1,1,169,0,2.189541," ","integrate((d*x+c)^4*sinh(b*x+a),x, algorithm=""fricas"")","\frac{{\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + b^{4} c^{4} + 12 \, b^{2} c^{2} d^{2} + 24 \, d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} + 2 \, b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d + 6 \, b^{2} c d^{3}\right)} x\right)} \cosh\left(b x + a\right) - 4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + b^{3} c^{3} d + 6 \, b c d^{3} + 3 \, {\left(b^{3} c^{2} d^{2} + 2 \, b d^{4}\right)} x\right)} \sinh\left(b x + a\right)}{b^{5}}"," ",0,"((b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + b^4*c^4 + 12*b^2*c^2*d^2 + 24*d^4 + 6*(b^4*c^2*d^2 + 2*b^2*d^4)*x^2 + 4*(b^4*c^3*d + 6*b^2*c*d^3)*x)*cosh(b*x + a) - 4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + b^3*c^3*d + 6*b*c*d^3 + 3*(b^3*c^2*d^2 + 2*b*d^4)*x)*sinh(b*x + a))/b^5","A",0
2,1,109,0,0.403636," ","integrate((d*x+c)^3*sinh(b*x+a),x, algorithm=""fricas"")","\frac{{\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d + 2 \, d^{3}\right)} \sinh\left(b x + a\right)}{b^{4}}"," ",0,"((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 6*b*c*d^2 + 3*(b^3*c^2*d + 2*b*d^3)*x)*cosh(b*x + a) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d + 2*d^3)*sinh(b*x + a))/b^4","A",0
3,1,62,0,0.381851," ","integrate((d*x+c)^2*sinh(b*x+a),x, algorithm=""fricas"")","\frac{{\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + 2 \, d^{2}\right)} \cosh\left(b x + a\right) - 2 \, {\left(b d^{2} x + b c d\right)} \sinh\left(b x + a\right)}{b^{3}}"," ",0,"((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + 2*d^2)*cosh(b*x + a) - 2*(b*d^2*x + b*c*d)*sinh(b*x + a))/b^3","A",0
4,1,29,0,0.387867," ","integrate((d*x+c)*sinh(b*x+a),x, algorithm=""fricas"")","\frac{{\left(b d x + b c\right)} \cosh\left(b x + a\right) - d \sinh\left(b x + a\right)}{b^{2}}"," ",0,"((b*d*x + b*c)*cosh(b*x + a) - d*sinh(b*x + a))/b^2","A",0
5,1,94,0,0.410770," ","integrate(sinh(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{{\left({\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left({\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right)}{2 \, d}"," ",0,"1/2*((Ei((b*d*x + b*c)/d) - Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) + (Ei((b*d*x + b*c)/d) + Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d))/d","A",0
6,1,148,0,0.390389," ","integrate(sinh(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) - 2 \, d \sinh\left(b x + a\right) + {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/2*(((b*d*x + b*c)*Ei((b*d*x + b*c)/d) + (b*d*x + b*c)*Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) - 2*d*sinh(b*x + a) + ((b*d*x + b*c)*Ei((b*d*x + b*c)/d) - (b*d*x + b*c)*Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d))/(d^3*x + c*d^2)","B",0
7,1,254,0,0.391001," ","integrate(sinh(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, d^{2} \sinh\left(b x + a\right) + 2 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) - {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(2*d^2*sinh(b*x + a) + 2*(b*d^2*x + b*c*d)*cosh(b*x + a) - ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei((b*d*x + b*c)/d) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) - ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei((b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
8,1,312,0,0.402788," ","integrate((d*x+c)^4*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{5} d^{4} x^{5} + 10 \, b^{5} c d^{3} x^{4} + 20 \, b^{5} c^{2} d^{2} x^{3} + 20 \, b^{5} c^{3} d x^{2} + 10 \, b^{5} c^{4} x + 5 \, {\left(2 \, b^{3} d^{4} x^{3} + 6 \, b^{3} c d^{3} x^{2} + 2 \, b^{3} c^{3} d + 3 \, b c d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} + b d^{4}\right)} x\right)} \cosh\left(b x + a\right)^{2} - 5 \, {\left(2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} + 2 \, b^{4} c^{4} + 6 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 6 \, {\left(2 \, b^{4} c^{2} d^{2} + b^{2} d^{4}\right)} x^{2} + 4 \, {\left(2 \, b^{4} c^{3} d + 3 \, b^{2} c d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + 5 \, {\left(2 \, b^{3} d^{4} x^{3} + 6 \, b^{3} c d^{3} x^{2} + 2 \, b^{3} c^{3} d + 3 \, b c d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} + b d^{4}\right)} x\right)} \sinh\left(b x + a\right)^{2}}{20 \, b^{5}}"," ",0,"-1/20*(2*b^5*d^4*x^5 + 10*b^5*c*d^3*x^4 + 20*b^5*c^2*d^2*x^3 + 20*b^5*c^3*d*x^2 + 10*b^5*c^4*x + 5*(2*b^3*d^4*x^3 + 6*b^3*c*d^3*x^2 + 2*b^3*c^3*d + 3*b*c*d^3 + 3*(2*b^3*c^2*d^2 + b*d^4)*x)*cosh(b*x + a)^2 - 5*(2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 + 2*b^4*c^4 + 6*b^2*c^2*d^2 + 3*d^4 + 6*(2*b^4*c^2*d^2 + b^2*d^4)*x^2 + 4*(2*b^4*c^3*d + 3*b^2*c*d^3)*x)*cosh(b*x + a)*sinh(b*x + a) + 5*(2*b^3*d^4*x^3 + 6*b^3*c*d^3*x^2 + 2*b^3*c^3*d + 3*b*c*d^3 + 3*(2*b^3*c^2*d^2 + b*d^4)*x)*sinh(b*x + a)^2)/b^5","B",0
9,1,209,0,0.403988," ","integrate((d*x+c)^3*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{4} d^{3} x^{4} + 8 \, b^{4} c d^{2} x^{3} + 12 \, b^{4} c^{2} d x^{2} + 8 \, b^{4} c^{3} x + 3 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d + d^{3}\right)} \cosh\left(b x + a\right)^{2} - 4 \, {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} + 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + 3 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d + d^{3}\right)} \sinh\left(b x + a\right)^{2}}{16 \, b^{4}}"," ",0,"-1/16*(2*b^4*d^3*x^4 + 8*b^4*c*d^2*x^3 + 12*b^4*c^2*d*x^2 + 8*b^4*c^3*x + 3*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d + d^3)*cosh(b*x + a)^2 - 4*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 + 3*b*c*d^2 + 3*(2*b^3*c^2*d + b*d^3)*x)*cosh(b*x + a)*sinh(b*x + a) + 3*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d + d^3)*sinh(b*x + a)^2)/b^4","A",0
10,1,123,0,0.382028," ","integrate((d*x+c)^2*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{3} d^{2} x^{3} + 6 \, b^{3} c d x^{2} + 6 \, b^{3} c^{2} x + 3 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{2} - 3 \, {\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} + d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + 3 \, {\left(b d^{2} x + b c d\right)} \sinh\left(b x + a\right)^{2}}{12 \, b^{3}}"," ",0,"-1/12*(2*b^3*d^2*x^3 + 6*b^3*c*d*x^2 + 6*b^3*c^2*x + 3*(b*d^2*x + b*c*d)*cosh(b*x + a)^2 - 3*(2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 + d^2)*cosh(b*x + a)*sinh(b*x + a) + 3*(b*d^2*x + b*c*d)*sinh(b*x + a)^2)/b^3","A",0
11,1,64,0,0.391274," ","integrate((d*x+c)*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{2} d x^{2} + 4 \, b^{2} c x + d \cosh\left(b x + a\right)^{2} - 4 \, {\left(b d x + b c\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d \sinh\left(b x + a\right)^{2}}{8 \, b^{2}}"," ",0,"-1/8*(2*b^2*d*x^2 + 4*b^2*c*x + d*cosh(b*x + a)^2 - 4*(b*d*x + b*c)*cosh(b*x + a)*sinh(b*x + a) + d*sinh(b*x + a)^2)/b^2","A",0
12,1,104,0,0.419015," ","integrate(sinh(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","\frac{{\left({\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, \log\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((Ei(2*(b*d*x + b*c)/d) + Ei(-2*(b*d*x + b*c)/d))*cosh(-2*(b*c - a*d)/d) + (Ei(2*(b*d*x + b*c)/d) - Ei(-2*(b*d*x + b*c)/d))*sinh(-2*(b*c - a*d)/d) - 2*log(d*x + c))/d","A",0
13,1,166,0,0.411969," ","integrate(sinh(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{d \cosh\left(b x + a\right)^{2} + d \sinh\left(b x + a\right)^{2} - {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(d*cosh(b*x + a)^2 + d*sinh(b*x + a)^2 - ((b*d*x + b*c)*Ei(2*(b*d*x + b*c)/d) - (b*d*x + b*c)*Ei(-2*(b*d*x + b*c)/d))*cosh(-2*(b*c - a*d)/d) - ((b*d*x + b*c)*Ei(2*(b*d*x + b*c)/d) + (b*d*x + b*c)*Ei(-2*(b*d*x + b*c)/d))*sinh(-2*(b*c - a*d)/d) - d)/(d^3*x + c*d^2)","B",0
14,1,280,0,0.384225," ","integrate(sinh(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{d^{2} \cosh\left(b x + a\right)^{2} + d^{2} \sinh\left(b x + a\right)^{2} + 4 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - d^{2} - 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(d^2*cosh(b*x + a)^2 + d^2*sinh(b*x + a)^2 + 4*(b*d^2*x + b*c*d)*cosh(b*x + a)*sinh(b*x + a) - d^2 - 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(2*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-2*(b*d*x + b*c)/d))*cosh(-2*(b*c - a*d)/d) - 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(2*(b*d*x + b*c)/d) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-2*(b*d*x + b*c)/d))*sinh(-2*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
15,1,411,0,0.399863," ","integrate(sinh(b*x+a)^2/(d*x+c)^4,x, algorithm=""fricas"")","\frac{d^{3} - {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d + d^{3}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d + d^{3}\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{6 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"1/6*(d^3 - (2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d + d^3)*cosh(b*x + a)^2 - 2*(b*d^3*x + b*c*d^2)*cosh(b*x + a)*sinh(b*x + a) - (2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d + d^3)*sinh(b*x + a)^2 + 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*Ei(2*(b*d*x + b*c)/d) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*Ei(-2*(b*d*x + b*c)/d))*cosh(-2*(b*c - a*d)/d) + 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*Ei(2*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*Ei(-2*(b*d*x + b*c)/d))*sinh(-2*(b*c - a*d)/d))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
16,1,528,0,0.398858," ","integrate((d*x+c)^4*sinh(b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left(27 \, b^{4} d^{4} x^{4} + 108 \, b^{4} c d^{3} x^{3} + 27 \, b^{4} c^{4} + 36 \, b^{2} c^{2} d^{2} + 8 \, d^{4} + 18 \, {\left(9 \, b^{4} c^{2} d^{2} + 2 \, b^{2} d^{4}\right)} x^{2} + 36 \, {\left(3 \, b^{4} c^{3} d + 2 \, b^{2} c d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{3} + 3 \, {\left(27 \, b^{4} d^{4} x^{4} + 108 \, b^{4} c d^{3} x^{3} + 27 \, b^{4} c^{4} + 36 \, b^{2} c^{2} d^{2} + 8 \, d^{4} + 18 \, {\left(9 \, b^{4} c^{2} d^{2} + 2 \, b^{2} d^{4}\right)} x^{2} + 36 \, {\left(3 \, b^{4} c^{3} d + 2 \, b^{2} c d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} - 12 \, {\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{3} d + 2 \, b c d^{3} + {\left(9 \, b^{3} c^{2} d^{2} + 2 \, b d^{4}\right)} x\right)} \sinh\left(b x + a\right)^{3} - 243 \, {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + b^{4} c^{4} + 12 \, b^{2} c^{2} d^{2} + 24 \, d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} + 2 \, b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d + 6 \, b^{2} c d^{3}\right)} x\right)} \cosh\left(b x + a\right) + 36 \, {\left(27 \, b^{3} d^{4} x^{3} + 81 \, b^{3} c d^{3} x^{2} + 27 \, b^{3} c^{3} d + 162 \, b c d^{3} - {\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{3} d + 2 \, b c d^{3} + {\left(9 \, b^{3} c^{2} d^{2} + 2 \, b d^{4}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 81 \, {\left(b^{3} c^{2} d^{2} + 2 \, b d^{4}\right)} x\right)} \sinh\left(b x + a\right)}{324 \, b^{5}}"," ",0,"1/324*((27*b^4*d^4*x^4 + 108*b^4*c*d^3*x^3 + 27*b^4*c^4 + 36*b^2*c^2*d^2 + 8*d^4 + 18*(9*b^4*c^2*d^2 + 2*b^2*d^4)*x^2 + 36*(3*b^4*c^3*d + 2*b^2*c*d^3)*x)*cosh(b*x + a)^3 + 3*(27*b^4*d^4*x^4 + 108*b^4*c*d^3*x^3 + 27*b^4*c^4 + 36*b^2*c^2*d^2 + 8*d^4 + 18*(9*b^4*c^2*d^2 + 2*b^2*d^4)*x^2 + 36*(3*b^4*c^3*d + 2*b^2*c*d^3)*x)*cosh(b*x + a)*sinh(b*x + a)^2 - 12*(3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 3*b^3*c^3*d + 2*b*c*d^3 + (9*b^3*c^2*d^2 + 2*b*d^4)*x)*sinh(b*x + a)^3 - 243*(b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + b^4*c^4 + 12*b^2*c^2*d^2 + 24*d^4 + 6*(b^4*c^2*d^2 + 2*b^2*d^4)*x^2 + 4*(b^4*c^3*d + 6*b^2*c*d^3)*x)*cosh(b*x + a) + 36*(27*b^3*d^4*x^3 + 81*b^3*c*d^3*x^2 + 27*b^3*c^3*d + 162*b*c*d^3 - (3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 3*b^3*c^3*d + 2*b*c*d^3 + (9*b^3*c^2*d^2 + 2*b*d^4)*x)*cosh(b*x + a)^2 + 81*(b^3*c^2*d^2 + 2*b*d^4)*x)*sinh(b*x + a))/b^5","B",0
17,1,345,0,0.409591," ","integrate((d*x+c)^3*sinh(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, b^{3} d^{3} x^{3} + 9 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{3} + 2 \, b c d^{2} + {\left(9 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{3} + 9 \, {\left(3 \, b^{3} d^{3} x^{3} + 9 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{3} + 2 \, b c d^{2} + {\left(9 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} - {\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d + 2 \, d^{3}\right)} \sinh\left(b x + a\right)^{3} - 81 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right) + 3 \, {\left(81 \, b^{2} d^{3} x^{2} + 162 \, b^{2} c d^{2} x + 81 \, b^{2} c^{2} d + 162 \, d^{3} - {\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d + 2 \, d^{3}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)}{108 \, b^{4}}"," ",0,"1/108*(3*(3*b^3*d^3*x^3 + 9*b^3*c*d^2*x^2 + 3*b^3*c^3 + 2*b*c*d^2 + (9*b^3*c^2*d + 2*b*d^3)*x)*cosh(b*x + a)^3 + 9*(3*b^3*d^3*x^3 + 9*b^3*c*d^2*x^2 + 3*b^3*c^3 + 2*b*c*d^2 + (9*b^3*c^2*d + 2*b*d^3)*x)*cosh(b*x + a)*sinh(b*x + a)^2 - (9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d + 2*d^3)*sinh(b*x + a)^3 - 81*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 6*b*c*d^2 + 3*(b^3*c^2*d + 2*b*d^3)*x)*cosh(b*x + a) + 3*(81*b^2*d^3*x^2 + 162*b^2*c*d^2*x + 81*b^2*c^2*d + 162*d^3 - (9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d + 2*d^3)*cosh(b*x + a)^2)*sinh(b*x + a))/b^4","B",0
18,1,199,0,0.400896," ","integrate((d*x+c)^2*sinh(b*x+a)^3,x, algorithm=""fricas"")","\frac{{\left(9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x + 9 \, b^{2} c^{2} + 2 \, d^{2}\right)} \cosh\left(b x + a\right)^{3} + 3 \, {\left(9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x + 9 \, b^{2} c^{2} + 2 \, d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} - 6 \, {\left(b d^{2} x + b c d\right)} \sinh\left(b x + a\right)^{3} - 81 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + 2 \, d^{2}\right)} \cosh\left(b x + a\right) + 18 \, {\left(9 \, b d^{2} x + 9 \, b c d - {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)}{108 \, b^{3}}"," ",0,"1/108*((9*b^2*d^2*x^2 + 18*b^2*c*d*x + 9*b^2*c^2 + 2*d^2)*cosh(b*x + a)^3 + 3*(9*b^2*d^2*x^2 + 18*b^2*c*d*x + 9*b^2*c^2 + 2*d^2)*cosh(b*x + a)*sinh(b*x + a)^2 - 6*(b*d^2*x + b*c*d)*sinh(b*x + a)^3 - 81*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + 2*d^2)*cosh(b*x + a) + 18*(9*b*d^2*x + 9*b*c*d - (b*d^2*x + b*c*d)*cosh(b*x + a)^2)*sinh(b*x + a))/b^3","A",0
19,1,97,0,0.593202," ","integrate((d*x+c)*sinh(b*x+a)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(b d x + b c\right)} \cosh\left(b x + a\right)^{3} + 9 \, {\left(b d x + b c\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} - d \sinh\left(b x + a\right)^{3} - 27 \, {\left(b d x + b c\right)} \cosh\left(b x + a\right) - 3 \, {\left(d \cosh\left(b x + a\right)^{2} - 9 \, d\right)} \sinh\left(b x + a\right)}{36 \, b^{2}}"," ",0,"1/36*(3*(b*d*x + b*c)*cosh(b*x + a)^3 + 9*(b*d*x + b*c)*cosh(b*x + a)*sinh(b*x + a)^2 - d*sinh(b*x + a)^3 - 27*(b*d*x + b*c)*cosh(b*x + a) - 3*(d*cosh(b*x + a)^2 - 9*d)*sinh(b*x + a))/b^2","A",0
20,1,188,0,0.772158," ","integrate(sinh(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","-\frac{3 \, {\left({\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left({\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 3 \, {\left({\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right) - {\left({\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, d}"," ",0,"-1/8*(3*(Ei((b*d*x + b*c)/d) - Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) - (Ei(3*(b*d*x + b*c)/d) - Ei(-3*(b*d*x + b*c)/d))*cosh(-3*(b*c - a*d)/d) + 3*(Ei((b*d*x + b*c)/d) + Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d) - (Ei(3*(b*d*x + b*c)/d) + Ei(-3*(b*d*x + b*c)/d))*sinh(-3*(b*c - a*d)/d))/d","A",0
21,1,301,0,0.768837," ","integrate(sinh(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, d \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) - 3 \, {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 6 \, {\left(d \cosh\left(b x + a\right)^{2} - d\right)} \sinh\left(b x + a\right) + 3 \, {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right) - 3 \, {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/8*(2*d*sinh(b*x + a)^3 + 3*((b*d*x + b*c)*Ei((b*d*x + b*c)/d) + (b*d*x + b*c)*Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) - 3*((b*d*x + b*c)*Ei(3*(b*d*x + b*c)/d) + (b*d*x + b*c)*Ei(-3*(b*d*x + b*c)/d))*cosh(-3*(b*c - a*d)/d) + 6*(d*cosh(b*x + a)^2 - d)*sinh(b*x + a) + 3*((b*d*x + b*c)*Ei((b*d*x + b*c)/d) - (b*d*x + b*c)*Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d) - 3*((b*d*x + b*c)*Ei(3*(b*d*x + b*c)/d) - (b*d*x + b*c)*Ei(-3*(b*d*x + b*c)/d))*sinh(-3*(b*c - a*d)/d))/(d^3*x + c*d^2)","B",0
22,1,529,0,0.719950," ","integrate(sinh(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, d^{2} \sinh\left(b x + a\right)^{3} + 6 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{3} + 18 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} - 6 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) + 3 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) - 9 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 6 \, {\left(d^{2} \cosh\left(b x + a\right)^{2} - d^{2}\right)} \sinh\left(b x + a\right) + 3 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right) - 9 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{16 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/16*(2*d^2*sinh(b*x + a)^3 + 6*(b*d^2*x + b*c*d)*cosh(b*x + a)^3 + 18*(b*d^2*x + b*c*d)*cosh(b*x + a)*sinh(b*x + a)^2 - 6*(b*d^2*x + b*c*d)*cosh(b*x + a) + 3*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei((b*d*x + b*c)/d) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) - 9*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(3*(b*d*x + b*c)/d) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-3*(b*d*x + b*c)/d))*cosh(-3*(b*c - a*d)/d) + 6*(d^2*cosh(b*x + a)^2 - d^2)*sinh(b*x + a) + 3*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei((b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d) - 9*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(3*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-3*(b*d*x + b*c)/d))*sinh(-3*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
23,1,396,0,0.473481," ","integrate((d*x+c)^3*csch(b*x+a),x, algorithm=""fricas"")","\frac{6 \, d^{3} {\rm polylog}\left(4, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 6 \, d^{3} {\rm polylog}\left(4, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) - 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2}\right)} {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{b^{4}}"," ",0,"(6*d^3*polylog(4, cosh(b*x + a) + sinh(b*x + a)) - 6*d^3*polylog(4, -cosh(b*x + a) - sinh(b*x + a)) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*dilog(cosh(b*x + a) + sinh(b*x + a)) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*dilog(-cosh(b*x + a) - sinh(b*x + a)) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*log(cosh(b*x + a) + sinh(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*log(cosh(b*x + a) + sinh(b*x + a) - 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) - 6*(b*d^3*x + b*c*d^2)*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 6*(b*d^3*x + b*c*d^2)*polylog(3, -cosh(b*x + a) - sinh(b*x + a)))/b^4","C",0
24,1,242,0,0.494132," ","integrate((d*x+c)^2*csch(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, d^{2} {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 2 \, d^{2} {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - 2 \, {\left(b d^{2} x + b c d\right)} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 2 \, {\left(b d^{2} x + b c d\right)} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) - {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right)}{b^{3}}"," ",0,"-(2*d^2*polylog(3, cosh(b*x + a) + sinh(b*x + a)) - 2*d^2*polylog(3, -cosh(b*x + a) - sinh(b*x + a)) - 2*(b*d^2*x + b*c*d)*dilog(cosh(b*x + a) + sinh(b*x + a)) + 2*(b*d^2*x + b*c*d)*dilog(-cosh(b*x + a) - sinh(b*x + a)) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*log(cosh(b*x + a) + sinh(b*x + a) + 1) - (b^2*c^2 - 2*a*b*c*d + a^2*d^2)*log(cosh(b*x + a) + sinh(b*x + a) - 1) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*log(-cosh(b*x + a) - sinh(b*x + a) + 1))/b^3","C",0
25,1,119,0,0.611101," ","integrate((d*x+c)*csch(b*x+a),x, algorithm=""fricas"")","\frac{d {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - d {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - {\left(b d x + b c\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + {\left(b c - a d\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) + {\left(b d x + a d\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right)}{b^{2}}"," ",0,"(d*dilog(cosh(b*x + a) + sinh(b*x + a)) - d*dilog(-cosh(b*x + a) - sinh(b*x + a)) - (b*d*x + b*c)*log(cosh(b*x + a) + sinh(b*x + a) + 1) + (b*c - a*d)*log(cosh(b*x + a) + sinh(b*x + a) - 1) + (b*d*x + a*d)*log(-cosh(b*x + a) - sinh(b*x + a) + 1))/b^2","B",0
26,0,0,0,0.563254," ","integrate(csch(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(csch(b*x + a)/(d*x + c), x)","F",0
27,0,0,0,0.482502," ","integrate(csch(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csch(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
28,1,1159,0,0.611300," ","integrate((d*x+c)^3*csch(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3} + 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cosh\left(b x + a\right)^{2} + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sinh\left(b x + a\right)^{2} + 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b d^{3} x + b c d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2} - {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b d^{3} x + b c d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3} - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3} - {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right) + 6 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} + 2 \, d^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d^{3} \sinh\left(b x + a\right)^{2} - d^{3}\right)} {\rm polylog}\left(3, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) + 6 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} + 2 \, d^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d^{3} \sinh\left(b x + a\right)^{2} - d^{3}\right)} {\rm polylog}\left(3, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right)}{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}}"," ",0,"-(2*b^3*c^3 - 6*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 2*a^3*d^3 + 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cosh(b*x + a)^2 + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cosh(b*x + a)*sinh(b*x + a) + 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*sinh(b*x + a)^2 + 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cosh(b*x + a)^2 - 2*(b*d^3*x + b*c*d^2)*cosh(b*x + a)*sinh(b*x + a) - (b*d^3*x + b*c*d^2)*sinh(b*x + a)^2)*dilog(cosh(b*x + a) + sinh(b*x + a)) + 6*(b*d^3*x + b*c*d^2 - (b*d^3*x + b*c*d^2)*cosh(b*x + a)^2 - 2*(b*d^3*x + b*c*d^2)*cosh(b*x + a)*sinh(b*x + a) - (b*d^3*x + b*c*d^2)*sinh(b*x + a)^2)*dilog(-cosh(b*x + a) - sinh(b*x + a)) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - (b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cosh(b*x + a)^2 - 2*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*cosh(b*x + a)*sinh(b*x + a) - (b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d)*sinh(b*x + a)^2)*log(cosh(b*x + a) + sinh(b*x + a) + 1) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3 - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cosh(b*x + a)^2 - 2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cosh(b*x + a)*sinh(b*x + a) - (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sinh(b*x + a)^2)*log(cosh(b*x + a) + sinh(b*x + a) - 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3 - (b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cosh(b*x + a)^2 - 2*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cosh(b*x + a)*sinh(b*x + a) - (b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*sinh(b*x + a)^2)*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + 6*(d^3*cosh(b*x + a)^2 + 2*d^3*cosh(b*x + a)*sinh(b*x + a) + d^3*sinh(b*x + a)^2 - d^3)*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 6*(d^3*cosh(b*x + a)^2 + 2*d^3*cosh(b*x + a)*sinh(b*x + a) + d^3*sinh(b*x + a)^2 - d^3)*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
29,1,623,0,0.571308," ","integrate((d*x+c)^2*csch(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \sinh\left(b x + a\right)^{2} - {\left(d^{2} \cosh\left(b x + a\right)^{2} + 2 \, d^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d^{2} \sinh\left(b x + a\right)^{2} - d^{2}\right)} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - {\left(d^{2} \cosh\left(b x + a\right)^{2} + 2 \, d^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d^{2} \sinh\left(b x + a\right)^{2} - d^{2}\right)} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) + {\left(b d^{2} x + b c d - {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b d^{2} x + b c d\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + 1\right) + {\left(b c d - a d^{2} - {\left(b c d - a d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b c d - a d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b c d - a d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - 1\right) + {\left(b d^{2} x + a d^{2} - {\left(b d^{2} x + a d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d^{2} x + a d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b d^{2} x + a d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right) + 1\right)\right)}}{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}}"," ",0,"-2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cosh(b*x + a)^2 + 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cosh(b*x + a)*sinh(b*x + a) + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*sinh(b*x + a)^2 - (d^2*cosh(b*x + a)^2 + 2*d^2*cosh(b*x + a)*sinh(b*x + a) + d^2*sinh(b*x + a)^2 - d^2)*dilog(cosh(b*x + a) + sinh(b*x + a)) - (d^2*cosh(b*x + a)^2 + 2*d^2*cosh(b*x + a)*sinh(b*x + a) + d^2*sinh(b*x + a)^2 - d^2)*dilog(-cosh(b*x + a) - sinh(b*x + a)) + (b*d^2*x + b*c*d - (b*d^2*x + b*c*d)*cosh(b*x + a)^2 - 2*(b*d^2*x + b*c*d)*cosh(b*x + a)*sinh(b*x + a) - (b*d^2*x + b*c*d)*sinh(b*x + a)^2)*log(cosh(b*x + a) + sinh(b*x + a) + 1) + (b*c*d - a*d^2 - (b*c*d - a*d^2)*cosh(b*x + a)^2 - 2*(b*c*d - a*d^2)*cosh(b*x + a)*sinh(b*x + a) - (b*c*d - a*d^2)*sinh(b*x + a)^2)*log(cosh(b*x + a) + sinh(b*x + a) - 1) + (b*d^2*x + a*d^2 - (b*d^2*x + a*d^2)*cosh(b*x + a)^2 - 2*(b*d^2*x + a*d^2)*cosh(b*x + a)*sinh(b*x + a) - (b*d^2*x + a*d^2)*sinh(b*x + a)^2)*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
30,1,166,0,0.589643," ","integrate((d*x+c)*csch(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b d x \cosh\left(b x + a\right)^{2} + 4 \, b d x \cosh\left(b x + a\right) \sinh\left(b x + a\right) + 2 \, b d x \sinh\left(b x + a\right)^{2} + 2 \, b c - {\left(d \cosh\left(b x + a\right)^{2} + 2 \, d \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d \sinh\left(b x + a\right)^{2} - d\right)} \log\left(\frac{2 \, \sinh\left(b x + a\right)}{\cosh\left(b x + a\right) - \sinh\left(b x + a\right)}\right)}{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}}"," ",0,"-(2*b*d*x*cosh(b*x + a)^2 + 4*b*d*x*cosh(b*x + a)*sinh(b*x + a) + 2*b*d*x*sinh(b*x + a)^2 + 2*b*c - (d*cosh(b*x + a)^2 + 2*d*cosh(b*x + a)*sinh(b*x + a) + d*sinh(b*x + a)^2 - d)*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
31,0,0,0,0.483029," ","integrate(csch(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(csch(b*x + a)^2/(d*x + c), x)","F",0
32,0,0,0,0.460492," ","integrate(csch(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csch(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
33,1,4008,0,0.757384," ","integrate((d*x+c)^3*csch(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} + 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b^{2} c d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} + 6 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} + 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b^{2} c d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + 2 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} + 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b^{2} c d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{3} + 2 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} - 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} - b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b^{2} c d^{2}\right)} x\right)} \cosh\left(b x + a\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \sinh\left(b x + a\right)^{4} - 2 \, d^{3} - 2 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3} - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \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(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \sinh\left(b x + a\right)^{4} - 2 \, d^{3} - 2 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3} - 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d - 2 \, d^{3}\right)} \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) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{4} - 6 \, b c d^{2} - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} - 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x + 4 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} - 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} 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) + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \sinh\left(b x + a\right)^{4} - {\left(a^{3} - 6 \, a\right)} d^{3} - 2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3} - 3 \, {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, {\left(a^{2} - 2\right)} b c d^{2} - {\left(a^{3} - 6 \, a\right)} d^{3}\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) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{4} + {\left(a^{3} - 6 \, a\right)} d^{3} - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} - 3 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x + 4 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + {\left(a^{3} - 6 \, a\right)} d^{3} + 3 \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} 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) + 6 \, {\left(d^{3} \cosh\left(b x + a\right)^{4} + 4 \, d^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + d^{3} \sinh\left(b x + a\right)^{4} - 2 \, d^{3} \cosh\left(b x + a\right)^{2} + d^{3} + 2 \, {\left(3 \, d^{3} \cosh\left(b x + a\right)^{2} - d^{3}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(d^{3} \cosh\left(b x + a\right)^{3} - d^{3} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm polylog}\left(4, \cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - 6 \, {\left(d^{3} \cosh\left(b x + a\right)^{4} + 4 \, d^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + d^{3} \sinh\left(b x + a\right)^{4} - 2 \, d^{3} \cosh\left(b x + a\right)^{2} + d^{3} + 2 \, {\left(3 \, d^{3} \cosh\left(b x + a\right)^{2} - d^{3}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(d^{3} \cosh\left(b x + a\right)^{3} - d^{3} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm polylog}\left(4, -\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - 6 \, {\left(b d^{3} x + {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b d^{3} x + b c d^{2}\right)} \sinh\left(b x + a\right)^{4} + b c d^{2} - 2 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d^{3} x + b c d^{2} - 3 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{3} - {\left(b d^{3} x + b c d^{2}\right)} \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) + 6 \, {\left(b d^{3} x + {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b d^{3} x + b c d^{2}\right)} \sinh\left(b x + a\right)^{4} + b c d^{2} - 2 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d^{3} x + b c d^{2} - 3 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{3} - {\left(b d^{3} x + b c d^{2}\right)} \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) + 2 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} - 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} - b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} + 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b^{2} c d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b^{2} c d^{2}\right)} x\right)} \sinh\left(b x + a\right)}{2 \, {\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,"-1/2*(2*(b^3*d^3*x^3 + b^3*c^3 + 3*b^2*c^2*d + 3*(b^3*c*d^2 + b^2*d^3)*x^2 + 3*(b^3*c^2*d + 2*b^2*c*d^2)*x)*cosh(b*x + a)^3 + 6*(b^3*d^3*x^3 + b^3*c^3 + 3*b^2*c^2*d + 3*(b^3*c*d^2 + b^2*d^3)*x^2 + 3*(b^3*c^2*d + 2*b^2*c*d^2)*x)*cosh(b*x + a)*sinh(b*x + a)^2 + 2*(b^3*d^3*x^3 + b^3*c^3 + 3*b^2*c^2*d + 3*(b^3*c*d^2 + b^2*d^3)*x^2 + 3*(b^3*c^2*d + 2*b^2*c*d^2)*x)*sinh(b*x + a)^3 + 2*(b^3*d^3*x^3 + b^3*c^3 - 3*b^2*c^2*d + 3*(b^3*c*d^2 - b^2*d^3)*x^2 + 3*(b^3*c^2*d - 2*b^2*c*d^2)*x)*cosh(b*x + a) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a)^4 + 4*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*sinh(b*x + a)^4 - 2*d^3 - 2*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a)^2 - 2*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3 - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*((b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a)^3 - (b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a))*sinh(b*x + a))*dilog(cosh(b*x + a) + sinh(b*x + a)) - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a)^4 + 4*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*sinh(b*x + a)^4 - 2*d^3 - 2*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a)^2 - 2*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3 - 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*((b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a)^3 - (b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d - 2*d^3)*cosh(b*x + a))*sinh(b*x + a))*dilog(-cosh(b*x + a) - sinh(b*x + a)) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^4 + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*sinh(b*x + a)^4 - 6*b*c*d^2 - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^2 - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 - 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*sinh(b*x + a)^2 + 3*(b^3*c^2*d - 2*b*d^3)*x + 4*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 - 6*b*c*d^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) + 1) + (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 + (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cosh(b*x + a)^4 + 4*(b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*sinh(b*x + a)^4 - (a^3 - 6*a)*d^3 - 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cosh(b*x + a)^2 - 2*(b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3 - 3*(b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*((b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cosh(b*x + a)^3 - (b^3*c^3 - 3*a*b^2*c^2*d + 3*(a^2 - 2)*b*c*d^2 - (a^3 - 6*a)*d^3)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) - 1) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^4 + 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*sinh(b*x + a)^4 + (a^3 - 6*a)*d^3 - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^2 - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 - 3*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^2 + 3*(b^3*c^2*d - 2*b*d^3)*x)*sinh(b*x + a)^2 + 3*(b^3*c^2*d - 2*b*d^3)*x + 4*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^3 - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + (a^3 - 6*a)*d^3 + 3*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a))*sinh(b*x + a))*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + 6*(d^3*cosh(b*x + a)^4 + 4*d^3*cosh(b*x + a)*sinh(b*x + a)^3 + d^3*sinh(b*x + a)^4 - 2*d^3*cosh(b*x + a)^2 + d^3 + 2*(3*d^3*cosh(b*x + a)^2 - d^3)*sinh(b*x + a)^2 + 4*(d^3*cosh(b*x + a)^3 - d^3*cosh(b*x + a))*sinh(b*x + a))*polylog(4, cosh(b*x + a) + sinh(b*x + a)) - 6*(d^3*cosh(b*x + a)^4 + 4*d^3*cosh(b*x + a)*sinh(b*x + a)^3 + d^3*sinh(b*x + a)^4 - 2*d^3*cosh(b*x + a)^2 + d^3 + 2*(3*d^3*cosh(b*x + a)^2 - d^3)*sinh(b*x + a)^2 + 4*(d^3*cosh(b*x + a)^3 - d^3*cosh(b*x + a))*sinh(b*x + a))*polylog(4, -cosh(b*x + a) - sinh(b*x + a)) - 6*(b*d^3*x + (b*d^3*x + b*c*d^2)*cosh(b*x + a)^4 + 4*(b*d^3*x + b*c*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (b*d^3*x + b*c*d^2)*sinh(b*x + a)^4 + b*c*d^2 - 2*(b*d^3*x + b*c*d^2)*cosh(b*x + a)^2 - 2*(b*d^3*x + b*c*d^2 - 3*(b*d^3*x + b*c*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*((b*d^3*x + b*c*d^2)*cosh(b*x + a)^3 - (b*d^3*x + b*c*d^2)*cosh(b*x + a))*sinh(b*x + a))*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 6*(b*d^3*x + (b*d^3*x + b*c*d^2)*cosh(b*x + a)^4 + 4*(b*d^3*x + b*c*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (b*d^3*x + b*c*d^2)*sinh(b*x + a)^4 + b*c*d^2 - 2*(b*d^3*x + b*c*d^2)*cosh(b*x + a)^2 - 2*(b*d^3*x + b*c*d^2 - 3*(b*d^3*x + b*c*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*((b*d^3*x + b*c*d^2)*cosh(b*x + a)^3 - (b*d^3*x + b*c*d^2)*cosh(b*x + a))*sinh(b*x + a))*polylog(3, -cosh(b*x + a) - sinh(b*x + a)) + 2*(b^3*d^3*x^3 + b^3*c^3 - 3*b^2*c^2*d + 3*(b^3*c*d^2 - b^2*d^3)*x^2 + 3*(b^3*d^3*x^3 + b^3*c^3 + 3*b^2*c^2*d + 3*(b^3*c*d^2 + b^2*d^3)*x^2 + 3*(b^3*c^2*d + 2*b^2*c*d^2)*x)*cosh(b*x + a)^2 + 3*(b^3*c^2*d - 2*b^2*c*d^2)*x)*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
34,1,2218,0,0.545893," ","integrate((d*x+c)^2*csch(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 \, b c d + 2 \, {\left(b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} + 6 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 \, b c d + 2 \, {\left(b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 \, b c d + 2 \, {\left(b^{2} c d + b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{3} + 2 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} - 2 \, b c d + 2 \, {\left(b^{2} c d - b d^{2}\right)} x\right)} \cosh\left(b x + a\right) + 2 \, {\left({\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b d^{2} x + b c d\right)} \sinh\left(b x + a\right)^{4} + b d^{2} x + b c d - 2 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d^{2} x + b c d - 3 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{3} - {\left(b d^{2} x + b c d\right)} \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) - 2 \, {\left({\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b d^{2} x + b c d\right)} \sinh\left(b x + a\right)^{4} + b d^{2} x + b c d - 2 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d^{2} x + b c d - 3 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{3} - {\left(b d^{2} x + b c d\right)} \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) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \sinh\left(b x + a\right)^{4} + b^{2} c^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, d^{2}\right)} \sinh\left(b x + a\right)^{2} - 2 \, d^{2} + 4 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{2}\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} - 2 \, d^{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) + {\left({\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \sinh\left(b x + a\right)^{4} + b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2} - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2} - 3 \, {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{2} c^{2} - 2 \, a b c d + {\left(a^{2} - 2\right)} d^{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) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \sinh\left(b x + a\right)^{4} + 2 \, a b c d - a^{2} d^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2} - 3 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{3} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{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) - 2 \, {\left(d^{2} \cosh\left(b x + a\right)^{4} + 4 \, d^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + d^{2} \sinh\left(b x + a\right)^{4} - 2 \, d^{2} \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, d^{2} \cosh\left(b x + a\right)^{2} - d^{2}\right)} \sinh\left(b x + a\right)^{2} + d^{2} + 4 \, {\left(d^{2} \cosh\left(b x + a\right)^{3} - d^{2} \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) + 2 \, {\left(d^{2} \cosh\left(b x + a\right)^{4} + 4 \, d^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + d^{2} \sinh\left(b x + a\right)^{4} - 2 \, d^{2} \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, d^{2} \cosh\left(b x + a\right)^{2} - d^{2}\right)} \sinh\left(b x + a\right)^{2} + d^{2} + 4 \, {\left(d^{2} \cosh\left(b x + a\right)^{3} - d^{2} \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) + 2 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} - 2 \, b c d + 3 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 \, b c d + 2 \, {\left(b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b^{2} c d - b d^{2}\right)} x\right)} \sinh\left(b x + a\right)}{2 \, {\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,"-1/2*(2*(b^2*d^2*x^2 + b^2*c^2 + 2*b*c*d + 2*(b^2*c*d + b*d^2)*x)*cosh(b*x + a)^3 + 6*(b^2*d^2*x^2 + b^2*c^2 + 2*b*c*d + 2*(b^2*c*d + b*d^2)*x)*cosh(b*x + a)*sinh(b*x + a)^2 + 2*(b^2*d^2*x^2 + b^2*c^2 + 2*b*c*d + 2*(b^2*c*d + b*d^2)*x)*sinh(b*x + a)^3 + 2*(b^2*d^2*x^2 + b^2*c^2 - 2*b*c*d + 2*(b^2*c*d - b*d^2)*x)*cosh(b*x + a) + 2*((b*d^2*x + b*c*d)*cosh(b*x + a)^4 + 4*(b*d^2*x + b*c*d)*cosh(b*x + a)*sinh(b*x + a)^3 + (b*d^2*x + b*c*d)*sinh(b*x + a)^4 + b*d^2*x + b*c*d - 2*(b*d^2*x + b*c*d)*cosh(b*x + a)^2 - 2*(b*d^2*x + b*c*d - 3*(b*d^2*x + b*c*d)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*((b*d^2*x + b*c*d)*cosh(b*x + a)^3 - (b*d^2*x + b*c*d)*cosh(b*x + a))*sinh(b*x + a))*dilog(cosh(b*x + a) + sinh(b*x + a)) - 2*((b*d^2*x + b*c*d)*cosh(b*x + a)^4 + 4*(b*d^2*x + b*c*d)*cosh(b*x + a)*sinh(b*x + a)^3 + (b*d^2*x + b*c*d)*sinh(b*x + a)^4 + b*d^2*x + b*c*d - 2*(b*d^2*x + b*c*d)*cosh(b*x + a)^2 - 2*(b*d^2*x + b*c*d - 3*(b*d^2*x + b*c*d)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*((b*d^2*x + b*c*d)*cosh(b*x + a)^3 - (b*d^2*x + b*c*d)*cosh(b*x + a))*sinh(b*x + a))*dilog(-cosh(b*x + a) - sinh(b*x + a)) - (b^2*d^2*x^2 + 2*b^2*c*d*x + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cosh(b*x + a)^4 + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*sinh(b*x + a)^4 + b^2*c^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cosh(b*x + a)^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 3*(b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cosh(b*x + a)^2 - 2*d^2)*sinh(b*x + a)^2 - 2*d^2 + 4*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cosh(b*x + a)^3 - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 - 2*d^2)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) + 1) + ((b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cosh(b*x + a)^4 + 4*(b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*sinh(b*x + a)^4 + b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2 - 2*(b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cosh(b*x + a)^2 - 2*(b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2 - 3*(b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*((b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cosh(b*x + a)^3 - (b^2*c^2 - 2*a*b*c*d + (a^2 - 2)*d^2)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) - 1) + (b^2*d^2*x^2 + 2*b^2*c*d*x + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cosh(b*x + a)^4 + 4*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*sinh(b*x + a)^4 + 2*a*b*c*d - a^2*d^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cosh(b*x + a)^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2 - 3*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*((b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cosh(b*x + a)^3 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cosh(b*x + a))*sinh(b*x + a))*log(-cosh(b*x + a) - sinh(b*x + a) + 1) - 2*(d^2*cosh(b*x + a)^4 + 4*d^2*cosh(b*x + a)*sinh(b*x + a)^3 + d^2*sinh(b*x + a)^4 - 2*d^2*cosh(b*x + a)^2 + 2*(3*d^2*cosh(b*x + a)^2 - d^2)*sinh(b*x + a)^2 + d^2 + 4*(d^2*cosh(b*x + a)^3 - d^2*cosh(b*x + a))*sinh(b*x + a))*polylog(3, cosh(b*x + a) + sinh(b*x + a)) + 2*(d^2*cosh(b*x + a)^4 + 4*d^2*cosh(b*x + a)*sinh(b*x + a)^3 + d^2*sinh(b*x + a)^4 - 2*d^2*cosh(b*x + a)^2 + 2*(3*d^2*cosh(b*x + a)^2 - d^2)*sinh(b*x + a)^2 + d^2 + 4*(d^2*cosh(b*x + a)^3 - d^2*cosh(b*x + a))*sinh(b*x + a))*polylog(3, -cosh(b*x + a) - sinh(b*x + a)) + 2*(b^2*d^2*x^2 + b^2*c^2 - 2*b*c*d + 3*(b^2*d^2*x^2 + b^2*c^2 + 2*b*c*d + 2*(b^2*c*d + b*d^2)*x)*cosh(b*x + a)^2 + 2*(b^2*c*d - b*d^2)*x)*sinh(b*x + 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
35,1,1026,0,0.444408," ","integrate((d*x+c)*csch(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(b d x + b c + d\right)} \cosh\left(b x + a\right)^{3} + 6 \, {\left(b d x + b c + d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + 2 \, {\left(b d x + b c + d\right)} \sinh\left(b x + a\right)^{3} + 2 \, {\left(b d x + b c - d\right)} \cosh\left(b x + a\right) + {\left(d \cosh\left(b x + a\right)^{4} + 4 \, d \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + d \sinh\left(b x + a\right)^{4} - 2 \, d \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, d \cosh\left(b x + a\right)^{2} - d\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(d \cosh\left(b x + a\right)^{3} - d \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + d\right)} {\rm Li}_2\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right)\right) - {\left(d \cosh\left(b x + a\right)^{4} + 4 \, d \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + d \sinh\left(b x + a\right)^{4} - 2 \, d \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, d \cosh\left(b x + a\right)^{2} - d\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(d \cosh\left(b x + a\right)^{3} - d \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + d\right)} {\rm Li}_2\left(-\cosh\left(b x + a\right) - \sinh\left(b x + a\right)\right) - {\left({\left(b d x + b c\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b d x + b c\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b d x + b c\right)} \sinh\left(b x + a\right)^{4} + b d x - 2 \, {\left(b d x + b c\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d x - 3 \, {\left(b d x + b c\right)} \cosh\left(b x + a\right)^{2} + b c\right)} \sinh\left(b x + a\right)^{2} + b c + 4 \, {\left({\left(b d x + b c\right)} \cosh\left(b x + a\right)^{3} - {\left(b d x + b c\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) + {\left({\left(b c - a d\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b c - a d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b c - a d\right)} \sinh\left(b x + a\right)^{4} - 2 \, {\left(b c - a d\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, {\left(b c - a d\right)} \cosh\left(b x + a\right)^{2} - b c + a d\right)} \sinh\left(b x + a\right)^{2} + b c - a d + 4 \, {\left({\left(b c - a d\right)} \cosh\left(b x + a\right)^{3} - {\left(b c - a d\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) + {\left({\left(b d x + a d\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(b d x + a d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(b d x + a d\right)} \sinh\left(b x + a\right)^{4} + b d x - 2 \, {\left(b d x + a d\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b d x - 3 \, {\left(b d x + a d\right)} \cosh\left(b x + a\right)^{2} + a d\right)} \sinh\left(b x + a\right)^{2} + a d + 4 \, {\left({\left(b d x + a d\right)} \cosh\left(b x + a\right)^{3} - {\left(b d x + a d\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) + 2 \, {\left(b d x + 3 \, {\left(b d x + b c + d\right)} \cosh\left(b x + a\right)^{2} + b c - d\right)} \sinh\left(b x + a\right)}{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*(2*(b*d*x + b*c + d)*cosh(b*x + a)^3 + 6*(b*d*x + b*c + d)*cosh(b*x + a)*sinh(b*x + a)^2 + 2*(b*d*x + b*c + d)*sinh(b*x + a)^3 + 2*(b*d*x + b*c - d)*cosh(b*x + a) + (d*cosh(b*x + a)^4 + 4*d*cosh(b*x + a)*sinh(b*x + a)^3 + d*sinh(b*x + a)^4 - 2*d*cosh(b*x + a)^2 + 2*(3*d*cosh(b*x + a)^2 - d)*sinh(b*x + a)^2 + 4*(d*cosh(b*x + a)^3 - d*cosh(b*x + a))*sinh(b*x + a) + d)*dilog(cosh(b*x + a) + sinh(b*x + a)) - (d*cosh(b*x + a)^4 + 4*d*cosh(b*x + a)*sinh(b*x + a)^3 + d*sinh(b*x + a)^4 - 2*d*cosh(b*x + a)^2 + 2*(3*d*cosh(b*x + a)^2 - d)*sinh(b*x + a)^2 + 4*(d*cosh(b*x + a)^3 - d*cosh(b*x + a))*sinh(b*x + a) + d)*dilog(-cosh(b*x + a) - sinh(b*x + a)) - ((b*d*x + b*c)*cosh(b*x + a)^4 + 4*(b*d*x + b*c)*cosh(b*x + a)*sinh(b*x + a)^3 + (b*d*x + b*c)*sinh(b*x + a)^4 + b*d*x - 2*(b*d*x + b*c)*cosh(b*x + a)^2 - 2*(b*d*x - 3*(b*d*x + b*c)*cosh(b*x + a)^2 + b*c)*sinh(b*x + a)^2 + b*c + 4*((b*d*x + b*c)*cosh(b*x + a)^3 - (b*d*x + b*c)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) + 1) + ((b*c - a*d)*cosh(b*x + a)^4 + 4*(b*c - a*d)*cosh(b*x + a)*sinh(b*x + a)^3 + (b*c - a*d)*sinh(b*x + a)^4 - 2*(b*c - a*d)*cosh(b*x + a)^2 + 2*(3*(b*c - a*d)*cosh(b*x + a)^2 - b*c + a*d)*sinh(b*x + a)^2 + b*c - a*d + 4*((b*c - a*d)*cosh(b*x + a)^3 - (b*c - a*d)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) - 1) + ((b*d*x + a*d)*cosh(b*x + a)^4 + 4*(b*d*x + a*d)*cosh(b*x + a)*sinh(b*x + a)^3 + (b*d*x + a*d)*sinh(b*x + a)^4 + b*d*x - 2*(b*d*x + a*d)*cosh(b*x + a)^2 - 2*(b*d*x - 3*(b*d*x + a*d)*cosh(b*x + a)^2 + a*d)*sinh(b*x + a)^2 + a*d + 4*((b*d*x + a*d)*cosh(b*x + a)^3 - (b*d*x + a*d)*cosh(b*x + a))*sinh(b*x + a))*log(-cosh(b*x + a) - sinh(b*x + a) + 1) + 2*(b*d*x + 3*(b*d*x + b*c + d)*cosh(b*x + a)^2 + b*c - d)*sinh(b*x + a))/(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
36,0,0,0,0.515561," ","integrate(csch(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(b x + a\right)^{3}}{d x + c}, x\right)"," ",0,"integral(csch(b*x + a)^3/(d*x + c), x)","F",0
37,0,0,0,0.483386," ","integrate(csch(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(b x + a\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(csch(b*x + a)^3/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
38,1,521,0,0.490944," ","integrate((d*x+c)^(5/2)*sinh(b*x+a),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{3} \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 15 \, \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{3} \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 2 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} + 10 \, b^{2} c d + 15 \, b d^{2} + {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(4 \, b^{3} c d + 5 \, b^{2} d^{2}\right)} x\right)} \sqrt{d x + c}}{16 \, {\left(b^{4} \cosh\left(b x + a\right) + b^{4} \sinh\left(b x + a\right)\right)}}"," ",0,"-1/16*(15*sqrt(pi)*(d^3*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d^3*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d^3*cosh(-(b*c - a*d)/d) - d^3*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) - 15*sqrt(pi)*(d^3*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d^3*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d^3*cosh(-(b*c - a*d)/d) + d^3*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - 2*(4*b^3*d^2*x^2 + 4*b^3*c^2 + 10*b^2*c*d + 15*b*d^2 + (4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^2 + 2*(4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)*sinh(b*x + a) + (4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*sinh(b*x + a)^2 + 2*(4*b^3*c*d + 5*b^2*d^2)*x)*sqrt(d*x + c))/(b^4*cosh(b*x + a) + b^4*sinh(b*x + a))","B",0
39,1,385,0,0.439240," ","integrate((d*x+c)^(3/2)*sinh(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{2} \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 3 \, \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{2} \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 2 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c + {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \sinh\left(b x + a\right)^{2} + 3 \, b d\right)} \sqrt{d x + c}}{8 \, {\left(b^{3} \cosh\left(b x + a\right) + b^{3} \sinh\left(b x + a\right)\right)}}"," ",0,"-1/8*(3*sqrt(pi)*(d^2*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d^2*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d^2*cosh(-(b*c - a*d)/d) - d^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 3*sqrt(pi)*(d^2*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d^2*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d^2*cosh(-(b*c - a*d)/d) + d^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - 2*(2*b^2*d*x + 2*b^2*c + (2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a)^2 + 2*(2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a)*sinh(b*x + a) + (2*b^2*d*x + 2*b^2*c - 3*b*d)*sinh(b*x + a)^2 + 3*b*d)*sqrt(d*x + c))/(b^3*cosh(b*x + a) + b^3*sinh(b*x + a))","B",0
40,1,301,0,0.439967," ","integrate(sinh(b*x+a)*(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d \cosh\left(-\frac{b c - a d}{d}\right) - d \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - \sqrt{\pi} {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d \cosh\left(-\frac{b c - a d}{d}\right) + d \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 2 \, {\left(b \cosh\left(b x + a\right)^{2} + 2 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b \sinh\left(b x + a\right)^{2} + b\right)} \sqrt{d x + c}}{4 \, {\left(b^{2} \cosh\left(b x + a\right) + b^{2} \sinh\left(b x + a\right)\right)}}"," ",0,"-1/4*(sqrt(pi)*(d*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d*cosh(-(b*c - a*d)/d) - d*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) - sqrt(pi)*(d*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d*cosh(-(b*c - a*d)/d) + d*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - 2*(b*cosh(b*x + a)^2 + 2*b*cosh(b*x + a)*sinh(b*x + a) + b*sinh(b*x + a)^2 + b)*sqrt(d*x + c))/(b^2*cosh(b*x + a) + b^2*sinh(b*x + a))","B",0
41,1,122,0,0.466913," ","integrate(sinh(b*x+a)/(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} \sqrt{\frac{b}{d}} {\left(\cosh\left(-\frac{b c - a d}{d}\right) - \sinh\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + \sqrt{\pi} \sqrt{-\frac{b}{d}} {\left(\cosh\left(-\frac{b c - a d}{d}\right) + \sinh\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right)}{2 \, b}"," ",0,"-1/2*(sqrt(pi)*sqrt(b/d)*(cosh(-(b*c - a*d)/d) - sinh(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(b/d)) + sqrt(pi)*sqrt(-b/d)*(cosh(-(b*c - a*d)/d) + sinh(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-b/d)))/b","A",0
42,1,339,0,0.462815," ","integrate(sinh(b*x+a)/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - \sqrt{d x + c} {\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)}}{{\left(d^{2} x + c d\right)} \cosh\left(b x + a\right) + {\left(d^{2} x + c d\right)} \sinh\left(b x + a\right)}"," ",0,"(sqrt(pi)*((d*x + c)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((d*x + c)*cosh(-(b*c - a*d)/d) - (d*x + c)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) - sqrt(pi)*((d*x + c)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((d*x + c)*cosh(-(b*c - a*d)/d) + (d*x + c)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - sqrt(d*x + c)*(cosh(b*x + a)^2 + 2*cosh(b*x + a)*sinh(b*x + a) + sinh(b*x + a)^2 - 1))/((d^2*x + c*d)*cosh(b*x + a) + (d^2*x + c*d)*sinh(b*x + a))","B",0
43,1,532,0,0.573179," ","integrate(sinh(b*x+a)/(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 2 \, \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left(2 \, b d x + {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(2 \, b d x + 2 \, b c + d\right)} \sinh\left(b x + a\right)^{2} + 2 \, b c - d\right)} \sqrt{d x + c}}{3 \, {\left({\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right) + {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"-1/3*(2*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 2*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + (2*b*d*x + (2*b*d*x + 2*b*c + d)*cosh(b*x + a)^2 + 2*(2*b*d*x + 2*b*c + d)*cosh(b*x + a)*sinh(b*x + a) + (2*b*d*x + 2*b*c + d)*sinh(b*x + a)^2 + 2*b*c - d)*sqrt(d*x + c))/((d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a) + (d^4*x^2 + 2*c*d^3*x + c^2*d^2)*sinh(b*x + a))","B",0
44,1,855,0,0.511229," ","integrate(sinh(b*x+a)/(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 4 \, \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} - 2 \, b c d - {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{2} + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d - b d^{2}\right)} x\right)} \sqrt{d x + c}}{15 \, {\left({\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right) + {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"1/15*(4*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) - 4*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + (4*b^2*d^2*x^2 + 4*b^2*c^2 - 2*b*c*d - (4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^2 - 2*(4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a)*sinh(b*x + a) - (4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*sinh(b*x + a)^2 + 3*d^2 + 2*(4*b^2*c*d - b*d^2)*x)*sqrt(d*x + c))/((d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a) + (d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*sinh(b*x + a))","B",0
45,1,1001,0,0.528781," ","integrate((d*x+c)^(5/2)*sinh(b*x+a)^2,x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} \sqrt{\pi} {\left(d^{4} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{4} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{4} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{4} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{4} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{4} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 105 \, \sqrt{2} \sqrt{\pi} {\left(d^{4} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{4} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{4} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{4} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{4} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{4} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 4 \, {\left(112 \, b^{3} d^{3} x^{2} + 112 \, b^{3} c^{2} d + 140 \, b^{2} c d^{2} - 7 \, {\left(16 \, b^{3} d^{3} x^{2} + 16 \, b^{3} c^{2} d - 20 \, b^{2} c d^{2} + 15 \, b d^{3} + 4 \, {\left(8 \, b^{3} c d^{2} - 5 \, b^{2} d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{4} - 28 \, {\left(16 \, b^{3} d^{3} x^{2} + 16 \, b^{3} c^{2} d - 20 \, b^{2} c d^{2} + 15 \, b d^{3} + 4 \, {\left(8 \, b^{3} c d^{2} - 5 \, b^{2} d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - 7 \, {\left(16 \, b^{3} d^{3} x^{2} + 16 \, b^{3} c^{2} d - 20 \, b^{2} c d^{2} + 15 \, b d^{3} + 4 \, {\left(8 \, b^{3} c d^{2} - 5 \, b^{2} d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{4} + 105 \, b d^{3} + 128 \, {\left(b^{4} d^{3} x^{3} + 3 \, b^{4} c d^{2} x^{2} + 3 \, b^{4} c^{2} d x + b^{4} c^{3}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(64 \, b^{4} d^{3} x^{3} + 192 \, b^{4} c d^{2} x^{2} + 192 \, b^{4} c^{2} d x + 64 \, b^{4} c^{3} - 21 \, {\left(16 \, b^{3} d^{3} x^{2} + 16 \, b^{3} c^{2} d - 20 \, b^{2} c d^{2} + 15 \, b d^{3} + 4 \, {\left(8 \, b^{3} c d^{2} - 5 \, b^{2} d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 28 \, {\left(8 \, b^{3} c d^{2} + 5 \, b^{2} d^{3}\right)} x - 4 \, {\left(7 \, {\left(16 \, b^{3} d^{3} x^{2} + 16 \, b^{3} c^{2} d - 20 \, b^{2} c d^{2} + 15 \, b d^{3} + 4 \, {\left(8 \, b^{3} c d^{2} - 5 \, b^{2} d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{3} - 64 \, {\left(b^{4} d^{3} x^{3} + 3 \, b^{4} c d^{2} x^{2} + 3 \, b^{4} c^{2} d x + b^{4} c^{3}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{3584 \, {\left(b^{4} d \cosh\left(b x + a\right)^{2} + 2 \, b^{4} d \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{4} d \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"1/3584*(105*sqrt(2)*sqrt(pi)*(d^4*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - d^4*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^4*cosh(-2*(b*c - a*d)/d) - d^4*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^4*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - d^4*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) + 105*sqrt(2)*sqrt(pi)*(d^4*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + d^4*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^4*cosh(-2*(b*c - a*d)/d) + d^4*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^4*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + d^4*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) - 4*(112*b^3*d^3*x^2 + 112*b^3*c^2*d + 140*b^2*c*d^2 - 7*(16*b^3*d^3*x^2 + 16*b^3*c^2*d - 20*b^2*c*d^2 + 15*b*d^3 + 4*(8*b^3*c*d^2 - 5*b^2*d^3)*x)*cosh(b*x + a)^4 - 28*(16*b^3*d^3*x^2 + 16*b^3*c^2*d - 20*b^2*c*d^2 + 15*b*d^3 + 4*(8*b^3*c*d^2 - 5*b^2*d^3)*x)*cosh(b*x + a)*sinh(b*x + a)^3 - 7*(16*b^3*d^3*x^2 + 16*b^3*c^2*d - 20*b^2*c*d^2 + 15*b*d^3 + 4*(8*b^3*c*d^2 - 5*b^2*d^3)*x)*sinh(b*x + a)^4 + 105*b*d^3 + 128*(b^4*d^3*x^3 + 3*b^4*c*d^2*x^2 + 3*b^4*c^2*d*x + b^4*c^3)*cosh(b*x + a)^2 + 2*(64*b^4*d^3*x^3 + 192*b^4*c*d^2*x^2 + 192*b^4*c^2*d*x + 64*b^4*c^3 - 21*(16*b^3*d^3*x^2 + 16*b^3*c^2*d - 20*b^2*c*d^2 + 15*b*d^3 + 4*(8*b^3*c*d^2 - 5*b^2*d^3)*x)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 28*(8*b^3*c*d^2 + 5*b^2*d^3)*x - 4*(7*(16*b^3*d^3*x^2 + 16*b^3*c^2*d - 20*b^2*c*d^2 + 15*b*d^3 + 4*(8*b^3*c*d^2 - 5*b^2*d^3)*x)*cosh(b*x + a)^3 - 64*(b^4*d^3*x^3 + 3*b^4*c*d^2*x^2 + 3*b^4*c^2*d*x + b^4*c^3)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/(b^4*d*cosh(b*x + a)^2 + 2*b^4*d*cosh(b*x + a)*sinh(b*x + a) + b^4*d*sinh(b*x + a)^2)","B",0
46,1,755,0,0.509631," ","integrate((d*x+c)^(3/2)*sinh(b*x+a)^2,x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{3} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 15 \, \sqrt{2} \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{3} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 4 \, {\left(20 \, b^{2} d^{2} x - 5 \, {\left(4 \, b^{2} d^{2} x + 4 \, b^{2} c d - 3 \, b d^{2}\right)} \cosh\left(b x + a\right)^{4} - 20 \, {\left(4 \, b^{2} d^{2} x + 4 \, b^{2} c d - 3 \, b d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - 5 \, {\left(4 \, b^{2} d^{2} x + 4 \, b^{2} c d - 3 \, b d^{2}\right)} \sinh\left(b x + a\right)^{4} + 20 \, b^{2} c d + 15 \, b d^{2} + 32 \, {\left(b^{3} d^{2} x^{2} + 2 \, b^{3} c d x + b^{3} c^{2}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(16 \, b^{3} d^{2} x^{2} + 32 \, b^{3} c d x + 16 \, b^{3} c^{2} - 15 \, {\left(4 \, b^{2} d^{2} x + 4 \, b^{2} c d - 3 \, b d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} - 4 \, {\left(5 \, {\left(4 \, b^{2} d^{2} x + 4 \, b^{2} c d - 3 \, b d^{2}\right)} \cosh\left(b x + a\right)^{3} - 16 \, {\left(b^{3} d^{2} x^{2} + 2 \, b^{3} c d x + b^{3} c^{2}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{640 \, {\left(b^{3} d \cosh\left(b x + a\right)^{2} + 2 \, b^{3} d \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{3} d \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"1/640*(15*sqrt(2)*sqrt(pi)*(d^3*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - d^3*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^3*cosh(-2*(b*c - a*d)/d) - d^3*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^3*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - d^3*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) - 15*sqrt(2)*sqrt(pi)*(d^3*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + d^3*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^3*cosh(-2*(b*c - a*d)/d) + d^3*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^3*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + d^3*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) - 4*(20*b^2*d^2*x - 5*(4*b^2*d^2*x + 4*b^2*c*d - 3*b*d^2)*cosh(b*x + a)^4 - 20*(4*b^2*d^2*x + 4*b^2*c*d - 3*b*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 - 5*(4*b^2*d^2*x + 4*b^2*c*d - 3*b*d^2)*sinh(b*x + a)^4 + 20*b^2*c*d + 15*b*d^2 + 32*(b^3*d^2*x^2 + 2*b^3*c*d*x + b^3*c^2)*cosh(b*x + a)^2 + 2*(16*b^3*d^2*x^2 + 32*b^3*c*d*x + 16*b^3*c^2 - 15*(4*b^2*d^2*x + 4*b^2*c*d - 3*b*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 - 4*(5*(4*b^2*d^2*x + 4*b^2*c*d - 3*b*d^2)*cosh(b*x + a)^3 - 16*(b^3*d^2*x^2 + 2*b^3*c*d*x + b^3*c^2)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/(b^3*d*cosh(b*x + a)^2 + 2*b^3*d*cosh(b*x + a)*sinh(b*x + a) + b^3*d*sinh(b*x + a)^2)","B",0
47,1,590,0,0.501828," ","integrate(sinh(b*x+a)^2*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 3 \, \sqrt{2} \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 4 \, {\left(3 \, b d \cosh\left(b x + a\right)^{4} + 12 \, b d \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + 3 \, b d \sinh\left(b x + a\right)^{4} - 8 \, {\left(b^{2} d x + b^{2} c\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(4 \, b^{2} d x - 9 \, b d \cosh\left(b x + a\right)^{2} + 4 \, b^{2} c\right)} \sinh\left(b x + a\right)^{2} - 3 \, b d + 4 \, {\left(3 \, b d \cosh\left(b x + a\right)^{3} - 4 \, {\left(b^{2} d x + b^{2} c\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{96 \, {\left(b^{2} d \cosh\left(b x + a\right)^{2} + 2 \, b^{2} d \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{2} d \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"1/96*(3*sqrt(2)*sqrt(pi)*(d^2*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - d^2*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^2*cosh(-2*(b*c - a*d)/d) - d^2*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^2*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - d^2*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) + 3*sqrt(2)*sqrt(pi)*(d^2*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + d^2*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^2*cosh(-2*(b*c - a*d)/d) + d^2*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^2*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + d^2*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) + 4*(3*b*d*cosh(b*x + a)^4 + 12*b*d*cosh(b*x + a)*sinh(b*x + a)^3 + 3*b*d*sinh(b*x + a)^4 - 8*(b^2*d*x + b^2*c)*cosh(b*x + a)^2 - 2*(4*b^2*d*x - 9*b*d*cosh(b*x + a)^2 + 4*b^2*c)*sinh(b*x + a)^2 - 3*b*d + 4*(3*b*d*cosh(b*x + a)^3 - 4*(b^2*d*x + b^2*c)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/(b^2*d*cosh(b*x + a)^2 + 2*b^2*d*cosh(b*x + a)*sinh(b*x + a) + b^2*d*sinh(b*x + a)^2)","B",0
48,1,155,0,1.185882," ","integrate(sinh(b*x+a)^2/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\pi} {\left(d \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - \sqrt{2} \sqrt{\pi} {\left(d \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 8 \, \sqrt{d x + c} b}{8 \, b d}"," ",0,"1/8*(sqrt(2)*sqrt(pi)*(d*cosh(-2*(b*c - a*d)/d) - d*sinh(-2*(b*c - a*d)/d))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) - sqrt(2)*sqrt(pi)*(d*cosh(-2*(b*c - a*d)/d) + d*sinh(-2*(b*c - a*d)/d))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) - 8*sqrt(d*x + c)*b)/(b*d)","A",0
49,1,571,0,1.164406," ","integrate(sinh(b*x+a)^2/(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + \sqrt{2} \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\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)} \sqrt{d x + c}}{2 \, {\left({\left(d^{2} x + c d\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(d^{2} x + c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(d^{2} x + c d\right)} \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"-1/2*(sqrt(2)*sqrt(pi)*((d*x + c)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((d*x + c)*cosh(-2*(b*c - a*d)/d) - (d*x + c)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((d*x + c)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) + sqrt(2)*sqrt(pi)*((d*x + c)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((d*x + c)*cosh(-2*(b*c - a*d)/d) + (d*x + c)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((d*x + c)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) + (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)*sqrt(d*x + c))/((d^2*x + c*d)*cosh(b*x + a)^2 + 2*(d^2*x + c*d)*cosh(b*x + a)*sinh(b*x + a) + (d^2*x + c*d)*sinh(b*x + a)^2)","B",0
50,1,864,0,0.780077," ","integrate(sinh(b*x+a)^2/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 4 \, \sqrt{2} \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - {\left({\left(4 \, b d x + 4 \, b c + d\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(4 \, b d x + 4 \, b c + d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(4 \, b d x + 4 \, b c + d\right)} \sinh\left(b x + a\right)^{4} - 4 \, b d x - 2 \, d \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, {\left(4 \, b d x + 4 \, b c + d\right)} \cosh\left(b x + a\right)^{2} - d\right)} \sinh\left(b x + a\right)^{2} - 4 \, b c + 4 \, {\left({\left(4 \, b d x + 4 \, b c + d\right)} \cosh\left(b x + a\right)^{3} - d \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + d\right)} \sqrt{d x + c}}{6 \, {\left({\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"1/6*(4*sqrt(2)*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-2*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) - 4*sqrt(2)*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-2*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) - ((4*b*d*x + 4*b*c + d)*cosh(b*x + a)^4 + 4*(4*b*d*x + 4*b*c + d)*cosh(b*x + a)*sinh(b*x + a)^3 + (4*b*d*x + 4*b*c + d)*sinh(b*x + a)^4 - 4*b*d*x - 2*d*cosh(b*x + a)^2 + 2*(3*(4*b*d*x + 4*b*c + d)*cosh(b*x + a)^2 - d)*sinh(b*x + a)^2 - 4*b*c + 4*((4*b*d*x + 4*b*c + d)*cosh(b*x + a)^3 - d*cosh(b*x + a))*sinh(b*x + a) + d)*sqrt(d*x + c))/((d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a)^2 + 2*(d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a)*sinh(b*x + a) + (d^4*x^2 + 2*c*d^3*x + c^2*d^2)*sinh(b*x + a)^2)","B",0
51,1,1352,0,0.907303," ","integrate(sinh(b*x+a)^2/(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{16 \, \sqrt{2} \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 16 \, \sqrt{2} \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left(16 \, b^{2} d^{2} x^{2} + {\left(16 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c^{2} + 4 \, b c d + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(16 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c^{2} + 4 \, b c d + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(16 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c^{2} + 4 \, b c d + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d + b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{4} + 16 \, b^{2} c^{2} - 6 \, d^{2} \cosh\left(b x + a\right)^{2} - 4 \, b c d + 6 \, {\left({\left(16 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c^{2} + 4 \, b c d + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} - d^{2}\right)} \sinh\left(b x + a\right)^{2} + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d - b d^{2}\right)} x + 4 \, {\left({\left(16 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c^{2} + 4 \, b c d + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} - 3 \, d^{2} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{30 \, {\left({\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"-1/30*(16*sqrt(2)*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-2*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) + 16*sqrt(2)*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-2*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) + (16*b^2*d^2*x^2 + (16*b^2*d^2*x^2 + 16*b^2*c^2 + 4*b*c*d + 3*d^2 + 4*(8*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^4 + 4*(16*b^2*d^2*x^2 + 16*b^2*c^2 + 4*b*c*d + 3*d^2 + 4*(8*b^2*c*d + b*d^2)*x)*cosh(b*x + a)*sinh(b*x + a)^3 + (16*b^2*d^2*x^2 + 16*b^2*c^2 + 4*b*c*d + 3*d^2 + 4*(8*b^2*c*d + b*d^2)*x)*sinh(b*x + a)^4 + 16*b^2*c^2 - 6*d^2*cosh(b*x + a)^2 - 4*b*c*d + 6*((16*b^2*d^2*x^2 + 16*b^2*c^2 + 4*b*c*d + 3*d^2 + 4*(8*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^2 - d^2)*sinh(b*x + a)^2 + 3*d^2 + 4*(8*b^2*c*d - b*d^2)*x + 4*((16*b^2*d^2*x^2 + 16*b^2*c^2 + 4*b*c*d + 3*d^2 + 4*(8*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^3 - 3*d^2*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/((d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a)^2 + 2*(d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a)*sinh(b*x + a) + (d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*sinh(b*x + a)^2)","B",0
52,1,1827,0,0.575556," ","integrate(sinh(b*x+a)^2/(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{64 \, \sqrt{2} \sqrt{\pi} {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 64 \, \sqrt{2} \sqrt{\pi} {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} - 16 \, b^{2} c^{2} d + 30 \, d^{3} \cosh\left(b x + a\right)^{2} - {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} + 16 \, b^{2} c^{2} d + 12 \, b c d^{2} + 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 4 \, {\left(48 \, b^{3} c^{2} d + 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{4} - 4 \, {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} + 16 \, b^{2} c^{2} d + 12 \, b c d^{2} + 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 4 \, {\left(48 \, b^{3} c^{2} d + 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} + 16 \, b^{2} c^{2} d + 12 \, b c d^{2} + 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 4 \, {\left(48 \, b^{3} c^{2} d + 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{4} + 12 \, b c d^{2} - 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} - b^{2} d^{3}\right)} x^{2} + 6 \, {\left(5 \, d^{3} - {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} + 16 \, b^{2} c^{2} d + 12 \, b c d^{2} + 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 4 \, {\left(48 \, b^{3} c^{2} d + 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(48 \, b^{3} c^{2} d - 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x + 4 \, {\left(15 \, d^{3} \cosh\left(b x + a\right) - {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} + 16 \, b^{2} c^{2} d + 12 \, b c d^{2} + 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 4 \, {\left(48 \, b^{3} c^{2} d + 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{3}\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{210 \, {\left({\left(d^{8} x^{4} + 4 \, c d^{7} x^{3} + 6 \, c^{2} d^{6} x^{2} + 4 \, c^{3} d^{5} x + c^{4} d^{4}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(d^{8} x^{4} + 4 \, c d^{7} x^{3} + 6 \, c^{2} d^{6} x^{2} + 4 \, c^{3} d^{5} x + c^{4} d^{4}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(d^{8} x^{4} + 4 \, c d^{7} x^{3} + 6 \, c^{2} d^{6} x^{2} + 4 \, c^{3} d^{5} x + c^{4} d^{4}\right)} \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"1/210*(64*sqrt(2)*sqrt(pi)*((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(-2*(b*c - a*d)/d) - (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) - 64*sqrt(2)*sqrt(pi)*((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(-2*(b*c - a*d)/d) + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) + (64*b^3*d^3*x^3 + 64*b^3*c^3 - 16*b^2*c^2*d + 30*d^3*cosh(b*x + a)^2 - (64*b^3*d^3*x^3 + 64*b^3*c^3 + 16*b^2*c^2*d + 12*b*c*d^2 + 15*d^3 + 16*(12*b^3*c*d^2 + b^2*d^3)*x^2 + 4*(48*b^3*c^2*d + 8*b^2*c*d^2 + 3*b*d^3)*x)*cosh(b*x + a)^4 - 4*(64*b^3*d^3*x^3 + 64*b^3*c^3 + 16*b^2*c^2*d + 12*b*c*d^2 + 15*d^3 + 16*(12*b^3*c*d^2 + b^2*d^3)*x^2 + 4*(48*b^3*c^2*d + 8*b^2*c*d^2 + 3*b*d^3)*x)*cosh(b*x + a)*sinh(b*x + a)^3 - (64*b^3*d^3*x^3 + 64*b^3*c^3 + 16*b^2*c^2*d + 12*b*c*d^2 + 15*d^3 + 16*(12*b^3*c*d^2 + b^2*d^3)*x^2 + 4*(48*b^3*c^2*d + 8*b^2*c*d^2 + 3*b*d^3)*x)*sinh(b*x + a)^4 + 12*b*c*d^2 - 15*d^3 + 16*(12*b^3*c*d^2 - b^2*d^3)*x^2 + 6*(5*d^3 - (64*b^3*d^3*x^3 + 64*b^3*c^3 + 16*b^2*c^2*d + 12*b*c*d^2 + 15*d^3 + 16*(12*b^3*c*d^2 + b^2*d^3)*x^2 + 4*(48*b^3*c^2*d + 8*b^2*c*d^2 + 3*b*d^3)*x)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*(48*b^3*c^2*d - 8*b^2*c*d^2 + 3*b*d^3)*x + 4*(15*d^3*cosh(b*x + a) - (64*b^3*d^3*x^3 + 64*b^3*c^3 + 16*b^2*c^2*d + 12*b*c*d^2 + 15*d^3 + 16*(12*b^3*c*d^2 + b^2*d^3)*x^2 + 4*(48*b^3*c^2*d + 8*b^2*c*d^2 + 3*b*d^3)*x)*cosh(b*x + a)^3)*sinh(b*x + a))*sqrt(d*x + c))/((d^8*x^4 + 4*c*d^7*x^3 + 6*c^2*d^6*x^2 + 4*c^3*d^5*x + c^4*d^4)*cosh(b*x + a)^2 + 2*(d^8*x^4 + 4*c*d^7*x^3 + 6*c^2*d^6*x^2 + 4*c^3*d^5*x + c^4*d^4)*cosh(b*x + a)*sinh(b*x + a) + (d^8*x^4 + 4*c*d^7*x^3 + 6*c^2*d^6*x^2 + 4*c^3*d^5*x + c^4*d^4)*sinh(b*x + a)^2)","B",0
53,1,2090,0,0.509273," ","integrate((d*x+c)^(5/2)*sinh(b*x+a)^3,x, algorithm=""fricas"")","-\frac{5 \, \sqrt{3} \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 5 \, \sqrt{3} \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 1215 \, \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{3} \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 1215 \, \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{3} \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 6 \, {\left(12 \, b^{3} d^{2} x^{2} + {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{6} + 6 \, {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{6} + 12 \, b^{3} c^{2} - 27 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{4} - 3 \, {\left(36 \, b^{3} d^{2} x^{2} + 36 \, b^{3} c^{2} - 90 \, b^{2} c d + 135 \, b d^{2} - 5 \, {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 18 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{4} + 10 \, b^{2} c d + 4 \, {\left(5 \, {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} - 27 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 5 \, b d^{2} - 27 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} + 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d + 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} - 3 \, {\left(36 \, b^{3} d^{2} x^{2} + 36 \, b^{3} c^{2} - 5 \, {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{4} + 90 \, b^{2} c d + 135 \, b d^{2} + 54 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 18 \, {\left(4 \, b^{3} c d + 5 \, b^{2} d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(12 \, b^{3} c d + 5 \, b^{2} d^{2}\right)} x + 6 \, {\left({\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{5} - 18 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} - 9 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} + 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d + 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{1728 \, {\left(b^{4} \cosh\left(b x + a\right)^{3} + 3 \, b^{4} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, b^{4} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + b^{4} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"-1/1728*(5*sqrt(3)*sqrt(pi)*(d^3*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - d^3*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d^3*cosh(-3*(b*c - a*d)/d) - d^3*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^3*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - d^3*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^3*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - d^3*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) - 5*sqrt(3)*sqrt(pi)*(d^3*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + d^3*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d^3*cosh(-3*(b*c - a*d)/d) + d^3*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^3*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + d^3*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^3*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + d^3*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) - 1215*sqrt(pi)*(d^3*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - d^3*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d^3*cosh(-(b*c - a*d)/d) - d^3*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^3*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d^3*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^3*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - d^3*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 1215*sqrt(pi)*(d^3*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + d^3*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d^3*cosh(-(b*c - a*d)/d) + d^3*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^3*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d^3*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^3*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + d^3*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - 6*(12*b^3*d^2*x^2 + (12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^6 + 6*(12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)*sinh(b*x + a)^5 + (12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*sinh(b*x + a)^6 + 12*b^3*c^2 - 27*(4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^4 - 3*(36*b^3*d^2*x^2 + 36*b^3*c^2 - 90*b^2*c*d + 135*b*d^2 - 5*(12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^2 + 18*(4*b^3*c*d - 5*b^2*d^2)*x)*sinh(b*x + a)^4 + 10*b^2*c*d + 4*(5*(12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^3 - 27*(4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a))*sinh(b*x + a)^3 + 5*b*d^2 - 27*(4*b^3*d^2*x^2 + 4*b^3*c^2 + 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d + 5*b^2*d^2)*x)*cosh(b*x + a)^2 - 3*(36*b^3*d^2*x^2 + 36*b^3*c^2 - 5*(12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^4 + 90*b^2*c*d + 135*b*d^2 + 54*(4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^2 + 18*(4*b^3*c*d + 5*b^2*d^2)*x)*sinh(b*x + a)^2 + 2*(12*b^3*c*d + 5*b^2*d^2)*x + 6*((12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^5 - 18*(4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^3 - 9*(4*b^3*d^2*x^2 + 4*b^3*c^2 + 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d + 5*b^2*d^2)*x)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/(b^4*cosh(b*x + a)^3 + 3*b^4*cosh(b*x + a)^2*sinh(b*x + a) + 3*b^4*cosh(b*x + a)*sinh(b*x + a)^2 + b^4*sinh(b*x + a)^3)","B",0
54,1,1543,0,0.547126," ","integrate((d*x+c)^(3/2)*sinh(b*x+a)^3,x, algorithm=""fricas"")","-\frac{\sqrt{3} \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + \sqrt{3} \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 81 \, \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{2} \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 81 \, \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{2} \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 6 \, {\left({\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right)^{6} + 6 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + {\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \sinh\left(b x + a\right)^{6} - 9 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right)^{4} - 3 \, {\left(6 \, b^{2} d x + 6 \, b^{2} c - 5 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right)^{2} - 9 \, b d\right)} \sinh\left(b x + a\right)^{4} + 2 \, b^{2} d x + 4 \, {\left(5 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right)^{3} - 9 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 2 \, b^{2} c - 9 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c + 3 \, b d\right)} \cosh\left(b x + a\right)^{2} + 3 \, {\left(5 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right)^{4} - 6 \, b^{2} d x - 6 \, b^{2} c - 18 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right)^{2} - 9 \, b d\right)} \sinh\left(b x + a\right)^{2} + b d + 6 \, {\left({\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right)^{5} - 6 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right)^{3} - 3 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c + 3 \, b d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{288 \, {\left(b^{3} \cosh\left(b x + a\right)^{3} + 3 \, b^{3} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, b^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + b^{3} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"-1/288*(sqrt(3)*sqrt(pi)*(d^2*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - d^2*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d^2*cosh(-3*(b*c - a*d)/d) - d^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^2*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - d^2*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^2*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - d^2*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) + sqrt(3)*sqrt(pi)*(d^2*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + d^2*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d^2*cosh(-3*(b*c - a*d)/d) + d^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^2*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + d^2*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^2*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + d^2*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) - 81*sqrt(pi)*(d^2*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - d^2*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d^2*cosh(-(b*c - a*d)/d) - d^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^2*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d^2*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^2*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - d^2*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) - 81*sqrt(pi)*(d^2*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + d^2*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d^2*cosh(-(b*c - a*d)/d) + d^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^2*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d^2*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^2*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + d^2*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - 6*((2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)^6 + 6*(2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)*sinh(b*x + a)^5 + (2*b^2*d*x + 2*b^2*c - b*d)*sinh(b*x + a)^6 - 9*(2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a)^4 - 3*(6*b^2*d*x + 6*b^2*c - 5*(2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)^2 - 9*b*d)*sinh(b*x + a)^4 + 2*b^2*d*x + 4*(5*(2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)^3 - 9*(2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a))*sinh(b*x + a)^3 + 2*b^2*c - 9*(2*b^2*d*x + 2*b^2*c + 3*b*d)*cosh(b*x + a)^2 + 3*(5*(2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)^4 - 6*b^2*d*x - 6*b^2*c - 18*(2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a)^2 - 9*b*d)*sinh(b*x + a)^2 + b*d + 6*((2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)^5 - 6*(2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a)^3 - 3*(2*b^2*d*x + 2*b^2*c + 3*b*d)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/(b^3*cosh(b*x + a)^3 + 3*b^3*cosh(b*x + a)^2*sinh(b*x + a) + 3*b^3*cosh(b*x + a)*sinh(b*x + a)^2 + b^3*sinh(b*x + a)^3)","B",0
55,1,1216,0,0.467991," ","integrate(sinh(b*x+a)^3*(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{3} \sqrt{\pi} {\left(d \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - \sqrt{3} \sqrt{\pi} {\left(d \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 27 \, \sqrt{\pi} {\left(d \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - d \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d \cosh\left(-\frac{b c - a d}{d}\right) - d \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - d \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 27 \, \sqrt{\pi} {\left(d \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + d \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d \cosh\left(-\frac{b c - a d}{d}\right) + d \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + d \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 6 \, {\left(b \cosh\left(b x + a\right)^{6} + 6 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + b \sinh\left(b x + a\right)^{6} - 9 \, b \cosh\left(b x + a\right)^{4} + 3 \, {\left(5 \, b \cosh\left(b x + a\right)^{2} - 3 \, b\right)} \sinh\left(b x + a\right)^{4} + 4 \, {\left(5 \, b \cosh\left(b x + a\right)^{3} - 9 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} - 9 \, b \cosh\left(b x + a\right)^{2} + 3 \, {\left(5 \, b \cosh\left(b x + a\right)^{4} - 18 \, b \cosh\left(b x + a\right)^{2} - 3 \, b\right)} \sinh\left(b x + a\right)^{2} + 6 \, {\left(b \cosh\left(b x + a\right)^{5} - 6 \, b \cosh\left(b x + a\right)^{3} - 3 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + b\right)} \sqrt{d x + c}}{144 \, {\left(b^{2} \cosh\left(b x + a\right)^{3} + 3 \, b^{2} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, b^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + b^{2} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"-1/144*(sqrt(3)*sqrt(pi)*(d*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - d*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d*cosh(-3*(b*c - a*d)/d) - d*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - d*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - d*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) - sqrt(3)*sqrt(pi)*(d*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + d*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d*cosh(-3*(b*c - a*d)/d) + d*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + d*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + d*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) - 27*sqrt(pi)*(d*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - d*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d*cosh(-(b*c - a*d)/d) - d*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - d*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 27*sqrt(pi)*(d*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + d*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d*cosh(-(b*c - a*d)/d) + d*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + d*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - 6*(b*cosh(b*x + a)^6 + 6*b*cosh(b*x + a)*sinh(b*x + a)^5 + b*sinh(b*x + a)^6 - 9*b*cosh(b*x + a)^4 + 3*(5*b*cosh(b*x + a)^2 - 3*b)*sinh(b*x + a)^4 + 4*(5*b*cosh(b*x + a)^3 - 9*b*cosh(b*x + a))*sinh(b*x + a)^3 - 9*b*cosh(b*x + a)^2 + 3*(5*b*cosh(b*x + a)^4 - 18*b*cosh(b*x + a)^2 - 3*b)*sinh(b*x + a)^2 + 6*(b*cosh(b*x + a)^5 - 6*b*cosh(b*x + a)^3 - 3*b*cosh(b*x + a))*sinh(b*x + a) + b)*sqrt(d*x + c))/(b^2*cosh(b*x + a)^3 + 3*b^2*cosh(b*x + a)^2*sinh(b*x + a) + 3*b^2*cosh(b*x + a)*sinh(b*x + a)^2 + b^2*sinh(b*x + a)^3)","B",0
56,1,252,0,0.525320," ","integrate(sinh(b*x+a)^3/(d*x+c)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{3} \sqrt{\pi} \sqrt{\frac{b}{d}} {\left(\cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + \sqrt{3} \sqrt{\pi} \sqrt{-\frac{b}{d}} {\left(\cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 9 \, \sqrt{\pi} \sqrt{\frac{b}{d}} {\left(\cosh\left(-\frac{b c - a d}{d}\right) - \sinh\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 9 \, \sqrt{\pi} \sqrt{-\frac{b}{d}} {\left(\cosh\left(-\frac{b c - a d}{d}\right) + \sinh\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right)}{24 \, b}"," ",0,"-1/24*(sqrt(3)*sqrt(pi)*sqrt(b/d)*(cosh(-3*(b*c - a*d)/d) - sinh(-3*(b*c - a*d)/d))*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) + sqrt(3)*sqrt(pi)*sqrt(-b/d)*(cosh(-3*(b*c - a*d)/d) + sinh(-3*(b*c - a*d)/d))*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) - 9*sqrt(pi)*sqrt(b/d)*(cosh(-(b*c - a*d)/d) - sinh(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(b/d)) - 9*sqrt(pi)*sqrt(-b/d)*(cosh(-(b*c - a*d)/d) + sinh(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-b/d)))/b","A",0
57,1,1346,0,0.493489," ","integrate(sinh(b*x+a)^3/(d*x+c)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{3} \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - \sqrt{3} \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 3 \, \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 3 \, \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - {\left(\cosh\left(b x + a\right)^{6} + 6 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + \sinh\left(b x + a\right)^{6} + 3 \, {\left(5 \, \cosh\left(b x + a\right)^{2} - 1\right)} \sinh\left(b x + a\right)^{4} - 3 \, \cosh\left(b x + a\right)^{4} + 4 \, {\left(5 \, \cosh\left(b x + a\right)^{3} - 3 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(5 \, \cosh\left(b x + a\right)^{4} - 6 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 3 \, \cosh\left(b x + a\right)^{2} + 6 \, {\left(\cosh\left(b x + a\right)^{5} - 2 \, \cosh\left(b x + a\right)^{3} + \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) - 1\right)} \sqrt{d x + c}}{4 \, {\left({\left(d^{2} x + c d\right)} \cosh\left(b x + a\right)^{3} + 3 \, {\left(d^{2} x + c d\right)} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, {\left(d^{2} x + c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + {\left(d^{2} x + c d\right)} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"1/4*(sqrt(3)*sqrt(pi)*((d*x + c)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((d*x + c)*cosh(-3*(b*c - a*d)/d) - (d*x + c)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((d*x + c)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((d*x + c)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) - sqrt(3)*sqrt(pi)*((d*x + c)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((d*x + c)*cosh(-3*(b*c - a*d)/d) + (d*x + c)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((d*x + c)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((d*x + c)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) - 3*sqrt(pi)*((d*x + c)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((d*x + c)*cosh(-(b*c - a*d)/d) - (d*x + c)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((d*x + c)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((d*x + c)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 3*sqrt(pi)*((d*x + c)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((d*x + c)*cosh(-(b*c - a*d)/d) + (d*x + c)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((d*x + c)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((d*x + c)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - (cosh(b*x + a)^6 + 6*cosh(b*x + a)*sinh(b*x + a)^5 + sinh(b*x + a)^6 + 3*(5*cosh(b*x + a)^2 - 1)*sinh(b*x + a)^4 - 3*cosh(b*x + a)^4 + 4*(5*cosh(b*x + a)^3 - 3*cosh(b*x + a))*sinh(b*x + a)^3 + 3*(5*cosh(b*x + a)^4 - 6*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 3*cosh(b*x + a)^2 + 6*(cosh(b*x + a)^5 - 2*cosh(b*x + a)^3 + cosh(b*x + a))*sinh(b*x + a) - 1)*sqrt(d*x + c))/((d^2*x + c*d)*cosh(b*x + a)^3 + 3*(d^2*x + c*d)*cosh(b*x + a)^2*sinh(b*x + a) + 3*(d^2*x + c*d)*cosh(b*x + a)*sinh(b*x + a)^2 + (d^2*x + c*d)*sinh(b*x + a)^3)","B",0
58,1,2059,0,0.571080," ","integrate(sinh(b*x+a)^3/(d*x+c)^(5/2),x, algorithm=""fricas"")","-\frac{6 \, \sqrt{3} \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 6 \, \sqrt{3} \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 6 \, \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 6 \, \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left({\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right)^{6} + 6 \, {\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + {\left(6 \, b d x + 6 \, b c + d\right)} \sinh\left(b x + a\right)^{6} - 3 \, {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right)^{4} - 3 \, {\left(2 \, b d x - 5 \, {\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right)^{2} + 2 \, b c + d\right)} \sinh\left(b x + a\right)^{4} + 4 \, {\left(5 \, {\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right)^{3} - 3 \, {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 6 \, b d x - 3 \, {\left(2 \, b d x + 2 \, b c - d\right)} \cosh\left(b x + a\right)^{2} + 3 \, {\left(5 \, {\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right)^{4} - 2 \, b d x - 6 \, {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right)^{2} - 2 \, b c + d\right)} \sinh\left(b x + a\right)^{2} + 6 \, b c + 6 \, {\left({\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right)^{5} - 2 \, {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right)^{3} - {\left(2 \, b d x + 2 \, b c - d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) - d\right)} \sqrt{d x + c}}{12 \, {\left({\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right)^{3} + 3 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"-1/12*(6*sqrt(3)*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-3*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) + 6*sqrt(3)*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-3*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) - 6*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) - 6*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + ((6*b*d*x + 6*b*c + d)*cosh(b*x + a)^6 + 6*(6*b*d*x + 6*b*c + d)*cosh(b*x + a)*sinh(b*x + a)^5 + (6*b*d*x + 6*b*c + d)*sinh(b*x + a)^6 - 3*(2*b*d*x + 2*b*c + d)*cosh(b*x + a)^4 - 3*(2*b*d*x - 5*(6*b*d*x + 6*b*c + d)*cosh(b*x + a)^2 + 2*b*c + d)*sinh(b*x + a)^4 + 4*(5*(6*b*d*x + 6*b*c + d)*cosh(b*x + a)^3 - 3*(2*b*d*x + 2*b*c + d)*cosh(b*x + a))*sinh(b*x + a)^3 + 6*b*d*x - 3*(2*b*d*x + 2*b*c - d)*cosh(b*x + a)^2 + 3*(5*(6*b*d*x + 6*b*c + d)*cosh(b*x + a)^4 - 2*b*d*x - 6*(2*b*d*x + 2*b*c + d)*cosh(b*x + a)^2 - 2*b*c + d)*sinh(b*x + a)^2 + 6*b*c + 6*((6*b*d*x + 6*b*c + d)*cosh(b*x + a)^5 - 2*(2*b*d*x + 2*b*c + d)*cosh(b*x + a)^3 - (2*b*d*x + 2*b*c - d)*cosh(b*x + a))*sinh(b*x + a) - d)*sqrt(d*x + c))/((d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a)^3 + 3*(d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a)^2*sinh(b*x + a) + 3*(d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a)*sinh(b*x + a)^2 + (d^4*x^2 + 2*c*d^3*x + c^2*d^2)*sinh(b*x + a)^3)","B",0
59,1,3286,0,0.710811," ","integrate(sinh(b*x+a)^3/(d*x+c)^(7/2),x, algorithm=""fricas"")","\frac{12 \, \sqrt{3} \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 12 \, \sqrt{3} \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 4 \, \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 4 \, \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - {\left({\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{6} + 6 \, {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{6} - 12 \, b^{2} d^{2} x^{2} - {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{4} - {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d - 15 \, {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{4} - 12 \, b^{2} c^{2} + 4 \, {\left(5 \, {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} - {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 2 \, b c d + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} - 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d - b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + {\left(4 \, b^{2} d^{2} x^{2} + 15 \, {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{4} + 4 \, b^{2} c^{2} - 2 \, b c d - 6 \, {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d - b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{2} - d^{2} - 2 \, {\left(12 \, b^{2} c d - b d^{2}\right)} x + 2 \, {\left(3 \, {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{5} - 2 \, {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} - 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d - b d^{2}\right)} x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{20 \, {\left({\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right)^{3} + 3 \, {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"1/20*(12*sqrt(3)*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-3*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) - 12*sqrt(3)*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-3*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) - 4*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 4*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - ((12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^6 + 6*(12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)*sinh(b*x + a)^5 + (12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*sinh(b*x + a)^6 - 12*b^2*d^2*x^2 - (4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^4 - (4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d - 15*(12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^2 + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*sinh(b*x + a)^4 - 12*b^2*c^2 + 4*(5*(12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^3 - (4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a))*sinh(b*x + a)^3 + 2*b*c*d + (4*b^2*d^2*x^2 + 4*b^2*c^2 - 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d - b*d^2)*x)*cosh(b*x + a)^2 + (4*b^2*d^2*x^2 + 15*(12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^4 + 4*b^2*c^2 - 2*b*c*d - 6*(4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^2 + 3*d^2 + 2*(4*b^2*c*d - b*d^2)*x)*sinh(b*x + a)^2 - d^2 - 2*(12*b^2*c*d - b*d^2)*x + 2*(3*(12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^5 - 2*(4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^3 + (4*b^2*d^2*x^2 + 4*b^2*c^2 - 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d - b*d^2)*x)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/((d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a)^3 + 3*(d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a)^2*sinh(b*x + a) + 3*(d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a)*sinh(b*x + a)^2 + (d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*sinh(b*x + a)^3)","B",0
60,1,189,0,0.681544," ","integrate((d*x)^(3/2)*sinh(f*x),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{\pi} {\left(d^{2} \cosh\left(f x\right) + d^{2} \sinh\left(f x\right)\right)} \sqrt{\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{f}{d}}\right) + 3 \, \sqrt{\pi} {\left(d^{2} \cosh\left(f x\right) + d^{2} \sinh\left(f x\right)\right)} \sqrt{-\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{f}{d}}\right) - 2 \, {\left(2 \, d f^{2} x + {\left(2 \, d f^{2} x - 3 \, d f\right)} \cosh\left(f x\right)^{2} + 2 \, {\left(2 \, d f^{2} x - 3 \, d f\right)} \cosh\left(f x\right) \sinh\left(f x\right) + {\left(2 \, d f^{2} x - 3 \, d f\right)} \sinh\left(f x\right)^{2} + 3 \, d f\right)} \sqrt{d x}}{8 \, {\left(f^{3} \cosh\left(f x\right) + f^{3} \sinh\left(f x\right)\right)}}"," ",0,"-1/8*(3*sqrt(pi)*(d^2*cosh(f*x) + d^2*sinh(f*x))*sqrt(f/d)*erf(sqrt(d*x)*sqrt(f/d)) + 3*sqrt(pi)*(d^2*cosh(f*x) + d^2*sinh(f*x))*sqrt(-f/d)*erf(sqrt(d*x)*sqrt(-f/d)) - 2*(2*d*f^2*x + (2*d*f^2*x - 3*d*f)*cosh(f*x)^2 + 2*(2*d*f^2*x - 3*d*f)*cosh(f*x)*sinh(f*x) + (2*d*f^2*x - 3*d*f)*sinh(f*x)^2 + 3*d*f)*sqrt(d*x))/(f^3*cosh(f*x) + f^3*sinh(f*x))","B",0
61,1,137,0,0.622543," ","integrate(sinh(f*x)*(d*x)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(d \cosh\left(f x\right) + d \sinh\left(f x\right)\right)} \sqrt{\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{f}{d}}\right) - \sqrt{\pi} {\left(d \cosh\left(f x\right) + d \sinh\left(f x\right)\right)} \sqrt{-\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{f}{d}}\right) - 2 \, {\left(f \cosh\left(f x\right)^{2} + 2 \, f \cosh\left(f x\right) \sinh\left(f x\right) + f \sinh\left(f x\right)^{2} + f\right)} \sqrt{d x}}{4 \, {\left(f^{2} \cosh\left(f x\right) + f^{2} \sinh\left(f x\right)\right)}}"," ",0,"-1/4*(sqrt(pi)*(d*cosh(f*x) + d*sinh(f*x))*sqrt(f/d)*erf(sqrt(d*x)*sqrt(f/d)) - sqrt(pi)*(d*cosh(f*x) + d*sinh(f*x))*sqrt(-f/d)*erf(sqrt(d*x)*sqrt(-f/d)) - 2*(f*cosh(f*x)^2 + 2*f*cosh(f*x)*sinh(f*x) + f*sinh(f*x)^2 + f)*sqrt(d*x))/(f^2*cosh(f*x) + f^2*sinh(f*x))","B",0
62,1,58,0,0.668152," ","integrate(sinh(f*x)/(d*x)^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} \sqrt{\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{f}{d}}\right) + \sqrt{\pi} \sqrt{-\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{f}{d}}\right)}{2 \, f}"," ",0,"-1/2*(sqrt(pi)*sqrt(f/d)*erf(sqrt(d*x)*sqrt(f/d)) + sqrt(pi)*sqrt(-f/d)*erf(sqrt(d*x)*sqrt(-f/d)))/f","A",0
63,1,137,0,0.570545," ","integrate(sinh(f*x)/(d*x)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(d x \cosh\left(f x\right) + d x \sinh\left(f x\right)\right)} \sqrt{\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{f}{d}}\right) - \sqrt{\pi} {\left(d x \cosh\left(f x\right) + d x \sinh\left(f x\right)\right)} \sqrt{-\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{f}{d}}\right) - \sqrt{d x} {\left(\cosh\left(f x\right)^{2} + 2 \, \cosh\left(f x\right) \sinh\left(f x\right) + \sinh\left(f x\right)^{2} - 1\right)}}{d^{2} x \cosh\left(f x\right) + d^{2} x \sinh\left(f x\right)}"," ",0,"(sqrt(pi)*(d*x*cosh(f*x) + d*x*sinh(f*x))*sqrt(f/d)*erf(sqrt(d*x)*sqrt(f/d)) - sqrt(pi)*(d*x*cosh(f*x) + d*x*sinh(f*x))*sqrt(-f/d)*erf(sqrt(d*x)*sqrt(-f/d)) - sqrt(d*x)*(cosh(f*x)^2 + 2*cosh(f*x)*sinh(f*x) + sinh(f*x)^2 - 1))/(d^2*x*cosh(f*x) + d^2*x*sinh(f*x))","B",0
64,1,178,0,0.575217," ","integrate(sinh(f*x)/(d*x)^(5/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{\pi} {\left(d f x^{2} \cosh\left(f x\right) + d f x^{2} \sinh\left(f x\right)\right)} \sqrt{\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{f}{d}}\right) + 2 \, \sqrt{\pi} {\left(d f x^{2} \cosh\left(f x\right) + d f x^{2} \sinh\left(f x\right)\right)} \sqrt{-\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{f}{d}}\right) + {\left({\left(2 \, f x + 1\right)} \cosh\left(f x\right)^{2} + 2 \, {\left(2 \, f x + 1\right)} \cosh\left(f x\right) \sinh\left(f x\right) + {\left(2 \, f x + 1\right)} \sinh\left(f x\right)^{2} + 2 \, f x - 1\right)} \sqrt{d x}}{3 \, {\left(d^{3} x^{2} \cosh\left(f x\right) + d^{3} x^{2} \sinh\left(f x\right)\right)}}"," ",0,"-1/3*(2*sqrt(pi)*(d*f*x^2*cosh(f*x) + d*f*x^2*sinh(f*x))*sqrt(f/d)*erf(sqrt(d*x)*sqrt(f/d)) + 2*sqrt(pi)*(d*f*x^2*cosh(f*x) + d*f*x^2*sinh(f*x))*sqrt(-f/d)*erf(sqrt(d*x)*sqrt(-f/d)) + ((2*f*x + 1)*cosh(f*x)^2 + 2*(2*f*x + 1)*cosh(f*x)*sinh(f*x) + (2*f*x + 1)*sinh(f*x)^2 + 2*f*x - 1)*sqrt(d*x))/(d^3*x^2*cosh(f*x) + d^3*x^2*sinh(f*x))","B",0
65,0,0,0,0.471802," ","integrate(csch(b*x+a)*(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x + c} \operatorname{csch}\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*x + c)*csch(b*x + a), x)","F",0
66,0,0,0,0.555031," ","integrate(csch(b*x+a)/(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(b x + a\right)}{\sqrt{d x + c}}, x\right)"," ",0,"integral(csch(b*x + a)/sqrt(d*x + c), x)","F",0
67,-2,0,0,0.000000," ","integrate(sinh(x)^(3/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
68,-2,0,0,0.000000," ","integrate(x/sinh(x)^(3/2)-x*sinh(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
69,1,108,0,0.554197," ","integrate(x/sinh(x)^(5/2)+1/3*x/sinh(x)^(1/2),x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(x + 2\right)} \cosh\left(x\right)^{3} + 3 \, {\left(x + 2\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(x + 2\right)} \sinh\left(x\right)^{3} + {\left(x - 2\right)} \cosh\left(x\right) + {\left(3 \, {\left(x + 2\right)} \cosh\left(x\right)^{2} + x - 2\right)} \sinh\left(x\right)\right)} \sqrt{\sinh\left(x\right)}}{3 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"-4/3*((x + 2)*cosh(x)^3 + 3*(x + 2)*cosh(x)*sinh(x)^2 + (x + 2)*sinh(x)^3 + (x - 2)*cosh(x) + (3*(x + 2)*cosh(x)^2 + x - 2)*sinh(x))*sqrt(sinh(x))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 - 1)*sinh(x)^2 - 2*cosh(x)^2 + 4*(cosh(x)^3 - cosh(x))*sinh(x) + 1)","B",0
70,-2,0,0,0.000000," ","integrate(x/sinh(x)^(7/2)+3/5*x*sinh(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
71,-2,0,0,0.000000," ","integrate(x^2/sinh(x)^(3/2)-x^2*sinh(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
72,0,0,0,0.654305," ","integrate((d*x+c)^m*(b*sinh(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \left(b \sinh\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((d*x + c)^m*(b*sinh(f*x + e))^n, x)","F",0
73,1,340,0,0.507327," ","integrate((d*x+c)^m*sinh(b*x+a)^3,x, algorithm=""fricas"")","\frac{\cosh\left(\frac{d m \log\left(\frac{3 \, b}{d}\right) - 3 \, b c + 3 \, a d}{d}\right) \Gamma\left(m + 1, \frac{3 \, {\left(b d x + b c\right)}}{d}\right) - 9 \, \cosh\left(\frac{d m \log\left(\frac{b}{d}\right) - b c + a d}{d}\right) \Gamma\left(m + 1, \frac{b d x + b c}{d}\right) - 9 \, \cosh\left(\frac{d m \log\left(-\frac{b}{d}\right) + b c - a d}{d}\right) \Gamma\left(m + 1, -\frac{b d x + b c}{d}\right) + \cosh\left(\frac{d m \log\left(-\frac{3 \, b}{d}\right) + 3 \, b c - 3 \, a d}{d}\right) \Gamma\left(m + 1, -\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - \Gamma\left(m + 1, \frac{3 \, {\left(b d x + b c\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{3 \, b}{d}\right) - 3 \, b c + 3 \, a d}{d}\right) + 9 \, \Gamma\left(m + 1, \frac{b d x + b c}{d}\right) \sinh\left(\frac{d m \log\left(\frac{b}{d}\right) - b c + a d}{d}\right) + 9 \, \Gamma\left(m + 1, -\frac{b d x + b c}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{b}{d}\right) + b c - a d}{d}\right) - \Gamma\left(m + 1, -\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{3 \, b}{d}\right) + 3 \, b c - 3 \, a d}{d}\right)}{24 \, b}"," ",0,"1/24*(cosh((d*m*log(3*b/d) - 3*b*c + 3*a*d)/d)*gamma(m + 1, 3*(b*d*x + b*c)/d) - 9*cosh((d*m*log(b/d) - b*c + a*d)/d)*gamma(m + 1, (b*d*x + b*c)/d) - 9*cosh((d*m*log(-b/d) + b*c - a*d)/d)*gamma(m + 1, -(b*d*x + b*c)/d) + cosh((d*m*log(-3*b/d) + 3*b*c - 3*a*d)/d)*gamma(m + 1, -3*(b*d*x + b*c)/d) - gamma(m + 1, 3*(b*d*x + b*c)/d)*sinh((d*m*log(3*b/d) - 3*b*c + 3*a*d)/d) + 9*gamma(m + 1, (b*d*x + b*c)/d)*sinh((d*m*log(b/d) - b*c + a*d)/d) + 9*gamma(m + 1, -(b*d*x + b*c)/d)*sinh((d*m*log(-b/d) + b*c - a*d)/d) - gamma(m + 1, -3*(b*d*x + b*c)/d)*sinh((d*m*log(-3*b/d) + 3*b*c - 3*a*d)/d))/b","A",0
74,1,241,0,0.543962," ","integrate((d*x+c)^m*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(d m + d\right)} \cosh\left(\frac{d m \log\left(\frac{2 \, b}{d}\right) - 2 \, b c + 2 \, a d}{d}\right) \Gamma\left(m + 1, \frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left(d m + d\right)} \cosh\left(\frac{d m \log\left(-\frac{2 \, b}{d}\right) + 2 \, b c - 2 \, a d}{d}\right) \Gamma\left(m + 1, -\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left(d m + d\right)} \Gamma\left(m + 1, \frac{2 \, {\left(b d x + b c\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{2 \, b}{d}\right) - 2 \, b c + 2 \, a d}{d}\right) + {\left(d m + d\right)} \Gamma\left(m + 1, -\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{2 \, b}{d}\right) + 2 \, b c - 2 \, a d}{d}\right) + 4 \, {\left(b d x + b c\right)} \cosh\left(m \log\left(d x + c\right)\right) + 4 \, {\left(b d x + b c\right)} \sinh\left(m \log\left(d x + c\right)\right)}{8 \, {\left(b d m + b d\right)}}"," ",0,"-1/8*((d*m + d)*cosh((d*m*log(2*b/d) - 2*b*c + 2*a*d)/d)*gamma(m + 1, 2*(b*d*x + b*c)/d) - (d*m + d)*cosh((d*m*log(-2*b/d) + 2*b*c - 2*a*d)/d)*gamma(m + 1, -2*(b*d*x + b*c)/d) - (d*m + d)*gamma(m + 1, 2*(b*d*x + b*c)/d)*sinh((d*m*log(2*b/d) - 2*b*c + 2*a*d)/d) + (d*m + d)*gamma(m + 1, -2*(b*d*x + b*c)/d)*sinh((d*m*log(-2*b/d) + 2*b*c - 2*a*d)/d) + 4*(b*d*x + b*c)*cosh(m*log(d*x + c)) + 4*(b*d*x + b*c)*sinh(m*log(d*x + c)))/(b*d*m + b*d)","A",0
75,1,168,0,0.495462," ","integrate((d*x+c)^m*sinh(b*x+a),x, algorithm=""fricas"")","\frac{\cosh\left(\frac{d m \log\left(\frac{b}{d}\right) - b c + a d}{d}\right) \Gamma\left(m + 1, \frac{b d x + b c}{d}\right) + \cosh\left(\frac{d m \log\left(-\frac{b}{d}\right) + b c - a d}{d}\right) \Gamma\left(m + 1, -\frac{b d x + b c}{d}\right) - \Gamma\left(m + 1, \frac{b d x + b c}{d}\right) \sinh\left(\frac{d m \log\left(\frac{b}{d}\right) - b c + a d}{d}\right) - \Gamma\left(m + 1, -\frac{b d x + b c}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{b}{d}\right) + b c - a d}{d}\right)}{2 \, b}"," ",0,"1/2*(cosh((d*m*log(b/d) - b*c + a*d)/d)*gamma(m + 1, (b*d*x + b*c)/d) + cosh((d*m*log(-b/d) + b*c - a*d)/d)*gamma(m + 1, -(b*d*x + b*c)/d) - gamma(m + 1, (b*d*x + b*c)/d)*sinh((d*m*log(b/d) - b*c + a*d)/d) - gamma(m + 1, -(b*d*x + b*c)/d)*sinh((d*m*log(-b/d) + b*c - a*d)/d))/b","A",0
76,0,0,0,0.457257," ","integrate((d*x+c)^m*csch(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \operatorname{csch}\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*csch(b*x + a), x)","F",0
77,0,0,0,0.452916," ","integrate((d*x+c)^m*csch(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \operatorname{csch}\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*csch(b*x + a)^2, x)","F",0
78,1,86,0,0.604570," ","integrate(x^(3+m)*sinh(b*x+a),x, algorithm=""fricas"")","\frac{\cosh\left({\left(m + 3\right)} \log\left(b\right) + a\right) \Gamma\left(m + 4, b x\right) + \cosh\left({\left(m + 3\right)} \log\left(-b\right) - a\right) \Gamma\left(m + 4, -b x\right) - \Gamma\left(m + 4, -b x\right) \sinh\left({\left(m + 3\right)} \log\left(-b\right) - a\right) - \Gamma\left(m + 4, b x\right) \sinh\left({\left(m + 3\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"1/2*(cosh((m + 3)*log(b) + a)*gamma(m + 4, b*x) + cosh((m + 3)*log(-b) - a)*gamma(m + 4, -b*x) - gamma(m + 4, -b*x)*sinh((m + 3)*log(-b) - a) - gamma(m + 4, b*x)*sinh((m + 3)*log(b) + a))/b","A",0
79,1,86,0,0.488638," ","integrate(x^(2+m)*sinh(b*x+a),x, algorithm=""fricas"")","\frac{\cosh\left({\left(m + 2\right)} \log\left(b\right) + a\right) \Gamma\left(m + 3, b x\right) + \cosh\left({\left(m + 2\right)} \log\left(-b\right) - a\right) \Gamma\left(m + 3, -b x\right) - \Gamma\left(m + 3, -b x\right) \sinh\left({\left(m + 2\right)} \log\left(-b\right) - a\right) - \Gamma\left(m + 3, b x\right) \sinh\left({\left(m + 2\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"1/2*(cosh((m + 2)*log(b) + a)*gamma(m + 3, b*x) + cosh((m + 2)*log(-b) - a)*gamma(m + 3, -b*x) - gamma(m + 3, -b*x)*sinh((m + 2)*log(-b) - a) - gamma(m + 3, b*x)*sinh((m + 2)*log(b) + a))/b","A",0
80,1,86,0,0.582640," ","integrate(x^(1+m)*sinh(b*x+a),x, algorithm=""fricas"")","\frac{\cosh\left({\left(m + 1\right)} \log\left(b\right) + a\right) \Gamma\left(m + 2, b x\right) + \cosh\left({\left(m + 1\right)} \log\left(-b\right) - a\right) \Gamma\left(m + 2, -b x\right) - \Gamma\left(m + 2, -b x\right) \sinh\left({\left(m + 1\right)} \log\left(-b\right) - a\right) - \Gamma\left(m + 2, b x\right) \sinh\left({\left(m + 1\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"1/2*(cosh((m + 1)*log(b) + a)*gamma(m + 2, b*x) + cosh((m + 1)*log(-b) - a)*gamma(m + 2, -b*x) - gamma(m + 2, -b*x)*sinh((m + 1)*log(-b) - a) - gamma(m + 2, b*x)*sinh((m + 1)*log(b) + a))/b","A",0
81,1,78,0,0.481375," ","integrate(x^m*sinh(b*x+a),x, algorithm=""fricas"")","\frac{\cosh\left(m \log\left(b\right) + a\right) \Gamma\left(m + 1, b x\right) + \cosh\left(m \log\left(-b\right) - a\right) \Gamma\left(m + 1, -b x\right) - \Gamma\left(m + 1, -b x\right) \sinh\left(m \log\left(-b\right) - a\right) - \Gamma\left(m + 1, b x\right) \sinh\left(m \log\left(b\right) + a\right)}{2 \, b}"," ",0,"1/2*(cosh(m*log(b) + a)*gamma(m + 1, b*x) + cosh(m*log(-b) - a)*gamma(m + 1, -b*x) - gamma(m + 1, -b*x)*sinh(m*log(-b) - a) - gamma(m + 1, b*x)*sinh(m*log(b) + a))/b","A",0
82,1,78,0,0.648732," ","integrate(x^(-1+m)*sinh(b*x+a),x, algorithm=""fricas"")","\frac{\cosh\left({\left(m - 1\right)} \log\left(b\right) + a\right) \Gamma\left(m, b x\right) + \cosh\left({\left(m - 1\right)} \log\left(-b\right) - a\right) \Gamma\left(m, -b x\right) - \Gamma\left(m, -b x\right) \sinh\left({\left(m - 1\right)} \log\left(-b\right) - a\right) - \Gamma\left(m, b x\right) \sinh\left({\left(m - 1\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"1/2*(cosh((m - 1)*log(b) + a)*gamma(m, b*x) + cosh((m - 1)*log(-b) - a)*gamma(m, -b*x) - gamma(m, -b*x)*sinh((m - 1)*log(-b) - a) - gamma(m, b*x)*sinh((m - 1)*log(b) + a))/b","A",0
83,1,86,0,0.508986," ","integrate(x^(-2+m)*sinh(b*x+a),x, algorithm=""fricas"")","\frac{\cosh\left({\left(m - 2\right)} \log\left(b\right) + a\right) \Gamma\left(m - 1, b x\right) + \cosh\left({\left(m - 2\right)} \log\left(-b\right) - a\right) \Gamma\left(m - 1, -b x\right) - \Gamma\left(m - 1, -b x\right) \sinh\left({\left(m - 2\right)} \log\left(-b\right) - a\right) - \Gamma\left(m - 1, b x\right) \sinh\left({\left(m - 2\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"1/2*(cosh((m - 2)*log(b) + a)*gamma(m - 1, b*x) + cosh((m - 2)*log(-b) - a)*gamma(m - 1, -b*x) - gamma(m - 1, -b*x)*sinh((m - 2)*log(-b) - a) - gamma(m - 1, b*x)*sinh((m - 2)*log(b) + a))/b","A",0
84,1,86,0,0.534913," ","integrate(x^(-3+m)*sinh(b*x+a),x, algorithm=""fricas"")","\frac{\cosh\left({\left(m - 3\right)} \log\left(b\right) + a\right) \Gamma\left(m - 2, b x\right) + \cosh\left({\left(m - 3\right)} \log\left(-b\right) - a\right) \Gamma\left(m - 2, -b x\right) - \Gamma\left(m - 2, -b x\right) \sinh\left({\left(m - 3\right)} \log\left(-b\right) - a\right) - \Gamma\left(m - 2, b x\right) \sinh\left({\left(m - 3\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"1/2*(cosh((m - 3)*log(b) + a)*gamma(m - 2, b*x) + cosh((m - 3)*log(-b) - a)*gamma(m - 2, -b*x) - gamma(m - 2, -b*x)*sinh((m - 3)*log(-b) - a) - gamma(m - 2, b*x)*sinh((m - 3)*log(b) + a))/b","A",0
85,1,136,0,0.492571," ","integrate(x^(3+m)*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b x \cosh\left({\left(m + 3\right)} \log\left(x\right)\right) + {\left(m + 4\right)} \cosh\left({\left(m + 3\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m + 4, 2 \, b x\right) - {\left(m + 4\right)} \cosh\left({\left(m + 3\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m + 4, -2 \, b x\right) - {\left(m + 4\right)} \Gamma\left(m + 4, 2 \, b x\right) \sinh\left({\left(m + 3\right)} \log\left(2 \, b\right) + 2 \, a\right) + {\left(m + 4\right)} \Gamma\left(m + 4, -2 \, b x\right) \sinh\left({\left(m + 3\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m + 3\right)} \log\left(x\right)\right)}{8 \, {\left(b m + 4 \, b\right)}}"," ",0,"-1/8*(4*b*x*cosh((m + 3)*log(x)) + (m + 4)*cosh((m + 3)*log(2*b) + 2*a)*gamma(m + 4, 2*b*x) - (m + 4)*cosh((m + 3)*log(-2*b) - 2*a)*gamma(m + 4, -2*b*x) - (m + 4)*gamma(m + 4, 2*b*x)*sinh((m + 3)*log(2*b) + 2*a) + (m + 4)*gamma(m + 4, -2*b*x)*sinh((m + 3)*log(-2*b) - 2*a) + 4*b*x*sinh((m + 3)*log(x)))/(b*m + 4*b)","A",0
86,1,136,0,0.593010," ","integrate(x^(2+m)*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b x \cosh\left({\left(m + 2\right)} \log\left(x\right)\right) + {\left(m + 3\right)} \cosh\left({\left(m + 2\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m + 3, 2 \, b x\right) - {\left(m + 3\right)} \cosh\left({\left(m + 2\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m + 3, -2 \, b x\right) - {\left(m + 3\right)} \Gamma\left(m + 3, 2 \, b x\right) \sinh\left({\left(m + 2\right)} \log\left(2 \, b\right) + 2 \, a\right) + {\left(m + 3\right)} \Gamma\left(m + 3, -2 \, b x\right) \sinh\left({\left(m + 2\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m + 2\right)} \log\left(x\right)\right)}{8 \, {\left(b m + 3 \, b\right)}}"," ",0,"-1/8*(4*b*x*cosh((m + 2)*log(x)) + (m + 3)*cosh((m + 2)*log(2*b) + 2*a)*gamma(m + 3, 2*b*x) - (m + 3)*cosh((m + 2)*log(-2*b) - 2*a)*gamma(m + 3, -2*b*x) - (m + 3)*gamma(m + 3, 2*b*x)*sinh((m + 2)*log(2*b) + 2*a) + (m + 3)*gamma(m + 3, -2*b*x)*sinh((m + 2)*log(-2*b) - 2*a) + 4*b*x*sinh((m + 2)*log(x)))/(b*m + 3*b)","A",0
87,1,136,0,0.542793," ","integrate(x^(1+m)*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b x \cosh\left({\left(m + 1\right)} \log\left(x\right)\right) + {\left(m + 2\right)} \cosh\left({\left(m + 1\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m + 2, 2 \, b x\right) - {\left(m + 2\right)} \cosh\left({\left(m + 1\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m + 2, -2 \, b x\right) - {\left(m + 2\right)} \Gamma\left(m + 2, 2 \, b x\right) \sinh\left({\left(m + 1\right)} \log\left(2 \, b\right) + 2 \, a\right) + {\left(m + 2\right)} \Gamma\left(m + 2, -2 \, b x\right) \sinh\left({\left(m + 1\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m + 1\right)} \log\left(x\right)\right)}{8 \, {\left(b m + 2 \, b\right)}}"," ",0,"-1/8*(4*b*x*cosh((m + 1)*log(x)) + (m + 2)*cosh((m + 1)*log(2*b) + 2*a)*gamma(m + 2, 2*b*x) - (m + 2)*cosh((m + 1)*log(-2*b) - 2*a)*gamma(m + 2, -2*b*x) - (m + 2)*gamma(m + 2, 2*b*x)*sinh((m + 1)*log(2*b) + 2*a) + (m + 2)*gamma(m + 2, -2*b*x)*sinh((m + 1)*log(-2*b) - 2*a) + 4*b*x*sinh((m + 1)*log(x)))/(b*m + 2*b)","A",0
88,1,122,0,0.791396," ","integrate(x^m*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b x \cosh\left(m \log\left(x\right)\right) + {\left(m + 1\right)} \cosh\left(m \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m + 1, 2 \, b x\right) - {\left(m + 1\right)} \cosh\left(m \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m + 1, -2 \, b x\right) - {\left(m + 1\right)} \Gamma\left(m + 1, 2 \, b x\right) \sinh\left(m \log\left(2 \, b\right) + 2 \, a\right) + {\left(m + 1\right)} \Gamma\left(m + 1, -2 \, b x\right) \sinh\left(m \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left(m \log\left(x\right)\right)}{8 \, {\left(b m + b\right)}}"," ",0,"-1/8*(4*b*x*cosh(m*log(x)) + (m + 1)*cosh(m*log(2*b) + 2*a)*gamma(m + 1, 2*b*x) - (m + 1)*cosh(m*log(-2*b) - 2*a)*gamma(m + 1, -2*b*x) - (m + 1)*gamma(m + 1, 2*b*x)*sinh(m*log(2*b) + 2*a) + (m + 1)*gamma(m + 1, -2*b*x)*sinh(m*log(-2*b) - 2*a) + 4*b*x*sinh(m*log(x)))/(b*m + b)","A",0
89,1,117,0,0.552343," ","integrate(x^(-1+m)*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b x \cosh\left({\left(m - 1\right)} \log\left(x\right)\right) + m \cosh\left({\left(m - 1\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m, 2 \, b x\right) - m \cosh\left({\left(m - 1\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m, -2 \, b x\right) - m \Gamma\left(m, 2 \, b x\right) \sinh\left({\left(m - 1\right)} \log\left(2 \, b\right) + 2 \, a\right) + m \Gamma\left(m, -2 \, b x\right) \sinh\left({\left(m - 1\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m - 1\right)} \log\left(x\right)\right)}{8 \, b m}"," ",0,"-1/8*(4*b*x*cosh((m - 1)*log(x)) + m*cosh((m - 1)*log(2*b) + 2*a)*gamma(m, 2*b*x) - m*cosh((m - 1)*log(-2*b) - 2*a)*gamma(m, -2*b*x) - m*gamma(m, 2*b*x)*sinh((m - 1)*log(2*b) + 2*a) + m*gamma(m, -2*b*x)*sinh((m - 1)*log(-2*b) - 2*a) + 4*b*x*sinh((m - 1)*log(x)))/(b*m)","A",0
90,1,136,0,0.500327," ","integrate(x^(-2+m)*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b x \cosh\left({\left(m - 2\right)} \log\left(x\right)\right) + {\left(m - 1\right)} \cosh\left({\left(m - 2\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m - 1, 2 \, b x\right) - {\left(m - 1\right)} \cosh\left({\left(m - 2\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m - 1, -2 \, b x\right) - {\left(m - 1\right)} \Gamma\left(m - 1, 2 \, b x\right) \sinh\left({\left(m - 2\right)} \log\left(2 \, b\right) + 2 \, a\right) + {\left(m - 1\right)} \Gamma\left(m - 1, -2 \, b x\right) \sinh\left({\left(m - 2\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m - 2\right)} \log\left(x\right)\right)}{8 \, {\left(b m - b\right)}}"," ",0,"-1/8*(4*b*x*cosh((m - 2)*log(x)) + (m - 1)*cosh((m - 2)*log(2*b) + 2*a)*gamma(m - 1, 2*b*x) - (m - 1)*cosh((m - 2)*log(-2*b) - 2*a)*gamma(m - 1, -2*b*x) - (m - 1)*gamma(m - 1, 2*b*x)*sinh((m - 2)*log(2*b) + 2*a) + (m - 1)*gamma(m - 1, -2*b*x)*sinh((m - 2)*log(-2*b) - 2*a) + 4*b*x*sinh((m - 2)*log(x)))/(b*m - b)","A",0
91,1,136,0,0.710300," ","integrate(x^(-3+m)*sinh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{4 \, b x \cosh\left({\left(m - 3\right)} \log\left(x\right)\right) + {\left(m - 2\right)} \cosh\left({\left(m - 3\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m - 2, 2 \, b x\right) - {\left(m - 2\right)} \cosh\left({\left(m - 3\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m - 2, -2 \, b x\right) - {\left(m - 2\right)} \Gamma\left(m - 2, 2 \, b x\right) \sinh\left({\left(m - 3\right)} \log\left(2 \, b\right) + 2 \, a\right) + {\left(m - 2\right)} \Gamma\left(m - 2, -2 \, b x\right) \sinh\left({\left(m - 3\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m - 3\right)} \log\left(x\right)\right)}{8 \, {\left(b m - 2 \, b\right)}}"," ",0,"-1/8*(4*b*x*cosh((m - 3)*log(x)) + (m - 2)*cosh((m - 3)*log(2*b) + 2*a)*gamma(m - 2, 2*b*x) - (m - 2)*cosh((m - 3)*log(-2*b) - 2*a)*gamma(m - 2, -2*b*x) - (m - 2)*gamma(m - 2, 2*b*x)*sinh((m - 3)*log(2*b) + 2*a) + (m - 2)*gamma(m - 2, -2*b*x)*sinh((m - 3)*log(-2*b) - 2*a) + 4*b*x*sinh((m - 3)*log(x)))/(b*m - 2*b)","A",0
92,-2,0,0,0.000000," ","integrate(x/csch(x)^(3/2)+1/3*x*csch(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
93,-2,0,0,0.000000," ","integrate(x/csch(x)^(5/2)+3/5*x/csch(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
94,-2,0,0,0.000000," ","integrate(x/csch(x)^(7/2)-5/21*x*csch(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
95,-2,0,0,0.000000," ","integrate(x^2/csch(x)^(3/2)+1/3*x^2*csch(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
96,1,279,0,0.557381," ","integrate((d*x+c)^3*(a+I*a*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 i \, a d^{3} f^{3} x^{3} + 2 i \, a c^{3} f^{3} + 6 i \, a c^{2} d f^{2} + 12 i \, a c d^{2} f + 12 i \, a d^{3} + {\left(6 i \, a c d^{2} f^{3} + 6 i \, a d^{3} f^{2}\right)} x^{2} + {\left(6 i \, a c^{2} d f^{3} + 12 i \, a c d^{2} f^{2} + 12 i \, a d^{3} f\right)} x + {\left(2 i \, a d^{3} f^{3} x^{3} + 2 i \, a c^{3} f^{3} - 6 i \, a c^{2} d f^{2} + 12 i \, a c d^{2} f - 12 i \, a d^{3} + {\left(6 i \, a c d^{2} f^{3} - 6 i \, a d^{3} f^{2}\right)} x^{2} + {\left(6 i \, a c^{2} d f^{3} - 12 i \, a c d^{2} f^{2} + 12 i \, a d^{3} f\right)} x\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(a d^{3} f^{4} x^{4} + 4 \, a c d^{2} f^{4} x^{3} + 6 \, a c^{2} d f^{4} x^{2} + 4 \, a c^{3} f^{4} x\right)} e^{\left(f x + e\right)}\right)} e^{\left(-f x - e\right)}}{4 \, f^{4}}"," ",0,"1/4*(2*I*a*d^3*f^3*x^3 + 2*I*a*c^3*f^3 + 6*I*a*c^2*d*f^2 + 12*I*a*c*d^2*f + 12*I*a*d^3 + (6*I*a*c*d^2*f^3 + 6*I*a*d^3*f^2)*x^2 + (6*I*a*c^2*d*f^3 + 12*I*a*c*d^2*f^2 + 12*I*a*d^3*f)*x + (2*I*a*d^3*f^3*x^3 + 2*I*a*c^3*f^3 - 6*I*a*c^2*d*f^2 + 12*I*a*c*d^2*f - 12*I*a*d^3 + (6*I*a*c*d^2*f^3 - 6*I*a*d^3*f^2)*x^2 + (6*I*a*c^2*d*f^3 - 12*I*a*c*d^2*f^2 + 12*I*a*d^3*f)*x)*e^(2*f*x + 2*e) + (a*d^3*f^4*x^4 + 4*a*c*d^2*f^4*x^3 + 6*a*c^2*d*f^4*x^2 + 4*a*c^3*f^4*x)*e^(f*x + e))*e^(-f*x - e)/f^4","B",0
97,1,169,0,0.524921," ","integrate((d*x+c)^2*(a+I*a*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(3 i \, a d^{2} f^{2} x^{2} + 3 i \, a c^{2} f^{2} + 6 i \, a c d f + 6 i \, a d^{2} + {\left(6 i \, a c d f^{2} + 6 i \, a d^{2} f\right)} x + {\left(3 i \, a d^{2} f^{2} x^{2} + 3 i \, a c^{2} f^{2} - 6 i \, a c d f + 6 i \, a d^{2} + {\left(6 i \, a c d f^{2} - 6 i \, a d^{2} f\right)} x\right)} e^{\left(2 \, f x + 2 \, e\right)} + 2 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a c d f^{3} x^{2} + 3 \, a c^{2} f^{3} x\right)} e^{\left(f x + e\right)}\right)} e^{\left(-f x - e\right)}}{6 \, f^{3}}"," ",0,"1/6*(3*I*a*d^2*f^2*x^2 + 3*I*a*c^2*f^2 + 6*I*a*c*d*f + 6*I*a*d^2 + (6*I*a*c*d*f^2 + 6*I*a*d^2*f)*x + (3*I*a*d^2*f^2*x^2 + 3*I*a*c^2*f^2 - 6*I*a*c*d*f + 6*I*a*d^2 + (6*I*a*c*d*f^2 - 6*I*a*d^2*f)*x)*e^(2*f*x + 2*e) + 2*(a*d^2*f^3*x^3 + 3*a*c*d*f^3*x^2 + 3*a*c^2*f^3*x)*e^(f*x + e))*e^(-f*x - e)/f^3","B",0
98,1,81,0,0.474276," ","integrate((d*x+c)*(a+I*a*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(i \, a d f x + i \, a c f + i \, a d + {\left(i \, a d f x + i \, a c f - i \, a d\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(a d f^{2} x^{2} + 2 \, a c f^{2} x\right)} e^{\left(f x + e\right)}\right)} e^{\left(-f x - e\right)}}{2 \, f^{2}}"," ",0,"1/2*(I*a*d*f*x + I*a*c*f + I*a*d + (I*a*d*f*x + I*a*c*f - I*a*d)*e^(2*f*x + 2*e) + (a*d*f^2*x^2 + 2*a*c*f^2*x)*e^(f*x + e))*e^(-f*x - e)/f^2","A",0
99,1,79,0,0.440559," ","integrate((a+I*a*sinh(f*x+e))/(d*x+c),x, algorithm=""fricas"")","\frac{i \, a {\rm Ei}\left(\frac{d f x + c f}{d}\right) e^{\left(\frac{d e - c f}{d}\right)} - i \, a {\rm Ei}\left(-\frac{d f x + c f}{d}\right) e^{\left(-\frac{d e - c f}{d}\right)} + 2 \, a \log\left(\frac{d x + c}{d}\right)}{2 \, d}"," ",0,"1/2*(I*a*Ei((d*f*x + c*f)/d)*e^((d*e - c*f)/d) - I*a*Ei(-(d*f*x + c*f)/d)*e^(-(d*e - c*f)/d) + 2*a*log((d*x + c)/d))/d","A",0
100,1,134,0,1.295701," ","integrate((a+I*a*sinh(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(-i \, a d e^{\left(2 \, f x + 2 \, e\right)} + i \, a d + {\left({\left(i \, a d f x + i \, a c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) e^{\left(\frac{d e - c f}{d}\right)} + {\left(i \, a d f x + i \, a c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right) e^{\left(-\frac{d e - c f}{d}\right)} - 2 \, a d\right)} e^{\left(f x + e\right)}\right)} e^{\left(-f x - e\right)}}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/2*(-I*a*d*e^(2*f*x + 2*e) + I*a*d + ((I*a*d*f*x + I*a*c*f)*Ei((d*f*x + c*f)/d)*e^((d*e - c*f)/d) + (I*a*d*f*x + I*a*c*f)*Ei(-(d*f*x + c*f)/d)*e^(-(d*e - c*f)/d) - 2*a*d)*e^(f*x + e))*e^(-f*x - e)/(d^3*x + c*d^2)","A",0
101,1,222,0,0.467346," ","integrate((a+I*a*sinh(f*x+e))/(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(-i \, a d^{2} f x - i \, a c d f + i \, a d^{2} + {\left(-i \, a d^{2} f x - i \, a c d f - i \, a d^{2}\right)} e^{\left(2 \, f x + 2 \, e\right)} - {\left(2 \, a d^{2} - {\left(i \, a d^{2} f^{2} x^{2} + 2 i \, a c d f^{2} x + i \, a c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) e^{\left(\frac{d e - c f}{d}\right)} - {\left(-i \, a d^{2} f^{2} x^{2} - 2 i \, a c d f^{2} x - i \, a c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right) e^{\left(-\frac{d e - c f}{d}\right)}\right)} e^{\left(f x + e\right)}\right)} e^{\left(-f x - e\right)}}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/4*(-I*a*d^2*f*x - I*a*c*d*f + I*a*d^2 + (-I*a*d^2*f*x - I*a*c*d*f - I*a*d^2)*e^(2*f*x + 2*e) - (2*a*d^2 - (I*a*d^2*f^2*x^2 + 2*I*a*c*d*f^2*x + I*a*c^2*f^2)*Ei((d*f*x + c*f)/d)*e^((d*e - c*f)/d) - (-I*a*d^2*f^2*x^2 - 2*I*a*c*d*f^2*x - I*a*c^2*f^2)*Ei(-(d*f*x + c*f)/d)*e^(-(d*e - c*f)/d))*e^(f*x + e))*e^(-f*x - e)/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
102,1,590,0,0.648325," ","integrate((d*x+c)^3*(a+I*a*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(4 \, a^{2} d^{3} f^{3} x^{3} + 4 \, a^{2} c^{3} f^{3} + 6 \, a^{2} c^{2} d f^{2} + 6 \, a^{2} c d^{2} f + 3 \, a^{2} d^{3} + 6 \, {\left(2 \, a^{2} c d^{2} f^{3} + a^{2} d^{3} f^{2}\right)} x^{2} + 6 \, {\left(2 \, a^{2} c^{2} d f^{3} + 2 \, a^{2} c d^{2} f^{2} + a^{2} d^{3} f\right)} x - {\left(4 \, a^{2} d^{3} f^{3} x^{3} + 4 \, a^{2} c^{3} f^{3} - 6 \, a^{2} c^{2} d f^{2} + 6 \, a^{2} c d^{2} f - 3 \, a^{2} d^{3} + 6 \, {\left(2 \, a^{2} c d^{2} f^{3} - a^{2} d^{3} f^{2}\right)} x^{2} + 6 \, {\left(2 \, a^{2} c^{2} d f^{3} - 2 \, a^{2} c d^{2} f^{2} + a^{2} d^{3} f\right)} x\right)} e^{\left(4 \, f x + 4 \, e\right)} + {\left(32 i \, a^{2} d^{3} f^{3} x^{3} + 32 i \, a^{2} c^{3} f^{3} - 96 i \, a^{2} c^{2} d f^{2} + 192 i \, a^{2} c d^{2} f - 192 i \, a^{2} d^{3} + {\left(96 i \, a^{2} c d^{2} f^{3} - 96 i \, a^{2} d^{3} f^{2}\right)} x^{2} + {\left(96 i \, a^{2} c^{2} d f^{3} - 192 i \, a^{2} c d^{2} f^{2} + 192 i \, a^{2} d^{3} f\right)} x\right)} e^{\left(3 \, f x + 3 \, e\right)} + 12 \, {\left(a^{2} d^{3} f^{4} x^{4} + 4 \, a^{2} c d^{2} f^{4} x^{3} + 6 \, a^{2} c^{2} d f^{4} x^{2} + 4 \, a^{2} c^{3} f^{4} x\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(32 i \, a^{2} d^{3} f^{3} x^{3} + 32 i \, a^{2} c^{3} f^{3} + 96 i \, a^{2} c^{2} d f^{2} + 192 i \, a^{2} c d^{2} f + 192 i \, a^{2} d^{3} + {\left(96 i \, a^{2} c d^{2} f^{3} + 96 i \, a^{2} d^{3} f^{2}\right)} x^{2} + {\left(96 i \, a^{2} c^{2} d f^{3} + 192 i \, a^{2} c d^{2} f^{2} + 192 i \, a^{2} d^{3} f\right)} x\right)} e^{\left(f x + e\right)}\right)} e^{\left(-2 \, f x - 2 \, e\right)}}{32 \, f^{4}}"," ",0,"1/32*(4*a^2*d^3*f^3*x^3 + 4*a^2*c^3*f^3 + 6*a^2*c^2*d*f^2 + 6*a^2*c*d^2*f + 3*a^2*d^3 + 6*(2*a^2*c*d^2*f^3 + a^2*d^3*f^2)*x^2 + 6*(2*a^2*c^2*d*f^3 + 2*a^2*c*d^2*f^2 + a^2*d^3*f)*x - (4*a^2*d^3*f^3*x^3 + 4*a^2*c^3*f^3 - 6*a^2*c^2*d*f^2 + 6*a^2*c*d^2*f - 3*a^2*d^3 + 6*(2*a^2*c*d^2*f^3 - a^2*d^3*f^2)*x^2 + 6*(2*a^2*c^2*d*f^3 - 2*a^2*c*d^2*f^2 + a^2*d^3*f)*x)*e^(4*f*x + 4*e) + (32*I*a^2*d^3*f^3*x^3 + 32*I*a^2*c^3*f^3 - 96*I*a^2*c^2*d*f^2 + 192*I*a^2*c*d^2*f - 192*I*a^2*d^3 + (96*I*a^2*c*d^2*f^3 - 96*I*a^2*d^3*f^2)*x^2 + (96*I*a^2*c^2*d*f^3 - 192*I*a^2*c*d^2*f^2 + 192*I*a^2*d^3*f)*x)*e^(3*f*x + 3*e) + 12*(a^2*d^3*f^4*x^4 + 4*a^2*c*d^2*f^4*x^3 + 6*a^2*c^2*d*f^4*x^2 + 4*a^2*c^3*f^4*x)*e^(2*f*x + 2*e) + (32*I*a^2*d^3*f^3*x^3 + 32*I*a^2*c^3*f^3 + 96*I*a^2*c^2*d*f^2 + 192*I*a^2*c*d^2*f + 192*I*a^2*d^3 + (96*I*a^2*c*d^2*f^3 + 96*I*a^2*d^3*f^2)*x^2 + (96*I*a^2*c^2*d*f^3 + 192*I*a^2*c*d^2*f^2 + 192*I*a^2*d^3*f)*x)*e^(f*x + e))*e^(-2*f*x - 2*e)/f^4","B",0
103,1,347,0,0.437265," ","integrate((d*x+c)^2*(a+I*a*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c^{2} f^{2} + 2 \, a^{2} c d f + a^{2} d^{2} + 2 \, {\left(2 \, a^{2} c d f^{2} + a^{2} d^{2} f\right)} x - {\left(2 \, a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c^{2} f^{2} - 2 \, a^{2} c d f + a^{2} d^{2} + 2 \, {\left(2 \, a^{2} c d f^{2} - a^{2} d^{2} f\right)} x\right)} e^{\left(4 \, f x + 4 \, e\right)} + {\left(16 i \, a^{2} d^{2} f^{2} x^{2} + 16 i \, a^{2} c^{2} f^{2} - 32 i \, a^{2} c d f + 32 i \, a^{2} d^{2} + {\left(32 i \, a^{2} c d f^{2} - 32 i \, a^{2} d^{2} f\right)} x\right)} e^{\left(3 \, f x + 3 \, e\right)} + 8 \, {\left(a^{2} d^{2} f^{3} x^{3} + 3 \, a^{2} c d f^{3} x^{2} + 3 \, a^{2} c^{2} f^{3} x\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(16 i \, a^{2} d^{2} f^{2} x^{2} + 16 i \, a^{2} c^{2} f^{2} + 32 i \, a^{2} c d f + 32 i \, a^{2} d^{2} + {\left(32 i \, a^{2} c d f^{2} + 32 i \, a^{2} d^{2} f\right)} x\right)} e^{\left(f x + e\right)}\right)} e^{\left(-2 \, f x - 2 \, e\right)}}{16 \, f^{3}}"," ",0,"1/16*(2*a^2*d^2*f^2*x^2 + 2*a^2*c^2*f^2 + 2*a^2*c*d*f + a^2*d^2 + 2*(2*a^2*c*d*f^2 + a^2*d^2*f)*x - (2*a^2*d^2*f^2*x^2 + 2*a^2*c^2*f^2 - 2*a^2*c*d*f + a^2*d^2 + 2*(2*a^2*c*d*f^2 - a^2*d^2*f)*x)*e^(4*f*x + 4*e) + (16*I*a^2*d^2*f^2*x^2 + 16*I*a^2*c^2*f^2 - 32*I*a^2*c*d*f + 32*I*a^2*d^2 + (32*I*a^2*c*d*f^2 - 32*I*a^2*d^2*f)*x)*e^(3*f*x + 3*e) + 8*(a^2*d^2*f^3*x^3 + 3*a^2*c*d*f^3*x^2 + 3*a^2*c^2*f^3*x)*e^(2*f*x + 2*e) + (16*I*a^2*d^2*f^2*x^2 + 16*I*a^2*c^2*f^2 + 32*I*a^2*c*d*f + 32*I*a^2*d^2 + (32*I*a^2*c*d*f^2 + 32*I*a^2*d^2*f)*x)*e^(f*x + e))*e^(-2*f*x - 2*e)/f^3","B",0
104,1,162,0,0.498126," ","integrate((d*x+c)*(a+I*a*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} d f x + 2 \, a^{2} c f + a^{2} d - {\left(2 \, a^{2} d f x + 2 \, a^{2} c f - a^{2} d\right)} e^{\left(4 \, f x + 4 \, e\right)} + {\left(16 i \, a^{2} d f x + 16 i \, a^{2} c f - 16 i \, a^{2} d\right)} e^{\left(3 \, f x + 3 \, e\right)} + 12 \, {\left(a^{2} d f^{2} x^{2} + 2 \, a^{2} c f^{2} x\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(16 i \, a^{2} d f x + 16 i \, a^{2} c f + 16 i \, a^{2} d\right)} e^{\left(f x + e\right)}\right)} e^{\left(-2 \, f x - 2 \, e\right)}}{16 \, f^{2}}"," ",0,"1/16*(2*a^2*d*f*x + 2*a^2*c*f + a^2*d - (2*a^2*d*f*x + 2*a^2*c*f - a^2*d)*e^(4*f*x + 4*e) + (16*I*a^2*d*f*x + 16*I*a^2*c*f - 16*I*a^2*d)*e^(3*f*x + 3*e) + 12*(a^2*d*f^2*x^2 + 2*a^2*c*f^2*x)*e^(2*f*x + 2*e) + (16*I*a^2*d*f*x + 16*I*a^2*c*f + 16*I*a^2*d)*e^(f*x + e))*e^(-2*f*x - 2*e)/f^2","A",0
105,1,149,0,0.496183," ","integrate((a+I*a*sinh(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","-\frac{a^{2} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) e^{\left(\frac{2 \, {\left(d e - c f\right)}}{d}\right)} - 4 i \, a^{2} {\rm Ei}\left(\frac{d f x + c f}{d}\right) e^{\left(\frac{d e - c f}{d}\right)} + 4 i \, a^{2} {\rm Ei}\left(-\frac{d f x + c f}{d}\right) e^{\left(-\frac{d e - c f}{d}\right)} + a^{2} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) e^{\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)} - 6 \, a^{2} \log\left(\frac{d x + c}{d}\right)}{4 \, d}"," ",0,"-1/4*(a^2*Ei(2*(d*f*x + c*f)/d)*e^(2*(d*e - c*f)/d) - 4*I*a^2*Ei((d*f*x + c*f)/d)*e^((d*e - c*f)/d) + 4*I*a^2*Ei(-(d*f*x + c*f)/d)*e^(-(d*e - c*f)/d) + a^2*Ei(-2*(d*f*x + c*f)/d)*e^(-2*(d*e - c*f)/d) - 6*a^2*log((d*x + c)/d))/d","A",0
106,1,267,0,0.895466," ","integrate((a+I*a*sinh(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} d e^{\left(4 \, f x + 4 \, e\right)} - 4 i \, a^{2} d e^{\left(3 \, f x + 3 \, e\right)} + 4 i \, a^{2} d e^{\left(f x + e\right)} + a^{2} d - {\left(6 \, a^{2} d + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) e^{\left(\frac{2 \, {\left(d e - c f\right)}}{d}\right)} - {\left(4 i \, a^{2} d f x + 4 i \, a^{2} c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) e^{\left(\frac{d e - c f}{d}\right)} - {\left(4 i \, a^{2} d f x + 4 i \, a^{2} c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right) e^{\left(-\frac{d e - c f}{d}\right)} - 2 \, {\left(a^{2} d f x + a^{2} c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) e^{\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} e^{\left(-2 \, f x - 2 \, e\right)}}{4 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"1/4*(a^2*d*e^(4*f*x + 4*e) - 4*I*a^2*d*e^(3*f*x + 3*e) + 4*I*a^2*d*e^(f*x + e) + a^2*d - (6*a^2*d + 2*(a^2*d*f*x + a^2*c*f)*Ei(2*(d*f*x + c*f)/d)*e^(2*(d*e - c*f)/d) - (4*I*a^2*d*f*x + 4*I*a^2*c*f)*Ei((d*f*x + c*f)/d)*e^((d*e - c*f)/d) - (4*I*a^2*d*f*x + 4*I*a^2*c*f)*Ei(-(d*f*x + c*f)/d)*e^(-(d*e - c*f)/d) - 2*(a^2*d*f*x + a^2*c*f)*Ei(-2*(d*f*x + c*f)/d)*e^(-2*(d*e - c*f)/d))*e^(2*f*x + 2*e))*e^(-2*f*x - 2*e)/(d^3*x + c*d^2)","A",0
107,1,453,0,0.745105," ","integrate((a+I*a*sinh(f*x+e))^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} d^{2} f x + 2 \, a^{2} c d f - a^{2} d^{2} - {\left(2 \, a^{2} d^{2} f x + 2 \, a^{2} c d f + a^{2} d^{2}\right)} e^{\left(4 \, f x + 4 \, e\right)} - {\left(-4 i \, a^{2} d^{2} f x - 4 i \, a^{2} c d f - 4 i \, a^{2} d^{2}\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(6 \, a^{2} d^{2} + 4 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) e^{\left(\frac{2 \, {\left(d e - c f\right)}}{d}\right)} - {\left(4 i \, a^{2} d^{2} f^{2} x^{2} + 8 i \, a^{2} c d f^{2} x + 4 i \, a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) e^{\left(\frac{d e - c f}{d}\right)} - {\left(-4 i \, a^{2} d^{2} f^{2} x^{2} - 8 i \, a^{2} c d f^{2} x - 4 i \, a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right) e^{\left(-\frac{d e - c f}{d}\right)} + 4 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right) e^{\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}\right)} e^{\left(2 \, f x + 2 \, e\right)} - {\left(-4 i \, a^{2} d^{2} f x - 4 i \, a^{2} c d f + 4 i \, a^{2} d^{2}\right)} e^{\left(f x + e\right)}\right)} e^{\left(-2 \, f x - 2 \, e\right)}}{8 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/8*(2*a^2*d^2*f*x + 2*a^2*c*d*f - a^2*d^2 - (2*a^2*d^2*f*x + 2*a^2*c*d*f + a^2*d^2)*e^(4*f*x + 4*e) - (-4*I*a^2*d^2*f*x - 4*I*a^2*c*d*f - 4*I*a^2*d^2)*e^(3*f*x + 3*e) + (6*a^2*d^2 + 4*(a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*Ei(2*(d*f*x + c*f)/d)*e^(2*(d*e - c*f)/d) - (4*I*a^2*d^2*f^2*x^2 + 8*I*a^2*c*d*f^2*x + 4*I*a^2*c^2*f^2)*Ei((d*f*x + c*f)/d)*e^((d*e - c*f)/d) - (-4*I*a^2*d^2*f^2*x^2 - 8*I*a^2*c*d*f^2*x - 4*I*a^2*c^2*f^2)*Ei(-(d*f*x + c*f)/d)*e^(-(d*e - c*f)/d) + 4*(a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*Ei(-2*(d*f*x + c*f)/d)*e^(-2*(d*e - c*f)/d))*e^(2*f*x + 2*e) - (-4*I*a^2*d^2*f*x - 4*I*a^2*c*d*f + 4*I*a^2*d^2)*e^(f*x + e))*e^(-2*f*x - 2*e)/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
108,1,363,0,0.499083," ","integrate((d*x+c)^3/(a+I*a*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{-2 i \, d^{3} e^{3} + 6 i \, c d^{2} e^{2} f - 6 i \, c^{2} d e f^{2} + 2 i \, c^{3} f^{3} + {\left(12 i \, d^{3} f x + 12 i \, c d^{2} f - 12 \, {\left(d^{3} f x + c d^{2} f\right)} e^{\left(f x + e\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(f x + e\right)}\right) + 2 \, {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + 3 \, c^{2} d f^{3} x + d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2}\right)} e^{\left(f x + e\right)} + {\left(6 i \, d^{3} e^{2} - 12 i \, c d^{2} e f + 6 i \, c^{2} d f^{2} - 6 \, {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2}\right)} e^{\left(f x + e\right)}\right)} \log\left(e^{\left(f x + e\right)} - i\right) + {\left(6 i \, d^{3} f^{2} x^{2} + 12 i \, c d^{2} f^{2} x - 6 i \, d^{3} e^{2} + 12 i \, c d^{2} e f - 6 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} e^{\left(f x + e\right)}\right)} \log\left(i \, e^{\left(f x + e\right)} + 1\right) + {\left(12 \, d^{3} e^{\left(f x + e\right)} - 12 i \, d^{3}\right)} {\rm polylog}\left(3, -i \, e^{\left(f x + e\right)}\right)}{a f^{4} e^{\left(f x + e\right)} - i \, a f^{4}}"," ",0,"(-2*I*d^3*e^3 + 6*I*c*d^2*e^2*f - 6*I*c^2*d*e*f^2 + 2*I*c^3*f^3 + (12*I*d^3*f*x + 12*I*c*d^2*f - 12*(d^3*f*x + c*d^2*f)*e^(f*x + e))*dilog(-I*e^(f*x + e)) + 2*(d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + 3*c^2*d*f^3*x + d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2)*e^(f*x + e) + (6*I*d^3*e^2 - 12*I*c*d^2*e*f + 6*I*c^2*d*f^2 - 6*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2)*e^(f*x + e))*log(e^(f*x + e) - I) + (6*I*d^3*f^2*x^2 + 12*I*c*d^2*f^2*x - 6*I*d^3*e^2 + 12*I*c*d^2*e*f - 6*(d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*e^(f*x + e))*log(I*e^(f*x + e) + 1) + (12*d^3*e^(f*x + e) - 12*I*d^3)*polylog(3, -I*e^(f*x + e)))/(a*f^4*e^(f*x + e) - I*a*f^4)","C",0
109,1,200,0,0.564933," ","integrate((d*x+c)^2/(a+I*a*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{2 i \, d^{2} e^{2} - 4 i \, c d e f + 2 i \, c^{2} f^{2} - {\left(4 \, d^{2} e^{\left(f x + e\right)} - 4 i \, d^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(f x + e\right)}\right) + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x - d^{2} e^{2} + 2 \, c d e f\right)} e^{\left(f x + e\right)} + {\left(-4 i \, d^{2} e + 4 i \, c d f + 4 \, {\left(d^{2} e - c d f\right)} e^{\left(f x + e\right)}\right)} \log\left(e^{\left(f x + e\right)} - i\right) + {\left(4 i \, d^{2} f x + 4 i \, d^{2} e - 4 \, {\left(d^{2} f x + d^{2} e\right)} e^{\left(f x + e\right)}\right)} \log\left(i \, e^{\left(f x + e\right)} + 1\right)}{a f^{3} e^{\left(f x + e\right)} - i \, a f^{3}}"," ",0,"(2*I*d^2*e^2 - 4*I*c*d*e*f + 2*I*c^2*f^2 - (4*d^2*e^(f*x + e) - 4*I*d^2)*dilog(-I*e^(f*x + e)) + 2*(d^2*f^2*x^2 + 2*c*d*f^2*x - d^2*e^2 + 2*c*d*e*f)*e^(f*x + e) + (-4*I*d^2*e + 4*I*c*d*f + 4*(d^2*e - c*d*f)*e^(f*x + e))*log(e^(f*x + e) - I) + (4*I*d^2*f*x + 4*I*d^2*e - 4*(d^2*f*x + d^2*e)*e^(f*x + e))*log(I*e^(f*x + e) + 1))/(a*f^3*e^(f*x + e) - I*a*f^3)","B",0
110,1,61,0,0.762244," ","integrate((d*x+c)/(a+I*a*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, d f x e^{\left(f x + e\right)} + 2 i \, c f - {\left(2 \, d e^{\left(f x + e\right)} - 2 i \, d\right)} \log\left(e^{\left(f x + e\right)} - i\right)}{a f^{2} e^{\left(f x + e\right)} - i \, a f^{2}}"," ",0,"(2*d*f*x*e^(f*x + e) + 2*I*c*f - (2*d*e^(f*x + e) - 2*I*d)*log(e^(f*x + e) - I))/(a*f^2*e^(f*x + e) - I*a*f^2)","A",0
111,0,0,0,0.674933," ","integrate(1/(d*x+c)/(a+I*a*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(-i \, a d f x - i \, a c f + {\left(a d f x + a c f\right)} e^{\left(f x + e\right)}\right)} {\rm integral}\left(\frac{2 i \, d}{-i \, a d^{2} f x^{2} - 2 i \, a c d f x - i \, a c^{2} f + {\left(a d^{2} f x^{2} + 2 \, a c d f x + a c^{2} f\right)} e^{\left(f x + e\right)}}, x\right) + 2 i}{-i \, a d f x - i \, a c f + {\left(a d f x + a c f\right)} e^{\left(f x + e\right)}}"," ",0,"((-I*a*d*f*x - I*a*c*f + (a*d*f*x + a*c*f)*e^(f*x + e))*integral(2*I*d/(-I*a*d^2*f*x^2 - 2*I*a*c*d*f*x - I*a*c^2*f + (a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*e^(f*x + e)), x) + 2*I)/(-I*a*d*f*x - I*a*c*f + (a*d*f*x + a*c*f)*e^(f*x + e))","F",0
112,0,0,0,0.549829," ","integrate(1/(d*x+c)^2/(a+I*a*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(-i \, a d^{2} f x^{2} - 2 i \, a c d f x - i \, a c^{2} f + {\left(a d^{2} f x^{2} + 2 \, a c d f x + a c^{2} f\right)} e^{\left(f x + e\right)}\right)} {\rm integral}\left(\frac{4 i \, d}{-i \, a d^{3} f x^{3} - 3 i \, a c d^{2} f x^{2} - 3 i \, a c^{2} d f x - i \, a c^{3} f + {\left(a d^{3} f x^{3} + 3 \, a c d^{2} f x^{2} + 3 \, a c^{2} d f x + a c^{3} f\right)} e^{\left(f x + e\right)}}, x\right) + 2 i}{-i \, a d^{2} f x^{2} - 2 i \, a c d f x - i \, a c^{2} f + {\left(a d^{2} f x^{2} + 2 \, a c d f x + a c^{2} f\right)} e^{\left(f x + e\right)}}"," ",0,"((-I*a*d^2*f*x^2 - 2*I*a*c*d*f*x - I*a*c^2*f + (a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*e^(f*x + e))*integral(4*I*d/(-I*a*d^3*f*x^3 - 3*I*a*c*d^2*f*x^2 - 3*I*a*c^2*d*f*x - I*a*c^3*f + (a*d^3*f*x^3 + 3*a*c*d^2*f*x^2 + 3*a*c^2*d*f*x + a*c^3*f)*e^(f*x + e)), x) + 2*I)/(-I*a*d^2*f*x^2 - 2*I*a*c*d*f*x - I*a*c^2*f + (a*d^2*f*x^2 + 2*a*c*d*f*x + a*c^2*f)*e^(f*x + e))","F",0
113,1,912,0,0.581189," ","integrate((d*x+c)^3/(a+I*a*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 i \, d^{3} e^{3} + 6 i \, c^{2} d e f^{2} - 2 i \, c^{3} f^{3} - 12 i \, d^{3} e + {\left(-6 i \, c d^{2} e^{2} + 12 i \, c d^{2}\right)} f + {\left(-12 i \, d^{3} f x - 12 i \, c d^{2} f - 12 \, {\left(d^{3} f x + c d^{2} f\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(36 i \, d^{3} f x + 36 i \, c d^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 36 \, {\left(d^{3} f x + c d^{2} f\right)} e^{\left(f x + e\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(f x + e\right)}\right) + 2 \, {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - 6 \, d^{3} e + 3 \, {\left(c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(-6 i \, d^{3} f^{3} x^{3} - 6 i \, d^{3} e^{3} + 36 i \, d^{3} e + {\left(-18 i \, c^{2} d e - 6 i \, c^{2} d\right)} f^{2} + {\left(-18 i \, c d^{2} f^{3} - 6 i \, d^{3} f^{2}\right)} x^{2} + {\left(18 i \, c d^{2} e^{2} - 12 i \, c d^{2}\right)} f + {\left(-18 i \, c^{2} d f^{3} - 12 i \, c d^{2} f^{2} + 24 i \, d^{3} f\right)} x\right)} e^{\left(2 \, f x + 2 \, e\right)} - 6 \, {\left(d^{3} f^{2} x^{2} + d^{3} e^{3} - c^{3} f^{3} - 6 \, d^{3} e + {\left(3 \, c^{2} d e + c^{2} d\right)} f^{2} - {\left(3 \, c d^{2} e^{2} - 4 \, c d^{2}\right)} f + 2 \, {\left(c d^{2} f^{2} - d^{3} f\right)} x\right)} e^{\left(f x + e\right)} + {\left(-6 i \, d^{3} e^{2} + 12 i \, c d^{2} e f - 6 i \, c^{2} d f^{2} + 12 i \, d^{3} - 6 \, {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, d^{3}\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(18 i \, d^{3} e^{2} - 36 i \, c d^{2} e f + 18 i \, c^{2} d f^{2} - 36 i \, d^{3}\right)} e^{\left(2 \, f x + 2 \, e\right)} + 18 \, {\left(d^{3} e^{2} - 2 \, c d^{2} e f + c^{2} d f^{2} - 2 \, d^{3}\right)} e^{\left(f x + e\right)}\right)} \log\left(e^{\left(f x + e\right)} - i\right) + {\left(-6 i \, d^{3} f^{2} x^{2} - 12 i \, c d^{2} f^{2} x + 6 i \, d^{3} e^{2} - 12 i \, c d^{2} e f - 6 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(18 i \, d^{3} f^{2} x^{2} + 36 i \, c d^{2} f^{2} x - 18 i \, d^{3} e^{2} + 36 i \, c d^{2} e f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 18 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x - d^{3} e^{2} + 2 \, c d^{2} e f\right)} e^{\left(f x + e\right)}\right)} \log\left(i \, e^{\left(f x + e\right)} + 1\right) + {\left(12 \, d^{3} e^{\left(3 \, f x + 3 \, e\right)} - 36 i \, d^{3} e^{\left(2 \, f x + 2 \, e\right)} - 36 \, d^{3} e^{\left(f x + e\right)} + 12 i \, d^{3}\right)} {\rm polylog}\left(3, -i \, e^{\left(f x + e\right)}\right)}{3 \, a^{2} f^{4} e^{\left(3 \, f x + 3 \, e\right)} - 9 i \, a^{2} f^{4} e^{\left(2 \, f x + 2 \, e\right)} - 9 \, a^{2} f^{4} e^{\left(f x + e\right)} + 3 i \, a^{2} f^{4}}"," ",0,"(2*I*d^3*e^3 + 6*I*c^2*d*e*f^2 - 2*I*c^3*f^3 - 12*I*d^3*e + (-6*I*c*d^2*e^2 + 12*I*c*d^2)*f + (-12*I*d^3*f*x - 12*I*c*d^2*f - 12*(d^3*f*x + c*d^2*f)*e^(3*f*x + 3*e) + (36*I*d^3*f*x + 36*I*c*d^2*f)*e^(2*f*x + 2*e) + 36*(d^3*f*x + c*d^2*f)*e^(f*x + e))*dilog(-I*e^(f*x + e)) + 2*(d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - 6*d^3*e + 3*(c^2*d*f^3 - 2*d^3*f)*x)*e^(3*f*x + 3*e) + (-6*I*d^3*f^3*x^3 - 6*I*d^3*e^3 + 36*I*d^3*e + (-18*I*c^2*d*e - 6*I*c^2*d)*f^2 + (-18*I*c*d^2*f^3 - 6*I*d^3*f^2)*x^2 + (18*I*c*d^2*e^2 - 12*I*c*d^2)*f + (-18*I*c^2*d*f^3 - 12*I*c*d^2*f^2 + 24*I*d^3*f)*x)*e^(2*f*x + 2*e) - 6*(d^3*f^2*x^2 + d^3*e^3 - c^3*f^3 - 6*d^3*e + (3*c^2*d*e + c^2*d)*f^2 - (3*c*d^2*e^2 - 4*c*d^2)*f + 2*(c*d^2*f^2 - d^3*f)*x)*e^(f*x + e) + (-6*I*d^3*e^2 + 12*I*c*d^2*e*f - 6*I*c^2*d*f^2 + 12*I*d^3 - 6*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*d^3)*e^(3*f*x + 3*e) + (18*I*d^3*e^2 - 36*I*c*d^2*e*f + 18*I*c^2*d*f^2 - 36*I*d^3)*e^(2*f*x + 2*e) + 18*(d^3*e^2 - 2*c*d^2*e*f + c^2*d*f^2 - 2*d^3)*e^(f*x + e))*log(e^(f*x + e) - I) + (-6*I*d^3*f^2*x^2 - 12*I*c*d^2*f^2*x + 6*I*d^3*e^2 - 12*I*c*d^2*e*f - 6*(d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*e^(3*f*x + 3*e) + (18*I*d^3*f^2*x^2 + 36*I*c*d^2*f^2*x - 18*I*d^3*e^2 + 36*I*c*d^2*e*f)*e^(2*f*x + 2*e) + 18*(d^3*f^2*x^2 + 2*c*d^2*f^2*x - d^3*e^2 + 2*c*d^2*e*f)*e^(f*x + e))*log(I*e^(f*x + e) + 1) + (12*d^3*e^(3*f*x + 3*e) - 36*I*d^3*e^(2*f*x + 2*e) - 36*d^3*e^(f*x + e) + 12*I*d^3)*polylog(3, -I*e^(f*x + e)))/(3*a^2*f^4*e^(3*f*x + 3*e) - 9*I*a^2*f^4*e^(2*f*x + 2*e) - 9*a^2*f^4*e^(f*x + e) + 3*I*a^2*f^4)","C",0
114,1,478,0,0.532800," ","integrate((d*x+c)^2/(a+I*a*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{-2 i \, d^{2} e^{2} + 4 i \, c d e f - 2 i \, c^{2} f^{2} + 4 i \, d^{2} - {\left(4 \, d^{2} e^{\left(3 \, f x + 3 \, e\right)} - 12 i \, d^{2} e^{\left(2 \, f x + 2 \, e\right)} - 12 \, d^{2} e^{\left(f x + e\right)} + 4 i \, d^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(f x + e\right)}\right) + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x - d^{2} e^{2} + 2 \, c d e f\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(-6 i \, d^{2} f^{2} x^{2} + 6 i \, d^{2} e^{2} - 4 i \, d^{2} + {\left(-12 i \, c d e - 4 i \, c d\right)} f + {\left(-12 i \, c d f^{2} - 4 i \, d^{2} f\right)} x\right)} e^{\left(2 \, f x + 2 \, e\right)} + 2 \, {\left(3 \, d^{2} e^{2} + 3 \, c^{2} f^{2} - 2 \, d^{2} f x - 4 \, d^{2} - 2 \, {\left(3 \, c d e + c d\right)} f\right)} e^{\left(f x + e\right)} + {\left(4 i \, d^{2} e - 4 i \, c d f + 4 \, {\left(d^{2} e - c d f\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(-12 i \, d^{2} e + 12 i \, c d f\right)} e^{\left(2 \, f x + 2 \, e\right)} - 12 \, {\left(d^{2} e - c d f\right)} e^{\left(f x + e\right)}\right)} \log\left(e^{\left(f x + e\right)} - i\right) + {\left(-4 i \, d^{2} f x - 4 i \, d^{2} e - 4 \, {\left(d^{2} f x + d^{2} e\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(12 i \, d^{2} f x + 12 i \, d^{2} e\right)} e^{\left(2 \, f x + 2 \, e\right)} + 12 \, {\left(d^{2} f x + d^{2} e\right)} e^{\left(f x + e\right)}\right)} \log\left(i \, e^{\left(f x + e\right)} + 1\right)}{3 \, a^{2} f^{3} e^{\left(3 \, f x + 3 \, e\right)} - 9 i \, a^{2} f^{3} e^{\left(2 \, f x + 2 \, e\right)} - 9 \, a^{2} f^{3} e^{\left(f x + e\right)} + 3 i \, a^{2} f^{3}}"," ",0,"(-2*I*d^2*e^2 + 4*I*c*d*e*f - 2*I*c^2*f^2 + 4*I*d^2 - (4*d^2*e^(3*f*x + 3*e) - 12*I*d^2*e^(2*f*x + 2*e) - 12*d^2*e^(f*x + e) + 4*I*d^2)*dilog(-I*e^(f*x + e)) + 2*(d^2*f^2*x^2 + 2*c*d*f^2*x - d^2*e^2 + 2*c*d*e*f)*e^(3*f*x + 3*e) + (-6*I*d^2*f^2*x^2 + 6*I*d^2*e^2 - 4*I*d^2 + (-12*I*c*d*e - 4*I*c*d)*f + (-12*I*c*d*f^2 - 4*I*d^2*f)*x)*e^(2*f*x + 2*e) + 2*(3*d^2*e^2 + 3*c^2*f^2 - 2*d^2*f*x - 4*d^2 - 2*(3*c*d*e + c*d)*f)*e^(f*x + e) + (4*I*d^2*e - 4*I*c*d*f + 4*(d^2*e - c*d*f)*e^(3*f*x + 3*e) + (-12*I*d^2*e + 12*I*c*d*f)*e^(2*f*x + 2*e) - 12*(d^2*e - c*d*f)*e^(f*x + e))*log(e^(f*x + e) - I) + (-4*I*d^2*f*x - 4*I*d^2*e - 4*(d^2*f*x + d^2*e)*e^(3*f*x + 3*e) + (12*I*d^2*f*x + 12*I*d^2*e)*e^(2*f*x + 2*e) + 12*(d^2*f*x + d^2*e)*e^(f*x + e))*log(I*e^(f*x + e) + 1))/(3*a^2*f^3*e^(3*f*x + 3*e) - 9*I*a^2*f^3*e^(2*f*x + 2*e) - 9*a^2*f^3*e^(f*x + e) + 3*I*a^2*f^3)","B",0
115,1,162,0,0.439728," ","integrate((d*x+c)/(a+I*a*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, d f x e^{\left(3 \, f x + 3 \, e\right)} - 2 i \, c f + {\left(-6 i \, d f x - 2 i \, d\right)} e^{\left(2 \, f x + 2 \, e\right)} + 2 \, {\left(3 \, c f - d\right)} e^{\left(f x + e\right)} - {\left(2 \, d e^{\left(3 \, f x + 3 \, e\right)} - 6 i \, d e^{\left(2 \, f x + 2 \, e\right)} - 6 \, d e^{\left(f x + e\right)} + 2 i \, d\right)} \log\left(e^{\left(f x + e\right)} - i\right)}{3 \, a^{2} f^{2} e^{\left(3 \, f x + 3 \, e\right)} - 9 i \, a^{2} f^{2} e^{\left(2 \, f x + 2 \, e\right)} - 9 \, a^{2} f^{2} e^{\left(f x + e\right)} + 3 i \, a^{2} f^{2}}"," ",0,"(2*d*f*x*e^(3*f*x + 3*e) - 2*I*c*f + (-6*I*d*f*x - 2*I*d)*e^(2*f*x + 2*e) + 2*(3*c*f - d)*e^(f*x + e) - (2*d*e^(3*f*x + 3*e) - 6*I*d*e^(2*f*x + 2*e) - 6*d*e^(f*x + e) + 2*I*d)*log(e^(f*x + e) - I))/(3*a^2*f^2*e^(3*f*x + 3*e) - 9*I*a^2*f^2*e^(2*f*x + 2*e) - 9*a^2*f^2*e^(f*x + e) + 3*I*a^2*f^2)","A",0
116,0,0,0,0.633114," ","integrate(1/(d*x+c)/(a+I*a*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{-2 i \, d^{2} f^{2} x^{2} - 4 i \, c d f^{2} x - 2 i \, c^{2} f^{2} + 4 i \, d^{2} + {\left(2 i \, d^{2} f x + 2 i \, c d f - 4 i \, d^{2}\right)} e^{\left(2 \, f x + 2 \, e\right)} + 2 \, {\left(3 \, d^{2} f^{2} x^{2} + 3 \, c^{2} f^{2} + c d f - 4 \, d^{2} + {\left(6 \, c d f^{2} + d^{2} f\right)} x\right)} e^{\left(f x + e\right)} + {\left(3 i \, a^{2} d^{3} f^{3} x^{3} + 9 i \, a^{2} c d^{2} f^{3} x^{2} + 9 i \, a^{2} c^{2} d f^{3} x + 3 i \, a^{2} c^{3} f^{3} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(-9 i \, a^{2} d^{3} f^{3} x^{3} - 27 i \, a^{2} c d^{2} f^{3} x^{2} - 27 i \, a^{2} c^{2} d f^{3} x - 9 i \, a^{2} c^{3} f^{3}\right)} e^{\left(2 \, f x + 2 \, e\right)} - 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} e^{\left(f x + e\right)}\right)} {\rm integral}\left(\frac{2 i \, d^{3} f^{2} x^{2} + 4 i \, c d^{2} f^{2} x + 2 i \, c^{2} d f^{2} - 12 i \, d^{3}}{-3 i \, a^{2} d^{4} f^{3} x^{4} - 12 i \, a^{2} c d^{3} f^{3} x^{3} - 18 i \, a^{2} c^{2} d^{2} f^{3} x^{2} - 12 i \, a^{2} c^{3} d f^{3} x - 3 i \, a^{2} c^{4} f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} e^{\left(f x + e\right)}}, x\right)}{3 i \, a^{2} d^{3} f^{3} x^{3} + 9 i \, a^{2} c d^{2} f^{3} x^{2} + 9 i \, a^{2} c^{2} d f^{3} x + 3 i \, a^{2} c^{3} f^{3} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(-9 i \, a^{2} d^{3} f^{3} x^{3} - 27 i \, a^{2} c d^{2} f^{3} x^{2} - 27 i \, a^{2} c^{2} d f^{3} x - 9 i \, a^{2} c^{3} f^{3}\right)} e^{\left(2 \, f x + 2 \, e\right)} - 9 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} e^{\left(f x + e\right)}}"," ",0,"(-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x - 2*I*c^2*f^2 + 4*I*d^2 + (2*I*d^2*f*x + 2*I*c*d*f - 4*I*d^2)*e^(2*f*x + 2*e) + 2*(3*d^2*f^2*x^2 + 3*c^2*f^2 + c*d*f - 4*d^2 + (6*c*d*f^2 + d^2*f)*x)*e^(f*x + e) + (3*I*a^2*d^3*f^3*x^3 + 9*I*a^2*c*d^2*f^3*x^2 + 9*I*a^2*c^2*d*f^3*x + 3*I*a^2*c^3*f^3 + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*e^(3*f*x + 3*e) + (-9*I*a^2*d^3*f^3*x^3 - 27*I*a^2*c*d^2*f^3*x^2 - 27*I*a^2*c^2*d*f^3*x - 9*I*a^2*c^3*f^3)*e^(2*f*x + 2*e) - 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*e^(f*x + e))*integral((2*I*d^3*f^2*x^2 + 4*I*c*d^2*f^2*x + 2*I*c^2*d*f^2 - 12*I*d^3)/(-3*I*a^2*d^4*f^3*x^4 - 12*I*a^2*c*d^3*f^3*x^3 - 18*I*a^2*c^2*d^2*f^3*x^2 - 12*I*a^2*c^3*d*f^3*x - 3*I*a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*e^(f*x + e)), x))/(3*I*a^2*d^3*f^3*x^3 + 9*I*a^2*c*d^2*f^3*x^2 + 9*I*a^2*c^2*d*f^3*x + 3*I*a^2*c^3*f^3 + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*e^(3*f*x + 3*e) + (-9*I*a^2*d^3*f^3*x^3 - 27*I*a^2*c*d^2*f^3*x^2 - 27*I*a^2*c^2*d*f^3*x - 9*I*a^2*c^3*f^3)*e^(2*f*x + 2*e) - 9*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*e^(f*x + e))","F",0
117,0,0,0,1.189077," ","integrate(1/(d*x+c)^2/(a+I*a*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{-2 i \, d^{2} f^{2} x^{2} - 4 i \, c d f^{2} x - 2 i \, c^{2} f^{2} + 12 i \, d^{2} + {\left(4 i \, d^{2} f x + 4 i \, c d f - 12 i \, d^{2}\right)} e^{\left(2 \, f x + 2 \, e\right)} + 2 \, {\left(3 \, d^{2} f^{2} x^{2} + 3 \, c^{2} f^{2} + 2 \, c d f - 12 \, d^{2} + 2 \, {\left(3 \, c d f^{2} + d^{2} f\right)} x\right)} e^{\left(f x + e\right)} + {\left(3 i \, a^{2} d^{4} f^{3} x^{4} + 12 i \, a^{2} c d^{3} f^{3} x^{3} + 18 i \, a^{2} c^{2} d^{2} f^{3} x^{2} + 12 i \, a^{2} c^{3} d f^{3} x + 3 i \, a^{2} c^{4} f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(-9 i \, a^{2} d^{4} f^{3} x^{4} - 36 i \, a^{2} c d^{3} f^{3} x^{3} - 54 i \, a^{2} c^{2} d^{2} f^{3} x^{2} - 36 i \, a^{2} c^{3} d f^{3} x - 9 i \, a^{2} c^{4} f^{3}\right)} e^{\left(2 \, f x + 2 \, e\right)} - 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} e^{\left(f x + e\right)}\right)} {\rm integral}\left(\frac{4 i \, d^{3} f^{2} x^{2} + 8 i \, c d^{2} f^{2} x + 4 i \, c^{2} d f^{2} - 48 i \, d^{3}}{-3 i \, a^{2} d^{5} f^{3} x^{5} - 15 i \, a^{2} c d^{4} f^{3} x^{4} - 30 i \, a^{2} c^{2} d^{3} f^{3} x^{3} - 30 i \, a^{2} c^{3} d^{2} f^{3} x^{2} - 15 i \, a^{2} c^{4} d f^{3} x - 3 i \, a^{2} c^{5} f^{3} + 3 \, {\left(a^{2} d^{5} f^{3} x^{5} + 5 \, a^{2} c d^{4} f^{3} x^{4} + 10 \, a^{2} c^{2} d^{3} f^{3} x^{3} + 10 \, a^{2} c^{3} d^{2} f^{3} x^{2} + 5 \, a^{2} c^{4} d f^{3} x + a^{2} c^{5} f^{3}\right)} e^{\left(f x + e\right)}}, x\right)}{3 i \, a^{2} d^{4} f^{3} x^{4} + 12 i \, a^{2} c d^{3} f^{3} x^{3} + 18 i \, a^{2} c^{2} d^{2} f^{3} x^{2} + 12 i \, a^{2} c^{3} d f^{3} x + 3 i \, a^{2} c^{4} f^{3} + 3 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(-9 i \, a^{2} d^{4} f^{3} x^{4} - 36 i \, a^{2} c d^{3} f^{3} x^{3} - 54 i \, a^{2} c^{2} d^{2} f^{3} x^{2} - 36 i \, a^{2} c^{3} d f^{3} x - 9 i \, a^{2} c^{4} f^{3}\right)} e^{\left(2 \, f x + 2 \, e\right)} - 9 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} c d^{3} f^{3} x^{3} + 6 \, a^{2} c^{2} d^{2} f^{3} x^{2} + 4 \, a^{2} c^{3} d f^{3} x + a^{2} c^{4} f^{3}\right)} e^{\left(f x + e\right)}}"," ",0,"(-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x - 2*I*c^2*f^2 + 12*I*d^2 + (4*I*d^2*f*x + 4*I*c*d*f - 12*I*d^2)*e^(2*f*x + 2*e) + 2*(3*d^2*f^2*x^2 + 3*c^2*f^2 + 2*c*d*f - 12*d^2 + 2*(3*c*d*f^2 + d^2*f)*x)*e^(f*x + e) + (3*I*a^2*d^4*f^3*x^4 + 12*I*a^2*c*d^3*f^3*x^3 + 18*I*a^2*c^2*d^2*f^3*x^2 + 12*I*a^2*c^3*d*f^3*x + 3*I*a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*e^(3*f*x + 3*e) + (-9*I*a^2*d^4*f^3*x^4 - 36*I*a^2*c*d^3*f^3*x^3 - 54*I*a^2*c^2*d^2*f^3*x^2 - 36*I*a^2*c^3*d*f^3*x - 9*I*a^2*c^4*f^3)*e^(2*f*x + 2*e) - 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*e^(f*x + e))*integral((4*I*d^3*f^2*x^2 + 8*I*c*d^2*f^2*x + 4*I*c^2*d*f^2 - 48*I*d^3)/(-3*I*a^2*d^5*f^3*x^5 - 15*I*a^2*c*d^4*f^3*x^4 - 30*I*a^2*c^2*d^3*f^3*x^3 - 30*I*a^2*c^3*d^2*f^3*x^2 - 15*I*a^2*c^4*d*f^3*x - 3*I*a^2*c^5*f^3 + 3*(a^2*d^5*f^3*x^5 + 5*a^2*c*d^4*f^3*x^4 + 10*a^2*c^2*d^3*f^3*x^3 + 10*a^2*c^3*d^2*f^3*x^2 + 5*a^2*c^4*d*f^3*x + a^2*c^5*f^3)*e^(f*x + e)), x))/(3*I*a^2*d^4*f^3*x^4 + 12*I*a^2*c*d^3*f^3*x^3 + 18*I*a^2*c^2*d^2*f^3*x^2 + 12*I*a^2*c^3*d*f^3*x + 3*I*a^2*c^4*f^3 + 3*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*e^(3*f*x + 3*e) + (-9*I*a^2*d^4*f^3*x^4 - 36*I*a^2*c*d^3*f^3*x^3 - 54*I*a^2*c^2*d^2*f^3*x^2 - 36*I*a^2*c^3*d*f^3*x - 9*I*a^2*c^4*f^3)*e^(2*f*x + 2*e) - 9*(a^2*d^4*f^3*x^4 + 4*a^2*c*d^3*f^3*x^3 + 6*a^2*c^2*d^2*f^3*x^2 + 4*a^2*c^3*d*f^3*x + a^2*c^4*f^3)*e^(f*x + e))","F",0
118,-2,0,0,0.000000," ","integrate(x^4*(a+I*a*sinh(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
119,-2,0,0,0.000000," ","integrate(x^3*(a+I*a*sinh(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
120,-2,0,0,0.000000," ","integrate(x^2*(a+I*a*sinh(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
121,-2,0,0,0.000000," ","integrate(x*(a+I*a*sinh(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
122,-2,0,0,0.000000," ","integrate((a+I*a*sinh(f*x+e))^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
123,-2,0,0,0.000000," ","integrate((a+I*a*sinh(f*x+e))^(1/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
124,-2,0,0,0.000000," ","integrate((a+I*a*sinh(f*x+e))^(1/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
125,-2,0,0,0.000000," ","integrate(x^3*(a+I*a*sinh(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
126,-2,0,0,0.000000," ","integrate(x^2*(a+I*a*sinh(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
127,-2,0,0,0.000000," ","integrate(x*(a+I*a*sinh(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
128,-2,0,0,0.000000," ","integrate((a+I*a*sinh(f*x+e))^(3/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
129,-2,0,0,0.000000," ","integrate((a+I*a*sinh(f*x+e))^(3/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
130,-2,0,0,0.000000," ","integrate(x^3*(a+I*a*sinh(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
131,-2,0,0,0.000000," ","integrate(x^2*(a+I*a*sinh(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
132,-2,0,0,0.000000," ","integrate(x*(a+I*a*sinh(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
133,-2,0,0,0.000000," ","integrate((a+I*a*sinh(d*x+c))^(5/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
134,-2,0,0,0.000000," ","integrate((a+I*a*sinh(d*x+c))^(5/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
135,-2,0,0,0.000000," ","integrate((a+I*a*sinh(d*x+c))^(5/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
136,0,0,0,0.699033," ","integrate(x^3/(a+I*a*sinh(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}} x^{3} e^{\left(f x + e\right)}}{a e^{\left(f x + e\right)} - i \, a}, x\right)"," ",0,"integral(-2*I*sqrt(1/2*I*a*e^(-f*x - e))*x^3*e^(f*x + e)/(a*e^(f*x + e) - I*a), x)","F",0
137,0,0,0,0.516941," ","integrate(x^2/(a+I*a*sinh(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}} x^{2} e^{\left(f x + e\right)}}{a e^{\left(f x + e\right)} - i \, a}, x\right)"," ",0,"integral(-2*I*sqrt(1/2*I*a*e^(-f*x - e))*x^2*e^(f*x + e)/(a*e^(f*x + e) - I*a), x)","F",0
138,0,0,0,0.786167," ","integrate(x/(a+I*a*sinh(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}} x e^{\left(f x + e\right)}}{a e^{\left(f x + e\right)} - i \, a}, x\right)"," ",0,"integral(-2*I*sqrt(1/2*I*a*e^(-f*x - e))*x*e^(f*x + e)/(a*e^(f*x + e) - I*a), x)","F",0
139,0,0,0,0.743345," ","integrate(1/x/(a+I*a*sinh(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}} e^{\left(f x + e\right)}}{a x e^{\left(f x + e\right)} - i \, a x}, x\right)"," ",0,"integral(-2*I*sqrt(1/2*I*a*e^(-f*x - e))*e^(f*x + e)/(a*x*e^(f*x + e) - I*a*x), x)","F",0
140,0,0,0,0.468583," ","integrate(1/x^2/(a+I*a*sinh(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{2 i \, \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}} e^{\left(f x + e\right)}}{a x^{2} e^{\left(f x + e\right)} - i \, a x^{2}}, x\right)"," ",0,"integral(-2*I*sqrt(1/2*I*a*e^(-f*x - e))*e^(f*x + e)/(a*x^2*e^(f*x + e) - I*a*x^2), x)","F",0
141,0,0,0,0.836708," ","integrate(x^3/(a+I*a*sinh(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} f^{2} e^{\left(2 \, f x + 2 \, e\right)} - 2 i \, a^{2} f^{2} e^{\left(f x + e\right)} - a^{2} f^{2}\right)} {\rm integral}\left(\frac{{\left(-i \, f^{2} x^{3} + 24 i \, x\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}} e^{\left(f x + e\right)}}{2 \, {\left(a^{2} f^{2} e^{\left(f x + e\right)} - i \, a^{2} f^{2}\right)}}, x\right) + {\left({\left(-i \, f x^{3} - 6 i \, x^{2}\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(f x^{3} - 6 \, x^{2}\right)} e^{\left(f x + e\right)}\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}}}{a^{2} f^{2} e^{\left(2 \, f x + 2 \, e\right)} - 2 i \, a^{2} f^{2} e^{\left(f x + e\right)} - a^{2} f^{2}}"," ",0,"((a^2*f^2*e^(2*f*x + 2*e) - 2*I*a^2*f^2*e^(f*x + e) - a^2*f^2)*integral(1/2*(-I*f^2*x^3 + 24*I*x)*sqrt(1/2*I*a*e^(-f*x - e))*e^(f*x + e)/(a^2*f^2*e^(f*x + e) - I*a^2*f^2), x) + ((-I*f*x^3 - 6*I*x^2)*e^(2*f*x + 2*e) + (f*x^3 - 6*x^2)*e^(f*x + e))*sqrt(1/2*I*a*e^(-f*x - e)))/(a^2*f^2*e^(2*f*x + 2*e) - 2*I*a^2*f^2*e^(f*x + e) - a^2*f^2)","F",0
142,0,0,0,0.691643," ","integrate(x^2/(a+I*a*sinh(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} f^{2} e^{\left(2 \, f x + 2 \, e\right)} - 2 i \, a^{2} f^{2} e^{\left(f x + e\right)} - a^{2} f^{2}\right)} {\rm integral}\left(\frac{{\left(-i \, f^{2} x^{2} + 8 i\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}} e^{\left(f x + e\right)}}{2 \, {\left(a^{2} f^{2} e^{\left(f x + e\right)} - i \, a^{2} f^{2}\right)}}, x\right) + {\left({\left(-i \, f x^{2} - 4 i \, x\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(f x^{2} - 4 \, x\right)} e^{\left(f x + e\right)}\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}}}{a^{2} f^{2} e^{\left(2 \, f x + 2 \, e\right)} - 2 i \, a^{2} f^{2} e^{\left(f x + e\right)} - a^{2} f^{2}}"," ",0,"((a^2*f^2*e^(2*f*x + 2*e) - 2*I*a^2*f^2*e^(f*x + e) - a^2*f^2)*integral(1/2*(-I*f^2*x^2 + 8*I)*sqrt(1/2*I*a*e^(-f*x - e))*e^(f*x + e)/(a^2*f^2*e^(f*x + e) - I*a^2*f^2), x) + ((-I*f*x^2 - 4*I*x)*e^(2*f*x + 2*e) + (f*x^2 - 4*x)*e^(f*x + e))*sqrt(1/2*I*a*e^(-f*x - e)))/(a^2*f^2*e^(2*f*x + 2*e) - 2*I*a^2*f^2*e^(f*x + e) - a^2*f^2)","F",0
143,0,0,0,0.491418," ","integrate(x/(a+I*a*sinh(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} f^{2} e^{\left(2 \, f x + 2 \, e\right)} - 2 i \, a^{2} f^{2} e^{\left(f x + e\right)} - a^{2} f^{2}\right)} {\rm integral}\left(-\frac{i \, \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}} x e^{\left(f x + e\right)}}{2 \, a^{2} e^{\left(f x + e\right)} - 2 i \, a^{2}}, x\right) + {\left({\left(-i \, f x - 2 i\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(f x - 2\right)} e^{\left(f x + e\right)}\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}}}{a^{2} f^{2} e^{\left(2 \, f x + 2 \, e\right)} - 2 i \, a^{2} f^{2} e^{\left(f x + e\right)} - a^{2} f^{2}}"," ",0,"((a^2*f^2*e^(2*f*x + 2*e) - 2*I*a^2*f^2*e^(f*x + e) - a^2*f^2)*integral(-I*sqrt(1/2*I*a*e^(-f*x - e))*x*e^(f*x + e)/(2*a^2*e^(f*x + e) - 2*I*a^2), x) + ((-I*f*x - 2*I)*e^(2*f*x + 2*e) + (f*x - 2)*e^(f*x + e))*sqrt(1/2*I*a*e^(-f*x - e)))/(a^2*f^2*e^(2*f*x + 2*e) - 2*I*a^2*f^2*e^(f*x + e) - a^2*f^2)","F",0
144,0,0,0,0.597495," ","integrate(1/x/(a+I*a*sinh(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} f^{2} x^{2} e^{\left(2 \, f x + 2 \, e\right)} - 2 i \, a^{2} f^{2} x^{2} e^{\left(f x + e\right)} - a^{2} f^{2} x^{2}\right)} {\rm integral}\left(\frac{{\left(-i \, f^{2} x^{2} + 8 i\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}} e^{\left(f x + e\right)}}{2 \, a^{2} f^{2} x^{3} e^{\left(f x + e\right)} - 2 i \, a^{2} f^{2} x^{3}}, x\right) + {\left({\left(-i \, f x + 2 i\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(f x + 2\right)} e^{\left(f x + e\right)}\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}}}{a^{2} f^{2} x^{2} e^{\left(2 \, f x + 2 \, e\right)} - 2 i \, a^{2} f^{2} x^{2} e^{\left(f x + e\right)} - a^{2} f^{2} x^{2}}"," ",0,"((a^2*f^2*x^2*e^(2*f*x + 2*e) - 2*I*a^2*f^2*x^2*e^(f*x + e) - a^2*f^2*x^2)*integral((-I*f^2*x^2 + 8*I)*sqrt(1/2*I*a*e^(-f*x - e))*e^(f*x + e)/(2*a^2*f^2*x^3*e^(f*x + e) - 2*I*a^2*f^2*x^3), x) + ((-I*f*x + 2*I)*e^(2*f*x + 2*e) + (f*x + 2)*e^(f*x + e))*sqrt(1/2*I*a*e^(-f*x - e)))/(a^2*f^2*x^2*e^(2*f*x + 2*e) - 2*I*a^2*f^2*x^2*e^(f*x + e) - a^2*f^2*x^2)","F",0
145,0,0,0,0.931048," ","integrate(1/x^2/(a+I*a*sinh(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} f^{2} x^{3} e^{\left(2 \, f x + 2 \, e\right)} - 2 i \, a^{2} f^{2} x^{3} e^{\left(f x + e\right)} - a^{2} f^{2} x^{3}\right)} {\rm integral}\left(\frac{{\left(-i \, f^{2} x^{2} + 24 i\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}} e^{\left(f x + e\right)}}{2 \, a^{2} f^{2} x^{4} e^{\left(f x + e\right)} - 2 i \, a^{2} f^{2} x^{4}}, x\right) + {\left({\left(-i \, f x + 4 i\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(f x + 4\right)} e^{\left(f x + e\right)}\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-f x - e\right)}}}{a^{2} f^{2} x^{3} e^{\left(2 \, f x + 2 \, e\right)} - 2 i \, a^{2} f^{2} x^{3} e^{\left(f x + e\right)} - a^{2} f^{2} x^{3}}"," ",0,"((a^2*f^2*x^3*e^(2*f*x + 2*e) - 2*I*a^2*f^2*x^3*e^(f*x + e) - a^2*f^2*x^3)*integral((-I*f^2*x^2 + 24*I)*sqrt(1/2*I*a*e^(-f*x - e))*e^(f*x + e)/(2*a^2*f^2*x^4*e^(f*x + e) - 2*I*a^2*f^2*x^4), x) + ((-I*f*x + 4*I)*e^(2*f*x + 2*e) + (f*x + 4)*e^(f*x + e))*sqrt(1/2*I*a*e^(-f*x - e)))/(a^2*f^2*x^3*e^(2*f*x + 2*e) - 2*I*a^2*f^2*x^3*e^(f*x + e) - a^2*f^2*x^3)","F",0
146,0,0,0,0.546221," ","integrate(x^3/(a+I*a*sinh(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(8 \, a^{3} d^{4} e^{\left(4 \, d x + 4 \, c\right)} - 32 i \, a^{3} d^{4} e^{\left(3 \, d x + 3 \, c\right)} - 48 \, a^{3} d^{4} e^{\left(2 \, d x + 2 \, c\right)} + 32 i \, a^{3} d^{4} e^{\left(d x + c\right)} + 8 \, a^{3} d^{4}\right)} {\rm integral}\left(\frac{{\left(-3 i \, d^{2} x^{3} + 80 i \, x\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-d x - c\right)}} e^{\left(d x + c\right)}}{16 \, {\left(a^{3} d^{2} e^{\left(d x + c\right)} - i \, a^{3} d^{2}\right)}}, x\right) + {\left({\left(-3 i \, d^{3} x^{3} - 18 i \, d^{2} x^{2} + 8 i \, d x + 16 i\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(11 \, d^{3} x^{3} + 70 \, d^{2} x^{2} - 8 \, d x - 48\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-11 i \, d^{3} x^{3} + 70 i \, d^{2} x^{2} + 8 i \, d x - 48 i\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(3 \, d^{3} x^{3} - 18 \, d^{2} x^{2} - 8 \, d x + 16\right)} e^{\left(d x + c\right)}\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-d x - c\right)}}}{8 \, a^{3} d^{4} e^{\left(4 \, d x + 4 \, c\right)} - 32 i \, a^{3} d^{4} e^{\left(3 \, d x + 3 \, c\right)} - 48 \, a^{3} d^{4} e^{\left(2 \, d x + 2 \, c\right)} + 32 i \, a^{3} d^{4} e^{\left(d x + c\right)} + 8 \, a^{3} d^{4}}"," ",0,"((8*a^3*d^4*e^(4*d*x + 4*c) - 32*I*a^3*d^4*e^(3*d*x + 3*c) - 48*a^3*d^4*e^(2*d*x + 2*c) + 32*I*a^3*d^4*e^(d*x + c) + 8*a^3*d^4)*integral(1/16*(-3*I*d^2*x^3 + 80*I*x)*sqrt(1/2*I*a*e^(-d*x - c))*e^(d*x + c)/(a^3*d^2*e^(d*x + c) - I*a^3*d^2), x) + ((-3*I*d^3*x^3 - 18*I*d^2*x^2 + 8*I*d*x + 16*I)*e^(4*d*x + 4*c) - (11*d^3*x^3 + 70*d^2*x^2 - 8*d*x - 48)*e^(3*d*x + 3*c) + (-11*I*d^3*x^3 + 70*I*d^2*x^2 + 8*I*d*x - 48*I)*e^(2*d*x + 2*c) - (3*d^3*x^3 - 18*d^2*x^2 - 8*d*x + 16)*e^(d*x + c))*sqrt(1/2*I*a*e^(-d*x - c)))/(8*a^3*d^4*e^(4*d*x + 4*c) - 32*I*a^3*d^4*e^(3*d*x + 3*c) - 48*a^3*d^4*e^(2*d*x + 2*c) + 32*I*a^3*d^4*e^(d*x + c) + 8*a^3*d^4)","F",0
147,0,0,0,0.559718," ","integrate(x^2/(a+I*a*sinh(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(24 \, a^{3} d^{3} e^{\left(4 \, d x + 4 \, c\right)} - 96 i \, a^{3} d^{3} e^{\left(3 \, d x + 3 \, c\right)} - 144 \, a^{3} d^{3} e^{\left(2 \, d x + 2 \, c\right)} + 96 i \, a^{3} d^{3} e^{\left(d x + c\right)} + 24 \, a^{3} d^{3}\right)} {\rm integral}\left(\frac{{\left(-9 i \, d^{2} x^{2} + 80 i\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-d x - c\right)}} e^{\left(d x + c\right)}}{48 \, {\left(a^{3} d^{2} e^{\left(d x + c\right)} - i \, a^{3} d^{2}\right)}}, x\right) + {\left({\left(-9 i \, d^{2} x^{2} - 36 i \, d x + 8 i\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(33 \, d^{2} x^{2} + 140 \, d x - 8\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-33 i \, d^{2} x^{2} + 140 i \, d x + 8 i\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(9 \, d^{2} x^{2} - 36 \, d x - 8\right)} e^{\left(d x + c\right)}\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-d x - c\right)}}}{24 \, a^{3} d^{3} e^{\left(4 \, d x + 4 \, c\right)} - 96 i \, a^{3} d^{3} e^{\left(3 \, d x + 3 \, c\right)} - 144 \, a^{3} d^{3} e^{\left(2 \, d x + 2 \, c\right)} + 96 i \, a^{3} d^{3} e^{\left(d x + c\right)} + 24 \, a^{3} d^{3}}"," ",0,"((24*a^3*d^3*e^(4*d*x + 4*c) - 96*I*a^3*d^3*e^(3*d*x + 3*c) - 144*a^3*d^3*e^(2*d*x + 2*c) + 96*I*a^3*d^3*e^(d*x + c) + 24*a^3*d^3)*integral(1/48*(-9*I*d^2*x^2 + 80*I)*sqrt(1/2*I*a*e^(-d*x - c))*e^(d*x + c)/(a^3*d^2*e^(d*x + c) - I*a^3*d^2), x) + ((-9*I*d^2*x^2 - 36*I*d*x + 8*I)*e^(4*d*x + 4*c) - (33*d^2*x^2 + 140*d*x - 8)*e^(3*d*x + 3*c) + (-33*I*d^2*x^2 + 140*I*d*x + 8*I)*e^(2*d*x + 2*c) - (9*d^2*x^2 - 36*d*x - 8)*e^(d*x + c))*sqrt(1/2*I*a*e^(-d*x - c)))/(24*a^3*d^3*e^(4*d*x + 4*c) - 96*I*a^3*d^3*e^(3*d*x + 3*c) - 144*a^3*d^3*e^(2*d*x + 2*c) + 96*I*a^3*d^3*e^(d*x + c) + 24*a^3*d^3)","F",0
148,0,0,0,0.520107," ","integrate(x/(a+I*a*sinh(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(24 \, a^{3} d^{2} e^{\left(4 \, d x + 4 \, c\right)} - 96 i \, a^{3} d^{2} e^{\left(3 \, d x + 3 \, c\right)} - 144 \, a^{3} d^{2} e^{\left(2 \, d x + 2 \, c\right)} + 96 i \, a^{3} d^{2} e^{\left(d x + c\right)} + 24 \, a^{3} d^{2}\right)} {\rm integral}\left(-\frac{3 i \, \sqrt{\frac{1}{2} i \, a e^{\left(-d x - c\right)}} x e^{\left(d x + c\right)}}{16 \, a^{3} e^{\left(d x + c\right)} - 16 i \, a^{3}}, x\right) + {\left({\left(-9 i \, d x - 18 i\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(33 \, d x + 70\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-33 i \, d x + 70 i\right)} e^{\left(2 \, d x + 2 \, c\right)} - 9 \, {\left(d x - 2\right)} e^{\left(d x + c\right)}\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-d x - c\right)}}}{24 \, a^{3} d^{2} e^{\left(4 \, d x + 4 \, c\right)} - 96 i \, a^{3} d^{2} e^{\left(3 \, d x + 3 \, c\right)} - 144 \, a^{3} d^{2} e^{\left(2 \, d x + 2 \, c\right)} + 96 i \, a^{3} d^{2} e^{\left(d x + c\right)} + 24 \, a^{3} d^{2}}"," ",0,"((24*a^3*d^2*e^(4*d*x + 4*c) - 96*I*a^3*d^2*e^(3*d*x + 3*c) - 144*a^3*d^2*e^(2*d*x + 2*c) + 96*I*a^3*d^2*e^(d*x + c) + 24*a^3*d^2)*integral(-3*I*sqrt(1/2*I*a*e^(-d*x - c))*x*e^(d*x + c)/(16*a^3*e^(d*x + c) - 16*I*a^3), x) + ((-9*I*d*x - 18*I)*e^(4*d*x + 4*c) - (33*d*x + 70)*e^(3*d*x + 3*c) + (-33*I*d*x + 70*I)*e^(2*d*x + 2*c) - 9*(d*x - 2)*e^(d*x + c))*sqrt(1/2*I*a*e^(-d*x - c)))/(24*a^3*d^2*e^(4*d*x + 4*c) - 96*I*a^3*d^2*e^(3*d*x + 3*c) - 144*a^3*d^2*e^(2*d*x + 2*c) + 96*I*a^3*d^2*e^(d*x + c) + 24*a^3*d^2)","F",0
149,0,0,0,0.914332," ","integrate(1/x/(a+I*a*sinh(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{{\left(24 \, a^{3} d^{4} x^{4} e^{\left(4 \, d x + 4 \, c\right)} - 96 i \, a^{3} d^{4} x^{4} e^{\left(3 \, d x + 3 \, c\right)} - 144 \, a^{3} d^{4} x^{4} e^{\left(2 \, d x + 2 \, c\right)} + 96 i \, a^{3} d^{4} x^{4} e^{\left(d x + c\right)} + 24 \, a^{3} d^{4} x^{4}\right)} {\rm integral}\left(\frac{{\left(-9 i \, d^{4} x^{4} + 80 i \, d^{2} x^{2} - 384 i\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-d x - c\right)}} e^{\left(d x + c\right)}}{48 \, a^{3} d^{4} x^{5} e^{\left(d x + c\right)} - 48 i \, a^{3} d^{4} x^{5}}, x\right) + {\left({\left(-9 i \, d^{3} x^{3} + 18 i \, d^{2} x^{2} + 8 i \, d x - 48 i\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(33 \, d^{3} x^{3} - 70 \, d^{2} x^{2} - 8 \, d x + 144\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-33 i \, d^{3} x^{3} - 70 i \, d^{2} x^{2} + 8 i \, d x + 144 i\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(9 \, d^{3} x^{3} + 18 \, d^{2} x^{2} - 8 \, d x - 48\right)} e^{\left(d x + c\right)}\right)} \sqrt{\frac{1}{2} i \, a e^{\left(-d x - c\right)}}}{24 \, a^{3} d^{4} x^{4} e^{\left(4 \, d x + 4 \, c\right)} - 96 i \, a^{3} d^{4} x^{4} e^{\left(3 \, d x + 3 \, c\right)} - 144 \, a^{3} d^{4} x^{4} e^{\left(2 \, d x + 2 \, c\right)} + 96 i \, a^{3} d^{4} x^{4} e^{\left(d x + c\right)} + 24 \, a^{3} d^{4} x^{4}}"," ",0,"((24*a^3*d^4*x^4*e^(4*d*x + 4*c) - 96*I*a^3*d^4*x^4*e^(3*d*x + 3*c) - 144*a^3*d^4*x^4*e^(2*d*x + 2*c) + 96*I*a^3*d^4*x^4*e^(d*x + c) + 24*a^3*d^4*x^4)*integral((-9*I*d^4*x^4 + 80*I*d^2*x^2 - 384*I)*sqrt(1/2*I*a*e^(-d*x - c))*e^(d*x + c)/(48*a^3*d^4*x^5*e^(d*x + c) - 48*I*a^3*d^4*x^5), x) + ((-9*I*d^3*x^3 + 18*I*d^2*x^2 + 8*I*d*x - 48*I)*e^(4*d*x + 4*c) - (33*d^3*x^3 - 70*d^2*x^2 - 8*d*x + 144)*e^(3*d*x + 3*c) + (-33*I*d^3*x^3 - 70*I*d^2*x^2 + 8*I*d*x + 144*I)*e^(2*d*x + 2*c) - (9*d^3*x^3 + 18*d^2*x^2 - 8*d*x - 48)*e^(d*x + c))*sqrt(1/2*I*a*e^(-d*x - c)))/(24*a^3*d^4*x^4*e^(4*d*x + 4*c) - 96*I*a^3*d^4*x^4*e^(3*d*x + 3*c) - 144*a^3*d^4*x^4*e^(2*d*x + 2*c) + 96*I*a^3*d^4*x^4*e^(d*x + c) + 24*a^3*d^4*x^4)","F",0
150,-2,0,0,0.000000," ","integrate((a+I*a*sinh(f*x+e))^(1/3)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
151,0,0,0,0.573061," ","integrate((d*x+c)^m*(a+I*a*sinh(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \left(\frac{1}{2} \, {\left(i \, a e^{\left(2 \, f x + 2 \, e\right)} + 2 \, a e^{\left(f x + e\right)} - i \, a\right)} e^{\left(-f x - e\right)}\right)^{n}, x\right)"," ",0,"integral((d*x + c)^m*(1/2*(I*a*e^(2*f*x + 2*e) + 2*a*e^(f*x + e) - I*a)*e^(-f*x - e))^n, x)","F",0
152,1,372,0,0.655252," ","integrate((d*x+c)^m*(a+I*a*sinh(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(-i \, a^{3} d m - i \, a^{3} d\right)} e^{\left(-\frac{d m \log\left(\frac{3 \, f}{d}\right) + 3 \, d e - 3 \, c f}{d}\right)} \Gamma\left(m + 1, \frac{3 \, {\left(d f x + c f\right)}}{d}\right) + 9 \, {\left(a^{3} d m + a^{3} d\right)} e^{\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(45 i \, a^{3} d m + 45 i \, a^{3} d\right)} e^{\left(-\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) + {\left(45 i \, a^{3} d m + 45 i \, a^{3} d\right)} e^{\left(-\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) - 9 \, {\left(a^{3} d m + a^{3} d\right)} e^{\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(-i \, a^{3} d m - i \, a^{3} d\right)} e^{\left(-\frac{d m \log\left(-\frac{3 \, f}{d}\right) - 3 \, d e + 3 \, c f}{d}\right)} \Gamma\left(m + 1, -\frac{3 \, {\left(d f x + c f\right)}}{d}\right) + 60 \, {\left(a^{3} d f x + a^{3} c f\right)} {\left(d x + c\right)}^{m}}{24 \, {\left(d f m + d f\right)}}"," ",0,"1/24*((-I*a^3*d*m - I*a^3*d)*e^(-(d*m*log(3*f/d) + 3*d*e - 3*c*f)/d)*gamma(m + 1, 3*(d*f*x + c*f)/d) + 9*(a^3*d*m + a^3*d)*e^(-(d*m*log(2*f/d) + 2*d*e - 2*c*f)/d)*gamma(m + 1, 2*(d*f*x + c*f)/d) + (45*I*a^3*d*m + 45*I*a^3*d)*e^(-(d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) + (45*I*a^3*d*m + 45*I*a^3*d)*e^(-(d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) - 9*(a^3*d*m + a^3*d)*e^(-(d*m*log(-2*f/d) - 2*d*e + 2*c*f)/d)*gamma(m + 1, -2*(d*f*x + c*f)/d) + (-I*a^3*d*m - I*a^3*d)*e^(-(d*m*log(-3*f/d) - 3*d*e + 3*c*f)/d)*gamma(m + 1, -3*(d*f*x + c*f)/d) + 60*(a^3*d*f*x + a^3*c*f)*(d*x + c)^m)/(d*f*m + d*f)","A",0
153,1,257,0,0.528308," ","integrate((d*x+c)^m*(a+I*a*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} d m + a^{2} d\right)} e^{\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(8 i \, a^{2} d m + 8 i \, a^{2} d\right)} e^{\left(-\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) + {\left(8 i \, a^{2} d m + 8 i \, a^{2} d\right)} e^{\left(-\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) - {\left(a^{2} d m + a^{2} d\right)} e^{\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) + 12 \, {\left(a^{2} d f x + a^{2} c f\right)} {\left(d x + c\right)}^{m}}{8 \, {\left(d f m + d f\right)}}"," ",0,"1/8*((a^2*d*m + a^2*d)*e^(-(d*m*log(2*f/d) + 2*d*e - 2*c*f)/d)*gamma(m + 1, 2*(d*f*x + c*f)/d) + (8*I*a^2*d*m + 8*I*a^2*d)*e^(-(d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) + (8*I*a^2*d*m + 8*I*a^2*d)*e^(-(d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) - (a^2*d*m + a^2*d)*e^(-(d*m*log(-2*f/d) - 2*d*e + 2*c*f)/d)*gamma(m + 1, -2*(d*f*x + c*f)/d) + 12*(a^2*d*f*x + a^2*c*f)*(d*x + c)^m)/(d*f*m + d*f)","A",0
154,1,134,0,0.923007," ","integrate((d*x+c)^m*(a+I*a*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(i \, a d m + i \, a d\right)} e^{\left(-\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) + {\left(i \, a d m + i \, a d\right)} e^{\left(-\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) + 2 \, {\left(a d f x + a c f\right)} {\left(d x + c\right)}^{m}}{2 \, {\left(d f m + d f\right)}}"," ",0,"1/2*((I*a*d*m + I*a*d)*e^(-(d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) + (I*a*d*m + I*a*d)*e^(-(d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) + 2*(a*d*f*x + a*c*f)*(d*x + c)^m)/(d*f*m + d*f)","A",0
155,0,0,0,0.523849," ","integrate((d*x+c)^m/(a+I*a*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a f e^{\left(f x + e\right)} - i \, a f\right)} {\rm integral}\left(-\frac{2 i \, {\left(d x + c\right)}^{m} d m}{-i \, a d f x - i \, a c f + {\left(a d f x + a c f\right)} e^{\left(f x + e\right)}}, x\right) + 2 i \, {\left(d x + c\right)}^{m}}{a f e^{\left(f x + e\right)} - i \, a f}"," ",0,"((a*f*e^(f*x + e) - I*a*f)*integral(-2*I*(d*x + c)^m*d*m/(-I*a*d*f*x - I*a*c*f + (a*d*f*x + a*c*f)*e^(f*x + e)), x) + 2*I*(d*x + c)^m)/(a*f*e^(f*x + e) - I*a*f)","F",0
156,0,0,0,0.445677," ","integrate((d*x+c)^m/(a+I*a*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(-2 i \, d^{2} f^{2} x^{2} - 4 i \, c d f^{2} x - 2 i \, c^{2} f^{2} + 2 i \, d^{2} m^{2} - 2 i \, d^{2} m + {\left(-2 i \, d^{2} f m x - 2 i \, d^{2} m^{2} + {\left(-2 i \, c d f + 2 i \, d^{2}\right)} m\right)} e^{\left(2 \, f x + 2 \, e\right)} + 2 \, {\left(3 \, d^{2} f^{2} x^{2} + 3 \, c^{2} f^{2} - 2 \, d^{2} m^{2} - {\left(c d f - 2 \, d^{2}\right)} m + {\left(6 \, c d f^{2} - d^{2} f m\right)} x\right)} e^{\left(f x + e\right)}\right)} {\left(d x + c\right)}^{m} + {\left(3 i \, a^{2} d^{2} f^{3} x^{2} + 6 i \, a^{2} c d f^{3} x + 3 i \, a^{2} c^{2} f^{3} + 3 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} c d f^{3} x + a^{2} c^{2} f^{3}\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(-9 i \, a^{2} d^{2} f^{3} x^{2} - 18 i \, a^{2} c d f^{3} x - 9 i \, a^{2} c^{2} f^{3}\right)} e^{\left(2 \, f x + 2 \, e\right)} - 9 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} c d f^{3} x + a^{2} c^{2} f^{3}\right)} e^{\left(f x + e\right)}\right)} {\rm integral}\left(\frac{{\left(-2 i \, d^{3} f^{2} m x^{2} - 4 i \, c d^{2} f^{2} m x + 2 i \, d^{3} m^{3} - 6 i \, d^{3} m^{2} + {\left(-2 i \, c^{2} d f^{2} + 4 i \, d^{3}\right)} m\right)} {\left(d x + c\right)}^{m}}{-3 i \, a^{2} d^{3} f^{3} x^{3} - 9 i \, a^{2} c d^{2} f^{3} x^{2} - 9 i \, a^{2} c^{2} d f^{3} x - 3 i \, a^{2} c^{3} f^{3} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} x + a^{2} c^{3} f^{3}\right)} e^{\left(f x + e\right)}}, x\right)}{3 i \, a^{2} d^{2} f^{3} x^{2} + 6 i \, a^{2} c d f^{3} x + 3 i \, a^{2} c^{2} f^{3} + 3 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} c d f^{3} x + a^{2} c^{2} f^{3}\right)} e^{\left(3 \, f x + 3 \, e\right)} + {\left(-9 i \, a^{2} d^{2} f^{3} x^{2} - 18 i \, a^{2} c d f^{3} x - 9 i \, a^{2} c^{2} f^{3}\right)} e^{\left(2 \, f x + 2 \, e\right)} - 9 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} c d f^{3} x + a^{2} c^{2} f^{3}\right)} e^{\left(f x + e\right)}}"," ",0,"((-2*I*d^2*f^2*x^2 - 4*I*c*d*f^2*x - 2*I*c^2*f^2 + 2*I*d^2*m^2 - 2*I*d^2*m + (-2*I*d^2*f*m*x - 2*I*d^2*m^2 + (-2*I*c*d*f + 2*I*d^2)*m)*e^(2*f*x + 2*e) + 2*(3*d^2*f^2*x^2 + 3*c^2*f^2 - 2*d^2*m^2 - (c*d*f - 2*d^2)*m + (6*c*d*f^2 - d^2*f*m)*x)*e^(f*x + e))*(d*x + c)^m + (3*I*a^2*d^2*f^3*x^2 + 6*I*a^2*c*d*f^3*x + 3*I*a^2*c^2*f^3 + 3*(a^2*d^2*f^3*x^2 + 2*a^2*c*d*f^3*x + a^2*c^2*f^3)*e^(3*f*x + 3*e) + (-9*I*a^2*d^2*f^3*x^2 - 18*I*a^2*c*d*f^3*x - 9*I*a^2*c^2*f^3)*e^(2*f*x + 2*e) - 9*(a^2*d^2*f^3*x^2 + 2*a^2*c*d*f^3*x + a^2*c^2*f^3)*e^(f*x + e))*integral((-2*I*d^3*f^2*m*x^2 - 4*I*c*d^2*f^2*m*x + 2*I*d^3*m^3 - 6*I*d^3*m^2 + (-2*I*c^2*d*f^2 + 4*I*d^3)*m)*(d*x + c)^m/(-3*I*a^2*d^3*f^3*x^3 - 9*I*a^2*c*d^2*f^3*x^2 - 9*I*a^2*c^2*d*f^3*x - 3*I*a^2*c^3*f^3 + 3*(a^2*d^3*f^3*x^3 + 3*a^2*c*d^2*f^3*x^2 + 3*a^2*c^2*d*f^3*x + a^2*c^3*f^3)*e^(f*x + e)), x))/(3*I*a^2*d^2*f^3*x^2 + 6*I*a^2*c*d*f^3*x + 3*I*a^2*c^2*f^3 + 3*(a^2*d^2*f^3*x^2 + 2*a^2*c*d*f^3*x + a^2*c^2*f^3)*e^(3*f*x + 3*e) + (-9*I*a^2*d^2*f^3*x^2 - 18*I*a^2*c*d*f^3*x - 9*I*a^2*c^2*f^3)*e^(2*f*x + 2*e) - 9*(a^2*d^2*f^3*x^2 + 2*a^2*c*d*f^3*x + a^2*c^2*f^3)*e^(f*x + e))","F",0
157,1,168,0,0.523279," ","integrate((d*x+c)^3*(a+b*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{3} f^{4} x^{4} + 4 \, a c d^{2} f^{4} x^{3} + 6 \, a c^{2} d f^{4} x^{2} + 4 \, a c^{3} f^{4} x + 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + b c^{3} f^{3} + 6 \, b c d^{2} f + 3 \, {\left(b c^{2} d f^{3} + 2 \, b d^{3} f\right)} x\right)} \cosh\left(f x + e\right) - 12 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2} + 2 \, b d^{3}\right)} \sinh\left(f x + e\right)}{4 \, f^{4}}"," ",0,"1/4*(a*d^3*f^4*x^4 + 4*a*c*d^2*f^4*x^3 + 6*a*c^2*d*f^4*x^2 + 4*a*c^3*f^4*x + 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + b*c^3*f^3 + 6*b*c*d^2*f + 3*(b*c^2*d*f^3 + 2*b*d^3*f)*x)*cosh(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 + 2*b*d^3)*sinh(f*x + e))/f^4","A",0
158,1,102,0,1.058825," ","integrate((d*x+c)^2*(a+b*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{2} f^{3} x^{3} + 3 \, a c d f^{3} x^{2} + 3 \, a c^{2} f^{3} x + 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2} + 2 \, b d^{2}\right)} \cosh\left(f x + e\right) - 6 \, {\left(b d^{2} f x + b c d f\right)} \sinh\left(f x + e\right)}{3 \, f^{3}}"," ",0,"1/3*(a*d^2*f^3*x^3 + 3*a*c*d*f^3*x^2 + 3*a*c^2*f^3*x + 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2 + 2*b*d^2)*cosh(f*x + e) - 6*(b*d^2*f*x + b*c*d*f)*sinh(f*x + e))/f^3","A",0
159,1,51,0,0.456695," ","integrate((d*x+c)*(a+b*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{a d f^{2} x^{2} + 2 \, a c f^{2} x - 2 \, b d \sinh\left(f x + e\right) + 2 \, {\left(b d f x + b c f\right)} \cosh\left(f x + e\right)}{2 \, f^{2}}"," ",0,"1/2*(a*d*f^2*x^2 + 2*a*c*f^2*x - 2*b*d*sinh(f*x + e) + 2*(b*d*f*x + b*c*f)*cosh(f*x + e))/f^2","A",0
160,1,111,0,0.459513," ","integrate((a+b*sinh(f*x+e))/(d*x+c),x, algorithm=""fricas"")","\frac{{\left(b {\rm Ei}\left(\frac{d f x + c f}{d}\right) - b {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + 2 \, a \log\left(d x + c\right) - {\left(b {\rm Ei}\left(\frac{d f x + c f}{d}\right) + b {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right)}{2 \, d}"," ",0,"1/2*((b*Ei((d*f*x + c*f)/d) - b*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + 2*a*log(d*x + c) - (b*Ei((d*f*x + c*f)/d) + b*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d))/d","A",0
161,1,162,0,0.511998," ","integrate((a+b*sinh(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, b d \sinh\left(f x + e\right) + 2 \, a d - {\left({\left(b d f x + b c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(b d f x + b c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + {\left({\left(b d f x + b c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(b d f x + b c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(2*b*d*sinh(f*x + e) + 2*a*d - ((b*d*f*x + b*c*f)*Ei((d*f*x + c*f)/d) + (b*d*f*x + b*c*f)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + ((b*d*f*x + b*c*f)*Ei((d*f*x + c*f)/d) - (b*d*f*x + b*c*f)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d))/(d^3*x + c*d^2)","A",0
162,1,274,0,0.446877," ","integrate((a+b*sinh(f*x+e))/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, b d^{2} \sinh\left(f x + e\right) + 2 \, a d^{2} + 2 \, {\left(b d^{2} f x + b c d f\right)} \cosh\left(f x + e\right) - {\left({\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + {\left({\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(2*b*d^2*sinh(f*x + e) + 2*a*d^2 + 2*(b*d^2*f*x + b*c*d*f)*cosh(f*x + e) - ((b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*Ei((d*f*x + c*f)/d) - (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + ((b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*Ei((d*f*x + c*f)/d) + (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
163,1,418,0,0.472446," ","integrate((d*x+c)^3*(a+b*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} - b^{2}\right)} d^{3} f^{4} x^{4} + 8 \, {\left(2 \, a^{2} - b^{2}\right)} c d^{2} f^{4} x^{3} + 12 \, {\left(2 \, a^{2} - b^{2}\right)} c^{2} d f^{4} x^{2} + 8 \, {\left(2 \, a^{2} - b^{2}\right)} c^{3} f^{4} x - 3 \, {\left(2 \, b^{2} d^{3} f^{2} x^{2} + 4 \, b^{2} c d^{2} f^{2} x + 2 \, b^{2} c^{2} d f^{2} + b^{2} d^{3}\right)} \cosh\left(f x + e\right)^{2} - 3 \, {\left(2 \, b^{2} d^{3} f^{2} x^{2} + 4 \, b^{2} c d^{2} f^{2} x + 2 \, b^{2} c^{2} d f^{2} + b^{2} d^{3}\right)} \sinh\left(f x + e\right)^{2} + 32 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b c d^{2} f^{3} x^{2} + a b c^{3} f^{3} + 6 \, a b c d^{2} f + 3 \, {\left(a b c^{2} d f^{3} + 2 \, a b d^{3} f\right)} x\right)} \cosh\left(f x + e\right) - 4 \, {\left(24 \, a b d^{3} f^{2} x^{2} + 48 \, a b c d^{2} f^{2} x + 24 \, a b c^{2} d f^{2} + 48 \, a b d^{3} - {\left(2 \, b^{2} d^{3} f^{3} x^{3} + 6 \, b^{2} c d^{2} f^{3} x^{2} + 2 \, b^{2} c^{3} f^{3} + 3 \, b^{2} c d^{2} f + 3 \, {\left(2 \, b^{2} c^{2} d f^{3} + b^{2} d^{3} f\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{16 \, f^{4}}"," ",0,"1/16*(2*(2*a^2 - b^2)*d^3*f^4*x^4 + 8*(2*a^2 - b^2)*c*d^2*f^4*x^3 + 12*(2*a^2 - b^2)*c^2*d*f^4*x^2 + 8*(2*a^2 - b^2)*c^3*f^4*x - 3*(2*b^2*d^3*f^2*x^2 + 4*b^2*c*d^2*f^2*x + 2*b^2*c^2*d*f^2 + b^2*d^3)*cosh(f*x + e)^2 - 3*(2*b^2*d^3*f^2*x^2 + 4*b^2*c*d^2*f^2*x + 2*b^2*c^2*d*f^2 + b^2*d^3)*sinh(f*x + e)^2 + 32*(a*b*d^3*f^3*x^3 + 3*a*b*c*d^2*f^3*x^2 + a*b*c^3*f^3 + 6*a*b*c*d^2*f + 3*(a*b*c^2*d*f^3 + 2*a*b*d^3*f)*x)*cosh(f*x + e) - 4*(24*a*b*d^3*f^2*x^2 + 48*a*b*c*d^2*f^2*x + 24*a*b*c^2*d*f^2 + 48*a*b*d^3 - (2*b^2*d^3*f^3*x^3 + 6*b^2*c*d^2*f^3*x^2 + 2*b^2*c^3*f^3 + 3*b^2*c*d^2*f + 3*(2*b^2*c^2*d*f^3 + b^2*d^3*f)*x)*cosh(f*x + e))*sinh(f*x + e))/f^4","A",0
164,1,247,0,0.667838," ","integrate((d*x+c)^2*(a+b*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} - b^{2}\right)} d^{2} f^{3} x^{3} + 6 \, {\left(2 \, a^{2} - b^{2}\right)} c d f^{3} x^{2} + 6 \, {\left(2 \, a^{2} - b^{2}\right)} c^{2} f^{3} x - 3 \, {\left(b^{2} d^{2} f x + b^{2} c d f\right)} \cosh\left(f x + e\right)^{2} - 3 \, {\left(b^{2} d^{2} f x + b^{2} c d f\right)} \sinh\left(f x + e\right)^{2} + 24 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2} + 2 \, a b d^{2}\right)} \cosh\left(f x + e\right) - 3 \, {\left(16 \, a b d^{2} f x + 16 \, a b c d f - {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 4 \, b^{2} c d f^{2} x + 2 \, b^{2} c^{2} f^{2} + b^{2} d^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{12 \, f^{3}}"," ",0,"1/12*(2*(2*a^2 - b^2)*d^2*f^3*x^3 + 6*(2*a^2 - b^2)*c*d*f^3*x^2 + 6*(2*a^2 - b^2)*c^2*f^3*x - 3*(b^2*d^2*f*x + b^2*c*d*f)*cosh(f*x + e)^2 - 3*(b^2*d^2*f*x + b^2*c*d*f)*sinh(f*x + e)^2 + 24*(a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2 + 2*a*b*d^2)*cosh(f*x + e) - 3*(16*a*b*d^2*f*x + 16*a*b*c*d*f - (2*b^2*d^2*f^2*x^2 + 4*b^2*c*d*f^2*x + 2*b^2*c^2*f^2 + b^2*d^2)*cosh(f*x + e))*sinh(f*x + e))/f^3","A",0
165,1,128,0,0.608159," ","integrate((d*x+c)*(a+b*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} - b^{2}\right)} d f^{2} x^{2} + 4 \, {\left(2 \, a^{2} - b^{2}\right)} c f^{2} x - b^{2} d \cosh\left(f x + e\right)^{2} - b^{2} d \sinh\left(f x + e\right)^{2} + 16 \, {\left(a b d f x + a b c f\right)} \cosh\left(f x + e\right) - 4 \, {\left(4 \, a b d - {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{8 \, f^{2}}"," ",0,"1/8*(2*(2*a^2 - b^2)*d*f^2*x^2 + 4*(2*a^2 - b^2)*c*f^2*x - b^2*d*cosh(f*x + e)^2 - b^2*d*sinh(f*x + e)^2 + 16*(a*b*d*f*x + a*b*c*f)*cosh(f*x + e) - 4*(4*a*b*d - (b^2*d*f*x + b^2*c*f)*cosh(f*x + e))*sinh(f*x + e))/f^2","A",0
166,1,232,0,0.885392," ","integrate((a+b*sinh(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","\frac{4 \, {\left(a b {\rm Ei}\left(\frac{d f x + c f}{d}\right) - a b {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + {\left(b^{2} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + b^{2} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 2 \, {\left(2 \, a^{2} - b^{2}\right)} \log\left(d x + c\right) - 4 \, {\left(a b {\rm Ei}\left(\frac{d f x + c f}{d}\right) + a b {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right) - {\left(b^{2} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - b^{2} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{4 \, d}"," ",0,"1/4*(4*(a*b*Ei((d*f*x + c*f)/d) - a*b*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + (b^2*Ei(2*(d*f*x + c*f)/d) + b^2*Ei(-2*(d*f*x + c*f)/d))*cosh(-2*(d*e - c*f)/d) + 2*(2*a^2 - b^2)*log(d*x + c) - 4*(a*b*Ei((d*f*x + c*f)/d) + a*b*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d) - (b^2*Ei(2*(d*f*x + c*f)/d) - b^2*Ei(-2*(d*f*x + c*f)/d))*sinh(-2*(d*e - c*f)/d))/d","A",0
167,1,357,0,0.584439," ","integrate((a+b*sinh(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{b^{2} d \cosh\left(f x + e\right)^{2} + b^{2} d \sinh\left(f x + e\right)^{2} + 4 \, a b d \sinh\left(f x + e\right) + {\left(2 \, a^{2} - b^{2}\right)} d - 2 \, {\left({\left(a b d f x + a b c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(a b d f x + a b c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) - {\left({\left(b^{2} d f x + b^{2} c f\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(b^{2} d f x + b^{2} c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 2 \, {\left({\left(a b d f x + a b c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(a b d f x + a b c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right) + {\left({\left(b^{2} d f x + b^{2} c f\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + {\left(b^{2} d f x + b^{2} c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(b^2*d*cosh(f*x + e)^2 + b^2*d*sinh(f*x + e)^2 + 4*a*b*d*sinh(f*x + e) + (2*a^2 - b^2)*d - 2*((a*b*d*f*x + a*b*c*f)*Ei((d*f*x + c*f)/d) + (a*b*d*f*x + a*b*c*f)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) - ((b^2*d*f*x + b^2*c*f)*Ei(2*(d*f*x + c*f)/d) - (b^2*d*f*x + b^2*c*f)*Ei(-2*(d*f*x + c*f)/d))*cosh(-2*(d*e - c*f)/d) + 2*((a*b*d*f*x + a*b*c*f)*Ei((d*f*x + c*f)/d) - (a*b*d*f*x + a*b*c*f)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d) + ((b^2*d*f*x + b^2*c*f)*Ei(2*(d*f*x + c*f)/d) + (b^2*d*f*x + b^2*c*f)*Ei(-2*(d*f*x + c*f)/d))*sinh(-2*(d*e - c*f)/d))/(d^3*x + c*d^2)","A",0
168,1,590,0,0.501984," ","integrate((a+b*sinh(f*x+e))^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{b^{2} d^{2} \cosh\left(f x + e\right)^{2} + b^{2} d^{2} \sinh\left(f x + e\right)^{2} + {\left(2 \, a^{2} - b^{2}\right)} d^{2} + 4 \, {\left(a b d^{2} f x + a b c d f\right)} \cosh\left(f x + e\right) - 2 \, {\left({\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) - 2 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 4 \, {\left(a b d^{2} + {\left(b^{2} d^{2} f x + b^{2} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 2 \, {\left({\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right) + 2 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(b^2*d^2*cosh(f*x + e)^2 + b^2*d^2*sinh(f*x + e)^2 + (2*a^2 - b^2)*d^2 + 4*(a*b*d^2*f*x + a*b*c*d*f)*cosh(f*x + e) - 2*((a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*Ei((d*f*x + c*f)/d) - (a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) - 2*((b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*Ei(2*(d*f*x + c*f)/d) + (b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*Ei(-2*(d*f*x + c*f)/d))*cosh(-2*(d*e - c*f)/d) + 4*(a*b*d^2 + (b^2*d^2*f*x + b^2*c*d*f)*cosh(f*x + e))*sinh(f*x + e) + 2*((a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*Ei((d*f*x + c*f)/d) + (a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d) + 2*((b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*Ei(2*(d*f*x + c*f)/d) - (b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*Ei(-2*(d*f*x + c*f)/d))*sinh(-2*(d*e - c*f)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
169,1,1004,0,0.736857," ","integrate((d*x+c)^3/(a+b*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{6 \, b d^{3} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, b d^{3} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 3 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\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)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\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)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\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)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\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)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left(b d^{3} f x + b c d^{2} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b d^{3} f x + b c d^{2} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right)}{{\left(a^{2} + b^{2}\right)} f^{4}}"," ",0,"(6*b*d^3*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))/b) - 6*b*d^3*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))/b) + 3*(b*d^3*f^2*x^2 + 2*b*c*d^2*f^2*x + b*c^2*d*f^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*(b*d^3*f^2*x^2 + 2*b*c*d^2*f^2*x + b*c^2*d*f^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (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)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (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)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (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)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b) - (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)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b) - 6*(b*d^3*f*x + b*c*d^2*f)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b*d^3*f*x + b*c*d^2*f)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))/b))/((a^2 + b^2)*f^4)","C",0
170,1,708,0,0.517483," ","integrate((d*x+c)^2/(a+b*sinh(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, b d^{2} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, b d^{2} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(b d^{2} f x + b c d f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b d^{2} f x + b c d f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\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)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\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)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right)}{{\left(a^{2} + b^{2}\right)} f^{3}}"," ",0,"-(2*b*d^2*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))/b) - 2*b*d^2*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))/b) - 2*(b*d^2*f*x + b*c*d*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b*d^2*f*x + b*c*d*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (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)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b) + (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)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b))/((a^2 + b^2)*f^3)","C",0
171,1,455,0,0.472354," ","integrate((d*x+c)/(a+b*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{b d \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - b d \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b d e - b c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b d e - b c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d f x + b d e\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b d f x + b d e\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right)}{{\left(a^{2} + b^{2}\right)} f^{2}}"," ",0,"(b*d*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - b*d*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (b*d*e - b*c*f)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b*d*e - b*c*f)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d*f*x + b*d*e)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b*d*f*x + b*d*e)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b))/((a^2 + b^2)*f^2)","B",0
172,0,0,0,0.512948," ","integrate(1/(d*x+c)/(a+b*sinh(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(b d x + b c\right)} \sinh\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (b*d*x + b*c)*sinh(f*x + e)), x)","F",0
173,0,0,0,0.753030," ","integrate(1/(d*x+c)^2/(a+b*sinh(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)} \sinh\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)*sinh(f*x + e)), x)","F",0
174,1,3957,0,0.785227," ","integrate((d*x+c)^2/(a+b*sinh(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d f^{2} x - {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d f^{2} x - {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a b^{2} d^{2} \cosh\left(f x + e\right)^{2} + a b^{2} d^{2} \sinh\left(f x + e\right)^{2} + 2 \, a^{2} b d^{2} \cosh\left(f x + e\right) - a b^{2} d^{2} + 2 \, {\left(a b^{2} d^{2} \cosh\left(f x + e\right) + a^{2} b d^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(a b^{2} d^{2} \cosh\left(f x + e\right)^{2} + a b^{2} d^{2} \sinh\left(f x + e\right)^{2} + 2 \, a^{2} b d^{2} \cosh\left(f x + e\right) - a b^{2} d^{2} + 2 \, {\left(a b^{2} d^{2} \cosh\left(f x + e\right) + a^{2} b d^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c d f^{2} x - 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(f x + e\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} \cosh\left(f x + e\right) - {\left(a^{2} b + b^{3}\right)} d^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right) + {\left(a^{3} + a b^{2}\right)} d^{2}\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d^{2} f x + a b^{2} c d f - {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \cosh\left(f x + e\right)^{2} - {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a^{2} b d^{2} f x + a^{2} b c d f\right)} \cosh\left(f x + e\right) - 2 \, {\left(a^{2} b d^{2} f x + a^{2} b c d f + {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} \cosh\left(f x + e\right) - {\left(a^{2} b + b^{3}\right)} d^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} \cosh\left(f x + e\right) + {\left(a^{3} + a b^{2}\right)} d^{2}\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d^{2} f x + a b^{2} c d f - {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \cosh\left(f x + e\right)^{2} - {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a^{2} b d^{2} f x + a^{2} b c d f\right)} \cosh\left(f x + e\right) - 2 \, {\left(a^{2} b d^{2} f x + a^{2} b c d f + {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e - 2 \, {\left(a^{2} b + b^{3}\right)} c d f - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e - {\left(a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e - {\left(a^{2} b + b^{3}\right)} c d f\right)} \sinh\left(f x + e\right)^{2} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e - {\left(a^{3} + a b^{2}\right)} c d f\right)} \cosh\left(f x + e\right) - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e - {\left(a^{3} + a b^{2}\right)} c d f + {\left({\left(a^{2} b + b^{3}\right)} d^{2} e - {\left(a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2} - {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(f x + e\right)^{2} - {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(f x + e\right) - 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e - 2 \, {\left(a^{2} b + b^{3}\right)} c d f - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e - {\left(a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e - {\left(a^{2} b + b^{3}\right)} c d f\right)} \sinh\left(f x + e\right)^{2} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e - {\left(a^{3} + a b^{2}\right)} c d f\right)} \cosh\left(f x + e\right) - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e - {\left(a^{3} + a b^{2}\right)} c d f + {\left({\left(a^{2} b + b^{3}\right)} d^{2} e - {\left(a^{2} b + b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2} - {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(f x + e\right)^{2} - {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(f x + e\right) - 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} f x + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f x + {\left(a^{2} b + b^{3}\right)} d^{2} e\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f x + {\left(a^{2} b + b^{3}\right)} d^{2} e\right)} \sinh\left(f x + e\right)^{2} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x + {\left(a^{3} + a b^{2}\right)} d^{2} e\right)} \cosh\left(f x + e\right) - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x + {\left(a^{3} + a b^{2}\right)} d^{2} e + {\left({\left(a^{2} b + b^{3}\right)} d^{2} f x + {\left(a^{2} b + b^{3}\right)} d^{2} e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f - {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \cosh\left(f x + e\right)^{2} - {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f\right)} \cosh\left(f x + e\right) - 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} f x + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f x + {\left(a^{2} b + b^{3}\right)} d^{2} e\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f x + {\left(a^{2} b + b^{3}\right)} d^{2} e\right)} \sinh\left(f x + e\right)^{2} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x + {\left(a^{3} + a b^{2}\right)} d^{2} e\right)} \cosh\left(f x + e\right) - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x + {\left(a^{3} + a b^{2}\right)} d^{2} e + {\left({\left(a^{2} b + b^{3}\right)} d^{2} f x + {\left(a^{2} b + b^{3}\right)} d^{2} e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f - {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \cosh\left(f x + e\right)^{2} - {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f\right)} \cosh\left(f x + e\right) - 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c d f^{2} x - 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d f^{2} x - {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} \cosh\left(f x + e\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{3} \cosh\left(f x + e\right) - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} \cosh\left(f x + e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{3}\right)} \sinh\left(f x + e\right)}"," ",0,"-(2*(a^2*b + b^3)*d^2*e^2 - 4*(a^2*b + b^3)*c*d*e*f + 2*(a^2*b + b^3)*c^2*f^2 + 2*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*f^2*x - (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*c*d*e*f)*cosh(f*x + e)^2 + 2*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*f^2*x - (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*c*d*e*f)*sinh(f*x + e)^2 + 2*(a*b^2*d^2*cosh(f*x + e)^2 + a*b^2*d^2*sinh(f*x + e)^2 + 2*a^2*b*d^2*cosh(f*x + e) - a*b^2*d^2 + 2*(a*b^2*d^2*cosh(f*x + e) + a^2*b*d^2)*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))/b) - 2*(a*b^2*d^2*cosh(f*x + e)^2 + a*b^2*d^2*sinh(f*x + e)^2 + 2*a^2*b*d^2*cosh(f*x + e) - a*b^2*d^2 + 2*(a*b^2*d^2*cosh(f*x + e) + a^2*b*d^2)*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))/b) + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*c*d*f^2*x - 2*(a^3 + a*b^2)*d^2*e^2 + 4*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(f*x + e) - 2*((a^2*b + b^3)*d^2*cosh(f*x + e)^2 + (a^2*b + b^3)*d^2*sinh(f*x + e)^2 + 2*(a^3 + a*b^2)*d^2*cosh(f*x + e) - (a^2*b + b^3)*d^2 + 2*((a^2*b + b^3)*d^2*cosh(f*x + e) + (a^3 + a*b^2)*d^2)*sinh(f*x + e) - (a*b^2*d^2*f*x + a*b^2*c*d*f - (a*b^2*d^2*f*x + a*b^2*c*d*f)*cosh(f*x + e)^2 - (a*b^2*d^2*f*x + a*b^2*c*d*f)*sinh(f*x + e)^2 - 2*(a^2*b*d^2*f*x + a^2*b*c*d*f)*cosh(f*x + e) - 2*(a^2*b*d^2*f*x + a^2*b*c*d*f + (a*b^2*d^2*f*x + a*b^2*c*d*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))*dilog((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*((a^2*b + b^3)*d^2*cosh(f*x + e)^2 + (a^2*b + b^3)*d^2*sinh(f*x + e)^2 + 2*(a^3 + a*b^2)*d^2*cosh(f*x + e) - (a^2*b + b^3)*d^2 + 2*((a^2*b + b^3)*d^2*cosh(f*x + e) + (a^3 + a*b^2)*d^2)*sinh(f*x + e) + (a*b^2*d^2*f*x + a*b^2*c*d*f - (a*b^2*d^2*f*x + a*b^2*c*d*f)*cosh(f*x + e)^2 - (a*b^2*d^2*f*x + a*b^2*c*d*f)*sinh(f*x + e)^2 - 2*(a^2*b*d^2*f*x + a^2*b*c*d*f)*cosh(f*x + e) - 2*(a^2*b*d^2*f*x + a^2*b*c*d*f + (a*b^2*d^2*f*x + a*b^2*c*d*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))*dilog((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (2*(a^2*b + b^3)*d^2*e - 2*(a^2*b + b^3)*c*d*f - 2*((a^2*b + b^3)*d^2*e - (a^2*b + b^3)*c*d*f)*cosh(f*x + e)^2 - 2*((a^2*b + b^3)*d^2*e - (a^2*b + b^3)*c*d*f)*sinh(f*x + e)^2 - 4*((a^3 + a*b^2)*d^2*e - (a^3 + a*b^2)*c*d*f)*cosh(f*x + e) - 4*((a^3 + a*b^2)*d^2*e - (a^3 + a*b^2)*c*d*f + ((a^2*b + b^3)*d^2*e - (a^2*b + b^3)*c*d*f)*cosh(f*x + e))*sinh(f*x + e) + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2 - (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(f*x + e)^2 - (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sinh(f*x + e)^2 - 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(f*x + e) - 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (2*(a^2*b + b^3)*d^2*e - 2*(a^2*b + b^3)*c*d*f - 2*((a^2*b + b^3)*d^2*e - (a^2*b + b^3)*c*d*f)*cosh(f*x + e)^2 - 2*((a^2*b + b^3)*d^2*e - (a^2*b + b^3)*c*d*f)*sinh(f*x + e)^2 - 4*((a^3 + a*b^2)*d^2*e - (a^3 + a*b^2)*c*d*f)*cosh(f*x + e) - 4*((a^3 + a*b^2)*d^2*e - (a^3 + a*b^2)*c*d*f + ((a^2*b + b^3)*d^2*e - (a^2*b + b^3)*c*d*f)*cosh(f*x + e))*sinh(f*x + e) - (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2 - (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(f*x + e)^2 - (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sinh(f*x + e)^2 - 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(f*x + e) - 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (2*(a^2*b + b^3)*d^2*f*x + 2*(a^2*b + b^3)*d^2*e - 2*((a^2*b + b^3)*d^2*f*x + (a^2*b + b^3)*d^2*e)*cosh(f*x + e)^2 - 2*((a^2*b + b^3)*d^2*f*x + (a^2*b + b^3)*d^2*e)*sinh(f*x + e)^2 - 4*((a^3 + a*b^2)*d^2*f*x + (a^3 + a*b^2)*d^2*e)*cosh(f*x + e) - 4*((a^3 + a*b^2)*d^2*f*x + (a^3 + a*b^2)*d^2*e + ((a^2*b + b^3)*d^2*f*x + (a^2*b + b^3)*d^2*e)*cosh(f*x + e))*sinh(f*x + e) + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f - (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*cosh(f*x + e)^2 - (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*sinh(f*x + e)^2 - 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f)*cosh(f*x + e) - 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))*log(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b) + (2*(a^2*b + b^3)*d^2*f*x + 2*(a^2*b + b^3)*d^2*e - 2*((a^2*b + b^3)*d^2*f*x + (a^2*b + b^3)*d^2*e)*cosh(f*x + e)^2 - 2*((a^2*b + b^3)*d^2*f*x + (a^2*b + b^3)*d^2*e)*sinh(f*x + e)^2 - 4*((a^3 + a*b^2)*d^2*f*x + (a^3 + a*b^2)*d^2*e)*cosh(f*x + e) - 4*((a^3 + a*b^2)*d^2*f*x + (a^3 + a*b^2)*d^2*e + ((a^2*b + b^3)*d^2*f*x + (a^2*b + b^3)*d^2*e)*cosh(f*x + e))*sinh(f*x + e) - (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f - (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*cosh(f*x + e)^2 - (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*sinh(f*x + e)^2 - 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f)*cosh(f*x + e) - 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))*log(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*c*d*f^2*x - 2*(a^3 + a*b^2)*d^2*e^2 + 4*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2 + 2*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*f^2*x - (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*c*d*e*f)*cosh(f*x + e))*sinh(f*x + e))/((a^4*b + 2*a^2*b^3 + b^5)*f^3*cosh(f*x + e)^2 + (a^4*b + 2*a^2*b^3 + b^5)*f^3*sinh(f*x + e)^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*f^3*cosh(f*x + e) - (a^4*b + 2*a^2*b^3 + b^5)*f^3 + 2*((a^4*b + 2*a^2*b^3 + b^5)*f^3*cosh(f*x + e) + (a^5 + 2*a^3*b^2 + a*b^4)*f^3)*sinh(f*x + e))","C",0
175,1,1717,0,0.504593," ","integrate((d*x+c)/(a+b*sinh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} b + b^{3}\right)} d e - 2 \, {\left(a^{2} b + b^{3}\right)} c f - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e\right)} \sinh\left(f x + e\right)^{2} + {\left(a b^{2} d \cosh\left(f x + e\right)^{2} + a b^{2} d \sinh\left(f x + e\right)^{2} + 2 \, a^{2} b d \cosh\left(f x + e\right) - a b^{2} d + 2 \, {\left(a b^{2} d \cosh\left(f x + e\right) + a^{2} b d\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a b^{2} d \cosh\left(f x + e\right)^{2} + a b^{2} d \sinh\left(f x + e\right)^{2} + 2 \, a^{2} b d \cosh\left(f x + e\right) - a b^{2} d + 2 \, {\left(a b^{2} d \cosh\left(f x + e\right) + a^{2} b d\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a b^{2} d f x + a b^{2} d e - {\left(a b^{2} d f x + a b^{2} d e\right)} \cosh\left(f x + e\right)^{2} - {\left(a b^{2} d f x + a b^{2} d e\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a^{2} b d f x + a^{2} b d e\right)} \cosh\left(f x + e\right) - 2 \, {\left(a^{2} b d f x + a^{2} b d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(a b^{2} d f x + a b^{2} d e - {\left(a b^{2} d f x + a b^{2} d e\right)} \cosh\left(f x + e\right)^{2} - {\left(a b^{2} d f x + a b^{2} d e\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a^{2} b d f x + a^{2} b d e\right)} \cosh\left(f x + e\right) - 2 \, {\left(a^{2} b d f x + a^{2} b d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + 2 \, {\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(f x + e\right) + {\left({\left(a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)^{2} + {\left(a^{2} b + b^{3}\right)} d \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d \cosh\left(f x + e\right) - {\left(a^{2} b + b^{3}\right)} d + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right) + {\left(a^{3} + a b^{2}\right)} d\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d e - a b^{2} c f - {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(f x + e\right)^{2} - {\left(a b^{2} d e - a b^{2} c f\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(f x + e\right) - 2 \, {\left(a^{2} b d e - a^{2} b c f + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left({\left(a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right)^{2} + {\left(a^{2} b + b^{3}\right)} d \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d \cosh\left(f x + e\right) - {\left(a^{2} b + b^{3}\right)} d + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d \cosh\left(f x + e\right) + {\left(a^{3} + a b^{2}\right)} d\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d e - a b^{2} c f - {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(f x + e\right)^{2} - {\left(a b^{2} d e - a b^{2} c f\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(f x + e\right) - 2 \, {\left(a^{2} b d e - a^{2} b c f + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + 2 \, {\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} c f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(f x + e\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} \cosh\left(f x + e\right) - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(f x + e\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \sinh\left(f x + e\right)}"," ",0,"(2*(a^2*b + b^3)*d*e - 2*(a^2*b + b^3)*c*f - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e)*cosh(f*x + e)^2 - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e)*sinh(f*x + e)^2 + (a*b^2*d*cosh(f*x + e)^2 + a*b^2*d*sinh(f*x + e)^2 + 2*a^2*b*d*cosh(f*x + e) - a*b^2*d + 2*(a*b^2*d*cosh(f*x + e) + a^2*b*d)*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (a*b^2*d*cosh(f*x + e)^2 + a*b^2*d*sinh(f*x + e)^2 + 2*a^2*b*d*cosh(f*x + e) - a*b^2*d + 2*(a*b^2*d*cosh(f*x + e) + a^2*b*d)*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (a*b^2*d*f*x + a*b^2*d*e - (a*b^2*d*f*x + a*b^2*d*e)*cosh(f*x + e)^2 - (a*b^2*d*f*x + a*b^2*d*e)*sinh(f*x + e)^2 - 2*(a^2*b*d*f*x + a^2*b*d*e)*cosh(f*x + e) - 2*(a^2*b*d*f*x + a^2*b*d*e + (a*b^2*d*f*x + a*b^2*d*e)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b) + (a*b^2*d*f*x + a*b^2*d*e - (a*b^2*d*f*x + a*b^2*d*e)*cosh(f*x + e)^2 - (a*b^2*d*f*x + a*b^2*d*e)*sinh(f*x + e)^2 - 2*(a^2*b*d*f*x + a^2*b*d*e)*cosh(f*x + e) - 2*(a^2*b*d*f*x + a^2*b*d*e + (a*b^2*d*f*x + a*b^2*d*e)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((a^3 + a*b^2)*d*f*x + 2*(a^3 + a*b^2)*d*e - (a^3 + a*b^2)*c*f)*cosh(f*x + e) + ((a^2*b + b^3)*d*cosh(f*x + e)^2 + (a^2*b + b^3)*d*sinh(f*x + e)^2 + 2*(a^3 + a*b^2)*d*cosh(f*x + e) - (a^2*b + b^3)*d + 2*((a^2*b + b^3)*d*cosh(f*x + e) + (a^3 + a*b^2)*d)*sinh(f*x + e) - (a*b^2*d*e - a*b^2*c*f - (a*b^2*d*e - a*b^2*c*f)*cosh(f*x + e)^2 - (a*b^2*d*e - a*b^2*c*f)*sinh(f*x + e)^2 - 2*(a^2*b*d*e - a^2*b*c*f)*cosh(f*x + e) - 2*(a^2*b*d*e - a^2*b*c*f + (a*b^2*d*e - a*b^2*c*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + ((a^2*b + b^3)*d*cosh(f*x + e)^2 + (a^2*b + b^3)*d*sinh(f*x + e)^2 + 2*(a^3 + a*b^2)*d*cosh(f*x + e) - (a^2*b + b^3)*d + 2*((a^2*b + b^3)*d*cosh(f*x + e) + (a^3 + a*b^2)*d)*sinh(f*x + e) + (a*b^2*d*e - a*b^2*c*f - (a*b^2*d*e - a*b^2*c*f)*cosh(f*x + e)^2 - (a*b^2*d*e - a*b^2*c*f)*sinh(f*x + e)^2 - 2*(a^2*b*d*e - a^2*b*c*f)*cosh(f*x + e) - 2*(a^2*b*d*e - a^2*b*c*f + (a*b^2*d*e - a*b^2*c*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*((a^3 + a*b^2)*d*f*x + 2*(a^3 + a*b^2)*d*e - (a^3 + a*b^2)*c*f + 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e)*cosh(f*x + e))*sinh(f*x + e))/((a^4*b + 2*a^2*b^3 + b^5)*f^2*cosh(f*x + e)^2 + (a^4*b + 2*a^2*b^3 + b^5)*f^2*sinh(f*x + e)^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*f^2*cosh(f*x + e) - (a^4*b + 2*a^2*b^3 + b^5)*f^2 + 2*((a^4*b + 2*a^2*b^3 + b^5)*f^2*cosh(f*x + e) + (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*sinh(f*x + e))","B",0
176,0,0,0,0.525871," ","integrate(1/(d*x+c)/(a+b*sinh(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)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a b d x + a b c\right)} \sinh\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d*x + a^2*c + (b^2*d*x + b^2*c)*sinh(f*x + e)^2 + 2*(a*b*d*x + a*b*c)*sinh(f*x + e)), x)","F",0
177,0,0,0,0.489693," ","integrate(1/(d*x+c)^2/(a+b*sinh(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)} \sinh\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)} \sinh\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)*sinh(f*x + e)^2 + 2*(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*sinh(f*x + e)), x)","F",0
178,1,6396,0,0.674517," ","integrate((f*x+e)/(a+b*sinh(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{3} b^{2} + a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{3} b^{2} + a b^{4}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left({\left(10 \, a^{4} b + 11 \, a^{2} b^{3} + b^{5}\right)} d f x - {\left(2 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} d e + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} + 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(10 \, a^{4} b + 11 \, a^{2} b^{3} + b^{5}\right)} d f x - {\left(2 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} d e + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} + 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} c\right)} f + 12 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{3} b^{2} + a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} d e + 6 \, {\left(a^{3} b^{2} + a b^{4}\right)} c f + 2 \, {\left(3 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} d f x - 3 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} d e + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + 3 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} d f x - 3 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} d e + 18 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{3} b^{2} + a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + 3 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} c\right)} f + 3 \, {\left({\left(10 \, a^{4} b + 11 \, a^{2} b^{3} + b^{5}\right)} d f x - {\left(2 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} d e + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} + 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} c\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} f \cosh\left(d x + c\right)^{4} + {\left(2 \, a^{2} b^{3} - b^{5}\right)} f \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} f \cosh\left(d x + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(2 \, a^{2} b^{3} - b^{5}\right)} f \cosh\left(d x + c\right)^{2} + 6 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right) + {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(2 \, a^{2} b^{3} - b^{5}\right)} f + 4 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} f \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right) - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} f \cosh\left(d x + c\right)^{4} + {\left(2 \, a^{2} b^{3} - b^{5}\right)} f \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} f \cosh\left(d x + c\right) + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(2 \, a^{2} b^{3} - b^{5}\right)} f \cosh\left(d x + c\right)^{2} + 6 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right) + {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(2 \, a^{2} b^{3} - b^{5}\right)} f + 4 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} f \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right) - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left({\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f + {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f + 2 \, {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f + 3 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right) - 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x - {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f - 3 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f + {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f + 2 \, {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f + 3 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right) - 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x - {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f - 3 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d f x + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} d f x - {\left(10 \, a^{4} b + 11 \, a^{2} b^{3} + b^{5}\right)} d e + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} + 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} c\right)} f\right)} \cosh\left(d x + c\right) - {\left(3 \, {\left(a^{3} b^{2} + a b^{4}\right)} f \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} f \sinh\left(d x + c\right)^{4} + 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right)^{3} + 6 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 12 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} f \cosh\left(d x + c\right) + {\left(a^{4} b + a^{2} b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{3} - 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right) + 6 \, {\left(3 \, {\left(a^{3} b^{2} + a b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right) + {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} f + 12 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} f \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right) - {\left(a^{4} b + a^{2} b^{3}\right)} f\right)} \sinh\left(d x + c\right) - {\left({\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f + {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f + 2 \, {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f + 3 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f + 3 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(3 \, {\left(a^{3} b^{2} + a b^{4}\right)} f \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} f \sinh\left(d x + c\right)^{4} + 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right)^{3} + 6 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 12 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} f \cosh\left(d x + c\right) + {\left(a^{4} b + a^{2} b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{3} - 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right) + 6 \, {\left(3 \, {\left(a^{3} b^{2} + a b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right) + {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(a^{3} b^{2} + a b^{4}\right)} f + 12 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} f \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} f \cosh\left(d x + c\right) - {\left(a^{4} b + a^{2} b^{3}\right)} f\right)} \sinh\left(d x + c\right) + {\left({\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f + {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f + 2 \, {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f + 3 \, {\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left({\left(2 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(2 \, a^{2} b^{3} - b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e + {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f + 3 \, {\left({\left(2 \, a^{3} b^{2} - a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{4} b - 4 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left({\left(2 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} d f x - 12 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{3} b^{2} + a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(10 \, a^{4} b + 11 \, a^{2} b^{3} + b^{5}\right)} d e - 3 \, {\left({\left(10 \, a^{4} b + 11 \, a^{2} b^{3} + b^{5}\right)} d f x - {\left(2 \, a^{4} b + a^{2} b^{3} - b^{5}\right)} d e + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} + 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} + 12 \, {\left(a^{4} b + a^{2} b^{3}\right)} c\right)} f - 2 \, {\left(3 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} d f x - 3 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} d e + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + 3 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{2} \cosh\left(d x + c\right)^{4} + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{2} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{8} + 5 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} d^{2} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d^{2} \cosh\left(d x + c\right) + 4 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{2} \cosh\left(d x + c\right) + {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{2} + 2 \, {\left(3 \, {\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{8} + 5 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{6} b^{2} + 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} + b^{8}\right)} d^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{8} + 5 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6} - b^{8}\right)} d^{2} \cosh\left(d x + c\right) - {\left(a^{7} b + 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + a b^{7}\right)} d^{2}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(6*((a^3*b^2 + a*b^4)*d*f*x + (a^3*b^2 + a*b^4)*c*f)*cosh(d*x + c)^4 + 6*((a^3*b^2 + a*b^4)*d*f*x + (a^3*b^2 + a*b^4)*c*f)*sinh(d*x + c)^4 + 2*((10*a^4*b + 11*a^2*b^3 + b^5)*d*f*x - (2*a^4*b + a^2*b^3 - b^5)*d*e + (a^4*b + 2*a^2*b^3 + b^5 + 12*(a^4*b + a^2*b^3)*c)*f)*cosh(d*x + c)^3 + 2*((10*a^4*b + 11*a^2*b^3 + b^5)*d*f*x - (2*a^4*b + a^2*b^3 - b^5)*d*e + (a^4*b + 2*a^2*b^3 + b^5 + 12*(a^4*b + a^2*b^3)*c)*f + 12*((a^3*b^2 + a*b^4)*d*f*x + (a^3*b^2 + a*b^4)*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(a^3*b^2 + a*b^4)*d*e + 6*(a^3*b^2 + a*b^4)*c*f + 2*(3*(2*a^5 + a^3*b^2 - a*b^4)*d*f*x - 3*(2*a^5 + a^3*b^2 - a*b^4)*d*e + 2*(a^5 + 2*a^3*b^2 + a*b^4 + 3*(2*a^5 + a^3*b^2 - a*b^4)*c)*f)*cosh(d*x + c)^2 + 2*(3*(2*a^5 + a^3*b^2 - a*b^4)*d*f*x - 3*(2*a^5 + a^3*b^2 - a*b^4)*d*e + 18*((a^3*b^2 + a*b^4)*d*f*x + (a^3*b^2 + a*b^4)*c*f)*cosh(d*x + c)^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4 + 3*(2*a^5 + a^3*b^2 - a*b^4)*c)*f + 3*((10*a^4*b + 11*a^2*b^3 + b^5)*d*f*x - (2*a^4*b + a^2*b^3 - b^5)*d*e + (a^4*b + 2*a^2*b^3 + b^5 + 12*(a^4*b + a^2*b^3)*c)*f)*cosh(d*x + c))*sinh(d*x + c)^2 - ((2*a^2*b^3 - b^5)*f*cosh(d*x + c)^4 + (2*a^2*b^3 - b^5)*f*sinh(d*x + c)^4 + 4*(2*a^3*b^2 - a*b^4)*f*cosh(d*x + c)^3 + 2*(4*a^4*b - 4*a^2*b^3 + b^5)*f*cosh(d*x + c)^2 + 4*((2*a^2*b^3 - b^5)*f*cosh(d*x + c) + (2*a^3*b^2 - a*b^4)*f)*sinh(d*x + c)^3 - 4*(2*a^3*b^2 - a*b^4)*f*cosh(d*x + c) + 2*(3*(2*a^2*b^3 - b^5)*f*cosh(d*x + c)^2 + 6*(2*a^3*b^2 - a*b^4)*f*cosh(d*x + c) + (4*a^4*b - 4*a^2*b^3 + b^5)*f)*sinh(d*x + c)^2 + (2*a^2*b^3 - b^5)*f + 4*((2*a^2*b^3 - b^5)*f*cosh(d*x + c)^3 + 3*(2*a^3*b^2 - a*b^4)*f*cosh(d*x + c)^2 + (4*a^4*b - 4*a^2*b^3 + b^5)*f*cosh(d*x + c) - (2*a^3*b^2 - a*b^4)*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + ((2*a^2*b^3 - b^5)*f*cosh(d*x + c)^4 + (2*a^2*b^3 - b^5)*f*sinh(d*x + c)^4 + 4*(2*a^3*b^2 - a*b^4)*f*cosh(d*x + c)^3 + 2*(4*a^4*b - 4*a^2*b^3 + b^5)*f*cosh(d*x + c)^2 + 4*((2*a^2*b^3 - b^5)*f*cosh(d*x + c) + (2*a^3*b^2 - a*b^4)*f)*sinh(d*x + c)^3 - 4*(2*a^3*b^2 - a*b^4)*f*cosh(d*x + c) + 2*(3*(2*a^2*b^3 - b^5)*f*cosh(d*x + c)^2 + 6*(2*a^3*b^2 - a*b^4)*f*cosh(d*x + c) + (4*a^4*b - 4*a^2*b^3 + b^5)*f)*sinh(d*x + c)^2 + (2*a^2*b^3 - b^5)*f + 4*((2*a^2*b^3 - b^5)*f*cosh(d*x + c)^3 + 3*(2*a^3*b^2 - a*b^4)*f*cosh(d*x + c)^2 + (4*a^4*b - 4*a^2*b^3 + b^5)*f*cosh(d*x + c) - (2*a^3*b^2 - a*b^4)*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (((2*a^2*b^3 - b^5)*d*f*x + (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^4 + ((2*a^2*b^3 - b^5)*d*f*x + (2*a^2*b^3 - b^5)*c*f)*sinh(d*x + c)^4 + (2*a^2*b^3 - b^5)*d*f*x + 4*((2*a^3*b^2 - a*b^4)*d*f*x + (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c)^3 + 4*((2*a^3*b^2 - a*b^4)*d*f*x + (2*a^3*b^2 - a*b^4)*c*f + ((2*a^2*b^3 - b^5)*d*f*x + (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 + (2*a^2*b^3 - b^5)*c*f + 2*((4*a^4*b - 4*a^2*b^3 + b^5)*d*f*x + (4*a^4*b - 4*a^2*b^3 + b^5)*c*f)*cosh(d*x + c)^2 + 2*((4*a^4*b - 4*a^2*b^3 + b^5)*d*f*x + (4*a^4*b - 4*a^2*b^3 + b^5)*c*f + 3*((2*a^2*b^3 - b^5)*d*f*x + (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^2 + 6*((2*a^3*b^2 - a*b^4)*d*f*x + (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*((2*a^3*b^2 - a*b^4)*d*f*x + (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c) - 4*((2*a^3*b^2 - a*b^4)*d*f*x - ((2*a^2*b^3 - b^5)*d*f*x + (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^3 + (2*a^3*b^2 - a*b^4)*c*f - 3*((2*a^3*b^2 - a*b^4)*d*f*x + (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c)^2 - ((4*a^4*b - 4*a^2*b^3 + b^5)*d*f*x + (4*a^4*b - 4*a^2*b^3 + b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (((2*a^2*b^3 - b^5)*d*f*x + (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^4 + ((2*a^2*b^3 - b^5)*d*f*x + (2*a^2*b^3 - b^5)*c*f)*sinh(d*x + c)^4 + (2*a^2*b^3 - b^5)*d*f*x + 4*((2*a^3*b^2 - a*b^4)*d*f*x + (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c)^3 + 4*((2*a^3*b^2 - a*b^4)*d*f*x + (2*a^3*b^2 - a*b^4)*c*f + ((2*a^2*b^3 - b^5)*d*f*x + (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 + (2*a^2*b^3 - b^5)*c*f + 2*((4*a^4*b - 4*a^2*b^3 + b^5)*d*f*x + (4*a^4*b - 4*a^2*b^3 + b^5)*c*f)*cosh(d*x + c)^2 + 2*((4*a^4*b - 4*a^2*b^3 + b^5)*d*f*x + (4*a^4*b - 4*a^2*b^3 + b^5)*c*f + 3*((2*a^2*b^3 - b^5)*d*f*x + (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^2 + 6*((2*a^3*b^2 - a*b^4)*d*f*x + (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*((2*a^3*b^2 - a*b^4)*d*f*x + (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c) - 4*((2*a^3*b^2 - a*b^4)*d*f*x - ((2*a^2*b^3 - b^5)*d*f*x + (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^3 + (2*a^3*b^2 - a*b^4)*c*f - 3*((2*a^3*b^2 - a*b^4)*d*f*x + (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c)^2 - ((4*a^4*b - 4*a^2*b^3 + b^5)*d*f*x + (4*a^4*b - 4*a^2*b^3 + b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((2*a^4*b + a^2*b^3 - b^5)*d*f*x - (10*a^4*b + 11*a^2*b^3 + b^5)*d*e + (a^4*b + 2*a^2*b^3 + b^5 + 12*(a^4*b + a^2*b^3)*c)*f)*cosh(d*x + c) - (3*(a^3*b^2 + a*b^4)*f*cosh(d*x + c)^4 + 3*(a^3*b^2 + a*b^4)*f*sinh(d*x + c)^4 + 12*(a^4*b + a^2*b^3)*f*cosh(d*x + c)^3 + 6*(2*a^5 + a^3*b^2 - a*b^4)*f*cosh(d*x + c)^2 + 12*((a^3*b^2 + a*b^4)*f*cosh(d*x + c) + (a^4*b + a^2*b^3)*f)*sinh(d*x + c)^3 - 12*(a^4*b + a^2*b^3)*f*cosh(d*x + c) + 6*(3*(a^3*b^2 + a*b^4)*f*cosh(d*x + c)^2 + 6*(a^4*b + a^2*b^3)*f*cosh(d*x + c) + (2*a^5 + a^3*b^2 - a*b^4)*f)*sinh(d*x + c)^2 + 3*(a^3*b^2 + a*b^4)*f + 12*((a^3*b^2 + a*b^4)*f*cosh(d*x + c)^3 + 3*(a^4*b + a^2*b^3)*f*cosh(d*x + c)^2 + (2*a^5 + a^3*b^2 - a*b^4)*f*cosh(d*x + c) - (a^4*b + a^2*b^3)*f)*sinh(d*x + c) - (((2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^4 + ((2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f)*sinh(d*x + c)^4 + 4*((2*a^3*b^2 - a*b^4)*d*e - (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c)^3 + 4*((2*a^3*b^2 - a*b^4)*d*e - (2*a^3*b^2 - a*b^4)*c*f + ((2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 + (2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f + 2*((4*a^4*b - 4*a^2*b^3 + b^5)*d*e - (4*a^4*b - 4*a^2*b^3 + b^5)*c*f)*cosh(d*x + c)^2 + 2*((4*a^4*b - 4*a^2*b^3 + b^5)*d*e - (4*a^4*b - 4*a^2*b^3 + b^5)*c*f + 3*((2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^2 + 6*((2*a^3*b^2 - a*b^4)*d*e - (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*((2*a^3*b^2 - a*b^4)*d*e - (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c) + 4*(((2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^3 - (2*a^3*b^2 - a*b^4)*d*e + (2*a^3*b^2 - a*b^4)*c*f + 3*((2*a^3*b^2 - a*b^4)*d*e - (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c)^2 + ((4*a^4*b - 4*a^2*b^3 + b^5)*d*e - (4*a^4*b - 4*a^2*b^3 + b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (3*(a^3*b^2 + a*b^4)*f*cosh(d*x + c)^4 + 3*(a^3*b^2 + a*b^4)*f*sinh(d*x + c)^4 + 12*(a^4*b + a^2*b^3)*f*cosh(d*x + c)^3 + 6*(2*a^5 + a^3*b^2 - a*b^4)*f*cosh(d*x + c)^2 + 12*((a^3*b^2 + a*b^4)*f*cosh(d*x + c) + (a^4*b + a^2*b^3)*f)*sinh(d*x + c)^3 - 12*(a^4*b + a^2*b^3)*f*cosh(d*x + c) + 6*(3*(a^3*b^2 + a*b^4)*f*cosh(d*x + c)^2 + 6*(a^4*b + a^2*b^3)*f*cosh(d*x + c) + (2*a^5 + a^3*b^2 - a*b^4)*f)*sinh(d*x + c)^2 + 3*(a^3*b^2 + a*b^4)*f + 12*((a^3*b^2 + a*b^4)*f*cosh(d*x + c)^3 + 3*(a^4*b + a^2*b^3)*f*cosh(d*x + c)^2 + (2*a^5 + a^3*b^2 - a*b^4)*f*cosh(d*x + c) - (a^4*b + a^2*b^3)*f)*sinh(d*x + c) + (((2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^4 + ((2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f)*sinh(d*x + c)^4 + 4*((2*a^3*b^2 - a*b^4)*d*e - (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c)^3 + 4*((2*a^3*b^2 - a*b^4)*d*e - (2*a^3*b^2 - a*b^4)*c*f + ((2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 + (2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f + 2*((4*a^4*b - 4*a^2*b^3 + b^5)*d*e - (4*a^4*b - 4*a^2*b^3 + b^5)*c*f)*cosh(d*x + c)^2 + 2*((4*a^4*b - 4*a^2*b^3 + b^5)*d*e - (4*a^4*b - 4*a^2*b^3 + b^5)*c*f + 3*((2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^2 + 6*((2*a^3*b^2 - a*b^4)*d*e - (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*((2*a^3*b^2 - a*b^4)*d*e - (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c) + 4*(((2*a^2*b^3 - b^5)*d*e - (2*a^2*b^3 - b^5)*c*f)*cosh(d*x + c)^3 - (2*a^3*b^2 - a*b^4)*d*e + (2*a^3*b^2 - a*b^4)*c*f + 3*((2*a^3*b^2 - a*b^4)*d*e - (2*a^3*b^2 - a*b^4)*c*f)*cosh(d*x + c)^2 + ((4*a^4*b - 4*a^2*b^3 + b^5)*d*e - (4*a^4*b - 4*a^2*b^3 + b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*((2*a^4*b + a^2*b^3 - b^5)*d*f*x - 12*((a^3*b^2 + a*b^4)*d*f*x + (a^3*b^2 + a*b^4)*c*f)*cosh(d*x + c)^3 - (10*a^4*b + 11*a^2*b^3 + b^5)*d*e - 3*((10*a^4*b + 11*a^2*b^3 + b^5)*d*f*x - (2*a^4*b + a^2*b^3 - b^5)*d*e + (a^4*b + 2*a^2*b^3 + b^5 + 12*(a^4*b + a^2*b^3)*c)*f)*cosh(d*x + c)^2 + (a^4*b + 2*a^2*b^3 + b^5 + 12*(a^4*b + a^2*b^3)*c)*f - 2*(3*(2*a^5 + a^3*b^2 - a*b^4)*d*f*x - 3*(2*a^5 + a^3*b^2 - a*b^4)*d*e + 2*(a^5 + 2*a^3*b^2 + a*b^4 + 3*(2*a^5 + a^3*b^2 - a*b^4)*c)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^2*cosh(d*x + c)^4 + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^2*sinh(d*x + c)^4 + 4*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d^2*cosh(d*x + c)^3 + 2*(2*a^8 + 5*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - b^8)*d^2*cosh(d*x + c)^2 - 4*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d^2*cosh(d*x + c) + 4*((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^2*cosh(d*x + c) + (a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d^2)*sinh(d*x + c)^3 + (a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^2 + 2*(3*(a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^2*cosh(d*x + c)^2 + 6*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d^2*cosh(d*x + c) + (2*a^8 + 5*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - b^8)*d^2)*sinh(d*x + c)^2 + 4*((a^6*b^2 + 3*a^4*b^4 + 3*a^2*b^6 + b^8)*d^2*cosh(d*x + c)^3 + 3*(a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d^2*cosh(d*x + c)^2 + (2*a^8 + 5*a^6*b^2 + 3*a^4*b^4 - a^2*b^6 - b^8)*d^2*cosh(d*x + c) - (a^7*b + 3*a^5*b^3 + 3*a^3*b^5 + a*b^7)*d^2)*sinh(d*x + c))","B",0
179,0,0,0,0.948696," ","integrate(1/(f*x+e)/(a+b*sinh(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{3} f x + a^{3} e + {\left(b^{3} f x + b^{3} e\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} f x + a b^{2} e\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(a^{2} b f x + a^{2} b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(1/(a^3*f*x + a^3*e + (b^3*f*x + b^3*e)*sinh(d*x + c)^3 + 3*(a*b^2*f*x + a*b^2*e)*sinh(d*x + c)^2 + 3*(a^2*b*f*x + a^2*b*e)*sinh(d*x + c)), x)","F",0
180,0,0,0,0.501487," ","integrate(1/(f*x+e)^2/(a+b*sinh(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{3} f^{2} x^{2} + 2 \, a^{3} e f x + a^{3} e^{2} + {\left(b^{3} f^{2} x^{2} + 2 \, b^{3} e f x + b^{3} e^{2}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a b^{2} f^{2} x^{2} + 2 \, a b^{2} e f x + a b^{2} e^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(a^{2} b f^{2} x^{2} + 2 \, a^{2} b e f x + a^{2} b e^{2}\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(1/(a^3*f^2*x^2 + 2*a^3*e*f*x + a^3*e^2 + (b^3*f^2*x^2 + 2*b^3*e*f*x + b^3*e^2)*sinh(d*x + c)^3 + 3*(a*b^2*f^2*x^2 + 2*a*b^2*e*f*x + a*b^2*e^2)*sinh(d*x + c)^2 + 3*(a^2*b*f^2*x^2 + 2*a^2*b*e*f*x + a^2*b*e^2)*sinh(d*x + c)), x)","F",0
181,0,0,0,0.475411," ","integrate((d*x+c)^m*(a+b*sinh(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} {\left(b \sinh\left(f x + e\right) + a\right)}^{n}, x\right)"," ",0,"integral((d*x + c)^m*(b*sinh(f*x + e) + a)^n, x)","F",0
182,1,829,0,0.905547," ","integrate((d*x+c)^m*(a+b*sinh(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(b^{3} d m + b^{3} d\right)} \cosh\left(\frac{d m \log\left(\frac{3 \, f}{d}\right) + 3 \, d e - 3 \, c f}{d}\right) \Gamma\left(m + 1, \frac{3 \, {\left(d f x + c f\right)}}{d}\right) - 9 \, {\left(a b^{2} d m + a b^{2} 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) + 9 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d m + {\left(4 \, a^{2} b - b^{3}\right)} d\right)} \cosh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) + 9 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d m + {\left(4 \, a^{2} b - b^{3}\right)} d\right)} \cosh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) + 9 \, {\left(a b^{2} d m + a b^{2} 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(b^{3} d m + b^{3} d\right)} \cosh\left(\frac{d m \log\left(-\frac{3 \, f}{d}\right) - 3 \, d e + 3 \, c f}{d}\right) \Gamma\left(m + 1, -\frac{3 \, {\left(d f x + c f\right)}}{d}\right) - {\left(b^{3} d m + b^{3} d\right)} \Gamma\left(m + 1, \frac{3 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{3 \, f}{d}\right) + 3 \, d e - 3 \, c f}{d}\right) + 9 \, {\left(a b^{2} d m + a b^{2} 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) - 9 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d m + {\left(4 \, a^{2} b - b^{3}\right)} d\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) - 9 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d m + {\left(4 \, a^{2} b - b^{3}\right)} d\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) - 9 \, {\left(a b^{2} d m + a b^{2} 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) - {\left(b^{3} d m + b^{3} d\right)} \Gamma\left(m + 1, -\frac{3 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{3 \, f}{d}\right) - 3 \, d e + 3 \, c f}{d}\right) + 12 \, {\left({\left(2 \, a^{3} - 3 \, a b^{2}\right)} d f x + {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c f\right)} \cosh\left(m \log\left(d x + c\right)\right) + 12 \, {\left({\left(2 \, a^{3} - 3 \, a b^{2}\right)} d f x + {\left(2 \, a^{3} - 3 \, a b^{2}\right)} c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{24 \, {\left(d f m + d f\right)}}"," ",0,"1/24*((b^3*d*m + b^3*d)*cosh((d*m*log(3*f/d) + 3*d*e - 3*c*f)/d)*gamma(m + 1, 3*(d*f*x + c*f)/d) - 9*(a*b^2*d*m + a*b^2*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) + 9*((4*a^2*b - b^3)*d*m + (4*a^2*b - b^3)*d)*cosh((d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) + 9*((4*a^2*b - b^3)*d*m + (4*a^2*b - b^3)*d)*cosh((d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) + 9*(a*b^2*d*m + a*b^2*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) + (b^3*d*m + b^3*d)*cosh((d*m*log(-3*f/d) - 3*d*e + 3*c*f)/d)*gamma(m + 1, -3*(d*f*x + c*f)/d) - (b^3*d*m + b^3*d)*gamma(m + 1, 3*(d*f*x + c*f)/d)*sinh((d*m*log(3*f/d) + 3*d*e - 3*c*f)/d) + 9*(a*b^2*d*m + a*b^2*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) - 9*((4*a^2*b - b^3)*d*m + (4*a^2*b - b^3)*d)*gamma(m + 1, (d*f*x + c*f)/d)*sinh((d*m*log(f/d) + d*e - c*f)/d) - 9*((4*a^2*b - b^3)*d*m + (4*a^2*b - b^3)*d)*gamma(m + 1, -(d*f*x + c*f)/d)*sinh((d*m*log(-f/d) - d*e + c*f)/d) - 9*(a*b^2*d*m + a*b^2*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) - (b^3*d*m + b^3*d)*gamma(m + 1, -3*(d*f*x + c*f)/d)*sinh((d*m*log(-3*f/d) - 3*d*e + 3*c*f)/d) + 12*((2*a^3 - 3*a*b^2)*d*f*x + (2*a^3 - 3*a*b^2)*c*f)*cosh(m*log(d*x + c)) + 12*((2*a^3 - 3*a*b^2)*d*f*x + (2*a^3 - 3*a*b^2)*c*f)*sinh(m*log(d*x + c)))/(d*f*m + d*f)","A",0
183,1,517,0,0.795424," ","integrate((d*x+c)^m*(a+b*sinh(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(b^{2} d m + b^{2} 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) - 8 \, {\left(a b d m + a b d\right)} \cosh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) - 8 \, {\left(a b d m + a b d\right)} \cosh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) - {\left(b^{2} d m + b^{2} 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(b^{2} d m + b^{2} 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) + 8 \, {\left(a b d m + a b d\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) + 8 \, {\left(a b d m + a b d\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) + {\left(b^{2} d m + b^{2} 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({\left(2 \, a^{2} - b^{2}\right)} d f x + {\left(2 \, a^{2} - b^{2}\right)} c f\right)} \cosh\left(m \log\left(d x + c\right)\right) - 4 \, {\left({\left(2 \, a^{2} - b^{2}\right)} d f x + {\left(2 \, a^{2} - b^{2}\right)} c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{8 \, {\left(d f m + d f\right)}}"," ",0,"-1/8*((b^2*d*m + b^2*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) - 8*(a*b*d*m + a*b*d)*cosh((d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) - 8*(a*b*d*m + a*b*d)*cosh((d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) - (b^2*d*m + b^2*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) - (b^2*d*m + b^2*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) + 8*(a*b*d*m + a*b*d)*gamma(m + 1, (d*f*x + c*f)/d)*sinh((d*m*log(f/d) + d*e - c*f)/d) + 8*(a*b*d*m + a*b*d)*gamma(m + 1, -(d*f*x + c*f)/d)*sinh((d*m*log(-f/d) - d*e + c*f)/d) + (b^2*d*m + b^2*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*((2*a^2 - b^2)*d*f*x + (2*a^2 - b^2)*c*f)*cosh(m*log(d*x + c)) - 4*((2*a^2 - b^2)*d*f*x + (2*a^2 - b^2)*c*f)*sinh(m*log(d*x + c)))/(d*f*m + d*f)","A",0
184,1,249,0,0.489284," ","integrate((d*x+c)^m*(a+b*sinh(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(b d m + b d\right)} \cosh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) + {\left(b d m + b d\right)} \cosh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) - {\left(b d m + b d\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) - {\left(b d m + b d\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) + 2 \, {\left(a d f x + a c f\right)} \cosh\left(m \log\left(d x + c\right)\right) + 2 \, {\left(a d f x + a c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{2 \, {\left(d f m + d f\right)}}"," ",0,"1/2*((b*d*m + b*d)*cosh((d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) + (b*d*m + b*d)*cosh((d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) - (b*d*m + b*d)*gamma(m + 1, (d*f*x + c*f)/d)*sinh((d*m*log(f/d) + d*e - c*f)/d) - (b*d*m + b*d)*gamma(m + 1, -(d*f*x + c*f)/d)*sinh((d*m*log(-f/d) - d*e + c*f)/d) + 2*(a*d*f*x + a*c*f)*cosh(m*log(d*x + c)) + 2*(a*d*f*x + a*c*f)*sinh(m*log(d*x + c)))/(d*f*m + d*f)","A",0
185,0,0,0,0.473380," ","integrate((d*x+c)^m/(a+b*sinh(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{b \sinh\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*x + c)^m/(b*sinh(f*x + e) + a), x)","F",0
186,0,0,0,0.394787," ","integrate((d*x+c)^m/(a+b*sinh(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{b^{2} \sinh\left(f x + e\right)^{2} + 2 \, a b \sinh\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((d*x + c)^m/(b^2*sinh(f*x + e)^2 + 2*a*b*sinh(f*x + e) + a^2), x)","F",0
187,1,458,0,0.912829," ","integrate((f*x+e)^3*sinh(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{d^{4} f^{3} x^{4} + 4 \, d^{4} e f^{2} x^{3} + 6 \, d^{4} e^{2} f x^{2} + 4 \, d^{4} e^{3} x + 8 \, d^{3} e^{3} - 24 \, c d^{2} e^{2} f + 24 \, c^{2} d e f^{2} - 8 \, c^{3} f^{3} + {\left(48 \, d f^{3} x + 48 \, d e f^{2} - {\left(-48 i \, d f^{3} x - 48 i \, d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) - {\left(-i \, d^{4} f^{3} x^{4} + 24 i \, c d^{2} e^{2} f - 24 i \, c^{2} d e f^{2} + 8 i \, c^{3} f^{3} + {\left(-4 i \, d^{4} e f^{2} + 8 i \, d^{3} f^{3}\right)} x^{3} + {\left(-6 i \, d^{4} e^{2} f + 24 i \, d^{3} e f^{2}\right)} x^{2} + {\left(-4 i \, d^{4} e^{3} + 24 i \, d^{3} e^{2} f\right)} x\right)} e^{\left(d x + c\right)} + {\left(24 \, d^{2} e^{2} f - 48 \, c d e f^{2} + 24 \, c^{2} f^{3} - {\left(-24 i \, d^{2} e^{2} f + 48 i \, c d e f^{2} - 24 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(24 \, d^{2} f^{3} x^{2} + 48 \, d^{2} e f^{2} x + 48 \, c d e f^{2} - 24 \, c^{2} f^{3} - {\left(-24 i \, d^{2} f^{3} x^{2} - 48 i \, d^{2} e f^{2} x - 48 i \, c d e f^{2} + 24 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + 48 \, {\left(-i \, f^{3} e^{\left(d x + c\right)} - f^{3}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right)}{4 \, {\left(a d^{4} e^{\left(d x + c\right)} - i \, a d^{4}\right)}}"," ",0,"-1/4*(d^4*f^3*x^4 + 4*d^4*e*f^2*x^3 + 6*d^4*e^2*f*x^2 + 4*d^4*e^3*x + 8*d^3*e^3 - 24*c*d^2*e^2*f + 24*c^2*d*e*f^2 - 8*c^3*f^3 + (48*d*f^3*x + 48*d*e*f^2 - (-48*I*d*f^3*x - 48*I*d*e*f^2)*e^(d*x + c))*dilog(-I*e^(d*x + c)) - (-I*d^4*f^3*x^4 + 24*I*c*d^2*e^2*f - 24*I*c^2*d*e*f^2 + 8*I*c^3*f^3 + (-4*I*d^4*e*f^2 + 8*I*d^3*f^3)*x^3 + (-6*I*d^4*e^2*f + 24*I*d^3*e*f^2)*x^2 + (-4*I*d^4*e^3 + 24*I*d^3*e^2*f)*x)*e^(d*x + c) + (24*d^2*e^2*f - 48*c*d*e*f^2 + 24*c^2*f^3 - (-24*I*d^2*e^2*f + 48*I*c*d*e*f^2 - 24*I*c^2*f^3)*e^(d*x + c))*log(e^(d*x + c) - I) + (24*d^2*f^3*x^2 + 48*d^2*e*f^2*x + 48*c*d*e*f^2 - 24*c^2*f^3 - (-24*I*d^2*f^3*x^2 - 48*I*d^2*e*f^2*x - 48*I*c*d*e*f^2 + 24*I*c^2*f^3)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + 48*(-I*f^3*e^(d*x + c) - f^3)*polylog(3, -I*e^(d*x + c)))/(a*d^4*e^(d*x + c) - I*a*d^4)","C",0
188,1,262,0,0.532272," ","integrate((f*x+e)^2*sinh(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{d^{3} f^{2} x^{3} + 3 \, d^{3} e f x^{2} + 3 \, d^{3} e^{2} x + 6 \, d^{2} e^{2} - 12 \, c d e f + 6 \, c^{2} f^{2} + 12 \, {\left(i \, f^{2} e^{\left(d x + c\right)} + f^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) - {\left(-i \, d^{3} f^{2} x^{3} + 12 i \, c d e f - 6 i \, c^{2} f^{2} + {\left(-3 i \, d^{3} e f + 6 i \, d^{2} f^{2}\right)} x^{2} + {\left(-3 i \, d^{3} e^{2} + 12 i \, d^{2} e f\right)} x\right)} e^{\left(d x + c\right)} + {\left(12 \, d e f - 12 \, c f^{2} - {\left(-12 i \, d e f + 12 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(12 \, d f^{2} x + 12 \, c f^{2} - {\left(-12 i \, d f^{2} x - 12 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right)}{3 \, {\left(a d^{3} e^{\left(d x + c\right)} - i \, a d^{3}\right)}}"," ",0,"-1/3*(d^3*f^2*x^3 + 3*d^3*e*f*x^2 + 3*d^3*e^2*x + 6*d^2*e^2 - 12*c*d*e*f + 6*c^2*f^2 + 12*(I*f^2*e^(d*x + c) + f^2)*dilog(-I*e^(d*x + c)) - (-I*d^3*f^2*x^3 + 12*I*c*d*e*f - 6*I*c^2*f^2 + (-3*I*d^3*e*f + 6*I*d^2*f^2)*x^2 + (-3*I*d^3*e^2 + 12*I*d^2*e*f)*x)*e^(d*x + c) + (12*d*e*f - 12*c*f^2 - (-12*I*d*e*f + 12*I*c*f^2)*e^(d*x + c))*log(e^(d*x + c) - I) + (12*d*f^2*x + 12*c*f^2 - (-12*I*d*f^2*x - 12*I*c*f^2)*e^(d*x + c))*log(I*e^(d*x + c) + 1))/(a*d^3*e^(d*x + c) - I*a*d^3)","B",0
189,1,95,0,0.927317," ","integrate((f*x+e)*sinh(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{d^{2} f x^{2} + 2 \, d^{2} e x + 4 \, d e - {\left(-i \, d^{2} f x^{2} + {\left(-2 i \, d^{2} e + 4 i \, d f\right)} x\right)} e^{\left(d x + c\right)} + 4 \, {\left(i \, f e^{\left(d x + c\right)} + f\right)} \log\left(e^{\left(d x + c\right)} - i\right)}{2 \, {\left(a d^{2} e^{\left(d x + c\right)} - i \, a d^{2}\right)}}"," ",0,"-1/2*(d^2*f*x^2 + 2*d^2*e*x + 4*d*e - (-I*d^2*f*x^2 + (-2*I*d^2*e + 4*I*d*f)*x)*e^(d*x + c) + 4*(I*f*e^(d*x + c) + f)*log(e^(d*x + c) - I))/(a*d^2*e^(d*x + c) - I*a*d^2)","A",0
190,1,33,0,0.445921," ","integrate(sinh(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{-i \, d x e^{\left(d x + c\right)} - d x - 2}{a d e^{\left(d x + c\right)} - i \, a d}"," ",0,"(-I*d*x*e^(d*x + c) - d*x - 2)/(a*d*e^(d*x + c) - I*a*d)","A",0
191,0,0,0,0.508277," ","integrate(sinh(d*x+c)/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, a d f x - i \, a d e + {\left(a d f x + a d e\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(-\frac{d f x + d e - {\left(-i \, d f x - i \, d e\right)} e^{\left(d x + c\right)} + 2 \, f}{-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}}, x\right) - 2}{-i \, a d f x - i \, a d e + {\left(a d f x + a d e\right)} e^{\left(d x + c\right)}}"," ",0,"((-I*a*d*f*x - I*a*d*e + (a*d*f*x + a*d*e)*e^(d*x + c))*integral(-(d*f*x + d*e - (-I*d*f*x - I*d*e)*e^(d*x + c) + 2*f)/(-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c)), x) - 2)/(-I*a*d*f*x - I*a*d*e + (a*d*f*x + a*d*e)*e^(d*x + c))","F",0
192,0,0,0,0.474396," ","integrate(sinh(d*x+c)/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(-\frac{d f x + d e - {\left(-i \, d f x - i \, d e\right)} e^{\left(d x + c\right)} + 4 \, f}{-i \, a d f^{3} x^{3} - 3 i \, a d e f^{2} x^{2} - 3 i \, a d e^{2} f x - i \, a d e^{3} + {\left(a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3}\right)} e^{\left(d x + c\right)}}, x\right) - 2}{-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}}"," ",0,"((-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c))*integral(-(d*f*x + d*e - (-I*d*f*x - I*d*e)*e^(d*x + c) + 4*f)/(-I*a*d*f^3*x^3 - 3*I*a*d*e*f^2*x^2 - 3*I*a*d*e^2*f*x - I*a*d*e^3 + (a*d*f^3*x^3 + 3*a*d*e*f^2*x^2 + 3*a*d*e^2*f*x + a*d*e^3)*e^(d*x + c)), x) - 2)/(-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c))","F",0
193,1,816,0,0.523735," ","integrate((f*x+e)^3*sinh(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, d^{3} f^{3} x^{3} + 2 \, d^{3} e^{3} + 6 \, d^{2} e^{2} f + 12 \, d e f^{2} + 12 \, f^{3} + 6 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 6 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x - {\left(48 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-48 i \, d f^{3} x - 48 i \, d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) - {\left(-2 i \, d^{3} f^{3} x^{3} - 2 i \, d^{3} e^{3} + 6 i \, d^{2} e^{2} f - 12 i \, d e f^{2} + 12 i \, f^{3} + {\left(-6 i \, d^{3} e f^{2} + 6 i \, d^{2} f^{3}\right)} x^{2} + {\left(-6 i \, d^{3} e^{2} f + 12 i \, d^{2} e f^{2} - 12 i \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d^{4} f^{3} x^{4} - 2 \, d^{3} e^{3} - 6 \, {\left(4 \, c - 1\right)} d^{2} e^{2} f + 12 \, {\left(2 \, c^{2} - 1\right)} d e f^{2} - 4 \, {\left(2 \, c^{3} - 3\right)} f^{3} + 2 \, {\left(2 \, d^{4} e f^{2} - 5 \, d^{3} f^{3}\right)} x^{3} + 6 \, {\left(d^{4} e^{2} f - 5 \, d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 2 \, {\left(2 \, d^{4} e^{3} - 15 \, d^{3} e^{2} f + 6 \, d^{2} e f^{2} - 6 \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-i \, d^{4} f^{3} x^{4} - 10 i \, d^{3} e^{3} + {\left(24 i \, c - 6 i\right)} d^{2} e^{2} f + {\left(-24 i \, c^{2} - 12 i\right)} d e f^{2} + {\left(8 i \, c^{3} - 12 i\right)} f^{3} + {\left(-4 i \, d^{4} e f^{2} - 2 i \, d^{3} f^{3}\right)} x^{3} + {\left(-6 i \, d^{4} e^{2} f - 6 i \, d^{3} e f^{2} - 6 i \, d^{2} f^{3}\right)} x^{2} + {\left(-4 i \, d^{4} e^{3} - 6 i \, d^{3} e^{2} f - 12 i \, d^{2} e f^{2} - 12 i \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)} - {\left(24 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-24 i \, d^{2} e^{2} f + 48 i \, c d e f^{2} - 24 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) - {\left(24 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-24 i \, d^{2} f^{3} x^{2} - 48 i \, d^{2} e f^{2} x - 48 i \, c d e f^{2} + 24 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(48 \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} - 48 i \, f^{3} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right)}{4 \, a d^{4} e^{\left(2 \, d x + 2 \, c\right)} - 4 i \, a d^{4} e^{\left(d x + c\right)}}"," ",0,"-(2*d^3*f^3*x^3 + 2*d^3*e^3 + 6*d^2*e^2*f + 12*d*e*f^2 + 12*f^3 + 6*(d^3*e*f^2 + d^2*f^3)*x^2 + 6*(d^3*e^2*f + 2*d^2*e*f^2 + 2*d*f^3)*x - (48*(d*f^3*x + d*e*f^2)*e^(2*d*x + 2*c) + (-48*I*d*f^3*x - 48*I*d*e*f^2)*e^(d*x + c))*dilog(-I*e^(d*x + c)) - (-2*I*d^3*f^3*x^3 - 2*I*d^3*e^3 + 6*I*d^2*e^2*f - 12*I*d*e*f^2 + 12*I*f^3 + (-6*I*d^3*e*f^2 + 6*I*d^2*f^3)*x^2 + (-6*I*d^3*e^2*f + 12*I*d^2*e*f^2 - 12*I*d*f^3)*x)*e^(3*d*x + 3*c) - (d^4*f^3*x^4 - 2*d^3*e^3 - 6*(4*c - 1)*d^2*e^2*f + 12*(2*c^2 - 1)*d*e*f^2 - 4*(2*c^3 - 3)*f^3 + 2*(2*d^4*e*f^2 - 5*d^3*f^3)*x^3 + 6*(d^4*e^2*f - 5*d^3*e*f^2 + d^2*f^3)*x^2 + 2*(2*d^4*e^3 - 15*d^3*e^2*f + 6*d^2*e*f^2 - 6*d*f^3)*x)*e^(2*d*x + 2*c) - (-I*d^4*f^3*x^4 - 10*I*d^3*e^3 + (24*I*c - 6*I)*d^2*e^2*f + (-24*I*c^2 - 12*I)*d*e*f^2 + (8*I*c^3 - 12*I)*f^3 + (-4*I*d^4*e*f^2 - 2*I*d^3*f^3)*x^3 + (-6*I*d^4*e^2*f - 6*I*d^3*e*f^2 - 6*I*d^2*f^3)*x^2 + (-4*I*d^4*e^3 - 6*I*d^3*e^2*f - 12*I*d^2*e*f^2 - 12*I*d*f^3)*x)*e^(d*x + c) - (24*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*e^(2*d*x + 2*c) + (-24*I*d^2*e^2*f + 48*I*c*d*e*f^2 - 24*I*c^2*f^3)*e^(d*x + c))*log(e^(d*x + c) - I) - (24*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*e^(2*d*x + 2*c) + (-24*I*d^2*f^3*x^2 - 48*I*d^2*e*f^2*x - 48*I*c*d*e*f^2 + 24*I*c^2*f^3)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (48*f^3*e^(2*d*x + 2*c) - 48*I*f^3*e^(d*x + c))*polylog(3, -I*e^(d*x + c)))/(4*a*d^4*e^(2*d*x + 2*c) - 4*I*a*d^4*e^(d*x + c))","C",0
194,1,471,0,0.508087," ","integrate((f*x+e)^2*sinh(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 6 \, d e f + 6 \, f^{2} + 6 \, {\left(d^{2} e f + d f^{2}\right)} x - {\left(24 \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} - 24 i \, f^{2} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) - {\left(-3 i \, d^{2} f^{2} x^{2} - 3 i \, d^{2} e^{2} + 6 i \, d e f - 6 i \, f^{2} + {\left(-6 i \, d^{2} e f + 6 i \, d f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(2 \, d^{3} f^{2} x^{3} - 3 \, d^{2} e^{2} - 6 \, {\left(4 \, c - 1\right)} d e f + 6 \, {\left(2 \, c^{2} - 1\right)} f^{2} + 3 \, {\left(2 \, d^{3} e f - 5 \, d^{2} f^{2}\right)} x^{2} + 6 \, {\left(d^{3} e^{2} - 5 \, d^{2} e f + d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-2 i \, d^{3} f^{2} x^{3} - 15 i \, d^{2} e^{2} + {\left(24 i \, c - 6 i\right)} d e f + {\left(-12 i \, c^{2} - 6 i\right)} f^{2} + {\left(-6 i \, d^{3} e f - 3 i \, d^{2} f^{2}\right)} x^{2} + {\left(-6 i \, d^{3} e^{2} - 6 i \, d^{2} e f - 6 i \, d f^{2}\right)} x\right)} e^{\left(d x + c\right)} - {\left(24 \, {\left(d e f - c f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-24 i \, d e f + 24 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) - {\left(24 \, {\left(d f^{2} x + c f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-24 i \, d f^{2} x - 24 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right)}{6 \, a d^{3} e^{\left(2 \, d x + 2 \, c\right)} - 6 i \, a d^{3} e^{\left(d x + c\right)}}"," ",0,"-(3*d^2*f^2*x^2 + 3*d^2*e^2 + 6*d*e*f + 6*f^2 + 6*(d^2*e*f + d*f^2)*x - (24*f^2*e^(2*d*x + 2*c) - 24*I*f^2*e^(d*x + c))*dilog(-I*e^(d*x + c)) - (-3*I*d^2*f^2*x^2 - 3*I*d^2*e^2 + 6*I*d*e*f - 6*I*f^2 + (-6*I*d^2*e*f + 6*I*d*f^2)*x)*e^(3*d*x + 3*c) - (2*d^3*f^2*x^3 - 3*d^2*e^2 - 6*(4*c - 1)*d*e*f + 6*(2*c^2 - 1)*f^2 + 3*(2*d^3*e*f - 5*d^2*f^2)*x^2 + 6*(d^3*e^2 - 5*d^2*e*f + d*f^2)*x)*e^(2*d*x + 2*c) - (-2*I*d^3*f^2*x^3 - 15*I*d^2*e^2 + (24*I*c - 6*I)*d*e*f + (-12*I*c^2 - 6*I)*f^2 + (-6*I*d^3*e*f - 3*I*d^2*f^2)*x^2 + (-6*I*d^3*e^2 - 6*I*d^2*e*f - 6*I*d*f^2)*x)*e^(d*x + c) - (24*(d*e*f - c*f^2)*e^(2*d*x + 2*c) + (-24*I*d*e*f + 24*I*c*f^2)*e^(d*x + c))*log(e^(d*x + c) - I) - (24*(d*f^2*x + c*f^2)*e^(2*d*x + 2*c) + (-24*I*d*f^2*x - 24*I*c*f^2)*e^(d*x + c))*log(I*e^(d*x + c) + 1))/(6*a*d^3*e^(2*d*x + 2*c) - 6*I*a*d^3*e^(d*x + c))","B",0
195,1,174,0,0.522684," ","integrate((f*x+e)*sinh(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{d f x + d e - {\left(-i \, d f x - i \, d e + i \, f\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d^{2} f x^{2} - d e + {\left(2 \, d^{2} e - 5 \, d f\right)} x + f\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-i \, d^{2} f x^{2} - 5 i \, d e + {\left(-2 i \, d^{2} e - i \, d f\right)} x - i \, f\right)} e^{\left(d x + c\right)} - {\left(4 \, f e^{\left(2 \, d x + 2 \, c\right)} - 4 i \, f e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + f}{2 \, a d^{2} e^{\left(2 \, d x + 2 \, c\right)} - 2 i \, a d^{2} e^{\left(d x + c\right)}}"," ",0,"-(d*f*x + d*e - (-I*d*f*x - I*d*e + I*f)*e^(3*d*x + 3*c) - (d^2*f*x^2 - d*e + (2*d^2*e - 5*d*f)*x + f)*e^(2*d*x + 2*c) - (-I*d^2*f*x^2 - 5*I*d*e + (-2*I*d^2*e - I*d*f)*x - I*f)*e^(d*x + c) - (4*f*e^(2*d*x + 2*c) - 4*I*f*e^(d*x + c))*log(e^(d*x + c) - I) + f)/(2*a*d^2*e^(2*d*x + 2*c) - 2*I*a*d^2*e^(d*x + c))","A",0
196,1,69,0,0.547291," ","integrate(sinh(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, d x - 1\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-2 i \, d x - 5 i\right)} e^{\left(d x + c\right)} - i \, e^{\left(3 \, d x + 3 \, c\right)} - 1}{2 \, a d e^{\left(2 \, d x + 2 \, c\right)} - 2 i \, a d e^{\left(d x + c\right)}}"," ",0,"((2*d*x - 1)*e^(2*d*x + 2*c) + (-2*I*d*x - 5*I)*e^(d*x + c) - I*e^(3*d*x + 3*c) - 1)/(2*a*d*e^(2*d*x + 2*c) - 2*I*a*d*e^(d*x + c))","A",0
197,0,0,0,0.534386," ","integrate(sinh(d*x+c)^2/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, a d f x - i \, a d e + {\left(a d f x + a d e\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{d f x + d e + {\left(-i \, d f x - i \, d e\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(d f x + d e\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-i \, d f x - i \, d e - 4 i \, f\right)} e^{\left(d x + c\right)}}{2 \, {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-2 i \, a d f^{2} x^{2} - 4 i \, a d e f x - 2 i \, a d e^{2}\right)} e^{\left(d x + c\right)}}, x\right) - 2 i}{-i \, a d f x - i \, a d e + {\left(a d f x + a d e\right)} e^{\left(d x + c\right)}}"," ",0,"((-I*a*d*f*x - I*a*d*e + (a*d*f*x + a*d*e)*e^(d*x + c))*integral((d*f*x + d*e + (-I*d*f*x - I*d*e)*e^(3*d*x + 3*c) + (d*f*x + d*e)*e^(2*d*x + 2*c) + (-I*d*f*x - I*d*e - 4*I*f)*e^(d*x + c))/(2*(a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(2*d*x + 2*c) + (-2*I*a*d*f^2*x^2 - 4*I*a*d*e*f*x - 2*I*a*d*e^2)*e^(d*x + c)), x) - 2*I)/(-I*a*d*f*x - I*a*d*e + (a*d*f*x + a*d*e)*e^(d*x + c))","F",0
198,0,0,0,0.552403," ","integrate(sinh(d*x+c)^2/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{d f x + d e + {\left(-i \, d f x - i \, d e\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(d f x + d e\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-i \, d f x - i \, d e - 8 i \, f\right)} e^{\left(d x + c\right)}}{2 \, {\left(a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-2 i \, a d f^{3} x^{3} - 6 i \, a d e f^{2} x^{2} - 6 i \, a d e^{2} f x - 2 i \, a d e^{3}\right)} e^{\left(d x + c\right)}}, x\right) - 2 i}{-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}}"," ",0,"((-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c))*integral((d*f*x + d*e + (-I*d*f*x - I*d*e)*e^(3*d*x + 3*c) + (d*f*x + d*e)*e^(2*d*x + 2*c) + (-I*d*f*x - I*d*e - 8*I*f)*e^(d*x + c))/(2*(a*d*f^3*x^3 + 3*a*d*e*f^2*x^2 + 3*a*d*e^2*f*x + a*d*e^3)*e^(2*d*x + 2*c) + (-2*I*a*d*f^3*x^3 - 6*I*a*d*e*f^2*x^2 - 6*I*a*d*e^2*f*x - 2*I*a*d*e^3)*e^(d*x + c)), x) - 2*I)/(-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c))","F",0
199,1,1029,0,0.896649," ","integrate((f*x+e)^3*sinh(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, d^{3} f^{3} x^{3} + 4 \, d^{3} e^{3} + 6 \, d^{2} e^{2} f + 6 \, d e f^{2} + 3 \, f^{3} + 6 \, {\left(2 \, d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, d^{3} e^{2} f + 2 \, d^{2} e f^{2} + d f^{3}\right)} x + {\left({\left(384 i \, d f^{3} x + 384 i \, d e f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + 384 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(-4 i \, d^{3} f^{3} x^{3} - 4 i \, d^{3} e^{3} + 6 i \, d^{2} e^{2} f - 6 i \, d e f^{2} + 3 i \, f^{3} + {\left(-12 i \, d^{3} e f^{2} + 6 i \, d^{2} f^{3}\right)} x^{2} + {\left(-12 i \, d^{3} e^{2} f + 12 i \, d^{2} e f^{2} - 6 i \, d f^{3}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + 3 \, {\left(4 \, d^{3} f^{3} x^{3} + 4 \, d^{3} e^{3} - 14 \, d^{2} e^{2} f + 30 \, d e f^{2} - 31 \, f^{3} + 2 \, {\left(6 \, d^{3} e f^{2} - 7 \, d^{2} f^{3}\right)} x^{2} + 2 \, {\left(6 \, d^{3} e^{2} f - 14 \, d^{2} e f^{2} + 15 \, d f^{3}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(12 i \, d^{4} f^{3} x^{4} - 16 i \, d^{3} e^{3} + {\left(-192 i \, c + 48 i\right)} d^{2} e^{2} f + {\left(192 i \, c^{2} - 96 i\right)} d e f^{2} + {\left(-64 i \, c^{3} + 96 i\right)} f^{3} + {\left(48 i \, d^{4} e f^{2} - 80 i \, d^{3} f^{3}\right)} x^{3} + {\left(72 i \, d^{4} e^{2} f - 240 i \, d^{3} e f^{2} + 48 i \, d^{2} f^{3}\right)} x^{2} + {\left(48 i \, d^{4} e^{3} - 240 i \, d^{3} e^{2} f + 96 i \, d^{2} e f^{2} - 96 i \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + 4 \, {\left(3 \, d^{4} f^{3} x^{4} + 20 \, d^{3} e^{3} - 12 \, {\left(4 \, c - 1\right)} d^{2} e^{2} f + 24 \, {\left(2 \, c^{2} + 1\right)} d e f^{2} - 8 \, {\left(2 \, c^{3} - 3\right)} f^{3} + 4 \, {\left(3 \, d^{4} e f^{2} + d^{3} f^{3}\right)} x^{3} + 6 \, {\left(3 \, d^{4} e^{2} f + 2 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + 12 \, {\left(d^{4} e^{3} + d^{3} e^{2} f + 2 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-12 i \, d^{3} f^{3} x^{3} - 12 i \, d^{3} e^{3} - 42 i \, d^{2} e^{2} f - 90 i \, d e f^{2} - 93 i \, f^{3} + {\left(-36 i \, d^{3} e f^{2} - 42 i \, d^{2} f^{3}\right)} x^{2} + {\left(-36 i \, d^{3} e^{2} f - 84 i \, d^{2} e f^{2} - 90 i \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)} + {\left({\left(192 i \, d^{2} e^{2} f - 384 i \, c d e f^{2} + 192 i \, c^{2} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + 192 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left({\left(192 i \, d^{2} f^{3} x^{2} + 384 i \, d^{2} e f^{2} x + 384 i \, c d e f^{2} - 192 i \, c^{2} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + 192 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(-384 i \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} - 384 \, f^{3} e^{\left(2 \, d x + 2 \, c\right)}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right)}{32 \, a d^{4} e^{\left(3 \, d x + 3 \, c\right)} - 32 i \, a d^{4} e^{\left(2 \, d x + 2 \, c\right)}}"," ",0,"(4*d^3*f^3*x^3 + 4*d^3*e^3 + 6*d^2*e^2*f + 6*d*e*f^2 + 3*f^3 + 6*(2*d^3*e*f^2 + d^2*f^3)*x^2 + 6*(2*d^3*e^2*f + 2*d^2*e*f^2 + d*f^3)*x + ((384*I*d*f^3*x + 384*I*d*e*f^2)*e^(3*d*x + 3*c) + 384*(d*f^3*x + d*e*f^2)*e^(2*d*x + 2*c))*dilog(-I*e^(d*x + c)) + (-4*I*d^3*f^3*x^3 - 4*I*d^3*e^3 + 6*I*d^2*e^2*f - 6*I*d*e*f^2 + 3*I*f^3 + (-12*I*d^3*e*f^2 + 6*I*d^2*f^3)*x^2 + (-12*I*d^3*e^2*f + 12*I*d^2*e*f^2 - 6*I*d*f^3)*x)*e^(5*d*x + 5*c) + 3*(4*d^3*f^3*x^3 + 4*d^3*e^3 - 14*d^2*e^2*f + 30*d*e*f^2 - 31*f^3 + 2*(6*d^3*e*f^2 - 7*d^2*f^3)*x^2 + 2*(6*d^3*e^2*f - 14*d^2*e*f^2 + 15*d*f^3)*x)*e^(4*d*x + 4*c) + (12*I*d^4*f^3*x^4 - 16*I*d^3*e^3 + (-192*I*c + 48*I)*d^2*e^2*f + (192*I*c^2 - 96*I)*d*e*f^2 + (-64*I*c^3 + 96*I)*f^3 + (48*I*d^4*e*f^2 - 80*I*d^3*f^3)*x^3 + (72*I*d^4*e^2*f - 240*I*d^3*e*f^2 + 48*I*d^2*f^3)*x^2 + (48*I*d^4*e^3 - 240*I*d^3*e^2*f + 96*I*d^2*e*f^2 - 96*I*d*f^3)*x)*e^(3*d*x + 3*c) + 4*(3*d^4*f^3*x^4 + 20*d^3*e^3 - 12*(4*c - 1)*d^2*e^2*f + 24*(2*c^2 + 1)*d*e*f^2 - 8*(2*c^3 - 3)*f^3 + 4*(3*d^4*e*f^2 + d^3*f^3)*x^3 + 6*(3*d^4*e^2*f + 2*d^3*e*f^2 + 2*d^2*f^3)*x^2 + 12*(d^4*e^3 + d^3*e^2*f + 2*d^2*e*f^2 + 2*d*f^3)*x)*e^(2*d*x + 2*c) + (-12*I*d^3*f^3*x^3 - 12*I*d^3*e^3 - 42*I*d^2*e^2*f - 90*I*d*e*f^2 - 93*I*f^3 + (-36*I*d^3*e*f^2 - 42*I*d^2*f^3)*x^2 + (-36*I*d^3*e^2*f - 84*I*d^2*e*f^2 - 90*I*d*f^3)*x)*e^(d*x + c) + ((192*I*d^2*e^2*f - 384*I*c*d*e*f^2 + 192*I*c^2*f^3)*e^(3*d*x + 3*c) + 192*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*e^(2*d*x + 2*c))*log(e^(d*x + c) - I) + ((192*I*d^2*f^3*x^2 + 384*I*d^2*e*f^2*x + 384*I*c*d*e*f^2 - 192*I*c^2*f^3)*e^(3*d*x + 3*c) + 192*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*e^(2*d*x + 2*c))*log(I*e^(d*x + c) + 1) + (-384*I*f^3*e^(3*d*x + 3*c) - 384*f^3*e^(2*d*x + 2*c))*polylog(3, -I*e^(d*x + c)))/(32*a*d^4*e^(3*d*x + 3*c) - 32*I*a*d^4*e^(2*d*x + 2*c))","C",0
200,1,587,0,0.533894," ","integrate((f*x+e)^2*sinh(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{2} f^{2} x^{2} + 2 \, d^{2} e^{2} + 2 \, d e f + f^{2} + 2 \, {\left(2 \, d^{2} e f + d f^{2}\right)} x + {\left(64 i \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} + 64 \, f^{2} e^{\left(2 \, d x + 2 \, c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(-2 i \, d^{2} f^{2} x^{2} - 2 i \, d^{2} e^{2} + 2 i \, d e f - i \, f^{2} + {\left(-4 i \, d^{2} e f + 2 i \, d f^{2}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(6 \, d^{2} f^{2} x^{2} + 6 \, d^{2} e^{2} - 14 \, d e f + 15 \, f^{2} + 2 \, {\left(6 \, d^{2} e f - 7 \, d f^{2}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(8 i \, d^{3} f^{2} x^{3} - 8 i \, d^{2} e^{2} + {\left(-64 i \, c + 16 i\right)} d e f + {\left(32 i \, c^{2} - 16 i\right)} f^{2} + {\left(24 i \, d^{3} e f - 40 i \, d^{2} f^{2}\right)} x^{2} + {\left(24 i \, d^{3} e^{2} - 80 i \, d^{2} e f + 16 i \, d f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + 8 \, {\left(d^{3} f^{2} x^{3} + 5 \, d^{2} e^{2} - 2 \, {\left(4 \, c - 1\right)} d e f + 2 \, {\left(2 \, c^{2} + 1\right)} f^{2} + {\left(3 \, d^{3} e f + d^{2} f^{2}\right)} x^{2} + {\left(3 \, d^{3} e^{2} + 2 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-6 i \, d^{2} f^{2} x^{2} - 6 i \, d^{2} e^{2} - 14 i \, d e f - 15 i \, f^{2} + {\left(-12 i \, d^{2} e f - 14 i \, d f^{2}\right)} x\right)} e^{\left(d x + c\right)} + {\left({\left(64 i \, d e f - 64 i \, c f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + 64 \, {\left(d e f - c f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left({\left(64 i \, d f^{2} x + 64 i \, c f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + 64 \, {\left(d f^{2} x + c f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right)}{16 \, a d^{3} e^{\left(3 \, d x + 3 \, c\right)} - 16 i \, a d^{3} e^{\left(2 \, d x + 2 \, c\right)}}"," ",0,"(2*d^2*f^2*x^2 + 2*d^2*e^2 + 2*d*e*f + f^2 + 2*(2*d^2*e*f + d*f^2)*x + (64*I*f^2*e^(3*d*x + 3*c) + 64*f^2*e^(2*d*x + 2*c))*dilog(-I*e^(d*x + c)) + (-2*I*d^2*f^2*x^2 - 2*I*d^2*e^2 + 2*I*d*e*f - I*f^2 + (-4*I*d^2*e*f + 2*I*d*f^2)*x)*e^(5*d*x + 5*c) + (6*d^2*f^2*x^2 + 6*d^2*e^2 - 14*d*e*f + 15*f^2 + 2*(6*d^2*e*f - 7*d*f^2)*x)*e^(4*d*x + 4*c) + (8*I*d^3*f^2*x^3 - 8*I*d^2*e^2 + (-64*I*c + 16*I)*d*e*f + (32*I*c^2 - 16*I)*f^2 + (24*I*d^3*e*f - 40*I*d^2*f^2)*x^2 + (24*I*d^3*e^2 - 80*I*d^2*e*f + 16*I*d*f^2)*x)*e^(3*d*x + 3*c) + 8*(d^3*f^2*x^3 + 5*d^2*e^2 - 2*(4*c - 1)*d*e*f + 2*(2*c^2 + 1)*f^2 + (3*d^3*e*f + d^2*f^2)*x^2 + (3*d^3*e^2 + 2*d^2*e*f + 2*d*f^2)*x)*e^(2*d*x + 2*c) + (-6*I*d^2*f^2*x^2 - 6*I*d^2*e^2 - 14*I*d*e*f - 15*I*f^2 + (-12*I*d^2*e*f - 14*I*d*f^2)*x)*e^(d*x + c) + ((64*I*d*e*f - 64*I*c*f^2)*e^(3*d*x + 3*c) + 64*(d*e*f - c*f^2)*e^(2*d*x + 2*c))*log(e^(d*x + c) - I) + ((64*I*d*f^2*x + 64*I*c*f^2)*e^(3*d*x + 3*c) + 64*(d*f^2*x + c*f^2)*e^(2*d*x + 2*c))*log(I*e^(d*x + c) + 1))/(16*a*d^3*e^(3*d*x + 3*c) - 16*I*a*d^3*e^(2*d*x + 2*c))","B",0
201,1,227,0,0.496715," ","integrate((f*x+e)*sinh(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d f x + 2 \, d e + {\left(-2 i \, d f x - 2 i \, d e + i \, f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(6 \, d f x + 6 \, d e - 7 \, f\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(12 i \, d^{2} f x^{2} - 8 i \, d e + {\left(24 i \, d^{2} e - 40 i \, d f\right)} x + 8 i \, f\right)} e^{\left(3 \, d x + 3 \, c\right)} + 4 \, {\left(3 \, d^{2} f x^{2} + 10 \, d e + 2 \, {\left(3 \, d^{2} e + d f\right)} x + 2 \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-6 i \, d f x - 6 i \, d e - 7 i \, f\right)} e^{\left(d x + c\right)} + {\left(32 i \, f e^{\left(3 \, d x + 3 \, c\right)} + 32 \, f e^{\left(2 \, d x + 2 \, c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + f}{16 \, a d^{2} e^{\left(3 \, d x + 3 \, c\right)} - 16 i \, a d^{2} e^{\left(2 \, d x + 2 \, c\right)}}"," ",0,"(2*d*f*x + 2*d*e + (-2*I*d*f*x - 2*I*d*e + I*f)*e^(5*d*x + 5*c) + (6*d*f*x + 6*d*e - 7*f)*e^(4*d*x + 4*c) + (12*I*d^2*f*x^2 - 8*I*d*e + (24*I*d^2*e - 40*I*d*f)*x + 8*I*f)*e^(3*d*x + 3*c) + 4*(3*d^2*f*x^2 + 10*d*e + 2*(3*d^2*e + d*f)*x + 2*f)*e^(2*d*x + 2*c) + (-6*I*d*f*x - 6*I*d*e - 7*I*f)*e^(d*x + c) + (32*I*f*e^(3*d*x + 3*c) + 32*f*e^(2*d*x + 2*c))*log(e^(d*x + c) - I) + f)/(16*a*d^2*e^(3*d*x + 3*c) - 16*I*a*d^2*e^(2*d*x + 2*c))","A",0
202,1,95,0,0.719727," ","integrate(sinh(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(12 i \, d x - 4 i\right)} e^{\left(3 \, d x + 3 \, c\right)} + 4 \, {\left(3 \, d x + 5\right)} e^{\left(2 \, d x + 2 \, c\right)} - i \, e^{\left(5 \, d x + 5 \, c\right)} + 3 \, e^{\left(4 \, d x + 4 \, c\right)} - 3 i \, e^{\left(d x + c\right)} + 1}{8 \, a d e^{\left(3 \, d x + 3 \, c\right)} - 8 i \, a d e^{\left(2 \, d x + 2 \, c\right)}}"," ",0,"((12*I*d*x - 4*I)*e^(3*d*x + 3*c) + 4*(3*d*x + 5)*e^(2*d*x + 2*c) - I*e^(5*d*x + 5*c) + 3*e^(4*d*x + 4*c) - 3*I*e^(d*x + c) + 1)/(8*a*d*e^(3*d*x + 3*c) - 8*I*a*d*e^(2*d*x + 2*c))","A",0
203,0,0,0,0.797806," ","integrate(sinh(d*x+c)^3/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, a d f x - i \, a d e + {\left(a d f x + a d e\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(-\frac{d f x + d e - {\left(-i \, d f x - i \, d e\right)} e^{\left(5 \, d x + 5 \, c\right)} - {\left(d f x + d e\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(4 i \, d f x + 4 i \, d e\right)} e^{\left(3 \, d x + 3 \, c\right)} - 4 \, {\left(d f x + d e + 2 \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(i \, d f x + i \, d e\right)} e^{\left(d x + c\right)}}{4 \, {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-4 i \, a d f^{2} x^{2} - 8 i \, a d e f x - 4 i \, a d e^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)}}, x\right) + 2}{-i \, a d f x - i \, a d e + {\left(a d f x + a d e\right)} e^{\left(d x + c\right)}}"," ",0,"((-I*a*d*f*x - I*a*d*e + (a*d*f*x + a*d*e)*e^(d*x + c))*integral(-(d*f*x + d*e - (-I*d*f*x - I*d*e)*e^(5*d*x + 5*c) - (d*f*x + d*e)*e^(4*d*x + 4*c) - (4*I*d*f*x + 4*I*d*e)*e^(3*d*x + 3*c) - 4*(d*f*x + d*e + 2*f)*e^(2*d*x + 2*c) - (I*d*f*x + I*d*e)*e^(d*x + c))/(4*(a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(3*d*x + 3*c) + (-4*I*a*d*f^2*x^2 - 8*I*a*d*e*f*x - 4*I*a*d*e^2)*e^(2*d*x + 2*c)), x) + 2)/(-I*a*d*f*x - I*a*d*e + (a*d*f*x + a*d*e)*e^(d*x + c))","F",0
204,0,0,0,0.523023," ","integrate(sinh(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(-\frac{d f x + d e - {\left(-i \, d f x - i \, d e\right)} e^{\left(5 \, d x + 5 \, c\right)} - {\left(d f x + d e\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(4 i \, d f x + 4 i \, d e\right)} e^{\left(3 \, d x + 3 \, c\right)} - 4 \, {\left(d f x + d e + 4 \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(i \, d f x + i \, d e\right)} e^{\left(d x + c\right)}}{4 \, {\left(a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-4 i \, a d f^{3} x^{3} - 12 i \, a d e f^{2} x^{2} - 12 i \, a d e^{2} f x - 4 i \, a d e^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}, x\right) + 2}{-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}}"," ",0,"((-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c))*integral(-(d*f*x + d*e - (-I*d*f*x - I*d*e)*e^(5*d*x + 5*c) - (d*f*x + d*e)*e^(4*d*x + 4*c) - (4*I*d*f*x + 4*I*d*e)*e^(3*d*x + 3*c) - 4*(d*f*x + d*e + 4*f)*e^(2*d*x + 2*c) - (I*d*f*x + I*d*e)*e^(d*x + c))/(4*(a*d*f^3*x^3 + 3*a*d*e*f^2*x^2 + 3*a*d*e^2*f*x + a*d*e^3)*e^(3*d*x + 3*c) + (-4*I*a*d*f^3*x^3 - 12*I*a*d*e*f^2*x^2 - 12*I*a*d*e^2*f*x - 4*I*a*d*e^3)*e^(2*d*x + 2*c)), x) + 2)/(-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c))","F",0
205,1,997,0,0.861705," ","integrate((f*x+e)^3*csch(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{3} e^{3} - 6 \, c d^{2} e^{2} f + 6 \, c^{2} d e f^{2} - 2 \, c^{3} f^{3} + {\left(12 \, d f^{3} x + 12 \, d e f^{2} + {\left(12 i \, d f^{3} x + 12 i \, d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f - 3 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-e^{\left(d x + c\right)}\right) + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f + 3 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(e^{\left(d x + c\right)}\right) + {\left(-2 i \, d^{3} f^{3} x^{3} - 6 i \, d^{3} e f^{2} x^{2} - 6 i \, d^{3} e^{2} f x - 6 i \, c d^{2} e^{2} f + 6 i \, c^{2} d e f^{2} - 2 i \, c^{3} f^{3}\right)} e^{\left(d x + c\right)} + {\left(i \, d^{3} f^{3} x^{3} + 3 i \, d^{3} e f^{2} x^{2} + 3 i \, d^{3} e^{2} f x + i \, d^{3} e^{3} - {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + 1\right) + {\left(6 \, d^{2} e^{2} f - 12 \, c d e f^{2} + 6 \, c^{2} f^{3} + {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(-i \, d^{3} e^{3} + 3 i \, c d^{2} e^{2} f - 3 i \, c^{2} d e f^{2} + i \, c^{3} f^{3} + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - 1\right) + {\left(6 \, d^{2} f^{3} x^{2} + 12 \, d^{2} e f^{2} x + 12 \, c d e f^{2} - 6 \, c^{2} f^{3} + {\left(6 i \, d^{2} f^{3} x^{2} + 12 i \, d^{2} e f^{2} x + 12 i \, c d e f^{2} - 6 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(-i \, d^{3} f^{3} x^{3} - 3 i \, d^{3} e f^{2} x^{2} - 3 i \, d^{3} e^{2} f x - 3 i \, c d^{2} e^{2} f + 3 i \, c^{2} d e f^{2} - i \, c^{3} f^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(-e^{\left(d x + c\right)} + 1\right) - {\left(6 \, f^{3} e^{\left(d x + c\right)} - 6 i \, f^{3}\right)} {\rm polylog}\left(4, -e^{\left(d x + c\right)}\right) + {\left(6 \, f^{3} e^{\left(d x + c\right)} - 6 i \, f^{3}\right)} {\rm polylog}\left(4, e^{\left(d x + c\right)}\right) - 12 \, {\left(i \, f^{3} e^{\left(d x + c\right)} + f^{3}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right) + {\left(-6 i \, d f^{3} x - 6 i \, d e f^{2} + 6 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, -e^{\left(d x + c\right)}\right) + {\left(6 i \, d f^{3} x + 6 i \, d e f^{2} - 6 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, e^{\left(d x + c\right)}\right)}{a d^{4} e^{\left(d x + c\right)} - i \, a d^{4}}"," ",0,"(2*d^3*e^3 - 6*c*d^2*e^2*f + 6*c^2*d*e*f^2 - 2*c^3*f^3 + (12*d*f^3*x + 12*d*e*f^2 + (12*I*d*f^3*x + 12*I*d*e*f^2)*e^(d*x + c))*dilog(-I*e^(d*x + c)) + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f - 3*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*e^(d*x + c))*dilog(-e^(d*x + c)) + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f + 3*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*e^(d*x + c))*dilog(e^(d*x + c)) + (-2*I*d^3*f^3*x^3 - 6*I*d^3*e*f^2*x^2 - 6*I*d^3*e^2*f*x - 6*I*c*d^2*e^2*f + 6*I*c^2*d*e*f^2 - 2*I*c^3*f^3)*e^(d*x + c) + (I*d^3*f^3*x^3 + 3*I*d^3*e*f^2*x^2 + 3*I*d^3*e^2*f*x + I*d^3*e^3 - (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*e^(d*x + c))*log(e^(d*x + c) + 1) + (6*d^2*e^2*f - 12*c*d*e*f^2 + 6*c^2*f^3 + (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*c^2*f^3)*e^(d*x + c))*log(e^(d*x + c) - I) + (-I*d^3*e^3 + 3*I*c*d^2*e^2*f - 3*I*c^2*d*e*f^2 + I*c^3*f^3 + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*e^(d*x + c))*log(e^(d*x + c) - 1) + (6*d^2*f^3*x^2 + 12*d^2*e*f^2*x + 12*c*d*e*f^2 - 6*c^2*f^3 + (6*I*d^2*f^3*x^2 + 12*I*d^2*e*f^2*x + 12*I*c*d*e*f^2 - 6*I*c^2*f^3)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (-I*d^3*f^3*x^3 - 3*I*d^3*e*f^2*x^2 - 3*I*d^3*e^2*f*x - 3*I*c*d^2*e^2*f + 3*I*c^2*d*e*f^2 - I*c^3*f^3 + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*e^(d*x + c))*log(-e^(d*x + c) + 1) - (6*f^3*e^(d*x + c) - 6*I*f^3)*polylog(4, -e^(d*x + c)) + (6*f^3*e^(d*x + c) - 6*I*f^3)*polylog(4, e^(d*x + c)) - 12*(I*f^3*e^(d*x + c) + f^3)*polylog(3, -I*e^(d*x + c)) + (-6*I*d*f^3*x - 6*I*d*e*f^2 + 6*(d*f^3*x + d*e*f^2)*e^(d*x + c))*polylog(3, -e^(d*x + c)) + (6*I*d*f^3*x + 6*I*d*e*f^2 - 6*(d*f^3*x + d*e*f^2)*e^(d*x + c))*polylog(3, e^(d*x + c)))/(a*d^4*e^(d*x + c) - I*a*d^4)","C",0
206,1,557,0,0.446267," ","integrate((f*x+e)^2*csch(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, d^{2} e^{2} - 4 \, c d e f + 2 \, c^{2} f^{2} - 4 \, {\left(-i \, f^{2} e^{\left(d x + c\right)} - f^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f - 2 \, {\left(d f^{2} x + d e f\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-e^{\left(d x + c\right)}\right) + {\left(-2 i \, d f^{2} x - 2 i \, d e f + 2 \, {\left(d f^{2} x + d e f\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(e^{\left(d x + c\right)}\right) + {\left(-2 i \, d^{2} f^{2} x^{2} - 4 i \, d^{2} e f x - 4 i \, c d e f + 2 i \, c^{2} f^{2}\right)} e^{\left(d x + c\right)} + {\left(i \, d^{2} f^{2} x^{2} + 2 i \, d^{2} e f x + i \, d^{2} e^{2} - {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + 1\right) + {\left(4 \, d e f - 4 \, c f^{2} + {\left(4 i \, d e f - 4 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(-i \, d^{2} e^{2} + 2 i \, c d e f - i \, c^{2} f^{2} + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - 1\right) + {\left(4 \, d f^{2} x + 4 \, c f^{2} + {\left(4 i \, d f^{2} x + 4 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(-i \, d^{2} f^{2} x^{2} - 2 i \, d^{2} e f x - 2 i \, c d e f + i \, c^{2} f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(-e^{\left(d x + c\right)} + 1\right) + {\left(2 \, f^{2} e^{\left(d x + c\right)} - 2 i \, f^{2}\right)} {\rm polylog}\left(3, -e^{\left(d x + c\right)}\right) - {\left(2 \, f^{2} e^{\left(d x + c\right)} - 2 i \, f^{2}\right)} {\rm polylog}\left(3, e^{\left(d x + c\right)}\right)}{a d^{3} e^{\left(d x + c\right)} - i \, a d^{3}}"," ",0,"(2*d^2*e^2 - 4*c*d*e*f + 2*c^2*f^2 - 4*(-I*f^2*e^(d*x + c) - f^2)*dilog(-I*e^(d*x + c)) + (2*I*d*f^2*x + 2*I*d*e*f - 2*(d*f^2*x + d*e*f)*e^(d*x + c))*dilog(-e^(d*x + c)) + (-2*I*d*f^2*x - 2*I*d*e*f + 2*(d*f^2*x + d*e*f)*e^(d*x + c))*dilog(e^(d*x + c)) + (-2*I*d^2*f^2*x^2 - 4*I*d^2*e*f*x - 4*I*c*d*e*f + 2*I*c^2*f^2)*e^(d*x + c) + (I*d^2*f^2*x^2 + 2*I*d^2*e*f*x + I*d^2*e^2 - (d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*e^(d*x + c))*log(e^(d*x + c) + 1) + (4*d*e*f - 4*c*f^2 + (4*I*d*e*f - 4*I*c*f^2)*e^(d*x + c))*log(e^(d*x + c) - I) + (-I*d^2*e^2 + 2*I*c*d*e*f - I*c^2*f^2 + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*e^(d*x + c))*log(e^(d*x + c) - 1) + (4*d*f^2*x + 4*c*f^2 + (4*I*d*f^2*x + 4*I*c*f^2)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (-I*d^2*f^2*x^2 - 2*I*d^2*e*f*x - 2*I*c*d*e*f + I*c^2*f^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(d*x + c))*log(-e^(d*x + c) + 1) + (2*f^2*e^(d*x + c) - 2*I*f^2)*polylog(3, -e^(d*x + c)) - (2*f^2*e^(d*x + c) - 2*I*f^2)*polylog(3, e^(d*x + c)))/(a*d^3*e^(d*x + c) - I*a*d^3)","C",0
207,1,211,0,0.484537," ","integrate((f*x+e)*csch(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{-2 i \, d f x e^{\left(d x + c\right)} + 2 \, d e - {\left(f e^{\left(d x + c\right)} - i \, f\right)} {\rm Li}_2\left(-e^{\left(d x + c\right)}\right) + {\left(f e^{\left(d x + c\right)} - i \, f\right)} {\rm Li}_2\left(e^{\left(d x + c\right)}\right) + {\left(i \, d f x + i \, d e - {\left(d f x + d e\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + 1\right) - 2 \, {\left(-i \, f e^{\left(d x + c\right)} - f\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(-i \, d e + i \, c f + {\left(d e - c f\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - 1\right) + {\left(-i \, d f x - i \, c f + {\left(d f x + c f\right)} e^{\left(d x + c\right)}\right)} \log\left(-e^{\left(d x + c\right)} + 1\right)}{a d^{2} e^{\left(d x + c\right)} - i \, a d^{2}}"," ",0,"(-2*I*d*f*x*e^(d*x + c) + 2*d*e - (f*e^(d*x + c) - I*f)*dilog(-e^(d*x + c)) + (f*e^(d*x + c) - I*f)*dilog(e^(d*x + c)) + (I*d*f*x + I*d*e - (d*f*x + d*e)*e^(d*x + c))*log(e^(d*x + c) + 1) - 2*(-I*f*e^(d*x + c) - f)*log(e^(d*x + c) - I) + (-I*d*e + I*c*f + (d*e - c*f)*e^(d*x + c))*log(e^(d*x + c) - 1) + (-I*d*f*x - I*c*f + (d*f*x + c*f)*e^(d*x + c))*log(-e^(d*x + c) + 1))/(a*d^2*e^(d*x + c) - I*a*d^2)","B",0
208,1,57,0,1.599534," ","integrate(csch(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(e^{\left(d x + c\right)} - i\right)} \log\left(e^{\left(d x + c\right)} + 1\right) - {\left(e^{\left(d x + c\right)} - i\right)} \log\left(e^{\left(d x + c\right)} - 1\right) - 2}{a d e^{\left(d x + c\right)} - i \, a d}"," ",0,"-((e^(d*x + c) - I)*log(e^(d*x + c) + 1) - (e^(d*x + c) - I)*log(e^(d*x + c) - 1) - 2)/(a*d*e^(d*x + c) - I*a*d)","A",0
209,0,0,0,0.726816," ","integrate(csch(d*x+c)/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, a d f x - i \, a d e + {\left(a d f x + a d e\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{2 \, {\left(d f x + d e + f\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-2 i \, d f x - 2 i \, d e\right)} e^{\left(d x + c\right)} - 2 \, f}{i \, a d f^{2} x^{2} + 2 i \, a d e f x + i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}}, x\right) + 2}{-i \, a d f x - i \, a d e + {\left(a d f x + a d e\right)} e^{\left(d x + c\right)}}"," ",0,"((-I*a*d*f*x - I*a*d*e + (a*d*f*x + a*d*e)*e^(d*x + c))*integral((2*(d*f*x + d*e + f)*e^(2*d*x + 2*c) + (-2*I*d*f*x - 2*I*d*e)*e^(d*x + c) - 2*f)/(I*a*d*f^2*x^2 + 2*I*a*d*e*f*x + I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(3*d*x + 3*c) + (-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2)*e^(2*d*x + 2*c) - (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c)), x) + 2)/(-I*a*d*f*x - I*a*d*e + (a*d*f*x + a*d*e)*e^(d*x + c))","F",0
210,0,0,0,0.466793," ","integrate(csch(d*x+c)/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{2 \, {\left(d f x + d e + 2 \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-2 i \, d f x - 2 i \, d e\right)} e^{\left(d x + c\right)} - 4 \, f}{i \, a d f^{3} x^{3} + 3 i \, a d e f^{2} x^{2} + 3 i \, a d e^{2} f x + i \, a d e^{3} + {\left(a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-i \, a d f^{3} x^{3} - 3 i \, a d e f^{2} x^{2} - 3 i \, a d e^{2} f x - i \, a d e^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3}\right)} e^{\left(d x + c\right)}}, x\right) + 2}{-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}}"," ",0,"((-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c))*integral((2*(d*f*x + d*e + 2*f)*e^(2*d*x + 2*c) + (-2*I*d*f*x - 2*I*d*e)*e^(d*x + c) - 4*f)/(I*a*d*f^3*x^3 + 3*I*a*d*e*f^2*x^2 + 3*I*a*d*e^2*f*x + I*a*d*e^3 + (a*d*f^3*x^3 + 3*a*d*e*f^2*x^2 + 3*a*d*e^2*f*x + a*d*e^3)*e^(3*d*x + 3*c) + (-I*a*d*f^3*x^3 - 3*I*a*d*e*f^2*x^2 - 3*I*a*d*e^2*f*x - I*a*d*e^3)*e^(2*d*x + 2*c) - (a*d*f^3*x^3 + 3*a*d*e*f^2*x^2 + 3*a*d*e^2*f*x + a*d*e^3)*e^(d*x + c)), x) + 2)/(-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c))","F",0
211,1,2577,0,0.979816," ","integrate((f*x+e)^3*csch(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 i \, d^{3} e^{3} - 12 i \, c d^{2} e^{2} f + 12 i \, c^{2} d e f^{2} - 4 i \, c^{3} f^{3} + {\left(12 i \, d f^{3} x + 12 i \, d e f^{2} + 12 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-12 i \, d f^{3} x - 12 i \, d e f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 12 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) - {\left(3 \, d^{2} f^{3} x^{2} + 3 \, d^{2} e^{2} f - 6 i \, d e f^{2} + {\left(6 \, d^{2} e f^{2} - 6 i \, d f^{3}\right)} x - {\left(3 i \, d^{2} f^{3} x^{2} + 3 i \, d^{2} e^{2} f + 6 \, d e f^{2} - 6 \, {\left(-i \, d^{2} e f^{2} - d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(3 \, d^{2} f^{3} x^{2} + 3 \, d^{2} e^{2} f - 6 i \, d e f^{2} + {\left(6 \, d^{2} e f^{2} - 6 i \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-3 i \, d^{2} f^{3} x^{2} - 3 i \, d^{2} e^{2} f - 6 \, d e f^{2} - 6 \, {\left(i \, d^{2} e f^{2} + d f^{3}\right)} x\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-e^{\left(d x + c\right)}\right) + {\left(3 \, d^{2} f^{3} x^{2} + 3 \, d^{2} e^{2} f + 6 i \, d e f^{2} + {\left(6 \, d^{2} e f^{2} + 6 i \, d f^{3}\right)} x + {\left(-3 i \, d^{2} f^{3} x^{2} - 3 i \, d^{2} e^{2} f + 6 \, d e f^{2} - 6 \, {\left(i \, d^{2} e f^{2} - d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(3 \, d^{2} f^{3} x^{2} + 3 \, d^{2} e^{2} f + 6 i \, d e f^{2} + {\left(6 \, d^{2} e f^{2} + 6 i \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(3 i \, d^{2} f^{3} x^{2} + 3 i \, d^{2} e^{2} f - 6 \, d e f^{2} - 6 \, {\left(-i \, d^{2} e f^{2} + d f^{3}\right)} x\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(e^{\left(d x + c\right)}\right) - 4 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(2 i \, d^{3} f^{3} x^{3} + 6 i \, d^{3} e f^{2} x^{2} + 6 i \, d^{3} e^{2} f x - 2 i \, d^{3} e^{3} + 12 i \, c d^{2} e^{2} f - 12 i \, c^{2} d e f^{2} + 4 i \, c^{3} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x - d^{3} e^{3} + 6 \, c d^{2} e^{2} f - 6 \, c^{2} d e f^{2} + 2 \, c^{3} f^{3}\right)} e^{\left(d x + c\right)} - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} - 3 i \, d^{2} e^{2} f + {\left(3 \, d^{3} e f^{2} - 3 i \, d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 i \, d^{2} e f^{2}\right)} x - {\left(i \, d^{3} f^{3} x^{3} + i \, d^{3} e^{3} + 3 \, d^{2} e^{2} f - 3 \, {\left(-i \, d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + {\left(3 i \, d^{3} e^{2} f + 6 \, d^{2} e f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} - 3 i \, d^{2} e^{2} f + {\left(3 \, d^{3} e f^{2} - 3 i \, d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 i \, d^{2} e f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-i \, d^{3} f^{3} x^{3} - i \, d^{3} e^{3} - 3 \, d^{2} e^{2} f - 3 \, {\left(i \, d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + {\left(-3 i \, d^{3} e^{2} f - 6 \, d^{2} e f^{2}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + 1\right) + {\left(6 i \, d^{2} e^{2} f - 12 i \, c d e f^{2} + 6 i \, c^{2} f^{3} + 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} - 6 i \, c^{2} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 6 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(d^{3} e^{3} - {\left(3 \, c - 3 i\right)} d^{2} e^{2} f + 3 \, {\left(c^{2} - 2 i \, c\right)} d e f^{2} - {\left(c^{3} - 3 i \, c^{2}\right)} f^{3} + {\left(-i \, d^{3} e^{3} - 3 \, {\left(-i \, c - 1\right)} d^{2} e^{2} f + {\left(-3 i \, c^{2} - 6 \, c\right)} d e f^{2} + {\left(i \, c^{3} + 3 \, c^{2}\right)} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d^{3} e^{3} - {\left(3 \, c - 3 i\right)} d^{2} e^{2} f + 3 \, {\left(c^{2} - 2 i \, c\right)} d e f^{2} - {\left(c^{3} - 3 i \, c^{2}\right)} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(i \, d^{3} e^{3} - 3 \, {\left(i \, c + 1\right)} d^{2} e^{2} f + {\left(3 i \, c^{2} + 6 \, c\right)} d e f^{2} + {\left(-i \, c^{3} - 3 \, c^{2}\right)} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - 1\right) + {\left(6 i \, d^{2} f^{3} x^{2} + 12 i \, d^{2} e f^{2} x + 12 i \, c d e f^{2} - 6 i \, c^{2} f^{3} + 6 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-6 i \, d^{2} f^{3} x^{2} - 12 i \, d^{2} e f^{2} x - 12 i \, c d e f^{2} + 6 i \, c^{2} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 6 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - 3 \, {\left(c^{2} - 2 i \, c\right)} d e f^{2} + {\left(c^{3} - 3 i \, c^{2}\right)} f^{3} + {\left(3 \, d^{3} e f^{2} + 3 i \, d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f + 2 i \, d^{2} e f^{2}\right)} x + {\left(-i \, d^{3} f^{3} x^{3} - 3 i \, c d^{2} e^{2} f + {\left(3 i \, c^{2} + 6 \, c\right)} d e f^{2} + {\left(-i \, c^{3} - 3 \, c^{2}\right)} f^{3} - 3 \, {\left(i \, d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + {\left(-3 i \, d^{3} e^{2} f + 6 \, d^{2} e f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} e^{2} f - 3 \, {\left(c^{2} - 2 i \, c\right)} d e f^{2} + {\left(c^{3} - 3 i \, c^{2}\right)} f^{3} + {\left(3 \, d^{3} e f^{2} + 3 i \, d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f + 2 i \, d^{2} e f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(i \, d^{3} f^{3} x^{3} + 3 i \, c d^{2} e^{2} f + {\left(-3 i \, c^{2} - 6 \, c\right)} d e f^{2} + {\left(i \, c^{3} + 3 \, c^{2}\right)} f^{3} - 3 \, {\left(-i \, d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + {\left(3 i \, d^{3} e^{2} f - 6 \, d^{2} e f^{2}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(-e^{\left(d x + c\right)} + 1\right) + {\left(6 i \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} + 6 \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} - 6 i \, f^{3} e^{\left(d x + c\right)} - 6 \, f^{3}\right)} {\rm polylog}\left(4, -e^{\left(d x + c\right)}\right) + {\left(-6 i \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} - 6 \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} + 6 i \, f^{3} e^{\left(d x + c\right)} + 6 \, f^{3}\right)} {\rm polylog}\left(4, e^{\left(d x + c\right)}\right) - {\left(12 \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} - 12 i \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} - 12 \, f^{3} e^{\left(d x + c\right)} + 12 i \, f^{3}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right) + {\left(6 \, d f^{3} x + 6 \, d e f^{2} - 6 i \, f^{3} + {\left(-6 i \, d f^{3} x - 6 i \, d e f^{2} - 6 \, f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(6 \, d f^{3} x + 6 \, d e f^{2} - 6 i \, f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(6 i \, d f^{3} x + 6 i \, d e f^{2} + 6 \, f^{3}\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, -e^{\left(d x + c\right)}\right) - {\left(6 \, d f^{3} x + 6 \, d e f^{2} + 6 i \, f^{3} - {\left(6 i \, d f^{3} x + 6 i \, d e f^{2} - 6 \, f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(6 \, d f^{3} x + 6 \, d e f^{2} + 6 i \, f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-6 i \, d f^{3} x - 6 i \, d e f^{2} + 6 \, f^{3}\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, e^{\left(d x + c\right)}\right)}{a d^{4} e^{\left(3 \, d x + 3 \, c\right)} - i \, a d^{4} e^{\left(2 \, d x + 2 \, c\right)} - a d^{4} e^{\left(d x + c\right)} + i \, a d^{4}}"," ",0,"(4*I*d^3*e^3 - 12*I*c*d^2*e^2*f + 12*I*c^2*d*e*f^2 - 4*I*c^3*f^3 + (12*I*d*f^3*x + 12*I*d*e*f^2 + 12*(d*f^3*x + d*e*f^2)*e^(3*d*x + 3*c) + (-12*I*d*f^3*x - 12*I*d*e*f^2)*e^(2*d*x + 2*c) - 12*(d*f^3*x + d*e*f^2)*e^(d*x + c))*dilog(-I*e^(d*x + c)) - (3*d^2*f^3*x^2 + 3*d^2*e^2*f - 6*I*d*e*f^2 + (6*d^2*e*f^2 - 6*I*d*f^3)*x - (3*I*d^2*f^3*x^2 + 3*I*d^2*e^2*f + 6*d*e*f^2 - 6*(-I*d^2*e*f^2 - d*f^3)*x)*e^(3*d*x + 3*c) - (3*d^2*f^3*x^2 + 3*d^2*e^2*f - 6*I*d*e*f^2 + (6*d^2*e*f^2 - 6*I*d*f^3)*x)*e^(2*d*x + 2*c) - (-3*I*d^2*f^3*x^2 - 3*I*d^2*e^2*f - 6*d*e*f^2 - 6*(I*d^2*e*f^2 + d*f^3)*x)*e^(d*x + c))*dilog(-e^(d*x + c)) + (3*d^2*f^3*x^2 + 3*d^2*e^2*f + 6*I*d*e*f^2 + (6*d^2*e*f^2 + 6*I*d*f^3)*x + (-3*I*d^2*f^3*x^2 - 3*I*d^2*e^2*f + 6*d*e*f^2 - 6*(I*d^2*e*f^2 - d*f^3)*x)*e^(3*d*x + 3*c) - (3*d^2*f^3*x^2 + 3*d^2*e^2*f + 6*I*d*e*f^2 + (6*d^2*e*f^2 + 6*I*d*f^3)*x)*e^(2*d*x + 2*c) + (3*I*d^2*f^3*x^2 + 3*I*d^2*e^2*f - 6*d*e*f^2 - 6*(-I*d^2*e*f^2 + d*f^3)*x)*e^(d*x + c))*dilog(e^(d*x + c)) - 4*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*e^(3*d*x + 3*c) + (2*I*d^3*f^3*x^3 + 6*I*d^3*e*f^2*x^2 + 6*I*d^3*e^2*f*x - 2*I*d^3*e^3 + 12*I*c*d^2*e^2*f - 12*I*c^2*d*e*f^2 + 4*I*c^3*f^3)*e^(2*d*x + 2*c) + 2*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x - d^3*e^3 + 6*c*d^2*e^2*f - 6*c^2*d*e*f^2 + 2*c^3*f^3)*e^(d*x + c) - (d^3*f^3*x^3 + d^3*e^3 - 3*I*d^2*e^2*f + (3*d^3*e*f^2 - 3*I*d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*I*d^2*e*f^2)*x - (I*d^3*f^3*x^3 + I*d^3*e^3 + 3*d^2*e^2*f - 3*(-I*d^3*e*f^2 - d^2*f^3)*x^2 + (3*I*d^3*e^2*f + 6*d^2*e*f^2)*x)*e^(3*d*x + 3*c) - (d^3*f^3*x^3 + d^3*e^3 - 3*I*d^2*e^2*f + (3*d^3*e*f^2 - 3*I*d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*I*d^2*e*f^2)*x)*e^(2*d*x + 2*c) - (-I*d^3*f^3*x^3 - I*d^3*e^3 - 3*d^2*e^2*f - 3*(I*d^3*e*f^2 + d^2*f^3)*x^2 + (-3*I*d^3*e^2*f - 6*d^2*e*f^2)*x)*e^(d*x + c))*log(e^(d*x + c) + 1) + (6*I*d^2*e^2*f - 12*I*c*d*e*f^2 + 6*I*c^2*f^3 + 6*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*e^(3*d*x + 3*c) + (-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 - 6*I*c^2*f^3)*e^(2*d*x + 2*c) - 6*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*e^(d*x + c))*log(e^(d*x + c) - I) + (d^3*e^3 - (3*c - 3*I)*d^2*e^2*f + 3*(c^2 - 2*I*c)*d*e*f^2 - (c^3 - 3*I*c^2)*f^3 + (-I*d^3*e^3 - 3*(-I*c - 1)*d^2*e^2*f + (-3*I*c^2 - 6*c)*d*e*f^2 + (I*c^3 + 3*c^2)*f^3)*e^(3*d*x + 3*c) - (d^3*e^3 - (3*c - 3*I)*d^2*e^2*f + 3*(c^2 - 2*I*c)*d*e*f^2 - (c^3 - 3*I*c^2)*f^3)*e^(2*d*x + 2*c) + (I*d^3*e^3 - 3*(I*c + 1)*d^2*e^2*f + (3*I*c^2 + 6*c)*d*e*f^2 + (-I*c^3 - 3*c^2)*f^3)*e^(d*x + c))*log(e^(d*x + c) - 1) + (6*I*d^2*f^3*x^2 + 12*I*d^2*e*f^2*x + 12*I*c*d*e*f^2 - 6*I*c^2*f^3 + 6*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*e^(3*d*x + 3*c) + (-6*I*d^2*f^3*x^2 - 12*I*d^2*e*f^2*x - 12*I*c*d*e*f^2 + 6*I*c^2*f^3)*e^(2*d*x + 2*c) - 6*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (d^3*f^3*x^3 + 3*c*d^2*e^2*f - 3*(c^2 - 2*I*c)*d*e*f^2 + (c^3 - 3*I*c^2)*f^3 + (3*d^3*e*f^2 + 3*I*d^2*f^3)*x^2 + 3*(d^3*e^2*f + 2*I*d^2*e*f^2)*x + (-I*d^3*f^3*x^3 - 3*I*c*d^2*e^2*f + (3*I*c^2 + 6*c)*d*e*f^2 + (-I*c^3 - 3*c^2)*f^3 - 3*(I*d^3*e*f^2 - d^2*f^3)*x^2 + (-3*I*d^3*e^2*f + 6*d^2*e*f^2)*x)*e^(3*d*x + 3*c) - (d^3*f^3*x^3 + 3*c*d^2*e^2*f - 3*(c^2 - 2*I*c)*d*e*f^2 + (c^3 - 3*I*c^2)*f^3 + (3*d^3*e*f^2 + 3*I*d^2*f^3)*x^2 + 3*(d^3*e^2*f + 2*I*d^2*e*f^2)*x)*e^(2*d*x + 2*c) + (I*d^3*f^3*x^3 + 3*I*c*d^2*e^2*f + (-3*I*c^2 - 6*c)*d*e*f^2 + (I*c^3 + 3*c^2)*f^3 - 3*(-I*d^3*e*f^2 + d^2*f^3)*x^2 + (3*I*d^3*e^2*f - 6*d^2*e*f^2)*x)*e^(d*x + c))*log(-e^(d*x + c) + 1) + (6*I*f^3*e^(3*d*x + 3*c) + 6*f^3*e^(2*d*x + 2*c) - 6*I*f^3*e^(d*x + c) - 6*f^3)*polylog(4, -e^(d*x + c)) + (-6*I*f^3*e^(3*d*x + 3*c) - 6*f^3*e^(2*d*x + 2*c) + 6*I*f^3*e^(d*x + c) + 6*f^3)*polylog(4, e^(d*x + c)) - (12*f^3*e^(3*d*x + 3*c) - 12*I*f^3*e^(2*d*x + 2*c) - 12*f^3*e^(d*x + c) + 12*I*f^3)*polylog(3, -I*e^(d*x + c)) + (6*d*f^3*x + 6*d*e*f^2 - 6*I*f^3 + (-6*I*d*f^3*x - 6*I*d*e*f^2 - 6*f^3)*e^(3*d*x + 3*c) - (6*d*f^3*x + 6*d*e*f^2 - 6*I*f^3)*e^(2*d*x + 2*c) + (6*I*d*f^3*x + 6*I*d*e*f^2 + 6*f^3)*e^(d*x + c))*polylog(3, -e^(d*x + c)) - (6*d*f^3*x + 6*d*e*f^2 + 6*I*f^3 - (6*I*d*f^3*x + 6*I*d*e*f^2 - 6*f^3)*e^(3*d*x + 3*c) - (6*d*f^3*x + 6*d*e*f^2 + 6*I*f^3)*e^(2*d*x + 2*c) - (-6*I*d*f^3*x - 6*I*d*e*f^2 + 6*f^3)*e^(d*x + c))*polylog(3, e^(d*x + c)))/(a*d^4*e^(3*d*x + 3*c) - I*a*d^4*e^(2*d*x + 2*c) - a*d^4*e^(d*x + c) + I*a*d^4)","C",0
212,1,1370,0,0.664235," ","integrate((f*x+e)^2*csch(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 i \, d^{2} e^{2} - 8 i \, c d e f + 4 i \, c^{2} f^{2} + {\left(4 \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} - 4 i \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} - 4 \, f^{2} e^{\left(d x + c\right)} + 4 i \, f^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) - {\left(2 \, d f^{2} x + 2 \, d e f - 2 i \, f^{2} - {\left(2 i \, d f^{2} x + 2 i \, d e f + 2 \, f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(2 \, d f^{2} x + 2 \, d e f - 2 i \, f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-2 i \, d f^{2} x - 2 i \, d e f - 2 \, f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-e^{\left(d x + c\right)}\right) + {\left(2 \, d f^{2} x + 2 \, d e f + 2 i \, f^{2} + {\left(-2 i \, d f^{2} x - 2 i \, d e f + 2 \, f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(2 \, d f^{2} x + 2 \, d e f + 2 i \, f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(2 i \, d f^{2} x + 2 i \, d e f - 2 \, f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(e^{\left(d x + c\right)}\right) - 4 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(2 i \, d^{2} f^{2} x^{2} + 4 i \, d^{2} e f x - 2 i \, d^{2} e^{2} + 8 i \, c d e f - 4 i \, c^{2} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x - d^{2} e^{2} + 4 \, c d e f - 2 \, c^{2} f^{2}\right)} e^{\left(d x + c\right)} - {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} - 2 i \, d e f + {\left(2 \, d^{2} e f - 2 i \, d f^{2}\right)} x - {\left(i \, d^{2} f^{2} x^{2} + i \, d^{2} e^{2} + 2 \, d e f - 2 \, {\left(-i \, d^{2} e f - d f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} - 2 i \, d e f + {\left(2 \, d^{2} e f - 2 i \, d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-i \, d^{2} f^{2} x^{2} - i \, d^{2} e^{2} - 2 \, d e f - 2 \, {\left(i \, d^{2} e f + d f^{2}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + 1\right) + {\left(4 i \, d e f - 4 i \, c f^{2} + 4 \, {\left(d e f - c f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-4 i \, d e f + 4 i \, c f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 4 \, {\left(d e f - c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(d^{2} e^{2} - {\left(2 \, c - 2 i\right)} d e f + {\left(c^{2} - 2 i \, c\right)} f^{2} + {\left(-i \, d^{2} e^{2} - 2 \, {\left(-i \, c - 1\right)} d e f + {\left(-i \, c^{2} - 2 \, c\right)} f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d^{2} e^{2} - {\left(2 \, c - 2 i\right)} d e f + {\left(c^{2} - 2 i \, c\right)} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(i \, d^{2} e^{2} - 2 \, {\left(i \, c + 1\right)} d e f + {\left(i \, c^{2} + 2 \, c\right)} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - 1\right) + {\left(4 i \, d f^{2} x + 4 i \, c f^{2} + 4 \, {\left(d f^{2} x + c f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-4 i \, d f^{2} x - 4 i \, c f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 4 \, {\left(d f^{2} x + c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(d^{2} f^{2} x^{2} + 2 \, c d e f - {\left(c^{2} - 2 i \, c\right)} f^{2} + {\left(2 \, d^{2} e f + 2 i \, d f^{2}\right)} x + {\left(-i \, d^{2} f^{2} x^{2} - 2 i \, c d e f + {\left(i \, c^{2} + 2 \, c\right)} f^{2} - 2 \, {\left(i \, d^{2} e f - d f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d^{2} f^{2} x^{2} + 2 \, c d e f - {\left(c^{2} - 2 i \, c\right)} f^{2} + {\left(2 \, d^{2} e f + 2 i \, d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(i \, d^{2} f^{2} x^{2} + 2 i \, c d e f + {\left(-i \, c^{2} - 2 \, c\right)} f^{2} - 2 \, {\left(-i \, d^{2} e f + d f^{2}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(-e^{\left(d x + c\right)} + 1\right) + {\left(-2 i \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} - 2 \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} + 2 i \, f^{2} e^{\left(d x + c\right)} + 2 \, f^{2}\right)} {\rm polylog}\left(3, -e^{\left(d x + c\right)}\right) + {\left(2 i \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} + 2 \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} - 2 i \, f^{2} e^{\left(d x + c\right)} - 2 \, f^{2}\right)} {\rm polylog}\left(3, e^{\left(d x + c\right)}\right)}{a d^{3} e^{\left(3 \, d x + 3 \, c\right)} - i \, a d^{3} e^{\left(2 \, d x + 2 \, c\right)} - a d^{3} e^{\left(d x + c\right)} + i \, a d^{3}}"," ",0,"(4*I*d^2*e^2 - 8*I*c*d*e*f + 4*I*c^2*f^2 + (4*f^2*e^(3*d*x + 3*c) - 4*I*f^2*e^(2*d*x + 2*c) - 4*f^2*e^(d*x + c) + 4*I*f^2)*dilog(-I*e^(d*x + c)) - (2*d*f^2*x + 2*d*e*f - 2*I*f^2 - (2*I*d*f^2*x + 2*I*d*e*f + 2*f^2)*e^(3*d*x + 3*c) - (2*d*f^2*x + 2*d*e*f - 2*I*f^2)*e^(2*d*x + 2*c) - (-2*I*d*f^2*x - 2*I*d*e*f - 2*f^2)*e^(d*x + c))*dilog(-e^(d*x + c)) + (2*d*f^2*x + 2*d*e*f + 2*I*f^2 + (-2*I*d*f^2*x - 2*I*d*e*f + 2*f^2)*e^(3*d*x + 3*c) - (2*d*f^2*x + 2*d*e*f + 2*I*f^2)*e^(2*d*x + 2*c) + (2*I*d*f^2*x + 2*I*d*e*f - 2*f^2)*e^(d*x + c))*dilog(e^(d*x + c)) - 4*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(3*d*x + 3*c) + (2*I*d^2*f^2*x^2 + 4*I*d^2*e*f*x - 2*I*d^2*e^2 + 8*I*c*d*e*f - 4*I*c^2*f^2)*e^(2*d*x + 2*c) + 2*(d^2*f^2*x^2 + 2*d^2*e*f*x - d^2*e^2 + 4*c*d*e*f - 2*c^2*f^2)*e^(d*x + c) - (d^2*f^2*x^2 + d^2*e^2 - 2*I*d*e*f + (2*d^2*e*f - 2*I*d*f^2)*x - (I*d^2*f^2*x^2 + I*d^2*e^2 + 2*d*e*f - 2*(-I*d^2*e*f - d*f^2)*x)*e^(3*d*x + 3*c) - (d^2*f^2*x^2 + d^2*e^2 - 2*I*d*e*f + (2*d^2*e*f - 2*I*d*f^2)*x)*e^(2*d*x + 2*c) - (-I*d^2*f^2*x^2 - I*d^2*e^2 - 2*d*e*f - 2*(I*d^2*e*f + d*f^2)*x)*e^(d*x + c))*log(e^(d*x + c) + 1) + (4*I*d*e*f - 4*I*c*f^2 + 4*(d*e*f - c*f^2)*e^(3*d*x + 3*c) + (-4*I*d*e*f + 4*I*c*f^2)*e^(2*d*x + 2*c) - 4*(d*e*f - c*f^2)*e^(d*x + c))*log(e^(d*x + c) - I) + (d^2*e^2 - (2*c - 2*I)*d*e*f + (c^2 - 2*I*c)*f^2 + (-I*d^2*e^2 - 2*(-I*c - 1)*d*e*f + (-I*c^2 - 2*c)*f^2)*e^(3*d*x + 3*c) - (d^2*e^2 - (2*c - 2*I)*d*e*f + (c^2 - 2*I*c)*f^2)*e^(2*d*x + 2*c) + (I*d^2*e^2 - 2*(I*c + 1)*d*e*f + (I*c^2 + 2*c)*f^2)*e^(d*x + c))*log(e^(d*x + c) - 1) + (4*I*d*f^2*x + 4*I*c*f^2 + 4*(d*f^2*x + c*f^2)*e^(3*d*x + 3*c) + (-4*I*d*f^2*x - 4*I*c*f^2)*e^(2*d*x + 2*c) - 4*(d*f^2*x + c*f^2)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (d^2*f^2*x^2 + 2*c*d*e*f - (c^2 - 2*I*c)*f^2 + (2*d^2*e*f + 2*I*d*f^2)*x + (-I*d^2*f^2*x^2 - 2*I*c*d*e*f + (I*c^2 + 2*c)*f^2 - 2*(I*d^2*e*f - d*f^2)*x)*e^(3*d*x + 3*c) - (d^2*f^2*x^2 + 2*c*d*e*f - (c^2 - 2*I*c)*f^2 + (2*d^2*e*f + 2*I*d*f^2)*x)*e^(2*d*x + 2*c) + (I*d^2*f^2*x^2 + 2*I*c*d*e*f + (-I*c^2 - 2*c)*f^2 - 2*(-I*d^2*e*f + d*f^2)*x)*e^(d*x + c))*log(-e^(d*x + c) + 1) + (-2*I*f^2*e^(3*d*x + 3*c) - 2*f^2*e^(2*d*x + 2*c) + 2*I*f^2*e^(d*x + c) + 2*f^2)*polylog(3, -e^(d*x + c)) + (2*I*f^2*e^(3*d*x + 3*c) + 2*f^2*e^(2*d*x + 2*c) - 2*I*f^2*e^(d*x + c) - 2*f^2)*polylog(3, e^(d*x + c)))/(a*d^3*e^(3*d*x + 3*c) - I*a*d^3*e^(2*d*x + 2*c) - a*d^3*e^(d*x + c) + I*a*d^3)","C",0
213,1,505,0,0.550853," ","integrate((f*x+e)*csch(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 i \, d e - 2 i \, c f + {\left(i \, f e^{\left(3 \, d x + 3 \, c\right)} + f e^{\left(2 \, d x + 2 \, c\right)} - i \, f e^{\left(d x + c\right)} - f\right)} {\rm Li}_2\left(-e^{\left(d x + c\right)}\right) + {\left(-i \, f e^{\left(3 \, d x + 3 \, c\right)} - f e^{\left(2 \, d x + 2 \, c\right)} + i \, f e^{\left(d x + c\right)} + f\right)} {\rm Li}_2\left(e^{\left(d x + c\right)}\right) - 2 \, {\left(2 \, d f x + c f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(2 i \, d f x - 2 i \, d e + 2 i \, c f\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d f x - d e + c f\right)} e^{\left(d x + c\right)} - {\left(d f x + d e - {\left(i \, d f x + i \, d e + f\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d f x + d e - i \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-i \, d f x - i \, d e - f\right)} e^{\left(d x + c\right)} - i \, f\right)} \log\left(e^{\left(d x + c\right)} + 1\right) + {\left(2 \, f e^{\left(3 \, d x + 3 \, c\right)} - 2 i \, f e^{\left(2 \, d x + 2 \, c\right)} - 2 \, f e^{\left(d x + c\right)} + 2 i \, f\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(d e - {\left(c - i\right)} f + {\left(-i \, d e + {\left(i \, c + 1\right)} f\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d e - {\left(c - i\right)} f\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(i \, d e + {\left(-i \, c - 1\right)} f\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - 1\right) + {\left(d f x + c f + {\left(-i \, d f x - i \, c f\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(d f x + c f\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(i \, d f x + i \, c f\right)} e^{\left(d x + c\right)}\right)} \log\left(-e^{\left(d x + c\right)} + 1\right)}{a d^{2} e^{\left(3 \, d x + 3 \, c\right)} - i \, a d^{2} e^{\left(2 \, d x + 2 \, c\right)} - a d^{2} e^{\left(d x + c\right)} + i \, a d^{2}}"," ",0,"(4*I*d*e - 2*I*c*f + (I*f*e^(3*d*x + 3*c) + f*e^(2*d*x + 2*c) - I*f*e^(d*x + c) - f)*dilog(-e^(d*x + c)) + (-I*f*e^(3*d*x + 3*c) - f*e^(2*d*x + 2*c) + I*f*e^(d*x + c) + f)*dilog(e^(d*x + c)) - 2*(2*d*f*x + c*f)*e^(3*d*x + 3*c) + (2*I*d*f*x - 2*I*d*e + 2*I*c*f)*e^(2*d*x + 2*c) + 2*(d*f*x - d*e + c*f)*e^(d*x + c) - (d*f*x + d*e - (I*d*f*x + I*d*e + f)*e^(3*d*x + 3*c) - (d*f*x + d*e - I*f)*e^(2*d*x + 2*c) - (-I*d*f*x - I*d*e - f)*e^(d*x + c) - I*f)*log(e^(d*x + c) + 1) + (2*f*e^(3*d*x + 3*c) - 2*I*f*e^(2*d*x + 2*c) - 2*f*e^(d*x + c) + 2*I*f)*log(e^(d*x + c) - I) + (d*e - (c - I)*f + (-I*d*e + (I*c + 1)*f)*e^(3*d*x + 3*c) - (d*e - (c - I)*f)*e^(2*d*x + 2*c) + (I*d*e + (-I*c - 1)*f)*e^(d*x + c))*log(e^(d*x + c) - 1) + (d*f*x + c*f + (-I*d*f*x - I*c*f)*e^(3*d*x + 3*c) - (d*f*x + c*f)*e^(2*d*x + 2*c) + (I*d*f*x + I*c*f)*e^(d*x + c))*log(-e^(d*x + c) + 1))/(a*d^2*e^(3*d*x + 3*c) - I*a*d^2*e^(2*d*x + 2*c) - a*d^2*e^(d*x + c) + I*a*d^2)","B",0
214,1,146,0,0.564791," ","integrate(csch(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(i \, e^{\left(3 \, d x + 3 \, c\right)} + e^{\left(2 \, d x + 2 \, c\right)} - i \, e^{\left(d x + c\right)} - 1\right)} \log\left(e^{\left(d x + c\right)} + 1\right) + {\left(-i \, e^{\left(3 \, d x + 3 \, c\right)} - e^{\left(2 \, d x + 2 \, c\right)} + i \, e^{\left(d x + c\right)} + 1\right)} \log\left(e^{\left(d x + c\right)} - 1\right) - 2 i \, e^{\left(2 \, d x + 2 \, c\right)} - 2 \, e^{\left(d x + c\right)} + 4 i}{a d e^{\left(3 \, d x + 3 \, c\right)} - i \, a d e^{\left(2 \, d x + 2 \, c\right)} - a d e^{\left(d x + c\right)} + i \, a d}"," ",0,"((I*e^(3*d*x + 3*c) + e^(2*d*x + 2*c) - I*e^(d*x + c) - 1)*log(e^(d*x + c) + 1) + (-I*e^(3*d*x + 3*c) - e^(2*d*x + 2*c) + I*e^(d*x + c) + 1)*log(e^(d*x + c) - 1) - 2*I*e^(2*d*x + 2*c) - 2*e^(d*x + c) + 4*I)/(a*d*e^(3*d*x + 3*c) - I*a*d*e^(2*d*x + 2*c) - a*d*e^(d*x + c) + I*a*d)","B",0
215,0,0,0,0.535576," ","integrate(csch(d*x+c)^2/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(i \, a d f x + i \, a d e + {\left(a d f x + a d e\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-i \, a d f x - i \, a d e\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a d f x + a d e\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{{\left(-2 i \, d f x - 2 i \, d e - 2 i \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(d f x + d e + f\right)} e^{\left(d x + c\right)} + 4 i \, f}{i \, a d f^{2} x^{2} + 2 i \, a d e f x + i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}}, x\right) - 2 i \, e^{\left(2 \, d x + 2 \, c\right)} - 2 \, e^{\left(d x + c\right)} + 4 i}{i \, a d f x + i \, a d e + {\left(a d f x + a d e\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-i \, a d f x - i \, a d e\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a d f x + a d e\right)} e^{\left(d x + c\right)}}"," ",0,"((I*a*d*f*x + I*a*d*e + (a*d*f*x + a*d*e)*e^(3*d*x + 3*c) + (-I*a*d*f*x - I*a*d*e)*e^(2*d*x + 2*c) - (a*d*f*x + a*d*e)*e^(d*x + c))*integral(((-2*I*d*f*x - 2*I*d*e - 2*I*f)*e^(2*d*x + 2*c) - 2*(d*f*x + d*e + f)*e^(d*x + c) + 4*I*f)/(I*a*d*f^2*x^2 + 2*I*a*d*e*f*x + I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(3*d*x + 3*c) + (-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2)*e^(2*d*x + 2*c) - (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c)), x) - 2*I*e^(2*d*x + 2*c) - 2*e^(d*x + c) + 4*I)/(I*a*d*f*x + I*a*d*e + (a*d*f*x + a*d*e)*e^(3*d*x + 3*c) + (-I*a*d*f*x - I*a*d*e)*e^(2*d*x + 2*c) - (a*d*f*x + a*d*e)*e^(d*x + c))","F",0
216,0,0,0,0.663685," ","integrate(csch(d*x+c)^2/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(i \, a d f^{2} x^{2} + 2 i \, a d e f x + i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{{\left(-2 i \, d f x - 2 i \, d e - 4 i \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(d f x + d e + 2 \, f\right)} e^{\left(d x + c\right)} + 8 i \, f}{i \, a d f^{3} x^{3} + 3 i \, a d e f^{2} x^{2} + 3 i \, a d e^{2} f x + i \, a d e^{3} + {\left(a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-i \, a d f^{3} x^{3} - 3 i \, a d e f^{2} x^{2} - 3 i \, a d e^{2} f x - i \, a d e^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a d f^{3} x^{3} + 3 \, a d e f^{2} x^{2} + 3 \, a d e^{2} f x + a d e^{3}\right)} e^{\left(d x + c\right)}}, x\right) - 2 i \, e^{\left(2 \, d x + 2 \, c\right)} - 2 \, e^{\left(d x + c\right)} + 4 i}{i \, a d f^{2} x^{2} + 2 i \, a d e f x + i \, a d e^{2} + {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-i \, a d f^{2} x^{2} - 2 i \, a d e f x - i \, a d e^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a d f^{2} x^{2} + 2 \, a d e f x + a d e^{2}\right)} e^{\left(d x + c\right)}}"," ",0,"((I*a*d*f^2*x^2 + 2*I*a*d*e*f*x + I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(3*d*x + 3*c) + (-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2)*e^(2*d*x + 2*c) - (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c))*integral(((-2*I*d*f*x - 2*I*d*e - 4*I*f)*e^(2*d*x + 2*c) - 2*(d*f*x + d*e + 2*f)*e^(d*x + c) + 8*I*f)/(I*a*d*f^3*x^3 + 3*I*a*d*e*f^2*x^2 + 3*I*a*d*e^2*f*x + I*a*d*e^3 + (a*d*f^3*x^3 + 3*a*d*e*f^2*x^2 + 3*a*d*e^2*f*x + a*d*e^3)*e^(3*d*x + 3*c) + (-I*a*d*f^3*x^3 - 3*I*a*d*e*f^2*x^2 - 3*I*a*d*e^2*f*x - I*a*d*e^3)*e^(2*d*x + 2*c) - (a*d*f^3*x^3 + 3*a*d*e*f^2*x^2 + 3*a*d*e^2*f*x + a*d*e^3)*e^(d*x + c)), x) - 2*I*e^(2*d*x + 2*c) - 2*e^(d*x + c) + 4*I)/(I*a*d*f^2*x^2 + 2*I*a*d*e*f*x + I*a*d*e^2 + (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(3*d*x + 3*c) + (-I*a*d*f^2*x^2 - 2*I*a*d*e*f*x - I*a*d*e^2)*e^(2*d*x + 2*c) - (a*d*f^2*x^2 + 2*a*d*e*f*x + a*d*e^2)*e^(d*x + c))","F",0
217,1,4289,0,0.706635," ","integrate((f*x+e)^3*csch(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, d^{3} e^{3} - 24 \, c d^{2} e^{2} f + 24 \, c^{2} d e f^{2} - 8 \, c^{3} f^{3} + {\left(24 \, d f^{3} x + 24 \, d e f^{2} - {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + 24 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(48 i \, d f^{3} x + 48 i \, d e f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} - 48 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-24 i \, d f^{3} x - 24 i \, d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) - {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f - 12 \, d e f^{2} + 6 i \, f^{3} - 6 \, {\left(3 i \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x + {\left(9 \, d^{2} f^{3} x^{2} + 9 \, d^{2} e^{2} f - 12 i \, d e f^{2} - 6 \, f^{3} + {\left(18 \, d^{2} e f^{2} - 12 i \, d f^{3}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-9 i \, d^{2} f^{3} x^{2} - 9 i \, d^{2} e^{2} f - 12 \, d e f^{2} + 6 i \, f^{3} - 6 \, {\left(3 i \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(18 \, d^{2} f^{3} x^{2} + 18 \, d^{2} e^{2} f - 24 i \, d e f^{2} - 12 \, f^{3} + {\left(36 \, d^{2} e f^{2} - 24 i \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(18 i \, d^{2} f^{3} x^{2} + 18 i \, d^{2} e^{2} f + 24 \, d e f^{2} - 12 i \, f^{3} - 12 \, {\left(-3 i \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(9 \, d^{2} f^{3} x^{2} + 9 \, d^{2} e^{2} f - 12 i \, d e f^{2} - 6 \, f^{3} + {\left(18 \, d^{2} e f^{2} - 12 i \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-e^{\left(d x + c\right)}\right) - {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f - 12 \, d e f^{2} - 6 i \, f^{3} - 6 \, {\left(-3 i \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x - {\left(9 \, d^{2} f^{3} x^{2} + 9 \, d^{2} e^{2} f + 12 i \, d e f^{2} - 6 \, f^{3} + {\left(18 \, d^{2} e f^{2} + 12 i \, d f^{3}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(9 i \, d^{2} f^{3} x^{2} + 9 i \, d^{2} e^{2} f - 12 \, d e f^{2} - 6 i \, f^{3} - 6 \, {\left(-3 i \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(18 \, d^{2} f^{3} x^{2} + 18 \, d^{2} e^{2} f + 24 i \, d e f^{2} - 12 \, f^{3} + {\left(36 \, d^{2} e f^{2} + 24 i \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-18 i \, d^{2} f^{3} x^{2} - 18 i \, d^{2} e^{2} f + 24 \, d e f^{2} + 12 i \, f^{3} - 12 \, {\left(3 i \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(9 \, d^{2} f^{3} x^{2} + 9 \, d^{2} e^{2} f + 12 i \, d e f^{2} - 6 \, f^{3} + {\left(18 \, d^{2} e f^{2} + 12 i \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(e^{\left(d x + c\right)}\right) - {\left(8 i \, d^{3} f^{3} x^{3} + 24 i \, d^{3} e f^{2} x^{2} + 24 i \, d^{3} e^{2} f x + 24 i \, c d^{2} e^{2} f - 24 i \, c^{2} d e f^{2} + 8 i \, c^{3} f^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} - 2 \, {\left(d^{3} f^{3} x^{3} - 3 \, d^{3} e^{3} + 3 \, {\left(4 \, c - 1\right)} d^{2} e^{2} f - 12 \, c^{2} d e f^{2} + 4 \, c^{3} f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-10 i \, d^{3} f^{3} x^{3} + 6 i \, d^{3} e^{3} + {\left(-48 i \, c + 6 i\right)} d^{2} e^{2} f + 48 i \, c^{2} d e f^{2} - 16 i \, c^{3} f^{3} + {\left(-30 i \, d^{3} e f^{2} + 6 i \, d^{2} f^{3}\right)} x^{2} + {\left(-30 i \, d^{3} e^{2} f + 12 i \, d^{2} e f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + 2 \, {\left(3 \, d^{3} f^{3} x^{3} - 5 \, d^{3} e^{3} + 3 \, {\left(8 \, c - 1\right)} d^{2} e^{2} f - 24 \, c^{2} d e f^{2} + 8 \, c^{3} f^{3} + 3 \, {\left(3 \, d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(3 \, d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(6 i \, d^{3} f^{3} x^{3} - 2 i \, d^{3} e^{3} + {\left(24 i \, c - 6 i\right)} d^{2} e^{2} f - 24 i \, c^{2} d e f^{2} + 8 i \, c^{3} f^{3} + {\left(18 i \, d^{3} e f^{2} - 6 i \, d^{2} f^{3}\right)} x^{2} + {\left(18 i \, d^{3} e^{2} f - 12 i \, d^{2} e f^{2}\right)} x\right)} e^{\left(d x + c\right)} - {\left(-3 i \, d^{3} f^{3} x^{3} - 3 i \, d^{3} e^{3} - 6 \, d^{2} e^{2} f + 6 i \, d e f^{2} - 3 \, {\left(3 i \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(-9 i \, d^{3} e^{2} f - 12 \, d^{2} e f^{2} + 6 i \, d f^{3}\right)} x + {\left(3 \, d^{3} f^{3} x^{3} + 3 \, d^{3} e^{3} - 6 i \, d^{2} e^{2} f - 6 \, d e f^{2} + {\left(9 \, d^{3} e f^{2} - 6 i \, d^{2} f^{3}\right)} x^{2} + 3 \, {\left(3 \, d^{3} e^{2} f - 4 i \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-3 i \, d^{3} f^{3} x^{3} - 3 i \, d^{3} e^{3} - 6 \, d^{2} e^{2} f + 6 i \, d e f^{2} - 3 \, {\left(3 i \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(-9 i \, d^{3} e^{2} f - 12 \, d^{2} e f^{2} + 6 i \, d f^{3}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(6 \, d^{3} f^{3} x^{3} + 6 \, d^{3} e^{3} - 12 i \, d^{2} e^{2} f - 12 \, d e f^{2} + {\left(18 \, d^{3} e f^{2} - 12 i \, d^{2} f^{3}\right)} x^{2} + 6 \, {\left(3 \, d^{3} e^{2} f - 4 i \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(6 i \, d^{3} f^{3} x^{3} + 6 i \, d^{3} e^{3} + 12 \, d^{2} e^{2} f - 12 i \, d e f^{2} - 6 \, {\left(-3 i \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(18 i \, d^{3} e^{2} f + 24 \, d^{2} e f^{2} - 12 i \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(3 \, d^{3} f^{3} x^{3} + 3 \, d^{3} e^{3} - 6 i \, d^{2} e^{2} f - 6 \, d e f^{2} + {\left(9 \, d^{3} e f^{2} - 6 i \, d^{2} f^{3}\right)} x^{2} + 3 \, {\left(3 \, d^{3} e^{2} f - 4 i \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + 1\right) + {\left(12 \, d^{2} e^{2} f - 24 \, c d e f^{2} + 12 \, c^{2} f^{3} - {\left(-12 i \, d^{2} e^{2} f + 24 i \, c d e f^{2} - 12 i \, c^{2} f^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + 12 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(24 i \, d^{2} e^{2} f - 48 i \, c d e f^{2} + 24 i \, c^{2} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} - 24 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-12 i \, d^{2} e^{2} f + 24 i \, c d e f^{2} - 12 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) - {\left(3 i \, d^{3} e^{3} - 3 \, {\left(3 i \, c + 2\right)} d^{2} e^{2} f + {\left(9 i \, c^{2} + 12 \, c - 6 i\right)} d e f^{2} + {\left(-3 i \, c^{3} - 6 \, c^{2} + 6 i \, c\right)} f^{3} - {\left(3 \, d^{3} e^{3} - {\left(9 \, c - 6 i\right)} d^{2} e^{2} f + 3 \, {\left(3 \, c^{2} - 4 i \, c - 2\right)} d e f^{2} - {\left(3 \, c^{3} - 6 i \, c^{2} - 6 \, c\right)} f^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(3 i \, d^{3} e^{3} - 3 \, {\left(3 i \, c + 2\right)} d^{2} e^{2} f + {\left(9 i \, c^{2} + 12 \, c - 6 i\right)} d e f^{2} + {\left(-3 i \, c^{3} - 6 \, c^{2} + 6 i \, c\right)} f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(6 \, d^{3} e^{3} - {\left(18 \, c - 12 i\right)} d^{2} e^{2} f + 6 \, {\left(3 \, c^{2} - 4 i \, c - 2\right)} d e f^{2} - {\left(6 \, c^{3} - 12 i \, c^{2} - 12 \, c\right)} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-6 i \, d^{3} e^{3} - 6 \, {\left(-3 i \, c - 2\right)} d^{2} e^{2} f + {\left(-18 i \, c^{2} - 24 \, c + 12 i\right)} d e f^{2} + {\left(6 i \, c^{3} + 12 \, c^{2} - 12 i \, c\right)} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(3 \, d^{3} e^{3} - {\left(9 \, c - 6 i\right)} d^{2} e^{2} f + 3 \, {\left(3 \, c^{2} - 4 i \, c - 2\right)} d e f^{2} - {\left(3 \, c^{3} - 6 i \, c^{2} - 6 \, c\right)} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - 1\right) + {\left(12 \, d^{2} f^{3} x^{2} + 24 \, d^{2} e f^{2} x + 24 \, c d e f^{2} - 12 \, c^{2} f^{3} - {\left(-12 i \, d^{2} f^{3} x^{2} - 24 i \, d^{2} e f^{2} x - 24 i \, c d e f^{2} + 12 i \, c^{2} f^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + 12 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(24 i \, d^{2} f^{3} x^{2} + 48 i \, d^{2} e f^{2} x + 48 i \, c d e f^{2} - 24 i \, c^{2} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} - 24 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-12 i \, d^{2} f^{3} x^{2} - 24 i \, d^{2} e f^{2} x - 24 i \, c d e f^{2} + 12 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) - {\left(3 i \, d^{3} f^{3} x^{3} + 9 i \, c d^{2} e^{2} f + {\left(-9 i \, c^{2} - 12 \, c\right)} d e f^{2} + {\left(3 i \, c^{3} + 6 \, c^{2} - 6 i \, c\right)} f^{3} - 3 \, {\left(-3 i \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(9 i \, d^{3} e^{2} f - 12 \, d^{2} e f^{2} - 6 i \, d f^{3}\right)} x - {\left(3 \, d^{3} f^{3} x^{3} + 9 \, c d^{2} e^{2} f - 3 \, {\left(3 \, c^{2} - 4 i \, c\right)} d e f^{2} + {\left(3 \, c^{3} - 6 i \, c^{2} - 6 \, c\right)} f^{3} + {\left(9 \, d^{3} e f^{2} + 6 i \, d^{2} f^{3}\right)} x^{2} + 3 \, {\left(3 \, d^{3} e^{2} f + 4 i \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(3 i \, d^{3} f^{3} x^{3} + 9 i \, c d^{2} e^{2} f + {\left(-9 i \, c^{2} - 12 \, c\right)} d e f^{2} + {\left(3 i \, c^{3} + 6 \, c^{2} - 6 i \, c\right)} f^{3} - 3 \, {\left(-3 i \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(9 i \, d^{3} e^{2} f - 12 \, d^{2} e f^{2} - 6 i \, d f^{3}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(6 \, d^{3} f^{3} x^{3} + 18 \, c d^{2} e^{2} f - 6 \, {\left(3 \, c^{2} - 4 i \, c\right)} d e f^{2} + {\left(6 \, c^{3} - 12 i \, c^{2} - 12 \, c\right)} f^{3} + {\left(18 \, d^{3} e f^{2} + 12 i \, d^{2} f^{3}\right)} x^{2} + 6 \, {\left(3 \, d^{3} e^{2} f + 4 i \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-6 i \, d^{3} f^{3} x^{3} - 18 i \, c d^{2} e^{2} f + {\left(18 i \, c^{2} + 24 \, c\right)} d e f^{2} + {\left(-6 i \, c^{3} - 12 \, c^{2} + 12 i \, c\right)} f^{3} - 6 \, {\left(3 i \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(-18 i \, d^{3} e^{2} f + 24 \, d^{2} e f^{2} + 12 i \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(3 \, d^{3} f^{3} x^{3} + 9 \, c d^{2} e^{2} f - 3 \, {\left(3 \, c^{2} - 4 i \, c\right)} d e f^{2} + {\left(3 \, c^{3} - 6 i \, c^{2} - 6 \, c\right)} f^{3} + {\left(9 \, d^{3} e f^{2} + 6 i \, d^{2} f^{3}\right)} x^{2} + 3 \, {\left(3 \, d^{3} e^{2} f + 4 i \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(-e^{\left(d x + c\right)} + 1\right) - {\left(18 \, f^{3} e^{\left(5 \, d x + 5 \, c\right)} - 18 i \, f^{3} e^{\left(4 \, d x + 4 \, c\right)} - 36 \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} + 36 i \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} + 18 \, f^{3} e^{\left(d x + c\right)} - 18 i \, f^{3}\right)} {\rm polylog}\left(4, -e^{\left(d x + c\right)}\right) + {\left(18 \, f^{3} e^{\left(5 \, d x + 5 \, c\right)} - 18 i \, f^{3} e^{\left(4 \, d x + 4 \, c\right)} - 36 \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} + 36 i \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} + 18 \, f^{3} e^{\left(d x + c\right)} - 18 i \, f^{3}\right)} {\rm polylog}\left(4, e^{\left(d x + c\right)}\right) - {\left(24 i \, f^{3} e^{\left(5 \, d x + 5 \, c\right)} + 24 \, f^{3} e^{\left(4 \, d x + 4 \, c\right)} - 48 i \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} - 48 \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} + 24 i \, f^{3} e^{\left(d x + c\right)} + 24 \, f^{3}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right) - {\left(18 i \, d f^{3} x + 18 i \, d e f^{2} + 12 \, f^{3} - {\left(18 \, d f^{3} x + 18 \, d e f^{2} - 12 i \, f^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(18 i \, d f^{3} x + 18 i \, d e f^{2} + 12 \, f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(36 \, d f^{3} x + 36 \, d e f^{2} - 24 i \, f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-36 i \, d f^{3} x - 36 i \, d e f^{2} - 24 \, f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(18 \, d f^{3} x + 18 \, d e f^{2} - 12 i \, f^{3}\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, -e^{\left(d x + c\right)}\right) - {\left(-18 i \, d f^{3} x - 18 i \, d e f^{2} + 12 \, f^{3} + {\left(18 \, d f^{3} x + 18 \, d e f^{2} + 12 i \, f^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-18 i \, d f^{3} x - 18 i \, d e f^{2} + 12 \, f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(36 \, d f^{3} x + 36 \, d e f^{2} + 24 i \, f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(36 i \, d f^{3} x + 36 i \, d e f^{2} - 24 \, f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(18 \, d f^{3} x + 18 \, d e f^{2} + 12 i \, f^{3}\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, e^{\left(d x + c\right)}\right)}{2 \, a d^{4} e^{\left(5 \, d x + 5 \, c\right)} - 2 i \, a d^{4} e^{\left(4 \, d x + 4 \, c\right)} - 4 \, a d^{4} e^{\left(3 \, d x + 3 \, c\right)} + 4 i \, a d^{4} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a d^{4} e^{\left(d x + c\right)} - 2 i \, a d^{4}}"," ",0,"-(8*d^3*e^3 - 24*c*d^2*e^2*f + 24*c^2*d*e*f^2 - 8*c^3*f^3 + (24*d*f^3*x + 24*d*e*f^2 - (-24*I*d*f^3*x - 24*I*d*e*f^2)*e^(5*d*x + 5*c) + 24*(d*f^3*x + d*e*f^2)*e^(4*d*x + 4*c) - (48*I*d*f^3*x + 48*I*d*e*f^2)*e^(3*d*x + 3*c) - 48*(d*f^3*x + d*e*f^2)*e^(2*d*x + 2*c) - (-24*I*d*f^3*x - 24*I*d*e*f^2)*e^(d*x + c))*dilog(-I*e^(d*x + c)) - (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f - 12*d*e*f^2 + 6*I*f^3 - 6*(3*I*d^2*e*f^2 + 2*d*f^3)*x + (9*d^2*f^3*x^2 + 9*d^2*e^2*f - 12*I*d*e*f^2 - 6*f^3 + (18*d^2*e*f^2 - 12*I*d*f^3)*x)*e^(5*d*x + 5*c) + (-9*I*d^2*f^3*x^2 - 9*I*d^2*e^2*f - 12*d*e*f^2 + 6*I*f^3 - 6*(3*I*d^2*e*f^2 + 2*d*f^3)*x)*e^(4*d*x + 4*c) - (18*d^2*f^3*x^2 + 18*d^2*e^2*f - 24*I*d*e*f^2 - 12*f^3 + (36*d^2*e*f^2 - 24*I*d*f^3)*x)*e^(3*d*x + 3*c) + (18*I*d^2*f^3*x^2 + 18*I*d^2*e^2*f + 24*d*e*f^2 - 12*I*f^3 - 12*(-3*I*d^2*e*f^2 - 2*d*f^3)*x)*e^(2*d*x + 2*c) + (9*d^2*f^3*x^2 + 9*d^2*e^2*f - 12*I*d*e*f^2 - 6*f^3 + (18*d^2*e*f^2 - 12*I*d*f^3)*x)*e^(d*x + c))*dilog(-e^(d*x + c)) - (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f - 12*d*e*f^2 - 6*I*f^3 - 6*(-3*I*d^2*e*f^2 + 2*d*f^3)*x - (9*d^2*f^3*x^2 + 9*d^2*e^2*f + 12*I*d*e*f^2 - 6*f^3 + (18*d^2*e*f^2 + 12*I*d*f^3)*x)*e^(5*d*x + 5*c) + (9*I*d^2*f^3*x^2 + 9*I*d^2*e^2*f - 12*d*e*f^2 - 6*I*f^3 - 6*(-3*I*d^2*e*f^2 + 2*d*f^3)*x)*e^(4*d*x + 4*c) + (18*d^2*f^3*x^2 + 18*d^2*e^2*f + 24*I*d*e*f^2 - 12*f^3 + (36*d^2*e*f^2 + 24*I*d*f^3)*x)*e^(3*d*x + 3*c) + (-18*I*d^2*f^3*x^2 - 18*I*d^2*e^2*f + 24*d*e*f^2 + 12*I*f^3 - 12*(3*I*d^2*e*f^2 - 2*d*f^3)*x)*e^(2*d*x + 2*c) - (9*d^2*f^3*x^2 + 9*d^2*e^2*f + 12*I*d*e*f^2 - 6*f^3 + (18*d^2*e*f^2 + 12*I*d*f^3)*x)*e^(d*x + c))*dilog(e^(d*x + c)) - (8*I*d^3*f^3*x^3 + 24*I*d^3*e*f^2*x^2 + 24*I*d^3*e^2*f*x + 24*I*c*d^2*e^2*f - 24*I*c^2*d*e*f^2 + 8*I*c^3*f^3)*e^(5*d*x + 5*c) - 2*(d^3*f^3*x^3 - 3*d^3*e^3 + 3*(4*c - 1)*d^2*e^2*f - 12*c^2*d*e*f^2 + 4*c^3*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x)*e^(4*d*x + 4*c) - (-10*I*d^3*f^3*x^3 + 6*I*d^3*e^3 + (-48*I*c + 6*I)*d^2*e^2*f + 48*I*c^2*d*e*f^2 - 16*I*c^3*f^3 + (-30*I*d^3*e*f^2 + 6*I*d^2*f^3)*x^2 + (-30*I*d^3*e^2*f + 12*I*d^2*e*f^2)*x)*e^(3*d*x + 3*c) + 2*(3*d^3*f^3*x^3 - 5*d^3*e^3 + 3*(8*c - 1)*d^2*e^2*f - 24*c^2*d*e*f^2 + 8*c^3*f^3 + 3*(3*d^3*e*f^2 - d^2*f^3)*x^2 + 3*(3*d^3*e^2*f - 2*d^2*e*f^2)*x)*e^(2*d*x + 2*c) - (6*I*d^3*f^3*x^3 - 2*I*d^3*e^3 + (24*I*c - 6*I)*d^2*e^2*f - 24*I*c^2*d*e*f^2 + 8*I*c^3*f^3 + (18*I*d^3*e*f^2 - 6*I*d^2*f^3)*x^2 + (18*I*d^3*e^2*f - 12*I*d^2*e*f^2)*x)*e^(d*x + c) - (-3*I*d^3*f^3*x^3 - 3*I*d^3*e^3 - 6*d^2*e^2*f + 6*I*d*e*f^2 - 3*(3*I*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (-9*I*d^3*e^2*f - 12*d^2*e*f^2 + 6*I*d*f^3)*x + (3*d^3*f^3*x^3 + 3*d^3*e^3 - 6*I*d^2*e^2*f - 6*d*e*f^2 + (9*d^3*e*f^2 - 6*I*d^2*f^3)*x^2 + 3*(3*d^3*e^2*f - 4*I*d^2*e*f^2 - 2*d*f^3)*x)*e^(5*d*x + 5*c) + (-3*I*d^3*f^3*x^3 - 3*I*d^3*e^3 - 6*d^2*e^2*f + 6*I*d*e*f^2 - 3*(3*I*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (-9*I*d^3*e^2*f - 12*d^2*e*f^2 + 6*I*d*f^3)*x)*e^(4*d*x + 4*c) - (6*d^3*f^3*x^3 + 6*d^3*e^3 - 12*I*d^2*e^2*f - 12*d*e*f^2 + (18*d^3*e*f^2 - 12*I*d^2*f^3)*x^2 + 6*(3*d^3*e^2*f - 4*I*d^2*e*f^2 - 2*d*f^3)*x)*e^(3*d*x + 3*c) + (6*I*d^3*f^3*x^3 + 6*I*d^3*e^3 + 12*d^2*e^2*f - 12*I*d*e*f^2 - 6*(-3*I*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (18*I*d^3*e^2*f + 24*d^2*e*f^2 - 12*I*d*f^3)*x)*e^(2*d*x + 2*c) + (3*d^3*f^3*x^3 + 3*d^3*e^3 - 6*I*d^2*e^2*f - 6*d*e*f^2 + (9*d^3*e*f^2 - 6*I*d^2*f^3)*x^2 + 3*(3*d^3*e^2*f - 4*I*d^2*e*f^2 - 2*d*f^3)*x)*e^(d*x + c))*log(e^(d*x + c) + 1) + (12*d^2*e^2*f - 24*c*d*e*f^2 + 12*c^2*f^3 - (-12*I*d^2*e^2*f + 24*I*c*d*e*f^2 - 12*I*c^2*f^3)*e^(5*d*x + 5*c) + 12*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*e^(4*d*x + 4*c) - (24*I*d^2*e^2*f - 48*I*c*d*e*f^2 + 24*I*c^2*f^3)*e^(3*d*x + 3*c) - 24*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*e^(2*d*x + 2*c) - (-12*I*d^2*e^2*f + 24*I*c*d*e*f^2 - 12*I*c^2*f^3)*e^(d*x + c))*log(e^(d*x + c) - I) - (3*I*d^3*e^3 - 3*(3*I*c + 2)*d^2*e^2*f + (9*I*c^2 + 12*c - 6*I)*d*e*f^2 + (-3*I*c^3 - 6*c^2 + 6*I*c)*f^3 - (3*d^3*e^3 - (9*c - 6*I)*d^2*e^2*f + 3*(3*c^2 - 4*I*c - 2)*d*e*f^2 - (3*c^3 - 6*I*c^2 - 6*c)*f^3)*e^(5*d*x + 5*c) + (3*I*d^3*e^3 - 3*(3*I*c + 2)*d^2*e^2*f + (9*I*c^2 + 12*c - 6*I)*d*e*f^2 + (-3*I*c^3 - 6*c^2 + 6*I*c)*f^3)*e^(4*d*x + 4*c) + (6*d^3*e^3 - (18*c - 12*I)*d^2*e^2*f + 6*(3*c^2 - 4*I*c - 2)*d*e*f^2 - (6*c^3 - 12*I*c^2 - 12*c)*f^3)*e^(3*d*x + 3*c) + (-6*I*d^3*e^3 - 6*(-3*I*c - 2)*d^2*e^2*f + (-18*I*c^2 - 24*c + 12*I)*d*e*f^2 + (6*I*c^3 + 12*c^2 - 12*I*c)*f^3)*e^(2*d*x + 2*c) - (3*d^3*e^3 - (9*c - 6*I)*d^2*e^2*f + 3*(3*c^2 - 4*I*c - 2)*d*e*f^2 - (3*c^3 - 6*I*c^2 - 6*c)*f^3)*e^(d*x + c))*log(e^(d*x + c) - 1) + (12*d^2*f^3*x^2 + 24*d^2*e*f^2*x + 24*c*d*e*f^2 - 12*c^2*f^3 - (-12*I*d^2*f^3*x^2 - 24*I*d^2*e*f^2*x - 24*I*c*d*e*f^2 + 12*I*c^2*f^3)*e^(5*d*x + 5*c) + 12*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*e^(4*d*x + 4*c) - (24*I*d^2*f^3*x^2 + 48*I*d^2*e*f^2*x + 48*I*c*d*e*f^2 - 24*I*c^2*f^3)*e^(3*d*x + 3*c) - 24*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*e^(2*d*x + 2*c) - (-12*I*d^2*f^3*x^2 - 24*I*d^2*e*f^2*x - 24*I*c*d*e*f^2 + 12*I*c^2*f^3)*e^(d*x + c))*log(I*e^(d*x + c) + 1) - (3*I*d^3*f^3*x^3 + 9*I*c*d^2*e^2*f + (-9*I*c^2 - 12*c)*d*e*f^2 + (3*I*c^3 + 6*c^2 - 6*I*c)*f^3 - 3*(-3*I*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (9*I*d^3*e^2*f - 12*d^2*e*f^2 - 6*I*d*f^3)*x - (3*d^3*f^3*x^3 + 9*c*d^2*e^2*f - 3*(3*c^2 - 4*I*c)*d*e*f^2 + (3*c^3 - 6*I*c^2 - 6*c)*f^3 + (9*d^3*e*f^2 + 6*I*d^2*f^3)*x^2 + 3*(3*d^3*e^2*f + 4*I*d^2*e*f^2 - 2*d*f^3)*x)*e^(5*d*x + 5*c) + (3*I*d^3*f^3*x^3 + 9*I*c*d^2*e^2*f + (-9*I*c^2 - 12*c)*d*e*f^2 + (3*I*c^3 + 6*c^2 - 6*I*c)*f^3 - 3*(-3*I*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (9*I*d^3*e^2*f - 12*d^2*e*f^2 - 6*I*d*f^3)*x)*e^(4*d*x + 4*c) + (6*d^3*f^3*x^3 + 18*c*d^2*e^2*f - 6*(3*c^2 - 4*I*c)*d*e*f^2 + (6*c^3 - 12*I*c^2 - 12*c)*f^3 + (18*d^3*e*f^2 + 12*I*d^2*f^3)*x^2 + 6*(3*d^3*e^2*f + 4*I*d^2*e*f^2 - 2*d*f^3)*x)*e^(3*d*x + 3*c) + (-6*I*d^3*f^3*x^3 - 18*I*c*d^2*e^2*f + (18*I*c^2 + 24*c)*d*e*f^2 + (-6*I*c^3 - 12*c^2 + 12*I*c)*f^3 - 6*(3*I*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (-18*I*d^3*e^2*f + 24*d^2*e*f^2 + 12*I*d*f^3)*x)*e^(2*d*x + 2*c) - (3*d^3*f^3*x^3 + 9*c*d^2*e^2*f - 3*(3*c^2 - 4*I*c)*d*e*f^2 + (3*c^3 - 6*I*c^2 - 6*c)*f^3 + (9*d^3*e*f^2 + 6*I*d^2*f^3)*x^2 + 3*(3*d^3*e^2*f + 4*I*d^2*e*f^2 - 2*d*f^3)*x)*e^(d*x + c))*log(-e^(d*x + c) + 1) - (18*f^3*e^(5*d*x + 5*c) - 18*I*f^3*e^(4*d*x + 4*c) - 36*f^3*e^(3*d*x + 3*c) + 36*I*f^3*e^(2*d*x + 2*c) + 18*f^3*e^(d*x + c) - 18*I*f^3)*polylog(4, -e^(d*x + c)) + (18*f^3*e^(5*d*x + 5*c) - 18*I*f^3*e^(4*d*x + 4*c) - 36*f^3*e^(3*d*x + 3*c) + 36*I*f^3*e^(2*d*x + 2*c) + 18*f^3*e^(d*x + c) - 18*I*f^3)*polylog(4, e^(d*x + c)) - (24*I*f^3*e^(5*d*x + 5*c) + 24*f^3*e^(4*d*x + 4*c) - 48*I*f^3*e^(3*d*x + 3*c) - 48*f^3*e^(2*d*x + 2*c) + 24*I*f^3*e^(d*x + c) + 24*f^3)*polylog(3, -I*e^(d*x + c)) - (18*I*d*f^3*x + 18*I*d*e*f^2 + 12*f^3 - (18*d*f^3*x + 18*d*e*f^2 - 12*I*f^3)*e^(5*d*x + 5*c) + (18*I*d*f^3*x + 18*I*d*e*f^2 + 12*f^3)*e^(4*d*x + 4*c) + (36*d*f^3*x + 36*d*e*f^2 - 24*I*f^3)*e^(3*d*x + 3*c) + (-36*I*d*f^3*x - 36*I*d*e*f^2 - 24*f^3)*e^(2*d*x + 2*c) - (18*d*f^3*x + 18*d*e*f^2 - 12*I*f^3)*e^(d*x + c))*polylog(3, -e^(d*x + c)) - (-18*I*d*f^3*x - 18*I*d*e*f^2 + 12*f^3 + (18*d*f^3*x + 18*d*e*f^2 + 12*I*f^3)*e^(5*d*x + 5*c) + (-18*I*d*f^3*x - 18*I*d*e*f^2 + 12*f^3)*e^(4*d*x + 4*c) - (36*d*f^3*x + 36*d*e*f^2 + 24*I*f^3)*e^(3*d*x + 3*c) + (36*I*d*f^3*x + 36*I*d*e*f^2 - 24*f^3)*e^(2*d*x + 2*c) + (18*d*f^3*x + 18*d*e*f^2 + 12*I*f^3)*e^(d*x + c))*polylog(3, e^(d*x + c)))/(2*a*d^4*e^(5*d*x + 5*c) - 2*I*a*d^4*e^(4*d*x + 4*c) - 4*a*d^4*e^(3*d*x + 3*c) + 4*I*a*d^4*e^(2*d*x + 2*c) + 2*a*d^4*e^(d*x + c) - 2*I*a*d^4)","C",0
218,1,2213,0,0.533737," ","integrate((f*x+e)^2*csch(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, d^{2} e^{2} - 16 \, c d e f + 8 \, c^{2} f^{2} - {\left(-8 i \, f^{2} e^{\left(5 \, d x + 5 \, c\right)} - 8 \, f^{2} e^{\left(4 \, d x + 4 \, c\right)} + 16 i \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} + 16 \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} - 8 i \, f^{2} e^{\left(d x + c\right)} - 8 \, f^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) - {\left(-6 i \, d f^{2} x - 6 i \, d e f - 4 \, f^{2} + {\left(6 \, d f^{2} x + 6 \, d e f - 4 i \, f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-6 i \, d f^{2} x - 6 i \, d e f - 4 \, f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(12 \, d f^{2} x + 12 \, d e f - 8 i \, f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(12 i \, d f^{2} x + 12 i \, d e f + 8 \, f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(6 \, d f^{2} x + 6 \, d e f - 4 i \, f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-e^{\left(d x + c\right)}\right) - {\left(6 i \, d f^{2} x + 6 i \, d e f - 4 \, f^{2} - {\left(6 \, d f^{2} x + 6 \, d e f + 4 i \, f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(6 i \, d f^{2} x + 6 i \, d e f - 4 \, f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(12 \, d f^{2} x + 12 \, d e f + 8 i \, f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-12 i \, d f^{2} x - 12 i \, d e f + 8 \, f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(6 \, d f^{2} x + 6 \, d e f + 4 i \, f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(e^{\left(d x + c\right)}\right) - {\left(8 i \, d^{2} f^{2} x^{2} + 16 i \, d^{2} e f x + 16 i \, c d e f - 8 i \, c^{2} f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} - 2 \, {\left(d^{2} f^{2} x^{2} - 3 \, d^{2} e^{2} + 2 \, {\left(4 \, c - 1\right)} d e f - 4 \, c^{2} f^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-10 i \, d^{2} f^{2} x^{2} + 6 i \, d^{2} e^{2} + {\left(-32 i \, c + 4 i\right)} d e f + 16 i \, c^{2} f^{2} + {\left(-20 i \, d^{2} e f + 4 i \, d f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + 2 \, {\left(3 \, d^{2} f^{2} x^{2} - 5 \, d^{2} e^{2} + 2 \, {\left(8 \, c - 1\right)} d e f - 8 \, c^{2} f^{2} + 2 \, {\left(3 \, d^{2} e f - d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(6 i \, d^{2} f^{2} x^{2} - 2 i \, d^{2} e^{2} + {\left(16 i \, c - 4 i\right)} d e f - 8 i \, c^{2} f^{2} + {\left(12 i \, d^{2} e f - 4 i \, d f^{2}\right)} x\right)} e^{\left(d x + c\right)} - {\left(-3 i \, d^{2} f^{2} x^{2} - 3 i \, d^{2} e^{2} - 4 \, d e f + 2 i \, f^{2} - 2 \, {\left(3 i \, d^{2} e f + 2 \, d f^{2}\right)} x + {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} - 4 i \, d e f - 2 \, f^{2} + {\left(6 \, d^{2} e f - 4 i \, d f^{2}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-3 i \, d^{2} f^{2} x^{2} - 3 i \, d^{2} e^{2} - 4 \, d e f + 2 i \, f^{2} - 2 \, {\left(3 i \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(6 \, d^{2} f^{2} x^{2} + 6 \, d^{2} e^{2} - 8 i \, d e f - 4 \, f^{2} + {\left(12 \, d^{2} e f - 8 i \, d f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(6 i \, d^{2} f^{2} x^{2} + 6 i \, d^{2} e^{2} + 8 \, d e f - 4 i \, f^{2} - 4 \, {\left(-3 i \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} - 4 i \, d e f - 2 \, f^{2} + {\left(6 \, d^{2} e f - 4 i \, d f^{2}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + 1\right) + {\left(8 \, d e f - 8 \, c f^{2} - {\left(-8 i \, d e f + 8 i \, c f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + 8 \, {\left(d e f - c f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(16 i \, d e f - 16 i \, c f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} - 16 \, {\left(d e f - c f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-8 i \, d e f + 8 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) - {\left(3 i \, d^{2} e^{2} - 2 \, {\left(3 i \, c + 2\right)} d e f + {\left(3 i \, c^{2} + 4 \, c - 2 i\right)} f^{2} - {\left(3 \, d^{2} e^{2} - {\left(6 \, c - 4 i\right)} d e f + {\left(3 \, c^{2} - 4 i \, c - 2\right)} f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(3 i \, d^{2} e^{2} - 2 \, {\left(3 i \, c + 2\right)} d e f + {\left(3 i \, c^{2} + 4 \, c - 2 i\right)} f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(6 \, d^{2} e^{2} - {\left(12 \, c - 8 i\right)} d e f + 2 \, {\left(3 \, c^{2} - 4 i \, c - 2\right)} f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-6 i \, d^{2} e^{2} - 4 \, {\left(-3 i \, c - 2\right)} d e f + {\left(-6 i \, c^{2} - 8 \, c + 4 i\right)} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(3 \, d^{2} e^{2} - {\left(6 \, c - 4 i\right)} d e f + {\left(3 \, c^{2} - 4 i \, c - 2\right)} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - 1\right) + {\left(8 \, d f^{2} x + 8 \, c f^{2} - {\left(-8 i \, d f^{2} x - 8 i \, c f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + 8 \, {\left(d f^{2} x + c f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(16 i \, d f^{2} x + 16 i \, c f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} - 16 \, {\left(d f^{2} x + c f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-8 i \, d f^{2} x - 8 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) - {\left(3 i \, d^{2} f^{2} x^{2} + 6 i \, c d e f + {\left(-3 i \, c^{2} - 4 \, c\right)} f^{2} - 2 \, {\left(-3 i \, d^{2} e f + 2 \, d f^{2}\right)} x - {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} - 4 i \, c\right)} f^{2} + {\left(6 \, d^{2} e f + 4 i \, d f^{2}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(3 i \, d^{2} f^{2} x^{2} + 6 i \, c d e f + {\left(-3 i \, c^{2} - 4 \, c\right)} f^{2} - 2 \, {\left(-3 i \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(6 \, d^{2} f^{2} x^{2} + 12 \, c d e f - 2 \, {\left(3 \, c^{2} - 4 i \, c\right)} f^{2} + {\left(12 \, d^{2} e f + 8 i \, d f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-6 i \, d^{2} f^{2} x^{2} - 12 i \, c d e f + {\left(6 i \, c^{2} + 8 \, c\right)} f^{2} - 4 \, {\left(3 i \, d^{2} e f - 2 \, d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(3 \, d^{2} f^{2} x^{2} + 6 \, c d e f - {\left(3 \, c^{2} - 4 i \, c\right)} f^{2} + {\left(6 \, d^{2} e f + 4 i \, d f^{2}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(-e^{\left(d x + c\right)} + 1\right) + {\left(6 \, f^{2} e^{\left(5 \, d x + 5 \, c\right)} - 6 i \, f^{2} e^{\left(4 \, d x + 4 \, c\right)} - 12 \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} + 12 i \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, f^{2} e^{\left(d x + c\right)} - 6 i \, f^{2}\right)} {\rm polylog}\left(3, -e^{\left(d x + c\right)}\right) - {\left(6 \, f^{2} e^{\left(5 \, d x + 5 \, c\right)} - 6 i \, f^{2} e^{\left(4 \, d x + 4 \, c\right)} - 12 \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} + 12 i \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, f^{2} e^{\left(d x + c\right)} - 6 i \, f^{2}\right)} {\rm polylog}\left(3, e^{\left(d x + c\right)}\right)}{2 \, a d^{3} e^{\left(5 \, d x + 5 \, c\right)} - 2 i \, a d^{3} e^{\left(4 \, d x + 4 \, c\right)} - 4 \, a d^{3} e^{\left(3 \, d x + 3 \, c\right)} + 4 i \, a d^{3} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a d^{3} e^{\left(d x + c\right)} - 2 i \, a d^{3}}"," ",0,"-(8*d^2*e^2 - 16*c*d*e*f + 8*c^2*f^2 - (-8*I*f^2*e^(5*d*x + 5*c) - 8*f^2*e^(4*d*x + 4*c) + 16*I*f^2*e^(3*d*x + 3*c) + 16*f^2*e^(2*d*x + 2*c) - 8*I*f^2*e^(d*x + c) - 8*f^2)*dilog(-I*e^(d*x + c)) - (-6*I*d*f^2*x - 6*I*d*e*f - 4*f^2 + (6*d*f^2*x + 6*d*e*f - 4*I*f^2)*e^(5*d*x + 5*c) + (-6*I*d*f^2*x - 6*I*d*e*f - 4*f^2)*e^(4*d*x + 4*c) - (12*d*f^2*x + 12*d*e*f - 8*I*f^2)*e^(3*d*x + 3*c) + (12*I*d*f^2*x + 12*I*d*e*f + 8*f^2)*e^(2*d*x + 2*c) + (6*d*f^2*x + 6*d*e*f - 4*I*f^2)*e^(d*x + c))*dilog(-e^(d*x + c)) - (6*I*d*f^2*x + 6*I*d*e*f - 4*f^2 - (6*d*f^2*x + 6*d*e*f + 4*I*f^2)*e^(5*d*x + 5*c) + (6*I*d*f^2*x + 6*I*d*e*f - 4*f^2)*e^(4*d*x + 4*c) + (12*d*f^2*x + 12*d*e*f + 8*I*f^2)*e^(3*d*x + 3*c) + (-12*I*d*f^2*x - 12*I*d*e*f + 8*f^2)*e^(2*d*x + 2*c) - (6*d*f^2*x + 6*d*e*f + 4*I*f^2)*e^(d*x + c))*dilog(e^(d*x + c)) - (8*I*d^2*f^2*x^2 + 16*I*d^2*e*f*x + 16*I*c*d*e*f - 8*I*c^2*f^2)*e^(5*d*x + 5*c) - 2*(d^2*f^2*x^2 - 3*d^2*e^2 + 2*(4*c - 1)*d*e*f - 4*c^2*f^2 + 2*(d^2*e*f - d*f^2)*x)*e^(4*d*x + 4*c) - (-10*I*d^2*f^2*x^2 + 6*I*d^2*e^2 + (-32*I*c + 4*I)*d*e*f + 16*I*c^2*f^2 + (-20*I*d^2*e*f + 4*I*d*f^2)*x)*e^(3*d*x + 3*c) + 2*(3*d^2*f^2*x^2 - 5*d^2*e^2 + 2*(8*c - 1)*d*e*f - 8*c^2*f^2 + 2*(3*d^2*e*f - d*f^2)*x)*e^(2*d*x + 2*c) - (6*I*d^2*f^2*x^2 - 2*I*d^2*e^2 + (16*I*c - 4*I)*d*e*f - 8*I*c^2*f^2 + (12*I*d^2*e*f - 4*I*d*f^2)*x)*e^(d*x + c) - (-3*I*d^2*f^2*x^2 - 3*I*d^2*e^2 - 4*d*e*f + 2*I*f^2 - 2*(3*I*d^2*e*f + 2*d*f^2)*x + (3*d^2*f^2*x^2 + 3*d^2*e^2 - 4*I*d*e*f - 2*f^2 + (6*d^2*e*f - 4*I*d*f^2)*x)*e^(5*d*x + 5*c) + (-3*I*d^2*f^2*x^2 - 3*I*d^2*e^2 - 4*d*e*f + 2*I*f^2 - 2*(3*I*d^2*e*f + 2*d*f^2)*x)*e^(4*d*x + 4*c) - (6*d^2*f^2*x^2 + 6*d^2*e^2 - 8*I*d*e*f - 4*f^2 + (12*d^2*e*f - 8*I*d*f^2)*x)*e^(3*d*x + 3*c) + (6*I*d^2*f^2*x^2 + 6*I*d^2*e^2 + 8*d*e*f - 4*I*f^2 - 4*(-3*I*d^2*e*f - 2*d*f^2)*x)*e^(2*d*x + 2*c) + (3*d^2*f^2*x^2 + 3*d^2*e^2 - 4*I*d*e*f - 2*f^2 + (6*d^2*e*f - 4*I*d*f^2)*x)*e^(d*x + c))*log(e^(d*x + c) + 1) + (8*d*e*f - 8*c*f^2 - (-8*I*d*e*f + 8*I*c*f^2)*e^(5*d*x + 5*c) + 8*(d*e*f - c*f^2)*e^(4*d*x + 4*c) - (16*I*d*e*f - 16*I*c*f^2)*e^(3*d*x + 3*c) - 16*(d*e*f - c*f^2)*e^(2*d*x + 2*c) - (-8*I*d*e*f + 8*I*c*f^2)*e^(d*x + c))*log(e^(d*x + c) - I) - (3*I*d^2*e^2 - 2*(3*I*c + 2)*d*e*f + (3*I*c^2 + 4*c - 2*I)*f^2 - (3*d^2*e^2 - (6*c - 4*I)*d*e*f + (3*c^2 - 4*I*c - 2)*f^2)*e^(5*d*x + 5*c) + (3*I*d^2*e^2 - 2*(3*I*c + 2)*d*e*f + (3*I*c^2 + 4*c - 2*I)*f^2)*e^(4*d*x + 4*c) + (6*d^2*e^2 - (12*c - 8*I)*d*e*f + 2*(3*c^2 - 4*I*c - 2)*f^2)*e^(3*d*x + 3*c) + (-6*I*d^2*e^2 - 4*(-3*I*c - 2)*d*e*f + (-6*I*c^2 - 8*c + 4*I)*f^2)*e^(2*d*x + 2*c) - (3*d^2*e^2 - (6*c - 4*I)*d*e*f + (3*c^2 - 4*I*c - 2)*f^2)*e^(d*x + c))*log(e^(d*x + c) - 1) + (8*d*f^2*x + 8*c*f^2 - (-8*I*d*f^2*x - 8*I*c*f^2)*e^(5*d*x + 5*c) + 8*(d*f^2*x + c*f^2)*e^(4*d*x + 4*c) - (16*I*d*f^2*x + 16*I*c*f^2)*e^(3*d*x + 3*c) - 16*(d*f^2*x + c*f^2)*e^(2*d*x + 2*c) - (-8*I*d*f^2*x - 8*I*c*f^2)*e^(d*x + c))*log(I*e^(d*x + c) + 1) - (3*I*d^2*f^2*x^2 + 6*I*c*d*e*f + (-3*I*c^2 - 4*c)*f^2 - 2*(-3*I*d^2*e*f + 2*d*f^2)*x - (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 - 4*I*c)*f^2 + (6*d^2*e*f + 4*I*d*f^2)*x)*e^(5*d*x + 5*c) + (3*I*d^2*f^2*x^2 + 6*I*c*d*e*f + (-3*I*c^2 - 4*c)*f^2 - 2*(-3*I*d^2*e*f + 2*d*f^2)*x)*e^(4*d*x + 4*c) + (6*d^2*f^2*x^2 + 12*c*d*e*f - 2*(3*c^2 - 4*I*c)*f^2 + (12*d^2*e*f + 8*I*d*f^2)*x)*e^(3*d*x + 3*c) + (-6*I*d^2*f^2*x^2 - 12*I*c*d*e*f + (6*I*c^2 + 8*c)*f^2 - 4*(3*I*d^2*e*f - 2*d*f^2)*x)*e^(2*d*x + 2*c) - (3*d^2*f^2*x^2 + 6*c*d*e*f - (3*c^2 - 4*I*c)*f^2 + (6*d^2*e*f + 4*I*d*f^2)*x)*e^(d*x + c))*log(-e^(d*x + c) + 1) + (6*f^2*e^(5*d*x + 5*c) - 6*I*f^2*e^(4*d*x + 4*c) - 12*f^2*e^(3*d*x + 3*c) + 12*I*f^2*e^(2*d*x + 2*c) + 6*f^2*e^(d*x + c) - 6*I*f^2)*polylog(3, -e^(d*x + c)) - (6*f^2*e^(5*d*x + 5*c) - 6*I*f^2*e^(4*d*x + 4*c) - 12*f^2*e^(3*d*x + 3*c) + 12*I*f^2*e^(2*d*x + 2*c) + 6*f^2*e^(d*x + c) - 6*I*f^2)*polylog(3, e^(d*x + c)))/(2*a*d^3*e^(5*d*x + 5*c) - 2*I*a*d^3*e^(4*d*x + 4*c) - 4*a*d^3*e^(3*d*x + 3*c) + 4*I*a*d^3*e^(2*d*x + 2*c) + 2*a*d^3*e^(d*x + c) - 2*I*a*d^3)","C",0
219,1,824,0,0.558551," ","integrate((f*x+e)*csch(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, d e - 4 \, c f - {\left(3 \, f e^{\left(5 \, d x + 5 \, c\right)} - 3 i \, f e^{\left(4 \, d x + 4 \, c\right)} - 6 \, f e^{\left(3 \, d x + 3 \, c\right)} + 6 i \, f e^{\left(2 \, d x + 2 \, c\right)} + 3 \, f e^{\left(d x + c\right)} - 3 i \, f\right)} {\rm Li}_2\left(-e^{\left(d x + c\right)}\right) + {\left(3 \, f e^{\left(5 \, d x + 5 \, c\right)} - 3 i \, f e^{\left(4 \, d x + 4 \, c\right)} - 6 \, f e^{\left(3 \, d x + 3 \, c\right)} + 6 i \, f e^{\left(2 \, d x + 2 \, c\right)} + 3 \, f e^{\left(d x + c\right)} - 3 i \, f\right)} {\rm Li}_2\left(e^{\left(d x + c\right)}\right) - {\left(8 i \, d f x + 4 i \, c f\right)} e^{\left(5 \, d x + 5 \, c\right)} - 2 \, {\left(d f x - 3 \, d e + {\left(2 \, c - 1\right)} f\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-10 i \, d f x + 6 i \, d e + {\left(-8 i \, c + 2 i\right)} f\right)} e^{\left(3 \, d x + 3 \, c\right)} + 2 \, {\left(3 \, d f x - 5 \, d e + {\left(4 \, c - 1\right)} f\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(6 i \, d f x - 2 i \, d e + {\left(4 i \, c - 2 i\right)} f\right)} e^{\left(d x + c\right)} - {\left(-3 i \, d f x - 3 i \, d e + {\left(3 \, d f x + 3 \, d e - 2 i \, f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-3 i \, d f x - 3 i \, d e - 2 \, f\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(6 \, d f x + 6 \, d e - 4 i \, f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(6 i \, d f x + 6 i \, d e + 4 \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(3 \, d f x + 3 \, d e - 2 i \, f\right)} e^{\left(d x + c\right)} - 2 \, f\right)} \log\left(e^{\left(d x + c\right)} + 1\right) - {\left(-4 i \, f e^{\left(5 \, d x + 5 \, c\right)} - 4 \, f e^{\left(4 \, d x + 4 \, c\right)} + 8 i \, f e^{\left(3 \, d x + 3 \, c\right)} + 8 \, f e^{\left(2 \, d x + 2 \, c\right)} - 4 i \, f e^{\left(d x + c\right)} - 4 \, f\right)} \log\left(e^{\left(d x + c\right)} - i\right) - {\left(3 i \, d e + {\left(-3 i \, c - 2\right)} f - {\left(3 \, d e - {\left(3 \, c - 2 i\right)} f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(3 i \, d e + {\left(-3 i \, c - 2\right)} f\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(6 \, d e - {\left(6 \, c - 4 i\right)} f\right)} e^{\left(3 \, d x + 3 \, c\right)} - 2 \, {\left(3 i \, d e + {\left(-3 i \, c - 2\right)} f\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(3 \, d e - {\left(3 \, c - 2 i\right)} f\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - 1\right) - {\left(3 i \, d f x + 3 i \, c f - 3 \, {\left(d f x + c f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(3 i \, d f x + 3 i \, c f\right)} e^{\left(4 \, d x + 4 \, c\right)} + 6 \, {\left(d f x + c f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-6 i \, d f x - 6 i \, c f\right)} e^{\left(2 \, d x + 2 \, c\right)} - 3 \, {\left(d f x + c f\right)} e^{\left(d x + c\right)}\right)} \log\left(-e^{\left(d x + c\right)} + 1\right)}{2 \, a d^{2} e^{\left(5 \, d x + 5 \, c\right)} - 2 i \, a d^{2} e^{\left(4 \, d x + 4 \, c\right)} - 4 \, a d^{2} e^{\left(3 \, d x + 3 \, c\right)} + 4 i \, a d^{2} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a d^{2} e^{\left(d x + c\right)} - 2 i \, a d^{2}}"," ",0,"-(8*d*e - 4*c*f - (3*f*e^(5*d*x + 5*c) - 3*I*f*e^(4*d*x + 4*c) - 6*f*e^(3*d*x + 3*c) + 6*I*f*e^(2*d*x + 2*c) + 3*f*e^(d*x + c) - 3*I*f)*dilog(-e^(d*x + c)) + (3*f*e^(5*d*x + 5*c) - 3*I*f*e^(4*d*x + 4*c) - 6*f*e^(3*d*x + 3*c) + 6*I*f*e^(2*d*x + 2*c) + 3*f*e^(d*x + c) - 3*I*f)*dilog(e^(d*x + c)) - (8*I*d*f*x + 4*I*c*f)*e^(5*d*x + 5*c) - 2*(d*f*x - 3*d*e + (2*c - 1)*f)*e^(4*d*x + 4*c) - (-10*I*d*f*x + 6*I*d*e + (-8*I*c + 2*I)*f)*e^(3*d*x + 3*c) + 2*(3*d*f*x - 5*d*e + (4*c - 1)*f)*e^(2*d*x + 2*c) - (6*I*d*f*x - 2*I*d*e + (4*I*c - 2*I)*f)*e^(d*x + c) - (-3*I*d*f*x - 3*I*d*e + (3*d*f*x + 3*d*e - 2*I*f)*e^(5*d*x + 5*c) + (-3*I*d*f*x - 3*I*d*e - 2*f)*e^(4*d*x + 4*c) - (6*d*f*x + 6*d*e - 4*I*f)*e^(3*d*x + 3*c) + (6*I*d*f*x + 6*I*d*e + 4*f)*e^(2*d*x + 2*c) + (3*d*f*x + 3*d*e - 2*I*f)*e^(d*x + c) - 2*f)*log(e^(d*x + c) + 1) - (-4*I*f*e^(5*d*x + 5*c) - 4*f*e^(4*d*x + 4*c) + 8*I*f*e^(3*d*x + 3*c) + 8*f*e^(2*d*x + 2*c) - 4*I*f*e^(d*x + c) - 4*f)*log(e^(d*x + c) - I) - (3*I*d*e + (-3*I*c - 2)*f - (3*d*e - (3*c - 2*I)*f)*e^(5*d*x + 5*c) + (3*I*d*e + (-3*I*c - 2)*f)*e^(4*d*x + 4*c) + (6*d*e - (6*c - 4*I)*f)*e^(3*d*x + 3*c) - 2*(3*I*d*e + (-3*I*c - 2)*f)*e^(2*d*x + 2*c) - (3*d*e - (3*c - 2*I)*f)*e^(d*x + c))*log(e^(d*x + c) - 1) - (3*I*d*f*x + 3*I*c*f - 3*(d*f*x + c*f)*e^(5*d*x + 5*c) + (3*I*d*f*x + 3*I*c*f)*e^(4*d*x + 4*c) + 6*(d*f*x + c*f)*e^(3*d*x + 3*c) + (-6*I*d*f*x - 6*I*c*f)*e^(2*d*x + 2*c) - 3*(d*f*x + c*f)*e^(d*x + c))*log(-e^(d*x + c) + 1))/(2*a*d^2*e^(5*d*x + 5*c) - 2*I*a*d^2*e^(4*d*x + 4*c) - 4*a*d^2*e^(3*d*x + 3*c) + 4*I*a*d^2*e^(2*d*x + 2*c) + 2*a*d^2*e^(d*x + c) - 2*I*a*d^2)","B",0
220,1,242,0,0.579363," ","integrate(csch(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, e^{\left(5 \, d x + 5 \, c\right)} - 3 i \, e^{\left(4 \, d x + 4 \, c\right)} - 6 \, e^{\left(3 \, d x + 3 \, c\right)} + 6 i \, e^{\left(2 \, d x + 2 \, c\right)} + 3 \, e^{\left(d x + c\right)} - 3 i\right)} \log\left(e^{\left(d x + c\right)} + 1\right) - {\left(3 \, e^{\left(5 \, d x + 5 \, c\right)} - 3 i \, e^{\left(4 \, d x + 4 \, c\right)} - 6 \, e^{\left(3 \, d x + 3 \, c\right)} + 6 i \, e^{\left(2 \, d x + 2 \, c\right)} + 3 \, e^{\left(d x + c\right)} - 3 i\right)} \log\left(e^{\left(d x + c\right)} - 1\right) - 6 \, e^{\left(4 \, d x + 4 \, c\right)} + 6 i \, e^{\left(3 \, d x + 3 \, c\right)} + 10 \, e^{\left(2 \, d x + 2 \, c\right)} - 2 i \, e^{\left(d x + c\right)} - 8}{2 \, a d e^{\left(5 \, d x + 5 \, c\right)} - 2 i \, a d e^{\left(4 \, d x + 4 \, c\right)} - 4 \, a d e^{\left(3 \, d x + 3 \, c\right)} + 4 i \, a d e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a d e^{\left(d x + c\right)} - 2 i \, a d}"," ",0,"((3*e^(5*d*x + 5*c) - 3*I*e^(4*d*x + 4*c) - 6*e^(3*d*x + 3*c) + 6*I*e^(2*d*x + 2*c) + 3*e^(d*x + c) - 3*I)*log(e^(d*x + c) + 1) - (3*e^(5*d*x + 5*c) - 3*I*e^(4*d*x + 4*c) - 6*e^(3*d*x + 3*c) + 6*I*e^(2*d*x + 2*c) + 3*e^(d*x + c) - 3*I)*log(e^(d*x + c) - 1) - 6*e^(4*d*x + 4*c) + 6*I*e^(3*d*x + 3*c) + 10*e^(2*d*x + 2*c) - 2*I*e^(d*x + c) - 8)/(2*a*d*e^(5*d*x + 5*c) - 2*I*a*d*e^(4*d*x + 4*c) - 4*a*d*e^(3*d*x + 3*c) + 4*I*a*d*e^(2*d*x + 2*c) + 2*a*d*e^(d*x + c) - 2*I*a*d)","B",0
221,0,0,0,0.901934," ","integrate(csch(d*x+c)^3/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, d f x + 4 \, d e + {\left(3 \, d f x + 3 \, d e - f\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(3 i \, d f x + 3 i \, d e - i \, f\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(5 \, d f x + 5 \, d e - f\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-i \, d f x - i \, d e + i \, f\right)} e^{\left(d x + c\right)} - {\left(-i \, a d^{2} f^{2} x^{2} - 2 i \, a d^{2} e f x - i \, a d^{2} e^{2} + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-i \, a d^{2} f^{2} x^{2} - 2 i \, a d^{2} e f x - i \, a d^{2} e^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(2 i \, a d^{2} f^{2} x^{2} + 4 i \, a d^{2} e f x + 2 i \, a d^{2} e^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{4 \, d f^{2} x + 4 \, d e f - {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 2 \, d e f - 2 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(3 i \, d^{2} f^{2} x^{2} + 3 i \, d^{2} e^{2} + 2 i \, d e f - 2 i \, f^{2} + {\left(6 i \, d^{2} e f + 2 i \, d f^{2}\right)} x\right)} e^{\left(d x + c\right)}}{i \, a d^{2} f^{3} x^{3} + 3 i \, a d^{2} e f^{2} x^{2} + 3 i \, a d^{2} e^{2} f x + i \, a d^{2} e^{3} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-i \, a d^{2} f^{3} x^{3} - 3 i \, a d^{2} e f^{2} x^{2} - 3 i \, a d^{2} e^{2} f x - i \, a d^{2} e^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(d x + c\right)}}, x\right)}{-i \, a d^{2} f^{2} x^{2} - 2 i \, a d^{2} e f x - i \, a d^{2} e^{2} + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-i \, a d^{2} f^{2} x^{2} - 2 i \, a d^{2} e f x - i \, a d^{2} e^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(2 i \, a d^{2} f^{2} x^{2} + 4 i \, a d^{2} e f x + 2 i \, a d^{2} e^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} e^{\left(d x + c\right)}}"," ",0,"-(4*d*f*x + 4*d*e + (3*d*f*x + 3*d*e - f)*e^(4*d*x + 4*c) - (3*I*d*f*x + 3*I*d*e - I*f)*e^(3*d*x + 3*c) - (5*d*f*x + 5*d*e - f)*e^(2*d*x + 2*c) - (-I*d*f*x - I*d*e + I*f)*e^(d*x + c) - (-I*a*d^2*f^2*x^2 - 2*I*a*d^2*e*f*x - I*a*d^2*e^2 + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*e^(5*d*x + 5*c) + (-I*a*d^2*f^2*x^2 - 2*I*a*d^2*e*f*x - I*a*d^2*e^2)*e^(4*d*x + 4*c) - 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*e^(3*d*x + 3*c) + (2*I*a*d^2*f^2*x^2 + 4*I*a*d^2*e*f*x + 2*I*a*d^2*e^2)*e^(2*d*x + 2*c) + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*e^(d*x + c))*integral((4*d*f^2*x + 4*d*e*f - (3*d^2*f^2*x^2 + 3*d^2*e^2 + 2*d*e*f - 2*f^2 + 2*(3*d^2*e*f + d*f^2)*x)*e^(2*d*x + 2*c) + (3*I*d^2*f^2*x^2 + 3*I*d^2*e^2 + 2*I*d*e*f - 2*I*f^2 + (6*I*d^2*e*f + 2*I*d*f^2)*x)*e^(d*x + c))/(I*a*d^2*f^3*x^3 + 3*I*a*d^2*e*f^2*x^2 + 3*I*a*d^2*e^2*f*x + I*a*d^2*e^3 + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(3*d*x + 3*c) + (-I*a*d^2*f^3*x^3 - 3*I*a*d^2*e*f^2*x^2 - 3*I*a*d^2*e^2*f*x - I*a*d^2*e^3)*e^(2*d*x + 2*c) - (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(d*x + c)), x))/(-I*a*d^2*f^2*x^2 - 2*I*a*d^2*e*f*x - I*a*d^2*e^2 + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*e^(5*d*x + 5*c) + (-I*a*d^2*f^2*x^2 - 2*I*a*d^2*e*f*x - I*a*d^2*e^2)*e^(4*d*x + 4*c) - 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*e^(3*d*x + 3*c) + (2*I*a*d^2*f^2*x^2 + 4*I*a*d^2*e*f*x + 2*I*a*d^2*e^2)*e^(2*d*x + 2*c) + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*e^(d*x + c))","F",0
222,0,0,0,0.729699," ","integrate(csch(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, d f x + 4 \, d e + {\left(3 \, d f x + 3 \, d e - 2 \, f\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(3 i \, d f x + 3 i \, d e - 2 i \, f\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(5 \, d f x + 5 \, d e - 2 \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-i \, d f x - i \, d e + 2 i \, f\right)} e^{\left(d x + c\right)} - {\left(-i \, a d^{2} f^{3} x^{3} - 3 i \, a d^{2} e f^{2} x^{2} - 3 i \, a d^{2} e^{2} f x - i \, a d^{2} e^{3} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-i \, a d^{2} f^{3} x^{3} - 3 i \, a d^{2} e f^{2} x^{2} - 3 i \, a d^{2} e^{2} f x - i \, a d^{2} e^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(2 i \, a d^{2} f^{3} x^{3} + 6 i \, a d^{2} e f^{2} x^{2} + 6 i \, a d^{2} e^{2} f x + 2 i \, a d^{2} e^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{8 \, d f^{2} x + 8 \, d e f - {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 4 \, d e f - 6 \, f^{2} + 2 \, {\left(3 \, d^{2} e f + 2 \, d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(3 i \, d^{2} f^{2} x^{2} + 3 i \, d^{2} e^{2} + 4 i \, d e f - 6 i \, f^{2} + {\left(6 i \, d^{2} e f + 4 i \, d f^{2}\right)} x\right)} e^{\left(d x + c\right)}}{i \, a d^{2} f^{4} x^{4} + 4 i \, a d^{2} e f^{3} x^{3} + 6 i \, a d^{2} e^{2} f^{2} x^{2} + 4 i \, a d^{2} e^{3} f x + i \, a d^{2} e^{4} + {\left(a d^{2} f^{4} x^{4} + 4 \, a d^{2} e f^{3} x^{3} + 6 \, a d^{2} e^{2} f^{2} x^{2} + 4 \, a d^{2} e^{3} f x + a d^{2} e^{4}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-i \, a d^{2} f^{4} x^{4} - 4 i \, a d^{2} e f^{3} x^{3} - 6 i \, a d^{2} e^{2} f^{2} x^{2} - 4 i \, a d^{2} e^{3} f x - i \, a d^{2} e^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a d^{2} f^{4} x^{4} + 4 \, a d^{2} e f^{3} x^{3} + 6 \, a d^{2} e^{2} f^{2} x^{2} + 4 \, a d^{2} e^{3} f x + a d^{2} e^{4}\right)} e^{\left(d x + c\right)}}, x\right)}{-i \, a d^{2} f^{3} x^{3} - 3 i \, a d^{2} e f^{2} x^{2} - 3 i \, a d^{2} e^{2} f x - i \, a d^{2} e^{3} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-i \, a d^{2} f^{3} x^{3} - 3 i \, a d^{2} e f^{2} x^{2} - 3 i \, a d^{2} e^{2} f x - i \, a d^{2} e^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 2 \, {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(2 i \, a d^{2} f^{3} x^{3} + 6 i \, a d^{2} e f^{2} x^{2} + 6 i \, a d^{2} e^{2} f x + 2 i \, a d^{2} e^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(d x + c\right)}}"," ",0,"-(4*d*f*x + 4*d*e + (3*d*f*x + 3*d*e - 2*f)*e^(4*d*x + 4*c) - (3*I*d*f*x + 3*I*d*e - 2*I*f)*e^(3*d*x + 3*c) - (5*d*f*x + 5*d*e - 2*f)*e^(2*d*x + 2*c) - (-I*d*f*x - I*d*e + 2*I*f)*e^(d*x + c) - (-I*a*d^2*f^3*x^3 - 3*I*a*d^2*e*f^2*x^2 - 3*I*a*d^2*e^2*f*x - I*a*d^2*e^3 + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(5*d*x + 5*c) + (-I*a*d^2*f^3*x^3 - 3*I*a*d^2*e*f^2*x^2 - 3*I*a*d^2*e^2*f*x - I*a*d^2*e^3)*e^(4*d*x + 4*c) - 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(3*d*x + 3*c) + (2*I*a*d^2*f^3*x^3 + 6*I*a*d^2*e*f^2*x^2 + 6*I*a*d^2*e^2*f*x + 2*I*a*d^2*e^3)*e^(2*d*x + 2*c) + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(d*x + c))*integral((8*d*f^2*x + 8*d*e*f - (3*d^2*f^2*x^2 + 3*d^2*e^2 + 4*d*e*f - 6*f^2 + 2*(3*d^2*e*f + 2*d*f^2)*x)*e^(2*d*x + 2*c) + (3*I*d^2*f^2*x^2 + 3*I*d^2*e^2 + 4*I*d*e*f - 6*I*f^2 + (6*I*d^2*e*f + 4*I*d*f^2)*x)*e^(d*x + c))/(I*a*d^2*f^4*x^4 + 4*I*a*d^2*e*f^3*x^3 + 6*I*a*d^2*e^2*f^2*x^2 + 4*I*a*d^2*e^3*f*x + I*a*d^2*e^4 + (a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3*f*x + a*d^2*e^4)*e^(3*d*x + 3*c) + (-I*a*d^2*f^4*x^4 - 4*I*a*d^2*e*f^3*x^3 - 6*I*a*d^2*e^2*f^2*x^2 - 4*I*a*d^2*e^3*f*x - I*a*d^2*e^4)*e^(2*d*x + 2*c) - (a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3*f*x + a*d^2*e^4)*e^(d*x + c)), x))/(-I*a*d^2*f^3*x^3 - 3*I*a*d^2*e*f^2*x^2 - 3*I*a*d^2*e^2*f*x - I*a*d^2*e^3 + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(5*d*x + 5*c) + (-I*a*d^2*f^3*x^3 - 3*I*a*d^2*e*f^2*x^2 - 3*I*a*d^2*e^2*f*x - I*a*d^2*e^3)*e^(4*d*x + 4*c) - 2*(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(3*d*x + 3*c) + (2*I*a*d^2*f^3*x^3 + 6*I*a*d^2*e*f^2*x^2 + 6*I*a*d^2*e^2*f*x + 2*I*a*d^2*e^3)*e^(2*d*x + 2*c) + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(d*x + c))","F",0
223,1,1112,0,1.006320," ","integrate((f*x+e)^3*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{2} + b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{2} + b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{2} + b^{2}\right)} d^{4} e^{3} x - 24 \, a b f^{3} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, a b f^{3} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + a b d^{2} e^{2} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + a b d^{2} e^{2} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 \, {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 24 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right)}{4 \, {\left(a^{2} b + b^{3}\right)} d^{4}}"," ",0,"1/4*((a^2 + b^2)*d^4*f^3*x^4 + 4*(a^2 + b^2)*d^4*e*f^2*x^3 + 6*(a^2 + b^2)*d^4*e^2*f*x^2 + 4*(a^2 + b^2)*d^4*e^3*x - 24*a*b*f^3*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*a*b*f^3*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + a*b*d^2*e^2*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + a*b*d^2*e^2*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 4*(a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*(a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 24*(a*b*d*f^3*x + a*b*d*e*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*(a*b*d*f^3*x + a*b*d*e*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b))/((a^2*b + b^3)*d^4)","C",0
224,1,782,0,0.535784," ","integrate((f*x+e)^2*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} x + 6 \, a b f^{2} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, a b f^{2} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(a b d f^{2} x + a b d e f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 6 \, {\left(a b d f^{2} x + a b d e f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 3 \, {\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 3 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right)}{3 \, {\left(a^{2} b + b^{3}\right)} d^{3}}"," ",0,"1/3*((a^2 + b^2)*d^3*f^2*x^3 + 3*(a^2 + b^2)*d^3*e*f*x^2 + 3*(a^2 + b^2)*d^3*e^2*x + 6*a*b*f^2*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*a*b*f^2*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(a*b*d*f^2*x + a*b*d*e*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 6*(a*b*d*f^2*x + a*b*d*e*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 3*(a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 3*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 3*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b))/((a^2*b + b^3)*d^3)","C",0
225,1,500,0,0.489241," ","integrate((f*x+e)*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e x - 2 \, a b f \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, a b f \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(a b d e - a b c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a b d e - a b c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a b d f x + a b c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a b d f x + a b c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right)}{2 \, {\left(a^{2} b + b^{3}\right)} d^{2}}"," ",0,"1/2*((a^2 + b^2)*d^2*f*x^2 + 2*(a^2 + b^2)*d^2*e*x - 2*a*b*f*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*a*b*f*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(a*b*d*e - a*b*c*f)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a*b*d*e - a*b*c*f)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a*b*d*f*x + a*b*c*f)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(a*b*d*f*x + a*b*c*f)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b))/((a^2*b + b^3)*d^2)","B",0
226,1,186,0,0.585833," ","integrate(sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} + b^{2}\right)} d x + \sqrt{a^{2} + b^{2}} a \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right)}{{\left(a^{2} b + b^{3}\right)} d}"," ",0,"((a^2 + b^2)*d*x + sqrt(a^2 + b^2)*a*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)))/((a^2*b + b^3)*d)","B",0
227,0,0,0,0.441384," ","integrate(sinh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sinh\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sinh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
228,1,2612,0,0.645817," ","integrate((f*x+e)^3*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 12 \, {\left(a^{2} b + b^{3}\right)} d e f^{2} + 12 \, {\left(a^{2} b + b^{3}\right)} f^{3} + 6 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b + b^{3}\right)} d e f^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b + b^{3}\right)} d e f^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 12 \, {\left({\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left({\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 4 \, {\left({\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 4 \, {\left({\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left({\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 24 \, {\left(a^{2} b f^{3} \cosh\left(d x + c\right) + a^{2} b f^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left(a^{2} b f^{3} \cosh\left(d x + c\right) + a^{2} b f^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left({\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d f^{3}\right)} x - {\left({\left(a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right) - {\left({\left(a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{3} x - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b + b^{3}\right)} d e f^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{4} \sinh\left(d x + c\right)\right)}}"," ",0,"1/4*(2*(a^2*b + b^3)*d^3*f^3*x^3 + 2*(a^2*b + b^3)*d^3*e^3 + 6*(a^2*b + b^3)*d^2*e^2*f + 12*(a^2*b + b^3)*d*e*f^2 + 12*(a^2*b + b^3)*f^3 + 6*((a^2*b + b^3)*d^3*e*f^2 + (a^2*b + b^3)*d^2*f^3)*x^2 + 2*((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 - 3*(a^2*b + b^3)*d^2*e^2*f + 6*(a^2*b + b^3)*d*e*f^2 - 6*(a^2*b + b^3)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^2*b + b^3)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^2*b + b^3)*d^2*e*f^2 + 2*(a^2*b + b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 2*((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 - 3*(a^2*b + b^3)*d^2*e^2*f + 6*(a^2*b + b^3)*d*e*f^2 - 6*(a^2*b + b^3)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^2*b + b^3)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^2*b + b^3)*d^2*e*f^2 + 2*(a^2*b + b^3)*d*f^3)*x)*sinh(d*x + c)^2 + 12*((a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c) + (a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 12*((a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c) + (a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 4*((a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c) + (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 4*((a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c) + (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 4*((a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c) + (a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*((a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c) + (a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 24*(a^2*b*f^3*cosh(d*x + c) + a^2*b*f^3*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*(a^2*b*f^3*cosh(d*x + c) + a^2*b*f^3*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*((a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c) + (a^2*b*d*f^3*x + a^2*b*d*e*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*((a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c) + (a^2*b*d*f^3*x + a^2*b*d*e*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*((a^2*b + b^3)*d^3*e^2*f + 2*(a^2*b + b^3)*d^2*e*f^2 + 2*(a^2*b + b^3)*d*f^3)*x - ((a^3 + a*b^2)*d^4*f^3*x^4 + 4*(a^3 + a*b^2)*d^4*e*f^2*x^3 + 6*(a^3 + a*b^2)*d^4*e^2*f*x^2 + 4*(a^3 + a*b^2)*d^4*e^3*x)*cosh(d*x + c) - ((a^3 + a*b^2)*d^4*f^3*x^4 + 4*(a^3 + a*b^2)*d^4*e*f^2*x^3 + 6*(a^3 + a*b^2)*d^4*e^2*f*x^2 + 4*(a^3 + a*b^2)*d^4*e^3*x - 4*((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 - 3*(a^2*b + b^3)*d^2*e^2*f + 6*(a^2*b + b^3)*d*e*f^2 - 6*(a^2*b + b^3)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^2*b + b^3)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^2*b + b^3)*d^2*e*f^2 + 2*(a^2*b + b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^2 + b^4)*d^4*cosh(d*x + c) + (a^2*b^2 + b^4)*d^4*sinh(d*x + c))","C",0
229,1,1689,0,0.612134," ","integrate((f*x+e)^2*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 6 \, {\left(a^{2} b + b^{3}\right)} d e f + 6 \, {\left(a^{2} b + b^{3}\right)} f^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left(a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left(a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 12 \, {\left({\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left({\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 6 \, {\left({\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 6 \, {\left({\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left({\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left(a^{2} b f^{2} \cosh\left(d x + c\right) + a^{2} b f^{2} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a^{2} b f^{2} \cosh\left(d x + c\right) + a^{2} b f^{2} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right) - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} x - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left(a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)\right)}}"," ",0,"1/6*(3*(a^2*b + b^3)*d^2*f^2*x^2 + 3*(a^2*b + b^3)*d^2*e^2 + 6*(a^2*b + b^3)*d*e*f + 6*(a^2*b + b^3)*f^2 + 3*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 - 2*(a^2*b + b^3)*d*e*f + 2*(a^2*b + b^3)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 3*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 - 2*(a^2*b + b^3)*d*e*f + 2*(a^2*b + b^3)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*sinh(d*x + c)^2 + 12*((a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c) + (a^2*b*d*f^2*x + a^2*b*d*e*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 12*((a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c) + (a^2*b*d*f^2*x + a^2*b*d*e*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 6*((a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c) + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 6*((a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c) + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 6*((a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c) + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 6*((a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c) + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 12*(a^2*b*f^2*cosh(d*x + c) + a^2*b*f^2*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(a^2*b*f^2*cosh(d*x + c) + a^2*b*f^2*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*((a^2*b + b^3)*d^2*e*f + (a^2*b + b^3)*d*f^2)*x - 2*((a^3 + a*b^2)*d^3*f^2*x^3 + 3*(a^3 + a*b^2)*d^3*e*f*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*x)*cosh(d*x + c) - 2*((a^3 + a*b^2)*d^3*f^2*x^3 + 3*(a^3 + a*b^2)*d^3*e*f*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*x - 3*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 - 2*(a^2*b + b^3)*d*e*f + 2*(a^2*b + b^3)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^2 + b^4)*d^3*cosh(d*x + c) + (a^2*b^2 + b^4)*d^3*sinh(d*x + c))","C",0
230,1,946,0,0.536965," ","integrate((f*x+e)*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left(a^{2} b + b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b f \cosh\left(d x + c\right) + a^{2} b f \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a^{2} b f \cosh\left(d x + c\right) + a^{2} b f \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left({\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d e - a^{2} b c f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d e - a^{2} b c f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d f x + a^{2} b c f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right) + {\left(a^{2} b d f x + a^{2} b c f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(a^{2} b + b^{3}\right)} f - {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e x\right)} \cosh\left(d x + c\right) - {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e x - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - (a^2*b + b^3)*f)*cosh(d*x + c)^2 + ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - (a^2*b + b^3)*f)*sinh(d*x + c)^2 + 2*(a^2*b*f*cosh(d*x + c) + a^2*b*f*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(a^2*b*f*cosh(d*x + c) + a^2*b*f*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*((a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c) + (a^2*b*d*e - a^2*b*c*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*((a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c) + (a^2*b*d*e - a^2*b*c*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*((a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c) + (a^2*b*d*f*x + a^2*b*c*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c) + (a^2*b*d*f*x + a^2*b*c*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (a^2*b + b^3)*f - ((a^3 + a*b^2)*d^2*f*x^2 + 2*(a^3 + a*b^2)*d^2*e*x)*cosh(d*x + c) - ((a^3 + a*b^2)*d^2*f*x^2 + 2*(a^3 + a*b^2)*d^2*e*x - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - (a^2*b + b^3)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^2 + b^4)*d^2*cosh(d*x + c) + (a^2*b^2 + b^4)*d^2*sinh(d*x + c))","B",0
231,1,331,0,0.764769," ","integrate(sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} + a b^{2}\right)} d x \cosh\left(d x + c\right) - a^{2} b - b^{3} - {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} \cosh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d x - {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*(a^3 + a*b^2)*d*x*cosh(d*x + c) - a^2*b - b^3 - (a^2*b + b^3)*cosh(d*x + c)^2 - (a^2*b + b^3)*sinh(d*x + c)^2 - 2*(a^2*cosh(d*x + c) + a^2*sinh(d*x + c))*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 2*((a^3 + a*b^2)*d*x - (a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^2 + b^4)*d*cosh(d*x + c) + (a^2*b^2 + b^4)*d*sinh(d*x + c))","B",0
232,0,0,0,0.607855," ","integrate(sinh(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sinh\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sinh(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
233,1,5191,0,0.708926," ","integrate((f*x+e)^3*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} - {\left(4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + 16 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{3} b + a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} - 6 \, {\left(a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, {\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e^{3} - 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 24 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} - 24 \, {\left(a^{3} b + a b^{3}\right)} f^{3} + 12 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 12 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{3}\right)} x - {\left(4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} - 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} f^{3} x^{4} + 8 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} e f^{2} x^{3} + 12 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} e^{2} f x^{2} + 8 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} e^{3} x + 3 \, {\left(4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 24 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{3} b + a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} - 6 \, {\left(a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 96 \, {\left({\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 96 \, {\left({\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 32 \, {\left({\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 32 \, {\left({\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 32 \, {\left({\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 32 \, {\left({\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 192 \, {\left(a^{3} b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f^{3} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 192 \, {\left(a^{3} b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f^{3} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 192 \, {\left({\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 192 \, {\left({\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x + 16 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{3} b + a b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) + 4 \, {\left(4 \, {\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e^{3} + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 24 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + 24 \, {\left(a^{3} b + a b^{3}\right)} f^{3} - {\left(4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 12 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{3} b + a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} - 6 \, {\left(a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{3}\right)} x - 2 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{32 \, {\left({\left(a^{2} b^{3} + b^{5}\right)} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{3} + b^{5}\right)} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} d^{4} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/32*(4*(a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(a^2*b^2 + b^4)*d^3*e^3 + 6*(a^2*b^2 + b^4)*d^2*e^2*f + 6*(a^2*b^2 + b^4)*d*e*f^2 - (4*(a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(a^2*b^2 + b^4)*d^3*e^3 - 6*(a^2*b^2 + b^4)*d^2*e^2*f + 6*(a^2*b^2 + b^4)*d*e*f^2 - 3*(a^2*b^2 + b^4)*f^3 + 6*(2*(a^2*b^2 + b^4)*d^3*e*f^2 - (a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(a^2*b^2 + b^4)*d^3*e^2*f - 2*(a^2*b^2 + b^4)*d^2*e*f^2 + (a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c)^4 - (4*(a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(a^2*b^2 + b^4)*d^3*e^3 - 6*(a^2*b^2 + b^4)*d^2*e^2*f + 6*(a^2*b^2 + b^4)*d*e*f^2 - 3*(a^2*b^2 + b^4)*f^3 + 6*(2*(a^2*b^2 + b^4)*d^3*e*f^2 - (a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(a^2*b^2 + b^4)*d^3*e^2*f - 2*(a^2*b^2 + b^4)*d^2*e*f^2 + (a^2*b^2 + b^4)*d*f^3)*x)*sinh(d*x + c)^4 + 3*(a^2*b^2 + b^4)*f^3 + 16*((a^3*b + a*b^3)*d^3*f^3*x^3 + (a^3*b + a*b^3)*d^3*e^3 - 3*(a^3*b + a*b^3)*d^2*e^2*f + 6*(a^3*b + a*b^3)*d*e*f^2 - 6*(a^3*b + a*b^3)*f^3 + 3*((a^3*b + a*b^3)*d^3*e*f^2 - (a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((a^3*b + a*b^3)*d^3*e^2*f - 2*(a^3*b + a*b^3)*d^2*e*f^2 + 2*(a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c)^3 + 4*(4*(a^3*b + a*b^3)*d^3*f^3*x^3 + 4*(a^3*b + a*b^3)*d^3*e^3 - 12*(a^3*b + a*b^3)*d^2*e^2*f + 24*(a^3*b + a*b^3)*d*e*f^2 - 24*(a^3*b + a*b^3)*f^3 + 12*((a^3*b + a*b^3)*d^3*e*f^2 - (a^3*b + a*b^3)*d^2*f^3)*x^2 + 12*((a^3*b + a*b^3)*d^3*e^2*f - 2*(a^3*b + a*b^3)*d^2*e*f^2 + 2*(a^3*b + a*b^3)*d*f^3)*x - (4*(a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(a^2*b^2 + b^4)*d^3*e^3 - 6*(a^2*b^2 + b^4)*d^2*e^2*f + 6*(a^2*b^2 + b^4)*d*e*f^2 - 3*(a^2*b^2 + b^4)*f^3 + 6*(2*(a^2*b^2 + b^4)*d^3*e*f^2 - (a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(a^2*b^2 + b^4)*d^3*e^2*f - 2*(a^2*b^2 + b^4)*d^2*e*f^2 + (a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(2*(a^2*b^2 + b^4)*d^3*e*f^2 + (a^2*b^2 + b^4)*d^2*f^3)*x^2 - 4*((2*a^4 + a^2*b^2 - b^4)*d^4*f^3*x^4 + 4*(2*a^4 + a^2*b^2 - b^4)*d^4*e*f^2*x^3 + 6*(2*a^4 + a^2*b^2 - b^4)*d^4*e^2*f*x^2 + 4*(2*a^4 + a^2*b^2 - b^4)*d^4*e^3*x)*cosh(d*x + c)^2 - 2*(2*(2*a^4 + a^2*b^2 - b^4)*d^4*f^3*x^4 + 8*(2*a^4 + a^2*b^2 - b^4)*d^4*e*f^2*x^3 + 12*(2*a^4 + a^2*b^2 - b^4)*d^4*e^2*f*x^2 + 8*(2*a^4 + a^2*b^2 - b^4)*d^4*e^3*x + 3*(4*(a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(a^2*b^2 + b^4)*d^3*e^3 - 6*(a^2*b^2 + b^4)*d^2*e^2*f + 6*(a^2*b^2 + b^4)*d*e*f^2 - 3*(a^2*b^2 + b^4)*f^3 + 6*(2*(a^2*b^2 + b^4)*d^3*e*f^2 - (a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(a^2*b^2 + b^4)*d^3*e^2*f - 2*(a^2*b^2 + b^4)*d^2*e*f^2 + (a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c)^2 - 24*((a^3*b + a*b^3)*d^3*f^3*x^3 + (a^3*b + a*b^3)*d^3*e^3 - 3*(a^3*b + a*b^3)*d^2*e^2*f + 6*(a^3*b + a*b^3)*d*e*f^2 - 6*(a^3*b + a*b^3)*f^3 + 3*((a^3*b + a*b^3)*d^3*e*f^2 - (a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((a^3*b + a*b^3)*d^3*e^2*f - 2*(a^3*b + a*b^3)*d^2*e*f^2 + 2*(a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 96*((a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 96*((a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 32*((a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 32*((a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 32*((a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 32*((a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 192*(a^3*b*f^3*cosh(d*x + c)^2 + 2*a^3*b*f^3*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f^3*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 192*(a^3*b*f^3*cosh(d*x + c)^2 + 2*a^3*b*f^3*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f^3*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 192*((a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f^3*x + a^3*b*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 192*((a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f^3*x + a^3*b*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(2*(a^2*b^2 + b^4)*d^3*e^2*f + 2*(a^2*b^2 + b^4)*d^2*e*f^2 + (a^2*b^2 + b^4)*d*f^3)*x + 16*((a^3*b + a*b^3)*d^3*f^3*x^3 + (a^3*b + a*b^3)*d^3*e^3 + 3*(a^3*b + a*b^3)*d^2*e^2*f + 6*(a^3*b + a*b^3)*d*e*f^2 + 6*(a^3*b + a*b^3)*f^3 + 3*((a^3*b + a*b^3)*d^3*e*f^2 + (a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((a^3*b + a*b^3)*d^3*e^2*f + 2*(a^3*b + a*b^3)*d^2*e*f^2 + 2*(a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c) + 4*(4*(a^3*b + a*b^3)*d^3*f^3*x^3 + 4*(a^3*b + a*b^3)*d^3*e^3 + 12*(a^3*b + a*b^3)*d^2*e^2*f + 24*(a^3*b + a*b^3)*d*e*f^2 + 24*(a^3*b + a*b^3)*f^3 - (4*(a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(a^2*b^2 + b^4)*d^3*e^3 - 6*(a^2*b^2 + b^4)*d^2*e^2*f + 6*(a^2*b^2 + b^4)*d*e*f^2 - 3*(a^2*b^2 + b^4)*f^3 + 6*(2*(a^2*b^2 + b^4)*d^3*e*f^2 - (a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(a^2*b^2 + b^4)*d^3*e^2*f - 2*(a^2*b^2 + b^4)*d^2*e*f^2 + (a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c)^3 + 12*((a^3*b + a*b^3)*d^3*e*f^2 + (a^3*b + a*b^3)*d^2*f^3)*x^2 + 12*((a^3*b + a*b^3)*d^3*f^3*x^3 + (a^3*b + a*b^3)*d^3*e^3 - 3*(a^3*b + a*b^3)*d^2*e^2*f + 6*(a^3*b + a*b^3)*d*e*f^2 - 6*(a^3*b + a*b^3)*f^3 + 3*((a^3*b + a*b^3)*d^3*e*f^2 - (a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((a^3*b + a*b^3)*d^3*e^2*f - 2*(a^3*b + a*b^3)*d^2*e*f^2 + 2*(a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 12*((a^3*b + a*b^3)*d^3*e^2*f + 2*(a^3*b + a*b^3)*d^2*e*f^2 + 2*(a^3*b + a*b^3)*d*f^3)*x - 2*((2*a^4 + a^2*b^2 - b^4)*d^4*f^3*x^4 + 4*(2*a^4 + a^2*b^2 - b^4)*d^4*e*f^2*x^3 + 6*(2*a^4 + a^2*b^2 - b^4)*d^4*e^2*f*x^2 + 4*(2*a^4 + a^2*b^2 - b^4)*d^4*e^3*x)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^3 + b^5)*d^4*cosh(d*x + c)^2 + 2*(a^2*b^3 + b^5)*d^4*cosh(d*x + c)*sinh(d*x + c) + (a^2*b^3 + b^5)*d^4*sinh(d*x + c)^2)","C",0
234,1,3247,0,0.511506," ","integrate((f*x+e)^2*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + 24 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x - {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2} - 8 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{3} e f x^{2} + 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(4 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{3} f^{2} x^{3} + 12 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{3} e f x^{2} + 12 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{3} e^{2} x + 9 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 36 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 96 \, {\left({\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 96 \, {\left({\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 48 \, {\left({\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 48 \, {\left({\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 48 \, {\left({\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 48 \, {\left({\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 96 \, {\left(a^{3} b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 96 \, {\left(a^{3} b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f + {\left(a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x + 24 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 4 \, {\left(6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} d e f - 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 18 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x - 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{3} e f x^{2} + 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{48 \, {\left({\left(a^{2} b^{3} + b^{5}\right)} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{3} + b^{5}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} d^{3} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/48*(6*(a^2*b^2 + b^4)*d^2*f^2*x^2 + 6*(a^2*b^2 + b^4)*d^2*e^2 - 3*(2*(a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^2*b^2 + b^4)*d^2*e^2 - 2*(a^2*b^2 + b^4)*d*e*f + (a^2*b^2 + b^4)*f^2 + 2*(2*(a^2*b^2 + b^4)*d^2*e*f - (a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c)^4 - 3*(2*(a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^2*b^2 + b^4)*d^2*e^2 - 2*(a^2*b^2 + b^4)*d*e*f + (a^2*b^2 + b^4)*f^2 + 2*(2*(a^2*b^2 + b^4)*d^2*e*f - (a^2*b^2 + b^4)*d*f^2)*x)*sinh(d*x + c)^4 + 6*(a^2*b^2 + b^4)*d*e*f + 24*((a^3*b + a*b^3)*d^2*f^2*x^2 + (a^3*b + a*b^3)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f + 2*(a^3*b + a*b^3)*f^2 + 2*((a^3*b + a*b^3)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^3 + 12*(2*(a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e^2 - 4*(a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*f^2 + 4*((a^3*b + a*b^3)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x - (2*(a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^2*b^2 + b^4)*d^2*e^2 - 2*(a^2*b^2 + b^4)*d*e*f + (a^2*b^2 + b^4)*f^2 + 2*(2*(a^2*b^2 + b^4)*d^2*e*f - (a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a^2*b^2 + b^4)*f^2 - 8*((2*a^4 + a^2*b^2 - b^4)*d^3*f^2*x^3 + 3*(2*a^4 + a^2*b^2 - b^4)*d^3*e*f*x^2 + 3*(2*a^4 + a^2*b^2 - b^4)*d^3*e^2*x)*cosh(d*x + c)^2 - 2*(4*(2*a^4 + a^2*b^2 - b^4)*d^3*f^2*x^3 + 12*(2*a^4 + a^2*b^2 - b^4)*d^3*e*f*x^2 + 12*(2*a^4 + a^2*b^2 - b^4)*d^3*e^2*x + 9*(2*(a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^2*b^2 + b^4)*d^2*e^2 - 2*(a^2*b^2 + b^4)*d*e*f + (a^2*b^2 + b^4)*f^2 + 2*(2*(a^2*b^2 + b^4)*d^2*e*f - (a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c)^2 - 36*((a^3*b + a*b^3)*d^2*f^2*x^2 + (a^3*b + a*b^3)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f + 2*(a^3*b + a*b^3)*f^2 + 2*((a^3*b + a*b^3)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 96*((a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f^2*x + a^3*b*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 96*((a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f^2*x + a^3*b*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 48*((a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 48*((a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 48*((a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 48*((a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 96*(a^3*b*f^2*cosh(d*x + c)^2 + 2*a^3*b*f^2*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f^2*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 96*(a^3*b*f^2*cosh(d*x + c)^2 + 2*a^3*b*f^2*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f^2*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(2*(a^2*b^2 + b^4)*d^2*e*f + (a^2*b^2 + b^4)*d*f^2)*x + 24*((a^3*b + a*b^3)*d^2*f^2*x^2 + (a^3*b + a*b^3)*d^2*e^2 + 2*(a^3*b + a*b^3)*d*e*f + 2*(a^3*b + a*b^3)*f^2 + 2*((a^3*b + a*b^3)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c) + 4*(6*(a^3*b + a*b^3)*d^2*f^2*x^2 + 6*(a^3*b + a*b^3)*d^2*e^2 + 12*(a^3*b + a*b^3)*d*e*f - 3*(2*(a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^2*b^2 + b^4)*d^2*e^2 - 2*(a^2*b^2 + b^4)*d*e*f + (a^2*b^2 + b^4)*f^2 + 2*(2*(a^2*b^2 + b^4)*d^2*e*f - (a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c)^3 + 12*(a^3*b + a*b^3)*f^2 + 18*((a^3*b + a*b^3)*d^2*f^2*x^2 + (a^3*b + a*b^3)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f + 2*(a^3*b + a*b^3)*f^2 + 2*((a^3*b + a*b^3)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 12*((a^3*b + a*b^3)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x - 4*((2*a^4 + a^2*b^2 - b^4)*d^3*f^2*x^3 + 3*(2*a^4 + a^2*b^2 - b^4)*d^3*e*f*x^2 + 3*(2*a^4 + a^2*b^2 - b^4)*d^3*e^2*x)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^3 + b^5)*d^3*cosh(d*x + c)^2 + 2*(a^2*b^3 + b^5)*d^3*cosh(d*x + c)*sinh(d*x + c) + (a^2*b^3 + b^5)*d^3*sinh(d*x + c)^2)","C",0
235,1,1727,0,0.787761," ","integrate((f*x+e)*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{2} b^{2} + b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f x - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d f x + 2 \, {\left(a^{3} b + a b^{3}\right)} d e - 2 \, {\left(a^{3} b + a b^{3}\right)} f - {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 4 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e x + 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 12 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 16 \, {\left(a^{3} b f \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 16 \, {\left(a^{3} b f \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 16 \, {\left({\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d e - a^{3} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 16 \, {\left({\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d e - a^{3} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 16 \, {\left({\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f x + a^{3} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 16 \, {\left({\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f x + a^{3} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(a^{2} b^{2} + b^{4}\right)} f - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e + {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right) - 4 \, {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d f x - {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b + a b^{3}\right)} d e + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} f - 2 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} d^{2} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*((2*(a^2*b^2 + b^4)*d*f*x + 2*(a^2*b^2 + b^4)*d*e - (a^2*b^2 + b^4)*f)*cosh(d*x + c)^4 + (2*(a^2*b^2 + b^4)*d*f*x + 2*(a^2*b^2 + b^4)*d*e - (a^2*b^2 + b^4)*f)*sinh(d*x + c)^4 - 2*(a^2*b^2 + b^4)*d*f*x - 8*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e - (a^3*b + a*b^3)*f)*cosh(d*x + c)^3 - 4*(2*(a^3*b + a*b^3)*d*f*x + 2*(a^3*b + a*b^3)*d*e - 2*(a^3*b + a*b^3)*f - (2*(a^2*b^2 + b^4)*d*f*x + 2*(a^2*b^2 + b^4)*d*e - (a^2*b^2 + b^4)*f)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(a^2*b^2 + b^4)*d*e + 4*((2*a^4 + a^2*b^2 - b^4)*d^2*f*x^2 + 2*(2*a^4 + a^2*b^2 - b^4)*d^2*e*x)*cosh(d*x + c)^2 + 2*(2*(2*a^4 + a^2*b^2 - b^4)*d^2*f*x^2 + 4*(2*a^4 + a^2*b^2 - b^4)*d^2*e*x + 3*(2*(a^2*b^2 + b^4)*d*f*x + 2*(a^2*b^2 + b^4)*d*e - (a^2*b^2 + b^4)*f)*cosh(d*x + c)^2 - 12*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e - (a^3*b + a*b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 16*(a^3*b*f*cosh(d*x + c)^2 + 2*a^3*b*f*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 16*(a^3*b*f*cosh(d*x + c)^2 + 2*a^3*b*f*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 16*((a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*e - a^3*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 16*((a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*e - a^3*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 16*((a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f*x + a^3*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 16*((a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f*x + a^3*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (a^2*b^2 + b^4)*f - 8*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e + (a^3*b + a*b^3)*f)*cosh(d*x + c) - 4*(2*(a^3*b + a*b^3)*d*f*x - (2*(a^2*b^2 + b^4)*d*f*x + 2*(a^2*b^2 + b^4)*d*e - (a^2*b^2 + b^4)*f)*cosh(d*x + c)^3 + 2*(a^3*b + a*b^3)*d*e + 6*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e - (a^3*b + a*b^3)*f)*cosh(d*x + c)^2 + 2*(a^3*b + a*b^3)*f - 2*((2*a^4 + a^2*b^2 - b^4)*d^2*f*x^2 + 2*(2*a^4 + a^2*b^2 - b^4)*d^2*e*x)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^3 + b^5)*d^2*cosh(d*x + c)^2 + 2*(a^2*b^3 + b^5)*d^2*cosh(d*x + c)*sinh(d*x + c) + (a^2*b^3 + b^5)*d^2*sinh(d*x + c)^2)","B",0
236,1,601,0,0.515931," ","integrate(sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{2} b^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{4} - a^{2} b^{2} - b^{4} - 4 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a^{3} b + a b^{3} - {\left(a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d x + 3 \, {\left(a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} \sinh\left(d x + c\right)^{2}\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) - 4 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{3} b + a b^{3} - 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d x \cosh\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{2} b^{3} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{3} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b^{3} + b^{5}\right)} d \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/8*(4*(2*a^4 + a^2*b^2 - b^4)*d*x*cosh(d*x + c)^2 + (a^2*b^2 + b^4)*cosh(d*x + c)^4 + (a^2*b^2 + b^4)*sinh(d*x + c)^4 - a^2*b^2 - b^4 - 4*(a^3*b + a*b^3)*cosh(d*x + c)^3 - 4*(a^3*b + a*b^3 - (a^2*b^2 + b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(2*(2*a^4 + a^2*b^2 - b^4)*d*x + 3*(a^2*b^2 + b^4)*cosh(d*x + c)^2 - 6*(a^3*b + a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*(a^3*cosh(d*x + c)^2 + 2*a^3*cosh(d*x + c)*sinh(d*x + c) + a^3*sinh(d*x + c)^2)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) - 4*(a^3*b + a*b^3)*cosh(d*x + c) - 4*(a^3*b + a*b^3 - 2*(2*a^4 + a^2*b^2 - b^4)*d*x*cosh(d*x + c) - (a^2*b^2 + b^4)*cosh(d*x + c)^3 + 3*(a^3*b + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^2*b^3 + b^5)*d*cosh(d*x + c)^2 + 2*(a^2*b^3 + b^5)*d*cosh(d*x + c)*sinh(d*x + c) + (a^2*b^3 + b^5)*d*sinh(d*x + c)^2)","B",0
237,0,0,0,0.454892," ","integrate(sinh(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sinh\left(d x + c\right)^{3}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sinh(d*x + c)^3/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
238,1,1645,0,0.569794," ","integrate((f*x+e)^3*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, b^{2} f^{3} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, b^{2} f^{3} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(a^{2} + b^{2}\right)} f^{3} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left(a^{2} + b^{2}\right)} f^{3} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + {\left(a^{2} + b^{2}\right)} d^{3} e^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 6 \, {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 6 \, {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right)}{{\left(a^{3} + a b^{2}\right)} d^{4}}"," ",0,"-(6*b^2*f^3*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*b^2*f^3*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(a^2 + b^2)*f^3*polylog(4, cosh(d*x + c) + sinh(d*x + c)) + 6*(a^2 + b^2)*f^3*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) + 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 6*(b^2*d*f^3*x + b^2*d*e*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b^2*d*f^3*x + b^2*d*e*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 3*((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) + 3*((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + (a^2 + b^2)*d^3*e^3)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 6*((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 6*((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)))/((a^3 + a*b^2)*d^4)","C",0
239,1,1096,0,0.584516," ","integrate((f*x+e)^2*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b^{2} f^{2} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, b^{2} f^{2} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(a^{2} + b^{2}\right)} f^{2} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left(a^{2} + b^{2}\right)} f^{2} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right)}{{\left(a^{3} + a b^{2}\right)} d^{3}}"," ",0,"(2*b^2*f^2*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*b^2*f^2*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(a^2 + b^2)*f^2*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 2*(a^2 + b^2)*f^2*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 2*(b^2*d*f^2*x + b^2*d*e*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^2*d*f^2*x + b^2*d*e*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + (a^2 + b^2)*d^2*e^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1))/((a^3 + a*b^2)*d^3)","C",0
240,1,649,0,0.508137," ","integrate((f*x+e)*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{b^{2} f \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - b^{2} f \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a^{2} + b^{2}\right)} f {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(a^{2} + b^{2}\right)} f {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left(b^{2} d e - b^{2} c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{2} d e - b^{2} c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{2} d f x + b^{2} c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{2} d f x + b^{2} c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right)}{{\left(a^{3} + a b^{2}\right)} d^{2}}"," ",0,"-(b^2*f*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - b^2*f*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (a^2 + b^2)*f*dilog(cosh(d*x + c) + sinh(d*x + c)) + (a^2 + b^2)*f*dilog(-cosh(d*x + c) - sinh(d*x + c)) - (b^2*d*e - b^2*c*f)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^2*d*e - b^2*c*f)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^2*d*f*x + b^2*c*f)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^2*d*f*x + b^2*c*f)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + ((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*log(-cosh(d*x + c) - sinh(d*x + c) + 1))/((a^3 + a*b^2)*d^2)","B",0
241,1,223,0,0.551147," ","integrate(csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} b \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) - {\left(a^{2} + b^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left(a^{2} + b^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right)}{{\left(a^{3} + a b^{2}\right)} d}"," ",0,"(sqrt(a^2 + b^2)*b*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) - (a^2 + b^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (a^2 + b^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1))/((a^3 + a*b^2)*d)","B",0
242,0,0,0,0.535448," ","integrate(csch(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(csch(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
243,1,6416,0,1.393282," ","integrate((f*x+e)^3*csch(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c^{3} f^{3} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f - {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f - {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3} - {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3} - {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3} - {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3} - {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left(b^{3} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{3} \sinh\left(d x + c\right)^{2} - b^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b^{3} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{3} \sinh\left(d x + c\right)^{2} - b^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2} - {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2} - {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} - {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} - {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} - {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} - {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3} - {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} + {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} + {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} + {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} + {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 6 \, {\left({\left(a^{2} b + b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f^{3} \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f^{3}\right)} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 6 \, {\left({\left(a^{2} b + b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f^{3} \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f^{3}\right)} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 6 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} - {\left(a^{3} + a b^{2}\right)} f^{3} - {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} - {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} - {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} - {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 6 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(a^{3} + a b^{2}\right)} f^{3} - {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right)}{{\left(a^{4} + a^{2} b^{2}\right)} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{2} b^{2}\right)} d^{4} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d^{4}}"," ",0,"-(2*(a^3 + a*b^2)*d^3*e^3 - 6*(a^3 + a*b^2)*c*d^2*e^2*f + 6*(a^3 + a*b^2)*c^2*d*e*f^2 - 2*(a^3 + a*b^2)*c^3*f^3 + 2*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^2 + 4*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + 2*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*sinh(d*x + c)^2 + 3*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f - (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f - (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3 - (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3 - (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3 - (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3 - (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 6*(b^3*f^3*cosh(d*x + c)^2 + 2*b^3*f^3*cosh(d*x + c)*sinh(d*x + c) + b^3*f^3*sinh(d*x + c)^2 - b^3*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b^3*f^3*cosh(d*x + c)^2 + 2*b^3*f^3*cosh(d*x + c)*sinh(d*x + c) + b^3*f^3*sinh(d*x + c)^2 - b^3*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b^3*d*f^3*x + b^3*d*e*f^2 - (b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)^2 - 2*(b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f^3*x + b^3*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b^3*d*f^3*x + b^3*d*e*f^2 - (b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)^2 - 2*(b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f^3*x + b^3*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 3*((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f - 2*(a^3 + a*b^2)*d*e*f^2 - ((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f - 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 - (a^3 + a*b^2)*d*f^3)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f - 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 - (a^3 + a*b^2)*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f - 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 - (a^3 + a*b^2)*d*f^3)*x)*sinh(d*x + c)^2 + 2*((a^2*b + b^3)*d^2*e*f^2 - (a^3 + a*b^2)*d*f^3)*x)*dilog(cosh(d*x + c) + sinh(d*x + c)) + 3*((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f + 2*(a^3 + a*b^2)*d*e*f^2 - ((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f + 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 + (a^3 + a*b^2)*d*f^3)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f + 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 + (a^3 + a*b^2)*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f + 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 + (a^3 + a*b^2)*d*f^3)*x)*sinh(d*x + c)^2 + 2*((a^2*b + b^3)*d^2*e*f^2 + (a^3 + a*b^2)*d*f^3)*x)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + ((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 + 3*(a^3 + a*b^2)*d^2*e^2*f + 3*((a^2*b + b^3)*d^3*e*f^2 + (a^3 + a*b^2)*d^2*f^3)*x^2 - ((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 + 3*(a^3 + a*b^2)*d^2*e^2*f + 3*((a^2*b + b^3)*d^3*e*f^2 + (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f + 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 + 3*(a^3 + a*b^2)*d^2*e^2*f + 3*((a^2*b + b^3)*d^3*e*f^2 + (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f + 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 + 3*(a^3 + a*b^2)*d^2*e^2*f + 3*((a^2*b + b^3)*d^3*e*f^2 + (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f + 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*sinh(d*x + c)^2 + 3*((a^2*b + b^3)*d^3*e^2*f + 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((a^2*b + b^3)*d^3*e^3 - 3*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d^2*e^2*f + 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 - ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3 - ((a^2*b + b^3)*d^3*e^3 - 3*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d^2*e^2*f + 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 - ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^3*e^3 - 3*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d^2*e^2*f + 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 - ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^3*e^3 - 3*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d^2*e^2*f + 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 - ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - ((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 + ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^3 + a*b^2)*d^2*f^3)*x^2 - ((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 + ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 + ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 + ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*sinh(d*x + c)^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 6*((a^2*b + b^3)*f^3*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f^3*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f^3*sinh(d*x + c)^2 - (a^2*b + b^3)*f^3)*polylog(4, cosh(d*x + c) + sinh(d*x + c)) - 6*((a^2*b + b^3)*f^3*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f^3*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f^3*sinh(d*x + c)^2 - (a^2*b + b^3)*f^3)*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) + 6*((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 - (a^3 + a*b^2)*f^3 - ((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 - (a^3 + a*b^2)*f^3)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 - (a^3 + a*b^2)*f^3)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 - (a^3 + a*b^2)*f^3)*sinh(d*x + c)^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 6*((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 + (a^3 + a*b^2)*f^3 - ((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 + (a^3 + a*b^2)*f^3)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 + (a^3 + a*b^2)*f^3)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 + (a^3 + a*b^2)*f^3)*sinh(d*x + c)^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)))/((a^4 + a^2*b^2)*d^4*cosh(d*x + c)^2 + 2*(a^4 + a^2*b^2)*d^4*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^2*b^2)*d^4*sinh(d*x + c)^2 - (a^4 + a^2*b^2)*d^4)","C",0
244,1,3805,0,1.026515," ","integrate((f*x+e)^2*csch(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} + a b^{2}\right)} c d e f + 2 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f - {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f - {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2} - {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2} - {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2} - {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2} - {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{3} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{2} \sinh\left(d x + c\right)^{2} - b^{3} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(b^{3} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{2} \sinh\left(d x + c\right)^{2} - b^{3} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f - {\left(a^{3} + a b^{2}\right)} f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f - {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f - {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f - {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f + {\left(a^{3} + a b^{2}\right)} f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f + {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f + {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f + {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d e f + {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d e f + {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d e f + {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d e f + {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f^{2} \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{2} b + b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f^{2} \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right)}{{\left(a^{4} + a^{2} b^{2}\right)} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{2} b^{2}\right)} d^{3} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d^{3}}"," ",0,"-(2*(a^3 + a*b^2)*d^2*e^2 - 4*(a^3 + a*b^2)*c*d*e*f + 2*(a^3 + a*b^2)*c^2*f^2 + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^2 + 4*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*sinh(d*x + c)^2 + 2*(b^3*d*f^2*x + b^3*d*e*f - (b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^2 - 2*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f^2*x + b^3*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b^3*d*f^2*x + b^3*d*e*f - (b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^2 - 2*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f^2*x + b^3*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2 - (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2 - (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2 - (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2 - (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^3*f^2*cosh(d*x + c)^2 + 2*b^3*f^2*cosh(d*x + c)*sinh(d*x + c) + b^3*f^2*sinh(d*x + c)^2 - b^3*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(b^3*f^2*cosh(d*x + c)^2 + 2*b^3*f^2*cosh(d*x + c)*sinh(d*x + c) + b^3*f^2*sinh(d*x + c)^2 - b^3*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f - (a^3 + a*b^2)*f^2 - ((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f - (a^3 + a*b^2)*f^2)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f - (a^3 + a*b^2)*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f - (a^3 + a*b^2)*f^2)*sinh(d*x + c)^2)*dilog(cosh(d*x + c) + sinh(d*x + c)) + 2*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f + (a^3 + a*b^2)*f^2 - ((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f + (a^3 + a*b^2)*f^2)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f + (a^3 + a*b^2)*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f + (a^3 + a*b^2)*f^2)*sinh(d*x + c)^2)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + ((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f - ((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^2*b + b^3)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((a^2*b + b^3)*d^2*e^2 - 2*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d*e*f + ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2 - ((a^2*b + b^3)*d^2*e^2 - 2*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d*e*f + ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*e^2 - 2*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d*e*f + ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^2*e^2 - 2*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d*e*f + ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - ((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*e*f - ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2 - ((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*e*f - ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*e*f - ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*e*f - ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*((a^2*b + b^3)*f^2*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f^2*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f^2*sinh(d*x + c)^2 - (a^2*b + b^3)*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 2*((a^2*b + b^3)*f^2*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f^2*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f^2*sinh(d*x + c)^2 - (a^2*b + b^3)*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)))/((a^4 + a^2*b^2)*d^3*cosh(d*x + c)^2 + 2*(a^4 + a^2*b^2)*d^3*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^2*b^2)*d^3*sinh(d*x + c)^2 - (a^4 + a^2*b^2)*d^3)","C",0
245,1,1830,0,0.995384," ","integrate((f*x+e)*csch(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} + a b^{2}\right)} d e - 2 \, {\left(a^{3} + a b^{2}\right)} c f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{2} - {\left(b^{3} f \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f \sinh\left(d x + c\right)^{2} - b^{3} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b^{3} f \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f \sinh\left(d x + c\right)^{2} - b^{3} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{3} d e - b^{3} c f - {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d e - b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d e - b^{3} c f - {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d e - b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d f x + b^{3} c f - {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f x + b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{3} d f x + b^{3} c f - {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f x + b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left({\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} b + b^{3}\right)} d e - {\left({\left(a^{2} b + b^{3}\right)} d e - {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d e - {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d e - {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} c f - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right)}{{\left(a^{4} + a^{2} b^{2}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d^{2}}"," ",0,"-(2*(a^3 + a*b^2)*d*e - 2*(a^3 + a*b^2)*c*f + 2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*cosh(d*x + c)^2 + 4*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c) + 2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*sinh(d*x + c)^2 - (b^3*f*cosh(d*x + c)^2 + 2*b^3*f*cosh(d*x + c)*sinh(d*x + c) + b^3*f*sinh(d*x + c)^2 - b^3*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (b^3*f*cosh(d*x + c)^2 + 2*b^3*f*cosh(d*x + c)*sinh(d*x + c) + b^3*f*sinh(d*x + c)^2 - b^3*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^3*d*e - b^3*c*f - (b^3*d*e - b^3*c*f)*cosh(d*x + c)^2 - 2*(b^3*d*e - b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*e - b^3*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d*e - b^3*c*f - (b^3*d*e - b^3*c*f)*cosh(d*x + c)^2 - 2*(b^3*d*e - b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*e - b^3*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d*f*x + b^3*c*f - (b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^2 - 2*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f*x + b^3*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^3*d*f*x + b^3*c*f - (b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^2 - 2*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f*x + b^3*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + ((a^2*b + b^3)*f*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f*sinh(d*x + c)^2 - (a^2*b + b^3)*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) - ((a^2*b + b^3)*f*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f*sinh(d*x + c)^2 - (a^2*b + b^3)*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^3 + a*b^2)*f)*sinh(d*x + c)^2 + (a^3 + a*b^2)*f)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((a^2*b + b^3)*d*e - ((a^2*b + b^3)*d*e - (a^3 + a*b^2 + (a^2*b + b^3)*c)*f)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*e - (a^3 + a*b^2 + (a^2*b + b^3)*c)*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*e - (a^3 + a*b^2 + (a^2*b + b^3)*c)*f)*sinh(d*x + c)^2 - (a^3 + a*b^2 + (a^2*b + b^3)*c)*f)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*c*f - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*c*f)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*c*f)*sinh(d*x + c)^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1))/((a^4 + a^2*b^2)*d^2*cosh(d*x + c)^2 + 2*(a^4 + a^2*b^2)*d^2*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^2*b^2)*d^2*sinh(d*x + c)^2 - (a^4 + a^2*b^2)*d^2)","B",0
246,1,479,0,0.617415," ","integrate(csch(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a^{3} + 2 \, a b^{2} - {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} - b^{2}\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + {\left(a^{2} b + b^{3} - {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(a^{2} b + b^{3} - {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right)}{{\left(a^{4} + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d}"," ",0,"-(2*a^3 + 2*a*b^2 - (b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 - b^2)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + (a^2*b + b^3 - (a^2*b + b^3)*cosh(d*x + c)^2 - 2*(a^2*b + b^3)*cosh(d*x + c)*sinh(d*x + c) - (a^2*b + b^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (a^2*b + b^3 - (a^2*b + b^3)*cosh(d*x + c)^2 - 2*(a^2*b + b^3)*cosh(d*x + c)*sinh(d*x + c) - (a^2*b + b^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1))/((a^4 + a^2*b^2)*d*cosh(d*x + c)^2 + 2*(a^4 + a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^2*b^2)*d*sinh(d*x + c)^2 - (a^4 + a^2*b^2)*d)","B",0
247,0,0,0,0.587092," ","integrate(csch(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(csch(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
248,-1,0,0,0.000000," ","integrate((f*x+e)^3*csch(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,1,10341,0,0.905992," ","integrate((f*x+e)^2*csch(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} - 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2} - 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f + {\left(a^{4} + a^{2} b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f + {\left(a^{4} + a^{2} b^{2}\right)} d f^{2}\right)} x - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x - {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x - 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2} - 12 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f + {\left(a^{4} + a^{2} b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} d f^{2} x + b^{4} d e f + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f - 3 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left(b^{4} d f^{2} x + b^{4} d e f + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f - 3 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2} - 3 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2} - 3 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2} - 3 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2} - 3 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left(b^{4} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{4} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{4} f^{2} \cosh\left(d x + c\right)^{2} + b^{4} f^{2} + 2 \, {\left(3 \, b^{4} f^{2} \cosh\left(d x + c\right)^{2} - b^{4} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} f^{2} \cosh\left(d x + c\right)^{3} - b^{4} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(b^{4} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{4} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{4} f^{2} \cosh\left(d x + c\right)^{2} + b^{4} f^{2} + 2 \, {\left(3 \, b^{4} f^{2} \cosh\left(d x + c\right)^{2} - b^{4} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} f^{2} \cosh\left(d x + c\right)^{3} - b^{4} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f - {\left(a^{4} + a^{2} b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2} - 3 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f + 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2} - 3 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f^{2} x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f - 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f - 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f - 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f - 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} - 3 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f - 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f - 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f - 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x + 4 \, {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f - 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f - 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} d e f - {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} d e f - {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} d e f - {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} d e f - {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} d e f - {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} d e f - {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} - 3 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} d e f - {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} d e f - {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} d e f - {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c d e f + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c d e f - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c d e f - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c d e f - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c d e f - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c d e f - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} - 3 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c d e f - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x + 4 \, {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c d e f - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c d e f - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d^{2} e f + 2 \, {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e f - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f + {\left(a^{4} + a^{2} b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f - {\left(a^{4} + a^{2} b^{2}\right)} d f^{2}\right)} x + 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x - {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c d e f - 2 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + a^{3} b^{2}\right)} d^{3} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d^{3} + 2 \, {\left(3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right)^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right)^{3} - {\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(4*(a^3*b + a*b^3)*d^2*e^2 - 8*(a^3*b + a*b^3)*c*d*e*f + 4*(a^3*b + a*b^3)*c^2*f^2 - 4*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + 2*(a^3*b + a*b^3)*c*d*e*f - (a^3*b + a*b^3)*c^2*f^2)*cosh(d*x + c)^4 - 4*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + 2*(a^3*b + a*b^3)*c*d*e*f - (a^3*b + a*b^3)*c^2*f^2)*sinh(d*x + c)^4 + 2*((a^4 + a^2*b^2)*d^2*f^2*x^2 + (a^4 + a^2*b^2)*d^2*e^2 + 2*(a^4 + a^2*b^2)*d*e*f + 2*((a^4 + a^2*b^2)*d^2*e*f + (a^4 + a^2*b^2)*d*f^2)*x)*cosh(d*x + c)^3 + 2*((a^4 + a^2*b^2)*d^2*f^2*x^2 + (a^4 + a^2*b^2)*d^2*e^2 + 2*(a^4 + a^2*b^2)*d*e*f + 2*((a^4 + a^2*b^2)*d^2*e*f + (a^4 + a^2*b^2)*d*f^2)*x - 8*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + 2*(a^3*b + a*b^3)*c*d*e*f - (a^3*b + a*b^3)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x - (a^3*b + a*b^3)*d^2*e^2 + 4*(a^3*b + a*b^3)*c*d*e*f - 2*(a^3*b + a*b^3)*c^2*f^2)*cosh(d*x + c)^2 + 2*(2*(a^3*b + a*b^3)*d^2*f^2*x^2 + 4*(a^3*b + a*b^3)*d^2*e*f*x - 2*(a^3*b + a*b^3)*d^2*e^2 + 8*(a^3*b + a*b^3)*c*d*e*f - 4*(a^3*b + a*b^3)*c^2*f^2 - 12*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + 2*(a^3*b + a*b^3)*c*d*e*f - (a^3*b + a*b^3)*c^2*f^2)*cosh(d*x + c)^2 + 3*((a^4 + a^2*b^2)*d^2*f^2*x^2 + (a^4 + a^2*b^2)*d^2*e^2 + 2*(a^4 + a^2*b^2)*d*e*f + 2*((a^4 + a^2*b^2)*d^2*e*f + (a^4 + a^2*b^2)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 4*(b^4*d*f^2*x + b^4*d*e*f + (b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^4 + 4*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*f^2*x + b^4*d*e*f)*sinh(d*x + c)^4 - 2*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^2 - 2*(b^4*d*f^2*x + b^4*d*e*f - 3*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^3 - (b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 4*(b^4*d*f^2*x + b^4*d*e*f + (b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^4 + 4*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*f^2*x + b^4*d*e*f)*sinh(d*x + c)^4 - 2*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^2 - 2*(b^4*d*f^2*x + b^4*d*e*f - 3*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^3 - (b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2 - 3*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^3 - (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2 - 3*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^3 - (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2 - 3*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^3 - (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2 - 3*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^3 - (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*(b^4*f^2*cosh(d*x + c)^4 + 4*b^4*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*f^2*sinh(d*x + c)^4 - 2*b^4*f^2*cosh(d*x + c)^2 + b^4*f^2 + 2*(3*b^4*f^2*cosh(d*x + c)^2 - b^4*f^2)*sinh(d*x + c)^2 + 4*(b^4*f^2*cosh(d*x + c)^3 - b^4*f^2*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*(b^4*f^2*cosh(d*x + c)^4 + 4*b^4*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*f^2*sinh(d*x + c)^4 - 2*b^4*f^2*cosh(d*x + c)^2 + b^4*f^2 + 2*(3*b^4*f^2*cosh(d*x + c)^2 - b^4*f^2)*sinh(d*x + c)^2 + 4*(b^4*f^2*cosh(d*x + c)^3 - b^4*f^2*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*((a^4 + a^2*b^2)*d^2*f^2*x^2 + (a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*d*e*f + 2*((a^4 + a^2*b^2)*d^2*e*f - (a^4 + a^2*b^2)*d*f^2)*x)*cosh(d*x + c) + 2*((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + ((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f + 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c)^4 + 4*((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f + 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f + 2*(a^3*b + a*b^3)*f^2)*sinh(d*x + c)^4 + (a^4 - a^2*b^2 - 2*b^4)*d*e*f + 2*(a^3*b + a*b^3)*f^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f + 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c)^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f + 2*(a^3*b + a*b^3)*f^2 - 3*((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f + 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f + 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c)^3 - ((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f + 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) - 2*((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + ((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f - 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c)^4 + 4*((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f - 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f - 2*(a^3*b + a*b^3)*f^2)*sinh(d*x + c)^4 + (a^4 - a^2*b^2 - 2*b^4)*d*e*f - 2*(a^3*b + a*b^3)*f^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f - 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c)^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f - 2*(a^3*b + a*b^3)*f^2 - 3*((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f - 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f - 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c)^3 - ((a^4 - a^2*b^2 - 2*b^4)*d*f^2*x + (a^4 - a^2*b^2 - 2*b^4)*d*e*f - 2*(a^3*b + a*b^3)*f^2)*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) - ((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + (a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 + ((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + (a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 - 4*(a^3*b + a*b^3)*d*e*f - 2*(a^4 + a^2*b^2)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f - 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^4 + 4*((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + (a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 - 4*(a^3*b + a*b^3)*d*e*f - 2*(a^4 + a^2*b^2)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f - 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + (a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 - 4*(a^3*b + a*b^3)*d*e*f - 2*(a^4 + a^2*b^2)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f - 2*(a^3*b + a*b^3)*d*f^2)*x)*sinh(d*x + c)^4 - 4*(a^3*b + a*b^3)*d*e*f - 2*(a^4 + a^2*b^2)*f^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + (a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 - 4*(a^3*b + a*b^3)*d*e*f - 2*(a^4 + a^2*b^2)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f - 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + (a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 - 4*(a^3*b + a*b^3)*d*e*f - 2*(a^4 + a^2*b^2)*f^2 - 3*((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + (a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 - 4*(a^3*b + a*b^3)*d*e*f - 2*(a^4 + a^2*b^2)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f - 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f - 2*(a^3*b + a*b^3)*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f - 2*(a^3*b + a*b^3)*d*f^2)*x + 4*(((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + (a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 - 4*(a^3*b + a*b^3)*d*e*f - 2*(a^4 + a^2*b^2)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f - 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^3 - ((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + (a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 - 4*(a^3*b + a*b^3)*d*e*f - 2*(a^4 + a^2*b^2)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f - 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 + ((a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 + 2*(2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*d*e*f - (2*a^4 + 2*a^2*b^2 - (a^4 - a^2*b^2 - 2*b^4)*c^2 + 4*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c)^4 + 4*((a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 + 2*(2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*d*e*f - (2*a^4 + 2*a^2*b^2 - (a^4 - a^2*b^2 - 2*b^4)*c^2 + 4*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 + 2*(2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*d*e*f - (2*a^4 + 2*a^2*b^2 - (a^4 - a^2*b^2 - 2*b^4)*c^2 + 4*(a^3*b + a*b^3)*c)*f^2)*sinh(d*x + c)^4 + 2*(2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*d*e*f - (2*a^4 + 2*a^2*b^2 - (a^4 - a^2*b^2 - 2*b^4)*c^2 + 4*(a^3*b + a*b^3)*c)*f^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 + 2*(2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*d*e*f - (2*a^4 + 2*a^2*b^2 - (a^4 - a^2*b^2 - 2*b^4)*c^2 + 4*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c)^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 + 2*(2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*d*e*f - (2*a^4 + 2*a^2*b^2 - (a^4 - a^2*b^2 - 2*b^4)*c^2 + 4*(a^3*b + a*b^3)*c)*f^2 - 3*((a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 + 2*(2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*d*e*f - (2*a^4 + 2*a^2*b^2 - (a^4 - a^2*b^2 - 2*b^4)*c^2 + 4*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 + 2*(2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*d*e*f - (2*a^4 + 2*a^2*b^2 - (a^4 - a^2*b^2 - 2*b^4)*c^2 + 4*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c)^3 - ((a^4 - a^2*b^2 - 2*b^4)*d^2*e^2 + 2*(2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*d*e*f - (2*a^4 + 2*a^2*b^2 - (a^4 - a^2*b^2 - 2*b^4)*c^2 + 4*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + ((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + 2*(a^4 - a^2*b^2 - 2*b^4)*c*d*e*f + ((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + 2*(a^4 - a^2*b^2 - 2*b^4)*c*d*e*f - ((a^4 - a^2*b^2 - 2*b^4)*c^2 - 4*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f + 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^4 + 4*((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + 2*(a^4 - a^2*b^2 - 2*b^4)*c*d*e*f - ((a^4 - a^2*b^2 - 2*b^4)*c^2 - 4*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f + 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + 2*(a^4 - a^2*b^2 - 2*b^4)*c*d*e*f - ((a^4 - a^2*b^2 - 2*b^4)*c^2 - 4*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f + 2*(a^3*b + a*b^3)*d*f^2)*x)*sinh(d*x + c)^4 - ((a^4 - a^2*b^2 - 2*b^4)*c^2 - 4*(a^3*b + a*b^3)*c)*f^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + 2*(a^4 - a^2*b^2 - 2*b^4)*c*d*e*f - ((a^4 - a^2*b^2 - 2*b^4)*c^2 - 4*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f + 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + 2*(a^4 - a^2*b^2 - 2*b^4)*c*d*e*f - ((a^4 - a^2*b^2 - 2*b^4)*c^2 - 4*(a^3*b + a*b^3)*c)*f^2 - 3*((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + 2*(a^4 - a^2*b^2 - 2*b^4)*c*d*e*f - ((a^4 - a^2*b^2 - 2*b^4)*c^2 - 4*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f + 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f + 2*(a^3*b + a*b^3)*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f + 2*(a^3*b + a*b^3)*d*f^2)*x + 4*(((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + 2*(a^4 - a^2*b^2 - 2*b^4)*c*d*e*f - ((a^4 - a^2*b^2 - 2*b^4)*c^2 - 4*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f + 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^3 - ((a^4 - a^2*b^2 - 2*b^4)*d^2*f^2*x^2 + 2*(a^4 - a^2*b^2 - 2*b^4)*c*d*e*f - ((a^4 - a^2*b^2 - 2*b^4)*c^2 - 4*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - a^2*b^2 - 2*b^4)*d^2*e*f + 2*(a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*((a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c)^4 + 4*(a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - a^2*b^2 - 2*b^4)*f^2*sinh(d*x + c)^4 - 2*(a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c)^2 + (a^4 - a^2*b^2 - 2*b^4)*f^2 + 2*(3*(a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c)^2 - (a^4 - a^2*b^2 - 2*b^4)*f^2)*sinh(d*x + c)^2 + 4*((a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c)^3 - (a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 2*((a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c)^4 + 4*(a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - a^2*b^2 - 2*b^4)*f^2*sinh(d*x + c)^4 - 2*(a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c)^2 + (a^4 - a^2*b^2 - 2*b^4)*f^2 + 2*(3*(a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c)^2 - (a^4 - a^2*b^2 - 2*b^4)*f^2)*sinh(d*x + c)^2 + 4*((a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c)^3 - (a^4 - a^2*b^2 - 2*b^4)*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) + 2*((a^4 + a^2*b^2)*d^2*f^2*x^2 + (a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*d*e*f - 8*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + 2*(a^3*b + a*b^3)*c*d*e*f - (a^3*b + a*b^3)*c^2*f^2)*cosh(d*x + c)^3 + 3*((a^4 + a^2*b^2)*d^2*f^2*x^2 + (a^4 + a^2*b^2)*d^2*e^2 + 2*(a^4 + a^2*b^2)*d*e*f + 2*((a^4 + a^2*b^2)*d^2*e*f + (a^4 + a^2*b^2)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^4 + a^2*b^2)*d^2*e*f - (a^4 + a^2*b^2)*d*f^2)*x + 4*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x - (a^3*b + a*b^3)*d^2*e^2 + 4*(a^3*b + a*b^3)*c*d*e*f - 2*(a^3*b + a*b^3)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + a^3*b^2)*d^3*cosh(d*x + c)^4 + 4*(a^5 + a^3*b^2)*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + a^3*b^2)*d^3*sinh(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d^3*cosh(d*x + c)^2 + (a^5 + a^3*b^2)*d^3 + 2*(3*(a^5 + a^3*b^2)*d^3*cosh(d*x + c)^2 - (a^5 + a^3*b^2)*d^3)*sinh(d*x + c)^2 + 4*((a^5 + a^3*b^2)*d^3*cosh(d*x + c)^3 - (a^5 + a^3*b^2)*d^3*cosh(d*x + c))*sinh(d*x + c))","C",0
250,1,4720,0,0.578771," ","integrate((f*x+e)*csch(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} d e + {\left(a^{4} + a^{2} b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} d e + {\left(a^{4} + a^{2} b^{2}\right)} f - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a^{3} b + a b^{3}\right)} d e + 4 \, {\left(a^{3} b + a b^{3}\right)} c f - 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x - {\left(a^{3} b + a b^{3}\right)} d e + 2 \, {\left(a^{3} b + a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d f x - 2 \, {\left(a^{3} b + a b^{3}\right)} d e + 4 \, {\left(a^{3} b + a b^{3}\right)} c f - 12 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} d e + {\left(a^{4} + a^{2} b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} f \cosh\left(d x + c\right)^{4} + 4 \, b^{4} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} f \sinh\left(d x + c\right)^{4} - 2 \, b^{4} f \cosh\left(d x + c\right)^{2} + b^{4} f + 2 \, {\left(3 \, b^{4} f \cosh\left(d x + c\right)^{2} - b^{4} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} f \cosh\left(d x + c\right)^{3} - b^{4} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{4} f \cosh\left(d x + c\right)^{4} + 4 \, b^{4} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} f \sinh\left(d x + c\right)^{4} - 2 \, b^{4} f \cosh\left(d x + c\right)^{2} + b^{4} f + 2 \, {\left(3 \, b^{4} f \cosh\left(d x + c\right)^{2} - b^{4} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} f \cosh\left(d x + c\right)^{3} - b^{4} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{4} d e - b^{4} c f + {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d e - b^{4} c f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d e - b^{4} c f - 3 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{4} d e - b^{4} c f + {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d e - b^{4} c f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d e - b^{4} c f - 3 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{4} d f x + b^{4} c f + {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d f x + b^{4} c f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d f x + b^{4} c f - 3 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{4} d f x + b^{4} c f + {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d f x + b^{4} c f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d f x + b^{4} c f - 3 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} f\right)} \cosh\left(d x + c\right) - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 2 \, {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 2 \, {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 2 \, {\left(a^{3} b + a b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 2 \, {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 3 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 2 \, {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} f + 4 \, {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 2 \, {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 2 \, {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e + {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e + {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e + {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e + {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e - 3 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e + {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} f + 4 \, {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e + {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d e + {\left(2 \, a^{3} b + 2 \, a b^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c f - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c f - 3 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} d f x + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + a^{2} b^{2}\right)} d e + 3 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} d e + {\left(a^{4} + a^{2} b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} f + 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x - {\left(a^{3} b + a b^{3}\right)} d e + 2 \, {\left(a^{3} b + a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + a^{3} b^{2}\right)} d^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(4*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*c*f)*cosh(d*x + c)^4 + 4*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*c*f)*sinh(d*x + c)^4 - 2*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*d*e + (a^4 + a^2*b^2)*f)*cosh(d*x + c)^3 - 2*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*d*e + (a^4 + a^2*b^2)*f - 8*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a^3*b + a*b^3)*d*e + 4*(a^3*b + a*b^3)*c*f - 4*((a^3*b + a*b^3)*d*f*x - (a^3*b + a*b^3)*d*e + 2*(a^3*b + a*b^3)*c*f)*cosh(d*x + c)^2 - 2*(2*(a^3*b + a*b^3)*d*f*x - 2*(a^3*b + a*b^3)*d*e + 4*(a^3*b + a*b^3)*c*f - 12*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*c*f)*cosh(d*x + c)^2 + 3*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*d*e + (a^4 + a^2*b^2)*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(b^4*f*cosh(d*x + c)^4 + 4*b^4*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*f*sinh(d*x + c)^4 - 2*b^4*f*cosh(d*x + c)^2 + b^4*f + 2*(3*b^4*f*cosh(d*x + c)^2 - b^4*f)*sinh(d*x + c)^2 + 4*(b^4*f*cosh(d*x + c)^3 - b^4*f*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^4*f*cosh(d*x + c)^4 + 4*b^4*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*f*sinh(d*x + c)^4 - 2*b^4*f*cosh(d*x + c)^2 + b^4*f + 2*(3*b^4*f*cosh(d*x + c)^2 - b^4*f)*sinh(d*x + c)^2 + 4*(b^4*f*cosh(d*x + c)^3 - b^4*f*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^4*d*e - b^4*c*f + (b^4*d*e - b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*e - b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*e - b^4*c*f)*sinh(d*x + c)^4 - 2*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2 - 2*(b^4*d*e - b^4*c*f - 3*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*e - b^4*c*f)*cosh(d*x + c)^3 - (b^4*d*e - b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^4*d*e - b^4*c*f + (b^4*d*e - b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*e - b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*e - b^4*c*f)*sinh(d*x + c)^4 - 2*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2 - 2*(b^4*d*e - b^4*c*f - 3*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*e - b^4*c*f)*cosh(d*x + c)^3 - (b^4*d*e - b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^4*d*f*x + b^4*c*f + (b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*f*x + b^4*c*f)*sinh(d*x + c)^4 - 2*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2 - 2*(b^4*d*f*x + b^4*c*f - 3*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^3 - (b^4*d*f*x + b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^4*d*f*x + b^4*c*f + (b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*f*x + b^4*c*f)*sinh(d*x + c)^4 - 2*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2 - 2*(b^4*d*f*x + b^4*c*f - 3*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^3 - (b^4*d*f*x + b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*f)*cosh(d*x + c) - ((a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c)^4 + 4*(a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - a^2*b^2 - 2*b^4)*f*sinh(d*x + c)^4 - 2*(a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c)^2 + 2*(3*(a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c)^2 - (a^4 - a^2*b^2 - 2*b^4)*f)*sinh(d*x + c)^2 + (a^4 - a^2*b^2 - 2*b^4)*f + 4*((a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c)^3 - (a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + ((a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c)^4 + 4*(a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - a^2*b^2 - 2*b^4)*f*sinh(d*x + c)^4 - 2*(a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c)^2 + 2*(3*(a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c)^2 - (a^4 - a^2*b^2 - 2*b^4)*f)*sinh(d*x + c)^2 + (a^4 - a^2*b^2 - 2*b^4)*f + 4*((a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c)^3 - (a^4 - a^2*b^2 - 2*b^4)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*d*e - 2*(a^3*b + a*b^3)*f)*cosh(d*x + c)^4 + 4*((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*d*e - 2*(a^3*b + a*b^3)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*d*e - 2*(a^3*b + a*b^3)*f)*sinh(d*x + c)^4 + (a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*d*e - 2*((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*d*e - 2*(a^3*b + a*b^3)*f)*cosh(d*x + c)^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*d*e - 3*((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*d*e - 2*(a^3*b + a*b^3)*f)*cosh(d*x + c)^2 - 2*(a^3*b + a*b^3)*f)*sinh(d*x + c)^2 - 2*(a^3*b + a*b^3)*f + 4*(((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*d*e - 2*(a^3*b + a*b^3)*f)*cosh(d*x + c)^3 - ((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*d*e - 2*(a^3*b + a*b^3)*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (((a^4 - a^2*b^2 - 2*b^4)*d*e + (2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*f)*cosh(d*x + c)^4 + 4*((a^4 - a^2*b^2 - 2*b^4)*d*e + (2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - a^2*b^2 - 2*b^4)*d*e + (2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*f)*sinh(d*x + c)^4 + (a^4 - a^2*b^2 - 2*b^4)*d*e - 2*((a^4 - a^2*b^2 - 2*b^4)*d*e + (2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*f)*cosh(d*x + c)^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d*e - 3*((a^4 - a^2*b^2 - 2*b^4)*d*e + (2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*f)*cosh(d*x + c)^2 + (2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*f)*sinh(d*x + c)^2 + (2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*f + 4*(((a^4 - a^2*b^2 - 2*b^4)*d*e + (2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*f)*cosh(d*x + c)^3 - ((a^4 - a^2*b^2 - 2*b^4)*d*e + (2*a^3*b + 2*a*b^3 - (a^4 - a^2*b^2 - 2*b^4)*c)*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*c*f)*cosh(d*x + c)^4 + 4*((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*c*f)*sinh(d*x + c)^4 + (a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*c*f - 2*((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*c*f)*cosh(d*x + c)^2 - 2*((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*c*f - 3*((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*c*f)*cosh(d*x + c)^3 - ((a^4 - a^2*b^2 - 2*b^4)*d*f*x + (a^4 - a^2*b^2 - 2*b^4)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*((a^4 + a^2*b^2)*d*f*x - 8*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*c*f)*cosh(d*x + c)^3 + (a^4 + a^2*b^2)*d*e + 3*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*d*e + (a^4 + a^2*b^2)*f)*cosh(d*x + c)^2 - (a^4 + a^2*b^2)*f + 4*((a^3*b + a*b^3)*d*f*x - (a^3*b + a*b^3)*d*e + 2*(a^3*b + a*b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + a^3*b^2)*d^2*cosh(d*x + c)^4 + 4*(a^5 + a^3*b^2)*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + a^3*b^2)*d^2*sinh(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d^2*cosh(d*x + c)^2 + (a^5 + a^3*b^2)*d^2 + 2*(3*(a^5 + a^3*b^2)*d^2*cosh(d*x + c)^2 - (a^5 + a^3*b^2)*d^2)*sinh(d*x + c)^2 + 4*((a^5 + a^3*b^2)*d^2*cosh(d*x + c)^3 - (a^5 + a^3*b^2)*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
251,1,1203,0,0.664047," ","integrate(csch(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a^{3} b + 4 \, a b^{3} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{3} b + 2 \, a b^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3} + 2 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} \cosh\left(d x + c\right)^{3} - b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \sinh\left(d x + c\right)^{4} + a^{4} - a^{2} b^{2} - 2 \, b^{4} - 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4} - 3 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \sinh\left(d x + c\right)^{4} + a^{4} - a^{2} b^{2} - 2 \, b^{4} - 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4} - 3 \, {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(a^{4} + a^{2} b^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d + 4 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(4*a^3*b + 4*a*b^3 + 2*(a^4 + a^2*b^2)*cosh(d*x + c)^3 + 2*(a^4 + a^2*b^2)*sinh(d*x + c)^3 - 4*(a^3*b + a*b^3)*cosh(d*x + c)^2 - 2*(2*a^3*b + 2*a*b^3 - 3*(a^4 + a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(b^3*cosh(d*x + c)^4 + 4*b^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*sinh(d*x + c)^4 - 2*b^3*cosh(d*x + c)^2 + b^3 + 2*(3*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^2 + 4*(b^3*cosh(d*x + c)^3 - b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 2*(a^4 + a^2*b^2)*cosh(d*x + c) - ((a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c)^4 + 4*(a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - a^2*b^2 - 2*b^4)*sinh(d*x + c)^4 + a^4 - a^2*b^2 - 2*b^4 - 2*(a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c)^2 - 2*(a^4 - a^2*b^2 - 2*b^4 - 3*(a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c)^3 - (a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c)^4 + 4*(a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - a^2*b^2 - 2*b^4)*sinh(d*x + c)^4 + a^4 - a^2*b^2 - 2*b^4 - 2*(a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c)^2 - 2*(a^4 - a^2*b^2 - 2*b^4 - 3*(a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c)^3 - (a^4 - a^2*b^2 - 2*b^4)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(a^4 + a^2*b^2 + 3*(a^4 + a^2*b^2)*cosh(d*x + c)^2 - 4*(a^3*b + a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + a^3*b^2)*d*cosh(d*x + c)^4 + 4*(a^5 + a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + a^3*b^2)*d*sinh(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^5 + a^3*b^2)*d*cosh(d*x + c)^2 - (a^5 + a^3*b^2)*d)*sinh(d*x + c)^2 + (a^5 + a^3*b^2)*d + 4*((a^5 + a^3*b^2)*d*cosh(d*x + c)^3 - (a^5 + a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
252,0,0,0,0.679415," ","integrate(csch(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(d x + c\right)^{3}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(csch(d*x + c)^3/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
253,1,295,0,0.578971," ","integrate((f*x+e)^3*cosh(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{i \, d^{4} f^{3} x^{4} + 4 i \, d^{4} e f^{2} x^{3} + 6 i \, d^{4} e^{2} f x^{2} + 4 i \, d^{4} e^{3} x + 8 i \, c d^{3} e^{3} - 12 i \, c^{2} d^{2} e^{2} f + 8 i \, c^{3} d e f^{2} - 2 i \, c^{4} f^{3} - 48 i \, f^{3} {\rm polylog}\left(4, -i \, e^{\left(d x + c\right)}\right) + {\left(-24 i \, d^{2} f^{3} x^{2} - 48 i \, d^{2} e f^{2} x - 24 i \, d^{2} e^{2} f\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(-8 i \, d^{3} e^{3} + 24 i \, c d^{2} e^{2} f - 24 i \, c^{2} d e f^{2} + 8 i \, c^{3} f^{3}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(-8 i \, d^{3} f^{3} x^{3} - 24 i \, d^{3} e f^{2} x^{2} - 24 i \, d^{3} e^{2} f x - 24 i \, c d^{2} e^{2} f + 24 i \, c^{2} d e f^{2} - 8 i \, c^{3} f^{3}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(48 i \, d f^{3} x + 48 i \, d e f^{2}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right)}{4 \, a d^{4}}"," ",0,"1/4*(I*d^4*f^3*x^4 + 4*I*d^4*e*f^2*x^3 + 6*I*d^4*e^2*f*x^2 + 4*I*d^4*e^3*x + 8*I*c*d^3*e^3 - 12*I*c^2*d^2*e^2*f + 8*I*c^3*d*e*f^2 - 2*I*c^4*f^3 - 48*I*f^3*polylog(4, -I*e^(d*x + c)) + (-24*I*d^2*f^3*x^2 - 48*I*d^2*e*f^2*x - 24*I*d^2*e^2*f)*dilog(-I*e^(d*x + c)) + (-8*I*d^3*e^3 + 24*I*c*d^2*e^2*f - 24*I*c^2*d*e*f^2 + 8*I*c^3*f^3)*log(e^(d*x + c) - I) + (-8*I*d^3*f^3*x^3 - 24*I*d^3*e*f^2*x^2 - 24*I*d^3*e^2*f*x - 24*I*c*d^2*e^2*f + 24*I*c^2*d*e*f^2 - 8*I*c^3*f^3)*log(I*e^(d*x + c) + 1) + (48*I*d*f^3*x + 48*I*d*e*f^2)*polylog(3, -I*e^(d*x + c)))/(a*d^4)","C",0
254,1,181,0,0.457657," ","integrate((f*x+e)^2*cosh(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{i \, d^{3} f^{2} x^{3} + 3 i \, d^{3} e f x^{2} + 3 i \, d^{3} e^{2} x + 6 i \, c d^{2} e^{2} - 6 i \, c^{2} d e f + 2 i \, c^{3} f^{2} + 12 i \, f^{2} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right) + {\left(-12 i \, d f^{2} x - 12 i \, d e f\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(-6 i \, d^{2} e^{2} + 12 i \, c d e f - 6 i \, c^{2} f^{2}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(-6 i \, d^{2} f^{2} x^{2} - 12 i \, d^{2} e f x - 12 i \, c d e f + 6 i \, c^{2} f^{2}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right)}{3 \, a d^{3}}"," ",0,"1/3*(I*d^3*f^2*x^3 + 3*I*d^3*e*f*x^2 + 3*I*d^3*e^2*x + 6*I*c*d^2*e^2 - 6*I*c^2*d*e*f + 2*I*c^3*f^2 + 12*I*f^2*polylog(3, -I*e^(d*x + c)) + (-12*I*d*f^2*x - 12*I*d*e*f)*dilog(-I*e^(d*x + c)) + (-6*I*d^2*e^2 + 12*I*c*d*e*f - 6*I*c^2*f^2)*log(e^(d*x + c) - I) + (-6*I*d^2*f^2*x^2 - 12*I*d^2*e*f*x - 12*I*c*d*e*f + 6*I*c^2*f^2)*log(I*e^(d*x + c) + 1))/(a*d^3)","C",0
255,1,89,0,0.467693," ","integrate((f*x+e)*cosh(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{i \, d^{2} f x^{2} + 2 i \, d^{2} e x + 4 i \, c d e - 2 i \, c^{2} f - 4 i \, f {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(-4 i \, d e + 4 i \, c f\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(-4 i \, d f x - 4 i \, c f\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right)}{2 \, a d^{2}}"," ",0,"1/2*(I*d^2*f*x^2 + 2*I*d^2*e*x + 4*I*c*d*e - 2*I*c^2*f - 4*I*f*dilog(-I*e^(d*x + c)) + (-4*I*d*e + 4*I*c*f)*log(e^(d*x + c) - I) + (-4*I*d*f*x - 4*I*c*f)*log(I*e^(d*x + c) + 1))/(a*d^2)","A",0
256,1,23,0,0.480670," ","integrate(cosh(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{i \, d x - 2 i \, \log\left(e^{\left(d x + c\right)} - i\right)}{a d}"," ",0,"(I*d*x - 2*I*log(e^(d*x + c) - I))/(a*d)","A",0
257,0,0,0,0.425103," ","integrate(cosh(d*x+c)/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, e^{\left(d x + c\right)} + 1}{-i \, a f x - i \, a e + {\left(a f x + a e\right)} e^{\left(d x + c\right)}}, x\right)"," ",0,"integral((-I*e^(d*x + c) + 1)/(-I*a*f*x - I*a*e + (a*f*x + a*e)*e^(d*x + c)), x)","F",0
258,0,0,0,0.567475," ","integrate(cosh(d*x+c)/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{-i \, e^{\left(d x + c\right)} + 1}{-i \, a f^{2} x^{2} - 2 i \, a e f x - i \, a e^{2} + {\left(a f^{2} x^{2} + 2 \, a e f x + a e^{2}\right)} e^{\left(d x + c\right)}}, x\right)"," ",0,"integral((-I*e^(d*x + c) + 1)/(-I*a*f^2*x^2 - 2*I*a*e*f*x - I*a*e^2 + (a*f^2*x^2 + 2*a*e*f*x + a*e^2)*e^(d*x + c)), x)","F",0
259,1,258,0,0.474526," ","integrate((f*x+e)^3*cosh(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-2 i \, d^{3} f^{3} x^{3} - 2 i \, d^{3} e^{3} - 6 i \, d^{2} e^{2} f - 12 i \, d e f^{2} - 12 i \, f^{3} + {\left(-6 i \, d^{3} e f^{2} - 6 i \, d^{2} f^{3}\right)} x^{2} + {\left(-6 i \, d^{3} e^{2} f - 12 i \, d^{2} e f^{2} - 12 i \, d f^{3}\right)} x + {\left(-2 i \, d^{3} f^{3} x^{3} - 2 i \, d^{3} e^{3} + 6 i \, d^{2} e^{2} f - 12 i \, d e f^{2} + 12 i \, f^{3} + {\left(-6 i \, d^{3} e f^{2} + 6 i \, d^{2} f^{3}\right)} x^{2} + {\left(-6 i \, d^{3} e^{2} f + 12 i \, d^{2} e f^{2} - 12 i \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(d^{4} f^{3} x^{4} + 4 \, d^{4} e f^{2} x^{3} + 6 \, d^{4} e^{2} f x^{2} + 4 \, d^{4} e^{3} x\right)} e^{\left(d x + c\right)}\right)} e^{\left(-d x - c\right)}}{4 \, a d^{4}}"," ",0,"1/4*(-2*I*d^3*f^3*x^3 - 2*I*d^3*e^3 - 6*I*d^2*e^2*f - 12*I*d*e*f^2 - 12*I*f^3 + (-6*I*d^3*e*f^2 - 6*I*d^2*f^3)*x^2 + (-6*I*d^3*e^2*f - 12*I*d^2*e*f^2 - 12*I*d*f^3)*x + (-2*I*d^3*f^3*x^3 - 2*I*d^3*e^3 + 6*I*d^2*e^2*f - 12*I*d*e*f^2 + 12*I*f^3 + (-6*I*d^3*e*f^2 + 6*I*d^2*f^3)*x^2 + (-6*I*d^3*e^2*f + 12*I*d^2*e*f^2 - 12*I*d*f^3)*x)*e^(2*d*x + 2*c) + (d^4*f^3*x^4 + 4*d^4*e*f^2*x^3 + 6*d^4*e^2*f*x^2 + 4*d^4*e^3*x)*e^(d*x + c))*e^(-d*x - c)/(a*d^4)","B",0
260,1,157,0,0.493166," ","integrate((f*x+e)^2*cosh(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-3 i \, d^{2} f^{2} x^{2} - 3 i \, d^{2} e^{2} - 6 i \, d e f - 6 i \, f^{2} + {\left(-6 i \, d^{2} e f - 6 i \, d f^{2}\right)} x + {\left(-3 i \, d^{2} f^{2} x^{2} - 3 i \, d^{2} e^{2} + 6 i \, d e f - 6 i \, f^{2} + {\left(-6 i \, d^{2} e f + 6 i \, d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d^{3} f^{2} x^{3} + 3 \, d^{3} e f x^{2} + 3 \, d^{3} e^{2} x\right)} e^{\left(d x + c\right)}\right)} e^{\left(-d x - c\right)}}{6 \, a d^{3}}"," ",0,"1/6*(-3*I*d^2*f^2*x^2 - 3*I*d^2*e^2 - 6*I*d*e*f - 6*I*f^2 + (-6*I*d^2*e*f - 6*I*d*f^2)*x + (-3*I*d^2*f^2*x^2 - 3*I*d^2*e^2 + 6*I*d*e*f - 6*I*f^2 + (-6*I*d^2*e*f + 6*I*d*f^2)*x)*e^(2*d*x + 2*c) + 2*(d^3*f^2*x^3 + 3*d^3*e*f*x^2 + 3*d^3*e^2*x)*e^(d*x + c))*e^(-d*x - c)/(a*d^3)","B",0
261,1,76,0,0.471235," ","integrate((f*x+e)*cosh(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, d f x - i \, d e + {\left(-i \, d f x - i \, d e + i \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(d^{2} f x^{2} + 2 \, d^{2} e x\right)} e^{\left(d x + c\right)} - i \, f\right)} e^{\left(-d x - c\right)}}{2 \, a d^{2}}"," ",0,"1/2*(-I*d*f*x - I*d*e + (-I*d*f*x - I*d*e + I*f)*e^(2*d*x + 2*c) + (d^2*f*x^2 + 2*d^2*e*x)*e^(d*x + c) - I*f)*e^(-d*x - c)/(a*d^2)","A",0
262,1,40,0,0.450730," ","integrate(cosh(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, d x e^{\left(d x + c\right)} - i \, e^{\left(2 \, d x + 2 \, c\right)} - i\right)} e^{\left(-d x - c\right)}}{2 \, a d}"," ",0,"1/2*(2*d*x*e^(d*x + c) - I*e^(2*d*x + 2*c) - I)*e^(-d*x - c)/(a*d)","A",0
263,1,79,0,0.487369," ","integrate(cosh(d*x+c)^2/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{i \, {\rm Ei}\left(-\frac{d f x + d e}{f}\right) e^{\left(\frac{d e - c f}{f}\right)} - i \, {\rm Ei}\left(\frac{d f x + d e}{f}\right) e^{\left(-\frac{d e - c f}{f}\right)} + 2 \, \log\left(\frac{f x + e}{f}\right)}{2 \, a f}"," ",0,"1/2*(I*Ei(-(d*f*x + d*e)/f)*e^((d*e - c*f)/f) - I*Ei((d*f*x + d*e)/f)*e^(-(d*e - c*f)/f) + 2*log((f*x + e)/f))/(a*f)","A",0
264,1,129,0,0.509347," ","integrate(cosh(d*x+c)^2/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(i \, f e^{\left(2 \, d x + 2 \, c\right)} + {\left({\left(-i \, d f x - i \, d e\right)} {\rm Ei}\left(-\frac{d f x + d e}{f}\right) e^{\left(\frac{d e - c f}{f}\right)} + {\left(-i \, d f x - i \, d e\right)} {\rm Ei}\left(\frac{d f x + d e}{f}\right) e^{\left(-\frac{d e - c f}{f}\right)} - 2 \, f\right)} e^{\left(d x + c\right)} - i \, f\right)} e^{\left(-d x - c\right)}}{2 \, {\left(a f^{3} x + a e f^{2}\right)}}"," ",0,"1/2*(I*f*e^(2*d*x + 2*c) + ((-I*d*f*x - I*d*e)*Ei(-(d*f*x + d*e)/f)*e^((d*e - c*f)/f) + (-I*d*f*x - I*d*e)*Ei((d*f*x + d*e)/f)*e^(-(d*e - c*f)/f) - 2*f)*e^(d*x + c) - I*f)*e^(-d*x - c)/(a*f^3*x + a*e*f^2)","A",0
265,1,401,0,0.467381," ","integrate((f*x+e)^3*cosh(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-4 i \, d^{3} f^{3} x^{3} - 4 i \, d^{3} e^{3} - 6 i \, d^{2} e^{2} f - 6 i \, d e f^{2} - 3 i \, f^{3} + {\left(-12 i \, d^{3} e f^{2} - 6 i \, d^{2} f^{3}\right)} x^{2} + {\left(-12 i \, d^{3} e^{2} f - 12 i \, d^{2} e f^{2} - 6 i \, d f^{3}\right)} x + {\left(-4 i \, d^{3} f^{3} x^{3} - 4 i \, d^{3} e^{3} + 6 i \, d^{2} e^{2} f - 6 i \, d e f^{2} + 3 i \, f^{3} + {\left(-12 i \, d^{3} e f^{2} + 6 i \, d^{2} f^{3}\right)} x^{2} + {\left(-12 i \, d^{3} e^{2} f + 12 i \, d^{2} e f^{2} - 6 i \, d f^{3}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + 16 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} - 3 \, d^{2} e^{2} f + 6 \, d e f^{2} - 6 \, f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - 16 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f + 6 \, d e f^{2} + 6 \, f^{3} + 3 \, {\left(d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f + 2 \, d^{2} e f^{2} + 2 \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{32 \, a d^{4}}"," ",0,"1/32*(-4*I*d^3*f^3*x^3 - 4*I*d^3*e^3 - 6*I*d^2*e^2*f - 6*I*d*e*f^2 - 3*I*f^3 + (-12*I*d^3*e*f^2 - 6*I*d^2*f^3)*x^2 + (-12*I*d^3*e^2*f - 12*I*d^2*e*f^2 - 6*I*d*f^3)*x + (-4*I*d^3*f^3*x^3 - 4*I*d^3*e^3 + 6*I*d^2*e^2*f - 6*I*d*e*f^2 + 3*I*f^3 + (-12*I*d^3*e*f^2 + 6*I*d^2*f^3)*x^2 + (-12*I*d^3*e^2*f + 12*I*d^2*e*f^2 - 6*I*d*f^3)*x)*e^(4*d*x + 4*c) + 16*(d^3*f^3*x^3 + d^3*e^3 - 3*d^2*e^2*f + 6*d*e*f^2 - 6*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2 + 2*d*f^3)*x)*e^(3*d*x + 3*c) - 16*(d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f + 6*d*e*f^2 + 6*f^3 + 3*(d^3*e*f^2 + d^2*f^3)*x^2 + 3*(d^3*e^2*f + 2*d^2*e*f^2 + 2*d*f^3)*x)*e^(d*x + c))*e^(-2*d*x - 2*c)/(a*d^4)","A",0
266,1,225,0,0.491076," ","integrate((f*x+e)^2*cosh(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-2 i \, d^{2} f^{2} x^{2} - 2 i \, d^{2} e^{2} - 2 i \, d e f - i \, f^{2} + {\left(-4 i \, d^{2} e f - 2 i \, d f^{2}\right)} x + {\left(-2 i \, d^{2} f^{2} x^{2} - 2 i \, d^{2} e^{2} + 2 i \, d e f - i \, f^{2} + {\left(-4 i \, d^{2} e f + 2 i \, d f^{2}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + 8 \, {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} - 2 \, d e f + 2 \, f^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - 8 \, {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f + 2 \, f^{2} + 2 \, {\left(d^{2} e f + d f^{2}\right)} x\right)} e^{\left(d x + c\right)}\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{16 \, a d^{3}}"," ",0,"1/16*(-2*I*d^2*f^2*x^2 - 2*I*d^2*e^2 - 2*I*d*e*f - I*f^2 + (-4*I*d^2*e*f - 2*I*d*f^2)*x + (-2*I*d^2*f^2*x^2 - 2*I*d^2*e^2 + 2*I*d*e*f - I*f^2 + (-4*I*d^2*e*f + 2*I*d*f^2)*x)*e^(4*d*x + 4*c) + 8*(d^2*f^2*x^2 + d^2*e^2 - 2*d*e*f + 2*f^2 + 2*(d^2*e*f - d*f^2)*x)*e^(3*d*x + 3*c) - 8*(d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f + 2*f^2 + 2*(d^2*e*f + d*f^2)*x)*e^(d*x + c))*e^(-2*d*x - 2*c)/(a*d^3)","A",0
267,1,92,0,0.468637," ","integrate((f*x+e)*cosh(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-2 i \, d f x - 2 i \, d e + {\left(-2 i \, d f x - 2 i \, d e + i \, f\right)} e^{\left(4 \, d x + 4 \, c\right)} + 8 \, {\left(d f x + d e - f\right)} e^{\left(3 \, d x + 3 \, c\right)} - 8 \, {\left(d f x + d e + f\right)} e^{\left(d x + c\right)} - i \, f\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{16 \, a d^{2}}"," ",0,"1/16*(-2*I*d*f*x - 2*I*d*e + (-2*I*d*f*x - 2*I*d*e + I*f)*e^(4*d*x + 4*c) + 8*(d*f*x + d*e - f)*e^(3*d*x + 3*c) - 8*(d*f*x + d*e + f)*e^(d*x + c) - I*f)*e^(-2*d*x - 2*c)/(a*d^2)","A",0
268,1,49,0,0.522622," ","integrate(cosh(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(-i \, e^{\left(4 \, d x + 4 \, c\right)} + 4 \, e^{\left(3 \, d x + 3 \, c\right)} - 4 \, e^{\left(d x + c\right)} - i\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{8 \, a d}"," ",0,"1/8*(-I*e^(4*d*x + 4*c) + 4*e^(3*d*x + 3*c) - 4*e^(d*x + c) - I)*e^(-2*d*x - 2*c)/(a*d)","A",0
269,1,127,0,0.536739," ","integrate(cosh(d*x+c)^3/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{i \, {\rm Ei}\left(-\frac{2 \, {\left(d f x + d e\right)}}{f}\right) e^{\left(\frac{2 \, {\left(d e - c f\right)}}{f}\right)} + 2 \, {\rm Ei}\left(-\frac{d f x + d e}{f}\right) e^{\left(\frac{d e - c f}{f}\right)} + 2 \, {\rm Ei}\left(\frac{d f x + d e}{f}\right) e^{\left(-\frac{d e - c f}{f}\right)} - i \, {\rm Ei}\left(\frac{2 \, {\left(d f x + d e\right)}}{f}\right) e^{\left(-\frac{2 \, {\left(d e - c f\right)}}{f}\right)}}{4 \, a f}"," ",0,"1/4*(I*Ei(-2*(d*f*x + d*e)/f)*e^(2*(d*e - c*f)/f) + 2*Ei(-(d*f*x + d*e)/f)*e^((d*e - c*f)/f) + 2*Ei((d*f*x + d*e)/f)*e^(-(d*e - c*f)/f) - I*Ei(2*(d*f*x + d*e)/f)*e^(-2*(d*e - c*f)/f))/(a*f)","A",0
270,1,226,0,0.517971," ","integrate(cosh(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(i \, f e^{\left(4 \, d x + 4 \, c\right)} - 2 \, f e^{\left(3 \, d x + 3 \, c\right)} + {\left({\left(-2 i \, d f x - 2 i \, d e\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + d e\right)}}{f}\right) e^{\left(\frac{2 \, {\left(d e - c f\right)}}{f}\right)} - 2 \, {\left(d f x + d e\right)} {\rm Ei}\left(-\frac{d f x + d e}{f}\right) e^{\left(\frac{d e - c f}{f}\right)} + 2 \, {\left(d f x + d e\right)} {\rm Ei}\left(\frac{d f x + d e}{f}\right) e^{\left(-\frac{d e - c f}{f}\right)} + {\left(-2 i \, d f x - 2 i \, d e\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + d e\right)}}{f}\right) e^{\left(-\frac{2 \, {\left(d e - c f\right)}}{f}\right)}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, f e^{\left(d x + c\right)} - i \, f\right)} e^{\left(-2 \, d x - 2 \, c\right)}}{4 \, {\left(a f^{3} x + a e f^{2}\right)}}"," ",0,"1/4*(I*f*e^(4*d*x + 4*c) - 2*f*e^(3*d*x + 3*c) + ((-2*I*d*f*x - 2*I*d*e)*Ei(-2*(d*f*x + d*e)/f)*e^(2*(d*e - c*f)/f) - 2*(d*f*x + d*e)*Ei(-(d*f*x + d*e)/f)*e^((d*e - c*f)/f) + 2*(d*f*x + d*e)*Ei((d*f*x + d*e)/f)*e^(-(d*e - c*f)/f) + (-2*I*d*f*x - 2*I*d*e)*Ei(2*(d*f*x + d*e)/f)*e^(-2*(d*e - c*f)/f))*e^(2*d*x + 2*c) - 2*f*e^(d*x + c) - I*f)*e^(-2*d*x - 2*c)/(a*f^3*x + a*e*f^2)","A",0
271,1,1450,0,0.549387," ","integrate((f*x+e)^3*sech(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{-6 i \, d^{2} e^{2} f + 12 i \, c d e f^{2} - 6 i \, c^{2} f^{3} + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(i \, e^{\left(d x + c\right)}\right) + {\left(3 i \, d^{2} f^{3} x^{2} + 6 i \, d^{2} e f^{2} x + 3 i \, d^{2} e^{2} f - 12 i \, f^{3} + {\left(-3 i \, d^{2} f^{3} x^{2} - 6 i \, d^{2} e f^{2} x - 3 i \, d^{2} e^{2} f + 12 i \, f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 6 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f - 4 \, f^{3}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(-6 i \, d^{2} f^{3} x^{2} - 12 i \, d^{2} e f^{2} x - 12 i \, c d e f^{2} + 6 i \, c^{2} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 3 \, d^{2} e^{2} f - 12 \, c d e f^{2} + 6 \, c^{2} f^{3} + 3 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + 3 \, {\left(d^{3} e^{2} f - 2 \, d^{2} e f^{2}\right)} x\right)} e^{\left(d x + c\right)} + {\left(-i \, d^{3} e^{3} + 3 i \, c d^{2} e^{2} f - 3 i \, c^{2} d e f^{2} + i \, c^{3} f^{3} + {\left(i \, d^{3} e^{3} - 3 i \, c d^{2} e^{2} f + 3 i \, c^{2} d e f^{2} - i \, c^{3} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + i\right) + {\left(i \, d^{3} e^{3} - 3 i \, c d^{2} e^{2} f + {\left(3 i \, c^{2} - 12 i\right)} d e f^{2} + {\left(-i \, c^{3} + 12 i \, c\right)} f^{3} + {\left(-i \, d^{3} e^{3} + 3 i \, c d^{2} e^{2} f + {\left(-3 i \, c^{2} + 12 i\right)} d e f^{2} + {\left(i \, c^{3} - 12 i \, c\right)} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, {\left(c^{2} - 4\right)} d e f^{2} - {\left(c^{3} - 12 \, c\right)} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(i \, d^{3} f^{3} x^{3} + 3 i \, d^{3} e f^{2} x^{2} + 3 i \, c d^{2} e^{2} f - 3 i \, c^{2} d e f^{2} + {\left(i \, c^{3} - 12 i \, c\right)} f^{3} + {\left(3 i \, d^{3} e^{2} f - 12 i \, d f^{3}\right)} x + {\left(-i \, d^{3} f^{3} x^{3} - 3 i \, d^{3} e f^{2} x^{2} - 3 i \, c d^{2} e^{2} f + 3 i \, c^{2} d e f^{2} + {\left(-i \, c^{3} + 12 i \, c\right)} f^{3} + {\left(-3 i \, d^{3} e^{2} f + 12 i \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} - 12 \, c\right)} f^{3} + 3 \, {\left(d^{3} e^{2} f - 4 \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(-i \, d^{3} f^{3} x^{3} - 3 i \, d^{3} e f^{2} x^{2} - 3 i \, d^{3} e^{2} f x - 3 i \, c d^{2} e^{2} f + 3 i \, c^{2} d e f^{2} - i \, c^{3} f^{3} + {\left(i \, d^{3} f^{3} x^{3} + 3 i \, d^{3} e f^{2} x^{2} + 3 i \, d^{3} e^{2} f x + 3 i \, c d^{2} e^{2} f - 3 i \, c^{2} d e f^{2} + i \, c^{3} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(-i \, e^{\left(d x + c\right)} + 1\right) + {\left(6 i \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} + 12 \, f^{3} e^{\left(d x + c\right)} - 6 i \, f^{3}\right)} {\rm polylog}\left(4, i \, e^{\left(d x + c\right)}\right) + {\left(-6 i \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} - 12 \, f^{3} e^{\left(d x + c\right)} + 6 i \, f^{3}\right)} {\rm polylog}\left(4, -i \, e^{\left(d x + c\right)}\right) + {\left(6 i \, d f^{3} x + 6 i \, d e f^{2} + {\left(-6 i \, d f^{3} x - 6 i \, d e f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 12 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, i \, e^{\left(d x + c\right)}\right) + {\left(-6 i \, d f^{3} x - 6 i \, d e f^{2} + {\left(6 i \, d f^{3} x + 6 i \, d e f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 12 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right)}{2 \, a d^{4} e^{\left(2 \, d x + 2 \, c\right)} - 4 i \, a d^{4} e^{\left(d x + c\right)} - 2 \, a d^{4}}"," ",0,"(-6*I*d^2*e^2*f + 12*I*c*d*e*f^2 - 6*I*c^2*f^3 + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f)*e^(2*d*x + 2*c) + 6*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*e^(d*x + c))*dilog(I*e^(d*x + c)) + (3*I*d^2*f^3*x^2 + 6*I*d^2*e*f^2*x + 3*I*d^2*e^2*f - 12*I*f^3 + (-3*I*d^2*f^3*x^2 - 6*I*d^2*e*f^2*x - 3*I*d^2*e^2*f + 12*I*f^3)*e^(2*d*x + 2*c) - 6*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f - 4*f^3)*e^(d*x + c))*dilog(-I*e^(d*x + c)) + (-6*I*d^2*f^3*x^2 - 12*I*d^2*e*f^2*x - 12*I*c*d*e*f^2 + 6*I*c^2*f^3)*e^(2*d*x + 2*c) + 2*(d^3*f^3*x^3 + d^3*e^3 + 3*d^2*e^2*f - 12*c*d*e*f^2 + 6*c^2*f^3 + 3*(d^3*e*f^2 - d^2*f^3)*x^2 + 3*(d^3*e^2*f - 2*d^2*e*f^2)*x)*e^(d*x + c) + (-I*d^3*e^3 + 3*I*c*d^2*e^2*f - 3*I*c^2*d*e*f^2 + I*c^3*f^3 + (I*d^3*e^3 - 3*I*c*d^2*e^2*f + 3*I*c^2*d*e*f^2 - I*c^3*f^3)*e^(2*d*x + 2*c) + 2*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*e^(d*x + c))*log(e^(d*x + c) + I) + (I*d^3*e^3 - 3*I*c*d^2*e^2*f + (3*I*c^2 - 12*I)*d*e*f^2 + (-I*c^3 + 12*I*c)*f^3 + (-I*d^3*e^3 + 3*I*c*d^2*e^2*f + (-3*I*c^2 + 12*I)*d*e*f^2 + (I*c^3 - 12*I*c)*f^3)*e^(2*d*x + 2*c) - 2*(d^3*e^3 - 3*c*d^2*e^2*f + 3*(c^2 - 4)*d*e*f^2 - (c^3 - 12*c)*f^3)*e^(d*x + c))*log(e^(d*x + c) - I) + (I*d^3*f^3*x^3 + 3*I*d^3*e*f^2*x^2 + 3*I*c*d^2*e^2*f - 3*I*c^2*d*e*f^2 + (I*c^3 - 12*I*c)*f^3 + (3*I*d^3*e^2*f - 12*I*d*f^3)*x + (-I*d^3*f^3*x^3 - 3*I*d^3*e*f^2*x^2 - 3*I*c*d^2*e^2*f + 3*I*c^2*d*e*f^2 + (-I*c^3 + 12*I*c)*f^3 + (-3*I*d^3*e^2*f + 12*I*d*f^3)*x)*e^(2*d*x + 2*c) - 2*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 - 12*c)*f^3 + 3*(d^3*e^2*f - 4*d*f^3)*x)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (-I*d^3*f^3*x^3 - 3*I*d^3*e*f^2*x^2 - 3*I*d^3*e^2*f*x - 3*I*c*d^2*e^2*f + 3*I*c^2*d*e*f^2 - I*c^3*f^3 + (I*d^3*f^3*x^3 + 3*I*d^3*e*f^2*x^2 + 3*I*d^3*e^2*f*x + 3*I*c*d^2*e^2*f - 3*I*c^2*d*e*f^2 + I*c^3*f^3)*e^(2*d*x + 2*c) + 2*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*e^(d*x + c))*log(-I*e^(d*x + c) + 1) + (6*I*f^3*e^(2*d*x + 2*c) + 12*f^3*e^(d*x + c) - 6*I*f^3)*polylog(4, I*e^(d*x + c)) + (-6*I*f^3*e^(2*d*x + 2*c) - 12*f^3*e^(d*x + c) + 6*I*f^3)*polylog(4, -I*e^(d*x + c)) + (6*I*d*f^3*x + 6*I*d*e*f^2 + (-6*I*d*f^3*x - 6*I*d*e*f^2)*e^(2*d*x + 2*c) - 12*(d*f^3*x + d*e*f^2)*e^(d*x + c))*polylog(3, I*e^(d*x + c)) + (-6*I*d*f^3*x - 6*I*d*e*f^2 + (6*I*d*f^3*x + 6*I*d*e*f^2)*e^(2*d*x + 2*c) + 12*(d*f^3*x + d*e*f^2)*e^(d*x + c))*polylog(3, -I*e^(d*x + c)))/(2*a*d^4*e^(2*d*x + 2*c) - 4*I*a*d^4*e^(d*x + c) - 2*a*d^4)","C",0
272,1,800,0,0.608015," ","integrate((f*x+e)^2*sech(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{-4 i \, d e f + 4 i \, c f^{2} + {\left(-2 i \, d f^{2} x - 2 i \, d e f + {\left(2 i \, d f^{2} x + 2 i \, d e f\right)} e^{\left(2 \, d x + 2 \, c\right)} + 4 \, {\left(d f^{2} x + d e f\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(i \, e^{\left(d x + c\right)}\right) + {\left(2 i \, d f^{2} x + 2 i \, d e f + {\left(-2 i \, d f^{2} x - 2 i \, d e f\right)} e^{\left(2 \, d x + 2 \, c\right)} - 4 \, {\left(d f^{2} x + d e f\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(-4 i \, d f^{2} x - 4 i \, c f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d^{2} f^{2} x^{2} + d^{2} e^{2} + 2 \, d e f - 4 \, c f^{2} + 2 \, {\left(d^{2} e f - d f^{2}\right)} x\right)} e^{\left(d x + c\right)} + {\left(-i \, d^{2} e^{2} + 2 i \, c d e f - i \, c^{2} f^{2} + {\left(i \, d^{2} e^{2} - 2 i \, c d e f + i \, c^{2} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + i\right) + {\left(i \, d^{2} e^{2} - 2 i \, c d e f + {\left(i \, c^{2} - 4 i\right)} f^{2} + {\left(-i \, d^{2} e^{2} + 2 i \, c d e f + {\left(-i \, c^{2} + 4 i\right)} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(d^{2} e^{2} - 2 \, c d e f + {\left(c^{2} - 4\right)} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(i \, d^{2} f^{2} x^{2} + 2 i \, d^{2} e f x + 2 i \, c d e f - i \, c^{2} f^{2} + {\left(-i \, d^{2} f^{2} x^{2} - 2 i \, d^{2} e f x - 2 i \, c d e f + i \, c^{2} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(-i \, d^{2} f^{2} x^{2} - 2 i \, d^{2} e f x - 2 i \, c d e f + i \, c^{2} f^{2} + {\left(i \, d^{2} f^{2} x^{2} + 2 i \, d^{2} e f x + 2 i \, c d e f - i \, c^{2} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(-i \, e^{\left(d x + c\right)} + 1\right) + {\left(-2 i \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} - 4 \, f^{2} e^{\left(d x + c\right)} + 2 i \, f^{2}\right)} {\rm polylog}\left(3, i \, e^{\left(d x + c\right)}\right) + {\left(2 i \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} + 4 \, f^{2} e^{\left(d x + c\right)} - 2 i \, f^{2}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right)}{2 \, a d^{3} e^{\left(2 \, d x + 2 \, c\right)} - 4 i \, a d^{3} e^{\left(d x + c\right)} - 2 \, a d^{3}}"," ",0,"(-4*I*d*e*f + 4*I*c*f^2 + (-2*I*d*f^2*x - 2*I*d*e*f + (2*I*d*f^2*x + 2*I*d*e*f)*e^(2*d*x + 2*c) + 4*(d*f^2*x + d*e*f)*e^(d*x + c))*dilog(I*e^(d*x + c)) + (2*I*d*f^2*x + 2*I*d*e*f + (-2*I*d*f^2*x - 2*I*d*e*f)*e^(2*d*x + 2*c) - 4*(d*f^2*x + d*e*f)*e^(d*x + c))*dilog(-I*e^(d*x + c)) + (-4*I*d*f^2*x - 4*I*c*f^2)*e^(2*d*x + 2*c) + 2*(d^2*f^2*x^2 + d^2*e^2 + 2*d*e*f - 4*c*f^2 + 2*(d^2*e*f - d*f^2)*x)*e^(d*x + c) + (-I*d^2*e^2 + 2*I*c*d*e*f - I*c^2*f^2 + (I*d^2*e^2 - 2*I*c*d*e*f + I*c^2*f^2)*e^(2*d*x + 2*c) + 2*(d^2*e^2 - 2*c*d*e*f + c^2*f^2)*e^(d*x + c))*log(e^(d*x + c) + I) + (I*d^2*e^2 - 2*I*c*d*e*f + (I*c^2 - 4*I)*f^2 + (-I*d^2*e^2 + 2*I*c*d*e*f + (-I*c^2 + 4*I)*f^2)*e^(2*d*x + 2*c) - 2*(d^2*e^2 - 2*c*d*e*f + (c^2 - 4)*f^2)*e^(d*x + c))*log(e^(d*x + c) - I) + (I*d^2*f^2*x^2 + 2*I*d^2*e*f*x + 2*I*c*d*e*f - I*c^2*f^2 + (-I*d^2*f^2*x^2 - 2*I*d^2*e*f*x - 2*I*c*d*e*f + I*c^2*f^2)*e^(2*d*x + 2*c) - 2*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (-I*d^2*f^2*x^2 - 2*I*d^2*e*f*x - 2*I*c*d*e*f + I*c^2*f^2 + (I*d^2*f^2*x^2 + 2*I*d^2*e*f*x + 2*I*c*d*e*f - I*c^2*f^2)*e^(2*d*x + 2*c) + 2*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(d*x + c))*log(-I*e^(d*x + c) + 1) + (-2*I*f^2*e^(2*d*x + 2*c) - 4*f^2*e^(d*x + c) + 2*I*f^2)*polylog(3, I*e^(d*x + c)) + (2*I*f^2*e^(2*d*x + 2*c) + 4*f^2*e^(d*x + c) - 2*I*f^2)*polylog(3, -I*e^(d*x + c)))/(2*a*d^3*e^(2*d*x + 2*c) - 4*I*a*d^3*e^(d*x + c) - 2*a*d^3)","C",0
273,1,352,0,0.512506," ","integrate((f*x+e)*sech(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(i \, f e^{\left(2 \, d x + 2 \, c\right)} + 2 \, f e^{\left(d x + c\right)} - i \, f\right)} {\rm Li}_2\left(i \, e^{\left(d x + c\right)}\right) + {\left(-i \, f e^{\left(2 \, d x + 2 \, c\right)} - 2 \, f e^{\left(d x + c\right)} + i \, f\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + 2 \, {\left(d f x + d e + f\right)} e^{\left(d x + c\right)} + {\left(-i \, d e + i \, c f + {\left(i \, d e - i \, c f\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d e - c f\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + i\right) + {\left(i \, d e - i \, c f + {\left(-i \, d e + i \, c f\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(d e - c f\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(i \, d f x + i \, c f + {\left(-i \, d f x - i \, c f\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(d f x + c f\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(-i \, d f x - i \, c f + {\left(i \, d f x + i \, c f\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(d f x + c f\right)} e^{\left(d x + c\right)}\right)} \log\left(-i \, e^{\left(d x + c\right)} + 1\right) - 2 i \, f}{2 \, a d^{2} e^{\left(2 \, d x + 2 \, c\right)} - 4 i \, a d^{2} e^{\left(d x + c\right)} - 2 \, a d^{2}}"," ",0,"((I*f*e^(2*d*x + 2*c) + 2*f*e^(d*x + c) - I*f)*dilog(I*e^(d*x + c)) + (-I*f*e^(2*d*x + 2*c) - 2*f*e^(d*x + c) + I*f)*dilog(-I*e^(d*x + c)) + 2*(d*f*x + d*e + f)*e^(d*x + c) + (-I*d*e + I*c*f + (I*d*e - I*c*f)*e^(2*d*x + 2*c) + 2*(d*e - c*f)*e^(d*x + c))*log(e^(d*x + c) + I) + (I*d*e - I*c*f + (-I*d*e + I*c*f)*e^(2*d*x + 2*c) - 2*(d*e - c*f)*e^(d*x + c))*log(e^(d*x + c) - I) + (I*d*f*x + I*c*f + (-I*d*f*x - I*c*f)*e^(2*d*x + 2*c) - 2*(d*f*x + c*f)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (-I*d*f*x - I*c*f + (I*d*f*x + I*c*f)*e^(2*d*x + 2*c) + 2*(d*f*x + c*f)*e^(d*x + c))*log(-I*e^(d*x + c) + 1) - 2*I*f)/(2*a*d^2*e^(2*d*x + 2*c) - 4*I*a*d^2*e^(d*x + c) - 2*a*d^2)","B",0
274,1,102,0,0.455736," ","integrate(sech(d*x+c)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(i \, e^{\left(2 \, d x + 2 \, c\right)} + 2 \, e^{\left(d x + c\right)} - i\right)} \log\left(e^{\left(d x + c\right)} + i\right) + {\left(-i \, e^{\left(2 \, d x + 2 \, c\right)} - 2 \, e^{\left(d x + c\right)} + i\right)} \log\left(e^{\left(d x + c\right)} - i\right) + 2 \, e^{\left(d x + c\right)}}{2 \, a d e^{\left(2 \, d x + 2 \, c\right)} - 4 i \, a d e^{\left(d x + c\right)} - 2 \, a d}"," ",0,"((I*e^(2*d*x + 2*c) + 2*e^(d*x + c) - I)*log(e^(d*x + c) + I) + (-I*e^(2*d*x + 2*c) - 2*e^(d*x + c) + I)*log(e^(d*x + c) - I) + 2*e^(d*x + c))/(2*a*d*e^(2*d*x + 2*c) - 4*I*a*d*e^(d*x + c) - 2*a*d)","B",0
275,0,0,0,0.551081," ","integrate(sech(d*x+c)/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(d f x + d e - f\right)} e^{\left(d x + c\right)} - {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2} - {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-2 i \, a d^{2} f^{2} x^{2} - 4 i \, a d^{2} e f x - 2 i \, a d^{2} e^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{-2 i \, f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2} - 2 \, f^{2}\right)} e^{\left(d x + c\right)}}{a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3} + {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}, x\right) + i \, f}{a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2} - {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-2 i \, a d^{2} f^{2} x^{2} - 4 i \, a d^{2} e f x - 2 i \, a d^{2} e^{2}\right)} e^{\left(d x + c\right)}}"," ",0,"-((d*f*x + d*e - f)*e^(d*x + c) - (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2 - (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*e^(2*d*x + 2*c) - (-2*I*a*d^2*f^2*x^2 - 4*I*a*d^2*e*f*x - 2*I*a*d^2*e^2)*e^(d*x + c))*integral((-2*I*f^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2 - 2*f^2)*e^(d*x + c))/(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3 + (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(2*d*x + 2*c)), x) + I*f)/(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2 - (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*e^(2*d*x + 2*c) - (-2*I*a*d^2*f^2*x^2 - 4*I*a*d^2*e*f*x - 2*I*a*d^2*e^2)*e^(d*x + c))","F",0
276,0,0,0,0.539448," ","integrate(sech(d*x+c)/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(d f x + d e - 2 \, f\right)} e^{\left(d x + c\right)} - {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3} - {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-2 i \, a d^{2} f^{3} x^{3} - 6 i \, a d^{2} e f^{2} x^{2} - 6 i \, a d^{2} e^{2} f x - 2 i \, a d^{2} e^{3}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{-6 i \, f^{2} + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2} - 6 \, f^{2}\right)} e^{\left(d x + c\right)}}{a d^{2} f^{4} x^{4} + 4 \, a d^{2} e f^{3} x^{3} + 6 \, a d^{2} e^{2} f^{2} x^{2} + 4 \, a d^{2} e^{3} f x + a d^{2} e^{4} + {\left(a d^{2} f^{4} x^{4} + 4 \, a d^{2} e f^{3} x^{3} + 6 \, a d^{2} e^{2} f^{2} x^{2} + 4 \, a d^{2} e^{3} f x + a d^{2} e^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}}, x\right) + 2 i \, f}{a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3} - {\left(a d^{2} f^{3} x^{3} + 3 \, a d^{2} e f^{2} x^{2} + 3 \, a d^{2} e^{2} f x + a d^{2} e^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-2 i \, a d^{2} f^{3} x^{3} - 6 i \, a d^{2} e f^{2} x^{2} - 6 i \, a d^{2} e^{2} f x - 2 i \, a d^{2} e^{3}\right)} e^{\left(d x + c\right)}}"," ",0,"-((d*f*x + d*e - 2*f)*e^(d*x + c) - (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3 - (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(2*d*x + 2*c) - (-2*I*a*d^2*f^3*x^3 - 6*I*a*d^2*e*f^2*x^2 - 6*I*a*d^2*e^2*f*x - 2*I*a*d^2*e^3)*e^(d*x + c))*integral((-6*I*f^2 + (d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2 - 6*f^2)*e^(d*x + c))/(a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3*f*x + a*d^2*e^4 + (a*d^2*f^4*x^4 + 4*a*d^2*e*f^3*x^3 + 6*a*d^2*e^2*f^2*x^2 + 4*a*d^2*e^3*f*x + a*d^2*e^4)*e^(2*d*x + 2*c)), x) + 2*I*f)/(a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3 - (a*d^2*f^3*x^3 + 3*a*d^2*e*f^2*x^2 + 3*a*d^2*e^2*f*x + a*d^2*e^3)*e^(2*d*x + 2*c) - (-2*I*a*d^2*f^3*x^3 - 6*I*a*d^2*e*f^2*x^2 - 6*I*a*d^2*e^2*f*x - 2*I*a*d^2*e^3)*e^(d*x + c))","F",0
277,1,1385,0,0.503253," ","integrate((f*x+e)^3*sech(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, d^{3} e^{3} - 24 \, c d^{2} e^{2} f + 12 \, {\left(2 \, c^{2} - 1\right)} d e f^{2} - 4 \, {\left(2 \, c^{3} - 3 \, c\right)} f^{3} + {\left(18 \, d f^{3} x + 18 \, d e f^{2} - 18 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(36 i \, d f^{3} x + 36 i \, d e f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(36 i \, d f^{3} x + 36 i \, d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(i \, e^{\left(d x + c\right)}\right) + {\left(30 \, d f^{3} x + 30 \, d e f^{2} - 30 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(60 i \, d f^{3} x + 60 i \, d e f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(60 i \, d f^{3} x + 60 i \, d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + 4 \, {\left(2 \, d^{3} f^{3} x^{3} + 6 \, d^{3} e f^{2} x^{2} + 6 \, c d^{2} e^{2} f - 6 \, c^{2} d e f^{2} + {\left(2 \, c^{3} - 3 \, c\right)} f^{3} + 3 \, {\left(2 \, d^{3} e^{2} f - d f^{3}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(-16 i \, d^{3} f^{3} x^{3} + {\left(-48 i \, c - 6 i\right)} d^{2} e^{2} f + {\left(48 i \, c^{2} - 12 i\right)} d e f^{2} + {\left(-16 i \, c^{3} + 24 i \, c\right)} f^{3} + {\left(-48 i \, d^{3} e f^{2} - 6 i \, d^{2} f^{3}\right)} x^{2} + {\left(-48 i \, d^{3} e^{2} f - 12 i \, d^{2} e f^{2} + 12 i \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} - 12 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(-6 i \, d^{2} f^{3} x^{2} + 16 i \, d^{3} e^{3} + {\left(-48 i \, c - 6 i\right)} d^{2} e^{2} f + {\left(48 i \, c^{2} - 12 i\right)} d e f^{2} + {\left(-16 i \, c^{3} + 24 i \, c\right)} f^{3} + {\left(-12 i \, d^{2} e f^{2} + 12 i \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)} + {\left(9 \, d^{2} e^{2} f - 18 \, c d e f^{2} + 9 \, c^{2} f^{3} - 9 \, {\left(d^{2} e^{2} f - 2 \, c d e f^{2} + c^{2} f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(18 i \, d^{2} e^{2} f - 36 i \, c d e f^{2} + 18 i \, c^{2} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(18 i \, d^{2} e^{2} f - 36 i \, c d e f^{2} + 18 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + i\right) + {\left(15 \, d^{2} e^{2} f - 30 \, c d e f^{2} + 3 \, {\left(5 \, c^{2} - 4\right)} f^{3} - 3 \, {\left(5 \, d^{2} e^{2} f - 10 \, c d e f^{2} + {\left(5 \, c^{2} - 4\right)} f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(30 i \, d^{2} e^{2} f - 60 i \, c d e f^{2} + {\left(30 i \, c^{2} - 24 i\right)} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(30 i \, d^{2} e^{2} f - 60 i \, c d e f^{2} + {\left(30 i \, c^{2} - 24 i\right)} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(15 \, d^{2} f^{3} x^{2} + 30 \, d^{2} e f^{2} x + 30 \, c d e f^{2} - 15 \, c^{2} f^{3} - 15 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(30 i \, d^{2} f^{3} x^{2} + 60 i \, d^{2} e f^{2} x + 60 i \, c d e f^{2} - 30 i \, c^{2} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(30 i \, d^{2} f^{3} x^{2} + 60 i \, d^{2} e f^{2} x + 60 i \, c d e f^{2} - 30 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(9 \, d^{2} f^{3} x^{2} + 18 \, d^{2} e f^{2} x + 18 \, c d e f^{2} - 9 \, c^{2} f^{3} - 9 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + 2 \, c d e f^{2} - c^{2} f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(18 i \, d^{2} f^{3} x^{2} + 36 i \, d^{2} e f^{2} x + 36 i \, c d e f^{2} - 18 i \, c^{2} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(18 i \, d^{2} f^{3} x^{2} + 36 i \, d^{2} e f^{2} x + 36 i \, c d e f^{2} - 18 i \, c^{2} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(-i \, e^{\left(d x + c\right)} + 1\right) + {\left(18 \, f^{3} e^{\left(4 \, d x + 4 \, c\right)} - 36 i \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} - 36 i \, f^{3} e^{\left(d x + c\right)} - 18 \, f^{3}\right)} {\rm polylog}\left(3, i \, e^{\left(d x + c\right)}\right) + {\left(30 \, f^{3} e^{\left(4 \, d x + 4 \, c\right)} - 60 i \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} - 60 i \, f^{3} e^{\left(d x + c\right)} - 30 \, f^{3}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right)}{6 \, a d^{4} e^{\left(4 \, d x + 4 \, c\right)} - 12 i \, a d^{4} e^{\left(3 \, d x + 3 \, c\right)} - 12 i \, a d^{4} e^{\left(d x + c\right)} - 6 \, a d^{4}}"," ",0,"(8*d^3*e^3 - 24*c*d^2*e^2*f + 12*(2*c^2 - 1)*d*e*f^2 - 4*(2*c^3 - 3*c)*f^3 + (18*d*f^3*x + 18*d*e*f^2 - 18*(d*f^3*x + d*e*f^2)*e^(4*d*x + 4*c) + (36*I*d*f^3*x + 36*I*d*e*f^2)*e^(3*d*x + 3*c) + (36*I*d*f^3*x + 36*I*d*e*f^2)*e^(d*x + c))*dilog(I*e^(d*x + c)) + (30*d*f^3*x + 30*d*e*f^2 - 30*(d*f^3*x + d*e*f^2)*e^(4*d*x + 4*c) + (60*I*d*f^3*x + 60*I*d*e*f^2)*e^(3*d*x + 3*c) + (60*I*d*f^3*x + 60*I*d*e*f^2)*e^(d*x + c))*dilog(-I*e^(d*x + c)) + 4*(2*d^3*f^3*x^3 + 6*d^3*e*f^2*x^2 + 6*c*d^2*e^2*f - 6*c^2*d*e*f^2 + (2*c^3 - 3*c)*f^3 + 3*(2*d^3*e^2*f - d*f^3)*x)*e^(4*d*x + 4*c) + (-16*I*d^3*f^3*x^3 + (-48*I*c - 6*I)*d^2*e^2*f + (48*I*c^2 - 12*I)*d*e*f^2 + (-16*I*c^3 + 24*I*c)*f^3 + (-48*I*d^3*e*f^2 - 6*I*d^2*f^3)*x^2 + (-48*I*d^3*e^2*f - 12*I*d^2*e*f^2 + 12*I*d*f^3)*x)*e^(3*d*x + 3*c) - 12*(d*f^3*x + d*e*f^2)*e^(2*d*x + 2*c) + (-6*I*d^2*f^3*x^2 + 16*I*d^3*e^3 + (-48*I*c - 6*I)*d^2*e^2*f + (48*I*c^2 - 12*I)*d*e*f^2 + (-16*I*c^3 + 24*I*c)*f^3 + (-12*I*d^2*e*f^2 + 12*I*d*f^3)*x)*e^(d*x + c) + (9*d^2*e^2*f - 18*c*d*e*f^2 + 9*c^2*f^3 - 9*(d^2*e^2*f - 2*c*d*e*f^2 + c^2*f^3)*e^(4*d*x + 4*c) + (18*I*d^2*e^2*f - 36*I*c*d*e*f^2 + 18*I*c^2*f^3)*e^(3*d*x + 3*c) + (18*I*d^2*e^2*f - 36*I*c*d*e*f^2 + 18*I*c^2*f^3)*e^(d*x + c))*log(e^(d*x + c) + I) + (15*d^2*e^2*f - 30*c*d*e*f^2 + 3*(5*c^2 - 4)*f^3 - 3*(5*d^2*e^2*f - 10*c*d*e*f^2 + (5*c^2 - 4)*f^3)*e^(4*d*x + 4*c) + (30*I*d^2*e^2*f - 60*I*c*d*e*f^2 + (30*I*c^2 - 24*I)*f^3)*e^(3*d*x + 3*c) + (30*I*d^2*e^2*f - 60*I*c*d*e*f^2 + (30*I*c^2 - 24*I)*f^3)*e^(d*x + c))*log(e^(d*x + c) - I) + (15*d^2*f^3*x^2 + 30*d^2*e*f^2*x + 30*c*d*e*f^2 - 15*c^2*f^3 - 15*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*e^(4*d*x + 4*c) + (30*I*d^2*f^3*x^2 + 60*I*d^2*e*f^2*x + 60*I*c*d*e*f^2 - 30*I*c^2*f^3)*e^(3*d*x + 3*c) + (30*I*d^2*f^3*x^2 + 60*I*d^2*e*f^2*x + 60*I*c*d*e*f^2 - 30*I*c^2*f^3)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (9*d^2*f^3*x^2 + 18*d^2*e*f^2*x + 18*c*d*e*f^2 - 9*c^2*f^3 - 9*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + 2*c*d*e*f^2 - c^2*f^3)*e^(4*d*x + 4*c) + (18*I*d^2*f^3*x^2 + 36*I*d^2*e*f^2*x + 36*I*c*d*e*f^2 - 18*I*c^2*f^3)*e^(3*d*x + 3*c) + (18*I*d^2*f^3*x^2 + 36*I*d^2*e*f^2*x + 36*I*c*d*e*f^2 - 18*I*c^2*f^3)*e^(d*x + c))*log(-I*e^(d*x + c) + 1) + (18*f^3*e^(4*d*x + 4*c) - 36*I*f^3*e^(3*d*x + 3*c) - 36*I*f^3*e^(d*x + c) - 18*f^3)*polylog(3, I*e^(d*x + c)) + (30*f^3*e^(4*d*x + 4*c) - 60*I*f^3*e^(3*d*x + 3*c) - 60*I*f^3*e^(d*x + c) - 30*f^3)*polylog(3, -I*e^(d*x + c)))/(6*a*d^4*e^(4*d*x + 4*c) - 12*I*a*d^4*e^(3*d*x + 3*c) - 12*I*a*d^4*e^(d*x + c) - 6*a*d^4)","C",0
278,1,708,0,0.479775," ","integrate((f*x+e)^2*sech(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, d^{2} e^{2} - 8 \, c d e f + 2 \, {\left(2 \, c^{2} - 1\right)} f^{2} - 2 \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} - {\left(3 \, f^{2} e^{\left(4 \, d x + 4 \, c\right)} - 6 i \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} - 6 i \, f^{2} e^{\left(d x + c\right)} - 3 \, f^{2}\right)} {\rm Li}_2\left(i \, e^{\left(d x + c\right)}\right) - {\left(5 \, f^{2} e^{\left(4 \, d x + 4 \, c\right)} - 10 i \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} - 10 i \, f^{2} e^{\left(d x + c\right)} - 5 \, f^{2}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + 4 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(-8 i \, d^{2} f^{2} x^{2} + {\left(-16 i \, c - 2 i\right)} d e f + {\left(8 i \, c^{2} - 2 i\right)} f^{2} + {\left(-16 i \, d^{2} e f - 2 i \, d f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(8 i \, d^{2} e^{2} + {\left(-16 i \, c - 2 i\right)} d e f - 2 i \, d f^{2} x + {\left(8 i \, c^{2} - 2 i\right)} f^{2}\right)} e^{\left(d x + c\right)} + {\left(3 \, d e f - 3 \, c f^{2} - 3 \, {\left(d e f - c f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(6 i \, d e f - 6 i \, c f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(6 i \, d e f - 6 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + i\right) + {\left(5 \, d e f - 5 \, c f^{2} - 5 \, {\left(d e f - c f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(10 i \, d e f - 10 i \, c f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(10 i \, d e f - 10 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(5 \, d f^{2} x + 5 \, c f^{2} - 5 \, {\left(d f^{2} x + c f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(10 i \, d f^{2} x + 10 i \, c f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(10 i \, d f^{2} x + 10 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(3 \, d f^{2} x + 3 \, c f^{2} - 3 \, {\left(d f^{2} x + c f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + {\left(6 i \, d f^{2} x + 6 i \, c f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(6 i \, d f^{2} x + 6 i \, c f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(-i \, e^{\left(d x + c\right)} + 1\right)}{3 \, a d^{3} e^{\left(4 \, d x + 4 \, c\right)} - 6 i \, a d^{3} e^{\left(3 \, d x + 3 \, c\right)} - 6 i \, a d^{3} e^{\left(d x + c\right)} - 3 \, a d^{3}}"," ",0,"(4*d^2*e^2 - 8*c*d*e*f + 2*(2*c^2 - 1)*f^2 - 2*f^2*e^(2*d*x + 2*c) - (3*f^2*e^(4*d*x + 4*c) - 6*I*f^2*e^(3*d*x + 3*c) - 6*I*f^2*e^(d*x + c) - 3*f^2)*dilog(I*e^(d*x + c)) - (5*f^2*e^(4*d*x + 4*c) - 10*I*f^2*e^(3*d*x + 3*c) - 10*I*f^2*e^(d*x + c) - 5*f^2)*dilog(-I*e^(d*x + c)) + 4*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(4*d*x + 4*c) + (-8*I*d^2*f^2*x^2 + (-16*I*c - 2*I)*d*e*f + (8*I*c^2 - 2*I)*f^2 + (-16*I*d^2*e*f - 2*I*d*f^2)*x)*e^(3*d*x + 3*c) + (8*I*d^2*e^2 + (-16*I*c - 2*I)*d*e*f - 2*I*d*f^2*x + (8*I*c^2 - 2*I)*f^2)*e^(d*x + c) + (3*d*e*f - 3*c*f^2 - 3*(d*e*f - c*f^2)*e^(4*d*x + 4*c) + (6*I*d*e*f - 6*I*c*f^2)*e^(3*d*x + 3*c) + (6*I*d*e*f - 6*I*c*f^2)*e^(d*x + c))*log(e^(d*x + c) + I) + (5*d*e*f - 5*c*f^2 - 5*(d*e*f - c*f^2)*e^(4*d*x + 4*c) + (10*I*d*e*f - 10*I*c*f^2)*e^(3*d*x + 3*c) + (10*I*d*e*f - 10*I*c*f^2)*e^(d*x + c))*log(e^(d*x + c) - I) + (5*d*f^2*x + 5*c*f^2 - 5*(d*f^2*x + c*f^2)*e^(4*d*x + 4*c) + (10*I*d*f^2*x + 10*I*c*f^2)*e^(3*d*x + 3*c) + (10*I*d*f^2*x + 10*I*c*f^2)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (3*d*f^2*x + 3*c*f^2 - 3*(d*f^2*x + c*f^2)*e^(4*d*x + 4*c) + (6*I*d*f^2*x + 6*I*c*f^2)*e^(3*d*x + 3*c) + (6*I*d*f^2*x + 6*I*c*f^2)*e^(d*x + c))*log(-I*e^(d*x + c) + 1))/(3*a*d^3*e^(4*d*x + 4*c) - 6*I*a*d^3*e^(3*d*x + 3*c) - 6*I*a*d^3*e^(d*x + c) - 3*a*d^3)","B",0
279,1,201,0,0.494601," ","integrate((f*x+e)*sech(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, d f x e^{\left(4 \, d x + 4 \, c\right)} + 8 \, d e + {\left(-16 i \, d f x - 2 i \, f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(16 i \, d e - 2 i \, f\right)} e^{\left(d x + c\right)} - {\left(3 \, f e^{\left(4 \, d x + 4 \, c\right)} - 6 i \, f e^{\left(3 \, d x + 3 \, c\right)} - 6 i \, f e^{\left(d x + c\right)} - 3 \, f\right)} \log\left(e^{\left(d x + c\right)} + i\right) - {\left(5 \, f e^{\left(4 \, d x + 4 \, c\right)} - 10 i \, f e^{\left(3 \, d x + 3 \, c\right)} - 10 i \, f e^{\left(d x + c\right)} - 5 \, f\right)} \log\left(e^{\left(d x + c\right)} - i\right)}{6 \, a d^{2} e^{\left(4 \, d x + 4 \, c\right)} - 12 i \, a d^{2} e^{\left(3 \, d x + 3 \, c\right)} - 12 i \, a d^{2} e^{\left(d x + c\right)} - 6 \, a d^{2}}"," ",0,"(8*d*f*x*e^(4*d*x + 4*c) + 8*d*e + (-16*I*d*f*x - 2*I*f)*e^(3*d*x + 3*c) + (16*I*d*e - 2*I*f)*e^(d*x + c) - (3*f*e^(4*d*x + 4*c) - 6*I*f*e^(3*d*x + 3*c) - 6*I*f*e^(d*x + c) - 3*f)*log(e^(d*x + c) + I) - (5*f*e^(4*d*x + 4*c) - 10*I*f*e^(3*d*x + 3*c) - 10*I*f*e^(d*x + c) - 5*f)*log(e^(d*x + c) - I))/(6*a*d^2*e^(4*d*x + 4*c) - 12*I*a*d^2*e^(3*d*x + 3*c) - 12*I*a*d^2*e^(d*x + c) - 6*a*d^2)","A",0
280,1,55,0,0.496098," ","integrate(sech(d*x+c)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(-2 i \, e^{\left(d x + c\right)} - 1\right)}}{3 \, a d e^{\left(4 \, d x + 4 \, c\right)} - 6 i \, a d e^{\left(3 \, d x + 3 \, c\right)} - 6 i \, a d e^{\left(d x + c\right)} - 3 \, a d}"," ",0,"-4*(-2*I*e^(d*x + c) - 1)/(3*a*d*e^(4*d*x + 4*c) - 6*I*a*d*e^(3*d*x + 3*c) - 6*I*a*d*e^(d*x + c) - 3*a*d)","A",0
281,0,0,0,0.507317," ","integrate(sech(d*x+c)^2/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, d^{2} f^{2} x^{2} + 8 \, d^{2} e f x + 4 \, d^{2} e^{2} - 2 \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, f^{2} + {\left(i \, d f^{2} x + i \, d e f - 2 i \, f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(8 i \, d^{2} f^{2} x^{2} + 8 i \, d^{2} e^{2} + i \, d e f - 2 i \, f^{2} + {\left(16 i \, d^{2} e f + i \, d f^{2}\right)} x\right)} e^{\left(d x + c\right)} - {\left(3 \, a d^{3} f^{3} x^{3} + 9 \, a d^{3} e f^{2} x^{2} + 9 \, a d^{3} e^{2} f x + 3 \, a d^{3} e^{3} - 3 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-6 i \, a d^{3} f^{3} x^{3} - 18 i \, a d^{3} e f^{2} x^{2} - 18 i \, a d^{3} e^{2} f x - 6 i \, a d^{3} e^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(-6 i \, a d^{3} f^{3} x^{3} - 18 i \, a d^{3} e f^{2} x^{2} - 18 i \, a d^{3} e^{2} f x - 6 i \, a d^{3} e^{3}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(-\frac{4 \, d^{2} f^{3} x^{2} + 8 \, d^{2} e f^{2} x + 4 \, d^{2} e^{2} f - 6 \, f^{3} - {\left(i \, d^{2} f^{3} x^{2} + 2 i \, d^{2} e f^{2} x + i \, d^{2} e^{2} f - 6 i \, f^{3}\right)} e^{\left(d x + c\right)}}{3 \, {\left(a d^{3} f^{4} x^{4} + 4 \, a d^{3} e f^{3} x^{3} + 6 \, a d^{3} e^{2} f^{2} x^{2} + 4 \, a d^{3} e^{3} f x + a d^{3} e^{4} + {\left(a d^{3} f^{4} x^{4} + 4 \, a d^{3} e f^{3} x^{3} + 6 \, a d^{3} e^{2} f^{2} x^{2} + 4 \, a d^{3} e^{3} f x + a d^{3} e^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}, x\right)}{3 \, a d^{3} f^{3} x^{3} + 9 \, a d^{3} e f^{2} x^{2} + 9 \, a d^{3} e^{2} f x + 3 \, a d^{3} e^{3} - 3 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-6 i \, a d^{3} f^{3} x^{3} - 18 i \, a d^{3} e f^{2} x^{2} - 18 i \, a d^{3} e^{2} f x - 6 i \, a d^{3} e^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(-6 i \, a d^{3} f^{3} x^{3} - 18 i \, a d^{3} e f^{2} x^{2} - 18 i \, a d^{3} e^{2} f x - 6 i \, a d^{3} e^{3}\right)} e^{\left(d x + c\right)}}"," ",0,"-(4*d^2*f^2*x^2 + 8*d^2*e*f*x + 4*d^2*e^2 - 2*f^2*e^(2*d*x + 2*c) - 2*f^2 + (I*d*f^2*x + I*d*e*f - 2*I*f^2)*e^(3*d*x + 3*c) + (8*I*d^2*f^2*x^2 + 8*I*d^2*e^2 + I*d*e*f - 2*I*f^2 + (16*I*d^2*e*f + I*d*f^2)*x)*e^(d*x + c) - (3*a*d^3*f^3*x^3 + 9*a*d^3*e*f^2*x^2 + 9*a*d^3*e^2*f*x + 3*a*d^3*e^3 - 3*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*e^(4*d*x + 4*c) - (-6*I*a*d^3*f^3*x^3 - 18*I*a*d^3*e*f^2*x^2 - 18*I*a*d^3*e^2*f*x - 6*I*a*d^3*e^3)*e^(3*d*x + 3*c) - (-6*I*a*d^3*f^3*x^3 - 18*I*a*d^3*e*f^2*x^2 - 18*I*a*d^3*e^2*f*x - 6*I*a*d^3*e^3)*e^(d*x + c))*integral(-1/3*(4*d^2*f^3*x^2 + 8*d^2*e*f^2*x + 4*d^2*e^2*f - 6*f^3 - (I*d^2*f^3*x^2 + 2*I*d^2*e*f^2*x + I*d^2*e^2*f - 6*I*f^3)*e^(d*x + c))/(a*d^3*f^4*x^4 + 4*a*d^3*e*f^3*x^3 + 6*a*d^3*e^2*f^2*x^2 + 4*a*d^3*e^3*f*x + a*d^3*e^4 + (a*d^3*f^4*x^4 + 4*a*d^3*e*f^3*x^3 + 6*a*d^3*e^2*f^2*x^2 + 4*a*d^3*e^3*f*x + a*d^3*e^4)*e^(2*d*x + 2*c)), x))/(3*a*d^3*f^3*x^3 + 9*a*d^3*e*f^2*x^2 + 9*a*d^3*e^2*f*x + 3*a*d^3*e^3 - 3*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*e^(4*d*x + 4*c) - (-6*I*a*d^3*f^3*x^3 - 18*I*a*d^3*e*f^2*x^2 - 18*I*a*d^3*e^2*f*x - 6*I*a*d^3*e^3)*e^(3*d*x + 3*c) - (-6*I*a*d^3*f^3*x^3 - 18*I*a*d^3*e*f^2*x^2 - 18*I*a*d^3*e^2*f*x - 6*I*a*d^3*e^3)*e^(d*x + c))","F",0
282,0,0,0,0.571777," ","integrate(sech(d*x+c)^2/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, d^{2} f^{2} x^{2} + 8 \, d^{2} e f x + 4 \, d^{2} e^{2} - 6 \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} - 6 \, f^{2} + {\left(2 i \, d f^{2} x + 2 i \, d e f - 6 i \, f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(8 i \, d^{2} f^{2} x^{2} + 8 i \, d^{2} e^{2} + 2 i \, d e f - 6 i \, f^{2} + {\left(16 i \, d^{2} e f + 2 i \, d f^{2}\right)} x\right)} e^{\left(d x + c\right)} - {\left(3 \, a d^{3} f^{4} x^{4} + 12 \, a d^{3} e f^{3} x^{3} + 18 \, a d^{3} e^{2} f^{2} x^{2} + 12 \, a d^{3} e^{3} f x + 3 \, a d^{3} e^{4} - 3 \, {\left(a d^{3} f^{4} x^{4} + 4 \, a d^{3} e f^{3} x^{3} + 6 \, a d^{3} e^{2} f^{2} x^{2} + 4 \, a d^{3} e^{3} f x + a d^{3} e^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-6 i \, a d^{3} f^{4} x^{4} - 24 i \, a d^{3} e f^{3} x^{3} - 36 i \, a d^{3} e^{2} f^{2} x^{2} - 24 i \, a d^{3} e^{3} f x - 6 i \, a d^{3} e^{4}\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(-6 i \, a d^{3} f^{4} x^{4} - 24 i \, a d^{3} e f^{3} x^{3} - 36 i \, a d^{3} e^{2} f^{2} x^{2} - 24 i \, a d^{3} e^{3} f x - 6 i \, a d^{3} e^{4}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(-\frac{8 \, d^{2} f^{3} x^{2} + 16 \, d^{2} e f^{2} x + 8 \, d^{2} e^{2} f - 24 \, f^{3} - {\left(2 i \, d^{2} f^{3} x^{2} + 4 i \, d^{2} e f^{2} x + 2 i \, d^{2} e^{2} f - 24 i \, f^{3}\right)} e^{\left(d x + c\right)}}{3 \, {\left(a d^{3} f^{5} x^{5} + 5 \, a d^{3} e f^{4} x^{4} + 10 \, a d^{3} e^{2} f^{3} x^{3} + 10 \, a d^{3} e^{3} f^{2} x^{2} + 5 \, a d^{3} e^{4} f x + a d^{3} e^{5} + {\left(a d^{3} f^{5} x^{5} + 5 \, a d^{3} e f^{4} x^{4} + 10 \, a d^{3} e^{2} f^{3} x^{3} + 10 \, a d^{3} e^{3} f^{2} x^{2} + 5 \, a d^{3} e^{4} f x + a d^{3} e^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}, x\right)}{3 \, a d^{3} f^{4} x^{4} + 12 \, a d^{3} e f^{3} x^{3} + 18 \, a d^{3} e^{2} f^{2} x^{2} + 12 \, a d^{3} e^{3} f x + 3 \, a d^{3} e^{4} - 3 \, {\left(a d^{3} f^{4} x^{4} + 4 \, a d^{3} e f^{3} x^{3} + 6 \, a d^{3} e^{2} f^{2} x^{2} + 4 \, a d^{3} e^{3} f x + a d^{3} e^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-6 i \, a d^{3} f^{4} x^{4} - 24 i \, a d^{3} e f^{3} x^{3} - 36 i \, a d^{3} e^{2} f^{2} x^{2} - 24 i \, a d^{3} e^{3} f x - 6 i \, a d^{3} e^{4}\right)} e^{\left(3 \, d x + 3 \, c\right)} - {\left(-6 i \, a d^{3} f^{4} x^{4} - 24 i \, a d^{3} e f^{3} x^{3} - 36 i \, a d^{3} e^{2} f^{2} x^{2} - 24 i \, a d^{3} e^{3} f x - 6 i \, a d^{3} e^{4}\right)} e^{\left(d x + c\right)}}"," ",0,"-(4*d^2*f^2*x^2 + 8*d^2*e*f*x + 4*d^2*e^2 - 6*f^2*e^(2*d*x + 2*c) - 6*f^2 + (2*I*d*f^2*x + 2*I*d*e*f - 6*I*f^2)*e^(3*d*x + 3*c) + (8*I*d^2*f^2*x^2 + 8*I*d^2*e^2 + 2*I*d*e*f - 6*I*f^2 + (16*I*d^2*e*f + 2*I*d*f^2)*x)*e^(d*x + c) - (3*a*d^3*f^4*x^4 + 12*a*d^3*e*f^3*x^3 + 18*a*d^3*e^2*f^2*x^2 + 12*a*d^3*e^3*f*x + 3*a*d^3*e^4 - 3*(a*d^3*f^4*x^4 + 4*a*d^3*e*f^3*x^3 + 6*a*d^3*e^2*f^2*x^2 + 4*a*d^3*e^3*f*x + a*d^3*e^4)*e^(4*d*x + 4*c) - (-6*I*a*d^3*f^4*x^4 - 24*I*a*d^3*e*f^3*x^3 - 36*I*a*d^3*e^2*f^2*x^2 - 24*I*a*d^3*e^3*f*x - 6*I*a*d^3*e^4)*e^(3*d*x + 3*c) - (-6*I*a*d^3*f^4*x^4 - 24*I*a*d^3*e*f^3*x^3 - 36*I*a*d^3*e^2*f^2*x^2 - 24*I*a*d^3*e^3*f*x - 6*I*a*d^3*e^4)*e^(d*x + c))*integral(-1/3*(8*d^2*f^3*x^2 + 16*d^2*e*f^2*x + 8*d^2*e^2*f - 24*f^3 - (2*I*d^2*f^3*x^2 + 4*I*d^2*e*f^2*x + 2*I*d^2*e^2*f - 24*I*f^3)*e^(d*x + c))/(a*d^3*f^5*x^5 + 5*a*d^3*e*f^4*x^4 + 10*a*d^3*e^2*f^3*x^3 + 10*a*d^3*e^3*f^2*x^2 + 5*a*d^3*e^4*f*x + a*d^3*e^5 + (a*d^3*f^5*x^5 + 5*a*d^3*e*f^4*x^4 + 10*a*d^3*e^2*f^3*x^3 + 10*a*d^3*e^3*f^2*x^2 + 5*a*d^3*e^4*f*x + a*d^3*e^5)*e^(2*d*x + 2*c)), x))/(3*a*d^3*f^4*x^4 + 12*a*d^3*e*f^3*x^3 + 18*a*d^3*e^2*f^2*x^2 + 12*a*d^3*e^3*f*x + 3*a*d^3*e^4 - 3*(a*d^3*f^4*x^4 + 4*a*d^3*e*f^3*x^3 + 6*a*d^3*e^2*f^2*x^2 + 4*a*d^3*e^3*f*x + a*d^3*e^4)*e^(4*d*x + 4*c) - (-6*I*a*d^3*f^4*x^4 - 24*I*a*d^3*e*f^3*x^3 - 36*I*a*d^3*e^2*f^2*x^2 - 24*I*a*d^3*e^3*f*x - 6*I*a*d^3*e^4)*e^(3*d*x + 3*c) - (-6*I*a*d^3*f^4*x^4 - 24*I*a*d^3*e*f^3*x^3 - 36*I*a*d^3*e^2*f^2*x^2 - 24*I*a*d^3*e^3*f*x - 6*I*a*d^3*e^4)*e^(d*x + c))","F",0
283,1,3841,0,0.593685," ","integrate((f*x+e)^3*sech(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{-8 i \, d^{2} e^{2} f + 16 i \, c d e f^{2} + {\left(-8 i \, c^{2} + 4 i\right)} f^{3} + {\left(-9 i \, d^{2} f^{3} x^{2} - 18 i \, d^{2} e f^{2} x - 9 i \, d^{2} e^{2} f + 12 i \, f^{3} + {\left(9 i \, d^{2} f^{3} x^{2} + 18 i \, d^{2} e f^{2} x + 9 i \, d^{2} e^{2} f - 12 i \, f^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 6 \, {\left(3 \, d^{2} f^{3} x^{2} + 6 \, d^{2} e f^{2} x + 3 \, d^{2} e^{2} f - 4 \, f^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(9 i \, d^{2} f^{3} x^{2} + 18 i \, d^{2} e f^{2} x + 9 i \, d^{2} e^{2} f - 12 i \, f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 12 \, {\left(3 \, d^{2} f^{3} x^{2} + 6 \, d^{2} e f^{2} x + 3 \, d^{2} e^{2} f - 4 \, f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-9 i \, d^{2} f^{3} x^{2} - 18 i \, d^{2} e f^{2} x - 9 i \, d^{2} e^{2} f + 12 i \, f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, {\left(3 \, d^{2} f^{3} x^{2} + 6 \, d^{2} e f^{2} x + 3 \, d^{2} e^{2} f - 4 \, f^{3}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(i \, e^{\left(d x + c\right)}\right) + {\left(9 i \, d^{2} f^{3} x^{2} + 18 i \, d^{2} e f^{2} x + 9 i \, d^{2} e^{2} f - 28 i \, f^{3} + {\left(-9 i \, d^{2} f^{3} x^{2} - 18 i \, d^{2} e f^{2} x - 9 i \, d^{2} e^{2} f + 28 i \, f^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(9 \, d^{2} f^{3} x^{2} + 18 \, d^{2} e f^{2} x + 9 \, d^{2} e^{2} f - 28 \, f^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-9 i \, d^{2} f^{3} x^{2} - 18 i \, d^{2} e f^{2} x - 9 i \, d^{2} e^{2} f + 28 i \, f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 4 \, {\left(9 \, d^{2} f^{3} x^{2} + 18 \, d^{2} e f^{2} x + 9 \, d^{2} e^{2} f - 28 \, f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(9 i \, d^{2} f^{3} x^{2} + 18 i \, d^{2} e f^{2} x + 9 i \, d^{2} e^{2} f - 28 i \, f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(9 \, d^{2} f^{3} x^{2} + 18 \, d^{2} e f^{2} x + 9 \, d^{2} e^{2} f - 28 \, f^{3}\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(-8 i \, d^{2} f^{3} x^{2} - 16 i \, d^{2} e f^{2} x - 16 i \, c d e f^{2} + 8 i \, c^{2} f^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(3 \, d^{3} f^{3} x^{3} + 3 \, d^{3} e^{3} + 9 \, d^{2} e^{2} f - 2 \, {\left(8 \, c + 1\right)} d e f^{2} + 2 \, {\left(4 \, c^{2} - 1\right)} f^{3} + {\left(9 \, d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + {\left(9 \, d^{3} e^{2} f + 2 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-12 i \, d^{3} f^{3} x^{3} - 12 i \, d^{3} e^{3} - 36 i \, d^{2} e^{2} f - 16 i \, c d e f^{2} + {\left(8 i \, c^{2} + 4 i\right)} f^{3} + {\left(-36 i \, d^{3} e f^{2} - 44 i \, d^{2} f^{3}\right)} x^{2} + {\left(-36 i \, d^{3} e^{2} f - 88 i \, d^{2} e f^{2}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} + 4 \, d^{2} e^{2} f - 2 \, {\left(8 \, c + 1\right)} d e f^{2} + 2 \, {\left(4 \, c^{2} - 1\right)} f^{3} + {\left(3 \, d^{3} e f^{2} - 4 \, d^{2} f^{3}\right)} x^{2} + {\left(3 \, d^{3} e^{2} f - 8 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(12 i \, d^{3} f^{3} x^{3} + 12 i \, d^{3} e^{3} - 44 i \, d^{2} e^{2} f + 16 i \, c d e f^{2} + {\left(-8 i \, c^{2} + 8 i\right)} f^{3} + {\left(36 i \, d^{3} e f^{2} - 36 i \, d^{2} f^{3}\right)} x^{2} + {\left(36 i \, d^{3} e^{2} f - 72 i \, d^{2} e f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(3 \, d^{3} f^{3} x^{3} + 3 \, d^{3} e^{3} - d^{2} e^{2} f - 2 \, {\left(8 \, c + 1\right)} d e f^{2} + 2 \, {\left(4 \, c^{2} - 1\right)} f^{3} + 9 \, {\left(d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + {\left(9 \, d^{3} e^{2} f - 18 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)} + {\left(-3 i \, d^{3} e^{3} + 9 i \, c d^{2} e^{2} f + {\left(-9 i \, c^{2} + 12 i\right)} d e f^{2} + {\left(3 i \, c^{3} - 12 i \, c\right)} f^{3} + {\left(3 i \, d^{3} e^{3} - 9 i \, c d^{2} e^{2} f + {\left(9 i \, c^{2} - 12 i\right)} d e f^{2} + {\left(-3 i \, c^{3} + 12 i \, c\right)} f^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 6 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + {\left(3 \, c^{2} - 4\right)} d e f^{2} - {\left(c^{3} - 4 \, c\right)} f^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(3 i \, d^{3} e^{3} - 9 i \, c d^{2} e^{2} f + {\left(9 i \, c^{2} - 12 i\right)} d e f^{2} + {\left(-3 i \, c^{3} + 12 i \, c\right)} f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 12 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + {\left(3 \, c^{2} - 4\right)} d e f^{2} - {\left(c^{3} - 4 \, c\right)} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-3 i \, d^{3} e^{3} + 9 i \, c d^{2} e^{2} f + {\left(-9 i \, c^{2} + 12 i\right)} d e f^{2} + {\left(3 i \, c^{3} - 12 i \, c\right)} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + {\left(3 \, c^{2} - 4\right)} d e f^{2} - {\left(c^{3} - 4 \, c\right)} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + i\right) + {\left(3 i \, d^{3} e^{3} - 9 i \, c d^{2} e^{2} f + {\left(9 i \, c^{2} - 28 i\right)} d e f^{2} + {\left(-3 i \, c^{3} + 28 i \, c\right)} f^{3} + {\left(-3 i \, d^{3} e^{3} + 9 i \, c d^{2} e^{2} f + {\left(-9 i \, c^{2} + 28 i\right)} d e f^{2} + {\left(3 i \, c^{3} - 28 i \, c\right)} f^{3}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(3 \, d^{3} e^{3} - 9 \, c d^{2} e^{2} f + {\left(9 \, c^{2} - 28\right)} d e f^{2} - {\left(3 \, c^{3} - 28 \, c\right)} f^{3}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-3 i \, d^{3} e^{3} + 9 i \, c d^{2} e^{2} f + {\left(-9 i \, c^{2} + 28 i\right)} d e f^{2} + {\left(3 i \, c^{3} - 28 i \, c\right)} f^{3}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 4 \, {\left(3 \, d^{3} e^{3} - 9 \, c d^{2} e^{2} f + {\left(9 \, c^{2} - 28\right)} d e f^{2} - {\left(3 \, c^{3} - 28 \, c\right)} f^{3}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(3 i \, d^{3} e^{3} - 9 i \, c d^{2} e^{2} f + {\left(9 i \, c^{2} - 28 i\right)} d e f^{2} + {\left(-3 i \, c^{3} + 28 i \, c\right)} f^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(3 \, d^{3} e^{3} - 9 \, c d^{2} e^{2} f + {\left(9 \, c^{2} - 28\right)} d e f^{2} - {\left(3 \, c^{3} - 28 \, c\right)} f^{3}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(3 i \, d^{3} f^{3} x^{3} + 9 i \, d^{3} e f^{2} x^{2} + 9 i \, c d^{2} e^{2} f - 9 i \, c^{2} d e f^{2} + {\left(3 i \, c^{3} - 28 i \, c\right)} f^{3} + {\left(9 i \, d^{3} e^{2} f - 28 i \, d f^{3}\right)} x + {\left(-3 i \, d^{3} f^{3} x^{3} - 9 i \, d^{3} e f^{2} x^{2} - 9 i \, c d^{2} e^{2} f + 9 i \, c^{2} d e f^{2} + {\left(-3 i \, c^{3} + 28 i \, c\right)} f^{3} + {\left(-9 i \, d^{3} e^{2} f + 28 i \, d f^{3}\right)} x\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(3 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e f^{2} x^{2} + 9 \, c d^{2} e^{2} f - 9 \, c^{2} d e f^{2} + {\left(3 \, c^{3} - 28 \, c\right)} f^{3} + {\left(9 \, d^{3} e^{2} f - 28 \, d f^{3}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-3 i \, d^{3} f^{3} x^{3} - 9 i \, d^{3} e f^{2} x^{2} - 9 i \, c d^{2} e^{2} f + 9 i \, c^{2} d e f^{2} + {\left(-3 i \, c^{3} + 28 i \, c\right)} f^{3} + {\left(-9 i \, d^{3} e^{2} f + 28 i \, d f^{3}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} - 4 \, {\left(3 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e f^{2} x^{2} + 9 \, c d^{2} e^{2} f - 9 \, c^{2} d e f^{2} + {\left(3 \, c^{3} - 28 \, c\right)} f^{3} + {\left(9 \, d^{3} e^{2} f - 28 \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(3 i \, d^{3} f^{3} x^{3} + 9 i \, d^{3} e f^{2} x^{2} + 9 i \, c d^{2} e^{2} f - 9 i \, c^{2} d e f^{2} + {\left(3 i \, c^{3} - 28 i \, c\right)} f^{3} + {\left(9 i \, d^{3} e^{2} f - 28 i \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(3 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e f^{2} x^{2} + 9 \, c d^{2} e^{2} f - 9 \, c^{2} d e f^{2} + {\left(3 \, c^{3} - 28 \, c\right)} f^{3} + {\left(9 \, d^{3} e^{2} f - 28 \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(-3 i \, d^{3} f^{3} x^{3} - 9 i \, d^{3} e f^{2} x^{2} - 9 i \, c d^{2} e^{2} f + 9 i \, c^{2} d e f^{2} + {\left(-3 i \, c^{3} + 12 i \, c\right)} f^{3} + {\left(-9 i \, d^{3} e^{2} f + 12 i \, d f^{3}\right)} x + {\left(3 i \, d^{3} f^{3} x^{3} + 9 i \, d^{3} e f^{2} x^{2} + 9 i \, c d^{2} e^{2} f - 9 i \, c^{2} d e f^{2} + {\left(3 i \, c^{3} - 12 i \, c\right)} f^{3} + {\left(9 i \, d^{3} e^{2} f - 12 i \, d f^{3}\right)} x\right)} e^{\left(6 \, d x + 6 \, c\right)} + 6 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} - 4 \, c\right)} f^{3} + {\left(3 \, d^{3} e^{2} f - 4 \, d f^{3}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(3 i \, d^{3} f^{3} x^{3} + 9 i \, d^{3} e f^{2} x^{2} + 9 i \, c d^{2} e^{2} f - 9 i \, c^{2} d e f^{2} + {\left(3 i \, c^{3} - 12 i \, c\right)} f^{3} + {\left(9 i \, d^{3} e^{2} f - 12 i \, d f^{3}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + 12 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} - 4 \, c\right)} f^{3} + {\left(3 \, d^{3} e^{2} f - 4 \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-3 i \, d^{3} f^{3} x^{3} - 9 i \, d^{3} e f^{2} x^{2} - 9 i \, c d^{2} e^{2} f + 9 i \, c^{2} d e f^{2} + {\left(-3 i \, c^{3} + 12 i \, c\right)} f^{3} + {\left(-9 i \, d^{3} e^{2} f + 12 i \, d f^{3}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + {\left(c^{3} - 4 \, c\right)} f^{3} + {\left(3 \, d^{3} e^{2} f - 4 \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)}\right)} \log\left(-i \, e^{\left(d x + c\right)} + 1\right) + {\left(18 i \, f^{3} e^{\left(6 \, d x + 6 \, c\right)} + 36 \, f^{3} e^{\left(5 \, d x + 5 \, c\right)} + 18 i \, f^{3} e^{\left(4 \, d x + 4 \, c\right)} + 72 \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} - 18 i \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} + 36 \, f^{3} e^{\left(d x + c\right)} - 18 i \, f^{3}\right)} {\rm polylog}\left(4, i \, e^{\left(d x + c\right)}\right) + {\left(-18 i \, f^{3} e^{\left(6 \, d x + 6 \, c\right)} - 36 \, f^{3} e^{\left(5 \, d x + 5 \, c\right)} - 18 i \, f^{3} e^{\left(4 \, d x + 4 \, c\right)} - 72 \, f^{3} e^{\left(3 \, d x + 3 \, c\right)} + 18 i \, f^{3} e^{\left(2 \, d x + 2 \, c\right)} - 36 \, f^{3} e^{\left(d x + c\right)} + 18 i \, f^{3}\right)} {\rm polylog}\left(4, -i \, e^{\left(d x + c\right)}\right) + {\left(18 i \, d f^{3} x + 18 i \, d e f^{2} + {\left(-18 i \, d f^{3} x - 18 i \, d e f^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 36 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-18 i \, d f^{3} x - 18 i \, d e f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 72 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(18 i \, d f^{3} x + 18 i \, d e f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 36 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, i \, e^{\left(d x + c\right)}\right) + {\left(-18 i \, d f^{3} x - 18 i \, d e f^{2} + {\left(18 i \, d f^{3} x + 18 i \, d e f^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 36 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(18 i \, d f^{3} x + 18 i \, d e f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 72 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-18 i \, d f^{3} x - 18 i \, d e f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 36 \, {\left(d f^{3} x + d e f^{2}\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right)}{8 \, a d^{4} e^{\left(6 \, d x + 6 \, c\right)} - 16 i \, a d^{4} e^{\left(5 \, d x + 5 \, c\right)} + 8 \, a d^{4} e^{\left(4 \, d x + 4 \, c\right)} - 32 i \, a d^{4} e^{\left(3 \, d x + 3 \, c\right)} - 8 \, a d^{4} e^{\left(2 \, d x + 2 \, c\right)} - 16 i \, a d^{4} e^{\left(d x + c\right)} - 8 \, a d^{4}}"," ",0,"(-8*I*d^2*e^2*f + 16*I*c*d*e*f^2 + (-8*I*c^2 + 4*I)*f^3 + (-9*I*d^2*f^3*x^2 - 18*I*d^2*e*f^2*x - 9*I*d^2*e^2*f + 12*I*f^3 + (9*I*d^2*f^3*x^2 + 18*I*d^2*e*f^2*x + 9*I*d^2*e^2*f - 12*I*f^3)*e^(6*d*x + 6*c) + 6*(3*d^2*f^3*x^2 + 6*d^2*e*f^2*x + 3*d^2*e^2*f - 4*f^3)*e^(5*d*x + 5*c) + (9*I*d^2*f^3*x^2 + 18*I*d^2*e*f^2*x + 9*I*d^2*e^2*f - 12*I*f^3)*e^(4*d*x + 4*c) + 12*(3*d^2*f^3*x^2 + 6*d^2*e*f^2*x + 3*d^2*e^2*f - 4*f^3)*e^(3*d*x + 3*c) + (-9*I*d^2*f^3*x^2 - 18*I*d^2*e*f^2*x - 9*I*d^2*e^2*f + 12*I*f^3)*e^(2*d*x + 2*c) + 6*(3*d^2*f^3*x^2 + 6*d^2*e*f^2*x + 3*d^2*e^2*f - 4*f^3)*e^(d*x + c))*dilog(I*e^(d*x + c)) + (9*I*d^2*f^3*x^2 + 18*I*d^2*e*f^2*x + 9*I*d^2*e^2*f - 28*I*f^3 + (-9*I*d^2*f^3*x^2 - 18*I*d^2*e*f^2*x - 9*I*d^2*e^2*f + 28*I*f^3)*e^(6*d*x + 6*c) - 2*(9*d^2*f^3*x^2 + 18*d^2*e*f^2*x + 9*d^2*e^2*f - 28*f^3)*e^(5*d*x + 5*c) + (-9*I*d^2*f^3*x^2 - 18*I*d^2*e*f^2*x - 9*I*d^2*e^2*f + 28*I*f^3)*e^(4*d*x + 4*c) - 4*(9*d^2*f^3*x^2 + 18*d^2*e*f^2*x + 9*d^2*e^2*f - 28*f^3)*e^(3*d*x + 3*c) + (9*I*d^2*f^3*x^2 + 18*I*d^2*e*f^2*x + 9*I*d^2*e^2*f - 28*I*f^3)*e^(2*d*x + 2*c) - 2*(9*d^2*f^3*x^2 + 18*d^2*e*f^2*x + 9*d^2*e^2*f - 28*f^3)*e^(d*x + c))*dilog(-I*e^(d*x + c)) + (-8*I*d^2*f^3*x^2 - 16*I*d^2*e*f^2*x - 16*I*c*d*e*f^2 + 8*I*c^2*f^3)*e^(6*d*x + 6*c) + 2*(3*d^3*f^3*x^3 + 3*d^3*e^3 + 9*d^2*e^2*f - 2*(8*c + 1)*d*e*f^2 + 2*(4*c^2 - 1)*f^3 + (9*d^3*e*f^2 + d^2*f^3)*x^2 + (9*d^3*e^2*f + 2*d^2*e*f^2 - 2*d*f^3)*x)*e^(5*d*x + 5*c) + (-12*I*d^3*f^3*x^3 - 12*I*d^3*e^3 - 36*I*d^2*e^2*f - 16*I*c*d*e*f^2 + (8*I*c^2 + 4*I)*f^3 + (-36*I*d^3*e*f^2 - 44*I*d^2*f^3)*x^2 + (-36*I*d^3*e^2*f - 88*I*d^2*e*f^2)*x)*e^(4*d*x + 4*c) + 4*(d^3*f^3*x^3 + d^3*e^3 + 4*d^2*e^2*f - 2*(8*c + 1)*d*e*f^2 + 2*(4*c^2 - 1)*f^3 + (3*d^3*e*f^2 - 4*d^2*f^3)*x^2 + (3*d^3*e^2*f - 8*d^2*e*f^2 - 2*d*f^3)*x)*e^(3*d*x + 3*c) + (12*I*d^3*f^3*x^3 + 12*I*d^3*e^3 - 44*I*d^2*e^2*f + 16*I*c*d*e*f^2 + (-8*I*c^2 + 8*I)*f^3 + (36*I*d^3*e*f^2 - 36*I*d^2*f^3)*x^2 + (36*I*d^3*e^2*f - 72*I*d^2*e*f^2)*x)*e^(2*d*x + 2*c) + 2*(3*d^3*f^3*x^3 + 3*d^3*e^3 - d^2*e^2*f - 2*(8*c + 1)*d*e*f^2 + 2*(4*c^2 - 1)*f^3 + 9*(d^3*e*f^2 - d^2*f^3)*x^2 + (9*d^3*e^2*f - 18*d^2*e*f^2 - 2*d*f^3)*x)*e^(d*x + c) + (-3*I*d^3*e^3 + 9*I*c*d^2*e^2*f + (-9*I*c^2 + 12*I)*d*e*f^2 + (3*I*c^3 - 12*I*c)*f^3 + (3*I*d^3*e^3 - 9*I*c*d^2*e^2*f + (9*I*c^2 - 12*I)*d*e*f^2 + (-3*I*c^3 + 12*I*c)*f^3)*e^(6*d*x + 6*c) + 6*(d^3*e^3 - 3*c*d^2*e^2*f + (3*c^2 - 4)*d*e*f^2 - (c^3 - 4*c)*f^3)*e^(5*d*x + 5*c) + (3*I*d^3*e^3 - 9*I*c*d^2*e^2*f + (9*I*c^2 - 12*I)*d*e*f^2 + (-3*I*c^3 + 12*I*c)*f^3)*e^(4*d*x + 4*c) + 12*(d^3*e^3 - 3*c*d^2*e^2*f + (3*c^2 - 4)*d*e*f^2 - (c^3 - 4*c)*f^3)*e^(3*d*x + 3*c) + (-3*I*d^3*e^3 + 9*I*c*d^2*e^2*f + (-9*I*c^2 + 12*I)*d*e*f^2 + (3*I*c^3 - 12*I*c)*f^3)*e^(2*d*x + 2*c) + 6*(d^3*e^3 - 3*c*d^2*e^2*f + (3*c^2 - 4)*d*e*f^2 - (c^3 - 4*c)*f^3)*e^(d*x + c))*log(e^(d*x + c) + I) + (3*I*d^3*e^3 - 9*I*c*d^2*e^2*f + (9*I*c^2 - 28*I)*d*e*f^2 + (-3*I*c^3 + 28*I*c)*f^3 + (-3*I*d^3*e^3 + 9*I*c*d^2*e^2*f + (-9*I*c^2 + 28*I)*d*e*f^2 + (3*I*c^3 - 28*I*c)*f^3)*e^(6*d*x + 6*c) - 2*(3*d^3*e^3 - 9*c*d^2*e^2*f + (9*c^2 - 28)*d*e*f^2 - (3*c^3 - 28*c)*f^3)*e^(5*d*x + 5*c) + (-3*I*d^3*e^3 + 9*I*c*d^2*e^2*f + (-9*I*c^2 + 28*I)*d*e*f^2 + (3*I*c^3 - 28*I*c)*f^3)*e^(4*d*x + 4*c) - 4*(3*d^3*e^3 - 9*c*d^2*e^2*f + (9*c^2 - 28)*d*e*f^2 - (3*c^3 - 28*c)*f^3)*e^(3*d*x + 3*c) + (3*I*d^3*e^3 - 9*I*c*d^2*e^2*f + (9*I*c^2 - 28*I)*d*e*f^2 + (-3*I*c^3 + 28*I*c)*f^3)*e^(2*d*x + 2*c) - 2*(3*d^3*e^3 - 9*c*d^2*e^2*f + (9*c^2 - 28)*d*e*f^2 - (3*c^3 - 28*c)*f^3)*e^(d*x + c))*log(e^(d*x + c) - I) + (3*I*d^3*f^3*x^3 + 9*I*d^3*e*f^2*x^2 + 9*I*c*d^2*e^2*f - 9*I*c^2*d*e*f^2 + (3*I*c^3 - 28*I*c)*f^3 + (9*I*d^3*e^2*f - 28*I*d*f^3)*x + (-3*I*d^3*f^3*x^3 - 9*I*d^3*e*f^2*x^2 - 9*I*c*d^2*e^2*f + 9*I*c^2*d*e*f^2 + (-3*I*c^3 + 28*I*c)*f^3 + (-9*I*d^3*e^2*f + 28*I*d*f^3)*x)*e^(6*d*x + 6*c) - 2*(3*d^3*f^3*x^3 + 9*d^3*e*f^2*x^2 + 9*c*d^2*e^2*f - 9*c^2*d*e*f^2 + (3*c^3 - 28*c)*f^3 + (9*d^3*e^2*f - 28*d*f^3)*x)*e^(5*d*x + 5*c) + (-3*I*d^3*f^3*x^3 - 9*I*d^3*e*f^2*x^2 - 9*I*c*d^2*e^2*f + 9*I*c^2*d*e*f^2 + (-3*I*c^3 + 28*I*c)*f^3 + (-9*I*d^3*e^2*f + 28*I*d*f^3)*x)*e^(4*d*x + 4*c) - 4*(3*d^3*f^3*x^3 + 9*d^3*e*f^2*x^2 + 9*c*d^2*e^2*f - 9*c^2*d*e*f^2 + (3*c^3 - 28*c)*f^3 + (9*d^3*e^2*f - 28*d*f^3)*x)*e^(3*d*x + 3*c) + (3*I*d^3*f^3*x^3 + 9*I*d^3*e*f^2*x^2 + 9*I*c*d^2*e^2*f - 9*I*c^2*d*e*f^2 + (3*I*c^3 - 28*I*c)*f^3 + (9*I*d^3*e^2*f - 28*I*d*f^3)*x)*e^(2*d*x + 2*c) - 2*(3*d^3*f^3*x^3 + 9*d^3*e*f^2*x^2 + 9*c*d^2*e^2*f - 9*c^2*d*e*f^2 + (3*c^3 - 28*c)*f^3 + (9*d^3*e^2*f - 28*d*f^3)*x)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (-3*I*d^3*f^3*x^3 - 9*I*d^3*e*f^2*x^2 - 9*I*c*d^2*e^2*f + 9*I*c^2*d*e*f^2 + (-3*I*c^3 + 12*I*c)*f^3 + (-9*I*d^3*e^2*f + 12*I*d*f^3)*x + (3*I*d^3*f^3*x^3 + 9*I*d^3*e*f^2*x^2 + 9*I*c*d^2*e^2*f - 9*I*c^2*d*e*f^2 + (3*I*c^3 - 12*I*c)*f^3 + (9*I*d^3*e^2*f - 12*I*d*f^3)*x)*e^(6*d*x + 6*c) + 6*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 - 4*c)*f^3 + (3*d^3*e^2*f - 4*d*f^3)*x)*e^(5*d*x + 5*c) + (3*I*d^3*f^3*x^3 + 9*I*d^3*e*f^2*x^2 + 9*I*c*d^2*e^2*f - 9*I*c^2*d*e*f^2 + (3*I*c^3 - 12*I*c)*f^3 + (9*I*d^3*e^2*f - 12*I*d*f^3)*x)*e^(4*d*x + 4*c) + 12*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 - 4*c)*f^3 + (3*d^3*e^2*f - 4*d*f^3)*x)*e^(3*d*x + 3*c) + (-3*I*d^3*f^3*x^3 - 9*I*d^3*e*f^2*x^2 - 9*I*c*d^2*e^2*f + 9*I*c^2*d*e*f^2 + (-3*I*c^3 + 12*I*c)*f^3 + (-9*I*d^3*e^2*f + 12*I*d*f^3)*x)*e^(2*d*x + 2*c) + 6*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + (c^3 - 4*c)*f^3 + (3*d^3*e^2*f - 4*d*f^3)*x)*e^(d*x + c))*log(-I*e^(d*x + c) + 1) + (18*I*f^3*e^(6*d*x + 6*c) + 36*f^3*e^(5*d*x + 5*c) + 18*I*f^3*e^(4*d*x + 4*c) + 72*f^3*e^(3*d*x + 3*c) - 18*I*f^3*e^(2*d*x + 2*c) + 36*f^3*e^(d*x + c) - 18*I*f^3)*polylog(4, I*e^(d*x + c)) + (-18*I*f^3*e^(6*d*x + 6*c) - 36*f^3*e^(5*d*x + 5*c) - 18*I*f^3*e^(4*d*x + 4*c) - 72*f^3*e^(3*d*x + 3*c) + 18*I*f^3*e^(2*d*x + 2*c) - 36*f^3*e^(d*x + c) + 18*I*f^3)*polylog(4, -I*e^(d*x + c)) + (18*I*d*f^3*x + 18*I*d*e*f^2 + (-18*I*d*f^3*x - 18*I*d*e*f^2)*e^(6*d*x + 6*c) - 36*(d*f^3*x + d*e*f^2)*e^(5*d*x + 5*c) + (-18*I*d*f^3*x - 18*I*d*e*f^2)*e^(4*d*x + 4*c) - 72*(d*f^3*x + d*e*f^2)*e^(3*d*x + 3*c) + (18*I*d*f^3*x + 18*I*d*e*f^2)*e^(2*d*x + 2*c) - 36*(d*f^3*x + d*e*f^2)*e^(d*x + c))*polylog(3, I*e^(d*x + c)) + (-18*I*d*f^3*x - 18*I*d*e*f^2 + (18*I*d*f^3*x + 18*I*d*e*f^2)*e^(6*d*x + 6*c) + 36*(d*f^3*x + d*e*f^2)*e^(5*d*x + 5*c) + (18*I*d*f^3*x + 18*I*d*e*f^2)*e^(4*d*x + 4*c) + 72*(d*f^3*x + d*e*f^2)*e^(3*d*x + 3*c) + (-18*I*d*f^3*x - 18*I*d*e*f^2)*e^(2*d*x + 2*c) + 36*(d*f^3*x + d*e*f^2)*e^(d*x + c))*polylog(3, -I*e^(d*x + c)))/(8*a*d^4*e^(6*d*x + 6*c) - 16*I*a*d^4*e^(5*d*x + 5*c) + 8*a*d^4*e^(4*d*x + 4*c) - 32*I*a*d^4*e^(3*d*x + 3*c) - 8*a*d^4*e^(2*d*x + 2*c) - 16*I*a*d^4*e^(d*x + c) - 8*a*d^4)","C",0
284,1,2055,0,0.698248," ","integrate((f*x+e)^2*sech(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{-16 i \, d e f + 16 i \, c f^{2} + {\left(-18 i \, d f^{2} x - 18 i \, d e f + {\left(18 i \, d f^{2} x + 18 i \, d e f\right)} e^{\left(6 \, d x + 6 \, c\right)} + 36 \, {\left(d f^{2} x + d e f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(18 i \, d f^{2} x + 18 i \, d e f\right)} e^{\left(4 \, d x + 4 \, c\right)} + 72 \, {\left(d f^{2} x + d e f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-18 i \, d f^{2} x - 18 i \, d e f\right)} e^{\left(2 \, d x + 2 \, c\right)} + 36 \, {\left(d f^{2} x + d e f\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(i \, e^{\left(d x + c\right)}\right) + {\left(18 i \, d f^{2} x + 18 i \, d e f + {\left(-18 i \, d f^{2} x - 18 i \, d e f\right)} e^{\left(6 \, d x + 6 \, c\right)} - 36 \, {\left(d f^{2} x + d e f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-18 i \, d f^{2} x - 18 i \, d e f\right)} e^{\left(4 \, d x + 4 \, c\right)} - 72 \, {\left(d f^{2} x + d e f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(18 i \, d f^{2} x + 18 i \, d e f\right)} e^{\left(2 \, d x + 2 \, c\right)} - 36 \, {\left(d f^{2} x + d e f\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + {\left(-16 i \, d f^{2} x - 16 i \, c f^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 2 \, {\left(9 \, d^{2} f^{2} x^{2} + 9 \, d^{2} e^{2} + 18 \, d e f - 2 \, {\left(8 \, c + 1\right)} f^{2} + 2 \, {\left(9 \, d^{2} e f + d f^{2}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-36 i \, d^{2} f^{2} x^{2} - 36 i \, d^{2} e^{2} - 72 i \, d e f - 16 i \, c f^{2} + {\left(-72 i \, d^{2} e f - 88 i \, d f^{2}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(3 \, d^{2} f^{2} x^{2} + 3 \, d^{2} e^{2} + 8 \, d e f - 2 \, {\left(8 \, c + 1\right)} f^{2} + 2 \, {\left(3 \, d^{2} e f - 4 \, d f^{2}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(36 i \, d^{2} f^{2} x^{2} + 36 i \, d^{2} e^{2} - 88 i \, d e f + 16 i \, c f^{2} + {\left(72 i \, d^{2} e f - 72 i \, d f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(9 \, d^{2} f^{2} x^{2} + 9 \, d^{2} e^{2} - 2 \, d e f - 2 \, {\left(8 \, c + 1\right)} f^{2} + 18 \, {\left(d^{2} e f - d f^{2}\right)} x\right)} e^{\left(d x + c\right)} + {\left(-9 i \, d^{2} e^{2} + 18 i \, c d e f + {\left(-9 i \, c^{2} + 12 i\right)} f^{2} + {\left(9 i \, d^{2} e^{2} - 18 i \, c d e f + {\left(9 i \, c^{2} - 12 i\right)} f^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 6 \, {\left(3 \, d^{2} e^{2} - 6 \, c d e f + {\left(3 \, c^{2} - 4\right)} f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(9 i \, d^{2} e^{2} - 18 i \, c d e f + {\left(9 i \, c^{2} - 12 i\right)} f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 12 \, {\left(3 \, d^{2} e^{2} - 6 \, c d e f + {\left(3 \, c^{2} - 4\right)} f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-9 i \, d^{2} e^{2} + 18 i \, c d e f + {\left(-9 i \, c^{2} + 12 i\right)} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 6 \, {\left(3 \, d^{2} e^{2} - 6 \, c d e f + {\left(3 \, c^{2} - 4\right)} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + i\right) + {\left(9 i \, d^{2} e^{2} - 18 i \, c d e f + {\left(9 i \, c^{2} - 28 i\right)} f^{2} + {\left(-9 i \, d^{2} e^{2} + 18 i \, c d e f + {\left(-9 i \, c^{2} + 28 i\right)} f^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 2 \, {\left(9 \, d^{2} e^{2} - 18 \, c d e f + {\left(9 \, c^{2} - 28\right)} f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-9 i \, d^{2} e^{2} + 18 i \, c d e f + {\left(-9 i \, c^{2} + 28 i\right)} f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 4 \, {\left(9 \, d^{2} e^{2} - 18 \, c d e f + {\left(9 \, c^{2} - 28\right)} f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(9 i \, d^{2} e^{2} - 18 i \, c d e f + {\left(9 i \, c^{2} - 28 i\right)} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left(9 \, d^{2} e^{2} - 18 \, c d e f + {\left(9 \, c^{2} - 28\right)} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(9 i \, d^{2} f^{2} x^{2} + 18 i \, d^{2} e f x + 18 i \, c d e f - 9 i \, c^{2} f^{2} + {\left(-9 i \, d^{2} f^{2} x^{2} - 18 i \, d^{2} e f x - 18 i \, c d e f + 9 i \, c^{2} f^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} - 18 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-9 i \, d^{2} f^{2} x^{2} - 18 i \, d^{2} e f x - 18 i \, c d e f + 9 i \, c^{2} f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} - 36 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(9 i \, d^{2} f^{2} x^{2} + 18 i \, d^{2} e f x + 18 i \, c d e f - 9 i \, c^{2} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} - 18 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(-9 i \, d^{2} f^{2} x^{2} - 18 i \, d^{2} e f x - 18 i \, c d e f + 9 i \, c^{2} f^{2} + {\left(9 i \, d^{2} f^{2} x^{2} + 18 i \, d^{2} e f x + 18 i \, c d e f - 9 i \, c^{2} f^{2}\right)} e^{\left(6 \, d x + 6 \, c\right)} + 18 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(9 i \, d^{2} f^{2} x^{2} + 18 i \, d^{2} e f x + 18 i \, c d e f - 9 i \, c^{2} f^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 36 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-9 i \, d^{2} f^{2} x^{2} - 18 i \, d^{2} e f x - 18 i \, c d e f + 9 i \, c^{2} f^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 18 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(-i \, e^{\left(d x + c\right)} + 1\right) + {\left(-18 i \, f^{2} e^{\left(6 \, d x + 6 \, c\right)} - 36 \, f^{2} e^{\left(5 \, d x + 5 \, c\right)} - 18 i \, f^{2} e^{\left(4 \, d x + 4 \, c\right)} - 72 \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} + 18 i \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} - 36 \, f^{2} e^{\left(d x + c\right)} + 18 i \, f^{2}\right)} {\rm polylog}\left(3, i \, e^{\left(d x + c\right)}\right) + {\left(18 i \, f^{2} e^{\left(6 \, d x + 6 \, c\right)} + 36 \, f^{2} e^{\left(5 \, d x + 5 \, c\right)} + 18 i \, f^{2} e^{\left(4 \, d x + 4 \, c\right)} + 72 \, f^{2} e^{\left(3 \, d x + 3 \, c\right)} - 18 i \, f^{2} e^{\left(2 \, d x + 2 \, c\right)} + 36 \, f^{2} e^{\left(d x + c\right)} - 18 i \, f^{2}\right)} {\rm polylog}\left(3, -i \, e^{\left(d x + c\right)}\right)}{24 \, a d^{3} e^{\left(6 \, d x + 6 \, c\right)} - 48 i \, a d^{3} e^{\left(5 \, d x + 5 \, c\right)} + 24 \, a d^{3} e^{\left(4 \, d x + 4 \, c\right)} - 96 i \, a d^{3} e^{\left(3 \, d x + 3 \, c\right)} - 24 \, a d^{3} e^{\left(2 \, d x + 2 \, c\right)} - 48 i \, a d^{3} e^{\left(d x + c\right)} - 24 \, a d^{3}}"," ",0,"(-16*I*d*e*f + 16*I*c*f^2 + (-18*I*d*f^2*x - 18*I*d*e*f + (18*I*d*f^2*x + 18*I*d*e*f)*e^(6*d*x + 6*c) + 36*(d*f^2*x + d*e*f)*e^(5*d*x + 5*c) + (18*I*d*f^2*x + 18*I*d*e*f)*e^(4*d*x + 4*c) + 72*(d*f^2*x + d*e*f)*e^(3*d*x + 3*c) + (-18*I*d*f^2*x - 18*I*d*e*f)*e^(2*d*x + 2*c) + 36*(d*f^2*x + d*e*f)*e^(d*x + c))*dilog(I*e^(d*x + c)) + (18*I*d*f^2*x + 18*I*d*e*f + (-18*I*d*f^2*x - 18*I*d*e*f)*e^(6*d*x + 6*c) - 36*(d*f^2*x + d*e*f)*e^(5*d*x + 5*c) + (-18*I*d*f^2*x - 18*I*d*e*f)*e^(4*d*x + 4*c) - 72*(d*f^2*x + d*e*f)*e^(3*d*x + 3*c) + (18*I*d*f^2*x + 18*I*d*e*f)*e^(2*d*x + 2*c) - 36*(d*f^2*x + d*e*f)*e^(d*x + c))*dilog(-I*e^(d*x + c)) + (-16*I*d*f^2*x - 16*I*c*f^2)*e^(6*d*x + 6*c) + 2*(9*d^2*f^2*x^2 + 9*d^2*e^2 + 18*d*e*f - 2*(8*c + 1)*f^2 + 2*(9*d^2*e*f + d*f^2)*x)*e^(5*d*x + 5*c) + (-36*I*d^2*f^2*x^2 - 36*I*d^2*e^2 - 72*I*d*e*f - 16*I*c*f^2 + (-72*I*d^2*e*f - 88*I*d*f^2)*x)*e^(4*d*x + 4*c) + 4*(3*d^2*f^2*x^2 + 3*d^2*e^2 + 8*d*e*f - 2*(8*c + 1)*f^2 + 2*(3*d^2*e*f - 4*d*f^2)*x)*e^(3*d*x + 3*c) + (36*I*d^2*f^2*x^2 + 36*I*d^2*e^2 - 88*I*d*e*f + 16*I*c*f^2 + (72*I*d^2*e*f - 72*I*d*f^2)*x)*e^(2*d*x + 2*c) + 2*(9*d^2*f^2*x^2 + 9*d^2*e^2 - 2*d*e*f - 2*(8*c + 1)*f^2 + 18*(d^2*e*f - d*f^2)*x)*e^(d*x + c) + (-9*I*d^2*e^2 + 18*I*c*d*e*f + (-9*I*c^2 + 12*I)*f^2 + (9*I*d^2*e^2 - 18*I*c*d*e*f + (9*I*c^2 - 12*I)*f^2)*e^(6*d*x + 6*c) + 6*(3*d^2*e^2 - 6*c*d*e*f + (3*c^2 - 4)*f^2)*e^(5*d*x + 5*c) + (9*I*d^2*e^2 - 18*I*c*d*e*f + (9*I*c^2 - 12*I)*f^2)*e^(4*d*x + 4*c) + 12*(3*d^2*e^2 - 6*c*d*e*f + (3*c^2 - 4)*f^2)*e^(3*d*x + 3*c) + (-9*I*d^2*e^2 + 18*I*c*d*e*f + (-9*I*c^2 + 12*I)*f^2)*e^(2*d*x + 2*c) + 6*(3*d^2*e^2 - 6*c*d*e*f + (3*c^2 - 4)*f^2)*e^(d*x + c))*log(e^(d*x + c) + I) + (9*I*d^2*e^2 - 18*I*c*d*e*f + (9*I*c^2 - 28*I)*f^2 + (-9*I*d^2*e^2 + 18*I*c*d*e*f + (-9*I*c^2 + 28*I)*f^2)*e^(6*d*x + 6*c) - 2*(9*d^2*e^2 - 18*c*d*e*f + (9*c^2 - 28)*f^2)*e^(5*d*x + 5*c) + (-9*I*d^2*e^2 + 18*I*c*d*e*f + (-9*I*c^2 + 28*I)*f^2)*e^(4*d*x + 4*c) - 4*(9*d^2*e^2 - 18*c*d*e*f + (9*c^2 - 28)*f^2)*e^(3*d*x + 3*c) + (9*I*d^2*e^2 - 18*I*c*d*e*f + (9*I*c^2 - 28*I)*f^2)*e^(2*d*x + 2*c) - 2*(9*d^2*e^2 - 18*c*d*e*f + (9*c^2 - 28)*f^2)*e^(d*x + c))*log(e^(d*x + c) - I) + (9*I*d^2*f^2*x^2 + 18*I*d^2*e*f*x + 18*I*c*d*e*f - 9*I*c^2*f^2 + (-9*I*d^2*f^2*x^2 - 18*I*d^2*e*f*x - 18*I*c*d*e*f + 9*I*c^2*f^2)*e^(6*d*x + 6*c) - 18*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(5*d*x + 5*c) + (-9*I*d^2*f^2*x^2 - 18*I*d^2*e*f*x - 18*I*c*d*e*f + 9*I*c^2*f^2)*e^(4*d*x + 4*c) - 36*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(3*d*x + 3*c) + (9*I*d^2*f^2*x^2 + 18*I*d^2*e*f*x + 18*I*c*d*e*f - 9*I*c^2*f^2)*e^(2*d*x + 2*c) - 18*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (-9*I*d^2*f^2*x^2 - 18*I*d^2*e*f*x - 18*I*c*d*e*f + 9*I*c^2*f^2 + (9*I*d^2*f^2*x^2 + 18*I*d^2*e*f*x + 18*I*c*d*e*f - 9*I*c^2*f^2)*e^(6*d*x + 6*c) + 18*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(5*d*x + 5*c) + (9*I*d^2*f^2*x^2 + 18*I*d^2*e*f*x + 18*I*c*d*e*f - 9*I*c^2*f^2)*e^(4*d*x + 4*c) + 36*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(3*d*x + 3*c) + (-9*I*d^2*f^2*x^2 - 18*I*d^2*e*f*x - 18*I*c*d*e*f + 9*I*c^2*f^2)*e^(2*d*x + 2*c) + 18*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*e^(d*x + c))*log(-I*e^(d*x + c) + 1) + (-18*I*f^2*e^(6*d*x + 6*c) - 36*f^2*e^(5*d*x + 5*c) - 18*I*f^2*e^(4*d*x + 4*c) - 72*f^2*e^(3*d*x + 3*c) + 18*I*f^2*e^(2*d*x + 2*c) - 36*f^2*e^(d*x + c) + 18*I*f^2)*polylog(3, I*e^(d*x + c)) + (18*I*f^2*e^(6*d*x + 6*c) + 36*f^2*e^(5*d*x + 5*c) + 18*I*f^2*e^(4*d*x + 4*c) + 72*f^2*e^(3*d*x + 3*c) - 18*I*f^2*e^(2*d*x + 2*c) + 36*f^2*e^(d*x + c) - 18*I*f^2)*polylog(3, -I*e^(d*x + c)))/(24*a*d^3*e^(6*d*x + 6*c) - 48*I*a*d^3*e^(5*d*x + 5*c) + 24*a*d^3*e^(4*d*x + 4*c) - 96*I*a*d^3*e^(3*d*x + 3*c) - 24*a*d^3*e^(2*d*x + 2*c) - 48*I*a*d^3*e^(d*x + c) - 24*a*d^3)","C",0
285,1,910,0,0.528455," ","integrate((f*x+e)*sech(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(9 i \, f e^{\left(6 \, d x + 6 \, c\right)} + 18 \, f e^{\left(5 \, d x + 5 \, c\right)} + 9 i \, f e^{\left(4 \, d x + 4 \, c\right)} + 36 \, f e^{\left(3 \, d x + 3 \, c\right)} - 9 i \, f e^{\left(2 \, d x + 2 \, c\right)} + 18 \, f e^{\left(d x + c\right)} - 9 i \, f\right)} {\rm Li}_2\left(i \, e^{\left(d x + c\right)}\right) + {\left(-9 i \, f e^{\left(6 \, d x + 6 \, c\right)} - 18 \, f e^{\left(5 \, d x + 5 \, c\right)} - 9 i \, f e^{\left(4 \, d x + 4 \, c\right)} - 36 \, f e^{\left(3 \, d x + 3 \, c\right)} + 9 i \, f e^{\left(2 \, d x + 2 \, c\right)} - 18 \, f e^{\left(d x + c\right)} + 9 i \, f\right)} {\rm Li}_2\left(-i \, e^{\left(d x + c\right)}\right) + 18 \, {\left(d f x + d e + f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-36 i \, d f x - 36 i \, d e - 36 i \, f\right)} e^{\left(4 \, d x + 4 \, c\right)} + 4 \, {\left(3 \, d f x + 3 \, d e + 4 \, f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(36 i \, d f x + 36 i \, d e - 44 i \, f\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(9 \, d f x + 9 \, d e - f\right)} e^{\left(d x + c\right)} + {\left(-9 i \, d e + 9 i \, c f + {\left(9 i \, d e - 9 i \, c f\right)} e^{\left(6 \, d x + 6 \, c\right)} + 18 \, {\left(d e - c f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(9 i \, d e - 9 i \, c f\right)} e^{\left(4 \, d x + 4 \, c\right)} + 36 \, {\left(d e - c f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-9 i \, d e + 9 i \, c f\right)} e^{\left(2 \, d x + 2 \, c\right)} + 18 \, {\left(d e - c f\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} + i\right) + {\left(9 i \, d e - 9 i \, c f + {\left(-9 i \, d e + 9 i \, c f\right)} e^{\left(6 \, d x + 6 \, c\right)} - 18 \, {\left(d e - c f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-9 i \, d e + 9 i \, c f\right)} e^{\left(4 \, d x + 4 \, c\right)} - 36 \, {\left(d e - c f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(9 i \, d e - 9 i \, c f\right)} e^{\left(2 \, d x + 2 \, c\right)} - 18 \, {\left(d e - c f\right)} e^{\left(d x + c\right)}\right)} \log\left(e^{\left(d x + c\right)} - i\right) + {\left(9 i \, d f x + 9 i \, c f + {\left(-9 i \, d f x - 9 i \, c f\right)} e^{\left(6 \, d x + 6 \, c\right)} - 18 \, {\left(d f x + c f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-9 i \, d f x - 9 i \, c f\right)} e^{\left(4 \, d x + 4 \, c\right)} - 36 \, {\left(d f x + c f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(9 i \, d f x + 9 i \, c f\right)} e^{\left(2 \, d x + 2 \, c\right)} - 18 \, {\left(d f x + c f\right)} e^{\left(d x + c\right)}\right)} \log\left(i \, e^{\left(d x + c\right)} + 1\right) + {\left(-9 i \, d f x - 9 i \, c f + {\left(9 i \, d f x + 9 i \, c f\right)} e^{\left(6 \, d x + 6 \, c\right)} + 18 \, {\left(d f x + c f\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(9 i \, d f x + 9 i \, c f\right)} e^{\left(4 \, d x + 4 \, c\right)} + 36 \, {\left(d f x + c f\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(-9 i \, d f x - 9 i \, c f\right)} e^{\left(2 \, d x + 2 \, c\right)} + 18 \, {\left(d f x + c f\right)} e^{\left(d x + c\right)}\right)} \log\left(-i \, e^{\left(d x + c\right)} + 1\right) - 8 i \, f}{24 \, a d^{2} e^{\left(6 \, d x + 6 \, c\right)} - 48 i \, a d^{2} e^{\left(5 \, d x + 5 \, c\right)} + 24 \, a d^{2} e^{\left(4 \, d x + 4 \, c\right)} - 96 i \, a d^{2} e^{\left(3 \, d x + 3 \, c\right)} - 24 \, a d^{2} e^{\left(2 \, d x + 2 \, c\right)} - 48 i \, a d^{2} e^{\left(d x + c\right)} - 24 \, a d^{2}}"," ",0,"((9*I*f*e^(6*d*x + 6*c) + 18*f*e^(5*d*x + 5*c) + 9*I*f*e^(4*d*x + 4*c) + 36*f*e^(3*d*x + 3*c) - 9*I*f*e^(2*d*x + 2*c) + 18*f*e^(d*x + c) - 9*I*f)*dilog(I*e^(d*x + c)) + (-9*I*f*e^(6*d*x + 6*c) - 18*f*e^(5*d*x + 5*c) - 9*I*f*e^(4*d*x + 4*c) - 36*f*e^(3*d*x + 3*c) + 9*I*f*e^(2*d*x + 2*c) - 18*f*e^(d*x + c) + 9*I*f)*dilog(-I*e^(d*x + c)) + 18*(d*f*x + d*e + f)*e^(5*d*x + 5*c) + (-36*I*d*f*x - 36*I*d*e - 36*I*f)*e^(4*d*x + 4*c) + 4*(3*d*f*x + 3*d*e + 4*f)*e^(3*d*x + 3*c) + (36*I*d*f*x + 36*I*d*e - 44*I*f)*e^(2*d*x + 2*c) + 2*(9*d*f*x + 9*d*e - f)*e^(d*x + c) + (-9*I*d*e + 9*I*c*f + (9*I*d*e - 9*I*c*f)*e^(6*d*x + 6*c) + 18*(d*e - c*f)*e^(5*d*x + 5*c) + (9*I*d*e - 9*I*c*f)*e^(4*d*x + 4*c) + 36*(d*e - c*f)*e^(3*d*x + 3*c) + (-9*I*d*e + 9*I*c*f)*e^(2*d*x + 2*c) + 18*(d*e - c*f)*e^(d*x + c))*log(e^(d*x + c) + I) + (9*I*d*e - 9*I*c*f + (-9*I*d*e + 9*I*c*f)*e^(6*d*x + 6*c) - 18*(d*e - c*f)*e^(5*d*x + 5*c) + (-9*I*d*e + 9*I*c*f)*e^(4*d*x + 4*c) - 36*(d*e - c*f)*e^(3*d*x + 3*c) + (9*I*d*e - 9*I*c*f)*e^(2*d*x + 2*c) - 18*(d*e - c*f)*e^(d*x + c))*log(e^(d*x + c) - I) + (9*I*d*f*x + 9*I*c*f + (-9*I*d*f*x - 9*I*c*f)*e^(6*d*x + 6*c) - 18*(d*f*x + c*f)*e^(5*d*x + 5*c) + (-9*I*d*f*x - 9*I*c*f)*e^(4*d*x + 4*c) - 36*(d*f*x + c*f)*e^(3*d*x + 3*c) + (9*I*d*f*x + 9*I*c*f)*e^(2*d*x + 2*c) - 18*(d*f*x + c*f)*e^(d*x + c))*log(I*e^(d*x + c) + 1) + (-9*I*d*f*x - 9*I*c*f + (9*I*d*f*x + 9*I*c*f)*e^(6*d*x + 6*c) + 18*(d*f*x + c*f)*e^(5*d*x + 5*c) + (9*I*d*f*x + 9*I*c*f)*e^(4*d*x + 4*c) + 36*(d*f*x + c*f)*e^(3*d*x + 3*c) + (-9*I*d*f*x - 9*I*c*f)*e^(2*d*x + 2*c) + 18*(d*f*x + c*f)*e^(d*x + c))*log(-I*e^(d*x + c) + 1) - 8*I*f)/(24*a*d^2*e^(6*d*x + 6*c) - 48*I*a*d^2*e^(5*d*x + 5*c) + 24*a*d^2*e^(4*d*x + 4*c) - 96*I*a*d^2*e^(3*d*x + 3*c) - 24*a*d^2*e^(2*d*x + 2*c) - 48*I*a*d^2*e^(d*x + c) - 24*a*d^2)","B",0
286,1,286,0,0.577181," ","integrate(sech(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 i \, e^{\left(6 \, d x + 6 \, c\right)} + 6 \, e^{\left(5 \, d x + 5 \, c\right)} + 3 i \, e^{\left(4 \, d x + 4 \, c\right)} + 12 \, e^{\left(3 \, d x + 3 \, c\right)} - 3 i \, e^{\left(2 \, d x + 2 \, c\right)} + 6 \, e^{\left(d x + c\right)} - 3 i\right)} \log\left(e^{\left(d x + c\right)} + i\right) + {\left(-3 i \, e^{\left(6 \, d x + 6 \, c\right)} - 6 \, e^{\left(5 \, d x + 5 \, c\right)} - 3 i \, e^{\left(4 \, d x + 4 \, c\right)} - 12 \, e^{\left(3 \, d x + 3 \, c\right)} + 3 i \, e^{\left(2 \, d x + 2 \, c\right)} - 6 \, e^{\left(d x + c\right)} + 3 i\right)} \log\left(e^{\left(d x + c\right)} - i\right) + 6 \, e^{\left(5 \, d x + 5 \, c\right)} - 12 i \, e^{\left(4 \, d x + 4 \, c\right)} + 4 \, e^{\left(3 \, d x + 3 \, c\right)} + 12 i \, e^{\left(2 \, d x + 2 \, c\right)} + 6 \, e^{\left(d x + c\right)}}{8 \, a d e^{\left(6 \, d x + 6 \, c\right)} - 16 i \, a d e^{\left(5 \, d x + 5 \, c\right)} + 8 \, a d e^{\left(4 \, d x + 4 \, c\right)} - 32 i \, a d e^{\left(3 \, d x + 3 \, c\right)} - 8 \, a d e^{\left(2 \, d x + 2 \, c\right)} - 16 i \, a d e^{\left(d x + c\right)} - 8 \, a d}"," ",0,"((3*I*e^(6*d*x + 6*c) + 6*e^(5*d*x + 5*c) + 3*I*e^(4*d*x + 4*c) + 12*e^(3*d*x + 3*c) - 3*I*e^(2*d*x + 2*c) + 6*e^(d*x + c) - 3*I)*log(e^(d*x + c) + I) + (-3*I*e^(6*d*x + 6*c) - 6*e^(5*d*x + 5*c) - 3*I*e^(4*d*x + 4*c) - 12*e^(3*d*x + 3*c) + 3*I*e^(2*d*x + 2*c) - 6*e^(d*x + c) + 3*I)*log(e^(d*x + c) - I) + 6*e^(5*d*x + 5*c) - 12*I*e^(4*d*x + 4*c) + 4*e^(3*d*x + 3*c) + 12*I*e^(2*d*x + 2*c) + 6*e^(d*x + c))/(8*a*d*e^(6*d*x + 6*c) - 16*I*a*d*e^(5*d*x + 5*c) + 8*a*d*e^(4*d*x + 4*c) - 32*I*a*d*e^(3*d*x + 3*c) - 8*a*d*e^(2*d*x + 2*c) - 16*I*a*d*e^(d*x + c) - 8*a*d)","B",0
287,0,0,0,0.728433," ","integrate(sech(d*x+c)^3/(f*x+e)/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 i \, d^{2} f^{3} x^{2} + 8 i \, d^{2} e f^{2} x + 4 i \, d^{2} e^{2} f - 6 i \, f^{3} + {\left(9 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e^{3} - 9 \, d^{2} e^{2} f - 2 \, d e f^{2} + 6 \, f^{3} + 9 \, {\left(3 \, d^{3} e f^{2} - d^{2} f^{3}\right)} x^{2} + {\left(27 \, d^{3} e^{2} f - 18 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-18 i \, d^{3} f^{3} x^{3} - 18 i \, d^{3} e^{3} + 18 i \, d^{2} e^{2} f - 6 i \, f^{3} + {\left(-54 i \, d^{3} e f^{2} + 18 i \, d^{2} f^{3}\right)} x^{2} + {\left(-54 i \, d^{3} e^{2} f + 36 i \, d^{2} e f^{2}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(3 \, d^{3} f^{3} x^{3} + 3 \, d^{3} e^{3} - 4 \, d^{2} e^{2} f - 2 \, d e f^{2} + 6 \, f^{3} + {\left(9 \, d^{3} e f^{2} - 4 \, d^{2} f^{3}\right)} x^{2} + {\left(9 \, d^{3} e^{2} f - 8 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(18 i \, d^{3} f^{3} x^{3} + 18 i \, d^{3} e^{3} + 22 i \, d^{2} e^{2} f - 12 i \, f^{3} + {\left(54 i \, d^{3} e f^{2} + 22 i \, d^{2} f^{3}\right)} x^{2} + {\left(54 i \, d^{3} e^{2} f + 44 i \, d^{2} e f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(9 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e^{3} + d^{2} e^{2} f - 2 \, d e f^{2} + 6 \, f^{3} + {\left(27 \, d^{3} e f^{2} + d^{2} f^{3}\right)} x^{2} + {\left(27 \, d^{3} e^{2} f + 2 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)} - {\left(12 \, a d^{4} f^{4} x^{4} + 48 \, a d^{4} e f^{3} x^{3} + 72 \, a d^{4} e^{2} f^{2} x^{2} + 48 \, a d^{4} e^{3} f x + 12 \, a d^{4} e^{4} - 12 \, {\left(a d^{4} f^{4} x^{4} + 4 \, a d^{4} e f^{3} x^{3} + 6 \, a d^{4} e^{2} f^{2} x^{2} + 4 \, a d^{4} e^{3} f x + a d^{4} e^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(-24 i \, a d^{4} f^{4} x^{4} - 96 i \, a d^{4} e f^{3} x^{3} - 144 i \, a d^{4} e^{2} f^{2} x^{2} - 96 i \, a d^{4} e^{3} f x - 24 i \, a d^{4} e^{4}\right)} e^{\left(5 \, d x + 5 \, c\right)} - 12 \, {\left(a d^{4} f^{4} x^{4} + 4 \, a d^{4} e f^{3} x^{3} + 6 \, a d^{4} e^{2} f^{2} x^{2} + 4 \, a d^{4} e^{3} f x + a d^{4} e^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-48 i \, a d^{4} f^{4} x^{4} - 192 i \, a d^{4} e f^{3} x^{3} - 288 i \, a d^{4} e^{2} f^{2} x^{2} - 192 i \, a d^{4} e^{3} f x - 48 i \, a d^{4} e^{4}\right)} e^{\left(3 \, d x + 3 \, c\right)} + 12 \, {\left(a d^{4} f^{4} x^{4} + 4 \, a d^{4} e f^{3} x^{3} + 6 \, a d^{4} e^{2} f^{2} x^{2} + 4 \, a d^{4} e^{3} f x + a d^{4} e^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-24 i \, a d^{4} f^{4} x^{4} - 96 i \, a d^{4} e f^{3} x^{3} - 144 i \, a d^{4} e^{2} f^{2} x^{2} - 96 i \, a d^{4} e^{3} f x - 24 i \, a d^{4} e^{4}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{-8 i \, d^{2} f^{4} x^{2} - 16 i \, d^{2} e f^{3} x - 8 i \, d^{2} e^{2} f^{2} + 24 i \, f^{4} + {\left(9 \, d^{4} f^{4} x^{4} + 36 \, d^{4} e f^{3} x^{3} + 9 \, d^{4} e^{4} - 20 \, d^{2} e^{2} f^{2} + 24 \, f^{4} + 2 \, {\left(27 \, d^{4} e^{2} f^{2} - 10 \, d^{2} f^{4}\right)} x^{2} + 4 \, {\left(9 \, d^{4} e^{3} f - 10 \, d^{2} e f^{3}\right)} x\right)} e^{\left(d x + c\right)}}{12 \, {\left(a d^{4} f^{5} x^{5} + 5 \, a d^{4} e f^{4} x^{4} + 10 \, a d^{4} e^{2} f^{3} x^{3} + 10 \, a d^{4} e^{3} f^{2} x^{2} + 5 \, a d^{4} e^{4} f x + a d^{4} e^{5} + {\left(a d^{4} f^{5} x^{5} + 5 \, a d^{4} e f^{4} x^{4} + 10 \, a d^{4} e^{2} f^{3} x^{3} + 10 \, a d^{4} e^{3} f^{2} x^{2} + 5 \, a d^{4} e^{4} f x + a d^{4} e^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}, x\right)}{12 \, a d^{4} f^{4} x^{4} + 48 \, a d^{4} e f^{3} x^{3} + 72 \, a d^{4} e^{2} f^{2} x^{2} + 48 \, a d^{4} e^{3} f x + 12 \, a d^{4} e^{4} - 12 \, {\left(a d^{4} f^{4} x^{4} + 4 \, a d^{4} e f^{3} x^{3} + 6 \, a d^{4} e^{2} f^{2} x^{2} + 4 \, a d^{4} e^{3} f x + a d^{4} e^{4}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(-24 i \, a d^{4} f^{4} x^{4} - 96 i \, a d^{4} e f^{3} x^{3} - 144 i \, a d^{4} e^{2} f^{2} x^{2} - 96 i \, a d^{4} e^{3} f x - 24 i \, a d^{4} e^{4}\right)} e^{\left(5 \, d x + 5 \, c\right)} - 12 \, {\left(a d^{4} f^{4} x^{4} + 4 \, a d^{4} e f^{3} x^{3} + 6 \, a d^{4} e^{2} f^{2} x^{2} + 4 \, a d^{4} e^{3} f x + a d^{4} e^{4}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-48 i \, a d^{4} f^{4} x^{4} - 192 i \, a d^{4} e f^{3} x^{3} - 288 i \, a d^{4} e^{2} f^{2} x^{2} - 192 i \, a d^{4} e^{3} f x - 48 i \, a d^{4} e^{4}\right)} e^{\left(3 \, d x + 3 \, c\right)} + 12 \, {\left(a d^{4} f^{4} x^{4} + 4 \, a d^{4} e f^{3} x^{3} + 6 \, a d^{4} e^{2} f^{2} x^{2} + 4 \, a d^{4} e^{3} f x + a d^{4} e^{4}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-24 i \, a d^{4} f^{4} x^{4} - 96 i \, a d^{4} e f^{3} x^{3} - 144 i \, a d^{4} e^{2} f^{2} x^{2} - 96 i \, a d^{4} e^{3} f x - 24 i \, a d^{4} e^{4}\right)} e^{\left(d x + c\right)}}"," ",0,"-(4*I*d^2*f^3*x^2 + 8*I*d^2*e*f^2*x + 4*I*d^2*e^2*f - 6*I*f^3 + (9*d^3*f^3*x^3 + 9*d^3*e^3 - 9*d^2*e^2*f - 2*d*e*f^2 + 6*f^3 + 9*(3*d^3*e*f^2 - d^2*f^3)*x^2 + (27*d^3*e^2*f - 18*d^2*e*f^2 - 2*d*f^3)*x)*e^(5*d*x + 5*c) + (-18*I*d^3*f^3*x^3 - 18*I*d^3*e^3 + 18*I*d^2*e^2*f - 6*I*f^3 + (-54*I*d^3*e*f^2 + 18*I*d^2*f^3)*x^2 + (-54*I*d^3*e^2*f + 36*I*d^2*e*f^2)*x)*e^(4*d*x + 4*c) + 2*(3*d^3*f^3*x^3 + 3*d^3*e^3 - 4*d^2*e^2*f - 2*d*e*f^2 + 6*f^3 + (9*d^3*e*f^2 - 4*d^2*f^3)*x^2 + (9*d^3*e^2*f - 8*d^2*e*f^2 - 2*d*f^3)*x)*e^(3*d*x + 3*c) + (18*I*d^3*f^3*x^3 + 18*I*d^3*e^3 + 22*I*d^2*e^2*f - 12*I*f^3 + (54*I*d^3*e*f^2 + 22*I*d^2*f^3)*x^2 + (54*I*d^3*e^2*f + 44*I*d^2*e*f^2)*x)*e^(2*d*x + 2*c) + (9*d^3*f^3*x^3 + 9*d^3*e^3 + d^2*e^2*f - 2*d*e*f^2 + 6*f^3 + (27*d^3*e*f^2 + d^2*f^3)*x^2 + (27*d^3*e^2*f + 2*d^2*e*f^2 - 2*d*f^3)*x)*e^(d*x + c) - (12*a*d^4*f^4*x^4 + 48*a*d^4*e*f^3*x^3 + 72*a*d^4*e^2*f^2*x^2 + 48*a*d^4*e^3*f*x + 12*a*d^4*e^4 - 12*(a*d^4*f^4*x^4 + 4*a*d^4*e*f^3*x^3 + 6*a*d^4*e^2*f^2*x^2 + 4*a*d^4*e^3*f*x + a*d^4*e^4)*e^(6*d*x + 6*c) - (-24*I*a*d^4*f^4*x^4 - 96*I*a*d^4*e*f^3*x^3 - 144*I*a*d^4*e^2*f^2*x^2 - 96*I*a*d^4*e^3*f*x - 24*I*a*d^4*e^4)*e^(5*d*x + 5*c) - 12*(a*d^4*f^4*x^4 + 4*a*d^4*e*f^3*x^3 + 6*a*d^4*e^2*f^2*x^2 + 4*a*d^4*e^3*f*x + a*d^4*e^4)*e^(4*d*x + 4*c) - (-48*I*a*d^4*f^4*x^4 - 192*I*a*d^4*e*f^3*x^3 - 288*I*a*d^4*e^2*f^2*x^2 - 192*I*a*d^4*e^3*f*x - 48*I*a*d^4*e^4)*e^(3*d*x + 3*c) + 12*(a*d^4*f^4*x^4 + 4*a*d^4*e*f^3*x^3 + 6*a*d^4*e^2*f^2*x^2 + 4*a*d^4*e^3*f*x + a*d^4*e^4)*e^(2*d*x + 2*c) - (-24*I*a*d^4*f^4*x^4 - 96*I*a*d^4*e*f^3*x^3 - 144*I*a*d^4*e^2*f^2*x^2 - 96*I*a*d^4*e^3*f*x - 24*I*a*d^4*e^4)*e^(d*x + c))*integral(1/12*(-8*I*d^2*f^4*x^2 - 16*I*d^2*e*f^3*x - 8*I*d^2*e^2*f^2 + 24*I*f^4 + (9*d^4*f^4*x^4 + 36*d^4*e*f^3*x^3 + 9*d^4*e^4 - 20*d^2*e^2*f^2 + 24*f^4 + 2*(27*d^4*e^2*f^2 - 10*d^2*f^4)*x^2 + 4*(9*d^4*e^3*f - 10*d^2*e*f^3)*x)*e^(d*x + c))/(a*d^4*f^5*x^5 + 5*a*d^4*e*f^4*x^4 + 10*a*d^4*e^2*f^3*x^3 + 10*a*d^4*e^3*f^2*x^2 + 5*a*d^4*e^4*f*x + a*d^4*e^5 + (a*d^4*f^5*x^5 + 5*a*d^4*e*f^4*x^4 + 10*a*d^4*e^2*f^3*x^3 + 10*a*d^4*e^3*f^2*x^2 + 5*a*d^4*e^4*f*x + a*d^4*e^5)*e^(2*d*x + 2*c)), x))/(12*a*d^4*f^4*x^4 + 48*a*d^4*e*f^3*x^3 + 72*a*d^4*e^2*f^2*x^2 + 48*a*d^4*e^3*f*x + 12*a*d^4*e^4 - 12*(a*d^4*f^4*x^4 + 4*a*d^4*e*f^3*x^3 + 6*a*d^4*e^2*f^2*x^2 + 4*a*d^4*e^3*f*x + a*d^4*e^4)*e^(6*d*x + 6*c) - (-24*I*a*d^4*f^4*x^4 - 96*I*a*d^4*e*f^3*x^3 - 144*I*a*d^4*e^2*f^2*x^2 - 96*I*a*d^4*e^3*f*x - 24*I*a*d^4*e^4)*e^(5*d*x + 5*c) - 12*(a*d^4*f^4*x^4 + 4*a*d^4*e*f^3*x^3 + 6*a*d^4*e^2*f^2*x^2 + 4*a*d^4*e^3*f*x + a*d^4*e^4)*e^(4*d*x + 4*c) - (-48*I*a*d^4*f^4*x^4 - 192*I*a*d^4*e*f^3*x^3 - 288*I*a*d^4*e^2*f^2*x^2 - 192*I*a*d^4*e^3*f*x - 48*I*a*d^4*e^4)*e^(3*d*x + 3*c) + 12*(a*d^4*f^4*x^4 + 4*a*d^4*e*f^3*x^3 + 6*a*d^4*e^2*f^2*x^2 + 4*a*d^4*e^3*f*x + a*d^4*e^4)*e^(2*d*x + 2*c) - (-24*I*a*d^4*f^4*x^4 - 96*I*a*d^4*e*f^3*x^3 - 144*I*a*d^4*e^2*f^2*x^2 - 96*I*a*d^4*e^3*f*x - 24*I*a*d^4*e^4)*e^(d*x + c))","F",0
288,0,0,0,0.624318," ","integrate(sech(d*x+c)^3/(f*x+e)^2/(a+I*a*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{8 i \, d^{2} f^{3} x^{2} + 16 i \, d^{2} e f^{2} x + 8 i \, d^{2} e^{2} f - 24 i \, f^{3} + 3 \, {\left(3 \, d^{3} f^{3} x^{3} + 3 \, d^{3} e^{3} - 6 \, d^{2} e^{2} f - 2 \, d e f^{2} + 8 \, f^{3} + 3 \, {\left(3 \, d^{3} e f^{2} - 2 \, d^{2} f^{3}\right)} x^{2} + {\left(9 \, d^{3} e^{2} f - 12 \, d^{2} e f^{2} - 2 \, d f^{3}\right)} x\right)} e^{\left(5 \, d x + 5 \, c\right)} + {\left(-18 i \, d^{3} f^{3} x^{3} - 18 i \, d^{3} e^{3} + 36 i \, d^{2} e^{2} f - 24 i \, f^{3} + {\left(-54 i \, d^{3} e f^{2} + 36 i \, d^{2} f^{3}\right)} x^{2} + {\left(-54 i \, d^{3} e^{2} f + 72 i \, d^{2} e f^{2}\right)} x\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(3 \, d^{3} f^{3} x^{3} + 3 \, d^{3} e^{3} - 8 \, d^{2} e^{2} f - 6 \, d e f^{2} + 24 \, f^{3} + {\left(9 \, d^{3} e f^{2} - 8 \, d^{2} f^{3}\right)} x^{2} + {\left(9 \, d^{3} e^{2} f - 16 \, d^{2} e f^{2} - 6 \, d f^{3}\right)} x\right)} e^{\left(3 \, d x + 3 \, c\right)} + {\left(18 i \, d^{3} f^{3} x^{3} + 18 i \, d^{3} e^{3} + 44 i \, d^{2} e^{2} f - 48 i \, f^{3} + {\left(54 i \, d^{3} e f^{2} + 44 i \, d^{2} f^{3}\right)} x^{2} + {\left(54 i \, d^{3} e^{2} f + 88 i \, d^{2} e f^{2}\right)} x\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(9 \, d^{3} f^{3} x^{3} + 9 \, d^{3} e^{3} + 2 \, d^{2} e^{2} f - 6 \, d e f^{2} + 24 \, f^{3} + {\left(27 \, d^{3} e f^{2} + 2 \, d^{2} f^{3}\right)} x^{2} + {\left(27 \, d^{3} e^{2} f + 4 \, d^{2} e f^{2} - 6 \, d f^{3}\right)} x\right)} e^{\left(d x + c\right)} - {\left(12 \, a d^{4} f^{5} x^{5} + 60 \, a d^{4} e f^{4} x^{4} + 120 \, a d^{4} e^{2} f^{3} x^{3} + 120 \, a d^{4} e^{3} f^{2} x^{2} + 60 \, a d^{4} e^{4} f x + 12 \, a d^{4} e^{5} - 12 \, {\left(a d^{4} f^{5} x^{5} + 5 \, a d^{4} e f^{4} x^{4} + 10 \, a d^{4} e^{2} f^{3} x^{3} + 10 \, a d^{4} e^{3} f^{2} x^{2} + 5 \, a d^{4} e^{4} f x + a d^{4} e^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(-24 i \, a d^{4} f^{5} x^{5} - 120 i \, a d^{4} e f^{4} x^{4} - 240 i \, a d^{4} e^{2} f^{3} x^{3} - 240 i \, a d^{4} e^{3} f^{2} x^{2} - 120 i \, a d^{4} e^{4} f x - 24 i \, a d^{4} e^{5}\right)} e^{\left(5 \, d x + 5 \, c\right)} - 12 \, {\left(a d^{4} f^{5} x^{5} + 5 \, a d^{4} e f^{4} x^{4} + 10 \, a d^{4} e^{2} f^{3} x^{3} + 10 \, a d^{4} e^{3} f^{2} x^{2} + 5 \, a d^{4} e^{4} f x + a d^{4} e^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-48 i \, a d^{4} f^{5} x^{5} - 240 i \, a d^{4} e f^{4} x^{4} - 480 i \, a d^{4} e^{2} f^{3} x^{3} - 480 i \, a d^{4} e^{3} f^{2} x^{2} - 240 i \, a d^{4} e^{4} f x - 48 i \, a d^{4} e^{5}\right)} e^{\left(3 \, d x + 3 \, c\right)} + 12 \, {\left(a d^{4} f^{5} x^{5} + 5 \, a d^{4} e f^{4} x^{4} + 10 \, a d^{4} e^{2} f^{3} x^{3} + 10 \, a d^{4} e^{3} f^{2} x^{2} + 5 \, a d^{4} e^{4} f x + a d^{4} e^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-24 i \, a d^{4} f^{5} x^{5} - 120 i \, a d^{4} e f^{4} x^{4} - 240 i \, a d^{4} e^{2} f^{3} x^{3} - 240 i \, a d^{4} e^{3} f^{2} x^{2} - 120 i \, a d^{4} e^{4} f x - 24 i \, a d^{4} e^{5}\right)} e^{\left(d x + c\right)}\right)} {\rm integral}\left(\frac{-8 i \, d^{2} f^{4} x^{2} - 16 i \, d^{2} e f^{3} x - 8 i \, d^{2} e^{2} f^{2} + 40 i \, f^{4} + {\left(3 \, d^{4} f^{4} x^{4} + 12 \, d^{4} e f^{3} x^{3} + 3 \, d^{4} e^{4} - 20 \, d^{2} e^{2} f^{2} + 40 \, f^{4} + 2 \, {\left(9 \, d^{4} e^{2} f^{2} - 10 \, d^{2} f^{4}\right)} x^{2} + 4 \, {\left(3 \, d^{4} e^{3} f - 10 \, d^{2} e f^{3}\right)} x\right)} e^{\left(d x + c\right)}}{4 \, {\left(a d^{4} f^{6} x^{6} + 6 \, a d^{4} e f^{5} x^{5} + 15 \, a d^{4} e^{2} f^{4} x^{4} + 20 \, a d^{4} e^{3} f^{3} x^{3} + 15 \, a d^{4} e^{4} f^{2} x^{2} + 6 \, a d^{4} e^{5} f x + a d^{4} e^{6} + {\left(a d^{4} f^{6} x^{6} + 6 \, a d^{4} e f^{5} x^{5} + 15 \, a d^{4} e^{2} f^{4} x^{4} + 20 \, a d^{4} e^{3} f^{3} x^{3} + 15 \, a d^{4} e^{4} f^{2} x^{2} + 6 \, a d^{4} e^{5} f x + a d^{4} e^{6}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right)}}, x\right)}{12 \, a d^{4} f^{5} x^{5} + 60 \, a d^{4} e f^{4} x^{4} + 120 \, a d^{4} e^{2} f^{3} x^{3} + 120 \, a d^{4} e^{3} f^{2} x^{2} + 60 \, a d^{4} e^{4} f x + 12 \, a d^{4} e^{5} - 12 \, {\left(a d^{4} f^{5} x^{5} + 5 \, a d^{4} e f^{4} x^{4} + 10 \, a d^{4} e^{2} f^{3} x^{3} + 10 \, a d^{4} e^{3} f^{2} x^{2} + 5 \, a d^{4} e^{4} f x + a d^{4} e^{5}\right)} e^{\left(6 \, d x + 6 \, c\right)} - {\left(-24 i \, a d^{4} f^{5} x^{5} - 120 i \, a d^{4} e f^{4} x^{4} - 240 i \, a d^{4} e^{2} f^{3} x^{3} - 240 i \, a d^{4} e^{3} f^{2} x^{2} - 120 i \, a d^{4} e^{4} f x - 24 i \, a d^{4} e^{5}\right)} e^{\left(5 \, d x + 5 \, c\right)} - 12 \, {\left(a d^{4} f^{5} x^{5} + 5 \, a d^{4} e f^{4} x^{4} + 10 \, a d^{4} e^{2} f^{3} x^{3} + 10 \, a d^{4} e^{3} f^{2} x^{2} + 5 \, a d^{4} e^{4} f x + a d^{4} e^{5}\right)} e^{\left(4 \, d x + 4 \, c\right)} - {\left(-48 i \, a d^{4} f^{5} x^{5} - 240 i \, a d^{4} e f^{4} x^{4} - 480 i \, a d^{4} e^{2} f^{3} x^{3} - 480 i \, a d^{4} e^{3} f^{2} x^{2} - 240 i \, a d^{4} e^{4} f x - 48 i \, a d^{4} e^{5}\right)} e^{\left(3 \, d x + 3 \, c\right)} + 12 \, {\left(a d^{4} f^{5} x^{5} + 5 \, a d^{4} e f^{4} x^{4} + 10 \, a d^{4} e^{2} f^{3} x^{3} + 10 \, a d^{4} e^{3} f^{2} x^{2} + 5 \, a d^{4} e^{4} f x + a d^{4} e^{5}\right)} e^{\left(2 \, d x + 2 \, c\right)} - {\left(-24 i \, a d^{4} f^{5} x^{5} - 120 i \, a d^{4} e f^{4} x^{4} - 240 i \, a d^{4} e^{2} f^{3} x^{3} - 240 i \, a d^{4} e^{3} f^{2} x^{2} - 120 i \, a d^{4} e^{4} f x - 24 i \, a d^{4} e^{5}\right)} e^{\left(d x + c\right)}}"," ",0,"-(8*I*d^2*f^3*x^2 + 16*I*d^2*e*f^2*x + 8*I*d^2*e^2*f - 24*I*f^3 + 3*(3*d^3*f^3*x^3 + 3*d^3*e^3 - 6*d^2*e^2*f - 2*d*e*f^2 + 8*f^3 + 3*(3*d^3*e*f^2 - 2*d^2*f^3)*x^2 + (9*d^3*e^2*f - 12*d^2*e*f^2 - 2*d*f^3)*x)*e^(5*d*x + 5*c) + (-18*I*d^3*f^3*x^3 - 18*I*d^3*e^3 + 36*I*d^2*e^2*f - 24*I*f^3 + (-54*I*d^3*e*f^2 + 36*I*d^2*f^3)*x^2 + (-54*I*d^3*e^2*f + 72*I*d^2*e*f^2)*x)*e^(4*d*x + 4*c) + 2*(3*d^3*f^3*x^3 + 3*d^3*e^3 - 8*d^2*e^2*f - 6*d*e*f^2 + 24*f^3 + (9*d^3*e*f^2 - 8*d^2*f^3)*x^2 + (9*d^3*e^2*f - 16*d^2*e*f^2 - 6*d*f^3)*x)*e^(3*d*x + 3*c) + (18*I*d^3*f^3*x^3 + 18*I*d^3*e^3 + 44*I*d^2*e^2*f - 48*I*f^3 + (54*I*d^3*e*f^2 + 44*I*d^2*f^3)*x^2 + (54*I*d^3*e^2*f + 88*I*d^2*e*f^2)*x)*e^(2*d*x + 2*c) + (9*d^3*f^3*x^3 + 9*d^3*e^3 + 2*d^2*e^2*f - 6*d*e*f^2 + 24*f^3 + (27*d^3*e*f^2 + 2*d^2*f^3)*x^2 + (27*d^3*e^2*f + 4*d^2*e*f^2 - 6*d*f^3)*x)*e^(d*x + c) - (12*a*d^4*f^5*x^5 + 60*a*d^4*e*f^4*x^4 + 120*a*d^4*e^2*f^3*x^3 + 120*a*d^4*e^3*f^2*x^2 + 60*a*d^4*e^4*f*x + 12*a*d^4*e^5 - 12*(a*d^4*f^5*x^5 + 5*a*d^4*e*f^4*x^4 + 10*a*d^4*e^2*f^3*x^3 + 10*a*d^4*e^3*f^2*x^2 + 5*a*d^4*e^4*f*x + a*d^4*e^5)*e^(6*d*x + 6*c) - (-24*I*a*d^4*f^5*x^5 - 120*I*a*d^4*e*f^4*x^4 - 240*I*a*d^4*e^2*f^3*x^3 - 240*I*a*d^4*e^3*f^2*x^2 - 120*I*a*d^4*e^4*f*x - 24*I*a*d^4*e^5)*e^(5*d*x + 5*c) - 12*(a*d^4*f^5*x^5 + 5*a*d^4*e*f^4*x^4 + 10*a*d^4*e^2*f^3*x^3 + 10*a*d^4*e^3*f^2*x^2 + 5*a*d^4*e^4*f*x + a*d^4*e^5)*e^(4*d*x + 4*c) - (-48*I*a*d^4*f^5*x^5 - 240*I*a*d^4*e*f^4*x^4 - 480*I*a*d^4*e^2*f^3*x^3 - 480*I*a*d^4*e^3*f^2*x^2 - 240*I*a*d^4*e^4*f*x - 48*I*a*d^4*e^5)*e^(3*d*x + 3*c) + 12*(a*d^4*f^5*x^5 + 5*a*d^4*e*f^4*x^4 + 10*a*d^4*e^2*f^3*x^3 + 10*a*d^4*e^3*f^2*x^2 + 5*a*d^4*e^4*f*x + a*d^4*e^5)*e^(2*d*x + 2*c) - (-24*I*a*d^4*f^5*x^5 - 120*I*a*d^4*e*f^4*x^4 - 240*I*a*d^4*e^2*f^3*x^3 - 240*I*a*d^4*e^3*f^2*x^2 - 120*I*a*d^4*e^4*f*x - 24*I*a*d^4*e^5)*e^(d*x + c))*integral(1/4*(-8*I*d^2*f^4*x^2 - 16*I*d^2*e*f^3*x - 8*I*d^2*e^2*f^2 + 40*I*f^4 + (3*d^4*f^4*x^4 + 12*d^4*e*f^3*x^3 + 3*d^4*e^4 - 20*d^2*e^2*f^2 + 40*f^4 + 2*(9*d^4*e^2*f^2 - 10*d^2*f^4)*x^2 + 4*(3*d^4*e^3*f - 10*d^2*e*f^3)*x)*e^(d*x + c))/(a*d^4*f^6*x^6 + 6*a*d^4*e*f^5*x^5 + 15*a*d^4*e^2*f^4*x^4 + 20*a*d^4*e^3*f^3*x^3 + 15*a*d^4*e^4*f^2*x^2 + 6*a*d^4*e^5*f*x + a*d^4*e^6 + (a*d^4*f^6*x^6 + 6*a*d^4*e*f^5*x^5 + 15*a*d^4*e^2*f^4*x^4 + 20*a*d^4*e^3*f^3*x^3 + 15*a*d^4*e^4*f^2*x^2 + 6*a*d^4*e^5*f*x + a*d^4*e^6)*e^(2*d*x + 2*c)), x))/(12*a*d^4*f^5*x^5 + 60*a*d^4*e*f^4*x^4 + 120*a*d^4*e^2*f^3*x^3 + 120*a*d^4*e^3*f^2*x^2 + 60*a*d^4*e^4*f*x + 12*a*d^4*e^5 - 12*(a*d^4*f^5*x^5 + 5*a*d^4*e*f^4*x^4 + 10*a*d^4*e^2*f^3*x^3 + 10*a*d^4*e^3*f^2*x^2 + 5*a*d^4*e^4*f*x + a*d^4*e^5)*e^(6*d*x + 6*c) - (-24*I*a*d^4*f^5*x^5 - 120*I*a*d^4*e*f^4*x^4 - 240*I*a*d^4*e^2*f^3*x^3 - 240*I*a*d^4*e^3*f^2*x^2 - 120*I*a*d^4*e^4*f*x - 24*I*a*d^4*e^5)*e^(5*d*x + 5*c) - 12*(a*d^4*f^5*x^5 + 5*a*d^4*e*f^4*x^4 + 10*a*d^4*e^2*f^3*x^3 + 10*a*d^4*e^3*f^2*x^2 + 5*a*d^4*e^4*f*x + a*d^4*e^5)*e^(4*d*x + 4*c) - (-48*I*a*d^4*f^5*x^5 - 240*I*a*d^4*e*f^4*x^4 - 480*I*a*d^4*e^2*f^3*x^3 - 480*I*a*d^4*e^3*f^2*x^2 - 240*I*a*d^4*e^4*f*x - 48*I*a*d^4*e^5)*e^(3*d*x + 3*c) + 12*(a*d^4*f^5*x^5 + 5*a*d^4*e*f^4*x^4 + 10*a*d^4*e^2*f^3*x^3 + 10*a*d^4*e^3*f^2*x^2 + 5*a*d^4*e^4*f*x + a*d^4*e^5)*e^(2*d*x + 2*c) - (-24*I*a*d^4*f^5*x^5 - 120*I*a*d^4*e*f^4*x^4 - 240*I*a*d^4*e^2*f^3*x^3 - 240*I*a*d^4*e^3*f^2*x^2 - 120*I*a*d^4*e^4*f*x - 24*I*a*d^4*e^5)*e^(d*x + c))","F",0
289,1,882,0,0.522656," ","integrate((f*x+e)^3*cosh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{d^{4} f^{3} x^{4} + 4 \, d^{4} e f^{2} x^{3} + 6 \, d^{4} e^{2} f x^{2} + 4 \, d^{4} e^{3} x - 24 \, f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 12 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 24 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right)}{4 \, b d^{4}}"," ",0,"-1/4*(d^4*f^3*x^4 + 4*d^4*e*f^2*x^3 + 6*d^4*e^2*f*x^2 + 4*d^4*e^3*x - 24*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 12*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 4*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*(d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 24*(d*f^3*x + d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*(d*f^3*x + d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b))/(b*d^4)","C",0
290,1,609,0,0.541982," ","integrate((f*x+e)^2*cosh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{d^{3} f^{2} x^{3} + 3 \, d^{3} e f x^{2} + 3 \, d^{3} e^{2} x + 6 \, f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(d f^{2} x + d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left(d f^{2} x + d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 3 \, {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right)}{3 \, b d^{3}}"," ",0,"-1/3*(d^3*f^2*x^3 + 3*d^3*e*f*x^2 + 3*d^3*e^2*x + 6*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(d*f^2*x + d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 6*(d*f^2*x + d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*(d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 3*(d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 3*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 3*(d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b))/(b*d^3)","C",0
291,1,380,0,0.532882," ","integrate((f*x+e)*cosh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{d^{2} f x^{2} + 2 \, d^{2} e x - 2 \, f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(d e - c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(d e - c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(d f x + c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(d f x + c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right)}{2 \, b d^{2}}"," ",0,"-1/2*(d^2*f*x^2 + 2*d^2*e*x - 2*f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(d*e - c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(d*e - c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(d*f*x + c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(d*f*x + c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b))/(b*d^2)","B",0
292,1,44,0,0.432335," ","integrate(cosh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{d x - \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{b d}"," ",0,"-(d*x - log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))))/(b*d)","B",0
293,0,0,0,0.541664," ","integrate(cosh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
294,1,2020,0,0.789093," ","integrate((f*x+e)^3*cosh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b d^{3} f^{3} x^{3} + 2 \, b d^{3} e^{3} + 6 \, b d^{2} e^{2} f + 12 \, b d e f^{2} + 12 \, b f^{3} + 6 \, {\left(b d^{3} e f^{2} + b d^{2} f^{3}\right)} x^{2} + 2 \, {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} - 3 \, b d^{2} e^{2} f + 6 \, b d e f^{2} - 6 \, b f^{3} + 3 \, {\left(b d^{3} e f^{2} - b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, b d^{2} e f^{2} + 2 \, b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} - 3 \, b d^{2} e^{2} f + 6 \, b d e f^{2} - 6 \, b f^{3} + 3 \, {\left(b d^{3} e f^{2} - b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, b d^{2} e f^{2} + 2 \, b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 12 \, {\left({\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left({\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)} \cosh\left(d x + c\right) + {\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)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 4 \, {\left({\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)} \cosh\left(d x + c\right) + {\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)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 4 \, {\left({\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left({\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 24 \, {\left(b f^{3} \cosh\left(d x + c\right) + b f^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left(b f^{3} \cosh\left(d x + c\right) + b f^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left({\left(b d f^{3} x + b d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(b d f^{3} x + b d e f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(b d f^{3} x + b d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(b d f^{3} x + b d e f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b d^{3} e^{2} f + 2 \, b d^{2} e f^{2} + 2 \, b d f^{3}\right)} x - {\left(a d^{4} f^{3} x^{4} + 4 \, a d^{4} e f^{2} x^{3} + 6 \, a d^{4} e^{2} f x^{2} + 4 \, a d^{4} e^{3} x\right)} \cosh\left(d x + c\right) - {\left(a d^{4} f^{3} x^{4} + 4 \, a d^{4} e f^{2} x^{3} + 6 \, a d^{4} e^{2} f x^{2} + 4 \, a d^{4} e^{3} x - 4 \, {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} - 3 \, b d^{2} e^{2} f + 6 \, b d e f^{2} - 6 \, b f^{3} + 3 \, {\left(b d^{3} e f^{2} - b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, b d^{2} e f^{2} + 2 \, b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left(b^{2} d^{4} \cosh\left(d x + c\right) + b^{2} d^{4} \sinh\left(d x + c\right)\right)}}"," ",0,"1/4*(2*b*d^3*f^3*x^3 + 2*b*d^3*e^3 + 6*b*d^2*e^2*f + 12*b*d*e*f^2 + 12*b*f^3 + 6*(b*d^3*e*f^2 + b*d^2*f^3)*x^2 + 2*(b*d^3*f^3*x^3 + b*d^3*e^3 - 3*b*d^2*e^2*f + 6*b*d*e*f^2 - 6*b*f^3 + 3*(b*d^3*e*f^2 - b*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*b*d^2*e*f^2 + 2*b*d*f^3)*x)*cosh(d*x + c)^2 + 2*(b*d^3*f^3*x^3 + b*d^3*e^3 - 3*b*d^2*e^2*f + 6*b*d*e*f^2 - 6*b*f^3 + 3*(b*d^3*e*f^2 - b*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*b*d^2*e*f^2 + 2*b*d*f^3)*x)*sinh(d*x + c)^2 + 12*((b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*cosh(d*x + c) + (b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 12*((b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*cosh(d*x + c) + (b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 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)*cosh(d*x + c) + (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)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 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)*cosh(d*x + c) + (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)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 4*((b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*cosh(d*x + c) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*((b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*cosh(d*x + c) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 24*(b*f^3*cosh(d*x + c) + b*f^3*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*(b*f^3*cosh(d*x + c) + b*f^3*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*((b*d*f^3*x + b*d*e*f^2)*cosh(d*x + c) + (b*d*f^3*x + b*d*e*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*((b*d*f^3*x + b*d*e*f^2)*cosh(d*x + c) + (b*d*f^3*x + b*d*e*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b*d^3*e^2*f + 2*b*d^2*e*f^2 + 2*b*d*f^3)*x - (a*d^4*f^3*x^4 + 4*a*d^4*e*f^2*x^3 + 6*a*d^4*e^2*f*x^2 + 4*a*d^4*e^3*x)*cosh(d*x + c) - (a*d^4*f^3*x^4 + 4*a*d^4*e*f^2*x^3 + 6*a*d^4*e^2*f*x^2 + 4*a*d^4*e^3*x - 4*(b*d^3*f^3*x^3 + b*d^3*e^3 - 3*b*d^2*e^2*f + 6*b*d*e*f^2 - 6*b*f^3 + 3*(b*d^3*e*f^2 - b*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*b*d^2*e*f^2 + 2*b*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^2*d^4*cosh(d*x + c) + b^2*d^4*sinh(d*x + c))","C",0
295,1,1313,0,0.717753," ","integrate((f*x+e)^2*cosh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, b d^{2} f^{2} x^{2} + 3 \, b d^{2} e^{2} + 6 \, b d e f + 6 \, b f^{2} + 3 \, {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} - 2 \, b d e f + 2 \, b f^{2} + 2 \, {\left(b d^{2} e f - b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} - 2 \, b d e f + 2 \, b f^{2} + 2 \, {\left(b d^{2} e f - b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(b d f^{2} x + b d e f\right)} \cosh\left(d x + c\right) + {\left(b d f^{2} x + b d e f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 12 \, {\left({\left(b d f^{2} x + b d e f\right)} \cosh\left(d x + c\right) + {\left(b d f^{2} x + b d e f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left({\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 6 \, {\left({\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 6 \, {\left({\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left({\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left(b f^{2} \cosh\left(d x + c\right) + b f^{2} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b f^{2} \cosh\left(d x + c\right) + b f^{2} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b d^{2} e f + b d f^{2}\right)} x - 2 \, {\left(a d^{3} f^{2} x^{3} + 3 \, a d^{3} e f x^{2} + 3 \, a d^{3} e^{2} x\right)} \cosh\left(d x + c\right) - 2 \, {\left(a d^{3} f^{2} x^{3} + 3 \, a d^{3} e f x^{2} + 3 \, a d^{3} e^{2} x - 3 \, {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} - 2 \, b d e f + 2 \, b f^{2} + 2 \, {\left(b d^{2} e f - b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left(b^{2} d^{3} \cosh\left(d x + c\right) + b^{2} d^{3} \sinh\left(d x + c\right)\right)}}"," ",0,"1/6*(3*b*d^2*f^2*x^2 + 3*b*d^2*e^2 + 6*b*d*e*f + 6*b*f^2 + 3*(b*d^2*f^2*x^2 + b*d^2*e^2 - 2*b*d*e*f + 2*b*f^2 + 2*(b*d^2*e*f - b*d*f^2)*x)*cosh(d*x + c)^2 + 3*(b*d^2*f^2*x^2 + b*d^2*e^2 - 2*b*d*e*f + 2*b*f^2 + 2*(b*d^2*e*f - b*d*f^2)*x)*sinh(d*x + c)^2 + 12*((b*d*f^2*x + b*d*e*f)*cosh(d*x + c) + (b*d*f^2*x + b*d*e*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 12*((b*d*f^2*x + b*d*e*f)*cosh(d*x + c) + (b*d*f^2*x + b*d*e*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 6*((b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cosh(d*x + c) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 6*((b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cosh(d*x + c) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 6*((b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*cosh(d*x + c) + (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 6*((b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*cosh(d*x + c) + (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 12*(b*f^2*cosh(d*x + c) + b*f^2*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(b*f^2*cosh(d*x + c) + b*f^2*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b*d^2*e*f + b*d*f^2)*x - 2*(a*d^3*f^2*x^3 + 3*a*d^3*e*f*x^2 + 3*a*d^3*e^2*x)*cosh(d*x + c) - 2*(a*d^3*f^2*x^3 + 3*a*d^3*e*f*x^2 + 3*a*d^3*e^2*x - 3*(b*d^2*f^2*x^2 + b*d^2*e^2 - 2*b*d*e*f + 2*b*f^2 + 2*(b*d^2*e*f - b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^2*d^3*cosh(d*x + c) + b^2*d^3*sinh(d*x + c))","C",0
296,1,742,0,0.664660," ","integrate((f*x+e)*cosh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{b d f x + b d e + {\left(b d f x + b d e - b f\right)} \cosh\left(d x + c\right)^{2} + {\left(b d f x + b d e - b f\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b f \cosh\left(d x + c\right) + b f \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b f \cosh\left(d x + c\right) + b f \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left({\left(b d e - b c f\right)} \cosh\left(d x + c\right) + {\left(b d e - b c f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left(b d e - b c f\right)} \cosh\left(d x + c\right) + {\left(b d e - b c f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left(b d f x + b c f\right)} \cosh\left(d x + c\right) + {\left(b d f x + b c f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(b d f x + b c f\right)} \cosh\left(d x + c\right) + {\left(b d f x + b c f\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + b f - {\left(a d^{2} f x^{2} + 2 \, a d^{2} e x\right)} \cosh\left(d x + c\right) - {\left(a d^{2} f x^{2} + 2 \, a d^{2} e x - 2 \, {\left(b d f x + b d e - b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(b^{2} d^{2} \cosh\left(d x + c\right) + b^{2} d^{2} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(b*d*f*x + b*d*e + (b*d*f*x + b*d*e - b*f)*cosh(d*x + c)^2 + (b*d*f*x + b*d*e - b*f)*sinh(d*x + c)^2 + 2*(b*f*cosh(d*x + c) + b*f*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b*f*cosh(d*x + c) + b*f*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*((b*d*e - b*c*f)*cosh(d*x + c) + (b*d*e - b*c*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*((b*d*e - b*c*f)*cosh(d*x + c) + (b*d*e - b*c*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*((b*d*f*x + b*c*f)*cosh(d*x + c) + (b*d*f*x + b*c*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((b*d*f*x + b*c*f)*cosh(d*x + c) + (b*d*f*x + b*c*f)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + b*f - (a*d^2*f*x^2 + 2*a*d^2*e*x)*cosh(d*x + c) - (a*d^2*f*x^2 + 2*a*d^2*e*x - 2*(b*d*f*x + b*d*e - b*f)*cosh(d*x + c))*sinh(d*x + c))/(b^2*d^2*cosh(d*x + c) + b^2*d^2*sinh(d*x + c))","B",0
297,1,259,0,0.601230," ","integrate(cosh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a d x \cosh\left(d x + c\right) - b \cosh\left(d x + c\right)^{2} - b \sinh\left(d x + c\right)^{2} - 2 \, \sqrt{a^{2} + b^{2}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 2 \, {\left(a d x - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - b}{2 \, {\left(b^{2} d \cosh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*a*d*x*cosh(d*x + c) - b*cosh(d*x + c)^2 - b*sinh(d*x + c)^2 - 2*sqrt(a^2 + b^2)*(cosh(d*x + c) + sinh(d*x + c))*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 2*(a*d*x - b*cosh(d*x + c))*sinh(d*x + c) - b)/(b^2*d*cosh(d*x + c) + b^2*d*sinh(d*x + c))","B",0
298,0,0,0,0.787894," ","integrate(cosh(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
299,1,4371,0,0.670930," ","integrate((f*x+e)^3*cosh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} + 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} + 3 \, b^{2} f^{3} + {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} - 16 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(4 \, a b d^{3} f^{3} x^{3} + 4 \, a b d^{3} e^{3} - 12 \, a b d^{2} e^{2} f + 24 \, a b d e f^{2} - 24 \, a b f^{3} + 12 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 12 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x - {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} + b^{2} d^{2} f^{3}\right)} x^{2} - 8 \, {\left({\left(a^{2} + b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{2} + b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{2} + b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{2} + b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{2} + b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{2} + b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c^{4} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(4 \, {\left(a^{2} + b^{2}\right)} d^{4} f^{3} x^{4} + 16 \, {\left(a^{2} + b^{2}\right)} d^{4} e f^{2} x^{3} + 24 \, {\left(a^{2} + b^{2}\right)} d^{4} e^{2} f x^{2} + 16 \, {\left(a^{2} + b^{2}\right)} d^{4} e^{3} x + 32 \, {\left(a^{2} + b^{2}\right)} c d^{3} e^{3} - 48 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{2} e^{2} f + 32 \, {\left(a^{2} + b^{2}\right)} c^{3} d e f^{2} - 8 \, {\left(a^{2} + b^{2}\right)} c^{4} f^{3} - 3 \, {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 24 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f + 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x + 16 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} + 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right) + 96 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 96 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 32 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 32 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 32 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 32 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 192 \, {\left({\left(a^{2} + b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{3} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 192 \, {\left({\left(a^{2} + b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{3} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 192 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 192 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(4 \, a b d^{3} f^{3} x^{3} + 4 \, a b d^{3} e^{3} + 12 \, a b d^{2} e^{2} f + 24 \, a b d e f^{2} + 24 \, a b f^{3} + {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(a b d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} - 12 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(a b d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x - 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{2} + b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{2} + b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{2} + b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{2} + b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{2} + b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{2} + b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c^{4} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{32 \, {\left(b^{3} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d^{4} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/32*(4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 + 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 + 3*b^2*f^3 + (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c)^4 + (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*sinh(d*x + c)^4 - 16*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^3 - 4*(4*a*b*d^3*f^3*x^3 + 4*a*b*d^3*e^3 - 12*a*b*d^2*e^2*f + 24*a*b*d*e*f^2 - 24*a*b*f^3 + 12*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 12*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x - (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(2*b^2*d^3*e*f^2 + b^2*d^2*f^3)*x^2 - 8*((a^2 + b^2)*d^4*f^3*x^4 + 4*(a^2 + b^2)*d^4*e*f^2*x^3 + 6*(a^2 + b^2)*d^4*e^2*f*x^2 + 4*(a^2 + b^2)*d^4*e^3*x + 8*(a^2 + b^2)*c*d^3*e^3 - 12*(a^2 + b^2)*c^2*d^2*e^2*f + 8*(a^2 + b^2)*c^3*d*e*f^2 - 2*(a^2 + b^2)*c^4*f^3)*cosh(d*x + c)^2 - 2*(4*(a^2 + b^2)*d^4*f^3*x^4 + 16*(a^2 + b^2)*d^4*e*f^2*x^3 + 24*(a^2 + b^2)*d^4*e^2*f*x^2 + 16*(a^2 + b^2)*d^4*e^3*x + 32*(a^2 + b^2)*c*d^3*e^3 - 48*(a^2 + b^2)*c^2*d^2*e^2*f + 32*(a^2 + b^2)*c^3*d*e*f^2 - 8*(a^2 + b^2)*c^4*f^3 - 3*(4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c)^2 + 24*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 6*(2*b^2*d^3*e^2*f + 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x + 16*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 + 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 + 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f + 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c) + 96*(((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 96*(((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 32*(((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 32*(((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 32*(((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 32*(((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 192*((a^2 + b^2)*f^3*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f^3*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f^3*sinh(d*x + c)^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 192*((a^2 + b^2)*f^3*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f^3*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f^3*sinh(d*x + c)^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 192*(((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 192*(((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*(4*a*b*d^3*f^3*x^3 + 4*a*b*d^3*e^3 + 12*a*b*d^2*e^2*f + 24*a*b*d*e*f^2 + 24*a*b*f^3 + (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c)^3 + 12*(a*b*d^3*e*f^2 + a*b*d^2*f^3)*x^2 - 12*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^2 + 12*(a*b*d^3*e^2*f + 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x - 4*((a^2 + b^2)*d^4*f^3*x^4 + 4*(a^2 + b^2)*d^4*e*f^2*x^3 + 6*(a^2 + b^2)*d^4*e^2*f*x^2 + 4*(a^2 + b^2)*d^4*e^3*x + 8*(a^2 + b^2)*c*d^3*e^3 - 12*(a^2 + b^2)*c^2*d^2*e^2*f + 8*(a^2 + b^2)*c^3*d*e*f^2 - 2*(a^2 + b^2)*c^4*f^3)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d^4*cosh(d*x + c)^2 + 2*b^3*d^4*cosh(d*x + c)*sinh(d*x + c) + b^3*d^4*sinh(d*x + c)^2)","C",0
300,1,2726,0,0.534936," ","integrate((f*x+e)^2*cosh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, b^{2} d^{2} f^{2} x^{2} + 6 \, b^{2} d^{2} e^{2} + 6 \, b^{2} d e f + 3 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} + 3 \, b^{2} f^{2} - 24 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(2 \, a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e^{2} - 4 \, a b d e f + 4 \, a b f^{2} + 4 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x - {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 16 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{2} + b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(8 \, {\left(a^{2} + b^{2}\right)} d^{3} f^{2} x^{3} + 24 \, {\left(a^{2} + b^{2}\right)} d^{3} e f x^{2} + 24 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} x + 48 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} - 48 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f + 16 \, {\left(a^{2} + b^{2}\right)} c^{3} f^{2} - 9 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 36 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(2 \, b^{2} d^{2} e f + b^{2} d f^{2}\right)} x + 24 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} + 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 96 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 96 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 48 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 48 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 48 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 48 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 96 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 96 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(6 \, a b d^{2} f^{2} x^{2} + 6 \, a b d^{2} e^{2} + 12 \, a b d e f + 12 \, a b f^{2} + 3 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 18 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(a b d^{2} e f + a b d f^{2}\right)} x - 8 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{2} + b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{48 \, {\left(b^{3} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d^{3} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/48*(6*b^2*d^2*f^2*x^2 + 6*b^2*d^2*e^2 + 6*b^2*d*e*f + 3*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c)^4 + 3*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*sinh(d*x + c)^4 + 3*b^2*f^2 - 24*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^3 - 12*(2*a*b*d^2*f^2*x^2 + 2*a*b*d^2*e^2 - 4*a*b*d*e*f + 4*a*b*f^2 + 4*(a*b*d^2*e*f - a*b*d*f^2)*x - (2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 16*((a^2 + b^2)*d^3*f^2*x^3 + 3*(a^2 + b^2)*d^3*e*f*x^2 + 3*(a^2 + b^2)*d^3*e^2*x + 6*(a^2 + b^2)*c*d^2*e^2 - 6*(a^2 + b^2)*c^2*d*e*f + 2*(a^2 + b^2)*c^3*f^2)*cosh(d*x + c)^2 - 2*(8*(a^2 + b^2)*d^3*f^2*x^3 + 24*(a^2 + b^2)*d^3*e*f*x^2 + 24*(a^2 + b^2)*d^3*e^2*x + 48*(a^2 + b^2)*c*d^2*e^2 - 48*(a^2 + b^2)*c^2*d*e*f + 16*(a^2 + b^2)*c^3*f^2 - 9*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c)^2 + 36*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 6*(2*b^2*d^2*e*f + b^2*d*f^2)*x + 24*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 + 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c) + 96*(((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 96*(((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 48*(((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 48*(((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 48*(((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 48*(((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 96*((a^2 + b^2)*f^2*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f^2*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f^2*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 96*((a^2 + b^2)*f^2*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f^2*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f^2*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*(6*a*b*d^2*f^2*x^2 + 6*a*b*d^2*e^2 + 12*a*b*d*e*f + 12*a*b*f^2 + 3*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c)^3 - 18*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^2 + 12*(a*b*d^2*e*f + a*b*d*f^2)*x - 8*((a^2 + b^2)*d^3*f^2*x^3 + 3*(a^2 + b^2)*d^3*e*f*x^2 + 3*(a^2 + b^2)*d^3*e^2*x + 6*(a^2 + b^2)*c*d^2*e^2 - 6*(a^2 + b^2)*c^2*d*e*f + 2*(a^2 + b^2)*c^3*f^2)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d^3*cosh(d*x + c)^2 + 2*b^3*d^3*cosh(d*x + c)*sinh(d*x + c) + b^3*d^3*sinh(d*x + c)^2)","C",0
301,1,1416,0,0.503519," ","integrate((f*x+e)*cosh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b^{2} d f x + {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, b^{2} d e - 8 \, {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a b d f x + 2 \, a b d e - 2 \, a b f - {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{2} f - 8 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e x + 4 \, {\left(a^{2} + b^{2}\right)} c d e - 2 \, {\left(a^{2} + b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(4 \, {\left(a^{2} + b^{2}\right)} d^{2} f x^{2} + 8 \, {\left(a^{2} + b^{2}\right)} d^{2} e x + 16 \, {\left(a^{2} + b^{2}\right)} c d e - 8 \, {\left(a^{2} + b^{2}\right)} c^{2} f - 3 \, {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a b d f x + a b d e + a b f\right)} \cosh\left(d x + c\right) + 16 \, {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 16 \, {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 16 \, {\left({\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 16 \, {\left({\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 16 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 16 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(2 \, a b d f x + 2 \, a b d e + {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, a b f - 6 \, {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e x + 4 \, {\left(a^{2} + b^{2}\right)} c d e - 2 \, {\left(a^{2} + b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left(b^{3} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d^{2} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(2*b^2*d*f*x + (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c)^4 + (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*sinh(d*x + c)^4 + 2*b^2*d*e - 8*(a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c)^3 - 4*(2*a*b*d*f*x + 2*a*b*d*e - 2*a*b*f - (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c))*sinh(d*x + c)^3 + b^2*f - 8*((a^2 + b^2)*d^2*f*x^2 + 2*(a^2 + b^2)*d^2*e*x + 4*(a^2 + b^2)*c*d*e - 2*(a^2 + b^2)*c^2*f)*cosh(d*x + c)^2 - 2*(4*(a^2 + b^2)*d^2*f*x^2 + 8*(a^2 + b^2)*d^2*e*x + 16*(a^2 + b^2)*c*d*e - 8*(a^2 + b^2)*c^2*f - 3*(2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c)^2 + 12*(a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*(a*b*d*f*x + a*b*d*e + a*b*f)*cosh(d*x + c) + 16*((a^2 + b^2)*f*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 16*((a^2 + b^2)*f*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 16*(((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 16*(((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 16*(((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 16*(((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*(2*a*b*d*f*x + 2*a*b*d*e + (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c)^3 + 2*a*b*f - 6*(a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c)^2 - 4*((a^2 + b^2)*d^2*f*x^2 + 2*(a^2 + b^2)*d^2*e*x + 4*(a^2 + b^2)*c*d*e - 2*(a^2 + b^2)*c^2*f)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d^2*cosh(d*x + c)^2 + 2*b^3*d^2*cosh(d*x + c)*sinh(d*x + c) + b^3*d^2*sinh(d*x + c)^2)","B",0
302,1,327,0,0.557710," ","integrate(cosh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{4} + b^{2} \sinh\left(d x + c\right)^{4} - 8 \, {\left(a^{2} + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(b^{2} \cosh\left(d x + c\right) - a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} + b^{2}\right)} d x - 6 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left({\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a^{2} + b^{2}\right)} d x \cosh\left(d x + c\right) - 3 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)}{8 \, {\left(b^{3} d \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/8*(b^2*cosh(d*x + c)^4 + b^2*sinh(d*x + c)^4 - 8*(a^2 + b^2)*d*x*cosh(d*x + c)^2 - 4*a*b*cosh(d*x + c)^3 + 4*(b^2*cosh(d*x + c) - a*b)*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) + 2*(3*b^2*cosh(d*x + c)^2 - 4*(a^2 + b^2)*d*x - 6*a*b*cosh(d*x + c))*sinh(d*x + c)^2 + b^2 + 8*((a^2 + b^2)*cosh(d*x + c)^2 + 2*(a^2 + b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*sinh(d*x + c)^2)*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(b^2*cosh(d*x + c)^3 - 4*(a^2 + b^2)*d*x*cosh(d*x + c) - 3*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c))/(b^3*d*cosh(d*x + c)^2 + 2*b^3*d*cosh(d*x + c)*sinh(d*x + c) + b^3*d*sinh(d*x + c)^2)","B",0
303,0,0,0,0.770599," ","integrate(cosh(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{3}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)^3/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
304,1,1718,0,0.764766," ","integrate((f*x+e)^3*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, b f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, b f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 3 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(3 i \, a d^{2} f^{3} x^{2} - 3 \, b d^{2} f^{3} x^{2} + 6 i \, a d^{2} e f^{2} x - 6 \, b d^{2} e f^{2} x + 3 i \, a d^{2} e^{2} f - 3 \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(-3 i \, a d^{2} f^{3} x^{2} - 3 \, b d^{2} f^{3} x^{2} - 6 i \, a d^{2} e f^{2} x - 6 \, b d^{2} e f^{2} x - 3 i \, a d^{2} e^{2} f - 3 \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\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 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\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 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(i \, a d^{3} e^{3} - b d^{3} e^{3} - 3 i \, a c d^{2} e^{2} f + 3 \, b c d^{2} e^{2} f + 3 i \, a c^{2} d e f^{2} - 3 \, b c^{2} d e f^{2} - i \, a c^{3} f^{3} + b c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(-i \, a d^{3} e^{3} - b d^{3} e^{3} + 3 i \, a c d^{2} e^{2} f + 3 \, b c d^{2} e^{2} f - 3 i \, a c^{2} d e f^{2} - 3 \, b c^{2} d e f^{2} + i \, a c^{3} f^{3} + b c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(-i \, a d^{3} f^{3} x^{3} - b d^{3} f^{3} x^{3} - 3 i \, a d^{3} e f^{2} x^{2} - 3 \, b d^{3} e f^{2} x^{2} - 3 i \, a d^{3} e^{2} f x - 3 \, b d^{3} e^{2} f x - 3 i \, a c d^{2} e^{2} f - 3 \, b c d^{2} e^{2} f + 3 i \, a c^{2} d e f^{2} + 3 \, b c^{2} d e f^{2} - i \, a c^{3} f^{3} - b c^{3} f^{3}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(i \, a d^{3} f^{3} x^{3} - b d^{3} f^{3} x^{3} + 3 i \, a d^{3} e f^{2} x^{2} - 3 \, b d^{3} e f^{2} x^{2} + 3 i \, a d^{3} e^{2} f x - 3 \, b d^{3} e^{2} f x + 3 i \, a c d^{2} e^{2} f - 3 \, b c d^{2} e^{2} f - 3 i \, a c^{2} d e f^{2} + 3 \, b c^{2} d e f^{2} + i \, a c^{3} f^{3} - b c^{3} f^{3}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 6 \, {\left(-i \, a f^{3} + b f^{3}\right)} {\rm polylog}\left(4, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - 6 \, {\left(i \, a f^{3} + b f^{3}\right)} {\rm polylog}\left(4, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 6 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + {\left(-6 i \, a d f^{3} x + 6 \, b d f^{3} x - 6 i \, a d e f^{2} + 6 \, b d e f^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(6 i \, a d f^{3} x + 6 \, b d f^{3} x + 6 i \, a d e f^{2} + 6 \, b d e f^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right)}{{\left(a^{2} + b^{2}\right)} d^{4}}"," ",0,"(6*b*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*b*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 3*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (3*I*a*d^2*f^3*x^2 - 3*b*d^2*f^3*x^2 + 6*I*a*d^2*e*f^2*x - 6*b*d^2*e*f^2*x + 3*I*a*d^2*e^2*f - 3*b*d^2*e^2*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (-3*I*a*d^2*f^3*x^2 - 3*b*d^2*f^3*x^2 - 6*I*a*d^2*e*f^2*x - 6*b*d^2*e*f^2*x - 3*I*a*d^2*e^2*f - 3*b*d^2*e^2*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (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*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (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*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (I*a*d^3*e^3 - b*d^3*e^3 - 3*I*a*c*d^2*e^2*f + 3*b*c*d^2*e^2*f + 3*I*a*c^2*d*e*f^2 - 3*b*c^2*d*e*f^2 - I*a*c^3*f^3 + b*c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (-I*a*d^3*e^3 - b*d^3*e^3 + 3*I*a*c*d^2*e^2*f + 3*b*c*d^2*e^2*f - 3*I*a*c^2*d*e*f^2 - 3*b*c^2*d*e*f^2 + I*a*c^3*f^3 + b*c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) - I) + (-I*a*d^3*f^3*x^3 - b*d^3*f^3*x^3 - 3*I*a*d^3*e*f^2*x^2 - 3*b*d^3*e*f^2*x^2 - 3*I*a*d^3*e^2*f*x - 3*b*d^3*e^2*f*x - 3*I*a*c*d^2*e^2*f - 3*b*c*d^2*e^2*f + 3*I*a*c^2*d*e*f^2 + 3*b*c^2*d*e*f^2 - I*a*c^3*f^3 - b*c^3*f^3)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (I*a*d^3*f^3*x^3 - b*d^3*f^3*x^3 + 3*I*a*d^3*e*f^2*x^2 - 3*b*d^3*e*f^2*x^2 + 3*I*a*d^3*e^2*f*x - 3*b*d^3*e^2*f*x + 3*I*a*c*d^2*e^2*f - 3*b*c*d^2*e^2*f - 3*I*a*c^2*d*e*f^2 + 3*b*c^2*d*e*f^2 + I*a*c^3*f^3 - b*c^3*f^3)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 6*(-I*a*f^3 + b*f^3)*polylog(4, I*cosh(d*x + c) + I*sinh(d*x + c)) - 6*(I*a*f^3 + b*f^3)*polylog(4, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 6*(b*d*f^3*x + b*d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b*d*f^3*x + b*d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + (-6*I*a*d*f^3*x + 6*b*d*f^3*x - 6*I*a*d*e*f^2 + 6*b*d*e*f^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + (6*I*a*d*f^3*x + 6*b*d*f^3*x + 6*I*a*d*e*f^2 + 6*b*d*e*f^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)))/((a^2 + b^2)*d^4)","C",0
305,1,1098,0,0.475153," ","integrate((f*x+e)^2*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, b f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(b d f^{2} x + b d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b d f^{2} x + b d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(2 i \, a d f^{2} x - 2 \, b d f^{2} x + 2 i \, a d e f - 2 \, b d e f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(-2 i \, a d f^{2} x - 2 \, b d f^{2} x - 2 i \, a d e f - 2 \, b d e f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(i \, a d^{2} e^{2} - b d^{2} e^{2} - 2 i \, a c d e f + 2 \, b c d e f + i \, a c^{2} f^{2} - b c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(-i \, a d^{2} e^{2} - b d^{2} e^{2} + 2 i \, a c d e f + 2 \, b c d e f - i \, a c^{2} f^{2} - b c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(-i \, a d^{2} f^{2} x^{2} - b d^{2} f^{2} x^{2} - 2 i \, a d^{2} e f x - 2 \, b d^{2} e f x - 2 i \, a c d e f - 2 \, b c d e f + i \, a c^{2} f^{2} + b c^{2} f^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(i \, a d^{2} f^{2} x^{2} - b d^{2} f^{2} x^{2} + 2 i \, a d^{2} e f x - 2 \, b d^{2} e f x + 2 i \, a c d e f - 2 \, b c d e f - i \, a c^{2} f^{2} + b c^{2} f^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(i \, a f^{2} - b f^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + 2 \, {\left(-i \, a f^{2} - b f^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right)}{{\left(a^{2} + b^{2}\right)} d^{3}}"," ",0,"-(2*b*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*b*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(b*d*f^2*x + b*d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b*d*f^2*x + b*d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (2*I*a*d*f^2*x - 2*b*d*f^2*x + 2*I*a*d*e*f - 2*b*d*e*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (-2*I*a*d*f^2*x - 2*b*d*f^2*x - 2*I*a*d*e*f - 2*b*d*e*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (I*a*d^2*e^2 - b*d^2*e^2 - 2*I*a*c*d*e*f + 2*b*c*d*e*f + I*a*c^2*f^2 - b*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (-I*a*d^2*e^2 - b*d^2*e^2 + 2*I*a*c*d*e*f + 2*b*c*d*e*f - I*a*c^2*f^2 - b*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) - (-I*a*d^2*f^2*x^2 - b*d^2*f^2*x^2 - 2*I*a*d^2*e*f*x - 2*b*d^2*e*f*x - 2*I*a*c*d*e*f - 2*b*c*d*e*f + I*a*c^2*f^2 + b*c^2*f^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (I*a*d^2*f^2*x^2 - b*d^2*f^2*x^2 + 2*I*a*d^2*e*f*x - 2*b*d^2*e*f*x + 2*I*a*c*d*e*f - 2*b*c*d*e*f - I*a*c^2*f^2 + b*c^2*f^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + 2*(I*a*f^2 - b*f^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + 2*(-I*a*f^2 - b*f^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)))/((a^2 + b^2)*d^3)","C",0
306,1,588,0,0.817953," ","integrate((f*x+e)*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{b f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + b f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(i \, a f - b f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(-i \, a f - b f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left(b d e - b c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d e - b c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d f x + b c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d f x + b c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(i \, a d e - b d e - i \, a c f + b c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(-i \, a d e - b d e + i \, a c f + b c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(-i \, a d f x - b d f x - i \, a c f - b c f\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(i \, a d f x - b d f x + i \, a c f - b c f\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right)}{{\left(a^{2} + b^{2}\right)} d^{2}}"," ",0,"(b*f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + b*f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (I*a*f - b*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (-I*a*f - b*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (b*d*e - b*c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d*e - b*c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d*f*x + b*c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b*d*f*x + b*c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (I*a*d*e - b*d*e - I*a*c*f + b*c*f)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (-I*a*d*e - b*d*e + I*a*c*f + b*c*f)*log(cosh(d*x + c) + sinh(d*x + c) - I) + (-I*a*d*f*x - b*d*f*x - I*a*c*f - b*c*f)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (I*a*d*f*x - b*d*f*x + I*a*c*f - b*c*f)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1))/((a^2 + b^2)*d^2)","A",0
307,1,92,0,0.499331," ","integrate(sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + b \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - b \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{{\left(a^{2} + b^{2}\right)} d}"," ",0,"(2*a*arctan(cosh(d*x + c) + sinh(d*x + c)) + b*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) - b*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/((a^2 + b^2)*d)","A",0
308,0,0,0,1.006146," ","integrate(sech(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sech(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
309,1,6397,0,0.767232," ","integrate((f*x+e)^3*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 12 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - 4 \, {\left(a^{3} + a b^{2}\right)} c^{3} f^{3} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f + {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 6 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f + {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3} + {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3} + {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3} + {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3} + {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left(b^{3} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{3} \sinh\left(d x + c\right)^{2} + b^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b^{3} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{3} \sinh\left(d x + c\right)^{2} + b^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2} + {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2} + {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f x + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3}\right)} \cosh\left(d x + c\right) + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x + 24 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 24 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 24 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 24 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 24 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 24 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 24 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 24 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 12 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 24 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 24 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 12 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 24 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 24 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 24 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 12 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 24 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + 24 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 24 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 12 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 12 \, {\left({\left(a^{3} + a b^{2}\right)} f^{3} + i \, {\left(a^{2} b + b^{3}\right)} f^{3} + {\left({\left(a^{3} + a b^{2}\right)} f^{3} + i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} f^{3} + i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{3} + a b^{2}\right)} f^{3} + i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - 12 \, {\left({\left(a^{3} + a b^{2}\right)} f^{3} - i \, {\left(a^{2} b + b^{3}\right)} f^{3} + {\left({\left(a^{3} + a b^{2}\right)} f^{3} - i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} f^{3} - i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{3} + a b^{2}\right)} f^{3} - i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f x + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}\right)}}"," ",0,"-1/2*(4*(a^3 + a*b^2)*d^3*e^3 - 12*(a^3 + a*b^2)*c*d^2*e^2*f + 12*(a^3 + a*b^2)*c^2*d*e*f^2 - 4*(a^3 + a*b^2)*c^3*f^3 - 4*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^2 - 4*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*sinh(d*x + c)^2 - 6*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f + (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 6*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f + (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3 + (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)^2 + 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3 + (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)^2 + 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3 + (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)^2 + 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3 + (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)^2 + 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 12*(b^3*f^3*cosh(d*x + c)^2 + 2*b^3*f^3*cosh(d*x + c)*sinh(d*x + c) + b^3*f^3*sinh(d*x + c)^2 + b^3*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(b^3*f^3*cosh(d*x + c)^2 + 2*b^3*f^3*cosh(d*x + c)*sinh(d*x + c) + b^3*f^3*sinh(d*x + c)^2 + b^3*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(b^3*d*f^3*x + b^3*d*e*f^2 + (b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)^2 + 2*(b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d*f^3*x + b^3*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(b^3*d*f^3*x + b^3*d*e*f^2 + (b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)^2 + 2*(b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d*f^3*x + b^3*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 4*((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*d^3*e*f^2*x^2 + 3*(a^2*b + b^3)*d^3*e^2*f*x + (a^2*b + b^3)*d^3*e^3)*cosh(d*x + c) + (12*(a^3 + a*b^2)*d*f^3*x + 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 + 12*I*(a^2*b + b^3)*d*e*f^2 + (12*(a^3 + a*b^2)*d*f^3*x + 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 + 12*I*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)^2 + (24*(a^3 + a*b^2)*d*f^3*x + 24*I*(a^2*b + b^3)*d*f^3*x + 24*(a^3 + a*b^2)*d*e*f^2 + 24*I*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (12*(a^3 + a*b^2)*d*f^3*x + 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 + 12*I*(a^2*b + b^3)*d*e*f^2)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (12*(a^3 + a*b^2)*d*f^3*x - 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 - 12*I*(a^2*b + b^3)*d*e*f^2 + (12*(a^3 + a*b^2)*d*f^3*x - 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 - 12*I*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)^2 + (24*(a^3 + a*b^2)*d*f^3*x - 24*I*(a^2*b + b^3)*d*f^3*x + 24*(a^3 + a*b^2)*d*e*f^2 - 24*I*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (12*(a^3 + a*b^2)*d*f^3*x - 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 - 12*I*(a^2*b + b^3)*d*e*f^2)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (6*(a^3 + a*b^2)*d^2*e^2*f + 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3 + (6*(a^3 + a*b^2)*d^2*e^2*f + 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*(a^3 + a*b^2)*d^2*e^2*f + 12*I*(a^2*b + b^3)*d^2*e^2*f - 24*(a^3 + a*b^2)*c*d*e*f^2 - 24*I*(a^2*b + b^3)*c*d*e*f^2 + 12*(a^3 + a*b^2)*c^2*f^3 + 12*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*(a^3 + a*b^2)*d^2*e^2*f + 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (6*(a^3 + a*b^2)*d^2*e^2*f - 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3 + (6*(a^3 + a*b^2)*d^2*e^2*f - 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*(a^3 + a*b^2)*d^2*e^2*f - 12*I*(a^2*b + b^3)*d^2*e^2*f - 24*(a^3 + a*b^2)*c*d*e*f^2 + 24*I*(a^2*b + b^3)*c*d*e*f^2 + 12*(a^3 + a*b^2)*c^2*f^3 - 12*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*(a^3 + a*b^2)*d^2*e^2*f - 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) + (6*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x - 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3 + (6*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x - 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*(a^3 + a*b^2)*d^2*f^3*x^2 - 12*I*(a^2*b + b^3)*d^2*f^3*x^2 + 24*(a^3 + a*b^2)*d^2*e*f^2*x - 24*I*(a^2*b + b^3)*d^2*e*f^2*x + 24*(a^3 + a*b^2)*c*d*e*f^2 - 24*I*(a^2*b + b^3)*c*d*e*f^2 - 12*(a^3 + a*b^2)*c^2*f^3 + 12*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x - 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (6*(a^3 + a*b^2)*d^2*f^3*x^2 + 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x + 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3 + (6*(a^3 + a*b^2)*d^2*f^3*x^2 + 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x + 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*(a^3 + a*b^2)*d^2*f^3*x^2 + 12*I*(a^2*b + b^3)*d^2*f^3*x^2 + 24*(a^3 + a*b^2)*d^2*e*f^2*x + 24*I*(a^2*b + b^3)*d^2*e*f^2*x + 24*(a^3 + a*b^2)*c*d*e*f^2 + 24*I*(a^2*b + b^3)*c*d*e*f^2 - 12*(a^3 + a*b^2)*c^2*f^3 - 12*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*(a^3 + a*b^2)*d^2*f^3*x^2 + 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x + 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 12*((a^3 + a*b^2)*f^3 + I*(a^2*b + b^3)*f^3 + ((a^3 + a*b^2)*f^3 + I*(a^2*b + b^3)*f^3)*cosh(d*x + c)^2 + 2*((a^3 + a*b^2)*f^3 + I*(a^2*b + b^3)*f^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^3 + a*b^2)*f^3 + I*(a^2*b + b^3)*f^3)*sinh(d*x + c)^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - 12*((a^3 + a*b^2)*f^3 - I*(a^2*b + b^3)*f^3 + ((a^3 + a*b^2)*f^3 - I*(a^2*b + b^3)*f^3)*cosh(d*x + c)^2 + 2*((a^3 + a*b^2)*f^3 - I*(a^2*b + b^3)*f^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^3 + a*b^2)*f^3 - I*(a^2*b + b^3)*f^3)*sinh(d*x + c)^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 4*((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*d^3*e*f^2*x^2 + 3*(a^2*b + b^3)*d^3*e^2*f*x + (a^2*b + b^3)*d^3*e^3 + 2*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^4*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^4*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d^4*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^4)","C",0
310,1,3600,0,1.059561," ","integrate((f*x+e)^2*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 8 \, {\left(a^{3} + a b^{2}\right)} c d e f + 4 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{2} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{3} d f^{2} x + b^{3} d e f + {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 \, {\left(b^{3} d f^{2} x + b^{3} d e f + {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2} + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2} + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2} + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2} + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(b^{3} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{2} \sinh\left(d x + c\right)^{2} + b^{3} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(b^{3} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{2} \sinh\left(d x + c\right)^{2} + b^{3} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f x + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(a^{3} + a b^{2}\right)} f^{2} + i \, {\left(a^{2} b + b^{3}\right)} f^{2} + {\left({\left(a^{3} + a b^{2}\right)} f^{2} + i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} f^{2} + i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{3} + a b^{2}\right)} f^{2} + i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + 4 \, {\left({\left(a^{3} + a b^{2}\right)} f^{2} - i \, {\left(a^{2} b + b^{3}\right)} f^{2} + {\left({\left(a^{3} + a b^{2}\right)} f^{2} - i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} f^{2} - i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{3} + a b^{2}\right)} f^{2} - i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f + 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f + 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, {\left(a^{3} + a b^{2}\right)} d e f + 8 i \, {\left(a^{2} b + b^{3}\right)} d e f - 8 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 8 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f + 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f - 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f - 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, {\left(a^{3} + a b^{2}\right)} d e f - 8 i \, {\left(a^{2} b + b^{3}\right)} d e f - 8 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 8 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f - 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 8 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 8 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 8 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x + 8 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 8 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 8 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f x + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3}\right)}}"," ",0,"-1/2*(4*(a^3 + a*b^2)*d^2*e^2 - 8*(a^3 + a*b^2)*c*d*e*f + 4*(a^3 + a*b^2)*c^2*f^2 - 4*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^2 - 4*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*sinh(d*x + c)^2 - 4*(b^3*d*f^2*x + b^3*d*e*f + (b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^2 + 2*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d*f^2*x + b^3*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 4*(b^3*d*f^2*x + b^3*d*e*f + (b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^2 + 2*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d*f^2*x + b^3*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2 + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2 + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2 + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2 + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*(b^3*f^2*cosh(d*x + c)^2 + 2*b^3*f^2*cosh(d*x + c)*sinh(d*x + c) + b^3*f^2*sinh(d*x + c)^2 + b^3*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 4*(b^3*f^2*cosh(d*x + c)^2 + 2*b^3*f^2*cosh(d*x + c)*sinh(d*x + c) + b^3*f^2*sinh(d*x + c)^2 + b^3*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 4*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*d^2*e*f*x + (a^2*b + b^3)*d^2*e^2)*cosh(d*x + c) + 4*((a^3 + a*b^2)*f^2 + I*(a^2*b + b^3)*f^2 + ((a^3 + a*b^2)*f^2 + I*(a^2*b + b^3)*f^2)*cosh(d*x + c)^2 + 2*((a^3 + a*b^2)*f^2 + I*(a^2*b + b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^3 + a*b^2)*f^2 + I*(a^2*b + b^3)*f^2)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + 4*((a^3 + a*b^2)*f^2 - I*(a^2*b + b^3)*f^2 + ((a^3 + a*b^2)*f^2 - I*(a^2*b + b^3)*f^2)*cosh(d*x + c)^2 + 2*((a^3 + a*b^2)*f^2 - I*(a^2*b + b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^3 + a*b^2)*f^2 - I*(a^2*b + b^3)*f^2)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (4*(a^3 + a*b^2)*d*e*f + 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2 + (4*(a^3 + a*b^2)*d*e*f + 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (8*(a^3 + a*b^2)*d*e*f + 8*I*(a^2*b + b^3)*d*e*f - 8*(a^3 + a*b^2)*c*f^2 - 8*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*(a^3 + a*b^2)*d*e*f + 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (4*(a^3 + a*b^2)*d*e*f - 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2 + (4*(a^3 + a*b^2)*d*e*f - 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (8*(a^3 + a*b^2)*d*e*f - 8*I*(a^2*b + b^3)*d*e*f - 8*(a^3 + a*b^2)*c*f^2 + 8*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*(a^3 + a*b^2)*d*e*f - 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) + (4*(a^3 + a*b^2)*d*f^2*x - 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2 + (4*(a^3 + a*b^2)*d*f^2*x - 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (8*(a^3 + a*b^2)*d*f^2*x - 8*I*(a^2*b + b^3)*d*f^2*x + 8*(a^3 + a*b^2)*c*f^2 - 8*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*(a^3 + a*b^2)*d*f^2*x - 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (4*(a^3 + a*b^2)*d*f^2*x + 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2 + (4*(a^3 + a*b^2)*d*f^2*x + 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (8*(a^3 + a*b^2)*d*f^2*x + 8*I*(a^2*b + b^3)*d*f^2*x + 8*(a^3 + a*b^2)*c*f^2 + 8*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*(a^3 + a*b^2)*d*f^2*x + 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 4*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*d^2*e*f*x + (a^2*b + b^3)*d^2*e^2 + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d^3*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3)","C",0
311,1,1296,0,0.781237," ","integrate((f*x+e)*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} + a b^{2}\right)} d f x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d f x \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} d e + {\left(b^{3} f \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f \sinh\left(d x + c\right)^{2} + b^{3} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{3} f \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f \sinh\left(d x + c\right)^{2} + b^{3} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{3} d e - b^{3} c f + {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d e - b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d e - b^{3} c f + {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d e - b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d f x + b^{3} c f + {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d f x + b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{3} d f x + b^{3} c f + {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{3} d f x + b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{2} b + b^{3}\right)} f\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e\right)} \cosh\left(d x + c\right) - {\left({\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} + a b^{2}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d f x \cosh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}"," ",0,"(2*(a^3 + a*b^2)*d*f*x*cosh(d*x + c)^2 + 2*(a^3 + a*b^2)*d*f*x*sinh(d*x + c)^2 - 2*(a^3 + a*b^2)*d*e + (b^3*f*cosh(d*x + c)^2 + 2*b^3*f*cosh(d*x + c)*sinh(d*x + c) + b^3*f*sinh(d*x + c)^2 + b^3*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^3*f*cosh(d*x + c)^2 + 2*b^3*f*cosh(d*x + c)*sinh(d*x + c) + b^3*f*sinh(d*x + c)^2 + b^3*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^3*d*e - b^3*c*f + (b^3*d*e - b^3*c*f)*cosh(d*x + c)^2 + 2*(b^3*d*e - b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d*e - b^3*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d*e - b^3*c*f + (b^3*d*e - b^3*c*f)*cosh(d*x + c)^2 + 2*(b^3*d*e - b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d*e - b^3*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d*f*x + b^3*c*f + (b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^2 + 2*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d*f*x + b^3*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^3*d*f*x + b^3*c*f + (b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^2 + 2*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) + (b^3*d*f*x + b^3*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((a^2*b + b^3)*f*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f*sinh(d*x + c)^2 + (a^2*b + b^3)*f)*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e)*cosh(d*x + c) - ((a^3 + a*b^2)*f*cosh(d*x + c)^2 + 2*(a^3 + a*b^2)*f*cosh(d*x + c)*sinh(d*x + c) + (a^3 + a*b^2)*f*sinh(d*x + c)^2 + (a^3 + a*b^2)*f)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(2*(a^3 + a*b^2)*d*f*x*cosh(d*x + c) + (a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e)*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d^2*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)","B",0
312,1,353,0,0.536023," ","integrate(sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a^{3} + 2 \, a b^{2} - {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + b^{2}\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d}"," ",0,"-(2*a^3 + 2*a*b^2 - (b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + b^2)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) - 2*(a^2*b + b^3)*cosh(d*x + c) - 2*(a^2*b + b^3)*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d)","B",0
313,0,0,0,0.625685," ","integrate(sech(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sech(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
314,1,10600,0,1.018219," ","integrate((f*x+e)^2*sech(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b + b^{3}\right)} d e f + 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2} - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x - 8 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + {\left(a^{2} b + b^{3}\right)} d e f - 2 \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2} - 12 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) - 4 \, {\left(b^{3} d f^{2} x + b^{3} d e f + {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f + 3 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left(b^{3} d f^{2} x + b^{3} d e f + {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f + 3 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(4 \, b^{3} d f^{2} x + 4 \, b^{3} d e f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x + {\left(4 \, b^{3} d f^{2} x + 4 \, b^{3} d e f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, b^{3} d f^{2} x + 16 \, b^{3} d e f - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, b^{3} d f^{2} x + 4 \, b^{3} d e f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f + {\left(8 \, b^{3} d f^{2} x + 8 \, b^{3} d e f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, b^{3} d f^{2} x + 8 \, b^{3} d e f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f + {\left(24 \, b^{3} d f^{2} x + 24 \, b^{3} d e f - 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x - 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, b^{3} d f^{2} x + 16 \, b^{3} d e f - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, b^{3} d f^{2} x + 16 \, b^{3} d e f - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(4 \, b^{3} d f^{2} x + 4 \, b^{3} d e f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x + {\left(4 \, b^{3} d f^{2} x + 4 \, b^{3} d e f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, b^{3} d f^{2} x + 16 \, b^{3} d e f + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, b^{3} d f^{2} x + 4 \, b^{3} d e f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{4} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f + {\left(8 \, b^{3} d f^{2} x + 8 \, b^{3} d e f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, b^{3} d f^{2} x + 8 \, b^{3} d e f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f + {\left(24 \, b^{3} d f^{2} x + 24 \, b^{3} d e f + 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x + 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, b^{3} d f^{2} x + 16 \, b^{3} d e f + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, b^{3} d f^{2} x + 16 \, b^{3} d e f + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f^{2} x + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2} + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2} + 3 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2} + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2} + 3 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2} + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2} + 3 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2} + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2} + 3 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(2 \, b^{3} d^{2} e^{2} - 4 \, b^{3} c d e f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + {\left(2 \, b^{3} d^{2} e^{2} - 4 \, b^{3} c d e f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 2 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} + i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, b^{3} d^{2} e^{2} - 16 \, b^{3} c d e f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 8 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} + 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, b^{3} d^{2} e^{2} - 4 \, b^{3} c d e f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 2 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} + i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} + i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2} + {\left(4 \, b^{3} d^{2} e^{2} - 8 \, b^{3} c d e f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 4 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} + 2 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, b^{3} d^{2} e^{2} - 8 \, b^{3} c d e f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 4 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} + 2 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2} + {\left(12 \, b^{3} d^{2} e^{2} - 24 \, b^{3} c d e f - 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} + 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 12 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} + 6 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, b^{3} d^{2} e^{2} - 16 \, b^{3} c d e f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 8 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} + 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, b^{3} d^{2} e^{2} - 16 \, b^{3} c d e f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 8 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} + 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(2 \, b^{3} d^{2} e^{2} - 4 \, b^{3} c d e f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + {\left(2 \, b^{3} d^{2} e^{2} - 4 \, b^{3} c d e f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 2 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} - i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, b^{3} d^{2} e^{2} - 16 \, b^{3} c d e f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 8 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} - 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, b^{3} d^{2} e^{2} - 4 \, b^{3} c d e f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 2 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} - i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} - i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2} + {\left(4 \, b^{3} d^{2} e^{2} - 8 \, b^{3} c d e f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 4 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} - 2 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, b^{3} d^{2} e^{2} - 8 \, b^{3} c d e f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 4 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} - 2 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2} + {\left(12 \, b^{3} d^{2} e^{2} - 24 \, b^{3} c d e f + 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} - 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 12 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} - 6 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, b^{3} d^{2} e^{2} - 16 \, b^{3} c d e f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 8 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} - 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, b^{3} d^{2} e^{2} - 16 \, b^{3} c d e f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e^{2} - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 8 \, {\left(b^{3} c^{2} - a^{2} b - b^{3}\right)} f^{2} - 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(2 \, b^{3} d^{2} f^{2} x^{2} + 4 \, b^{3} d^{2} e f x + 4 \, b^{3} c d e f - 2 \, b^{3} c^{2} f^{2} + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2} + {\left(2 \, b^{3} d^{2} f^{2} x^{2} + 4 \, b^{3} d^{2} e f x + 4 \, b^{3} c d e f - 2 \, b^{3} c^{2} f^{2} + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, b^{3} d^{2} f^{2} x^{2} + 16 \, b^{3} d^{2} e f x + 16 \, b^{3} c d e f - 8 \, b^{3} c^{2} f^{2} + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, b^{3} d^{2} f^{2} x^{2} + 4 \, b^{3} d^{2} e f x + 4 \, b^{3} c d e f - 2 \, b^{3} c^{2} f^{2} + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, b^{3} d^{2} f^{2} x^{2} + 8 \, b^{3} d^{2} e f x + 8 \, b^{3} c d e f - 4 \, b^{3} c^{2} f^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, b^{3} d^{2} f^{2} x^{2} + 8 \, b^{3} d^{2} e f x + 8 \, b^{3} c d e f - 4 \, b^{3} c^{2} f^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2} + {\left(12 \, b^{3} d^{2} f^{2} x^{2} + 24 \, b^{3} d^{2} e f x + 24 \, b^{3} c d e f - 12 \, b^{3} c^{2} f^{2} + 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x + 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f - 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, b^{3} d^{2} f^{2} x^{2} + 16 \, b^{3} d^{2} e f x + 16 \, b^{3} c d e f - 8 \, b^{3} c^{2} f^{2} + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, b^{3} d^{2} f^{2} x^{2} + 16 \, b^{3} d^{2} e f x + 16 \, b^{3} c d e f - 8 \, b^{3} c^{2} f^{2} + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(2 \, b^{3} d^{2} f^{2} x^{2} + 4 \, b^{3} d^{2} e f x + 4 \, b^{3} c d e f - 2 \, b^{3} c^{2} f^{2} - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2} + {\left(2 \, b^{3} d^{2} f^{2} x^{2} + 4 \, b^{3} d^{2} e f x + 4 \, b^{3} c d e f - 2 \, b^{3} c^{2} f^{2} - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, b^{3} d^{2} f^{2} x^{2} + 16 \, b^{3} d^{2} e f x + 16 \, b^{3} c d e f - 8 \, b^{3} c^{2} f^{2} - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, b^{3} d^{2} f^{2} x^{2} + 4 \, b^{3} d^{2} e f x + 4 \, b^{3} c d e f - 2 \, b^{3} c^{2} f^{2} - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, b^{3} d^{2} f^{2} x^{2} + 8 \, b^{3} d^{2} e f x + 8 \, b^{3} c d e f - 4 \, b^{3} c^{2} f^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, b^{3} d^{2} f^{2} x^{2} + 8 \, b^{3} d^{2} e f x + 8 \, b^{3} c d e f - 4 \, b^{3} c^{2} f^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2} + {\left(12 \, b^{3} d^{2} f^{2} x^{2} + 24 \, b^{3} d^{2} e f x + 24 \, b^{3} c d e f - 12 \, b^{3} c^{2} f^{2} - 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} - 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x - 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, b^{3} d^{2} f^{2} x^{2} + 16 \, b^{3} d^{2} e f x + 16 \, b^{3} c d e f - 8 \, b^{3} c^{2} f^{2} - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, b^{3} d^{2} f^{2} x^{2} + 16 \, b^{3} d^{2} e f x + 16 \, b^{3} c d e f - 8 \, b^{3} c^{2} f^{2} - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d^{2} e f x - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c d e f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + 4 \, {\left(b^{3} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} f^{2} \sinh\left(d x + c\right)^{4} + 2 \, b^{3} f^{2} \cosh\left(d x + c\right)^{2} + b^{3} f^{2} + 2 \, {\left(3 \, b^{3} f^{2} \cosh\left(d x + c\right)^{2} + b^{3} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} f^{2} \cosh\left(d x + c\right)^{3} + b^{3} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(b^{3} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} f^{2} \sinh\left(d x + c\right)^{4} + 2 \, b^{3} f^{2} \cosh\left(d x + c\right)^{2} + b^{3} f^{2} + 2 \, {\left(3 \, b^{3} f^{2} \cosh\left(d x + c\right)^{2} + b^{3} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} f^{2} \cosh\left(d x + c\right)^{3} + b^{3} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - {\left(4 \, b^{3} f^{2} + {\left(4 \, b^{3} f^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, b^{3} f^{2} - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, b^{3} f^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2} + {\left(8 \, b^{3} f^{2} - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, b^{3} f^{2} - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2} + {\left(24 \, b^{3} f^{2} - 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, b^{3} f^{2} - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, b^{3} f^{2} - 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(4 \, b^{3} f^{2} + {\left(4 \, b^{3} f^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, b^{3} f^{2} + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, b^{3} f^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2} + {\left(8 \, b^{3} f^{2} + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, b^{3} f^{2} + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2} + {\left(24 \, b^{3} f^{2} + 12 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, b^{3} f^{2} + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, b^{3} f^{2} + 8 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 8 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + {\left(a^{2} b + b^{3}\right)} d e f - 2 \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(4*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*c*f^2)*cosh(d*x + c)^4 + 4*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*c*f^2)*sinh(d*x + c)^4 - 4*(a^2*b + b^3)*d*e*f + 4*(a^2*b + b^3)*c*f^2 - 2*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^3 + a*b^2)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)^3 - 2*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^3 + a*b^2)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x - 8*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + (a^2*b + b^3)*d*e*f - 2*(a^2*b + b^3)*c*f^2 + (2*(a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^2 - 2*(2*(a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*d*e*f - 4*(a^2*b + b^3)*c*f^2 - 12*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + 2*(2*(a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x + 3*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^3 + a*b^2)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*d*e*f + 2*((a^3 + a*b^2)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c) - 4*(b^3*d*f^2*x + b^3*d*e*f + (b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^4 + 4*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^3*d*f^2*x + b^3*d*e*f)*sinh(d*x + c)^4 + 2*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^2 + 2*(b^3*d*f^2*x + b^3*d*e*f + 3*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^3 + (b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 4*(b^3*d*f^2*x + b^3*d*e*f + (b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^4 + 4*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^3*d*f^2*x + b^3*d*e*f)*sinh(d*x + c)^4 + 2*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^2 + 2*(b^3*d*f^2*x + b^3*d*e*f + 3*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^3 + (b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (4*b^3*d*f^2*x + 4*b^3*d*e*f - 2*I*(a^3 + 3*a*b^2)*d*f^2*x + (4*b^3*d*f^2*x + 4*b^3*d*e*f - 2*I*(a^3 + 3*a*b^2)*d*f^2*x - 2*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c)^4 + (16*b^3*d*f^2*x + 16*b^3*d*e*f - 8*I*(a^3 + 3*a*b^2)*d*f^2*x - 8*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*b^3*d*f^2*x + 4*b^3*d*e*f - 2*I*(a^3 + 3*a*b^2)*d*f^2*x - 2*I*(a^3 + 3*a*b^2)*d*e*f)*sinh(d*x + c)^4 - 2*I*(a^3 + 3*a*b^2)*d*e*f + (8*b^3*d*f^2*x + 8*b^3*d*e*f - 4*I*(a^3 + 3*a*b^2)*d*f^2*x - 4*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c)^2 + (8*b^3*d*f^2*x + 8*b^3*d*e*f - 4*I*(a^3 + 3*a*b^2)*d*f^2*x - 4*I*(a^3 + 3*a*b^2)*d*e*f + (24*b^3*d*f^2*x + 24*b^3*d*e*f - 12*I*(a^3 + 3*a*b^2)*d*f^2*x - 12*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*b^3*d*f^2*x + 16*b^3*d*e*f - 8*I*(a^3 + 3*a*b^2)*d*f^2*x - 8*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c)^3 + (16*b^3*d*f^2*x + 16*b^3*d*e*f - 8*I*(a^3 + 3*a*b^2)*d*f^2*x - 8*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (4*b^3*d*f^2*x + 4*b^3*d*e*f + 2*I*(a^3 + 3*a*b^2)*d*f^2*x + (4*b^3*d*f^2*x + 4*b^3*d*e*f + 2*I*(a^3 + 3*a*b^2)*d*f^2*x + 2*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c)^4 + (16*b^3*d*f^2*x + 16*b^3*d*e*f + 8*I*(a^3 + 3*a*b^2)*d*f^2*x + 8*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*b^3*d*f^2*x + 4*b^3*d*e*f + 2*I*(a^3 + 3*a*b^2)*d*f^2*x + 2*I*(a^3 + 3*a*b^2)*d*e*f)*sinh(d*x + c)^4 + 2*I*(a^3 + 3*a*b^2)*d*e*f + (8*b^3*d*f^2*x + 8*b^3*d*e*f + 4*I*(a^3 + 3*a*b^2)*d*f^2*x + 4*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c)^2 + (8*b^3*d*f^2*x + 8*b^3*d*e*f + 4*I*(a^3 + 3*a*b^2)*d*f^2*x + 4*I*(a^3 + 3*a*b^2)*d*e*f + (24*b^3*d*f^2*x + 24*b^3*d*e*f + 12*I*(a^3 + 3*a*b^2)*d*f^2*x + 12*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*b^3*d*f^2*x + 16*b^3*d*e*f + 8*I*(a^3 + 3*a*b^2)*d*f^2*x + 8*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c)^3 + (16*b^3*d*f^2*x + 16*b^3*d*e*f + 8*I*(a^3 + 3*a*b^2)*d*f^2*x + 8*I*(a^3 + 3*a*b^2)*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2 + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sinh(d*x + c)^4 + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2 + 3*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^3 + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2 + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sinh(d*x + c)^4 + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2 + 3*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^3 + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2 + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sinh(d*x + c)^4 + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2 + 3*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^3 + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2 + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sinh(d*x + c)^4 + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2 + 3*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^3 + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (2*b^3*d^2*e^2 - 4*b^3*c*d*e*f - I*(a^3 + 3*a*b^2)*d^2*e^2 + 2*I*(a^3 + 3*a*b^2)*c*d*e*f + (2*b^3*d^2*e^2 - 4*b^3*c*d*e*f - I*(a^3 + 3*a*b^2)*d^2*e^2 + 2*I*(a^3 + 3*a*b^2)*c*d*e*f + 2*(b^3*c^2 - a^2*b - b^3)*f^2 + I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c)^4 + (8*b^3*d^2*e^2 - 16*b^3*c*d*e*f - 4*I*(a^3 + 3*a*b^2)*d^2*e^2 + 8*I*(a^3 + 3*a*b^2)*c*d*e*f + 8*(b^3*c^2 - a^2*b - b^3)*f^2 + 4*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*b^3*d^2*e^2 - 4*b^3*c*d*e*f - I*(a^3 + 3*a*b^2)*d^2*e^2 + 2*I*(a^3 + 3*a*b^2)*c*d*e*f + 2*(b^3*c^2 - a^2*b - b^3)*f^2 + I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*sinh(d*x + c)^4 + 2*(b^3*c^2 - a^2*b - b^3)*f^2 + I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2 + (4*b^3*d^2*e^2 - 8*b^3*c*d*e*f - 2*I*(a^3 + 3*a*b^2)*d^2*e^2 + 4*I*(a^3 + 3*a*b^2)*c*d*e*f + 4*(b^3*c^2 - a^2*b - b^3)*f^2 + 2*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c)^2 + (4*b^3*d^2*e^2 - 8*b^3*c*d*e*f - 2*I*(a^3 + 3*a*b^2)*d^2*e^2 + 4*I*(a^3 + 3*a*b^2)*c*d*e*f + 4*(b^3*c^2 - a^2*b - b^3)*f^2 + 2*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2 + (12*b^3*d^2*e^2 - 24*b^3*c*d*e*f - 6*I*(a^3 + 3*a*b^2)*d^2*e^2 + 12*I*(a^3 + 3*a*b^2)*c*d*e*f + 12*(b^3*c^2 - a^2*b - b^3)*f^2 + 6*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*b^3*d^2*e^2 - 16*b^3*c*d*e*f - 4*I*(a^3 + 3*a*b^2)*d^2*e^2 + 8*I*(a^3 + 3*a*b^2)*c*d*e*f + 8*(b^3*c^2 - a^2*b - b^3)*f^2 + 4*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c)^3 + (8*b^3*d^2*e^2 - 16*b^3*c*d*e*f - 4*I*(a^3 + 3*a*b^2)*d^2*e^2 + 8*I*(a^3 + 3*a*b^2)*c*d*e*f + 8*(b^3*c^2 - a^2*b - b^3)*f^2 + 4*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) + (2*b^3*d^2*e^2 - 4*b^3*c*d*e*f + I*(a^3 + 3*a*b^2)*d^2*e^2 - 2*I*(a^3 + 3*a*b^2)*c*d*e*f + (2*b^3*d^2*e^2 - 4*b^3*c*d*e*f + I*(a^3 + 3*a*b^2)*d^2*e^2 - 2*I*(a^3 + 3*a*b^2)*c*d*e*f + 2*(b^3*c^2 - a^2*b - b^3)*f^2 - I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c)^4 + (8*b^3*d^2*e^2 - 16*b^3*c*d*e*f + 4*I*(a^3 + 3*a*b^2)*d^2*e^2 - 8*I*(a^3 + 3*a*b^2)*c*d*e*f + 8*(b^3*c^2 - a^2*b - b^3)*f^2 - 4*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*b^3*d^2*e^2 - 4*b^3*c*d*e*f + I*(a^3 + 3*a*b^2)*d^2*e^2 - 2*I*(a^3 + 3*a*b^2)*c*d*e*f + 2*(b^3*c^2 - a^2*b - b^3)*f^2 - I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*sinh(d*x + c)^4 + 2*(b^3*c^2 - a^2*b - b^3)*f^2 - I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2 + (4*b^3*d^2*e^2 - 8*b^3*c*d*e*f + 2*I*(a^3 + 3*a*b^2)*d^2*e^2 - 4*I*(a^3 + 3*a*b^2)*c*d*e*f + 4*(b^3*c^2 - a^2*b - b^3)*f^2 - 2*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c)^2 + (4*b^3*d^2*e^2 - 8*b^3*c*d*e*f + 2*I*(a^3 + 3*a*b^2)*d^2*e^2 - 4*I*(a^3 + 3*a*b^2)*c*d*e*f + 4*(b^3*c^2 - a^2*b - b^3)*f^2 - 2*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2 + (12*b^3*d^2*e^2 - 24*b^3*c*d*e*f + 6*I*(a^3 + 3*a*b^2)*d^2*e^2 - 12*I*(a^3 + 3*a*b^2)*c*d*e*f + 12*(b^3*c^2 - a^2*b - b^3)*f^2 - 6*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*b^3*d^2*e^2 - 16*b^3*c*d*e*f + 4*I*(a^3 + 3*a*b^2)*d^2*e^2 - 8*I*(a^3 + 3*a*b^2)*c*d*e*f + 8*(b^3*c^2 - a^2*b - b^3)*f^2 - 4*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c)^3 + (8*b^3*d^2*e^2 - 16*b^3*c*d*e*f + 4*I*(a^3 + 3*a*b^2)*d^2*e^2 - 8*I*(a^3 + 3*a*b^2)*c*d*e*f + 8*(b^3*c^2 - a^2*b - b^3)*f^2 - 4*I*(2*a^3 + 2*a*b^2 - (a^3 + 3*a*b^2)*c^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) + (2*b^3*d^2*f^2*x^2 + 4*b^3*d^2*e*f*x + 4*b^3*c*d*e*f - 2*b^3*c^2*f^2 + I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 + 2*I*(a^3 + 3*a*b^2)*d^2*e*f*x + 2*I*(a^3 + 3*a*b^2)*c*d*e*f - I*(a^3 + 3*a*b^2)*c^2*f^2 + (2*b^3*d^2*f^2*x^2 + 4*b^3*d^2*e*f*x + 4*b^3*c*d*e*f - 2*b^3*c^2*f^2 + I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 + 2*I*(a^3 + 3*a*b^2)*d^2*e*f*x + 2*I*(a^3 + 3*a*b^2)*c*d*e*f - I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c)^4 + (8*b^3*d^2*f^2*x^2 + 16*b^3*d^2*e*f*x + 16*b^3*c*d*e*f - 8*b^3*c^2*f^2 + 4*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 + 8*I*(a^3 + 3*a*b^2)*d^2*e*f*x + 8*I*(a^3 + 3*a*b^2)*c*d*e*f - 4*I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*b^3*d^2*f^2*x^2 + 4*b^3*d^2*e*f*x + 4*b^3*c*d*e*f - 2*b^3*c^2*f^2 + I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 + 2*I*(a^3 + 3*a*b^2)*d^2*e*f*x + 2*I*(a^3 + 3*a*b^2)*c*d*e*f - I*(a^3 + 3*a*b^2)*c^2*f^2)*sinh(d*x + c)^4 + (4*b^3*d^2*f^2*x^2 + 8*b^3*d^2*e*f*x + 8*b^3*c*d*e*f - 4*b^3*c^2*f^2 + 2*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 + 4*I*(a^3 + 3*a*b^2)*d^2*e*f*x + 4*I*(a^3 + 3*a*b^2)*c*d*e*f - 2*I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c)^2 + (4*b^3*d^2*f^2*x^2 + 8*b^3*d^2*e*f*x + 8*b^3*c*d*e*f - 4*b^3*c^2*f^2 + 2*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 + 4*I*(a^3 + 3*a*b^2)*d^2*e*f*x + 4*I*(a^3 + 3*a*b^2)*c*d*e*f - 2*I*(a^3 + 3*a*b^2)*c^2*f^2 + (12*b^3*d^2*f^2*x^2 + 24*b^3*d^2*e*f*x + 24*b^3*c*d*e*f - 12*b^3*c^2*f^2 + 6*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 + 12*I*(a^3 + 3*a*b^2)*d^2*e*f*x + 12*I*(a^3 + 3*a*b^2)*c*d*e*f - 6*I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*b^3*d^2*f^2*x^2 + 16*b^3*d^2*e*f*x + 16*b^3*c*d*e*f - 8*b^3*c^2*f^2 + 4*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 + 8*I*(a^3 + 3*a*b^2)*d^2*e*f*x + 8*I*(a^3 + 3*a*b^2)*c*d*e*f - 4*I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c)^3 + (8*b^3*d^2*f^2*x^2 + 16*b^3*d^2*e*f*x + 16*b^3*c*d*e*f - 8*b^3*c^2*f^2 + 4*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 + 8*I*(a^3 + 3*a*b^2)*d^2*e*f*x + 8*I*(a^3 + 3*a*b^2)*c*d*e*f - 4*I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (2*b^3*d^2*f^2*x^2 + 4*b^3*d^2*e*f*x + 4*b^3*c*d*e*f - 2*b^3*c^2*f^2 - I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 - 2*I*(a^3 + 3*a*b^2)*d^2*e*f*x - 2*I*(a^3 + 3*a*b^2)*c*d*e*f + I*(a^3 + 3*a*b^2)*c^2*f^2 + (2*b^3*d^2*f^2*x^2 + 4*b^3*d^2*e*f*x + 4*b^3*c*d*e*f - 2*b^3*c^2*f^2 - I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 - 2*I*(a^3 + 3*a*b^2)*d^2*e*f*x - 2*I*(a^3 + 3*a*b^2)*c*d*e*f + I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c)^4 + (8*b^3*d^2*f^2*x^2 + 16*b^3*d^2*e*f*x + 16*b^3*c*d*e*f - 8*b^3*c^2*f^2 - 4*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 - 8*I*(a^3 + 3*a*b^2)*d^2*e*f*x - 8*I*(a^3 + 3*a*b^2)*c*d*e*f + 4*I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*b^3*d^2*f^2*x^2 + 4*b^3*d^2*e*f*x + 4*b^3*c*d*e*f - 2*b^3*c^2*f^2 - I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 - 2*I*(a^3 + 3*a*b^2)*d^2*e*f*x - 2*I*(a^3 + 3*a*b^2)*c*d*e*f + I*(a^3 + 3*a*b^2)*c^2*f^2)*sinh(d*x + c)^4 + (4*b^3*d^2*f^2*x^2 + 8*b^3*d^2*e*f*x + 8*b^3*c*d*e*f - 4*b^3*c^2*f^2 - 2*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 - 4*I*(a^3 + 3*a*b^2)*d^2*e*f*x - 4*I*(a^3 + 3*a*b^2)*c*d*e*f + 2*I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c)^2 + (4*b^3*d^2*f^2*x^2 + 8*b^3*d^2*e*f*x + 8*b^3*c*d*e*f - 4*b^3*c^2*f^2 - 2*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 - 4*I*(a^3 + 3*a*b^2)*d^2*e*f*x - 4*I*(a^3 + 3*a*b^2)*c*d*e*f + 2*I*(a^3 + 3*a*b^2)*c^2*f^2 + (12*b^3*d^2*f^2*x^2 + 24*b^3*d^2*e*f*x + 24*b^3*c*d*e*f - 12*b^3*c^2*f^2 - 6*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 - 12*I*(a^3 + 3*a*b^2)*d^2*e*f*x - 12*I*(a^3 + 3*a*b^2)*c*d*e*f + 6*I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*b^3*d^2*f^2*x^2 + 16*b^3*d^2*e*f*x + 16*b^3*c*d*e*f - 8*b^3*c^2*f^2 - 4*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 - 8*I*(a^3 + 3*a*b^2)*d^2*e*f*x - 8*I*(a^3 + 3*a*b^2)*c*d*e*f + 4*I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c)^3 + (8*b^3*d^2*f^2*x^2 + 16*b^3*d^2*e*f*x + 16*b^3*c*d*e*f - 8*b^3*c^2*f^2 - 4*I*(a^3 + 3*a*b^2)*d^2*f^2*x^2 - 8*I*(a^3 + 3*a*b^2)*d^2*e*f*x - 8*I*(a^3 + 3*a*b^2)*c*d*e*f + 4*I*(a^3 + 3*a*b^2)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + 4*(b^3*f^2*cosh(d*x + c)^4 + 4*b^3*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*f^2*sinh(d*x + c)^4 + 2*b^3*f^2*cosh(d*x + c)^2 + b^3*f^2 + 2*(3*b^3*f^2*cosh(d*x + c)^2 + b^3*f^2)*sinh(d*x + c)^2 + 4*(b^3*f^2*cosh(d*x + c)^3 + b^3*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*(b^3*f^2*cosh(d*x + c)^4 + 4*b^3*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*f^2*sinh(d*x + c)^4 + 2*b^3*f^2*cosh(d*x + c)^2 + b^3*f^2 + 2*(3*b^3*f^2*cosh(d*x + c)^2 + b^3*f^2)*sinh(d*x + c)^2 + 4*(b^3*f^2*cosh(d*x + c)^3 + b^3*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - (4*b^3*f^2 + (4*b^3*f^2 - 2*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c)^4 + (16*b^3*f^2 - 8*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*b^3*f^2 - 2*I*(a^3 + 3*a*b^2)*f^2)*sinh(d*x + c)^4 - 2*I*(a^3 + 3*a*b^2)*f^2 + (8*b^3*f^2 - 4*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c)^2 + (8*b^3*f^2 - 4*I*(a^3 + 3*a*b^2)*f^2 + (24*b^3*f^2 - 12*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*b^3*f^2 - 8*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c)^3 + (16*b^3*f^2 - 8*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - (4*b^3*f^2 + (4*b^3*f^2 + 2*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c)^4 + (16*b^3*f^2 + 8*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*b^3*f^2 + 2*I*(a^3 + 3*a*b^2)*f^2)*sinh(d*x + c)^4 + 2*I*(a^3 + 3*a*b^2)*f^2 + (8*b^3*f^2 + 4*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c)^2 + (8*b^3*f^2 + 4*I*(a^3 + 3*a*b^2)*f^2 + (24*b^3*f^2 + 12*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*b^3*f^2 + 8*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c)^3 + (16*b^3*f^2 + 8*I*(a^3 + 3*a*b^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*d*e*f + 8*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*c*f^2)*cosh(d*x + c)^3 - 3*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^3 + a*b^2)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^3 + a*b^2)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x - 4*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + (a^2*b + b^3)*d*e*f - 2*(a^2*b + b^3)*c*f^2 + (2*(a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^3*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3)*sinh(d*x + c)^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c))*sinh(d*x + c))","C",0
315,1,4699,0,1.000695," ","integrate((f*x+e)*sech(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d f x + 2 \, {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d f x + 2 \, {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right) + 2 \, {\left(b^{3} f \cosh\left(d x + c\right)^{4} + 4 \, b^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} f \sinh\left(d x + c\right)^{4} + 2 \, b^{3} f \cosh\left(d x + c\right)^{2} + b^{3} f + 2 \, {\left(3 \, b^{3} f \cosh\left(d x + c\right)^{2} + b^{3} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} f \cosh\left(d x + c\right)^{3} + b^{3} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{3} f \cosh\left(d x + c\right)^{4} + 4 \, b^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} f \sinh\left(d x + c\right)^{4} + 2 \, b^{3} f \cosh\left(d x + c\right)^{2} + b^{3} f + 2 \, {\left(3 \, b^{3} f \cosh\left(d x + c\right)^{2} + b^{3} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} f \cosh\left(d x + c\right)^{3} + b^{3} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left({\left(2 \, b^{3} f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, b^{3} f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, b^{3} f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, b^{3} f + {\left(4 \, b^{3} f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, b^{3} f + {\left(12 \, b^{3} f - 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} - i \, {\left(a^{3} + 3 \, a b^{2}\right)} f + {\left({\left(8 \, b^{3} f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, b^{3} f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left({\left(2 \, b^{3} f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, b^{3} f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, b^{3} f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, b^{3} f + {\left(4 \, b^{3} f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, b^{3} f + {\left(12 \, b^{3} f + 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + i \, {\left(a^{3} + 3 \, a b^{2}\right)} f + {\left({\left(8 \, b^{3} f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, b^{3} f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 2 \, {\left(b^{3} d e - b^{3} c f + {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{3} d e - b^{3} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d e - b^{3} c f + 3 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{3} d e - b^{3} c f + {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{3} d e - b^{3} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d e - b^{3} c f + 3 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{3} d f x + b^{3} c f + {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{3} d f x + b^{3} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f x + b^{3} c f + 3 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{3} d f x + b^{3} c f + {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{3} d f x + b^{3} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{3} d f x + b^{3} c f + 3 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(2 \, b^{3} d e - 2 \, b^{3} c f + {\left(2 \, b^{3} d e - 2 \, b^{3} c f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e + i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, b^{3} d e - 8 \, b^{3} c f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, b^{3} d e - 2 \, b^{3} c f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e + i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e + i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f + {\left(4 \, b^{3} d e - 4 \, b^{3} c f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, b^{3} d e - 4 \, b^{3} c f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f + {\left(12 \, b^{3} d e - 12 \, b^{3} c f - 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e + 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, b^{3} d e - 8 \, b^{3} c f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, b^{3} d e - 8 \, b^{3} c f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(2 \, b^{3} d e - 2 \, b^{3} c f + {\left(2 \, b^{3} d e - 2 \, b^{3} c f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e - i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, b^{3} d e - 8 \, b^{3} c f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, b^{3} d e - 2 \, b^{3} c f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e - i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e - i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f + {\left(4 \, b^{3} d e - 4 \, b^{3} c f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, b^{3} d e - 4 \, b^{3} c f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f + {\left(12 \, b^{3} d e - 12 \, b^{3} c f + 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e - 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, b^{3} d e - 8 \, b^{3} c f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, b^{3} d e - 8 \, b^{3} c f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d e - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(2 \, b^{3} d f x + 2 \, b^{3} c f + {\left(2 \, b^{3} d f x + 2 \, b^{3} c f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x + i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, b^{3} d f x + 8 \, b^{3} c f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, b^{3} d f x + 2 \, b^{3} c f + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x + i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x + i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f + {\left(4 \, b^{3} d f x + 4 \, b^{3} c f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, b^{3} d f x + 4 \, b^{3} c f + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x + 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f + {\left(12 \, b^{3} d f x + 12 \, b^{3} c f + 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x + 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, b^{3} d f x + 8 \, b^{3} c f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, b^{3} d f x + 8 \, b^{3} c f + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x + 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(2 \, b^{3} d f x + 2 \, b^{3} c f + {\left(2 \, b^{3} d f x + 2 \, b^{3} c f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x - i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, b^{3} d f x + 8 \, b^{3} c f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, b^{3} d f x + 2 \, b^{3} c f - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x - i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} - i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x - i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f + {\left(4 \, b^{3} d f x + 4 \, b^{3} c f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, b^{3} d f x + 4 \, b^{3} c f - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x - 2 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f + {\left(12 \, b^{3} d f x + 12 \, b^{3} c f - 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x - 6 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, b^{3} d f x + 8 \, b^{3} c f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, b^{3} d f x + 8 \, b^{3} c f - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} d f x - 4 i \, {\left(a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e - 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} f - 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d f x + 2 \, {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c)^3 + 2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*sinh(d*x + c)^3 + 2*(2*(a^2*b + b^3)*d*f*x + 2*(a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*cosh(d*x + c)^2 + 2*(2*(a^2*b + b^3)*d*f*x + 2*(a^2*b + b^3)*d*e + (a^2*b + b^3)*f + 3*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*(a^2*b + b^3)*f - 2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e - (a^3 + a*b^2)*f)*cosh(d*x + c) + 2*(b^3*f*cosh(d*x + c)^4 + 4*b^3*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*f*sinh(d*x + c)^4 + 2*b^3*f*cosh(d*x + c)^2 + b^3*f + 2*(3*b^3*f*cosh(d*x + c)^2 + b^3*f)*sinh(d*x + c)^2 + 4*(b^3*f*cosh(d*x + c)^3 + b^3*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^3*f*cosh(d*x + c)^4 + 4*b^3*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*f*sinh(d*x + c)^4 + 2*b^3*f*cosh(d*x + c)^2 + b^3*f + 2*(3*b^3*f*cosh(d*x + c)^2 + b^3*f)*sinh(d*x + c)^2 + 4*(b^3*f*cosh(d*x + c)^3 + b^3*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - ((2*b^3*f - I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c)^4 + (8*b^3*f - 4*I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*b^3*f - I*(a^3 + 3*a*b^2)*f)*sinh(d*x + c)^4 + 2*b^3*f + (4*b^3*f - 2*I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c)^2 + (4*b^3*f + (12*b^3*f - 6*I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c)^2 - 2*I*(a^3 + 3*a*b^2)*f)*sinh(d*x + c)^2 - I*(a^3 + 3*a*b^2)*f + ((8*b^3*f - 4*I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c)^3 + (8*b^3*f - 4*I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - ((2*b^3*f + I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c)^4 + (8*b^3*f + 4*I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*b^3*f + I*(a^3 + 3*a*b^2)*f)*sinh(d*x + c)^4 + 2*b^3*f + (4*b^3*f + 2*I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c)^2 + (4*b^3*f + (12*b^3*f + 6*I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c)^2 + 2*I*(a^3 + 3*a*b^2)*f)*sinh(d*x + c)^2 + I*(a^3 + 3*a*b^2)*f + ((8*b^3*f + 4*I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c)^3 + (8*b^3*f + 4*I*(a^3 + 3*a*b^2)*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + 2*(b^3*d*e - b^3*c*f + (b^3*d*e - b^3*c*f)*cosh(d*x + c)^4 + 4*(b^3*d*e - b^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^3*d*e - b^3*c*f)*sinh(d*x + c)^4 + 2*(b^3*d*e - b^3*c*f)*cosh(d*x + c)^2 + 2*(b^3*d*e - b^3*c*f + 3*(b^3*d*e - b^3*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^3*d*e - b^3*c*f)*cosh(d*x + c)^3 + (b^3*d*e - b^3*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^3*d*e - b^3*c*f + (b^3*d*e - b^3*c*f)*cosh(d*x + c)^4 + 4*(b^3*d*e - b^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^3*d*e - b^3*c*f)*sinh(d*x + c)^4 + 2*(b^3*d*e - b^3*c*f)*cosh(d*x + c)^2 + 2*(b^3*d*e - b^3*c*f + 3*(b^3*d*e - b^3*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^3*d*e - b^3*c*f)*cosh(d*x + c)^3 + (b^3*d*e - b^3*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^3*d*f*x + b^3*c*f + (b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^4 + 4*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^3*d*f*x + b^3*c*f)*sinh(d*x + c)^4 + 2*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^2 + 2*(b^3*d*f*x + b^3*c*f + 3*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^3 + (b^3*d*f*x + b^3*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^3*d*f*x + b^3*c*f + (b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^4 + 4*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^3*d*f*x + b^3*c*f)*sinh(d*x + c)^4 + 2*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^2 + 2*(b^3*d*f*x + b^3*c*f + 3*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^3 + (b^3*d*f*x + b^3*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (2*b^3*d*e - 2*b^3*c*f + (2*b^3*d*e - 2*b^3*c*f - I*(a^3 + 3*a*b^2)*d*e + I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^4 + (8*b^3*d*e - 8*b^3*c*f - 4*I*(a^3 + 3*a*b^2)*d*e + 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*b^3*d*e - 2*b^3*c*f - I*(a^3 + 3*a*b^2)*d*e + I*(a^3 + 3*a*b^2)*c*f)*sinh(d*x + c)^4 - I*(a^3 + 3*a*b^2)*d*e + I*(a^3 + 3*a*b^2)*c*f + (4*b^3*d*e - 4*b^3*c*f - 2*I*(a^3 + 3*a*b^2)*d*e + 2*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^2 + (4*b^3*d*e - 4*b^3*c*f - 2*I*(a^3 + 3*a*b^2)*d*e + 2*I*(a^3 + 3*a*b^2)*c*f + (12*b^3*d*e - 12*b^3*c*f - 6*I*(a^3 + 3*a*b^2)*d*e + 6*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*b^3*d*e - 8*b^3*c*f - 4*I*(a^3 + 3*a*b^2)*d*e + 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^3 + (8*b^3*d*e - 8*b^3*c*f - 4*I*(a^3 + 3*a*b^2)*d*e + 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) - (2*b^3*d*e - 2*b^3*c*f + (2*b^3*d*e - 2*b^3*c*f + I*(a^3 + 3*a*b^2)*d*e - I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^4 + (8*b^3*d*e - 8*b^3*c*f + 4*I*(a^3 + 3*a*b^2)*d*e - 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*b^3*d*e - 2*b^3*c*f + I*(a^3 + 3*a*b^2)*d*e - I*(a^3 + 3*a*b^2)*c*f)*sinh(d*x + c)^4 + I*(a^3 + 3*a*b^2)*d*e - I*(a^3 + 3*a*b^2)*c*f + (4*b^3*d*e - 4*b^3*c*f + 2*I*(a^3 + 3*a*b^2)*d*e - 2*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^2 + (4*b^3*d*e - 4*b^3*c*f + 2*I*(a^3 + 3*a*b^2)*d*e - 2*I*(a^3 + 3*a*b^2)*c*f + (12*b^3*d*e - 12*b^3*c*f + 6*I*(a^3 + 3*a*b^2)*d*e - 6*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*b^3*d*e - 8*b^3*c*f + 4*I*(a^3 + 3*a*b^2)*d*e - 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^3 + (8*b^3*d*e - 8*b^3*c*f + 4*I*(a^3 + 3*a*b^2)*d*e - 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) - (2*b^3*d*f*x + 2*b^3*c*f + (2*b^3*d*f*x + 2*b^3*c*f + I*(a^3 + 3*a*b^2)*d*f*x + I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^4 + (8*b^3*d*f*x + 8*b^3*c*f + 4*I*(a^3 + 3*a*b^2)*d*f*x + 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*b^3*d*f*x + 2*b^3*c*f + I*(a^3 + 3*a*b^2)*d*f*x + I*(a^3 + 3*a*b^2)*c*f)*sinh(d*x + c)^4 + I*(a^3 + 3*a*b^2)*d*f*x + I*(a^3 + 3*a*b^2)*c*f + (4*b^3*d*f*x + 4*b^3*c*f + 2*I*(a^3 + 3*a*b^2)*d*f*x + 2*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^2 + (4*b^3*d*f*x + 4*b^3*c*f + 2*I*(a^3 + 3*a*b^2)*d*f*x + 2*I*(a^3 + 3*a*b^2)*c*f + (12*b^3*d*f*x + 12*b^3*c*f + 6*I*(a^3 + 3*a*b^2)*d*f*x + 6*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*b^3*d*f*x + 8*b^3*c*f + 4*I*(a^3 + 3*a*b^2)*d*f*x + 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^3 + (8*b^3*d*f*x + 8*b^3*c*f + 4*I*(a^3 + 3*a*b^2)*d*f*x + 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (2*b^3*d*f*x + 2*b^3*c*f + (2*b^3*d*f*x + 2*b^3*c*f - I*(a^3 + 3*a*b^2)*d*f*x - I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^4 + (8*b^3*d*f*x + 8*b^3*c*f - 4*I*(a^3 + 3*a*b^2)*d*f*x - 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*b^3*d*f*x + 2*b^3*c*f - I*(a^3 + 3*a*b^2)*d*f*x - I*(a^3 + 3*a*b^2)*c*f)*sinh(d*x + c)^4 - I*(a^3 + 3*a*b^2)*d*f*x - I*(a^3 + 3*a*b^2)*c*f + (4*b^3*d*f*x + 4*b^3*c*f - 2*I*(a^3 + 3*a*b^2)*d*f*x - 2*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^2 + (4*b^3*d*f*x + 4*b^3*c*f - 2*I*(a^3 + 3*a*b^2)*d*f*x - 2*I*(a^3 + 3*a*b^2)*c*f + (12*b^3*d*f*x + 12*b^3*c*f - 6*I*(a^3 + 3*a*b^2)*d*f*x - 6*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*b^3*d*f*x + 8*b^3*c*f - 4*I*(a^3 + 3*a*b^2)*d*f*x - 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c)^3 + (8*b^3*d*f*x + 8*b^3*c*f - 4*I*(a^3 + 3*a*b^2)*d*f*x - 4*I*(a^3 + 3*a*b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e - 3*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c)^2 - (a^3 + a*b^2)*f - 2*(2*(a^2*b + b^3)*d*f*x + 2*(a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^2*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)*sinh(d*x + c)^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
316,1,893,0,0.503782," ","integrate(sech(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + a b^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} b + 2 \, b^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} + 3 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a b^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{3} + 3 \, a b^{2} + 2 \, {\left(a^{3} + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + 3 \, a b^{2} + 3 \, {\left(a^{3} + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right) + {\left(b^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} \sinh\left(d x + c\right)^{4} + 2 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3} + 2 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} \cosh\left(d x + c\right)^{3} + b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(b^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} \sinh\left(d x + c\right)^{4} + 2 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3} + 2 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{3} \cosh\left(d x + c\right)^{3} + b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{3} + a b^{2} - 3 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"((a^3 + a*b^2)*cosh(d*x + c)^3 + (a^3 + a*b^2)*sinh(d*x + c)^3 + 2*(a^2*b + b^3)*cosh(d*x + c)^2 + (2*a^2*b + 2*b^3 + 3*(a^3 + a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + ((a^3 + 3*a*b^2)*cosh(d*x + c)^4 + 4*(a^3 + 3*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 3*a*b^2)*sinh(d*x + c)^4 + a^3 + 3*a*b^2 + 2*(a^3 + 3*a*b^2)*cosh(d*x + c)^2 + 2*(a^3 + 3*a*b^2 + 3*(a^3 + 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3 + 3*a*b^2)*cosh(d*x + c)^3 + (a^3 + 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - (a^3 + a*b^2)*cosh(d*x + c) + (b^3*cosh(d*x + c)^4 + 4*b^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*sinh(d*x + c)^4 + 2*b^3*cosh(d*x + c)^2 + b^3 + 2*(3*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^2 + 4*(b^3*cosh(d*x + c)^3 + b^3*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) - (b^3*cosh(d*x + c)^4 + 4*b^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*sinh(d*x + c)^4 + 2*b^3*cosh(d*x + c)^2 + b^3 + 2*(3*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^2 + 4*(b^3*cosh(d*x + c)^3 + b^3*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (a^3 + a*b^2 - 3*(a^3 + a*b^2)*cosh(d*x + c)^2 - 4*(a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d)*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d + 4*((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
317,0,0,0,12.851768," ","integrate(sech(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(d x + c\right)^{3}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sech(d*x + c)^3/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
318,0,0,0,0.537359," ","integrate(x^m*cosh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \cosh\left(d x + c\right)^{3}}{b \sinh\left(d x + c\right) + a}, x\right)"," ",0,"integral(x^m*cosh(d*x + c)^3/(b*sinh(d*x + c) + a), x)","F",0
319,0,0,0,0.592474," ","integrate(x^m*cosh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \cosh\left(d x + c\right)^{2}}{b \sinh\left(d x + c\right) + a}, x\right)"," ",0,"integral(x^m*cosh(d*x + c)^2/(b*sinh(d*x + c) + a), x)","F",0
320,0,0,0,0.398792," ","integrate(x^m*cosh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{m} \cosh\left(d x + c\right)}{b \sinh\left(d x + c\right) + a}, x\right)"," ",0,"integral(x^m*cosh(d*x + c)/(b*sinh(d*x + c) + a), x)","F",0
321,1,411,0,0.551183," ","integrate((f*x+e)*cosh(d*x+c)/(a+b*sinh(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(b f \cosh\left(d x + c\right)^{2} + b f \sinh\left(d x + c\right)^{2} + 2 \, a f \cosh\left(d x + c\right) - b f + 2 \, {\left(b f \cosh\left(d x + c\right) + a f\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e\right)} \cosh\left(d x + c\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e\right)} \sinh\left(d x + c\right)}{{\left(a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} \cosh\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} d^{2}\right)} \sinh\left(d x + c\right)}"," ",0,"((b*f*cosh(d*x + c)^2 + b*f*sinh(d*x + c)^2 + 2*a*f*cosh(d*x + c) - b*f + 2*(b*f*cosh(d*x + c) + a*f)*sinh(d*x + c))*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e)*cosh(d*x + c) - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e)*sinh(d*x + c))/((a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + (a^2*b^2 + b^4)*d^2*sinh(d*x + c)^2 + 2*(a^3*b + a*b^3)*d^2*cosh(d*x + c) - (a^2*b^2 + b^4)*d^2 + 2*((a^2*b^2 + b^4)*d^2*cosh(d*x + c) + (a^3*b + a*b^3)*d^2)*sinh(d*x + c))","B",0
322,1,1378,0,0.547057," ","integrate((f*x+e)^2*cosh(d*x+c)/(a+b*sinh(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left({\left(b^{2} f^{2} \cosh\left(d x + c\right)^{2} + b^{2} f^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b f^{2} \cosh\left(d x + c\right) - b^{2} f^{2} + 2 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right) + a b f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{2} + b^{2} f^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b f^{2} \cosh\left(d x + c\right) - b^{2} f^{2} + 2 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right) + a b f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b^{2} d e f - b^{2} c f^{2} - {\left(b^{2} d e f - b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d e f - b^{2} c f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d e f - a b c f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d e f - a b c f^{2} + {\left(b^{2} d e f - b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d e f - b^{2} c f^{2} - {\left(b^{2} d e f - b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d e f - b^{2} c f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d e f - a b c f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d e f - a b c f^{2} + {\left(b^{2} d e f - b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d f^{2} x + b^{2} c f^{2} - {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d f^{2} x + a b c f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d f^{2} x + a b c f^{2} + {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{2} d f^{2} x + b^{2} c f^{2} - {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d f^{2} x + a b c f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d f^{2} x + a b c f^{2} + {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2}\right)} \sinh\left(d x + c\right)\right)}}{{\left(a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \cosh\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{3} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} d^{3}\right)} \sinh\left(d x + c\right)}"," ",0,"2*((b^2*f^2*cosh(d*x + c)^2 + b^2*f^2*sinh(d*x + c)^2 + 2*a*b*f^2*cosh(d*x + c) - b^2*f^2 + 2*(b^2*f^2*cosh(d*x + c) + a*b*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^2*f^2*cosh(d*x + c)^2 + b^2*f^2*sinh(d*x + c)^2 + 2*a*b*f^2*cosh(d*x + c) - b^2*f^2 + 2*(b^2*f^2*cosh(d*x + c) + a*b*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (b^2*d*e*f - b^2*c*f^2 - (b^2*d*e*f - b^2*c*f^2)*cosh(d*x + c)^2 - (b^2*d*e*f - b^2*c*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*e*f - a*b*c*f^2)*cosh(d*x + c) - 2*(a*b*d*e*f - a*b*c*f^2 + (b^2*d*e*f - b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d*e*f - b^2*c*f^2 - (b^2*d*e*f - b^2*c*f^2)*cosh(d*x + c)^2 - (b^2*d*e*f - b^2*c*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*e*f - a*b*c*f^2)*cosh(d*x + c) - 2*(a*b*d*e*f - a*b*c*f^2 + (b^2*d*e*f - b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d*f^2*x + b^2*c*f^2 - (b^2*d*f^2*x + b^2*c*f^2)*cosh(d*x + c)^2 - (b^2*d*f^2*x + b^2*c*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*f^2*x + a*b*c*f^2)*cosh(d*x + c) - 2*(a*b*d*f^2*x + a*b*c*f^2 + (b^2*d*f^2*x + b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^2*d*f^2*x + b^2*c*f^2 - (b^2*d*f^2*x + b^2*c*f^2)*cosh(d*x + c)^2 - (b^2*d*f^2*x + b^2*c*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*f^2*x + a*b*c*f^2)*cosh(d*x + c) - 2*(a*b*d*f^2*x + a*b*c*f^2 + (b^2*d*f^2*x + b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + (a^2 + b^2)*d^2*e^2)*cosh(d*x + c) - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + (a^2 + b^2)*d^2*e^2)*sinh(d*x + c))/((a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + (a^2*b^2 + b^4)*d^3*sinh(d*x + c)^2 + 2*(a^3*b + a*b^3)*d^3*cosh(d*x + c) - (a^2*b^2 + b^4)*d^3 + 2*((a^2*b^2 + b^4)*d^3*cosh(d*x + c) + (a^3*b + a*b^3)*d^3)*sinh(d*x + c))","B",0
323,1,2420,0,0.599964," ","integrate((f*x+e)^3*cosh(d*x+c)/(a+b*sinh(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d f^{3} x + a b d e f^{2} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d f^{3} x + a b d e f^{2} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3} - {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 3 \, {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3} - {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{2} + b^{2} f^{3} \sinh\left(d x + c\right)^{2} + 2 \, a b f^{3} \cosh\left(d x + c\right) - b^{2} f^{3} + 2 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right) + a b f^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{2} + b^{2} f^{3} \sinh\left(d x + c\right)^{2} + 2 \, a b f^{3} \cosh\left(d x + c\right) - b^{2} f^{3} + 2 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right) + a b f^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + {\left(a^{2} + b^{2}\right)} d^{3} e^{3}\right)} \cosh\left(d x + c\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + {\left(a^{2} + b^{2}\right)} d^{3} e^{3}\right)} \sinh\left(d x + c\right)}{{\left(a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d^{4} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{4} \cosh\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} d^{4}\right)} \sinh\left(d x + c\right)}"," ",0,"-(6*(b^2*d*f^3*x + b^2*d*e*f^2 - (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2 - (b^2*d*f^3*x + b^2*d*e*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*f^3*x + a*b*d*e*f^2)*cosh(d*x + c) - 2*(a*b*d*f^3*x + a*b*d*e*f^2 + (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 6*(b^2*d*f^3*x + b^2*d*e*f^2 - (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2 - (b^2*d*f^3*x + b^2*d*e*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*f^3*x + a*b*d*e*f^2)*cosh(d*x + c) - 2*(a*b*d*f^3*x + a*b*d*e*f^2 + (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*(b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3 - (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*cosh(d*x + c)^2 - (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*sinh(d*x + c)^2 - 2*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3)*cosh(d*x + c) - 2*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 3*(b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3 - (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*cosh(d*x + c)^2 - (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*sinh(d*x + c)^2 - 2*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3)*cosh(d*x + c) - 2*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*cosh(d*x + c)^2 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*sinh(d*x + c)^2 - 2*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3)*cosh(d*x + c) - 2*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*cosh(d*x + c)^2 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*sinh(d*x + c)^2 - 2*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3)*cosh(d*x + c) - 2*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 6*(b^2*f^3*cosh(d*x + c)^2 + b^2*f^3*sinh(d*x + c)^2 + 2*a*b*f^3*cosh(d*x + c) - b^2*f^3 + 2*(b^2*f^3*cosh(d*x + c) + a*b*f^3)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b^2*f^3*cosh(d*x + c)^2 + b^2*f^3*sinh(d*x + c)^2 + 2*a*b*f^3*cosh(d*x + c) - b^2*f^3 + 2*(b^2*f^3*cosh(d*x + c) + a*b*f^3)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + (a^2 + b^2)*d^3*e^3)*cosh(d*x + c) + 2*((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + (a^2 + b^2)*d^3*e^3)*sinh(d*x + c))/((a^2*b^2 + b^4)*d^4*cosh(d*x + c)^2 + (a^2*b^2 + b^4)*d^4*sinh(d*x + c)^2 + 2*(a^3*b + a*b^3)*d^4*cosh(d*x + c) - (a^2*b^2 + b^4)*d^4 + 2*((a^2*b^2 + b^4)*d^4*cosh(d*x + c) + (a^3*b + a*b^3)*d^4)*sinh(d*x + c))","C",0
324,1,411,0,0.483486," ","integrate((f*x+e)*cosh(d*x+c)/(a+b*sinh(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(b f \cosh\left(d x + c\right)^{2} + b f \sinh\left(d x + c\right)^{2} + 2 \, a f \cosh\left(d x + c\right) - b f + 2 \, {\left(b f \cosh\left(d x + c\right) + a f\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e\right)} \cosh\left(d x + c\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e\right)} \sinh\left(d x + c\right)}{{\left(a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} \cosh\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{2} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} d^{2}\right)} \sinh\left(d x + c\right)}"," ",0,"((b*f*cosh(d*x + c)^2 + b*f*sinh(d*x + c)^2 + 2*a*f*cosh(d*x + c) - b*f + 2*(b*f*cosh(d*x + c) + a*f)*sinh(d*x + c))*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e)*cosh(d*x + c) - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e)*sinh(d*x + c))/((a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + (a^2*b^2 + b^4)*d^2*sinh(d*x + c)^2 + 2*(a^3*b + a*b^3)*d^2*cosh(d*x + c) - (a^2*b^2 + b^4)*d^2 + 2*((a^2*b^2 + b^4)*d^2*cosh(d*x + c) + (a^3*b + a*b^3)*d^2)*sinh(d*x + c))","B",0
325,1,1378,0,0.511542," ","integrate((f*x+e)^2*cosh(d*x+c)/(a+b*sinh(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left({\left(b^{2} f^{2} \cosh\left(d x + c\right)^{2} + b^{2} f^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b f^{2} \cosh\left(d x + c\right) - b^{2} f^{2} + 2 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right) + a b f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{2} + b^{2} f^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b f^{2} \cosh\left(d x + c\right) - b^{2} f^{2} + 2 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right) + a b f^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b^{2} d e f - b^{2} c f^{2} - {\left(b^{2} d e f - b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d e f - b^{2} c f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d e f - a b c f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d e f - a b c f^{2} + {\left(b^{2} d e f - b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d e f - b^{2} c f^{2} - {\left(b^{2} d e f - b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d e f - b^{2} c f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d e f - a b c f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d e f - a b c f^{2} + {\left(b^{2} d e f - b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d f^{2} x + b^{2} c f^{2} - {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d f^{2} x + a b c f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d f^{2} x + a b c f^{2} + {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{2} d f^{2} x + b^{2} c f^{2} - {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d f^{2} x + a b c f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d f^{2} x + a b c f^{2} + {\left(b^{2} d f^{2} x + b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2}\right)} \sinh\left(d x + c\right)\right)}}{{\left(a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{3} \cosh\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{3} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} d^{3}\right)} \sinh\left(d x + c\right)}"," ",0,"2*((b^2*f^2*cosh(d*x + c)^2 + b^2*f^2*sinh(d*x + c)^2 + 2*a*b*f^2*cosh(d*x + c) - b^2*f^2 + 2*(b^2*f^2*cosh(d*x + c) + a*b*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^2*f^2*cosh(d*x + c)^2 + b^2*f^2*sinh(d*x + c)^2 + 2*a*b*f^2*cosh(d*x + c) - b^2*f^2 + 2*(b^2*f^2*cosh(d*x + c) + a*b*f^2)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (b^2*d*e*f - b^2*c*f^2 - (b^2*d*e*f - b^2*c*f^2)*cosh(d*x + c)^2 - (b^2*d*e*f - b^2*c*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*e*f - a*b*c*f^2)*cosh(d*x + c) - 2*(a*b*d*e*f - a*b*c*f^2 + (b^2*d*e*f - b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d*e*f - b^2*c*f^2 - (b^2*d*e*f - b^2*c*f^2)*cosh(d*x + c)^2 - (b^2*d*e*f - b^2*c*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*e*f - a*b*c*f^2)*cosh(d*x + c) - 2*(a*b*d*e*f - a*b*c*f^2 + (b^2*d*e*f - b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d*f^2*x + b^2*c*f^2 - (b^2*d*f^2*x + b^2*c*f^2)*cosh(d*x + c)^2 - (b^2*d*f^2*x + b^2*c*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*f^2*x + a*b*c*f^2)*cosh(d*x + c) - 2*(a*b*d*f^2*x + a*b*c*f^2 + (b^2*d*f^2*x + b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^2*d*f^2*x + b^2*c*f^2 - (b^2*d*f^2*x + b^2*c*f^2)*cosh(d*x + c)^2 - (b^2*d*f^2*x + b^2*c*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*f^2*x + a*b*c*f^2)*cosh(d*x + c) - 2*(a*b*d*f^2*x + a*b*c*f^2 + (b^2*d*f^2*x + b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + (a^2 + b^2)*d^2*e^2)*cosh(d*x + c) - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + (a^2 + b^2)*d^2*e^2)*sinh(d*x + c))/((a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + (a^2*b^2 + b^4)*d^3*sinh(d*x + c)^2 + 2*(a^3*b + a*b^3)*d^3*cosh(d*x + c) - (a^2*b^2 + b^4)*d^3 + 2*((a^2*b^2 + b^4)*d^3*cosh(d*x + c) + (a^3*b + a*b^3)*d^3)*sinh(d*x + c))","B",0
326,1,2420,0,0.627527," ","integrate((f*x+e)^3*cosh(d*x+c)/(a+b*sinh(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d f^{3} x + a b d e f^{2} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d f^{3} x + a b d e f^{2} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3} - {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 3 \, {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3} - {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d^{2} e^{2} f - 2 \, a b c d e f^{2} + a b c^{2} f^{3} + {\left(b^{2} d^{2} e^{2} f - 2 \, b^{2} c d e f^{2} + b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + 2 \, a b c d e f^{2} - a b c^{2} f^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + 2 \, b^{2} c d e f^{2} - b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{2} + b^{2} f^{3} \sinh\left(d x + c\right)^{2} + 2 \, a b f^{3} \cosh\left(d x + c\right) - b^{2} f^{3} + 2 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right) + a b f^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{2} + b^{2} f^{3} \sinh\left(d x + c\right)^{2} + 2 \, a b f^{3} \cosh\left(d x + c\right) - b^{2} f^{3} + 2 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right) + a b f^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + {\left(a^{2} + b^{2}\right)} d^{3} e^{3}\right)} \cosh\left(d x + c\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + {\left(a^{2} + b^{2}\right)} d^{3} e^{3}\right)} \sinh\left(d x + c\right)}{{\left(a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} d^{4} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{4} \cosh\left(d x + c\right) - {\left(a^{2} b^{2} + b^{4}\right)} d^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} d^{4}\right)} \sinh\left(d x + c\right)}"," ",0,"-(6*(b^2*d*f^3*x + b^2*d*e*f^2 - (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2 - (b^2*d*f^3*x + b^2*d*e*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*f^3*x + a*b*d*e*f^2)*cosh(d*x + c) - 2*(a*b*d*f^3*x + a*b*d*e*f^2 + (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 6*(b^2*d*f^3*x + b^2*d*e*f^2 - (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2 - (b^2*d*f^3*x + b^2*d*e*f^2)*sinh(d*x + c)^2 - 2*(a*b*d*f^3*x + a*b*d*e*f^2)*cosh(d*x + c) - 2*(a*b*d*f^3*x + a*b*d*e*f^2 + (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*(b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3 - (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*cosh(d*x + c)^2 - (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*sinh(d*x + c)^2 - 2*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3)*cosh(d*x + c) - 2*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 3*(b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3 - (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*cosh(d*x + c)^2 - (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*sinh(d*x + c)^2 - 2*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3)*cosh(d*x + c) - 2*(a*b*d^2*e^2*f - 2*a*b*c*d*e*f^2 + a*b*c^2*f^3 + (b^2*d^2*e^2*f - 2*b^2*c*d*e*f^2 + b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*cosh(d*x + c)^2 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*sinh(d*x + c)^2 - 2*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3)*cosh(d*x + c) - 2*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*cosh(d*x + c)^2 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*sinh(d*x + c)^2 - 2*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3)*cosh(d*x + c) - 2*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + 2*a*b*c*d*e*f^2 - a*b*c^2*f^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + 2*b^2*c*d*e*f^2 - b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 6*(b^2*f^3*cosh(d*x + c)^2 + b^2*f^3*sinh(d*x + c)^2 + 2*a*b*f^3*cosh(d*x + c) - b^2*f^3 + 2*(b^2*f^3*cosh(d*x + c) + a*b*f^3)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b^2*f^3*cosh(d*x + c)^2 + b^2*f^3*sinh(d*x + c)^2 + 2*a*b*f^3*cosh(d*x + c) - b^2*f^3 + 2*(b^2*f^3*cosh(d*x + c) + a*b*f^3)*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + (a^2 + b^2)*d^3*e^3)*cosh(d*x + c) + 2*((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + (a^2 + b^2)*d^3*e^3)*sinh(d*x + c))/((a^2*b^2 + b^4)*d^4*cosh(d*x + c)^2 + (a^2*b^2 + b^4)*d^4*sinh(d*x + c)^2 + 2*(a^3*b + a*b^3)*d^4*cosh(d*x + c) - (a^2*b^2 + b^4)*d^4 + 2*((a^2*b^2 + b^4)*d^4*cosh(d*x + c) + (a^3*b + a*b^3)*d^4)*sinh(d*x + c))","C",0
327,1,1230,0,0.467452," ","integrate((f*x+e)*cosh(d*x+c)/(a+b*sinh(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b + a b^{3}\right)} f \sinh\left(d x + c\right)^{3} - 6 \, {\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right) - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - 3 \, {\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right) - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} f \cosh\left(d x + c\right)^{4} + a b^{2} f \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b f \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b f \cosh\left(d x + c\right) + a b^{2} f + 2 \, {\left(2 \, a^{3} - a b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} f \cosh\left(d x + c\right) + a^{2} b f\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a b^{2} f \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b f \cosh\left(d x + c\right) + {\left(2 \, a^{3} - a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} f \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b f \cosh\left(d x + c\right)^{2} - a^{2} b f + {\left(2 \, a^{3} - a b^{2}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} f + 2 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right)^{2} - 3 \, {\left(a^{3} b + a b^{3}\right)} f - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \cosh\left(d x + c\right)^{4} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{2} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2} \cosh\left(d x + c\right) + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \cosh\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} + 2 \, {\left(3 \, {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{2} \cosh\left(d x + c\right) - {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(2*(a^3*b + a*b^3)*f*cosh(d*x + c)^3 + 2*(a^3*b + a*b^3)*f*sinh(d*x + c)^3 - 6*(a^3*b + a*b^3)*f*cosh(d*x + c) - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d*f*x + 2*(a^4 + 2*a^2*b^2 + b^4)*d*e - (2*a^4 + a^2*b^2 - b^4)*f)*cosh(d*x + c)^2 - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d*f*x + 2*(a^4 + 2*a^2*b^2 + b^4)*d*e - 3*(a^3*b + a*b^3)*f*cosh(d*x + c) - (2*a^4 + a^2*b^2 - b^4)*f)*sinh(d*x + c)^2 + (a*b^2*f*cosh(d*x + c)^4 + a*b^2*f*sinh(d*x + c)^4 + 4*a^2*b*f*cosh(d*x + c)^3 - 4*a^2*b*f*cosh(d*x + c) + a*b^2*f + 2*(2*a^3 - a*b^2)*f*cosh(d*x + c)^2 + 4*(a*b^2*f*cosh(d*x + c) + a^2*b*f)*sinh(d*x + c)^3 + 2*(3*a*b^2*f*cosh(d*x + c)^2 + 6*a^2*b*f*cosh(d*x + c) + (2*a^3 - a*b^2)*f)*sinh(d*x + c)^2 + 4*(a*b^2*f*cosh(d*x + c)^3 + 3*a^2*b*f*cosh(d*x + c)^2 - a^2*b*f + (2*a^3 - a*b^2)*f*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 2*(a^2*b^2 + b^4)*f + 2*(3*(a^3*b + a*b^3)*f*cosh(d*x + c)^2 - 3*(a^3*b + a*b^3)*f - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d*f*x + 2*(a^4 + 2*a^2*b^2 + b^4)*d*e - (2*a^4 + a^2*b^2 - b^4)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b^3 + 2*a^2*b^5 + b^7)*d^2*cosh(d*x + c)^4 + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^2*sinh(d*x + c)^4 + 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2*cosh(d*x + c)^3 + 2*(2*a^6*b + 3*a^4*b^3 - b^7)*d^2*cosh(d*x + c)^2 - 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2*cosh(d*x + c) + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^2*cosh(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2)*sinh(d*x + c)^3 + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^2 + 2*(3*(a^4*b^3 + 2*a^2*b^5 + b^7)*d^2*cosh(d*x + c)^2 + 6*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2*cosh(d*x + c) + (2*a^6*b + 3*a^4*b^3 - b^7)*d^2)*sinh(d*x + c)^2 + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^2*cosh(d*x + c)^3 + 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2*cosh(d*x + c)^2 + (2*a^6*b + 3*a^4*b^3 - b^7)*d^2*cosh(d*x + c) - (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2)*sinh(d*x + c))","B",0
328,1,5233,0,0.806793," ","integrate((f*x+e)^2*cosh(d*x+c)/(a+b*sinh(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2} + 2 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{2} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{2} + 6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{2}\right)} x + 3 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left(a b^{3} f^{2} \cosh\left(d x + c\right)^{4} + a b^{3} f^{2} \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right) + a b^{3} f^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{2} \cosh\left(d x + c\right) + a^{2} b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a b^{3} f^{2} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{3} b - a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right)^{2} - a^{2} b^{2} f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(a b^{3} f^{2} \cosh\left(d x + c\right)^{4} + a b^{3} f^{2} \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right) + a b^{3} f^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{2} \cosh\left(d x + c\right) + a^{2} b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a b^{3} f^{2} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{3} b - a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right)^{2} - a^{2} b^{2} f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a b^{3} d f^{2} x + a b^{3} c f^{2} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2} + 3 \, {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2} - {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2} + 3 \, {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2} - {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{2} x - 3 \, {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{4} + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right) + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2} \cosh\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right) - {\left(a b^{3} d e f - a b^{3} c f^{2} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2} + 3 \, {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2} - {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{4} + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right) + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2} \cosh\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right) + {\left(a b^{3} d e f - a b^{3} c f^{2} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2} + 3 \, {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2} - {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{2} x - 3 \, {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2} - 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{2} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \cosh\left(d x + c\right)^{4} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{3} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{3} \cosh\left(d x + c\right) - {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3}\right)} \sinh\left(d x + c\right)}"," ",0,"-(2*((a^2*b^2 + b^4)*d*f^2*x + (a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)^4 + 2*((a^2*b^2 + b^4)*d*f^2*x + (a^2*b^2 + b^4)*c*f^2)*sinh(d*x + c)^4 - 2*(a^2*b^2 + b^4)*d*e*f + 2*(a^2*b^2 + b^4)*c*f^2 + 2*(3*(a^3*b + a*b^3)*d*f^2*x - (a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)^3 + 2*(3*(a^3*b + a*b^3)*d*f^2*x - (a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2 + 4*((a^2*b^2 + b^4)*d*f^2*x + (a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 - (2*a^4 + a^2*b^2 - b^4)*d*e*f + 2*(2*a^4 + a^2*b^2 - b^4)*c*f^2 + (2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f + (2*a^4 + a^2*b^2 - b^4)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 - (2*a^4 + a^2*b^2 - b^4)*d*e*f + 2*(2*a^4 + a^2*b^2 - b^4)*c*f^2 + 6*((a^2*b^2 + b^4)*d*f^2*x + (a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)^2 + (2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f + (2*a^4 + a^2*b^2 - b^4)*d*f^2)*x + 3*(3*(a^3*b + a*b^3)*d*f^2*x - (a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - (a*b^3*f^2*cosh(d*x + c)^4 + a*b^3*f^2*sinh(d*x + c)^4 + 4*a^2*b^2*f^2*cosh(d*x + c)^3 - 4*a^2*b^2*f^2*cosh(d*x + c) + a*b^3*f^2 + 2*(2*a^3*b - a*b^3)*f^2*cosh(d*x + c)^2 + 4*(a*b^3*f^2*cosh(d*x + c) + a^2*b^2*f^2)*sinh(d*x + c)^3 + 2*(3*a*b^3*f^2*cosh(d*x + c)^2 + 6*a^2*b^2*f^2*cosh(d*x + c) + (2*a^3*b - a*b^3)*f^2)*sinh(d*x + c)^2 + 4*(a*b^3*f^2*cosh(d*x + c)^3 + 3*a^2*b^2*f^2*cosh(d*x + c)^2 - a^2*b^2*f^2 + (2*a^3*b - a*b^3)*f^2*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (a*b^3*f^2*cosh(d*x + c)^4 + a*b^3*f^2*sinh(d*x + c)^4 + 4*a^2*b^2*f^2*cosh(d*x + c)^3 - 4*a^2*b^2*f^2*cosh(d*x + c) + a*b^3*f^2 + 2*(2*a^3*b - a*b^3)*f^2*cosh(d*x + c)^2 + 4*(a*b^3*f^2*cosh(d*x + c) + a^2*b^2*f^2)*sinh(d*x + c)^3 + 2*(3*a*b^3*f^2*cosh(d*x + c)^2 + 6*a^2*b^2*f^2*cosh(d*x + c) + (2*a^3*b - a*b^3)*f^2)*sinh(d*x + c)^2 + 4*(a*b^3*f^2*cosh(d*x + c)^3 + 3*a^2*b^2*f^2*cosh(d*x + c)^2 - a^2*b^2*f^2 + (2*a^3*b - a*b^3)*f^2*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (a*b^3*d*f^2*x + a*b^3*c*f^2 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^4 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2 + 3*(a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2 - (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (a*b^3*d*f^2*x + a*b^3*c*f^2 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^4 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2 + 3*(a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2 - (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((a^3*b + a*b^3)*d*f^2*x - 3*(a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c) - ((a^2*b^2 + b^4)*f^2*cosh(d*x + c)^4 + (a^2*b^2 + b^4)*f^2*sinh(d*x + c)^4 + 4*(a^3*b + a*b^3)*f^2*cosh(d*x + c)^3 + 2*(2*a^4 + a^2*b^2 - b^4)*f^2*cosh(d*x + c)^2 - 4*(a^3*b + a*b^3)*f^2*cosh(d*x + c) + 4*((a^2*b^2 + b^4)*f^2*cosh(d*x + c) + (a^3*b + a*b^3)*f^2)*sinh(d*x + c)^3 + (a^2*b^2 + b^4)*f^2 + 2*(3*(a^2*b^2 + b^4)*f^2*cosh(d*x + c)^2 + 6*(a^3*b + a*b^3)*f^2*cosh(d*x + c) + (2*a^4 + a^2*b^2 - b^4)*f^2)*sinh(d*x + c)^2 + 4*((a^2*b^2 + b^4)*f^2*cosh(d*x + c)^3 + 3*(a^3*b + a*b^3)*f^2*cosh(d*x + c)^2 + (2*a^4 + a^2*b^2 - b^4)*f^2*cosh(d*x + c) - (a^3*b + a*b^3)*f^2)*sinh(d*x + c) - (a*b^3*d*e*f - a*b^3*c*f^2 + (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^4 + (a*b^3*d*e*f - a*b^3*c*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2 + (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2 + 3*(a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2 - (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - ((a^2*b^2 + b^4)*f^2*cosh(d*x + c)^4 + (a^2*b^2 + b^4)*f^2*sinh(d*x + c)^4 + 4*(a^3*b + a*b^3)*f^2*cosh(d*x + c)^3 + 2*(2*a^4 + a^2*b^2 - b^4)*f^2*cosh(d*x + c)^2 - 4*(a^3*b + a*b^3)*f^2*cosh(d*x + c) + 4*((a^2*b^2 + b^4)*f^2*cosh(d*x + c) + (a^3*b + a*b^3)*f^2)*sinh(d*x + c)^3 + (a^2*b^2 + b^4)*f^2 + 2*(3*(a^2*b^2 + b^4)*f^2*cosh(d*x + c)^2 + 6*(a^3*b + a*b^3)*f^2*cosh(d*x + c) + (2*a^4 + a^2*b^2 - b^4)*f^2)*sinh(d*x + c)^2 + 4*((a^2*b^2 + b^4)*f^2*cosh(d*x + c)^3 + 3*(a^3*b + a*b^3)*f^2*cosh(d*x + c)^2 + (2*a^4 + a^2*b^2 - b^4)*f^2*cosh(d*x + c) - (a^3*b + a*b^3)*f^2)*sinh(d*x + c) + (a*b^3*d*e*f - a*b^3*c*f^2 + (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^4 + (a*b^3*d*e*f - a*b^3*c*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2 + (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2 + 3*(a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2 - (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*((a^3*b + a*b^3)*d*f^2*x - 3*(a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2 - 4*((a^2*b^2 + b^4)*d*f^2*x + (a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)^3 - 3*(3*(a^3*b + a*b^3)*d*f^2*x - (a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)^2 - 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 - (2*a^4 + a^2*b^2 - b^4)*d*e*f + 2*(2*a^4 + a^2*b^2 - b^4)*c*f^2 + (2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f + (2*a^4 + a^2*b^2 - b^4)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*cosh(d*x + c)^4 + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*sinh(d*x + c)^4 + 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3*cosh(d*x + c)^3 + 2*(2*a^6*b + 3*a^4*b^3 - b^7)*d^3*cosh(d*x + c)^2 - 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3*cosh(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^3 + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*cosh(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3)*sinh(d*x + c)^3 + 2*(3*(a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*cosh(d*x + c)^2 + 6*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3*cosh(d*x + c) + (2*a^6*b + 3*a^4*b^3 - b^7)*d^3)*sinh(d*x + c)^2 + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*cosh(d*x + c)^3 + 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3*cosh(d*x + c)^2 + (2*a^6*b + 3*a^4*b^3 - b^7)*d^3*cosh(d*x + c) - (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3)*sinh(d*x + c))","B",0
329,1,11757,0,0.786194," ","integrate((f*x+e)^3*cosh(d*x+c)/(a+b*sinh(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3} - 6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} - 6 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e^{2} f + 12 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c d e f^{2} - 6 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c^{2} f^{3} + 3 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e^{2} f + 12 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c d e f^{2} - 6 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c^{2} f^{3} + 3 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 18 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e f^{2}\right)} x + 9 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right)^{4} + a b^{3} f^{3} \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right) + a b^{3} f^{3} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right) + a^{2} b^{2} f^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a b^{3} f^{3} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{3} b - a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right)^{2} - a^{2} b^{2} f^{3} + {\left(2 \, a^{3} b - a b^{3}\right)} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right)^{4} + a b^{3} f^{3} \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right) + a b^{3} f^{3} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right) + a^{2} b^{2} f^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a b^{3} f^{3} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{3} b - a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right)^{2} - a^{2} b^{2} f^{3} + {\left(2 \, a^{3} b - a b^{3}\right)} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - 3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) + 6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{4} + {\left(a^{2} b^{2} + b^{4}\right)} f^{3} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3} \cosh\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right) + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2} + 3 \, {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2} - {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{4} + {\left(a^{2} b^{2} + b^{4}\right)} f^{3} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3} \cosh\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right) - {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2} + 3 \, {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2} - {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{3} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3} + {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3} + 3 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right) - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3} - {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3} + 3 \, {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3} - {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{3} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3} + {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3} + 3 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right) - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3} - {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3} + 3 \, {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3} - {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{3} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3} + {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3} + 3 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right) - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3} - {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3} + 3 \, {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3} - {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{3} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3} + {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3} + 3 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right) - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3} - {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3} + 3 \, {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3} - {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - 9 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 24 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 12 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - 12 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 9 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e^{2} f + 12 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c d e f^{2} - 6 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c^{2} f^{3} + 3 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \cosh\left(d x + c\right)^{4} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{4} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4} \cosh\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \cosh\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4} \cosh\left(d x + c\right) + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{4} \cosh\left(d x + c\right) - {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(6*(a^2*b^2 + b^4)*d^2*e^2*f - 12*(a^2*b^2 + b^4)*c*d*e*f^2 + 6*(a^2*b^2 + b^4)*c^2*f^3 - 6*((a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 + b^4)*d^2*e*f^2*x + 2*(a^2*b^2 + b^4)*c*d*e*f^2 - (a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)^4 - 6*((a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 + b^4)*d^2*e*f^2*x + 2*(a^2*b^2 + b^4)*c*d*e*f^2 - (a^2*b^2 + b^4)*c^2*f^3)*sinh(d*x + c)^4 - 6*(3*(a^3*b + a*b^3)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f^2*x - (a^3*b + a*b^3)*d^2*e^2*f + 8*(a^3*b + a*b^3)*c*d*e*f^2 - 4*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)^3 - 6*(3*(a^3*b + a*b^3)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f^2*x - (a^3*b + a*b^3)*d^2*e^2*f + 8*(a^3*b + a*b^3)*c*d*e*f^2 - 4*(a^3*b + a*b^3)*c^2*f^3 + 4*((a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 + b^4)*d^2*e*f^2*x + 2*(a^2*b^2 + b^4)*c*d*e*f^2 - (a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(2*a^4 + a^2*b^2 - b^4)*d^2*e^2*f + 12*(2*a^4 + a^2*b^2 - b^4)*c*d*e*f^2 - 6*(2*a^4 + a^2*b^2 - b^4)*c^2*f^3 + 3*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2 + (2*a^4 + a^2*b^2 - b^4)*d^2*f^3)*x^2 + 6*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f + (2*a^4 + a^2*b^2 - b^4)*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(2*a^4 + a^2*b^2 - b^4)*d^2*e^2*f + 12*(2*a^4 + a^2*b^2 - b^4)*c*d*e*f^2 - 6*(2*a^4 + a^2*b^2 - b^4)*c^2*f^3 + 3*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2 + (2*a^4 + a^2*b^2 - b^4)*d^2*f^3)*x^2 + 18*((a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 + b^4)*d^2*e*f^2*x + 2*(a^2*b^2 + b^4)*c*d*e*f^2 - (a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)^2 + 6*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f + (2*a^4 + a^2*b^2 - b^4)*d^2*e*f^2)*x + 9*(3*(a^3*b + a*b^3)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f^2*x - (a^3*b + a*b^3)*d^2*e^2*f + 8*(a^3*b + a*b^3)*c*d*e*f^2 - 4*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 6*(a*b^3*f^3*cosh(d*x + c)^4 + a*b^3*f^3*sinh(d*x + c)^4 + 4*a^2*b^2*f^3*cosh(d*x + c)^3 - 4*a^2*b^2*f^3*cosh(d*x + c) + a*b^3*f^3 + 2*(2*a^3*b - a*b^3)*f^3*cosh(d*x + c)^2 + 4*(a*b^3*f^3*cosh(d*x + c) + a^2*b^2*f^3)*sinh(d*x + c)^3 + 2*(3*a*b^3*f^3*cosh(d*x + c)^2 + 6*a^2*b^2*f^3*cosh(d*x + c) + (2*a^3*b - a*b^3)*f^3)*sinh(d*x + c)^2 + 4*(a*b^3*f^3*cosh(d*x + c)^3 + 3*a^2*b^2*f^3*cosh(d*x + c)^2 - a^2*b^2*f^3 + (2*a^3*b - a*b^3)*f^3*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(a*b^3*f^3*cosh(d*x + c)^4 + a*b^3*f^3*sinh(d*x + c)^4 + 4*a^2*b^2*f^3*cosh(d*x + c)^3 - 4*a^2*b^2*f^3*cosh(d*x + c) + a*b^3*f^3 + 2*(2*a^3*b - a*b^3)*f^3*cosh(d*x + c)^2 + 4*(a*b^3*f^3*cosh(d*x + c) + a^2*b^2*f^3)*sinh(d*x + c)^3 + 2*(3*a*b^3*f^3*cosh(d*x + c)^2 + 6*a^2*b^2*f^3*cosh(d*x + c) + (2*a^3*b - a*b^3)*f^3)*sinh(d*x + c)^2 + 4*(a*b^3*f^3*cosh(d*x + c)^3 + 3*a^2*b^2*f^3*cosh(d*x + c)^2 - a^2*b^2*f^3 + (2*a^3*b - a*b^3)*f^3*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*((a^3*b + a*b^3)*d^2*f^3*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f^2*x - 3*(a^3*b + a*b^3)*d^2*e^2*f + 8*(a^3*b + a*b^3)*c*d*e*f^2 - 4*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c) + 6*((a^2*b^2 + b^4)*f^3*cosh(d*x + c)^4 + (a^2*b^2 + b^4)*f^3*sinh(d*x + c)^4 + 4*(a^3*b + a*b^3)*f^3*cosh(d*x + c)^3 + 2*(2*a^4 + a^2*b^2 - b^4)*f^3*cosh(d*x + c)^2 - 4*(a^3*b + a*b^3)*f^3*cosh(d*x + c) + (a^2*b^2 + b^4)*f^3 + 4*((a^2*b^2 + b^4)*f^3*cosh(d*x + c) + (a^3*b + a*b^3)*f^3)*sinh(d*x + c)^3 + 2*(3*(a^2*b^2 + b^4)*f^3*cosh(d*x + c)^2 + 6*(a^3*b + a*b^3)*f^3*cosh(d*x + c) + (2*a^4 + a^2*b^2 - b^4)*f^3)*sinh(d*x + c)^2 + 4*((a^2*b^2 + b^4)*f^3*cosh(d*x + c)^3 + 3*(a^3*b + a*b^3)*f^3*cosh(d*x + c)^2 + (2*a^4 + a^2*b^2 - b^4)*f^3*cosh(d*x + c) - (a^3*b + a*b^3)*f^3)*sinh(d*x + c) + (a*b^3*d*f^3*x + a*b^3*d*e*f^2 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^4 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2 + 3*(a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2 - (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 6*((a^2*b^2 + b^4)*f^3*cosh(d*x + c)^4 + (a^2*b^2 + b^4)*f^3*sinh(d*x + c)^4 + 4*(a^3*b + a*b^3)*f^3*cosh(d*x + c)^3 + 2*(2*a^4 + a^2*b^2 - b^4)*f^3*cosh(d*x + c)^2 - 4*(a^3*b + a*b^3)*f^3*cosh(d*x + c) + (a^2*b^2 + b^4)*f^3 + 4*((a^2*b^2 + b^4)*f^3*cosh(d*x + c) + (a^3*b + a*b^3)*f^3)*sinh(d*x + c)^3 + 2*(3*(a^2*b^2 + b^4)*f^3*cosh(d*x + c)^2 + 6*(a^3*b + a*b^3)*f^3*cosh(d*x + c) + (2*a^4 + a^2*b^2 - b^4)*f^3)*sinh(d*x + c)^2 + 4*((a^2*b^2 + b^4)*f^3*cosh(d*x + c)^3 + 3*(a^3*b + a*b^3)*f^3*cosh(d*x + c)^2 + (2*a^4 + a^2*b^2 - b^4)*f^3*cosh(d*x + c) - (a^3*b + a*b^3)*f^3)*sinh(d*x + c) - (a*b^3*d*f^3*x + a*b^3*d*e*f^2 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^4 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2 + 3*(a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2 - (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(2*(a^2*b^2 + b^4)*d*e*f^2 - 2*(a^2*b^2 + b^4)*c*f^3 + 2*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^4 + 2*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*sinh(d*x + c)^4 + 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^3 + 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3 + ((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c)^2 + 4*((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3 + 3*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^2 + 6*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c) - 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3 - ((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^3 - 3*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^2 - ((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c) - (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^4 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*sinh(d*x + c)^4 + 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c)^3 + 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3 + 3*(a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^2 + 6*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c) - 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3 - (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^3 - 3*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 3*(2*(a^2*b^2 + b^4)*d*e*f^2 - 2*(a^2*b^2 + b^4)*c*f^3 + 2*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^4 + 2*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*sinh(d*x + c)^4 + 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^3 + 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3 + ((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c)^2 + 4*((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3 + 3*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^2 + 6*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c) - 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3 - ((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^3 - 3*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^2 - ((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c) + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^4 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*sinh(d*x + c)^4 + 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c)^3 + 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3 + 3*(a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^2 + 6*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c) - 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3 - (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^3 - 3*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 3*(2*(a^2*b^2 + b^4)*d*f^3*x + 2*(a^2*b^2 + b^4)*c*f^3 + 2*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^4 + 2*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*sinh(d*x + c)^4 + 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^3 + 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3 + ((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c)^2 + 4*((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3 + 3*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^2 + 6*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c) - 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3 - ((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^3 - 3*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^2 - ((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c) + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^4 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*sinh(d*x + c)^4 + 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c)^3 + 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3 + 3*(a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^2 + 6*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c) - 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3 - (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^3 - 3*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 3*(2*(a^2*b^2 + b^4)*d*f^3*x + 2*(a^2*b^2 + b^4)*c*f^3 + 2*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^4 + 2*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*sinh(d*x + c)^4 + 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^3 + 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3 + ((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c)^2 + 4*((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3 + 3*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^2 + 6*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c) - 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3 - ((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^3 - 3*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^2 - ((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c) - (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^4 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*sinh(d*x + c)^4 + 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c)^3 + 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3 + 3*(a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^2 + 6*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c) - 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3 - (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^3 - 3*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(3*(a^3*b + a*b^3)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f^2*x - 9*(a^3*b + a*b^3)*d^2*e^2*f + 24*(a^3*b + a*b^3)*c*d*e*f^2 - 12*(a^3*b + a*b^3)*c^2*f^3 - 12*((a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 + b^4)*d^2*e*f^2*x + 2*(a^2*b^2 + b^4)*c*d*e*f^2 - (a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)^3 - 9*(3*(a^3*b + a*b^3)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f^2*x - (a^3*b + a*b^3)*d^2*e^2*f + 8*(a^3*b + a*b^3)*c*d*e*f^2 - 4*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)^2 - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(2*a^4 + a^2*b^2 - b^4)*d^2*e^2*f + 12*(2*a^4 + a^2*b^2 - b^4)*c*d*e*f^2 - 6*(2*a^4 + a^2*b^2 - b^4)*c^2*f^3 + 3*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2 + (2*a^4 + a^2*b^2 - b^4)*d^2*f^3)*x^2 + 6*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f + (2*a^4 + a^2*b^2 - b^4)*d^2*e*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b^3 + 2*a^2*b^5 + b^7)*d^4*cosh(d*x + c)^4 + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^4*sinh(d*x + c)^4 + 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4*cosh(d*x + c)^3 + 2*(2*a^6*b + 3*a^4*b^3 - b^7)*d^4*cosh(d*x + c)^2 - 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4*cosh(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^4 + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^4*cosh(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4)*sinh(d*x + c)^3 + 2*(3*(a^4*b^3 + 2*a^2*b^5 + b^7)*d^4*cosh(d*x + c)^2 + 6*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4*cosh(d*x + c) + (2*a^6*b + 3*a^4*b^3 - b^7)*d^4)*sinh(d*x + c)^2 + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^4*cosh(d*x + c)^3 + 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4*cosh(d*x + c)^2 + (2*a^6*b + 3*a^4*b^3 - b^7)*d^4*cosh(d*x + c) - (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4)*sinh(d*x + c))","C",0
330,1,1230,0,0.609559," ","integrate((f*x+e)*cosh(d*x+c)/(a+b*sinh(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b + a b^{3}\right)} f \sinh\left(d x + c\right)^{3} - 6 \, {\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right) - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - 3 \, {\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right) - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} f \cosh\left(d x + c\right)^{4} + a b^{2} f \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b f \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b f \cosh\left(d x + c\right) + a b^{2} f + 2 \, {\left(2 \, a^{3} - a b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} f \cosh\left(d x + c\right) + a^{2} b f\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a b^{2} f \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b f \cosh\left(d x + c\right) + {\left(2 \, a^{3} - a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} f \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b f \cosh\left(d x + c\right)^{2} - a^{2} b f + {\left(2 \, a^{3} - a b^{2}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} f + 2 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right)^{2} - 3 \, {\left(a^{3} b + a b^{3}\right)} f - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \cosh\left(d x + c\right)^{4} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{2} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2} \cosh\left(d x + c\right) + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \cosh\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} + 2 \, {\left(3 \, {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{2} \cosh\left(d x + c\right) - {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{2}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(2*(a^3*b + a*b^3)*f*cosh(d*x + c)^3 + 2*(a^3*b + a*b^3)*f*sinh(d*x + c)^3 - 6*(a^3*b + a*b^3)*f*cosh(d*x + c) - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d*f*x + 2*(a^4 + 2*a^2*b^2 + b^4)*d*e - (2*a^4 + a^2*b^2 - b^4)*f)*cosh(d*x + c)^2 - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d*f*x + 2*(a^4 + 2*a^2*b^2 + b^4)*d*e - 3*(a^3*b + a*b^3)*f*cosh(d*x + c) - (2*a^4 + a^2*b^2 - b^4)*f)*sinh(d*x + c)^2 + (a*b^2*f*cosh(d*x + c)^4 + a*b^2*f*sinh(d*x + c)^4 + 4*a^2*b*f*cosh(d*x + c)^3 - 4*a^2*b*f*cosh(d*x + c) + a*b^2*f + 2*(2*a^3 - a*b^2)*f*cosh(d*x + c)^2 + 4*(a*b^2*f*cosh(d*x + c) + a^2*b*f)*sinh(d*x + c)^3 + 2*(3*a*b^2*f*cosh(d*x + c)^2 + 6*a^2*b*f*cosh(d*x + c) + (2*a^3 - a*b^2)*f)*sinh(d*x + c)^2 + 4*(a*b^2*f*cosh(d*x + c)^3 + 3*a^2*b*f*cosh(d*x + c)^2 - a^2*b*f + (2*a^3 - a*b^2)*f*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 2*(a^2*b^2 + b^4)*f + 2*(3*(a^3*b + a*b^3)*f*cosh(d*x + c)^2 - 3*(a^3*b + a*b^3)*f - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d*f*x + 2*(a^4 + 2*a^2*b^2 + b^4)*d*e - (2*a^4 + a^2*b^2 - b^4)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b^3 + 2*a^2*b^5 + b^7)*d^2*cosh(d*x + c)^4 + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^2*sinh(d*x + c)^4 + 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2*cosh(d*x + c)^3 + 2*(2*a^6*b + 3*a^4*b^3 - b^7)*d^2*cosh(d*x + c)^2 - 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2*cosh(d*x + c) + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^2*cosh(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2)*sinh(d*x + c)^3 + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^2 + 2*(3*(a^4*b^3 + 2*a^2*b^5 + b^7)*d^2*cosh(d*x + c)^2 + 6*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2*cosh(d*x + c) + (2*a^6*b + 3*a^4*b^3 - b^7)*d^2)*sinh(d*x + c)^2 + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^2*cosh(d*x + c)^3 + 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2*cosh(d*x + c)^2 + (2*a^6*b + 3*a^4*b^3 - b^7)*d^2*cosh(d*x + c) - (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^2)*sinh(d*x + c))","B",0
331,1,5233,0,0.706597," ","integrate((f*x+e)^2*cosh(d*x+c)/(a+b*sinh(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2} + 2 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{2} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{2} + 6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{2}\right)} x + 3 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left(a b^{3} f^{2} \cosh\left(d x + c\right)^{4} + a b^{3} f^{2} \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right) + a b^{3} f^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{2} \cosh\left(d x + c\right) + a^{2} b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a b^{3} f^{2} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{3} b - a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right)^{2} - a^{2} b^{2} f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(a b^{3} f^{2} \cosh\left(d x + c\right)^{4} + a b^{3} f^{2} \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right) + a b^{3} f^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{2} \cosh\left(d x + c\right) + a^{2} b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a b^{3} f^{2} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{3} b - a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b^{2} f^{2} \cosh\left(d x + c\right)^{2} - a^{2} b^{2} f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a b^{3} d f^{2} x + a b^{3} c f^{2} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2} + 3 \, {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2} - {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2} + {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2} + 3 \, {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2} - {\left(a b^{3} d f^{2} x + a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d f^{2} x + a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{2} x + {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{2} x - 3 \, {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{4} + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right) + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2} \cosh\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right) - {\left(a b^{3} d e f - a b^{3} c f^{2} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2} + 3 \, {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2} - {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{4} + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right) + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right) + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{2} \cosh\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right) + {\left(a b^{3} d e f - a b^{3} c f^{2} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2} + {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2} + 3 \, {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2} - {\left(a b^{3} d e f - a b^{3} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d e f - a^{2} b^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d e f - {\left(2 \, a^{3} b - a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{2} x - 3 \, {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2} - 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - {\left(a^{3} b + a b^{3}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{2} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \cosh\left(d x + c\right)^{4} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{3} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{3} \cosh\left(d x + c\right) - {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{3}\right)} \sinh\left(d x + c\right)}"," ",0,"-(2*((a^2*b^2 + b^4)*d*f^2*x + (a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)^4 + 2*((a^2*b^2 + b^4)*d*f^2*x + (a^2*b^2 + b^4)*c*f^2)*sinh(d*x + c)^4 - 2*(a^2*b^2 + b^4)*d*e*f + 2*(a^2*b^2 + b^4)*c*f^2 + 2*(3*(a^3*b + a*b^3)*d*f^2*x - (a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)^3 + 2*(3*(a^3*b + a*b^3)*d*f^2*x - (a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2 + 4*((a^2*b^2 + b^4)*d*f^2*x + (a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 - (2*a^4 + a^2*b^2 - b^4)*d*e*f + 2*(2*a^4 + a^2*b^2 - b^4)*c*f^2 + (2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f + (2*a^4 + a^2*b^2 - b^4)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 - (2*a^4 + a^2*b^2 - b^4)*d*e*f + 2*(2*a^4 + a^2*b^2 - b^4)*c*f^2 + 6*((a^2*b^2 + b^4)*d*f^2*x + (a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)^2 + (2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f + (2*a^4 + a^2*b^2 - b^4)*d*f^2)*x + 3*(3*(a^3*b + a*b^3)*d*f^2*x - (a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - (a*b^3*f^2*cosh(d*x + c)^4 + a*b^3*f^2*sinh(d*x + c)^4 + 4*a^2*b^2*f^2*cosh(d*x + c)^3 - 4*a^2*b^2*f^2*cosh(d*x + c) + a*b^3*f^2 + 2*(2*a^3*b - a*b^3)*f^2*cosh(d*x + c)^2 + 4*(a*b^3*f^2*cosh(d*x + c) + a^2*b^2*f^2)*sinh(d*x + c)^3 + 2*(3*a*b^3*f^2*cosh(d*x + c)^2 + 6*a^2*b^2*f^2*cosh(d*x + c) + (2*a^3*b - a*b^3)*f^2)*sinh(d*x + c)^2 + 4*(a*b^3*f^2*cosh(d*x + c)^3 + 3*a^2*b^2*f^2*cosh(d*x + c)^2 - a^2*b^2*f^2 + (2*a^3*b - a*b^3)*f^2*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (a*b^3*f^2*cosh(d*x + c)^4 + a*b^3*f^2*sinh(d*x + c)^4 + 4*a^2*b^2*f^2*cosh(d*x + c)^3 - 4*a^2*b^2*f^2*cosh(d*x + c) + a*b^3*f^2 + 2*(2*a^3*b - a*b^3)*f^2*cosh(d*x + c)^2 + 4*(a*b^3*f^2*cosh(d*x + c) + a^2*b^2*f^2)*sinh(d*x + c)^3 + 2*(3*a*b^3*f^2*cosh(d*x + c)^2 + 6*a^2*b^2*f^2*cosh(d*x + c) + (2*a^3*b - a*b^3)*f^2)*sinh(d*x + c)^2 + 4*(a*b^3*f^2*cosh(d*x + c)^3 + 3*a^2*b^2*f^2*cosh(d*x + c)^2 - a^2*b^2*f^2 + (2*a^3*b - a*b^3)*f^2*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (a*b^3*d*f^2*x + a*b^3*c*f^2 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^4 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2 + 3*(a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2 - (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (a*b^3*d*f^2*x + a*b^3*c*f^2 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^4 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2 + (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2 + 3*(a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2 - (a*b^3*d*f^2*x + a*b^3*c*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*f^2*x + a^2*b^2*c*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*f^2*x + (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((a^3*b + a*b^3)*d*f^2*x - 3*(a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c) - ((a^2*b^2 + b^4)*f^2*cosh(d*x + c)^4 + (a^2*b^2 + b^4)*f^2*sinh(d*x + c)^4 + 4*(a^3*b + a*b^3)*f^2*cosh(d*x + c)^3 + 2*(2*a^4 + a^2*b^2 - b^4)*f^2*cosh(d*x + c)^2 - 4*(a^3*b + a*b^3)*f^2*cosh(d*x + c) + 4*((a^2*b^2 + b^4)*f^2*cosh(d*x + c) + (a^3*b + a*b^3)*f^2)*sinh(d*x + c)^3 + (a^2*b^2 + b^4)*f^2 + 2*(3*(a^2*b^2 + b^4)*f^2*cosh(d*x + c)^2 + 6*(a^3*b + a*b^3)*f^2*cosh(d*x + c) + (2*a^4 + a^2*b^2 - b^4)*f^2)*sinh(d*x + c)^2 + 4*((a^2*b^2 + b^4)*f^2*cosh(d*x + c)^3 + 3*(a^3*b + a*b^3)*f^2*cosh(d*x + c)^2 + (2*a^4 + a^2*b^2 - b^4)*f^2*cosh(d*x + c) - (a^3*b + a*b^3)*f^2)*sinh(d*x + c) - (a*b^3*d*e*f - a*b^3*c*f^2 + (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^4 + (a*b^3*d*e*f - a*b^3*c*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2 + (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2 + 3*(a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2 - (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - ((a^2*b^2 + b^4)*f^2*cosh(d*x + c)^4 + (a^2*b^2 + b^4)*f^2*sinh(d*x + c)^4 + 4*(a^3*b + a*b^3)*f^2*cosh(d*x + c)^3 + 2*(2*a^4 + a^2*b^2 - b^4)*f^2*cosh(d*x + c)^2 - 4*(a^3*b + a*b^3)*f^2*cosh(d*x + c) + 4*((a^2*b^2 + b^4)*f^2*cosh(d*x + c) + (a^3*b + a*b^3)*f^2)*sinh(d*x + c)^3 + (a^2*b^2 + b^4)*f^2 + 2*(3*(a^2*b^2 + b^4)*f^2*cosh(d*x + c)^2 + 6*(a^3*b + a*b^3)*f^2*cosh(d*x + c) + (2*a^4 + a^2*b^2 - b^4)*f^2)*sinh(d*x + c)^2 + 4*((a^2*b^2 + b^4)*f^2*cosh(d*x + c)^3 + 3*(a^3*b + a*b^3)*f^2*cosh(d*x + c)^2 + (2*a^4 + a^2*b^2 - b^4)*f^2*cosh(d*x + c) - (a^3*b + a*b^3)*f^2)*sinh(d*x + c) + (a*b^3*d*e*f - a*b^3*c*f^2 + (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^4 + (a*b^3*d*e*f - a*b^3*c*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2 + (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2 + 3*(a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*e*f - a^2*b^2*c*f^2 - (a*b^3*d*e*f - a*b^3*c*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*e*f - a^2*b^2*c*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*e*f - (2*a^3*b - a*b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*((a^3*b + a*b^3)*d*f^2*x - 3*(a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2 - 4*((a^2*b^2 + b^4)*d*f^2*x + (a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)^3 - 3*(3*(a^3*b + a*b^3)*d*f^2*x - (a^3*b + a*b^3)*d*e*f + 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)^2 - 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 - (2*a^4 + a^2*b^2 - b^4)*d*e*f + 2*(2*a^4 + a^2*b^2 - b^4)*c*f^2 + (2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f + (2*a^4 + a^2*b^2 - b^4)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*cosh(d*x + c)^4 + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*sinh(d*x + c)^4 + 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3*cosh(d*x + c)^3 + 2*(2*a^6*b + 3*a^4*b^3 - b^7)*d^3*cosh(d*x + c)^2 - 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3*cosh(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^3 + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*cosh(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3)*sinh(d*x + c)^3 + 2*(3*(a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*cosh(d*x + c)^2 + 6*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3*cosh(d*x + c) + (2*a^6*b + 3*a^4*b^3 - b^7)*d^3)*sinh(d*x + c)^2 + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^3*cosh(d*x + c)^3 + 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3*cosh(d*x + c)^2 + (2*a^6*b + 3*a^4*b^3 - b^7)*d^3*cosh(d*x + c) - (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^3)*sinh(d*x + c))","B",0
332,1,11757,0,0.811205," ","integrate((f*x+e)^3*cosh(d*x+c)/(a+b*sinh(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3} - 6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} - 6 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e^{2} f + 12 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c d e f^{2} - 6 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c^{2} f^{3} + 3 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e^{2} f + 12 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c d e f^{2} - 6 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c^{2} f^{3} + 3 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 18 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e f^{2}\right)} x + 9 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right)^{4} + a b^{3} f^{3} \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right) + a b^{3} f^{3} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right) + a^{2} b^{2} f^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a b^{3} f^{3} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{3} b - a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right)^{2} - a^{2} b^{2} f^{3} + {\left(2 \, a^{3} b - a b^{3}\right)} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right)^{4} + a b^{3} f^{3} \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right) + a b^{3} f^{3} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right) + a^{2} b^{2} f^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a b^{3} f^{3} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{3} b - a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b^{2} f^{3} \cosh\left(d x + c\right)^{2} - a^{2} b^{2} f^{3} + {\left(2 \, a^{3} b - a b^{3}\right)} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - 3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) + 6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{4} + {\left(a^{2} b^{2} + b^{4}\right)} f^{3} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3} \cosh\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right) + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2} + 3 \, {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2} - {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{4} + {\left(a^{2} b^{2} + b^{4}\right)} f^{3} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} f^{3} \cosh\left(d x + c\right) - {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right) - {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2} + {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2} + 3 \, {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2} - {\left(a b^{3} d f^{3} x + a b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d f^{3} x + a^{2} b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d f^{3} x + {\left(2 \, a^{3} b - a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{3} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3} + {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3} + 3 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right) - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3} - {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3} + 3 \, {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3} - {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{3} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3} + {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3} + 3 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right) - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3} - {\left({\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d e f^{2} - {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d e f^{2} - {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3} + {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3} + 3 \, {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3} - {\left(a b^{3} d^{2} e^{2} f - 2 \, a b^{3} c d e f^{2} + a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d^{2} e^{2} f - 2 \, a^{2} b^{2} c d e f^{2} + a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} + {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{3} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3} + {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3} + 3 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right) - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3} - {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3} + 3 \, {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3} - {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{3} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3} + {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3} + 3 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right) - 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3} - {\left({\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{2} b^{2} + b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d f^{3} x + {\left(a^{3} b + a b^{3}\right)} c f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d f^{3} x + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3} + {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3} + 3 \, {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3} - {\left(a b^{3} d^{2} f^{3} x^{2} + 2 \, a b^{3} d^{2} e f^{2} x + 2 \, a b^{3} c d e f^{2} - a b^{3} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} b^{2} d^{2} e f^{2} x + 2 \, a^{2} b^{2} c d e f^{2} - a^{2} b^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(2 \, a^{3} b - a b^{3}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} d^{2} e f^{2} x + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} c d e f^{2} - {\left(2 \, a^{3} b - a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - 9 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 24 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 12 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - 12 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 9 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e^{2} f + 12 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c d e f^{2} - 6 \, {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} c^{2} f^{3} + 3 \, {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f + {\left(2 \, a^{4} + a^{2} b^{2} - b^{4}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \cosh\left(d x + c\right)^{4} + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{4} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4} \cosh\left(d x + c\right) + {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \cosh\left(d x + c\right) + {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, {\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4} \cosh\left(d x + c\right) + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} b^{3} + 2 \, a^{2} b^{5} + b^{7}\right)} d^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b + 3 \, a^{4} b^{3} - b^{7}\right)} d^{4} \cosh\left(d x + c\right) - {\left(a^{5} b^{2} + 2 \, a^{3} b^{4} + a b^{6}\right)} d^{4}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(6*(a^2*b^2 + b^4)*d^2*e^2*f - 12*(a^2*b^2 + b^4)*c*d*e*f^2 + 6*(a^2*b^2 + b^4)*c^2*f^3 - 6*((a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 + b^4)*d^2*e*f^2*x + 2*(a^2*b^2 + b^4)*c*d*e*f^2 - (a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)^4 - 6*((a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 + b^4)*d^2*e*f^2*x + 2*(a^2*b^2 + b^4)*c*d*e*f^2 - (a^2*b^2 + b^4)*c^2*f^3)*sinh(d*x + c)^4 - 6*(3*(a^3*b + a*b^3)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f^2*x - (a^3*b + a*b^3)*d^2*e^2*f + 8*(a^3*b + a*b^3)*c*d*e*f^2 - 4*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)^3 - 6*(3*(a^3*b + a*b^3)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f^2*x - (a^3*b + a*b^3)*d^2*e^2*f + 8*(a^3*b + a*b^3)*c*d*e*f^2 - 4*(a^3*b + a*b^3)*c^2*f^3 + 4*((a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 + b^4)*d^2*e*f^2*x + 2*(a^2*b^2 + b^4)*c*d*e*f^2 - (a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(2*a^4 + a^2*b^2 - b^4)*d^2*e^2*f + 12*(2*a^4 + a^2*b^2 - b^4)*c*d*e*f^2 - 6*(2*a^4 + a^2*b^2 - b^4)*c^2*f^3 + 3*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2 + (2*a^4 + a^2*b^2 - b^4)*d^2*f^3)*x^2 + 6*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f + (2*a^4 + a^2*b^2 - b^4)*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(2*a^4 + a^2*b^2 - b^4)*d^2*e^2*f + 12*(2*a^4 + a^2*b^2 - b^4)*c*d*e*f^2 - 6*(2*a^4 + a^2*b^2 - b^4)*c^2*f^3 + 3*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2 + (2*a^4 + a^2*b^2 - b^4)*d^2*f^3)*x^2 + 18*((a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 + b^4)*d^2*e*f^2*x + 2*(a^2*b^2 + b^4)*c*d*e*f^2 - (a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)^2 + 6*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f + (2*a^4 + a^2*b^2 - b^4)*d^2*e*f^2)*x + 9*(3*(a^3*b + a*b^3)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f^2*x - (a^3*b + a*b^3)*d^2*e^2*f + 8*(a^3*b + a*b^3)*c*d*e*f^2 - 4*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 6*(a*b^3*f^3*cosh(d*x + c)^4 + a*b^3*f^3*sinh(d*x + c)^4 + 4*a^2*b^2*f^3*cosh(d*x + c)^3 - 4*a^2*b^2*f^3*cosh(d*x + c) + a*b^3*f^3 + 2*(2*a^3*b - a*b^3)*f^3*cosh(d*x + c)^2 + 4*(a*b^3*f^3*cosh(d*x + c) + a^2*b^2*f^3)*sinh(d*x + c)^3 + 2*(3*a*b^3*f^3*cosh(d*x + c)^2 + 6*a^2*b^2*f^3*cosh(d*x + c) + (2*a^3*b - a*b^3)*f^3)*sinh(d*x + c)^2 + 4*(a*b^3*f^3*cosh(d*x + c)^3 + 3*a^2*b^2*f^3*cosh(d*x + c)^2 - a^2*b^2*f^3 + (2*a^3*b - a*b^3)*f^3*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(a*b^3*f^3*cosh(d*x + c)^4 + a*b^3*f^3*sinh(d*x + c)^4 + 4*a^2*b^2*f^3*cosh(d*x + c)^3 - 4*a^2*b^2*f^3*cosh(d*x + c) + a*b^3*f^3 + 2*(2*a^3*b - a*b^3)*f^3*cosh(d*x + c)^2 + 4*(a*b^3*f^3*cosh(d*x + c) + a^2*b^2*f^3)*sinh(d*x + c)^3 + 2*(3*a*b^3*f^3*cosh(d*x + c)^2 + 6*a^2*b^2*f^3*cosh(d*x + c) + (2*a^3*b - a*b^3)*f^3)*sinh(d*x + c)^2 + 4*(a*b^3*f^3*cosh(d*x + c)^3 + 3*a^2*b^2*f^3*cosh(d*x + c)^2 - a^2*b^2*f^3 + (2*a^3*b - a*b^3)*f^3*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*((a^3*b + a*b^3)*d^2*f^3*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f^2*x - 3*(a^3*b + a*b^3)*d^2*e^2*f + 8*(a^3*b + a*b^3)*c*d*e*f^2 - 4*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c) + 6*((a^2*b^2 + b^4)*f^3*cosh(d*x + c)^4 + (a^2*b^2 + b^4)*f^3*sinh(d*x + c)^4 + 4*(a^3*b + a*b^3)*f^3*cosh(d*x + c)^3 + 2*(2*a^4 + a^2*b^2 - b^4)*f^3*cosh(d*x + c)^2 - 4*(a^3*b + a*b^3)*f^3*cosh(d*x + c) + (a^2*b^2 + b^4)*f^3 + 4*((a^2*b^2 + b^4)*f^3*cosh(d*x + c) + (a^3*b + a*b^3)*f^3)*sinh(d*x + c)^3 + 2*(3*(a^2*b^2 + b^4)*f^3*cosh(d*x + c)^2 + 6*(a^3*b + a*b^3)*f^3*cosh(d*x + c) + (2*a^4 + a^2*b^2 - b^4)*f^3)*sinh(d*x + c)^2 + 4*((a^2*b^2 + b^4)*f^3*cosh(d*x + c)^3 + 3*(a^3*b + a*b^3)*f^3*cosh(d*x + c)^2 + (2*a^4 + a^2*b^2 - b^4)*f^3*cosh(d*x + c) - (a^3*b + a*b^3)*f^3)*sinh(d*x + c) + (a*b^3*d*f^3*x + a*b^3*d*e*f^2 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^4 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2 + 3*(a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2 - (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 6*((a^2*b^2 + b^4)*f^3*cosh(d*x + c)^4 + (a^2*b^2 + b^4)*f^3*sinh(d*x + c)^4 + 4*(a^3*b + a*b^3)*f^3*cosh(d*x + c)^3 + 2*(2*a^4 + a^2*b^2 - b^4)*f^3*cosh(d*x + c)^2 - 4*(a^3*b + a*b^3)*f^3*cosh(d*x + c) + (a^2*b^2 + b^4)*f^3 + 4*((a^2*b^2 + b^4)*f^3*cosh(d*x + c) + (a^3*b + a*b^3)*f^3)*sinh(d*x + c)^3 + 2*(3*(a^2*b^2 + b^4)*f^3*cosh(d*x + c)^2 + 6*(a^3*b + a*b^3)*f^3*cosh(d*x + c) + (2*a^4 + a^2*b^2 - b^4)*f^3)*sinh(d*x + c)^2 + 4*((a^2*b^2 + b^4)*f^3*cosh(d*x + c)^3 + 3*(a^3*b + a*b^3)*f^3*cosh(d*x + c)^2 + (2*a^4 + a^2*b^2 - b^4)*f^3*cosh(d*x + c) - (a^3*b + a*b^3)*f^3)*sinh(d*x + c) - (a*b^3*d*f^3*x + a*b^3*d*e*f^2 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^4 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*sinh(d*x + c)^4 + 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c)^3 + 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2 + (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2 + 3*(a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^2 + 6*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c) - 4*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2 - (a*b^3*d*f^3*x + a*b^3*d*e*f^2)*cosh(d*x + c)^3 - 3*(a^2*b^2*d*f^3*x + a^2*b^2*d*e*f^2)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d*f^3*x + (2*a^3*b - a*b^3)*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(2*(a^2*b^2 + b^4)*d*e*f^2 - 2*(a^2*b^2 + b^4)*c*f^3 + 2*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^4 + 2*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*sinh(d*x + c)^4 + 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^3 + 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3 + ((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c)^2 + 4*((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3 + 3*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^2 + 6*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c) - 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3 - ((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^3 - 3*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^2 - ((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c) - (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^4 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*sinh(d*x + c)^4 + 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c)^3 + 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3 + 3*(a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^2 + 6*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c) - 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3 - (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^3 - 3*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 3*(2*(a^2*b^2 + b^4)*d*e*f^2 - 2*(a^2*b^2 + b^4)*c*f^3 + 2*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^4 + 2*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*sinh(d*x + c)^4 + 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^3 + 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3 + ((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c)^2 + 4*((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3 + 3*((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^2 + 6*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c) - 8*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3 - ((a^2*b^2 + b^4)*d*e*f^2 - (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^3 - 3*((a^3*b + a*b^3)*d*e*f^2 - (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^2 - ((2*a^4 + a^2*b^2 - b^4)*d*e*f^2 - (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c) + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^4 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*sinh(d*x + c)^4 + 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c)^3 + 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3 + (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3 + 3*(a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^2 + 6*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c) - 4*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3 - (a*b^3*d^2*e^2*f - 2*a*b^3*c*d*e*f^2 + a*b^3*c^2*f^3)*cosh(d*x + c)^3 - 3*(a^2*b^2*d^2*e^2*f - 2*a^2*b^2*c*d*e*f^2 + a^2*b^2*c^2*f^3)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d^2*e^2*f - 2*(2*a^3*b - a*b^3)*c*d*e*f^2 + (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 3*(2*(a^2*b^2 + b^4)*d*f^3*x + 2*(a^2*b^2 + b^4)*c*f^3 + 2*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^4 + 2*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*sinh(d*x + c)^4 + 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^3 + 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3 + ((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c)^2 + 4*((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3 + 3*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^2 + 6*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c) - 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3 - ((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^3 - 3*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^2 - ((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c) + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^4 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*sinh(d*x + c)^4 + 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c)^3 + 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3 + 3*(a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^2 + 6*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c) - 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3 - (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^3 - 3*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 3*(2*(a^2*b^2 + b^4)*d*f^3*x + 2*(a^2*b^2 + b^4)*c*f^3 + 2*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^4 + 2*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*sinh(d*x + c)^4 + 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^3 + 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3 + ((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c)^2 + 4*((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3 + 3*((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^2 + 6*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c) - 8*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3 - ((a^2*b^2 + b^4)*d*f^3*x + (a^2*b^2 + b^4)*c*f^3)*cosh(d*x + c)^3 - 3*((a^3*b + a*b^3)*d*f^3*x + (a^3*b + a*b^3)*c*f^3)*cosh(d*x + c)^2 - ((2*a^4 + a^2*b^2 - b^4)*d*f^3*x + (2*a^4 + a^2*b^2 - b^4)*c*f^3)*cosh(d*x + c))*sinh(d*x + c) - (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^4 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*sinh(d*x + c)^4 + 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c)^3 + 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3 + (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + 2*((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3 + 3*(a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^2 + 6*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c) - 4*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3 - (a*b^3*d^2*f^3*x^2 + 2*a*b^3*d^2*e*f^2*x + 2*a*b^3*c*d*e*f^2 - a*b^3*c^2*f^3)*cosh(d*x + c)^3 - 3*(a^2*b^2*d^2*f^3*x^2 + 2*a^2*b^2*d^2*e*f^2*x + 2*a^2*b^2*c*d*e*f^2 - a^2*b^2*c^2*f^3)*cosh(d*x + c)^2 - ((2*a^3*b - a*b^3)*d^2*f^3*x^2 + 2*(2*a^3*b - a*b^3)*d^2*e*f^2*x + 2*(2*a^3*b - a*b^3)*c*d*e*f^2 - (2*a^3*b - a*b^3)*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(3*(a^3*b + a*b^3)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f^2*x - 9*(a^3*b + a*b^3)*d^2*e^2*f + 24*(a^3*b + a*b^3)*c*d*e*f^2 - 12*(a^3*b + a*b^3)*c^2*f^3 - 12*((a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^2*b^2 + b^4)*d^2*e*f^2*x + 2*(a^2*b^2 + b^4)*c*d*e*f^2 - (a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)^3 - 9*(3*(a^3*b + a*b^3)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f^2*x - (a^3*b + a*b^3)*d^2*e^2*f + 8*(a^3*b + a*b^3)*c*d*e*f^2 - 4*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)^2 - 2*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(2*a^4 + a^2*b^2 - b^4)*d^2*e^2*f + 12*(2*a^4 + a^2*b^2 - b^4)*c*d*e*f^2 - 6*(2*a^4 + a^2*b^2 - b^4)*c^2*f^3 + 3*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2 + (2*a^4 + a^2*b^2 - b^4)*d^2*f^3)*x^2 + 6*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f + (2*a^4 + a^2*b^2 - b^4)*d^2*e*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b^3 + 2*a^2*b^5 + b^7)*d^4*cosh(d*x + c)^4 + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^4*sinh(d*x + c)^4 + 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4*cosh(d*x + c)^3 + 2*(2*a^6*b + 3*a^4*b^3 - b^7)*d^4*cosh(d*x + c)^2 - 4*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4*cosh(d*x + c) + (a^4*b^3 + 2*a^2*b^5 + b^7)*d^4 + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^4*cosh(d*x + c) + (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4)*sinh(d*x + c)^3 + 2*(3*(a^4*b^3 + 2*a^2*b^5 + b^7)*d^4*cosh(d*x + c)^2 + 6*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4*cosh(d*x + c) + (2*a^6*b + 3*a^4*b^3 - b^7)*d^4)*sinh(d*x + c)^2 + 4*((a^4*b^3 + 2*a^2*b^5 + b^7)*d^4*cosh(d*x + c)^3 + 3*(a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4*cosh(d*x + c)^2 + (2*a^6*b + 3*a^4*b^3 - b^7)*d^4*cosh(d*x + c) - (a^5*b^2 + 2*a^3*b^4 + a*b^6)*d^4)*sinh(d*x + c))","C",0
333,1,1976,0,0.494635," ","integrate((f*x+e)^3*cosh(d*x+c)*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b d^{3} f^{3} x^{3} + 2 \, b d^{3} e^{3} + 6 \, b d^{2} e^{2} f + 12 \, b d e f^{2} + 12 \, b f^{3} + 6 \, {\left(b d^{3} e f^{2} + b d^{2} f^{3}\right)} x^{2} - 2 \, {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} - 3 \, b d^{2} e^{2} f + 6 \, b d e f^{2} - 6 \, b f^{3} + 3 \, {\left(b d^{3} e f^{2} - b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, b d^{2} e f^{2} + 2 \, b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} - 3 \, b d^{2} e^{2} f + 6 \, b d e f^{2} - 6 \, b f^{3} + 3 \, {\left(b d^{3} e f^{2} - b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, b d^{2} e f^{2} + 2 \, b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b d^{3} e^{2} f + 2 \, b d^{2} e f^{2} + 2 \, b d f^{3}\right)} x - {\left(a d^{4} f^{3} x^{4} + 4 \, a d^{4} e f^{2} x^{3} + 6 \, a d^{4} e^{2} f x^{2} + 4 \, a d^{4} e^{3} x + 8 \, a c d^{3} e^{3} - 12 \, a c^{2} d^{2} e^{2} f + 8 \, a c^{3} d e f^{2} - 2 \, a c^{4} f^{3}\right)} \cosh\left(d x + c\right) + 12 \, {\left({\left(a d^{2} f^{3} x^{2} + 2 \, a d^{2} e f^{2} x + a d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(a d^{2} f^{3} x^{2} + 2 \, a d^{2} e f^{2} x + a d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left({\left(a d^{2} f^{3} x^{2} + 2 \, a d^{2} e f^{2} x + a d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(a d^{2} f^{3} x^{2} + 2 \, a d^{2} e f^{2} x + a d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 \, {\left({\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 4 \, {\left({\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 4 \, {\left({\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} + a c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} + a c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left({\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} + a c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} + a c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 24 \, {\left(a f^{3} \cosh\left(d x + c\right) + a f^{3} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left(a f^{3} \cosh\left(d x + c\right) + a f^{3} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left({\left(a d f^{3} x + a d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(a d f^{3} x + a d e f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left({\left(a d f^{3} x + a d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(a d f^{3} x + a d e f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - {\left(a d^{4} f^{3} x^{4} + 4 \, a d^{4} e f^{2} x^{3} + 6 \, a d^{4} e^{2} f x^{2} + 4 \, a d^{4} e^{3} x + 8 \, a c d^{3} e^{3} - 12 \, a c^{2} d^{2} e^{2} f + 8 \, a c^{3} d e f^{2} - 2 \, a c^{4} f^{3} + 4 \, {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} - 3 \, b d^{2} e^{2} f + 6 \, b d e f^{2} - 6 \, b f^{3} + 3 \, {\left(b d^{3} e f^{2} - b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, b d^{2} e f^{2} + 2 \, b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left(b^{2} d^{4} \cosh\left(d x + c\right) + b^{2} d^{4} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/4*(2*b*d^3*f^3*x^3 + 2*b*d^3*e^3 + 6*b*d^2*e^2*f + 12*b*d*e*f^2 + 12*b*f^3 + 6*(b*d^3*e*f^2 + b*d^2*f^3)*x^2 - 2*(b*d^3*f^3*x^3 + b*d^3*e^3 - 3*b*d^2*e^2*f + 6*b*d*e*f^2 - 6*b*f^3 + 3*(b*d^3*e*f^2 - b*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*b*d^2*e*f^2 + 2*b*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b*d^3*f^3*x^3 + b*d^3*e^3 - 3*b*d^2*e^2*f + 6*b*d*e*f^2 - 6*b*f^3 + 3*(b*d^3*e*f^2 - b*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*b*d^2*e*f^2 + 2*b*d*f^3)*x)*sinh(d*x + c)^2 + 6*(b*d^3*e^2*f + 2*b*d^2*e*f^2 + 2*b*d*f^3)*x - (a*d^4*f^3*x^4 + 4*a*d^4*e*f^2*x^3 + 6*a*d^4*e^2*f*x^2 + 4*a*d^4*e^3*x + 8*a*c*d^3*e^3 - 12*a*c^2*d^2*e^2*f + 8*a*c^3*d*e*f^2 - 2*a*c^4*f^3)*cosh(d*x + c) + 12*((a*d^2*f^3*x^2 + 2*a*d^2*e*f^2*x + a*d^2*e^2*f)*cosh(d*x + c) + (a*d^2*f^3*x^2 + 2*a*d^2*e*f^2*x + a*d^2*e^2*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*((a*d^2*f^3*x^2 + 2*a*d^2*e*f^2*x + a*d^2*e^2*f)*cosh(d*x + c) + (a*d^2*f^3*x^2 + 2*a*d^2*e*f^2*x + a*d^2*e^2*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 4*((a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*cosh(d*x + c) + (a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 4*((a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*cosh(d*x + c) + (a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 4*((a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + 3*a*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 + a*c^3*f^3)*cosh(d*x + c) + (a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + 3*a*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 + a*c^3*f^3)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*((a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + 3*a*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 + a*c^3*f^3)*cosh(d*x + c) + (a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + 3*a*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 + a*c^3*f^3)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 24*(a*f^3*cosh(d*x + c) + a*f^3*sinh(d*x + c))*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*(a*f^3*cosh(d*x + c) + a*f^3*sinh(d*x + c))*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*((a*d*f^3*x + a*d*e*f^2)*cosh(d*x + c) + (a*d*f^3*x + a*d*e*f^2)*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*((a*d*f^3*x + a*d*e*f^2)*cosh(d*x + c) + (a*d*f^3*x + a*d*e*f^2)*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - (a*d^4*f^3*x^4 + 4*a*d^4*e*f^2*x^3 + 6*a*d^4*e^2*f*x^2 + 4*a*d^4*e^3*x + 8*a*c*d^3*e^3 - 12*a*c^2*d^2*e^2*f + 8*a*c^3*d*e*f^2 - 2*a*c^4*f^3 + 4*(b*d^3*f^3*x^3 + b*d^3*e^3 - 3*b*d^2*e^2*f + 6*b*d*e*f^2 - 6*b*f^3 + 3*(b*d^3*e*f^2 - b*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*b*d^2*e*f^2 + 2*b*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^2*d^4*cosh(d*x + c) + b^2*d^4*sinh(d*x + c))","C",0
334,1,1265,0,0.466929," ","integrate((f*x+e)^2*cosh(d*x+c)*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, b d^{2} f^{2} x^{2} + 3 \, b d^{2} e^{2} + 6 \, b d e f + 6 \, b f^{2} - 3 \, {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} - 2 \, b d e f + 2 \, b f^{2} + 2 \, {\left(b d^{2} e f - b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} - 2 \, b d e f + 2 \, b f^{2} + 2 \, {\left(b d^{2} e f - b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b d^{2} e f + b d f^{2}\right)} x - 2 \, {\left(a d^{3} f^{2} x^{3} + 3 \, a d^{3} e f x^{2} + 3 \, a d^{3} e^{2} x + 6 \, a c d^{2} e^{2} - 6 \, a c^{2} d e f + 2 \, a c^{3} f^{2}\right)} \cosh\left(d x + c\right) + 12 \, {\left({\left(a d f^{2} x + a d e f\right)} \cosh\left(d x + c\right) + {\left(a d f^{2} x + a d e f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left({\left(a d f^{2} x + a d e f\right)} \cosh\left(d x + c\right) + {\left(a d f^{2} x + a d e f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 6 \, {\left({\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 6 \, {\left({\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 6 \, {\left({\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + 2 \, a c d e f - a c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + 2 \, a c d e f - a c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left({\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + 2 \, a c d e f - a c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + 2 \, a c d e f - a c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left(a f^{2} \cosh\left(d x + c\right) + a f^{2} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a f^{2} \cosh\left(d x + c\right) + a f^{2} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(a d^{3} f^{2} x^{3} + 3 \, a d^{3} e f x^{2} + 3 \, a d^{3} e^{2} x + 6 \, a c d^{2} e^{2} - 6 \, a c^{2} d e f + 2 \, a c^{3} f^{2} + 3 \, {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} - 2 \, b d e f + 2 \, b f^{2} + 2 \, {\left(b d^{2} e f - b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left(b^{2} d^{3} \cosh\left(d x + c\right) + b^{2} d^{3} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/6*(3*b*d^2*f^2*x^2 + 3*b*d^2*e^2 + 6*b*d*e*f + 6*b*f^2 - 3*(b*d^2*f^2*x^2 + b*d^2*e^2 - 2*b*d*e*f + 2*b*f^2 + 2*(b*d^2*e*f - b*d*f^2)*x)*cosh(d*x + c)^2 - 3*(b*d^2*f^2*x^2 + b*d^2*e^2 - 2*b*d*e*f + 2*b*f^2 + 2*(b*d^2*e*f - b*d*f^2)*x)*sinh(d*x + c)^2 + 6*(b*d^2*e*f + b*d*f^2)*x - 2*(a*d^3*f^2*x^3 + 3*a*d^3*e*f*x^2 + 3*a*d^3*e^2*x + 6*a*c*d^2*e^2 - 6*a*c^2*d*e*f + 2*a*c^3*f^2)*cosh(d*x + c) + 12*((a*d*f^2*x + a*d*e*f)*cosh(d*x + c) + (a*d*f^2*x + a*d*e*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*((a*d*f^2*x + a*d*e*f)*cosh(d*x + c) + (a*d*f^2*x + a*d*e*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 6*((a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*cosh(d*x + c) + (a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 6*((a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*cosh(d*x + c) + (a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 6*((a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + 2*a*c*d*e*f - a*c^2*f^2)*cosh(d*x + c) + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + 2*a*c*d*e*f - a*c^2*f^2)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 6*((a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + 2*a*c*d*e*f - a*c^2*f^2)*cosh(d*x + c) + (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + 2*a*c*d*e*f - a*c^2*f^2)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 12*(a*f^2*cosh(d*x + c) + a*f^2*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(a*f^2*cosh(d*x + c) + a*f^2*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(a*d^3*f^2*x^3 + 3*a*d^3*e*f*x^2 + 3*a*d^3*e^2*x + 6*a*c*d^2*e^2 - 6*a*c^2*d*e*f + 2*a*c^3*f^2 + 3*(b*d^2*f^2*x^2 + b*d^2*e^2 - 2*b*d*e*f + 2*b*f^2 + 2*(b*d^2*e*f - b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^2*d^3*cosh(d*x + c) + b^2*d^3*sinh(d*x + c))","C",0
335,1,692,0,0.493062," ","integrate((f*x+e)*cosh(d*x+c)*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{b d f x + b d e - {\left(b d f x + b d e - b f\right)} \cosh\left(d x + c\right)^{2} - {\left(b d f x + b d e - b f\right)} \sinh\left(d x + c\right)^{2} + b f - {\left(a d^{2} f x^{2} + 2 \, a d^{2} e x + 4 \, a c d e - 2 \, a c^{2} f\right)} \cosh\left(d x + c\right) + 2 \, {\left(a f \cosh\left(d x + c\right) + a f \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(a f \cosh\left(d x + c\right) + a f \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left({\left(a d e - a c f\right)} \cosh\left(d x + c\right) + {\left(a d e - a c f\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left(a d e - a c f\right)} \cosh\left(d x + c\right) + {\left(a d e - a c f\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left(a d f x + a c f\right)} \cosh\left(d x + c\right) + {\left(a d f x + a c f\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a d f x + a c f\right)} \cosh\left(d x + c\right) + {\left(a d f x + a c f\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(a d^{2} f x^{2} + 2 \, a d^{2} e x + 4 \, a c d e - 2 \, a c^{2} f + 2 \, {\left(b d f x + b d e - b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(b^{2} d^{2} \cosh\left(d x + c\right) + b^{2} d^{2} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(b*d*f*x + b*d*e - (b*d*f*x + b*d*e - b*f)*cosh(d*x + c)^2 - (b*d*f*x + b*d*e - b*f)*sinh(d*x + c)^2 + b*f - (a*d^2*f*x^2 + 2*a*d^2*e*x + 4*a*c*d*e - 2*a*c^2*f)*cosh(d*x + c) + 2*(a*f*cosh(d*x + c) + a*f*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(a*f*cosh(d*x + c) + a*f*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*((a*d*e - a*c*f)*cosh(d*x + c) + (a*d*e - a*c*f)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*((a*d*e - a*c*f)*cosh(d*x + c) + (a*d*e - a*c*f)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*((a*d*f*x + a*c*f)*cosh(d*x + c) + (a*d*f*x + a*c*f)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*((a*d*f*x + a*c*f)*cosh(d*x + c) + (a*d*f*x + a*c*f)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (a*d^2*f*x^2 + 2*a*d^2*e*x + 4*a*c*d*e - 2*a*c^2*f + 2*(b*d*f*x + b*d*e - b*f)*cosh(d*x + c))*sinh(d*x + c))/(b^2*d^2*cosh(d*x + c) + b^2*d^2*sinh(d*x + c))","B",0
336,1,132,0,0.488162," ","integrate(cosh(d*x+c)*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a d x \cosh\left(d x + c\right) + b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} - 2 \, {\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(a d x + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - b}{2 \, {\left(b^{2} d \cosh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(2*a*d*x*cosh(d*x + c) + b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 - 2*(a*cosh(d*x + c) + a*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(a*d*x + b*cosh(d*x + c))*sinh(d*x + c) - b)/(b^2*d*cosh(d*x + c) + b^2*d*sinh(d*x + c))","B",0
337,0,0,0,0.459912," ","integrate(cosh(d*x+c)*sinh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right) \sinh\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)*sinh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
338,1,3847,0,0.592823," ","integrate((f*x+e)^3*cosh(d*x+c)^2*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} + 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} + 3 \, b^{2} f^{3} - {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} - {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a b d^{3} f^{3} x^{3} + 4 \, a b d^{3} e^{3} - 12 \, a b d^{2} e^{2} f + 24 \, a b d e f^{2} - 24 \, a b f^{3} + 12 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 12 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x - {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} + b^{2} d^{2} f^{3}\right)} x^{2} - 4 \, {\left({\left(2 \, a^{2} + b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(2 \, a^{2} + b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(2 \, a^{2} + b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(2 \, a^{2} + b^{2}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(2 \, a^{2} + b^{2}\right)} d^{4} f^{3} x^{4} + 8 \, {\left(2 \, a^{2} + b^{2}\right)} d^{4} e f^{2} x^{3} + 12 \, {\left(2 \, a^{2} + b^{2}\right)} d^{4} e^{2} f x^{2} + 8 \, {\left(2 \, a^{2} + b^{2}\right)} d^{4} e^{3} x + 3 \, {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 24 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 96 \, {\left({\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + a b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + a b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + a b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 96 \, {\left({\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + a b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + a b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d^{2} f^{3} x^{2} + 2 \, a b d^{2} e f^{2} x + a b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 32 \, {\left({\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 32 \, {\left({\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 32 \, {\left({\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 32 \, {\left({\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 192 \, {\left(a b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b f^{3} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 192 \, {\left(a b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b f^{3} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 192 \, {\left({\left(a b d f^{3} x + a b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d f^{3} x + a b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 192 \, {\left({\left(a b d f^{3} x + a b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d f^{3} x + a b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d f^{3} x + a b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f + 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x + 16 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} + 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right) + 4 \, {\left(4 \, a b d^{3} f^{3} x^{3} + 4 \, a b d^{3} e^{3} + 12 \, a b d^{2} e^{2} f + 24 \, a b d e f^{2} + 24 \, a b f^{3} - {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(a b d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 12 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(a b d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x - 2 \, {\left({\left(2 \, a^{2} + b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(2 \, a^{2} + b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(2 \, a^{2} + b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(2 \, a^{2} + b^{2}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{32 \, {\left(b^{3} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d^{4} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/32*(4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 + 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 + 3*b^2*f^3 - (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c)^4 - (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*sinh(d*x + c)^4 + 16*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^3 + 4*(4*a*b*d^3*f^3*x^3 + 4*a*b*d^3*e^3 - 12*a*b*d^2*e^2*f + 24*a*b*d*e*f^2 - 24*a*b*f^3 + 12*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 12*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x - (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(2*b^2*d^3*e*f^2 + b^2*d^2*f^3)*x^2 - 4*((2*a^2 + b^2)*d^4*f^3*x^4 + 4*(2*a^2 + b^2)*d^4*e*f^2*x^3 + 6*(2*a^2 + b^2)*d^4*e^2*f*x^2 + 4*(2*a^2 + b^2)*d^4*e^3*x)*cosh(d*x + c)^2 - 2*(2*(2*a^2 + b^2)*d^4*f^3*x^4 + 8*(2*a^2 + b^2)*d^4*e*f^2*x^3 + 12*(2*a^2 + b^2)*d^4*e^2*f*x^2 + 8*(2*a^2 + b^2)*d^4*e^3*x + 3*(4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c)^2 - 24*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 96*((a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + a*b*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + a*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + a*b*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 96*((a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + a*b*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + a*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d^2*f^3*x^2 + 2*a*b*d^2*e*f^2*x + a*b*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 32*((a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 32*((a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 32*((a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 32*((a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 192*(a*b*f^3*cosh(d*x + c)^2 + 2*a*b*f^3*cosh(d*x + c)*sinh(d*x + c) + a*b*f^3*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 192*(a*b*f^3*cosh(d*x + c)^2 + 2*a*b*f^3*cosh(d*x + c)*sinh(d*x + c) + a*b*f^3*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 192*((a*b*d*f^3*x + a*b*d*e*f^2)*cosh(d*x + c)^2 + 2*(a*b*d*f^3*x + a*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d*f^3*x + a*b*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 192*((a*b*d*f^3*x + a*b*d*e*f^2)*cosh(d*x + c)^2 + 2*(a*b*d*f^3*x + a*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d*f^3*x + a*b*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(2*b^2*d^3*e^2*f + 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x + 16*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 + 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 + 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f + 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c) + 4*(4*a*b*d^3*f^3*x^3 + 4*a*b*d^3*e^3 + 12*a*b*d^2*e^2*f + 24*a*b*d*e*f^2 + 24*a*b*f^3 - (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c)^3 + 12*(a*b*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 12*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^2 + 12*(a*b*d^3*e^2*f + 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x - 2*((2*a^2 + b^2)*d^4*f^3*x^4 + 4*(2*a^2 + b^2)*d^4*e*f^2*x^3 + 6*(2*a^2 + b^2)*d^4*e^2*f*x^2 + 4*(2*a^2 + b^2)*d^4*e^3*x)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d^4*cosh(d*x + c)^2 + 2*b^3*d^4*cosh(d*x + c)*sinh(d*x + c) + b^3*d^4*sinh(d*x + c)^2)","C",0
339,1,2410,0,0.556834," ","integrate((f*x+e)^2*cosh(d*x+c)^2*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, b^{2} d^{2} f^{2} x^{2} + 6 \, b^{2} d^{2} e^{2} + 6 \, b^{2} d e f - 3 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} + 3 \, b^{2} f^{2} + 24 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(2 \, a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e^{2} - 4 \, a b d e f + 4 \, a b f^{2} + 4 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x - {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left({\left(2 \, a^{2} + b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(2 \, a^{2} + b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(2 \, a^{2} + b^{2}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(4 \, {\left(2 \, a^{2} + b^{2}\right)} d^{3} f^{2} x^{3} + 12 \, {\left(2 \, a^{2} + b^{2}\right)} d^{3} e f x^{2} + 12 \, {\left(2 \, a^{2} + b^{2}\right)} d^{3} e^{2} x + 9 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 36 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 96 \, {\left({\left(a b d f^{2} x + a b d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d f^{2} x + a b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d f^{2} x + a b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 96 \, {\left({\left(a b d f^{2} x + a b d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d f^{2} x + a b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d f^{2} x + a b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 48 \, {\left({\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 48 \, {\left({\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 48 \, {\left({\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 48 \, {\left({\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 96 \, {\left(a b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b f^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 96 \, {\left(a b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b f^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(2 \, b^{2} d^{2} e f + b^{2} d f^{2}\right)} x + 24 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} + 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 4 \, {\left(6 \, a b d^{2} f^{2} x^{2} + 6 \, a b d^{2} e^{2} + 12 \, a b d e f + 12 \, a b f^{2} - 3 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 18 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(a b d^{2} e f + a b d f^{2}\right)} x - 4 \, {\left({\left(2 \, a^{2} + b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(2 \, a^{2} + b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(2 \, a^{2} + b^{2}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{48 \, {\left(b^{3} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d^{3} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/48*(6*b^2*d^2*f^2*x^2 + 6*b^2*d^2*e^2 + 6*b^2*d*e*f - 3*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c)^4 - 3*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*sinh(d*x + c)^4 + 3*b^2*f^2 + 24*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^3 + 12*(2*a*b*d^2*f^2*x^2 + 2*a*b*d^2*e^2 - 4*a*b*d*e*f + 4*a*b*f^2 + 4*(a*b*d^2*e*f - a*b*d*f^2)*x - (2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*((2*a^2 + b^2)*d^3*f^2*x^3 + 3*(2*a^2 + b^2)*d^3*e*f*x^2 + 3*(2*a^2 + b^2)*d^3*e^2*x)*cosh(d*x + c)^2 - 2*(4*(2*a^2 + b^2)*d^3*f^2*x^3 + 12*(2*a^2 + b^2)*d^3*e*f*x^2 + 12*(2*a^2 + b^2)*d^3*e^2*x + 9*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c)^2 - 36*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 96*((a*b*d*f^2*x + a*b*d*e*f)*cosh(d*x + c)^2 + 2*(a*b*d*f^2*x + a*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d*f^2*x + a*b*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 96*((a*b*d*f^2*x + a*b*d*e*f)*cosh(d*x + c)^2 + 2*(a*b*d*f^2*x + a*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d*f^2*x + a*b*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 48*((a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 48*((a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 48*((a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 48*((a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 96*(a*b*f^2*cosh(d*x + c)^2 + 2*a*b*f^2*cosh(d*x + c)*sinh(d*x + c) + a*b*f^2*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 96*(a*b*f^2*cosh(d*x + c)^2 + 2*a*b*f^2*cosh(d*x + c)*sinh(d*x + c) + a*b*f^2*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(2*b^2*d^2*e*f + b^2*d*f^2)*x + 24*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 + 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c) + 4*(6*a*b*d^2*f^2*x^2 + 6*a*b*d^2*e^2 + 12*a*b*d*e*f + 12*a*b*f^2 - 3*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c)^3 + 18*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^2 + 12*(a*b*d^2*e*f + a*b*d*f^2)*x - 4*((2*a^2 + b^2)*d^3*f^2*x^3 + 3*(2*a^2 + b^2)*d^3*e*f*x^2 + 3*(2*a^2 + b^2)*d^3*e^2*x)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d^3*cosh(d*x + c)^2 + 2*b^3*d^3*cosh(d*x + c)*sinh(d*x + c) + b^3*d^3*sinh(d*x + c)^2)","C",0
340,1,1284,0,0.543353," ","integrate((f*x+e)*cosh(d*x+c)^2*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b^{2} d f x - {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)^{4} - {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, b^{2} d e + 8 \, {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b d f x + 2 \, a b d e - 2 \, a b f - {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{2} f - 4 \, {\left({\left(2 \, a^{2} + b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(2 \, a^{2} + b^{2}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(2 \, a^{2} + b^{2}\right)} d^{2} f x^{2} + 4 \, {\left(2 \, a^{2} + b^{2}\right)} d^{2} e x + 3 \, {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)^{2} - 12 \, {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 16 \, {\left(a b f \cosh\left(d x + c\right)^{2} + 2 \, a b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b f \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 16 \, {\left(a b f \cosh\left(d x + c\right)^{2} + 2 \, a b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b f \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 16 \, {\left({\left(a b d e - a b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d e - a b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d e - a b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 16 \, {\left({\left(a b d e - a b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d e - a b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d e - a b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 16 \, {\left({\left(a b d f x + a b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d f x + a b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d f x + a b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 16 \, {\left({\left(a b d f x + a b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b d f x + a b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b d f x + a b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 8 \, {\left(a b d f x + a b d e + a b f\right)} \cosh\left(d x + c\right) + 4 \, {\left(2 \, a b d f x + 2 \, a b d e - {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, a b f + 6 \, {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(2 \, a^{2} + b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(2 \, a^{2} + b^{2}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left(b^{3} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d^{2} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/16*(2*b^2*d*f*x - (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c)^4 - (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*sinh(d*x + c)^4 + 2*b^2*d*e + 8*(a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c)^3 + 4*(2*a*b*d*f*x + 2*a*b*d*e - 2*a*b*f - (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c))*sinh(d*x + c)^3 + b^2*f - 4*((2*a^2 + b^2)*d^2*f*x^2 + 2*(2*a^2 + b^2)*d^2*e*x)*cosh(d*x + c)^2 - 2*(2*(2*a^2 + b^2)*d^2*f*x^2 + 4*(2*a^2 + b^2)*d^2*e*x + 3*(2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c)^2 - 12*(a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c))*sinh(d*x + c)^2 + 16*(a*b*f*cosh(d*x + c)^2 + 2*a*b*f*cosh(d*x + c)*sinh(d*x + c) + a*b*f*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 16*(a*b*f*cosh(d*x + c)^2 + 2*a*b*f*cosh(d*x + c)*sinh(d*x + c) + a*b*f*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 16*((a*b*d*e - a*b*c*f)*cosh(d*x + c)^2 + 2*(a*b*d*e - a*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d*e - a*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 16*((a*b*d*e - a*b*c*f)*cosh(d*x + c)^2 + 2*(a*b*d*e - a*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d*e - a*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 16*((a*b*d*f*x + a*b*c*f)*cosh(d*x + c)^2 + 2*(a*b*d*f*x + a*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d*f*x + a*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 16*((a*b*d*f*x + a*b*c*f)*cosh(d*x + c)^2 + 2*(a*b*d*f*x + a*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b*d*f*x + a*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 8*(a*b*d*f*x + a*b*d*e + a*b*f)*cosh(d*x + c) + 4*(2*a*b*d*f*x + 2*a*b*d*e - (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c)^3 + 2*a*b*f + 6*(a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c)^2 - 2*((2*a^2 + b^2)*d^2*f*x^2 + 2*(2*a^2 + b^2)*d^2*e*x)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d^2*cosh(d*x + c)^2 + 2*b^3*d^2*cosh(d*x + c)*sinh(d*x + c) + b^3*d^2*sinh(d*x + c)^2)","B",0
341,1,446,0,0.485221," ","integrate(cosh(d*x+c)^2*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{4} + b^{2} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 4 \, a b \cosh\left(d x + c\right)^{3} + 4 \, {\left(b^{2} \cosh\left(d x + c\right) - a b\right)} \sinh\left(d x + c\right)^{3} - 4 \, a b \cosh\left(d x + c\right) + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} + b^{2}\right)} d x - 6 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2}\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) - b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{2} + b^{2}\right)} d x \cosh\left(d x + c\right) - 3 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)}{8 \, {\left(b^{3} d \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/8*(b^2*cosh(d*x + c)^4 + b^2*sinh(d*x + c)^4 + 4*(2*a^2 + b^2)*d*x*cosh(d*x + c)^2 - 4*a*b*cosh(d*x + c)^3 + 4*(b^2*cosh(d*x + c) - a*b)*sinh(d*x + c)^3 - 4*a*b*cosh(d*x + c) + 2*(3*b^2*cosh(d*x + c)^2 + 2*(2*a^2 + b^2)*d*x - 6*a*b*cosh(d*x + c))*sinh(d*x + c)^2 + 8*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) - b^2 + 4*(b^2*cosh(d*x + c)^3 + 2*(2*a^2 + b^2)*d*x*cosh(d*x + c) - 3*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c))/(b^3*d*cosh(d*x + c)^2 + 2*b^3*d*cosh(d*x + c)*sinh(d*x + c) + b^3*d*sinh(d*x + c)^2)","B",0
342,0,0,0,0.492466," ","integrate(cosh(d*x+c)^2*sinh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)^2*sinh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
343,1,7980,0,0.627171," ","integrate((f*x+e)^3*cosh(d*x+c)^3*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{36 \, b^{3} d^{3} f^{3} x^{3} + 36 \, b^{3} d^{3} e^{3} + 36 \, b^{3} d^{2} e^{2} f + 24 \, b^{3} d e f^{2} - 4 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{6} + 8 \, b^{3} f^{3} + 27 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(36 \, a b^{2} d^{3} f^{3} x^{3} + 36 \, a b^{2} d^{3} e^{3} - 54 \, a b^{2} d^{2} e^{2} f + 54 \, a b^{2} d e f^{2} - 27 \, a b^{2} f^{3} + 54 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 54 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x - 8 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 108 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(36 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} f^{3} x^{3} + 36 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{3} - 108 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} f + 216 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f^{2} - 216 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{3} + 108 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 20 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 108 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{3}\right)} x - 45 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 216 \, {\left({\left(a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{3} + a b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{3} + a b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c^{4} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(108 \, {\left(a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 432 \, {\left(a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 648 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 432 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{3} x + 864 \, {\left(a^{3} + a b^{2}\right)} c d^{3} e^{3} - 1296 \, {\left(a^{3} + a b^{2}\right)} c^{2} d^{2} e^{2} f + 864 \, {\left(a^{3} + a b^{2}\right)} c^{3} d e f^{2} - 216 \, {\left(a^{3} + a b^{2}\right)} c^{4} f^{3} + 40 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 135 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 216 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 36 \, {\left(3 \, b^{3} d^{3} e f^{2} + b^{3} d^{2} f^{3}\right)} x^{2} + 108 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(18 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} f^{3} x^{3} + 18 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{3} + 54 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} f + 108 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f^{2} - 10 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 108 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{3} + 45 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 54 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{3}\right)} x^{2} - 108 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 54 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{3}\right)} x - 108 \, {\left({\left(a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{3} + a b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{3} + a b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c^{4} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left(9 \, b^{3} d^{3} e^{2} f + 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x + 27 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} + 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} + 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} + a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f + 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) + 2592 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2592 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 864 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 864 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 864 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 864 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 5184 \, {\left({\left(a^{3} + a b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} + a b^{2}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f^{3} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 5184 \, {\left({\left(a^{3} + a b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} + a b^{2}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f^{3} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 5184 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d f^{3} x + {\left(a^{3} + a b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{3} x + {\left(a^{3} + a b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{3} x + {\left(a^{3} + a b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d f^{3} x + {\left(a^{3} + a b^{2}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 5184 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d f^{3} x + {\left(a^{3} + a b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{3} x + {\left(a^{3} + a b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{3} x + {\left(a^{3} + a b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d f^{3} x + {\left(a^{3} + a b^{2}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 3 \, {\left(36 \, a b^{2} d^{3} f^{3} x^{3} + 36 \, a b^{2} d^{3} e^{3} + 54 \, a b^{2} d^{2} e^{2} f + 54 \, a b^{2} d e f^{2} + 27 \, a b^{2} f^{3} - 8 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 45 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 144 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 54 \, {\left(2 \, a b^{2} d^{3} e f^{2} + a b^{2} d^{2} f^{3}\right)} x^{2} - 216 \, {\left({\left(a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{3} + a b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{3} + a b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c^{4} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 54 \, {\left(2 \, a b^{2} d^{3} e^{2} f + 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x + 72 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{864 \, {\left(b^{4} d^{4} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d^{4} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d^{4} \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"-1/864*(36*b^3*d^3*f^3*x^3 + 36*b^3*d^3*e^3 + 36*b^3*d^2*e^2*f + 24*b^3*d*e*f^2 - 4*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^6 - 4*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*sinh(d*x + c)^6 + 8*b^3*f^3 + 27*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^5 + 3*(36*a*b^2*d^3*f^3*x^3 + 36*a*b^2*d^3*e^3 - 54*a*b^2*d^2*e^2*f + 54*a*b^2*d*e*f^2 - 27*a*b^2*f^3 + 54*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 54*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x - 8*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 108*((4*a^2*b + 3*b^3)*d^3*f^3*x^3 + (4*a^2*b + 3*b^3)*d^3*e^3 - 3*(4*a^2*b + 3*b^3)*d^2*e^2*f + 6*(4*a^2*b + 3*b^3)*d*e*f^2 - 6*(4*a^2*b + 3*b^3)*f^3 + 3*((4*a^2*b + 3*b^3)*d^3*e*f^2 - (4*a^2*b + 3*b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + 3*b^3)*d^3*e^2*f - 2*(4*a^2*b + 3*b^3)*d^2*e*f^2 + 2*(4*a^2*b + 3*b^3)*d*f^3)*x)*cosh(d*x + c)^4 - 3*(36*(4*a^2*b + 3*b^3)*d^3*f^3*x^3 + 36*(4*a^2*b + 3*b^3)*d^3*e^3 - 108*(4*a^2*b + 3*b^3)*d^2*e^2*f + 216*(4*a^2*b + 3*b^3)*d*e*f^2 - 216*(4*a^2*b + 3*b^3)*f^3 + 108*((4*a^2*b + 3*b^3)*d^3*e*f^2 - (4*a^2*b + 3*b^3)*d^2*f^3)*x^2 + 20*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^2 + 108*((4*a^2*b + 3*b^3)*d^3*e^2*f - 2*(4*a^2*b + 3*b^3)*d^2*e*f^2 + 2*(4*a^2*b + 3*b^3)*d*f^3)*x - 45*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^4 - 216*((a^3 + a*b^2)*d^4*f^3*x^4 + 4*(a^3 + a*b^2)*d^4*e*f^2*x^3 + 6*(a^3 + a*b^2)*d^4*e^2*f*x^2 + 4*(a^3 + a*b^2)*d^4*e^3*x + 8*(a^3 + a*b^2)*c*d^3*e^3 - 12*(a^3 + a*b^2)*c^2*d^2*e^2*f + 8*(a^3 + a*b^2)*c^3*d*e*f^2 - 2*(a^3 + a*b^2)*c^4*f^3)*cosh(d*x + c)^3 - 2*(108*(a^3 + a*b^2)*d^4*f^3*x^4 + 432*(a^3 + a*b^2)*d^4*e*f^2*x^3 + 648*(a^3 + a*b^2)*d^4*e^2*f*x^2 + 432*(a^3 + a*b^2)*d^4*e^3*x + 864*(a^3 + a*b^2)*c*d^3*e^3 - 1296*(a^3 + a*b^2)*c^2*d^2*e^2*f + 864*(a^3 + a*b^2)*c^3*d*e*f^2 - 216*(a^3 + a*b^2)*c^4*f^3 + 40*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^3 - 135*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^2 + 216*((4*a^2*b + 3*b^3)*d^3*f^3*x^3 + (4*a^2*b + 3*b^3)*d^3*e^3 - 3*(4*a^2*b + 3*b^3)*d^2*e^2*f + 6*(4*a^2*b + 3*b^3)*d*e*f^2 - 6*(4*a^2*b + 3*b^3)*f^3 + 3*((4*a^2*b + 3*b^3)*d^3*e*f^2 - (4*a^2*b + 3*b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + 3*b^3)*d^3*e^2*f - 2*(4*a^2*b + 3*b^3)*d^2*e*f^2 + 2*(4*a^2*b + 3*b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 36*(3*b^3*d^3*e*f^2 + b^3*d^2*f^3)*x^2 + 108*((4*a^2*b + 3*b^3)*d^3*f^3*x^3 + (4*a^2*b + 3*b^3)*d^3*e^3 + 3*(4*a^2*b + 3*b^3)*d^2*e^2*f + 6*(4*a^2*b + 3*b^3)*d*e*f^2 + 6*(4*a^2*b + 3*b^3)*f^3 + 3*((4*a^2*b + 3*b^3)*d^3*e*f^2 + (4*a^2*b + 3*b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + 3*b^3)*d^3*e^2*f + 2*(4*a^2*b + 3*b^3)*d^2*e*f^2 + 2*(4*a^2*b + 3*b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 6*(18*(4*a^2*b + 3*b^3)*d^3*f^3*x^3 + 18*(4*a^2*b + 3*b^3)*d^3*e^3 + 54*(4*a^2*b + 3*b^3)*d^2*e^2*f + 108*(4*a^2*b + 3*b^3)*d*e*f^2 - 10*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^4 + 108*(4*a^2*b + 3*b^3)*f^3 + 45*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^3 + 54*((4*a^2*b + 3*b^3)*d^3*e*f^2 + (4*a^2*b + 3*b^3)*d^2*f^3)*x^2 - 108*((4*a^2*b + 3*b^3)*d^3*f^3*x^3 + (4*a^2*b + 3*b^3)*d^3*e^3 - 3*(4*a^2*b + 3*b^3)*d^2*e^2*f + 6*(4*a^2*b + 3*b^3)*d*e*f^2 - 6*(4*a^2*b + 3*b^3)*f^3 + 3*((4*a^2*b + 3*b^3)*d^3*e*f^2 - (4*a^2*b + 3*b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + 3*b^3)*d^3*e^2*f - 2*(4*a^2*b + 3*b^3)*d^2*e*f^2 + 2*(4*a^2*b + 3*b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 54*((4*a^2*b + 3*b^3)*d^3*e^2*f + 2*(4*a^2*b + 3*b^3)*d^2*e*f^2 + 2*(4*a^2*b + 3*b^3)*d*f^3)*x - 108*((a^3 + a*b^2)*d^4*f^3*x^4 + 4*(a^3 + a*b^2)*d^4*e*f^2*x^3 + 6*(a^3 + a*b^2)*d^4*e^2*f*x^2 + 4*(a^3 + a*b^2)*d^4*e^3*x + 8*(a^3 + a*b^2)*c*d^3*e^3 - 12*(a^3 + a*b^2)*c^2*d^2*e^2*f + 8*(a^3 + a*b^2)*c^3*d*e*f^2 - 2*(a^3 + a*b^2)*c^4*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 12*(9*b^3*d^3*e^2*f + 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x + 27*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 + 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 + 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 + a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f + 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c) + 2592*(((a^3 + a*b^2)*d^2*f^3*x^2 + 2*(a^3 + a*b^2)*d^2*e*f^2*x + (a^3 + a*b^2)*d^2*e^2*f)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d^2*f^3*x^2 + 2*(a^3 + a*b^2)*d^2*e*f^2*x + (a^3 + a*b^2)*d^2*e^2*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d^2*f^3*x^2 + 2*(a^3 + a*b^2)*d^2*e*f^2*x + (a^3 + a*b^2)*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d^2*f^3*x^2 + 2*(a^3 + a*b^2)*d^2*e*f^2*x + (a^3 + a*b^2)*d^2*e^2*f)*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2592*(((a^3 + a*b^2)*d^2*f^3*x^2 + 2*(a^3 + a*b^2)*d^2*e*f^2*x + (a^3 + a*b^2)*d^2*e^2*f)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d^2*f^3*x^2 + 2*(a^3 + a*b^2)*d^2*e*f^2*x + (a^3 + a*b^2)*d^2*e^2*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d^2*f^3*x^2 + 2*(a^3 + a*b^2)*d^2*e*f^2*x + (a^3 + a*b^2)*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d^2*f^3*x^2 + 2*(a^3 + a*b^2)*d^2*e*f^2*x + (a^3 + a*b^2)*d^2*e^2*f)*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 864*(((a^3 + a*b^2)*d^3*e^3 - 3*(a^3 + a*b^2)*c*d^2*e^2*f + 3*(a^3 + a*b^2)*c^2*d*e*f^2 - (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d^3*e^3 - 3*(a^3 + a*b^2)*c*d^2*e^2*f + 3*(a^3 + a*b^2)*c^2*d*e*f^2 - (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d^3*e^3 - 3*(a^3 + a*b^2)*c*d^2*e^2*f + 3*(a^3 + a*b^2)*c^2*d*e*f^2 - (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d^3*e^3 - 3*(a^3 + a*b^2)*c*d^2*e^2*f + 3*(a^3 + a*b^2)*c^2*d*e*f^2 - (a^3 + a*b^2)*c^3*f^3)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 864*(((a^3 + a*b^2)*d^3*e^3 - 3*(a^3 + a*b^2)*c*d^2*e^2*f + 3*(a^3 + a*b^2)*c^2*d*e*f^2 - (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d^3*e^3 - 3*(a^3 + a*b^2)*c*d^2*e^2*f + 3*(a^3 + a*b^2)*c^2*d*e*f^2 - (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d^3*e^3 - 3*(a^3 + a*b^2)*c*d^2*e^2*f + 3*(a^3 + a*b^2)*c^2*d*e*f^2 - (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d^3*e^3 - 3*(a^3 + a*b^2)*c*d^2*e^2*f + 3*(a^3 + a*b^2)*c^2*d*e*f^2 - (a^3 + a*b^2)*c^3*f^3)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 864*(((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 864*(((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 5184*((a^3 + a*b^2)*f^3*cosh(d*x + c)^3 + 3*(a^3 + a*b^2)*f^3*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3 + a*b^2)*f^3*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3 + a*b^2)*f^3*sinh(d*x + c)^3)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 5184*((a^3 + a*b^2)*f^3*cosh(d*x + c)^3 + 3*(a^3 + a*b^2)*f^3*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3 + a*b^2)*f^3*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3 + a*b^2)*f^3*sinh(d*x + c)^3)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 5184*(((a^3 + a*b^2)*d*f^3*x + (a^3 + a*b^2)*d*e*f^2)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d*f^3*x + (a^3 + a*b^2)*d*e*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d*f^3*x + (a^3 + a*b^2)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d*f^3*x + (a^3 + a*b^2)*d*e*f^2)*sinh(d*x + c)^3)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 5184*(((a^3 + a*b^2)*d*f^3*x + (a^3 + a*b^2)*d*e*f^2)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d*f^3*x + (a^3 + a*b^2)*d*e*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d*f^3*x + (a^3 + a*b^2)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d*f^3*x + (a^3 + a*b^2)*d*e*f^2)*sinh(d*x + c)^3)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 3*(36*a*b^2*d^3*f^3*x^3 + 36*a*b^2*d^3*e^3 + 54*a*b^2*d^2*e^2*f + 54*a*b^2*d*e*f^2 + 27*a*b^2*f^3 - 8*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^5 + 45*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^4 - 144*((4*a^2*b + 3*b^3)*d^3*f^3*x^3 + (4*a^2*b + 3*b^3)*d^3*e^3 - 3*(4*a^2*b + 3*b^3)*d^2*e^2*f + 6*(4*a^2*b + 3*b^3)*d*e*f^2 - 6*(4*a^2*b + 3*b^3)*f^3 + 3*((4*a^2*b + 3*b^3)*d^3*e*f^2 - (4*a^2*b + 3*b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + 3*b^3)*d^3*e^2*f - 2*(4*a^2*b + 3*b^3)*d^2*e*f^2 + 2*(4*a^2*b + 3*b^3)*d*f^3)*x)*cosh(d*x + c)^3 + 54*(2*a*b^2*d^3*e*f^2 + a*b^2*d^2*f^3)*x^2 - 216*((a^3 + a*b^2)*d^4*f^3*x^4 + 4*(a^3 + a*b^2)*d^4*e*f^2*x^3 + 6*(a^3 + a*b^2)*d^4*e^2*f*x^2 + 4*(a^3 + a*b^2)*d^4*e^3*x + 8*(a^3 + a*b^2)*c*d^3*e^3 - 12*(a^3 + a*b^2)*c^2*d^2*e^2*f + 8*(a^3 + a*b^2)*c^3*d*e*f^2 - 2*(a^3 + a*b^2)*c^4*f^3)*cosh(d*x + c)^2 + 54*(2*a*b^2*d^3*e^2*f + 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x + 72*((4*a^2*b + 3*b^3)*d^3*f^3*x^3 + (4*a^2*b + 3*b^3)*d^3*e^3 + 3*(4*a^2*b + 3*b^3)*d^2*e^2*f + 6*(4*a^2*b + 3*b^3)*d*e*f^2 + 6*(4*a^2*b + 3*b^3)*f^3 + 3*((4*a^2*b + 3*b^3)*d^3*e*f^2 + (4*a^2*b + 3*b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + 3*b^3)*d^3*e^2*f + 2*(4*a^2*b + 3*b^3)*d^2*e*f^2 + 2*(4*a^2*b + 3*b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d^4*cosh(d*x + c)^3 + 3*b^4*d^4*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d^4*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d^4*sinh(d*x + c)^3)","C",0
344,1,4887,0,0.609433," ","integrate((f*x+e)^2*cosh(d*x+c)^3*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{18 \, b^{3} d^{2} f^{2} x^{2} + 18 \, b^{3} d^{2} e^{2} - 2 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 2 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{6} + 12 \, b^{3} d e f + 27 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(18 \, a b^{2} d^{2} f^{2} x^{2} + 18 \, a b^{2} d^{2} e^{2} - 18 \, a b^{2} d e f + 9 \, a b^{2} f^{2} + 18 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x - 4 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, b^{3} f^{2} - 54 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(18 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{2} x^{2} + 18 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} - 36 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f + 36 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{2} + 10 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 36 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{2}\right)} x - 45 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 144 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{3} + a b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(72 \, {\left(a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 216 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 216 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} x + 432 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} - 432 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f + 144 \, {\left(a^{3} + a b^{2}\right)} c^{3} f^{2} + 20 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 135 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 108 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 54 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(9 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} - 5 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f + 45 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 18 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{2} - 54 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 18 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{2}\right)} x - 72 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{3} + a b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left(3 \, b^{3} d^{2} e f + b^{3} d f^{2}\right)} x + 27 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} + 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f + a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 864 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 864 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 432 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c d e f + {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c d e f + {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c d e f + {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c d e f + {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 432 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c d e f + {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c d e f + {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c d e f + {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c d e f + {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 432 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 432 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 864 \, {\left({\left(a^{3} + a b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} + a b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 864 \, {\left({\left(a^{3} + a b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} + a b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 3 \, {\left(18 \, a b^{2} d^{2} f^{2} x^{2} + 18 \, a b^{2} d^{2} e^{2} + 18 \, a b^{2} d e f - 4 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 9 \, a b^{2} f^{2} + 45 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 72 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 144 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{3} + a b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 18 \, {\left(2 \, a b^{2} d^{2} e f + a b^{2} d f^{2}\right)} x + 36 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d^{2} e f + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{432 \, {\left(b^{4} d^{3} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d^{3} \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"-1/432*(18*b^3*d^2*f^2*x^2 + 18*b^3*d^2*e^2 - 2*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^6 - 2*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*sinh(d*x + c)^6 + 12*b^3*d*e*f + 27*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^5 + 3*(18*a*b^2*d^2*f^2*x^2 + 18*a*b^2*d^2*e^2 - 18*a*b^2*d*e*f + 9*a*b^2*f^2 + 18*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x - 4*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*b^3*f^2 - 54*((4*a^2*b + 3*b^3)*d^2*f^2*x^2 + (4*a^2*b + 3*b^3)*d^2*e^2 - 2*(4*a^2*b + 3*b^3)*d*e*f + 2*(4*a^2*b + 3*b^3)*f^2 + 2*((4*a^2*b + 3*b^3)*d^2*e*f - (4*a^2*b + 3*b^3)*d*f^2)*x)*cosh(d*x + c)^4 - 3*(18*(4*a^2*b + 3*b^3)*d^2*f^2*x^2 + 18*(4*a^2*b + 3*b^3)*d^2*e^2 - 36*(4*a^2*b + 3*b^3)*d*e*f + 36*(4*a^2*b + 3*b^3)*f^2 + 10*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^2 + 36*((4*a^2*b + 3*b^3)*d^2*e*f - (4*a^2*b + 3*b^3)*d*f^2)*x - 45*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^4 - 144*((a^3 + a*b^2)*d^3*f^2*x^3 + 3*(a^3 + a*b^2)*d^3*e*f*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*x + 6*(a^3 + a*b^2)*c*d^2*e^2 - 6*(a^3 + a*b^2)*c^2*d*e*f + 2*(a^3 + a*b^2)*c^3*f^2)*cosh(d*x + c)^3 - 2*(72*(a^3 + a*b^2)*d^3*f^2*x^3 + 216*(a^3 + a*b^2)*d^3*e*f*x^2 + 216*(a^3 + a*b^2)*d^3*e^2*x + 432*(a^3 + a*b^2)*c*d^2*e^2 - 432*(a^3 + a*b^2)*c^2*d*e*f + 144*(a^3 + a*b^2)*c^3*f^2 + 20*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^3 - 135*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^2 + 108*((4*a^2*b + 3*b^3)*d^2*f^2*x^2 + (4*a^2*b + 3*b^3)*d^2*e^2 - 2*(4*a^2*b + 3*b^3)*d*e*f + 2*(4*a^2*b + 3*b^3)*f^2 + 2*((4*a^2*b + 3*b^3)*d^2*e*f - (4*a^2*b + 3*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 54*((4*a^2*b + 3*b^3)*d^2*f^2*x^2 + (4*a^2*b + 3*b^3)*d^2*e^2 + 2*(4*a^2*b + 3*b^3)*d*e*f + 2*(4*a^2*b + 3*b^3)*f^2 + 2*((4*a^2*b + 3*b^3)*d^2*e*f + (4*a^2*b + 3*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 6*(9*(4*a^2*b + 3*b^3)*d^2*f^2*x^2 + 9*(4*a^2*b + 3*b^3)*d^2*e^2 - 5*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^4 + 18*(4*a^2*b + 3*b^3)*d*e*f + 45*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^3 + 18*(4*a^2*b + 3*b^3)*f^2 - 54*((4*a^2*b + 3*b^3)*d^2*f^2*x^2 + (4*a^2*b + 3*b^3)*d^2*e^2 - 2*(4*a^2*b + 3*b^3)*d*e*f + 2*(4*a^2*b + 3*b^3)*f^2 + 2*((4*a^2*b + 3*b^3)*d^2*e*f - (4*a^2*b + 3*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 18*((4*a^2*b + 3*b^3)*d^2*e*f + (4*a^2*b + 3*b^3)*d*f^2)*x - 72*((a^3 + a*b^2)*d^3*f^2*x^3 + 3*(a^3 + a*b^2)*d^3*e*f*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*x + 6*(a^3 + a*b^2)*c*d^2*e^2 - 6*(a^3 + a*b^2)*c^2*d*e*f + 2*(a^3 + a*b^2)*c^3*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 12*(3*b^3*d^2*e*f + b^3*d*f^2)*x + 27*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 + 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f + a*b^2*d*f^2)*x)*cosh(d*x + c) + 864*(((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*d*e*f)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*d*e*f)*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 864*(((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*d*e*f)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*d*e*f)*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 432*(((a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*c*d*e*f + (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*c*d*e*f + (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*c*d*e*f + (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*c*d*e*f + (a^3 + a*b^2)*c^2*f^2)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 432*(((a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*c*d*e*f + (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*c*d*e*f + (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*c*d*e*f + (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*c*d*e*f + (a^3 + a*b^2)*c^2*f^2)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 432*(((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 432*(((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 864*((a^3 + a*b^2)*f^2*cosh(d*x + c)^3 + 3*(a^3 + a*b^2)*f^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3 + a*b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3 + a*b^2)*f^2*sinh(d*x + c)^3)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 864*((a^3 + a*b^2)*f^2*cosh(d*x + c)^3 + 3*(a^3 + a*b^2)*f^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3 + a*b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3 + a*b^2)*f^2*sinh(d*x + c)^3)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 3*(18*a*b^2*d^2*f^2*x^2 + 18*a*b^2*d^2*e^2 + 18*a*b^2*d*e*f - 4*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^5 + 9*a*b^2*f^2 + 45*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^4 - 72*((4*a^2*b + 3*b^3)*d^2*f^2*x^2 + (4*a^2*b + 3*b^3)*d^2*e^2 - 2*(4*a^2*b + 3*b^3)*d*e*f + 2*(4*a^2*b + 3*b^3)*f^2 + 2*((4*a^2*b + 3*b^3)*d^2*e*f - (4*a^2*b + 3*b^3)*d*f^2)*x)*cosh(d*x + c)^3 - 144*((a^3 + a*b^2)*d^3*f^2*x^3 + 3*(a^3 + a*b^2)*d^3*e*f*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*x + 6*(a^3 + a*b^2)*c*d^2*e^2 - 6*(a^3 + a*b^2)*c^2*d*e*f + 2*(a^3 + a*b^2)*c^3*f^2)*cosh(d*x + c)^2 + 18*(2*a*b^2*d^2*e*f + a*b^2*d*f^2)*x + 36*((4*a^2*b + 3*b^3)*d^2*f^2*x^2 + (4*a^2*b + 3*b^3)*d^2*e^2 + 2*(4*a^2*b + 3*b^3)*d*e*f + 2*(4*a^2*b + 3*b^3)*f^2 + 2*((4*a^2*b + 3*b^3)*d^2*e*f + (4*a^2*b + 3*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d^3*cosh(d*x + c)^3 + 3*b^4*d^3*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d^3*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d^3*sinh(d*x + c)^3)","C",0
345,1,2465,0,0.551988," ","integrate((f*x+e)*cosh(d*x+c)^3*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \sinh\left(d x + c\right)^{6} - 6 \, b^{3} d f x - 9 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{5} - 3 \, {\left(6 \, a b^{2} d f x + 6 \, a b^{2} d e - 3 \, a b^{2} f - 4 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 6 \, b^{3} d e + 18 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f x + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f x + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e + 10 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f - 15 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, b^{3} f + 72 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e x + 4 \, {\left(a^{3} + a b^{2}\right)} c d e - 2 \, {\left(a^{3} + a b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(36 \, {\left(a^{3} + a b^{2}\right)} d^{2} f x^{2} + 72 \, {\left(a^{3} + a b^{2}\right)} d^{2} e x + 144 \, {\left(a^{3} + a b^{2}\right)} c d e - 72 \, {\left(a^{3} + a b^{2}\right)} c^{2} f + 20 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{3} - 45 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{2} + 36 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f x + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 18 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f x + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(5 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f x - 15 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e + 18 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f x + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f + 36 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e x + 4 \, {\left(a^{3} + a b^{2}\right)} c d e - 2 \, {\left(a^{3} + a b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 9 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e + a b^{2} f\right)} \cosh\left(d x + c\right) - 144 \, {\left({\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 144 \, {\left({\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 144 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 144 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 144 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 144 \, {\left({\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(6 \, a b^{2} d f x - 4 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{5} + 6 \, a b^{2} d e + 15 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{4} + 3 \, a b^{2} f - 24 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f x + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e - {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} - 72 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e x + 4 \, {\left(a^{3} + a b^{2}\right)} c d e - 2 \, {\left(a^{3} + a b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left({\left(4 \, a^{2} b + 3 \, b^{3}\right)} d f x + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} d e + {\left(4 \, a^{2} b + 3 \, b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{144 \, {\left(b^{4} d^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d^{2} \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/144*(2*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^6 + 2*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*sinh(d*x + c)^6 - 6*b^3*d*f*x - 9*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^5 - 3*(6*a*b^2*d*f*x + 6*a*b^2*d*e - 3*a*b^2*f - 4*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c))*sinh(d*x + c)^5 - 6*b^3*d*e + 18*((4*a^2*b + 3*b^3)*d*f*x + (4*a^2*b + 3*b^3)*d*e - (4*a^2*b + 3*b^3)*f)*cosh(d*x + c)^4 + 3*(6*(4*a^2*b + 3*b^3)*d*f*x + 6*(4*a^2*b + 3*b^3)*d*e + 10*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^2 - 6*(4*a^2*b + 3*b^3)*f - 15*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*b^3*f + 72*((a^3 + a*b^2)*d^2*f*x^2 + 2*(a^3 + a*b^2)*d^2*e*x + 4*(a^3 + a*b^2)*c*d*e - 2*(a^3 + a*b^2)*c^2*f)*cosh(d*x + c)^3 + 2*(36*(a^3 + a*b^2)*d^2*f*x^2 + 72*(a^3 + a*b^2)*d^2*e*x + 144*(a^3 + a*b^2)*c*d*e - 72*(a^3 + a*b^2)*c^2*f + 20*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^3 - 45*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^2 + 36*((4*a^2*b + 3*b^3)*d*f*x + (4*a^2*b + 3*b^3)*d*e - (4*a^2*b + 3*b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^3 - 18*((4*a^2*b + 3*b^3)*d*f*x + (4*a^2*b + 3*b^3)*d*e + (4*a^2*b + 3*b^3)*f)*cosh(d*x + c)^2 + 6*(5*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^4 - 3*(4*a^2*b + 3*b^3)*d*f*x - 15*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^3 - 3*(4*a^2*b + 3*b^3)*d*e + 18*((4*a^2*b + 3*b^3)*d*f*x + (4*a^2*b + 3*b^3)*d*e - (4*a^2*b + 3*b^3)*f)*cosh(d*x + c)^2 - 3*(4*a^2*b + 3*b^3)*f + 36*((a^3 + a*b^2)*d^2*f*x^2 + 2*(a^3 + a*b^2)*d^2*e*x + 4*(a^3 + a*b^2)*c*d*e - 2*(a^3 + a*b^2)*c^2*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 9*(2*a*b^2*d*f*x + 2*a*b^2*d*e + a*b^2*f)*cosh(d*x + c) - 144*((a^3 + a*b^2)*f*cosh(d*x + c)^3 + 3*(a^3 + a*b^2)*f*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3 + a*b^2)*f*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3 + a*b^2)*f*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 144*((a^3 + a*b^2)*f*cosh(d*x + c)^3 + 3*(a^3 + a*b^2)*f*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3 + a*b^2)*f*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3 + a*b^2)*f*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 144*(((a^3 + a*b^2)*d*e - (a^3 + a*b^2)*c*f)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d*e - (a^3 + a*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d*e - (a^3 + a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d*e - (a^3 + a*b^2)*c*f)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 144*(((a^3 + a*b^2)*d*e - (a^3 + a*b^2)*c*f)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d*e - (a^3 + a*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d*e - (a^3 + a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d*e - (a^3 + a*b^2)*c*f)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 144*(((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 144*(((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*cosh(d*x + c)^3 + 3*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + ((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*c*f)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 3*(6*a*b^2*d*f*x - 4*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^5 + 6*a*b^2*d*e + 15*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^4 + 3*a*b^2*f - 24*((4*a^2*b + 3*b^3)*d*f*x + (4*a^2*b + 3*b^3)*d*e - (4*a^2*b + 3*b^3)*f)*cosh(d*x + c)^3 - 72*((a^3 + a*b^2)*d^2*f*x^2 + 2*(a^3 + a*b^2)*d^2*e*x + 4*(a^3 + a*b^2)*c*d*e - 2*(a^3 + a*b^2)*c^2*f)*cosh(d*x + c)^2 + 12*((4*a^2*b + 3*b^3)*d*f*x + (4*a^2*b + 3*b^3)*d*e + (4*a^2*b + 3*b^3)*f)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d^2*cosh(d*x + c)^3 + 3*b^4*d^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d^2*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d^2*sinh(d*x + c)^3)","B",0
346,1,652,0,0.427233," ","integrate(cosh(d*x+c)^3*sinh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{b^{3} \cosh\left(d x + c\right)^{6} + b^{3} \sinh\left(d x + c\right)^{6} - 3 \, a b^{2} \cosh\left(d x + c\right)^{5} + 24 \, {\left(a^{3} + a b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, b^{3} \cosh\left(d x + c\right) - a b^{2}\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{2} - 5 \, a b^{2} \cosh\left(d x + c\right) + 4 \, a^{2} b + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{4} - 3 \, a b^{2} \cosh\left(d x + c\right) + 2 \, {\left(10 \, b^{3} \cosh\left(d x + c\right)^{3} - 15 \, a b^{2} \cosh\left(d x + c\right)^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d x + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - b^{3} - 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{4} - 10 \, a b^{2} \cosh\left(d x + c\right)^{3} + 24 \, {\left(a^{3} + a b^{2}\right)} d x \cosh\left(d x + c\right) - 4 \, a^{2} b - 3 \, b^{3} + 6 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 24 \, {\left({\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 3 \, {\left(2 \, b^{3} \cosh\left(d x + c\right)^{5} - 5 \, a b^{2} \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{3} + a b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 4 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - a b^{2} - 2 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/24*(b^3*cosh(d*x + c)^6 + b^3*sinh(d*x + c)^6 - 3*a*b^2*cosh(d*x + c)^5 + 24*(a^3 + a*b^2)*d*x*cosh(d*x + c)^3 + 3*(2*b^3*cosh(d*x + c) - a*b^2)*sinh(d*x + c)^5 + 3*(4*a^2*b + 3*b^3)*cosh(d*x + c)^4 + 3*(5*b^3*cosh(d*x + c)^2 - 5*a*b^2*cosh(d*x + c) + 4*a^2*b + 3*b^3)*sinh(d*x + c)^4 - 3*a*b^2*cosh(d*x + c) + 2*(10*b^3*cosh(d*x + c)^3 - 15*a*b^2*cosh(d*x + c)^2 + 12*(a^3 + a*b^2)*d*x + 6*(4*a^2*b + 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - b^3 - 3*(4*a^2*b + 3*b^3)*cosh(d*x + c)^2 + 3*(5*b^3*cosh(d*x + c)^4 - 10*a*b^2*cosh(d*x + c)^3 + 24*(a^3 + a*b^2)*d*x*cosh(d*x + c) - 4*a^2*b - 3*b^3 + 6*(4*a^2*b + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 24*((a^3 + a*b^2)*cosh(d*x + c)^3 + 3*(a^3 + a*b^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3 + a*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3 + a*b^2)*sinh(d*x + c)^3)*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + 3*(2*b^3*cosh(d*x + c)^5 - 5*a*b^2*cosh(d*x + c)^4 + 24*(a^3 + a*b^2)*d*x*cosh(d*x + c)^2 + 4*(4*a^2*b + 3*b^3)*cosh(d*x + c)^3 - a*b^2 - 2*(4*a^2*b + 3*b^3)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d*cosh(d*x + c)^3 + 3*b^4*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d*sinh(d*x + c)^3)","B",0
347,0,0,0,0.476495," ","integrate(cosh(d*x+c)^3*sinh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)^3*sinh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
348,1,1723,0,0.694895," ","integrate((f*x+e)^3*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, a f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, a f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 3 \, {\left(a d^{2} f^{3} x^{2} + 2 \, a d^{2} e f^{2} x + a d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(a d^{2} f^{3} x^{2} + 2 \, a d^{2} e f^{2} x + a d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(3 \, a d^{2} f^{3} x^{2} + 3 i \, b d^{2} f^{3} x^{2} + 6 \, a d^{2} e f^{2} x + 6 i \, b d^{2} e f^{2} x + 3 \, a d^{2} e^{2} f + 3 i \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(3 \, a d^{2} f^{3} x^{2} - 3 i \, b d^{2} f^{3} x^{2} + 6 \, a d^{2} e f^{2} x - 6 i \, b d^{2} e f^{2} x + 3 \, a d^{2} e^{2} f - 3 i \, b d^{2} e^{2} f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} + a c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} + a c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(a d^{3} e^{3} + i \, b d^{3} e^{3} - 3 \, a c d^{2} e^{2} f - 3 i \, b c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} + 3 i \, b c^{2} d e f^{2} - a c^{3} f^{3} - i \, b c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(a d^{3} e^{3} - i \, b d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 i \, b c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - 3 i \, b c^{2} d e f^{2} - a c^{3} f^{3} + i \, b c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(a d^{3} f^{3} x^{3} - i \, b d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} - 3 i \, b d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x - 3 i \, b d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f - 3 i \, b c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} + 3 i \, b c^{2} d e f^{2} + a c^{3} f^{3} - i \, b c^{3} f^{3}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(a d^{3} f^{3} x^{3} + i \, b d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 i \, b d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + 3 i \, b d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f + 3 i \, b c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} - 3 i \, b c^{2} d e f^{2} + a c^{3} f^{3} + i \, b c^{3} f^{3}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - {\left(6 \, a f^{3} + 6 i \, b f^{3}\right)} {\rm polylog}\left(4, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(6 \, a f^{3} - 6 i \, b f^{3}\right)} {\rm polylog}\left(4, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 6 \, {\left(a d f^{3} x + a d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(a d f^{3} x + a d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + {\left(6 \, a d f^{3} x + 6 i \, b d f^{3} x + 6 \, a d e f^{2} + 6 i \, b d e f^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(6 \, a d f^{3} x - 6 i \, b d f^{3} x + 6 \, a d e f^{2} - 6 i \, b d e f^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right)}{{\left(a^{2} + b^{2}\right)} d^{4}}"," ",0,"-(6*a*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*a*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 3*(a*d^2*f^3*x^2 + 2*a*d^2*e*f^2*x + a*d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(a*d^2*f^3*x^2 + 2*a*d^2*e*f^2*x + a*d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (3*a*d^2*f^3*x^2 + 3*I*b*d^2*f^3*x^2 + 6*a*d^2*e*f^2*x + 6*I*b*d^2*e*f^2*x + 3*a*d^2*e^2*f + 3*I*b*d^2*e^2*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (3*a*d^2*f^3*x^2 - 3*I*b*d^2*f^3*x^2 + 6*a*d^2*e*f^2*x - 6*I*b*d^2*e*f^2*x + 3*a*d^2*e^2*f - 3*I*b*d^2*e^2*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + 3*a*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 + a*c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + 3*a*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 + a*c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (a*d^3*e^3 + I*b*d^3*e^3 - 3*a*c*d^2*e^2*f - 3*I*b*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 + 3*I*b*c^2*d*e*f^2 - a*c^3*f^3 - I*b*c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (a*d^3*e^3 - I*b*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*I*b*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - 3*I*b*c^2*d*e*f^2 - a*c^3*f^3 + I*b*c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) - I) - (a*d^3*f^3*x^3 - I*b*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 - 3*I*b*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x - 3*I*b*d^3*e^2*f*x + 3*a*c*d^2*e^2*f - 3*I*b*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 + 3*I*b*c^2*d*e*f^2 + a*c^3*f^3 - I*b*c^3*f^3)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (a*d^3*f^3*x^3 + I*b*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*I*b*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + 3*I*b*d^3*e^2*f*x + 3*a*c*d^2*e^2*f + 3*I*b*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 - 3*I*b*c^2*d*e*f^2 + a*c^3*f^3 + I*b*c^3*f^3)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - (6*a*f^3 + 6*I*b*f^3)*polylog(4, I*cosh(d*x + c) + I*sinh(d*x + c)) - (6*a*f^3 - 6*I*b*f^3)*polylog(4, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 6*(a*d*f^3*x + a*d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(a*d*f^3*x + a*d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + (6*a*d*f^3*x + 6*I*b*d*f^3*x + 6*a*d*e*f^2 + 6*I*b*d*e*f^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + (6*a*d*f^3*x - 6*I*b*d*f^3*x + 6*a*d*e*f^2 - 6*I*b*d*e*f^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)))/((a^2 + b^2)*d^4)","C",0
349,1,1087,0,0.566545," ","integrate((f*x+e)^2*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, a f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(a d f^{2} x + a d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a d f^{2} x + a d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(2 \, a d f^{2} x + 2 i \, b d f^{2} x + 2 \, a d e f + 2 i \, b d e f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(2 \, a d f^{2} x - 2 i \, b d f^{2} x + 2 \, a d e f - 2 i \, b d e f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - {\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + 2 \, a c d e f - a c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + 2 \, a c d e f - a c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(a d^{2} e^{2} + i \, b d^{2} e^{2} - 2 \, a c d e f - 2 i \, b c d e f + a c^{2} f^{2} + i \, b c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(a d^{2} e^{2} - i \, b d^{2} e^{2} - 2 \, a c d e f + 2 i \, b c d e f + a c^{2} f^{2} - i \, b c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(a d^{2} f^{2} x^{2} - i \, b d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x - 2 i \, b d^{2} e f x + 2 \, a c d e f - 2 i \, b c d e f - a c^{2} f^{2} + i \, b c^{2} f^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(a d^{2} f^{2} x^{2} + i \, b d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + 2 i \, b d^{2} e f x + 2 \, a c d e f + 2 i \, b c d e f - a c^{2} f^{2} - i \, b c^{2} f^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - {\left(2 \, a f^{2} + 2 i \, b f^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(2 \, a f^{2} - 2 i \, b f^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right)}{{\left(a^{2} + b^{2}\right)} d^{3}}"," ",0,"(2*a*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*a*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(a*d*f^2*x + a*d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(a*d*f^2*x + a*d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (2*a*d*f^2*x + 2*I*b*d*f^2*x + 2*a*d*e*f + 2*I*b*d*e*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (2*a*d*f^2*x - 2*I*b*d*f^2*x + 2*a*d*e*f - 2*I*b*d*e*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - (a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + 2*a*c*d*e*f - a*c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + 2*a*c*d*e*f - a*c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (a*d^2*e^2 + I*b*d^2*e^2 - 2*a*c*d*e*f - 2*I*b*c*d*e*f + a*c^2*f^2 + I*b*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (a*d^2*e^2 - I*b*d^2*e^2 - 2*a*c*d*e*f + 2*I*b*c*d*e*f + a*c^2*f^2 - I*b*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) + (a*d^2*f^2*x^2 - I*b*d^2*f^2*x^2 + 2*a*d^2*e*f*x - 2*I*b*d^2*e*f*x + 2*a*c*d*e*f - 2*I*b*c*d*e*f - a*c^2*f^2 + I*b*c^2*f^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (a*d^2*f^2*x^2 + I*b*d^2*f^2*x^2 + 2*a*d^2*e*f*x + 2*I*b*d^2*e*f*x + 2*a*c*d*e*f + 2*I*b*c*d*e*f - a*c^2*f^2 - I*b*c^2*f^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - (2*a*f^2 + 2*I*b*f^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - (2*a*f^2 - 2*I*b*f^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)))/((a^2 + b^2)*d^3)","C",0
350,1,589,0,0.512289," ","integrate((f*x+e)*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{a f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + a f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a f + i \, b f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(a f - i \, b f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left(a d e - a c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(a d e - a c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(a d f x + a c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(a d f x + a c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(a d e + i \, b d e - a c f - i \, b c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(a d e - i \, b d e - a c f + i \, b c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(a d f x - i \, b d f x + a c f - i \, b c f\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(a d f x + i \, b d f x + a c f + i \, b c f\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right)}{{\left(a^{2} + b^{2}\right)} d^{2}}"," ",0,"-(a*f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + a*f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (a*f + I*b*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (a*f - I*b*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (a*d*e - a*c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (a*d*e - a*c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (a*d*f*x + a*c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (a*d*f*x + a*c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (a*d*e + I*b*d*e - a*c*f - I*b*c*f)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (a*d*e - I*b*d*e - a*c*f + I*b*c*f)*log(cosh(d*x + c) + sinh(d*x + c) - I) - (a*d*f*x - I*b*d*f*x + a*c*f - I*b*c*f)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (a*d*f*x + I*b*d*f*x + a*c*f + I*b*c*f)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1))/((a^2 + b^2)*d^2)","A",0
351,1,92,0,0.492303," ","integrate(tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - a \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + a \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{{\left(a^{2} + b^{2}\right)} d}"," ",0,"(2*b*arctan(cosh(d*x + c) + sinh(d*x + c)) - a*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + a*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/((a^2 + b^2)*d)","A",0
352,0,0,0,0.496262," ","integrate(tanh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tanh\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(tanh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
353,1,6537,0,0.804383," ","integrate((f*x+e)^3*sech(d*x+c)*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 12 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f + 12 \, {\left(a^{2} b + b^{3}\right)} c^{2} d e f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} c^{3} f^{3} - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b + b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b + b^{3}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b + b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b + b^{3}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a b^{2} d^{2} f^{3} x^{2} + 2 \, a b^{2} d^{2} e f^{2} x + a b^{2} d^{2} e^{2} f + {\left(a b^{2} d^{2} f^{3} x^{2} + 2 \, a b^{2} d^{2} e f^{2} x + a b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{2} f^{3} x^{2} + 2 \, a b^{2} d^{2} e f^{2} x + a b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d^{2} f^{3} x^{2} + 2 \, a b^{2} d^{2} e f^{2} x + a b^{2} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left(a b^{2} d^{2} f^{3} x^{2} + 2 \, a b^{2} d^{2} e f^{2} x + a b^{2} d^{2} e^{2} f + {\left(a b^{2} d^{2} f^{3} x^{2} + 2 \, a b^{2} d^{2} e f^{2} x + a b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{2} f^{3} x^{2} + 2 \, a b^{2} d^{2} e f^{2} x + a b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d^{2} f^{3} x^{2} + 2 \, a b^{2} d^{2} e f^{2} x + a b^{2} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} d^{3} e f^{2} x^{2} + 3 \, a b^{2} d^{3} e^{2} f x + 3 \, a b^{2} c d^{2} e^{2} f - 3 \, a b^{2} c^{2} d e f^{2} + a b^{2} c^{3} f^{3} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} d^{3} e f^{2} x^{2} + 3 \, a b^{2} d^{3} e^{2} f x + 3 \, a b^{2} c d^{2} e^{2} f - 3 \, a b^{2} c^{2} d e f^{2} + a b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} d^{3} e f^{2} x^{2} + 3 \, a b^{2} d^{3} e^{2} f x + 3 \, a b^{2} c d^{2} e^{2} f - 3 \, a b^{2} c^{2} d e f^{2} + a b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} d^{3} e f^{2} x^{2} + 3 \, a b^{2} d^{3} e^{2} f x + 3 \, a b^{2} c d^{2} e^{2} f - 3 \, a b^{2} c^{2} d e f^{2} + a b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} d^{3} e f^{2} x^{2} + 3 \, a b^{2} d^{3} e^{2} f x + 3 \, a b^{2} c d^{2} e^{2} f - 3 \, a b^{2} c^{2} d e f^{2} + a b^{2} c^{3} f^{3} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} d^{3} e f^{2} x^{2} + 3 \, a b^{2} d^{3} e^{2} f x + 3 \, a b^{2} c d^{2} e^{2} f - 3 \, a b^{2} c^{2} d e f^{2} + a b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} d^{3} e f^{2} x^{2} + 3 \, a b^{2} d^{3} e^{2} f x + 3 \, a b^{2} c d^{2} e^{2} f - 3 \, a b^{2} c^{2} d e f^{2} + a b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} d^{3} e f^{2} x^{2} + 3 \, a b^{2} d^{3} e^{2} f x + 3 \, a b^{2} c d^{2} e^{2} f - 3 \, a b^{2} c^{2} d e f^{2} + a b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 12 \, {\left(a b^{2} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a b^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b^{2} f^{3} \sinh\left(d x + c\right)^{2} + a b^{2} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a b^{2} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a b^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b^{2} f^{3} \sinh\left(d x + c\right)^{2} + a b^{2} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a b^{2} d f^{3} x + a b^{2} d e f^{2} + {\left(a b^{2} d f^{3} x + a b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d f^{3} x + a b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d f^{3} x + a b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a b^{2} d f^{3} x + a b^{2} d e f^{2} + {\left(a b^{2} d f^{3} x + a b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d f^{3} x + a b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d f^{3} x + a b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + {\left(a^{3} + a b^{2}\right)} d^{3} e^{3}\right)} \cosh\left(d x + c\right) - {\left(12 i \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 i \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(12 i \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 i \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 i \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 24 \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 24 i \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 24 \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 i \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 i \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(-12 i \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 \, {\left(a^{2} b + b^{3}\right)} d f^{3} x - 12 i \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(-12 i \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 \, {\left(a^{2} b + b^{3}\right)} d f^{3} x - 12 i \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-24 i \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 24 \, {\left(a^{2} b + b^{3}\right)} d f^{3} x - 24 i \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 24 \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-12 i \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 \, {\left(a^{2} b + b^{3}\right)} d f^{3} x - 12 i \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - {\left(6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 12 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 24 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 24 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 12 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 12 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(-6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(-6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(-12 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 12 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 24 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 24 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 12 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 12 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(-6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(-6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(-12 i \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} - 24 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 24 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x - 24 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 24 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 12 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 i \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 24 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 24 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 24 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 24 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 12 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 i \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - {\left(-12 i \, {\left(a^{3} + a b^{2}\right)} f^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} f^{3} + {\left(-12 i \, {\left(a^{3} + a b^{2}\right)} f^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(-24 i \, {\left(a^{3} + a b^{2}\right)} f^{3} + 24 \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-12 i \, {\left(a^{3} + a b^{2}\right)} f^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(12 i \, {\left(a^{3} + a b^{2}\right)} f^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} f^{3} + {\left(12 i \, {\left(a^{3} + a b^{2}\right)} f^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 i \, {\left(a^{3} + a b^{2}\right)} f^{3} + 24 \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 i \, {\left(a^{3} + a b^{2}\right)} f^{3} + 12 \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + {\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} b + b^{3}\right)} c^{2} d e f^{2} + {\left(a^{2} b + b^{3}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}\right)}}"," ",0,"-1/2*(4*(a^2*b + b^3)*d^3*e^3 - 12*(a^2*b + b^3)*c*d^2*e^2*f + 12*(a^2*b + b^3)*c^2*d*e*f^2 - 4*(a^2*b + b^3)*c^3*f^3 - 4*((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*d^3*e*f^2*x^2 + 3*(a^2*b + b^3)*d^3*e^2*f*x + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*(a^2*b + b^3)*c^2*d*e*f^2 + (a^2*b + b^3)*c^3*f^3)*cosh(d*x + c)^2 - 4*((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*d^3*e*f^2*x^2 + 3*(a^2*b + b^3)*d^3*e^2*f*x + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*(a^2*b + b^3)*c^2*d*e*f^2 + (a^2*b + b^3)*c^3*f^3)*sinh(d*x + c)^2 + 6*(a*b^2*d^2*f^3*x^2 + 2*a*b^2*d^2*e*f^2*x + a*b^2*d^2*e^2*f + (a*b^2*d^2*f^3*x^2 + 2*a*b^2*d^2*e*f^2*x + a*b^2*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a*b^2*d^2*f^3*x^2 + 2*a*b^2*d^2*e*f^2*x + a*b^2*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d^2*f^3*x^2 + 2*a*b^2*d^2*e*f^2*x + a*b^2*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 6*(a*b^2*d^2*f^3*x^2 + 2*a*b^2*d^2*e*f^2*x + a*b^2*d^2*e^2*f + (a*b^2*d^2*f^3*x^2 + 2*a*b^2*d^2*e*f^2*x + a*b^2*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a*b^2*d^2*f^3*x^2 + 2*a*b^2*d^2*e*f^2*x + a*b^2*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d^2*f^3*x^2 + 2*a*b^2*d^2*e*f^2*x + a*b^2*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*cosh(d*x + c)^2 + 2*(a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*cosh(d*x + c)^2 + 2*(a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a*b^2*d^3*f^3*x^3 + 3*a*b^2*d^3*e*f^2*x^2 + 3*a*b^2*d^3*e^2*f*x + 3*a*b^2*c*d^2*e^2*f - 3*a*b^2*c^2*d*e*f^2 + a*b^2*c^3*f^3 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*d^3*e*f^2*x^2 + 3*a*b^2*d^3*e^2*f*x + 3*a*b^2*c*d^2*e^2*f - 3*a*b^2*c^2*d*e*f^2 + a*b^2*c^3*f^3)*cosh(d*x + c)^2 + 2*(a*b^2*d^3*f^3*x^3 + 3*a*b^2*d^3*e*f^2*x^2 + 3*a*b^2*d^3*e^2*f*x + 3*a*b^2*c*d^2*e^2*f - 3*a*b^2*c^2*d*e*f^2 + a*b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*d^3*e*f^2*x^2 + 3*a*b^2*d^3*e^2*f*x + 3*a*b^2*c*d^2*e^2*f - 3*a*b^2*c^2*d*e*f^2 + a*b^2*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(a*b^2*d^3*f^3*x^3 + 3*a*b^2*d^3*e*f^2*x^2 + 3*a*b^2*d^3*e^2*f*x + 3*a*b^2*c*d^2*e^2*f - 3*a*b^2*c^2*d*e*f^2 + a*b^2*c^3*f^3 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*d^3*e*f^2*x^2 + 3*a*b^2*d^3*e^2*f*x + 3*a*b^2*c*d^2*e^2*f - 3*a*b^2*c^2*d*e*f^2 + a*b^2*c^3*f^3)*cosh(d*x + c)^2 + 2*(a*b^2*d^3*f^3*x^3 + 3*a*b^2*d^3*e*f^2*x^2 + 3*a*b^2*d^3*e^2*f*x + 3*a*b^2*c*d^2*e^2*f - 3*a*b^2*c^2*d*e*f^2 + a*b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*d^3*e*f^2*x^2 + 3*a*b^2*d^3*e^2*f*x + 3*a*b^2*c*d^2*e^2*f - 3*a*b^2*c^2*d*e*f^2 + a*b^2*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 12*(a*b^2*f^3*cosh(d*x + c)^2 + 2*a*b^2*f^3*cosh(d*x + c)*sinh(d*x + c) + a*b^2*f^3*sinh(d*x + c)^2 + a*b^2*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(a*b^2*f^3*cosh(d*x + c)^2 + 2*a*b^2*f^3*cosh(d*x + c)*sinh(d*x + c) + a*b^2*f^3*sinh(d*x + c)^2 + a*b^2*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(a*b^2*d*f^3*x + a*b^2*d*e*f^2 + (a*b^2*d*f^3*x + a*b^2*d*e*f^2)*cosh(d*x + c)^2 + 2*(a*b^2*d*f^3*x + a*b^2*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d*f^3*x + a*b^2*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(a*b^2*d*f^3*x + a*b^2*d*e*f^2 + (a*b^2*d*f^3*x + a*b^2*d*e*f^2)*cosh(d*x + c)^2 + 2*(a*b^2*d*f^3*x + a*b^2*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d*f^3*x + a*b^2*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + (a^3 + a*b^2)*d^3*e^3)*cosh(d*x + c) - (12*I*(a^3 + a*b^2)*d*f^3*x - 12*(a^2*b + b^3)*d*f^3*x + 12*I*(a^3 + a*b^2)*d*e*f^2 - 12*(a^2*b + b^3)*d*e*f^2 + (12*I*(a^3 + a*b^2)*d*f^3*x - 12*(a^2*b + b^3)*d*f^3*x + 12*I*(a^3 + a*b^2)*d*e*f^2 - 12*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)^2 + (24*I*(a^3 + a*b^2)*d*f^3*x - 24*(a^2*b + b^3)*d*f^3*x + 24*I*(a^3 + a*b^2)*d*e*f^2 - 24*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (12*I*(a^3 + a*b^2)*d*f^3*x - 12*(a^2*b + b^3)*d*f^3*x + 12*I*(a^3 + a*b^2)*d*e*f^2 - 12*(a^2*b + b^3)*d*e*f^2)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (-12*I*(a^3 + a*b^2)*d*f^3*x - 12*(a^2*b + b^3)*d*f^3*x - 12*I*(a^3 + a*b^2)*d*e*f^2 - 12*(a^2*b + b^3)*d*e*f^2 + (-12*I*(a^3 + a*b^2)*d*f^3*x - 12*(a^2*b + b^3)*d*f^3*x - 12*I*(a^3 + a*b^2)*d*e*f^2 - 12*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)^2 + (-24*I*(a^3 + a*b^2)*d*f^3*x - 24*(a^2*b + b^3)*d*f^3*x - 24*I*(a^3 + a*b^2)*d*e*f^2 - 24*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-12*I*(a^3 + a*b^2)*d*f^3*x - 12*(a^2*b + b^3)*d*f^3*x - 12*I*(a^3 + a*b^2)*d*e*f^2 - 12*(a^2*b + b^3)*d*e*f^2)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - (6*I*(a^3 + a*b^2)*d^2*e^2*f - 6*(a^2*b + b^3)*d^2*e^2*f - 12*I*(a^3 + a*b^2)*c*d*e*f^2 + 12*(a^2*b + b^3)*c*d*e*f^2 + 6*I*(a^3 + a*b^2)*c^2*f^3 - 6*(a^2*b + b^3)*c^2*f^3 + (6*I*(a^3 + a*b^2)*d^2*e^2*f - 6*(a^2*b + b^3)*d^2*e^2*f - 12*I*(a^3 + a*b^2)*c*d*e*f^2 + 12*(a^2*b + b^3)*c*d*e*f^2 + 6*I*(a^3 + a*b^2)*c^2*f^3 - 6*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*I*(a^3 + a*b^2)*d^2*e^2*f - 12*(a^2*b + b^3)*d^2*e^2*f - 24*I*(a^3 + a*b^2)*c*d*e*f^2 + 24*(a^2*b + b^3)*c*d*e*f^2 + 12*I*(a^3 + a*b^2)*c^2*f^3 - 12*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*I*(a^3 + a*b^2)*d^2*e^2*f - 6*(a^2*b + b^3)*d^2*e^2*f - 12*I*(a^3 + a*b^2)*c*d*e*f^2 + 12*(a^2*b + b^3)*c*d*e*f^2 + 6*I*(a^3 + a*b^2)*c^2*f^3 - 6*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (-6*I*(a^3 + a*b^2)*d^2*e^2*f - 6*(a^2*b + b^3)*d^2*e^2*f + 12*I*(a^3 + a*b^2)*c*d*e*f^2 + 12*(a^2*b + b^3)*c*d*e*f^2 - 6*I*(a^3 + a*b^2)*c^2*f^3 - 6*(a^2*b + b^3)*c^2*f^3 + (-6*I*(a^3 + a*b^2)*d^2*e^2*f - 6*(a^2*b + b^3)*d^2*e^2*f + 12*I*(a^3 + a*b^2)*c*d*e*f^2 + 12*(a^2*b + b^3)*c*d*e*f^2 - 6*I*(a^3 + a*b^2)*c^2*f^3 - 6*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (-12*I*(a^3 + a*b^2)*d^2*e^2*f - 12*(a^2*b + b^3)*d^2*e^2*f + 24*I*(a^3 + a*b^2)*c*d*e*f^2 + 24*(a^2*b + b^3)*c*d*e*f^2 - 12*I*(a^3 + a*b^2)*c^2*f^3 - 12*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (-6*I*(a^3 + a*b^2)*d^2*e^2*f - 6*(a^2*b + b^3)*d^2*e^2*f + 12*I*(a^3 + a*b^2)*c*d*e*f^2 + 12*(a^2*b + b^3)*c*d*e*f^2 - 6*I*(a^3 + a*b^2)*c^2*f^3 - 6*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) - (-6*I*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*(a^2*b + b^3)*d^2*f^3*x^2 - 12*I*(a^3 + a*b^2)*d^2*e*f^2*x - 12*(a^2*b + b^3)*d^2*e*f^2*x - 12*I*(a^3 + a*b^2)*c*d*e*f^2 - 12*(a^2*b + b^3)*c*d*e*f^2 + 6*I*(a^3 + a*b^2)*c^2*f^3 + 6*(a^2*b + b^3)*c^2*f^3 + (-6*I*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*(a^2*b + b^3)*d^2*f^3*x^2 - 12*I*(a^3 + a*b^2)*d^2*e*f^2*x - 12*(a^2*b + b^3)*d^2*e*f^2*x - 12*I*(a^3 + a*b^2)*c*d*e*f^2 - 12*(a^2*b + b^3)*c*d*e*f^2 + 6*I*(a^3 + a*b^2)*c^2*f^3 + 6*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (-12*I*(a^3 + a*b^2)*d^2*f^3*x^2 - 12*(a^2*b + b^3)*d^2*f^3*x^2 - 24*I*(a^3 + a*b^2)*d^2*e*f^2*x - 24*(a^2*b + b^3)*d^2*e*f^2*x - 24*I*(a^3 + a*b^2)*c*d*e*f^2 - 24*(a^2*b + b^3)*c*d*e*f^2 + 12*I*(a^3 + a*b^2)*c^2*f^3 + 12*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (-6*I*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*(a^2*b + b^3)*d^2*f^3*x^2 - 12*I*(a^3 + a*b^2)*d^2*e*f^2*x - 12*(a^2*b + b^3)*d^2*e*f^2*x - 12*I*(a^3 + a*b^2)*c*d*e*f^2 - 12*(a^2*b + b^3)*c*d*e*f^2 + 6*I*(a^3 + a*b^2)*c^2*f^3 + 6*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (6*I*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*(a^2*b + b^3)*d^2*f^3*x^2 + 12*I*(a^3 + a*b^2)*d^2*e*f^2*x - 12*(a^2*b + b^3)*d^2*e*f^2*x + 12*I*(a^3 + a*b^2)*c*d*e*f^2 - 12*(a^2*b + b^3)*c*d*e*f^2 - 6*I*(a^3 + a*b^2)*c^2*f^3 + 6*(a^2*b + b^3)*c^2*f^3 + (6*I*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*(a^2*b + b^3)*d^2*f^3*x^2 + 12*I*(a^3 + a*b^2)*d^2*e*f^2*x - 12*(a^2*b + b^3)*d^2*e*f^2*x + 12*I*(a^3 + a*b^2)*c*d*e*f^2 - 12*(a^2*b + b^3)*c*d*e*f^2 - 6*I*(a^3 + a*b^2)*c^2*f^3 + 6*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*I*(a^3 + a*b^2)*d^2*f^3*x^2 - 12*(a^2*b + b^3)*d^2*f^3*x^2 + 24*I*(a^3 + a*b^2)*d^2*e*f^2*x - 24*(a^2*b + b^3)*d^2*e*f^2*x + 24*I*(a^3 + a*b^2)*c*d*e*f^2 - 24*(a^2*b + b^3)*c*d*e*f^2 - 12*I*(a^3 + a*b^2)*c^2*f^3 + 12*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*I*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*(a^2*b + b^3)*d^2*f^3*x^2 + 12*I*(a^3 + a*b^2)*d^2*e*f^2*x - 12*(a^2*b + b^3)*d^2*e*f^2*x + 12*I*(a^3 + a*b^2)*c*d*e*f^2 - 12*(a^2*b + b^3)*c*d*e*f^2 - 6*I*(a^3 + a*b^2)*c^2*f^3 + 6*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - (-12*I*(a^3 + a*b^2)*f^3 + 12*(a^2*b + b^3)*f^3 + (-12*I*(a^3 + a*b^2)*f^3 + 12*(a^2*b + b^3)*f^3)*cosh(d*x + c)^2 + (-24*I*(a^3 + a*b^2)*f^3 + 24*(a^2*b + b^3)*f^3)*cosh(d*x + c)*sinh(d*x + c) + (-12*I*(a^3 + a*b^2)*f^3 + 12*(a^2*b + b^3)*f^3)*sinh(d*x + c)^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - (12*I*(a^3 + a*b^2)*f^3 + 12*(a^2*b + b^3)*f^3 + (12*I*(a^3 + a*b^2)*f^3 + 12*(a^2*b + b^3)*f^3)*cosh(d*x + c)^2 + (24*I*(a^3 + a*b^2)*f^3 + 24*(a^2*b + b^3)*f^3)*cosh(d*x + c)*sinh(d*x + c) + (12*I*(a^3 + a*b^2)*f^3 + 12*(a^2*b + b^3)*f^3)*sinh(d*x + c)^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) + 4*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + (a^3 + a*b^2)*d^3*e^3 - 2*((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*d^3*e*f^2*x^2 + 3*(a^2*b + b^3)*d^3*e^2*f*x + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*(a^2*b + b^3)*c^2*d*e*f^2 + (a^2*b + b^3)*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^4*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^4*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d^4*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^4)","C",0
354,1,3690,0,1.054948," ","integrate((f*x+e)^2*sech(d*x+c)*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 8 \, {\left(a^{2} b + b^{3}\right)} c d e f + 4 \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{2} - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left(a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left(a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f + {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f + {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2} + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2} + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left(a b^{2} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b^{2} f^{2} \sinh\left(d x + c\right)^{2} + a b^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(a b^{2} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b^{2} f^{2} \sinh\left(d x + c\right)^{2} + a b^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) - {\left(4 i \, {\left(a^{3} + a b^{2}\right)} f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} f^{2} + {\left(4 i \, {\left(a^{3} + a b^{2}\right)} f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 i \, {\left(a^{3} + a b^{2}\right)} f^{2} - 8 \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 i \, {\left(a^{3} + a b^{2}\right)} f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(-4 i \, {\left(a^{3} + a b^{2}\right)} f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} f^{2} + {\left(-4 i \, {\left(a^{3} + a b^{2}\right)} f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-8 i \, {\left(a^{3} + a b^{2}\right)} f^{2} - 8 \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-4 i \, {\left(a^{3} + a b^{2}\right)} f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - {\left(4 i \, {\left(a^{3} + a b^{2}\right)} d e f - 4 \, {\left(a^{2} b + b^{3}\right)} d e f - 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(4 i \, {\left(a^{3} + a b^{2}\right)} d e f - 4 \, {\left(a^{2} b + b^{3}\right)} d e f - 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 i \, {\left(a^{3} + a b^{2}\right)} d e f - 8 \, {\left(a^{2} b + b^{3}\right)} d e f - 8 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 8 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 i \, {\left(a^{3} + a b^{2}\right)} d e f - 4 \, {\left(a^{2} b + b^{3}\right)} d e f - 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(-4 i \, {\left(a^{3} + a b^{2}\right)} d e f - 4 \, {\left(a^{2} b + b^{3}\right)} d e f + 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(-4 i \, {\left(a^{3} + a b^{2}\right)} d e f - 4 \, {\left(a^{2} b + b^{3}\right)} d e f + 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-8 i \, {\left(a^{3} + a b^{2}\right)} d e f - 8 \, {\left(a^{2} b + b^{3}\right)} d e f + 8 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 8 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-4 i \, {\left(a^{3} + a b^{2}\right)} d e f - 4 \, {\left(a^{2} b + b^{3}\right)} d e f + 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(-4 i \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 \, {\left(a^{2} b + b^{3}\right)} d f^{2} x - 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(-4 i \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 \, {\left(a^{2} b + b^{3}\right)} d f^{2} x - 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-8 i \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 8 \, {\left(a^{2} b + b^{3}\right)} d f^{2} x - 8 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 8 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-4 i \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 \, {\left(a^{2} b + b^{3}\right)} d f^{2} x - 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(4 i \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(4 i \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 i \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 8 \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 8 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 8 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 i \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 i \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left(a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3}\right)}}"," ",0,"-1/2*(4*(a^2*b + b^3)*d^2*e^2 - 8*(a^2*b + b^3)*c*d*e*f + 4*(a^2*b + b^3)*c^2*f^2 - 4*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*d^2*e*f*x + 2*(a^2*b + b^3)*c*d*e*f - (a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)^2 - 4*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*d^2*e*f*x + 2*(a^2*b + b^3)*c*d*e*f - (a^2*b + b^3)*c^2*f^2)*sinh(d*x + c)^2 + 4*(a*b^2*d*f^2*x + a*b^2*d*e*f + (a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d*f^2*x + a*b^2*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 4*(a*b^2*d*f^2*x + a*b^2*d*e*f + (a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d*f^2*x + a*b^2*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2 + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2 + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*(a*b^2*f^2*cosh(d*x + c)^2 + 2*a*b^2*f^2*cosh(d*x + c)*sinh(d*x + c) + a*b^2*f^2*sinh(d*x + c)^2 + a*b^2*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*(a*b^2*f^2*cosh(d*x + c)^2 + 2*a*b^2*f^2*cosh(d*x + c)*sinh(d*x + c) + a*b^2*f^2*sinh(d*x + c)^2 + a*b^2*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + (a^3 + a*b^2)*d^2*e^2)*cosh(d*x + c) - (4*I*(a^3 + a*b^2)*f^2 - 4*(a^2*b + b^3)*f^2 + (4*I*(a^3 + a*b^2)*f^2 - 4*(a^2*b + b^3)*f^2)*cosh(d*x + c)^2 + (8*I*(a^3 + a*b^2)*f^2 - 8*(a^2*b + b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*I*(a^3 + a*b^2)*f^2 - 4*(a^2*b + b^3)*f^2)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (-4*I*(a^3 + a*b^2)*f^2 - 4*(a^2*b + b^3)*f^2 + (-4*I*(a^3 + a*b^2)*f^2 - 4*(a^2*b + b^3)*f^2)*cosh(d*x + c)^2 + (-8*I*(a^3 + a*b^2)*f^2 - 8*(a^2*b + b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-4*I*(a^3 + a*b^2)*f^2 - 4*(a^2*b + b^3)*f^2)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - (4*I*(a^3 + a*b^2)*d*e*f - 4*(a^2*b + b^3)*d*e*f - 4*I*(a^3 + a*b^2)*c*f^2 + 4*(a^2*b + b^3)*c*f^2 + (4*I*(a^3 + a*b^2)*d*e*f - 4*(a^2*b + b^3)*d*e*f - 4*I*(a^3 + a*b^2)*c*f^2 + 4*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (8*I*(a^3 + a*b^2)*d*e*f - 8*(a^2*b + b^3)*d*e*f - 8*I*(a^3 + a*b^2)*c*f^2 + 8*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*I*(a^3 + a*b^2)*d*e*f - 4*(a^2*b + b^3)*d*e*f - 4*I*(a^3 + a*b^2)*c*f^2 + 4*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (-4*I*(a^3 + a*b^2)*d*e*f - 4*(a^2*b + b^3)*d*e*f + 4*I*(a^3 + a*b^2)*c*f^2 + 4*(a^2*b + b^3)*c*f^2 + (-4*I*(a^3 + a*b^2)*d*e*f - 4*(a^2*b + b^3)*d*e*f + 4*I*(a^3 + a*b^2)*c*f^2 + 4*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (-8*I*(a^3 + a*b^2)*d*e*f - 8*(a^2*b + b^3)*d*e*f + 8*I*(a^3 + a*b^2)*c*f^2 + 8*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-4*I*(a^3 + a*b^2)*d*e*f - 4*(a^2*b + b^3)*d*e*f + 4*I*(a^3 + a*b^2)*c*f^2 + 4*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) - (-4*I*(a^3 + a*b^2)*d*f^2*x - 4*(a^2*b + b^3)*d*f^2*x - 4*I*(a^3 + a*b^2)*c*f^2 - 4*(a^2*b + b^3)*c*f^2 + (-4*I*(a^3 + a*b^2)*d*f^2*x - 4*(a^2*b + b^3)*d*f^2*x - 4*I*(a^3 + a*b^2)*c*f^2 - 4*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (-8*I*(a^3 + a*b^2)*d*f^2*x - 8*(a^2*b + b^3)*d*f^2*x - 8*I*(a^3 + a*b^2)*c*f^2 - 8*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-4*I*(a^3 + a*b^2)*d*f^2*x - 4*(a^2*b + b^3)*d*f^2*x - 4*I*(a^3 + a*b^2)*c*f^2 - 4*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (4*I*(a^3 + a*b^2)*d*f^2*x - 4*(a^2*b + b^3)*d*f^2*x + 4*I*(a^3 + a*b^2)*c*f^2 - 4*(a^2*b + b^3)*c*f^2 + (4*I*(a^3 + a*b^2)*d*f^2*x - 4*(a^2*b + b^3)*d*f^2*x + 4*I*(a^3 + a*b^2)*c*f^2 - 4*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (8*I*(a^3 + a*b^2)*d*f^2*x - 8*(a^2*b + b^3)*d*f^2*x + 8*I*(a^3 + a*b^2)*c*f^2 - 8*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*I*(a^3 + a*b^2)*d*f^2*x - 4*(a^2*b + b^3)*d*f^2*x + 4*I*(a^3 + a*b^2)*c*f^2 - 4*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + 4*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + (a^3 + a*b^2)*d^2*e^2 - 2*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*d^2*e*f*x + 2*(a^2*b + b^3)*c*d*e*f - (a^2*b + b^3)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d^3*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3)","C",0
355,1,1338,0,0.543092," ","integrate((f*x+e)*sech(d*x+c)*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} b + b^{3}\right)} d f x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d f x \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e - {\left(a b^{2} f \cosh\left(d x + c\right)^{2} + 2 \, a b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b^{2} f \sinh\left(d x + c\right)^{2} + a b^{2} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(a b^{2} f \cosh\left(d x + c\right)^{2} + 2 \, a b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b^{2} f \sinh\left(d x + c\right)^{2} + a b^{2} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(a b^{2} d e - a b^{2} c f + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d e - a b^{2} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(a b^{2} d e - a b^{2} c f + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d e - a b^{2} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(a b^{2} d f x + a b^{2} c f + {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d f x + a b^{2} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(a b^{2} d f x + a b^{2} c f + {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b^{2} d f x + a b^{2} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} + a b^{2}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{2} b + b^{3}\right)} f\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d f x \cosh\left(d x + c\right) - {\left(a^{3} + a b^{2}\right)} d f x - {\left(a^{3} + a b^{2}\right)} d e\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}"," ",0,"(2*(a^2*b + b^3)*d*f*x*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*d*f*x*sinh(d*x + c)^2 - 2*(a^2*b + b^3)*d*e - (a*b^2*f*cosh(d*x + c)^2 + 2*a*b^2*f*cosh(d*x + c)*sinh(d*x + c) + a*b^2*f*sinh(d*x + c)^2 + a*b^2*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (a*b^2*f*cosh(d*x + c)^2 + 2*a*b^2*f*cosh(d*x + c)*sinh(d*x + c) + a*b^2*f*sinh(d*x + c)^2 + a*b^2*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (a*b^2*d*e - a*b^2*c*f + (a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d*e - a*b^2*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (a*b^2*d*e - a*b^2*c*f + (a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d*e - a*b^2*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (a*b^2*d*f*x + a*b^2*c*f + (a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d*f*x + a*b^2*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (a*b^2*d*f*x + a*b^2*c*f + (a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a*b^2*d*f*x + a*b^2*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*((a^3 + a*b^2)*f*cosh(d*x + c)^2 + 2*(a^3 + a*b^2)*f*cosh(d*x + c)*sinh(d*x + c) + (a^3 + a*b^2)*f*sinh(d*x + c)^2 + (a^3 + a*b^2)*f)*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e)*cosh(d*x + c) - ((a^2*b + b^3)*f*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f*sinh(d*x + c)^2 + (a^2*b + b^3)*f)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(2*(a^2*b + b^3)*d*f*x*cosh(d*x + c) - (a^3 + a*b^2)*d*f*x - (a^3 + a*b^2)*d*e)*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d^2*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)","B",0
356,1,350,0,0.645725," ","integrate(sech(d*x+c)*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a^{2} b + 2 \, b^{3} - {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + a b\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 2 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(a^{3} + a b^{2}\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d}"," ",0,"-(2*a^2*b + 2*b^3 - (a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + a*b)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 2*(a^3 + a*b^2)*cosh(d*x + c) + 2*(a^3 + a*b^2)*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d)","B",0
357,0,0,0,0.516262," ","integrate(sech(d*x+c)*tanh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(d x + c\right) \tanh\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sech(d*x + c)*tanh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
358,1,11122,0,0.936558," ","integrate((f*x+e)^2*sech(d*x+c)^2*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{3} + a b^{2}\right)} d e f + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x + 8 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + {\left(a^{3} + a b^{2}\right)} d e f - 2 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + {\left(2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 12 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) - 4 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f + {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f + 3 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f + {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f + 3 \, {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(a b^{2} d f^{2} x + a b^{2} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(4 \, a b^{2} d f^{2} x + 4 \, a b^{2} d e f - 2 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + {\left(4 \, a b^{2} d f^{2} x + 4 \, a b^{2} d e f - 2 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 2 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a b^{2} d f^{2} x + 16 \, a b^{2} d e f - 8 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 8 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a b^{2} d f^{2} x + 4 \, a b^{2} d e f - 2 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 2 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 i \, {\left(a^{2} b - b^{3}\right)} d e f + {\left(8 \, a b^{2} d f^{2} x + 8 \, a b^{2} d e f - 4 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 4 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, a b^{2} d f^{2} x + 8 \, a b^{2} d e f - 4 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 4 i \, {\left(a^{2} b - b^{3}\right)} d e f + {\left(24 \, a b^{2} d f^{2} x + 24 \, a b^{2} d e f - 12 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 12 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, a b^{2} d f^{2} x + 16 \, a b^{2} d e f - 8 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 8 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a b^{2} d f^{2} x + 16 \, a b^{2} d e f - 8 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x - 8 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(4 \, a b^{2} d f^{2} x + 4 \, a b^{2} d e f + 2 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + {\left(4 \, a b^{2} d f^{2} x + 4 \, a b^{2} d e f + 2 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 2 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a b^{2} d f^{2} x + 16 \, a b^{2} d e f + 8 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 8 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a b^{2} d f^{2} x + 4 \, a b^{2} d e f + 2 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 2 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \sinh\left(d x + c\right)^{4} + 2 i \, {\left(a^{2} b - b^{3}\right)} d e f + {\left(8 \, a b^{2} d f^{2} x + 8 \, a b^{2} d e f + 4 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 4 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, a b^{2} d f^{2} x + 8 \, a b^{2} d e f + 4 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 4 i \, {\left(a^{2} b - b^{3}\right)} d e f + {\left(24 \, a b^{2} d f^{2} x + 24 \, a b^{2} d e f + 12 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 12 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, a b^{2} d f^{2} x + 16 \, a b^{2} d e f + 8 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 8 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a b^{2} d f^{2} x + 16 \, a b^{2} d e f + 8 i \, {\left(a^{2} b - b^{3}\right)} d f^{2} x + 8 i \, {\left(a^{2} b - b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2} + 3 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2} + 3 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2} + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2} + 3 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2} + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2} + 3 \, {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e f x + 2 \, a b^{2} c d e f - a b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(2 \, a b^{2} d^{2} e^{2} - 4 \, a b^{2} c d e f - i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f + {\left(2 \, a b^{2} d^{2} e^{2} - 4 \, a b^{2} c d e f - i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 2 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} - i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b^{2} d^{2} e^{2} - 16 \, a b^{2} c d e f - 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 8 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} - 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b^{2} d^{2} e^{2} - 4 \, a b^{2} c d e f - i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 2 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} - i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} - i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2} + {\left(4 \, a b^{2} d^{2} e^{2} - 8 \, a b^{2} c d e f - 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 4 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 4 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} - 2 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a b^{2} d^{2} e^{2} - 8 \, a b^{2} c d e f - 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 4 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 4 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} - 2 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2} + {\left(12 \, a b^{2} d^{2} e^{2} - 24 \, a b^{2} c d e f - 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 12 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 12 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} - 6 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a b^{2} d^{2} e^{2} - 16 \, a b^{2} c d e f - 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 8 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} - 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} d^{2} e^{2} - 16 \, a b^{2} c d e f - 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 8 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} - 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(2 \, a b^{2} d^{2} e^{2} - 4 \, a b^{2} c d e f + i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f + {\left(2 \, a b^{2} d^{2} e^{2} - 4 \, a b^{2} c d e f + i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 2 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} + i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b^{2} d^{2} e^{2} - 16 \, a b^{2} c d e f + 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 8 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} + 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b^{2} d^{2} e^{2} - 4 \, a b^{2} c d e f + i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 2 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} + i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} + i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2} + {\left(4 \, a b^{2} d^{2} e^{2} - 8 \, a b^{2} c d e f + 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 4 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 4 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} + 2 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a b^{2} d^{2} e^{2} - 8 \, a b^{2} c d e f + 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 4 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 4 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} + 2 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2} + {\left(12 \, a b^{2} d^{2} e^{2} - 24 \, a b^{2} c d e f + 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 12 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 12 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} + 6 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a b^{2} d^{2} e^{2} - 16 \, a b^{2} c d e f + 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 8 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} + 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} d^{2} e^{2} - 16 \, a b^{2} c d e f + 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 8 \, {\left(a b^{2} c^{2} - a^{3} - a b^{2}\right)} f^{2} + 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(a^{2} b - b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 4 \, a b^{2} d^{2} e f x + 4 \, a b^{2} c d e f - 2 \, a b^{2} c^{2} f^{2} + i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f - i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2} + {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 4 \, a b^{2} d^{2} e f x + 4 \, a b^{2} c d e f - 2 \, a b^{2} c^{2} f^{2} + i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f - i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b^{2} d^{2} f^{2} x^{2} + 16 \, a b^{2} d^{2} e f x + 16 \, a b^{2} c d e f - 8 \, a b^{2} c^{2} f^{2} + 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f - 4 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 4 \, a b^{2} d^{2} e f x + 4 \, a b^{2} c d e f - 2 \, a b^{2} c^{2} f^{2} + i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f - i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, a b^{2} d^{2} f^{2} x^{2} + 8 \, a b^{2} d^{2} e f x + 8 \, a b^{2} c d e f - 4 \, a b^{2} c^{2} f^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 4 i \, {\left(a^{2} b - b^{3}\right)} c d e f - 2 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a b^{2} d^{2} f^{2} x^{2} + 8 \, a b^{2} d^{2} e f x + 8 \, a b^{2} c d e f - 4 \, a b^{2} c^{2} f^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 4 i \, {\left(a^{2} b - b^{3}\right)} c d e f - 2 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2} + {\left(12 \, a b^{2} d^{2} f^{2} x^{2} + 24 \, a b^{2} d^{2} e f x + 24 \, a b^{2} c d e f - 12 \, a b^{2} c^{2} f^{2} + 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 12 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 12 i \, {\left(a^{2} b - b^{3}\right)} c d e f - 6 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a b^{2} d^{2} f^{2} x^{2} + 16 \, a b^{2} d^{2} e f x + 16 \, a b^{2} c d e f - 8 \, a b^{2} c^{2} f^{2} + 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f - 4 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} d^{2} f^{2} x^{2} + 16 \, a b^{2} d^{2} e f x + 16 \, a b^{2} c d e f - 8 \, a b^{2} c^{2} f^{2} + 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x + 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f - 4 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 4 \, a b^{2} d^{2} e f x + 4 \, a b^{2} c d e f - 2 \, a b^{2} c^{2} f^{2} - i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x - 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f + i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2} + {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 4 \, a b^{2} d^{2} e f x + 4 \, a b^{2} c d e f - 2 \, a b^{2} c^{2} f^{2} - i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x - 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f + i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b^{2} d^{2} f^{2} x^{2} + 16 \, a b^{2} d^{2} e f x + 16 \, a b^{2} c d e f - 8 \, a b^{2} c^{2} f^{2} - 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x - 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 4 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 4 \, a b^{2} d^{2} e f x + 4 \, a b^{2} c d e f - 2 \, a b^{2} c^{2} f^{2} - i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x - 2 i \, {\left(a^{2} b - b^{3}\right)} c d e f + i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, a b^{2} d^{2} f^{2} x^{2} + 8 \, a b^{2} d^{2} e f x + 8 \, a b^{2} c d e f - 4 \, a b^{2} c^{2} f^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x - 4 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 2 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a b^{2} d^{2} f^{2} x^{2} + 8 \, a b^{2} d^{2} e f x + 8 \, a b^{2} c d e f - 4 \, a b^{2} c^{2} f^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x - 4 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 2 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2} + {\left(12 \, a b^{2} d^{2} f^{2} x^{2} + 24 \, a b^{2} d^{2} e f x + 24 \, a b^{2} c d e f - 12 \, a b^{2} c^{2} f^{2} - 6 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 12 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x - 12 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 6 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a b^{2} d^{2} f^{2} x^{2} + 16 \, a b^{2} d^{2} e f x + 16 \, a b^{2} c d e f - 8 \, a b^{2} c^{2} f^{2} - 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x - 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 4 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} d^{2} f^{2} x^{2} + 16 \, a b^{2} d^{2} e f x + 16 \, a b^{2} c d e f - 8 \, a b^{2} c^{2} f^{2} - 4 i \, {\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(a^{2} b - b^{3}\right)} d^{2} e f x - 8 i \, {\left(a^{2} b - b^{3}\right)} c d e f + 4 i \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + 4 \, {\left(a b^{2} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, a b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b^{2} f^{2} \sinh\left(d x + c\right)^{4} + 2 \, a b^{2} f^{2} \cosh\left(d x + c\right)^{2} + a b^{2} f^{2} + 2 \, {\left(3 \, a b^{2} f^{2} \cosh\left(d x + c\right)^{2} + a b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} f^{2} \cosh\left(d x + c\right)^{3} + a b^{2} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(a b^{2} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, a b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b^{2} f^{2} \sinh\left(d x + c\right)^{4} + 2 \, a b^{2} f^{2} \cosh\left(d x + c\right)^{2} + a b^{2} f^{2} + 2 \, {\left(3 \, a b^{2} f^{2} \cosh\left(d x + c\right)^{2} + a b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} f^{2} \cosh\left(d x + c\right)^{3} + a b^{2} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - {\left(4 \, a b^{2} f^{2} + {\left(4 \, a b^{2} f^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a b^{2} f^{2} - 8 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a b^{2} f^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 i \, {\left(a^{2} b - b^{3}\right)} f^{2} + {\left(8 \, a b^{2} f^{2} - 4 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, a b^{2} f^{2} - 4 i \, {\left(a^{2} b - b^{3}\right)} f^{2} + {\left(24 \, a b^{2} f^{2} - 12 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, a b^{2} f^{2} - 8 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a b^{2} f^{2} - 8 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(4 \, a b^{2} f^{2} + {\left(4 \, a b^{2} f^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a b^{2} f^{2} + 8 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a b^{2} f^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 i \, {\left(a^{2} b - b^{3}\right)} f^{2} + {\left(8 \, a b^{2} f^{2} + 4 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, a b^{2} f^{2} + 4 i \, {\left(a^{2} b - b^{3}\right)} f^{2} + {\left(24 \, a b^{2} f^{2} + 12 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, a b^{2} f^{2} + 8 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a b^{2} f^{2} + 8 i \, {\left(a^{2} b - b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e f - 8 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + {\left(a^{3} + a b^{2}\right)} d e f - 2 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + {\left(2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(4*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*c*f^2)*cosh(d*x + c)^4 + 4*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*c*f^2)*sinh(d*x + c)^4 - 4*(a^3 + a*b^2)*d*e*f + 4*(a^3 + a*b^2)*c*f^2 + 2*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^3 + 2*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^2*b + b^3)*d*f^2)*x + 8*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + (a^3 + a*b^2)*d*e*f - 2*(a^3 + a*b^2)*c*f^2 + (2*(a^3 + a*b^2)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)^2 - 2*(2*(a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 - 12*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*c*f^2)*cosh(d*x + c)^2 + 2*(2*(a^3 + a*b^2)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x - 3*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 - 2*(a^2*b + b^3)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c) - 4*(a*b^2*d*f^2*x + a*b^2*d*e*f + (a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)^4 + 4*(a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2*d*f^2*x + a*b^2*d*e*f)*sinh(d*x + c)^4 + 2*(a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*f^2*x + a*b^2*d*e*f + 3*(a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)^3 + (a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 4*(a*b^2*d*f^2*x + a*b^2*d*e*f + (a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)^4 + 4*(a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2*d*f^2*x + a*b^2*d*e*f)*sinh(d*x + c)^4 + 2*(a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*f^2*x + a*b^2*d*e*f + 3*(a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c)^3 + (a*b^2*d*f^2*x + a*b^2*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (4*a*b^2*d*f^2*x + 4*a*b^2*d*e*f - 2*I*(a^2*b - b^3)*d*f^2*x + (4*a*b^2*d*f^2*x + 4*a*b^2*d*e*f - 2*I*(a^2*b - b^3)*d*f^2*x - 2*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c)^4 + (16*a*b^2*d*f^2*x + 16*a*b^2*d*e*f - 8*I*(a^2*b - b^3)*d*f^2*x - 8*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a*b^2*d*f^2*x + 4*a*b^2*d*e*f - 2*I*(a^2*b - b^3)*d*f^2*x - 2*I*(a^2*b - b^3)*d*e*f)*sinh(d*x + c)^4 - 2*I*(a^2*b - b^3)*d*e*f + (8*a*b^2*d*f^2*x + 8*a*b^2*d*e*f - 4*I*(a^2*b - b^3)*d*f^2*x - 4*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c)^2 + (8*a*b^2*d*f^2*x + 8*a*b^2*d*e*f - 4*I*(a^2*b - b^3)*d*f^2*x - 4*I*(a^2*b - b^3)*d*e*f + (24*a*b^2*d*f^2*x + 24*a*b^2*d*e*f - 12*I*(a^2*b - b^3)*d*f^2*x - 12*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*a*b^2*d*f^2*x + 16*a*b^2*d*e*f - 8*I*(a^2*b - b^3)*d*f^2*x - 8*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c)^3 + (16*a*b^2*d*f^2*x + 16*a*b^2*d*e*f - 8*I*(a^2*b - b^3)*d*f^2*x - 8*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (4*a*b^2*d*f^2*x + 4*a*b^2*d*e*f + 2*I*(a^2*b - b^3)*d*f^2*x + (4*a*b^2*d*f^2*x + 4*a*b^2*d*e*f + 2*I*(a^2*b - b^3)*d*f^2*x + 2*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c)^4 + (16*a*b^2*d*f^2*x + 16*a*b^2*d*e*f + 8*I*(a^2*b - b^3)*d*f^2*x + 8*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a*b^2*d*f^2*x + 4*a*b^2*d*e*f + 2*I*(a^2*b - b^3)*d*f^2*x + 2*I*(a^2*b - b^3)*d*e*f)*sinh(d*x + c)^4 + 2*I*(a^2*b - b^3)*d*e*f + (8*a*b^2*d*f^2*x + 8*a*b^2*d*e*f + 4*I*(a^2*b - b^3)*d*f^2*x + 4*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c)^2 + (8*a*b^2*d*f^2*x + 8*a*b^2*d*e*f + 4*I*(a^2*b - b^3)*d*f^2*x + 4*I*(a^2*b - b^3)*d*e*f + (24*a*b^2*d*f^2*x + 24*a*b^2*d*e*f + 12*I*(a^2*b - b^3)*d*f^2*x + 12*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*a*b^2*d*f^2*x + 16*a*b^2*d*e*f + 8*I*(a^2*b - b^3)*d*f^2*x + 8*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c)^3 + (16*a*b^2*d*f^2*x + 16*a*b^2*d*e*f + 8*I*(a^2*b - b^3)*d*f^2*x + 8*I*(a^2*b - b^3)*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sinh(d*x + c)^4 + 2*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2 + 3*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)^3 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sinh(d*x + c)^4 + 2*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2 + 3*(a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c)^3 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2 + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*sinh(d*x + c)^4 + 2*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2 + 3*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)^3 + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2 + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*sinh(d*x + c)^4 + 2*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2 + 3*(a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c)^3 + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e*f*x + 2*a*b^2*c*d*e*f - a*b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (2*a*b^2*d^2*e^2 - 4*a*b^2*c*d*e*f - I*(a^2*b - b^3)*d^2*e^2 + 2*I*(a^2*b - b^3)*c*d*e*f + (2*a*b^2*d^2*e^2 - 4*a*b^2*c*d*e*f - I*(a^2*b - b^3)*d^2*e^2 + 2*I*(a^2*b - b^3)*c*d*e*f + 2*(a*b^2*c^2 - a^3 - a*b^2)*f^2 - I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c)^4 + (8*a*b^2*d^2*e^2 - 16*a*b^2*c*d*e*f - 4*I*(a^2*b - b^3)*d^2*e^2 + 8*I*(a^2*b - b^3)*c*d*e*f + 8*(a*b^2*c^2 - a^3 - a*b^2)*f^2 - 4*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b^2*d^2*e^2 - 4*a*b^2*c*d*e*f - I*(a^2*b - b^3)*d^2*e^2 + 2*I*(a^2*b - b^3)*c*d*e*f + 2*(a*b^2*c^2 - a^3 - a*b^2)*f^2 - I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*sinh(d*x + c)^4 + 2*(a*b^2*c^2 - a^3 - a*b^2)*f^2 - I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2 + (4*a*b^2*d^2*e^2 - 8*a*b^2*c*d*e*f - 2*I*(a^2*b - b^3)*d^2*e^2 + 4*I*(a^2*b - b^3)*c*d*e*f + 4*(a*b^2*c^2 - a^3 - a*b^2)*f^2 - 2*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c)^2 + (4*a*b^2*d^2*e^2 - 8*a*b^2*c*d*e*f - 2*I*(a^2*b - b^3)*d^2*e^2 + 4*I*(a^2*b - b^3)*c*d*e*f + 4*(a*b^2*c^2 - a^3 - a*b^2)*f^2 - 2*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2 + (12*a*b^2*d^2*e^2 - 24*a*b^2*c*d*e*f - 6*I*(a^2*b - b^3)*d^2*e^2 + 12*I*(a^2*b - b^3)*c*d*e*f + 12*(a*b^2*c^2 - a^3 - a*b^2)*f^2 - 6*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a*b^2*d^2*e^2 - 16*a*b^2*c*d*e*f - 4*I*(a^2*b - b^3)*d^2*e^2 + 8*I*(a^2*b - b^3)*c*d*e*f + 8*(a*b^2*c^2 - a^3 - a*b^2)*f^2 - 4*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c)^3 + (8*a*b^2*d^2*e^2 - 16*a*b^2*c*d*e*f - 4*I*(a^2*b - b^3)*d^2*e^2 + 8*I*(a^2*b - b^3)*c*d*e*f + 8*(a*b^2*c^2 - a^3 - a*b^2)*f^2 - 4*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) + (2*a*b^2*d^2*e^2 - 4*a*b^2*c*d*e*f + I*(a^2*b - b^3)*d^2*e^2 - 2*I*(a^2*b - b^3)*c*d*e*f + (2*a*b^2*d^2*e^2 - 4*a*b^2*c*d*e*f + I*(a^2*b - b^3)*d^2*e^2 - 2*I*(a^2*b - b^3)*c*d*e*f + 2*(a*b^2*c^2 - a^3 - a*b^2)*f^2 + I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c)^4 + (8*a*b^2*d^2*e^2 - 16*a*b^2*c*d*e*f + 4*I*(a^2*b - b^3)*d^2*e^2 - 8*I*(a^2*b - b^3)*c*d*e*f + 8*(a*b^2*c^2 - a^3 - a*b^2)*f^2 + 4*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b^2*d^2*e^2 - 4*a*b^2*c*d*e*f + I*(a^2*b - b^3)*d^2*e^2 - 2*I*(a^2*b - b^3)*c*d*e*f + 2*(a*b^2*c^2 - a^3 - a*b^2)*f^2 + I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*sinh(d*x + c)^4 + 2*(a*b^2*c^2 - a^3 - a*b^2)*f^2 + I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2 + (4*a*b^2*d^2*e^2 - 8*a*b^2*c*d*e*f + 2*I*(a^2*b - b^3)*d^2*e^2 - 4*I*(a^2*b - b^3)*c*d*e*f + 4*(a*b^2*c^2 - a^3 - a*b^2)*f^2 + 2*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c)^2 + (4*a*b^2*d^2*e^2 - 8*a*b^2*c*d*e*f + 2*I*(a^2*b - b^3)*d^2*e^2 - 4*I*(a^2*b - b^3)*c*d*e*f + 4*(a*b^2*c^2 - a^3 - a*b^2)*f^2 + 2*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2 + (12*a*b^2*d^2*e^2 - 24*a*b^2*c*d*e*f + 6*I*(a^2*b - b^3)*d^2*e^2 - 12*I*(a^2*b - b^3)*c*d*e*f + 12*(a*b^2*c^2 - a^3 - a*b^2)*f^2 + 6*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a*b^2*d^2*e^2 - 16*a*b^2*c*d*e*f + 4*I*(a^2*b - b^3)*d^2*e^2 - 8*I*(a^2*b - b^3)*c*d*e*f + 8*(a*b^2*c^2 - a^3 - a*b^2)*f^2 + 4*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c)^3 + (8*a*b^2*d^2*e^2 - 16*a*b^2*c*d*e*f + 4*I*(a^2*b - b^3)*d^2*e^2 - 8*I*(a^2*b - b^3)*c*d*e*f + 8*(a*b^2*c^2 - a^3 - a*b^2)*f^2 + 4*I*(2*a^2*b + 2*b^3 + (a^2*b - b^3)*c^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) + (2*a*b^2*d^2*f^2*x^2 + 4*a*b^2*d^2*e*f*x + 4*a*b^2*c*d*e*f - 2*a*b^2*c^2*f^2 + I*(a^2*b - b^3)*d^2*f^2*x^2 + 2*I*(a^2*b - b^3)*d^2*e*f*x + 2*I*(a^2*b - b^3)*c*d*e*f - I*(a^2*b - b^3)*c^2*f^2 + (2*a*b^2*d^2*f^2*x^2 + 4*a*b^2*d^2*e*f*x + 4*a*b^2*c*d*e*f - 2*a*b^2*c^2*f^2 + I*(a^2*b - b^3)*d^2*f^2*x^2 + 2*I*(a^2*b - b^3)*d^2*e*f*x + 2*I*(a^2*b - b^3)*c*d*e*f - I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c)^4 + (8*a*b^2*d^2*f^2*x^2 + 16*a*b^2*d^2*e*f*x + 16*a*b^2*c*d*e*f - 8*a*b^2*c^2*f^2 + 4*I*(a^2*b - b^3)*d^2*f^2*x^2 + 8*I*(a^2*b - b^3)*d^2*e*f*x + 8*I*(a^2*b - b^3)*c*d*e*f - 4*I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b^2*d^2*f^2*x^2 + 4*a*b^2*d^2*e*f*x + 4*a*b^2*c*d*e*f - 2*a*b^2*c^2*f^2 + I*(a^2*b - b^3)*d^2*f^2*x^2 + 2*I*(a^2*b - b^3)*d^2*e*f*x + 2*I*(a^2*b - b^3)*c*d*e*f - I*(a^2*b - b^3)*c^2*f^2)*sinh(d*x + c)^4 + (4*a*b^2*d^2*f^2*x^2 + 8*a*b^2*d^2*e*f*x + 8*a*b^2*c*d*e*f - 4*a*b^2*c^2*f^2 + 2*I*(a^2*b - b^3)*d^2*f^2*x^2 + 4*I*(a^2*b - b^3)*d^2*e*f*x + 4*I*(a^2*b - b^3)*c*d*e*f - 2*I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c)^2 + (4*a*b^2*d^2*f^2*x^2 + 8*a*b^2*d^2*e*f*x + 8*a*b^2*c*d*e*f - 4*a*b^2*c^2*f^2 + 2*I*(a^2*b - b^3)*d^2*f^2*x^2 + 4*I*(a^2*b - b^3)*d^2*e*f*x + 4*I*(a^2*b - b^3)*c*d*e*f - 2*I*(a^2*b - b^3)*c^2*f^2 + (12*a*b^2*d^2*f^2*x^2 + 24*a*b^2*d^2*e*f*x + 24*a*b^2*c*d*e*f - 12*a*b^2*c^2*f^2 + 6*I*(a^2*b - b^3)*d^2*f^2*x^2 + 12*I*(a^2*b - b^3)*d^2*e*f*x + 12*I*(a^2*b - b^3)*c*d*e*f - 6*I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a*b^2*d^2*f^2*x^2 + 16*a*b^2*d^2*e*f*x + 16*a*b^2*c*d*e*f - 8*a*b^2*c^2*f^2 + 4*I*(a^2*b - b^3)*d^2*f^2*x^2 + 8*I*(a^2*b - b^3)*d^2*e*f*x + 8*I*(a^2*b - b^3)*c*d*e*f - 4*I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c)^3 + (8*a*b^2*d^2*f^2*x^2 + 16*a*b^2*d^2*e*f*x + 16*a*b^2*c*d*e*f - 8*a*b^2*c^2*f^2 + 4*I*(a^2*b - b^3)*d^2*f^2*x^2 + 8*I*(a^2*b - b^3)*d^2*e*f*x + 8*I*(a^2*b - b^3)*c*d*e*f - 4*I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (2*a*b^2*d^2*f^2*x^2 + 4*a*b^2*d^2*e*f*x + 4*a*b^2*c*d*e*f - 2*a*b^2*c^2*f^2 - I*(a^2*b - b^3)*d^2*f^2*x^2 - 2*I*(a^2*b - b^3)*d^2*e*f*x - 2*I*(a^2*b - b^3)*c*d*e*f + I*(a^2*b - b^3)*c^2*f^2 + (2*a*b^2*d^2*f^2*x^2 + 4*a*b^2*d^2*e*f*x + 4*a*b^2*c*d*e*f - 2*a*b^2*c^2*f^2 - I*(a^2*b - b^3)*d^2*f^2*x^2 - 2*I*(a^2*b - b^3)*d^2*e*f*x - 2*I*(a^2*b - b^3)*c*d*e*f + I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c)^4 + (8*a*b^2*d^2*f^2*x^2 + 16*a*b^2*d^2*e*f*x + 16*a*b^2*c*d*e*f - 8*a*b^2*c^2*f^2 - 4*I*(a^2*b - b^3)*d^2*f^2*x^2 - 8*I*(a^2*b - b^3)*d^2*e*f*x - 8*I*(a^2*b - b^3)*c*d*e*f + 4*I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b^2*d^2*f^2*x^2 + 4*a*b^2*d^2*e*f*x + 4*a*b^2*c*d*e*f - 2*a*b^2*c^2*f^2 - I*(a^2*b - b^3)*d^2*f^2*x^2 - 2*I*(a^2*b - b^3)*d^2*e*f*x - 2*I*(a^2*b - b^3)*c*d*e*f + I*(a^2*b - b^3)*c^2*f^2)*sinh(d*x + c)^4 + (4*a*b^2*d^2*f^2*x^2 + 8*a*b^2*d^2*e*f*x + 8*a*b^2*c*d*e*f - 4*a*b^2*c^2*f^2 - 2*I*(a^2*b - b^3)*d^2*f^2*x^2 - 4*I*(a^2*b - b^3)*d^2*e*f*x - 4*I*(a^2*b - b^3)*c*d*e*f + 2*I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c)^2 + (4*a*b^2*d^2*f^2*x^2 + 8*a*b^2*d^2*e*f*x + 8*a*b^2*c*d*e*f - 4*a*b^2*c^2*f^2 - 2*I*(a^2*b - b^3)*d^2*f^2*x^2 - 4*I*(a^2*b - b^3)*d^2*e*f*x - 4*I*(a^2*b - b^3)*c*d*e*f + 2*I*(a^2*b - b^3)*c^2*f^2 + (12*a*b^2*d^2*f^2*x^2 + 24*a*b^2*d^2*e*f*x + 24*a*b^2*c*d*e*f - 12*a*b^2*c^2*f^2 - 6*I*(a^2*b - b^3)*d^2*f^2*x^2 - 12*I*(a^2*b - b^3)*d^2*e*f*x - 12*I*(a^2*b - b^3)*c*d*e*f + 6*I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a*b^2*d^2*f^2*x^2 + 16*a*b^2*d^2*e*f*x + 16*a*b^2*c*d*e*f - 8*a*b^2*c^2*f^2 - 4*I*(a^2*b - b^3)*d^2*f^2*x^2 - 8*I*(a^2*b - b^3)*d^2*e*f*x - 8*I*(a^2*b - b^3)*c*d*e*f + 4*I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c)^3 + (8*a*b^2*d^2*f^2*x^2 + 16*a*b^2*d^2*e*f*x + 16*a*b^2*c*d*e*f - 8*a*b^2*c^2*f^2 - 4*I*(a^2*b - b^3)*d^2*f^2*x^2 - 8*I*(a^2*b - b^3)*d^2*e*f*x - 8*I*(a^2*b - b^3)*c*d*e*f + 4*I*(a^2*b - b^3)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + 4*(a*b^2*f^2*cosh(d*x + c)^4 + 4*a*b^2*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + a*b^2*f^2*sinh(d*x + c)^4 + 2*a*b^2*f^2*cosh(d*x + c)^2 + a*b^2*f^2 + 2*(3*a*b^2*f^2*cosh(d*x + c)^2 + a*b^2*f^2)*sinh(d*x + c)^2 + 4*(a*b^2*f^2*cosh(d*x + c)^3 + a*b^2*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*(a*b^2*f^2*cosh(d*x + c)^4 + 4*a*b^2*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + a*b^2*f^2*sinh(d*x + c)^4 + 2*a*b^2*f^2*cosh(d*x + c)^2 + a*b^2*f^2 + 2*(3*a*b^2*f^2*cosh(d*x + c)^2 + a*b^2*f^2)*sinh(d*x + c)^2 + 4*(a*b^2*f^2*cosh(d*x + c)^3 + a*b^2*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - (4*a*b^2*f^2 + (4*a*b^2*f^2 - 2*I*(a^2*b - b^3)*f^2)*cosh(d*x + c)^4 + (16*a*b^2*f^2 - 8*I*(a^2*b - b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a*b^2*f^2 - 2*I*(a^2*b - b^3)*f^2)*sinh(d*x + c)^4 - 2*I*(a^2*b - b^3)*f^2 + (8*a*b^2*f^2 - 4*I*(a^2*b - b^3)*f^2)*cosh(d*x + c)^2 + (8*a*b^2*f^2 - 4*I*(a^2*b - b^3)*f^2 + (24*a*b^2*f^2 - 12*I*(a^2*b - b^3)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*a*b^2*f^2 - 8*I*(a^2*b - b^3)*f^2)*cosh(d*x + c)^3 + (16*a*b^2*f^2 - 8*I*(a^2*b - b^3)*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - (4*a*b^2*f^2 + (4*a*b^2*f^2 + 2*I*(a^2*b - b^3)*f^2)*cosh(d*x + c)^4 + (16*a*b^2*f^2 + 8*I*(a^2*b - b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a*b^2*f^2 + 2*I*(a^2*b - b^3)*f^2)*sinh(d*x + c)^4 + 2*I*(a^2*b - b^3)*f^2 + (8*a*b^2*f^2 + 4*I*(a^2*b - b^3)*f^2)*cosh(d*x + c)^2 + (8*a*b^2*f^2 + 4*I*(a^2*b - b^3)*f^2 + (24*a*b^2*f^2 + 12*I*(a^2*b - b^3)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*a*b^2*f^2 + 8*I*(a^2*b - b^3)*f^2)*cosh(d*x + c)^3 + (16*a*b^2*f^2 + 8*I*(a^2*b - b^3)*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 - 2*(a^2*b + b^3)*d*e*f - 8*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*c*f^2)*cosh(d*x + c)^3 - 3*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x + 4*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + (a^3 + a*b^2)*d*e*f - 2*(a^3 + a*b^2)*c*f^2 + (2*(a^3 + a*b^2)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^3*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3)*sinh(d*x + c)^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c))*sinh(d*x + c))","C",0
359,1,4963,0,0.710436," ","integrate((f*x+e)*sech(d*x+c)^2*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d f x + 2 \, {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d f x + 2 \, {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} f - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right) - 2 \, {\left(a b^{2} f \cosh\left(d x + c\right)^{4} + 4 \, a b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b^{2} f \sinh\left(d x + c\right)^{4} + 2 \, a b^{2} f \cosh\left(d x + c\right)^{2} + a b^{2} f + 2 \, {\left(3 \, a b^{2} f \cosh\left(d x + c\right)^{2} + a b^{2} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} f \cosh\left(d x + c\right)^{3} + a b^{2} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a b^{2} f \cosh\left(d x + c\right)^{4} + 4 \, a b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b^{2} f \sinh\left(d x + c\right)^{4} + 2 \, a b^{2} f \cosh\left(d x + c\right)^{2} + a b^{2} f + 2 \, {\left(3 \, a b^{2} f \cosh\left(d x + c\right)^{2} + a b^{2} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} f \cosh\left(d x + c\right)^{3} + a b^{2} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left({\left(2 \, a b^{2} f - i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b^{2} f - 4 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b^{2} f - i \, {\left(a^{2} b - b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, a b^{2} f + {\left(4 \, a b^{2} f - 2 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a b^{2} f + {\left(12 \, a b^{2} f - 6 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} - i \, {\left(a^{2} b - b^{3}\right)} f + {\left({\left(8 \, a b^{2} f - 4 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} f - 4 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left({\left(2 \, a b^{2} f + i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b^{2} f + 4 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b^{2} f + i \, {\left(a^{2} b - b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, a b^{2} f + {\left(4 \, a b^{2} f + 2 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a b^{2} f + {\left(12 \, a b^{2} f + 6 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 2 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} + i \, {\left(a^{2} b - b^{3}\right)} f + {\left({\left(8 \, a b^{2} f + 4 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} f + 4 i \, {\left(a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left(a b^{2} d e - a b^{2} c f + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} d e - a b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d e - a b^{2} c f + 3 \, {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a b^{2} d e - a b^{2} c f + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} d e - a b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d e - a b^{2} c f + 3 \, {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a b^{2} d f x + a b^{2} c f + {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} d f x + a b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d f x + a b^{2} c f + 3 \, {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a b^{2} d f x + a b^{2} c f + {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} d f x + a b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b^{2} d f x + a b^{2} c f + 3 \, {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a b^{2} d f x + a b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f - i \, {\left(a^{2} b - b^{3}\right)} d e + i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b^{2} d e - 8 \, a b^{2} c f - 4 i \, {\left(a^{2} b - b^{3}\right)} d e + 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f - i \, {\left(a^{2} b - b^{3}\right)} d e + i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} - i \, {\left(a^{2} b - b^{3}\right)} d e + i \, {\left(a^{2} b - b^{3}\right)} c f + {\left(4 \, a b^{2} d e - 4 \, a b^{2} c f - 2 i \, {\left(a^{2} b - b^{3}\right)} d e + 2 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a b^{2} d e - 4 \, a b^{2} c f - 2 i \, {\left(a^{2} b - b^{3}\right)} d e + 2 i \, {\left(a^{2} b - b^{3}\right)} c f + {\left(12 \, a b^{2} d e - 12 \, a b^{2} c f - 6 i \, {\left(a^{2} b - b^{3}\right)} d e + 6 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a b^{2} d e - 8 \, a b^{2} c f - 4 i \, {\left(a^{2} b - b^{3}\right)} d e + 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} d e - 8 \, a b^{2} c f - 4 i \, {\left(a^{2} b - b^{3}\right)} d e + 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f + i \, {\left(a^{2} b - b^{3}\right)} d e - i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b^{2} d e - 8 \, a b^{2} c f + 4 i \, {\left(a^{2} b - b^{3}\right)} d e - 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b^{2} d e - 2 \, a b^{2} c f + i \, {\left(a^{2} b - b^{3}\right)} d e - i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + i \, {\left(a^{2} b - b^{3}\right)} d e - i \, {\left(a^{2} b - b^{3}\right)} c f + {\left(4 \, a b^{2} d e - 4 \, a b^{2} c f + 2 i \, {\left(a^{2} b - b^{3}\right)} d e - 2 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a b^{2} d e - 4 \, a b^{2} c f + 2 i \, {\left(a^{2} b - b^{3}\right)} d e - 2 i \, {\left(a^{2} b - b^{3}\right)} c f + {\left(12 \, a b^{2} d e - 12 \, a b^{2} c f + 6 i \, {\left(a^{2} b - b^{3}\right)} d e - 6 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a b^{2} d e - 8 \, a b^{2} c f + 4 i \, {\left(a^{2} b - b^{3}\right)} d e - 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} d e - 8 \, a b^{2} c f + 4 i \, {\left(a^{2} b - b^{3}\right)} d e - 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(2 \, a b^{2} d f x + 2 \, a b^{2} c f + {\left(2 \, a b^{2} d f x + 2 \, a b^{2} c f + i \, {\left(a^{2} b - b^{3}\right)} d f x + i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b^{2} d f x + 8 \, a b^{2} c f + 4 i \, {\left(a^{2} b - b^{3}\right)} d f x + 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b^{2} d f x + 2 \, a b^{2} c f + i \, {\left(a^{2} b - b^{3}\right)} d f x + i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + i \, {\left(a^{2} b - b^{3}\right)} d f x + i \, {\left(a^{2} b - b^{3}\right)} c f + {\left(4 \, a b^{2} d f x + 4 \, a b^{2} c f + 2 i \, {\left(a^{2} b - b^{3}\right)} d f x + 2 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a b^{2} d f x + 4 \, a b^{2} c f + 2 i \, {\left(a^{2} b - b^{3}\right)} d f x + 2 i \, {\left(a^{2} b - b^{3}\right)} c f + {\left(12 \, a b^{2} d f x + 12 \, a b^{2} c f + 6 i \, {\left(a^{2} b - b^{3}\right)} d f x + 6 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a b^{2} d f x + 8 \, a b^{2} c f + 4 i \, {\left(a^{2} b - b^{3}\right)} d f x + 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} d f x + 8 \, a b^{2} c f + 4 i \, {\left(a^{2} b - b^{3}\right)} d f x + 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(2 \, a b^{2} d f x + 2 \, a b^{2} c f + {\left(2 \, a b^{2} d f x + 2 \, a b^{2} c f - i \, {\left(a^{2} b - b^{3}\right)} d f x - i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b^{2} d f x + 8 \, a b^{2} c f - 4 i \, {\left(a^{2} b - b^{3}\right)} d f x - 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b^{2} d f x + 2 \, a b^{2} c f - i \, {\left(a^{2} b - b^{3}\right)} d f x - i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} - i \, {\left(a^{2} b - b^{3}\right)} d f x - i \, {\left(a^{2} b - b^{3}\right)} c f + {\left(4 \, a b^{2} d f x + 4 \, a b^{2} c f - 2 i \, {\left(a^{2} b - b^{3}\right)} d f x - 2 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a b^{2} d f x + 4 \, a b^{2} c f - 2 i \, {\left(a^{2} b - b^{3}\right)} d f x - 2 i \, {\left(a^{2} b - b^{3}\right)} c f + {\left(12 \, a b^{2} d f x + 12 \, a b^{2} c f - 6 i \, {\left(a^{2} b - b^{3}\right)} d f x - 6 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a b^{2} d f x + 8 \, a b^{2} c f - 4 i \, {\left(a^{2} b - b^{3}\right)} d f x - 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} d f x + 8 \, a b^{2} c f - 4 i \, {\left(a^{2} b - b^{3}\right)} d f x - 4 i \, {\left(a^{2} b - b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f + 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d f x + 2 \, {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*cosh(d*x + c)^3 + 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*sinh(d*x + c)^3 - 2*(2*(a^3 + a*b^2)*d*f*x + 2*(a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c)^2 - 2*(2*(a^3 + a*b^2)*d*f*x + 2*(a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f - 3*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(a^3 + a*b^2)*f - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - (a^2*b + b^3)*f)*cosh(d*x + c) - 2*(a*b^2*f*cosh(d*x + c)^4 + 4*a*b^2*f*cosh(d*x + c)*sinh(d*x + c)^3 + a*b^2*f*sinh(d*x + c)^4 + 2*a*b^2*f*cosh(d*x + c)^2 + a*b^2*f + 2*(3*a*b^2*f*cosh(d*x + c)^2 + a*b^2*f)*sinh(d*x + c)^2 + 4*(a*b^2*f*cosh(d*x + c)^3 + a*b^2*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(a*b^2*f*cosh(d*x + c)^4 + 4*a*b^2*f*cosh(d*x + c)*sinh(d*x + c)^3 + a*b^2*f*sinh(d*x + c)^4 + 2*a*b^2*f*cosh(d*x + c)^2 + a*b^2*f + 2*(3*a*b^2*f*cosh(d*x + c)^2 + a*b^2*f)*sinh(d*x + c)^2 + 4*(a*b^2*f*cosh(d*x + c)^3 + a*b^2*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + ((2*a*b^2*f - I*(a^2*b - b^3)*f)*cosh(d*x + c)^4 + (8*a*b^2*f - 4*I*(a^2*b - b^3)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b^2*f - I*(a^2*b - b^3)*f)*sinh(d*x + c)^4 + 2*a*b^2*f + (4*a*b^2*f - 2*I*(a^2*b - b^3)*f)*cosh(d*x + c)^2 + (4*a*b^2*f + (12*a*b^2*f - 6*I*(a^2*b - b^3)*f)*cosh(d*x + c)^2 - 2*I*(a^2*b - b^3)*f)*sinh(d*x + c)^2 - I*(a^2*b - b^3)*f + ((8*a*b^2*f - 4*I*(a^2*b - b^3)*f)*cosh(d*x + c)^3 + (8*a*b^2*f - 4*I*(a^2*b - b^3)*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + ((2*a*b^2*f + I*(a^2*b - b^3)*f)*cosh(d*x + c)^4 + (8*a*b^2*f + 4*I*(a^2*b - b^3)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b^2*f + I*(a^2*b - b^3)*f)*sinh(d*x + c)^4 + 2*a*b^2*f + (4*a*b^2*f + 2*I*(a^2*b - b^3)*f)*cosh(d*x + c)^2 + (4*a*b^2*f + (12*a*b^2*f + 6*I*(a^2*b - b^3)*f)*cosh(d*x + c)^2 + 2*I*(a^2*b - b^3)*f)*sinh(d*x + c)^2 + I*(a^2*b - b^3)*f + ((8*a*b^2*f + 4*I*(a^2*b - b^3)*f)*cosh(d*x + c)^3 + (8*a*b^2*f + 4*I*(a^2*b - b^3)*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*(a*b^2*d*e - a*b^2*c*f + (a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)^4 + 4*(a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2*d*e - a*b^2*c*f)*sinh(d*x + c)^4 + 2*(a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*e - a*b^2*c*f + 3*(a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)^3 + (a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a*b^2*d*e - a*b^2*c*f + (a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)^4 + 4*(a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2*d*e - a*b^2*c*f)*sinh(d*x + c)^4 + 2*(a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*e - a*b^2*c*f + 3*(a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c)^3 + (a*b^2*d*e - a*b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a*b^2*d*f*x + a*b^2*c*f + (a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)^4 + 4*(a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2*d*f*x + a*b^2*c*f)*sinh(d*x + c)^4 + 2*(a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*f*x + a*b^2*c*f + 3*(a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)^3 + (a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(a*b^2*d*f*x + a*b^2*c*f + (a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)^4 + 4*(a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2*d*f*x + a*b^2*c*f)*sinh(d*x + c)^4 + 2*(a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)^2 + 2*(a*b^2*d*f*x + a*b^2*c*f + 3*(a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c)^3 + (a*b^2*d*f*x + a*b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (2*a*b^2*d*e - 2*a*b^2*c*f + (2*a*b^2*d*e - 2*a*b^2*c*f - I*(a^2*b - b^3)*d*e + I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^4 + (8*a*b^2*d*e - 8*a*b^2*c*f - 4*I*(a^2*b - b^3)*d*e + 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b^2*d*e - 2*a*b^2*c*f - I*(a^2*b - b^3)*d*e + I*(a^2*b - b^3)*c*f)*sinh(d*x + c)^4 - I*(a^2*b - b^3)*d*e + I*(a^2*b - b^3)*c*f + (4*a*b^2*d*e - 4*a*b^2*c*f - 2*I*(a^2*b - b^3)*d*e + 2*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^2 + (4*a*b^2*d*e - 4*a*b^2*c*f - 2*I*(a^2*b - b^3)*d*e + 2*I*(a^2*b - b^3)*c*f + (12*a*b^2*d*e - 12*a*b^2*c*f - 6*I*(a^2*b - b^3)*d*e + 6*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a*b^2*d*e - 8*a*b^2*c*f - 4*I*(a^2*b - b^3)*d*e + 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^3 + (8*a*b^2*d*e - 8*a*b^2*c*f - 4*I*(a^2*b - b^3)*d*e + 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) + (2*a*b^2*d*e - 2*a*b^2*c*f + (2*a*b^2*d*e - 2*a*b^2*c*f + I*(a^2*b - b^3)*d*e - I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^4 + (8*a*b^2*d*e - 8*a*b^2*c*f + 4*I*(a^2*b - b^3)*d*e - 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b^2*d*e - 2*a*b^2*c*f + I*(a^2*b - b^3)*d*e - I*(a^2*b - b^3)*c*f)*sinh(d*x + c)^4 + I*(a^2*b - b^3)*d*e - I*(a^2*b - b^3)*c*f + (4*a*b^2*d*e - 4*a*b^2*c*f + 2*I*(a^2*b - b^3)*d*e - 2*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^2 + (4*a*b^2*d*e - 4*a*b^2*c*f + 2*I*(a^2*b - b^3)*d*e - 2*I*(a^2*b - b^3)*c*f + (12*a*b^2*d*e - 12*a*b^2*c*f + 6*I*(a^2*b - b^3)*d*e - 6*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a*b^2*d*e - 8*a*b^2*c*f + 4*I*(a^2*b - b^3)*d*e - 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^3 + (8*a*b^2*d*e - 8*a*b^2*c*f + 4*I*(a^2*b - b^3)*d*e - 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) + (2*a*b^2*d*f*x + 2*a*b^2*c*f + (2*a*b^2*d*f*x + 2*a*b^2*c*f + I*(a^2*b - b^3)*d*f*x + I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^4 + (8*a*b^2*d*f*x + 8*a*b^2*c*f + 4*I*(a^2*b - b^3)*d*f*x + 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b^2*d*f*x + 2*a*b^2*c*f + I*(a^2*b - b^3)*d*f*x + I*(a^2*b - b^3)*c*f)*sinh(d*x + c)^4 + I*(a^2*b - b^3)*d*f*x + I*(a^2*b - b^3)*c*f + (4*a*b^2*d*f*x + 4*a*b^2*c*f + 2*I*(a^2*b - b^3)*d*f*x + 2*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^2 + (4*a*b^2*d*f*x + 4*a*b^2*c*f + 2*I*(a^2*b - b^3)*d*f*x + 2*I*(a^2*b - b^3)*c*f + (12*a*b^2*d*f*x + 12*a*b^2*c*f + 6*I*(a^2*b - b^3)*d*f*x + 6*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a*b^2*d*f*x + 8*a*b^2*c*f + 4*I*(a^2*b - b^3)*d*f*x + 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^3 + (8*a*b^2*d*f*x + 8*a*b^2*c*f + 4*I*(a^2*b - b^3)*d*f*x + 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (2*a*b^2*d*f*x + 2*a*b^2*c*f + (2*a*b^2*d*f*x + 2*a*b^2*c*f - I*(a^2*b - b^3)*d*f*x - I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^4 + (8*a*b^2*d*f*x + 8*a*b^2*c*f - 4*I*(a^2*b - b^3)*d*f*x - 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b^2*d*f*x + 2*a*b^2*c*f - I*(a^2*b - b^3)*d*f*x - I*(a^2*b - b^3)*c*f)*sinh(d*x + c)^4 - I*(a^2*b - b^3)*d*f*x - I*(a^2*b - b^3)*c*f + (4*a*b^2*d*f*x + 4*a*b^2*c*f - 2*I*(a^2*b - b^3)*d*f*x - 2*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^2 + (4*a*b^2*d*f*x + 4*a*b^2*c*f - 2*I*(a^2*b - b^3)*d*f*x - 2*I*(a^2*b - b^3)*c*f + (12*a*b^2*d*f*x + 12*a*b^2*c*f - 6*I*(a^2*b - b^3)*d*f*x - 6*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a*b^2*d*f*x + 8*a*b^2*c*f - 4*I*(a^2*b - b^3)*d*f*x - 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c)^3 + (8*a*b^2*d*f*x + 8*a*b^2*c*f - 4*I*(a^2*b - b^3)*d*f*x - 4*I*(a^2*b - b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - 3*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*cosh(d*x + c)^2 - (a^2*b + b^3)*f + 2*(2*(a^3 + a*b^2)*d*f*x + 2*(a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^2*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)*sinh(d*x + c)^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
360,1,926,0,0.528907," ","integrate(sech(d*x+c)^2*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{3} + 2 \, a b^{2} - 3 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b - b^{3}\right)} \sinh\left(d x + c\right)^{4} + a^{2} b - b^{3} + 2 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b - b^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) - {\left(a b^{2} \cosh\left(d x + c\right)^{4} + 4 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b^{2} \sinh\left(d x + c\right)^{4} + 2 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(d x + c\right)^{3} + a b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left(a b^{2} \cosh\left(d x + c\right)^{4} + 4 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b^{2} \sinh\left(d x + c\right)^{4} + 2 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2} + 2 \, {\left(3 \, a b^{2} \cosh\left(d x + c\right)^{2} + a b^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{2} \cosh\left(d x + c\right)^{3} + a b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{2} b + b^{3} - 3 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"((a^2*b + b^3)*cosh(d*x + c)^3 + (a^2*b + b^3)*sinh(d*x + c)^3 - 2*(a^3 + a*b^2)*cosh(d*x + c)^2 - (2*a^3 + 2*a*b^2 - 3*(a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - ((a^2*b - b^3)*cosh(d*x + c)^4 + 4*(a^2*b - b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b - b^3)*sinh(d*x + c)^4 + a^2*b - b^3 + 2*(a^2*b - b^3)*cosh(d*x + c)^2 + 2*(a^2*b - b^3 + 3*(a^2*b - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b - b^3)*cosh(d*x + c)^3 + (a^2*b - b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - (a^2*b + b^3)*cosh(d*x + c) - (a*b^2*cosh(d*x + c)^4 + 4*a*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + a*b^2*sinh(d*x + c)^4 + 2*a*b^2*cosh(d*x + c)^2 + a*b^2 + 2*(3*a*b^2*cosh(d*x + c)^2 + a*b^2)*sinh(d*x + c)^2 + 4*(a*b^2*cosh(d*x + c)^3 + a*b^2*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + (a*b^2*cosh(d*x + c)^4 + 4*a*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + a*b^2*sinh(d*x + c)^4 + 2*a*b^2*cosh(d*x + c)^2 + a*b^2 + 2*(3*a*b^2*cosh(d*x + c)^2 + a*b^2)*sinh(d*x + c)^2 + 4*(a*b^2*cosh(d*x + c)^3 + a*b^2*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (a^2*b + b^3 - 3*(a^2*b + b^3)*cosh(d*x + c)^2 + 4*(a^3 + a*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d)*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d + 4*((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
361,0,0,0,9.077116," ","integrate(sech(d*x+c)^2*tanh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(d x + c\right)^{2} \tanh\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sech(d*x + c)^2*tanh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
362,1,3891,0,0.732733," ","integrate((f*x+e)^3*cosh(d*x+c)*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} + 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} + 3 \, b^{2} f^{3} + {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} - 16 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(4 \, a b d^{3} f^{3} x^{3} + 4 \, a b d^{3} e^{3} - 12 \, a b d^{2} e^{2} f + 24 \, a b d e f^{2} - 24 \, a b f^{3} + 12 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 12 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x - {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} + b^{2} d^{2} f^{3}\right)} x^{2} - 8 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} d^{4} e f^{2} x^{3} + 6 \, a^{2} d^{4} e^{2} f x^{2} + 4 \, a^{2} d^{4} e^{3} x + 8 \, a^{2} c d^{3} e^{3} - 12 \, a^{2} c^{2} d^{2} e^{2} f + 8 \, a^{2} c^{3} d e f^{2} - 2 \, a^{2} c^{4} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(4 \, a^{2} d^{4} f^{3} x^{4} + 16 \, a^{2} d^{4} e f^{2} x^{3} + 24 \, a^{2} d^{4} e^{2} f x^{2} + 16 \, a^{2} d^{4} e^{3} x + 32 \, a^{2} c d^{3} e^{3} - 48 \, a^{2} c^{2} d^{2} e^{2} f + 32 \, a^{2} c^{3} d e f^{2} - 8 \, a^{2} c^{4} f^{3} - 3 \, {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 24 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f + 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x + 16 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} + 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right) + 96 \, {\left({\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + a^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + a^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + a^{2} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 96 \, {\left({\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + a^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + a^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + a^{2} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 32 \, {\left({\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - a^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - a^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - a^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 32 \, {\left({\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - a^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - a^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - a^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 32 \, {\left({\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} d^{3} e f^{2} x^{2} + 3 \, a^{2} d^{3} e^{2} f x + 3 \, a^{2} c d^{2} e^{2} f - 3 \, a^{2} c^{2} d e f^{2} + a^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} d^{3} e f^{2} x^{2} + 3 \, a^{2} d^{3} e^{2} f x + 3 \, a^{2} c d^{2} e^{2} f - 3 \, a^{2} c^{2} d e f^{2} + a^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} d^{3} e f^{2} x^{2} + 3 \, a^{2} d^{3} e^{2} f x + 3 \, a^{2} c d^{2} e^{2} f - 3 \, a^{2} c^{2} d e f^{2} + a^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 32 \, {\left({\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} d^{3} e f^{2} x^{2} + 3 \, a^{2} d^{3} e^{2} f x + 3 \, a^{2} c d^{2} e^{2} f - 3 \, a^{2} c^{2} d e f^{2} + a^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} d^{3} e f^{2} x^{2} + 3 \, a^{2} d^{3} e^{2} f x + 3 \, a^{2} c d^{2} e^{2} f - 3 \, a^{2} c^{2} d e f^{2} + a^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} d^{3} e f^{2} x^{2} + 3 \, a^{2} d^{3} e^{2} f x + 3 \, a^{2} c d^{2} e^{2} f - 3 \, a^{2} c^{2} d e f^{2} + a^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 192 \, {\left(a^{2} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} f^{3} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 192 \, {\left(a^{2} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} f^{3} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 192 \, {\left({\left(a^{2} d f^{3} x + a^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d f^{3} x + a^{2} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d f^{3} x + a^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 192 \, {\left({\left(a^{2} d f^{3} x + a^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d f^{3} x + a^{2} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d f^{3} x + a^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(4 \, a b d^{3} f^{3} x^{3} + 4 \, a b d^{3} e^{3} + 12 \, a b d^{2} e^{2} f + 24 \, a b d e f^{2} + 24 \, a b f^{3} + {\left(4 \, b^{2} d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} e^{3} - 6 \, b^{2} d^{2} e^{2} f + 6 \, b^{2} d e f^{2} - 3 \, b^{2} f^{3} + 6 \, {\left(2 \, b^{2} d^{3} e f^{2} - b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, b^{2} d^{3} e^{2} f - 2 \, b^{2} d^{2} e f^{2} + b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(a b d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} - 12 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(a b d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x - 4 \, {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} d^{4} e f^{2} x^{3} + 6 \, a^{2} d^{4} e^{2} f x^{2} + 4 \, a^{2} d^{4} e^{3} x + 8 \, a^{2} c d^{3} e^{3} - 12 \, a^{2} c^{2} d^{2} e^{2} f + 8 \, a^{2} c^{3} d e f^{2} - 2 \, a^{2} c^{4} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{32 \, {\left(b^{3} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d^{4} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/32*(4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 + 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 + 3*b^2*f^3 + (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c)^4 + (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*sinh(d*x + c)^4 - 16*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^3 - 4*(4*a*b*d^3*f^3*x^3 + 4*a*b*d^3*e^3 - 12*a*b*d^2*e^2*f + 24*a*b*d*e*f^2 - 24*a*b*f^3 + 12*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 12*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x - (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(2*b^2*d^3*e*f^2 + b^2*d^2*f^3)*x^2 - 8*(a^2*d^4*f^3*x^4 + 4*a^2*d^4*e*f^2*x^3 + 6*a^2*d^4*e^2*f*x^2 + 4*a^2*d^4*e^3*x + 8*a^2*c*d^3*e^3 - 12*a^2*c^2*d^2*e^2*f + 8*a^2*c^3*d*e*f^2 - 2*a^2*c^4*f^3)*cosh(d*x + c)^2 - 2*(4*a^2*d^4*f^3*x^4 + 16*a^2*d^4*e*f^2*x^3 + 24*a^2*d^4*e^2*f*x^2 + 16*a^2*d^4*e^3*x + 32*a^2*c*d^3*e^3 - 48*a^2*c^2*d^2*e^2*f + 32*a^2*c^3*d*e*f^2 - 8*a^2*c^4*f^3 - 3*(4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c)^2 + 24*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 6*(2*b^2*d^3*e^2*f + 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x + 16*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 + 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 + 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f + 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c) + 96*((a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + a^2*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + a^2*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + a^2*d^2*e^2*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 96*((a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + a^2*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + a^2*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + a^2*d^2*e^2*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 32*((a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - a^2*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - a^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - a^2*c^3*f^3)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 32*((a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - a^2*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - a^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - a^2*c^3*f^3)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 32*((a^2*d^3*f^3*x^3 + 3*a^2*d^3*e*f^2*x^2 + 3*a^2*d^3*e^2*f*x + 3*a^2*c*d^2*e^2*f - 3*a^2*c^2*d*e*f^2 + a^2*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^2*d^3*f^3*x^3 + 3*a^2*d^3*e*f^2*x^2 + 3*a^2*d^3*e^2*f*x + 3*a^2*c*d^2*e^2*f - 3*a^2*c^2*d*e*f^2 + a^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d^3*f^3*x^3 + 3*a^2*d^3*e*f^2*x^2 + 3*a^2*d^3*e^2*f*x + 3*a^2*c*d^2*e^2*f - 3*a^2*c^2*d*e*f^2 + a^2*c^3*f^3)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 32*((a^2*d^3*f^3*x^3 + 3*a^2*d^3*e*f^2*x^2 + 3*a^2*d^3*e^2*f*x + 3*a^2*c*d^2*e^2*f - 3*a^2*c^2*d*e*f^2 + a^2*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^2*d^3*f^3*x^3 + 3*a^2*d^3*e*f^2*x^2 + 3*a^2*d^3*e^2*f*x + 3*a^2*c*d^2*e^2*f - 3*a^2*c^2*d*e*f^2 + a^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d^3*f^3*x^3 + 3*a^2*d^3*e*f^2*x^2 + 3*a^2*d^3*e^2*f*x + 3*a^2*c*d^2*e^2*f - 3*a^2*c^2*d*e*f^2 + a^2*c^3*f^3)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 192*(a^2*f^3*cosh(d*x + c)^2 + 2*a^2*f^3*cosh(d*x + c)*sinh(d*x + c) + a^2*f^3*sinh(d*x + c)^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 192*(a^2*f^3*cosh(d*x + c)^2 + 2*a^2*f^3*cosh(d*x + c)*sinh(d*x + c) + a^2*f^3*sinh(d*x + c)^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 192*((a^2*d*f^3*x + a^2*d*e*f^2)*cosh(d*x + c)^2 + 2*(a^2*d*f^3*x + a^2*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d*f^3*x + a^2*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 192*((a^2*d*f^3*x + a^2*d*e*f^2)*cosh(d*x + c)^2 + 2*(a^2*d*f^3*x + a^2*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d*f^3*x + a^2*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*(4*a*b*d^3*f^3*x^3 + 4*a*b*d^3*e^3 + 12*a*b*d^2*e^2*f + 24*a*b*d*e*f^2 + 24*a*b*f^3 + (4*b^2*d^3*f^3*x^3 + 4*b^2*d^3*e^3 - 6*b^2*d^2*e^2*f + 6*b^2*d*e*f^2 - 3*b^2*f^3 + 6*(2*b^2*d^3*e*f^2 - b^2*d^2*f^3)*x^2 + 6*(2*b^2*d^3*e^2*f - 2*b^2*d^2*e*f^2 + b^2*d*f^3)*x)*cosh(d*x + c)^3 + 12*(a*b*d^3*e*f^2 + a*b*d^2*f^3)*x^2 - 12*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^2 + 12*(a*b*d^3*e^2*f + 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x - 4*(a^2*d^4*f^3*x^4 + 4*a^2*d^4*e*f^2*x^3 + 6*a^2*d^4*e^2*f*x^2 + 4*a^2*d^4*e^3*x + 8*a^2*c*d^3*e^3 - 12*a^2*c^2*d^2*e^2*f + 8*a^2*c^3*d*e*f^2 - 2*a^2*c^4*f^3)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d^4*cosh(d*x + c)^2 + 2*b^3*d^4*cosh(d*x + c)*sinh(d*x + c) + b^3*d^4*sinh(d*x + c)^2)","C",0
363,1,2414,0,0.626183," ","integrate((f*x+e)^2*cosh(d*x+c)*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, b^{2} d^{2} f^{2} x^{2} + 6 \, b^{2} d^{2} e^{2} + 6 \, b^{2} d e f + 3 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} + 3 \, b^{2} f^{2} - 24 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(2 \, a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e^{2} - 4 \, a b d e f + 4 \, a b f^{2} + 4 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x - {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 16 \, {\left(a^{2} d^{3} f^{2} x^{3} + 3 \, a^{2} d^{3} e f x^{2} + 3 \, a^{2} d^{3} e^{2} x + 6 \, a^{2} c d^{2} e^{2} - 6 \, a^{2} c^{2} d e f + 2 \, a^{2} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(8 \, a^{2} d^{3} f^{2} x^{3} + 24 \, a^{2} d^{3} e f x^{2} + 24 \, a^{2} d^{3} e^{2} x + 48 \, a^{2} c d^{2} e^{2} - 48 \, a^{2} c^{2} d e f + 16 \, a^{2} c^{3} f^{2} - 9 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 36 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(2 \, b^{2} d^{2} e f + b^{2} d f^{2}\right)} x + 24 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} + 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 96 \, {\left({\left(a^{2} d f^{2} x + a^{2} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d f^{2} x + a^{2} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d f^{2} x + a^{2} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 96 \, {\left({\left(a^{2} d f^{2} x + a^{2} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d f^{2} x + a^{2} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d f^{2} x + a^{2} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 48 \, {\left({\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f + a^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f + a^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f + a^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 48 \, {\left({\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f + a^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f + a^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f + a^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 48 \, {\left({\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x + 2 \, a^{2} c d e f - a^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x + 2 \, a^{2} c d e f - a^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x + 2 \, a^{2} c d e f - a^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 48 \, {\left({\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x + 2 \, a^{2} c d e f - a^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x + 2 \, a^{2} c d e f - a^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x + 2 \, a^{2} c d e f - a^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 96 \, {\left(a^{2} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} f^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 96 \, {\left(a^{2} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} f^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(6 \, a b d^{2} f^{2} x^{2} + 6 \, a b d^{2} e^{2} + 12 \, a b d e f + 12 \, a b f^{2} + 3 \, {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e^{2} - 2 \, b^{2} d e f + b^{2} f^{2} + 2 \, {\left(2 \, b^{2} d^{2} e f - b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 18 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(a b d^{2} e f + a b d f^{2}\right)} x - 8 \, {\left(a^{2} d^{3} f^{2} x^{3} + 3 \, a^{2} d^{3} e f x^{2} + 3 \, a^{2} d^{3} e^{2} x + 6 \, a^{2} c d^{2} e^{2} - 6 \, a^{2} c^{2} d e f + 2 \, a^{2} c^{3} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{48 \, {\left(b^{3} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d^{3} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/48*(6*b^2*d^2*f^2*x^2 + 6*b^2*d^2*e^2 + 6*b^2*d*e*f + 3*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c)^4 + 3*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*sinh(d*x + c)^4 + 3*b^2*f^2 - 24*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^3 - 12*(2*a*b*d^2*f^2*x^2 + 2*a*b*d^2*e^2 - 4*a*b*d*e*f + 4*a*b*f^2 + 4*(a*b*d^2*e*f - a*b*d*f^2)*x - (2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 16*(a^2*d^3*f^2*x^3 + 3*a^2*d^3*e*f*x^2 + 3*a^2*d^3*e^2*x + 6*a^2*c*d^2*e^2 - 6*a^2*c^2*d*e*f + 2*a^2*c^3*f^2)*cosh(d*x + c)^2 - 2*(8*a^2*d^3*f^2*x^3 + 24*a^2*d^3*e*f*x^2 + 24*a^2*d^3*e^2*x + 48*a^2*c*d^2*e^2 - 48*a^2*c^2*d*e*f + 16*a^2*c^3*f^2 - 9*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c)^2 + 36*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 6*(2*b^2*d^2*e*f + b^2*d*f^2)*x + 24*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 + 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c) + 96*((a^2*d*f^2*x + a^2*d*e*f)*cosh(d*x + c)^2 + 2*(a^2*d*f^2*x + a^2*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d*f^2*x + a^2*d*e*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 96*((a^2*d*f^2*x + a^2*d*e*f)*cosh(d*x + c)^2 + 2*(a^2*d*f^2*x + a^2*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d*f^2*x + a^2*d*e*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 48*((a^2*d^2*e^2 - 2*a^2*c*d*e*f + a^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*d^2*e^2 - 2*a^2*c*d*e*f + a^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d^2*e^2 - 2*a^2*c*d*e*f + a^2*c^2*f^2)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 48*((a^2*d^2*e^2 - 2*a^2*c*d*e*f + a^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*d^2*e^2 - 2*a^2*c*d*e*f + a^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d^2*e^2 - 2*a^2*c*d*e*f + a^2*c^2*f^2)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 48*((a^2*d^2*f^2*x^2 + 2*a^2*d^2*e*f*x + 2*a^2*c*d*e*f - a^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*d^2*f^2*x^2 + 2*a^2*d^2*e*f*x + 2*a^2*c*d*e*f - a^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d^2*f^2*x^2 + 2*a^2*d^2*e*f*x + 2*a^2*c*d*e*f - a^2*c^2*f^2)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 48*((a^2*d^2*f^2*x^2 + 2*a^2*d^2*e*f*x + 2*a^2*c*d*e*f - a^2*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*d^2*f^2*x^2 + 2*a^2*d^2*e*f*x + 2*a^2*c*d*e*f - a^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d^2*f^2*x^2 + 2*a^2*d^2*e*f*x + 2*a^2*c*d*e*f - a^2*c^2*f^2)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 96*(a^2*f^2*cosh(d*x + c)^2 + 2*a^2*f^2*cosh(d*x + c)*sinh(d*x + c) + a^2*f^2*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 96*(a^2*f^2*cosh(d*x + c)^2 + 2*a^2*f^2*cosh(d*x + c)*sinh(d*x + c) + a^2*f^2*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*(6*a*b*d^2*f^2*x^2 + 6*a*b*d^2*e^2 + 12*a*b*d*e*f + 12*a*b*f^2 + 3*(2*b^2*d^2*f^2*x^2 + 2*b^2*d^2*e^2 - 2*b^2*d*e*f + b^2*f^2 + 2*(2*b^2*d^2*e*f - b^2*d*f^2)*x)*cosh(d*x + c)^3 - 18*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^2 + 12*(a*b*d^2*e*f + a*b*d*f^2)*x - 8*(a^2*d^3*f^2*x^3 + 3*a^2*d^3*e*f*x^2 + 3*a^2*d^3*e^2*x + 6*a^2*c*d^2*e^2 - 6*a^2*c^2*d*e*f + 2*a^2*c^3*f^2)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d^3*cosh(d*x + c)^2 + 2*b^3*d^3*cosh(d*x + c)*sinh(d*x + c) + b^3*d^3*sinh(d*x + c)^2)","C",0
364,1,1248,0,0.503240," ","integrate((f*x+e)*cosh(d*x+c)*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b^{2} d f x + {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, b^{2} d e - 8 \, {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a b d f x + 2 \, a b d e - 2 \, a b f - {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{2} f - 8 \, {\left(a^{2} d^{2} f x^{2} + 2 \, a^{2} d^{2} e x + 4 \, a^{2} c d e - 2 \, a^{2} c^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(4 \, a^{2} d^{2} f x^{2} + 8 \, a^{2} d^{2} e x + 16 \, a^{2} c d e - 8 \, a^{2} c^{2} f - 3 \, {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a b d f x + a b d e + a b f\right)} \cosh\left(d x + c\right) + 16 \, {\left(a^{2} f \cosh\left(d x + c\right)^{2} + 2 \, a^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} f \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 16 \, {\left(a^{2} f \cosh\left(d x + c\right)^{2} + 2 \, a^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} f \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 16 \, {\left({\left(a^{2} d e - a^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d e - a^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d e - a^{2} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 16 \, {\left({\left(a^{2} d e - a^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d e - a^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d e - a^{2} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 16 \, {\left({\left(a^{2} d f x + a^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d f x + a^{2} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 16 \, {\left({\left(a^{2} d f x + a^{2} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} d f x + a^{2} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(2 \, a b d f x + 2 \, a b d e + {\left(2 \, b^{2} d f x + 2 \, b^{2} d e - b^{2} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, a b f - 6 \, {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} d^{2} f x^{2} + 2 \, a^{2} d^{2} e x + 4 \, a^{2} c d e - 2 \, a^{2} c^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left(b^{3} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d^{2} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(2*b^2*d*f*x + (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c)^4 + (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*sinh(d*x + c)^4 + 2*b^2*d*e - 8*(a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c)^3 - 4*(2*a*b*d*f*x + 2*a*b*d*e - 2*a*b*f - (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c))*sinh(d*x + c)^3 + b^2*f - 8*(a^2*d^2*f*x^2 + 2*a^2*d^2*e*x + 4*a^2*c*d*e - 2*a^2*c^2*f)*cosh(d*x + c)^2 - 2*(4*a^2*d^2*f*x^2 + 8*a^2*d^2*e*x + 16*a^2*c*d*e - 8*a^2*c^2*f - 3*(2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c)^2 + 12*(a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c))*sinh(d*x + c)^2 + 8*(a*b*d*f*x + a*b*d*e + a*b*f)*cosh(d*x + c) + 16*(a^2*f*cosh(d*x + c)^2 + 2*a^2*f*cosh(d*x + c)*sinh(d*x + c) + a^2*f*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 16*(a^2*f*cosh(d*x + c)^2 + 2*a^2*f*cosh(d*x + c)*sinh(d*x + c) + a^2*f*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 16*((a^2*d*e - a^2*c*f)*cosh(d*x + c)^2 + 2*(a^2*d*e - a^2*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d*e - a^2*c*f)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 16*((a^2*d*e - a^2*c*f)*cosh(d*x + c)^2 + 2*(a^2*d*e - a^2*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d*e - a^2*c*f)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 16*((a^2*d*f*x + a^2*c*f)*cosh(d*x + c)^2 + 2*(a^2*d*f*x + a^2*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d*f*x + a^2*c*f)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 16*((a^2*d*f*x + a^2*c*f)*cosh(d*x + c)^2 + 2*(a^2*d*f*x + a^2*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*d*f*x + a^2*c*f)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*(2*a*b*d*f*x + 2*a*b*d*e + (2*b^2*d*f*x + 2*b^2*d*e - b^2*f)*cosh(d*x + c)^3 + 2*a*b*f - 6*(a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c)^2 - 4*(a^2*d^2*f*x^2 + 2*a^2*d^2*e*x + 4*a^2*c*d*e - 2*a^2*c^2*f)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d^2*cosh(d*x + c)^2 + 2*b^3*d^2*cosh(d*x + c)*sinh(d*x + c) + b^3*d^2*sinh(d*x + c)^2)","B",0
365,1,309,0,0.458347," ","integrate(cosh(d*x+c)*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, a^{2} d x \cosh\left(d x + c\right)^{2} - b^{2} \cosh\left(d x + c\right)^{4} - b^{2} \sinh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right)^{3} - 4 \, {\left(b^{2} \cosh\left(d x + c\right) - a b\right)} \sinh\left(d x + c\right)^{3} - 4 \, a b \cosh\left(d x + c\right) + 2 \, {\left(4 \, a^{2} d x - 3 \, b^{2} \cosh\left(d x + c\right)^{2} + 6 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - b^{2} - 8 \, {\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2}\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(4 \, a^{2} d x \cosh\left(d x + c\right) - b^{2} \cosh\left(d x + c\right)^{3} + 3 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)}{8 \, {\left(b^{3} d \cosh\left(d x + c\right)^{2} + 2 \, b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} d \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/8*(8*a^2*d*x*cosh(d*x + c)^2 - b^2*cosh(d*x + c)^4 - b^2*sinh(d*x + c)^4 + 4*a*b*cosh(d*x + c)^3 - 4*(b^2*cosh(d*x + c) - a*b)*sinh(d*x + c)^3 - 4*a*b*cosh(d*x + c) + 2*(4*a^2*d*x - 3*b^2*cosh(d*x + c)^2 + 6*a*b*cosh(d*x + c))*sinh(d*x + c)^2 - b^2 - 8*(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2)*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(4*a^2*d*x*cosh(d*x + c) - b^2*cosh(d*x + c)^3 + 3*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c))/(b^3*d*cosh(d*x + c)^2 + 2*b^3*d*cosh(d*x + c)*sinh(d*x + c) + b^3*d*sinh(d*x + c)^2)","B",0
366,0,0,0,0.451101," ","integrate(cosh(d*x+c)*sinh(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)*sinh(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
367,1,7042,0,0.680375," ","integrate((f*x+e)^3*cosh(d*x+c)^2*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{36 \, b^{3} d^{3} f^{3} x^{3} + 36 \, b^{3} d^{3} e^{3} + 36 \, b^{3} d^{2} e^{2} f + 24 \, b^{3} d e f^{2} + 4 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{6} + 8 \, b^{3} f^{3} - 27 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 3 \, {\left(36 \, a b^{2} d^{3} f^{3} x^{3} + 36 \, a b^{2} d^{3} e^{3} - 54 \, a b^{2} d^{2} e^{2} f + 54 \, a b^{2} d e f^{2} - 27 \, a b^{2} f^{3} + 54 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 54 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x - 8 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 108 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(36 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 36 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{3} - 108 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} f + 216 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f^{2} - 216 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{3} + 108 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 20 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 108 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d f^{3}\right)} x - 45 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 108 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(54 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 216 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 324 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 216 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e^{3} x - 40 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 135 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 216 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 36 \, {\left(3 \, b^{3} d^{3} e f^{2} + b^{3} d^{2} f^{3}\right)} x^{2} + 108 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(18 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 18 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 54 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} f + 108 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f^{2} + 10 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 108 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{3} - 45 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 54 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 108 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 54 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d f^{3}\right)} x - 54 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2592 \, {\left({\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2592 \, {\left({\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 864 \, {\left({\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 864 \, {\left({\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 864 \, {\left({\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 864 \, {\left({\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 5184 \, {\left(a^{2} b f^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b f^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} b f^{3} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 5184 \, {\left(a^{2} b f^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b f^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} b f^{3} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 5184 \, {\left({\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 5184 \, {\left({\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(9 \, b^{3} d^{3} e^{2} f + 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x + 27 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} + 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} + 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} + a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f + 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) + 3 \, {\left(36 \, a b^{2} d^{3} f^{3} x^{3} + 36 \, a b^{2} d^{3} e^{3} + 54 \, a b^{2} d^{2} e^{2} f + 54 \, a b^{2} d e f^{2} + 27 \, a b^{2} f^{3} + 8 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 45 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 144 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 54 \, {\left(2 \, a b^{2} d^{3} e f^{2} + a b^{2} d^{2} f^{3}\right)} x^{2} - 108 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)^{2} + 54 \, {\left(2 \, a b^{2} d^{3} e^{2} f + 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x + 72 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{864 \, {\left(b^{4} d^{4} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d^{4} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d^{4} \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/864*(36*b^3*d^3*f^3*x^3 + 36*b^3*d^3*e^3 + 36*b^3*d^2*e^2*f + 24*b^3*d*e*f^2 + 4*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^6 + 4*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*sinh(d*x + c)^6 + 8*b^3*f^3 - 27*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^5 - 3*(36*a*b^2*d^3*f^3*x^3 + 36*a*b^2*d^3*e^3 - 54*a*b^2*d^2*e^2*f + 54*a*b^2*d*e*f^2 - 27*a*b^2*f^3 + 54*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 54*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x - 8*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 108*((4*a^2*b + b^3)*d^3*f^3*x^3 + (4*a^2*b + b^3)*d^3*e^3 - 3*(4*a^2*b + b^3)*d^2*e^2*f + 6*(4*a^2*b + b^3)*d*e*f^2 - 6*(4*a^2*b + b^3)*f^3 + 3*((4*a^2*b + b^3)*d^3*e*f^2 - (4*a^2*b + b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + b^3)*d^3*e^2*f - 2*(4*a^2*b + b^3)*d^2*e*f^2 + 2*(4*a^2*b + b^3)*d*f^3)*x)*cosh(d*x + c)^4 + 3*(36*(4*a^2*b + b^3)*d^3*f^3*x^3 + 36*(4*a^2*b + b^3)*d^3*e^3 - 108*(4*a^2*b + b^3)*d^2*e^2*f + 216*(4*a^2*b + b^3)*d*e*f^2 - 216*(4*a^2*b + b^3)*f^3 + 108*((4*a^2*b + b^3)*d^3*e*f^2 - (4*a^2*b + b^3)*d^2*f^3)*x^2 + 20*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^2 + 108*((4*a^2*b + b^3)*d^3*e^2*f - 2*(4*a^2*b + b^3)*d^2*e*f^2 + 2*(4*a^2*b + b^3)*d*f^3)*x - 45*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^4 - 108*((2*a^3 + a*b^2)*d^4*f^3*x^4 + 4*(2*a^3 + a*b^2)*d^4*e*f^2*x^3 + 6*(2*a^3 + a*b^2)*d^4*e^2*f*x^2 + 4*(2*a^3 + a*b^2)*d^4*e^3*x)*cosh(d*x + c)^3 - 2*(54*(2*a^3 + a*b^2)*d^4*f^3*x^4 + 216*(2*a^3 + a*b^2)*d^4*e*f^2*x^3 + 324*(2*a^3 + a*b^2)*d^4*e^2*f*x^2 + 216*(2*a^3 + a*b^2)*d^4*e^3*x - 40*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^3 + 135*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^2 - 216*((4*a^2*b + b^3)*d^3*f^3*x^3 + (4*a^2*b + b^3)*d^3*e^3 - 3*(4*a^2*b + b^3)*d^2*e^2*f + 6*(4*a^2*b + b^3)*d*e*f^2 - 6*(4*a^2*b + b^3)*f^3 + 3*((4*a^2*b + b^3)*d^3*e*f^2 - (4*a^2*b + b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + b^3)*d^3*e^2*f - 2*(4*a^2*b + b^3)*d^2*e*f^2 + 2*(4*a^2*b + b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 36*(3*b^3*d^3*e*f^2 + b^3*d^2*f^3)*x^2 + 108*((4*a^2*b + b^3)*d^3*f^3*x^3 + (4*a^2*b + b^3)*d^3*e^3 + 3*(4*a^2*b + b^3)*d^2*e^2*f + 6*(4*a^2*b + b^3)*d*e*f^2 + 6*(4*a^2*b + b^3)*f^3 + 3*((4*a^2*b + b^3)*d^3*e*f^2 + (4*a^2*b + b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + b^3)*d^3*e^2*f + 2*(4*a^2*b + b^3)*d^2*e*f^2 + 2*(4*a^2*b + b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 6*(18*(4*a^2*b + b^3)*d^3*f^3*x^3 + 18*(4*a^2*b + b^3)*d^3*e^3 + 54*(4*a^2*b + b^3)*d^2*e^2*f + 108*(4*a^2*b + b^3)*d*e*f^2 + 10*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^4 + 108*(4*a^2*b + b^3)*f^3 - 45*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^3 + 54*((4*a^2*b + b^3)*d^3*e*f^2 + (4*a^2*b + b^3)*d^2*f^3)*x^2 + 108*((4*a^2*b + b^3)*d^3*f^3*x^3 + (4*a^2*b + b^3)*d^3*e^3 - 3*(4*a^2*b + b^3)*d^2*e^2*f + 6*(4*a^2*b + b^3)*d*e*f^2 - 6*(4*a^2*b + b^3)*f^3 + 3*((4*a^2*b + b^3)*d^3*e*f^2 - (4*a^2*b + b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + b^3)*d^3*e^2*f - 2*(4*a^2*b + b^3)*d^2*e*f^2 + 2*(4*a^2*b + b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 54*((4*a^2*b + b^3)*d^3*e^2*f + 2*(4*a^2*b + b^3)*d^2*e*f^2 + 2*(4*a^2*b + b^3)*d*f^3)*x - 54*((2*a^3 + a*b^2)*d^4*f^3*x^4 + 4*(2*a^3 + a*b^2)*d^4*e*f^2*x^3 + 6*(2*a^3 + a*b^2)*d^4*e^2*f*x^2 + 4*(2*a^3 + a*b^2)*d^4*e^3*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 2592*((a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c)^3 + 3*(a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2592*((a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c)^3 + 3*(a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 864*((a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c)^3 + 3*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 864*((a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c)^3 + 3*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 864*((a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c)^3 + 3*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 864*((a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c)^3 + 3*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 5184*(a^2*b*f^3*cosh(d*x + c)^3 + 3*a^2*b*f^3*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*b*f^3*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*b*f^3*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 5184*(a^2*b*f^3*cosh(d*x + c)^3 + 3*a^2*b*f^3*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*b*f^3*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*b*f^3*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 5184*((a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c)^3 + 3*(a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d*f^3*x + a^2*b*d*e*f^2)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 5184*((a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c)^3 + 3*(a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d*f^3*x + a^2*b*d*e*f^2)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(9*b^3*d^3*e^2*f + 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x + 27*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 + 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 + 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 + a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f + 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c) + 3*(36*a*b^2*d^3*f^3*x^3 + 36*a*b^2*d^3*e^3 + 54*a*b^2*d^2*e^2*f + 54*a*b^2*d*e*f^2 + 27*a*b^2*f^3 + 8*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^5 - 45*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^4 + 144*((4*a^2*b + b^3)*d^3*f^3*x^3 + (4*a^2*b + b^3)*d^3*e^3 - 3*(4*a^2*b + b^3)*d^2*e^2*f + 6*(4*a^2*b + b^3)*d*e*f^2 - 6*(4*a^2*b + b^3)*f^3 + 3*((4*a^2*b + b^3)*d^3*e*f^2 - (4*a^2*b + b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + b^3)*d^3*e^2*f - 2*(4*a^2*b + b^3)*d^2*e*f^2 + 2*(4*a^2*b + b^3)*d*f^3)*x)*cosh(d*x + c)^3 + 54*(2*a*b^2*d^3*e*f^2 + a*b^2*d^2*f^3)*x^2 - 108*((2*a^3 + a*b^2)*d^4*f^3*x^4 + 4*(2*a^3 + a*b^2)*d^4*e*f^2*x^3 + 6*(2*a^3 + a*b^2)*d^4*e^2*f*x^2 + 4*(2*a^3 + a*b^2)*d^4*e^3*x)*cosh(d*x + c)^2 + 54*(2*a*b^2*d^3*e^2*f + 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x + 72*((4*a^2*b + b^3)*d^3*f^3*x^3 + (4*a^2*b + b^3)*d^3*e^3 + 3*(4*a^2*b + b^3)*d^2*e^2*f + 6*(4*a^2*b + b^3)*d*e*f^2 + 6*(4*a^2*b + b^3)*f^3 + 3*((4*a^2*b + b^3)*d^3*e*f^2 + (4*a^2*b + b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b + b^3)*d^3*e^2*f + 2*(4*a^2*b + b^3)*d^2*e*f^2 + 2*(4*a^2*b + b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d^4*cosh(d*x + c)^3 + 3*b^4*d^4*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d^4*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d^4*sinh(d*x + c)^3)","C",0
368,1,4311,0,0.573980," ","integrate((f*x+e)^2*cosh(d*x+c)^2*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{18 \, b^{3} d^{2} f^{2} x^{2} + 18 \, b^{3} d^{2} e^{2} + 2 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{6} + 12 \, b^{3} d e f - 27 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 3 \, {\left(18 \, a b^{2} d^{2} f^{2} x^{2} + 18 \, a b^{2} d^{2} e^{2} - 18 \, a b^{2} d e f + 9 \, a b^{2} f^{2} + 18 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x - 4 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, b^{3} f^{2} + 54 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(18 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 18 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 36 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f + 36 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{2} + 10 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 36 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b + b^{3}\right)} d f^{2}\right)} x - 45 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 72 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(36 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 108 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 108 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{3} e^{2} x - 20 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 135 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 108 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 54 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f + {\left(4 \, a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(9 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 5 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f - 45 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 18 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{2} + 54 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 18 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f + {\left(4 \, a^{2} b + b^{3}\right)} d f^{2}\right)} x - 36 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 864 \, {\left({\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 864 \, {\left({\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 432 \, {\left({\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 432 \, {\left({\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 432 \, {\left({\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 432 \, {\left({\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 864 \, {\left(a^{2} b f^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} b f^{2} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 864 \, {\left(a^{2} b f^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} b f^{2} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(3 \, b^{3} d^{2} e f + b^{3} d f^{2}\right)} x + 27 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} + 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f + a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 3 \, {\left(18 \, a b^{2} d^{2} f^{2} x^{2} + 18 \, a b^{2} d^{2} e^{2} + 18 \, a b^{2} d e f + 4 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 9 \, a b^{2} f^{2} - 45 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 72 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 72 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)^{2} + 18 \, {\left(2 \, a b^{2} d^{2} e f + a b^{2} d f^{2}\right)} x + 36 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d^{2} e f + {\left(4 \, a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{432 \, {\left(b^{4} d^{3} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d^{3} \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/432*(18*b^3*d^2*f^2*x^2 + 18*b^3*d^2*e^2 + 2*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^6 + 2*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*sinh(d*x + c)^6 + 12*b^3*d*e*f - 27*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^5 - 3*(18*a*b^2*d^2*f^2*x^2 + 18*a*b^2*d^2*e^2 - 18*a*b^2*d*e*f + 9*a*b^2*f^2 + 18*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x - 4*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*b^3*f^2 + 54*((4*a^2*b + b^3)*d^2*f^2*x^2 + (4*a^2*b + b^3)*d^2*e^2 - 2*(4*a^2*b + b^3)*d*e*f + 2*(4*a^2*b + b^3)*f^2 + 2*((4*a^2*b + b^3)*d^2*e*f - (4*a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^4 + 3*(18*(4*a^2*b + b^3)*d^2*f^2*x^2 + 18*(4*a^2*b + b^3)*d^2*e^2 - 36*(4*a^2*b + b^3)*d*e*f + 36*(4*a^2*b + b^3)*f^2 + 10*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^2 + 36*((4*a^2*b + b^3)*d^2*e*f - (4*a^2*b + b^3)*d*f^2)*x - 45*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^4 - 72*((2*a^3 + a*b^2)*d^3*f^2*x^3 + 3*(2*a^3 + a*b^2)*d^3*e*f*x^2 + 3*(2*a^3 + a*b^2)*d^3*e^2*x)*cosh(d*x + c)^3 - 2*(36*(2*a^3 + a*b^2)*d^3*f^2*x^3 + 108*(2*a^3 + a*b^2)*d^3*e*f*x^2 + 108*(2*a^3 + a*b^2)*d^3*e^2*x - 20*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^3 + 135*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^2 - 108*((4*a^2*b + b^3)*d^2*f^2*x^2 + (4*a^2*b + b^3)*d^2*e^2 - 2*(4*a^2*b + b^3)*d*e*f + 2*(4*a^2*b + b^3)*f^2 + 2*((4*a^2*b + b^3)*d^2*e*f - (4*a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 54*((4*a^2*b + b^3)*d^2*f^2*x^2 + (4*a^2*b + b^3)*d^2*e^2 + 2*(4*a^2*b + b^3)*d*e*f + 2*(4*a^2*b + b^3)*f^2 + 2*((4*a^2*b + b^3)*d^2*e*f + (4*a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 6*(9*(4*a^2*b + b^3)*d^2*f^2*x^2 + 9*(4*a^2*b + b^3)*d^2*e^2 + 5*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^4 + 18*(4*a^2*b + b^3)*d*e*f - 45*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^3 + 18*(4*a^2*b + b^3)*f^2 + 54*((4*a^2*b + b^3)*d^2*f^2*x^2 + (4*a^2*b + b^3)*d^2*e^2 - 2*(4*a^2*b + b^3)*d*e*f + 2*(4*a^2*b + b^3)*f^2 + 2*((4*a^2*b + b^3)*d^2*e*f - (4*a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 18*((4*a^2*b + b^3)*d^2*e*f + (4*a^2*b + b^3)*d*f^2)*x - 36*((2*a^3 + a*b^2)*d^3*f^2*x^3 + 3*(2*a^3 + a*b^2)*d^3*e*f*x^2 + 3*(2*a^3 + a*b^2)*d^3*e^2*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 864*((a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^3 + 3*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d*f^2*x + a^2*b*d*e*f)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 864*((a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^3 + 3*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d*f^2*x + a^2*b*d*e*f)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 432*((a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^3 + 3*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 432*((a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^3 + 3*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 432*((a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^3 + 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 432*((a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^3 + 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 864*(a^2*b*f^2*cosh(d*x + c)^3 + 3*a^2*b*f^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*b*f^2*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*b*f^2*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 864*(a^2*b*f^2*cosh(d*x + c)^3 + 3*a^2*b*f^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*b*f^2*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*b*f^2*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(3*b^3*d^2*e*f + b^3*d*f^2)*x + 27*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 + 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f + a*b^2*d*f^2)*x)*cosh(d*x + c) + 3*(18*a*b^2*d^2*f^2*x^2 + 18*a*b^2*d^2*e^2 + 18*a*b^2*d*e*f + 4*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^5 + 9*a*b^2*f^2 - 45*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^4 + 72*((4*a^2*b + b^3)*d^2*f^2*x^2 + (4*a^2*b + b^3)*d^2*e^2 - 2*(4*a^2*b + b^3)*d*e*f + 2*(4*a^2*b + b^3)*f^2 + 2*((4*a^2*b + b^3)*d^2*e*f - (4*a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^3 - 72*((2*a^3 + a*b^2)*d^3*f^2*x^3 + 3*(2*a^3 + a*b^2)*d^3*e*f*x^2 + 3*(2*a^3 + a*b^2)*d^3*e^2*x)*cosh(d*x + c)^2 + 18*(2*a*b^2*d^2*e*f + a*b^2*d*f^2)*x + 36*((4*a^2*b + b^3)*d^2*f^2*x^2 + (4*a^2*b + b^3)*d^2*e^2 + 2*(4*a^2*b + b^3)*d*e*f + 2*(4*a^2*b + b^3)*f^2 + 2*((4*a^2*b + b^3)*d^2*e*f + (4*a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d^3*cosh(d*x + c)^3 + 3*b^4*d^3*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d^3*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d^3*sinh(d*x + c)^3)","C",0
369,1,2195,0,0.543599," ","integrate((f*x+e)*cosh(d*x+c)^2*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \sinh\left(d x + c\right)^{6} + 6 \, b^{3} d f x - 9 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{5} - 3 \, {\left(6 \, a b^{2} d f x + 6 \, a b^{2} d e - 3 \, a b^{2} f - 4 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, b^{3} d e + 18 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d f x + {\left(4 \, a^{2} b + b^{3}\right)} d e - {\left(4 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, {\left(4 \, a^{2} b + b^{3}\right)} d f x + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} d e + 10 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(4 \, a^{2} b + b^{3}\right)} f - 15 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, b^{3} f - 36 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(18 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{2} f x^{2} + 36 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{2} e x - 20 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{3} + 45 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{2} - 36 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d f x + {\left(4 \, a^{2} b + b^{3}\right)} d e - {\left(4 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 18 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d f x + {\left(4 \, a^{2} b + b^{3}\right)} d e + {\left(4 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(5 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(4 \, a^{2} b + b^{3}\right)} d f x - 15 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{2} b + b^{3}\right)} d e + 18 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d f x + {\left(4 \, a^{2} b + b^{3}\right)} d e - {\left(4 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(4 \, a^{2} b + b^{3}\right)} f - 18 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 144 \, {\left(a^{2} b f \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} b f \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 144 \, {\left(a^{2} b f \cosh\left(d x + c\right)^{3} + 3 \, a^{2} b f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} b f \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 144 \, {\left({\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d e - a^{2} b c f\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 144 \, {\left({\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d e - a^{2} b c f\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 144 \, {\left({\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d f x + a^{2} b c f\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 144 \, {\left({\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} b d f x + a^{2} b c f\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 9 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e + a b^{2} f\right)} \cosh\left(d x + c\right) + 3 \, {\left(6 \, a b^{2} d f x + 4 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{5} + 6 \, a b^{2} d e - 15 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{4} + 3 \, a b^{2} f + 24 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d f x + {\left(4 \, a^{2} b + b^{3}\right)} d e - {\left(4 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} - 36 \, {\left({\left(2 \, a^{3} + a b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(2 \, a^{3} + a b^{2}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d f x + {\left(4 \, a^{2} b + b^{3}\right)} d e + {\left(4 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{144 \, {\left(b^{4} d^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d^{2} \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/144*(2*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^6 + 2*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*sinh(d*x + c)^6 + 6*b^3*d*f*x - 9*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^5 - 3*(6*a*b^2*d*f*x + 6*a*b^2*d*e - 3*a*b^2*f - 4*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*b^3*d*e + 18*((4*a^2*b + b^3)*d*f*x + (4*a^2*b + b^3)*d*e - (4*a^2*b + b^3)*f)*cosh(d*x + c)^4 + 3*(6*(4*a^2*b + b^3)*d*f*x + 6*(4*a^2*b + b^3)*d*e + 10*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^2 - 6*(4*a^2*b + b^3)*f - 15*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c))*sinh(d*x + c)^4 + 2*b^3*f - 36*((2*a^3 + a*b^2)*d^2*f*x^2 + 2*(2*a^3 + a*b^2)*d^2*e*x)*cosh(d*x + c)^3 - 2*(18*(2*a^3 + a*b^2)*d^2*f*x^2 + 36*(2*a^3 + a*b^2)*d^2*e*x - 20*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^3 + 45*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^2 - 36*((4*a^2*b + b^3)*d*f*x + (4*a^2*b + b^3)*d*e - (4*a^2*b + b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^3 + 18*((4*a^2*b + b^3)*d*f*x + (4*a^2*b + b^3)*d*e + (4*a^2*b + b^3)*f)*cosh(d*x + c)^2 + 6*(5*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^4 + 3*(4*a^2*b + b^3)*d*f*x - 15*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^3 + 3*(4*a^2*b + b^3)*d*e + 18*((4*a^2*b + b^3)*d*f*x + (4*a^2*b + b^3)*d*e - (4*a^2*b + b^3)*f)*cosh(d*x + c)^2 + 3*(4*a^2*b + b^3)*f - 18*((2*a^3 + a*b^2)*d^2*f*x^2 + 2*(2*a^3 + a*b^2)*d^2*e*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 144*(a^2*b*f*cosh(d*x + c)^3 + 3*a^2*b*f*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*b*f*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*b*f*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 144*(a^2*b*f*cosh(d*x + c)^3 + 3*a^2*b*f*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*b*f*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*b*f*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 144*((a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^3 + 3*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d*e - a^2*b*c*f)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 144*((a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^3 + 3*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d*e - a^2*b*c*f)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 144*((a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^3 + 3*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d*f*x + a^2*b*c*f)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 144*((a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^3 + 3*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2*b*d*f*x + a^2*b*c*f)*sinh(d*x + c)^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 9*(2*a*b^2*d*f*x + 2*a*b^2*d*e + a*b^2*f)*cosh(d*x + c) + 3*(6*a*b^2*d*f*x + 4*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^5 + 6*a*b^2*d*e - 15*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^4 + 3*a*b^2*f + 24*((4*a^2*b + b^3)*d*f*x + (4*a^2*b + b^3)*d*e - (4*a^2*b + b^3)*f)*cosh(d*x + c)^3 - 36*((2*a^3 + a*b^2)*d^2*f*x^2 + 2*(2*a^3 + a*b^2)*d^2*e*x)*cosh(d*x + c)^2 + 12*((4*a^2*b + b^3)*d*f*x + (4*a^2*b + b^3)*d*e + (4*a^2*b + b^3)*f)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d^2*cosh(d*x + c)^3 + 3*b^4*d^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d^2*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d^2*sinh(d*x + c)^3)","B",0
370,1,745,0,0.536483," ","integrate(cosh(d*x+c)^2*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{b^{3} \cosh\left(d x + c\right)^{6} + b^{3} \sinh\left(d x + c\right)^{6} - 3 \, a b^{2} \cosh\left(d x + c\right)^{5} - 12 \, {\left(2 \, a^{3} + a b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, b^{3} \cosh\left(d x + c\right) - a b^{2}\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(4 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{2} - 5 \, a b^{2} \cosh\left(d x + c\right) + 4 \, a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a b^{2} \cosh\left(d x + c\right) + 2 \, {\left(10 \, b^{3} \cosh\left(d x + c\right)^{3} - 15 \, a b^{2} \cosh\left(d x + c\right)^{2} - 6 \, {\left(2 \, a^{3} + a b^{2}\right)} d x + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{3} + 3 \, {\left(4 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{4} - 10 \, a b^{2} \cosh\left(d x + c\right)^{3} - 12 \, {\left(2 \, a^{3} + a b^{2}\right)} d x \cosh\left(d x + c\right) + 4 \, a^{2} b + b^{3} + 6 \, {\left(4 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 24 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{3}\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 3 \, {\left(2 \, b^{3} \cosh\left(d x + c\right)^{5} - 5 \, a b^{2} \cosh\left(d x + c\right)^{4} - 12 \, {\left(2 \, a^{3} + a b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 4 \, {\left(4 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{3} + a b^{2} + 2 \, {\left(4 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/24*(b^3*cosh(d*x + c)^6 + b^3*sinh(d*x + c)^6 - 3*a*b^2*cosh(d*x + c)^5 - 12*(2*a^3 + a*b^2)*d*x*cosh(d*x + c)^3 + 3*(2*b^3*cosh(d*x + c) - a*b^2)*sinh(d*x + c)^5 + 3*(4*a^2*b + b^3)*cosh(d*x + c)^4 + 3*(5*b^3*cosh(d*x + c)^2 - 5*a*b^2*cosh(d*x + c) + 4*a^2*b + b^3)*sinh(d*x + c)^4 + 3*a*b^2*cosh(d*x + c) + 2*(10*b^3*cosh(d*x + c)^3 - 15*a*b^2*cosh(d*x + c)^2 - 6*(2*a^3 + a*b^2)*d*x + 6*(4*a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + b^3 + 3*(4*a^2*b + b^3)*cosh(d*x + c)^2 + 3*(5*b^3*cosh(d*x + c)^4 - 10*a*b^2*cosh(d*x + c)^3 - 12*(2*a^3 + a*b^2)*d*x*cosh(d*x + c) + 4*a^2*b + b^3 + 6*(4*a^2*b + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 24*(a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*sinh(d*x + c)^3)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 3*(2*b^3*cosh(d*x + c)^5 - 5*a*b^2*cosh(d*x + c)^4 - 12*(2*a^3 + a*b^2)*d*x*cosh(d*x + c)^2 + 4*(4*a^2*b + b^3)*cosh(d*x + c)^3 + a*b^2 + 2*(4*a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d*cosh(d*x + c)^3 + 3*b^4*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d*sinh(d*x + c)^3)","B",0
371,0,0,0,0.484092," ","integrate(cosh(d*x+c)^2*sinh(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)^2*sinh(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
372,1,12603,0,0.990062," ","integrate((f*x+e)^3*cosh(d*x+c)^3*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{864 \, b^{4} d^{3} f^{3} x^{3} + 864 \, b^{4} d^{3} e^{3} + 648 \, b^{4} d^{2} e^{2} f + 27 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{8} + 27 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{8} + 324 \, b^{4} d e f^{2} - 256 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{7} - 8 \, {\left(288 \, a b^{3} d^{3} f^{3} x^{3} + 288 \, a b^{3} d^{3} e^{3} - 288 \, a b^{3} d^{2} e^{2} f + 192 \, a b^{3} d e f^{2} - 64 \, a b^{3} f^{3} + 288 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 96 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x - 27 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 81 \, b^{4} f^{3} + 864 \, {\left(4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(864 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 864 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 1296 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 1296 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} - 648 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{3} + 1296 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 189 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 1296 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x - 448 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 6912 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 24 \, {\left(288 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} f^{3} x^{3} + 288 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{3} - 864 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} f + 1728 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f^{2} - 1728 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{3} - 63 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 864 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 224 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 864 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{3}\right)} x - 216 \, {\left(4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 13824 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{4} f^{3}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(6912 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} f^{3} x^{4} + 27648 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e f^{2} x^{3} + 41472 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e^{2} f x^{2} + 27648 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e^{3} x + 55296 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{3} e^{3} - 82944 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d^{2} e^{2} f + 55296 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} d e f^{2} - 13824 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{4} f^{3} - 945 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4480 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 6480 \, {\left(4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 17280 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 6912 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(864 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} f^{3} x^{3} + 864 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{3} + 2592 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} f + 189 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 5184 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f^{2} - 1120 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 5184 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{3} + 2160 \, {\left(4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 2592 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{3}\right)} x^{2} - 8640 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2592 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{3}\right)} x - 6912 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{4} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 648 \, {\left(4 \, b^{4} d^{3} e f^{2} + b^{4} d^{2} f^{3}\right)} x^{2} + 864 \, {\left(4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} + 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(288 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 288 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} + 63 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 432 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f - 448 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 432 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} + 1080 \, {\left(4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 216 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{3} - 5760 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 432 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} - 6912 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{4} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 432 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x + 1728 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 324 \, {\left(8 \, b^{4} d^{3} e^{2} f + 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x + 256 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} + 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} + 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} + a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f + 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) + 165888 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{4}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 165888 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{4}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 55296 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} - {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} - {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} - {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} - {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} - {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 55296 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} - {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} - {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} - {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} - {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} - {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 55296 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} + {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} + {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} + {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} + {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} + {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 55296 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} + {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} + {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} + {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} + {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f^{2} + {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 331776 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + a^{2} b^{2}\right)} f^{3} \sinh\left(d x + c\right)^{4}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 331776 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + a^{2} b^{2}\right)} f^{3} \sinh\left(d x + c\right)^{4}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 331776 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 331776 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 8 \, {\left(288 \, a b^{3} d^{3} f^{3} x^{3} + 288 \, a b^{3} d^{3} e^{3} + 288 \, a b^{3} d^{2} e^{2} f + 192 \, a b^{3} d e f^{2} + 27 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{7} + 64 \, a b^{3} f^{3} - 224 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 648 \, {\left(4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} - 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 4320 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 6912 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{4} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 288 \, {\left(3 \, a b^{3} d^{3} e f^{2} + a b^{3} d^{2} f^{3}\right)} x^{2} + 2592 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 96 \, {\left(9 \, a b^{3} d^{3} e^{2} f + 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x + 216 \, {\left(4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 4 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} + 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{3} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{55296 \, {\left(b^{5} d^{4} \cosh\left(d x + c\right)^{4} + 4 \, b^{5} d^{4} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} d^{4} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} d^{4} \sinh\left(d x + c\right)^{4}\right)}}"," ",0,"1/55296*(864*b^4*d^3*f^3*x^3 + 864*b^4*d^3*e^3 + 648*b^4*d^2*e^2*f + 27*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^8 + 27*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*sinh(d*x + c)^8 + 324*b^4*d*e*f^2 - 256*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^7 - 8*(288*a*b^3*d^3*f^3*x^3 + 288*a*b^3*d^3*e^3 - 288*a*b^3*d^2*e^2*f + 192*a*b^3*d*e*f^2 - 64*a*b^3*f^3 + 288*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 96*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x - 27*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 81*b^4*f^3 + 864*(4*(2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(2*a^2*b^2 + b^4)*d^3*e^3 - 6*(2*a^2*b^2 + b^4)*d^2*e^2*f + 6*(2*a^2*b^2 + b^4)*d*e*f^2 - 3*(2*a^2*b^2 + b^4)*f^3 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e*f^2 - (2*a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e^2*f - 2*(2*a^2*b^2 + b^4)*d^2*e*f^2 + (2*a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c)^6 + 4*(864*(2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 864*(2*a^2*b^2 + b^4)*d^3*e^3 - 1296*(2*a^2*b^2 + b^4)*d^2*e^2*f + 1296*(2*a^2*b^2 + b^4)*d*e*f^2 - 648*(2*a^2*b^2 + b^4)*f^3 + 1296*(2*(2*a^2*b^2 + b^4)*d^3*e*f^2 - (2*a^2*b^2 + b^4)*d^2*f^3)*x^2 + 189*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^2 + 1296*(2*(2*a^2*b^2 + b^4)*d^3*e^2*f - 2*(2*a^2*b^2 + b^4)*d^2*e*f^2 + (2*a^2*b^2 + b^4)*d*f^3)*x - 448*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^6 - 6912*((4*a^3*b + 3*a*b^3)*d^3*f^3*x^3 + (4*a^3*b + 3*a*b^3)*d^3*e^3 - 3*(4*a^3*b + 3*a*b^3)*d^2*e^2*f + 6*(4*a^3*b + 3*a*b^3)*d*e*f^2 - 6*(4*a^3*b + 3*a*b^3)*f^3 + 3*((4*a^3*b + 3*a*b^3)*d^3*e*f^2 - (4*a^3*b + 3*a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + 3*a*b^3)*d^3*e^2*f - 2*(4*a^3*b + 3*a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + 3*a*b^3)*d*f^3)*x)*cosh(d*x + c)^5 - 24*(288*(4*a^3*b + 3*a*b^3)*d^3*f^3*x^3 + 288*(4*a^3*b + 3*a*b^3)*d^3*e^3 - 864*(4*a^3*b + 3*a*b^3)*d^2*e^2*f + 1728*(4*a^3*b + 3*a*b^3)*d*e*f^2 - 1728*(4*a^3*b + 3*a*b^3)*f^3 - 63*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^3 + 864*((4*a^3*b + 3*a*b^3)*d^3*e*f^2 - (4*a^3*b + 3*a*b^3)*d^2*f^3)*x^2 + 224*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^2 + 864*((4*a^3*b + 3*a*b^3)*d^3*e^2*f - 2*(4*a^3*b + 3*a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + 3*a*b^3)*d*f^3)*x - 216*(4*(2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(2*a^2*b^2 + b^4)*d^3*e^3 - 6*(2*a^2*b^2 + b^4)*d^2*e^2*f + 6*(2*a^2*b^2 + b^4)*d*e*f^2 - 3*(2*a^2*b^2 + b^4)*f^3 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e*f^2 - (2*a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e^2*f - 2*(2*a^2*b^2 + b^4)*d^2*e*f^2 + (2*a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 13824*((a^4 + a^2*b^2)*d^4*f^3*x^4 + 4*(a^4 + a^2*b^2)*d^4*e*f^2*x^3 + 6*(a^4 + a^2*b^2)*d^4*e^2*f*x^2 + 4*(a^4 + a^2*b^2)*d^4*e^3*x + 8*(a^4 + a^2*b^2)*c*d^3*e^3 - 12*(a^4 + a^2*b^2)*c^2*d^2*e^2*f + 8*(a^4 + a^2*b^2)*c^3*d*e*f^2 - 2*(a^4 + a^2*b^2)*c^4*f^3)*cosh(d*x + c)^4 - 2*(6912*(a^4 + a^2*b^2)*d^4*f^3*x^4 + 27648*(a^4 + a^2*b^2)*d^4*e*f^2*x^3 + 41472*(a^4 + a^2*b^2)*d^4*e^2*f*x^2 + 27648*(a^4 + a^2*b^2)*d^4*e^3*x + 55296*(a^4 + a^2*b^2)*c*d^3*e^3 - 82944*(a^4 + a^2*b^2)*c^2*d^2*e^2*f + 55296*(a^4 + a^2*b^2)*c^3*d*e*f^2 - 13824*(a^4 + a^2*b^2)*c^4*f^3 - 945*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^4 + 4480*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^3 - 6480*(4*(2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(2*a^2*b^2 + b^4)*d^3*e^3 - 6*(2*a^2*b^2 + b^4)*d^2*e^2*f + 6*(2*a^2*b^2 + b^4)*d*e*f^2 - 3*(2*a^2*b^2 + b^4)*f^3 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e*f^2 - (2*a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e^2*f - 2*(2*a^2*b^2 + b^4)*d^2*e*f^2 + (2*a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c)^2 + 17280*((4*a^3*b + 3*a*b^3)*d^3*f^3*x^3 + (4*a^3*b + 3*a*b^3)*d^3*e^3 - 3*(4*a^3*b + 3*a*b^3)*d^2*e^2*f + 6*(4*a^3*b + 3*a*b^3)*d*e*f^2 - 6*(4*a^3*b + 3*a*b^3)*f^3 + 3*((4*a^3*b + 3*a*b^3)*d^3*e*f^2 - (4*a^3*b + 3*a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + 3*a*b^3)*d^3*e^2*f - 2*(4*a^3*b + 3*a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + 3*a*b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^4 + 6912*((4*a^3*b + 3*a*b^3)*d^3*f^3*x^3 + (4*a^3*b + 3*a*b^3)*d^3*e^3 + 3*(4*a^3*b + 3*a*b^3)*d^2*e^2*f + 6*(4*a^3*b + 3*a*b^3)*d*e*f^2 + 6*(4*a^3*b + 3*a*b^3)*f^3 + 3*((4*a^3*b + 3*a*b^3)*d^3*e*f^2 + (4*a^3*b + 3*a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + 3*a*b^3)*d^3*e^2*f + 2*(4*a^3*b + 3*a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + 3*a*b^3)*d*f^3)*x)*cosh(d*x + c)^3 + 8*(864*(4*a^3*b + 3*a*b^3)*d^3*f^3*x^3 + 864*(4*a^3*b + 3*a*b^3)*d^3*e^3 + 2592*(4*a^3*b + 3*a*b^3)*d^2*e^2*f + 189*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^5 + 5184*(4*a^3*b + 3*a*b^3)*d*e*f^2 - 1120*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^4 + 5184*(4*a^3*b + 3*a*b^3)*f^3 + 2160*(4*(2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(2*a^2*b^2 + b^4)*d^3*e^3 - 6*(2*a^2*b^2 + b^4)*d^2*e^2*f + 6*(2*a^2*b^2 + b^4)*d*e*f^2 - 3*(2*a^2*b^2 + b^4)*f^3 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e*f^2 - (2*a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e^2*f - 2*(2*a^2*b^2 + b^4)*d^2*e*f^2 + (2*a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c)^3 + 2592*((4*a^3*b + 3*a*b^3)*d^3*e*f^2 + (4*a^3*b + 3*a*b^3)*d^2*f^3)*x^2 - 8640*((4*a^3*b + 3*a*b^3)*d^3*f^3*x^3 + (4*a^3*b + 3*a*b^3)*d^3*e^3 - 3*(4*a^3*b + 3*a*b^3)*d^2*e^2*f + 6*(4*a^3*b + 3*a*b^3)*d*e*f^2 - 6*(4*a^3*b + 3*a*b^3)*f^3 + 3*((4*a^3*b + 3*a*b^3)*d^3*e*f^2 - (4*a^3*b + 3*a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + 3*a*b^3)*d^3*e^2*f - 2*(4*a^3*b + 3*a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + 3*a*b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 2592*((4*a^3*b + 3*a*b^3)*d^3*e^2*f + 2*(4*a^3*b + 3*a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + 3*a*b^3)*d*f^3)*x - 6912*((a^4 + a^2*b^2)*d^4*f^3*x^4 + 4*(a^4 + a^2*b^2)*d^4*e*f^2*x^3 + 6*(a^4 + a^2*b^2)*d^4*e^2*f*x^2 + 4*(a^4 + a^2*b^2)*d^4*e^3*x + 8*(a^4 + a^2*b^2)*c*d^3*e^3 - 12*(a^4 + a^2*b^2)*c^2*d^2*e^2*f + 8*(a^4 + a^2*b^2)*c^3*d*e*f^2 - 2*(a^4 + a^2*b^2)*c^4*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 648*(4*b^4*d^3*e*f^2 + b^4*d^2*f^3)*x^2 + 864*(4*(2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(2*a^2*b^2 + b^4)*d^3*e^3 + 6*(2*a^2*b^2 + b^4)*d^2*e^2*f + 6*(2*a^2*b^2 + b^4)*d*e*f^2 + 3*(2*a^2*b^2 + b^4)*f^3 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e*f^2 + (2*a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e^2*f + 2*(2*a^2*b^2 + b^4)*d^2*e*f^2 + (2*a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c)^2 + 12*(288*(2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 288*(2*a^2*b^2 + b^4)*d^3*e^3 + 63*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^6 + 432*(2*a^2*b^2 + b^4)*d^2*e^2*f - 448*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^5 + 432*(2*a^2*b^2 + b^4)*d*e*f^2 + 1080*(4*(2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(2*a^2*b^2 + b^4)*d^3*e^3 - 6*(2*a^2*b^2 + b^4)*d^2*e^2*f + 6*(2*a^2*b^2 + b^4)*d*e*f^2 - 3*(2*a^2*b^2 + b^4)*f^3 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e*f^2 - (2*a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e^2*f - 2*(2*a^2*b^2 + b^4)*d^2*e*f^2 + (2*a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c)^4 + 216*(2*a^2*b^2 + b^4)*f^3 - 5760*((4*a^3*b + 3*a*b^3)*d^3*f^3*x^3 + (4*a^3*b + 3*a*b^3)*d^3*e^3 - 3*(4*a^3*b + 3*a*b^3)*d^2*e^2*f + 6*(4*a^3*b + 3*a*b^3)*d*e*f^2 - 6*(4*a^3*b + 3*a*b^3)*f^3 + 3*((4*a^3*b + 3*a*b^3)*d^3*e*f^2 - (4*a^3*b + 3*a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + 3*a*b^3)*d^3*e^2*f - 2*(4*a^3*b + 3*a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + 3*a*b^3)*d*f^3)*x)*cosh(d*x + c)^3 + 432*(2*(2*a^2*b^2 + b^4)*d^3*e*f^2 + (2*a^2*b^2 + b^4)*d^2*f^3)*x^2 - 6912*((a^4 + a^2*b^2)*d^4*f^3*x^4 + 4*(a^4 + a^2*b^2)*d^4*e*f^2*x^3 + 6*(a^4 + a^2*b^2)*d^4*e^2*f*x^2 + 4*(a^4 + a^2*b^2)*d^4*e^3*x + 8*(a^4 + a^2*b^2)*c*d^3*e^3 - 12*(a^4 + a^2*b^2)*c^2*d^2*e^2*f + 8*(a^4 + a^2*b^2)*c^3*d*e*f^2 - 2*(a^4 + a^2*b^2)*c^4*f^3)*cosh(d*x + c)^2 + 432*(2*(2*a^2*b^2 + b^4)*d^3*e^2*f + 2*(2*a^2*b^2 + b^4)*d^2*e*f^2 + (2*a^2*b^2 + b^4)*d*f^3)*x + 1728*((4*a^3*b + 3*a*b^3)*d^3*f^3*x^3 + (4*a^3*b + 3*a*b^3)*d^3*e^3 + 3*(4*a^3*b + 3*a*b^3)*d^2*e^2*f + 6*(4*a^3*b + 3*a*b^3)*d*e*f^2 + 6*(4*a^3*b + 3*a*b^3)*f^3 + 3*((4*a^3*b + 3*a*b^3)*d^3*e*f^2 + (4*a^3*b + 3*a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + 3*a*b^3)*d^3*e^2*f + 2*(4*a^3*b + 3*a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + 3*a*b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 324*(8*b^4*d^3*e^2*f + 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x + 256*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 + 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 + 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 + a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f + 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c) + 165888*(((a^4 + a^2*b^2)*d^2*f^3*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f^2*x + (a^4 + a^2*b^2)*d^2*e^2*f)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d^2*f^3*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f^2*x + (a^4 + a^2*b^2)*d^2*e^2*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d^2*f^3*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f^2*x + (a^4 + a^2*b^2)*d^2*e^2*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d^2*f^3*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f^2*x + (a^4 + a^2*b^2)*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d^2*f^3*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f^2*x + (a^4 + a^2*b^2)*d^2*e^2*f)*sinh(d*x + c)^4)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 165888*(((a^4 + a^2*b^2)*d^2*f^3*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f^2*x + (a^4 + a^2*b^2)*d^2*e^2*f)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d^2*f^3*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f^2*x + (a^4 + a^2*b^2)*d^2*e^2*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d^2*f^3*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f^2*x + (a^4 + a^2*b^2)*d^2*e^2*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d^2*f^3*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f^2*x + (a^4 + a^2*b^2)*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d^2*f^3*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f^2*x + (a^4 + a^2*b^2)*d^2*e^2*f)*sinh(d*x + c)^4)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 55296*(((a^4 + a^2*b^2)*d^3*e^3 - 3*(a^4 + a^2*b^2)*c*d^2*e^2*f + 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 - (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d^3*e^3 - 3*(a^4 + a^2*b^2)*c*d^2*e^2*f + 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 - (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d^3*e^3 - 3*(a^4 + a^2*b^2)*c*d^2*e^2*f + 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 - (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d^3*e^3 - 3*(a^4 + a^2*b^2)*c*d^2*e^2*f + 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 - (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d^3*e^3 - 3*(a^4 + a^2*b^2)*c*d^2*e^2*f + 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 - (a^4 + a^2*b^2)*c^3*f^3)*sinh(d*x + c)^4)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 55296*(((a^4 + a^2*b^2)*d^3*e^3 - 3*(a^4 + a^2*b^2)*c*d^2*e^2*f + 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 - (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d^3*e^3 - 3*(a^4 + a^2*b^2)*c*d^2*e^2*f + 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 - (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d^3*e^3 - 3*(a^4 + a^2*b^2)*c*d^2*e^2*f + 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 - (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d^3*e^3 - 3*(a^4 + a^2*b^2)*c*d^2*e^2*f + 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 - (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d^3*e^3 - 3*(a^4 + a^2*b^2)*c*d^2*e^2*f + 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 - (a^4 + a^2*b^2)*c^3*f^3)*sinh(d*x + c)^4)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 55296*(((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + 3*(a^4 + a^2*b^2)*c*d^2*e^2*f - 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 + (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + 3*(a^4 + a^2*b^2)*c*d^2*e^2*f - 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 + (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + 3*(a^4 + a^2*b^2)*c*d^2*e^2*f - 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 + (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + 3*(a^4 + a^2*b^2)*c*d^2*e^2*f - 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 + (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + 3*(a^4 + a^2*b^2)*c*d^2*e^2*f - 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 + (a^4 + a^2*b^2)*c^3*f^3)*sinh(d*x + c)^4)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 55296*(((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + 3*(a^4 + a^2*b^2)*c*d^2*e^2*f - 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 + (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + 3*(a^4 + a^2*b^2)*c*d^2*e^2*f - 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 + (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + 3*(a^4 + a^2*b^2)*c*d^2*e^2*f - 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 + (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + 3*(a^4 + a^2*b^2)*c*d^2*e^2*f - 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 + (a^4 + a^2*b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + 3*(a^4 + a^2*b^2)*c*d^2*e^2*f - 3*(a^4 + a^2*b^2)*c^2*d*e*f^2 + (a^4 + a^2*b^2)*c^3*f^3)*sinh(d*x + c)^4)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 331776*((a^4 + a^2*b^2)*f^3*cosh(d*x + c)^4 + 4*(a^4 + a^2*b^2)*f^3*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4 + a^2*b^2)*f^3*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4 + a^2*b^2)*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + a^2*b^2)*f^3*sinh(d*x + c)^4)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 331776*((a^4 + a^2*b^2)*f^3*cosh(d*x + c)^4 + 4*(a^4 + a^2*b^2)*f^3*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4 + a^2*b^2)*f^3*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4 + a^2*b^2)*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + a^2*b^2)*f^3*sinh(d*x + c)^4)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 331776*(((a^4 + a^2*b^2)*d*f^3*x + (a^4 + a^2*b^2)*d*e*f^2)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d*f^3*x + (a^4 + a^2*b^2)*d*e*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d*f^3*x + (a^4 + a^2*b^2)*d*e*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d*f^3*x + (a^4 + a^2*b^2)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d*f^3*x + (a^4 + a^2*b^2)*d*e*f^2)*sinh(d*x + c)^4)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 331776*(((a^4 + a^2*b^2)*d*f^3*x + (a^4 + a^2*b^2)*d*e*f^2)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d*f^3*x + (a^4 + a^2*b^2)*d*e*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d*f^3*x + (a^4 + a^2*b^2)*d*e*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d*f^3*x + (a^4 + a^2*b^2)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d*f^3*x + (a^4 + a^2*b^2)*d*e*f^2)*sinh(d*x + c)^4)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 8*(288*a*b^3*d^3*f^3*x^3 + 288*a*b^3*d^3*e^3 + 288*a*b^3*d^2*e^2*f + 192*a*b^3*d*e*f^2 + 27*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^7 + 64*a*b^3*f^3 - 224*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^6 + 648*(4*(2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(2*a^2*b^2 + b^4)*d^3*e^3 - 6*(2*a^2*b^2 + b^4)*d^2*e^2*f + 6*(2*a^2*b^2 + b^4)*d*e*f^2 - 3*(2*a^2*b^2 + b^4)*f^3 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e*f^2 - (2*a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e^2*f - 2*(2*a^2*b^2 + b^4)*d^2*e*f^2 + (2*a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c)^5 - 4320*((4*a^3*b + 3*a*b^3)*d^3*f^3*x^3 + (4*a^3*b + 3*a*b^3)*d^3*e^3 - 3*(4*a^3*b + 3*a*b^3)*d^2*e^2*f + 6*(4*a^3*b + 3*a*b^3)*d*e*f^2 - 6*(4*a^3*b + 3*a*b^3)*f^3 + 3*((4*a^3*b + 3*a*b^3)*d^3*e*f^2 - (4*a^3*b + 3*a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + 3*a*b^3)*d^3*e^2*f - 2*(4*a^3*b + 3*a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + 3*a*b^3)*d*f^3)*x)*cosh(d*x + c)^4 - 6912*((a^4 + a^2*b^2)*d^4*f^3*x^4 + 4*(a^4 + a^2*b^2)*d^4*e*f^2*x^3 + 6*(a^4 + a^2*b^2)*d^4*e^2*f*x^2 + 4*(a^4 + a^2*b^2)*d^4*e^3*x + 8*(a^4 + a^2*b^2)*c*d^3*e^3 - 12*(a^4 + a^2*b^2)*c^2*d^2*e^2*f + 8*(a^4 + a^2*b^2)*c^3*d*e*f^2 - 2*(a^4 + a^2*b^2)*c^4*f^3)*cosh(d*x + c)^3 + 288*(3*a*b^3*d^3*e*f^2 + a*b^3*d^2*f^3)*x^2 + 2592*((4*a^3*b + 3*a*b^3)*d^3*f^3*x^3 + (4*a^3*b + 3*a*b^3)*d^3*e^3 + 3*(4*a^3*b + 3*a*b^3)*d^2*e^2*f + 6*(4*a^3*b + 3*a*b^3)*d*e*f^2 + 6*(4*a^3*b + 3*a*b^3)*f^3 + 3*((4*a^3*b + 3*a*b^3)*d^3*e*f^2 + (4*a^3*b + 3*a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + 3*a*b^3)*d^3*e^2*f + 2*(4*a^3*b + 3*a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + 3*a*b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 96*(9*a*b^3*d^3*e^2*f + 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x + 216*(4*(2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 4*(2*a^2*b^2 + b^4)*d^3*e^3 + 6*(2*a^2*b^2 + b^4)*d^2*e^2*f + 6*(2*a^2*b^2 + b^4)*d*e*f^2 + 3*(2*a^2*b^2 + b^4)*f^3 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e*f^2 + (2*a^2*b^2 + b^4)*d^2*f^3)*x^2 + 6*(2*(2*a^2*b^2 + b^4)*d^3*e^2*f + 2*(2*a^2*b^2 + b^4)*d^2*e*f^2 + (2*a^2*b^2 + b^4)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^5*d^4*cosh(d*x + c)^4 + 4*b^5*d^4*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*d^4*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*d^4*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*d^4*sinh(d*x + c)^4)","C",0
373,1,7645,0,0.632271," ","integrate((f*x+e)^2*cosh(d*x+c)^3*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{216 \, b^{4} d^{2} f^{2} x^{2} + 27 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{8} + 27 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{8} + 216 \, b^{4} d^{2} e^{2} - 64 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{7} - 8 \, {\left(72 \, a b^{3} d^{2} f^{2} x^{2} + 72 \, a b^{3} d^{2} e^{2} - 48 \, a b^{3} d e f + 16 \, a b^{3} f^{2} + 48 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x - 27 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 108 \, b^{4} d e f + 432 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(216 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 216 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 216 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f + 108 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{2} + 189 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 216 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x - 112 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 27 \, b^{4} f^{2} - 1728 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 24 \, {\left(72 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{2} x^{2} + 72 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} - 144 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f - 63 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 144 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{2} + 56 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 144 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{2}\right)} x - 108 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4608 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(2304 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{2} x^{3} + 6912 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f x^{2} + 6912 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} x + 13824 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} - 13824 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f + 4608 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{2} - 945 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 1120 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 3240 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 4320 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 1728 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(216 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{2} x^{2} + 189 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 216 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} - 280 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 432 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f + 1080 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 432 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{2} - 2160 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 432 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{2}\right)} x - 2304 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 432 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(72 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 63 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 112 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 72 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} + 540 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 72 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f - 1440 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 36 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{2} - 2304 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 72 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x + 432 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 108 \, {\left(4 \, b^{4} d^{2} e f + b^{4} d f^{2}\right)} x + 64 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} + 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f + a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 27648 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{4}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 27648 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{4}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 13824 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f + {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f + {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f + {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f + {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f + {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 13824 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f + {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f + {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f + {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f + {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f + {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 13824 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f - {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f - {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f - {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f - {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f - {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 13824 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f - {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f - {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f - {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f - {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f - {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 27648 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + a^{2} b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{4}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 27648 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + a^{2} b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{4}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 8 \, {\left(72 \, a b^{3} d^{2} f^{2} x^{2} + 72 \, a b^{3} d^{2} e^{2} + 27 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{7} + 48 \, a b^{3} d e f - 56 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 16 \, a b^{3} f^{2} + 324 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f - {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 1080 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 2304 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 648 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d^{2} e f + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 48 \, {\left(3 \, a b^{3} d^{2} e f + a b^{3} d f^{2}\right)} x + 108 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f + {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{13824 \, {\left(b^{5} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{5} d^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} d^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} d^{3} \sinh\left(d x + c\right)^{4}\right)}}"," ",0,"1/13824*(216*b^4*d^2*f^2*x^2 + 27*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^8 + 27*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*sinh(d*x + c)^8 + 216*b^4*d^2*e^2 - 64*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^7 - 8*(72*a*b^3*d^2*f^2*x^2 + 72*a*b^3*d^2*e^2 - 48*a*b^3*d*e*f + 16*a*b^3*f^2 + 48*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x - 27*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 108*b^4*d*e*f + 432*(2*(2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(2*a^2*b^2 + b^4)*d^2*e^2 - 2*(2*a^2*b^2 + b^4)*d*e*f + (2*a^2*b^2 + b^4)*f^2 + 2*(2*(2*a^2*b^2 + b^4)*d^2*e*f - (2*a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c)^6 + 4*(216*(2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 216*(2*a^2*b^2 + b^4)*d^2*e^2 - 216*(2*a^2*b^2 + b^4)*d*e*f + 108*(2*a^2*b^2 + b^4)*f^2 + 189*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^2 + 216*(2*(2*a^2*b^2 + b^4)*d^2*e*f - (2*a^2*b^2 + b^4)*d*f^2)*x - 112*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^6 + 27*b^4*f^2 - 1728*((4*a^3*b + 3*a*b^3)*d^2*f^2*x^2 + (4*a^3*b + 3*a*b^3)*d^2*e^2 - 2*(4*a^3*b + 3*a*b^3)*d*e*f + 2*(4*a^3*b + 3*a*b^3)*f^2 + 2*((4*a^3*b + 3*a*b^3)*d^2*e*f - (4*a^3*b + 3*a*b^3)*d*f^2)*x)*cosh(d*x + c)^5 - 24*(72*(4*a^3*b + 3*a*b^3)*d^2*f^2*x^2 + 72*(4*a^3*b + 3*a*b^3)*d^2*e^2 - 144*(4*a^3*b + 3*a*b^3)*d*e*f - 63*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^3 + 144*(4*a^3*b + 3*a*b^3)*f^2 + 56*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^2 + 144*((4*a^3*b + 3*a*b^3)*d^2*e*f - (4*a^3*b + 3*a*b^3)*d*f^2)*x - 108*(2*(2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(2*a^2*b^2 + b^4)*d^2*e^2 - 2*(2*a^2*b^2 + b^4)*d*e*f + (2*a^2*b^2 + b^4)*f^2 + 2*(2*(2*a^2*b^2 + b^4)*d^2*e*f - (2*a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 4608*((a^4 + a^2*b^2)*d^3*f^2*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*x + 6*(a^4 + a^2*b^2)*c*d^2*e^2 - 6*(a^4 + a^2*b^2)*c^2*d*e*f + 2*(a^4 + a^2*b^2)*c^3*f^2)*cosh(d*x + c)^4 - 2*(2304*(a^4 + a^2*b^2)*d^3*f^2*x^3 + 6912*(a^4 + a^2*b^2)*d^3*e*f*x^2 + 6912*(a^4 + a^2*b^2)*d^3*e^2*x + 13824*(a^4 + a^2*b^2)*c*d^2*e^2 - 13824*(a^4 + a^2*b^2)*c^2*d*e*f + 4608*(a^4 + a^2*b^2)*c^3*f^2 - 945*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^4 + 1120*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^3 - 3240*(2*(2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(2*a^2*b^2 + b^4)*d^2*e^2 - 2*(2*a^2*b^2 + b^4)*d*e*f + (2*a^2*b^2 + b^4)*f^2 + 2*(2*(2*a^2*b^2 + b^4)*d^2*e*f - (2*a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c)^2 + 4320*((4*a^3*b + 3*a*b^3)*d^2*f^2*x^2 + (4*a^3*b + 3*a*b^3)*d^2*e^2 - 2*(4*a^3*b + 3*a*b^3)*d*e*f + 2*(4*a^3*b + 3*a*b^3)*f^2 + 2*((4*a^3*b + 3*a*b^3)*d^2*e*f - (4*a^3*b + 3*a*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^4 + 1728*((4*a^3*b + 3*a*b^3)*d^2*f^2*x^2 + (4*a^3*b + 3*a*b^3)*d^2*e^2 + 2*(4*a^3*b + 3*a*b^3)*d*e*f + 2*(4*a^3*b + 3*a*b^3)*f^2 + 2*((4*a^3*b + 3*a*b^3)*d^2*e*f + (4*a^3*b + 3*a*b^3)*d*f^2)*x)*cosh(d*x + c)^3 + 8*(216*(4*a^3*b + 3*a*b^3)*d^2*f^2*x^2 + 189*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^5 + 216*(4*a^3*b + 3*a*b^3)*d^2*e^2 - 280*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^4 + 432*(4*a^3*b + 3*a*b^3)*d*e*f + 1080*(2*(2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(2*a^2*b^2 + b^4)*d^2*e^2 - 2*(2*a^2*b^2 + b^4)*d*e*f + (2*a^2*b^2 + b^4)*f^2 + 2*(2*(2*a^2*b^2 + b^4)*d^2*e*f - (2*a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c)^3 + 432*(4*a^3*b + 3*a*b^3)*f^2 - 2160*((4*a^3*b + 3*a*b^3)*d^2*f^2*x^2 + (4*a^3*b + 3*a*b^3)*d^2*e^2 - 2*(4*a^3*b + 3*a*b^3)*d*e*f + 2*(4*a^3*b + 3*a*b^3)*f^2 + 2*((4*a^3*b + 3*a*b^3)*d^2*e*f - (4*a^3*b + 3*a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 432*((4*a^3*b + 3*a*b^3)*d^2*e*f + (4*a^3*b + 3*a*b^3)*d*f^2)*x - 2304*((a^4 + a^2*b^2)*d^3*f^2*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*x + 6*(a^4 + a^2*b^2)*c*d^2*e^2 - 6*(a^4 + a^2*b^2)*c^2*d*e*f + 2*(a^4 + a^2*b^2)*c^3*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 432*(2*(2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(2*a^2*b^2 + b^4)*d^2*e^2 + 2*(2*a^2*b^2 + b^4)*d*e*f + (2*a^2*b^2 + b^4)*f^2 + 2*(2*(2*a^2*b^2 + b^4)*d^2*e*f + (2*a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c)^2 + 12*(72*(2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 63*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^6 - 112*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^5 + 72*(2*a^2*b^2 + b^4)*d^2*e^2 + 540*(2*(2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(2*a^2*b^2 + b^4)*d^2*e^2 - 2*(2*a^2*b^2 + b^4)*d*e*f + (2*a^2*b^2 + b^4)*f^2 + 2*(2*(2*a^2*b^2 + b^4)*d^2*e*f - (2*a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c)^4 + 72*(2*a^2*b^2 + b^4)*d*e*f - 1440*((4*a^3*b + 3*a*b^3)*d^2*f^2*x^2 + (4*a^3*b + 3*a*b^3)*d^2*e^2 - 2*(4*a^3*b + 3*a*b^3)*d*e*f + 2*(4*a^3*b + 3*a*b^3)*f^2 + 2*((4*a^3*b + 3*a*b^3)*d^2*e*f - (4*a^3*b + 3*a*b^3)*d*f^2)*x)*cosh(d*x + c)^3 + 36*(2*a^2*b^2 + b^4)*f^2 - 2304*((a^4 + a^2*b^2)*d^3*f^2*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*x + 6*(a^4 + a^2*b^2)*c*d^2*e^2 - 6*(a^4 + a^2*b^2)*c^2*d*e*f + 2*(a^4 + a^2*b^2)*c^3*f^2)*cosh(d*x + c)^2 + 72*(2*(2*a^2*b^2 + b^4)*d^2*e*f + (2*a^2*b^2 + b^4)*d*f^2)*x + 432*((4*a^3*b + 3*a*b^3)*d^2*f^2*x^2 + (4*a^3*b + 3*a*b^3)*d^2*e^2 + 2*(4*a^3*b + 3*a*b^3)*d*e*f + 2*(4*a^3*b + 3*a*b^3)*f^2 + 2*((4*a^3*b + 3*a*b^3)*d^2*e*f + (4*a^3*b + 3*a*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 108*(4*b^4*d^2*e*f + b^4*d*f^2)*x + 64*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 + 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f + a*b^3*d*f^2)*x)*cosh(d*x + c) + 27648*(((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*d*e*f)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*d*e*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*d*e*f)*sinh(d*x + c)^4)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 27648*(((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*d*e*f)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*d*e*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*d*e*f)*sinh(d*x + c)^4)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 13824*(((a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*c*d*e*f + (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*c*d*e*f + (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*c*d*e*f + (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*c*d*e*f + (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*c*d*e*f + (a^4 + a^2*b^2)*c^2*f^2)*sinh(d*x + c)^4)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 13824*(((a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*c*d*e*f + (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*c*d*e*f + (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*c*d*e*f + (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*c*d*e*f + (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d^2*e^2 - 2*(a^4 + a^2*b^2)*c*d*e*f + (a^4 + a^2*b^2)*c^2*f^2)*sinh(d*x + c)^4)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 13824*(((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + 2*(a^4 + a^2*b^2)*c*d*e*f - (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + 2*(a^4 + a^2*b^2)*c*d*e*f - (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + 2*(a^4 + a^2*b^2)*c*d*e*f - (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + 2*(a^4 + a^2*b^2)*c*d*e*f - (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + 2*(a^4 + a^2*b^2)*c*d*e*f - (a^4 + a^2*b^2)*c^2*f^2)*sinh(d*x + c)^4)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 13824*(((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + 2*(a^4 + a^2*b^2)*c*d*e*f - (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + 2*(a^4 + a^2*b^2)*c*d*e*f - (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + 2*(a^4 + a^2*b^2)*c*d*e*f - (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + 2*(a^4 + a^2*b^2)*c*d*e*f - (a^4 + a^2*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + 2*(a^4 + a^2*b^2)*c*d*e*f - (a^4 + a^2*b^2)*c^2*f^2)*sinh(d*x + c)^4)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 27648*((a^4 + a^2*b^2)*f^2*cosh(d*x + c)^4 + 4*(a^4 + a^2*b^2)*f^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4 + a^2*b^2)*f^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4 + a^2*b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + a^2*b^2)*f^2*sinh(d*x + c)^4)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 27648*((a^4 + a^2*b^2)*f^2*cosh(d*x + c)^4 + 4*(a^4 + a^2*b^2)*f^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4 + a^2*b^2)*f^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4 + a^2*b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + a^2*b^2)*f^2*sinh(d*x + c)^4)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 8*(72*a*b^3*d^2*f^2*x^2 + 72*a*b^3*d^2*e^2 + 27*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^7 + 48*a*b^3*d*e*f - 56*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^6 + 16*a*b^3*f^2 + 324*(2*(2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(2*a^2*b^2 + b^4)*d^2*e^2 - 2*(2*a^2*b^2 + b^4)*d*e*f + (2*a^2*b^2 + b^4)*f^2 + 2*(2*(2*a^2*b^2 + b^4)*d^2*e*f - (2*a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c)^5 - 1080*((4*a^3*b + 3*a*b^3)*d^2*f^2*x^2 + (4*a^3*b + 3*a*b^3)*d^2*e^2 - 2*(4*a^3*b + 3*a*b^3)*d*e*f + 2*(4*a^3*b + 3*a*b^3)*f^2 + 2*((4*a^3*b + 3*a*b^3)*d^2*e*f - (4*a^3*b + 3*a*b^3)*d*f^2)*x)*cosh(d*x + c)^4 - 2304*((a^4 + a^2*b^2)*d^3*f^2*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*x + 6*(a^4 + a^2*b^2)*c*d^2*e^2 - 6*(a^4 + a^2*b^2)*c^2*d*e*f + 2*(a^4 + a^2*b^2)*c^3*f^2)*cosh(d*x + c)^3 + 648*((4*a^3*b + 3*a*b^3)*d^2*f^2*x^2 + (4*a^3*b + 3*a*b^3)*d^2*e^2 + 2*(4*a^3*b + 3*a*b^3)*d*e*f + 2*(4*a^3*b + 3*a*b^3)*f^2 + 2*((4*a^3*b + 3*a*b^3)*d^2*e*f + (4*a^3*b + 3*a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 48*(3*a*b^3*d^2*e*f + a*b^3*d*f^2)*x + 108*(2*(2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(2*a^2*b^2 + b^4)*d^2*e^2 + 2*(2*a^2*b^2 + b^4)*d*e*f + (2*a^2*b^2 + b^4)*f^2 + 2*(2*(2*a^2*b^2 + b^4)*d^2*e*f + (2*a^2*b^2 + b^4)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^5*d^3*cosh(d*x + c)^4 + 4*b^5*d^3*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*d^3*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*d^3*sinh(d*x + c)^4)","C",0
374,1,3795,0,0.601797," ","integrate((f*x+e)*cosh(d*x+c)^3*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{8} + 9 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \sinh\left(d x + c\right)^{8} - 32 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{7} - 8 \, {\left(12 \, a b^{3} d f x + 12 \, a b^{3} d e - 4 \, a b^{3} f - 9 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 36 \, b^{4} d f x + 72 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(2 \, a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(36 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f x + 36 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e + 63 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{2} - 18 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f - 56 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 36 \, b^{4} d e - 288 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f x + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{5} - 24 \, {\left(12 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f x - 21 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e + 28 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{2} - 12 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f - 18 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(2 \, a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 9 \, b^{4} f - 1152 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e x + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(576 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} f x^{2} + 1152 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e x - 315 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{4} + 2304 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e - 1152 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f + 560 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{3} - 540 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(2 \, a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 720 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f x + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 288 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f x + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(63 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{4} + 36 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f x + 180 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(2 \, a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 36 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e - 360 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f x + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 36 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f - 576 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e x + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 72 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e + {\left(2 \, a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(21 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{6} - 56 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{5} + 90 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(2 \, a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f x - 240 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f x + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e - 576 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e x + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} f + 72 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f x + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 32 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e + a b^{3} f\right)} \cosh\left(d x + c\right) + 2304 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + a^{2} b^{2}\right)} f \sinh\left(d x + c\right)^{4}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2304 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + a^{2} b^{2}\right)} f \sinh\left(d x + c\right)^{4}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2304 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2304 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d e - {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2304 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2304 \, {\left({\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 8 \, {\left(9 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{7} + 12 \, a b^{3} d f x - 28 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{6} + 12 \, a b^{3} d e + 54 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(2 \, a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{5} + 4 \, a b^{3} f - 180 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f x + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e - {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} - 576 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e x + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} c d e - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)^{3} + 108 \, {\left({\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d f x + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} d e + {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 18 \, {\left(2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d f x + 2 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} d e + {\left(2 \, a^{2} b^{2} + b^{4}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2304 \, {\left(b^{5} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{5} d^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} d^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} d^{2} \sinh\left(d x + c\right)^{4}\right)}}"," ",0,"1/2304*(9*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^8 + 9*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*sinh(d*x + c)^8 - 32*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^7 - 8*(12*a*b^3*d*f*x + 12*a*b^3*d*e - 4*a*b^3*f - 9*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c))*sinh(d*x + c)^7 + 36*b^4*d*f*x + 72*(2*(2*a^2*b^2 + b^4)*d*f*x + 2*(2*a^2*b^2 + b^4)*d*e - (2*a^2*b^2 + b^4)*f)*cosh(d*x + c)^6 + 4*(36*(2*a^2*b^2 + b^4)*d*f*x + 36*(2*a^2*b^2 + b^4)*d*e + 63*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^2 - 18*(2*a^2*b^2 + b^4)*f - 56*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c))*sinh(d*x + c)^6 + 36*b^4*d*e - 288*((4*a^3*b + 3*a*b^3)*d*f*x + (4*a^3*b + 3*a*b^3)*d*e - (4*a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^5 - 24*(12*(4*a^3*b + 3*a*b^3)*d*f*x - 21*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^3 + 12*(4*a^3*b + 3*a*b^3)*d*e + 28*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^2 - 12*(4*a^3*b + 3*a*b^3)*f - 18*(2*(2*a^2*b^2 + b^4)*d*f*x + 2*(2*a^2*b^2 + b^4)*d*e - (2*a^2*b^2 + b^4)*f)*cosh(d*x + c))*sinh(d*x + c)^5 + 9*b^4*f - 1152*((a^4 + a^2*b^2)*d^2*f*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*x + 4*(a^4 + a^2*b^2)*c*d*e - 2*(a^4 + a^2*b^2)*c^2*f)*cosh(d*x + c)^4 - 2*(576*(a^4 + a^2*b^2)*d^2*f*x^2 + 1152*(a^4 + a^2*b^2)*d^2*e*x - 315*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^4 + 2304*(a^4 + a^2*b^2)*c*d*e - 1152*(a^4 + a^2*b^2)*c^2*f + 560*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^3 - 540*(2*(2*a^2*b^2 + b^4)*d*f*x + 2*(2*a^2*b^2 + b^4)*d*e - (2*a^2*b^2 + b^4)*f)*cosh(d*x + c)^2 + 720*((4*a^3*b + 3*a*b^3)*d*f*x + (4*a^3*b + 3*a*b^3)*d*e - (4*a^3*b + 3*a*b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^4 + 288*((4*a^3*b + 3*a*b^3)*d*f*x + (4*a^3*b + 3*a*b^3)*d*e + (4*a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^3 + 8*(63*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^5 - 140*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^4 + 36*(4*a^3*b + 3*a*b^3)*d*f*x + 180*(2*(2*a^2*b^2 + b^4)*d*f*x + 2*(2*a^2*b^2 + b^4)*d*e - (2*a^2*b^2 + b^4)*f)*cosh(d*x + c)^3 + 36*(4*a^3*b + 3*a*b^3)*d*e - 360*((4*a^3*b + 3*a*b^3)*d*f*x + (4*a^3*b + 3*a*b^3)*d*e - (4*a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^2 + 36*(4*a^3*b + 3*a*b^3)*f - 576*((a^4 + a^2*b^2)*d^2*f*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*x + 4*(a^4 + a^2*b^2)*c*d*e - 2*(a^4 + a^2*b^2)*c^2*f)*cosh(d*x + c))*sinh(d*x + c)^3 + 72*(2*(2*a^2*b^2 + b^4)*d*f*x + 2*(2*a^2*b^2 + b^4)*d*e + (2*a^2*b^2 + b^4)*f)*cosh(d*x + c)^2 + 12*(21*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^6 - 56*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^5 + 90*(2*(2*a^2*b^2 + b^4)*d*f*x + 2*(2*a^2*b^2 + b^4)*d*e - (2*a^2*b^2 + b^4)*f)*cosh(d*x + c)^4 + 12*(2*a^2*b^2 + b^4)*d*f*x - 240*((4*a^3*b + 3*a*b^3)*d*f*x + (4*a^3*b + 3*a*b^3)*d*e - (4*a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^3 + 12*(2*a^2*b^2 + b^4)*d*e - 576*((a^4 + a^2*b^2)*d^2*f*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*x + 4*(a^4 + a^2*b^2)*c*d*e - 2*(a^4 + a^2*b^2)*c^2*f)*cosh(d*x + c)^2 + 6*(2*a^2*b^2 + b^4)*f + 72*((4*a^3*b + 3*a*b^3)*d*f*x + (4*a^3*b + 3*a*b^3)*d*e + (4*a^3*b + 3*a*b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^2 + 32*(3*a*b^3*d*f*x + 3*a*b^3*d*e + a*b^3*f)*cosh(d*x + c) + 2304*((a^4 + a^2*b^2)*f*cosh(d*x + c)^4 + 4*(a^4 + a^2*b^2)*f*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4 + a^2*b^2)*f*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4 + a^2*b^2)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + a^2*b^2)*f*sinh(d*x + c)^4)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2304*((a^4 + a^2*b^2)*f*cosh(d*x + c)^4 + 4*(a^4 + a^2*b^2)*f*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4 + a^2*b^2)*f*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4 + a^2*b^2)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + a^2*b^2)*f*sinh(d*x + c)^4)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2304*(((a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*c*f)*sinh(d*x + c)^4)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2304*(((a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d*e - (a^4 + a^2*b^2)*c*f)*sinh(d*x + c)^4)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2304*(((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*c*f)*sinh(d*x + c)^4)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2304*(((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^4 + 4*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*c*f)*sinh(d*x + c)^4)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 8*(9*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^7 + 12*a*b^3*d*f*x - 28*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^6 + 12*a*b^3*d*e + 54*(2*(2*a^2*b^2 + b^4)*d*f*x + 2*(2*a^2*b^2 + b^4)*d*e - (2*a^2*b^2 + b^4)*f)*cosh(d*x + c)^5 + 4*a*b^3*f - 180*((4*a^3*b + 3*a*b^3)*d*f*x + (4*a^3*b + 3*a*b^3)*d*e - (4*a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^4 - 576*((a^4 + a^2*b^2)*d^2*f*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*x + 4*(a^4 + a^2*b^2)*c*d*e - 2*(a^4 + a^2*b^2)*c^2*f)*cosh(d*x + c)^3 + 108*((4*a^3*b + 3*a*b^3)*d*f*x + (4*a^3*b + 3*a*b^3)*d*e + (4*a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^2 + 18*(2*(2*a^2*b^2 + b^4)*d*f*x + 2*(2*a^2*b^2 + b^4)*d*e + (2*a^2*b^2 + b^4)*f)*cosh(d*x + c))*sinh(d*x + c))/(b^5*d^2*cosh(d*x + c)^4 + 4*b^5*d^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*d^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*d^2*sinh(d*x + c)^4)","B",0
375,1,1069,0,0.579921," ","integrate(cosh(d*x+c)^3*sinh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, b^{4} \cosh\left(d x + c\right)^{8} + 3 \, b^{4} \sinh\left(d x + c\right)^{8} - 8 \, a b^{3} \cosh\left(d x + c\right)^{7} + 8 \, {\left(3 \, b^{4} \cosh\left(d x + c\right) - a b^{3}\right)} \sinh\left(d x + c\right)^{7} - 192 \, {\left(a^{4} + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 12 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(21 \, b^{4} \cosh\left(d x + c\right)^{2} - 14 \, a b^{3} \cosh\left(d x + c\right) + 6 \, a^{2} b^{2} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{6} - 24 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 24 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{3} - 7 \, a b^{3} \cosh\left(d x + c\right)^{2} - 4 \, a^{3} b - 3 \, a b^{3} + 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, a b^{3} \cosh\left(d x + c\right) + 2 \, {\left(105 \, b^{4} \cosh\left(d x + c\right)^{4} - 140 \, a b^{3} \cosh\left(d x + c\right)^{3} - 96 \, {\left(a^{4} + a^{2} b^{2}\right)} d x + 90 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{2} - 60 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 3 \, b^{4} + 24 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(21 \, b^{4} \cosh\left(d x + c\right)^{5} - 35 \, a b^{3} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} b + 9 \, a b^{3} - 96 \, {\left(a^{4} + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right) + 30 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{3} - 30 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 12 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{6} - 14 \, a b^{3} \cosh\left(d x + c\right)^{5} - 96 \, {\left(a^{4} + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 15 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} b^{2} + b^{4} - 20 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 192 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left(3 \, b^{4} \cosh\left(d x + c\right)^{7} - 7 \, a b^{3} \cosh\left(d x + c\right)^{6} - 96 \, {\left(a^{4} + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 9 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + a b^{3} + 9 \, {\left(4 \, a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{192 \, {\left(b^{5} d \cosh\left(d x + c\right)^{4} + 4 \, b^{5} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} d \sinh\left(d x + c\right)^{4}\right)}}"," ",0,"1/192*(3*b^4*cosh(d*x + c)^8 + 3*b^4*sinh(d*x + c)^8 - 8*a*b^3*cosh(d*x + c)^7 + 8*(3*b^4*cosh(d*x + c) - a*b^3)*sinh(d*x + c)^7 - 192*(a^4 + a^2*b^2)*d*x*cosh(d*x + c)^4 + 12*(2*a^2*b^2 + b^4)*cosh(d*x + c)^6 + 4*(21*b^4*cosh(d*x + c)^2 - 14*a*b^3*cosh(d*x + c) + 6*a^2*b^2 + 3*b^4)*sinh(d*x + c)^6 - 24*(4*a^3*b + 3*a*b^3)*cosh(d*x + c)^5 + 24*(7*b^4*cosh(d*x + c)^3 - 7*a*b^3*cosh(d*x + c)^2 - 4*a^3*b - 3*a*b^3 + 3*(2*a^2*b^2 + b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*a*b^3*cosh(d*x + c) + 2*(105*b^4*cosh(d*x + c)^4 - 140*a*b^3*cosh(d*x + c)^3 - 96*(a^4 + a^2*b^2)*d*x + 90*(2*a^2*b^2 + b^4)*cosh(d*x + c)^2 - 60*(4*a^3*b + 3*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 3*b^4 + 24*(4*a^3*b + 3*a*b^3)*cosh(d*x + c)^3 + 8*(21*b^4*cosh(d*x + c)^5 - 35*a*b^3*cosh(d*x + c)^4 + 12*a^3*b + 9*a*b^3 - 96*(a^4 + a^2*b^2)*d*x*cosh(d*x + c) + 30*(2*a^2*b^2 + b^4)*cosh(d*x + c)^3 - 30*(4*a^3*b + 3*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 12*(2*a^2*b^2 + b^4)*cosh(d*x + c)^2 + 12*(7*b^4*cosh(d*x + c)^6 - 14*a*b^3*cosh(d*x + c)^5 - 96*(a^4 + a^2*b^2)*d*x*cosh(d*x + c)^2 + 15*(2*a^2*b^2 + b^4)*cosh(d*x + c)^4 + 2*a^2*b^2 + b^4 - 20*(4*a^3*b + 3*a*b^3)*cosh(d*x + c)^3 + 6*(4*a^3*b + 3*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 192*((a^4 + a^2*b^2)*cosh(d*x + c)^4 + 4*(a^4 + a^2*b^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4 + a^2*b^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4 + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + a^2*b^2)*sinh(d*x + c)^4)*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + 8*(3*b^4*cosh(d*x + c)^7 - 7*a*b^3*cosh(d*x + c)^6 - 96*(a^4 + a^2*b^2)*d*x*cosh(d*x + c)^3 + 9*(2*a^2*b^2 + b^4)*cosh(d*x + c)^5 - 15*(4*a^3*b + 3*a*b^3)*cosh(d*x + c)^4 + a*b^3 + 9*(4*a^3*b + 3*a*b^3)*cosh(d*x + c)^2 + 3*(2*a^2*b^2 + b^4)*cosh(d*x + c))*sinh(d*x + c))/(b^5*d*cosh(d*x + c)^4 + 4*b^5*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*d*sinh(d*x + c)^4)","B",0
376,0,0,0,0.602271," ","integrate(cosh(d*x+c)^3*sinh(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)^3*sinh(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
377,1,1968,0,0.666749," ","integrate((f*x+e)^3*sinh(d*x+c)*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a^{2} + b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{2} + b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{2} + b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{2} + b^{2}\right)} d^{4} e^{3} x - 24 \, a^{2} f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, a^{2} f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + a^{2} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 12 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + a^{2} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-12 i \, a b d^{2} f^{3} x^{2} + 12 \, b^{2} d^{2} f^{3} x^{2} - 24 i \, a b d^{2} e f^{2} x + 24 \, b^{2} d^{2} e f^{2} x - 12 i \, a b d^{2} e^{2} f + 12 \, b^{2} d^{2} e^{2} f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(12 i \, a b d^{2} f^{3} x^{2} + 12 \, b^{2} d^{2} f^{3} x^{2} + 24 i \, a b d^{2} e f^{2} x + 24 \, b^{2} d^{2} e f^{2} x + 12 i \, a b d^{2} e^{2} f + 12 \, b^{2} d^{2} e^{2} f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 4 \, {\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - a^{2} c^{3} f^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - a^{2} c^{3} f^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} d^{3} e f^{2} x^{2} + 3 \, a^{2} d^{3} e^{2} f x + 3 \, a^{2} c d^{2} e^{2} f - 3 \, a^{2} c^{2} d e f^{2} + a^{2} c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left(a^{2} d^{3} f^{3} x^{3} + 3 \, a^{2} d^{3} e f^{2} x^{2} + 3 \, a^{2} d^{3} e^{2} f x + 3 \, a^{2} c d^{2} e^{2} f - 3 \, a^{2} c^{2} d e f^{2} + a^{2} c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(-4 i \, a b d^{3} e^{3} + 4 \, b^{2} d^{3} e^{3} + 12 i \, a b c d^{2} e^{2} f - 12 \, b^{2} c d^{2} e^{2} f - 12 i \, a b c^{2} d e f^{2} + 12 \, b^{2} c^{2} d e f^{2} + 4 i \, a b c^{3} f^{3} - 4 \, b^{2} c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(4 i \, a b d^{3} e^{3} + 4 \, b^{2} d^{3} e^{3} - 12 i \, a b c d^{2} e^{2} f - 12 \, b^{2} c d^{2} e^{2} f + 12 i \, a b c^{2} d e f^{2} + 12 \, b^{2} c^{2} d e f^{2} - 4 i \, a b c^{3} f^{3} - 4 \, b^{2} c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(4 i \, a b d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} f^{3} x^{3} + 12 i \, a b d^{3} e f^{2} x^{2} + 12 \, b^{2} d^{3} e f^{2} x^{2} + 12 i \, a b d^{3} e^{2} f x + 12 \, b^{2} d^{3} e^{2} f x + 12 i \, a b c d^{2} e^{2} f + 12 \, b^{2} c d^{2} e^{2} f - 12 i \, a b c^{2} d e f^{2} - 12 \, b^{2} c^{2} d e f^{2} + 4 i \, a b c^{3} f^{3} + 4 \, b^{2} c^{3} f^{3}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(-4 i \, a b d^{3} f^{3} x^{3} + 4 \, b^{2} d^{3} f^{3} x^{3} - 12 i \, a b d^{3} e f^{2} x^{2} + 12 \, b^{2} d^{3} e f^{2} x^{2} - 12 i \, a b d^{3} e^{2} f x + 12 \, b^{2} d^{3} e^{2} f x - 12 i \, a b c d^{2} e^{2} f + 12 \, b^{2} c d^{2} e^{2} f + 12 i \, a b c^{2} d e f^{2} - 12 \, b^{2} c^{2} d e f^{2} - 4 i \, a b c^{3} f^{3} + 4 \, b^{2} c^{3} f^{3}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + 24 \, {\left(i \, a b f^{3} - b^{2} f^{3}\right)} {\rm polylog}\left(4, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + 24 \, {\left(-i \, a b f^{3} - b^{2} f^{3}\right)} {\rm polylog}\left(4, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 24 \, {\left(a^{2} d f^{3} x + a^{2} d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left(a^{2} d f^{3} x + a^{2} d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - {\left(24 i \, a b d f^{3} x - 24 \, b^{2} d f^{3} x + 24 i \, a b d e f^{2} - 24 \, b^{2} d e f^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(-24 i \, a b d f^{3} x - 24 \, b^{2} d f^{3} x - 24 i \, a b d e f^{2} - 24 \, b^{2} d e f^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right)}{4 \, {\left(a^{2} b + b^{3}\right)} d^{4}}"," ",0,"-1/4*((a^2 + b^2)*d^4*f^3*x^4 + 4*(a^2 + b^2)*d^4*e*f^2*x^3 + 6*(a^2 + b^2)*d^4*e^2*f*x^2 + 4*(a^2 + b^2)*d^4*e^3*x - 24*a^2*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*a^2*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + a^2*d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 12*(a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + a^2*d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (-12*I*a*b*d^2*f^3*x^2 + 12*b^2*d^2*f^3*x^2 - 24*I*a*b*d^2*e*f^2*x + 24*b^2*d^2*e*f^2*x - 12*I*a*b*d^2*e^2*f + 12*b^2*d^2*e^2*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (12*I*a*b*d^2*f^3*x^2 + 12*b^2*d^2*f^3*x^2 + 24*I*a*b*d^2*e*f^2*x + 24*b^2*d^2*e*f^2*x + 12*I*a*b*d^2*e^2*f + 12*b^2*d^2*e^2*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 4*(a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - a^2*c^3*f^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*(a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - a^2*c^3*f^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*(a^2*d^3*f^3*x^3 + 3*a^2*d^3*e*f^2*x^2 + 3*a^2*d^3*e^2*f*x + 3*a^2*c*d^2*e^2*f - 3*a^2*c^2*d*e*f^2 + a^2*c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*(a^2*d^3*f^3*x^3 + 3*a^2*d^3*e*f^2*x^2 + 3*a^2*d^3*e^2*f*x + 3*a^2*c*d^2*e^2*f - 3*a^2*c^2*d*e*f^2 + a^2*c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (-4*I*a*b*d^3*e^3 + 4*b^2*d^3*e^3 + 12*I*a*b*c*d^2*e^2*f - 12*b^2*c*d^2*e^2*f - 12*I*a*b*c^2*d*e*f^2 + 12*b^2*c^2*d*e*f^2 + 4*I*a*b*c^3*f^3 - 4*b^2*c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (4*I*a*b*d^3*e^3 + 4*b^2*d^3*e^3 - 12*I*a*b*c*d^2*e^2*f - 12*b^2*c*d^2*e^2*f + 12*I*a*b*c^2*d*e*f^2 + 12*b^2*c^2*d*e*f^2 - 4*I*a*b*c^3*f^3 - 4*b^2*c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) - I) - (4*I*a*b*d^3*f^3*x^3 + 4*b^2*d^3*f^3*x^3 + 12*I*a*b*d^3*e*f^2*x^2 + 12*b^2*d^3*e*f^2*x^2 + 12*I*a*b*d^3*e^2*f*x + 12*b^2*d^3*e^2*f*x + 12*I*a*b*c*d^2*e^2*f + 12*b^2*c*d^2*e^2*f - 12*I*a*b*c^2*d*e*f^2 - 12*b^2*c^2*d*e*f^2 + 4*I*a*b*c^3*f^3 + 4*b^2*c^3*f^3)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (-4*I*a*b*d^3*f^3*x^3 + 4*b^2*d^3*f^3*x^3 - 12*I*a*b*d^3*e*f^2*x^2 + 12*b^2*d^3*e*f^2*x^2 - 12*I*a*b*d^3*e^2*f*x + 12*b^2*d^3*e^2*f*x - 12*I*a*b*c*d^2*e^2*f + 12*b^2*c*d^2*e^2*f + 12*I*a*b*c^2*d*e*f^2 - 12*b^2*c^2*d*e*f^2 - 4*I*a*b*c^3*f^3 + 4*b^2*c^3*f^3)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + 24*(I*a*b*f^3 - b^2*f^3)*polylog(4, I*cosh(d*x + c) + I*sinh(d*x + c)) + 24*(-I*a*b*f^3 - b^2*f^3)*polylog(4, -I*cosh(d*x + c) - I*sinh(d*x + c)) + 24*(a^2*d*f^3*x + a^2*d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*(a^2*d*f^3*x + a^2*d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - (24*I*a*b*d*f^3*x - 24*b^2*d*f^3*x + 24*I*a*b*d*e*f^2 - 24*b^2*d*e*f^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - (-24*I*a*b*d*f^3*x - 24*b^2*d*f^3*x - 24*I*a*b*d*e*f^2 - 24*b^2*d*e*f^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)))/((a^2*b + b^3)*d^4)","C",0
378,1,1250,0,0.932000," ","integrate((f*x+e)^2*sinh(d*x+c)*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a^{2} + b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} x + 6 \, a^{2} f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, a^{2} f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(a^{2} d f^{2} x + a^{2} d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left(a^{2} d f^{2} x + a^{2} d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(-6 i \, a b d f^{2} x + 6 \, b^{2} d f^{2} x - 6 i \, a b d e f + 6 \, b^{2} d e f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(6 i \, a b d f^{2} x + 6 \, b^{2} d f^{2} x + 6 i \, a b d e f + 6 \, b^{2} d e f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 3 \, {\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f + a^{2} c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 3 \, {\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f + a^{2} c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 3 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x + 2 \, a^{2} c d e f - a^{2} c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x + 2 \, a^{2} c d e f - a^{2} c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(-3 i \, a b d^{2} e^{2} + 3 \, b^{2} d^{2} e^{2} + 6 i \, a b c d e f - 6 \, b^{2} c d e f - 3 i \, a b c^{2} f^{2} + 3 \, b^{2} c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(3 i \, a b d^{2} e^{2} + 3 \, b^{2} d^{2} e^{2} - 6 i \, a b c d e f - 6 \, b^{2} c d e f + 3 i \, a b c^{2} f^{2} + 3 \, b^{2} c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(3 i \, a b d^{2} f^{2} x^{2} + 3 \, b^{2} d^{2} f^{2} x^{2} + 6 i \, a b d^{2} e f x + 6 \, b^{2} d^{2} e f x + 6 i \, a b c d e f + 6 \, b^{2} c d e f - 3 i \, a b c^{2} f^{2} - 3 \, b^{2} c^{2} f^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(-3 i \, a b d^{2} f^{2} x^{2} + 3 \, b^{2} d^{2} f^{2} x^{2} - 6 i \, a b d^{2} e f x + 6 \, b^{2} d^{2} e f x - 6 i \, a b c d e f + 6 \, b^{2} c d e f + 3 i \, a b c^{2} f^{2} - 3 \, b^{2} c^{2} f^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + 6 \, {\left(-i \, a b f^{2} + b^{2} f^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + 6 \, {\left(i \, a b f^{2} + b^{2} f^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right)}{3 \, {\left(a^{2} b + b^{3}\right)} d^{3}}"," ",0,"-1/3*((a^2 + b^2)*d^3*f^2*x^3 + 3*(a^2 + b^2)*d^3*e*f*x^2 + 3*(a^2 + b^2)*d^3*e^2*x + 6*a^2*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*a^2*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(a^2*d*f^2*x + a^2*d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 6*(a^2*d*f^2*x + a^2*d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (-6*I*a*b*d*f^2*x + 6*b^2*d*f^2*x - 6*I*a*b*d*e*f + 6*b^2*d*e*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (6*I*a*b*d*f^2*x + 6*b^2*d*f^2*x + 6*I*a*b*d*e*f + 6*b^2*d*e*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 3*(a^2*d^2*e^2 - 2*a^2*c*d*e*f + a^2*c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 3*(a^2*d^2*e^2 - 2*a^2*c*d*e*f + a^2*c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 3*(a^2*d^2*f^2*x^2 + 2*a^2*d^2*e*f*x + 2*a^2*c*d*e*f - a^2*c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 3*(a^2*d^2*f^2*x^2 + 2*a^2*d^2*e*f*x + 2*a^2*c*d*e*f - a^2*c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (-3*I*a*b*d^2*e^2 + 3*b^2*d^2*e^2 + 6*I*a*b*c*d*e*f - 6*b^2*c*d*e*f - 3*I*a*b*c^2*f^2 + 3*b^2*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (3*I*a*b*d^2*e^2 + 3*b^2*d^2*e^2 - 6*I*a*b*c*d*e*f - 6*b^2*c*d*e*f + 3*I*a*b*c^2*f^2 + 3*b^2*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) - (3*I*a*b*d^2*f^2*x^2 + 3*b^2*d^2*f^2*x^2 + 6*I*a*b*d^2*e*f*x + 6*b^2*d^2*e*f*x + 6*I*a*b*c*d*e*f + 6*b^2*c*d*e*f - 3*I*a*b*c^2*f^2 - 3*b^2*c^2*f^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (-3*I*a*b*d^2*f^2*x^2 + 3*b^2*d^2*f^2*x^2 - 6*I*a*b*d^2*e*f*x + 6*b^2*d^2*e*f*x - 6*I*a*b*c*d*e*f + 6*b^2*c*d*e*f + 3*I*a*b*c^2*f^2 - 3*b^2*c^2*f^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + 6*(-I*a*b*f^2 + b^2*f^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + 6*(I*a*b*f^2 + b^2*f^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)))/((a^2*b + b^3)*d^3)","C",0
379,1,684,0,0.609673," ","integrate((f*x+e)*sinh(d*x+c)*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a^{2} + b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e x - 2 \, a^{2} f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, a^{2} f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(i \, a b f - b^{2} f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + 2 \, {\left(-i \, a b f - b^{2} f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left(a^{2} d e - a^{2} c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a^{2} d e - a^{2} c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a^{2} d f x + a^{2} c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(-2 i \, a b d e + 2 \, b^{2} d e + 2 i \, a b c f - 2 \, b^{2} c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(2 i \, a b d e + 2 \, b^{2} d e - 2 i \, a b c f - 2 \, b^{2} c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(2 i \, a b d f x + 2 \, b^{2} d f x + 2 i \, a b c f + 2 \, b^{2} c f\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(-2 i \, a b d f x + 2 \, b^{2} d f x - 2 i \, a b c f + 2 \, b^{2} c f\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right)}{2 \, {\left(a^{2} b + b^{3}\right)} d^{2}}"," ",0,"-1/2*((a^2 + b^2)*d^2*f*x^2 + 2*(a^2 + b^2)*d^2*e*x - 2*a^2*f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*a^2*f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(I*a*b*f - b^2*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + 2*(-I*a*b*f - b^2*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*(a^2*d*e - a^2*c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a^2*d*e - a^2*c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a^2*d*f*x + a^2*c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(a^2*d*f*x + a^2*c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (-2*I*a*b*d*e + 2*b^2*d*e + 2*I*a*b*c*f - 2*b^2*c*f)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (2*I*a*b*d*e + 2*b^2*d*e - 2*I*a*b*c*f - 2*b^2*c*f)*log(cosh(d*x + c) + sinh(d*x + c) - I) - (2*I*a*b*d*f*x + 2*b^2*d*f*x + 2*I*a*b*c*f + 2*b^2*c*f)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (-2*I*a*b*d*f*x + 2*b^2*d*f*x - 2*I*a*b*c*f + 2*b^2*c*f)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1))/((a^2*b + b^3)*d^2)","A",0
380,1,111,0,0.536709," ","integrate(sinh(d*x+c)*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a^{2} + b^{2}\right)} d x + 2 \, a b \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - a^{2} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - b^{2} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{{\left(a^{2} b + b^{3}\right)} d}"," ",0,"-((a^2 + b^2)*d*x + 2*a*b*arctan(cosh(d*x + c) + sinh(d*x + c)) - a^2*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) - b^2*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/((a^2*b + b^3)*d)","A",0
381,0,0,0,0.548162," ","integrate(sinh(d*x+c)*tanh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sinh\left(d x + c\right) \tanh\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sinh(d*x + c)*tanh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
382,1,6525,0,0.779403," ","integrate((f*x+e)^3*tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{3} - 12 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f + 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} - 4 \, {\left(a^{3} + a b^{2}\right)} c^{3} f^{3} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f + {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f + {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d^{2} f^{3} x^{2} + 2 \, a^{2} b d^{2} e f^{2} x + a^{2} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3} + {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3} + {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3} + {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3} + {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e^{2} f x + 3 \, a^{2} b c d^{2} e^{2} f - 3 \, a^{2} b c^{2} d e f^{2} + a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 12 \, {\left(a^{2} b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b f^{3} \sinh\left(d x + c\right)^{2} + a^{2} b f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a^{2} b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b f^{3} \sinh\left(d x + c\right)^{2} + a^{2} b f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2} + {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2} + {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d f^{3} x + a^{2} b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f x + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3}\right)} \cosh\left(d x + c\right) + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x + 24 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 24 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 24 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 24 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 24 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 24 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d f^{3} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d f^{3} x + 12 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 24 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 24 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 12 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 24 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 24 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 12 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} + 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 24 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 24 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 24 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 12 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} - 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} - 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} + 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3} + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 24 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + 24 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 24 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 12 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{3} x^{2} + 6 i \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} + a b^{2}\right)} c d e f^{2} + 12 i \, {\left(a^{2} b + b^{3}\right)} c d e f^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{3} - 6 i \, {\left(a^{2} b + b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 12 \, {\left({\left(a^{3} + a b^{2}\right)} f^{3} + i \, {\left(a^{2} b + b^{3}\right)} f^{3} + {\left({\left(a^{3} + a b^{2}\right)} f^{3} + i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} f^{3} + i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{3} + a b^{2}\right)} f^{3} + i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - 12 \, {\left({\left(a^{3} + a b^{2}\right)} f^{3} - i \, {\left(a^{2} b + b^{3}\right)} f^{3} + {\left({\left(a^{3} + a b^{2}\right)} f^{3} - i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} f^{3} - i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{3} + a b^{2}\right)} f^{3} - i \, {\left(a^{2} b + b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f x + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f^{2} + {\left(a^{3} + a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4}\right)}}"," ",0,"1/2*(4*(a^3 + a*b^2)*d^3*e^3 - 12*(a^3 + a*b^2)*c*d^2*e^2*f + 12*(a^3 + a*b^2)*c^2*d*e*f^2 - 4*(a^3 + a*b^2)*c^3*f^3 - 4*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c)^2 - 4*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*sinh(d*x + c)^2 + 6*(a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f + (a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 6*(a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f + (a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d^2*f^3*x^2 + 2*a^2*b*d^2*e*f^2*x + a^2*b*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3 + (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3 + (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3 + (a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3 + (a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d^3*f^3*x^3 + 3*a^2*b*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e^2*f*x + 3*a^2*b*c*d^2*e^2*f - 3*a^2*b*c^2*d*e*f^2 + a^2*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 12*(a^2*b*f^3*cosh(d*x + c)^2 + 2*a^2*b*f^3*cosh(d*x + c)*sinh(d*x + c) + a^2*b*f^3*sinh(d*x + c)^2 + a^2*b*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(a^2*b*f^3*cosh(d*x + c)^2 + 2*a^2*b*f^3*cosh(d*x + c)*sinh(d*x + c) + a^2*b*f^3*sinh(d*x + c)^2 + a^2*b*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(a^2*b*d*f^3*x + a^2*b*d*e*f^2 + (a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c)^2 + 2*(a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d*f^3*x + a^2*b*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(a^2*b*d*f^3*x + a^2*b*d*e*f^2 + (a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c)^2 + 2*(a^2*b*d*f^3*x + a^2*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d*f^3*x + a^2*b*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 4*((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*d^3*e*f^2*x^2 + 3*(a^2*b + b^3)*d^3*e^2*f*x + (a^2*b + b^3)*d^3*e^3)*cosh(d*x + c) + (12*(a^3 + a*b^2)*d*f^3*x + 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 + 12*I*(a^2*b + b^3)*d*e*f^2 + (12*(a^3 + a*b^2)*d*f^3*x + 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 + 12*I*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)^2 + (24*(a^3 + a*b^2)*d*f^3*x + 24*I*(a^2*b + b^3)*d*f^3*x + 24*(a^3 + a*b^2)*d*e*f^2 + 24*I*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (12*(a^3 + a*b^2)*d*f^3*x + 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 + 12*I*(a^2*b + b^3)*d*e*f^2)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (12*(a^3 + a*b^2)*d*f^3*x - 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 - 12*I*(a^2*b + b^3)*d*e*f^2 + (12*(a^3 + a*b^2)*d*f^3*x - 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 - 12*I*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)^2 + (24*(a^3 + a*b^2)*d*f^3*x - 24*I*(a^2*b + b^3)*d*f^3*x + 24*(a^3 + a*b^2)*d*e*f^2 - 24*I*(a^2*b + b^3)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (12*(a^3 + a*b^2)*d*f^3*x - 12*I*(a^2*b + b^3)*d*f^3*x + 12*(a^3 + a*b^2)*d*e*f^2 - 12*I*(a^2*b + b^3)*d*e*f^2)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (6*(a^3 + a*b^2)*d^2*e^2*f + 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3 + (6*(a^3 + a*b^2)*d^2*e^2*f + 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*(a^3 + a*b^2)*d^2*e^2*f + 12*I*(a^2*b + b^3)*d^2*e^2*f - 24*(a^3 + a*b^2)*c*d*e*f^2 - 24*I*(a^2*b + b^3)*c*d*e*f^2 + 12*(a^3 + a*b^2)*c^2*f^3 + 12*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*(a^3 + a*b^2)*d^2*e^2*f + 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (6*(a^3 + a*b^2)*d^2*e^2*f - 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3 + (6*(a^3 + a*b^2)*d^2*e^2*f - 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*(a^3 + a*b^2)*d^2*e^2*f - 12*I*(a^2*b + b^3)*d^2*e^2*f - 24*(a^3 + a*b^2)*c*d*e*f^2 + 24*I*(a^2*b + b^3)*c*d*e*f^2 + 12*(a^3 + a*b^2)*c^2*f^3 - 12*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*(a^3 + a*b^2)*d^2*e^2*f - 6*I*(a^2*b + b^3)*d^2*e^2*f - 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 + 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) + (6*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x - 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3 + (6*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x - 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*(a^3 + a*b^2)*d^2*f^3*x^2 - 12*I*(a^2*b + b^3)*d^2*f^3*x^2 + 24*(a^3 + a*b^2)*d^2*e*f^2*x - 24*I*(a^2*b + b^3)*d^2*e*f^2*x + 24*(a^3 + a*b^2)*c*d*e*f^2 - 24*I*(a^2*b + b^3)*c*d*e*f^2 - 12*(a^3 + a*b^2)*c^2*f^3 + 12*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*(a^3 + a*b^2)*d^2*f^3*x^2 - 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x - 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 - 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 + 6*I*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (6*(a^3 + a*b^2)*d^2*f^3*x^2 + 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x + 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3 + (6*(a^3 + a*b^2)*d^2*f^3*x^2 + 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x + 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*(a^3 + a*b^2)*d^2*f^3*x^2 + 12*I*(a^2*b + b^3)*d^2*f^3*x^2 + 24*(a^3 + a*b^2)*d^2*e*f^2*x + 24*I*(a^2*b + b^3)*d^2*e*f^2*x + 24*(a^3 + a*b^2)*c*d*e*f^2 + 24*I*(a^2*b + b^3)*c*d*e*f^2 - 12*(a^3 + a*b^2)*c^2*f^3 - 12*I*(a^2*b + b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*(a^3 + a*b^2)*d^2*f^3*x^2 + 6*I*(a^2*b + b^3)*d^2*f^3*x^2 + 12*(a^3 + a*b^2)*d^2*e*f^2*x + 12*I*(a^2*b + b^3)*d^2*e*f^2*x + 12*(a^3 + a*b^2)*c*d*e*f^2 + 12*I*(a^2*b + b^3)*c*d*e*f^2 - 6*(a^3 + a*b^2)*c^2*f^3 - 6*I*(a^2*b + b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 12*((a^3 + a*b^2)*f^3 + I*(a^2*b + b^3)*f^3 + ((a^3 + a*b^2)*f^3 + I*(a^2*b + b^3)*f^3)*cosh(d*x + c)^2 + 2*((a^3 + a*b^2)*f^3 + I*(a^2*b + b^3)*f^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^3 + a*b^2)*f^3 + I*(a^2*b + b^3)*f^3)*sinh(d*x + c)^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - 12*((a^3 + a*b^2)*f^3 - I*(a^2*b + b^3)*f^3 + ((a^3 + a*b^2)*f^3 - I*(a^2*b + b^3)*f^3)*cosh(d*x + c)^2 + 2*((a^3 + a*b^2)*f^3 - I*(a^2*b + b^3)*f^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^3 + a*b^2)*f^3 - I*(a^2*b + b^3)*f^3)*sinh(d*x + c)^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 4*((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*d^3*e*f^2*x^2 + 3*(a^2*b + b^3)*d^3*e^2*f*x + (a^2*b + b^3)*d^3*e^3 + 2*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + 3*(a^3 + a*b^2)*c*d^2*e^2*f - 3*(a^3 + a*b^2)*c^2*d*e*f^2 + (a^3 + a*b^2)*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^4*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^4*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d^4*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^4)","C",0
383,1,3680,0,0.688651," ","integrate((f*x+e)^2*tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 8 \, {\left(a^{3} + a b^{2}\right)} c d e f + 4 \, {\left(a^{3} + a b^{2}\right)} c^{2} f^{2} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2} + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2} + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left(a^{2} b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b f^{2} \sinh\left(d x + c\right)^{2} + a^{2} b f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(a^{2} b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b f^{2} \sinh\left(d x + c\right)^{2} + a^{2} b f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f x + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(a^{3} + a b^{2}\right)} f^{2} + i \, {\left(a^{2} b + b^{3}\right)} f^{2} + {\left({\left(a^{3} + a b^{2}\right)} f^{2} + i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} f^{2} + i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{3} + a b^{2}\right)} f^{2} + i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + 4 \, {\left({\left(a^{3} + a b^{2}\right)} f^{2} - i \, {\left(a^{2} b + b^{3}\right)} f^{2} + {\left({\left(a^{3} + a b^{2}\right)} f^{2} - i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} f^{2} - i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{3} + a b^{2}\right)} f^{2} - i \, {\left(a^{2} b + b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f + 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f + 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, {\left(a^{3} + a b^{2}\right)} d e f + 8 i \, {\left(a^{2} b + b^{3}\right)} d e f - 8 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 8 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f + 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f - 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f - 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, {\left(a^{3} + a b^{2}\right)} d e f - 8 i \, {\left(a^{2} b + b^{3}\right)} d e f - 8 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 8 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d e f - 4 i \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 8 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 8 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 8 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x + 8 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 8 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 8 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 \, {\left(a^{3} + a b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{2} b + b^{3}\right)} d f^{2} x + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 4 i \, {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f x + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{3} + a b^{2}\right)} c d e f - {\left(a^{3} + a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3}\right)}}"," ",0,"1/2*(4*(a^3 + a*b^2)*d^2*e^2 - 8*(a^3 + a*b^2)*c*d*e*f + 4*(a^3 + a*b^2)*c^2*f^2 - 4*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c)^2 - 4*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*sinh(d*x + c)^2 + 4*(a^2*b*d*f^2*x + a^2*b*d*e*f + (a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d*f^2*x + a^2*b*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 4*(a^2*b*d*f^2*x + a^2*b*d*e*f + (a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d*f^2*x + a^2*b*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2 + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2 + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*(a^2*b*f^2*cosh(d*x + c)^2 + 2*a^2*b*f^2*cosh(d*x + c)*sinh(d*x + c) + a^2*b*f^2*sinh(d*x + c)^2 + a^2*b*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*(a^2*b*f^2*cosh(d*x + c)^2 + 2*a^2*b*f^2*cosh(d*x + c)*sinh(d*x + c) + a^2*b*f^2*sinh(d*x + c)^2 + a^2*b*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 4*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*d^2*e*f*x + (a^2*b + b^3)*d^2*e^2)*cosh(d*x + c) + 4*((a^3 + a*b^2)*f^2 + I*(a^2*b + b^3)*f^2 + ((a^3 + a*b^2)*f^2 + I*(a^2*b + b^3)*f^2)*cosh(d*x + c)^2 + 2*((a^3 + a*b^2)*f^2 + I*(a^2*b + b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^3 + a*b^2)*f^2 + I*(a^2*b + b^3)*f^2)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + 4*((a^3 + a*b^2)*f^2 - I*(a^2*b + b^3)*f^2 + ((a^3 + a*b^2)*f^2 - I*(a^2*b + b^3)*f^2)*cosh(d*x + c)^2 + 2*((a^3 + a*b^2)*f^2 - I*(a^2*b + b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^3 + a*b^2)*f^2 - I*(a^2*b + b^3)*f^2)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (4*(a^3 + a*b^2)*d*e*f + 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2 + (4*(a^3 + a*b^2)*d*e*f + 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (8*(a^3 + a*b^2)*d*e*f + 8*I*(a^2*b + b^3)*d*e*f - 8*(a^3 + a*b^2)*c*f^2 - 8*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*(a^3 + a*b^2)*d*e*f + 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (4*(a^3 + a*b^2)*d*e*f - 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2 + (4*(a^3 + a*b^2)*d*e*f - 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (8*(a^3 + a*b^2)*d*e*f - 8*I*(a^2*b + b^3)*d*e*f - 8*(a^3 + a*b^2)*c*f^2 + 8*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*(a^3 + a*b^2)*d*e*f - 4*I*(a^2*b + b^3)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) + (4*(a^3 + a*b^2)*d*f^2*x - 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2 + (4*(a^3 + a*b^2)*d*f^2*x - 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (8*(a^3 + a*b^2)*d*f^2*x - 8*I*(a^2*b + b^3)*d*f^2*x + 8*(a^3 + a*b^2)*c*f^2 - 8*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*(a^3 + a*b^2)*d*f^2*x - 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 - 4*I*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (4*(a^3 + a*b^2)*d*f^2*x + 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2 + (4*(a^3 + a*b^2)*d*f^2*x + 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + (8*(a^3 + a*b^2)*d*f^2*x + 8*I*(a^2*b + b^3)*d*f^2*x + 8*(a^3 + a*b^2)*c*f^2 + 8*I*(a^2*b + b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*(a^3 + a*b^2)*d*f^2*x + 4*I*(a^2*b + b^3)*d*f^2*x + 4*(a^3 + a*b^2)*c*f^2 + 4*I*(a^2*b + b^3)*c*f^2)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 4*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*d^2*e*f*x + (a^2*b + b^3)*d^2*e^2 + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + 2*(a^3 + a*b^2)*c*d*e*f - (a^3 + a*b^2)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d^3*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3)","C",0
384,1,1337,0,0.553272," ","integrate((f*x+e)*tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} + a b^{2}\right)} d f x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d f x \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} d e - {\left(a^{2} b f \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b f \sinh\left(d x + c\right)^{2} + a^{2} b f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(a^{2} b f \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b f \sinh\left(d x + c\right)^{2} + a^{2} b f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(a^{2} b d e - a^{2} b c f + {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d e - a^{2} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(a^{2} b d e - a^{2} b c f + {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d e - a^{2} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(a^{2} b d f x + a^{2} b c f + {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d f x + a^{2} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(a^{2} b d f x + a^{2} b c f + {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b d f x + a^{2} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{2} b + b^{3}\right)} f\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e\right)} \cosh\left(d x + c\right) - {\left({\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} + a b^{2}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d f x \cosh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}}"," ",0,"-(2*(a^3 + a*b^2)*d*f*x*cosh(d*x + c)^2 + 2*(a^3 + a*b^2)*d*f*x*sinh(d*x + c)^2 - 2*(a^3 + a*b^2)*d*e - (a^2*b*f*cosh(d*x + c)^2 + 2*a^2*b*f*cosh(d*x + c)*sinh(d*x + c) + a^2*b*f*sinh(d*x + c)^2 + a^2*b*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (a^2*b*f*cosh(d*x + c)^2 + 2*a^2*b*f*cosh(d*x + c)*sinh(d*x + c) + a^2*b*f*sinh(d*x + c)^2 + a^2*b*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (a^2*b*d*e - a^2*b*c*f + (a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d*e - a^2*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (a^2*b*d*e - a^2*b*c*f + (a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d*e - a^2*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (a^2*b*d*f*x + a^2*b*c*f + (a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d*f*x + a^2*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (a^2*b*d*f*x + a^2*b*c*f + (a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^2*b*d*f*x + a^2*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((a^2*b + b^3)*f*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f*sinh(d*x + c)^2 + (a^2*b + b^3)*f)*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e)*cosh(d*x + c) - ((a^3 + a*b^2)*f*cosh(d*x + c)^2 + 2*(a^3 + a*b^2)*f*cosh(d*x + c)*sinh(d*x + c) + (a^3 + a*b^2)*f*sinh(d*x + c)^2 + (a^3 + a*b^2)*f)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(2*(a^3 + a*b^2)*d*f*x*cosh(d*x + c) + (a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e)*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d^2*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)","B",0
385,1,351,0,0.463057," ","integrate(tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a^{3} + 2 \, a b^{2} + {\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} + a^{2}\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d}"," ",0,"(2*a^3 + 2*a*b^2 + (a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 + a^2)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) - 2*(a^2*b + b^3)*cosh(d*x + c) - 2*(a^2*b + b^3)*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d)","B",0
386,0,0,0,0.544434," ","integrate(tanh(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tanh\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(tanh(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
387,1,10892,0,1.032277," ","integrate((f*x+e)^2*sech(d*x+c)*tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b + b^{3}\right)} d e f + 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2} - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x - 8 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + {\left(a^{2} b + b^{3}\right)} d e f - 2 \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d e f - 4 \, {\left(a^{2} b + b^{3}\right)} c f^{2} - 12 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 4 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f + 3 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f + 3 \, {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b d f^{2} x + a^{2} b d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(4 \, a^{2} b d f^{2} x + 4 \, a^{2} b d e f - 2 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x + {\left(4 \, a^{2} b d f^{2} x + 4 \, a^{2} b d e f - 2 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x - 2 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{2} b d f^{2} x + 16 \, a^{2} b d e f - 8 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x - 8 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b d f^{2} x + 4 \, a^{2} b d e f - 2 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x - 2 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 i \, {\left(a^{3} - a b^{2}\right)} d e f + {\left(8 \, a^{2} b d f^{2} x + 8 \, a^{2} b d e f - 4 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{2} b d f^{2} x + 8 \, a^{2} b d e f - 4 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{3} - a b^{2}\right)} d e f + {\left(24 \, a^{2} b d f^{2} x + 24 \, a^{2} b d e f - 12 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x - 12 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, a^{2} b d f^{2} x + 16 \, a^{2} b d e f - 8 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x - 8 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} b d f^{2} x + 16 \, a^{2} b d e f - 8 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x - 8 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(4 \, a^{2} b d f^{2} x + 4 \, a^{2} b d e f + 2 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x + {\left(4 \, a^{2} b d f^{2} x + 4 \, a^{2} b d e f + 2 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x + 2 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{2} b d f^{2} x + 16 \, a^{2} b d e f + 8 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x + 8 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b d f^{2} x + 4 \, a^{2} b d e f + 2 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x + 2 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{4} + 2 i \, {\left(a^{3} - a b^{2}\right)} d e f + {\left(8 \, a^{2} b d f^{2} x + 8 \, a^{2} b d e f + 4 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{2} b d f^{2} x + 8 \, a^{2} b d e f + 4 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{3} - a b^{2}\right)} d e f + {\left(24 \, a^{2} b d f^{2} x + 24 \, a^{2} b d e f + 12 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x + 12 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, a^{2} b d f^{2} x + 16 \, a^{2} b d e f + 8 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x + 8 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} b d f^{2} x + 16 \, a^{2} b d e f + 8 i \, {\left(a^{3} - a b^{2}\right)} d f^{2} x + 8 i \, {\left(a^{3} - a b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + 3 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + 3 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2} + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2} + 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2} + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2} + 3 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} e f x + 2 \, a^{2} b c d e f - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(2 \, a^{2} b d^{2} e^{2} - 4 \, a^{2} b c d e f - i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f + {\left(2 \, a^{2} b d^{2} e^{2} - 4 \, a^{2} b c d e f - i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 2 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} - i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} b d^{2} e^{2} - 16 \, a^{2} b c d e f - 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 8 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} - 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b d^{2} e^{2} - 4 \, a^{2} b c d e f - i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 2 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} - i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} - i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2} + {\left(4 \, a^{2} b d^{2} e^{2} - 8 \, a^{2} b c d e f - 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 4 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 4 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} - 2 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b d^{2} e^{2} - 8 \, a^{2} b c d e f - 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 4 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 4 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} - 2 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2} + {\left(12 \, a^{2} b d^{2} e^{2} - 24 \, a^{2} b c d e f - 6 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 12 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 12 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} - 6 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b d^{2} e^{2} - 16 \, a^{2} b c d e f - 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 8 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} - 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b d^{2} e^{2} - 16 \, a^{2} b c d e f - 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 8 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} - 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(2 \, a^{2} b d^{2} e^{2} - 4 \, a^{2} b c d e f + i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f + {\left(2 \, a^{2} b d^{2} e^{2} - 4 \, a^{2} b c d e f + i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 2 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} + i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} b d^{2} e^{2} - 16 \, a^{2} b c d e f + 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} - 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 8 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} + 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b d^{2} e^{2} - 4 \, a^{2} b c d e f + i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 2 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} + i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} + i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2} + {\left(4 \, a^{2} b d^{2} e^{2} - 8 \, a^{2} b c d e f + 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} - 4 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 4 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} + 2 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b d^{2} e^{2} - 8 \, a^{2} b c d e f + 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} - 4 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 4 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} + 2 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2} + {\left(12 \, a^{2} b d^{2} e^{2} - 24 \, a^{2} b c d e f + 6 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} - 12 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 12 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} + 6 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b d^{2} e^{2} - 16 \, a^{2} b c d e f + 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} - 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 8 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} + 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b d^{2} e^{2} - 16 \, a^{2} b c d e f + 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} - 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 8 \, {\left(a^{2} b c^{2} + a^{2} b + b^{3}\right)} f^{2} + 4 i \, {\left(2 \, a^{3} + 2 \, a b^{2} + {\left(a^{3} - a b^{2}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(2 \, a^{2} b d^{2} f^{2} x^{2} + 4 \, a^{2} b d^{2} e f x + 4 \, a^{2} b c d e f - 2 \, a^{2} b c^{2} f^{2} + i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f - i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2} + {\left(2 \, a^{2} b d^{2} f^{2} x^{2} + 4 \, a^{2} b d^{2} e f x + 4 \, a^{2} b c d e f - 2 \, a^{2} b c^{2} f^{2} + i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f - i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} b d^{2} f^{2} x^{2} + 16 \, a^{2} b d^{2} e f x + 16 \, a^{2} b c d e f - 8 \, a^{2} b c^{2} f^{2} + 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f - 4 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b d^{2} f^{2} x^{2} + 4 \, a^{2} b d^{2} e f x + 4 \, a^{2} b c d e f - 2 \, a^{2} b c^{2} f^{2} + i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f - i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{2} b d^{2} f^{2} x^{2} + 8 \, a^{2} b d^{2} e f x + 8 \, a^{2} b c d e f - 4 \, a^{2} b c^{2} f^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + 4 i \, {\left(a^{3} - a b^{2}\right)} c d e f - 2 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b d^{2} f^{2} x^{2} + 8 \, a^{2} b d^{2} e f x + 8 \, a^{2} b c d e f - 4 \, a^{2} b c^{2} f^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + 4 i \, {\left(a^{3} - a b^{2}\right)} c d e f - 2 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2} + {\left(12 \, a^{2} b d^{2} f^{2} x^{2} + 24 \, a^{2} b d^{2} e f x + 24 \, a^{2} b c d e f - 12 \, a^{2} b c^{2} f^{2} + 6 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 12 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + 12 i \, {\left(a^{3} - a b^{2}\right)} c d e f - 6 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b d^{2} f^{2} x^{2} + 16 \, a^{2} b d^{2} e f x + 16 \, a^{2} b c d e f - 8 \, a^{2} b c^{2} f^{2} + 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f - 4 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b d^{2} f^{2} x^{2} + 16 \, a^{2} b d^{2} e f x + 16 \, a^{2} b c d e f - 8 \, a^{2} b c^{2} f^{2} + 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x + 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f - 4 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(2 \, a^{2} b d^{2} f^{2} x^{2} + 4 \, a^{2} b d^{2} e f x + 4 \, a^{2} b c d e f - 2 \, a^{2} b c^{2} f^{2} - i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x - 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f + i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2} + {\left(2 \, a^{2} b d^{2} f^{2} x^{2} + 4 \, a^{2} b d^{2} e f x + 4 \, a^{2} b c d e f - 2 \, a^{2} b c^{2} f^{2} - i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x - 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f + i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} b d^{2} f^{2} x^{2} + 16 \, a^{2} b d^{2} e f x + 16 \, a^{2} b c d e f - 8 \, a^{2} b c^{2} f^{2} - 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x - 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 4 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b d^{2} f^{2} x^{2} + 4 \, a^{2} b d^{2} e f x + 4 \, a^{2} b c d e f - 2 \, a^{2} b c^{2} f^{2} - i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x - 2 i \, {\left(a^{3} - a b^{2}\right)} c d e f + i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{2} b d^{2} f^{2} x^{2} + 8 \, a^{2} b d^{2} e f x + 8 \, a^{2} b c d e f - 4 \, a^{2} b c^{2} f^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} - 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x - 4 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 2 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b d^{2} f^{2} x^{2} + 8 \, a^{2} b d^{2} e f x + 8 \, a^{2} b c d e f - 4 \, a^{2} b c^{2} f^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} - 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x - 4 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 2 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2} + {\left(12 \, a^{2} b d^{2} f^{2} x^{2} + 24 \, a^{2} b d^{2} e f x + 24 \, a^{2} b c d e f - 12 \, a^{2} b c^{2} f^{2} - 6 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} - 12 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x - 12 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 6 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b d^{2} f^{2} x^{2} + 16 \, a^{2} b d^{2} e f x + 16 \, a^{2} b c d e f - 8 \, a^{2} b c^{2} f^{2} - 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x - 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 4 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b d^{2} f^{2} x^{2} + 16 \, a^{2} b d^{2} e f x + 16 \, a^{2} b c d e f - 8 \, a^{2} b c^{2} f^{2} - 4 i \, {\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(a^{3} - a b^{2}\right)} d^{2} e f x - 8 i \, {\left(a^{3} - a b^{2}\right)} c d e f + 4 i \, {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 4 \, {\left(a^{2} b f^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} b f^{2} \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b f^{2} \cosh\left(d x + c\right)^{2} + a^{2} b f^{2} + 2 \, {\left(3 \, a^{2} b f^{2} \cosh\left(d x + c\right)^{2} + a^{2} b f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b f^{2} \cosh\left(d x + c\right)^{3} + a^{2} b f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(a^{2} b f^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} b f^{2} \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b f^{2} \cosh\left(d x + c\right)^{2} + a^{2} b f^{2} + 2 \, {\left(3 \, a^{2} b f^{2} \cosh\left(d x + c\right)^{2} + a^{2} b f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b f^{2} \cosh\left(d x + c\right)^{3} + a^{2} b f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + {\left(4 \, a^{2} b f^{2} + {\left(4 \, a^{2} b f^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{2} b f^{2} - 8 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b f^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 i \, {\left(a^{3} - a b^{2}\right)} f^{2} + {\left(8 \, a^{2} b f^{2} - 4 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{2} b f^{2} - 4 i \, {\left(a^{3} - a b^{2}\right)} f^{2} + {\left(24 \, a^{2} b f^{2} - 12 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, a^{2} b f^{2} - 8 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} b f^{2} - 8 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(4 \, a^{2} b f^{2} + {\left(4 \, a^{2} b f^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{2} b f^{2} + 8 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b f^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 i \, {\left(a^{3} - a b^{2}\right)} f^{2} + {\left(8 \, a^{2} b f^{2} + 4 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{2} b f^{2} + 4 i \, {\left(a^{3} - a b^{2}\right)} f^{2} + {\left(24 \, a^{2} b f^{2} + 12 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, a^{2} b f^{2} + 8 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} b f^{2} + 8 i \, {\left(a^{3} - a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 8 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x - 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + {\left(a^{2} b + b^{3}\right)} d e f - 2 \, {\left(a^{2} b + b^{3}\right)} c f^{2} + {\left(2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(4*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*c*f^2)*cosh(d*x + c)^4 + 4*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*c*f^2)*sinh(d*x + c)^4 - 4*(a^2*b + b^3)*d*e*f + 4*(a^2*b + b^3)*c*f^2 - 2*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^3 + a*b^2)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)^3 - 2*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^3 + a*b^2)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x - 8*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + (a^2*b + b^3)*d*e*f - 2*(a^2*b + b^3)*c*f^2 + (2*(a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^2 - 2*(2*(a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*d*e*f - 4*(a^2*b + b^3)*c*f^2 - 12*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*c*f^2)*cosh(d*x + c)^2 + 2*(2*(a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x + 3*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^3 + a*b^2)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*d*e*f + 2*((a^3 + a*b^2)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c) + 4*(a^2*b*d*f^2*x + a^2*b*d*e*f + (a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^4 + 4*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b*d*f^2*x + a^2*b*d*e*f)*sinh(d*x + c)^4 + 2*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*f^2*x + a^2*b*d*e*f + 3*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^3 + (a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 4*(a^2*b*d*f^2*x + a^2*b*d*e*f + (a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^4 + 4*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b*d*f^2*x + a^2*b*d*e*f)*sinh(d*x + c)^4 + 2*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*f^2*x + a^2*b*d*e*f + 3*(a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c)^3 + (a^2*b*d*f^2*x + a^2*b*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (4*a^2*b*d*f^2*x + 4*a^2*b*d*e*f - 2*I*(a^3 - a*b^2)*d*f^2*x + (4*a^2*b*d*f^2*x + 4*a^2*b*d*e*f - 2*I*(a^3 - a*b^2)*d*f^2*x - 2*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c)^4 + (16*a^2*b*d*f^2*x + 16*a^2*b*d*e*f - 8*I*(a^3 - a*b^2)*d*f^2*x - 8*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a^2*b*d*f^2*x + 4*a^2*b*d*e*f - 2*I*(a^3 - a*b^2)*d*f^2*x - 2*I*(a^3 - a*b^2)*d*e*f)*sinh(d*x + c)^4 - 2*I*(a^3 - a*b^2)*d*e*f + (8*a^2*b*d*f^2*x + 8*a^2*b*d*e*f - 4*I*(a^3 - a*b^2)*d*f^2*x - 4*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c)^2 + (8*a^2*b*d*f^2*x + 8*a^2*b*d*e*f - 4*I*(a^3 - a*b^2)*d*f^2*x - 4*I*(a^3 - a*b^2)*d*e*f + (24*a^2*b*d*f^2*x + 24*a^2*b*d*e*f - 12*I*(a^3 - a*b^2)*d*f^2*x - 12*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*a^2*b*d*f^2*x + 16*a^2*b*d*e*f - 8*I*(a^3 - a*b^2)*d*f^2*x - 8*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c)^3 + (16*a^2*b*d*f^2*x + 16*a^2*b*d*e*f - 8*I*(a^3 - a*b^2)*d*f^2*x - 8*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (4*a^2*b*d*f^2*x + 4*a^2*b*d*e*f + 2*I*(a^3 - a*b^2)*d*f^2*x + (4*a^2*b*d*f^2*x + 4*a^2*b*d*e*f + 2*I*(a^3 - a*b^2)*d*f^2*x + 2*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c)^4 + (16*a^2*b*d*f^2*x + 16*a^2*b*d*e*f + 8*I*(a^3 - a*b^2)*d*f^2*x + 8*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a^2*b*d*f^2*x + 4*a^2*b*d*e*f + 2*I*(a^3 - a*b^2)*d*f^2*x + 2*I*(a^3 - a*b^2)*d*e*f)*sinh(d*x + c)^4 + 2*I*(a^3 - a*b^2)*d*e*f + (8*a^2*b*d*f^2*x + 8*a^2*b*d*e*f + 4*I*(a^3 - a*b^2)*d*f^2*x + 4*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c)^2 + (8*a^2*b*d*f^2*x + 8*a^2*b*d*e*f + 4*I*(a^3 - a*b^2)*d*f^2*x + 4*I*(a^3 - a*b^2)*d*e*f + (24*a^2*b*d*f^2*x + 24*a^2*b*d*e*f + 12*I*(a^3 - a*b^2)*d*f^2*x + 12*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*a^2*b*d*f^2*x + 16*a^2*b*d*e*f + 8*I*(a^3 - a*b^2)*d*f^2*x + 8*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c)^3 + (16*a^2*b*d*f^2*x + 16*a^2*b*d*e*f + 8*I*(a^3 - a*b^2)*d*f^2*x + 8*I*(a^3 - a*b^2)*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sinh(d*x + c)^4 + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + 3*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^3 + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*sinh(d*x + c)^4 + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + 3*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c)^3 + (a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2 + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sinh(d*x + c)^4 + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2 + 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^3 + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2 + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*sinh(d*x + c)^4 + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2 + 3*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c)^3 + (a^2*b*d^2*f^2*x^2 + 2*a^2*b*d^2*e*f*x + 2*a^2*b*c*d*e*f - a^2*b*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (2*a^2*b*d^2*e^2 - 4*a^2*b*c*d*e*f - I*(a^3 - a*b^2)*d^2*e^2 + 2*I*(a^3 - a*b^2)*c*d*e*f + (2*a^2*b*d^2*e^2 - 4*a^2*b*c*d*e*f - I*(a^3 - a*b^2)*d^2*e^2 + 2*I*(a^3 - a*b^2)*c*d*e*f + 2*(a^2*b*c^2 + a^2*b + b^3)*f^2 - I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c)^4 + (8*a^2*b*d^2*e^2 - 16*a^2*b*c*d*e*f - 4*I*(a^3 - a*b^2)*d^2*e^2 + 8*I*(a^3 - a*b^2)*c*d*e*f + 8*(a^2*b*c^2 + a^2*b + b^3)*f^2 - 4*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b*d^2*e^2 - 4*a^2*b*c*d*e*f - I*(a^3 - a*b^2)*d^2*e^2 + 2*I*(a^3 - a*b^2)*c*d*e*f + 2*(a^2*b*c^2 + a^2*b + b^3)*f^2 - I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*sinh(d*x + c)^4 + 2*(a^2*b*c^2 + a^2*b + b^3)*f^2 - I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2 + (4*a^2*b*d^2*e^2 - 8*a^2*b*c*d*e*f - 2*I*(a^3 - a*b^2)*d^2*e^2 + 4*I*(a^3 - a*b^2)*c*d*e*f + 4*(a^2*b*c^2 + a^2*b + b^3)*f^2 - 2*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c)^2 + (4*a^2*b*d^2*e^2 - 8*a^2*b*c*d*e*f - 2*I*(a^3 - a*b^2)*d^2*e^2 + 4*I*(a^3 - a*b^2)*c*d*e*f + 4*(a^2*b*c^2 + a^2*b + b^3)*f^2 - 2*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2 + (12*a^2*b*d^2*e^2 - 24*a^2*b*c*d*e*f - 6*I*(a^3 - a*b^2)*d^2*e^2 + 12*I*(a^3 - a*b^2)*c*d*e*f + 12*(a^2*b*c^2 + a^2*b + b^3)*f^2 - 6*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b*d^2*e^2 - 16*a^2*b*c*d*e*f - 4*I*(a^3 - a*b^2)*d^2*e^2 + 8*I*(a^3 - a*b^2)*c*d*e*f + 8*(a^2*b*c^2 + a^2*b + b^3)*f^2 - 4*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c)^3 + (8*a^2*b*d^2*e^2 - 16*a^2*b*c*d*e*f - 4*I*(a^3 - a*b^2)*d^2*e^2 + 8*I*(a^3 - a*b^2)*c*d*e*f + 8*(a^2*b*c^2 + a^2*b + b^3)*f^2 - 4*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) - (2*a^2*b*d^2*e^2 - 4*a^2*b*c*d*e*f + I*(a^3 - a*b^2)*d^2*e^2 - 2*I*(a^3 - a*b^2)*c*d*e*f + (2*a^2*b*d^2*e^2 - 4*a^2*b*c*d*e*f + I*(a^3 - a*b^2)*d^2*e^2 - 2*I*(a^3 - a*b^2)*c*d*e*f + 2*(a^2*b*c^2 + a^2*b + b^3)*f^2 + I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c)^4 + (8*a^2*b*d^2*e^2 - 16*a^2*b*c*d*e*f + 4*I*(a^3 - a*b^2)*d^2*e^2 - 8*I*(a^3 - a*b^2)*c*d*e*f + 8*(a^2*b*c^2 + a^2*b + b^3)*f^2 + 4*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b*d^2*e^2 - 4*a^2*b*c*d*e*f + I*(a^3 - a*b^2)*d^2*e^2 - 2*I*(a^3 - a*b^2)*c*d*e*f + 2*(a^2*b*c^2 + a^2*b + b^3)*f^2 + I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*sinh(d*x + c)^4 + 2*(a^2*b*c^2 + a^2*b + b^3)*f^2 + I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2 + (4*a^2*b*d^2*e^2 - 8*a^2*b*c*d*e*f + 2*I*(a^3 - a*b^2)*d^2*e^2 - 4*I*(a^3 - a*b^2)*c*d*e*f + 4*(a^2*b*c^2 + a^2*b + b^3)*f^2 + 2*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c)^2 + (4*a^2*b*d^2*e^2 - 8*a^2*b*c*d*e*f + 2*I*(a^3 - a*b^2)*d^2*e^2 - 4*I*(a^3 - a*b^2)*c*d*e*f + 4*(a^2*b*c^2 + a^2*b + b^3)*f^2 + 2*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2 + (12*a^2*b*d^2*e^2 - 24*a^2*b*c*d*e*f + 6*I*(a^3 - a*b^2)*d^2*e^2 - 12*I*(a^3 - a*b^2)*c*d*e*f + 12*(a^2*b*c^2 + a^2*b + b^3)*f^2 + 6*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b*d^2*e^2 - 16*a^2*b*c*d*e*f + 4*I*(a^3 - a*b^2)*d^2*e^2 - 8*I*(a^3 - a*b^2)*c*d*e*f + 8*(a^2*b*c^2 + a^2*b + b^3)*f^2 + 4*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c)^3 + (8*a^2*b*d^2*e^2 - 16*a^2*b*c*d*e*f + 4*I*(a^3 - a*b^2)*d^2*e^2 - 8*I*(a^3 - a*b^2)*c*d*e*f + 8*(a^2*b*c^2 + a^2*b + b^3)*f^2 + 4*I*(2*a^3 + 2*a*b^2 + (a^3 - a*b^2)*c^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) - (2*a^2*b*d^2*f^2*x^2 + 4*a^2*b*d^2*e*f*x + 4*a^2*b*c*d*e*f - 2*a^2*b*c^2*f^2 + I*(a^3 - a*b^2)*d^2*f^2*x^2 + 2*I*(a^3 - a*b^2)*d^2*e*f*x + 2*I*(a^3 - a*b^2)*c*d*e*f - I*(a^3 - a*b^2)*c^2*f^2 + (2*a^2*b*d^2*f^2*x^2 + 4*a^2*b*d^2*e*f*x + 4*a^2*b*c*d*e*f - 2*a^2*b*c^2*f^2 + I*(a^3 - a*b^2)*d^2*f^2*x^2 + 2*I*(a^3 - a*b^2)*d^2*e*f*x + 2*I*(a^3 - a*b^2)*c*d*e*f - I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c)^4 + (8*a^2*b*d^2*f^2*x^2 + 16*a^2*b*d^2*e*f*x + 16*a^2*b*c*d*e*f - 8*a^2*b*c^2*f^2 + 4*I*(a^3 - a*b^2)*d^2*f^2*x^2 + 8*I*(a^3 - a*b^2)*d^2*e*f*x + 8*I*(a^3 - a*b^2)*c*d*e*f - 4*I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b*d^2*f^2*x^2 + 4*a^2*b*d^2*e*f*x + 4*a^2*b*c*d*e*f - 2*a^2*b*c^2*f^2 + I*(a^3 - a*b^2)*d^2*f^2*x^2 + 2*I*(a^3 - a*b^2)*d^2*e*f*x + 2*I*(a^3 - a*b^2)*c*d*e*f - I*(a^3 - a*b^2)*c^2*f^2)*sinh(d*x + c)^4 + (4*a^2*b*d^2*f^2*x^2 + 8*a^2*b*d^2*e*f*x + 8*a^2*b*c*d*e*f - 4*a^2*b*c^2*f^2 + 2*I*(a^3 - a*b^2)*d^2*f^2*x^2 + 4*I*(a^3 - a*b^2)*d^2*e*f*x + 4*I*(a^3 - a*b^2)*c*d*e*f - 2*I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c)^2 + (4*a^2*b*d^2*f^2*x^2 + 8*a^2*b*d^2*e*f*x + 8*a^2*b*c*d*e*f - 4*a^2*b*c^2*f^2 + 2*I*(a^3 - a*b^2)*d^2*f^2*x^2 + 4*I*(a^3 - a*b^2)*d^2*e*f*x + 4*I*(a^3 - a*b^2)*c*d*e*f - 2*I*(a^3 - a*b^2)*c^2*f^2 + (12*a^2*b*d^2*f^2*x^2 + 24*a^2*b*d^2*e*f*x + 24*a^2*b*c*d*e*f - 12*a^2*b*c^2*f^2 + 6*I*(a^3 - a*b^2)*d^2*f^2*x^2 + 12*I*(a^3 - a*b^2)*d^2*e*f*x + 12*I*(a^3 - a*b^2)*c*d*e*f - 6*I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b*d^2*f^2*x^2 + 16*a^2*b*d^2*e*f*x + 16*a^2*b*c*d*e*f - 8*a^2*b*c^2*f^2 + 4*I*(a^3 - a*b^2)*d^2*f^2*x^2 + 8*I*(a^3 - a*b^2)*d^2*e*f*x + 8*I*(a^3 - a*b^2)*c*d*e*f - 4*I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c)^3 + (8*a^2*b*d^2*f^2*x^2 + 16*a^2*b*d^2*e*f*x + 16*a^2*b*c*d*e*f - 8*a^2*b*c^2*f^2 + 4*I*(a^3 - a*b^2)*d^2*f^2*x^2 + 8*I*(a^3 - a*b^2)*d^2*e*f*x + 8*I*(a^3 - a*b^2)*c*d*e*f - 4*I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (2*a^2*b*d^2*f^2*x^2 + 4*a^2*b*d^2*e*f*x + 4*a^2*b*c*d*e*f - 2*a^2*b*c^2*f^2 - I*(a^3 - a*b^2)*d^2*f^2*x^2 - 2*I*(a^3 - a*b^2)*d^2*e*f*x - 2*I*(a^3 - a*b^2)*c*d*e*f + I*(a^3 - a*b^2)*c^2*f^2 + (2*a^2*b*d^2*f^2*x^2 + 4*a^2*b*d^2*e*f*x + 4*a^2*b*c*d*e*f - 2*a^2*b*c^2*f^2 - I*(a^3 - a*b^2)*d^2*f^2*x^2 - 2*I*(a^3 - a*b^2)*d^2*e*f*x - 2*I*(a^3 - a*b^2)*c*d*e*f + I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c)^4 + (8*a^2*b*d^2*f^2*x^2 + 16*a^2*b*d^2*e*f*x + 16*a^2*b*c*d*e*f - 8*a^2*b*c^2*f^2 - 4*I*(a^3 - a*b^2)*d^2*f^2*x^2 - 8*I*(a^3 - a*b^2)*d^2*e*f*x - 8*I*(a^3 - a*b^2)*c*d*e*f + 4*I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b*d^2*f^2*x^2 + 4*a^2*b*d^2*e*f*x + 4*a^2*b*c*d*e*f - 2*a^2*b*c^2*f^2 - I*(a^3 - a*b^2)*d^2*f^2*x^2 - 2*I*(a^3 - a*b^2)*d^2*e*f*x - 2*I*(a^3 - a*b^2)*c*d*e*f + I*(a^3 - a*b^2)*c^2*f^2)*sinh(d*x + c)^4 + (4*a^2*b*d^2*f^2*x^2 + 8*a^2*b*d^2*e*f*x + 8*a^2*b*c*d*e*f - 4*a^2*b*c^2*f^2 - 2*I*(a^3 - a*b^2)*d^2*f^2*x^2 - 4*I*(a^3 - a*b^2)*d^2*e*f*x - 4*I*(a^3 - a*b^2)*c*d*e*f + 2*I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c)^2 + (4*a^2*b*d^2*f^2*x^2 + 8*a^2*b*d^2*e*f*x + 8*a^2*b*c*d*e*f - 4*a^2*b*c^2*f^2 - 2*I*(a^3 - a*b^2)*d^2*f^2*x^2 - 4*I*(a^3 - a*b^2)*d^2*e*f*x - 4*I*(a^3 - a*b^2)*c*d*e*f + 2*I*(a^3 - a*b^2)*c^2*f^2 + (12*a^2*b*d^2*f^2*x^2 + 24*a^2*b*d^2*e*f*x + 24*a^2*b*c*d*e*f - 12*a^2*b*c^2*f^2 - 6*I*(a^3 - a*b^2)*d^2*f^2*x^2 - 12*I*(a^3 - a*b^2)*d^2*e*f*x - 12*I*(a^3 - a*b^2)*c*d*e*f + 6*I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b*d^2*f^2*x^2 + 16*a^2*b*d^2*e*f*x + 16*a^2*b*c*d*e*f - 8*a^2*b*c^2*f^2 - 4*I*(a^3 - a*b^2)*d^2*f^2*x^2 - 8*I*(a^3 - a*b^2)*d^2*e*f*x - 8*I*(a^3 - a*b^2)*c*d*e*f + 4*I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c)^3 + (8*a^2*b*d^2*f^2*x^2 + 16*a^2*b*d^2*e*f*x + 16*a^2*b*c*d*e*f - 8*a^2*b*c^2*f^2 - 4*I*(a^3 - a*b^2)*d^2*f^2*x^2 - 8*I*(a^3 - a*b^2)*d^2*e*f*x - 8*I*(a^3 - a*b^2)*c*d*e*f + 4*I*(a^3 - a*b^2)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 4*(a^2*b*f^2*cosh(d*x + c)^4 + 4*a^2*b*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*b*f^2*sinh(d*x + c)^4 + 2*a^2*b*f^2*cosh(d*x + c)^2 + a^2*b*f^2 + 2*(3*a^2*b*f^2*cosh(d*x + c)^2 + a^2*b*f^2)*sinh(d*x + c)^2 + 4*(a^2*b*f^2*cosh(d*x + c)^3 + a^2*b*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 4*(a^2*b*f^2*cosh(d*x + c)^4 + 4*a^2*b*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*b*f^2*sinh(d*x + c)^4 + 2*a^2*b*f^2*cosh(d*x + c)^2 + a^2*b*f^2 + 2*(3*a^2*b*f^2*cosh(d*x + c)^2 + a^2*b*f^2)*sinh(d*x + c)^2 + 4*(a^2*b*f^2*cosh(d*x + c)^3 + a^2*b*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + (4*a^2*b*f^2 + (4*a^2*b*f^2 - 2*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c)^4 + (16*a^2*b*f^2 - 8*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a^2*b*f^2 - 2*I*(a^3 - a*b^2)*f^2)*sinh(d*x + c)^4 - 2*I*(a^3 - a*b^2)*f^2 + (8*a^2*b*f^2 - 4*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c)^2 + (8*a^2*b*f^2 - 4*I*(a^3 - a*b^2)*f^2 + (24*a^2*b*f^2 - 12*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*a^2*b*f^2 - 8*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c)^3 + (16*a^2*b*f^2 - 8*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + (4*a^2*b*f^2 + (4*a^2*b*f^2 + 2*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c)^4 + (16*a^2*b*f^2 + 8*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a^2*b*f^2 + 2*I*(a^3 - a*b^2)*f^2)*sinh(d*x + c)^4 + 2*I*(a^3 - a*b^2)*f^2 + (8*a^2*b*f^2 + 4*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c)^2 + (8*a^2*b*f^2 + 4*I*(a^3 - a*b^2)*f^2 + (24*a^2*b*f^2 + 12*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*a^2*b*f^2 + 8*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c)^3 + (16*a^2*b*f^2 + 8*I*(a^3 - a*b^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 - 2*(a^3 + a*b^2)*d*e*f + 8*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*c*f^2)*cosh(d*x + c)^3 - 3*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^3 + a*b^2)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^3 + a*b^2)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x - 4*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + (a^2*b + b^3)*d*e*f - 2*(a^2*b + b^3)*c*f^2 + (2*(a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^3*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3)*sinh(d*x + c)^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c))*sinh(d*x + c))","C",0
388,1,4873,0,0.927505," ","integrate((f*x+e)*sech(d*x+c)*tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d f x + 2 \, {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d f x + 2 \, {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f + 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e - {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right) - 2 \, {\left(a^{2} b f \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} b f \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b f \cosh\left(d x + c\right)^{2} + a^{2} b f + 2 \, {\left(3 \, a^{2} b f \cosh\left(d x + c\right)^{2} + a^{2} b f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b f \cosh\left(d x + c\right)^{3} + a^{2} b f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(a^{2} b f \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} b f \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b f \cosh\left(d x + c\right)^{2} + a^{2} b f + 2 \, {\left(3 \, a^{2} b f \cosh\left(d x + c\right)^{2} + a^{2} b f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b f \cosh\left(d x + c\right)^{3} + a^{2} b f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left({\left(2 \, a^{2} b f - i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} b f - 4 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b f - i \, {\left(a^{3} - a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b f + {\left(4 \, a^{2} b f - 2 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b f + {\left(12 \, a^{2} b f - 6 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} - i \, {\left(a^{3} - a b^{2}\right)} f + {\left({\left(8 \, a^{2} b f - 4 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b f - 4 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left({\left(2 \, a^{2} b f + i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} b f + 4 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b f + i \, {\left(a^{3} - a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b f + {\left(4 \, a^{2} b f + 2 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b f + {\left(12 \, a^{2} b f + 6 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 2 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + i \, {\left(a^{3} - a b^{2}\right)} f + {\left({\left(8 \, a^{2} b f + 4 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b f + 4 i \, {\left(a^{3} - a b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left(a^{2} b d e - a^{2} b c f + {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b d e - a^{2} b c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d e - a^{2} b c f + 3 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a^{2} b d e - a^{2} b c f + {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b d e - a^{2} b c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d e - a^{2} b c f + 3 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a^{2} b d f x + a^{2} b c f + {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b d f x + a^{2} b c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d f x + a^{2} b c f + 3 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a^{2} b d f x + a^{2} b c f + {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b d f x + a^{2} b c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b d f x + a^{2} b c f + 3 \, {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b d f x + a^{2} b c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(2 \, a^{2} b d e - 2 \, a^{2} b c f + {\left(2 \, a^{2} b d e - 2 \, a^{2} b c f - i \, {\left(a^{3} - a b^{2}\right)} d e + i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} b d e - 8 \, a^{2} b c f - 4 i \, {\left(a^{3} - a b^{2}\right)} d e + 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b d e - 2 \, a^{2} b c f - i \, {\left(a^{3} - a b^{2}\right)} d e + i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} - i \, {\left(a^{3} - a b^{2}\right)} d e + i \, {\left(a^{3} - a b^{2}\right)} c f + {\left(4 \, a^{2} b d e - 4 \, a^{2} b c f - 2 i \, {\left(a^{3} - a b^{2}\right)} d e + 2 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b d e - 4 \, a^{2} b c f - 2 i \, {\left(a^{3} - a b^{2}\right)} d e + 2 i \, {\left(a^{3} - a b^{2}\right)} c f + {\left(12 \, a^{2} b d e - 12 \, a^{2} b c f - 6 i \, {\left(a^{3} - a b^{2}\right)} d e + 6 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b d e - 8 \, a^{2} b c f - 4 i \, {\left(a^{3} - a b^{2}\right)} d e + 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b d e - 8 \, a^{2} b c f - 4 i \, {\left(a^{3} - a b^{2}\right)} d e + 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(2 \, a^{2} b d e - 2 \, a^{2} b c f + {\left(2 \, a^{2} b d e - 2 \, a^{2} b c f + i \, {\left(a^{3} - a b^{2}\right)} d e - i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} b d e - 8 \, a^{2} b c f + 4 i \, {\left(a^{3} - a b^{2}\right)} d e - 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b d e - 2 \, a^{2} b c f + i \, {\left(a^{3} - a b^{2}\right)} d e - i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + i \, {\left(a^{3} - a b^{2}\right)} d e - i \, {\left(a^{3} - a b^{2}\right)} c f + {\left(4 \, a^{2} b d e - 4 \, a^{2} b c f + 2 i \, {\left(a^{3} - a b^{2}\right)} d e - 2 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b d e - 4 \, a^{2} b c f + 2 i \, {\left(a^{3} - a b^{2}\right)} d e - 2 i \, {\left(a^{3} - a b^{2}\right)} c f + {\left(12 \, a^{2} b d e - 12 \, a^{2} b c f + 6 i \, {\left(a^{3} - a b^{2}\right)} d e - 6 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b d e - 8 \, a^{2} b c f + 4 i \, {\left(a^{3} - a b^{2}\right)} d e - 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b d e - 8 \, a^{2} b c f + 4 i \, {\left(a^{3} - a b^{2}\right)} d e - 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(2 \, a^{2} b d f x + 2 \, a^{2} b c f + {\left(2 \, a^{2} b d f x + 2 \, a^{2} b c f + i \, {\left(a^{3} - a b^{2}\right)} d f x + i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} b d f x + 8 \, a^{2} b c f + 4 i \, {\left(a^{3} - a b^{2}\right)} d f x + 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b d f x + 2 \, a^{2} b c f + i \, {\left(a^{3} - a b^{2}\right)} d f x + i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + i \, {\left(a^{3} - a b^{2}\right)} d f x + i \, {\left(a^{3} - a b^{2}\right)} c f + {\left(4 \, a^{2} b d f x + 4 \, a^{2} b c f + 2 i \, {\left(a^{3} - a b^{2}\right)} d f x + 2 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b d f x + 4 \, a^{2} b c f + 2 i \, {\left(a^{3} - a b^{2}\right)} d f x + 2 i \, {\left(a^{3} - a b^{2}\right)} c f + {\left(12 \, a^{2} b d f x + 12 \, a^{2} b c f + 6 i \, {\left(a^{3} - a b^{2}\right)} d f x + 6 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b d f x + 8 \, a^{2} b c f + 4 i \, {\left(a^{3} - a b^{2}\right)} d f x + 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b d f x + 8 \, a^{2} b c f + 4 i \, {\left(a^{3} - a b^{2}\right)} d f x + 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(2 \, a^{2} b d f x + 2 \, a^{2} b c f + {\left(2 \, a^{2} b d f x + 2 \, a^{2} b c f - i \, {\left(a^{3} - a b^{2}\right)} d f x - i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{2} b d f x + 8 \, a^{2} b c f - 4 i \, {\left(a^{3} - a b^{2}\right)} d f x - 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b d f x + 2 \, a^{2} b c f - i \, {\left(a^{3} - a b^{2}\right)} d f x - i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} - i \, {\left(a^{3} - a b^{2}\right)} d f x - i \, {\left(a^{3} - a b^{2}\right)} c f + {\left(4 \, a^{2} b d f x + 4 \, a^{2} b c f - 2 i \, {\left(a^{3} - a b^{2}\right)} d f x - 2 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{2} b d f x + 4 \, a^{2} b c f - 2 i \, {\left(a^{3} - a b^{2}\right)} d f x - 2 i \, {\left(a^{3} - a b^{2}\right)} c f + {\left(12 \, a^{2} b d f x + 12 \, a^{2} b c f - 6 i \, {\left(a^{3} - a b^{2}\right)} d f x - 6 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b d f x + 8 \, a^{2} b c f - 4 i \, {\left(a^{3} - a b^{2}\right)} d f x - 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b d f x + 8 \, a^{2} b c f - 4 i \, {\left(a^{3} - a b^{2}\right)} d f x - 4 i \, {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e - 3 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2}\right)} f - 2 \, {\left(2 \, {\left(a^{2} b + b^{3}\right)} d f x + 2 \, {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c)^3 + 2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*sinh(d*x + c)^3 + 2*(2*(a^2*b + b^3)*d*f*x + 2*(a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*cosh(d*x + c)^2 + 2*(2*(a^2*b + b^3)*d*f*x + 2*(a^2*b + b^3)*d*e + (a^2*b + b^3)*f + 3*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*(a^2*b + b^3)*f - 2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e - (a^3 + a*b^2)*f)*cosh(d*x + c) - 2*(a^2*b*f*cosh(d*x + c)^4 + 4*a^2*b*f*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*b*f*sinh(d*x + c)^4 + 2*a^2*b*f*cosh(d*x + c)^2 + a^2*b*f + 2*(3*a^2*b*f*cosh(d*x + c)^2 + a^2*b*f)*sinh(d*x + c)^2 + 4*(a^2*b*f*cosh(d*x + c)^3 + a^2*b*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(a^2*b*f*cosh(d*x + c)^4 + 4*a^2*b*f*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*b*f*sinh(d*x + c)^4 + 2*a^2*b*f*cosh(d*x + c)^2 + a^2*b*f + 2*(3*a^2*b*f*cosh(d*x + c)^2 + a^2*b*f)*sinh(d*x + c)^2 + 4*(a^2*b*f*cosh(d*x + c)^3 + a^2*b*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + ((2*a^2*b*f - I*(a^3 - a*b^2)*f)*cosh(d*x + c)^4 + (8*a^2*b*f - 4*I*(a^3 - a*b^2)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b*f - I*(a^3 - a*b^2)*f)*sinh(d*x + c)^4 + 2*a^2*b*f + (4*a^2*b*f - 2*I*(a^3 - a*b^2)*f)*cosh(d*x + c)^2 + (4*a^2*b*f + (12*a^2*b*f - 6*I*(a^3 - a*b^2)*f)*cosh(d*x + c)^2 - 2*I*(a^3 - a*b^2)*f)*sinh(d*x + c)^2 - I*(a^3 - a*b^2)*f + ((8*a^2*b*f - 4*I*(a^3 - a*b^2)*f)*cosh(d*x + c)^3 + (8*a^2*b*f - 4*I*(a^3 - a*b^2)*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + ((2*a^2*b*f + I*(a^3 - a*b^2)*f)*cosh(d*x + c)^4 + (8*a^2*b*f + 4*I*(a^3 - a*b^2)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b*f + I*(a^3 - a*b^2)*f)*sinh(d*x + c)^4 + 2*a^2*b*f + (4*a^2*b*f + 2*I*(a^3 - a*b^2)*f)*cosh(d*x + c)^2 + (4*a^2*b*f + (12*a^2*b*f + 6*I*(a^3 - a*b^2)*f)*cosh(d*x + c)^2 + 2*I*(a^3 - a*b^2)*f)*sinh(d*x + c)^2 + I*(a^3 - a*b^2)*f + ((8*a^2*b*f + 4*I*(a^3 - a*b^2)*f)*cosh(d*x + c)^3 + (8*a^2*b*f + 4*I*(a^3 - a*b^2)*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*(a^2*b*d*e - a^2*b*c*f + (a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^4 + 4*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b*d*e - a^2*b*c*f)*sinh(d*x + c)^4 + 2*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*e - a^2*b*c*f + 3*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^3 + (a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a^2*b*d*e - a^2*b*c*f + (a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^4 + 4*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b*d*e - a^2*b*c*f)*sinh(d*x + c)^4 + 2*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*e - a^2*b*c*f + 3*(a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c)^3 + (a^2*b*d*e - a^2*b*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a^2*b*d*f*x + a^2*b*c*f + (a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^4 + 4*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b*d*f*x + a^2*b*c*f)*sinh(d*x + c)^4 + 2*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*f*x + a^2*b*c*f + 3*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^3 + (a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(a^2*b*d*f*x + a^2*b*c*f + (a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^4 + 4*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b*d*f*x + a^2*b*c*f)*sinh(d*x + c)^4 + 2*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^2 + 2*(a^2*b*d*f*x + a^2*b*c*f + 3*(a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c)^3 + (a^2*b*d*f*x + a^2*b*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (2*a^2*b*d*e - 2*a^2*b*c*f + (2*a^2*b*d*e - 2*a^2*b*c*f - I*(a^3 - a*b^2)*d*e + I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^4 + (8*a^2*b*d*e - 8*a^2*b*c*f - 4*I*(a^3 - a*b^2)*d*e + 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b*d*e - 2*a^2*b*c*f - I*(a^3 - a*b^2)*d*e + I*(a^3 - a*b^2)*c*f)*sinh(d*x + c)^4 - I*(a^3 - a*b^2)*d*e + I*(a^3 - a*b^2)*c*f + (4*a^2*b*d*e - 4*a^2*b*c*f - 2*I*(a^3 - a*b^2)*d*e + 2*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^2 + (4*a^2*b*d*e - 4*a^2*b*c*f - 2*I*(a^3 - a*b^2)*d*e + 2*I*(a^3 - a*b^2)*c*f + (12*a^2*b*d*e - 12*a^2*b*c*f - 6*I*(a^3 - a*b^2)*d*e + 6*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b*d*e - 8*a^2*b*c*f - 4*I*(a^3 - a*b^2)*d*e + 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^3 + (8*a^2*b*d*e - 8*a^2*b*c*f - 4*I*(a^3 - a*b^2)*d*e + 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) + (2*a^2*b*d*e - 2*a^2*b*c*f + (2*a^2*b*d*e - 2*a^2*b*c*f + I*(a^3 - a*b^2)*d*e - I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^4 + (8*a^2*b*d*e - 8*a^2*b*c*f + 4*I*(a^3 - a*b^2)*d*e - 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b*d*e - 2*a^2*b*c*f + I*(a^3 - a*b^2)*d*e - I*(a^3 - a*b^2)*c*f)*sinh(d*x + c)^4 + I*(a^3 - a*b^2)*d*e - I*(a^3 - a*b^2)*c*f + (4*a^2*b*d*e - 4*a^2*b*c*f + 2*I*(a^3 - a*b^2)*d*e - 2*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^2 + (4*a^2*b*d*e - 4*a^2*b*c*f + 2*I*(a^3 - a*b^2)*d*e - 2*I*(a^3 - a*b^2)*c*f + (12*a^2*b*d*e - 12*a^2*b*c*f + 6*I*(a^3 - a*b^2)*d*e - 6*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b*d*e - 8*a^2*b*c*f + 4*I*(a^3 - a*b^2)*d*e - 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^3 + (8*a^2*b*d*e - 8*a^2*b*c*f + 4*I*(a^3 - a*b^2)*d*e - 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) + (2*a^2*b*d*f*x + 2*a^2*b*c*f + (2*a^2*b*d*f*x + 2*a^2*b*c*f + I*(a^3 - a*b^2)*d*f*x + I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^4 + (8*a^2*b*d*f*x + 8*a^2*b*c*f + 4*I*(a^3 - a*b^2)*d*f*x + 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b*d*f*x + 2*a^2*b*c*f + I*(a^3 - a*b^2)*d*f*x + I*(a^3 - a*b^2)*c*f)*sinh(d*x + c)^4 + I*(a^3 - a*b^2)*d*f*x + I*(a^3 - a*b^2)*c*f + (4*a^2*b*d*f*x + 4*a^2*b*c*f + 2*I*(a^3 - a*b^2)*d*f*x + 2*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^2 + (4*a^2*b*d*f*x + 4*a^2*b*c*f + 2*I*(a^3 - a*b^2)*d*f*x + 2*I*(a^3 - a*b^2)*c*f + (12*a^2*b*d*f*x + 12*a^2*b*c*f + 6*I*(a^3 - a*b^2)*d*f*x + 6*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b*d*f*x + 8*a^2*b*c*f + 4*I*(a^3 - a*b^2)*d*f*x + 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^3 + (8*a^2*b*d*f*x + 8*a^2*b*c*f + 4*I*(a^3 - a*b^2)*d*f*x + 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (2*a^2*b*d*f*x + 2*a^2*b*c*f + (2*a^2*b*d*f*x + 2*a^2*b*c*f - I*(a^3 - a*b^2)*d*f*x - I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^4 + (8*a^2*b*d*f*x + 8*a^2*b*c*f - 4*I*(a^3 - a*b^2)*d*f*x - 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b*d*f*x + 2*a^2*b*c*f - I*(a^3 - a*b^2)*d*f*x - I*(a^3 - a*b^2)*c*f)*sinh(d*x + c)^4 - I*(a^3 - a*b^2)*d*f*x - I*(a^3 - a*b^2)*c*f + (4*a^2*b*d*f*x + 4*a^2*b*c*f - 2*I*(a^3 - a*b^2)*d*f*x - 2*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^2 + (4*a^2*b*d*f*x + 4*a^2*b*c*f - 2*I*(a^3 - a*b^2)*d*f*x - 2*I*(a^3 - a*b^2)*c*f + (12*a^2*b*d*f*x + 12*a^2*b*c*f - 6*I*(a^3 - a*b^2)*d*f*x - 6*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b*d*f*x + 8*a^2*b*c*f - 4*I*(a^3 - a*b^2)*d*f*x - 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c)^3 + (8*a^2*b*d*f*x + 8*a^2*b*c*f - 4*I*(a^3 - a*b^2)*d*f*x - 4*I*(a^3 - a*b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e - 3*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c)^2 - (a^3 + a*b^2)*f - 2*(2*(a^2*b + b^3)*d*f*x + 2*(a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^2*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)*sinh(d*x + c)^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
389,1,917,0,0.509167," ","integrate(sech(d*x+c)*tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + a b^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} b + 2 \, b^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} - a b^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{3} - a b^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} - a b^{2} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right) - {\left(a^{2} b \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} b \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b \cosh\left(d x + c\right)^{2} + a^{2} b + 2 \, {\left(3 \, a^{2} b \cosh\left(d x + c\right)^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b \cosh\left(d x + c\right)^{3} + a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left(a^{2} b \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} b \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b \cosh\left(d x + c\right)^{2} + a^{2} b + 2 \, {\left(3 \, a^{2} b \cosh\left(d x + c\right)^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b \cosh\left(d x + c\right)^{3} + a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{3} + a b^{2} - 3 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"-((a^3 + a*b^2)*cosh(d*x + c)^3 + (a^3 + a*b^2)*sinh(d*x + c)^3 + 2*(a^2*b + b^3)*cosh(d*x + c)^2 + (2*a^2*b + 2*b^3 + 3*(a^3 + a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - ((a^3 - a*b^2)*cosh(d*x + c)^4 + 4*(a^3 - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 - a*b^2)*sinh(d*x + c)^4 + a^3 - a*b^2 + 2*(a^3 - a*b^2)*cosh(d*x + c)^2 + 2*(a^3 - a*b^2 + 3*(a^3 - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3 - a*b^2)*cosh(d*x + c)^3 + (a^3 - a*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - (a^3 + a*b^2)*cosh(d*x + c) - (a^2*b*cosh(d*x + c)^4 + 4*a^2*b*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*b*sinh(d*x + c)^4 + 2*a^2*b*cosh(d*x + c)^2 + a^2*b + 2*(3*a^2*b*cosh(d*x + c)^2 + a^2*b)*sinh(d*x + c)^2 + 4*(a^2*b*cosh(d*x + c)^3 + a^2*b*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + (a^2*b*cosh(d*x + c)^4 + 4*a^2*b*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*b*sinh(d*x + c)^4 + 2*a^2*b*cosh(d*x + c)^2 + a^2*b + 2*(3*a^2*b*cosh(d*x + c)^2 + a^2*b)*sinh(d*x + c)^2 + 4*(a^2*b*cosh(d*x + c)^3 + a^2*b*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (a^3 + a*b^2 - 3*(a^3 + a*b^2)*cosh(d*x + c)^2 - 4*(a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d)*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d + 4*((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
390,0,0,0,8.058838," ","integrate(sech(d*x+c)*tanh(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(d x + c\right) \tanh\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sech(d*x + c)*tanh(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
391,1,7020,0,0.610200," ","integrate((f*x+e)^3*cosh(d*x+c)*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{36 \, b^{3} d^{3} f^{3} x^{3} + 36 \, b^{3} d^{3} e^{3} + 36 \, b^{3} d^{2} e^{2} f + 24 \, b^{3} d e f^{2} - 4 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{6} + 8 \, b^{3} f^{3} + 27 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(36 \, a b^{2} d^{3} f^{3} x^{3} + 36 \, a b^{2} d^{3} e^{3} - 54 \, a b^{2} d^{2} e^{2} f + 54 \, a b^{2} d e f^{2} - 27 \, a b^{2} f^{3} + 54 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 54 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x - 8 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 108 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(36 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 36 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{3} - 108 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} f + 216 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f^{2} - 216 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{3} + 108 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 20 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 108 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d f^{3}\right)} x - 45 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 216 \, {\left(a^{3} d^{4} f^{3} x^{4} + 4 \, a^{3} d^{4} e f^{2} x^{3} + 6 \, a^{3} d^{4} e^{2} f x^{2} + 4 \, a^{3} d^{4} e^{3} x + 8 \, a^{3} c d^{3} e^{3} - 12 \, a^{3} c^{2} d^{2} e^{2} f + 8 \, a^{3} c^{3} d e f^{2} - 2 \, a^{3} c^{4} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(108 \, a^{3} d^{4} f^{3} x^{4} + 432 \, a^{3} d^{4} e f^{2} x^{3} + 648 \, a^{3} d^{4} e^{2} f x^{2} + 432 \, a^{3} d^{4} e^{3} x + 864 \, a^{3} c d^{3} e^{3} - 1296 \, a^{3} c^{2} d^{2} e^{2} f + 864 \, a^{3} c^{3} d e f^{2} - 216 \, a^{3} c^{4} f^{3} + 40 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 135 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 216 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 36 \, {\left(3 \, b^{3} d^{3} e f^{2} + b^{3} d^{2} f^{3}\right)} x^{2} + 108 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(18 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 18 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + 54 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} f + 108 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f^{2} - 10 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 108 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{3} + 45 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 54 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{3}\right)} x^{2} - 108 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 54 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d f^{3}\right)} x - 108 \, {\left(a^{3} d^{4} f^{3} x^{4} + 4 \, a^{3} d^{4} e f^{2} x^{3} + 6 \, a^{3} d^{4} e^{2} f x^{2} + 4 \, a^{3} d^{4} e^{3} x + 8 \, a^{3} c d^{3} e^{3} - 12 \, a^{3} c^{2} d^{2} e^{2} f + 8 \, a^{3} c^{3} d e f^{2} - 2 \, a^{3} c^{4} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left(9 \, b^{3} d^{3} e^{2} f + 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x + 27 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} + 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} + 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} + a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f + 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) + 2592 \, {\left({\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2592 \, {\left({\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 864 \, {\left({\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 864 \, {\left({\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 864 \, {\left({\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 864 \, {\left({\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 5184 \, {\left(a^{3} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{3} f^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{3} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{3} f^{3} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 5184 \, {\left(a^{3} f^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{3} f^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{3} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{3} f^{3} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 5184 \, {\left({\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 5184 \, {\left({\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 3 \, {\left(36 \, a b^{2} d^{3} f^{3} x^{3} + 36 \, a b^{2} d^{3} e^{3} + 54 \, a b^{2} d^{2} e^{2} f + 54 \, a b^{2} d e f^{2} + 27 \, a b^{2} f^{3} - 8 \, {\left(9 \, b^{3} d^{3} f^{3} x^{3} + 9 \, b^{3} d^{3} e^{3} - 9 \, b^{3} d^{2} e^{2} f + 6 \, b^{3} d e f^{2} - 2 \, b^{3} f^{3} + 9 \, {\left(3 \, b^{3} d^{3} e f^{2} - b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, b^{3} d^{3} e^{2} f - 6 \, b^{3} d^{2} e f^{2} + 2 \, b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 45 \, {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 \, a b^{2} d^{3} e^{3} - 6 \, a b^{2} d^{2} e^{2} f + 6 \, a b^{2} d e f^{2} - 3 \, a b^{2} f^{3} + 6 \, {\left(2 \, a b^{2} d^{3} e f^{2} - a b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a b^{2} d^{3} e^{2} f - 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 144 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 54 \, {\left(2 \, a b^{2} d^{3} e f^{2} + a b^{2} d^{2} f^{3}\right)} x^{2} - 216 \, {\left(a^{3} d^{4} f^{3} x^{4} + 4 \, a^{3} d^{4} e f^{2} x^{3} + 6 \, a^{3} d^{4} e^{2} f x^{2} + 4 \, a^{3} d^{4} e^{3} x + 8 \, a^{3} c d^{3} e^{3} - 12 \, a^{3} c^{2} d^{2} e^{2} f + 8 \, a^{3} c^{3} d e f^{2} - 2 \, a^{3} c^{4} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 54 \, {\left(2 \, a b^{2} d^{3} e^{2} f + 2 \, a b^{2} d^{2} e f^{2} + a b^{2} d f^{3}\right)} x + 72 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{864 \, {\left(b^{4} d^{4} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d^{4} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d^{4} \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"-1/864*(36*b^3*d^3*f^3*x^3 + 36*b^3*d^3*e^3 + 36*b^3*d^2*e^2*f + 24*b^3*d*e*f^2 - 4*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^6 - 4*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*sinh(d*x + c)^6 + 8*b^3*f^3 + 27*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^5 + 3*(36*a*b^2*d^3*f^3*x^3 + 36*a*b^2*d^3*e^3 - 54*a*b^2*d^2*e^2*f + 54*a*b^2*d*e*f^2 - 27*a*b^2*f^3 + 54*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 54*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x - 8*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 108*((4*a^2*b - b^3)*d^3*f^3*x^3 + (4*a^2*b - b^3)*d^3*e^3 - 3*(4*a^2*b - b^3)*d^2*e^2*f + 6*(4*a^2*b - b^3)*d*e*f^2 - 6*(4*a^2*b - b^3)*f^3 + 3*((4*a^2*b - b^3)*d^3*e*f^2 - (4*a^2*b - b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b - b^3)*d^3*e^2*f - 2*(4*a^2*b - b^3)*d^2*e*f^2 + 2*(4*a^2*b - b^3)*d*f^3)*x)*cosh(d*x + c)^4 - 3*(36*(4*a^2*b - b^3)*d^3*f^3*x^3 + 36*(4*a^2*b - b^3)*d^3*e^3 - 108*(4*a^2*b - b^3)*d^2*e^2*f + 216*(4*a^2*b - b^3)*d*e*f^2 - 216*(4*a^2*b - b^3)*f^3 + 108*((4*a^2*b - b^3)*d^3*e*f^2 - (4*a^2*b - b^3)*d^2*f^3)*x^2 + 20*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^2 + 108*((4*a^2*b - b^3)*d^3*e^2*f - 2*(4*a^2*b - b^3)*d^2*e*f^2 + 2*(4*a^2*b - b^3)*d*f^3)*x - 45*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^4 - 216*(a^3*d^4*f^3*x^4 + 4*a^3*d^4*e*f^2*x^3 + 6*a^3*d^4*e^2*f*x^2 + 4*a^3*d^4*e^3*x + 8*a^3*c*d^3*e^3 - 12*a^3*c^2*d^2*e^2*f + 8*a^3*c^3*d*e*f^2 - 2*a^3*c^4*f^3)*cosh(d*x + c)^3 - 2*(108*a^3*d^4*f^3*x^4 + 432*a^3*d^4*e*f^2*x^3 + 648*a^3*d^4*e^2*f*x^2 + 432*a^3*d^4*e^3*x + 864*a^3*c*d^3*e^3 - 1296*a^3*c^2*d^2*e^2*f + 864*a^3*c^3*d*e*f^2 - 216*a^3*c^4*f^3 + 40*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^3 - 135*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^2 + 216*((4*a^2*b - b^3)*d^3*f^3*x^3 + (4*a^2*b - b^3)*d^3*e^3 - 3*(4*a^2*b - b^3)*d^2*e^2*f + 6*(4*a^2*b - b^3)*d*e*f^2 - 6*(4*a^2*b - b^3)*f^3 + 3*((4*a^2*b - b^3)*d^3*e*f^2 - (4*a^2*b - b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b - b^3)*d^3*e^2*f - 2*(4*a^2*b - b^3)*d^2*e*f^2 + 2*(4*a^2*b - b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 36*(3*b^3*d^3*e*f^2 + b^3*d^2*f^3)*x^2 + 108*((4*a^2*b - b^3)*d^3*f^3*x^3 + (4*a^2*b - b^3)*d^3*e^3 + 3*(4*a^2*b - b^3)*d^2*e^2*f + 6*(4*a^2*b - b^3)*d*e*f^2 + 6*(4*a^2*b - b^3)*f^3 + 3*((4*a^2*b - b^3)*d^3*e*f^2 + (4*a^2*b - b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b - b^3)*d^3*e^2*f + 2*(4*a^2*b - b^3)*d^2*e*f^2 + 2*(4*a^2*b - b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 6*(18*(4*a^2*b - b^3)*d^3*f^3*x^3 + 18*(4*a^2*b - b^3)*d^3*e^3 + 54*(4*a^2*b - b^3)*d^2*e^2*f + 108*(4*a^2*b - b^3)*d*e*f^2 - 10*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^4 + 108*(4*a^2*b - b^3)*f^3 + 45*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^3 + 54*((4*a^2*b - b^3)*d^3*e*f^2 + (4*a^2*b - b^3)*d^2*f^3)*x^2 - 108*((4*a^2*b - b^3)*d^3*f^3*x^3 + (4*a^2*b - b^3)*d^3*e^3 - 3*(4*a^2*b - b^3)*d^2*e^2*f + 6*(4*a^2*b - b^3)*d*e*f^2 - 6*(4*a^2*b - b^3)*f^3 + 3*((4*a^2*b - b^3)*d^3*e*f^2 - (4*a^2*b - b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b - b^3)*d^3*e^2*f - 2*(4*a^2*b - b^3)*d^2*e*f^2 + 2*(4*a^2*b - b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 54*((4*a^2*b - b^3)*d^3*e^2*f + 2*(4*a^2*b - b^3)*d^2*e*f^2 + 2*(4*a^2*b - b^3)*d*f^3)*x - 108*(a^3*d^4*f^3*x^4 + 4*a^3*d^4*e*f^2*x^3 + 6*a^3*d^4*e^2*f*x^2 + 4*a^3*d^4*e^3*x + 8*a^3*c*d^3*e^3 - 12*a^3*c^2*d^2*e^2*f + 8*a^3*c^3*d*e*f^2 - 2*a^3*c^4*f^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 12*(9*b^3*d^3*e^2*f + 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x + 27*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 + 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 + 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 + a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f + 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c) + 2592*((a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*cosh(d*x + c)^3 + 3*(a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2592*((a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*cosh(d*x + c)^3 + 3*(a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 864*((a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*cosh(d*x + c)^3 + 3*(a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 864*((a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*cosh(d*x + c)^3 + 3*(a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 864*((a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*cosh(d*x + c)^3 + 3*(a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 864*((a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*cosh(d*x + c)^3 + 3*(a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 5184*(a^3*f^3*cosh(d*x + c)^3 + 3*a^3*f^3*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^3*f^3*cosh(d*x + c)*sinh(d*x + c)^2 + a^3*f^3*sinh(d*x + c)^3)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 5184*(a^3*f^3*cosh(d*x + c)^3 + 3*a^3*f^3*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^3*f^3*cosh(d*x + c)*sinh(d*x + c)^2 + a^3*f^3*sinh(d*x + c)^3)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 5184*((a^3*d*f^3*x + a^3*d*e*f^2)*cosh(d*x + c)^3 + 3*(a^3*d*f^3*x + a^3*d*e*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d*f^3*x + a^3*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d*f^3*x + a^3*d*e*f^2)*sinh(d*x + c)^3)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 5184*((a^3*d*f^3*x + a^3*d*e*f^2)*cosh(d*x + c)^3 + 3*(a^3*d*f^3*x + a^3*d*e*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d*f^3*x + a^3*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d*f^3*x + a^3*d*e*f^2)*sinh(d*x + c)^3)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 3*(36*a*b^2*d^3*f^3*x^3 + 36*a*b^2*d^3*e^3 + 54*a*b^2*d^2*e^2*f + 54*a*b^2*d*e*f^2 + 27*a*b^2*f^3 - 8*(9*b^3*d^3*f^3*x^3 + 9*b^3*d^3*e^3 - 9*b^3*d^2*e^2*f + 6*b^3*d*e*f^2 - 2*b^3*f^3 + 9*(3*b^3*d^3*e*f^2 - b^3*d^2*f^3)*x^2 + 3*(9*b^3*d^3*e^2*f - 6*b^3*d^2*e*f^2 + 2*b^3*d*f^3)*x)*cosh(d*x + c)^5 + 45*(4*a*b^2*d^3*f^3*x^3 + 4*a*b^2*d^3*e^3 - 6*a*b^2*d^2*e^2*f + 6*a*b^2*d*e*f^2 - 3*a*b^2*f^3 + 6*(2*a*b^2*d^3*e*f^2 - a*b^2*d^2*f^3)*x^2 + 6*(2*a*b^2*d^3*e^2*f - 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x)*cosh(d*x + c)^4 - 144*((4*a^2*b - b^3)*d^3*f^3*x^3 + (4*a^2*b - b^3)*d^3*e^3 - 3*(4*a^2*b - b^3)*d^2*e^2*f + 6*(4*a^2*b - b^3)*d*e*f^2 - 6*(4*a^2*b - b^3)*f^3 + 3*((4*a^2*b - b^3)*d^3*e*f^2 - (4*a^2*b - b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b - b^3)*d^3*e^2*f - 2*(4*a^2*b - b^3)*d^2*e*f^2 + 2*(4*a^2*b - b^3)*d*f^3)*x)*cosh(d*x + c)^3 + 54*(2*a*b^2*d^3*e*f^2 + a*b^2*d^2*f^3)*x^2 - 216*(a^3*d^4*f^3*x^4 + 4*a^3*d^4*e*f^2*x^3 + 6*a^3*d^4*e^2*f*x^2 + 4*a^3*d^4*e^3*x + 8*a^3*c*d^3*e^3 - 12*a^3*c^2*d^2*e^2*f + 8*a^3*c^3*d*e*f^2 - 2*a^3*c^4*f^3)*cosh(d*x + c)^2 + 54*(2*a*b^2*d^3*e^2*f + 2*a*b^2*d^2*e*f^2 + a*b^2*d*f^3)*x + 72*((4*a^2*b - b^3)*d^3*f^3*x^3 + (4*a^2*b - b^3)*d^3*e^3 + 3*(4*a^2*b - b^3)*d^2*e^2*f + 6*(4*a^2*b - b^3)*d*e*f^2 + 6*(4*a^2*b - b^3)*f^3 + 3*((4*a^2*b - b^3)*d^3*e*f^2 + (4*a^2*b - b^3)*d^2*f^3)*x^2 + 3*((4*a^2*b - b^3)*d^3*e^2*f + 2*(4*a^2*b - b^3)*d^2*e*f^2 + 2*(4*a^2*b - b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d^4*cosh(d*x + c)^3 + 3*b^4*d^4*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d^4*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d^4*sinh(d*x + c)^3)","C",0
392,1,4263,0,0.498121," ","integrate((f*x+e)^2*cosh(d*x+c)*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{18 \, b^{3} d^{2} f^{2} x^{2} + 18 \, b^{3} d^{2} e^{2} - 2 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 2 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{6} + 12 \, b^{3} d e f + 27 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(18 \, a b^{2} d^{2} f^{2} x^{2} + 18 \, a b^{2} d^{2} e^{2} - 18 \, a b^{2} d e f + 9 \, a b^{2} f^{2} + 18 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x - 4 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, b^{3} f^{2} - 54 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b - b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(18 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 18 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} - 36 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f + 36 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{2} + 10 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 36 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b - b^{3}\right)} d f^{2}\right)} x - 45 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 144 \, {\left(a^{3} d^{3} f^{2} x^{3} + 3 \, a^{3} d^{3} e f x^{2} + 3 \, a^{3} d^{3} e^{2} x + 6 \, a^{3} c d^{2} e^{2} - 6 \, a^{3} c^{2} d e f + 2 \, a^{3} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(72 \, a^{3} d^{3} f^{2} x^{3} + 216 \, a^{3} d^{3} e f x^{2} + 216 \, a^{3} d^{3} e^{2} x + 432 \, a^{3} c d^{2} e^{2} - 432 \, a^{3} c^{2} d e f + 144 \, a^{3} c^{3} f^{2} + 20 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 135 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 108 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b - b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 54 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f + {\left(4 \, a^{2} b - b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(9 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} - 5 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f + 45 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 18 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{2} - 54 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b - b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 18 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f + {\left(4 \, a^{2} b - b^{3}\right)} d f^{2}\right)} x - 72 \, {\left(a^{3} d^{3} f^{2} x^{3} + 3 \, a^{3} d^{3} e f x^{2} + 3 \, a^{3} d^{3} e^{2} x + 6 \, a^{3} c d^{2} e^{2} - 6 \, a^{3} c^{2} d e f + 2 \, a^{3} c^{3} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left(3 \, b^{3} d^{2} e f + b^{3} d f^{2}\right)} x + 27 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} + 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f + a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 864 \, {\left({\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 864 \, {\left({\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 432 \, {\left({\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 432 \, {\left({\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 432 \, {\left({\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 432 \, {\left({\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 864 \, {\left(a^{3} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{3} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{3} f^{2} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 864 \, {\left(a^{3} f^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{3} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{3} f^{2} \sinh\left(d x + c\right)^{3}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 3 \, {\left(18 \, a b^{2} d^{2} f^{2} x^{2} + 18 \, a b^{2} d^{2} e^{2} + 18 \, a b^{2} d e f - 4 \, {\left(9 \, b^{3} d^{2} f^{2} x^{2} + 9 \, b^{3} d^{2} e^{2} - 6 \, b^{3} d e f + 2 \, b^{3} f^{2} + 6 \, {\left(3 \, b^{3} d^{2} e f - b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 9 \, a b^{2} f^{2} + 45 \, {\left(2 \, a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} d^{2} e^{2} - 2 \, a b^{2} d e f + a b^{2} f^{2} + 2 \, {\left(2 \, a b^{2} d^{2} e f - a b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 72 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f - {\left(4 \, a^{2} b - b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 144 \, {\left(a^{3} d^{3} f^{2} x^{3} + 3 \, a^{3} d^{3} e f x^{2} + 3 \, a^{3} d^{3} e^{2} x + 6 \, a^{3} c d^{2} e^{2} - 6 \, a^{3} c^{2} d e f + 2 \, a^{3} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 18 \, {\left(2 \, a b^{2} d^{2} e f + a b^{2} d f^{2}\right)} x + 36 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} d e f + 2 \, {\left(4 \, a^{2} b - b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d^{2} e f + {\left(4 \, a^{2} b - b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{432 \, {\left(b^{4} d^{3} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d^{3} \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"-1/432*(18*b^3*d^2*f^2*x^2 + 18*b^3*d^2*e^2 - 2*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^6 - 2*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*sinh(d*x + c)^6 + 12*b^3*d*e*f + 27*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^5 + 3*(18*a*b^2*d^2*f^2*x^2 + 18*a*b^2*d^2*e^2 - 18*a*b^2*d*e*f + 9*a*b^2*f^2 + 18*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x - 4*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*b^3*f^2 - 54*((4*a^2*b - b^3)*d^2*f^2*x^2 + (4*a^2*b - b^3)*d^2*e^2 - 2*(4*a^2*b - b^3)*d*e*f + 2*(4*a^2*b - b^3)*f^2 + 2*((4*a^2*b - b^3)*d^2*e*f - (4*a^2*b - b^3)*d*f^2)*x)*cosh(d*x + c)^4 - 3*(18*(4*a^2*b - b^3)*d^2*f^2*x^2 + 18*(4*a^2*b - b^3)*d^2*e^2 - 36*(4*a^2*b - b^3)*d*e*f + 36*(4*a^2*b - b^3)*f^2 + 10*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^2 + 36*((4*a^2*b - b^3)*d^2*e*f - (4*a^2*b - b^3)*d*f^2)*x - 45*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^4 - 144*(a^3*d^3*f^2*x^3 + 3*a^3*d^3*e*f*x^2 + 3*a^3*d^3*e^2*x + 6*a^3*c*d^2*e^2 - 6*a^3*c^2*d*e*f + 2*a^3*c^3*f^2)*cosh(d*x + c)^3 - 2*(72*a^3*d^3*f^2*x^3 + 216*a^3*d^3*e*f*x^2 + 216*a^3*d^3*e^2*x + 432*a^3*c*d^2*e^2 - 432*a^3*c^2*d*e*f + 144*a^3*c^3*f^2 + 20*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^3 - 135*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^2 + 108*((4*a^2*b - b^3)*d^2*f^2*x^2 + (4*a^2*b - b^3)*d^2*e^2 - 2*(4*a^2*b - b^3)*d*e*f + 2*(4*a^2*b - b^3)*f^2 + 2*((4*a^2*b - b^3)*d^2*e*f - (4*a^2*b - b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 54*((4*a^2*b - b^3)*d^2*f^2*x^2 + (4*a^2*b - b^3)*d^2*e^2 + 2*(4*a^2*b - b^3)*d*e*f + 2*(4*a^2*b - b^3)*f^2 + 2*((4*a^2*b - b^3)*d^2*e*f + (4*a^2*b - b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 6*(9*(4*a^2*b - b^3)*d^2*f^2*x^2 + 9*(4*a^2*b - b^3)*d^2*e^2 - 5*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^4 + 18*(4*a^2*b - b^3)*d*e*f + 45*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^3 + 18*(4*a^2*b - b^3)*f^2 - 54*((4*a^2*b - b^3)*d^2*f^2*x^2 + (4*a^2*b - b^3)*d^2*e^2 - 2*(4*a^2*b - b^3)*d*e*f + 2*(4*a^2*b - b^3)*f^2 + 2*((4*a^2*b - b^3)*d^2*e*f - (4*a^2*b - b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 18*((4*a^2*b - b^3)*d^2*e*f + (4*a^2*b - b^3)*d*f^2)*x - 72*(a^3*d^3*f^2*x^3 + 3*a^3*d^3*e*f*x^2 + 3*a^3*d^3*e^2*x + 6*a^3*c*d^2*e^2 - 6*a^3*c^2*d*e*f + 2*a^3*c^3*f^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 12*(3*b^3*d^2*e*f + b^3*d*f^2)*x + 27*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 + 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f + a*b^2*d*f^2)*x)*cosh(d*x + c) + 864*((a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^3 + 3*(a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d*f^2*x + a^3*d*e*f)*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 864*((a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^3 + 3*(a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d*f^2*x + a^3*d*e*f)*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 432*((a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^3 + 3*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 432*((a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^3 + 3*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 432*((a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^3 + 3*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 432*((a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^3 + 3*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 864*(a^3*f^2*cosh(d*x + c)^3 + 3*a^3*f^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^3*f^2*cosh(d*x + c)*sinh(d*x + c)^2 + a^3*f^2*sinh(d*x + c)^3)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 864*(a^3*f^2*cosh(d*x + c)^3 + 3*a^3*f^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^3*f^2*cosh(d*x + c)*sinh(d*x + c)^2 + a^3*f^2*sinh(d*x + c)^3)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 3*(18*a*b^2*d^2*f^2*x^2 + 18*a*b^2*d^2*e^2 + 18*a*b^2*d*e*f - 4*(9*b^3*d^2*f^2*x^2 + 9*b^3*d^2*e^2 - 6*b^3*d*e*f + 2*b^3*f^2 + 6*(3*b^3*d^2*e*f - b^3*d*f^2)*x)*cosh(d*x + c)^5 + 9*a*b^2*f^2 + 45*(2*a*b^2*d^2*f^2*x^2 + 2*a*b^2*d^2*e^2 - 2*a*b^2*d*e*f + a*b^2*f^2 + 2*(2*a*b^2*d^2*e*f - a*b^2*d*f^2)*x)*cosh(d*x + c)^4 - 72*((4*a^2*b - b^3)*d^2*f^2*x^2 + (4*a^2*b - b^3)*d^2*e^2 - 2*(4*a^2*b - b^3)*d*e*f + 2*(4*a^2*b - b^3)*f^2 + 2*((4*a^2*b - b^3)*d^2*e*f - (4*a^2*b - b^3)*d*f^2)*x)*cosh(d*x + c)^3 - 144*(a^3*d^3*f^2*x^3 + 3*a^3*d^3*e*f*x^2 + 3*a^3*d^3*e^2*x + 6*a^3*c*d^2*e^2 - 6*a^3*c^2*d*e*f + 2*a^3*c^3*f^2)*cosh(d*x + c)^2 + 18*(2*a*b^2*d^2*e*f + a*b^2*d*f^2)*x + 36*((4*a^2*b - b^3)*d^2*f^2*x^2 + (4*a^2*b - b^3)*d^2*e^2 + 2*(4*a^2*b - b^3)*d*e*f + 2*(4*a^2*b - b^3)*f^2 + 2*((4*a^2*b - b^3)*d^2*e*f + (4*a^2*b - b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d^3*cosh(d*x + c)^3 + 3*b^4*d^3*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d^3*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d^3*sinh(d*x + c)^3)","C",0
393,1,2129,0,0.521661," ","integrate((f*x+e)*cosh(d*x+c)*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \sinh\left(d x + c\right)^{6} - 6 \, b^{3} d f x - 9 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{5} - 3 \, {\left(6 \, a b^{2} d f x + 6 \, a b^{2} d e - 3 \, a b^{2} f - 4 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 6 \, b^{3} d e + 18 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d f x + {\left(4 \, a^{2} b - b^{3}\right)} d e - {\left(4 \, a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, {\left(4 \, a^{2} b - b^{3}\right)} d f x + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} d e + 10 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(4 \, a^{2} b - b^{3}\right)} f - 15 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, b^{3} f + 72 \, {\left(a^{3} d^{2} f x^{2} + 2 \, a^{3} d^{2} e x + 4 \, a^{3} c d e - 2 \, a^{3} c^{2} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(36 \, a^{3} d^{2} f x^{2} + 72 \, a^{3} d^{2} e x + 144 \, a^{3} c d e - 72 \, a^{3} c^{2} f + 20 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{3} - 45 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{2} + 36 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d f x + {\left(4 \, a^{2} b - b^{3}\right)} d e - {\left(4 \, a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 18 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d f x + {\left(4 \, a^{2} b - b^{3}\right)} d e + {\left(4 \, a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(5 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(4 \, a^{2} b - b^{3}\right)} d f x - 15 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{2} b - b^{3}\right)} d e + 18 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d f x + {\left(4 \, a^{2} b - b^{3}\right)} d e - {\left(4 \, a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(4 \, a^{2} b - b^{3}\right)} f + 36 \, {\left(a^{3} d^{2} f x^{2} + 2 \, a^{3} d^{2} e x + 4 \, a^{3} c d e - 2 \, a^{3} c^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 9 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e + a b^{2} f\right)} \cosh\left(d x + c\right) - 144 \, {\left(a^{3} f \cosh\left(d x + c\right)^{3} + 3 \, a^{3} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{3} f \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 144 \, {\left(a^{3} f \cosh\left(d x + c\right)^{3} + 3 \, a^{3} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{3} f \sinh\left(d x + c\right)^{3}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 144 \, {\left({\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d e - a^{3} c f\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 144 \, {\left({\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d e - a^{3} c f\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 144 \, {\left({\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d f x + a^{3} c f\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 144 \, {\left({\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{3} d f x + a^{3} c f\right)} \sinh\left(d x + c\right)^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left(6 \, a b^{2} d f x - 4 \, {\left(3 \, b^{3} d f x + 3 \, b^{3} d e - b^{3} f\right)} \cosh\left(d x + c\right)^{5} + 6 \, a b^{2} d e + 15 \, {\left(2 \, a b^{2} d f x + 2 \, a b^{2} d e - a b^{2} f\right)} \cosh\left(d x + c\right)^{4} + 3 \, a b^{2} f - 24 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d f x + {\left(4 \, a^{2} b - b^{3}\right)} d e - {\left(4 \, a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} - 72 \, {\left(a^{3} d^{2} f x^{2} + 2 \, a^{3} d^{2} e x + 4 \, a^{3} c d e - 2 \, a^{3} c^{2} f\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left({\left(4 \, a^{2} b - b^{3}\right)} d f x + {\left(4 \, a^{2} b - b^{3}\right)} d e + {\left(4 \, a^{2} b - b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{144 \, {\left(b^{4} d^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d^{2} \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/144*(2*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^6 + 2*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*sinh(d*x + c)^6 - 6*b^3*d*f*x - 9*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^5 - 3*(6*a*b^2*d*f*x + 6*a*b^2*d*e - 3*a*b^2*f - 4*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c))*sinh(d*x + c)^5 - 6*b^3*d*e + 18*((4*a^2*b - b^3)*d*f*x + (4*a^2*b - b^3)*d*e - (4*a^2*b - b^3)*f)*cosh(d*x + c)^4 + 3*(6*(4*a^2*b - b^3)*d*f*x + 6*(4*a^2*b - b^3)*d*e + 10*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^2 - 6*(4*a^2*b - b^3)*f - 15*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*b^3*f + 72*(a^3*d^2*f*x^2 + 2*a^3*d^2*e*x + 4*a^3*c*d*e - 2*a^3*c^2*f)*cosh(d*x + c)^3 + 2*(36*a^3*d^2*f*x^2 + 72*a^3*d^2*e*x + 144*a^3*c*d*e - 72*a^3*c^2*f + 20*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^3 - 45*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^2 + 36*((4*a^2*b - b^3)*d*f*x + (4*a^2*b - b^3)*d*e - (4*a^2*b - b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^3 - 18*((4*a^2*b - b^3)*d*f*x + (4*a^2*b - b^3)*d*e + (4*a^2*b - b^3)*f)*cosh(d*x + c)^2 + 6*(5*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^4 - 3*(4*a^2*b - b^3)*d*f*x - 15*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^3 - 3*(4*a^2*b - b^3)*d*e + 18*((4*a^2*b - b^3)*d*f*x + (4*a^2*b - b^3)*d*e - (4*a^2*b - b^3)*f)*cosh(d*x + c)^2 - 3*(4*a^2*b - b^3)*f + 36*(a^3*d^2*f*x^2 + 2*a^3*d^2*e*x + 4*a^3*c*d*e - 2*a^3*c^2*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 9*(2*a*b^2*d*f*x + 2*a*b^2*d*e + a*b^2*f)*cosh(d*x + c) - 144*(a^3*f*cosh(d*x + c)^3 + 3*a^3*f*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^3*f*cosh(d*x + c)*sinh(d*x + c)^2 + a^3*f*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 144*(a^3*f*cosh(d*x + c)^3 + 3*a^3*f*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^3*f*cosh(d*x + c)*sinh(d*x + c)^2 + a^3*f*sinh(d*x + c)^3)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 144*((a^3*d*e - a^3*c*f)*cosh(d*x + c)^3 + 3*(a^3*d*e - a^3*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d*e - a^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d*e - a^3*c*f)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 144*((a^3*d*e - a^3*c*f)*cosh(d*x + c)^3 + 3*(a^3*d*e - a^3*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d*e - a^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d*e - a^3*c*f)*sinh(d*x + c)^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 144*((a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^3 + 3*(a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d*f*x + a^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d*f*x + a^3*c*f)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 144*((a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^3 + 3*(a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^3*d*f*x + a^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^3*d*f*x + a^3*c*f)*sinh(d*x + c)^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 3*(6*a*b^2*d*f*x - 4*(3*b^3*d*f*x + 3*b^3*d*e - b^3*f)*cosh(d*x + c)^5 + 6*a*b^2*d*e + 15*(2*a*b^2*d*f*x + 2*a*b^2*d*e - a*b^2*f)*cosh(d*x + c)^4 + 3*a*b^2*f - 24*((4*a^2*b - b^3)*d*f*x + (4*a^2*b - b^3)*d*e - (4*a^2*b - b^3)*f)*cosh(d*x + c)^3 - 72*(a^3*d^2*f*x^2 + 2*a^3*d^2*e*x + 4*a^3*c*d*e - 2*a^3*c^2*f)*cosh(d*x + c)^2 + 12*((4*a^2*b - b^3)*d*f*x + (4*a^2*b - b^3)*d*e + (4*a^2*b - b^3)*f)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d^2*cosh(d*x + c)^3 + 3*b^4*d^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d^2*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d^2*sinh(d*x + c)^3)","B",0
394,1,602,0,0.431948," ","integrate(cosh(d*x+c)*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{b^{3} \cosh\left(d x + c\right)^{6} + b^{3} \sinh\left(d x + c\right)^{6} + 24 \, a^{3} d x \cosh\left(d x + c\right)^{3} - 3 \, a b^{2} \cosh\left(d x + c\right)^{5} + 3 \, {\left(2 \, b^{3} \cosh\left(d x + c\right) - a b^{2}\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(4 \, a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{2} - 5 \, a b^{2} \cosh\left(d x + c\right) + 4 \, a^{2} b - b^{3}\right)} \sinh\left(d x + c\right)^{4} - 3 \, a b^{2} \cosh\left(d x + c\right) + 2 \, {\left(10 \, b^{3} \cosh\left(d x + c\right)^{3} + 12 \, a^{3} d x - 15 \, a b^{2} \cosh\left(d x + c\right)^{2} + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - b^{3} - 3 \, {\left(4 \, a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{4} + 24 \, a^{3} d x \cosh\left(d x + c\right) - 10 \, a b^{2} \cosh\left(d x + c\right)^{3} - 4 \, a^{2} b + b^{3} + 6 \, {\left(4 \, a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 24 \, {\left(a^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{3} \sinh\left(d x + c\right)^{3}\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 3 \, {\left(2 \, b^{3} \cosh\left(d x + c\right)^{5} + 24 \, a^{3} d x \cosh\left(d x + c\right)^{2} - 5 \, a b^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{3} - a b^{2} - 2 \, {\left(4 \, a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, b^{4} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{4} d \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/24*(b^3*cosh(d*x + c)^6 + b^3*sinh(d*x + c)^6 + 24*a^3*d*x*cosh(d*x + c)^3 - 3*a*b^2*cosh(d*x + c)^5 + 3*(2*b^3*cosh(d*x + c) - a*b^2)*sinh(d*x + c)^5 + 3*(4*a^2*b - b^3)*cosh(d*x + c)^4 + 3*(5*b^3*cosh(d*x + c)^2 - 5*a*b^2*cosh(d*x + c) + 4*a^2*b - b^3)*sinh(d*x + c)^4 - 3*a*b^2*cosh(d*x + c) + 2*(10*b^3*cosh(d*x + c)^3 + 12*a^3*d*x - 15*a*b^2*cosh(d*x + c)^2 + 6*(4*a^2*b - b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - b^3 - 3*(4*a^2*b - b^3)*cosh(d*x + c)^2 + 3*(5*b^3*cosh(d*x + c)^4 + 24*a^3*d*x*cosh(d*x + c) - 10*a*b^2*cosh(d*x + c)^3 - 4*a^2*b + b^3 + 6*(4*a^2*b - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 24*(a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^3*cosh(d*x + c)*sinh(d*x + c)^2 + a^3*sinh(d*x + c)^3)*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + 3*(2*b^3*cosh(d*x + c)^5 + 24*a^3*d*x*cosh(d*x + c)^2 - 5*a*b^2*cosh(d*x + c)^4 + 4*(4*a^2*b - b^3)*cosh(d*x + c)^3 - a*b^2 - 2*(4*a^2*b - b^3)*cosh(d*x + c))*sinh(d*x + c))/(b^4*d*cosh(d*x + c)^3 + 3*b^4*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^4*d*cosh(d*x + c)*sinh(d*x + c)^2 + b^4*d*sinh(d*x + c)^3)","B",0
395,0,0,0,0.495190," ","integrate(cosh(d*x+c)*sinh(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)*sinh(d*x + c)^3/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
396,1,10658,0,0.668559," ","integrate((f*x+e)^3*cosh(d*x+c)^2*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{864 \, b^{4} d^{3} f^{3} x^{3} + 864 \, b^{4} d^{3} e^{3} + 648 \, b^{4} d^{2} e^{2} f - 27 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{8} - 27 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{8} + 324 \, b^{4} d e f^{2} + 256 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{7} + 8 \, {\left(288 \, a b^{3} d^{3} f^{3} x^{3} + 288 \, a b^{3} d^{3} e^{3} - 288 \, a b^{3} d^{2} e^{2} f + 192 \, a b^{3} d e f^{2} - 64 \, a b^{3} f^{3} + 288 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 96 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x - 27 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 81 \, b^{4} f^{3} - 1728 \, {\left(4 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 4 \, a^{2} b^{2} d^{3} e^{3} - 6 \, a^{2} b^{2} d^{2} e^{2} f + 6 \, a^{2} b^{2} d e f^{2} - 3 \, a^{2} b^{2} f^{3} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e f^{2} - a^{2} b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f - 2 \, a^{2} b^{2} d^{2} e f^{2} + a^{2} b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(1728 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 1728 \, a^{2} b^{2} d^{3} e^{3} - 2592 \, a^{2} b^{2} d^{2} e^{2} f + 2592 \, a^{2} b^{2} d e f^{2} - 1296 \, a^{2} b^{2} f^{3} + 2592 \, {\left(2 \, a^{2} b^{2} d^{3} e f^{2} - a^{2} b^{2} d^{2} f^{3}\right)} x^{2} + 189 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2592 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f - 2 \, a^{2} b^{2} d^{2} e f^{2} + a^{2} b^{2} d f^{3}\right)} x - 448 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6912 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 24 \, {\left(288 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + 288 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{3} - 864 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 1728 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f^{2} - 1728 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{3} - 63 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 864 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 224 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 864 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f^{3}\right)} x - 432 \, {\left(4 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 4 \, a^{2} b^{2} d^{3} e^{3} - 6 \, a^{2} b^{2} d^{2} e^{2} f + 6 \, a^{2} b^{2} d e f^{2} - 3 \, a^{2} b^{2} f^{3} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e f^{2} - a^{2} b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f - 2 \, a^{2} b^{2} d^{2} e f^{2} + a^{2} b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 1728 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(864 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} f^{3} x^{4} + 3456 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e f^{2} x^{3} + 5184 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e^{2} f x^{2} + 3456 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e^{3} x + 945 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 4480 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 12960 \, {\left(4 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 4 \, a^{2} b^{2} d^{3} e^{3} - 6 \, a^{2} b^{2} d^{2} e^{2} f + 6 \, a^{2} b^{2} d e f^{2} - 3 \, a^{2} b^{2} f^{3} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e f^{2} - a^{2} b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f - 2 \, a^{2} b^{2} d^{2} e f^{2} + a^{2} b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 17280 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 6912 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(864 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + 864 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{3} + 2592 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} f - 189 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 5184 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f^{2} + 1120 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 5184 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{3} - 4320 \, {\left(4 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 4 \, a^{2} b^{2} d^{3} e^{3} - 6 \, a^{2} b^{2} d^{2} e^{2} f + 6 \, a^{2} b^{2} d e f^{2} - 3 \, a^{2} b^{2} f^{3} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e f^{2} - a^{2} b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f - 2 \, a^{2} b^{2} d^{2} e f^{2} + a^{2} b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 2592 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 8640 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2592 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f^{3}\right)} x - 864 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 648 \, {\left(4 \, b^{4} d^{3} e f^{2} + b^{4} d^{2} f^{3}\right)} x^{2} + 1728 \, {\left(4 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 4 \, a^{2} b^{2} d^{3} e^{3} + 6 \, a^{2} b^{2} d^{2} e^{2} f + 6 \, a^{2} b^{2} d e f^{2} + 3 \, a^{2} b^{2} f^{3} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e f^{2} + a^{2} b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f + 2 \, a^{2} b^{2} d^{2} e f^{2} + a^{2} b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(576 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 576 \, a^{2} b^{2} d^{3} e^{3} + 864 \, a^{2} b^{2} d^{2} e^{2} f + 864 \, a^{2} b^{2} d e f^{2} + 432 \, a^{2} b^{2} f^{3} - 63 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 448 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 2160 \, {\left(4 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 4 \, a^{2} b^{2} d^{3} e^{3} - 6 \, a^{2} b^{2} d^{2} e^{2} f + 6 \, a^{2} b^{2} d e f^{2} - 3 \, a^{2} b^{2} f^{3} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e f^{2} - a^{2} b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f - 2 \, a^{2} b^{2} d^{2} e f^{2} + a^{2} b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 5760 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 864 \, {\left(2 \, a^{2} b^{2} d^{3} e f^{2} + a^{2} b^{2} d^{2} f^{3}\right)} x^{2} - 864 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)^{2} + 864 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f + 2 \, a^{2} b^{2} d^{2} e f^{2} + a^{2} b^{2} d f^{3}\right)} x + 1728 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 165888 \, {\left({\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 165888 \, {\left({\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 55296 \, {\left({\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 55296 \, {\left({\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 55296 \, {\left({\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 55296 \, {\left({\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 331776 \, {\left(a^{3} b f^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b f^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} b f^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} b f^{3} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 331776 \, {\left(a^{3} b f^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b f^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} b f^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} b f^{3} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 331776 \, {\left({\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 331776 \, {\left({\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 324 \, {\left(8 \, b^{4} d^{3} e^{2} f + 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x + 256 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} + 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} + 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} + a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f + 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) + 8 \, {\left(288 \, a b^{3} d^{3} f^{3} x^{3} + 288 \, a b^{3} d^{3} e^{3} + 288 \, a b^{3} d^{2} e^{2} f + 192 \, a b^{3} d e f^{2} - 27 \, {\left(32 \, b^{4} d^{3} f^{3} x^{3} + 32 \, b^{4} d^{3} e^{3} - 24 \, b^{4} d^{2} e^{2} f + 12 \, b^{4} d e f^{2} - 3 \, b^{4} f^{3} + 24 \, {\left(4 \, b^{4} d^{3} e f^{2} - b^{4} d^{2} f^{3}\right)} x^{2} + 12 \, {\left(8 \, b^{4} d^{3} e^{2} f - 4 \, b^{4} d^{2} e f^{2} + b^{4} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{7} + 64 \, a b^{3} f^{3} + 224 \, {\left(9 \, a b^{3} d^{3} f^{3} x^{3} + 9 \, a b^{3} d^{3} e^{3} - 9 \, a b^{3} d^{2} e^{2} f + 6 \, a b^{3} d e f^{2} - 2 \, a b^{3} f^{3} + 9 \, {\left(3 \, a b^{3} d^{3} e f^{2} - a b^{3} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(9 \, a b^{3} d^{3} e^{2} f - 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 1296 \, {\left(4 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 4 \, a^{2} b^{2} d^{3} e^{3} - 6 \, a^{2} b^{2} d^{2} e^{2} f + 6 \, a^{2} b^{2} d e f^{2} - 3 \, a^{2} b^{2} f^{3} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e f^{2} - a^{2} b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f - 2 \, a^{2} b^{2} d^{2} e f^{2} + a^{2} b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 4320 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{3} - 3 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f^{2} - 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e f^{2} - {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 864 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{4} e^{3} x\right)} \cosh\left(d x + c\right)^{3} + 288 \, {\left(3 \, a b^{3} d^{3} e f^{2} + a b^{3} d^{2} f^{3}\right)} x^{2} + 2592 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{3} + 3 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f^{2} + 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{3} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e f^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 96 \, {\left(9 \, a b^{3} d^{3} e^{2} f + 6 \, a b^{3} d^{2} e f^{2} + 2 \, a b^{3} d f^{3}\right)} x + 432 \, {\left(4 \, a^{2} b^{2} d^{3} f^{3} x^{3} + 4 \, a^{2} b^{2} d^{3} e^{3} + 6 \, a^{2} b^{2} d^{2} e^{2} f + 6 \, a^{2} b^{2} d e f^{2} + 3 \, a^{2} b^{2} f^{3} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e f^{2} + a^{2} b^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(2 \, a^{2} b^{2} d^{3} e^{2} f + 2 \, a^{2} b^{2} d^{2} e f^{2} + a^{2} b^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{55296 \, {\left(b^{5} d^{4} \cosh\left(d x + c\right)^{4} + 4 \, b^{5} d^{4} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} d^{4} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} d^{4} \sinh\left(d x + c\right)^{4}\right)}}"," ",0,"-1/55296*(864*b^4*d^3*f^3*x^3 + 864*b^4*d^3*e^3 + 648*b^4*d^2*e^2*f - 27*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^8 - 27*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*sinh(d*x + c)^8 + 324*b^4*d*e*f^2 + 256*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^7 + 8*(288*a*b^3*d^3*f^3*x^3 + 288*a*b^3*d^3*e^3 - 288*a*b^3*d^2*e^2*f + 192*a*b^3*d*e*f^2 - 64*a*b^3*f^3 + 288*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 96*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x - 27*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 81*b^4*f^3 - 1728*(4*a^2*b^2*d^3*f^3*x^3 + 4*a^2*b^2*d^3*e^3 - 6*a^2*b^2*d^2*e^2*f + 6*a^2*b^2*d*e*f^2 - 3*a^2*b^2*f^3 + 6*(2*a^2*b^2*d^3*e*f^2 - a^2*b^2*d^2*f^3)*x^2 + 6*(2*a^2*b^2*d^3*e^2*f - 2*a^2*b^2*d^2*e*f^2 + a^2*b^2*d*f^3)*x)*cosh(d*x + c)^6 - 4*(1728*a^2*b^2*d^3*f^3*x^3 + 1728*a^2*b^2*d^3*e^3 - 2592*a^2*b^2*d^2*e^2*f + 2592*a^2*b^2*d*e*f^2 - 1296*a^2*b^2*f^3 + 2592*(2*a^2*b^2*d^3*e*f^2 - a^2*b^2*d^2*f^3)*x^2 + 189*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^2 + 2592*(2*a^2*b^2*d^3*e^2*f - 2*a^2*b^2*d^2*e*f^2 + a^2*b^2*d*f^3)*x - 448*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^6 + 6912*((4*a^3*b + a*b^3)*d^3*f^3*x^3 + (4*a^3*b + a*b^3)*d^3*e^3 - 3*(4*a^3*b + a*b^3)*d^2*e^2*f + 6*(4*a^3*b + a*b^3)*d*e*f^2 - 6*(4*a^3*b + a*b^3)*f^3 + 3*((4*a^3*b + a*b^3)*d^3*e*f^2 - (4*a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + a*b^3)*d^3*e^2*f - 2*(4*a^3*b + a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c)^5 + 24*(288*(4*a^3*b + a*b^3)*d^3*f^3*x^3 + 288*(4*a^3*b + a*b^3)*d^3*e^3 - 864*(4*a^3*b + a*b^3)*d^2*e^2*f + 1728*(4*a^3*b + a*b^3)*d*e*f^2 - 1728*(4*a^3*b + a*b^3)*f^3 - 63*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^3 + 864*((4*a^3*b + a*b^3)*d^3*e*f^2 - (4*a^3*b + a*b^3)*d^2*f^3)*x^2 + 224*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^2 + 864*((4*a^3*b + a*b^3)*d^3*e^2*f - 2*(4*a^3*b + a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + a*b^3)*d*f^3)*x - 432*(4*a^2*b^2*d^3*f^3*x^3 + 4*a^2*b^2*d^3*e^3 - 6*a^2*b^2*d^2*e^2*f + 6*a^2*b^2*d*e*f^2 - 3*a^2*b^2*f^3 + 6*(2*a^2*b^2*d^3*e*f^2 - a^2*b^2*d^2*f^3)*x^2 + 6*(2*a^2*b^2*d^3*e^2*f - 2*a^2*b^2*d^2*e*f^2 + a^2*b^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 1728*((8*a^4 + 4*a^2*b^2 - b^4)*d^4*f^3*x^4 + 4*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e*f^2*x^3 + 6*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e^2*f*x^2 + 4*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e^3*x)*cosh(d*x + c)^4 - 2*(864*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*f^3*x^4 + 3456*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e*f^2*x^3 + 5184*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e^2*f*x^2 + 3456*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e^3*x + 945*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^4 - 4480*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^3 + 12960*(4*a^2*b^2*d^3*f^3*x^3 + 4*a^2*b^2*d^3*e^3 - 6*a^2*b^2*d^2*e^2*f + 6*a^2*b^2*d*e*f^2 - 3*a^2*b^2*f^3 + 6*(2*a^2*b^2*d^3*e*f^2 - a^2*b^2*d^2*f^3)*x^2 + 6*(2*a^2*b^2*d^3*e^2*f - 2*a^2*b^2*d^2*e*f^2 + a^2*b^2*d*f^3)*x)*cosh(d*x + c)^2 - 17280*((4*a^3*b + a*b^3)*d^3*f^3*x^3 + (4*a^3*b + a*b^3)*d^3*e^3 - 3*(4*a^3*b + a*b^3)*d^2*e^2*f + 6*(4*a^3*b + a*b^3)*d*e*f^2 - 6*(4*a^3*b + a*b^3)*f^3 + 3*((4*a^3*b + a*b^3)*d^3*e*f^2 - (4*a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + a*b^3)*d^3*e^2*f - 2*(4*a^3*b + a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^4 + 6912*((4*a^3*b + a*b^3)*d^3*f^3*x^3 + (4*a^3*b + a*b^3)*d^3*e^3 + 3*(4*a^3*b + a*b^3)*d^2*e^2*f + 6*(4*a^3*b + a*b^3)*d*e*f^2 + 6*(4*a^3*b + a*b^3)*f^3 + 3*((4*a^3*b + a*b^3)*d^3*e*f^2 + (4*a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + a*b^3)*d^3*e^2*f + 2*(4*a^3*b + a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c)^3 + 8*(864*(4*a^3*b + a*b^3)*d^3*f^3*x^3 + 864*(4*a^3*b + a*b^3)*d^3*e^3 + 2592*(4*a^3*b + a*b^3)*d^2*e^2*f - 189*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^5 + 5184*(4*a^3*b + a*b^3)*d*e*f^2 + 1120*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^4 + 5184*(4*a^3*b + a*b^3)*f^3 - 4320*(4*a^2*b^2*d^3*f^3*x^3 + 4*a^2*b^2*d^3*e^3 - 6*a^2*b^2*d^2*e^2*f + 6*a^2*b^2*d*e*f^2 - 3*a^2*b^2*f^3 + 6*(2*a^2*b^2*d^3*e*f^2 - a^2*b^2*d^2*f^3)*x^2 + 6*(2*a^2*b^2*d^3*e^2*f - 2*a^2*b^2*d^2*e*f^2 + a^2*b^2*d*f^3)*x)*cosh(d*x + c)^3 + 2592*((4*a^3*b + a*b^3)*d^3*e*f^2 + (4*a^3*b + a*b^3)*d^2*f^3)*x^2 + 8640*((4*a^3*b + a*b^3)*d^3*f^3*x^3 + (4*a^3*b + a*b^3)*d^3*e^3 - 3*(4*a^3*b + a*b^3)*d^2*e^2*f + 6*(4*a^3*b + a*b^3)*d*e*f^2 - 6*(4*a^3*b + a*b^3)*f^3 + 3*((4*a^3*b + a*b^3)*d^3*e*f^2 - (4*a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + a*b^3)*d^3*e^2*f - 2*(4*a^3*b + a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 2592*((4*a^3*b + a*b^3)*d^3*e^2*f + 2*(4*a^3*b + a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + a*b^3)*d*f^3)*x - 864*((8*a^4 + 4*a^2*b^2 - b^4)*d^4*f^3*x^4 + 4*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e*f^2*x^3 + 6*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e^2*f*x^2 + 4*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e^3*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 648*(4*b^4*d^3*e*f^2 + b^4*d^2*f^3)*x^2 + 1728*(4*a^2*b^2*d^3*f^3*x^3 + 4*a^2*b^2*d^3*e^3 + 6*a^2*b^2*d^2*e^2*f + 6*a^2*b^2*d*e*f^2 + 3*a^2*b^2*f^3 + 6*(2*a^2*b^2*d^3*e*f^2 + a^2*b^2*d^2*f^3)*x^2 + 6*(2*a^2*b^2*d^3*e^2*f + 2*a^2*b^2*d^2*e*f^2 + a^2*b^2*d*f^3)*x)*cosh(d*x + c)^2 + 12*(576*a^2*b^2*d^3*f^3*x^3 + 576*a^2*b^2*d^3*e^3 + 864*a^2*b^2*d^2*e^2*f + 864*a^2*b^2*d*e*f^2 + 432*a^2*b^2*f^3 - 63*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^6 + 448*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^5 - 2160*(4*a^2*b^2*d^3*f^3*x^3 + 4*a^2*b^2*d^3*e^3 - 6*a^2*b^2*d^2*e^2*f + 6*a^2*b^2*d*e*f^2 - 3*a^2*b^2*f^3 + 6*(2*a^2*b^2*d^3*e*f^2 - a^2*b^2*d^2*f^3)*x^2 + 6*(2*a^2*b^2*d^3*e^2*f - 2*a^2*b^2*d^2*e*f^2 + a^2*b^2*d*f^3)*x)*cosh(d*x + c)^4 + 5760*((4*a^3*b + a*b^3)*d^3*f^3*x^3 + (4*a^3*b + a*b^3)*d^3*e^3 - 3*(4*a^3*b + a*b^3)*d^2*e^2*f + 6*(4*a^3*b + a*b^3)*d*e*f^2 - 6*(4*a^3*b + a*b^3)*f^3 + 3*((4*a^3*b + a*b^3)*d^3*e*f^2 - (4*a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + a*b^3)*d^3*e^2*f - 2*(4*a^3*b + a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c)^3 + 864*(2*a^2*b^2*d^3*e*f^2 + a^2*b^2*d^2*f^3)*x^2 - 864*((8*a^4 + 4*a^2*b^2 - b^4)*d^4*f^3*x^4 + 4*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e*f^2*x^3 + 6*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e^2*f*x^2 + 4*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e^3*x)*cosh(d*x + c)^2 + 864*(2*a^2*b^2*d^3*e^2*f + 2*a^2*b^2*d^2*e*f^2 + a^2*b^2*d*f^3)*x + 1728*((4*a^3*b + a*b^3)*d^3*f^3*x^3 + (4*a^3*b + a*b^3)*d^3*e^3 + 3*(4*a^3*b + a*b^3)*d^2*e^2*f + 6*(4*a^3*b + a*b^3)*d*e*f^2 + 6*(4*a^3*b + a*b^3)*f^3 + 3*((4*a^3*b + a*b^3)*d^3*e*f^2 + (4*a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + a*b^3)*d^3*e^2*f + 2*(4*a^3*b + a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 165888*((a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)^4 + 4*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 165888*((a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)^4 + 4*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 55296*((a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)^4 + 4*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 55296*((a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)^4 + 4*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 55296*((a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)^4 + 4*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 55296*((a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)^4 + 4*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 331776*(a^3*b*f^3*cosh(d*x + c)^4 + 4*a^3*b*f^3*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*b*f^3*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*b*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*b*f^3*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 331776*(a^3*b*f^3*cosh(d*x + c)^4 + 4*a^3*b*f^3*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*b*f^3*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*b*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*b*f^3*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 331776*((a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)^4 + 4*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d*f^3*x + a^3*b*d*e*f^2)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 331776*((a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)^4 + 4*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d*f^3*x + a^3*b*d*e*f^2)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 324*(8*b^4*d^3*e^2*f + 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x + 256*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 + 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 + 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 + a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f + 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c) + 8*(288*a*b^3*d^3*f^3*x^3 + 288*a*b^3*d^3*e^3 + 288*a*b^3*d^2*e^2*f + 192*a*b^3*d*e*f^2 - 27*(32*b^4*d^3*f^3*x^3 + 32*b^4*d^3*e^3 - 24*b^4*d^2*e^2*f + 12*b^4*d*e*f^2 - 3*b^4*f^3 + 24*(4*b^4*d^3*e*f^2 - b^4*d^2*f^3)*x^2 + 12*(8*b^4*d^3*e^2*f - 4*b^4*d^2*e*f^2 + b^4*d*f^3)*x)*cosh(d*x + c)^7 + 64*a*b^3*f^3 + 224*(9*a*b^3*d^3*f^3*x^3 + 9*a*b^3*d^3*e^3 - 9*a*b^3*d^2*e^2*f + 6*a*b^3*d*e*f^2 - 2*a*b^3*f^3 + 9*(3*a*b^3*d^3*e*f^2 - a*b^3*d^2*f^3)*x^2 + 3*(9*a*b^3*d^3*e^2*f - 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x)*cosh(d*x + c)^6 - 1296*(4*a^2*b^2*d^3*f^3*x^3 + 4*a^2*b^2*d^3*e^3 - 6*a^2*b^2*d^2*e^2*f + 6*a^2*b^2*d*e*f^2 - 3*a^2*b^2*f^3 + 6*(2*a^2*b^2*d^3*e*f^2 - a^2*b^2*d^2*f^3)*x^2 + 6*(2*a^2*b^2*d^3*e^2*f - 2*a^2*b^2*d^2*e*f^2 + a^2*b^2*d*f^3)*x)*cosh(d*x + c)^5 + 4320*((4*a^3*b + a*b^3)*d^3*f^3*x^3 + (4*a^3*b + a*b^3)*d^3*e^3 - 3*(4*a^3*b + a*b^3)*d^2*e^2*f + 6*(4*a^3*b + a*b^3)*d*e*f^2 - 6*(4*a^3*b + a*b^3)*f^3 + 3*((4*a^3*b + a*b^3)*d^3*e*f^2 - (4*a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + a*b^3)*d^3*e^2*f - 2*(4*a^3*b + a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c)^4 - 864*((8*a^4 + 4*a^2*b^2 - b^4)*d^4*f^3*x^4 + 4*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e*f^2*x^3 + 6*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e^2*f*x^2 + 4*(8*a^4 + 4*a^2*b^2 - b^4)*d^4*e^3*x)*cosh(d*x + c)^3 + 288*(3*a*b^3*d^3*e*f^2 + a*b^3*d^2*f^3)*x^2 + 2592*((4*a^3*b + a*b^3)*d^3*f^3*x^3 + (4*a^3*b + a*b^3)*d^3*e^3 + 3*(4*a^3*b + a*b^3)*d^2*e^2*f + 6*(4*a^3*b + a*b^3)*d*e*f^2 + 6*(4*a^3*b + a*b^3)*f^3 + 3*((4*a^3*b + a*b^3)*d^3*e*f^2 + (4*a^3*b + a*b^3)*d^2*f^3)*x^2 + 3*((4*a^3*b + a*b^3)*d^3*e^2*f + 2*(4*a^3*b + a*b^3)*d^2*e*f^2 + 2*(4*a^3*b + a*b^3)*d*f^3)*x)*cosh(d*x + c)^2 + 96*(9*a*b^3*d^3*e^2*f + 6*a*b^3*d^2*e*f^2 + 2*a*b^3*d*f^3)*x + 432*(4*a^2*b^2*d^3*f^3*x^3 + 4*a^2*b^2*d^3*e^3 + 6*a^2*b^2*d^2*e^2*f + 6*a^2*b^2*d*e*f^2 + 3*a^2*b^2*f^3 + 6*(2*a^2*b^2*d^3*e*f^2 + a^2*b^2*d^2*f^3)*x^2 + 6*(2*a^2*b^2*d^3*e^2*f + 2*a^2*b^2*d^2*e*f^2 + a^2*b^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^5*d^4*cosh(d*x + c)^4 + 4*b^5*d^4*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*d^4*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*d^4*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*d^4*sinh(d*x + c)^4)","C",0
397,1,6459,0,0.764314," ","integrate((f*x+e)^2*cosh(d*x+c)^2*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{216 \, b^{4} d^{2} f^{2} x^{2} - 27 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{8} - 27 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{8} + 216 \, b^{4} d^{2} e^{2} + 64 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{7} + 8 \, {\left(72 \, a b^{3} d^{2} f^{2} x^{2} + 72 \, a b^{3} d^{2} e^{2} - 48 \, a b^{3} d e f + 16 \, a b^{3} f^{2} + 48 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x - 27 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 108 \, b^{4} d e f - 864 \, {\left(2 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{2} d^{2} e^{2} - 2 \, a^{2} b^{2} d e f + a^{2} b^{2} f^{2} + 2 \, {\left(2 \, a^{2} b^{2} d^{2} e f - a^{2} b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(432 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 432 \, a^{2} b^{2} d^{2} e^{2} - 432 \, a^{2} b^{2} d e f + 216 \, a^{2} b^{2} f^{2} + 189 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 432 \, {\left(2 \, a^{2} b^{2} d^{2} e f - a^{2} b^{2} d f^{2}\right)} x - 112 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 27 \, b^{4} f^{2} + 1728 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 24 \, {\left(72 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 72 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} - 144 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f - 63 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 144 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{2} + 56 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 144 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + a b^{3}\right)} d f^{2}\right)} x - 216 \, {\left(2 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{2} d^{2} e^{2} - 2 \, a^{2} b^{2} d e f + a^{2} b^{2} f^{2} + 2 \, {\left(2 \, a^{2} b^{2} d^{2} e f - a^{2} b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 576 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} e f x^{2} + 3 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(288 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} f^{2} x^{3} + 864 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} e f x^{2} + 864 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} e^{2} x + 945 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 1120 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 6480 \, {\left(2 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{2} d^{2} e^{2} - 2 \, a^{2} b^{2} d e f + a^{2} b^{2} f^{2} + 2 \, {\left(2 \, a^{2} b^{2} d^{2} e f - a^{2} b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 4320 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 1728 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f + {\left(4 \, a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(216 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} - 189 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 216 \, {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} + 280 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 432 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f - 2160 \, {\left(2 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{2} d^{2} e^{2} - 2 \, a^{2} b^{2} d e f + a^{2} b^{2} f^{2} + 2 \, {\left(2 \, a^{2} b^{2} d^{2} e f - a^{2} b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 432 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{2} + 2160 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 432 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f + {\left(4 \, a^{3} b + a b^{3}\right)} d f^{2}\right)} x - 288 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} e f x^{2} + 3 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 864 \, {\left(2 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{2} d^{2} e^{2} + 2 \, a^{2} b^{2} d e f + a^{2} b^{2} f^{2} + 2 \, {\left(2 \, a^{2} b^{2} d^{2} e f + a^{2} b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(144 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 144 \, a^{2} b^{2} d^{2} e^{2} + 144 \, a^{2} b^{2} d e f - 63 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 72 \, a^{2} b^{2} f^{2} + 112 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 1080 \, {\left(2 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{2} d^{2} e^{2} - 2 \, a^{2} b^{2} d e f + a^{2} b^{2} f^{2} + 2 \, {\left(2 \, a^{2} b^{2} d^{2} e f - a^{2} b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 1440 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 288 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} e f x^{2} + 3 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)^{2} + 144 \, {\left(2 \, a^{2} b^{2} d^{2} e f + a^{2} b^{2} d f^{2}\right)} x + 432 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f + {\left(4 \, a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 27648 \, {\left({\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 27648 \, {\left({\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 13824 \, {\left({\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 13824 \, {\left({\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 13824 \, {\left({\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 13824 \, {\left({\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 27648 \, {\left(a^{3} b f^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b f^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} b f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} b f^{2} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 27648 \, {\left(a^{3} b f^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b f^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} b f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} b f^{2} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 108 \, {\left(4 \, b^{4} d^{2} e f + b^{4} d f^{2}\right)} x + 64 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} + 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f + a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 8 \, {\left(72 \, a b^{3} d^{2} f^{2} x^{2} + 72 \, a b^{3} d^{2} e^{2} - 27 \, {\left(8 \, b^{4} d^{2} f^{2} x^{2} + 8 \, b^{4} d^{2} e^{2} - 4 \, b^{4} d e f + b^{4} f^{2} + 4 \, {\left(4 \, b^{4} d^{2} e f - b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{7} + 48 \, a b^{3} d e f + 56 \, {\left(9 \, a b^{3} d^{2} f^{2} x^{2} + 9 \, a b^{3} d^{2} e^{2} - 6 \, a b^{3} d e f + 2 \, a b^{3} f^{2} + 6 \, {\left(3 \, a b^{3} d^{2} e f - a b^{3} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 16 \, a b^{3} f^{2} - 648 \, {\left(2 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{2} d^{2} e^{2} - 2 \, a^{2} b^{2} d e f + a^{2} b^{2} f^{2} + 2 \, {\left(2 \, a^{2} b^{2} d^{2} e f - a^{2} b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 1080 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} - 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f - {\left(4 \, a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 288 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} e f x^{2} + 3 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{3} e^{2} x\right)} \cosh\left(d x + c\right)^{3} + 648 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + {\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e^{2} + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e f + 2 \, {\left(4 \, a^{3} b + a b^{3}\right)} f^{2} + 2 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d^{2} e f + {\left(4 \, a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 48 \, {\left(3 \, a b^{3} d^{2} e f + a b^{3} d f^{2}\right)} x + 216 \, {\left(2 \, a^{2} b^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} b^{2} d^{2} e^{2} + 2 \, a^{2} b^{2} d e f + a^{2} b^{2} f^{2} + 2 \, {\left(2 \, a^{2} b^{2} d^{2} e f + a^{2} b^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{13824 \, {\left(b^{5} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{5} d^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} d^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} d^{3} \sinh\left(d x + c\right)^{4}\right)}}"," ",0,"-1/13824*(216*b^4*d^2*f^2*x^2 - 27*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^8 - 27*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*sinh(d*x + c)^8 + 216*b^4*d^2*e^2 + 64*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^7 + 8*(72*a*b^3*d^2*f^2*x^2 + 72*a*b^3*d^2*e^2 - 48*a*b^3*d*e*f + 16*a*b^3*f^2 + 48*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x - 27*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 108*b^4*d*e*f - 864*(2*a^2*b^2*d^2*f^2*x^2 + 2*a^2*b^2*d^2*e^2 - 2*a^2*b^2*d*e*f + a^2*b^2*f^2 + 2*(2*a^2*b^2*d^2*e*f - a^2*b^2*d*f^2)*x)*cosh(d*x + c)^6 - 4*(432*a^2*b^2*d^2*f^2*x^2 + 432*a^2*b^2*d^2*e^2 - 432*a^2*b^2*d*e*f + 216*a^2*b^2*f^2 + 189*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^2 + 432*(2*a^2*b^2*d^2*e*f - a^2*b^2*d*f^2)*x - 112*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^6 + 27*b^4*f^2 + 1728*((4*a^3*b + a*b^3)*d^2*f^2*x^2 + (4*a^3*b + a*b^3)*d^2*e^2 - 2*(4*a^3*b + a*b^3)*d*e*f + 2*(4*a^3*b + a*b^3)*f^2 + 2*((4*a^3*b + a*b^3)*d^2*e*f - (4*a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^5 + 24*(72*(4*a^3*b + a*b^3)*d^2*f^2*x^2 + 72*(4*a^3*b + a*b^3)*d^2*e^2 - 144*(4*a^3*b + a*b^3)*d*e*f - 63*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^3 + 144*(4*a^3*b + a*b^3)*f^2 + 56*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^2 + 144*((4*a^3*b + a*b^3)*d^2*e*f - (4*a^3*b + a*b^3)*d*f^2)*x - 216*(2*a^2*b^2*d^2*f^2*x^2 + 2*a^2*b^2*d^2*e^2 - 2*a^2*b^2*d*e*f + a^2*b^2*f^2 + 2*(2*a^2*b^2*d^2*e*f - a^2*b^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 576*((8*a^4 + 4*a^2*b^2 - b^4)*d^3*f^2*x^3 + 3*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*e*f*x^2 + 3*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*e^2*x)*cosh(d*x + c)^4 - 2*(288*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*f^2*x^3 + 864*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*e*f*x^2 + 864*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*e^2*x + 945*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^4 - 1120*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^3 + 6480*(2*a^2*b^2*d^2*f^2*x^2 + 2*a^2*b^2*d^2*e^2 - 2*a^2*b^2*d*e*f + a^2*b^2*f^2 + 2*(2*a^2*b^2*d^2*e*f - a^2*b^2*d*f^2)*x)*cosh(d*x + c)^2 - 4320*((4*a^3*b + a*b^3)*d^2*f^2*x^2 + (4*a^3*b + a*b^3)*d^2*e^2 - 2*(4*a^3*b + a*b^3)*d*e*f + 2*(4*a^3*b + a*b^3)*f^2 + 2*((4*a^3*b + a*b^3)*d^2*e*f - (4*a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^4 + 1728*((4*a^3*b + a*b^3)*d^2*f^2*x^2 + (4*a^3*b + a*b^3)*d^2*e^2 + 2*(4*a^3*b + a*b^3)*d*e*f + 2*(4*a^3*b + a*b^3)*f^2 + 2*((4*a^3*b + a*b^3)*d^2*e*f + (4*a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^3 + 8*(216*(4*a^3*b + a*b^3)*d^2*f^2*x^2 - 189*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^5 + 216*(4*a^3*b + a*b^3)*d^2*e^2 + 280*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^4 + 432*(4*a^3*b + a*b^3)*d*e*f - 2160*(2*a^2*b^2*d^2*f^2*x^2 + 2*a^2*b^2*d^2*e^2 - 2*a^2*b^2*d*e*f + a^2*b^2*f^2 + 2*(2*a^2*b^2*d^2*e*f - a^2*b^2*d*f^2)*x)*cosh(d*x + c)^3 + 432*(4*a^3*b + a*b^3)*f^2 + 2160*((4*a^3*b + a*b^3)*d^2*f^2*x^2 + (4*a^3*b + a*b^3)*d^2*e^2 - 2*(4*a^3*b + a*b^3)*d*e*f + 2*(4*a^3*b + a*b^3)*f^2 + 2*((4*a^3*b + a*b^3)*d^2*e*f - (4*a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 432*((4*a^3*b + a*b^3)*d^2*e*f + (4*a^3*b + a*b^3)*d*f^2)*x - 288*((8*a^4 + 4*a^2*b^2 - b^4)*d^3*f^2*x^3 + 3*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*e*f*x^2 + 3*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*e^2*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 864*(2*a^2*b^2*d^2*f^2*x^2 + 2*a^2*b^2*d^2*e^2 + 2*a^2*b^2*d*e*f + a^2*b^2*f^2 + 2*(2*a^2*b^2*d^2*e*f + a^2*b^2*d*f^2)*x)*cosh(d*x + c)^2 + 12*(144*a^2*b^2*d^2*f^2*x^2 + 144*a^2*b^2*d^2*e^2 + 144*a^2*b^2*d*e*f - 63*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^6 + 72*a^2*b^2*f^2 + 112*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^5 - 1080*(2*a^2*b^2*d^2*f^2*x^2 + 2*a^2*b^2*d^2*e^2 - 2*a^2*b^2*d*e*f + a^2*b^2*f^2 + 2*(2*a^2*b^2*d^2*e*f - a^2*b^2*d*f^2)*x)*cosh(d*x + c)^4 + 1440*((4*a^3*b + a*b^3)*d^2*f^2*x^2 + (4*a^3*b + a*b^3)*d^2*e^2 - 2*(4*a^3*b + a*b^3)*d*e*f + 2*(4*a^3*b + a*b^3)*f^2 + 2*((4*a^3*b + a*b^3)*d^2*e*f - (4*a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^3 - 288*((8*a^4 + 4*a^2*b^2 - b^4)*d^3*f^2*x^3 + 3*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*e*f*x^2 + 3*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*e^2*x)*cosh(d*x + c)^2 + 144*(2*a^2*b^2*d^2*e*f + a^2*b^2*d*f^2)*x + 432*((4*a^3*b + a*b^3)*d^2*f^2*x^2 + (4*a^3*b + a*b^3)*d^2*e^2 + 2*(4*a^3*b + a*b^3)*d*e*f + 2*(4*a^3*b + a*b^3)*f^2 + 2*((4*a^3*b + a*b^3)*d^2*e*f + (4*a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 27648*((a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)^4 + 4*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d*f^2*x + a^3*b*d*e*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 27648*((a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)^4 + 4*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d*f^2*x + a^3*b*d*e*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 13824*((a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 13824*((a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 13824*((a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 13824*((a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 27648*(a^3*b*f^2*cosh(d*x + c)^4 + 4*a^3*b*f^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*b*f^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*b*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*b*f^2*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 27648*(a^3*b*f^2*cosh(d*x + c)^4 + 4*a^3*b*f^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*b*f^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*b*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*b*f^2*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 108*(4*b^4*d^2*e*f + b^4*d*f^2)*x + 64*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 + 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f + a*b^3*d*f^2)*x)*cosh(d*x + c) + 8*(72*a*b^3*d^2*f^2*x^2 + 72*a*b^3*d^2*e^2 - 27*(8*b^4*d^2*f^2*x^2 + 8*b^4*d^2*e^2 - 4*b^4*d*e*f + b^4*f^2 + 4*(4*b^4*d^2*e*f - b^4*d*f^2)*x)*cosh(d*x + c)^7 + 48*a*b^3*d*e*f + 56*(9*a*b^3*d^2*f^2*x^2 + 9*a*b^3*d^2*e^2 - 6*a*b^3*d*e*f + 2*a*b^3*f^2 + 6*(3*a*b^3*d^2*e*f - a*b^3*d*f^2)*x)*cosh(d*x + c)^6 + 16*a*b^3*f^2 - 648*(2*a^2*b^2*d^2*f^2*x^2 + 2*a^2*b^2*d^2*e^2 - 2*a^2*b^2*d*e*f + a^2*b^2*f^2 + 2*(2*a^2*b^2*d^2*e*f - a^2*b^2*d*f^2)*x)*cosh(d*x + c)^5 + 1080*((4*a^3*b + a*b^3)*d^2*f^2*x^2 + (4*a^3*b + a*b^3)*d^2*e^2 - 2*(4*a^3*b + a*b^3)*d*e*f + 2*(4*a^3*b + a*b^3)*f^2 + 2*((4*a^3*b + a*b^3)*d^2*e*f - (4*a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^4 - 288*((8*a^4 + 4*a^2*b^2 - b^4)*d^3*f^2*x^3 + 3*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*e*f*x^2 + 3*(8*a^4 + 4*a^2*b^2 - b^4)*d^3*e^2*x)*cosh(d*x + c)^3 + 648*((4*a^3*b + a*b^3)*d^2*f^2*x^2 + (4*a^3*b + a*b^3)*d^2*e^2 + 2*(4*a^3*b + a*b^3)*d*e*f + 2*(4*a^3*b + a*b^3)*f^2 + 2*((4*a^3*b + a*b^3)*d^2*e*f + (4*a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 48*(3*a*b^3*d^2*e*f + a*b^3*d*f^2)*x + 216*(2*a^2*b^2*d^2*f^2*x^2 + 2*a^2*b^2*d^2*e^2 + 2*a^2*b^2*d*e*f + a^2*b^2*f^2 + 2*(2*a^2*b^2*d^2*e*f + a^2*b^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^5*d^3*cosh(d*x + c)^4 + 4*b^5*d^3*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*d^3*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*d^3*sinh(d*x + c)^4)","C",0
398,1,3228,0,0.493536," ","integrate((f*x+e)*cosh(d*x+c)^2*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{8} + 9 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \sinh\left(d x + c\right)^{8} - 32 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{7} - 8 \, {\left(12 \, a b^{3} d f x + 12 \, a b^{3} d e - 4 \, a b^{3} f - 9 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 36 \, b^{4} d f x + 144 \, {\left(2 \, a^{2} b^{2} d f x + 2 \, a^{2} b^{2} d e - a^{2} b^{2} f\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(72 \, a^{2} b^{2} d f x + 72 \, a^{2} b^{2} d e - 36 \, a^{2} b^{2} f + 63 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{2} - 56 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 36 \, b^{4} d e - 288 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d f x + {\left(4 \, a^{3} b + a b^{3}\right)} d e - {\left(4 \, a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{5} - 24 \, {\left(12 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f x - 21 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e + 28 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{2} - 12 \, {\left(4 \, a^{3} b + a b^{3}\right)} f - 36 \, {\left(2 \, a^{2} b^{2} d f x + 2 \, a^{2} b^{2} d e - a^{2} b^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 9 \, b^{4} f + 144 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(72 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 144 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{2} e x + 315 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{4} - 560 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{3} + 1080 \, {\left(2 \, a^{2} b^{2} d f x + 2 \, a^{2} b^{2} d e - a^{2} b^{2} f\right)} \cosh\left(d x + c\right)^{2} - 720 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d f x + {\left(4 \, a^{3} b + a b^{3}\right)} d e - {\left(4 \, a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 288 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d f x + {\left(4 \, a^{3} b + a b^{3}\right)} d e + {\left(4 \, a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(63 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{4} - 36 \, {\left(4 \, a^{3} b + a b^{3}\right)} d f x + 360 \, {\left(2 \, a^{2} b^{2} d f x + 2 \, a^{2} b^{2} d e - a^{2} b^{2} f\right)} \cosh\left(d x + c\right)^{3} - 36 \, {\left(4 \, a^{3} b + a b^{3}\right)} d e - 360 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d f x + {\left(4 \, a^{3} b + a b^{3}\right)} d e - {\left(4 \, a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 36 \, {\left(4 \, a^{3} b + a b^{3}\right)} f + 72 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 144 \, {\left(2 \, a^{2} b^{2} d f x + 2 \, a^{2} b^{2} d e + a^{2} b^{2} f\right)} \cosh\left(d x + c\right)^{2} - 12 \, {\left(24 \, a^{2} b^{2} d f x - 21 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{6} + 24 \, a^{2} b^{2} d e + 56 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{5} + 12 \, a^{2} b^{2} f - 180 \, {\left(2 \, a^{2} b^{2} d f x + 2 \, a^{2} b^{2} d e - a^{2} b^{2} f\right)} \cosh\left(d x + c\right)^{4} + 240 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d f x + {\left(4 \, a^{3} b + a b^{3}\right)} d e - {\left(4 \, a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} - 72 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)^{2} + 72 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d f x + {\left(4 \, a^{3} b + a b^{3}\right)} d e + {\left(4 \, a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2304 \, {\left(a^{3} b f \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} b f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} b f \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2304 \, {\left(a^{3} b f \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} b f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} b f \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2304 \, {\left({\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d e - a^{3} b c f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2304 \, {\left({\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d e - a^{3} b c f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2304 \, {\left({\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d f x + a^{3} b c f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2304 \, {\left({\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b d f x + a^{3} b c f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 32 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e + a b^{3} f\right)} \cosh\left(d x + c\right) + 8 \, {\left(9 \, {\left(4 \, b^{4} d f x + 4 \, b^{4} d e - b^{4} f\right)} \cosh\left(d x + c\right)^{7} - 12 \, a b^{3} d f x - 28 \, {\left(3 \, a b^{3} d f x + 3 \, a b^{3} d e - a b^{3} f\right)} \cosh\left(d x + c\right)^{6} - 12 \, a b^{3} d e + 108 \, {\left(2 \, a^{2} b^{2} d f x + 2 \, a^{2} b^{2} d e - a^{2} b^{2} f\right)} \cosh\left(d x + c\right)^{5} - 4 \, a b^{3} f - 180 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d f x + {\left(4 \, a^{3} b + a b^{3}\right)} d e - {\left(4 \, a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 72 \, {\left({\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d^{2} e x\right)} \cosh\left(d x + c\right)^{3} - 108 \, {\left({\left(4 \, a^{3} b + a b^{3}\right)} d f x + {\left(4 \, a^{3} b + a b^{3}\right)} d e + {\left(4 \, a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 36 \, {\left(2 \, a^{2} b^{2} d f x + 2 \, a^{2} b^{2} d e + a^{2} b^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2304 \, {\left(b^{5} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{5} d^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} d^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} d^{2} \sinh\left(d x + c\right)^{4}\right)}}"," ",0,"1/2304*(9*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^8 + 9*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*sinh(d*x + c)^8 - 32*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^7 - 8*(12*a*b^3*d*f*x + 12*a*b^3*d*e - 4*a*b^3*f - 9*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c))*sinh(d*x + c)^7 - 36*b^4*d*f*x + 144*(2*a^2*b^2*d*f*x + 2*a^2*b^2*d*e - a^2*b^2*f)*cosh(d*x + c)^6 + 4*(72*a^2*b^2*d*f*x + 72*a^2*b^2*d*e - 36*a^2*b^2*f + 63*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^2 - 56*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c))*sinh(d*x + c)^6 - 36*b^4*d*e - 288*((4*a^3*b + a*b^3)*d*f*x + (4*a^3*b + a*b^3)*d*e - (4*a^3*b + a*b^3)*f)*cosh(d*x + c)^5 - 24*(12*(4*a^3*b + a*b^3)*d*f*x - 21*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^3 + 12*(4*a^3*b + a*b^3)*d*e + 28*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^2 - 12*(4*a^3*b + a*b^3)*f - 36*(2*a^2*b^2*d*f*x + 2*a^2*b^2*d*e - a^2*b^2*f)*cosh(d*x + c))*sinh(d*x + c)^5 - 9*b^4*f + 144*((8*a^4 + 4*a^2*b^2 - b^4)*d^2*f*x^2 + 2*(8*a^4 + 4*a^2*b^2 - b^4)*d^2*e*x)*cosh(d*x + c)^4 + 2*(72*(8*a^4 + 4*a^2*b^2 - b^4)*d^2*f*x^2 + 144*(8*a^4 + 4*a^2*b^2 - b^4)*d^2*e*x + 315*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^4 - 560*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^3 + 1080*(2*a^2*b^2*d*f*x + 2*a^2*b^2*d*e - a^2*b^2*f)*cosh(d*x + c)^2 - 720*((4*a^3*b + a*b^3)*d*f*x + (4*a^3*b + a*b^3)*d*e - (4*a^3*b + a*b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^4 - 288*((4*a^3*b + a*b^3)*d*f*x + (4*a^3*b + a*b^3)*d*e + (4*a^3*b + a*b^3)*f)*cosh(d*x + c)^3 + 8*(63*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^5 - 140*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^4 - 36*(4*a^3*b + a*b^3)*d*f*x + 360*(2*a^2*b^2*d*f*x + 2*a^2*b^2*d*e - a^2*b^2*f)*cosh(d*x + c)^3 - 36*(4*a^3*b + a*b^3)*d*e - 360*((4*a^3*b + a*b^3)*d*f*x + (4*a^3*b + a*b^3)*d*e - (4*a^3*b + a*b^3)*f)*cosh(d*x + c)^2 - 36*(4*a^3*b + a*b^3)*f + 72*((8*a^4 + 4*a^2*b^2 - b^4)*d^2*f*x^2 + 2*(8*a^4 + 4*a^2*b^2 - b^4)*d^2*e*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 144*(2*a^2*b^2*d*f*x + 2*a^2*b^2*d*e + a^2*b^2*f)*cosh(d*x + c)^2 - 12*(24*a^2*b^2*d*f*x - 21*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^6 + 24*a^2*b^2*d*e + 56*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^5 + 12*a^2*b^2*f - 180*(2*a^2*b^2*d*f*x + 2*a^2*b^2*d*e - a^2*b^2*f)*cosh(d*x + c)^4 + 240*((4*a^3*b + a*b^3)*d*f*x + (4*a^3*b + a*b^3)*d*e - (4*a^3*b + a*b^3)*f)*cosh(d*x + c)^3 - 72*((8*a^4 + 4*a^2*b^2 - b^4)*d^2*f*x^2 + 2*(8*a^4 + 4*a^2*b^2 - b^4)*d^2*e*x)*cosh(d*x + c)^2 + 72*((4*a^3*b + a*b^3)*d*f*x + (4*a^3*b + a*b^3)*d*e + (4*a^3*b + a*b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 2304*(a^3*b*f*cosh(d*x + c)^4 + 4*a^3*b*f*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*b*f*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*b*f*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*b*f*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2304*(a^3*b*f*cosh(d*x + c)^4 + 4*a^3*b*f*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*b*f*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*b*f*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*b*f*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2304*((a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)^4 + 4*(a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d*e - a^3*b*c*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2304*((a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)^4 + 4*(a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d*e - a^3*b*c*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2304*((a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)^4 + 4*(a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d*f*x + a^3*b*c*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2304*((a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)^4 + 4*(a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b*d*f*x + a^3*b*c*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 32*(3*a*b^3*d*f*x + 3*a*b^3*d*e + a*b^3*f)*cosh(d*x + c) + 8*(9*(4*b^4*d*f*x + 4*b^4*d*e - b^4*f)*cosh(d*x + c)^7 - 12*a*b^3*d*f*x - 28*(3*a*b^3*d*f*x + 3*a*b^3*d*e - a*b^3*f)*cosh(d*x + c)^6 - 12*a*b^3*d*e + 108*(2*a^2*b^2*d*f*x + 2*a^2*b^2*d*e - a^2*b^2*f)*cosh(d*x + c)^5 - 4*a*b^3*f - 180*((4*a^3*b + a*b^3)*d*f*x + (4*a^3*b + a*b^3)*d*e - (4*a^3*b + a*b^3)*f)*cosh(d*x + c)^4 + 72*((8*a^4 + 4*a^2*b^2 - b^4)*d^2*f*x^2 + 2*(8*a^4 + 4*a^2*b^2 - b^4)*d^2*e*x)*cosh(d*x + c)^3 - 108*((4*a^3*b + a*b^3)*d*f*x + (4*a^3*b + a*b^3)*d*e + (4*a^3*b + a*b^3)*f)*cosh(d*x + c)^2 - 36*(2*a^2*b^2*d*f*x + 2*a^2*b^2*d*e + a^2*b^2*f)*cosh(d*x + c))*sinh(d*x + c))/(b^5*d^2*cosh(d*x + c)^4 + 4*b^5*d^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*d^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*d^2*sinh(d*x + c)^4)","B",0
399,1,1134,0,0.611405," ","integrate(cosh(d*x+c)^2*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, b^{4} \cosh\left(d x + c\right)^{8} + 3 \, b^{4} \sinh\left(d x + c\right)^{8} - 8 \, a b^{3} \cosh\left(d x + c\right)^{7} + 24 \, a^{2} b^{2} \cosh\left(d x + c\right)^{6} + 8 \, {\left(3 \, b^{4} \cosh\left(d x + c\right) - a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 24 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d x \cosh\left(d x + c\right)^{4} + 4 \, {\left(21 \, b^{4} \cosh\left(d x + c\right)^{2} - 14 \, a b^{3} \cosh\left(d x + c\right) + 6 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{6} - 24 \, a^{2} b^{2} \cosh\left(d x + c\right)^{2} - 24 \, {\left(4 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 24 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{3} - 7 \, a b^{3} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} b^{2} \cosh\left(d x + c\right) - 4 \, a^{3} b - a b^{3}\right)} \sinh\left(d x + c\right)^{5} - 8 \, a b^{3} \cosh\left(d x + c\right) + 2 \, {\left(105 \, b^{4} \cosh\left(d x + c\right)^{4} - 140 \, a b^{3} \cosh\left(d x + c\right)^{3} + 180 \, a^{2} b^{2} \cosh\left(d x + c\right)^{2} + 12 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d x - 60 \, {\left(4 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 3 \, b^{4} - 24 \, {\left(4 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(21 \, b^{4} \cosh\left(d x + c\right)^{5} - 35 \, a b^{3} \cosh\left(d x + c\right)^{4} + 60 \, a^{2} b^{2} \cosh\left(d x + c\right)^{3} - 12 \, a^{3} b - 3 \, a b^{3} + 12 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d x \cosh\left(d x + c\right) - 30 \, {\left(4 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 12 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{6} - 14 \, a b^{3} \cosh\left(d x + c\right)^{5} + 30 \, a^{2} b^{2} \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, a^{2} b^{2} - 20 \, {\left(4 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(4 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 192 \, {\left(a^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} \sinh\left(d x + c\right)^{4}\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 8 \, {\left(3 \, b^{4} \cosh\left(d x + c\right)^{7} - 7 \, a b^{3} \cosh\left(d x + c\right)^{6} + 18 \, a^{2} b^{2} \cosh\left(d x + c\right)^{5} + 12 \, {\left(8 \, a^{4} + 4 \, a^{2} b^{2} - b^{4}\right)} d x \cosh\left(d x + c\right)^{3} - 6 \, a^{2} b^{2} \cosh\left(d x + c\right) - 15 \, {\left(4 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{4} - a b^{3} - 9 \, {\left(4 \, a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{192 \, {\left(b^{5} d \cosh\left(d x + c\right)^{4} + 4 \, b^{5} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} d \sinh\left(d x + c\right)^{4}\right)}}"," ",0,"1/192*(3*b^4*cosh(d*x + c)^8 + 3*b^4*sinh(d*x + c)^8 - 8*a*b^3*cosh(d*x + c)^7 + 24*a^2*b^2*cosh(d*x + c)^6 + 8*(3*b^4*cosh(d*x + c) - a*b^3)*sinh(d*x + c)^7 + 24*(8*a^4 + 4*a^2*b^2 - b^4)*d*x*cosh(d*x + c)^4 + 4*(21*b^4*cosh(d*x + c)^2 - 14*a*b^3*cosh(d*x + c) + 6*a^2*b^2)*sinh(d*x + c)^6 - 24*a^2*b^2*cosh(d*x + c)^2 - 24*(4*a^3*b + a*b^3)*cosh(d*x + c)^5 + 24*(7*b^4*cosh(d*x + c)^3 - 7*a*b^3*cosh(d*x + c)^2 + 6*a^2*b^2*cosh(d*x + c) - 4*a^3*b - a*b^3)*sinh(d*x + c)^5 - 8*a*b^3*cosh(d*x + c) + 2*(105*b^4*cosh(d*x + c)^4 - 140*a*b^3*cosh(d*x + c)^3 + 180*a^2*b^2*cosh(d*x + c)^2 + 12*(8*a^4 + 4*a^2*b^2 - b^4)*d*x - 60*(4*a^3*b + a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 3*b^4 - 24*(4*a^3*b + a*b^3)*cosh(d*x + c)^3 + 8*(21*b^4*cosh(d*x + c)^5 - 35*a*b^3*cosh(d*x + c)^4 + 60*a^2*b^2*cosh(d*x + c)^3 - 12*a^3*b - 3*a*b^3 + 12*(8*a^4 + 4*a^2*b^2 - b^4)*d*x*cosh(d*x + c) - 30*(4*a^3*b + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 12*(7*b^4*cosh(d*x + c)^6 - 14*a*b^3*cosh(d*x + c)^5 + 30*a^2*b^2*cosh(d*x + c)^4 + 12*(8*a^4 + 4*a^2*b^2 - b^4)*d*x*cosh(d*x + c)^2 - 2*a^2*b^2 - 20*(4*a^3*b + a*b^3)*cosh(d*x + c)^3 - 6*(4*a^3*b + a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 192*(a^3*cosh(d*x + c)^4 + 4*a^3*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^3*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^3*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*sinh(d*x + c)^4)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 8*(3*b^4*cosh(d*x + c)^7 - 7*a*b^3*cosh(d*x + c)^6 + 18*a^2*b^2*cosh(d*x + c)^5 + 12*(8*a^4 + 4*a^2*b^2 - b^4)*d*x*cosh(d*x + c)^3 - 6*a^2*b^2*cosh(d*x + c) - 15*(4*a^3*b + a*b^3)*cosh(d*x + c)^4 - a*b^3 - 9*(4*a^3*b + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(b^5*d*cosh(d*x + c)^4 + 4*b^5*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*d*sinh(d*x + c)^4)","B",0
400,0,0,0,0.423022," ","integrate(cosh(d*x+c)^2*sinh(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)^2*sinh(d*x + c)^3/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
401,-1,0,0,0.000000," ","integrate((f*x+e)^3*cosh(d*x+c)^3*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,1,11318,0,0.775943," ","integrate((f*x+e)^2*cosh(d*x+c)^3*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{10800 \, b^{5} d^{2} f^{2} x^{2} - 432 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{10} - 432 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{10} + 3375 \, {\left(8 \, a b^{4} d^{2} f^{2} x^{2} + 8 \, a b^{4} d^{2} e^{2} - 4 \, a b^{4} d e f + a b^{4} f^{2} + 4 \, {\left(4 \, a b^{4} d^{2} e f - a b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{9} + 135 \, {\left(200 \, a b^{4} d^{2} f^{2} x^{2} + 200 \, a b^{4} d^{2} e^{2} - 100 \, a b^{4} d e f + 25 \, a b^{4} f^{2} + 100 \, {\left(4 \, a b^{4} d^{2} e f - a b^{4} d f^{2}\right)} x - 32 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 10800 \, b^{5} d^{2} e^{2} - 2000 \, {\left(9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 6 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 2 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 6 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{8} - 5 \, {\left(3600 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 3600 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 2400 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 800 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 3888 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2400 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x - 6075 \, {\left(8 \, a b^{4} d^{2} f^{2} x^{2} + 8 \, a b^{4} d^{2} e^{2} - 4 \, a b^{4} d e f + a b^{4} f^{2} + 4 \, {\left(4 \, a b^{4} d^{2} e f - a b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 4320 \, b^{5} d e f + 54000 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{7} + 20 \, {\left(5400 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 5400 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} - 5400 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f - 2592 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 2700 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 6075 \, {\left(8 \, a b^{4} d^{2} f^{2} x^{2} + 8 \, a b^{4} d^{2} e^{2} - 4 \, a b^{4} d e f + a b^{4} f^{2} + 4 \, {\left(4 \, a b^{4} d^{2} e f - a b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 5400 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x - 800 \, {\left(9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 6 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 2 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 6 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 864 \, b^{5} f^{2} - 108000 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} - 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 20 \, {\left(5400 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + 5400 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} + 4536 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 10800 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f - 14175 \, {\left(8 \, a b^{4} d^{2} f^{2} x^{2} + 8 \, a b^{4} d^{2} e^{2} - 4 \, a b^{4} d e f + a b^{4} f^{2} + 4 \, {\left(4 \, a b^{4} d^{2} e f - a b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 10800 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2800 \, {\left(9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 6 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 2 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 6 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 10800 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x - 18900 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 576000 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{5} + a^{3} b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(288000 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} f^{2} x^{3} + 864000 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e f x^{2} + 864000 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e^{2} x + 1728000 \, {\left(a^{5} + a^{3} b^{2}\right)} c d^{2} e^{2} - 1728000 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} d e f + 576000 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{3} f^{2} + 54432 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 212625 \, {\left(8 \, a b^{4} d^{2} f^{2} x^{2} + 8 \, a b^{4} d^{2} e^{2} - 4 \, a b^{4} d e f + a b^{4} f^{2} + 4 \, {\left(4 \, a b^{4} d^{2} e f - a b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 56000 \, {\left(9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 6 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 2 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 6 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 567000 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 324000 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} - 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 108000 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(10800 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} - 9072 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 42525 \, {\left(8 \, a b^{4} d^{2} f^{2} x^{2} + 8 \, a b^{4} d^{2} e^{2} - 4 \, a b^{4} d e f + a b^{4} f^{2} + 4 \, {\left(4 \, a b^{4} d^{2} e f - a b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} + 10800 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} - 14000 \, {\left(9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 6 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 2 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 6 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 21600 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 189000 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 21600 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} - 162000 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} - 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 21600 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x - 288000 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{5} + a^{3} b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 54000 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 20 \, {\left(2592 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{7} - 5400 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} - 14175 \, {\left(8 \, a b^{4} d^{2} f^{2} x^{2} + 8 \, a b^{4} d^{2} e^{2} - 4 \, a b^{4} d e f + a b^{4} f^{2} + 4 \, {\left(4 \, a b^{4} d^{2} e f - a b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} + 5600 \, {\left(9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 6 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 2 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 6 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 5400 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} - 94500 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 5400 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + 108000 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} - 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - 2700 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 288000 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{5} + a^{3} b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 5400 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x - 21600 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2000 \, {\left(9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} + 6 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 2 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 6 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f + {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 20 \, {\left(972 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{8} - 6075 \, {\left(8 \, a b^{4} d^{2} f^{2} x^{2} + 8 \, a b^{4} d^{2} e^{2} - 4 \, a b^{4} d e f + a b^{4} f^{2} + 4 \, {\left(4 \, a b^{4} d^{2} e f - a b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{7} - 900 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 2800 \, {\left(9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 6 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 2 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 6 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 56700 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 900 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} + 81000 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} - 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 600 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 288000 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{5} + a^{3} b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{3} - 200 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} - 32400 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 600 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f + {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x - 8100 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 4320 \, {\left(5 \, b^{5} d^{2} e f + b^{5} d f^{2}\right)} x + 3375 \, {\left(8 \, a b^{4} d^{2} f^{2} x^{2} + 8 \, a b^{4} d^{2} e^{2} + 4 \, a b^{4} d e f + a b^{4} f^{2} + 4 \, {\left(4 \, a b^{4} d^{2} e f + a b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 3456000 \, {\left({\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{5}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3456000 \, {\left({\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left({\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + {\left(a^{5} + a^{3} b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{5}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 1728000 \, {\left({\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{5}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 1728000 \, {\left({\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f + {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{5}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 1728000 \, {\left({\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{5}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 1728000 \, {\left({\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e f - {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{5}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 3456000 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{5} + a^{3} b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{5}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 3456000 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{5} + a^{3} b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{5}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 5 \, {\left(5400 \, a b^{4} d^{2} f^{2} x^{2} - 864 \, {\left(25 \, b^{5} d^{2} f^{2} x^{2} + 25 \, b^{5} d^{2} e^{2} - 10 \, b^{5} d e f + 2 \, b^{5} f^{2} + 10 \, {\left(5 \, b^{5} d^{2} e f - b^{5} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{9} + 5400 \, a b^{4} d^{2} e^{2} + 6075 \, {\left(8 \, a b^{4} d^{2} f^{2} x^{2} + 8 \, a b^{4} d^{2} e^{2} - 4 \, a b^{4} d e f + a b^{4} f^{2} + 4 \, {\left(4 \, a b^{4} d^{2} e f - a b^{4} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{8} + 2700 \, a b^{4} d e f - 3200 \, {\left(9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 6 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 2 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 6 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{7} + 675 \, a b^{4} f^{2} + 75600 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{6} - 129600 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} - 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{5} - 576000 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{5} + a^{3} b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 86400 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} f^{2} x^{2} + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e^{2} + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e f + 2 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f^{2} + 2 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d^{2} e f + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 32400 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} + 2 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2700 \, {\left(4 \, a b^{4} d^{2} e f + a b^{4} d f^{2}\right)} x + 800 \, {\left(9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 9 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} + 6 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e f + 2 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 6 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f + {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{1728000 \, {\left(b^{6} d^{3} \cosh\left(d x + c\right)^{5} + 5 \, b^{6} d^{3} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, b^{6} d^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, b^{6} d^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, b^{6} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + b^{6} d^{3} \sinh\left(d x + c\right)^{5}\right)}}"," ",0,"-1/1728000*(10800*b^5*d^2*f^2*x^2 - 432*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*cosh(d*x + c)^10 - 432*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*sinh(d*x + c)^10 + 3375*(8*a*b^4*d^2*f^2*x^2 + 8*a*b^4*d^2*e^2 - 4*a*b^4*d*e*f + a*b^4*f^2 + 4*(4*a*b^4*d^2*e*f - a*b^4*d*f^2)*x)*cosh(d*x + c)^9 + 135*(200*a*b^4*d^2*f^2*x^2 + 200*a*b^4*d^2*e^2 - 100*a*b^4*d*e*f + 25*a*b^4*f^2 + 100*(4*a*b^4*d^2*e*f - a*b^4*d*f^2)*x - 32*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^9 + 10800*b^5*d^2*e^2 - 2000*(9*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 9*(4*a^2*b^3 + b^5)*d^2*e^2 - 6*(4*a^2*b^3 + b^5)*d*e*f + 2*(4*a^2*b^3 + b^5)*f^2 + 6*(3*(4*a^2*b^3 + b^5)*d^2*e*f - (4*a^2*b^3 + b^5)*d*f^2)*x)*cosh(d*x + c)^8 - 5*(3600*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 3600*(4*a^2*b^3 + b^5)*d^2*e^2 - 2400*(4*a^2*b^3 + b^5)*d*e*f + 800*(4*a^2*b^3 + b^5)*f^2 + 3888*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*cosh(d*x + c)^2 + 2400*(3*(4*a^2*b^3 + b^5)*d^2*e*f - (4*a^2*b^3 + b^5)*d*f^2)*x - 6075*(8*a*b^4*d^2*f^2*x^2 + 8*a*b^4*d^2*e^2 - 4*a*b^4*d*e*f + a*b^4*f^2 + 4*(4*a*b^4*d^2*e*f - a*b^4*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^8 + 4320*b^5*d*e*f + 54000*(2*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^3*b^2 + a*b^4)*d^2*e^2 - 2*(2*a^3*b^2 + a*b^4)*d*e*f + (2*a^3*b^2 + a*b^4)*f^2 + 2*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f - (2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^7 + 20*(5400*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 5400*(2*a^3*b^2 + a*b^4)*d^2*e^2 - 5400*(2*a^3*b^2 + a*b^4)*d*e*f - 2592*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*cosh(d*x + c)^3 + 2700*(2*a^3*b^2 + a*b^4)*f^2 + 6075*(8*a*b^4*d^2*f^2*x^2 + 8*a*b^4*d^2*e^2 - 4*a*b^4*d*e*f + a*b^4*f^2 + 4*(4*a*b^4*d^2*e*f - a*b^4*d*f^2)*x)*cosh(d*x + c)^2 + 5400*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f - (2*a^3*b^2 + a*b^4)*d*f^2)*x - 800*(9*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 9*(4*a^2*b^3 + b^5)*d^2*e^2 - 6*(4*a^2*b^3 + b^5)*d*e*f + 2*(4*a^2*b^3 + b^5)*f^2 + 6*(3*(4*a^2*b^3 + b^5)*d^2*e*f - (4*a^2*b^3 + b^5)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 864*b^5*f^2 - 108000*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + (8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 - 2*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f - (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x)*cosh(d*x + c)^6 - 20*(5400*(8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + 5400*(8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 + 4536*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*cosh(d*x + c)^4 - 10800*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f - 14175*(8*a*b^4*d^2*f^2*x^2 + 8*a*b^4*d^2*e^2 - 4*a*b^4*d*e*f + a*b^4*f^2 + 4*(4*a*b^4*d^2*e*f - a*b^4*d*f^2)*x)*cosh(d*x + c)^3 + 10800*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2800*(9*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 9*(4*a^2*b^3 + b^5)*d^2*e^2 - 6*(4*a^2*b^3 + b^5)*d*e*f + 2*(4*a^2*b^3 + b^5)*f^2 + 6*(3*(4*a^2*b^3 + b^5)*d^2*e*f - (4*a^2*b^3 + b^5)*d*f^2)*x)*cosh(d*x + c)^2 + 10800*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f - (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x - 18900*(2*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^3*b^2 + a*b^4)*d^2*e^2 - 2*(2*a^3*b^2 + a*b^4)*d*e*f + (2*a^3*b^2 + a*b^4)*f^2 + 2*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f - (2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^6 - 576000*((a^5 + a^3*b^2)*d^3*f^2*x^3 + 3*(a^5 + a^3*b^2)*d^3*e*f*x^2 + 3*(a^5 + a^3*b^2)*d^3*e^2*x + 6*(a^5 + a^3*b^2)*c*d^2*e^2 - 6*(a^5 + a^3*b^2)*c^2*d*e*f + 2*(a^5 + a^3*b^2)*c^3*f^2)*cosh(d*x + c)^5 - 2*(288000*(a^5 + a^3*b^2)*d^3*f^2*x^3 + 864000*(a^5 + a^3*b^2)*d^3*e*f*x^2 + 864000*(a^5 + a^3*b^2)*d^3*e^2*x + 1728000*(a^5 + a^3*b^2)*c*d^2*e^2 - 1728000*(a^5 + a^3*b^2)*c^2*d*e*f + 576000*(a^5 + a^3*b^2)*c^3*f^2 + 54432*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*cosh(d*x + c)^5 - 212625*(8*a*b^4*d^2*f^2*x^2 + 8*a*b^4*d^2*e^2 - 4*a*b^4*d*e*f + a*b^4*f^2 + 4*(4*a*b^4*d^2*e*f - a*b^4*d*f^2)*x)*cosh(d*x + c)^4 + 56000*(9*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 9*(4*a^2*b^3 + b^5)*d^2*e^2 - 6*(4*a^2*b^3 + b^5)*d*e*f + 2*(4*a^2*b^3 + b^5)*f^2 + 6*(3*(4*a^2*b^3 + b^5)*d^2*e*f - (4*a^2*b^3 + b^5)*d*f^2)*x)*cosh(d*x + c)^3 - 567000*(2*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^3*b^2 + a*b^4)*d^2*e^2 - 2*(2*a^3*b^2 + a*b^4)*d*e*f + (2*a^3*b^2 + a*b^4)*f^2 + 2*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f - (2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^2 + 324000*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + (8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 - 2*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f - (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 108000*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + (8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f + (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x)*cosh(d*x + c)^4 + 10*(10800*(8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 - 9072*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*cosh(d*x + c)^6 + 42525*(8*a*b^4*d^2*f^2*x^2 + 8*a*b^4*d^2*e^2 - 4*a*b^4*d*e*f + a*b^4*f^2 + 4*(4*a*b^4*d^2*e*f - a*b^4*d*f^2)*x)*cosh(d*x + c)^5 + 10800*(8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 - 14000*(9*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 9*(4*a^2*b^3 + b^5)*d^2*e^2 - 6*(4*a^2*b^3 + b^5)*d*e*f + 2*(4*a^2*b^3 + b^5)*f^2 + 6*(3*(4*a^2*b^3 + b^5)*d^2*e*f - (4*a^2*b^3 + b^5)*d*f^2)*x)*cosh(d*x + c)^4 + 21600*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 189000*(2*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^3*b^2 + a*b^4)*d^2*e^2 - 2*(2*a^3*b^2 + a*b^4)*d*e*f + (2*a^3*b^2 + a*b^4)*f^2 + 2*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f - (2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^3 + 21600*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 - 162000*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + (8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 - 2*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f - (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x)*cosh(d*x + c)^2 + 21600*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f + (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x - 288000*((a^5 + a^3*b^2)*d^3*f^2*x^3 + 3*(a^5 + a^3*b^2)*d^3*e*f*x^2 + 3*(a^5 + a^3*b^2)*d^3*e^2*x + 6*(a^5 + a^3*b^2)*c*d^2*e^2 - 6*(a^5 + a^3*b^2)*c^2*d*e*f + 2*(a^5 + a^3*b^2)*c^3*f^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 54000*(2*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^3*b^2 + a*b^4)*d^2*e^2 + 2*(2*a^3*b^2 + a*b^4)*d*e*f + (2*a^3*b^2 + a*b^4)*f^2 + 2*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f + (2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^3 - 20*(2592*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*cosh(d*x + c)^7 - 5400*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 - 14175*(8*a*b^4*d^2*f^2*x^2 + 8*a*b^4*d^2*e^2 - 4*a*b^4*d*e*f + a*b^4*f^2 + 4*(4*a*b^4*d^2*e*f - a*b^4*d*f^2)*x)*cosh(d*x + c)^6 + 5600*(9*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 9*(4*a^2*b^3 + b^5)*d^2*e^2 - 6*(4*a^2*b^3 + b^5)*d*e*f + 2*(4*a^2*b^3 + b^5)*f^2 + 6*(3*(4*a^2*b^3 + b^5)*d^2*e*f - (4*a^2*b^3 + b^5)*d*f^2)*x)*cosh(d*x + c)^5 - 5400*(2*a^3*b^2 + a*b^4)*d^2*e^2 - 94500*(2*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^3*b^2 + a*b^4)*d^2*e^2 - 2*(2*a^3*b^2 + a*b^4)*d*e*f + (2*a^3*b^2 + a*b^4)*f^2 + 2*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f - (2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^4 - 5400*(2*a^3*b^2 + a*b^4)*d*e*f + 108000*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + (8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 - 2*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f - (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x)*cosh(d*x + c)^3 - 2700*(2*a^3*b^2 + a*b^4)*f^2 + 288000*((a^5 + a^3*b^2)*d^3*f^2*x^3 + 3*(a^5 + a^3*b^2)*d^3*e*f*x^2 + 3*(a^5 + a^3*b^2)*d^3*e^2*x + 6*(a^5 + a^3*b^2)*c*d^2*e^2 - 6*(a^5 + a^3*b^2)*c^2*d*e*f + 2*(a^5 + a^3*b^2)*c^3*f^2)*cosh(d*x + c)^2 - 5400*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f + (2*a^3*b^2 + a*b^4)*d*f^2)*x - 21600*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + (8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f + (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 2000*(9*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 9*(4*a^2*b^3 + b^5)*d^2*e^2 + 6*(4*a^2*b^3 + b^5)*d*e*f + 2*(4*a^2*b^3 + b^5)*f^2 + 6*(3*(4*a^2*b^3 + b^5)*d^2*e*f + (4*a^2*b^3 + b^5)*d*f^2)*x)*cosh(d*x + c)^2 - 20*(972*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*cosh(d*x + c)^8 - 6075*(8*a*b^4*d^2*f^2*x^2 + 8*a*b^4*d^2*e^2 - 4*a*b^4*d*e*f + a*b^4*f^2 + 4*(4*a*b^4*d^2*e*f - a*b^4*d*f^2)*x)*cosh(d*x + c)^7 - 900*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 2800*(9*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 9*(4*a^2*b^3 + b^5)*d^2*e^2 - 6*(4*a^2*b^3 + b^5)*d*e*f + 2*(4*a^2*b^3 + b^5)*f^2 + 6*(3*(4*a^2*b^3 + b^5)*d^2*e*f - (4*a^2*b^3 + b^5)*d*f^2)*x)*cosh(d*x + c)^6 - 56700*(2*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^3*b^2 + a*b^4)*d^2*e^2 - 2*(2*a^3*b^2 + a*b^4)*d*e*f + (2*a^3*b^2 + a*b^4)*f^2 + 2*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f - (2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^5 - 900*(4*a^2*b^3 + b^5)*d^2*e^2 + 81000*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + (8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 - 2*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f - (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x)*cosh(d*x + c)^4 - 600*(4*a^2*b^3 + b^5)*d*e*f + 288000*((a^5 + a^3*b^2)*d^3*f^2*x^3 + 3*(a^5 + a^3*b^2)*d^3*e*f*x^2 + 3*(a^5 + a^3*b^2)*d^3*e^2*x + 6*(a^5 + a^3*b^2)*c*d^2*e^2 - 6*(a^5 + a^3*b^2)*c^2*d*e*f + 2*(a^5 + a^3*b^2)*c^3*f^2)*cosh(d*x + c)^3 - 200*(4*a^2*b^3 + b^5)*f^2 - 32400*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + (8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f + (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x)*cosh(d*x + c)^2 - 600*(3*(4*a^2*b^3 + b^5)*d^2*e*f + (4*a^2*b^3 + b^5)*d*f^2)*x - 8100*(2*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^3*b^2 + a*b^4)*d^2*e^2 + 2*(2*a^3*b^2 + a*b^4)*d*e*f + (2*a^3*b^2 + a*b^4)*f^2 + 2*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f + (2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 4320*(5*b^5*d^2*e*f + b^5*d*f^2)*x + 3375*(8*a*b^4*d^2*f^2*x^2 + 8*a*b^4*d^2*e^2 + 4*a*b^4*d*e*f + a*b^4*f^2 + 4*(4*a*b^4*d^2*e*f + a*b^4*d*f^2)*x)*cosh(d*x + c) + 3456000*(((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*cosh(d*x + c)^5 + 5*((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*cosh(d*x + c)^4*sinh(d*x + c) + 10*((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^4 + ((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*sinh(d*x + c)^5)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3456000*(((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*cosh(d*x + c)^5 + 5*((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*cosh(d*x + c)^4*sinh(d*x + c) + 10*((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^4 + ((a^5 + a^3*b^2)*d*f^2*x + (a^5 + a^3*b^2)*d*e*f)*sinh(d*x + c)^5)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 1728000*(((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^5 + 5*((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^4*sinh(d*x + c) + 10*((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^4 + ((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*sinh(d*x + c)^5)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 1728000*(((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^5 + 5*((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^4*sinh(d*x + c) + 10*((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^4 + ((a^5 + a^3*b^2)*d^2*e^2 - 2*(a^5 + a^3*b^2)*c*d*e*f + (a^5 + a^3*b^2)*c^2*f^2)*sinh(d*x + c)^5)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 1728000*(((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^5 + 5*((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^4*sinh(d*x + c) + 10*((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^4 + ((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*sinh(d*x + c)^5)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 1728000*(((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^5 + 5*((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^4*sinh(d*x + c) + 10*((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^4 + ((a^5 + a^3*b^2)*d^2*f^2*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*f*x + 2*(a^5 + a^3*b^2)*c*d*e*f - (a^5 + a^3*b^2)*c^2*f^2)*sinh(d*x + c)^5)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 3456000*((a^5 + a^3*b^2)*f^2*cosh(d*x + c)^5 + 5*(a^5 + a^3*b^2)*f^2*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a^5 + a^3*b^2)*f^2*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a^5 + a^3*b^2)*f^2*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a^5 + a^3*b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^4 + (a^5 + a^3*b^2)*f^2*sinh(d*x + c)^5)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 3456000*((a^5 + a^3*b^2)*f^2*cosh(d*x + c)^5 + 5*(a^5 + a^3*b^2)*f^2*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a^5 + a^3*b^2)*f^2*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a^5 + a^3*b^2)*f^2*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a^5 + a^3*b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^4 + (a^5 + a^3*b^2)*f^2*sinh(d*x + c)^5)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 5*(5400*a*b^4*d^2*f^2*x^2 - 864*(25*b^5*d^2*f^2*x^2 + 25*b^5*d^2*e^2 - 10*b^5*d*e*f + 2*b^5*f^2 + 10*(5*b^5*d^2*e*f - b^5*d*f^2)*x)*cosh(d*x + c)^9 + 5400*a*b^4*d^2*e^2 + 6075*(8*a*b^4*d^2*f^2*x^2 + 8*a*b^4*d^2*e^2 - 4*a*b^4*d*e*f + a*b^4*f^2 + 4*(4*a*b^4*d^2*e*f - a*b^4*d*f^2)*x)*cosh(d*x + c)^8 + 2700*a*b^4*d*e*f - 3200*(9*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 9*(4*a^2*b^3 + b^5)*d^2*e^2 - 6*(4*a^2*b^3 + b^5)*d*e*f + 2*(4*a^2*b^3 + b^5)*f^2 + 6*(3*(4*a^2*b^3 + b^5)*d^2*e*f - (4*a^2*b^3 + b^5)*d*f^2)*x)*cosh(d*x + c)^7 + 675*a*b^4*f^2 + 75600*(2*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^3*b^2 + a*b^4)*d^2*e^2 - 2*(2*a^3*b^2 + a*b^4)*d*e*f + (2*a^3*b^2 + a*b^4)*f^2 + 2*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f - (2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^6 - 129600*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + (8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 - 2*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f - (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x)*cosh(d*x + c)^5 - 576000*((a^5 + a^3*b^2)*d^3*f^2*x^3 + 3*(a^5 + a^3*b^2)*d^3*e*f*x^2 + 3*(a^5 + a^3*b^2)*d^3*e^2*x + 6*(a^5 + a^3*b^2)*c*d^2*e^2 - 6*(a^5 + a^3*b^2)*c^2*d*e*f + 2*(a^5 + a^3*b^2)*c^3*f^2)*cosh(d*x + c)^4 + 86400*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*f^2*x^2 + (8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e^2 + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e*f + 2*(8*a^4*b + 6*a^2*b^3 - b^5)*f^2 + 2*((8*a^4*b + 6*a^2*b^3 - b^5)*d^2*e*f + (8*a^4*b + 6*a^2*b^3 - b^5)*d*f^2)*x)*cosh(d*x + c)^3 + 32400*(2*(2*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^3*b^2 + a*b^4)*d^2*e^2 + 2*(2*a^3*b^2 + a*b^4)*d*e*f + (2*a^3*b^2 + a*b^4)*f^2 + 2*(2*(2*a^3*b^2 + a*b^4)*d^2*e*f + (2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^2 + 2700*(4*a*b^4*d^2*e*f + a*b^4*d*f^2)*x + 800*(9*(4*a^2*b^3 + b^5)*d^2*f^2*x^2 + 9*(4*a^2*b^3 + b^5)*d^2*e^2 + 6*(4*a^2*b^3 + b^5)*d*e*f + 2*(4*a^2*b^3 + b^5)*f^2 + 6*(3*(4*a^2*b^3 + b^5)*d^2*e*f + (4*a^2*b^3 + b^5)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(b^6*d^3*cosh(d*x + c)^5 + 5*b^6*d^3*cosh(d*x + c)^4*sinh(d*x + c) + 10*b^6*d^3*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*b^6*d^3*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*b^6*d^3*cosh(d*x + c)*sinh(d*x + c)^4 + b^6*d^3*sinh(d*x + c)^5)","C",0
403,1,5548,0,0.622535," ","integrate((f*x+e)*cosh(d*x+c)^3*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{72 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \cosh\left(d x + c\right)^{10} + 72 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \sinh\left(d x + c\right)^{10} - 225 \, {\left(4 \, a b^{4} d f x + 4 \, a b^{4} d e - a b^{4} f\right)} \cosh\left(d x + c\right)^{9} - 45 \, {\left(20 \, a b^{4} d f x + 20 \, a b^{4} d e - 5 \, a b^{4} f - 16 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 200 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{8} + 5 \, {\left(120 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 120 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e + 648 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \cosh\left(d x + c\right)^{2} - 40 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f - 405 \, {\left(4 \, a b^{4} d f x + 4 \, a b^{4} d e - a b^{4} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 360 \, b^{5} d f x - 1800 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{7} - 20 \, {\left(180 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x - 432 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \cosh\left(d x + c\right)^{3} + 180 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e + 405 \, {\left(4 \, a b^{4} d f x + 4 \, a b^{4} d e - a b^{4} f\right)} \cosh\left(d x + c\right)^{2} - 90 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f - 80 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 360 \, b^{5} d e + 3600 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(756 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \cosh\left(d x + c\right)^{4} + 180 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x - 945 \, {\left(4 \, a b^{4} d f x + 4 \, a b^{4} d e - a b^{4} f\right)} \cosh\left(d x + c\right)^{3} + 180 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e + 280 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 180 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f - 630 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 72 \, b^{5} f + 28800 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e x + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(14400 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} f x^{2} + 9072 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \cosh\left(d x + c\right)^{5} + 28800 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e x - 14175 \, {\left(4 \, a b^{4} d f x + 4 \, a b^{4} d e - a b^{4} f\right)} \cosh\left(d x + c\right)^{4} + 57600 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e - 28800 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f + 5600 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{3} - 18900 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 10800 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 3600 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(1512 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \cosh\left(d x + c\right)^{6} - 2835 \, {\left(4 \, a b^{4} d f x + 4 \, a b^{4} d e - a b^{4} f\right)} \cosh\left(d x + c\right)^{5} + 1400 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{4} - 360 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x - 6300 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{3} - 360 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e + 5400 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 360 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f + 14400 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e x + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 1800 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 20 \, {\left(432 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \cosh\left(d x + c\right)^{7} - 945 \, {\left(4 \, a b^{4} d f x + 4 \, a b^{4} d e - a b^{4} f\right)} \cosh\left(d x + c\right)^{6} + 560 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{5} - 3150 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{4} - 180 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 3600 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{3} - 180 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e + 14400 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e x + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)^{2} - 90 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f - 720 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 200 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e + {\left(4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 20 \, {\left(162 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \cosh\left(d x + c\right)^{8} - 405 \, {\left(4 \, a b^{4} d f x + 4 \, a b^{4} d e - a b^{4} f\right)} \cosh\left(d x + c\right)^{7} + 280 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{6} - 1890 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{5} + 2700 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 14400 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e x + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)^{3} - 30 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e - 1080 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 10 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} f - 270 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 225 \, {\left(4 \, a b^{4} d f x + 4 \, a b^{4} d e + a b^{4} f\right)} \cosh\left(d x + c\right) - 57600 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{5} + a^{3} b^{2}\right)} f \sinh\left(d x + c\right)^{5}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 57600 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{5} + a^{3} b^{2}\right)} f \sinh\left(d x + c\right)^{5}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 57600 \, {\left({\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{5}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 57600 \, {\left({\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left({\left(a^{5} + a^{3} b^{2}\right)} d e - {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{5}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 57600 \, {\left({\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{5}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 57600 \, {\left({\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left({\left(a^{5} + a^{3} b^{2}\right)} d f x + {\left(a^{5} + a^{3} b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{5}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 5 \, {\left(144 \, {\left(5 \, b^{5} d f x + 5 \, b^{5} d e - b^{5} f\right)} \cosh\left(d x + c\right)^{9} - 405 \, {\left(4 \, a b^{4} d f x + 4 \, a b^{4} d e - a b^{4} f\right)} \cosh\left(d x + c\right)^{8} - 180 \, a b^{4} d f x + 320 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{7} - 180 \, a b^{4} d e - 2520 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e - {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{6} - 45 \, a b^{4} f + 4320 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e - {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{5} + 28800 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} e x + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c d e - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right)^{4} - 2880 \, {\left({\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d f x + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} d e + {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{3} - 1080 \, {\left(2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d f x + 2 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} d e + {\left(2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 80 \, {\left(3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d f x + 3 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} d e + {\left(4 \, a^{2} b^{3} + b^{5}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{57600 \, {\left(b^{6} d^{2} \cosh\left(d x + c\right)^{5} + 5 \, b^{6} d^{2} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, b^{6} d^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, b^{6} d^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, b^{6} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + b^{6} d^{2} \sinh\left(d x + c\right)^{5}\right)}}"," ",0,"1/57600*(72*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*cosh(d*x + c)^10 + 72*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*sinh(d*x + c)^10 - 225*(4*a*b^4*d*f*x + 4*a*b^4*d*e - a*b^4*f)*cosh(d*x + c)^9 - 45*(20*a*b^4*d*f*x + 20*a*b^4*d*e - 5*a*b^4*f - 16*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*cosh(d*x + c))*sinh(d*x + c)^9 + 200*(3*(4*a^2*b^3 + b^5)*d*f*x + 3*(4*a^2*b^3 + b^5)*d*e - (4*a^2*b^3 + b^5)*f)*cosh(d*x + c)^8 + 5*(120*(4*a^2*b^3 + b^5)*d*f*x + 120*(4*a^2*b^3 + b^5)*d*e + 648*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*cosh(d*x + c)^2 - 40*(4*a^2*b^3 + b^5)*f - 405*(4*a*b^4*d*f*x + 4*a*b^4*d*e - a*b^4*f)*cosh(d*x + c))*sinh(d*x + c)^8 - 360*b^5*d*f*x - 1800*(2*(2*a^3*b^2 + a*b^4)*d*f*x + 2*(2*a^3*b^2 + a*b^4)*d*e - (2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^7 - 20*(180*(2*a^3*b^2 + a*b^4)*d*f*x - 432*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*cosh(d*x + c)^3 + 180*(2*a^3*b^2 + a*b^4)*d*e + 405*(4*a*b^4*d*f*x + 4*a*b^4*d*e - a*b^4*f)*cosh(d*x + c)^2 - 90*(2*a^3*b^2 + a*b^4)*f - 80*(3*(4*a^2*b^3 + b^5)*d*f*x + 3*(4*a^2*b^3 + b^5)*d*e - (4*a^2*b^3 + b^5)*f)*cosh(d*x + c))*sinh(d*x + c)^7 - 360*b^5*d*e + 3600*((8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x + (8*a^4*b + 6*a^2*b^3 - b^5)*d*e - (8*a^4*b + 6*a^2*b^3 - b^5)*f)*cosh(d*x + c)^6 + 20*(756*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*cosh(d*x + c)^4 + 180*(8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x - 945*(4*a*b^4*d*f*x + 4*a*b^4*d*e - a*b^4*f)*cosh(d*x + c)^3 + 180*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e + 280*(3*(4*a^2*b^3 + b^5)*d*f*x + 3*(4*a^2*b^3 + b^5)*d*e - (4*a^2*b^3 + b^5)*f)*cosh(d*x + c)^2 - 180*(8*a^4*b + 6*a^2*b^3 - b^5)*f - 630*(2*(2*a^3*b^2 + a*b^4)*d*f*x + 2*(2*a^3*b^2 + a*b^4)*d*e - (2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c))*sinh(d*x + c)^6 - 72*b^5*f + 28800*((a^5 + a^3*b^2)*d^2*f*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*x + 4*(a^5 + a^3*b^2)*c*d*e - 2*(a^5 + a^3*b^2)*c^2*f)*cosh(d*x + c)^5 + 2*(14400*(a^5 + a^3*b^2)*d^2*f*x^2 + 9072*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*cosh(d*x + c)^5 + 28800*(a^5 + a^3*b^2)*d^2*e*x - 14175*(4*a*b^4*d*f*x + 4*a*b^4*d*e - a*b^4*f)*cosh(d*x + c)^4 + 57600*(a^5 + a^3*b^2)*c*d*e - 28800*(a^5 + a^3*b^2)*c^2*f + 5600*(3*(4*a^2*b^3 + b^5)*d*f*x + 3*(4*a^2*b^3 + b^5)*d*e - (4*a^2*b^3 + b^5)*f)*cosh(d*x + c)^3 - 18900*(2*(2*a^3*b^2 + a*b^4)*d*f*x + 2*(2*a^3*b^2 + a*b^4)*d*e - (2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^2 + 10800*((8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x + (8*a^4*b + 6*a^2*b^3 - b^5)*d*e - (8*a^4*b + 6*a^2*b^3 - b^5)*f)*cosh(d*x + c))*sinh(d*x + c)^5 - 3600*((8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x + (8*a^4*b + 6*a^2*b^3 - b^5)*d*e + (8*a^4*b + 6*a^2*b^3 - b^5)*f)*cosh(d*x + c)^4 + 10*(1512*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*cosh(d*x + c)^6 - 2835*(4*a*b^4*d*f*x + 4*a*b^4*d*e - a*b^4*f)*cosh(d*x + c)^5 + 1400*(3*(4*a^2*b^3 + b^5)*d*f*x + 3*(4*a^2*b^3 + b^5)*d*e - (4*a^2*b^3 + b^5)*f)*cosh(d*x + c)^4 - 360*(8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x - 6300*(2*(2*a^3*b^2 + a*b^4)*d*f*x + 2*(2*a^3*b^2 + a*b^4)*d*e - (2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^3 - 360*(8*a^4*b + 6*a^2*b^3 - b^5)*d*e + 5400*((8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x + (8*a^4*b + 6*a^2*b^3 - b^5)*d*e - (8*a^4*b + 6*a^2*b^3 - b^5)*f)*cosh(d*x + c)^2 - 360*(8*a^4*b + 6*a^2*b^3 - b^5)*f + 14400*((a^5 + a^3*b^2)*d^2*f*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*x + 4*(a^5 + a^3*b^2)*c*d*e - 2*(a^5 + a^3*b^2)*c^2*f)*cosh(d*x + c))*sinh(d*x + c)^4 - 1800*(2*(2*a^3*b^2 + a*b^4)*d*f*x + 2*(2*a^3*b^2 + a*b^4)*d*e + (2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^3 + 20*(432*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*cosh(d*x + c)^7 - 945*(4*a*b^4*d*f*x + 4*a*b^4*d*e - a*b^4*f)*cosh(d*x + c)^6 + 560*(3*(4*a^2*b^3 + b^5)*d*f*x + 3*(4*a^2*b^3 + b^5)*d*e - (4*a^2*b^3 + b^5)*f)*cosh(d*x + c)^5 - 3150*(2*(2*a^3*b^2 + a*b^4)*d*f*x + 2*(2*a^3*b^2 + a*b^4)*d*e - (2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^4 - 180*(2*a^3*b^2 + a*b^4)*d*f*x + 3600*((8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x + (8*a^4*b + 6*a^2*b^3 - b^5)*d*e - (8*a^4*b + 6*a^2*b^3 - b^5)*f)*cosh(d*x + c)^3 - 180*(2*a^3*b^2 + a*b^4)*d*e + 14400*((a^5 + a^3*b^2)*d^2*f*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*x + 4*(a^5 + a^3*b^2)*c*d*e - 2*(a^5 + a^3*b^2)*c^2*f)*cosh(d*x + c)^2 - 90*(2*a^3*b^2 + a*b^4)*f - 720*((8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x + (8*a^4*b + 6*a^2*b^3 - b^5)*d*e + (8*a^4*b + 6*a^2*b^3 - b^5)*f)*cosh(d*x + c))*sinh(d*x + c)^3 - 200*(3*(4*a^2*b^3 + b^5)*d*f*x + 3*(4*a^2*b^3 + b^5)*d*e + (4*a^2*b^3 + b^5)*f)*cosh(d*x + c)^2 + 20*(162*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*cosh(d*x + c)^8 - 405*(4*a*b^4*d*f*x + 4*a*b^4*d*e - a*b^4*f)*cosh(d*x + c)^7 + 280*(3*(4*a^2*b^3 + b^5)*d*f*x + 3*(4*a^2*b^3 + b^5)*d*e - (4*a^2*b^3 + b^5)*f)*cosh(d*x + c)^6 - 1890*(2*(2*a^3*b^2 + a*b^4)*d*f*x + 2*(2*a^3*b^2 + a*b^4)*d*e - (2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^5 + 2700*((8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x + (8*a^4*b + 6*a^2*b^3 - b^5)*d*e - (8*a^4*b + 6*a^2*b^3 - b^5)*f)*cosh(d*x + c)^4 - 30*(4*a^2*b^3 + b^5)*d*f*x + 14400*((a^5 + a^3*b^2)*d^2*f*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*x + 4*(a^5 + a^3*b^2)*c*d*e - 2*(a^5 + a^3*b^2)*c^2*f)*cosh(d*x + c)^3 - 30*(4*a^2*b^3 + b^5)*d*e - 1080*((8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x + (8*a^4*b + 6*a^2*b^3 - b^5)*d*e + (8*a^4*b + 6*a^2*b^3 - b^5)*f)*cosh(d*x + c)^2 - 10*(4*a^2*b^3 + b^5)*f - 270*(2*(2*a^3*b^2 + a*b^4)*d*f*x + 2*(2*a^3*b^2 + a*b^4)*d*e + (2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 225*(4*a*b^4*d*f*x + 4*a*b^4*d*e + a*b^4*f)*cosh(d*x + c) - 57600*((a^5 + a^3*b^2)*f*cosh(d*x + c)^5 + 5*(a^5 + a^3*b^2)*f*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a^5 + a^3*b^2)*f*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a^5 + a^3*b^2)*f*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a^5 + a^3*b^2)*f*cosh(d*x + c)*sinh(d*x + c)^4 + (a^5 + a^3*b^2)*f*sinh(d*x + c)^5)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 57600*((a^5 + a^3*b^2)*f*cosh(d*x + c)^5 + 5*(a^5 + a^3*b^2)*f*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a^5 + a^3*b^2)*f*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a^5 + a^3*b^2)*f*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a^5 + a^3*b^2)*f*cosh(d*x + c)*sinh(d*x + c)^4 + (a^5 + a^3*b^2)*f*sinh(d*x + c)^5)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 57600*(((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^5 + 5*((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^4*sinh(d*x + c) + 10*((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^4 + ((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*sinh(d*x + c)^5)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 57600*(((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^5 + 5*((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^4*sinh(d*x + c) + 10*((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^4 + ((a^5 + a^3*b^2)*d*e - (a^5 + a^3*b^2)*c*f)*sinh(d*x + c)^5)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 57600*(((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^5 + 5*((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^4*sinh(d*x + c) + 10*((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^4 + ((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*sinh(d*x + c)^5)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 57600*(((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^5 + 5*((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^4*sinh(d*x + c) + 10*((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^4 + ((a^5 + a^3*b^2)*d*f*x + (a^5 + a^3*b^2)*c*f)*sinh(d*x + c)^5)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 5*(144*(5*b^5*d*f*x + 5*b^5*d*e - b^5*f)*cosh(d*x + c)^9 - 405*(4*a*b^4*d*f*x + 4*a*b^4*d*e - a*b^4*f)*cosh(d*x + c)^8 - 180*a*b^4*d*f*x + 320*(3*(4*a^2*b^3 + b^5)*d*f*x + 3*(4*a^2*b^3 + b^5)*d*e - (4*a^2*b^3 + b^5)*f)*cosh(d*x + c)^7 - 180*a*b^4*d*e - 2520*(2*(2*a^3*b^2 + a*b^4)*d*f*x + 2*(2*a^3*b^2 + a*b^4)*d*e - (2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^6 - 45*a*b^4*f + 4320*((8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x + (8*a^4*b + 6*a^2*b^3 - b^5)*d*e - (8*a^4*b + 6*a^2*b^3 - b^5)*f)*cosh(d*x + c)^5 + 28800*((a^5 + a^3*b^2)*d^2*f*x^2 + 2*(a^5 + a^3*b^2)*d^2*e*x + 4*(a^5 + a^3*b^2)*c*d*e - 2*(a^5 + a^3*b^2)*c^2*f)*cosh(d*x + c)^4 - 2880*((8*a^4*b + 6*a^2*b^3 - b^5)*d*f*x + (8*a^4*b + 6*a^2*b^3 - b^5)*d*e + (8*a^4*b + 6*a^2*b^3 - b^5)*f)*cosh(d*x + c)^3 - 1080*(2*(2*a^3*b^2 + a*b^4)*d*f*x + 2*(2*a^3*b^2 + a*b^4)*d*e + (2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^2 - 80*(3*(4*a^2*b^3 + b^5)*d*f*x + 3*(4*a^2*b^3 + b^5)*d*e + (4*a^2*b^3 + b^5)*f)*cosh(d*x + c))*sinh(d*x + c))/(b^6*d^2*cosh(d*x + c)^5 + 5*b^6*d^2*cosh(d*x + c)^4*sinh(d*x + c) + 10*b^6*d^2*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*b^6*d^2*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*b^6*d^2*cosh(d*x + c)*sinh(d*x + c)^4 + b^6*d^2*sinh(d*x + c)^5)","B",0
404,1,1660,0,0.477436," ","integrate(cosh(d*x+c)^3*sinh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, b^{5} \cosh\left(d x + c\right)^{10} + 6 \, b^{5} \sinh\left(d x + c\right)^{10} - 15 \, a b^{4} \cosh\left(d x + c\right)^{9} + 15 \, {\left(4 \, b^{5} \cosh\left(d x + c\right) - a b^{4}\right)} \sinh\left(d x + c\right)^{9} + 10 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{8} + 5 \, {\left(54 \, b^{5} \cosh\left(d x + c\right)^{2} - 27 \, a b^{4} \cosh\left(d x + c\right) + 8 \, a^{2} b^{3} + 2 \, b^{5}\right)} \sinh\left(d x + c\right)^{8} + 960 \, {\left(a^{5} + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 60 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 20 \, {\left(36 \, b^{5} \cosh\left(d x + c\right)^{3} - 27 \, a b^{4} \cosh\left(d x + c\right)^{2} - 6 \, a^{3} b^{2} - 3 \, a b^{4} + 4 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 60 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(63 \, b^{5} \cosh\left(d x + c\right)^{4} - 63 \, a b^{4} \cosh\left(d x + c\right)^{3} + 24 \, a^{4} b + 18 \, a^{2} b^{3} - 3 \, b^{5} + 14 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2} - 21 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 15 \, a b^{4} \cosh\left(d x + c\right) + 2 \, {\left(756 \, b^{5} \cosh\left(d x + c\right)^{5} - 945 \, a b^{4} \cosh\left(d x + c\right)^{4} + 280 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + 480 \, {\left(a^{5} + a^{3} b^{2}\right)} d x - 630 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 180 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 6 \, b^{5} - 60 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(126 \, b^{5} \cosh\left(d x + c\right)^{6} - 189 \, a b^{4} \cosh\left(d x + c\right)^{5} - 48 \, a^{4} b - 36 \, a^{2} b^{3} + 6 \, b^{5} + 70 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 480 \, {\left(a^{5} + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right) - 210 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 90 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 60 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 20 \, {\left(36 \, b^{5} \cosh\left(d x + c\right)^{7} - 63 \, a b^{4} \cosh\left(d x + c\right)^{6} + 28 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{5} - 6 \, a^{3} b^{2} - 3 \, a b^{4} + 480 \, {\left(a^{5} + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 105 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 60 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 10 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2} + 10 \, {\left(27 \, b^{5} \cosh\left(d x + c\right)^{8} - 54 \, a b^{4} \cosh\left(d x + c\right)^{7} + 28 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + 960 \, {\left(a^{5} + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 126 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 4 \, a^{2} b^{3} - b^{5} + 90 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)^{4} - 36 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)^{2} - 18 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 960 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{5} + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a^{5} + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{5} + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a^{5} + a^{3} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{5} + a^{3} b^{2}\right)} \sinh\left(d x + c\right)^{5}\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 5 \, {\left(12 \, b^{5} \cosh\left(d x + c\right)^{9} - 27 \, a b^{4} \cosh\left(d x + c\right)^{8} + 16 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{7} + 960 \, {\left(a^{5} + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 84 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 72 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)^{5} - 3 \, a b^{4} - 48 \, {\left(8 \, a^{4} b + 6 \, a^{2} b^{3} - b^{5}\right)} \cosh\left(d x + c\right)^{3} - 36 \, {\left(2 \, a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(4 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{960 \, {\left(b^{6} d \cosh\left(d x + c\right)^{5} + 5 \, b^{6} d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, b^{6} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, b^{6} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, b^{6} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + b^{6} d \sinh\left(d x + c\right)^{5}\right)}}"," ",0,"1/960*(6*b^5*cosh(d*x + c)^10 + 6*b^5*sinh(d*x + c)^10 - 15*a*b^4*cosh(d*x + c)^9 + 15*(4*b^5*cosh(d*x + c) - a*b^4)*sinh(d*x + c)^9 + 10*(4*a^2*b^3 + b^5)*cosh(d*x + c)^8 + 5*(54*b^5*cosh(d*x + c)^2 - 27*a*b^4*cosh(d*x + c) + 8*a^2*b^3 + 2*b^5)*sinh(d*x + c)^8 + 960*(a^5 + a^3*b^2)*d*x*cosh(d*x + c)^5 - 60*(2*a^3*b^2 + a*b^4)*cosh(d*x + c)^7 + 20*(36*b^5*cosh(d*x + c)^3 - 27*a*b^4*cosh(d*x + c)^2 - 6*a^3*b^2 - 3*a*b^4 + 4*(4*a^2*b^3 + b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 60*(8*a^4*b + 6*a^2*b^3 - b^5)*cosh(d*x + c)^6 + 20*(63*b^5*cosh(d*x + c)^4 - 63*a*b^4*cosh(d*x + c)^3 + 24*a^4*b + 18*a^2*b^3 - 3*b^5 + 14*(4*a^2*b^3 + b^5)*cosh(d*x + c)^2 - 21*(2*a^3*b^2 + a*b^4)*cosh(d*x + c))*sinh(d*x + c)^6 - 15*a*b^4*cosh(d*x + c) + 2*(756*b^5*cosh(d*x + c)^5 - 945*a*b^4*cosh(d*x + c)^4 + 280*(4*a^2*b^3 + b^5)*cosh(d*x + c)^3 + 480*(a^5 + a^3*b^2)*d*x - 630*(2*a^3*b^2 + a*b^4)*cosh(d*x + c)^2 + 180*(8*a^4*b + 6*a^2*b^3 - b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 6*b^5 - 60*(8*a^4*b + 6*a^2*b^3 - b^5)*cosh(d*x + c)^4 + 10*(126*b^5*cosh(d*x + c)^6 - 189*a*b^4*cosh(d*x + c)^5 - 48*a^4*b - 36*a^2*b^3 + 6*b^5 + 70*(4*a^2*b^3 + b^5)*cosh(d*x + c)^4 + 480*(a^5 + a^3*b^2)*d*x*cosh(d*x + c) - 210*(2*a^3*b^2 + a*b^4)*cosh(d*x + c)^3 + 90*(8*a^4*b + 6*a^2*b^3 - b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 60*(2*a^3*b^2 + a*b^4)*cosh(d*x + c)^3 + 20*(36*b^5*cosh(d*x + c)^7 - 63*a*b^4*cosh(d*x + c)^6 + 28*(4*a^2*b^3 + b^5)*cosh(d*x + c)^5 - 6*a^3*b^2 - 3*a*b^4 + 480*(a^5 + a^3*b^2)*d*x*cosh(d*x + c)^2 - 105*(2*a^3*b^2 + a*b^4)*cosh(d*x + c)^4 + 60*(8*a^4*b + 6*a^2*b^3 - b^5)*cosh(d*x + c)^3 - 12*(8*a^4*b + 6*a^2*b^3 - b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - 10*(4*a^2*b^3 + b^5)*cosh(d*x + c)^2 + 10*(27*b^5*cosh(d*x + c)^8 - 54*a*b^4*cosh(d*x + c)^7 + 28*(4*a^2*b^3 + b^5)*cosh(d*x + c)^6 + 960*(a^5 + a^3*b^2)*d*x*cosh(d*x + c)^3 - 126*(2*a^3*b^2 + a*b^4)*cosh(d*x + c)^5 - 4*a^2*b^3 - b^5 + 90*(8*a^4*b + 6*a^2*b^3 - b^5)*cosh(d*x + c)^4 - 36*(8*a^4*b + 6*a^2*b^3 - b^5)*cosh(d*x + c)^2 - 18*(2*a^3*b^2 + a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 - 960*((a^5 + a^3*b^2)*cosh(d*x + c)^5 + 5*(a^5 + a^3*b^2)*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a^5 + a^3*b^2)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a^5 + a^3*b^2)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a^5 + a^3*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + (a^5 + a^3*b^2)*sinh(d*x + c)^5)*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + 5*(12*b^5*cosh(d*x + c)^9 - 27*a*b^4*cosh(d*x + c)^8 + 16*(4*a^2*b^3 + b^5)*cosh(d*x + c)^7 + 960*(a^5 + a^3*b^2)*d*x*cosh(d*x + c)^4 - 84*(2*a^3*b^2 + a*b^4)*cosh(d*x + c)^6 + 72*(8*a^4*b + 6*a^2*b^3 - b^5)*cosh(d*x + c)^5 - 3*a*b^4 - 48*(8*a^4*b + 6*a^2*b^3 - b^5)*cosh(d*x + c)^3 - 36*(2*a^3*b^2 + a*b^4)*cosh(d*x + c)^2 - 4*(4*a^2*b^3 + b^5)*cosh(d*x + c))*sinh(d*x + c))/(b^6*d*cosh(d*x + c)^5 + 5*b^6*d*cosh(d*x + c)^4*sinh(d*x + c) + 10*b^6*d*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*b^6*d*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*b^6*d*cosh(d*x + c)*sinh(d*x + c)^4 + b^6*d*sinh(d*x + c)^5)","B",0
405,0,0,0,0.453042," ","integrate(cosh(d*x+c)^3*sinh(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{3}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)^3*sinh(d*x + c)^3/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
406,1,4546,0,0.736869," ","integrate((f*x+e)^3*sinh(d*x+c)^2*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 2 \, {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 6 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 12 \, {\left(a^{2} b + b^{3}\right)} d e f^{2} + 12 \, {\left(a^{2} b + b^{3}\right)} f^{3} + 6 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b + b^{3}\right)} d e f^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b + b^{3}\right)} d e f^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d f^{3}\right)} x - {\left({\left(a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{3} + a b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{3} + a b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c^{4} f^{3}\right)} \cosh\left(d x + c\right) + 12 \, {\left({\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left({\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{2} f^{3} x^{2} + 2 \, a^{3} d^{2} e f^{2} x + a^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left({\left(12 \, a b^{2} d^{2} f^{3} x^{2} + 12 i \, b^{3} d^{2} f^{3} x^{2} + 24 \, a b^{2} d^{2} e f^{2} x + 24 i \, b^{3} d^{2} e f^{2} x + 12 \, a b^{2} d^{2} e^{2} f + 12 i \, b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(12 \, a b^{2} d^{2} f^{3} x^{2} + 12 i \, b^{3} d^{2} f^{3} x^{2} + 24 \, a b^{2} d^{2} e f^{2} x + 24 i \, b^{3} d^{2} e f^{2} x + 12 \, a b^{2} d^{2} e^{2} f + 12 i \, b^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left({\left(12 \, a b^{2} d^{2} f^{3} x^{2} - 12 i \, b^{3} d^{2} f^{3} x^{2} + 24 \, a b^{2} d^{2} e f^{2} x - 24 i \, b^{3} d^{2} e f^{2} x + 12 \, a b^{2} d^{2} e^{2} f - 12 i \, b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(12 \, a b^{2} d^{2} f^{3} x^{2} - 12 i \, b^{3} d^{2} f^{3} x^{2} + 24 \, a b^{2} d^{2} e f^{2} x - 24 i \, b^{3} d^{2} e f^{2} x + 12 \, a b^{2} d^{2} e^{2} f - 12 i \, b^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 4 \, {\left({\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 4 \, {\left({\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{3} e^{3} - 3 \, a^{3} c d^{2} e^{2} f + 3 \, a^{3} c^{2} d e f^{2} - a^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 4 \, {\left({\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left({\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{3} f^{3} x^{3} + 3 \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{3} d^{3} e^{2} f x + 3 \, a^{3} c d^{2} e^{2} f - 3 \, a^{3} c^{2} d e f^{2} + a^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(4 \, a b^{2} d^{3} e^{3} + 4 i \, b^{3} d^{3} e^{3} - 12 \, a b^{2} c d^{2} e^{2} f - 12 i \, b^{3} c d^{2} e^{2} f + 12 \, a b^{2} c^{2} d e f^{2} + 12 i \, b^{3} c^{2} d e f^{2} - 4 \, a b^{2} c^{3} f^{3} - 4 i \, b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(4 \, a b^{2} d^{3} e^{3} + 4 i \, b^{3} d^{3} e^{3} - 12 \, a b^{2} c d^{2} e^{2} f - 12 i \, b^{3} c d^{2} e^{2} f + 12 \, a b^{2} c^{2} d e f^{2} + 12 i \, b^{3} c^{2} d e f^{2} - 4 \, a b^{2} c^{3} f^{3} - 4 i \, b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left({\left(4 \, a b^{2} d^{3} e^{3} - 4 i \, b^{3} d^{3} e^{3} - 12 \, a b^{2} c d^{2} e^{2} f + 12 i \, b^{3} c d^{2} e^{2} f + 12 \, a b^{2} c^{2} d e f^{2} - 12 i \, b^{3} c^{2} d e f^{2} - 4 \, a b^{2} c^{3} f^{3} + 4 i \, b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(4 \, a b^{2} d^{3} e^{3} - 4 i \, b^{3} d^{3} e^{3} - 12 \, a b^{2} c d^{2} e^{2} f + 12 i \, b^{3} c d^{2} e^{2} f + 12 \, a b^{2} c^{2} d e f^{2} - 12 i \, b^{3} c^{2} d e f^{2} - 4 \, a b^{2} c^{3} f^{3} + 4 i \, b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left({\left(4 \, a b^{2} d^{3} f^{3} x^{3} - 4 i \, b^{3} d^{3} f^{3} x^{3} + 12 \, a b^{2} d^{3} e f^{2} x^{2} - 12 i \, b^{3} d^{3} e f^{2} x^{2} + 12 \, a b^{2} d^{3} e^{2} f x - 12 i \, b^{3} d^{3} e^{2} f x + 12 \, a b^{2} c d^{2} e^{2} f - 12 i \, b^{3} c d^{2} e^{2} f - 12 \, a b^{2} c^{2} d e f^{2} + 12 i \, b^{3} c^{2} d e f^{2} + 4 \, a b^{2} c^{3} f^{3} - 4 i \, b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(4 \, a b^{2} d^{3} f^{3} x^{3} - 4 i \, b^{3} d^{3} f^{3} x^{3} + 12 \, a b^{2} d^{3} e f^{2} x^{2} - 12 i \, b^{3} d^{3} e f^{2} x^{2} + 12 \, a b^{2} d^{3} e^{2} f x - 12 i \, b^{3} d^{3} e^{2} f x + 12 \, a b^{2} c d^{2} e^{2} f - 12 i \, b^{3} c d^{2} e^{2} f - 12 \, a b^{2} c^{2} d e f^{2} + 12 i \, b^{3} c^{2} d e f^{2} + 4 \, a b^{2} c^{3} f^{3} - 4 i \, b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left({\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 i \, b^{3} d^{3} f^{3} x^{3} + 12 \, a b^{2} d^{3} e f^{2} x^{2} + 12 i \, b^{3} d^{3} e f^{2} x^{2} + 12 \, a b^{2} d^{3} e^{2} f x + 12 i \, b^{3} d^{3} e^{2} f x + 12 \, a b^{2} c d^{2} e^{2} f + 12 i \, b^{3} c d^{2} e^{2} f - 12 \, a b^{2} c^{2} d e f^{2} - 12 i \, b^{3} c^{2} d e f^{2} + 4 \, a b^{2} c^{3} f^{3} + 4 i \, b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(4 \, a b^{2} d^{3} f^{3} x^{3} + 4 i \, b^{3} d^{3} f^{3} x^{3} + 12 \, a b^{2} d^{3} e f^{2} x^{2} + 12 i \, b^{3} d^{3} e f^{2} x^{2} + 12 \, a b^{2} d^{3} e^{2} f x + 12 i \, b^{3} d^{3} e^{2} f x + 12 \, a b^{2} c d^{2} e^{2} f + 12 i \, b^{3} c d^{2} e^{2} f - 12 \, a b^{2} c^{2} d e f^{2} - 12 i \, b^{3} c^{2} d e f^{2} + 4 \, a b^{2} c^{3} f^{3} + 4 i \, b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + 24 \, {\left(a^{3} f^{3} \cosh\left(d x + c\right) + a^{3} f^{3} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left(a^{3} f^{3} \cosh\left(d x + c\right) + a^{3} f^{3} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + {\left({\left(24 \, a b^{2} f^{3} + 24 i \, b^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(24 \, a b^{2} f^{3} + 24 i \, b^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left({\left(24 \, a b^{2} f^{3} - 24 i \, b^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(24 \, a b^{2} f^{3} - 24 i \, b^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 24 \, {\left({\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left({\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{3} d f^{3} x + a^{3} d e f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - {\left({\left(24 \, a b^{2} d f^{3} x + 24 i \, b^{3} d f^{3} x + 24 \, a b^{2} d e f^{2} + 24 i \, b^{3} d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(24 \, a b^{2} d f^{3} x + 24 i \, b^{3} d f^{3} x + 24 \, a b^{2} d e f^{2} + 24 i \, b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left({\left(24 \, a b^{2} d f^{3} x - 24 i \, b^{3} d f^{3} x + 24 \, a b^{2} d e f^{2} - 24 i \, b^{3} d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(24 \, a b^{2} d f^{3} x - 24 i \, b^{3} d f^{3} x + 24 \, a b^{2} d e f^{2} - 24 i \, b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - {\left({\left(a^{3} + a b^{2}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} d^{4} e^{3} x + 8 \, {\left(a^{3} + a b^{2}\right)} c d^{3} e^{3} - 12 \, {\left(a^{3} + a b^{2}\right)} c^{2} d^{2} e^{2} f + 8 \, {\left(a^{3} + a b^{2}\right)} c^{3} d e f^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} c^{4} f^{3} + 4 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 6 \, {\left(a^{2} b + b^{3}\right)} d e f^{2} - 6 \, {\left(a^{2} b + b^{3}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{2} b + b^{3}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{4} \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{4} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/4*(2*(a^2*b + b^3)*d^3*f^3*x^3 + 2*(a^2*b + b^3)*d^3*e^3 + 6*(a^2*b + b^3)*d^2*e^2*f + 12*(a^2*b + b^3)*d*e*f^2 + 12*(a^2*b + b^3)*f^3 + 6*((a^2*b + b^3)*d^3*e*f^2 + (a^2*b + b^3)*d^2*f^3)*x^2 - 2*((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 - 3*(a^2*b + b^3)*d^2*e^2*f + 6*(a^2*b + b^3)*d*e*f^2 - 6*(a^2*b + b^3)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^2*b + b^3)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^2*b + b^3)*d^2*e*f^2 + 2*(a^2*b + b^3)*d*f^3)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 - 3*(a^2*b + b^3)*d^2*e^2*f + 6*(a^2*b + b^3)*d*e*f^2 - 6*(a^2*b + b^3)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^2*b + b^3)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^2*b + b^3)*d^2*e*f^2 + 2*(a^2*b + b^3)*d*f^3)*x)*sinh(d*x + c)^2 + 6*((a^2*b + b^3)*d^3*e^2*f + 2*(a^2*b + b^3)*d^2*e*f^2 + 2*(a^2*b + b^3)*d*f^3)*x - ((a^3 + a*b^2)*d^4*f^3*x^4 + 4*(a^3 + a*b^2)*d^4*e*f^2*x^3 + 6*(a^3 + a*b^2)*d^4*e^2*f*x^2 + 4*(a^3 + a*b^2)*d^4*e^3*x + 8*(a^3 + a*b^2)*c*d^3*e^3 - 12*(a^3 + a*b^2)*c^2*d^2*e^2*f + 8*(a^3 + a*b^2)*c^3*d*e*f^2 - 2*(a^3 + a*b^2)*c^4*f^3)*cosh(d*x + c) + 12*((a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*cosh(d*x + c) + (a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*((a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*cosh(d*x + c) + (a^3*d^2*f^3*x^2 + 2*a^3*d^2*e*f^2*x + a^3*d^2*e^2*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + ((12*a*b^2*d^2*f^3*x^2 + 12*I*b^3*d^2*f^3*x^2 + 24*a*b^2*d^2*e*f^2*x + 24*I*b^3*d^2*e*f^2*x + 12*a*b^2*d^2*e^2*f + 12*I*b^3*d^2*e^2*f)*cosh(d*x + c) + (12*a*b^2*d^2*f^3*x^2 + 12*I*b^3*d^2*f^3*x^2 + 24*a*b^2*d^2*e*f^2*x + 24*I*b^3*d^2*e*f^2*x + 12*a*b^2*d^2*e^2*f + 12*I*b^3*d^2*e^2*f)*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + ((12*a*b^2*d^2*f^3*x^2 - 12*I*b^3*d^2*f^3*x^2 + 24*a*b^2*d^2*e*f^2*x - 24*I*b^3*d^2*e*f^2*x + 12*a*b^2*d^2*e^2*f - 12*I*b^3*d^2*e^2*f)*cosh(d*x + c) + (12*a*b^2*d^2*f^3*x^2 - 12*I*b^3*d^2*f^3*x^2 + 24*a*b^2*d^2*e*f^2*x - 24*I*b^3*d^2*e*f^2*x + 12*a*b^2*d^2*e^2*f - 12*I*b^3*d^2*e^2*f)*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + 4*((a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*cosh(d*x + c) + (a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 4*((a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*cosh(d*x + c) + (a^3*d^3*e^3 - 3*a^3*c*d^2*e^2*f + 3*a^3*c^2*d*e*f^2 - a^3*c^3*f^3)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 4*((a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*cosh(d*x + c) + (a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*((a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*cosh(d*x + c) + (a^3*d^3*f^3*x^3 + 3*a^3*d^3*e*f^2*x^2 + 3*a^3*d^3*e^2*f*x + 3*a^3*c*d^2*e^2*f - 3*a^3*c^2*d*e*f^2 + a^3*c^3*f^3)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + ((4*a*b^2*d^3*e^3 + 4*I*b^3*d^3*e^3 - 12*a*b^2*c*d^2*e^2*f - 12*I*b^3*c*d^2*e^2*f + 12*a*b^2*c^2*d*e*f^2 + 12*I*b^3*c^2*d*e*f^2 - 4*a*b^2*c^3*f^3 - 4*I*b^3*c^3*f^3)*cosh(d*x + c) + (4*a*b^2*d^3*e^3 + 4*I*b^3*d^3*e^3 - 12*a*b^2*c*d^2*e^2*f - 12*I*b^3*c*d^2*e^2*f + 12*a*b^2*c^2*d*e*f^2 + 12*I*b^3*c^2*d*e*f^2 - 4*a*b^2*c^3*f^3 - 4*I*b^3*c^3*f^3)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) + ((4*a*b^2*d^3*e^3 - 4*I*b^3*d^3*e^3 - 12*a*b^2*c*d^2*e^2*f + 12*I*b^3*c*d^2*e^2*f + 12*a*b^2*c^2*d*e*f^2 - 12*I*b^3*c^2*d*e*f^2 - 4*a*b^2*c^3*f^3 + 4*I*b^3*c^3*f^3)*cosh(d*x + c) + (4*a*b^2*d^3*e^3 - 4*I*b^3*d^3*e^3 - 12*a*b^2*c*d^2*e^2*f + 12*I*b^3*c*d^2*e^2*f + 12*a*b^2*c^2*d*e*f^2 - 12*I*b^3*c^2*d*e*f^2 - 4*a*b^2*c^3*f^3 + 4*I*b^3*c^3*f^3)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) + ((4*a*b^2*d^3*f^3*x^3 - 4*I*b^3*d^3*f^3*x^3 + 12*a*b^2*d^3*e*f^2*x^2 - 12*I*b^3*d^3*e*f^2*x^2 + 12*a*b^2*d^3*e^2*f*x - 12*I*b^3*d^3*e^2*f*x + 12*a*b^2*c*d^2*e^2*f - 12*I*b^3*c*d^2*e^2*f - 12*a*b^2*c^2*d*e*f^2 + 12*I*b^3*c^2*d*e*f^2 + 4*a*b^2*c^3*f^3 - 4*I*b^3*c^3*f^3)*cosh(d*x + c) + (4*a*b^2*d^3*f^3*x^3 - 4*I*b^3*d^3*f^3*x^3 + 12*a*b^2*d^3*e*f^2*x^2 - 12*I*b^3*d^3*e*f^2*x^2 + 12*a*b^2*d^3*e^2*f*x - 12*I*b^3*d^3*e^2*f*x + 12*a*b^2*c*d^2*e^2*f - 12*I*b^3*c*d^2*e^2*f - 12*a*b^2*c^2*d*e*f^2 + 12*I*b^3*c^2*d*e*f^2 + 4*a*b^2*c^3*f^3 - 4*I*b^3*c^3*f^3)*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + ((4*a*b^2*d^3*f^3*x^3 + 4*I*b^3*d^3*f^3*x^3 + 12*a*b^2*d^3*e*f^2*x^2 + 12*I*b^3*d^3*e*f^2*x^2 + 12*a*b^2*d^3*e^2*f*x + 12*I*b^3*d^3*e^2*f*x + 12*a*b^2*c*d^2*e^2*f + 12*I*b^3*c*d^2*e^2*f - 12*a*b^2*c^2*d*e*f^2 - 12*I*b^3*c^2*d*e*f^2 + 4*a*b^2*c^3*f^3 + 4*I*b^3*c^3*f^3)*cosh(d*x + c) + (4*a*b^2*d^3*f^3*x^3 + 4*I*b^3*d^3*f^3*x^3 + 12*a*b^2*d^3*e*f^2*x^2 + 12*I*b^3*d^3*e*f^2*x^2 + 12*a*b^2*d^3*e^2*f*x + 12*I*b^3*d^3*e^2*f*x + 12*a*b^2*c*d^2*e^2*f + 12*I*b^3*c*d^2*e^2*f - 12*a*b^2*c^2*d*e*f^2 - 12*I*b^3*c^2*d*e*f^2 + 4*a*b^2*c^3*f^3 + 4*I*b^3*c^3*f^3)*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + 24*(a^3*f^3*cosh(d*x + c) + a^3*f^3*sinh(d*x + c))*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*(a^3*f^3*cosh(d*x + c) + a^3*f^3*sinh(d*x + c))*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + ((24*a*b^2*f^3 + 24*I*b^3*f^3)*cosh(d*x + c) + (24*a*b^2*f^3 + 24*I*b^3*f^3)*sinh(d*x + c))*polylog(4, I*cosh(d*x + c) + I*sinh(d*x + c)) + ((24*a*b^2*f^3 - 24*I*b^3*f^3)*cosh(d*x + c) + (24*a*b^2*f^3 - 24*I*b^3*f^3)*sinh(d*x + c))*polylog(4, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 24*((a^3*d*f^3*x + a^3*d*e*f^2)*cosh(d*x + c) + (a^3*d*f^3*x + a^3*d*e*f^2)*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*((a^3*d*f^3*x + a^3*d*e*f^2)*cosh(d*x + c) + (a^3*d*f^3*x + a^3*d*e*f^2)*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - ((24*a*b^2*d*f^3*x + 24*I*b^3*d*f^3*x + 24*a*b^2*d*e*f^2 + 24*I*b^3*d*e*f^2)*cosh(d*x + c) + (24*a*b^2*d*f^3*x + 24*I*b^3*d*f^3*x + 24*a*b^2*d*e*f^2 + 24*I*b^3*d*e*f^2)*sinh(d*x + c))*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - ((24*a*b^2*d*f^3*x - 24*I*b^3*d*f^3*x + 24*a*b^2*d*e*f^2 - 24*I*b^3*d*e*f^2)*cosh(d*x + c) + (24*a*b^2*d*f^3*x - 24*I*b^3*d*f^3*x + 24*a*b^2*d*e*f^2 - 24*I*b^3*d*e*f^2)*sinh(d*x + c))*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) - ((a^3 + a*b^2)*d^4*f^3*x^4 + 4*(a^3 + a*b^2)*d^4*e*f^2*x^3 + 6*(a^3 + a*b^2)*d^4*e^2*f*x^2 + 4*(a^3 + a*b^2)*d^4*e^3*x + 8*(a^3 + a*b^2)*c*d^3*e^3 - 12*(a^3 + a*b^2)*c^2*d^2*e^2*f + 8*(a^3 + a*b^2)*c^3*d*e*f^2 - 2*(a^3 + a*b^2)*c^4*f^3 + 4*((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 - 3*(a^2*b + b^3)*d^2*e^2*f + 6*(a^2*b + b^3)*d*e*f^2 - 6*(a^2*b + b^3)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^2*b + b^3)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^2*b + b^3)*d^2*e*f^2 + 2*(a^2*b + b^3)*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^2 + b^4)*d^4*cosh(d*x + c) + (a^2*b^2 + b^4)*d^4*sinh(d*x + c))","C",0
407,1,2793,0,0.645119," ","integrate((f*x+e)^2*sinh(d*x+c)^2*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 3 \, {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 6 \, {\left(a^{2} b + b^{3}\right)} d e f + 6 \, {\left(a^{2} b + b^{3}\right)} f^{2} - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left(a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left(a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{3} + a b^{2}\right)} c^{3} f^{2}\right)} \cosh\left(d x + c\right) + 12 \, {\left({\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right) + {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left({\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right) + {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left({\left(12 \, a b^{2} d f^{2} x + 12 i \, b^{3} d f^{2} x + 12 \, a b^{2} d e f + 12 i \, b^{3} d e f\right)} \cosh\left(d x + c\right) + {\left(12 \, a b^{2} d f^{2} x + 12 i \, b^{3} d f^{2} x + 12 \, a b^{2} d e f + 12 i \, b^{3} d e f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left({\left(12 \, a b^{2} d f^{2} x - 12 i \, b^{3} d f^{2} x + 12 \, a b^{2} d e f - 12 i \, b^{3} d e f\right)} \cosh\left(d x + c\right) + {\left(12 \, a b^{2} d f^{2} x - 12 i \, b^{3} d f^{2} x + 12 \, a b^{2} d e f - 12 i \, b^{3} d e f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 6 \, {\left({\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 6 \, {\left({\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 6 \, {\left({\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left({\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(6 \, a b^{2} d^{2} e^{2} + 6 i \, b^{3} d^{2} e^{2} - 12 \, a b^{2} c d e f - 12 i \, b^{3} c d e f + 6 \, a b^{2} c^{2} f^{2} + 6 i \, b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(6 \, a b^{2} d^{2} e^{2} + 6 i \, b^{3} d^{2} e^{2} - 12 \, a b^{2} c d e f - 12 i \, b^{3} c d e f + 6 \, a b^{2} c^{2} f^{2} + 6 i \, b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left({\left(6 \, a b^{2} d^{2} e^{2} - 6 i \, b^{3} d^{2} e^{2} - 12 \, a b^{2} c d e f + 12 i \, b^{3} c d e f + 6 \, a b^{2} c^{2} f^{2} - 6 i \, b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(6 \, a b^{2} d^{2} e^{2} - 6 i \, b^{3} d^{2} e^{2} - 12 \, a b^{2} c d e f + 12 i \, b^{3} c d e f + 6 \, a b^{2} c^{2} f^{2} - 6 i \, b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left({\left(6 \, a b^{2} d^{2} f^{2} x^{2} - 6 i \, b^{3} d^{2} f^{2} x^{2} + 12 \, a b^{2} d^{2} e f x - 12 i \, b^{3} d^{2} e f x + 12 \, a b^{2} c d e f - 12 i \, b^{3} c d e f - 6 \, a b^{2} c^{2} f^{2} + 6 i \, b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(6 \, a b^{2} d^{2} f^{2} x^{2} - 6 i \, b^{3} d^{2} f^{2} x^{2} + 12 \, a b^{2} d^{2} e f x - 12 i \, b^{3} d^{2} e f x + 12 \, a b^{2} c d e f - 12 i \, b^{3} c d e f - 6 \, a b^{2} c^{2} f^{2} + 6 i \, b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left({\left(6 \, a b^{2} d^{2} f^{2} x^{2} + 6 i \, b^{3} d^{2} f^{2} x^{2} + 12 \, a b^{2} d^{2} e f x + 12 i \, b^{3} d^{2} e f x + 12 \, a b^{2} c d e f + 12 i \, b^{3} c d e f - 6 \, a b^{2} c^{2} f^{2} - 6 i \, b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(6 \, a b^{2} d^{2} f^{2} x^{2} + 6 i \, b^{3} d^{2} f^{2} x^{2} + 12 \, a b^{2} d^{2} e f x + 12 i \, b^{3} d^{2} e f x + 12 \, a b^{2} c d e f + 12 i \, b^{3} c d e f - 6 \, a b^{2} c^{2} f^{2} - 6 i \, b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 12 \, {\left(a^{3} f^{2} \cosh\left(d x + c\right) + a^{3} f^{2} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a^{3} f^{2} \cosh\left(d x + c\right) + a^{3} f^{2} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - {\left({\left(12 \, a b^{2} f^{2} + 12 i \, b^{3} f^{2}\right)} \cosh\left(d x + c\right) + {\left(12 \, a b^{2} f^{2} + 12 i \, b^{3} f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left({\left(12 \, a b^{2} f^{2} - 12 i \, b^{3} f^{2}\right)} \cosh\left(d x + c\right) + {\left(12 \, a b^{2} f^{2} - 12 i \, b^{3} f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{2} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} x + 6 \, {\left(a^{3} + a b^{2}\right)} c d^{2} e^{2} - 6 \, {\left(a^{3} + a b^{2}\right)} c^{2} d e f + 2 \, {\left(a^{3} + a b^{2}\right)} c^{3} f^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left(a^{2} b + b^{3}\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/6*(3*(a^2*b + b^3)*d^2*f^2*x^2 + 3*(a^2*b + b^3)*d^2*e^2 + 6*(a^2*b + b^3)*d*e*f + 6*(a^2*b + b^3)*f^2 - 3*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 - 2*(a^2*b + b^3)*d*e*f + 2*(a^2*b + b^3)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^2 - 3*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 - 2*(a^2*b + b^3)*d*e*f + 2*(a^2*b + b^3)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*sinh(d*x + c)^2 + 6*((a^2*b + b^3)*d^2*e*f + (a^2*b + b^3)*d*f^2)*x - 2*((a^3 + a*b^2)*d^3*f^2*x^3 + 3*(a^3 + a*b^2)*d^3*e*f*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*x + 6*(a^3 + a*b^2)*c*d^2*e^2 - 6*(a^3 + a*b^2)*c^2*d*e*f + 2*(a^3 + a*b^2)*c^3*f^2)*cosh(d*x + c) + 12*((a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c) + (a^3*d*f^2*x + a^3*d*e*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*((a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c) + (a^3*d*f^2*x + a^3*d*e*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + ((12*a*b^2*d*f^2*x + 12*I*b^3*d*f^2*x + 12*a*b^2*d*e*f + 12*I*b^3*d*e*f)*cosh(d*x + c) + (12*a*b^2*d*f^2*x + 12*I*b^3*d*f^2*x + 12*a*b^2*d*e*f + 12*I*b^3*d*e*f)*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + ((12*a*b^2*d*f^2*x - 12*I*b^3*d*f^2*x + 12*a*b^2*d*e*f - 12*I*b^3*d*e*f)*cosh(d*x + c) + (12*a*b^2*d*f^2*x - 12*I*b^3*d*f^2*x + 12*a*b^2*d*e*f - 12*I*b^3*d*e*f)*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + 6*((a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c) + (a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 6*((a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c) + (a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 6*((a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c) + (a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 6*((a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c) + (a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + ((6*a*b^2*d^2*e^2 + 6*I*b^3*d^2*e^2 - 12*a*b^2*c*d*e*f - 12*I*b^3*c*d*e*f + 6*a*b^2*c^2*f^2 + 6*I*b^3*c^2*f^2)*cosh(d*x + c) + (6*a*b^2*d^2*e^2 + 6*I*b^3*d^2*e^2 - 12*a*b^2*c*d*e*f - 12*I*b^3*c*d*e*f + 6*a*b^2*c^2*f^2 + 6*I*b^3*c^2*f^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) + ((6*a*b^2*d^2*e^2 - 6*I*b^3*d^2*e^2 - 12*a*b^2*c*d*e*f + 12*I*b^3*c*d*e*f + 6*a*b^2*c^2*f^2 - 6*I*b^3*c^2*f^2)*cosh(d*x + c) + (6*a*b^2*d^2*e^2 - 6*I*b^3*d^2*e^2 - 12*a*b^2*c*d*e*f + 12*I*b^3*c*d*e*f + 6*a*b^2*c^2*f^2 - 6*I*b^3*c^2*f^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) + ((6*a*b^2*d^2*f^2*x^2 - 6*I*b^3*d^2*f^2*x^2 + 12*a*b^2*d^2*e*f*x - 12*I*b^3*d^2*e*f*x + 12*a*b^2*c*d*e*f - 12*I*b^3*c*d*e*f - 6*a*b^2*c^2*f^2 + 6*I*b^3*c^2*f^2)*cosh(d*x + c) + (6*a*b^2*d^2*f^2*x^2 - 6*I*b^3*d^2*f^2*x^2 + 12*a*b^2*d^2*e*f*x - 12*I*b^3*d^2*e*f*x + 12*a*b^2*c*d*e*f - 12*I*b^3*c*d*e*f - 6*a*b^2*c^2*f^2 + 6*I*b^3*c^2*f^2)*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + ((6*a*b^2*d^2*f^2*x^2 + 6*I*b^3*d^2*f^2*x^2 + 12*a*b^2*d^2*e*f*x + 12*I*b^3*d^2*e*f*x + 12*a*b^2*c*d*e*f + 12*I*b^3*c*d*e*f - 6*a*b^2*c^2*f^2 - 6*I*b^3*c^2*f^2)*cosh(d*x + c) + (6*a*b^2*d^2*f^2*x^2 + 6*I*b^3*d^2*f^2*x^2 + 12*a*b^2*d^2*e*f*x + 12*I*b^3*d^2*e*f*x + 12*a*b^2*c*d*e*f + 12*I*b^3*c*d*e*f - 6*a*b^2*c^2*f^2 - 6*I*b^3*c^2*f^2)*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 12*(a^3*f^2*cosh(d*x + c) + a^3*f^2*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(a^3*f^2*cosh(d*x + c) + a^3*f^2*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - ((12*a*b^2*f^2 + 12*I*b^3*f^2)*cosh(d*x + c) + (12*a*b^2*f^2 + 12*I*b^3*f^2)*sinh(d*x + c))*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - ((12*a*b^2*f^2 - 12*I*b^3*f^2)*cosh(d*x + c) + (12*a*b^2*f^2 - 12*I*b^3*f^2)*sinh(d*x + c))*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*((a^3 + a*b^2)*d^3*f^2*x^3 + 3*(a^3 + a*b^2)*d^3*e*f*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*x + 6*(a^3 + a*b^2)*c*d^2*e^2 - 6*(a^3 + a*b^2)*c^2*d*e*f + 2*(a^3 + a*b^2)*c^3*f^2 + 3*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 - 2*(a^2*b + b^3)*d*e*f + 2*(a^2*b + b^3)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^2 + b^4)*d^3*cosh(d*x + c) + (a^2*b^2 + b^4)*d^3*sinh(d*x + c))","C",0
408,1,1420,0,0.530902," ","integrate((f*x+e)*sinh(d*x+c)^2*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left(a^{2} b + b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b + b^{3}\right)} f - {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e x + 4 \, {\left(a^{3} + a b^{2}\right)} c d e - 2 \, {\left(a^{3} + a b^{2}\right)} c^{2} f\right)} \cosh\left(d x + c\right) + 2 \, {\left(a^{3} f \cosh\left(d x + c\right) + a^{3} f \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(a^{3} f \cosh\left(d x + c\right) + a^{3} f \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left({\left(2 \, a b^{2} f + 2 i \, b^{3} f\right)} \cosh\left(d x + c\right) + {\left(2 \, a b^{2} f + 2 i \, b^{3} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left({\left(2 \, a b^{2} f - 2 i \, b^{3} f\right)} \cosh\left(d x + c\right) + {\left(2 \, a b^{2} f - 2 i \, b^{3} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right) + {\left(a^{3} d e - a^{3} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right) + {\left(a^{3} d e - a^{3} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right) + {\left(a^{3} d f x + a^{3} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right) + {\left(a^{3} d f x + a^{3} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(2 \, a b^{2} d e + 2 i \, b^{3} d e - 2 \, a b^{2} c f - 2 i \, b^{3} c f\right)} \cosh\left(d x + c\right) + {\left(2 \, a b^{2} d e + 2 i \, b^{3} d e - 2 \, a b^{2} c f - 2 i \, b^{3} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left({\left(2 \, a b^{2} d e - 2 i \, b^{3} d e - 2 \, a b^{2} c f + 2 i \, b^{3} c f\right)} \cosh\left(d x + c\right) + {\left(2 \, a b^{2} d e - 2 i \, b^{3} d e - 2 \, a b^{2} c f + 2 i \, b^{3} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left({\left(2 \, a b^{2} d f x - 2 i \, b^{3} d f x + 2 \, a b^{2} c f - 2 i \, b^{3} c f\right)} \cosh\left(d x + c\right) + {\left(2 \, a b^{2} d f x - 2 i \, b^{3} d f x + 2 \, a b^{2} c f - 2 i \, b^{3} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left({\left(2 \, a b^{2} d f x + 2 i \, b^{3} d f x + 2 \, a b^{2} c f + 2 i \, b^{3} c f\right)} \cosh\left(d x + c\right) + {\left(2 \, a b^{2} d f x + 2 i \, b^{3} d f x + 2 \, a b^{2} c f + 2 i \, b^{3} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{3} + a b^{2}\right)} d^{2} f x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e x + 4 \, {\left(a^{3} + a b^{2}\right)} c d e - 2 \, {\left(a^{3} + a b^{2}\right)} c^{2} f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - (a^2*b + b^3)*f)*cosh(d*x + c)^2 - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - (a^2*b + b^3)*f)*sinh(d*x + c)^2 + (a^2*b + b^3)*f - ((a^3 + a*b^2)*d^2*f*x^2 + 2*(a^3 + a*b^2)*d^2*e*x + 4*(a^3 + a*b^2)*c*d*e - 2*(a^3 + a*b^2)*c^2*f)*cosh(d*x + c) + 2*(a^3*f*cosh(d*x + c) + a^3*f*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(a^3*f*cosh(d*x + c) + a^3*f*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + ((2*a*b^2*f + 2*I*b^3*f)*cosh(d*x + c) + (2*a*b^2*f + 2*I*b^3*f)*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + ((2*a*b^2*f - 2*I*b^3*f)*cosh(d*x + c) + (2*a*b^2*f - 2*I*b^3*f)*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + 2*((a^3*d*e - a^3*c*f)*cosh(d*x + c) + (a^3*d*e - a^3*c*f)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*((a^3*d*e - a^3*c*f)*cosh(d*x + c) + (a^3*d*e - a^3*c*f)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*((a^3*d*f*x + a^3*c*f)*cosh(d*x + c) + (a^3*d*f*x + a^3*c*f)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*((a^3*d*f*x + a^3*c*f)*cosh(d*x + c) + (a^3*d*f*x + a^3*c*f)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + ((2*a*b^2*d*e + 2*I*b^3*d*e - 2*a*b^2*c*f - 2*I*b^3*c*f)*cosh(d*x + c) + (2*a*b^2*d*e + 2*I*b^3*d*e - 2*a*b^2*c*f - 2*I*b^3*c*f)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) + ((2*a*b^2*d*e - 2*I*b^3*d*e - 2*a*b^2*c*f + 2*I*b^3*c*f)*cosh(d*x + c) + (2*a*b^2*d*e - 2*I*b^3*d*e - 2*a*b^2*c*f + 2*I*b^3*c*f)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) + ((2*a*b^2*d*f*x - 2*I*b^3*d*f*x + 2*a*b^2*c*f - 2*I*b^3*c*f)*cosh(d*x + c) + (2*a*b^2*d*f*x - 2*I*b^3*d*f*x + 2*a*b^2*c*f - 2*I*b^3*c*f)*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + ((2*a*b^2*d*f*x + 2*I*b^3*d*f*x + 2*a*b^2*c*f + 2*I*b^3*c*f)*cosh(d*x + c) + (2*a*b^2*d*f*x + 2*I*b^3*d*f*x + 2*a*b^2*c*f + 2*I*b^3*c*f)*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - ((a^3 + a*b^2)*d^2*f*x^2 + 2*(a^3 + a*b^2)*d^2*e*x + 4*(a^3 + a*b^2)*c*d*e - 2*(a^3 + a*b^2)*c^2*f + 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - (a^2*b + b^3)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^2 + b^4)*d^2*cosh(d*x + c) + (a^2*b^2 + b^4)*d^2*sinh(d*x + c))","B",0
409,1,288,0,0.501024," ","integrate(sinh(d*x+c)^2*tanh(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} + a b^{2}\right)} d x \cosh\left(d x + c\right) - a^{2} b - b^{3} + {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{3} \cosh\left(d x + c\right) + b^{3} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(a^{3} \cosh\left(d x + c\right) + a^{3} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - 2 \, {\left(a b^{2} \cosh\left(d x + c\right) + a b^{2} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d x + {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(2*(a^3 + a*b^2)*d*x*cosh(d*x + c) - a^2*b - b^3 + (a^2*b + b^3)*cosh(d*x + c)^2 + (a^2*b + b^3)*sinh(d*x + c)^2 - 4*(b^3*cosh(d*x + c) + b^3*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*(a^3*cosh(d*x + c) + a^3*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) - 2*(a*b^2*cosh(d*x + c) + a*b^2*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*((a^3 + a*b^2)*d*x + (a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^2*b^2 + b^4)*d*cosh(d*x + c) + (a^2*b^2 + b^4)*d*sinh(d*x + c))","B",0
410,0,0,0,0.632086," ","integrate(sinh(d*x+c)^2*tanh(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sinh\left(d x + c\right)^{2} \tanh\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sinh(d*x + c)^2*tanh(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
411,1,7331,0,0.698405," ","integrate((f*x+e)^3*sinh(d*x+c)*tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} f^{3} x^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e f^{2} x^{3} + 6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e^{2} f x^{2} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e^{3} x + 8 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - 8 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{3} f^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} f^{3} x^{4} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - 8 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{3} f^{3} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e f^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} f^{3}\right)} x^{3} + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e^{2} f - 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2}\right)} x^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e^{3} - 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f\right)} x\right)} \cosh\left(d x + c\right)^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} f^{3} x^{4} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - 8 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{3} f^{3} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e f^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} f^{3}\right)} x^{3} + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e^{2} f - 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2}\right)} x^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e^{3} - 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f\right)} x\right)} \sinh\left(d x + c\right)^{2} - 12 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f + {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f + {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} f^{3} x^{2} + 2 \, a^{3} b d^{2} e f^{2} x + a^{3} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3} + {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3} + {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{3} e^{3} - 3 \, a^{3} b c d^{2} e^{2} f + 3 \, a^{3} b c^{2} d e f^{2} - a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3} + {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3} + {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{3} f^{3} x^{3} + 3 \, a^{3} b d^{3} e f^{2} x^{2} + 3 \, a^{3} b d^{3} e^{2} f x + 3 \, a^{3} b c d^{2} e^{2} f - 3 \, a^{3} b c^{2} d e f^{2} + a^{3} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 24 \, {\left(a^{3} b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f^{3} \sinh\left(d x + c\right)^{2} + a^{3} b f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left(a^{3} b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f^{3} \sinh\left(d x + c\right)^{2} + a^{3} b f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2} + {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2} + {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f^{3} x + a^{3} b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 8 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f x + {\left(a^{3} b + a b^{3}\right)} d^{3} e^{3}\right)} \cosh\left(d x + c\right) + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x - 24 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x - 24 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-48 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 48 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x - 48 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + 48 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x - 24 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + 24 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2} + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + 24 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(48 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 48 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + 48 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + 48 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{3} x + 24 i \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3} + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 48 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 48 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - 24 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f - 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} + 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3} + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f - 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} + 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f - 48 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 48 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} + 24 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f - 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} + 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 24 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3} + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 24 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 48 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 48 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 48 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 48 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - 24 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 24 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} - 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} - 24 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x - 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} + 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3} + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} - 24 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x - 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} + 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} - 48 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 48 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x - 48 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 48 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} + 24 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} - 24 i \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x - 24 i \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f^{2} + 12 i \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} f^{3} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} f^{3} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(48 i \, {\left(a^{3} b + a b^{3}\right)} f^{3} - 48 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} f^{3} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} f^{3} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3} + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} f^{3} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(-48 i \, {\left(a^{3} b + a b^{3}\right)} f^{3} - 48 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} f^{3} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 2 \, {\left(4 \, {\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} x^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f x + 4 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} f^{3} x^{4} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - 8 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{3} f^{3} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e f^{2} - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} f^{3}\right)} x^{3} + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e^{2} f - 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2}\right)} x^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{4} e^{3} - 6 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{4} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{4}\right)}}"," ",0,"1/4*((a^4 + 2*a^2*b^2 + b^4)*d^4*f^3*x^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d^4*e*f^2*x^3 + 6*(a^4 + 2*a^2*b^2 + b^4)*d^4*e^2*f*x^2 + 4*(a^4 + 2*a^2*b^2 + b^4)*d^4*e^3*x + 8*(a^2*b^2 + b^4)*d^3*e^3 - 24*(a^2*b^2 + b^4)*c*d^2*e^2*f + 24*(a^2*b^2 + b^4)*c^2*d*e*f^2 - 8*(a^2*b^2 + b^4)*c^3*f^3 + ((a^4 + 2*a^2*b^2 + b^4)*d^4*f^3*x^4 - 24*(a^2*b^2 + b^4)*c*d^2*e^2*f + 24*(a^2*b^2 + b^4)*c^2*d*e*f^2 - 8*(a^2*b^2 + b^4)*c^3*f^3 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^4*e*f^2 - 2*(a^2*b^2 + b^4)*d^3*f^3)*x^3 + 6*((a^4 + 2*a^2*b^2 + b^4)*d^4*e^2*f - 4*(a^2*b^2 + b^4)*d^3*e*f^2)*x^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^4*e^3 - 6*(a^2*b^2 + b^4)*d^3*e^2*f)*x)*cosh(d*x + c)^2 + ((a^4 + 2*a^2*b^2 + b^4)*d^4*f^3*x^4 - 24*(a^2*b^2 + b^4)*c*d^2*e^2*f + 24*(a^2*b^2 + b^4)*c^2*d*e*f^2 - 8*(a^2*b^2 + b^4)*c^3*f^3 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^4*e*f^2 - 2*(a^2*b^2 + b^4)*d^3*f^3)*x^3 + 6*((a^4 + 2*a^2*b^2 + b^4)*d^4*e^2*f - 4*(a^2*b^2 + b^4)*d^3*e*f^2)*x^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^4*e^3 - 6*(a^2*b^2 + b^4)*d^3*e^2*f)*x)*sinh(d*x + c)^2 - 12*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f + (a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f + (a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*f^3*x^2 + 2*a^3*b*d^2*e*f^2*x + a^3*b*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 4*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3 + (a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3 + (a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^3*e^3 - 3*a^3*b*c*d^2*e^2*f + 3*a^3*b*c^2*d*e*f^2 - a^3*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3 + (a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3 + (a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^3*f^3*x^3 + 3*a^3*b*d^3*e*f^2*x^2 + 3*a^3*b*d^3*e^2*f*x + 3*a^3*b*c*d^2*e^2*f - 3*a^3*b*c^2*d*e*f^2 + a^3*b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 24*(a^3*b*f^3*cosh(d*x + c)^2 + 2*a^3*b*f^3*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f^3*sinh(d*x + c)^2 + a^3*b*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*(a^3*b*f^3*cosh(d*x + c)^2 + 2*a^3*b*f^3*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f^3*sinh(d*x + c)^2 + a^3*b*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*(a^3*b*d*f^3*x + a^3*b*d*e*f^2 + (a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f^3*x + a^3*b*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*(a^3*b*d*f^3*x + a^3*b*d*e*f^2 + (a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d*f^3*x + a^3*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f^3*x + a^3*b*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 8*((a^3*b + a*b^3)*d^3*f^3*x^3 + 3*(a^3*b + a*b^3)*d^3*e*f^2*x^2 + 3*(a^3*b + a*b^3)*d^3*e^2*f*x + (a^3*b + a*b^3)*d^3*e^3)*cosh(d*x + c) + (-24*I*(a^3*b + a*b^3)*d*f^3*x + 24*(a^2*b^2 + b^4)*d*f^3*x - 24*I*(a^3*b + a*b^3)*d*e*f^2 + 24*(a^2*b^2 + b^4)*d*e*f^2 + (-24*I*(a^3*b + a*b^3)*d*f^3*x + 24*(a^2*b^2 + b^4)*d*f^3*x - 24*I*(a^3*b + a*b^3)*d*e*f^2 + 24*(a^2*b^2 + b^4)*d*e*f^2)*cosh(d*x + c)^2 + (-48*I*(a^3*b + a*b^3)*d*f^3*x + 48*(a^2*b^2 + b^4)*d*f^3*x - 48*I*(a^3*b + a*b^3)*d*e*f^2 + 48*(a^2*b^2 + b^4)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-24*I*(a^3*b + a*b^3)*d*f^3*x + 24*(a^2*b^2 + b^4)*d*f^3*x - 24*I*(a^3*b + a*b^3)*d*e*f^2 + 24*(a^2*b^2 + b^4)*d*e*f^2)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (24*I*(a^3*b + a*b^3)*d*f^3*x + 24*(a^2*b^2 + b^4)*d*f^3*x + 24*I*(a^3*b + a*b^3)*d*e*f^2 + 24*(a^2*b^2 + b^4)*d*e*f^2 + (24*I*(a^3*b + a*b^3)*d*f^3*x + 24*(a^2*b^2 + b^4)*d*f^3*x + 24*I*(a^3*b + a*b^3)*d*e*f^2 + 24*(a^2*b^2 + b^4)*d*e*f^2)*cosh(d*x + c)^2 + (48*I*(a^3*b + a*b^3)*d*f^3*x + 48*(a^2*b^2 + b^4)*d*f^3*x + 48*I*(a^3*b + a*b^3)*d*e*f^2 + 48*(a^2*b^2 + b^4)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (24*I*(a^3*b + a*b^3)*d*f^3*x + 24*(a^2*b^2 + b^4)*d*f^3*x + 24*I*(a^3*b + a*b^3)*d*e*f^2 + 24*(a^2*b^2 + b^4)*d*e*f^2)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (-12*I*(a^3*b + a*b^3)*d^2*e^2*f + 12*(a^2*b^2 + b^4)*d^2*e^2*f + 24*I*(a^3*b + a*b^3)*c*d*e*f^2 - 24*(a^2*b^2 + b^4)*c*d*e*f^2 - 12*I*(a^3*b + a*b^3)*c^2*f^3 + 12*(a^2*b^2 + b^4)*c^2*f^3 + (-12*I*(a^3*b + a*b^3)*d^2*e^2*f + 12*(a^2*b^2 + b^4)*d^2*e^2*f + 24*I*(a^3*b + a*b^3)*c*d*e*f^2 - 24*(a^2*b^2 + b^4)*c*d*e*f^2 - 12*I*(a^3*b + a*b^3)*c^2*f^3 + 12*(a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)^2 + (-24*I*(a^3*b + a*b^3)*d^2*e^2*f + 24*(a^2*b^2 + b^4)*d^2*e^2*f + 48*I*(a^3*b + a*b^3)*c*d*e*f^2 - 48*(a^2*b^2 + b^4)*c*d*e*f^2 - 24*I*(a^3*b + a*b^3)*c^2*f^3 + 24*(a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (-12*I*(a^3*b + a*b^3)*d^2*e^2*f + 12*(a^2*b^2 + b^4)*d^2*e^2*f + 24*I*(a^3*b + a*b^3)*c*d*e*f^2 - 24*(a^2*b^2 + b^4)*c*d*e*f^2 - 12*I*(a^3*b + a*b^3)*c^2*f^3 + 12*(a^2*b^2 + b^4)*c^2*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (12*I*(a^3*b + a*b^3)*d^2*e^2*f + 12*(a^2*b^2 + b^4)*d^2*e^2*f - 24*I*(a^3*b + a*b^3)*c*d*e*f^2 - 24*(a^2*b^2 + b^4)*c*d*e*f^2 + 12*I*(a^3*b + a*b^3)*c^2*f^3 + 12*(a^2*b^2 + b^4)*c^2*f^3 + (12*I*(a^3*b + a*b^3)*d^2*e^2*f + 12*(a^2*b^2 + b^4)*d^2*e^2*f - 24*I*(a^3*b + a*b^3)*c*d*e*f^2 - 24*(a^2*b^2 + b^4)*c*d*e*f^2 + 12*I*(a^3*b + a*b^3)*c^2*f^3 + 12*(a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)^2 + (24*I*(a^3*b + a*b^3)*d^2*e^2*f + 24*(a^2*b^2 + b^4)*d^2*e^2*f - 48*I*(a^3*b + a*b^3)*c*d*e*f^2 - 48*(a^2*b^2 + b^4)*c*d*e*f^2 + 24*I*(a^3*b + a*b^3)*c^2*f^3 + 24*(a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (12*I*(a^3*b + a*b^3)*d^2*e^2*f + 12*(a^2*b^2 + b^4)*d^2*e^2*f - 24*I*(a^3*b + a*b^3)*c*d*e*f^2 - 24*(a^2*b^2 + b^4)*c*d*e*f^2 + 12*I*(a^3*b + a*b^3)*c^2*f^3 + 12*(a^2*b^2 + b^4)*c^2*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) + (12*I*(a^3*b + a*b^3)*d^2*f^3*x^2 + 12*(a^2*b^2 + b^4)*d^2*f^3*x^2 + 24*I*(a^3*b + a*b^3)*d^2*e*f^2*x + 24*(a^2*b^2 + b^4)*d^2*e*f^2*x + 24*I*(a^3*b + a*b^3)*c*d*e*f^2 + 24*(a^2*b^2 + b^4)*c*d*e*f^2 - 12*I*(a^3*b + a*b^3)*c^2*f^3 - 12*(a^2*b^2 + b^4)*c^2*f^3 + (12*I*(a^3*b + a*b^3)*d^2*f^3*x^2 + 12*(a^2*b^2 + b^4)*d^2*f^3*x^2 + 24*I*(a^3*b + a*b^3)*d^2*e*f^2*x + 24*(a^2*b^2 + b^4)*d^2*e*f^2*x + 24*I*(a^3*b + a*b^3)*c*d*e*f^2 + 24*(a^2*b^2 + b^4)*c*d*e*f^2 - 12*I*(a^3*b + a*b^3)*c^2*f^3 - 12*(a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)^2 + (24*I*(a^3*b + a*b^3)*d^2*f^3*x^2 + 24*(a^2*b^2 + b^4)*d^2*f^3*x^2 + 48*I*(a^3*b + a*b^3)*d^2*e*f^2*x + 48*(a^2*b^2 + b^4)*d^2*e*f^2*x + 48*I*(a^3*b + a*b^3)*c*d*e*f^2 + 48*(a^2*b^2 + b^4)*c*d*e*f^2 - 24*I*(a^3*b + a*b^3)*c^2*f^3 - 24*(a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (12*I*(a^3*b + a*b^3)*d^2*f^3*x^2 + 12*(a^2*b^2 + b^4)*d^2*f^3*x^2 + 24*I*(a^3*b + a*b^3)*d^2*e*f^2*x + 24*(a^2*b^2 + b^4)*d^2*e*f^2*x + 24*I*(a^3*b + a*b^3)*c*d*e*f^2 + 24*(a^2*b^2 + b^4)*c*d*e*f^2 - 12*I*(a^3*b + a*b^3)*c^2*f^3 - 12*(a^2*b^2 + b^4)*c^2*f^3)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (-12*I*(a^3*b + a*b^3)*d^2*f^3*x^2 + 12*(a^2*b^2 + b^4)*d^2*f^3*x^2 - 24*I*(a^3*b + a*b^3)*d^2*e*f^2*x + 24*(a^2*b^2 + b^4)*d^2*e*f^2*x - 24*I*(a^3*b + a*b^3)*c*d*e*f^2 + 24*(a^2*b^2 + b^4)*c*d*e*f^2 + 12*I*(a^3*b + a*b^3)*c^2*f^3 - 12*(a^2*b^2 + b^4)*c^2*f^3 + (-12*I*(a^3*b + a*b^3)*d^2*f^3*x^2 + 12*(a^2*b^2 + b^4)*d^2*f^3*x^2 - 24*I*(a^3*b + a*b^3)*d^2*e*f^2*x + 24*(a^2*b^2 + b^4)*d^2*e*f^2*x - 24*I*(a^3*b + a*b^3)*c*d*e*f^2 + 24*(a^2*b^2 + b^4)*c*d*e*f^2 + 12*I*(a^3*b + a*b^3)*c^2*f^3 - 12*(a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)^2 + (-24*I*(a^3*b + a*b^3)*d^2*f^3*x^2 + 24*(a^2*b^2 + b^4)*d^2*f^3*x^2 - 48*I*(a^3*b + a*b^3)*d^2*e*f^2*x + 48*(a^2*b^2 + b^4)*d^2*e*f^2*x - 48*I*(a^3*b + a*b^3)*c*d*e*f^2 + 48*(a^2*b^2 + b^4)*c*d*e*f^2 + 24*I*(a^3*b + a*b^3)*c^2*f^3 - 24*(a^2*b^2 + b^4)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (-12*I*(a^3*b + a*b^3)*d^2*f^3*x^2 + 12*(a^2*b^2 + b^4)*d^2*f^3*x^2 - 24*I*(a^3*b + a*b^3)*d^2*e*f^2*x + 24*(a^2*b^2 + b^4)*d^2*e*f^2*x - 24*I*(a^3*b + a*b^3)*c*d*e*f^2 + 24*(a^2*b^2 + b^4)*c*d*e*f^2 + 12*I*(a^3*b + a*b^3)*c^2*f^3 - 12*(a^2*b^2 + b^4)*c^2*f^3)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + (24*I*(a^3*b + a*b^3)*f^3 - 24*(a^2*b^2 + b^4)*f^3 + (24*I*(a^3*b + a*b^3)*f^3 - 24*(a^2*b^2 + b^4)*f^3)*cosh(d*x + c)^2 + (48*I*(a^3*b + a*b^3)*f^3 - 48*(a^2*b^2 + b^4)*f^3)*cosh(d*x + c)*sinh(d*x + c) + (24*I*(a^3*b + a*b^3)*f^3 - 24*(a^2*b^2 + b^4)*f^3)*sinh(d*x + c)^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + (-24*I*(a^3*b + a*b^3)*f^3 - 24*(a^2*b^2 + b^4)*f^3 + (-24*I*(a^3*b + a*b^3)*f^3 - 24*(a^2*b^2 + b^4)*f^3)*cosh(d*x + c)^2 + (-48*I*(a^3*b + a*b^3)*f^3 - 48*(a^2*b^2 + b^4)*f^3)*cosh(d*x + c)*sinh(d*x + c) + (-24*I*(a^3*b + a*b^3)*f^3 - 24*(a^2*b^2 + b^4)*f^3)*sinh(d*x + c)^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) + 2*(4*(a^3*b + a*b^3)*d^3*f^3*x^3 + 12*(a^3*b + a*b^3)*d^3*e*f^2*x^2 + 12*(a^3*b + a*b^3)*d^3*e^2*f*x + 4*(a^3*b + a*b^3)*d^3*e^3 + ((a^4 + 2*a^2*b^2 + b^4)*d^4*f^3*x^4 - 24*(a^2*b^2 + b^4)*c*d^2*e^2*f + 24*(a^2*b^2 + b^4)*c^2*d*e*f^2 - 8*(a^2*b^2 + b^4)*c^3*f^3 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^4*e*f^2 - 2*(a^2*b^2 + b^4)*d^3*f^3)*x^3 + 6*((a^4 + 2*a^2*b^2 + b^4)*d^4*e^2*f - 4*(a^2*b^2 + b^4)*d^3*e*f^2)*x^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^4*e^3 - 6*(a^2*b^2 + b^4)*d^3*e^2*f)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b + 2*a^2*b^3 + b^5)*d^4*cosh(d*x + c)^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*d^4*cosh(d*x + c)*sinh(d*x + c) + (a^4*b + 2*a^2*b^3 + b^5)*d^4*sinh(d*x + c)^2 + (a^4*b + 2*a^2*b^3 + b^5)*d^4)","C",0
412,1,4195,0,0.655452," ","integrate((f*x+e)^2*sinh(d*x+c)*tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{2} x^{3} + 6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f x^{2} + 6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} x + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{2} x^{3} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{2} + 3 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{2}\right)} x^{2} + 3 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{2} x^{3} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{2} + 3 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{2}\right)} x^{2} + 3 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f\right)} x\right)} \sinh\left(d x + c\right)^{2} - 12 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f + {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f + {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f^{2} x + a^{3} b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 6 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2} + {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 6 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2} + {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} e^{2} - 2 \, a^{3} b c d e f + a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 6 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2} + {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2} + {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{3} b d^{2} e f x + 2 \, a^{3} b c d e f - a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 12 \, {\left(a^{3} b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f^{2} \sinh\left(d x + c\right)^{2} + a^{3} b f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(a^{3} b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f^{2} \sinh\left(d x + c\right)^{2} + a^{3} b f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2} + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d e f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2} + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d e f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} d e f + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + 24 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d e f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f + 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d e f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f - 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2} + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d e f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f - 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} d e f + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f - 24 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} - 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d e f + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d e f - 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2} + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 i \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + 24 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 i \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x + 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x - 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2} + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x - 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-24 i \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x - 24 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + 24 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-12 i \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} d f^{2} x - 12 i \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + 4 \, {\left(3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{2} x^{3} - 12 \, {\left(a^{2} b^{2} + b^{4}\right)} c d e f + 6 \, {\left(a^{2} b^{2} + b^{4}\right)} c^{2} f^{2} + 3 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} f^{2}\right)} x^{2} + 3 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d^{2} e f\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{3} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{3}\right)}}"," ",0,"1/6*(2*(a^4 + 2*a^2*b^2 + b^4)*d^3*f^2*x^3 + 6*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f*x^2 + 6*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*x + 12*(a^2*b^2 + b^4)*d^2*e^2 - 24*(a^2*b^2 + b^4)*c*d*e*f + 12*(a^2*b^2 + b^4)*c^2*f^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^3*f^2*x^3 - 12*(a^2*b^2 + b^4)*c*d*e*f + 6*(a^2*b^2 + b^4)*c^2*f^2 + 3*((a^4 + 2*a^2*b^2 + b^4)*d^3*e*f - 2*(a^2*b^2 + b^4)*d^2*f^2)*x^2 + 3*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^2 - 4*(a^2*b^2 + b^4)*d^2*e*f)*x)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^3*f^2*x^3 - 12*(a^2*b^2 + b^4)*c*d*e*f + 6*(a^2*b^2 + b^4)*c^2*f^2 + 3*((a^4 + 2*a^2*b^2 + b^4)*d^3*e*f - 2*(a^2*b^2 + b^4)*d^2*f^2)*x^2 + 3*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^2 - 4*(a^2*b^2 + b^4)*d^2*e*f)*x)*sinh(d*x + c)^2 - 12*(a^3*b*d*f^2*x + a^3*b*d*e*f + (a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f^2*x + a^3*b*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*(a^3*b*d*f^2*x + a^3*b*d*e*f + (a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*f^2*x + a^3*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f^2*x + a^3*b*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 6*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2 + (a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 6*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2 + (a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*e^2 - 2*a^3*b*c*d*e*f + a^3*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 6*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2 + (a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 6*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2 + (a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d^2*f^2*x^2 + 2*a^3*b*d^2*e*f*x + 2*a^3*b*c*d*e*f - a^3*b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 12*(a^3*b*f^2*cosh(d*x + c)^2 + 2*a^3*b*f^2*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f^2*sinh(d*x + c)^2 + a^3*b*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(a^3*b*f^2*cosh(d*x + c)^2 + 2*a^3*b*f^2*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f^2*sinh(d*x + c)^2 + a^3*b*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + (a^3*b + a*b^3)*d^2*e^2)*cosh(d*x + c) + (-12*I*(a^3*b + a*b^3)*f^2 + 12*(a^2*b^2 + b^4)*f^2 + (-12*I*(a^3*b + a*b^3)*f^2 + 12*(a^2*b^2 + b^4)*f^2)*cosh(d*x + c)^2 + (-24*I*(a^3*b + a*b^3)*f^2 + 24*(a^2*b^2 + b^4)*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-12*I*(a^3*b + a*b^3)*f^2 + 12*(a^2*b^2 + b^4)*f^2)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (12*I*(a^3*b + a*b^3)*f^2 + 12*(a^2*b^2 + b^4)*f^2 + (12*I*(a^3*b + a*b^3)*f^2 + 12*(a^2*b^2 + b^4)*f^2)*cosh(d*x + c)^2 + (24*I*(a^3*b + a*b^3)*f^2 + 24*(a^2*b^2 + b^4)*f^2)*cosh(d*x + c)*sinh(d*x + c) + (12*I*(a^3*b + a*b^3)*f^2 + 12*(a^2*b^2 + b^4)*f^2)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (-12*I*(a^3*b + a*b^3)*d*e*f + 12*(a^2*b^2 + b^4)*d*e*f + 12*I*(a^3*b + a*b^3)*c*f^2 - 12*(a^2*b^2 + b^4)*c*f^2 + (-12*I*(a^3*b + a*b^3)*d*e*f + 12*(a^2*b^2 + b^4)*d*e*f + 12*I*(a^3*b + a*b^3)*c*f^2 - 12*(a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)^2 + (-24*I*(a^3*b + a*b^3)*d*e*f + 24*(a^2*b^2 + b^4)*d*e*f + 24*I*(a^3*b + a*b^3)*c*f^2 - 24*(a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-12*I*(a^3*b + a*b^3)*d*e*f + 12*(a^2*b^2 + b^4)*d*e*f + 12*I*(a^3*b + a*b^3)*c*f^2 - 12*(a^2*b^2 + b^4)*c*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (12*I*(a^3*b + a*b^3)*d*e*f + 12*(a^2*b^2 + b^4)*d*e*f - 12*I*(a^3*b + a*b^3)*c*f^2 - 12*(a^2*b^2 + b^4)*c*f^2 + (12*I*(a^3*b + a*b^3)*d*e*f + 12*(a^2*b^2 + b^4)*d*e*f - 12*I*(a^3*b + a*b^3)*c*f^2 - 12*(a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)^2 + (24*I*(a^3*b + a*b^3)*d*e*f + 24*(a^2*b^2 + b^4)*d*e*f - 24*I*(a^3*b + a*b^3)*c*f^2 - 24*(a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (12*I*(a^3*b + a*b^3)*d*e*f + 12*(a^2*b^2 + b^4)*d*e*f - 12*I*(a^3*b + a*b^3)*c*f^2 - 12*(a^2*b^2 + b^4)*c*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) + (12*I*(a^3*b + a*b^3)*d*f^2*x + 12*(a^2*b^2 + b^4)*d*f^2*x + 12*I*(a^3*b + a*b^3)*c*f^2 + 12*(a^2*b^2 + b^4)*c*f^2 + (12*I*(a^3*b + a*b^3)*d*f^2*x + 12*(a^2*b^2 + b^4)*d*f^2*x + 12*I*(a^3*b + a*b^3)*c*f^2 + 12*(a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)^2 + (24*I*(a^3*b + a*b^3)*d*f^2*x + 24*(a^2*b^2 + b^4)*d*f^2*x + 24*I*(a^3*b + a*b^3)*c*f^2 + 24*(a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (12*I*(a^3*b + a*b^3)*d*f^2*x + 12*(a^2*b^2 + b^4)*d*f^2*x + 12*I*(a^3*b + a*b^3)*c*f^2 + 12*(a^2*b^2 + b^4)*c*f^2)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (-12*I*(a^3*b + a*b^3)*d*f^2*x + 12*(a^2*b^2 + b^4)*d*f^2*x - 12*I*(a^3*b + a*b^3)*c*f^2 + 12*(a^2*b^2 + b^4)*c*f^2 + (-12*I*(a^3*b + a*b^3)*d*f^2*x + 12*(a^2*b^2 + b^4)*d*f^2*x - 12*I*(a^3*b + a*b^3)*c*f^2 + 12*(a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)^2 + (-24*I*(a^3*b + a*b^3)*d*f^2*x + 24*(a^2*b^2 + b^4)*d*f^2*x - 24*I*(a^3*b + a*b^3)*c*f^2 + 24*(a^2*b^2 + b^4)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-12*I*(a^3*b + a*b^3)*d*f^2*x + 12*(a^2*b^2 + b^4)*d*f^2*x - 12*I*(a^3*b + a*b^3)*c*f^2 + 12*(a^2*b^2 + b^4)*c*f^2)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + 4*(3*(a^3*b + a*b^3)*d^2*f^2*x^2 + 6*(a^3*b + a*b^3)*d^2*e*f*x + 3*(a^3*b + a*b^3)*d^2*e^2 + ((a^4 + 2*a^2*b^2 + b^4)*d^3*f^2*x^3 - 12*(a^2*b^2 + b^4)*c*d*e*f + 6*(a^2*b^2 + b^4)*c^2*f^2 + 3*((a^4 + 2*a^2*b^2 + b^4)*d^3*e*f - 2*(a^2*b^2 + b^4)*d^2*f^2)*x^2 + 3*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^2 - 4*(a^2*b^2 + b^4)*d^2*e*f)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b + 2*a^2*b^3 + b^5)*d^3*cosh(d*x + c)^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*d^3*cosh(d*x + c)*sinh(d*x + c) + (a^4*b + 2*a^2*b^3 + b^5)*d^3*sinh(d*x + c)^2 + (a^4*b + 2*a^2*b^3 + b^5)*d^3)","C",0
413,1,1571,0,0.490754," ","integrate((f*x+e)*sinh(d*x+c)*tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e x + 4 \, {\left(a^{2} b^{2} + b^{4}\right)} d e + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f x^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f\right)} x\right)} \cosh\left(d x + c\right)^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f x^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f\right)} x\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b f \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f \sinh\left(d x + c\right)^{2} + a^{3} b f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(a^{3} b f \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} b f \sinh\left(d x + c\right)^{2} + a^{3} b f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(a^{3} b d e - a^{3} b c f + {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d e - a^{3} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a^{3} b d e - a^{3} b c f + {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d e - a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d e - a^{3} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(a^{3} b d f x + a^{3} b c f + {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f x + a^{3} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a^{3} b d f x + a^{3} b c f + {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b d f x + a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b d f x + a^{3} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left({\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3}\right)} f\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e\right)} \cosh\left(d x + c\right) + 2 \, {\left({\left(a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b^{2} + b^{4}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + b^{4}\right)} f\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d f x + 2 \, {\left(a^{3} b + a b^{3}\right)} d e + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f x^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e - 2 \, {\left(a^{2} b^{2} + b^{4}\right)} d f\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2}\right)}}"," ",0,"1/2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*x + 4*(a^2*b^2 + b^4)*d*e + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f*x^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*e - 2*(a^2*b^2 + b^4)*d*f)*x)*cosh(d*x + c)^2 + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f*x^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*e - 2*(a^2*b^2 + b^4)*d*f)*x)*sinh(d*x + c)^2 - 2*(a^3*b*f*cosh(d*x + c)^2 + 2*a^3*b*f*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f*sinh(d*x + c)^2 + a^3*b*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(a^3*b*f*cosh(d*x + c)^2 + 2*a^3*b*f*cosh(d*x + c)*sinh(d*x + c) + a^3*b*f*sinh(d*x + c)^2 + a^3*b*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(a^3*b*d*e - a^3*b*c*f + (a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*e - a^3*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a^3*b*d*e - a^3*b*c*f + (a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*e - a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*e - a^3*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(a^3*b*d*f*x + a^3*b*c*f + (a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f*x + a^3*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(a^3*b*d*f*x + a^3*b*c*f + (a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)^2 + 2*(a^3*b*d*f*x + a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (a^3*b*d*f*x + a^3*b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*((a^3*b + a*b^3)*f*cosh(d*x + c)^2 + 2*(a^3*b + a*b^3)*f*cosh(d*x + c)*sinh(d*x + c) + (a^3*b + a*b^3)*f*sinh(d*x + c)^2 + (a^3*b + a*b^3)*f)*arctan(cosh(d*x + c) + sinh(d*x + c)) + 4*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e)*cosh(d*x + c) + 2*((a^2*b^2 + b^4)*f*cosh(d*x + c)^2 + 2*(a^2*b^2 + b^4)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2*b^2 + b^4)*f*sinh(d*x + c)^2 + (a^2*b^2 + b^4)*f)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(2*(a^3*b + a*b^3)*d*f*x + 2*(a^3*b + a*b^3)*d*e + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f*x^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*e - 2*(a^2*b^2 + b^4)*d*f)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh(d*x + c)^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*d^2*cosh(d*x + c)*sinh(d*x + c) + (a^4*b + 2*a^2*b^3 + b^5)*d^2*sinh(d*x + c)^2 + (a^4*b + 2*a^2*b^3 + b^5)*d^2)","B",0
414,1,459,0,0.443312," ","integrate(sinh(d*x+c)*tanh(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d x \sinh\left(d x + c\right)^{2} + 2 \, a^{2} b^{2} + 2 \, b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d x + {\left(a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} \sinh\left(d x + c\right)^{2} + a^{3}\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 2 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right) + 2 \, {\left(a^{3} b + a b^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d x \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d}"," ",0,"((a^4 + 2*a^2*b^2 + b^4)*d*x*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d*x*sinh(d*x + c)^2 + 2*a^2*b^2 + 2*b^4 + (a^4 + 2*a^2*b^2 + b^4)*d*x + (a^3*cosh(d*x + c)^2 + 2*a^3*cosh(d*x + c)*sinh(d*x + c) + a^3*sinh(d*x + c)^2 + a^3)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 2*(a^3*b + a*b^3)*cosh(d*x + c) + 2*(a^3*b + a*b^3 + (a^4 + 2*a^2*b^2 + b^4)*d*x*cosh(d*x + c))*sinh(d*x + c))/((a^4*b + 2*a^2*b^3 + b^5)*d*cosh(d*x + c)^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4*b + 2*a^2*b^3 + b^5)*d*sinh(d*x + c)^2 + (a^4*b + 2*a^2*b^3 + b^5)*d)","B",0
415,0,0,0,0.532221," ","integrate(sinh(d*x+c)*tanh(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sinh\left(d x + c\right) \tanh\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(sinh(d*x + c)*tanh(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
416,1,10546,0,0.900168," ","integrate((f*x+e)^2*tanh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{3} + a b^{2}\right)} d e f + 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x + 8 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + {\left(a^{3} + a b^{2}\right)} d e f - 2 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + {\left(2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f - 4 \, {\left(a^{3} + a b^{2}\right)} c f^{2} - 12 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) + 4 \, {\left(a^{3} d f^{2} x + a^{3} d e f + {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} d f^{2} x + a^{3} d e f + 3 \, {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 \, {\left(a^{3} d f^{2} x + a^{3} d e f + {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} d f^{2} x + a^{3} d e f + 3 \, {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} d f^{2} x + a^{3} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(4 \, a^{3} d f^{2} x + 4 \, a^{3} d e f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x + {\left(4 \, a^{3} d f^{2} x + 4 \, a^{3} d e f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{3} d f^{2} x + 16 \, a^{3} d e f + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{3} d f^{2} x + 4 \, a^{3} d e f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \sinh\left(d x + c\right)^{4} + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f + {\left(8 \, a^{3} d f^{2} x + 8 \, a^{3} d e f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{3} d f^{2} x + 8 \, a^{3} d e f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f + {\left(24 \, a^{3} d f^{2} x + 24 \, a^{3} d e f + 12 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x + 12 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, a^{3} d f^{2} x + 16 \, a^{3} d e f + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{3} d f^{2} x + 16 \, a^{3} d e f + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(4 \, a^{3} d f^{2} x + 4 \, a^{3} d e f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x + {\left(4 \, a^{3} d f^{2} x + 4 \, a^{3} d e f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{3} d f^{2} x + 16 \, a^{3} d e f - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{3} d f^{2} x + 4 \, a^{3} d e f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f + {\left(8 \, a^{3} d f^{2} x + 8 \, a^{3} d e f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{3} d f^{2} x + 8 \, a^{3} d e f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f + {\left(24 \, a^{3} d f^{2} x + 24 \, a^{3} d e f - 12 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x - 12 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(16 \, a^{3} d f^{2} x + 16 \, a^{3} d e f - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{3} d f^{2} x + 16 \, a^{3} d e f - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f^{2} x - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 2 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2} + {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2} + 3 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2} + {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2} + 3 \, {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} d^{2} e^{2} - 2 \, a^{3} c d e f + a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2} + {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2} + 3 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2} + {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2} + 3 \, {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} d^{2} f^{2} x^{2} + 2 \, a^{3} d^{2} e f x + 2 \, a^{3} c d e f - a^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(2 \, a^{3} d^{2} e^{2} - 4 \, a^{3} c d e f + i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + {\left(2 \, a^{3} d^{2} e^{2} - 4 \, a^{3} c d e f + i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} + i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{3} d^{2} e^{2} - 16 \, a^{3} c d e f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 8 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} + 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{3} d^{2} e^{2} - 4 \, a^{3} c d e f + i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} + i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} + i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2} + {\left(4 \, a^{3} d^{2} e^{2} - 8 \, a^{3} c d e f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 4 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} + 2 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{3} d^{2} e^{2} - 8 \, a^{3} c d e f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 4 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} + 2 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2} + {\left(12 \, a^{3} d^{2} e^{2} - 24 \, a^{3} c d e f + 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 12 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 12 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} + 6 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{3} d^{2} e^{2} - 16 \, a^{3} c d e f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 8 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} + 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} d^{2} e^{2} - 16 \, a^{3} c d e f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 8 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} + 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(2 \, a^{3} d^{2} e^{2} - 4 \, a^{3} c d e f - i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + {\left(2 \, a^{3} d^{2} e^{2} - 4 \, a^{3} c d e f - i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} - i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{3} d^{2} e^{2} - 16 \, a^{3} c d e f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 8 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} - 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{3} d^{2} e^{2} - 4 \, a^{3} c d e f - i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} - i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} - i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2} + {\left(4 \, a^{3} d^{2} e^{2} - 8 \, a^{3} c d e f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 4 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} - 2 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{3} d^{2} e^{2} - 8 \, a^{3} c d e f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 4 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} - 2 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2} + {\left(12 \, a^{3} d^{2} e^{2} - 24 \, a^{3} c d e f - 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 12 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 12 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} - 6 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{3} d^{2} e^{2} - 16 \, a^{3} c d e f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 8 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} - 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} d^{2} e^{2} - 16 \, a^{3} c d e f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e^{2} + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 8 \, {\left(a^{3} c^{2} + a^{3} + a b^{2}\right)} f^{2} - 4 i \, {\left(2 \, a^{2} b + 2 \, b^{3} + {\left(3 \, a^{2} b + b^{3}\right)} c^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(2 \, a^{3} d^{2} f^{2} x^{2} + 4 \, a^{3} d^{2} e f x + 4 \, a^{3} c d e f - 2 \, a^{3} c^{2} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + {\left(2 \, a^{3} d^{2} f^{2} x^{2} + 4 \, a^{3} d^{2} e f x + 4 \, a^{3} c d e f - 2 \, a^{3} c^{2} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{3} d^{2} f^{2} x^{2} + 16 \, a^{3} d^{2} e f x + 16 \, a^{3} c d e f - 8 \, a^{3} c^{2} f^{2} - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{3} d^{2} f^{2} x^{2} + 4 \, a^{3} d^{2} e f x + 4 \, a^{3} c d e f - 2 \, a^{3} c^{2} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{3} d^{2} f^{2} x^{2} + 8 \, a^{3} d^{2} e f x + 8 \, a^{3} c d e f - 4 \, a^{3} c^{2} f^{2} - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{3} d^{2} f^{2} x^{2} + 8 \, a^{3} d^{2} e f x + 8 \, a^{3} c d e f - 4 \, a^{3} c^{2} f^{2} - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + {\left(12 \, a^{3} d^{2} f^{2} x^{2} + 24 \, a^{3} d^{2} e f x + 24 \, a^{3} c d e f - 12 \, a^{3} c^{2} f^{2} - 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} - 12 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x - 12 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{3} d^{2} f^{2} x^{2} + 16 \, a^{3} d^{2} e f x + 16 \, a^{3} c d e f - 8 \, a^{3} c^{2} f^{2} - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} d^{2} f^{2} x^{2} + 16 \, a^{3} d^{2} e f x + 16 \, a^{3} c d e f - 8 \, a^{3} c^{2} f^{2} - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x - 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(2 \, a^{3} d^{2} f^{2} x^{2} + 4 \, a^{3} d^{2} e f x + 4 \, a^{3} c d e f - 2 \, a^{3} c^{2} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f - i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + {\left(2 \, a^{3} d^{2} f^{2} x^{2} + 4 \, a^{3} d^{2} e f x + 4 \, a^{3} c d e f - 2 \, a^{3} c^{2} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f - i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{3} d^{2} f^{2} x^{2} + 16 \, a^{3} d^{2} e f x + 16 \, a^{3} c d e f - 8 \, a^{3} c^{2} f^{2} + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{3} d^{2} f^{2} x^{2} + 4 \, a^{3} d^{2} e f x + 4 \, a^{3} c d e f - 2 \, a^{3} c^{2} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f - i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{3} d^{2} f^{2} x^{2} + 8 \, a^{3} d^{2} e f x + 8 \, a^{3} c d e f - 4 \, a^{3} c^{2} f^{2} + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{3} d^{2} f^{2} x^{2} + 8 \, a^{3} d^{2} e f x + 8 \, a^{3} c d e f - 4 \, a^{3} c^{2} f^{2} + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2} + {\left(12 \, a^{3} d^{2} f^{2} x^{2} + 24 \, a^{3} d^{2} e f x + 24 \, a^{3} c d e f - 12 \, a^{3} c^{2} f^{2} + 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 12 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x + 12 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f - 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{3} d^{2} f^{2} x^{2} + 16 \, a^{3} d^{2} e f x + 16 \, a^{3} c d e f - 8 \, a^{3} c^{2} f^{2} + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} d^{2} f^{2} x^{2} + 16 \, a^{3} d^{2} e f x + 16 \, a^{3} c d e f - 8 \, a^{3} c^{2} f^{2} + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} d^{2} e f x + 8 i \, {\left(3 \, a^{2} b + b^{3}\right)} c d e f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 4 \, {\left(a^{3} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} f^{2} \sinh\left(d x + c\right)^{4} + 2 \, a^{3} f^{2} \cosh\left(d x + c\right)^{2} + a^{3} f^{2} + 2 \, {\left(3 \, a^{3} f^{2} \cosh\left(d x + c\right)^{2} + a^{3} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} f^{2} \cosh\left(d x + c\right)^{3} + a^{3} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(a^{3} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} f^{2} \sinh\left(d x + c\right)^{4} + 2 \, a^{3} f^{2} \cosh\left(d x + c\right)^{2} + a^{3} f^{2} + 2 \, {\left(3 \, a^{3} f^{2} \cosh\left(d x + c\right)^{2} + a^{3} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} f^{2} \cosh\left(d x + c\right)^{3} + a^{3} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + {\left(4 \, a^{3} f^{2} + 2 \, {\left(2 \, a^{3} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(2 \, a^{3} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{3} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2} + 4 \, {\left(2 \, a^{3} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(2 \, a^{3} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2} + 3 \, {\left(2 \, a^{3} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(2 \, a^{3} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} f^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(4 \, a^{3} f^{2} + 2 \, {\left(2 \, a^{3} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(2 \, a^{3} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{3} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2} + 4 \, {\left(2 \, a^{3} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(2 \, a^{3} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2} + 3 \, {\left(2 \, a^{3} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(2 \, a^{3} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} f^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} d e f - 8 \, {\left({\left(a^{3} + a b^{2}\right)} d f^{2} x + {\left(a^{3} + a b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{2} b + b^{3}\right)} d f^{2}\right)} x + 4 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} + {\left(a^{3} + a b^{2}\right)} d e f - 2 \, {\left(a^{3} + a b^{2}\right)} c f^{2} + {\left(2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(4*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*c*f^2)*cosh(d*x + c)^4 + 4*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*c*f^2)*sinh(d*x + c)^4 - 4*(a^3 + a*b^2)*d*e*f + 4*(a^3 + a*b^2)*c*f^2 + 2*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^3 + 2*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^2*b + b^3)*d*f^2)*x + 8*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + (a^3 + a*b^2)*d*e*f - 2*(a^3 + a*b^2)*c*f^2 + (2*(a^3 + a*b^2)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)^2 - 2*(2*(a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f - 4*(a^3 + a*b^2)*c*f^2 - 12*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*c*f^2)*cosh(d*x + c)^2 + 2*(2*(a^3 + a*b^2)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x - 3*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 - 2*(a^2*b + b^3)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c) + 4*(a^3*d*f^2*x + a^3*d*e*f + (a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^4 + 4*(a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*d*f^2*x + a^3*d*e*f)*sinh(d*x + c)^4 + 2*(a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^2 + 2*(a^3*d*f^2*x + a^3*d*e*f + 3*(a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^3 + (a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 4*(a^3*d*f^2*x + a^3*d*e*f + (a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^4 + 4*(a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*d*f^2*x + a^3*d*e*f)*sinh(d*x + c)^4 + 2*(a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^2 + 2*(a^3*d*f^2*x + a^3*d*e*f + 3*(a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c)^3 + (a^3*d*f^2*x + a^3*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (4*a^3*d*f^2*x + 4*a^3*d*e*f + 2*I*(3*a^2*b + b^3)*d*f^2*x + (4*a^3*d*f^2*x + 4*a^3*d*e*f + 2*I*(3*a^2*b + b^3)*d*f^2*x + 2*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c)^4 + (16*a^3*d*f^2*x + 16*a^3*d*e*f + 8*I*(3*a^2*b + b^3)*d*f^2*x + 8*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a^3*d*f^2*x + 4*a^3*d*e*f + 2*I*(3*a^2*b + b^3)*d*f^2*x + 2*I*(3*a^2*b + b^3)*d*e*f)*sinh(d*x + c)^4 + 2*I*(3*a^2*b + b^3)*d*e*f + (8*a^3*d*f^2*x + 8*a^3*d*e*f + 4*I*(3*a^2*b + b^3)*d*f^2*x + 4*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c)^2 + (8*a^3*d*f^2*x + 8*a^3*d*e*f + 4*I*(3*a^2*b + b^3)*d*f^2*x + 4*I*(3*a^2*b + b^3)*d*e*f + (24*a^3*d*f^2*x + 24*a^3*d*e*f + 12*I*(3*a^2*b + b^3)*d*f^2*x + 12*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*a^3*d*f^2*x + 16*a^3*d*e*f + 8*I*(3*a^2*b + b^3)*d*f^2*x + 8*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c)^3 + (16*a^3*d*f^2*x + 16*a^3*d*e*f + 8*I*(3*a^2*b + b^3)*d*f^2*x + 8*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (4*a^3*d*f^2*x + 4*a^3*d*e*f - 2*I*(3*a^2*b + b^3)*d*f^2*x + (4*a^3*d*f^2*x + 4*a^3*d*e*f - 2*I*(3*a^2*b + b^3)*d*f^2*x - 2*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c)^4 + (16*a^3*d*f^2*x + 16*a^3*d*e*f - 8*I*(3*a^2*b + b^3)*d*f^2*x - 8*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a^3*d*f^2*x + 4*a^3*d*e*f - 2*I*(3*a^2*b + b^3)*d*f^2*x - 2*I*(3*a^2*b + b^3)*d*e*f)*sinh(d*x + c)^4 - 2*I*(3*a^2*b + b^3)*d*e*f + (8*a^3*d*f^2*x + 8*a^3*d*e*f - 4*I*(3*a^2*b + b^3)*d*f^2*x - 4*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c)^2 + (8*a^3*d*f^2*x + 8*a^3*d*e*f - 4*I*(3*a^2*b + b^3)*d*f^2*x - 4*I*(3*a^2*b + b^3)*d*e*f + (24*a^3*d*f^2*x + 24*a^3*d*e*f - 12*I*(3*a^2*b + b^3)*d*f^2*x - 12*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((16*a^3*d*f^2*x + 16*a^3*d*e*f - 8*I*(3*a^2*b + b^3)*d*f^2*x - 8*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c)^3 + (16*a^3*d*f^2*x + 16*a^3*d*e*f - 8*I*(3*a^2*b + b^3)*d*f^2*x - 8*I*(3*a^2*b + b^3)*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + 2*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2 + (a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*sinh(d*x + c)^4 + 2*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2 + 3*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^3 + (a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2 + (a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*sinh(d*x + c)^4 + 2*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2 + 3*(a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c)^3 + (a^3*d^2*e^2 - 2*a^3*c*d*e*f + a^3*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2 + (a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*sinh(d*x + c)^4 + 2*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2 + 3*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^3 + (a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2 + (a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^4 + 4*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*sinh(d*x + c)^4 + 2*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^2 + 2*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2 + 3*(a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c)^3 + (a^3*d^2*f^2*x^2 + 2*a^3*d^2*e*f*x + 2*a^3*c*d*e*f - a^3*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (2*a^3*d^2*e^2 - 4*a^3*c*d*e*f + I*(3*a^2*b + b^3)*d^2*e^2 - 2*I*(3*a^2*b + b^3)*c*d*e*f + (2*a^3*d^2*e^2 - 4*a^3*c*d*e*f + I*(3*a^2*b + b^3)*d^2*e^2 - 2*I*(3*a^2*b + b^3)*c*d*e*f + 2*(a^3*c^2 + a^3 + a*b^2)*f^2 + I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c)^4 + (8*a^3*d^2*e^2 - 16*a^3*c*d*e*f + 4*I*(3*a^2*b + b^3)*d^2*e^2 - 8*I*(3*a^2*b + b^3)*c*d*e*f + 8*(a^3*c^2 + a^3 + a*b^2)*f^2 + 4*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^3*d^2*e^2 - 4*a^3*c*d*e*f + I*(3*a^2*b + b^3)*d^2*e^2 - 2*I*(3*a^2*b + b^3)*c*d*e*f + 2*(a^3*c^2 + a^3 + a*b^2)*f^2 + I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*sinh(d*x + c)^4 + 2*(a^3*c^2 + a^3 + a*b^2)*f^2 + I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2 + (4*a^3*d^2*e^2 - 8*a^3*c*d*e*f + 2*I*(3*a^2*b + b^3)*d^2*e^2 - 4*I*(3*a^2*b + b^3)*c*d*e*f + 4*(a^3*c^2 + a^3 + a*b^2)*f^2 + 2*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c)^2 + (4*a^3*d^2*e^2 - 8*a^3*c*d*e*f + 2*I*(3*a^2*b + b^3)*d^2*e^2 - 4*I*(3*a^2*b + b^3)*c*d*e*f + 4*(a^3*c^2 + a^3 + a*b^2)*f^2 + 2*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2 + (12*a^3*d^2*e^2 - 24*a^3*c*d*e*f + 6*I*(3*a^2*b + b^3)*d^2*e^2 - 12*I*(3*a^2*b + b^3)*c*d*e*f + 12*(a^3*c^2 + a^3 + a*b^2)*f^2 + 6*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^3*d^2*e^2 - 16*a^3*c*d*e*f + 4*I*(3*a^2*b + b^3)*d^2*e^2 - 8*I*(3*a^2*b + b^3)*c*d*e*f + 8*(a^3*c^2 + a^3 + a*b^2)*f^2 + 4*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c)^3 + (8*a^3*d^2*e^2 - 16*a^3*c*d*e*f + 4*I*(3*a^2*b + b^3)*d^2*e^2 - 8*I*(3*a^2*b + b^3)*c*d*e*f + 8*(a^3*c^2 + a^3 + a*b^2)*f^2 + 4*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) - (2*a^3*d^2*e^2 - 4*a^3*c*d*e*f - I*(3*a^2*b + b^3)*d^2*e^2 + 2*I*(3*a^2*b + b^3)*c*d*e*f + (2*a^3*d^2*e^2 - 4*a^3*c*d*e*f - I*(3*a^2*b + b^3)*d^2*e^2 + 2*I*(3*a^2*b + b^3)*c*d*e*f + 2*(a^3*c^2 + a^3 + a*b^2)*f^2 - I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c)^4 + (8*a^3*d^2*e^2 - 16*a^3*c*d*e*f - 4*I*(3*a^2*b + b^3)*d^2*e^2 + 8*I*(3*a^2*b + b^3)*c*d*e*f + 8*(a^3*c^2 + a^3 + a*b^2)*f^2 - 4*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^3*d^2*e^2 - 4*a^3*c*d*e*f - I*(3*a^2*b + b^3)*d^2*e^2 + 2*I*(3*a^2*b + b^3)*c*d*e*f + 2*(a^3*c^2 + a^3 + a*b^2)*f^2 - I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*sinh(d*x + c)^4 + 2*(a^3*c^2 + a^3 + a*b^2)*f^2 - I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2 + (4*a^3*d^2*e^2 - 8*a^3*c*d*e*f - 2*I*(3*a^2*b + b^3)*d^2*e^2 + 4*I*(3*a^2*b + b^3)*c*d*e*f + 4*(a^3*c^2 + a^3 + a*b^2)*f^2 - 2*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c)^2 + (4*a^3*d^2*e^2 - 8*a^3*c*d*e*f - 2*I*(3*a^2*b + b^3)*d^2*e^2 + 4*I*(3*a^2*b + b^3)*c*d*e*f + 4*(a^3*c^2 + a^3 + a*b^2)*f^2 - 2*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2 + (12*a^3*d^2*e^2 - 24*a^3*c*d*e*f - 6*I*(3*a^2*b + b^3)*d^2*e^2 + 12*I*(3*a^2*b + b^3)*c*d*e*f + 12*(a^3*c^2 + a^3 + a*b^2)*f^2 - 6*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^3*d^2*e^2 - 16*a^3*c*d*e*f - 4*I*(3*a^2*b + b^3)*d^2*e^2 + 8*I*(3*a^2*b + b^3)*c*d*e*f + 8*(a^3*c^2 + a^3 + a*b^2)*f^2 - 4*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c)^3 + (8*a^3*d^2*e^2 - 16*a^3*c*d*e*f - 4*I*(3*a^2*b + b^3)*d^2*e^2 + 8*I*(3*a^2*b + b^3)*c*d*e*f + 8*(a^3*c^2 + a^3 + a*b^2)*f^2 - 4*I*(2*a^2*b + 2*b^3 + (3*a^2*b + b^3)*c^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) - (2*a^3*d^2*f^2*x^2 + 4*a^3*d^2*e*f*x + 4*a^3*c*d*e*f - 2*a^3*c^2*f^2 - I*(3*a^2*b + b^3)*d^2*f^2*x^2 - 2*I*(3*a^2*b + b^3)*d^2*e*f*x - 2*I*(3*a^2*b + b^3)*c*d*e*f + I*(3*a^2*b + b^3)*c^2*f^2 + (2*a^3*d^2*f^2*x^2 + 4*a^3*d^2*e*f*x + 4*a^3*c*d*e*f - 2*a^3*c^2*f^2 - I*(3*a^2*b + b^3)*d^2*f^2*x^2 - 2*I*(3*a^2*b + b^3)*d^2*e*f*x - 2*I*(3*a^2*b + b^3)*c*d*e*f + I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)^4 + (8*a^3*d^2*f^2*x^2 + 16*a^3*d^2*e*f*x + 16*a^3*c*d*e*f - 8*a^3*c^2*f^2 - 4*I*(3*a^2*b + b^3)*d^2*f^2*x^2 - 8*I*(3*a^2*b + b^3)*d^2*e*f*x - 8*I*(3*a^2*b + b^3)*c*d*e*f + 4*I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^3*d^2*f^2*x^2 + 4*a^3*d^2*e*f*x + 4*a^3*c*d*e*f - 2*a^3*c^2*f^2 - I*(3*a^2*b + b^3)*d^2*f^2*x^2 - 2*I*(3*a^2*b + b^3)*d^2*e*f*x - 2*I*(3*a^2*b + b^3)*c*d*e*f + I*(3*a^2*b + b^3)*c^2*f^2)*sinh(d*x + c)^4 + (4*a^3*d^2*f^2*x^2 + 8*a^3*d^2*e*f*x + 8*a^3*c*d*e*f - 4*a^3*c^2*f^2 - 2*I*(3*a^2*b + b^3)*d^2*f^2*x^2 - 4*I*(3*a^2*b + b^3)*d^2*e*f*x - 4*I*(3*a^2*b + b^3)*c*d*e*f + 2*I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)^2 + (4*a^3*d^2*f^2*x^2 + 8*a^3*d^2*e*f*x + 8*a^3*c*d*e*f - 4*a^3*c^2*f^2 - 2*I*(3*a^2*b + b^3)*d^2*f^2*x^2 - 4*I*(3*a^2*b + b^3)*d^2*e*f*x - 4*I*(3*a^2*b + b^3)*c*d*e*f + 2*I*(3*a^2*b + b^3)*c^2*f^2 + (12*a^3*d^2*f^2*x^2 + 24*a^3*d^2*e*f*x + 24*a^3*c*d*e*f - 12*a^3*c^2*f^2 - 6*I*(3*a^2*b + b^3)*d^2*f^2*x^2 - 12*I*(3*a^2*b + b^3)*d^2*e*f*x - 12*I*(3*a^2*b + b^3)*c*d*e*f + 6*I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^3*d^2*f^2*x^2 + 16*a^3*d^2*e*f*x + 16*a^3*c*d*e*f - 8*a^3*c^2*f^2 - 4*I*(3*a^2*b + b^3)*d^2*f^2*x^2 - 8*I*(3*a^2*b + b^3)*d^2*e*f*x - 8*I*(3*a^2*b + b^3)*c*d*e*f + 4*I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)^3 + (8*a^3*d^2*f^2*x^2 + 16*a^3*d^2*e*f*x + 16*a^3*c*d*e*f - 8*a^3*c^2*f^2 - 4*I*(3*a^2*b + b^3)*d^2*f^2*x^2 - 8*I*(3*a^2*b + b^3)*d^2*e*f*x - 8*I*(3*a^2*b + b^3)*c*d*e*f + 4*I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (2*a^3*d^2*f^2*x^2 + 4*a^3*d^2*e*f*x + 4*a^3*c*d*e*f - 2*a^3*c^2*f^2 + I*(3*a^2*b + b^3)*d^2*f^2*x^2 + 2*I*(3*a^2*b + b^3)*d^2*e*f*x + 2*I*(3*a^2*b + b^3)*c*d*e*f - I*(3*a^2*b + b^3)*c^2*f^2 + (2*a^3*d^2*f^2*x^2 + 4*a^3*d^2*e*f*x + 4*a^3*c*d*e*f - 2*a^3*c^2*f^2 + I*(3*a^2*b + b^3)*d^2*f^2*x^2 + 2*I*(3*a^2*b + b^3)*d^2*e*f*x + 2*I*(3*a^2*b + b^3)*c*d*e*f - I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)^4 + (8*a^3*d^2*f^2*x^2 + 16*a^3*d^2*e*f*x + 16*a^3*c*d*e*f - 8*a^3*c^2*f^2 + 4*I*(3*a^2*b + b^3)*d^2*f^2*x^2 + 8*I*(3*a^2*b + b^3)*d^2*e*f*x + 8*I*(3*a^2*b + b^3)*c*d*e*f - 4*I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^3*d^2*f^2*x^2 + 4*a^3*d^2*e*f*x + 4*a^3*c*d*e*f - 2*a^3*c^2*f^2 + I*(3*a^2*b + b^3)*d^2*f^2*x^2 + 2*I*(3*a^2*b + b^3)*d^2*e*f*x + 2*I*(3*a^2*b + b^3)*c*d*e*f - I*(3*a^2*b + b^3)*c^2*f^2)*sinh(d*x + c)^4 + (4*a^3*d^2*f^2*x^2 + 8*a^3*d^2*e*f*x + 8*a^3*c*d*e*f - 4*a^3*c^2*f^2 + 2*I*(3*a^2*b + b^3)*d^2*f^2*x^2 + 4*I*(3*a^2*b + b^3)*d^2*e*f*x + 4*I*(3*a^2*b + b^3)*c*d*e*f - 2*I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)^2 + (4*a^3*d^2*f^2*x^2 + 8*a^3*d^2*e*f*x + 8*a^3*c*d*e*f - 4*a^3*c^2*f^2 + 2*I*(3*a^2*b + b^3)*d^2*f^2*x^2 + 4*I*(3*a^2*b + b^3)*d^2*e*f*x + 4*I*(3*a^2*b + b^3)*c*d*e*f - 2*I*(3*a^2*b + b^3)*c^2*f^2 + (12*a^3*d^2*f^2*x^2 + 24*a^3*d^2*e*f*x + 24*a^3*c*d*e*f - 12*a^3*c^2*f^2 + 6*I*(3*a^2*b + b^3)*d^2*f^2*x^2 + 12*I*(3*a^2*b + b^3)*d^2*e*f*x + 12*I*(3*a^2*b + b^3)*c*d*e*f - 6*I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^3*d^2*f^2*x^2 + 16*a^3*d^2*e*f*x + 16*a^3*c*d*e*f - 8*a^3*c^2*f^2 + 4*I*(3*a^2*b + b^3)*d^2*f^2*x^2 + 8*I*(3*a^2*b + b^3)*d^2*e*f*x + 8*I*(3*a^2*b + b^3)*c*d*e*f - 4*I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c)^3 + (8*a^3*d^2*f^2*x^2 + 16*a^3*d^2*e*f*x + 16*a^3*c*d*e*f - 8*a^3*c^2*f^2 + 4*I*(3*a^2*b + b^3)*d^2*f^2*x^2 + 8*I*(3*a^2*b + b^3)*d^2*e*f*x + 8*I*(3*a^2*b + b^3)*c*d*e*f - 4*I*(3*a^2*b + b^3)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 4*(a^3*f^2*cosh(d*x + c)^4 + 4*a^3*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*f^2*sinh(d*x + c)^4 + 2*a^3*f^2*cosh(d*x + c)^2 + a^3*f^2 + 2*(3*a^3*f^2*cosh(d*x + c)^2 + a^3*f^2)*sinh(d*x + c)^2 + 4*(a^3*f^2*cosh(d*x + c)^3 + a^3*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 4*(a^3*f^2*cosh(d*x + c)^4 + 4*a^3*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*f^2*sinh(d*x + c)^4 + 2*a^3*f^2*cosh(d*x + c)^2 + a^3*f^2 + 2*(3*a^3*f^2*cosh(d*x + c)^2 + a^3*f^2)*sinh(d*x + c)^2 + 4*(a^3*f^2*cosh(d*x + c)^3 + a^3*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + (4*a^3*f^2 + 2*(2*a^3*f^2 + I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c)^4 + 8*(2*a^3*f^2 + I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(2*a^3*f^2 + I*(3*a^2*b + b^3)*f^2)*sinh(d*x + c)^4 + 2*I*(3*a^2*b + b^3)*f^2 + 4*(2*a^3*f^2 + I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c)^2 + 4*(2*a^3*f^2 + I*(3*a^2*b + b^3)*f^2 + 3*(2*a^3*f^2 + I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((2*a^3*f^2 + I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c)^3 + (2*a^3*f^2 + I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + (4*a^3*f^2 + 2*(2*a^3*f^2 - I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c)^4 + 8*(2*a^3*f^2 - I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(2*a^3*f^2 - I*(3*a^2*b + b^3)*f^2)*sinh(d*x + c)^4 - 2*I*(3*a^2*b + b^3)*f^2 + 4*(2*a^3*f^2 - I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c)^2 + 4*(2*a^3*f^2 - I*(3*a^2*b + b^3)*f^2 + 3*(2*a^3*f^2 - I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((2*a^3*f^2 - I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c)^3 + (2*a^3*f^2 - I*(3*a^2*b + b^3)*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 - 2*(a^2*b + b^3)*d*e*f - 8*((a^3 + a*b^2)*d*f^2*x + (a^3 + a*b^2)*c*f^2)*cosh(d*x + c)^3 - 3*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^2*b + b^3)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^2*b + b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^2*b + b^3)*d*f^2)*x + 4*((a^3 + a*b^2)*d^2*f^2*x^2 + (a^3 + a*b^2)*d^2*e^2 + (a^3 + a*b^2)*d*e*f - 2*(a^3 + a*b^2)*c*f^2 + (2*(a^3 + a*b^2)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^3*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^3)*sinh(d*x + c)^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^3*cosh(d*x + c))*sinh(d*x + c))","C",0
417,1,4709,0,0.740260," ","integrate((f*x+e)*tanh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d f x + 2 \, {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d f x + 2 \, {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} + a b^{2}\right)} f - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right) + 2 \, {\left(a^{3} f \cosh\left(d x + c\right)^{4} + 4 \, a^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} f \sinh\left(d x + c\right)^{4} + 2 \, a^{3} f \cosh\left(d x + c\right)^{2} + a^{3} f + 2 \, {\left(3 \, a^{3} f \cosh\left(d x + c\right)^{2} + a^{3} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} f \cosh\left(d x + c\right)^{3} + a^{3} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(a^{3} f \cosh\left(d x + c\right)^{4} + 4 \, a^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} f \sinh\left(d x + c\right)^{4} + 2 \, a^{3} f \cosh\left(d x + c\right)^{2} + a^{3} f + 2 \, {\left(3 \, a^{3} f \cosh\left(d x + c\right)^{2} + a^{3} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} f \cosh\left(d x + c\right)^{3} + a^{3} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left({\left(2 \, a^{3} f + i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{3} f + i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{3} f + i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{3} f + 2 \, {\left(2 \, a^{3} f + i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{3} f + 3 \, {\left(2 \, a^{3} f + i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} + i \, {\left(3 \, a^{2} b + b^{3}\right)} f + 4 \, {\left({\left(2 \, a^{3} f + i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} f + i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left({\left(2 \, a^{3} f - i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{3} f - i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{3} f - i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{3} f + 2 \, {\left(2 \, a^{3} f - i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{3} f + 3 \, {\left(2 \, a^{3} f - i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} - i \, {\left(3 \, a^{2} b + b^{3}\right)} f + 4 \, {\left({\left(2 \, a^{3} f - i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} f - i \, {\left(3 \, a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 2 \, {\left(a^{3} d e - a^{3} c f + {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} d e - a^{3} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} d e - a^{3} c f + 3 \, {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a^{3} d e - a^{3} c f + {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} d e - a^{3} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} d e - a^{3} c f + 3 \, {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} d e - a^{3} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(a^{3} d f x + a^{3} c f + {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} d f x + a^{3} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} d f x + a^{3} c f + 3 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(a^{3} d f x + a^{3} c f + {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} d f x + a^{3} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} d f x + a^{3} c f + 3 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(2 \, a^{3} d e - 2 \, a^{3} c f + {\left(2 \, a^{3} d e - 2 \, a^{3} c f + i \, {\left(3 \, a^{2} b + b^{3}\right)} d e - i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{3} d e - 8 \, a^{3} c f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{3} d e - 2 \, a^{3} c f + i \, {\left(3 \, a^{2} b + b^{3}\right)} d e - i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + i \, {\left(3 \, a^{2} b + b^{3}\right)} d e - i \, {\left(3 \, a^{2} b + b^{3}\right)} c f + {\left(4 \, a^{3} d e - 4 \, a^{3} c f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{3} d e - 4 \, a^{3} c f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f + {\left(12 \, a^{3} d e - 12 \, a^{3} c f + 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e - 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{3} d e - 8 \, a^{3} c f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} d e - 8 \, a^{3} c f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(2 \, a^{3} d e - 2 \, a^{3} c f + {\left(2 \, a^{3} d e - 2 \, a^{3} c f - i \, {\left(3 \, a^{2} b + b^{3}\right)} d e + i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{3} d e - 8 \, a^{3} c f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{3} d e - 2 \, a^{3} c f - i \, {\left(3 \, a^{2} b + b^{3}\right)} d e + i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} - i \, {\left(3 \, a^{2} b + b^{3}\right)} d e + i \, {\left(3 \, a^{2} b + b^{3}\right)} c f + {\left(4 \, a^{3} d e - 4 \, a^{3} c f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{3} d e - 4 \, a^{3} c f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f + {\left(12 \, a^{3} d e - 12 \, a^{3} c f - 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e + 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{3} d e - 8 \, a^{3} c f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} d e - 8 \, a^{3} c f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d e + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left(2 \, a^{3} d f x + 2 \, a^{3} c f + {\left(2 \, a^{3} d f x + 2 \, a^{3} c f - i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x - i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{3} d f x + 8 \, a^{3} c f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{3} d f x + 2 \, a^{3} c f - i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x - i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} - i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x - i \, {\left(3 \, a^{2} b + b^{3}\right)} c f + {\left(4 \, a^{3} d f x + 4 \, a^{3} c f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{3} d f x + 4 \, a^{3} c f - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x - 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f + {\left(12 \, a^{3} d f x + 12 \, a^{3} c f - 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x - 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{3} d f x + 8 \, a^{3} c f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} d f x + 8 \, a^{3} c f - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x - 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(2 \, a^{3} d f x + 2 \, a^{3} c f + {\left(2 \, a^{3} d f x + 2 \, a^{3} c f + i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x + i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{3} d f x + 8 \, a^{3} c f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{3} d f x + 2 \, a^{3} c f + i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x + i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x + i \, {\left(3 \, a^{2} b + b^{3}\right)} c f + {\left(4 \, a^{3} d f x + 4 \, a^{3} c f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{3} d f x + 4 \, a^{3} c f + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x + 2 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f + {\left(12 \, a^{3} d f x + 12 \, a^{3} c f + 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x + 6 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{3} d f x + 8 \, a^{3} c f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} d f x + 8 \, a^{3} c f + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} d f x + 4 i \, {\left(3 \, a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{2} b + b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f + 2 \, {\left(2 \, {\left(a^{3} + a b^{2}\right)} d f x + 2 \, {\left(a^{3} + a b^{2}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*cosh(d*x + c)^3 + 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*sinh(d*x + c)^3 - 2*(2*(a^3 + a*b^2)*d*f*x + 2*(a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c)^2 - 2*(2*(a^3 + a*b^2)*d*f*x + 2*(a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f - 3*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(a^3 + a*b^2)*f - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - (a^2*b + b^3)*f)*cosh(d*x + c) + 2*(a^3*f*cosh(d*x + c)^4 + 4*a^3*f*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*f*sinh(d*x + c)^4 + 2*a^3*f*cosh(d*x + c)^2 + a^3*f + 2*(3*a^3*f*cosh(d*x + c)^2 + a^3*f)*sinh(d*x + c)^2 + 4*(a^3*f*cosh(d*x + c)^3 + a^3*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(a^3*f*cosh(d*x + c)^4 + 4*a^3*f*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*f*sinh(d*x + c)^4 + 2*a^3*f*cosh(d*x + c)^2 + a^3*f + 2*(3*a^3*f*cosh(d*x + c)^2 + a^3*f)*sinh(d*x + c)^2 + 4*(a^3*f*cosh(d*x + c)^3 + a^3*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - ((2*a^3*f + I*(3*a^2*b + b^3)*f)*cosh(d*x + c)^4 + 4*(2*a^3*f + I*(3*a^2*b + b^3)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^3*f + I*(3*a^2*b + b^3)*f)*sinh(d*x + c)^4 + 2*a^3*f + 2*(2*a^3*f + I*(3*a^2*b + b^3)*f)*cosh(d*x + c)^2 + 2*(2*a^3*f + 3*(2*a^3*f + I*(3*a^2*b + b^3)*f)*cosh(d*x + c)^2 + I*(3*a^2*b + b^3)*f)*sinh(d*x + c)^2 + I*(3*a^2*b + b^3)*f + 4*((2*a^3*f + I*(3*a^2*b + b^3)*f)*cosh(d*x + c)^3 + (2*a^3*f + I*(3*a^2*b + b^3)*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - ((2*a^3*f - I*(3*a^2*b + b^3)*f)*cosh(d*x + c)^4 + 4*(2*a^3*f - I*(3*a^2*b + b^3)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^3*f - I*(3*a^2*b + b^3)*f)*sinh(d*x + c)^4 + 2*a^3*f + 2*(2*a^3*f - I*(3*a^2*b + b^3)*f)*cosh(d*x + c)^2 + 2*(2*a^3*f + 3*(2*a^3*f - I*(3*a^2*b + b^3)*f)*cosh(d*x + c)^2 - I*(3*a^2*b + b^3)*f)*sinh(d*x + c)^2 - I*(3*a^2*b + b^3)*f + 4*((2*a^3*f - I*(3*a^2*b + b^3)*f)*cosh(d*x + c)^3 + (2*a^3*f - I*(3*a^2*b + b^3)*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + 2*(a^3*d*e - a^3*c*f + (a^3*d*e - a^3*c*f)*cosh(d*x + c)^4 + 4*(a^3*d*e - a^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*d*e - a^3*c*f)*sinh(d*x + c)^4 + 2*(a^3*d*e - a^3*c*f)*cosh(d*x + c)^2 + 2*(a^3*d*e - a^3*c*f + 3*(a^3*d*e - a^3*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*d*e - a^3*c*f)*cosh(d*x + c)^3 + (a^3*d*e - a^3*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a^3*d*e - a^3*c*f + (a^3*d*e - a^3*c*f)*cosh(d*x + c)^4 + 4*(a^3*d*e - a^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*d*e - a^3*c*f)*sinh(d*x + c)^4 + 2*(a^3*d*e - a^3*c*f)*cosh(d*x + c)^2 + 2*(a^3*d*e - a^3*c*f + 3*(a^3*d*e - a^3*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*d*e - a^3*c*f)*cosh(d*x + c)^3 + (a^3*d*e - a^3*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(a^3*d*f*x + a^3*c*f + (a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^4 + 4*(a^3*d*f*x + a^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*d*f*x + a^3*c*f)*sinh(d*x + c)^4 + 2*(a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^2 + 2*(a^3*d*f*x + a^3*c*f + 3*(a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^3 + (a^3*d*f*x + a^3*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(a^3*d*f*x + a^3*c*f + (a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^4 + 4*(a^3*d*f*x + a^3*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*d*f*x + a^3*c*f)*sinh(d*x + c)^4 + 2*(a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^2 + 2*(a^3*d*f*x + a^3*c*f + 3*(a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*d*f*x + a^3*c*f)*cosh(d*x + c)^3 + (a^3*d*f*x + a^3*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (2*a^3*d*e - 2*a^3*c*f + (2*a^3*d*e - 2*a^3*c*f + I*(3*a^2*b + b^3)*d*e - I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^4 + (8*a^3*d*e - 8*a^3*c*f + 4*I*(3*a^2*b + b^3)*d*e - 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^3*d*e - 2*a^3*c*f + I*(3*a^2*b + b^3)*d*e - I*(3*a^2*b + b^3)*c*f)*sinh(d*x + c)^4 + I*(3*a^2*b + b^3)*d*e - I*(3*a^2*b + b^3)*c*f + (4*a^3*d*e - 4*a^3*c*f + 2*I*(3*a^2*b + b^3)*d*e - 2*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^2 + (4*a^3*d*e - 4*a^3*c*f + 2*I*(3*a^2*b + b^3)*d*e - 2*I*(3*a^2*b + b^3)*c*f + (12*a^3*d*e - 12*a^3*c*f + 6*I*(3*a^2*b + b^3)*d*e - 6*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^3*d*e - 8*a^3*c*f + 4*I*(3*a^2*b + b^3)*d*e - 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^3 + (8*a^3*d*e - 8*a^3*c*f + 4*I*(3*a^2*b + b^3)*d*e - 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) - (2*a^3*d*e - 2*a^3*c*f + (2*a^3*d*e - 2*a^3*c*f - I*(3*a^2*b + b^3)*d*e + I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^4 + (8*a^3*d*e - 8*a^3*c*f - 4*I*(3*a^2*b + b^3)*d*e + 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^3*d*e - 2*a^3*c*f - I*(3*a^2*b + b^3)*d*e + I*(3*a^2*b + b^3)*c*f)*sinh(d*x + c)^4 - I*(3*a^2*b + b^3)*d*e + I*(3*a^2*b + b^3)*c*f + (4*a^3*d*e - 4*a^3*c*f - 2*I*(3*a^2*b + b^3)*d*e + 2*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^2 + (4*a^3*d*e - 4*a^3*c*f - 2*I*(3*a^2*b + b^3)*d*e + 2*I*(3*a^2*b + b^3)*c*f + (12*a^3*d*e - 12*a^3*c*f - 6*I*(3*a^2*b + b^3)*d*e + 6*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^3*d*e - 8*a^3*c*f - 4*I*(3*a^2*b + b^3)*d*e + 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^3 + (8*a^3*d*e - 8*a^3*c*f - 4*I*(3*a^2*b + b^3)*d*e + 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) - (2*a^3*d*f*x + 2*a^3*c*f + (2*a^3*d*f*x + 2*a^3*c*f - I*(3*a^2*b + b^3)*d*f*x - I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^4 + (8*a^3*d*f*x + 8*a^3*c*f - 4*I*(3*a^2*b + b^3)*d*f*x - 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^3*d*f*x + 2*a^3*c*f - I*(3*a^2*b + b^3)*d*f*x - I*(3*a^2*b + b^3)*c*f)*sinh(d*x + c)^4 - I*(3*a^2*b + b^3)*d*f*x - I*(3*a^2*b + b^3)*c*f + (4*a^3*d*f*x + 4*a^3*c*f - 2*I*(3*a^2*b + b^3)*d*f*x - 2*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^2 + (4*a^3*d*f*x + 4*a^3*c*f - 2*I*(3*a^2*b + b^3)*d*f*x - 2*I*(3*a^2*b + b^3)*c*f + (12*a^3*d*f*x + 12*a^3*c*f - 6*I*(3*a^2*b + b^3)*d*f*x - 6*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^3*d*f*x + 8*a^3*c*f - 4*I*(3*a^2*b + b^3)*d*f*x - 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^3 + (8*a^3*d*f*x + 8*a^3*c*f - 4*I*(3*a^2*b + b^3)*d*f*x - 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (2*a^3*d*f*x + 2*a^3*c*f + (2*a^3*d*f*x + 2*a^3*c*f + I*(3*a^2*b + b^3)*d*f*x + I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^4 + (8*a^3*d*f*x + 8*a^3*c*f + 4*I*(3*a^2*b + b^3)*d*f*x + 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^3*d*f*x + 2*a^3*c*f + I*(3*a^2*b + b^3)*d*f*x + I*(3*a^2*b + b^3)*c*f)*sinh(d*x + c)^4 + I*(3*a^2*b + b^3)*d*f*x + I*(3*a^2*b + b^3)*c*f + (4*a^3*d*f*x + 4*a^3*c*f + 2*I*(3*a^2*b + b^3)*d*f*x + 2*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^2 + (4*a^3*d*f*x + 4*a^3*c*f + 2*I*(3*a^2*b + b^3)*d*f*x + 2*I*(3*a^2*b + b^3)*c*f + (12*a^3*d*f*x + 12*a^3*c*f + 6*I*(3*a^2*b + b^3)*d*f*x + 6*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^3*d*f*x + 8*a^3*c*f + 4*I*(3*a^2*b + b^3)*d*f*x + 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c)^3 + (8*a^3*d*f*x + 8*a^3*c*f + 4*I*(3*a^2*b + b^3)*d*f*x + 4*I*(3*a^2*b + b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - 3*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^2*b + b^3)*f)*cosh(d*x + c)^2 - (a^2*b + b^3)*f + 2*(2*(a^3 + a*b^2)*d*f*x + 2*(a^3 + a*b^2)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^2*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d^2)*sinh(d*x + c)^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
418,1,896,0,0.491499," ","integrate(tanh(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{3} + 2 \, a b^{2} - 3 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} b + b^{3} + 2 \, {\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b + b^{3} + 3 \, {\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) + {\left(a^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} \sinh\left(d x + c\right)^{4} + 2 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3} + 2 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} \sinh\left(d x + c\right)^{4} + 2 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3} + 2 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{2} b + b^{3} - 3 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"-((a^2*b + b^3)*cosh(d*x + c)^3 + (a^2*b + b^3)*sinh(d*x + c)^3 - 2*(a^3 + a*b^2)*cosh(d*x + c)^2 - (2*a^3 + 2*a*b^2 - 3*(a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - ((3*a^2*b + b^3)*cosh(d*x + c)^4 + 4*(3*a^2*b + b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2*b + b^3)*sinh(d*x + c)^4 + 3*a^2*b + b^3 + 2*(3*a^2*b + b^3)*cosh(d*x + c)^2 + 2*(3*a^2*b + b^3 + 3*(3*a^2*b + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((3*a^2*b + b^3)*cosh(d*x + c)^3 + (3*a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - (a^2*b + b^3)*cosh(d*x + c) + (a^3*cosh(d*x + c)^4 + 4*a^3*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*sinh(d*x + c)^4 + 2*a^3*cosh(d*x + c)^2 + a^3 + 2*(3*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^2 + 4*(a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) - (a^3*cosh(d*x + c)^4 + 4*a^3*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*sinh(d*x + c)^4 + 2*a^3*cosh(d*x + c)^2 + a^3 + 2*(3*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^2 + 4*(a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (a^2*b + b^3 - 3*(a^2*b + b^3)*cosh(d*x + c)^2 + 4*(a^3 + a*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d)*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*d + 4*((a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
419,0,0,0,7.751118," ","integrate(tanh(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tanh\left(d x + c\right)^{3}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(tanh(d*x + c)^3/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
420,1,1228,0,0.821467," ","integrate((f*x+e)^3*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, f^{3} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 6 \, f^{3} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 3 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 3 \, {\left(d^{2} f^{3} x^{2} + 2 \, d^{2} e f^{2} x + d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + d^{3} e^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(d^{3} f^{3} x^{3} + 3 \, d^{3} e f^{2} x^{2} + 3 \, d^{3} e^{2} f x + 3 \, c d^{2} e^{2} f - 3 \, c^{2} d e f^{2} + c^{3} f^{3}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 6 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left(d f^{3} x + d e f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right)}{a d^{4}}"," ",0,"-(6*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*f^3*polylog(4, cosh(d*x + c) + sinh(d*x + c)) - 6*f^3*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) + 3*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) - 3*(d^2*f^3*x^2 + 2*d^2*e*f^2*x + d^2*e^2*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + d^3*e^3)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (d^3*f^3*x^3 + 3*d^3*e*f^2*x^2 + 3*d^3*e^2*f*x + 3*c*d^2*e^2*f - 3*c^2*d*e*f^2 + c^3*f^3)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 6*(d*f^3*x + d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(d*f^3*x + d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(d*f^3*x + d*e*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 6*(d*f^3*x + d*e*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)))/(a*d^4)","C",0
421,1,813,0,0.621104," ","integrate((f*x+e)^2*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, f^{2} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, f^{2} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left(d f^{2} x + d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(d f^{2} x + d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(d f^{2} x + d e f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left(d f^{2} x + d e f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + d^{2} e^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(d^{2} f^{2} x^{2} + 2 \, d^{2} e f x + 2 \, c d e f - c^{2} f^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right)}{a d^{3}}"," ",0,"(2*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*f^2*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 2*f^2*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 2*(d*f^2*x + d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(d*f^2*x + d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(d*f^2*x + d*e*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) + 2*(d*f^2*x + d*e*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (d^2*f^2*x^2 + 2*d^2*e*f*x + d^2*e^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (d^2*e^2 - 2*c*d*e*f + c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (d^2*f^2*x^2 + 2*d^2*e*f*x + 2*c*d*e*f - c^2*f^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1))/(a*d^3)","C",0
422,1,476,0,0.497238," ","integrate((f*x+e)*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - f {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - f {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(d e - c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(d e - c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(d f x + c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(d f x + c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(d f x + d e\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(d e - c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(d f x + c f\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right)}{a d^{2}}"," ",0,"-(f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - f*dilog(cosh(d*x + c) + sinh(d*x + c)) - f*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (d*e - c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (d*e - c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (d*f*x + c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (d*f*x + c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (d*f*x + d*e)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (d*e - c*f)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (d*f*x + c*f)*log(-cosh(d*x + c) - sinh(d*x + c) + 1))/(a*d^2)","B",0
423,1,67,0,0.649239," ","integrate(coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{\log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{a d}"," ",0,"-(log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) - log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/(a*d)","A",0
424,0,0,0,0.534122," ","integrate(coth(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(coth(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
425,1,1470,0,0.511748," ","integrate((f*x+e)^3*cosh(d*x+c)*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{a d^{4} f^{3} x^{4} + 4 \, a d^{4} e f^{2} x^{3} + 6 \, a d^{4} e^{2} f x^{2} + 4 \, a d^{4} e^{3} x - 24 \, b f^{3} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, b f^{3} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, b f^{3} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 24 \, b f^{3} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 12 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 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)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\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)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 24 \, {\left(b d f^{3} x + b d e f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left(b d f^{3} x + b d e f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 12 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + b d^{3} e^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\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(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 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(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 24 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 24 \, {\left(b d f^{3} x + b d e f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right)}{4 \, a b d^{4}}"," ",0,"1/4*(a*d^4*f^3*x^4 + 4*a*d^4*e*f^2*x^3 + 6*a*d^4*e^2*f*x^2 + 4*a*d^4*e^3*x - 24*b*f^3*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*b*f^3*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*b*f^3*polylog(4, cosh(d*x + c) + sinh(d*x + c)) - 24*b*f^3*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) - 12*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 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)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 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)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 24*(b*d*f^3*x + b*d*e*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*(b*d*f^3*x + b*d*e*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) - 12*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - 4*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + b*d^3*e^3)*log(cosh(d*x + c) + sinh(d*x + c) + 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(d*x + c) + sinh(d*x + c) - 1) + 4*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 24*(b*d*f^3*x + b*d*e*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 24*(b*d*f^3*x + b*d*e*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)))/(a*b*d^4)","C",0
426,1,992,0,0.481078," ","integrate((f*x+e)^2*cosh(d*x+c)*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{a d^{3} f^{2} x^{3} + 3 \, a d^{3} e f x^{2} + 3 \, a d^{3} e^{2} x + 6 \, b f^{2} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, b f^{2} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, b f^{2} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, b f^{2} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 6 \, {\left(b d f^{2} x + b d e f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 6 \, {\left(b d f^{2} x + b d e f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 3 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left(b d f^{2} x + b d e f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 6 \, {\left(b d f^{2} x + b d e f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + b d^{2} e^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\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(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right)}{3 \, a b d^{3}}"," ",0,"1/3*(a*d^3*f^2*x^3 + 3*a*d^3*e*f*x^2 + 3*a*d^3*e^2*x + 6*b*f^2*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*b*f^2*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*b*f^2*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 6*b*f^2*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 6*(b*d*f^2*x + b*d*e*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 6*(b*d*f^2*x + b*d*e*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 3*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 3*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 6*(b*d*f^2*x + b*d*e*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) - 6*(b*d*f^2*x + b*d*e*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - 3*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + b*d^2*e^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 3*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 3*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1))/(a*b*d^3)","C",0
427,1,598,0,0.522910," ","integrate((f*x+e)*cosh(d*x+c)*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{a d^{2} f x^{2} + 2 \, a d^{2} e x - 2 \, b f \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, b f \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, b f {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, b f {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left(b d e - b c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b d e - b c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b d f x + b c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b d f x + b c f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b d f x + b d e\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(b d e - b c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(b d f x + b c f\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right)}{2 \, a b d^{2}}"," ",0,"1/2*(a*d^2*f*x^2 + 2*a*d^2*e*x - 2*b*f*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*b*f*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*b*f*dilog(cosh(d*x + c) + sinh(d*x + c)) - 2*b*f*dilog(-cosh(d*x + c) - sinh(d*x + c)) + 2*(b*d*e - b*c*f)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b*d*e - b*c*f)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b*d*f*x + b*c*f)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b*d*f*x + b*c*f)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(b*d*f*x + b*d*e)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 2*(b*d*e - b*c*f)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(b*d*f*x + b*c*f)*log(-cosh(d*x + c) - sinh(d*x + c) + 1))/(a*b*d^2)","B",0
428,1,209,0,0.517841," ","integrate(cosh(d*x+c)*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{a d x - b \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + b \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right)}{a b d}"," ",0,"(a*d*x - b*log(cosh(d*x + c) + sinh(d*x + c) + 1) + b*log(cosh(d*x + c) + sinh(d*x + c) - 1) + sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)))/(a*b*d)","B",0
429,0,0,0,0.597237," ","integrate(cosh(d*x+c)*coth(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right) \coth\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)*coth(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
430,1,3344,0,0.585294," ","integrate((f*x+e)^3*cosh(d*x+c)^2*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a b d^{3} f^{3} x^{3} + 2 \, a b d^{3} e^{3} + 6 \, a b d^{2} e^{2} f + 12 \, a b d e f^{2} + 12 \, a b f^{3} + 6 \, {\left(a b d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} - 2 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a b d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x - {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} d^{4} e f^{2} x^{3} + 6 \, a^{2} d^{4} e^{2} f x^{2} + 4 \, a^{2} d^{4} e^{3} x + 8 \, a^{2} c d^{3} e^{3} - 12 \, a^{2} c^{2} d^{2} e^{2} f + 8 \, a^{2} c^{3} d e f^{2} - 2 \, a^{2} c^{4} f^{3}\right)} \cosh\left(d x + c\right) + 12 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 12 \, {\left({\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 12 \, {\left({\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left({\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + b^{2} d^{3} e^{3}\right)} \cosh\left(d x + c\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + b^{2} d^{3} e^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 4 \, {\left({\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - 4 \, {\left({\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 24 \, {\left({\left(a^{2} + b^{2}\right)} f^{3} \cosh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{3} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(a^{2} + b^{2}\right)} f^{3} \cosh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{3} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right) + b^{2} f^{3} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 24 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right) + b^{2} f^{3} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 24 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 24 \, {\left({\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} d^{4} e f^{2} x^{3} + 6 \, a^{2} d^{4} e^{2} f x^{2} + 4 \, a^{2} d^{4} e^{3} x + 8 \, a^{2} c d^{3} e^{3} - 12 \, a^{2} c^{2} d^{2} e^{2} f + 8 \, a^{2} c^{3} d e f^{2} - 2 \, a^{2} c^{4} f^{3} + 4 \, {\left(a b d^{3} f^{3} x^{3} + a b d^{3} e^{3} - 3 \, a b d^{2} e^{2} f + 6 \, a b d e f^{2} - 6 \, a b f^{3} + 3 \, {\left(a b d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a b d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left(a b^{2} d^{4} \cosh\left(d x + c\right) + a b^{2} d^{4} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/4*(2*a*b*d^3*f^3*x^3 + 2*a*b*d^3*e^3 + 6*a*b*d^2*e^2*f + 12*a*b*d*e*f^2 + 12*a*b*f^3 + 6*(a*b*d^3*e*f^2 + a*b*d^2*f^3)*x^2 - 2*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^2 - 2*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*sinh(d*x + c)^2 + 6*(a*b*d^3*e^2*f + 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x - (a^2*d^4*f^3*x^4 + 4*a^2*d^4*e*f^2*x^3 + 6*a^2*d^4*e^2*f*x^2 + 4*a^2*d^4*e^3*x + 8*a^2*c*d^3*e^3 - 12*a^2*c^2*d^2*e^2*f + 8*a^2*c^3*d*e*f^2 - 2*a^2*c^4*f^3)*cosh(d*x + c) + 12*(((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*cosh(d*x + c) + ((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*(((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*cosh(d*x + c) + ((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 12*((b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c) + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) - 12*((b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c) + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) + 4*(((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*cosh(d*x + c) + ((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 4*(((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*cosh(d*x + c) + ((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 4*(((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*cosh(d*x + c) + ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*(((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*cosh(d*x + c) + ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*((b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + b^2*d^3*e^3)*cosh(d*x + c) + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + b^2*d^3*e^3)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 4*((b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c) + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) - 4*((b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c) + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 24*((a^2 + b^2)*f^3*cosh(d*x + c) + (a^2 + b^2)*f^3*sinh(d*x + c))*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*((a^2 + b^2)*f^3*cosh(d*x + c) + (a^2 + b^2)*f^3*sinh(d*x + c))*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*(b^2*f^3*cosh(d*x + c) + b^2*f^3*sinh(d*x + c))*polylog(4, cosh(d*x + c) + sinh(d*x + c)) - 24*(b^2*f^3*cosh(d*x + c) + b^2*f^3*sinh(d*x + c))*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) - 24*(((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*cosh(d*x + c) + ((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*(((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*cosh(d*x + c) + ((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*((b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c) + (b^2*d*f^3*x + b^2*d*e*f^2)*sinh(d*x + c))*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 24*((b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c) + (b^2*d*f^3*x + b^2*d*e*f^2)*sinh(d*x + c))*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - (a^2*d^4*f^3*x^4 + 4*a^2*d^4*e*f^2*x^3 + 6*a^2*d^4*e^2*f*x^2 + 4*a^2*d^4*e^3*x + 8*a^2*c*d^3*e^3 - 12*a^2*c^2*d^2*e^2*f + 8*a^2*c^3*d*e*f^2 - 2*a^2*c^4*f^3 + 4*(a*b*d^3*f^3*x^3 + a*b*d^3*e^3 - 3*a*b*d^2*e^2*f + 6*a*b*d*e*f^2 - 6*a*b*f^3 + 3*(a*b*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(a*b*d^3*e^2*f - 2*a*b*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))/(a*b^2*d^4*cosh(d*x + c) + a*b^2*d^4*sinh(d*x + c))","C",0
431,1,2101,0,0.523493," ","integrate((f*x+e)^2*cosh(d*x+c)^2*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, a b d^{2} f^{2} x^{2} + 3 \, a b d^{2} e^{2} + 6 \, a b d e f + 6 \, a b f^{2} - 3 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a b d^{2} e f + a b d f^{2}\right)} x - 2 \, {\left(a^{2} d^{3} f^{2} x^{3} + 3 \, a^{2} d^{3} e f x^{2} + 3 \, a^{2} d^{3} e^{2} x + 6 \, a^{2} c d^{2} e^{2} - 6 \, a^{2} c^{2} d e f + 2 \, a^{2} c^{3} f^{2}\right)} \cosh\left(d x + c\right) + 12 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 12 \, {\left({\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right) + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 12 \, {\left({\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right) + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 6 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 6 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 6 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 6 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + b^{2} d^{2} e^{2}\right)} \cosh\left(d x + c\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + b^{2} d^{2} e^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 6 \, {\left({\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - 6 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 12 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{2} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{2} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right) + b^{2} f^{2} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 12 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right) + b^{2} f^{2} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left(a^{2} d^{3} f^{2} x^{3} + 3 \, a^{2} d^{3} e f x^{2} + 3 \, a^{2} d^{3} e^{2} x + 6 \, a^{2} c d^{2} e^{2} - 6 \, a^{2} c^{2} d e f + 2 \, a^{2} c^{3} f^{2} + 3 \, {\left(a b d^{2} f^{2} x^{2} + a b d^{2} e^{2} - 2 \, a b d e f + 2 \, a b f^{2} + 2 \, {\left(a b d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left(a b^{2} d^{3} \cosh\left(d x + c\right) + a b^{2} d^{3} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/6*(3*a*b*d^2*f^2*x^2 + 3*a*b*d^2*e^2 + 6*a*b*d*e*f + 6*a*b*f^2 - 3*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^2 - 3*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*sinh(d*x + c)^2 + 6*(a*b*d^2*e*f + a*b*d*f^2)*x - 2*(a^2*d^3*f^2*x^3 + 3*a^2*d^3*e*f*x^2 + 3*a^2*d^3*e^2*x + 6*a^2*c*d^2*e^2 - 6*a^2*c^2*d*e*f + 2*a^2*c^3*f^2)*cosh(d*x + c) + 12*(((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c) + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*(((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c) + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 12*((b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c) + (b^2*d*f^2*x + b^2*d*e*f)*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) - 12*((b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c) + (b^2*d*f^2*x + b^2*d*e*f)*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) + 6*(((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c) + ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 6*(((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c) + ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 6*(((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c) + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 6*(((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c) + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 6*((b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + b^2*d^2*e^2)*cosh(d*x + c) + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + b^2*d^2*e^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 6*((b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c) + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) - 6*((b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c) + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 12*((a^2 + b^2)*f^2*cosh(d*x + c) + (a^2 + b^2)*f^2*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*((a^2 + b^2)*f^2*cosh(d*x + c) + (a^2 + b^2)*f^2*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(b^2*f^2*cosh(d*x + c) + b^2*f^2*sinh(d*x + c))*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 12*(b^2*f^2*cosh(d*x + c) + b^2*f^2*sinh(d*x + c))*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 2*(a^2*d^3*f^2*x^3 + 3*a^2*d^3*e*f*x^2 + 3*a^2*d^3*e^2*x + 6*a^2*c*d^2*e^2 - 6*a^2*c^2*d*e*f + 2*a^2*c^3*f^2 + 3*(a*b*d^2*f^2*x^2 + a*b*d^2*e^2 - 2*a*b*d*e*f + 2*a*b*f^2 + 2*(a*b*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(a*b^2*d^3*cosh(d*x + c) + a*b^2*d^3*sinh(d*x + c))","C",0
432,1,1108,0,0.534208," ","integrate((f*x+e)*cosh(d*x+c)^2*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{a b d f x + a b d e + a b f - {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d f x + a b d e - a b f\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{2} d^{2} f x^{2} + 2 \, a^{2} d^{2} e x + 4 \, a^{2} c d e - 2 \, a^{2} c^{2} f\right)} \cosh\left(d x + c\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b^{2} f \cosh\left(d x + c\right) + b^{2} f \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(b^{2} f \cosh\left(d x + c\right) + b^{2} f \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left({\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(b^{2} d f x + b^{2} d e\right)} \cosh\left(d x + c\right) + {\left(b^{2} d f x + b^{2} d e\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right) + {\left(b^{2} d e - b^{2} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - 2 \, {\left({\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right) + {\left(b^{2} d f x + b^{2} c f\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - {\left(a^{2} d^{2} f x^{2} + 2 \, a^{2} d^{2} e x + 4 \, a^{2} c d e - 2 \, a^{2} c^{2} f + 2 \, {\left(a b d f x + a b d e - a b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a b^{2} d^{2} \cosh\left(d x + c\right) + a b^{2} d^{2} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(a*b*d*f*x + a*b*d*e + a*b*f - (a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c)^2 - (a*b*d*f*x + a*b*d*e - a*b*f)*sinh(d*x + c)^2 - (a^2*d^2*f*x^2 + 2*a^2*d^2*e*x + 4*a^2*c*d*e - 2*a^2*c^2*f)*cosh(d*x + c) + 2*((a^2 + b^2)*f*cosh(d*x + c) + (a^2 + b^2)*f*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*((a^2 + b^2)*f*cosh(d*x + c) + (a^2 + b^2)*f*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b^2*f*cosh(d*x + c) + b^2*f*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) - 2*(b^2*f*cosh(d*x + c) + b^2*f*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) + 2*(((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c) + ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c) + ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c) + ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c) + ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((b^2*d*f*x + b^2*d*e)*cosh(d*x + c) + (b^2*d*f*x + b^2*d*e)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 2*((b^2*d*e - b^2*c*f)*cosh(d*x + c) + (b^2*d*e - b^2*c*f)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) - 2*((b^2*d*f*x + b^2*c*f)*cosh(d*x + c) + (b^2*d*f*x + b^2*c*f)*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - (a^2*d^2*f*x^2 + 2*a^2*d^2*e*x + 4*a^2*c*d*e - 2*a^2*c^2*f + 2*(a*b*d*f*x + a*b*d*e - a*b*f)*cosh(d*x + c))*sinh(d*x + c))/(a*b^2*d^2*cosh(d*x + c) + a*b^2*d^2*sinh(d*x + c))","B",0
433,1,203,0,0.739892," ","integrate(cosh(d*x+c)^2*coth(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a^{2} d x \cosh\left(d x + c\right) + a b \cosh\left(d x + c\right)^{2} + a b \sinh\left(d x + c\right)^{2} - a b - 2 \, {\left({\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(a^{2} d x + a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a b^{2} d \cosh\left(d x + c\right) + a b^{2} d \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(2*a^2*d*x*cosh(d*x + c) + a*b*cosh(d*x + c)^2 + a*b*sinh(d*x + c)^2 - a*b - 2*((a^2 + b^2)*cosh(d*x + c) + (a^2 + b^2)*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(b^2*cosh(d*x + c) + b^2*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(a^2*d*x + a*b*cosh(d*x + c))*sinh(d*x + c))/(a*b^2*d*cosh(d*x + c) + a*b^2*d*sinh(d*x + c))","B",0
434,0,0,0,0.629128," ","integrate(cosh(d*x+c)^2*coth(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{2} \coth\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)^2*coth(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
435,1,2454,0,0.674352," ","integrate((f*x+e)^3*csch(d*x+c)*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, b^{2} f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, b^{2} f^{3} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(a^{2} + b^{2}\right)} f^{3} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 6 \, {\left(a^{2} + b^{2}\right)} f^{3} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(3 \, a^{2} d^{2} f^{3} x^{2} + 3 i \, a b d^{2} f^{3} x^{2} + 6 \, a^{2} d^{2} e f^{2} x + 6 i \, a b d^{2} e f^{2} x + 3 \, a^{2} d^{2} e^{2} f + 3 i \, a b d^{2} e^{2} f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(3 \, a^{2} d^{2} f^{3} x^{2} - 3 i \, a b d^{2} f^{3} x^{2} + 6 \, a^{2} d^{2} e f^{2} x - 6 i \, a b d^{2} e f^{2} x + 3 \, a^{2} d^{2} e^{2} f - 3 i \, a b d^{2} e^{2} f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + {\left(a^{2} + b^{2}\right)} d^{3} e^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left(a^{2} d^{3} e^{3} + i \, a b d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f - 3 i \, a b c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} + 3 i \, a b c^{2} d e f^{2} - a^{2} c^{3} f^{3} - i \, a b c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(a^{2} d^{3} e^{3} - i \, a b d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 i \, a b c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - 3 i \, a b c^{2} d e f^{2} - a^{2} c^{3} f^{3} + i \, a b c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(a^{2} d^{3} f^{3} x^{3} - i \, a b d^{3} f^{3} x^{3} + 3 \, a^{2} d^{3} e f^{2} x^{2} - 3 i \, a b d^{3} e f^{2} x^{2} + 3 \, a^{2} d^{3} e^{2} f x - 3 i \, a b d^{3} e^{2} f x + 3 \, a^{2} c d^{2} e^{2} f - 3 i \, a b c d^{2} e^{2} f - 3 \, a^{2} c^{2} d e f^{2} + 3 i \, a b c^{2} d e f^{2} + a^{2} c^{3} f^{3} - i \, a b c^{3} f^{3}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(a^{2} d^{3} f^{3} x^{3} + i \, a b d^{3} f^{3} x^{3} + 3 \, a^{2} d^{3} e f^{2} x^{2} + 3 i \, a b d^{3} e f^{2} x^{2} + 3 \, a^{2} d^{3} e^{2} f x + 3 i \, a b d^{3} e^{2} f x + 3 \, a^{2} c d^{2} e^{2} f + 3 i \, a b c d^{2} e^{2} f - 3 \, a^{2} c^{2} d e f^{2} - 3 i \, a b c^{2} d e f^{2} + a^{2} c^{3} f^{3} + i \, a b c^{3} f^{3}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + {\left(6 \, a^{2} f^{3} + 6 i \, a b f^{3}\right)} {\rm polylog}\left(4, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(6 \, a^{2} f^{3} - 6 i \, a b f^{3}\right)} {\rm polylog}\left(4, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(6 \, a^{2} d f^{3} x + 6 i \, a b d f^{3} x + 6 \, a^{2} d e f^{2} + 6 i \, a b d e f^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(6 \, a^{2} d f^{3} x - 6 i \, a b d f^{3} x + 6 \, a^{2} d e f^{2} - 6 i \, a b d e f^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 6 \, {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right)}{{\left(a^{3} + a b^{2}\right)} d^{4}}"," ",0,"-(6*b^2*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*b^2*f^3*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(a^2 + b^2)*f^3*polylog(4, cosh(d*x + c) + sinh(d*x + c)) - 6*(a^2 + b^2)*f^3*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) + 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) + (3*a^2*d^2*f^3*x^2 + 3*I*a*b*d^2*f^3*x^2 + 6*a^2*d^2*e*f^2*x + 6*I*a*b*d^2*e*f^2*x + 3*a^2*d^2*e^2*f + 3*I*a*b*d^2*e^2*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (3*a^2*d^2*f^3*x^2 - 3*I*a*b*d^2*f^3*x^2 + 6*a^2*d^2*e*f^2*x - 6*I*a*b*d^2*e*f^2*x + 3*a^2*d^2*e^2*f - 3*I*a*b*d^2*e^2*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 3*((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + (a^2 + b^2)*d^3*e^3)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (a^2*d^3*e^3 + I*a*b*d^3*e^3 - 3*a^2*c*d^2*e^2*f - 3*I*a*b*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 + 3*I*a*b*c^2*d*e*f^2 - a^2*c^3*f^3 - I*a*b*c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (a^2*d^3*e^3 - I*a*b*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*I*a*b*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - 3*I*a*b*c^2*d*e*f^2 - a^2*c^3*f^3 + I*a*b*c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) - I) - ((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (a^2*d^3*f^3*x^3 - I*a*b*d^3*f^3*x^3 + 3*a^2*d^3*e*f^2*x^2 - 3*I*a*b*d^3*e*f^2*x^2 + 3*a^2*d^3*e^2*f*x - 3*I*a*b*d^3*e^2*f*x + 3*a^2*c*d^2*e^2*f - 3*I*a*b*c*d^2*e^2*f - 3*a^2*c^2*d*e*f^2 + 3*I*a*b*c^2*d*e*f^2 + a^2*c^3*f^3 - I*a*b*c^3*f^3)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (a^2*d^3*f^3*x^3 + I*a*b*d^3*f^3*x^3 + 3*a^2*d^3*e*f^2*x^2 + 3*I*a*b*d^3*e*f^2*x^2 + 3*a^2*d^3*e^2*f*x + 3*I*a*b*d^3*e^2*f*x + 3*a^2*c*d^2*e^2*f + 3*I*a*b*c*d^2*e^2*f - 3*a^2*c^2*d*e*f^2 - 3*I*a*b*c^2*d*e*f^2 + a^2*c^3*f^3 + I*a*b*c^3*f^3)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + (6*a^2*f^3 + 6*I*a*b*f^3)*polylog(4, I*cosh(d*x + c) + I*sinh(d*x + c)) + (6*a^2*f^3 - 6*I*a*b*f^3)*polylog(4, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 6*(b^2*d*f^3*x + b^2*d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b^2*d*f^3*x + b^2*d*e*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - (6*a^2*d*f^3*x + 6*I*a*b*d*f^3*x + 6*a^2*d*e*f^2 + 6*I*a*b*d*e*f^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - (6*a^2*d*f^3*x - 6*I*a*b*d*f^3*x + 6*a^2*d*e*f^2 - 6*I*a*b*d*e*f^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) + 6*((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)))/((a^3 + a*b^2)*d^4)","C",0
436,1,1539,0,0.519662," ","integrate((f*x+e)^2*csch(d*x+c)*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b^{2} f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, b^{2} f^{2} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(a^{2} + b^{2}\right)} f^{2} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(a^{2} + b^{2}\right)} f^{2} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(2 \, a^{2} d f^{2} x + 2 i \, a b d f^{2} x + 2 \, a^{2} d e f + 2 i \, a b d e f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(2 \, a^{2} d f^{2} x - 2 i \, a b d f^{2} x + 2 \, a^{2} d e f - 2 i \, a b d e f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(a^{2} d^{2} e^{2} + i \, a b d^{2} e^{2} - 2 \, a^{2} c d e f - 2 i \, a b c d e f + a^{2} c^{2} f^{2} + i \, a b c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(a^{2} d^{2} e^{2} - i \, a b d^{2} e^{2} - 2 \, a^{2} c d e f + 2 i \, a b c d e f + a^{2} c^{2} f^{2} - i \, a b c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(a^{2} d^{2} f^{2} x^{2} - i \, a b d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x - 2 i \, a b d^{2} e f x + 2 \, a^{2} c d e f - 2 i \, a b c d e f - a^{2} c^{2} f^{2} + i \, a b c^{2} f^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(a^{2} d^{2} f^{2} x^{2} + i \, a b d^{2} f^{2} x^{2} + 2 \, a^{2} d^{2} e f x + 2 i \, a b d^{2} e f x + 2 \, a^{2} c d e f + 2 i \, a b c d e f - a^{2} c^{2} f^{2} - i \, a b c^{2} f^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + {\left(2 \, a^{2} f^{2} + 2 i \, a b f^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(2 \, a^{2} f^{2} - 2 i \, a b f^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right)}{{\left(a^{3} + a b^{2}\right)} d^{3}}"," ",0,"(2*b^2*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*b^2*f^2*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(a^2 + b^2)*f^2*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 2*(a^2 + b^2)*f^2*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 2*(b^2*d*f^2*x + b^2*d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b^2*d*f^2*x + b^2*d*e*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) - (2*a^2*d*f^2*x + 2*I*a*b*d*f^2*x + 2*a^2*d*e*f + 2*I*a*b*d*e*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (2*a^2*d*f^2*x - 2*I*a*b*d*f^2*x + 2*a^2*d*e*f - 2*I*a*b*d*e*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + (a^2 + b^2)*d^2*e^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (a^2*d^2*e^2 + I*a*b*d^2*e^2 - 2*a^2*c*d*e*f - 2*I*a*b*c*d*e*f + a^2*c^2*f^2 + I*a*b*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (a^2*d^2*e^2 - I*a*b*d^2*e^2 - 2*a^2*c*d*e*f + 2*I*a*b*c*d*e*f + a^2*c^2*f^2 - I*a*b*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) + ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (a^2*d^2*f^2*x^2 - I*a*b*d^2*f^2*x^2 + 2*a^2*d^2*e*f*x - 2*I*a*b*d^2*e*f*x + 2*a^2*c*d*e*f - 2*I*a*b*c*d*e*f - a^2*c^2*f^2 + I*a*b*c^2*f^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (a^2*d^2*f^2*x^2 + I*a*b*d^2*f^2*x^2 + 2*a^2*d^2*e*f*x + 2*I*a*b*d^2*e*f*x + 2*a^2*c*d*e*f + 2*I*a*b*c*d*e*f - a^2*c^2*f^2 - I*a*b*c^2*f^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + (2*a^2*f^2 + 2*I*a*b*f^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + (2*a^2*f^2 - 2*I*a*b*f^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)))/((a^3 + a*b^2)*d^3)","C",0
437,1,808,0,0.520901," ","integrate((f*x+e)*csch(d*x+c)*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{b^{2} f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + b^{2} f {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(a^{2} + b^{2}\right)} f {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(a^{2} + b^{2}\right)} f {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(a^{2} f + i \, a b f\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(a^{2} f - i \, a b f\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left(b^{2} d e - b^{2} c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{2} d e - b^{2} c f\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{2} d f x + b^{2} c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{2} d f x + b^{2} c f\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left(a^{2} d e + i \, a b d e - a^{2} c f - i \, a b c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(a^{2} d e - i \, a b d e - a^{2} c f + i \, a b c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(a^{2} d f x - i \, a b d f x + a^{2} c f - i \, a b c f\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(a^{2} d f x + i \, a b d f x + a^{2} c f + i \, a b c f\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right)}{{\left(a^{3} + a b^{2}\right)} d^{2}}"," ",0,"-(b^2*f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + b^2*f*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (a^2 + b^2)*f*dilog(cosh(d*x + c) + sinh(d*x + c)) - (a^2 + b^2)*f*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (a^2*f + I*a*b*f)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (a^2*f - I*a*b*f)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + (b^2*d*e - b^2*c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^2*d*e - b^2*c*f)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^2*d*f*x + b^2*c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^2*d*f*x + b^2*c*f)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (a^2*d*e + I*a*b*d*e - a^2*c*f - I*a*b*c*f)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (a^2*d*e - I*a*b*d*e - a^2*c*f + I*a*b*c*f)*log(cosh(d*x + c) + sinh(d*x + c) - I) - ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (a^2*d*f*x - I*a*b*d*f*x + a^2*c*f - I*a*b*c*f)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (a^2*d*f*x + I*a*b*d*f*x + a^2*c*f + I*a*b*c*f)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*log(-cosh(d*x + c) - sinh(d*x + c) + 1))/((a^3 + a*b^2)*d^2)","B",0
438,1,134,0,0.600521," ","integrate(csch(d*x+c)*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a b \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + b^{2} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + a^{2} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{2} + b^{2}\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{{\left(a^{3} + a b^{2}\right)} d}"," ",0,"-(2*a*b*arctan(cosh(d*x + c) + sinh(d*x + c)) + b^2*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + a^2*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (a^2 + b^2)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/((a^3 + a*b^2)*d)","A",0
439,0,0,0,1.536308," ","integrate(csch(d*x+c)*sech(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(d x + c\right) \operatorname{sech}\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(csch(d*x + c)*sech(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
440,1,9712,0,1.084647," ","integrate((f*x+e)^3*csch(d*x+c)*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e^{3} - 12 \, {\left(a^{3} b + a b^{3}\right)} c d^{2} e^{2} f + 12 \, {\left(a^{3} b + a b^{3}\right)} c^{2} d e f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c^{3} f^{3} - 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} b + a b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} b + a b^{3}\right)} c^{2} d e f^{2} + {\left(a^{3} b + a b^{3}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} b + a b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} b + a b^{3}\right)} c^{2} d e f^{2} + {\left(a^{3} b + a b^{3}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left(b^{4} d^{2} f^{3} x^{2} + 2 \, b^{4} d^{2} e f^{2} x + b^{4} d^{2} e^{2} f + {\left(b^{4} d^{2} f^{3} x^{2} + 2 \, b^{4} d^{2} e f^{2} x + b^{4} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d^{2} f^{3} x^{2} + 2 \, b^{4} d^{2} e f^{2} x + b^{4} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d^{2} f^{3} x^{2} + 2 \, b^{4} d^{2} e f^{2} x + b^{4} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 6 \, {\left(b^{4} d^{2} f^{3} x^{2} + 2 \, b^{4} d^{2} e f^{2} x + b^{4} d^{2} e^{2} f + {\left(b^{4} d^{2} f^{3} x^{2} + 2 \, b^{4} d^{2} e f^{2} x + b^{4} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d^{2} f^{3} x^{2} + 2 \, b^{4} d^{2} e f^{2} x + b^{4} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d^{2} f^{3} x^{2} + 2 \, b^{4} d^{2} e f^{2} x + b^{4} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3} + {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3} + {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d^{3} e^{3} - 3 \, b^{4} c d^{2} e^{2} f + 3 \, b^{4} c^{2} d e f^{2} - b^{4} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3} + {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3} + {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d^{3} f^{3} x^{3} + 3 \, b^{4} d^{3} e f^{2} x^{2} + 3 \, b^{4} d^{3} e^{2} f x + 3 \, b^{4} c d^{2} e^{2} f - 3 \, b^{4} c^{2} d e f^{2} + b^{4} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 12 \, {\left(b^{4} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{4} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{4} f^{3} \sinh\left(d x + c\right)^{2} + b^{4} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b^{4} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{4} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{4} f^{3} \sinh\left(d x + c\right)^{2} + b^{4} f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b^{4} d f^{3} x + b^{4} d e f^{2} + {\left(b^{4} d f^{3} x + b^{4} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d f^{3} x + b^{4} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d f^{3} x + b^{4} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b^{4} d f^{3} x + b^{4} d e f^{2} + {\left(b^{4} d f^{3} x + b^{4} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d f^{3} x + b^{4} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d f^{3} x + b^{4} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3}\right)} \cosh\left(d x + c\right) + 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(-12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + {\left(-12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-24 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + 24 \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x - 24 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2} + 24 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2} + {\left(12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(24 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + 24 \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 24 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2} + 24 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{3} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d f^{3} x + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 6 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left(-6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + {\left(-6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(-12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 24 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} - 24 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} + 12 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + {\left(6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f - 24 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} - 24 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} + 12 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} f + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} f - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} - 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} + 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{3} - 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + {\left(6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 24 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 24 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} + 24 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} - 12 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} - 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(-6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3} + {\left(-6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(-12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} - 24 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + 24 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - 24 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} + 24 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} - 12 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-6 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{3} x^{2} + 6 \, {\left(a^{3} b + a b^{3}\right)} d^{2} f^{3} x^{2} - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f^{2} x + 12 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f^{2} x - 12 i \, {\left(a^{4} + a^{2} b^{2}\right)} c d e f^{2} + 12 \, {\left(a^{3} b + a b^{3}\right)} c d e f^{2} + 6 i \, {\left(a^{4} + a^{2} b^{2}\right)} c^{2} f^{3} - 6 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} d e f^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 12 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{3} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{3}\right)} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 12 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{3} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{3}\right)} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 12 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(12 i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} - 12 \, {\left(a^{3} b + a b^{3}\right)} f^{3} - 12 \, {\left(-i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} + {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 24 \, {\left(-i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} + {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - 12 \, {\left(-i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} + {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(-12 i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} - 12 \, {\left(a^{3} b + a b^{3}\right)} f^{3} - 12 \, {\left(i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} + {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 24 \, {\left(i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} + {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - 12 \, {\left(i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{3} + {\left(a^{3} b + a b^{3}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 12 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{3} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{2} f x + {\left(a^{4} + a^{2} b^{2}\right)} d^{3} e^{3} - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} b + a b^{3}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{3} b + a b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{3} b + a b^{3}\right)} c^{2} d e f^{2} + {\left(a^{3} b + a b^{3}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{4} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{4}\right)}}"," ",0,"1/2*(4*(a^3*b + a*b^3)*d^3*e^3 - 12*(a^3*b + a*b^3)*c*d^2*e^2*f + 12*(a^3*b + a*b^3)*c^2*d*e*f^2 - 4*(a^3*b + a*b^3)*c^3*f^3 - 4*((a^3*b + a*b^3)*d^3*f^3*x^3 + 3*(a^3*b + a*b^3)*d^3*e*f^2*x^2 + 3*(a^3*b + a*b^3)*d^3*e^2*f*x + 3*(a^3*b + a*b^3)*c*d^2*e^2*f - 3*(a^3*b + a*b^3)*c^2*d*e*f^2 + (a^3*b + a*b^3)*c^3*f^3)*cosh(d*x + c)^2 - 4*((a^3*b + a*b^3)*d^3*f^3*x^3 + 3*(a^3*b + a*b^3)*d^3*e*f^2*x^2 + 3*(a^3*b + a*b^3)*d^3*e^2*f*x + 3*(a^3*b + a*b^3)*c*d^2*e^2*f - 3*(a^3*b + a*b^3)*c^2*d*e*f^2 + (a^3*b + a*b^3)*c^3*f^3)*sinh(d*x + c)^2 - 6*(b^4*d^2*f^3*x^2 + 2*b^4*d^2*e*f^2*x + b^4*d^2*e^2*f + (b^4*d^2*f^3*x^2 + 2*b^4*d^2*e*f^2*x + b^4*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(b^4*d^2*f^3*x^2 + 2*b^4*d^2*e*f^2*x + b^4*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d^2*f^3*x^2 + 2*b^4*d^2*e*f^2*x + b^4*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 6*(b^4*d^2*f^3*x^2 + 2*b^4*d^2*e*f^2*x + b^4*d^2*e^2*f + (b^4*d^2*f^3*x^2 + 2*b^4*d^2*e*f^2*x + b^4*d^2*e^2*f)*cosh(d*x + c)^2 + 2*(b^4*d^2*f^3*x^2 + 2*b^4*d^2*e*f^2*x + b^4*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d^2*f^3*x^2 + 2*b^4*d^2*e*f^2*x + b^4*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3 + (b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3)*cosh(d*x + c)^2 + 2*(b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3 + (b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3)*cosh(d*x + c)^2 + 2*(b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d^3*e^3 - 3*b^4*c*d^2*e^2*f + 3*b^4*c^2*d*e*f^2 - b^4*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3 + (b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3)*cosh(d*x + c)^2 + 2*(b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3 + (b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3)*cosh(d*x + c)^2 + 2*(b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d^3*f^3*x^3 + 3*b^4*d^3*e*f^2*x^2 + 3*b^4*d^3*e^2*f*x + 3*b^4*c*d^2*e^2*f - 3*b^4*c^2*d*e*f^2 + b^4*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 12*(b^4*f^3*cosh(d*x + c)^2 + 2*b^4*f^3*cosh(d*x + c)*sinh(d*x + c) + b^4*f^3*sinh(d*x + c)^2 + b^4*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(b^4*f^3*cosh(d*x + c)^2 + 2*b^4*f^3*cosh(d*x + c)*sinh(d*x + c) + b^4*f^3*sinh(d*x + c)^2 + b^4*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(b^4*d*f^3*x + b^4*d*e*f^2 + (b^4*d*f^3*x + b^4*d*e*f^2)*cosh(d*x + c)^2 + 2*(b^4*d*f^3*x + b^4*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d*f^3*x + b^4*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(b^4*d*f^3*x + b^4*d*e*f^2 + (b^4*d*f^3*x + b^4*d*e*f^2)*cosh(d*x + c)^2 + 2*(b^4*d*f^3*x + b^4*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d*f^3*x + b^4*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + (a^4 + a^2*b^2)*d^3*e^3)*cosh(d*x + c) + 6*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2*f + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2*f)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2*f)*sinh(d*x + c)^2)*dilog(cosh(d*x + c) + sinh(d*x + c)) + (-12*I*(a^4 + a^2*b^2)*d*f^3*x + 12*(a^3*b + a*b^3)*d*f^3*x - 12*I*(a^4 + a^2*b^2)*d*e*f^2 + 12*(a^3*b + a*b^3)*d*e*f^2 + (-12*I*(a^4 + a^2*b^2)*d*f^3*x + 12*(a^3*b + a*b^3)*d*f^3*x - 12*I*(a^4 + a^2*b^2)*d*e*f^2 + 12*(a^3*b + a*b^3)*d*e*f^2)*cosh(d*x + c)^2 + (-24*I*(a^4 + a^2*b^2)*d*f^3*x + 24*(a^3*b + a*b^3)*d*f^3*x - 24*I*(a^4 + a^2*b^2)*d*e*f^2 + 24*(a^3*b + a*b^3)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-12*I*(a^4 + a^2*b^2)*d*f^3*x + 12*(a^3*b + a*b^3)*d*f^3*x - 12*I*(a^4 + a^2*b^2)*d*e*f^2 + 12*(a^3*b + a*b^3)*d*e*f^2)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (12*I*(a^4 + a^2*b^2)*d*f^3*x + 12*(a^3*b + a*b^3)*d*f^3*x + 12*I*(a^4 + a^2*b^2)*d*e*f^2 + 12*(a^3*b + a*b^3)*d*e*f^2 + (12*I*(a^4 + a^2*b^2)*d*f^3*x + 12*(a^3*b + a*b^3)*d*f^3*x + 12*I*(a^4 + a^2*b^2)*d*e*f^2 + 12*(a^3*b + a*b^3)*d*e*f^2)*cosh(d*x + c)^2 + (24*I*(a^4 + a^2*b^2)*d*f^3*x + 24*(a^3*b + a*b^3)*d*f^3*x + 24*I*(a^4 + a^2*b^2)*d*e*f^2 + 24*(a^3*b + a*b^3)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (12*I*(a^4 + a^2*b^2)*d*f^3*x + 12*(a^3*b + a*b^3)*d*f^3*x + 12*I*(a^4 + a^2*b^2)*d*e*f^2 + 12*(a^3*b + a*b^3)*d*e*f^2)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 6*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2*f + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2*f)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f^3*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2*f)*sinh(d*x + c)^2)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - 2*((a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f*x + (a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 + ((a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f*x + (a^4 + 2*a^2*b^2 + b^4)*d^3*e^3)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f*x + (a^4 + 2*a^2*b^2 + b^4)*d^3*e^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f*x + (a^4 + 2*a^2*b^2 + b^4)*d^3*e^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (-6*I*(a^4 + a^2*b^2)*d^2*e^2*f + 6*(a^3*b + a*b^3)*d^2*e^2*f + 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 - 12*(a^3*b + a*b^3)*c*d*e*f^2 - 6*I*(a^4 + a^2*b^2)*c^2*f^3 + 6*(a^3*b + a*b^3)*c^2*f^3 + (-6*I*(a^4 + a^2*b^2)*d^2*e^2*f + 6*(a^3*b + a*b^3)*d^2*e^2*f + 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 - 12*(a^3*b + a*b^3)*c*d*e*f^2 - 6*I*(a^4 + a^2*b^2)*c^2*f^3 + 6*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + (-12*I*(a^4 + a^2*b^2)*d^2*e^2*f + 12*(a^3*b + a*b^3)*d^2*e^2*f + 24*I*(a^4 + a^2*b^2)*c*d*e*f^2 - 24*(a^3*b + a*b^3)*c*d*e*f^2 - 12*I*(a^4 + a^2*b^2)*c^2*f^3 + 12*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (-6*I*(a^4 + a^2*b^2)*d^2*e^2*f + 6*(a^3*b + a*b^3)*d^2*e^2*f + 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 - 12*(a^3*b + a*b^3)*c*d*e*f^2 - 6*I*(a^4 + a^2*b^2)*c^2*f^3 + 6*(a^3*b + a*b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (6*I*(a^4 + a^2*b^2)*d^2*e^2*f + 6*(a^3*b + a*b^3)*d^2*e^2*f - 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 - 12*(a^3*b + a*b^3)*c*d*e*f^2 + 6*I*(a^4 + a^2*b^2)*c^2*f^3 + 6*(a^3*b + a*b^3)*c^2*f^3 + (6*I*(a^4 + a^2*b^2)*d^2*e^2*f + 6*(a^3*b + a*b^3)*d^2*e^2*f - 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 - 12*(a^3*b + a*b^3)*c*d*e*f^2 + 6*I*(a^4 + a^2*b^2)*c^2*f^3 + 6*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*I*(a^4 + a^2*b^2)*d^2*e^2*f + 12*(a^3*b + a*b^3)*d^2*e^2*f - 24*I*(a^4 + a^2*b^2)*c*d*e*f^2 - 24*(a^3*b + a*b^3)*c*d*e*f^2 + 12*I*(a^4 + a^2*b^2)*c^2*f^3 + 12*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*I*(a^4 + a^2*b^2)*d^2*e^2*f + 6*(a^3*b + a*b^3)*d^2*e^2*f - 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 - 12*(a^3*b + a*b^3)*c*d*e*f^2 + 6*I*(a^4 + a^2*b^2)*c^2*f^3 + 6*(a^3*b + a*b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) + 2*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(a^4 + 2*a^2*b^2 + b^4)*c*d^2*e^2*f + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d*e*f^2 - (a^4 + 2*a^2*b^2 + b^4)*c^3*f^3 + ((a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(a^4 + 2*a^2*b^2 + b^4)*c*d^2*e^2*f + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d*e*f^2 - (a^4 + 2*a^2*b^2 + b^4)*c^3*f^3)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(a^4 + 2*a^2*b^2 + b^4)*c*d^2*e^2*f + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d*e*f^2 - (a^4 + 2*a^2*b^2 + b^4)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d^3*e^3 - 3*(a^4 + 2*a^2*b^2 + b^4)*c*d^2*e^2*f + 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d*e*f^2 - (a^4 + 2*a^2*b^2 + b^4)*c^3*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (6*I*(a^4 + a^2*b^2)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*f^3*x^2 + 12*I*(a^4 + a^2*b^2)*d^2*e*f^2*x + 12*(a^3*b + a*b^3)*d^2*e*f^2*x + 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 + 12*(a^3*b + a*b^3)*c*d*e*f^2 - 6*I*(a^4 + a^2*b^2)*c^2*f^3 - 6*(a^3*b + a*b^3)*c^2*f^3 + (6*I*(a^4 + a^2*b^2)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*f^3*x^2 + 12*I*(a^4 + a^2*b^2)*d^2*e*f^2*x + 12*(a^3*b + a*b^3)*d^2*e*f^2*x + 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 + 12*(a^3*b + a*b^3)*c*d*e*f^2 - 6*I*(a^4 + a^2*b^2)*c^2*f^3 - 6*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + (12*I*(a^4 + a^2*b^2)*d^2*f^3*x^2 + 12*(a^3*b + a*b^3)*d^2*f^3*x^2 + 24*I*(a^4 + a^2*b^2)*d^2*e*f^2*x + 24*(a^3*b + a*b^3)*d^2*e*f^2*x + 24*I*(a^4 + a^2*b^2)*c*d*e*f^2 + 24*(a^3*b + a*b^3)*c*d*e*f^2 - 12*I*(a^4 + a^2*b^2)*c^2*f^3 - 12*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (6*I*(a^4 + a^2*b^2)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*f^3*x^2 + 12*I*(a^4 + a^2*b^2)*d^2*e*f^2*x + 12*(a^3*b + a*b^3)*d^2*e*f^2*x + 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 + 12*(a^3*b + a*b^3)*c*d*e*f^2 - 6*I*(a^4 + a^2*b^2)*c^2*f^3 - 6*(a^3*b + a*b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (-6*I*(a^4 + a^2*b^2)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*f^3*x^2 - 12*I*(a^4 + a^2*b^2)*d^2*e*f^2*x + 12*(a^3*b + a*b^3)*d^2*e*f^2*x - 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 + 12*(a^3*b + a*b^3)*c*d*e*f^2 + 6*I*(a^4 + a^2*b^2)*c^2*f^3 - 6*(a^3*b + a*b^3)*c^2*f^3 + (-6*I*(a^4 + a^2*b^2)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*f^3*x^2 - 12*I*(a^4 + a^2*b^2)*d^2*e*f^2*x + 12*(a^3*b + a*b^3)*d^2*e*f^2*x - 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 + 12*(a^3*b + a*b^3)*c*d*e*f^2 + 6*I*(a^4 + a^2*b^2)*c^2*f^3 - 6*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)^2 + (-12*I*(a^4 + a^2*b^2)*d^2*f^3*x^2 + 12*(a^3*b + a*b^3)*d^2*f^3*x^2 - 24*I*(a^4 + a^2*b^2)*d^2*e*f^2*x + 24*(a^3*b + a*b^3)*d^2*e*f^2*x - 24*I*(a^4 + a^2*b^2)*c*d*e*f^2 + 24*(a^3*b + a*b^3)*c*d*e*f^2 + 12*I*(a^4 + a^2*b^2)*c^2*f^3 - 12*(a^3*b + a*b^3)*c^2*f^3)*cosh(d*x + c)*sinh(d*x + c) + (-6*I*(a^4 + a^2*b^2)*d^2*f^3*x^2 + 6*(a^3*b + a*b^3)*d^2*f^3*x^2 - 12*I*(a^4 + a^2*b^2)*d^2*e*f^2*x + 12*(a^3*b + a*b^3)*d^2*e*f^2*x - 12*I*(a^4 + a^2*b^2)*c*d*e*f^2 + 12*(a^3*b + a*b^3)*c*d*e*f^2 + 6*I*(a^4 + a^2*b^2)*c^2*f^3 - 6*(a^3*b + a*b^3)*c^2*f^3)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + 2*((a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f*x + 3*(a^4 + 2*a^2*b^2 + b^4)*c*d^2*e^2*f - 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d*e*f^2 + (a^4 + 2*a^2*b^2 + b^4)*c^3*f^3 + ((a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f*x + 3*(a^4 + 2*a^2*b^2 + b^4)*c*d^2*e^2*f - 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d*e*f^2 + (a^4 + 2*a^2*b^2 + b^4)*c^3*f^3)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f*x + 3*(a^4 + 2*a^2*b^2 + b^4)*c*d^2*e^2*f - 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d*e*f^2 + (a^4 + 2*a^2*b^2 + b^4)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d^3*f^3*x^3 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e*f^2*x^2 + 3*(a^4 + 2*a^2*b^2 + b^4)*d^3*e^2*f*x + 3*(a^4 + 2*a^2*b^2 + b^4)*c*d^2*e^2*f - 3*(a^4 + 2*a^2*b^2 + b^4)*c^2*d*e*f^2 + (a^4 + 2*a^2*b^2 + b^4)*c^3*f^3)*sinh(d*x + c)^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 12*((a^4 + 2*a^2*b^2 + b^4)*f^3*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*f^3*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*f^3*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*f^3)*polylog(4, cosh(d*x + c) + sinh(d*x + c)) - 12*((a^4 + 2*a^2*b^2 + b^4)*f^3*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*f^3*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*f^3*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*f^3)*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) - 12*((a^4 + 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f^2 + ((a^4 + 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f^2)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + (12*I*(a^4 + a^2*b^2)*f^3 - 12*(a^3*b + a*b^3)*f^3 - 12*(-I*(a^4 + a^2*b^2)*f^3 + (a^3*b + a*b^3)*f^3)*cosh(d*x + c)^2 - 24*(-I*(a^4 + a^2*b^2)*f^3 + (a^3*b + a*b^3)*f^3)*cosh(d*x + c)*sinh(d*x + c) - 12*(-I*(a^4 + a^2*b^2)*f^3 + (a^3*b + a*b^3)*f^3)*sinh(d*x + c)^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + (-12*I*(a^4 + a^2*b^2)*f^3 - 12*(a^3*b + a*b^3)*f^3 - 12*(I*(a^4 + a^2*b^2)*f^3 + (a^3*b + a*b^3)*f^3)*cosh(d*x + c)^2 - 24*(I*(a^4 + a^2*b^2)*f^3 + (a^3*b + a*b^3)*f^3)*cosh(d*x + c)*sinh(d*x + c) - 12*(I*(a^4 + a^2*b^2)*f^3 + (a^3*b + a*b^3)*f^3)*sinh(d*x + c)^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) + 12*((a^4 + 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f^2 + ((a^4 + 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f^2)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d*f^3*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) + 4*((a^4 + a^2*b^2)*d^3*f^3*x^3 + 3*(a^4 + a^2*b^2)*d^3*e*f^2*x^2 + 3*(a^4 + a^2*b^2)*d^3*e^2*f*x + (a^4 + a^2*b^2)*d^3*e^3 - 2*((a^3*b + a*b^3)*d^3*f^3*x^3 + 3*(a^3*b + a*b^3)*d^3*e*f^2*x^2 + 3*(a^3*b + a*b^3)*d^3*e^2*f*x + 3*(a^3*b + a*b^3)*c*d^2*e^2*f - 3*(a^3*b + a*b^3)*c^2*d*e*f^2 + (a^3*b + a*b^3)*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 2*a^3*b^2 + a*b^4)*d^4*cosh(d*x + c)^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d^4*cosh(d*x + c)*sinh(d*x + c) + (a^5 + 2*a^3*b^2 + a*b^4)*d^4*sinh(d*x + c)^2 + (a^5 + 2*a^3*b^2 + a*b^4)*d^4)","C",0
441,1,5569,0,0.768630," ","integrate((f*x+e)^2*csch(d*x+c)*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} - 8 \, {\left(a^{3} b + a b^{3}\right)} c d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2} - 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{4} d f^{2} x + b^{4} d e f + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 4 \, {\left(b^{4} d f^{2} x + b^{4} d e f + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(b^{4} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{4} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{4} f^{2} \sinh\left(d x + c\right)^{2} + b^{4} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(b^{4} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{4} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{4} f^{2} \sinh\left(d x + c\right)^{2} + b^{4} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(-4 i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} - 4 \, {\left(i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - 4 \, {\left(i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(4 i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} f^{2} - 4 \, {\left(-i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(-i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - 4 \, {\left(-i \, {\left(a^{4} + a^{2} b^{2}\right)} f^{2} - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f^{2} x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left(-4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} d e f + 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + {\left(-4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} d e f + 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-8 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 8 \, {\left(a^{3} b + a b^{3}\right)} d e f + 8 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} - 8 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} d e f + 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + {\left(4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 8 \, {\left(a^{3} b + a b^{3}\right)} d e f - 8 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} - 8 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 4 \, {\left(a^{3} b + a b^{3}\right)} d e f - 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} - 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d e f + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d e f + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d e f + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d e f + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + 4 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + {\left(4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + 4 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(8 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + 8 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 8 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + 8 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + 4 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x + 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(-4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + 4 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2} + {\left(-4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + 4 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-8 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + 8 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - 8 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + 8 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-4 i \, {\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + 4 \, {\left(a^{3} b + a b^{3}\right)} d f^{2} x - 4 i \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + 4 \, {\left(a^{3} b + a b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d e f - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d e f - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d e f - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d^{2} e f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c d e f - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{2} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{2} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f x + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + 2 \, {\left(a^{3} b + a b^{3}\right)} c d e f - {\left(a^{3} b + a b^{3}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{3}\right)}}"," ",0,"1/2*(4*(a^3*b + a*b^3)*d^2*e^2 - 8*(a^3*b + a*b^3)*c*d*e*f + 4*(a^3*b + a*b^3)*c^2*f^2 - 4*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + 2*(a^3*b + a*b^3)*c*d*e*f - (a^3*b + a*b^3)*c^2*f^2)*cosh(d*x + c)^2 - 4*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + 2*(a^3*b + a*b^3)*c*d*e*f - (a^3*b + a*b^3)*c^2*f^2)*sinh(d*x + c)^2 - 4*(b^4*d*f^2*x + b^4*d*e*f + (b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^2 + 2*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d*f^2*x + b^4*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 4*(b^4*d*f^2*x + b^4*d*e*f + (b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^2 + 2*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d*f^2*x + b^4*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^2 + 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*(b^4*f^2*cosh(d*x + c)^2 + 2*b^4*f^2*cosh(d*x + c)*sinh(d*x + c) + b^4*f^2*sinh(d*x + c)^2 + b^4*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 4*(b^4*f^2*cosh(d*x + c)^2 + 2*b^4*f^2*cosh(d*x + c)*sinh(d*x + c) + b^4*f^2*sinh(d*x + c)^2 + b^4*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + (a^4 + a^2*b^2)*d^2*e^2)*cosh(d*x + c) + 4*((a^4 + 2*a^2*b^2 + b^4)*d*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f + ((a^4 + 2*a^2*b^2 + b^4)*d*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f)*sinh(d*x + c)^2)*dilog(cosh(d*x + c) + sinh(d*x + c)) + (-4*I*(a^4 + a^2*b^2)*f^2 + 4*(a^3*b + a*b^3)*f^2 - 4*(I*(a^4 + a^2*b^2)*f^2 - (a^3*b + a*b^3)*f^2)*cosh(d*x + c)^2 - 8*(I*(a^4 + a^2*b^2)*f^2 - (a^3*b + a*b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c) - 4*(I*(a^4 + a^2*b^2)*f^2 - (a^3*b + a*b^3)*f^2)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (4*I*(a^4 + a^2*b^2)*f^2 + 4*(a^3*b + a*b^3)*f^2 - 4*(-I*(a^4 + a^2*b^2)*f^2 - (a^3*b + a*b^3)*f^2)*cosh(d*x + c)^2 - 8*(-I*(a^4 + a^2*b^2)*f^2 - (a^3*b + a*b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c) - 4*(-I*(a^4 + a^2*b^2)*f^2 - (a^3*b + a*b^3)*f^2)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 4*((a^4 + 2*a^2*b^2 + b^4)*d*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f + ((a^4 + 2*a^2*b^2 + b^4)*d*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d*f^2*x + (a^4 + 2*a^2*b^2 + b^4)*d*e*f)*sinh(d*x + c)^2)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f*x + (a^4 + 2*a^2*b^2 + b^4)*d^2*e^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (-4*I*(a^4 + a^2*b^2)*d*e*f + 4*(a^3*b + a*b^3)*d*e*f + 4*I*(a^4 + a^2*b^2)*c*f^2 - 4*(a^3*b + a*b^3)*c*f^2 + (-4*I*(a^4 + a^2*b^2)*d*e*f + 4*(a^3*b + a*b^3)*d*e*f + 4*I*(a^4 + a^2*b^2)*c*f^2 - 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)^2 + (-8*I*(a^4 + a^2*b^2)*d*e*f + 8*(a^3*b + a*b^3)*d*e*f + 8*I*(a^4 + a^2*b^2)*c*f^2 - 8*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-4*I*(a^4 + a^2*b^2)*d*e*f + 4*(a^3*b + a*b^3)*d*e*f + 4*I*(a^4 + a^2*b^2)*c*f^2 - 4*(a^3*b + a*b^3)*c*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) + (4*I*(a^4 + a^2*b^2)*d*e*f + 4*(a^3*b + a*b^3)*d*e*f - 4*I*(a^4 + a^2*b^2)*c*f^2 - 4*(a^3*b + a*b^3)*c*f^2 + (4*I*(a^4 + a^2*b^2)*d*e*f + 4*(a^3*b + a*b^3)*d*e*f - 4*I*(a^4 + a^2*b^2)*c*f^2 - 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)^2 + (8*I*(a^4 + a^2*b^2)*d*e*f + 8*(a^3*b + a*b^3)*d*e*f - 8*I*(a^4 + a^2*b^2)*c*f^2 - 8*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*I*(a^4 + a^2*b^2)*d*e*f + 4*(a^3*b + a*b^3)*d*e*f - 4*I*(a^4 + a^2*b^2)*c*f^2 - 4*(a^3*b + a*b^3)*c*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 - 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*e*f + (a^4 + 2*a^2*b^2 + b^4)*c^2*f^2 + ((a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 - 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*e*f + (a^4 + 2*a^2*b^2 + b^4)*c^2*f^2)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 - 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*e*f + (a^4 + 2*a^2*b^2 + b^4)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d^2*e^2 - 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*e*f + (a^4 + 2*a^2*b^2 + b^4)*c^2*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (4*I*(a^4 + a^2*b^2)*d*f^2*x + 4*(a^3*b + a*b^3)*d*f^2*x + 4*I*(a^4 + a^2*b^2)*c*f^2 + 4*(a^3*b + a*b^3)*c*f^2 + (4*I*(a^4 + a^2*b^2)*d*f^2*x + 4*(a^3*b + a*b^3)*d*f^2*x + 4*I*(a^4 + a^2*b^2)*c*f^2 + 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)^2 + (8*I*(a^4 + a^2*b^2)*d*f^2*x + 8*(a^3*b + a*b^3)*d*f^2*x + 8*I*(a^4 + a^2*b^2)*c*f^2 + 8*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (4*I*(a^4 + a^2*b^2)*d*f^2*x + 4*(a^3*b + a*b^3)*d*f^2*x + 4*I*(a^4 + a^2*b^2)*c*f^2 + 4*(a^3*b + a*b^3)*c*f^2)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (-4*I*(a^4 + a^2*b^2)*d*f^2*x + 4*(a^3*b + a*b^3)*d*f^2*x - 4*I*(a^4 + a^2*b^2)*c*f^2 + 4*(a^3*b + a*b^3)*c*f^2 + (-4*I*(a^4 + a^2*b^2)*d*f^2*x + 4*(a^3*b + a*b^3)*d*f^2*x - 4*I*(a^4 + a^2*b^2)*c*f^2 + 4*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)^2 + (-8*I*(a^4 + a^2*b^2)*d*f^2*x + 8*(a^3*b + a*b^3)*d*f^2*x - 8*I*(a^4 + a^2*b^2)*c*f^2 + 8*(a^3*b + a*b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-4*I*(a^4 + a^2*b^2)*d*f^2*x + 4*(a^3*b + a*b^3)*d*f^2*x - 4*I*(a^4 + a^2*b^2)*c*f^2 + 4*(a^3*b + a*b^3)*c*f^2)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f*x + 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*e*f - (a^4 + 2*a^2*b^2 + b^4)*c^2*f^2 + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f*x + 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*e*f - (a^4 + 2*a^2*b^2 + b^4)*c^2*f^2)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f*x + 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*e*f - (a^4 + 2*a^2*b^2 + b^4)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d^2*f^2*x^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*d^2*e*f*x + 2*(a^4 + 2*a^2*b^2 + b^4)*c*d*e*f - (a^4 + 2*a^2*b^2 + b^4)*c^2*f^2)*sinh(d*x + c)^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 4*((a^4 + 2*a^2*b^2 + b^4)*f^2*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*f^2*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*f^2*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 4*((a^4 + 2*a^2*b^2 + b^4)*f^2*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*f^2*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*f^2*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) + 4*((a^4 + a^2*b^2)*d^2*f^2*x^2 + 2*(a^4 + a^2*b^2)*d^2*e*f*x + (a^4 + a^2*b^2)*d^2*e^2 - 2*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + 2*(a^3*b + a*b^3)*c*d*e*f - (a^3*b + a*b^3)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 2*a^3*b^2 + a*b^4)*d^3*cosh(d*x + c)^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d^3*cosh(d*x + c)*sinh(d*x + c) + (a^5 + 2*a^3*b^2 + a*b^4)*d^3*sinh(d*x + c)^2 + (a^5 + 2*a^3*b^2 + a*b^4)*d^3)","C",0
442,1,2176,0,0.595433," ","integrate((f*x+e)*csch(d*x+c)*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} b + a b^{3}\right)} d f x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d f x \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e + {\left(b^{4} f \cosh\left(d x + c\right)^{2} + 2 \, b^{4} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{4} f \sinh\left(d x + c\right)^{2} + b^{4} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{4} f \cosh\left(d x + c\right)^{2} + 2 \, b^{4} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{4} f \sinh\left(d x + c\right)^{2} + b^{4} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{4} d e - b^{4} c f + {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d e - b^{4} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{4} d e - b^{4} c f + {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d e - b^{4} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{4} d f x + b^{4} c f + {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d f x + b^{4} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{4} d f x + b^{4} c f + {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(b^{4} d f x + b^{4} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{2} b^{2}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{4} + a^{2} b^{2}\right)} f\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f x + {\left(a^{4} + a^{2} b^{2}\right)} d e\right)} \cosh\left(d x + c\right) - {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left({\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} b + a b^{3}\right)} f \sinh\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3}\right)} f\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, {\left(a^{3} b + a b^{3}\right)} d f x \cosh\left(d x + c\right) - {\left(a^{4} + a^{2} b^{2}\right)} d f x - {\left(a^{4} + a^{2} b^{2}\right)} d e\right)} \sinh\left(d x + c\right)}{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2}}"," ",0,"-(2*(a^3*b + a*b^3)*d*f*x*cosh(d*x + c)^2 + 2*(a^3*b + a*b^3)*d*f*x*sinh(d*x + c)^2 - 2*(a^3*b + a*b^3)*d*e + (b^4*f*cosh(d*x + c)^2 + 2*b^4*f*cosh(d*x + c)*sinh(d*x + c) + b^4*f*sinh(d*x + c)^2 + b^4*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^4*f*cosh(d*x + c)^2 + 2*b^4*f*cosh(d*x + c)*sinh(d*x + c) + b^4*f*sinh(d*x + c)^2 + b^4*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^4*d*e - b^4*c*f + (b^4*d*e - b^4*c*f)*cosh(d*x + c)^2 + 2*(b^4*d*e - b^4*c*f)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d*e - b^4*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^4*d*e - b^4*c*f + (b^4*d*e - b^4*c*f)*cosh(d*x + c)^2 + 2*(b^4*d*e - b^4*c*f)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d*e - b^4*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^4*d*f*x + b^4*c*f + (b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2 + 2*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d*f*x + b^4*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^4*d*f*x + b^4*c*f + (b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2 + 2*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)*sinh(d*x + c) + (b^4*d*f*x + b^4*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*((a^4 + a^2*b^2)*f*cosh(d*x + c)^2 + 2*(a^4 + a^2*b^2)*f*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^2*b^2)*f*sinh(d*x + c)^2 + (a^4 + a^2*b^2)*f)*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*((a^4 + a^2*b^2)*d*f*x + (a^4 + a^2*b^2)*d*e)*cosh(d*x + c) - ((a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*f*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) + ((a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*f*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - ((a^3*b + a*b^3)*f*cosh(d*x + c)^2 + 2*(a^3*b + a*b^3)*f*cosh(d*x + c)*sinh(d*x + c) + (a^3*b + a*b^3)*f*sinh(d*x + c)^2 + (a^3*b + a*b^3)*f)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + ((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e + ((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f + ((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - ((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f + ((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)*sinh(d*x + c) + ((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f)*sinh(d*x + c)^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 2*(2*(a^3*b + a*b^3)*d*f*x*cosh(d*x + c) - (a^4 + a^2*b^2)*d*f*x - (a^4 + a^2*b^2)*d*e)*sinh(d*x + c))/((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(d*x + c)^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(d*x + c)*sinh(d*x + c) + (a^5 + 2*a^3*b^2 + a*b^4)*d^2*sinh(d*x + c)^2 + (a^5 + 2*a^3*b^2 + a*b^4)*d^2)","B",0
443,1,581,0,0.676155," ","integrate(csch(d*x+c)*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a^{3} b + 2 \, a b^{3} + {\left(b^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} \sinh\left(d x + c\right)^{2} + b^{3}\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right) - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \sinh\left(d x + c\right)}{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d}"," ",0,"(2*a^3*b + 2*a*b^3 + (b^3*cosh(d*x + c)^2 + 2*b^3*cosh(d*x + c)*sinh(d*x + c) + b^3*sinh(d*x + c)^2 + b^3)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 2*(a^4 + a^2*b^2)*cosh(d*x + c) - (a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (a^4 + 2*a^2*b^2 + b^4 + (a^4 + 2*a^2*b^2 + b^4)*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4)*cosh(d*x + c)*sinh(d*x + c) + (a^4 + 2*a^2*b^2 + b^4)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(a^4 + a^2*b^2)*sinh(d*x + c))/((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(d*x + c)^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(d*x + c)*sinh(d*x + c) + (a^5 + 2*a^3*b^2 + a*b^4)*d*sinh(d*x + c)^2 + (a^5 + 2*a^3*b^2 + a*b^4)*d)","B",0
444,0,0,0,1.242929," ","integrate(csch(d*x+c)*sech(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(d x + c\right) \operatorname{sech}\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(csch(d*x + c)*sech(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
445,-1,0,0,0.000000," ","integrate((f*x+e)^2*csch(d*x+c)*sech(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,1,7615,0,0.729201," ","integrate((f*x+e)*csch(d*x+c)*sech(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e + {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e + {\left(a^{3} b + a b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} d f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e + {\left(a^{4} + a^{2} b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} d f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e + {\left(a^{4} + a^{2} b^{2}\right)} f - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e + {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} f - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right) + 2 \, {\left(b^{4} f \cosh\left(d x + c\right)^{4} + 4 \, b^{4} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} f \sinh\left(d x + c\right)^{4} + 2 \, b^{4} f \cosh\left(d x + c\right)^{2} + b^{4} f + 2 \, {\left(3 \, b^{4} f \cosh\left(d x + c\right)^{2} + b^{4} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} f \cosh\left(d x + c\right)^{3} + b^{4} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{4} f \cosh\left(d x + c\right)^{4} + 4 \, b^{4} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} f \sinh\left(d x + c\right)^{4} + 2 \, b^{4} f \cosh\left(d x + c\right)^{2} + b^{4} f + 2 \, {\left(3 \, b^{4} f \cosh\left(d x + c\right)^{2} + b^{4} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} f \cosh\left(d x + c\right)^{3} + b^{4} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left({\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f + 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left({\left(12 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f + 6 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f + 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f + {\left({\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left({\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f - 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left({\left(12 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f - 6 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f - 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f + {\left({\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} f - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left(b^{4} d e - b^{4} c f + {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d e - b^{4} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d e - b^{4} c f + 3 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{4} d e - b^{4} c f + {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d e - b^{4} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d e - b^{4} c f + 3 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{4} d f x + b^{4} c f + {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d f x + b^{4} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d f x + b^{4} c f + 3 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{4} d f x + b^{4} c f + {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d f x + b^{4} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{4} d f x + b^{4} c f + 3 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e + 3 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f + {\left(4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e + 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e + 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f + {\left(12 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e + 6 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 12 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 6 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left({\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f + {\left(4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e - 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e - 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f + {\left(12 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e - 6 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 12 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 6 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d e - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d e - 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - 2 \, {\left({\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f + 3 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d e - {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left({\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f + {\left(4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x - 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x - 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f + {\left(12 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x - 6 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 12 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 6 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f - 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left({\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f + {\left(4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x + 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x + 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 2 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f + {\left(12 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x + 6 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 12 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 6 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} d f x + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} d f x + 8 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} c f + 4 i \, {\left(a^{3} b + 3 \, a b^{3}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f + 3 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} d f x + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e + {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} b + a b^{3}\right)} f + 2 \, {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} d f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e + {\left(a^{4} + a^{2} b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} + 2 \, {\left(3 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e + (a^3*b + a*b^3)*f)*cosh(d*x + c)^3 + 2*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e + (a^3*b + a*b^3)*f)*sinh(d*x + c)^3 - 2*(2*(a^4 + a^2*b^2)*d*f*x + 2*(a^4 + a^2*b^2)*d*e + (a^4 + a^2*b^2)*f)*cosh(d*x + c)^2 - 2*(2*(a^4 + a^2*b^2)*d*f*x + 2*(a^4 + a^2*b^2)*d*e + (a^4 + a^2*b^2)*f - 3*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e + (a^3*b + a*b^3)*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(a^4 + a^2*b^2)*f - 2*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e - (a^3*b + a*b^3)*f)*cosh(d*x + c) + 2*(b^4*f*cosh(d*x + c)^4 + 4*b^4*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*f*sinh(d*x + c)^4 + 2*b^4*f*cosh(d*x + c)^2 + b^4*f + 2*(3*b^4*f*cosh(d*x + c)^2 + b^4*f)*sinh(d*x + c)^2 + 4*(b^4*f*cosh(d*x + c)^3 + b^4*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^4*f*cosh(d*x + c)^4 + 4*b^4*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*f*sinh(d*x + c)^4 + 2*b^4*f*cosh(d*x + c)^2 + b^4*f + 2*(3*b^4*f*cosh(d*x + c)^2 + b^4*f)*sinh(d*x + c)^2 + 4*(b^4*f*cosh(d*x + c)^3 + b^4*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*((a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*f*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)^2 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*f)*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*f + 4*((a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + ((2*(a^4 + 2*a^2*b^2)*f + I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^4 + (8*(a^4 + 2*a^2*b^2)*f + 4*I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*(a^4 + 2*a^2*b^2)*f + I*(a^3*b + 3*a*b^3)*f)*sinh(d*x + c)^4 + (4*(a^4 + 2*a^2*b^2)*f + 2*I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^2 + ((12*(a^4 + 2*a^2*b^2)*f + 6*I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^2 + 4*(a^4 + 2*a^2*b^2)*f + 2*I*(a^3*b + 3*a*b^3)*f)*sinh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2)*f + I*(a^3*b + 3*a*b^3)*f + ((8*(a^4 + 2*a^2*b^2)*f + 4*I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^3 + (8*(a^4 + 2*a^2*b^2)*f + 4*I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + ((2*(a^4 + 2*a^2*b^2)*f - I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^4 + (8*(a^4 + 2*a^2*b^2)*f - 4*I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*(a^4 + 2*a^2*b^2)*f - I*(a^3*b + 3*a*b^3)*f)*sinh(d*x + c)^4 + (4*(a^4 + 2*a^2*b^2)*f - 2*I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^2 + ((12*(a^4 + 2*a^2*b^2)*f - 6*I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^2 + 4*(a^4 + 2*a^2*b^2)*f - 2*I*(a^3*b + 3*a*b^3)*f)*sinh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2)*f - I*(a^3*b + 3*a*b^3)*f + ((8*(a^4 + 2*a^2*b^2)*f - 4*I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c)^3 + (8*(a^4 + 2*a^2*b^2)*f - 4*I*(a^3*b + 3*a*b^3)*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*((a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*f*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)^2 + 2*(3*(a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*f)*sinh(d*x + c)^2 + (a^4 + 2*a^2*b^2 + b^4)*f + 4*((a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) + 2*(b^4*d*e - b^4*c*f + (b^4*d*e - b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*e - b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*e - b^4*c*f)*sinh(d*x + c)^4 + 2*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2 + 2*(b^4*d*e - b^4*c*f + 3*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*e - b^4*c*f)*cosh(d*x + c)^3 + (b^4*d*e - b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^4*d*e - b^4*c*f + (b^4*d*e - b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*e - b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*e - b^4*c*f)*sinh(d*x + c)^4 + 2*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2 + 2*(b^4*d*e - b^4*c*f + 3*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*e - b^4*c*f)*cosh(d*x + c)^3 + (b^4*d*e - b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^4*d*f*x + b^4*c*f + (b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*f*x + b^4*c*f)*sinh(d*x + c)^4 + 2*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2 + 2*(b^4*d*f*x + b^4*c*f + 3*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^3 + (b^4*d*f*x + b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^4*d*f*x + b^4*c*f + (b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*f*x + b^4*c*f)*sinh(d*x + c)^4 + 2*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2 + 2*(b^4*d*f*x + b^4*c*f + 3*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^3 + (b^4*d*f*x + b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e)*cosh(d*x + c)^4 + 4*((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e)*sinh(d*x + c)^4 + (a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e + 2*((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e + 3*((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e)*cosh(d*x + c)^3 + ((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*d*e)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((2*(a^4 + 2*a^2*b^2)*d*e + I*(a^3*b + 3*a*b^3)*d*e - 2*(a^4 + 2*a^2*b^2)*c*f - I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^4 + (8*(a^4 + 2*a^2*b^2)*d*e + 4*I*(a^3*b + 3*a*b^3)*d*e - 8*(a^4 + 2*a^2*b^2)*c*f - 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*(a^4 + 2*a^2*b^2)*d*e + I*(a^3*b + 3*a*b^3)*d*e - 2*(a^4 + 2*a^2*b^2)*c*f - I*(a^3*b + 3*a*b^3)*c*f)*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2)*d*e + I*(a^3*b + 3*a*b^3)*d*e - 2*(a^4 + 2*a^2*b^2)*c*f - I*(a^3*b + 3*a*b^3)*c*f + (4*(a^4 + 2*a^2*b^2)*d*e + 2*I*(a^3*b + 3*a*b^3)*d*e - 4*(a^4 + 2*a^2*b^2)*c*f - 2*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^2 + (4*(a^4 + 2*a^2*b^2)*d*e + 2*I*(a^3*b + 3*a*b^3)*d*e - 4*(a^4 + 2*a^2*b^2)*c*f - 2*I*(a^3*b + 3*a*b^3)*c*f + (12*(a^4 + 2*a^2*b^2)*d*e + 6*I*(a^3*b + 3*a*b^3)*d*e - 12*(a^4 + 2*a^2*b^2)*c*f - 6*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*(a^4 + 2*a^2*b^2)*d*e + 4*I*(a^3*b + 3*a*b^3)*d*e - 8*(a^4 + 2*a^2*b^2)*c*f - 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^3 + (8*(a^4 + 2*a^2*b^2)*d*e + 4*I*(a^3*b + 3*a*b^3)*d*e - 8*(a^4 + 2*a^2*b^2)*c*f - 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) + ((2*(a^4 + 2*a^2*b^2)*d*e - I*(a^3*b + 3*a*b^3)*d*e - 2*(a^4 + 2*a^2*b^2)*c*f + I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^4 + (8*(a^4 + 2*a^2*b^2)*d*e - 4*I*(a^3*b + 3*a*b^3)*d*e - 8*(a^4 + 2*a^2*b^2)*c*f + 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*(a^4 + 2*a^2*b^2)*d*e - I*(a^3*b + 3*a*b^3)*d*e - 2*(a^4 + 2*a^2*b^2)*c*f + I*(a^3*b + 3*a*b^3)*c*f)*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2)*d*e - I*(a^3*b + 3*a*b^3)*d*e - 2*(a^4 + 2*a^2*b^2)*c*f + I*(a^3*b + 3*a*b^3)*c*f + (4*(a^4 + 2*a^2*b^2)*d*e - 2*I*(a^3*b + 3*a*b^3)*d*e - 4*(a^4 + 2*a^2*b^2)*c*f + 2*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^2 + (4*(a^4 + 2*a^2*b^2)*d*e - 2*I*(a^3*b + 3*a*b^3)*d*e - 4*(a^4 + 2*a^2*b^2)*c*f + 2*I*(a^3*b + 3*a*b^3)*c*f + (12*(a^4 + 2*a^2*b^2)*d*e - 6*I*(a^3*b + 3*a*b^3)*d*e - 12*(a^4 + 2*a^2*b^2)*c*f + 6*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*(a^4 + 2*a^2*b^2)*d*e - 4*I*(a^3*b + 3*a*b^3)*d*e - 8*(a^4 + 2*a^2*b^2)*c*f + 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^3 + (8*(a^4 + 2*a^2*b^2)*d*e - 4*I*(a^3*b + 3*a*b^3)*d*e - 8*(a^4 + 2*a^2*b^2)*c*f + 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) - 2*(((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)^4 + 4*((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f)*sinh(d*x + c)^4 + (a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f + 2*((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f + 3*((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)^3 + ((a^4 + 2*a^2*b^2 + b^4)*d*e - (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + ((2*(a^4 + 2*a^2*b^2)*d*f*x - I*(a^3*b + 3*a*b^3)*d*f*x + 2*(a^4 + 2*a^2*b^2)*c*f - I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^4 + (8*(a^4 + 2*a^2*b^2)*d*f*x - 4*I*(a^3*b + 3*a*b^3)*d*f*x + 8*(a^4 + 2*a^2*b^2)*c*f - 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*(a^4 + 2*a^2*b^2)*d*f*x - I*(a^3*b + 3*a*b^3)*d*f*x + 2*(a^4 + 2*a^2*b^2)*c*f - I*(a^3*b + 3*a*b^3)*c*f)*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2)*d*f*x - I*(a^3*b + 3*a*b^3)*d*f*x + 2*(a^4 + 2*a^2*b^2)*c*f - I*(a^3*b + 3*a*b^3)*c*f + (4*(a^4 + 2*a^2*b^2)*d*f*x - 2*I*(a^3*b + 3*a*b^3)*d*f*x + 4*(a^4 + 2*a^2*b^2)*c*f - 2*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^2 + (4*(a^4 + 2*a^2*b^2)*d*f*x - 2*I*(a^3*b + 3*a*b^3)*d*f*x + 4*(a^4 + 2*a^2*b^2)*c*f - 2*I*(a^3*b + 3*a*b^3)*c*f + (12*(a^4 + 2*a^2*b^2)*d*f*x - 6*I*(a^3*b + 3*a*b^3)*d*f*x + 12*(a^4 + 2*a^2*b^2)*c*f - 6*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*(a^4 + 2*a^2*b^2)*d*f*x - 4*I*(a^3*b + 3*a*b^3)*d*f*x + 8*(a^4 + 2*a^2*b^2)*c*f - 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^3 + (8*(a^4 + 2*a^2*b^2)*d*f*x - 4*I*(a^3*b + 3*a*b^3)*d*f*x + 8*(a^4 + 2*a^2*b^2)*c*f - 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + ((2*(a^4 + 2*a^2*b^2)*d*f*x + I*(a^3*b + 3*a*b^3)*d*f*x + 2*(a^4 + 2*a^2*b^2)*c*f + I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^4 + (8*(a^4 + 2*a^2*b^2)*d*f*x + 4*I*(a^3*b + 3*a*b^3)*d*f*x + 8*(a^4 + 2*a^2*b^2)*c*f + 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*(a^4 + 2*a^2*b^2)*d*f*x + I*(a^3*b + 3*a*b^3)*d*f*x + 2*(a^4 + 2*a^2*b^2)*c*f + I*(a^3*b + 3*a*b^3)*c*f)*sinh(d*x + c)^4 + 2*(a^4 + 2*a^2*b^2)*d*f*x + I*(a^3*b + 3*a*b^3)*d*f*x + 2*(a^4 + 2*a^2*b^2)*c*f + I*(a^3*b + 3*a*b^3)*c*f + (4*(a^4 + 2*a^2*b^2)*d*f*x + 2*I*(a^3*b + 3*a*b^3)*d*f*x + 4*(a^4 + 2*a^2*b^2)*c*f + 2*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^2 + (4*(a^4 + 2*a^2*b^2)*d*f*x + 2*I*(a^3*b + 3*a*b^3)*d*f*x + 4*(a^4 + 2*a^2*b^2)*c*f + 2*I*(a^3*b + 3*a*b^3)*c*f + (12*(a^4 + 2*a^2*b^2)*d*f*x + 6*I*(a^3*b + 3*a*b^3)*d*f*x + 12*(a^4 + 2*a^2*b^2)*c*f + 6*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*(a^4 + 2*a^2*b^2)*d*f*x + 4*I*(a^3*b + 3*a*b^3)*d*f*x + 8*(a^4 + 2*a^2*b^2)*c*f + 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c)^3 + (8*(a^4 + 2*a^2*b^2)*d*f*x + 4*I*(a^3*b + 3*a*b^3)*d*f*x + 8*(a^4 + 2*a^2*b^2)*c*f + 4*I*(a^3*b + 3*a*b^3)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 2*(((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)^4 + 4*((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f)*sinh(d*x + c)^4 + (a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f + 2*((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)^2 + 2*((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f + 3*((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c)^3 + ((a^4 + 2*a^2*b^2 + b^4)*d*f*x + (a^4 + 2*a^2*b^2 + b^4)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e - 3*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e + (a^3*b + a*b^3)*f)*cosh(d*x + c)^2 - (a^3*b + a*b^3)*f + 2*(2*(a^4 + a^2*b^2)*d*f*x + 2*(a^4 + a^2*b^2)*d*e + (a^4 + a^2*b^2)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(d*x + c)^4 + 4*(a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + 2*a^3*b^2 + a*b^4)*d^2*sinh(d*x + c)^4 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(d*x + c)^2 + (a^5 + 2*a^3*b^2 + a*b^4)*d^2 + 2*(3*(a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(d*x + c)^2 + (a^5 + 2*a^3*b^2 + a*b^4)*d^2)*sinh(d*x + c)^2 + 4*((a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(d*x + c)^3 + (a^5 + 2*a^3*b^2 + a*b^4)*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
447,1,1279,0,1.056519," ","integrate(csch(d*x+c)*sech(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} b + a b^{3}\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} + 2 \, a^{2} b^{2} - 3 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b + 3 \, a b^{3}\right)} \sinh\left(d x + c\right)^{4} + a^{3} b + 3 \, a b^{3} + 2 \, {\left(a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b + 3 \, a b^{3} + 3 \, {\left(a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} b + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right) + {\left(b^{4} \cosh\left(d x + c\right)^{4} + 4 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} \sinh\left(d x + c\right)^{4} + 2 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4} + 2 \, {\left(3 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} \cosh\left(d x + c\right)^{3} + b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left({\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + b^{4} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{2} b^{2} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{3} b + a b^{3} - 3 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d + 4 \, {\left({\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"-((a^3*b + a*b^3)*cosh(d*x + c)^3 + (a^3*b + a*b^3)*sinh(d*x + c)^3 - 2*(a^4 + a^2*b^2)*cosh(d*x + c)^2 - (2*a^4 + 2*a^2*b^2 - 3*(a^3*b + a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((a^3*b + 3*a*b^3)*cosh(d*x + c)^4 + 4*(a^3*b + 3*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b + 3*a*b^3)*sinh(d*x + c)^4 + a^3*b + 3*a*b^3 + 2*(a^3*b + 3*a*b^3)*cosh(d*x + c)^2 + 2*(a^3*b + 3*a*b^3 + 3*(a^3*b + 3*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3*b + 3*a*b^3)*cosh(d*x + c)^3 + (a^3*b + 3*a*b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - (a^3*b + a*b^3)*cosh(d*x + c) + (b^4*cosh(d*x + c)^4 + 4*b^4*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*sinh(d*x + c)^4 + 2*b^4*cosh(d*x + c)^2 + b^4 + 2*(3*b^4*cosh(d*x + c)^2 + b^4)*sinh(d*x + c)^2 + 4*(b^4*cosh(d*x + c)^3 + b^4*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + ((a^4 + 2*a^2*b^2)*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2)*sinh(d*x + c)^4 + a^4 + 2*a^2*b^2 + 2*(a^4 + 2*a^2*b^2)*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + 3*(a^4 + 2*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^4 + 2*a^2*b^2)*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - ((a^4 + 2*a^2*b^2 + b^4)*cosh(d*x + c)^4 + 4*(a^4 + 2*a^2*b^2 + b^4)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*sinh(d*x + c)^4 + a^4 + 2*a^2*b^2 + b^4 + 2*(a^4 + 2*a^2*b^2 + b^4)*cosh(d*x + c)^2 + 2*(a^4 + 2*a^2*b^2 + b^4 + 3*(a^4 + 2*a^2*b^2 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^4 + 2*a^2*b^2 + b^4)*cosh(d*x + c)^3 + (a^4 + 2*a^2*b^2 + b^4)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (a^3*b + a*b^3 - 3*(a^3*b + a*b^3)*cosh(d*x + c)^2 + 4*(a^4 + a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(d*x + c)^4 + 4*(a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + 2*a^3*b^2 + a*b^4)*d*sinh(d*x + c)^4 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 + 2*a^3*b^2 + a*b^4)*d)*sinh(d*x + c)^2 + (a^5 + 2*a^3*b^2 + a*b^4)*d + 4*((a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(d*x + c)^3 + (a^5 + 2*a^3*b^2 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
448,0,0,0,36.589237," ","integrate(csch(d*x+c)*sech(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(d x + c\right) \operatorname{sech}\left(d x + c\right)^{3}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(csch(d*x + c)*sech(d*x + c)^3/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
449,1,4313,0,0.676975," ","integrate((f*x+e)^3*coth(d*x+c)*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \cosh\left(d x + c\right) + 3 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f - {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f - {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f - 2 \, a d e f^{2} - {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f - 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} - a d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f - 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} - a d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f - 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} - a d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d^{2} e f^{2} - a d f^{3}\right)} x\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 3 \, {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f + 2 \, a d e f^{2} - {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f + 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} + a d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f + 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} + a d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f + 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} + a d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d^{2} e f^{2} + a d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\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} - {\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)} \cosh\left(d x + c\right)^{2} - 2 \, {\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)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\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)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\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} - {\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)} \cosh\left(d x + c\right)^{2} - 2 \, {\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)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\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)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3} - {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3} - {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} + 3 \, a d^{2} e^{2} f + 3 \, {\left(b d^{3} e f^{2} + a d^{2} f^{3}\right)} x^{2} - {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} + 3 \, a d^{2} e^{2} f + 3 \, {\left(b d^{3} e f^{2} + a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f + 2 \, a d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} + 3 \, a d^{2} e^{2} f + 3 \, {\left(b d^{3} e f^{2} + a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f + 2 \, a d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} + 3 \, a d^{2} e^{2} f + 3 \, {\left(b d^{3} e f^{2} + a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f + 2 \, a d^{2} e f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b d^{3} e^{2} f + 2 \, a d^{2} e f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(b d^{3} e^{3} - 3 \, {\left(b c + a\right)} d^{2} e^{2} f + 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} - {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3} - {\left(b d^{3} e^{3} - 3 \, {\left(b c + a\right)} d^{2} e^{2} f + 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} - {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} e^{3} - 3 \, {\left(b c + a\right)} d^{2} e^{2} f + 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} - {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{3} e^{3} - 3 \, {\left(b c + a\right)} d^{2} e^{2} f + 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} - {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} e^{2} f - 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} + {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3} + 3 \, {\left(b d^{3} e f^{2} - a d^{2} f^{3}\right)} x^{2} - {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} e^{2} f - 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} + {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3} + 3 \, {\left(b d^{3} e f^{2} - a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, a d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} e^{2} f - 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} + {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3} + 3 \, {\left(b d^{3} e f^{2} - a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, a d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} e^{2} f - 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} + {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3} + 3 \, {\left(b d^{3} e f^{2} - a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, a d^{2} e f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, a d^{2} e f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 6 \, {\left(b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{3} \sinh\left(d x + c\right)^{2} - b f^{3}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{3} \sinh\left(d x + c\right)^{2} - b f^{3}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{3} \sinh\left(d x + c\right)^{2} - b f^{3}\right)} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left(b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{3} \sinh\left(d x + c\right)^{2} - b f^{3}\right)} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 6 \, {\left(b d f^{3} x + b d e f^{2} - {\left(b d f^{3} x + b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{3} x + b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{3} x + b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b d f^{3} x + b d e f^{2} - {\left(b d f^{3} x + b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{3} x + b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{3} x + b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b d f^{3} x + b d e f^{2} - a f^{3} - {\left(b d f^{3} x + b d e f^{2} - a f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{3} x + b d e f^{2} - a f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{3} x + b d e f^{2} - a f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left(b d f^{3} x + b d e f^{2} + a f^{3} - {\left(b d f^{3} x + b d e f^{2} + a f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{3} x + b d e f^{2} + a f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{3} x + b d e f^{2} + a f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + a d^{3} e^{3}\right)} \sinh\left(d x + c\right)}{a^{2} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d^{4} \sinh\left(d x + c\right)^{2} - a^{2} d^{4}}"," ",0,"-(2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*cosh(d*x + c) + 3*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f - (b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f - (b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*(b*d^2*f^3*x^2 + b*d^2*e^2*f - 2*a*d*e*f^2 - (b*d^2*f^3*x^2 + b*d^2*e^2*f - 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 - a*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b*d^2*f^3*x^2 + b*d^2*e^2*f - 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 - a*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^3*x^2 + b*d^2*e^2*f - 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 - a*d*f^3)*x)*sinh(d*x + c)^2 + 2*(b*d^2*e*f^2 - a*d*f^3)*x)*dilog(cosh(d*x + c) + sinh(d*x + c)) - 3*(b*d^2*f^3*x^2 + b*d^2*e^2*f + 2*a*d*e*f^2 - (b*d^2*f^3*x^2 + b*d^2*e^2*f + 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 + a*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b*d^2*f^3*x^2 + b*d^2*e^2*f + 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 + a*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^3*x^2 + b*d^2*e^2*f + 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 + a*d*f^3)*x)*sinh(d*x + c)^2 + 2*(b*d^2*e*f^2 + a*d*f^3)*x)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (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 - (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)*cosh(d*x + c)^2 - 2*(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)*cosh(d*x + c)*sinh(d*x + c) - (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)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (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 - (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)*cosh(d*x + c)^2 - 2*(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)*cosh(d*x + c)*sinh(d*x + c) - (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)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3 - (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*cosh(d*x + c)^2 - 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3 - (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*cosh(d*x + c)^2 - 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b*d^3*f^3*x^3 + b*d^3*e^3 + 3*a*d^2*e^2*f + 3*(b*d^3*e*f^2 + a*d^2*f^3)*x^2 - (b*d^3*f^3*x^3 + b*d^3*e^3 + 3*a*d^2*e^2*f + 3*(b*d^3*e*f^2 + a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f + 2*a*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*(b*d^3*f^3*x^3 + b*d^3*e^3 + 3*a*d^2*e^2*f + 3*(b*d^3*e*f^2 + a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f + 2*a*d^2*e*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^3*f^3*x^3 + b*d^3*e^3 + 3*a*d^2*e^2*f + 3*(b*d^3*e*f^2 + a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f + 2*a*d^2*e*f^2)*x)*sinh(d*x + c)^2 + 3*(b*d^3*e^2*f + 2*a*d^2*e*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (b*d^3*e^3 - 3*(b*c + a)*d^2*e^2*f + 3*(b*c^2 + 2*a*c)*d*e*f^2 - (b*c^3 + 3*a*c^2)*f^3 - (b*d^3*e^3 - 3*(b*c + a)*d^2*e^2*f + 3*(b*c^2 + 2*a*c)*d*e*f^2 - (b*c^3 + 3*a*c^2)*f^3)*cosh(d*x + c)^2 - 2*(b*d^3*e^3 - 3*(b*c + a)*d^2*e^2*f + 3*(b*c^2 + 2*a*c)*d*e*f^2 - (b*c^3 + 3*a*c^2)*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b*d^3*e^3 - 3*(b*c + a)*d^2*e^2*f + 3*(b*c^2 + 2*a*c)*d*e*f^2 - (b*c^3 + 3*a*c^2)*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (b*d^3*f^3*x^3 + 3*b*c*d^2*e^2*f - 3*(b*c^2 + 2*a*c)*d*e*f^2 + (b*c^3 + 3*a*c^2)*f^3 + 3*(b*d^3*e*f^2 - a*d^2*f^3)*x^2 - (b*d^3*f^3*x^3 + 3*b*c*d^2*e^2*f - 3*(b*c^2 + 2*a*c)*d*e*f^2 + (b*c^3 + 3*a*c^2)*f^3 + 3*(b*d^3*e*f^2 - a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*a*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*(b*d^3*f^3*x^3 + 3*b*c*d^2*e^2*f - 3*(b*c^2 + 2*a*c)*d*e*f^2 + (b*c^3 + 3*a*c^2)*f^3 + 3*(b*d^3*e*f^2 - a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*a*d^2*e*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^3*f^3*x^3 + 3*b*c*d^2*e^2*f - 3*(b*c^2 + 2*a*c)*d*e*f^2 + (b*c^3 + 3*a*c^2)*f^3 + 3*(b*d^3*e*f^2 - a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*a*d^2*e*f^2)*x)*sinh(d*x + c)^2 + 3*(b*d^3*e^2*f - 2*a*d^2*e*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 6*(b*f^3*cosh(d*x + c)^2 + 2*b*f^3*cosh(d*x + c)*sinh(d*x + c) + b*f^3*sinh(d*x + c)^2 - b*f^3)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b*f^3*cosh(d*x + c)^2 + 2*b*f^3*cosh(d*x + c)*sinh(d*x + c) + b*f^3*sinh(d*x + c)^2 - b*f^3)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b*f^3*cosh(d*x + c)^2 + 2*b*f^3*cosh(d*x + c)*sinh(d*x + c) + b*f^3*sinh(d*x + c)^2 - b*f^3)*polylog(4, cosh(d*x + c) + sinh(d*x + c)) + 6*(b*f^3*cosh(d*x + c)^2 + 2*b*f^3*cosh(d*x + c)*sinh(d*x + c) + b*f^3*sinh(d*x + c)^2 - b*f^3)*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) - 6*(b*d*f^3*x + b*d*e*f^2 - (b*d*f^3*x + b*d*e*f^2)*cosh(d*x + c)^2 - 2*(b*d*f^3*x + b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^3*x + b*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b*d*f^3*x + b*d*e*f^2 - (b*d*f^3*x + b*d*e*f^2)*cosh(d*x + c)^2 - 2*(b*d*f^3*x + b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^3*x + b*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b*d*f^3*x + b*d*e*f^2 - a*f^3 - (b*d*f^3*x + b*d*e*f^2 - a*f^3)*cosh(d*x + c)^2 - 2*(b*d*f^3*x + b*d*e*f^2 - a*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^3*x + b*d*e*f^2 - a*f^3)*sinh(d*x + c)^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 6*(b*d*f^3*x + b*d*e*f^2 + a*f^3 - (b*d*f^3*x + b*d*e*f^2 + a*f^3)*cosh(d*x + c)^2 - 2*(b*d*f^3*x + b*d*e*f^2 + a*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^3*x + b*d*e*f^2 + a*f^3)*sinh(d*x + c)^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) + 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + a*d^3*e^3)*sinh(d*x + c))/(a^2*d^4*cosh(d*x + c)^2 + 2*a^2*d^4*cosh(d*x + c)*sinh(d*x + c) + a^2*d^4*sinh(d*x + c)^2 - a^2*d^4)","C",0
450,1,2528,0,0.729250," ","integrate((f*x+e)^2*coth(d*x+c)*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(b d f^{2} x + b d e f - {\left(b d f^{2} x + b d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{2} x + b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{2} x + b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b d f^{2} x + b d e f - {\left(b d f^{2} x + b d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{2} x + b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{2} x + b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b d f^{2} x + b d e f - a f^{2} - {\left(b d f^{2} x + b d e f - a f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{2} x + b d e f - a f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{2} x + b d e f - a f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(b d f^{2} x + b d e f + a f^{2} - {\left(b d f^{2} x + b d e f + a f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{2} x + b d e f + a f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{2} x + b d e f + a f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2} - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2} - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2} - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2} - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} + 2 \, a d e f - {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} + 2 \, a d e f + 2 \, {\left(b d^{2} e f + a d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} + 2 \, a d e f + 2 \, {\left(b d^{2} e f + a d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} + 2 \, a d e f + 2 \, {\left(b d^{2} e f + a d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d^{2} e f + a d f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(b d^{2} e^{2} - 2 \, {\left(b c + a\right)} d e f + {\left(b c^{2} + 2 \, a c\right)} f^{2} - {\left(b d^{2} e^{2} - 2 \, {\left(b c + a\right)} d e f + {\left(b c^{2} + 2 \, a c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} e^{2} - 2 \, {\left(b c + a\right)} d e f + {\left(b c^{2} + 2 \, a c\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} e^{2} - 2 \, {\left(b c + a\right)} d e f + {\left(b c^{2} + 2 \, a c\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d e f - {\left(b c^{2} + 2 \, a c\right)} f^{2} - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d e f - {\left(b c^{2} + 2 \, a c\right)} f^{2} + 2 \, {\left(b d^{2} e f - a d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d e f - {\left(b c^{2} + 2 \, a c\right)} f^{2} + 2 \, {\left(b d^{2} e f - a d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d e f - {\left(b c^{2} + 2 \, a c\right)} f^{2} + 2 \, {\left(b d^{2} e f - a d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d^{2} e f - a d f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{2} \sinh\left(d x + c\right)^{2} - b f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{2} \sinh\left(d x + c\right)^{2} - b f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{2} \sinh\left(d x + c\right)^{2} - b f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{2} \sinh\left(d x + c\right)^{2} - b f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + a d^{2} e^{2}\right)} \sinh\left(d x + c\right)}{a^{2} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d^{3} \sinh\left(d x + c\right)^{2} - a^{2} d^{3}}"," ",0,"-(2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*cosh(d*x + c) + 2*(b*d*f^2*x + b*d*e*f - (b*d*f^2*x + b*d*e*f)*cosh(d*x + c)^2 - 2*(b*d*f^2*x + b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^2*x + b*d*e*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b*d*f^2*x + b*d*e*f - (b*d*f^2*x + b*d*e*f)*cosh(d*x + c)^2 - 2*(b*d*f^2*x + b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^2*x + b*d*e*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b*d*f^2*x + b*d*e*f - a*f^2 - (b*d*f^2*x + b*d*e*f - a*f^2)*cosh(d*x + c)^2 - 2*(b*d*f^2*x + b*d*e*f - a*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^2*x + b*d*e*f - a*f^2)*sinh(d*x + c)^2)*dilog(cosh(d*x + c) + sinh(d*x + c)) - 2*(b*d*f^2*x + b*d*e*f + a*f^2 - (b*d*f^2*x + b*d*e*f + a*f^2)*cosh(d*x + c)^2 - 2*(b*d*f^2*x + b*d*e*f + a*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^2*x + b*d*e*f + a*f^2)*sinh(d*x + c)^2)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2 - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cosh(d*x + c)^2 - 2*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2 - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cosh(d*x + c)^2 - 2*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2 - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*cosh(d*x + c)^2 - 2*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2 - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*cosh(d*x + c)^2 - 2*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b*d^2*f^2*x^2 + b*d^2*e^2 + 2*a*d*e*f - (b*d^2*f^2*x^2 + b*d^2*e^2 + 2*a*d*e*f + 2*(b*d^2*e*f + a*d*f^2)*x)*cosh(d*x + c)^2 - 2*(b*d^2*f^2*x^2 + b*d^2*e^2 + 2*a*d*e*f + 2*(b*d^2*e*f + a*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^2*x^2 + b*d^2*e^2 + 2*a*d*e*f + 2*(b*d^2*e*f + a*d*f^2)*x)*sinh(d*x + c)^2 + 2*(b*d^2*e*f + a*d*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (b*d^2*e^2 - 2*(b*c + a)*d*e*f + (b*c^2 + 2*a*c)*f^2 - (b*d^2*e^2 - 2*(b*c + a)*d*e*f + (b*c^2 + 2*a*c)*f^2)*cosh(d*x + c)^2 - 2*(b*d^2*e^2 - 2*(b*c + a)*d*e*f + (b*c^2 + 2*a*c)*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*e^2 - 2*(b*c + a)*d*e*f + (b*c^2 + 2*a*c)*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (b*d^2*f^2*x^2 + 2*b*c*d*e*f - (b*c^2 + 2*a*c)*f^2 - (b*d^2*f^2*x^2 + 2*b*c*d*e*f - (b*c^2 + 2*a*c)*f^2 + 2*(b*d^2*e*f - a*d*f^2)*x)*cosh(d*x + c)^2 - 2*(b*d^2*f^2*x^2 + 2*b*c*d*e*f - (b*c^2 + 2*a*c)*f^2 + 2*(b*d^2*e*f - a*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^2*x^2 + 2*b*c*d*e*f - (b*c^2 + 2*a*c)*f^2 + 2*(b*d^2*e*f - a*d*f^2)*x)*sinh(d*x + c)^2 + 2*(b*d^2*e*f - a*d*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 2*(b*f^2*cosh(d*x + c)^2 + 2*b*f^2*cosh(d*x + c)*sinh(d*x + c) + b*f^2*sinh(d*x + c)^2 - b*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*(b*f^2*cosh(d*x + c)^2 + 2*b*f^2*cosh(d*x + c)*sinh(d*x + c) + b*f^2*sinh(d*x + c)^2 - b*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(b*f^2*cosh(d*x + c)^2 + 2*b*f^2*cosh(d*x + c)*sinh(d*x + c) + b*f^2*sinh(d*x + c)^2 - b*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 2*(b*f^2*cosh(d*x + c)^2 + 2*b*f^2*cosh(d*x + c)*sinh(d*x + c) + b*f^2*sinh(d*x + c)^2 - b*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) + 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + a*d^2*e^2)*sinh(d*x + c))/(a^2*d^3*cosh(d*x + c)^2 + 2*a^2*d^3*cosh(d*x + c)*sinh(d*x + c) + a^2*d^3*sinh(d*x + c)^2 - a^2*d^3)","C",0
451,1,1221,0,0.542534," ","integrate((f*x+e)*coth(d*x+c)*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a d f x + a d e\right)} \cosh\left(d x + c\right) - {\left(b f \cosh\left(d x + c\right)^{2} + 2 \, b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f \sinh\left(d x + c\right)^{2} - b f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b f \cosh\left(d x + c\right)^{2} + 2 \, b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f \sinh\left(d x + c\right)^{2} - b f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b f \cosh\left(d x + c\right)^{2} + 2 \, b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f \sinh\left(d x + c\right)^{2} - b f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(b f \cosh\left(d x + c\right)^{2} + 2 \, b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f \sinh\left(d x + c\right)^{2} - b f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(b d e - b c f - {\left(b d e - b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d e - b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d e - b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d e - b c f - {\left(b d e - b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d e - b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d e - b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d f x + b c f - {\left(b d f x + b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f x + b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f x + b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b d f x + b c f - {\left(b d f x + b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f x + b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f x + b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b d f x + b d e - {\left(b d f x + b d e + a f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f x + b d e + a f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f x + b d e + a f\right)} \sinh\left(d x + c\right)^{2} + a f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(b d e - {\left(b d e - {\left(b c + a\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d e - {\left(b c + a\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d e - {\left(b c + a\right)} f\right)} \sinh\left(d x + c\right)^{2} - {\left(b c + a\right)} f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(b d f x + b c f - {\left(b d f x + b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f x + b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f x + b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(a d f x + a d e\right)} \sinh\left(d x + c\right)}{a^{2} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d^{2} \sinh\left(d x + c\right)^{2} - a^{2} d^{2}}"," ",0,"-(2*(a*d*f*x + a*d*e)*cosh(d*x + c) - (b*f*cosh(d*x + c)^2 + 2*b*f*cosh(d*x + c)*sinh(d*x + c) + b*f*sinh(d*x + c)^2 - b*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b*f*cosh(d*x + c)^2 + 2*b*f*cosh(d*x + c)*sinh(d*x + c) + b*f*sinh(d*x + c)^2 - b*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (b*f*cosh(d*x + c)^2 + 2*b*f*cosh(d*x + c)*sinh(d*x + c) + b*f*sinh(d*x + c)^2 - b*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) + (b*f*cosh(d*x + c)^2 + 2*b*f*cosh(d*x + c)*sinh(d*x + c) + b*f*sinh(d*x + c)^2 - b*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (b*d*e - b*c*f - (b*d*e - b*c*f)*cosh(d*x + c)^2 - 2*(b*d*e - b*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*e - b*c*f)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d*e - b*c*f - (b*d*e - b*c*f)*cosh(d*x + c)^2 - 2*(b*d*e - b*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*e - b*c*f)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d*f*x + b*c*f - (b*d*f*x + b*c*f)*cosh(d*x + c)^2 - 2*(b*d*f*x + b*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f*x + b*c*f)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b*d*f*x + b*c*f - (b*d*f*x + b*c*f)*cosh(d*x + c)^2 - 2*(b*d*f*x + b*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f*x + b*c*f)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b*d*f*x + b*d*e - (b*d*f*x + b*d*e + a*f)*cosh(d*x + c)^2 - 2*(b*d*f*x + b*d*e + a*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f*x + b*d*e + a*f)*sinh(d*x + c)^2 + a*f)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (b*d*e - (b*d*e - (b*c + a)*f)*cosh(d*x + c)^2 - 2*(b*d*e - (b*c + a)*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*e - (b*c + a)*f)*sinh(d*x + c)^2 - (b*c + a)*f)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (b*d*f*x + b*c*f - (b*d*f*x + b*c*f)*cosh(d*x + c)^2 - 2*(b*d*f*x + b*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f*x + b*c*f)*sinh(d*x + c)^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 2*(a*d*f*x + a*d*e)*sinh(d*x + c))/(a^2*d^2*cosh(d*x + c)^2 + 2*a^2*d^2*cosh(d*x + c)*sinh(d*x + c) + a^2*d^2*sinh(d*x + c)^2 - a^2*d^2)","B",0
452,1,211,0,0.510737," ","integrate(coth(d*x+c)*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a \cosh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - b\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - b\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, a \sinh\left(d x + c\right)}{a^{2} d \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d \sinh\left(d x + c\right)^{2} - a^{2} d}"," ",0,"-(2*a*cosh(d*x + c) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*a*sinh(d*x + c))/(a^2*d*cosh(d*x + c)^2 + 2*a^2*d*cosh(d*x + c)*sinh(d*x + c) + a^2*d*sinh(d*x + c)^2 - a^2*d)","B",0
453,0,0,0,0.620236," ","integrate(coth(d*x+c)*csch(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(d x + c\right) \operatorname{csch}\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(coth(d*x + c)*csch(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
454,1,4612,0,0.690874," ","integrate((f*x+e)^3*coth(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a d^{3} e^{3} - 6 \, a c d^{2} e^{2} f + 6 \, a c^{2} d e f^{2} - 2 \, a c^{3} f^{3} + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} + a c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} + a c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a d^{3} e f^{2} x^{2} + 3 \, a d^{3} e^{2} f x + 3 \, a c d^{2} e^{2} f - 3 \, a c^{2} d e f^{2} + a c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f - {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f - {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{3} x^{2} + 2 \, b d^{2} e f^{2} x + b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\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} - {\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)} \cosh\left(d x + c\right)^{2} - 2 \, {\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)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\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)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\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} - {\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)} \cosh\left(d x + c\right)^{2} - 2 \, {\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)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\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)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3} - {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3} - {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{3} f^{3} x^{3} + 3 \, b d^{3} e f^{2} x^{2} + 3 \, b d^{3} e^{2} f x + 3 \, b c d^{2} e^{2} f - 3 \, b c^{2} d e f^{2} + b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 6 \, {\left(b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{3} \sinh\left(d x + c\right)^{2} - b f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{3} \sinh\left(d x + c\right)^{2} - b f^{3}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b d f^{3} x + b d e f^{2} - {\left(b d f^{3} x + b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{3} x + b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{3} x + b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b d f^{3} x + b d e f^{2} - {\left(b d f^{3} x + b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{3} x + b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{3} x + b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 3 \, {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f - 2 \, a d e f^{2} - {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f - 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} - a d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f - 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} - a d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f - 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} - a d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d^{2} e f^{2} - a d f^{3}\right)} x\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 3 \, {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f + 2 \, a d e f^{2} - {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f + 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} + a d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f + 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} + a d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{3} x^{2} + b d^{2} e^{2} f + 2 \, a d e f^{2} + 2 \, {\left(b d^{2} e f^{2} + a d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d^{2} e f^{2} + a d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} + 3 \, a d^{2} e^{2} f + 3 \, {\left(b d^{3} e f^{2} + a d^{2} f^{3}\right)} x^{2} - {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} + 3 \, a d^{2} e^{2} f + 3 \, {\left(b d^{3} e f^{2} + a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f + 2 \, a d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} + 3 \, a d^{2} e^{2} f + 3 \, {\left(b d^{3} e f^{2} + a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f + 2 \, a d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{3} f^{3} x^{3} + b d^{3} e^{3} + 3 \, a d^{2} e^{2} f + 3 \, {\left(b d^{3} e f^{2} + a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f + 2 \, a d^{2} e f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b d^{3} e^{2} f + 2 \, a d^{2} e f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(b d^{3} e^{3} - 3 \, {\left(b c + a\right)} d^{2} e^{2} f + 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} - {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3} - {\left(b d^{3} e^{3} - 3 \, {\left(b c + a\right)} d^{2} e^{2} f + 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} - {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} e^{3} - 3 \, {\left(b c + a\right)} d^{2} e^{2} f + 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} - {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{3} e^{3} - 3 \, {\left(b c + a\right)} d^{2} e^{2} f + 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} - {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} e^{2} f - 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} + {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3} + 3 \, {\left(b d^{3} e f^{2} - a d^{2} f^{3}\right)} x^{2} - {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} e^{2} f - 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} + {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3} + 3 \, {\left(b d^{3} e f^{2} - a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, a d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} e^{2} f - 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} + {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3} + 3 \, {\left(b d^{3} e f^{2} - a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, a d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} e^{2} f - 3 \, {\left(b c^{2} + 2 \, a c\right)} d e f^{2} + {\left(b c^{3} + 3 \, a c^{2}\right)} f^{3} + 3 \, {\left(b d^{3} e f^{2} - a d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, a d^{2} e f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b d^{3} e^{2} f - 2 \, a d^{2} e f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 6 \, {\left(b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{3} \sinh\left(d x + c\right)^{2} - b f^{3}\right)} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 6 \, {\left(b f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{3} \sinh\left(d x + c\right)^{2} - b f^{3}\right)} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 6 \, {\left(b d f^{3} x + b d e f^{2} - a f^{3} - {\left(b d f^{3} x + b d e f^{2} - a f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{3} x + b d e f^{2} - a f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{3} x + b d e f^{2} - a f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 6 \, {\left(b d f^{3} x + b d e f^{2} + a f^{3} - {\left(b d f^{3} x + b d e f^{2} + a f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{3} x + b d e f^{2} + a f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{3} x + b d e f^{2} + a f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right)}{a^{2} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d^{4} \sinh\left(d x + c\right)^{2} - a^{2} d^{4}}"," ",0,"-(2*a*d^3*e^3 - 6*a*c*d^2*e^2*f + 6*a*c^2*d*e*f^2 - 2*a*c^3*f^3 + 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + 3*a*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 + a*c^3*f^3)*cosh(d*x + c)^2 + 4*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + 3*a*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 + a*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + 2*(a*d^3*f^3*x^3 + 3*a*d^3*e*f^2*x^2 + 3*a*d^3*e^2*f*x + 3*a*c*d^2*e^2*f - 3*a*c^2*d*e*f^2 + a*c^3*f^3)*sinh(d*x + c)^2 + 3*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f - (b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f - (b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^3*x^2 + 2*b*d^2*e*f^2*x + b*d^2*e^2*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (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 - (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)*cosh(d*x + c)^2 - 2*(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)*cosh(d*x + c)*sinh(d*x + c) - (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)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (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 - (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)*cosh(d*x + c)^2 - 2*(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)*cosh(d*x + c)*sinh(d*x + c) - (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)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3 - (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*cosh(d*x + c)^2 - 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3 - (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*cosh(d*x + c)^2 - 2*(b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b*d^3*f^3*x^3 + 3*b*d^3*e*f^2*x^2 + 3*b*d^3*e^2*f*x + 3*b*c*d^2*e^2*f - 3*b*c^2*d*e*f^2 + b*c^3*f^3)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 6*(b*f^3*cosh(d*x + c)^2 + 2*b*f^3*cosh(d*x + c)*sinh(d*x + c) + b*f^3*sinh(d*x + c)^2 - b*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b*f^3*cosh(d*x + c)^2 + 2*b*f^3*cosh(d*x + c)*sinh(d*x + c) + b*f^3*sinh(d*x + c)^2 - b*f^3)*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b*d*f^3*x + b*d*e*f^2 - (b*d*f^3*x + b*d*e*f^2)*cosh(d*x + c)^2 - 2*(b*d*f^3*x + b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^3*x + b*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b*d*f^3*x + b*d*e*f^2 - (b*d*f^3*x + b*d*e*f^2)*cosh(d*x + c)^2 - 2*(b*d*f^3*x + b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^3*x + b*d*e*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 3*(b*d^2*f^3*x^2 + b*d^2*e^2*f - 2*a*d*e*f^2 - (b*d^2*f^3*x^2 + b*d^2*e^2*f - 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 - a*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b*d^2*f^3*x^2 + b*d^2*e^2*f - 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 - a*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^3*x^2 + b*d^2*e^2*f - 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 - a*d*f^3)*x)*sinh(d*x + c)^2 + 2*(b*d^2*e*f^2 - a*d*f^3)*x)*dilog(cosh(d*x + c) + sinh(d*x + c)) + 3*(b*d^2*f^3*x^2 + b*d^2*e^2*f + 2*a*d*e*f^2 - (b*d^2*f^3*x^2 + b*d^2*e^2*f + 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 + a*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b*d^2*f^3*x^2 + b*d^2*e^2*f + 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 + a*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^3*x^2 + b*d^2*e^2*f + 2*a*d*e*f^2 + 2*(b*d^2*e*f^2 + a*d*f^3)*x)*sinh(d*x + c)^2 + 2*(b*d^2*e*f^2 + a*d*f^3)*x)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (b*d^3*f^3*x^3 + b*d^3*e^3 + 3*a*d^2*e^2*f + 3*(b*d^3*e*f^2 + a*d^2*f^3)*x^2 - (b*d^3*f^3*x^3 + b*d^3*e^3 + 3*a*d^2*e^2*f + 3*(b*d^3*e*f^2 + a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f + 2*a*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*(b*d^3*f^3*x^3 + b*d^3*e^3 + 3*a*d^2*e^2*f + 3*(b*d^3*e*f^2 + a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f + 2*a*d^2*e*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^3*f^3*x^3 + b*d^3*e^3 + 3*a*d^2*e^2*f + 3*(b*d^3*e*f^2 + a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f + 2*a*d^2*e*f^2)*x)*sinh(d*x + c)^2 + 3*(b*d^3*e^2*f + 2*a*d^2*e*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (b*d^3*e^3 - 3*(b*c + a)*d^2*e^2*f + 3*(b*c^2 + 2*a*c)*d*e*f^2 - (b*c^3 + 3*a*c^2)*f^3 - (b*d^3*e^3 - 3*(b*c + a)*d^2*e^2*f + 3*(b*c^2 + 2*a*c)*d*e*f^2 - (b*c^3 + 3*a*c^2)*f^3)*cosh(d*x + c)^2 - 2*(b*d^3*e^3 - 3*(b*c + a)*d^2*e^2*f + 3*(b*c^2 + 2*a*c)*d*e*f^2 - (b*c^3 + 3*a*c^2)*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b*d^3*e^3 - 3*(b*c + a)*d^2*e^2*f + 3*(b*c^2 + 2*a*c)*d*e*f^2 - (b*c^3 + 3*a*c^2)*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (b*d^3*f^3*x^3 + 3*b*c*d^2*e^2*f - 3*(b*c^2 + 2*a*c)*d*e*f^2 + (b*c^3 + 3*a*c^2)*f^3 + 3*(b*d^3*e*f^2 - a*d^2*f^3)*x^2 - (b*d^3*f^3*x^3 + 3*b*c*d^2*e^2*f - 3*(b*c^2 + 2*a*c)*d*e*f^2 + (b*c^3 + 3*a*c^2)*f^3 + 3*(b*d^3*e*f^2 - a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*a*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*(b*d^3*f^3*x^3 + 3*b*c*d^2*e^2*f - 3*(b*c^2 + 2*a*c)*d*e*f^2 + (b*c^3 + 3*a*c^2)*f^3 + 3*(b*d^3*e*f^2 - a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*a*d^2*e*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^3*f^3*x^3 + 3*b*c*d^2*e^2*f - 3*(b*c^2 + 2*a*c)*d*e*f^2 + (b*c^3 + 3*a*c^2)*f^3 + 3*(b*d^3*e*f^2 - a*d^2*f^3)*x^2 + 3*(b*d^3*e^2*f - 2*a*d^2*e*f^2)*x)*sinh(d*x + c)^2 + 3*(b*d^3*e^2*f - 2*a*d^2*e*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 6*(b*f^3*cosh(d*x + c)^2 + 2*b*f^3*cosh(d*x + c)*sinh(d*x + c) + b*f^3*sinh(d*x + c)^2 - b*f^3)*polylog(4, cosh(d*x + c) + sinh(d*x + c)) - 6*(b*f^3*cosh(d*x + c)^2 + 2*b*f^3*cosh(d*x + c)*sinh(d*x + c) + b*f^3*sinh(d*x + c)^2 - b*f^3)*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) + 6*(b*d*f^3*x + b*d*e*f^2 - a*f^3 - (b*d*f^3*x + b*d*e*f^2 - a*f^3)*cosh(d*x + c)^2 - 2*(b*d*f^3*x + b*d*e*f^2 - a*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^3*x + b*d*e*f^2 - a*f^3)*sinh(d*x + c)^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 6*(b*d*f^3*x + b*d*e*f^2 + a*f^3 - (b*d*f^3*x + b*d*e*f^2 + a*f^3)*cosh(d*x + c)^2 - 2*(b*d*f^3*x + b*d*e*f^2 + a*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^3*x + b*d*e*f^2 + a*f^3)*sinh(d*x + c)^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)))/(a^2*d^4*cosh(d*x + c)^2 + 2*a^2*d^4*cosh(d*x + c)*sinh(d*x + c) + a^2*d^4*sinh(d*x + c)^2 - a^2*d^4)","C",0
455,1,2729,0,0.580907," ","integrate((f*x+e)^2*coth(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a d^{2} e^{2} - 4 \, a c d e f + 2 \, a c^{2} f^{2} + 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + 2 \, a c d e f - a c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + 2 \, a c d e f - a c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a d^{2} e f x + 2 \, a c d e f - a c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d f^{2} x + b d e f - {\left(b d f^{2} x + b d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{2} x + b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{2} x + b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b d f^{2} x + b d e f - {\left(b d f^{2} x + b d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{2} x + b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{2} x + b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2} - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2} - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2} - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2} - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b d^{2} e f x + 2 \, b c d e f - b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{2} \sinh\left(d x + c\right)^{2} - b f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{2} \sinh\left(d x + c\right)^{2} - b f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(b d f^{2} x + b d e f - a f^{2} - {\left(b d f^{2} x + b d e f - a f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{2} x + b d e f - a f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{2} x + b d e f - a f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left(b d f^{2} x + b d e f + a f^{2} - {\left(b d f^{2} x + b d e f + a f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f^{2} x + b d e f + a f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f^{2} x + b d e f + a f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} + 2 \, a d e f - {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} + 2 \, a d e f + 2 \, {\left(b d^{2} e f + a d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} + 2 \, a d e f + 2 \, {\left(b d^{2} e f + a d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{2} x^{2} + b d^{2} e^{2} + 2 \, a d e f + 2 \, {\left(b d^{2} e f + a d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d^{2} e f + a d f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(b d^{2} e^{2} - 2 \, {\left(b c + a\right)} d e f + {\left(b c^{2} + 2 \, a c\right)} f^{2} - {\left(b d^{2} e^{2} - 2 \, {\left(b c + a\right)} d e f + {\left(b c^{2} + 2 \, a c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} e^{2} - 2 \, {\left(b c + a\right)} d e f + {\left(b c^{2} + 2 \, a c\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} e^{2} - 2 \, {\left(b c + a\right)} d e f + {\left(b c^{2} + 2 \, a c\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d e f - {\left(b c^{2} + 2 \, a c\right)} f^{2} - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d e f - {\left(b c^{2} + 2 \, a c\right)} f^{2} + 2 \, {\left(b d^{2} e f - a d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d e f - {\left(b c^{2} + 2 \, a c\right)} f^{2} + 2 \, {\left(b d^{2} e f - a d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d e f - {\left(b c^{2} + 2 \, a c\right)} f^{2} + 2 \, {\left(b d^{2} e f - a d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d^{2} e f - a d f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left(b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{2} \sinh\left(d x + c\right)^{2} - b f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left(b f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f^{2} \sinh\left(d x + c\right)^{2} - b f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right)}{a^{2} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d^{3} \sinh\left(d x + c\right)^{2} - a^{2} d^{3}}"," ",0,"-(2*a*d^2*e^2 - 4*a*c*d*e*f + 2*a*c^2*f^2 + 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + 2*a*c*d*e*f - a*c^2*f^2)*cosh(d*x + c)^2 + 4*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + 2*a*c*d*e*f - a*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + 2*(a*d^2*f^2*x^2 + 2*a*d^2*e*f*x + 2*a*c*d*e*f - a*c^2*f^2)*sinh(d*x + c)^2 + 2*(b*d*f^2*x + b*d*e*f - (b*d*f^2*x + b*d*e*f)*cosh(d*x + c)^2 - 2*(b*d*f^2*x + b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^2*x + b*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b*d*f^2*x + b*d*e*f - (b*d*f^2*x + b*d*e*f)*cosh(d*x + c)^2 - 2*(b*d*f^2*x + b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^2*x + b*d*e*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2 - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cosh(d*x + c)^2 - 2*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2 - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cosh(d*x + c)^2 - 2*(b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2 - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*cosh(d*x + c)^2 - 2*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2 - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*cosh(d*x + c)^2 - 2*(b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^2*x^2 + 2*b*d^2*e*f*x + 2*b*c*d*e*f - b*c^2*f^2)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b*f^2*cosh(d*x + c)^2 + 2*b*f^2*cosh(d*x + c)*sinh(d*x + c) + b*f^2*sinh(d*x + c)^2 - b*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(b*f^2*cosh(d*x + c)^2 + 2*b*f^2*cosh(d*x + c)*sinh(d*x + c) + b*f^2*sinh(d*x + c)^2 - b*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(b*d*f^2*x + b*d*e*f - a*f^2 - (b*d*f^2*x + b*d*e*f - a*f^2)*cosh(d*x + c)^2 - 2*(b*d*f^2*x + b*d*e*f - a*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^2*x + b*d*e*f - a*f^2)*sinh(d*x + c)^2)*dilog(cosh(d*x + c) + sinh(d*x + c)) + 2*(b*d*f^2*x + b*d*e*f + a*f^2 - (b*d*f^2*x + b*d*e*f + a*f^2)*cosh(d*x + c)^2 - 2*(b*d*f^2*x + b*d*e*f + a*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f^2*x + b*d*e*f + a*f^2)*sinh(d*x + c)^2)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (b*d^2*f^2*x^2 + b*d^2*e^2 + 2*a*d*e*f - (b*d^2*f^2*x^2 + b*d^2*e^2 + 2*a*d*e*f + 2*(b*d^2*e*f + a*d*f^2)*x)*cosh(d*x + c)^2 - 2*(b*d^2*f^2*x^2 + b*d^2*e^2 + 2*a*d*e*f + 2*(b*d^2*e*f + a*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^2*x^2 + b*d^2*e^2 + 2*a*d*e*f + 2*(b*d^2*e*f + a*d*f^2)*x)*sinh(d*x + c)^2 + 2*(b*d^2*e*f + a*d*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (b*d^2*e^2 - 2*(b*c + a)*d*e*f + (b*c^2 + 2*a*c)*f^2 - (b*d^2*e^2 - 2*(b*c + a)*d*e*f + (b*c^2 + 2*a*c)*f^2)*cosh(d*x + c)^2 - 2*(b*d^2*e^2 - 2*(b*c + a)*d*e*f + (b*c^2 + 2*a*c)*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*e^2 - 2*(b*c + a)*d*e*f + (b*c^2 + 2*a*c)*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (b*d^2*f^2*x^2 + 2*b*c*d*e*f - (b*c^2 + 2*a*c)*f^2 - (b*d^2*f^2*x^2 + 2*b*c*d*e*f - (b*c^2 + 2*a*c)*f^2 + 2*(b*d^2*e*f - a*d*f^2)*x)*cosh(d*x + c)^2 - 2*(b*d^2*f^2*x^2 + 2*b*c*d*e*f - (b*c^2 + 2*a*c)*f^2 + 2*(b*d^2*e*f - a*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b*d^2*f^2*x^2 + 2*b*c*d*e*f - (b*c^2 + 2*a*c)*f^2 + 2*(b*d^2*e*f - a*d*f^2)*x)*sinh(d*x + c)^2 + 2*(b*d^2*e*f - a*d*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*(b*f^2*cosh(d*x + c)^2 + 2*b*f^2*cosh(d*x + c)*sinh(d*x + c) + b*f^2*sinh(d*x + c)^2 - b*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 2*(b*f^2*cosh(d*x + c)^2 + 2*b*f^2*cosh(d*x + c)*sinh(d*x + c) + b*f^2*sinh(d*x + c)^2 - b*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)))/(a^2*d^3*cosh(d*x + c)^2 + 2*a^2*d^3*cosh(d*x + c)*sinh(d*x + c) + a^2*d^3*sinh(d*x + c)^2 - a^2*d^3)","C",0
456,1,1338,0,0.491215," ","integrate((f*x+e)*coth(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a d e - 2 \, a c f + 2 \, {\left(a d f x + a c f\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a d f x + a c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(a d f x + a c f\right)} \sinh\left(d x + c\right)^{2} - {\left(b f \cosh\left(d x + c\right)^{2} + 2 \, b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f \sinh\left(d x + c\right)^{2} - b f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b f \cosh\left(d x + c\right)^{2} + 2 \, b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f \sinh\left(d x + c\right)^{2} - b f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b d e - b c f - {\left(b d e - b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d e - b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d e - b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d e - b c f - {\left(b d e - b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d e - b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d e - b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d f x + b c f - {\left(b d f x + b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f x + b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f x + b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b d f x + b c f - {\left(b d f x + b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f x + b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f x + b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b f \cosh\left(d x + c\right)^{2} + 2 \, b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f \sinh\left(d x + c\right)^{2} - b f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(b f \cosh\left(d x + c\right)^{2} + 2 \, b f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b f \sinh\left(d x + c\right)^{2} - b f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(b d f x + b d e - {\left(b d f x + b d e + a f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f x + b d e + a f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f x + b d e + a f\right)} \sinh\left(d x + c\right)^{2} + a f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(b d e - {\left(b d e - {\left(b c + a\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d e - {\left(b c + a\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d e - {\left(b c + a\right)} f\right)} \sinh\left(d x + c\right)^{2} - {\left(b c + a\right)} f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(b d f x + b c f - {\left(b d f x + b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b d f x + b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b d f x + b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right)}{a^{2} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d^{2} \sinh\left(d x + c\right)^{2} - a^{2} d^{2}}"," ",0,"-(2*a*d*e - 2*a*c*f + 2*(a*d*f*x + a*c*f)*cosh(d*x + c)^2 + 4*(a*d*f*x + a*c*f)*cosh(d*x + c)*sinh(d*x + c) + 2*(a*d*f*x + a*c*f)*sinh(d*x + c)^2 - (b*f*cosh(d*x + c)^2 + 2*b*f*cosh(d*x + c)*sinh(d*x + c) + b*f*sinh(d*x + c)^2 - b*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (b*f*cosh(d*x + c)^2 + 2*b*f*cosh(d*x + c)*sinh(d*x + c) + b*f*sinh(d*x + c)^2 - b*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b*d*e - b*c*f - (b*d*e - b*c*f)*cosh(d*x + c)^2 - 2*(b*d*e - b*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*e - b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d*e - b*c*f - (b*d*e - b*c*f)*cosh(d*x + c)^2 - 2*(b*d*e - b*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*e - b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b*d*f*x + b*c*f - (b*d*f*x + b*c*f)*cosh(d*x + c)^2 - 2*(b*d*f*x + b*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f*x + b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b*d*f*x + b*c*f - (b*d*f*x + b*c*f)*cosh(d*x + c)^2 - 2*(b*d*f*x + b*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f*x + b*c*f)*sinh(d*x + c)^2)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b*f*cosh(d*x + c)^2 + 2*b*f*cosh(d*x + c)*sinh(d*x + c) + b*f*sinh(d*x + c)^2 - b*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) - (b*f*cosh(d*x + c)^2 + 2*b*f*cosh(d*x + c)*sinh(d*x + c) + b*f*sinh(d*x + c)^2 - b*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (b*d*f*x + b*d*e - (b*d*f*x + b*d*e + a*f)*cosh(d*x + c)^2 - 2*(b*d*f*x + b*d*e + a*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f*x + b*d*e + a*f)*sinh(d*x + c)^2 + a*f)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (b*d*e - (b*d*e - (b*c + a)*f)*cosh(d*x + c)^2 - 2*(b*d*e - (b*c + a)*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*e - (b*c + a)*f)*sinh(d*x + c)^2 - (b*c + a)*f)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (b*d*f*x + b*c*f - (b*d*f*x + b*c*f)*cosh(d*x + c)^2 - 2*(b*d*f*x + b*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b*d*f*x + b*c*f)*sinh(d*x + c)^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1))/(a^2*d^2*cosh(d*x + c)^2 + 2*a^2*d^2*cosh(d*x + c)*sinh(d*x + c) + a^2*d^2*sinh(d*x + c)^2 - a^2*d^2)","B",0
457,1,360,0,0.488288," ","integrate(coth(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{\sqrt{a^{2} + b^{2}} {\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - 2 \, a}{a^{2} d \cosh\left(d x + c\right)^{2} + 2 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} d \sinh\left(d x + c\right)^{2} - a^{2} d}"," ",0,"(sqrt(a^2 + b^2)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - 2*a)/(a^2*d*cosh(d*x + c)^2 + 2*a^2*d*cosh(d*x + c)*sinh(d*x + c) + a^2*d*sinh(d*x + c)^2 - a^2*d)","B",0
458,0,0,0,0.637411," ","integrate(coth(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(coth(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
459,1,5829,0,0.722991," ","integrate((f*x+e)^3*cosh(d*x+c)*coth(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} d^{4} e f^{2} x^{3} + 6 \, a^{2} d^{4} e^{2} f x^{2} + 4 \, a^{2} d^{4} e^{3} x + 8 \, a^{2} c d^{3} e^{3} - 12 \, a^{2} c^{2} d^{2} e^{2} f + 8 \, a^{2} c^{3} d e f^{2} - 2 \, a^{2} c^{4} f^{3} - {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} d^{4} e f^{2} x^{3} + 6 \, a^{2} d^{4} e^{2} f x^{2} + 4 \, a^{2} d^{4} e^{3} x + 8 \, a^{2} c d^{3} e^{3} - 12 \, a^{2} c^{2} d^{2} e^{2} f + 8 \, a^{2} c^{3} d e f^{2} - 2 \, a^{2} c^{4} f^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} d^{4} e f^{2} x^{3} + 6 \, a^{2} d^{4} e^{2} f x^{2} + 4 \, a^{2} d^{4} e^{3} x + 8 \, a^{2} c d^{3} e^{3} - 12 \, a^{2} c^{2} d^{2} e^{2} f + 8 \, a^{2} c^{3} d e f^{2} - 2 \, a^{2} c^{4} f^{3}\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + a b d^{3} e^{3}\right)} \cosh\left(d x + c\right) - 12 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 12 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{3} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f^{2} x + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 12 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} - {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 12 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} - {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} - {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{2} + b^{2}\right)} d^{3} e^{2} f x + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d e f^{2} + {\left(a^{2} + b^{2}\right)} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} - {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 4 \, {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3} - {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} - {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2}\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 24 \, {\left({\left(a^{2} + b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{3} \sinh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f^{3}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(a^{2} + b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{3} \sinh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f^{3}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} f^{3} \sinh\left(d x + c\right)^{2} - b^{2} f^{3}\right)} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 24 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} f^{3} \sinh\left(d x + c\right)^{2} - b^{2} f^{3}\right)} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 24 \, {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2} - {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 24 \, {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2} - {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d f^{3} x + {\left(a^{2} + b^{2}\right)} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 24 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 24 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left(4 \, a b d^{3} f^{3} x^{3} + 12 \, a b d^{3} e f^{2} x^{2} + 12 \, a b d^{3} e^{2} f x + 4 \, a b d^{3} e^{3} + {\left(a^{2} d^{4} f^{3} x^{4} + 4 \, a^{2} d^{4} e f^{2} x^{3} + 6 \, a^{2} d^{4} e^{2} f x^{2} + 4 \, a^{2} d^{4} e^{3} x + 8 \, a^{2} c d^{3} e^{3} - 12 \, a^{2} c^{2} d^{2} e^{2} f + 8 \, a^{2} c^{3} d e f^{2} - 2 \, a^{2} c^{4} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left(a^{2} b d^{4} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b d^{4} \sinh\left(d x + c\right)^{2} - a^{2} b d^{4}\right)}}"," ",0,"1/4*(a^2*d^4*f^3*x^4 + 4*a^2*d^4*e*f^2*x^3 + 6*a^2*d^4*e^2*f*x^2 + 4*a^2*d^4*e^3*x + 8*a^2*c*d^3*e^3 - 12*a^2*c^2*d^2*e^2*f + 8*a^2*c^3*d*e*f^2 - 2*a^2*c^4*f^3 - (a^2*d^4*f^3*x^4 + 4*a^2*d^4*e*f^2*x^3 + 6*a^2*d^4*e^2*f*x^2 + 4*a^2*d^4*e^3*x + 8*a^2*c*d^3*e^3 - 12*a^2*c^2*d^2*e^2*f + 8*a^2*c^3*d*e*f^2 - 2*a^2*c^4*f^3)*cosh(d*x + c)^2 - (a^2*d^4*f^3*x^4 + 4*a^2*d^4*e*f^2*x^3 + 6*a^2*d^4*e^2*f*x^2 + 4*a^2*d^4*e^3*x + 8*a^2*c*d^3*e^3 - 12*a^2*c^2*d^2*e^2*f + 8*a^2*c^3*d*e*f^2 - 2*a^2*c^4*f^3)*sinh(d*x + c)^2 - 8*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + a*b*d^3*e^3)*cosh(d*x + c) - 12*((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f - ((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 12*((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f - ((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d^2*f^3*x^2 + 2*(a^2 + b^2)*d^2*e*f^2*x + (a^2 + b^2)*d^2*e^2*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 12*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 - (b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*sinh(d*x + c)^2 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*dilog(cosh(d*x + c) + sinh(d*x + c)) + 12*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 - (b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*sinh(d*x + c)^2 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - 4*((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3 - ((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3 - ((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d^3*e^3 - 3*(a^2 + b^2)*c*d^2*e^2*f + 3*(a^2 + b^2)*c^2*d*e*f^2 - (a^2 + b^2)*c^3*f^3)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 4*((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3 - ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3 - ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d^3*f^3*x^3 + 3*(a^2 + b^2)*d^3*e*f^2*x^2 + 3*(a^2 + b^2)*d^3*e^2*f*x + 3*(a^2 + b^2)*c*d^2*e^2*f - 3*(a^2 + b^2)*c^2*d*e*f^2 + (a^2 + b^2)*c^3*f^3)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*(b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 - (b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*(b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2)*x)*sinh(d*x + c)^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 4*(b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2)*f^3 - (b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2)*f^3)*cosh(d*x + c)^2 - 2*(b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2)*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2)*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 - (b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2)*x)*sinh(d*x + c)^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 24*((a^2 + b^2)*f^3*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f^3*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f^3*sinh(d*x + c)^2 - (a^2 + b^2)*f^3)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*((a^2 + b^2)*f^3*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f^3*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f^3*sinh(d*x + c)^2 - (a^2 + b^2)*f^3)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*(b^2*f^3*cosh(d*x + c)^2 + 2*b^2*f^3*cosh(d*x + c)*sinh(d*x + c) + b^2*f^3*sinh(d*x + c)^2 - b^2*f^3)*polylog(4, cosh(d*x + c) + sinh(d*x + c)) - 24*(b^2*f^3*cosh(d*x + c)^2 + 2*b^2*f^3*cosh(d*x + c)*sinh(d*x + c) + b^2*f^3*sinh(d*x + c)^2 - b^2*f^3)*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) + 24*((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2 - ((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 24*((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2 - ((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d*f^3*x + (a^2 + b^2)*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 24*(b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3 - (b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*cosh(d*x + c)^2 - 2*(b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*sinh(d*x + c)^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 24*(b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3 - (b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*cosh(d*x + c)^2 - 2*(b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*sinh(d*x + c)^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 2*(4*a*b*d^3*f^3*x^3 + 12*a*b*d^3*e*f^2*x^2 + 12*a*b*d^3*e^2*f*x + 4*a*b*d^3*e^3 + (a^2*d^4*f^3*x^4 + 4*a^2*d^4*e*f^2*x^3 + 6*a^2*d^4*e^2*f*x^2 + 4*a^2*d^4*e^3*x + 8*a^2*c*d^3*e^3 - 12*a^2*c^2*d^2*e^2*f + 8*a^2*c^3*d*e*f^2 - 2*a^2*c^4*f^3)*cosh(d*x + c))*sinh(d*x + c))/(a^2*b*d^4*cosh(d*x + c)^2 + 2*a^2*b*d^4*cosh(d*x + c)*sinh(d*x + c) + a^2*b*d^4*sinh(d*x + c)^2 - a^2*b*d^4)","C",0
460,1,3506,0,0.720093," ","integrate((f*x+e)^2*cosh(d*x+c)*coth(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{a^{2} d^{3} f^{2} x^{3} + 3 \, a^{2} d^{3} e f x^{2} + 3 \, a^{2} d^{3} e^{2} x + 6 \, a^{2} c d^{2} e^{2} - 6 \, a^{2} c^{2} d e f + 2 \, a^{2} c^{3} f^{2} - {\left(a^{2} d^{3} f^{2} x^{3} + 3 \, a^{2} d^{3} e f x^{2} + 3 \, a^{2} d^{3} e^{2} x + 6 \, a^{2} c d^{2} e^{2} - 6 \, a^{2} c^{2} d e f + 2 \, a^{2} c^{3} f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} d^{3} f^{2} x^{3} + 3 \, a^{2} d^{3} e f x^{2} + 3 \, a^{2} d^{3} e^{2} x + 6 \, a^{2} c d^{2} e^{2} - 6 \, a^{2} c^{2} d e f + 2 \, a^{2} c^{3} f^{2}\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2}\right)} \cosh\left(d x + c\right) - 6 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 6 \, {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2} - {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2} - {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2} - {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2} - {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2} - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2} - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 3 \, {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f - {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 3 \, {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} - {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 3 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 6 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} f^{2} \sinh\left(d x + c\right)^{2} - b^{2} f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} f^{2} \sinh\left(d x + c\right)^{2} - b^{2} f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left(3 \, a b d^{2} f^{2} x^{2} + 6 \, a b d^{2} e f x + 3 \, a b d^{2} e^{2} + {\left(a^{2} d^{3} f^{2} x^{3} + 3 \, a^{2} d^{3} e f x^{2} + 3 \, a^{2} d^{3} e^{2} x + 6 \, a^{2} c d^{2} e^{2} - 6 \, a^{2} c^{2} d e f + 2 \, a^{2} c^{3} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\left(a^{2} b d^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b d^{3} \sinh\left(d x + c\right)^{2} - a^{2} b d^{3}\right)}}"," ",0,"1/3*(a^2*d^3*f^2*x^3 + 3*a^2*d^3*e*f*x^2 + 3*a^2*d^3*e^2*x + 6*a^2*c*d^2*e^2 - 6*a^2*c^2*d*e*f + 2*a^2*c^3*f^2 - (a^2*d^3*f^2*x^3 + 3*a^2*d^3*e*f*x^2 + 3*a^2*d^3*e^2*x + 6*a^2*c*d^2*e^2 - 6*a^2*c^2*d*e*f + 2*a^2*c^3*f^2)*cosh(d*x + c)^2 - (a^2*d^3*f^2*x^3 + 3*a^2*d^3*e*f*x^2 + 3*a^2*d^3*e^2*x + 6*a^2*c*d^2*e^2 - 6*a^2*c^2*d*e*f + 2*a^2*c^3*f^2)*sinh(d*x + c)^2 - 6*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2)*cosh(d*x + c) - 6*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 6*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 6*(b^2*d*f^2*x + b^2*d*e*f - a*b*f^2 - (b^2*d*f^2*x + b^2*d*e*f - a*b*f^2)*cosh(d*x + c)^2 - 2*(b^2*d*f^2*x + b^2*d*e*f - a*b*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d*f^2*x + b^2*d*e*f - a*b*f^2)*sinh(d*x + c)^2)*dilog(cosh(d*x + c) + sinh(d*x + c)) + 6*(b^2*d*f^2*x + b^2*d*e*f + a*b*f^2 - (b^2*d*f^2*x + b^2*d*e*f + a*b*f^2)*cosh(d*x + c)^2 - 2*(b^2*d*f^2*x + b^2*d*e*f + a*b*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d*f^2*x + b^2*d*e*f + a*b*f^2)*sinh(d*x + c)^2)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - 3*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2 - ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 3*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2 - ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 3*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2 - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 3*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2 - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 3*(b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f - (b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*sinh(d*x + c)^2 + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 3*(b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c)*f^2 - (b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c)*f^2)*cosh(d*x + c)^2 - 2*(b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c)*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c)*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 3*(b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 - (b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*sinh(d*x + c)^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 6*((a^2 + b^2)*f^2*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f^2*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f^2*sinh(d*x + c)^2 - (a^2 + b^2)*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*((a^2 + b^2)*f^2*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f^2*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f^2*sinh(d*x + c)^2 - (a^2 + b^2)*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b^2*f^2*cosh(d*x + c)^2 + 2*b^2*f^2*cosh(d*x + c)*sinh(d*x + c) + b^2*f^2*sinh(d*x + c)^2 - b^2*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 6*(b^2*f^2*cosh(d*x + c)^2 + 2*b^2*f^2*cosh(d*x + c)*sinh(d*x + c) + b^2*f^2*sinh(d*x + c)^2 - b^2*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 2*(3*a*b*d^2*f^2*x^2 + 6*a*b*d^2*e*f*x + 3*a*b*d^2*e^2 + (a^2*d^3*f^2*x^3 + 3*a^2*d^3*e*f*x^2 + 3*a^2*d^3*e^2*x + 6*a^2*c*d^2*e^2 - 6*a^2*c^2*d*e*f + 2*a^2*c^3*f^2)*cosh(d*x + c))*sinh(d*x + c))/(a^2*b*d^3*cosh(d*x + c)^2 + 2*a^2*b*d^3*cosh(d*x + c)*sinh(d*x + c) + a^2*b*d^3*sinh(d*x + c)^2 - a^2*b*d^3)","C",0
461,1,1735,0,0.940045," ","integrate((f*x+e)*cosh(d*x+c)*coth(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{a^{2} d^{2} f x^{2} + 2 \, a^{2} d^{2} e x + 4 \, a^{2} c d e - 2 \, a^{2} c^{2} f - {\left(a^{2} d^{2} f x^{2} + 2 \, a^{2} d^{2} e x + 4 \, a^{2} c d e - 2 \, a^{2} c^{2} f\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} d^{2} f x^{2} + 2 \, a^{2} d^{2} e x + 4 \, a^{2} c d e - 2 \, a^{2} c^{2} f\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a b d f x + a b d e\right)} \cosh\left(d x + c\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f \sinh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} f \sinh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b^{2} f \cosh\left(d x + c\right)^{2} + 2 \, b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} f \sinh\left(d x + c\right)^{2} - b^{2} f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(b^{2} f \cosh\left(d x + c\right)^{2} + 2 \, b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} f \sinh\left(d x + c\right)^{2} - b^{2} f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f - {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f - {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{2} d f x + b^{2} d e + a b f - {\left(b^{2} d f x + b^{2} d e + a b f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f x + b^{2} d e + a b f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d f x + b^{2} d e + a b f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(b^{2} d e - {\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \sinh\left(d x + c\right)^{2} - {\left(b^{2} c + a b\right)} f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(b^{2} d f x + b^{2} c f - {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{2} d f x + b^{2} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, a b d f x + 2 \, a b d e + {\left(a^{2} d^{2} f x^{2} + 2 \, a^{2} d^{2} e x + 4 \, a^{2} c d e - 2 \, a^{2} c^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{2} b d^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b d^{2} \sinh\left(d x + c\right)^{2} - a^{2} b d^{2}\right)}}"," ",0,"1/2*(a^2*d^2*f*x^2 + 2*a^2*d^2*e*x + 4*a^2*c*d*e - 2*a^2*c^2*f - (a^2*d^2*f*x^2 + 2*a^2*d^2*e*x + 4*a^2*c*d*e - 2*a^2*c^2*f)*cosh(d*x + c)^2 - (a^2*d^2*f*x^2 + 2*a^2*d^2*e*x + 4*a^2*c*d*e - 2*a^2*c^2*f)*sinh(d*x + c)^2 - 4*(a*b*d*f*x + a*b*d*e)*cosh(d*x + c) + 2*((a^2 + b^2)*f*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f*sinh(d*x + c)^2 - (a^2 + b^2)*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*((a^2 + b^2)*f*cosh(d*x + c)^2 + 2*(a^2 + b^2)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*f*sinh(d*x + c)^2 - (a^2 + b^2)*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b^2*f*cosh(d*x + c)^2 + 2*b^2*f*cosh(d*x + c)*sinh(d*x + c) + b^2*f*sinh(d*x + c)^2 - b^2*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) - 2*(b^2*f*cosh(d*x + c)^2 + 2*b^2*f*cosh(d*x + c)*sinh(d*x + c) + b^2*f*sinh(d*x + c)^2 - b^2*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - 2*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f - ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f - ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^2*d*f*x + b^2*d*e + a*b*f - (b^2*d*f*x + b^2*d*e + a*b*f)*cosh(d*x + c)^2 - 2*(b^2*d*f*x + b^2*d*e + a*b*f)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d*f*x + b^2*d*e + a*b*f)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 2*(b^2*d*e - (b^2*d*e - (b^2*c + a*b)*f)*cosh(d*x + c)^2 - 2*(b^2*d*e - (b^2*c + a*b)*f)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d*e - (b^2*c + a*b)*f)*sinh(d*x + c)^2 - (b^2*c + a*b)*f)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(b^2*d*f*x + b^2*c*f - (b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2 - 2*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b^2*d*f*x + b^2*c*f)*sinh(d*x + c)^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*(2*a*b*d*f*x + 2*a*b*d*e + (a^2*d^2*f*x^2 + 2*a^2*d^2*e*x + 4*a^2*c*d*e - 2*a^2*c^2*f)*cosh(d*x + c))*sinh(d*x + c))/(a^2*b*d^2*cosh(d*x + c)^2 + 2*a^2*b*d^2*cosh(d*x + c)*sinh(d*x + c) + a^2*b*d^2*sinh(d*x + c)^2 - a^2*b*d^2)","B",0
462,1,299,0,0.642131," ","integrate(cosh(d*x+c)*coth(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{a^{2} d x \cosh\left(d x + c\right)^{2} + a^{2} d x \sinh\left(d x + c\right)^{2} - a^{2} d x + 2 \, a b \cosh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} - a^{2} - b^{2}\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} - b^{2}\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(a^{2} d x \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right)}{a^{2} b d \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b d \sinh\left(d x + c\right)^{2} - a^{2} b d}"," ",0,"-(a^2*d*x*cosh(d*x + c)^2 + a^2*d*x*sinh(d*x + c)^2 - a^2*d*x + 2*a*b*cosh(d*x + c) - ((a^2 + b^2)*cosh(d*x + c)^2 + 2*(a^2 + b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*sinh(d*x + c)^2 - a^2 - b^2)*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + (b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 - b^2)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(a^2*d*x*cosh(d*x + c) + a*b)*sinh(d*x + c))/(a^2*b*d*cosh(d*x + c)^2 + 2*a^2*b*d*cosh(d*x + c)*sinh(d*x + c) + a^2*b*d*sinh(d*x + c)^2 - a^2*b*d)","B",0
463,0,0,0,0.977627," ","integrate(cosh(d*x+c)*coth(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right) \coth\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(cosh(d*x + c)*coth(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
464,1,9779,0,1.023432," ","integrate((f*x+e)^3*csch(d*x+c)^2*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + {\left(a^{3} + a b^{2}\right)} d^{3} e^{3}\right)} \cosh\left(d x + c\right) + 3 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f - {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f - {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} f^{3} x^{2} + 2 \, b^{3} d^{2} e f^{2} x + b^{3} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} - {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} - {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} - {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} - {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(3 i \, a^{3} d^{2} f^{3} x^{2} - 3 \, a^{2} b d^{2} f^{3} x^{2} + 6 i \, a^{3} d^{2} e f^{2} x - 6 \, a^{2} b d^{2} e f^{2} x + 3 i \, a^{3} d^{2} e^{2} f - 3 \, a^{2} b d^{2} e^{2} f + {\left(-3 i \, a^{3} d^{2} f^{3} x^{2} + 3 \, a^{2} b d^{2} f^{3} x^{2} - 6 i \, a^{3} d^{2} e f^{2} x + 6 \, a^{2} b d^{2} e f^{2} x - 3 i \, a^{3} d^{2} e^{2} f + 3 \, a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + {\left(-6 i \, a^{3} d^{2} f^{3} x^{2} + 6 \, a^{2} b d^{2} f^{3} x^{2} - 12 i \, a^{3} d^{2} e f^{2} x + 12 \, a^{2} b d^{2} e f^{2} x - 6 i \, a^{3} d^{2} e^{2} f + 6 \, a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-3 i \, a^{3} d^{2} f^{3} x^{2} + 3 \, a^{2} b d^{2} f^{3} x^{2} - 6 i \, a^{3} d^{2} e f^{2} x + 6 \, a^{2} b d^{2} e f^{2} x - 3 i \, a^{3} d^{2} e^{2} f + 3 \, a^{2} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(-3 i \, a^{3} d^{2} f^{3} x^{2} - 3 \, a^{2} b d^{2} f^{3} x^{2} - 6 i \, a^{3} d^{2} e f^{2} x - 6 \, a^{2} b d^{2} e f^{2} x - 3 i \, a^{3} d^{2} e^{2} f - 3 \, a^{2} b d^{2} e^{2} f + {\left(3 i \, a^{3} d^{2} f^{3} x^{2} + 3 \, a^{2} b d^{2} f^{3} x^{2} + 6 i \, a^{3} d^{2} e f^{2} x + 6 \, a^{2} b d^{2} e f^{2} x + 3 i \, a^{3} d^{2} e^{2} f + 3 \, a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} + {\left(6 i \, a^{3} d^{2} f^{3} x^{2} + 6 \, a^{2} b d^{2} f^{3} x^{2} + 12 i \, a^{3} d^{2} e f^{2} x + 12 \, a^{2} b d^{2} e f^{2} x + 6 i \, a^{3} d^{2} e^{2} f + 6 \, a^{2} b d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(3 i \, a^{3} d^{2} f^{3} x^{2} + 3 \, a^{2} b d^{2} f^{3} x^{2} + 6 i \, a^{3} d^{2} e f^{2} x + 6 \, a^{2} b d^{2} e f^{2} x + 3 i \, a^{3} d^{2} e^{2} f + 3 \, a^{2} b d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d e f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f^{2} + {\left(a^{3} + a b^{2}\right)} d f^{3}\right)} x\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3} - {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3} - {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{3} e^{3} - 3 \, b^{3} c d^{2} e^{2} f + 3 \, b^{3} c^{2} d e f^{2} - b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3} - {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3} - {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{3} f^{3} x^{3} + 3 \, b^{3} d^{3} e f^{2} x^{2} + 3 \, b^{3} d^{3} e^{2} f x + 3 \, b^{3} c d^{2} e^{2} f - 3 \, b^{3} c^{2} d e f^{2} + b^{3} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} b + b^{3}\right)} d^{3} e^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} + {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(i \, a^{3} d^{3} e^{3} - a^{2} b d^{3} e^{3} - 3 i \, a^{3} c d^{2} e^{2} f + 3 \, a^{2} b c d^{2} e^{2} f + 3 i \, a^{3} c^{2} d e f^{2} - 3 \, a^{2} b c^{2} d e f^{2} - i \, a^{3} c^{3} f^{3} + a^{2} b c^{3} f^{3} + {\left(-i \, a^{3} d^{3} e^{3} + a^{2} b d^{3} e^{3} + 3 i \, a^{3} c d^{2} e^{2} f - 3 \, a^{2} b c d^{2} e^{2} f - 3 i \, a^{3} c^{2} d e f^{2} + 3 \, a^{2} b c^{2} d e f^{2} + i \, a^{3} c^{3} f^{3} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(-2 i \, a^{3} d^{3} e^{3} + 2 \, a^{2} b d^{3} e^{3} + 6 i \, a^{3} c d^{2} e^{2} f - 6 \, a^{2} b c d^{2} e^{2} f - 6 i \, a^{3} c^{2} d e f^{2} + 6 \, a^{2} b c^{2} d e f^{2} + 2 i \, a^{3} c^{3} f^{3} - 2 \, a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-i \, a^{3} d^{3} e^{3} + a^{2} b d^{3} e^{3} + 3 i \, a^{3} c d^{2} e^{2} f - 3 \, a^{2} b c d^{2} e^{2} f - 3 i \, a^{3} c^{2} d e f^{2} + 3 \, a^{2} b c^{2} d e f^{2} + i \, a^{3} c^{3} f^{3} - a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(-i \, a^{3} d^{3} e^{3} - a^{2} b d^{3} e^{3} + 3 i \, a^{3} c d^{2} e^{2} f + 3 \, a^{2} b c d^{2} e^{2} f - 3 i \, a^{3} c^{2} d e f^{2} - 3 \, a^{2} b c^{2} d e f^{2} + i \, a^{3} c^{3} f^{3} + a^{2} b c^{3} f^{3} + {\left(i \, a^{3} d^{3} e^{3} + a^{2} b d^{3} e^{3} - 3 i \, a^{3} c d^{2} e^{2} f - 3 \, a^{2} b c d^{2} e^{2} f + 3 i \, a^{3} c^{2} d e f^{2} + 3 \, a^{2} b c^{2} d e f^{2} - i \, a^{3} c^{3} f^{3} - a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 i \, a^{3} d^{3} e^{3} + 2 \, a^{2} b d^{3} e^{3} - 6 i \, a^{3} c d^{2} e^{2} f - 6 \, a^{2} b c d^{2} e^{2} f + 6 i \, a^{3} c^{2} d e f^{2} + 6 \, a^{2} b c^{2} d e f^{2} - 2 i \, a^{3} c^{3} f^{3} - 2 \, a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(i \, a^{3} d^{3} e^{3} + a^{2} b d^{3} e^{3} - 3 i \, a^{3} c d^{2} e^{2} f - 3 \, a^{2} b c d^{2} e^{2} f + 3 i \, a^{3} c^{2} d e f^{2} + 3 \, a^{2} b c^{2} d e f^{2} - i \, a^{3} c^{3} f^{3} - a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3} - {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} - {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(-i \, a^{3} d^{3} f^{3} x^{3} - a^{2} b d^{3} f^{3} x^{3} - 3 i \, a^{3} d^{3} e f^{2} x^{2} - 3 \, a^{2} b d^{3} e f^{2} x^{2} - 3 i \, a^{3} d^{3} e^{2} f x - 3 \, a^{2} b d^{3} e^{2} f x - 3 i \, a^{3} c d^{2} e^{2} f - 3 \, a^{2} b c d^{2} e^{2} f + 3 i \, a^{3} c^{2} d e f^{2} + 3 \, a^{2} b c^{2} d e f^{2} - i \, a^{3} c^{3} f^{3} - a^{2} b c^{3} f^{3} + {\left(i \, a^{3} d^{3} f^{3} x^{3} + a^{2} b d^{3} f^{3} x^{3} + 3 i \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 i \, a^{3} d^{3} e^{2} f x + 3 \, a^{2} b d^{3} e^{2} f x + 3 i \, a^{3} c d^{2} e^{2} f + 3 \, a^{2} b c d^{2} e^{2} f - 3 i \, a^{3} c^{2} d e f^{2} - 3 \, a^{2} b c^{2} d e f^{2} + i \, a^{3} c^{3} f^{3} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 i \, a^{3} d^{3} f^{3} x^{3} + 2 \, a^{2} b d^{3} f^{3} x^{3} + 6 i \, a^{3} d^{3} e f^{2} x^{2} + 6 \, a^{2} b d^{3} e f^{2} x^{2} + 6 i \, a^{3} d^{3} e^{2} f x + 6 \, a^{2} b d^{3} e^{2} f x + 6 i \, a^{3} c d^{2} e^{2} f + 6 \, a^{2} b c d^{2} e^{2} f - 6 i \, a^{3} c^{2} d e f^{2} - 6 \, a^{2} b c^{2} d e f^{2} + 2 i \, a^{3} c^{3} f^{3} + 2 \, a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(i \, a^{3} d^{3} f^{3} x^{3} + a^{2} b d^{3} f^{3} x^{3} + 3 i \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 i \, a^{3} d^{3} e^{2} f x + 3 \, a^{2} b d^{3} e^{2} f x + 3 i \, a^{3} c d^{2} e^{2} f + 3 \, a^{2} b c d^{2} e^{2} f - 3 i \, a^{3} c^{2} d e f^{2} - 3 \, a^{2} b c^{2} d e f^{2} + i \, a^{3} c^{3} f^{3} + a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(i \, a^{3} d^{3} f^{3} x^{3} - a^{2} b d^{3} f^{3} x^{3} + 3 i \, a^{3} d^{3} e f^{2} x^{2} - 3 \, a^{2} b d^{3} e f^{2} x^{2} + 3 i \, a^{3} d^{3} e^{2} f x - 3 \, a^{2} b d^{3} e^{2} f x + 3 i \, a^{3} c d^{2} e^{2} f - 3 \, a^{2} b c d^{2} e^{2} f - 3 i \, a^{3} c^{2} d e f^{2} + 3 \, a^{2} b c^{2} d e f^{2} + i \, a^{3} c^{3} f^{3} - a^{2} b c^{3} f^{3} + {\left(-i \, a^{3} d^{3} f^{3} x^{3} + a^{2} b d^{3} f^{3} x^{3} - 3 i \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e f^{2} x^{2} - 3 i \, a^{3} d^{3} e^{2} f x + 3 \, a^{2} b d^{3} e^{2} f x - 3 i \, a^{3} c d^{2} e^{2} f + 3 \, a^{2} b c d^{2} e^{2} f + 3 i \, a^{3} c^{2} d e f^{2} - 3 \, a^{2} b c^{2} d e f^{2} - i \, a^{3} c^{3} f^{3} + a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(-2 i \, a^{3} d^{3} f^{3} x^{3} + 2 \, a^{2} b d^{3} f^{3} x^{3} - 6 i \, a^{3} d^{3} e f^{2} x^{2} + 6 \, a^{2} b d^{3} e f^{2} x^{2} - 6 i \, a^{3} d^{3} e^{2} f x + 6 \, a^{2} b d^{3} e^{2} f x - 6 i \, a^{3} c d^{2} e^{2} f + 6 \, a^{2} b c d^{2} e^{2} f + 6 i \, a^{3} c^{2} d e f^{2} - 6 \, a^{2} b c^{2} d e f^{2} - 2 i \, a^{3} c^{3} f^{3} + 2 \, a^{2} b c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-i \, a^{3} d^{3} f^{3} x^{3} + a^{2} b d^{3} f^{3} x^{3} - 3 i \, a^{3} d^{3} e f^{2} x^{2} + 3 \, a^{2} b d^{3} e f^{2} x^{2} - 3 i \, a^{3} d^{3} e^{2} f x + 3 \, a^{2} b d^{3} e^{2} f x - 3 i \, a^{3} c d^{2} e^{2} f + 3 \, a^{2} b c d^{2} e^{2} f + 3 i \, a^{3} c^{2} d e f^{2} - 3 \, a^{2} b c^{2} d e f^{2} - i \, a^{3} c^{3} f^{3} + a^{2} b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} + {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} + {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} + {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b + b^{3}\right)} c d^{2} e^{2} f - 3 \, {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} d e f^{2} + {\left({\left(a^{2} b + b^{3}\right)} c^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} c^{2}\right)} f^{3} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e f^{2} - {\left(a^{3} + a b^{2}\right)} d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} b + b^{3}\right)} d^{3} e^{2} f - 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 6 \, {\left(b^{3} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{3} \sinh\left(d x + c\right)^{2} - b^{3} f^{3}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b^{3} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{3} \sinh\left(d x + c\right)^{2} - b^{3} f^{3}\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{2} b + b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f^{3} \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f^{3}\right)} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(6 i \, a^{3} f^{3} - 6 \, a^{2} b f^{3} - 6 \, {\left(i \, a^{3} f^{3} - a^{2} b f^{3}\right)} \cosh\left(d x + c\right)^{2} - 12 \, {\left(i \, a^{3} f^{3} - a^{2} b f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - 6 \, {\left(i \, a^{3} f^{3} - a^{2} b f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(4, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(-6 i \, a^{3} f^{3} - 6 \, a^{2} b f^{3} - 6 \, {\left(-i \, a^{3} f^{3} - a^{2} b f^{3}\right)} \cosh\left(d x + c\right)^{2} - 12 \, {\left(-i \, a^{3} f^{3} - a^{2} b f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - 6 \, {\left(-i \, a^{3} f^{3} - a^{2} b f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(4, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 6 \, {\left({\left(a^{2} b + b^{3}\right)} f^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f^{3} \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f^{3}\right)} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 6 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2} - {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2} - {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f^{3} x + b^{3} d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} - {\left(a^{3} + a b^{2}\right)} f^{3} - {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} - {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} - {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} - {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(-6 i \, a^{3} d f^{3} x + 6 \, a^{2} b d f^{3} x - 6 i \, a^{3} d e f^{2} + 6 \, a^{2} b d e f^{2} + {\left(6 i \, a^{3} d f^{3} x - 6 \, a^{2} b d f^{3} x + 6 i \, a^{3} d e f^{2} - 6 \, a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 i \, a^{3} d f^{3} x - 12 \, a^{2} b d f^{3} x + 12 i \, a^{3} d e f^{2} - 12 \, a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(6 i \, a^{3} d f^{3} x - 6 \, a^{2} b d f^{3} x + 6 i \, a^{3} d e f^{2} - 6 \, a^{2} b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(6 i \, a^{3} d f^{3} x + 6 \, a^{2} b d f^{3} x + 6 i \, a^{3} d e f^{2} + 6 \, a^{2} b d e f^{2} + {\left(-6 i \, a^{3} d f^{3} x - 6 \, a^{2} b d f^{3} x - 6 i \, a^{3} d e f^{2} - 6 \, a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-12 i \, a^{3} d f^{3} x - 12 \, a^{2} b d f^{3} x - 12 i \, a^{3} d e f^{2} - 12 \, a^{2} b d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-6 i \, a^{3} d f^{3} x - 6 \, a^{2} b d f^{3} x - 6 i \, a^{3} d e f^{2} - 6 \, a^{2} b d e f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 6 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(a^{3} + a b^{2}\right)} f^{3} - {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f^{3} x + {\left(a^{2} b + b^{3}\right)} d e f^{2} + {\left(a^{3} + a b^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e f^{2} x^{2} + 3 \, {\left(a^{3} + a b^{2}\right)} d^{3} e^{2} f x + {\left(a^{3} + a b^{2}\right)} d^{3} e^{3}\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + a^{2} b^{2}\right)} d^{4} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{2} b^{2}\right)} d^{4} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d^{4}}"," ",0,"-(2*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + (a^3 + a*b^2)*d^3*e^3)*cosh(d*x + c) + 3*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f - (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f - (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*f^3*x^2 + 2*b^3*d^2*e*f^2*x + b^3*d^2*e^2*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f - 2*(a^3 + a*b^2)*d*e*f^2 - ((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f - 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 - (a^3 + a*b^2)*d*f^3)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f - 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 - (a^3 + a*b^2)*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f - 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 - (a^3 + a*b^2)*d*f^3)*x)*sinh(d*x + c)^2 + 2*((a^2*b + b^3)*d^2*e*f^2 - (a^3 + a*b^2)*d*f^3)*x)*dilog(cosh(d*x + c) + sinh(d*x + c)) - (3*I*a^3*d^2*f^3*x^2 - 3*a^2*b*d^2*f^3*x^2 + 6*I*a^3*d^2*e*f^2*x - 6*a^2*b*d^2*e*f^2*x + 3*I*a^3*d^2*e^2*f - 3*a^2*b*d^2*e^2*f + (-3*I*a^3*d^2*f^3*x^2 + 3*a^2*b*d^2*f^3*x^2 - 6*I*a^3*d^2*e*f^2*x + 6*a^2*b*d^2*e*f^2*x - 3*I*a^3*d^2*e^2*f + 3*a^2*b*d^2*e^2*f)*cosh(d*x + c)^2 + (-6*I*a^3*d^2*f^3*x^2 + 6*a^2*b*d^2*f^3*x^2 - 12*I*a^3*d^2*e*f^2*x + 12*a^2*b*d^2*e*f^2*x - 6*I*a^3*d^2*e^2*f + 6*a^2*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (-3*I*a^3*d^2*f^3*x^2 + 3*a^2*b*d^2*f^3*x^2 - 6*I*a^3*d^2*e*f^2*x + 6*a^2*b*d^2*e*f^2*x - 3*I*a^3*d^2*e^2*f + 3*a^2*b*d^2*e^2*f)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (-3*I*a^3*d^2*f^3*x^2 - 3*a^2*b*d^2*f^3*x^2 - 6*I*a^3*d^2*e*f^2*x - 6*a^2*b*d^2*e*f^2*x - 3*I*a^3*d^2*e^2*f - 3*a^2*b*d^2*e^2*f + (3*I*a^3*d^2*f^3*x^2 + 3*a^2*b*d^2*f^3*x^2 + 6*I*a^3*d^2*e*f^2*x + 6*a^2*b*d^2*e*f^2*x + 3*I*a^3*d^2*e^2*f + 3*a^2*b*d^2*e^2*f)*cosh(d*x + c)^2 + (6*I*a^3*d^2*f^3*x^2 + 6*a^2*b*d^2*f^3*x^2 + 12*I*a^3*d^2*e*f^2*x + 12*a^2*b*d^2*e*f^2*x + 6*I*a^3*d^2*e^2*f + 6*a^2*b*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c) + (3*I*a^3*d^2*f^3*x^2 + 3*a^2*b*d^2*f^3*x^2 + 6*I*a^3*d^2*e*f^2*x + 6*a^2*b*d^2*e*f^2*x + 3*I*a^3*d^2*e^2*f + 3*a^2*b*d^2*e^2*f)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 3*((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f + 2*(a^3 + a*b^2)*d*e*f^2 - ((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f + 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 + (a^3 + a*b^2)*d*f^3)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f + 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 + (a^3 + a*b^2)*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^2*f^3*x^2 + (a^2*b + b^3)*d^2*e^2*f + 2*(a^3 + a*b^2)*d*e*f^2 + 2*((a^2*b + b^3)*d^2*e*f^2 + (a^3 + a*b^2)*d*f^3)*x)*sinh(d*x + c)^2 + 2*((a^2*b + b^3)*d^2*e*f^2 + (a^3 + a*b^2)*d*f^3)*x)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3 - (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3 - (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^3*e^3 - 3*b^3*c*d^2*e^2*f + 3*b^3*c^2*d*e*f^2 - b^3*c^3*f^3)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3 - (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3 - (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^3*f^3*x^3 + 3*b^3*d^3*e*f^2*x^2 + 3*b^3*d^3*e^2*f*x + 3*b^3*c*d^2*e^2*f - 3*b^3*c^2*d*e*f^2 + b^3*c^3*f^3)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - ((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 + 3*(a^3 + a*b^2)*d^2*e^2*f + 3*((a^2*b + b^3)*d^3*e*f^2 + (a^3 + a*b^2)*d^2*f^3)*x^2 - ((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 + 3*(a^3 + a*b^2)*d^2*e^2*f + 3*((a^2*b + b^3)*d^3*e*f^2 + (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f + 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 + 3*(a^3 + a*b^2)*d^2*e^2*f + 3*((a^2*b + b^3)*d^3*e*f^2 + (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f + 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^3*f^3*x^3 + (a^2*b + b^3)*d^3*e^3 + 3*(a^3 + a*b^2)*d^2*e^2*f + 3*((a^2*b + b^3)*d^3*e*f^2 + (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f + 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*sinh(d*x + c)^2 + 3*((a^2*b + b^3)*d^3*e^2*f + 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (I*a^3*d^3*e^3 - a^2*b*d^3*e^3 - 3*I*a^3*c*d^2*e^2*f + 3*a^2*b*c*d^2*e^2*f + 3*I*a^3*c^2*d*e*f^2 - 3*a^2*b*c^2*d*e*f^2 - I*a^3*c^3*f^3 + a^2*b*c^3*f^3 + (-I*a^3*d^3*e^3 + a^2*b*d^3*e^3 + 3*I*a^3*c*d^2*e^2*f - 3*a^2*b*c*d^2*e^2*f - 3*I*a^3*c^2*d*e*f^2 + 3*a^2*b*c^2*d*e*f^2 + I*a^3*c^3*f^3 - a^2*b*c^3*f^3)*cosh(d*x + c)^2 + (-2*I*a^3*d^3*e^3 + 2*a^2*b*d^3*e^3 + 6*I*a^3*c*d^2*e^2*f - 6*a^2*b*c*d^2*e^2*f - 6*I*a^3*c^2*d*e*f^2 + 6*a^2*b*c^2*d*e*f^2 + 2*I*a^3*c^3*f^3 - 2*a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (-I*a^3*d^3*e^3 + a^2*b*d^3*e^3 + 3*I*a^3*c*d^2*e^2*f - 3*a^2*b*c*d^2*e^2*f - 3*I*a^3*c^2*d*e*f^2 + 3*a^2*b*c^2*d*e*f^2 + I*a^3*c^3*f^3 - a^2*b*c^3*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (-I*a^3*d^3*e^3 - a^2*b*d^3*e^3 + 3*I*a^3*c*d^2*e^2*f + 3*a^2*b*c*d^2*e^2*f - 3*I*a^3*c^2*d*e*f^2 - 3*a^2*b*c^2*d*e*f^2 + I*a^3*c^3*f^3 + a^2*b*c^3*f^3 + (I*a^3*d^3*e^3 + a^2*b*d^3*e^3 - 3*I*a^3*c*d^2*e^2*f - 3*a^2*b*c*d^2*e^2*f + 3*I*a^3*c^2*d*e*f^2 + 3*a^2*b*c^2*d*e*f^2 - I*a^3*c^3*f^3 - a^2*b*c^3*f^3)*cosh(d*x + c)^2 + (2*I*a^3*d^3*e^3 + 2*a^2*b*d^3*e^3 - 6*I*a^3*c*d^2*e^2*f - 6*a^2*b*c*d^2*e^2*f + 6*I*a^3*c^2*d*e*f^2 + 6*a^2*b*c^2*d*e*f^2 - 2*I*a^3*c^3*f^3 - 2*a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (I*a^3*d^3*e^3 + a^2*b*d^3*e^3 - 3*I*a^3*c*d^2*e^2*f - 3*a^2*b*c*d^2*e^2*f + 3*I*a^3*c^2*d*e*f^2 + 3*a^2*b*c^2*d*e*f^2 - I*a^3*c^3*f^3 - a^2*b*c^3*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) - ((a^2*b + b^3)*d^3*e^3 - 3*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d^2*e^2*f + 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 - ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3 - ((a^2*b + b^3)*d^3*e^3 - 3*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d^2*e^2*f + 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 - ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^3*e^3 - 3*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d^2*e^2*f + 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 - ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^3*e^3 - 3*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d^2*e^2*f + 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 - ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (-I*a^3*d^3*f^3*x^3 - a^2*b*d^3*f^3*x^3 - 3*I*a^3*d^3*e*f^2*x^2 - 3*a^2*b*d^3*e*f^2*x^2 - 3*I*a^3*d^3*e^2*f*x - 3*a^2*b*d^3*e^2*f*x - 3*I*a^3*c*d^2*e^2*f - 3*a^2*b*c*d^2*e^2*f + 3*I*a^3*c^2*d*e*f^2 + 3*a^2*b*c^2*d*e*f^2 - I*a^3*c^3*f^3 - a^2*b*c^3*f^3 + (I*a^3*d^3*f^3*x^3 + a^2*b*d^3*f^3*x^3 + 3*I*a^3*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e*f^2*x^2 + 3*I*a^3*d^3*e^2*f*x + 3*a^2*b*d^3*e^2*f*x + 3*I*a^3*c*d^2*e^2*f + 3*a^2*b*c*d^2*e^2*f - 3*I*a^3*c^2*d*e*f^2 - 3*a^2*b*c^2*d*e*f^2 + I*a^3*c^3*f^3 + a^2*b*c^3*f^3)*cosh(d*x + c)^2 + (2*I*a^3*d^3*f^3*x^3 + 2*a^2*b*d^3*f^3*x^3 + 6*I*a^3*d^3*e*f^2*x^2 + 6*a^2*b*d^3*e*f^2*x^2 + 6*I*a^3*d^3*e^2*f*x + 6*a^2*b*d^3*e^2*f*x + 6*I*a^3*c*d^2*e^2*f + 6*a^2*b*c*d^2*e^2*f - 6*I*a^3*c^2*d*e*f^2 - 6*a^2*b*c^2*d*e*f^2 + 2*I*a^3*c^3*f^3 + 2*a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (I*a^3*d^3*f^3*x^3 + a^2*b*d^3*f^3*x^3 + 3*I*a^3*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e*f^2*x^2 + 3*I*a^3*d^3*e^2*f*x + 3*a^2*b*d^3*e^2*f*x + 3*I*a^3*c*d^2*e^2*f + 3*a^2*b*c*d^2*e^2*f - 3*I*a^3*c^2*d*e*f^2 - 3*a^2*b*c^2*d*e*f^2 + I*a^3*c^3*f^3 + a^2*b*c^3*f^3)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (I*a^3*d^3*f^3*x^3 - a^2*b*d^3*f^3*x^3 + 3*I*a^3*d^3*e*f^2*x^2 - 3*a^2*b*d^3*e*f^2*x^2 + 3*I*a^3*d^3*e^2*f*x - 3*a^2*b*d^3*e^2*f*x + 3*I*a^3*c*d^2*e^2*f - 3*a^2*b*c*d^2*e^2*f - 3*I*a^3*c^2*d*e*f^2 + 3*a^2*b*c^2*d*e*f^2 + I*a^3*c^3*f^3 - a^2*b*c^3*f^3 + (-I*a^3*d^3*f^3*x^3 + a^2*b*d^3*f^3*x^3 - 3*I*a^3*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e*f^2*x^2 - 3*I*a^3*d^3*e^2*f*x + 3*a^2*b*d^3*e^2*f*x - 3*I*a^3*c*d^2*e^2*f + 3*a^2*b*c*d^2*e^2*f + 3*I*a^3*c^2*d*e*f^2 - 3*a^2*b*c^2*d*e*f^2 - I*a^3*c^3*f^3 + a^2*b*c^3*f^3)*cosh(d*x + c)^2 + (-2*I*a^3*d^3*f^3*x^3 + 2*a^2*b*d^3*f^3*x^3 - 6*I*a^3*d^3*e*f^2*x^2 + 6*a^2*b*d^3*e*f^2*x^2 - 6*I*a^3*d^3*e^2*f*x + 6*a^2*b*d^3*e^2*f*x - 6*I*a^3*c*d^2*e^2*f + 6*a^2*b*c*d^2*e^2*f + 6*I*a^3*c^2*d*e*f^2 - 6*a^2*b*c^2*d*e*f^2 - 2*I*a^3*c^3*f^3 + 2*a^2*b*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c) + (-I*a^3*d^3*f^3*x^3 + a^2*b*d^3*f^3*x^3 - 3*I*a^3*d^3*e*f^2*x^2 + 3*a^2*b*d^3*e*f^2*x^2 - 3*I*a^3*d^3*e^2*f*x + 3*a^2*b*d^3*e^2*f*x - 3*I*a^3*c*d^2*e^2*f + 3*a^2*b*c*d^2*e^2*f + 3*I*a^3*c^2*d*e*f^2 - 3*a^2*b*c^2*d*e*f^2 - I*a^3*c^3*f^3 + a^2*b*c^3*f^3)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - ((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 + ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^3 + a*b^2)*d^2*f^3)*x^2 - ((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 + ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 + ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^3*f^3*x^3 + 3*(a^2*b + b^3)*c*d^2*e^2*f - 3*((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*d*e*f^2 + ((a^2*b + b^3)*c^3 + 3*(a^3 + a*b^2)*c^2)*f^3 + 3*((a^2*b + b^3)*d^3*e*f^2 - (a^3 + a*b^2)*d^2*f^3)*x^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*sinh(d*x + c)^2 + 3*((a^2*b + b^3)*d^3*e^2*f - 2*(a^3 + a*b^2)*d^2*e*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 6*(b^3*f^3*cosh(d*x + c)^2 + 2*b^3*f^3*cosh(d*x + c)*sinh(d*x + c) + b^3*f^3*sinh(d*x + c)^2 - b^3*f^3)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b^3*f^3*cosh(d*x + c)^2 + 2*b^3*f^3*cosh(d*x + c)*sinh(d*x + c) + b^3*f^3*sinh(d*x + c)^2 - b^3*f^3)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*((a^2*b + b^3)*f^3*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f^3*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f^3*sinh(d*x + c)^2 - (a^2*b + b^3)*f^3)*polylog(4, cosh(d*x + c) + sinh(d*x + c)) - (6*I*a^3*f^3 - 6*a^2*b*f^3 - 6*(I*a^3*f^3 - a^2*b*f^3)*cosh(d*x + c)^2 - 12*(I*a^3*f^3 - a^2*b*f^3)*cosh(d*x + c)*sinh(d*x + c) - 6*(I*a^3*f^3 - a^2*b*f^3)*sinh(d*x + c)^2)*polylog(4, I*cosh(d*x + c) + I*sinh(d*x + c)) - (-6*I*a^3*f^3 - 6*a^2*b*f^3 - 6*(-I*a^3*f^3 - a^2*b*f^3)*cosh(d*x + c)^2 - 12*(-I*a^3*f^3 - a^2*b*f^3)*cosh(d*x + c)*sinh(d*x + c) - 6*(-I*a^3*f^3 - a^2*b*f^3)*sinh(d*x + c)^2)*polylog(4, -I*cosh(d*x + c) - I*sinh(d*x + c)) + 6*((a^2*b + b^3)*f^3*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f^3*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f^3*sinh(d*x + c)^2 - (a^2*b + b^3)*f^3)*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) - 6*(b^3*d*f^3*x + b^3*d*e*f^2 - (b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)^2 - 2*(b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f^3*x + b^3*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b^3*d*f^3*x + b^3*d*e*f^2 - (b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)^2 - 2*(b^3*d*f^3*x + b^3*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f^3*x + b^3*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 - (a^3 + a*b^2)*f^3 - ((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 - (a^3 + a*b^2)*f^3)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 - (a^3 + a*b^2)*f^3)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 - (a^3 + a*b^2)*f^3)*sinh(d*x + c)^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - (-6*I*a^3*d*f^3*x + 6*a^2*b*d*f^3*x - 6*I*a^3*d*e*f^2 + 6*a^2*b*d*e*f^2 + (6*I*a^3*d*f^3*x - 6*a^2*b*d*f^3*x + 6*I*a^3*d*e*f^2 - 6*a^2*b*d*e*f^2)*cosh(d*x + c)^2 + (12*I*a^3*d*f^3*x - 12*a^2*b*d*f^3*x + 12*I*a^3*d*e*f^2 - 12*a^2*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (6*I*a^3*d*f^3*x - 6*a^2*b*d*f^3*x + 6*I*a^3*d*e*f^2 - 6*a^2*b*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) - (6*I*a^3*d*f^3*x + 6*a^2*b*d*f^3*x + 6*I*a^3*d*e*f^2 + 6*a^2*b*d*e*f^2 + (-6*I*a^3*d*f^3*x - 6*a^2*b*d*f^3*x - 6*I*a^3*d*e*f^2 - 6*a^2*b*d*e*f^2)*cosh(d*x + c)^2 + (-12*I*a^3*d*f^3*x - 12*a^2*b*d*f^3*x - 12*I*a^3*d*e*f^2 - 12*a^2*b*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-6*I*a^3*d*f^3*x - 6*a^2*b*d*f^3*x - 6*I*a^3*d*e*f^2 - 6*a^2*b*d*e*f^2)*sinh(d*x + c)^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) + 6*((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 + (a^3 + a*b^2)*f^3 - ((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 + (a^3 + a*b^2)*f^3)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 + (a^3 + a*b^2)*f^3)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f^3*x + (a^2*b + b^3)*d*e*f^2 + (a^3 + a*b^2)*f^3)*sinh(d*x + c)^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) + 2*((a^3 + a*b^2)*d^3*f^3*x^3 + 3*(a^3 + a*b^2)*d^3*e*f^2*x^2 + 3*(a^3 + a*b^2)*d^3*e^2*f*x + (a^3 + a*b^2)*d^3*e^3)*sinh(d*x + c))/((a^4 + a^2*b^2)*d^4*cosh(d*x + c)^2 + 2*(a^4 + a^2*b^2)*d^4*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^2*b^2)*d^4*sinh(d*x + c)^2 - (a^4 + a^2*b^2)*d^4)","C",0
465,1,5666,0,0.633574," ","integrate((f*x+e)^2*csch(d*x+c)^2*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f - {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f - {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f^{2} x + b^{3} d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f - {\left(a^{3} + a b^{2}\right)} f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f - {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f - {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f - {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(2 i \, a^{3} d f^{2} x - 2 \, a^{2} b d f^{2} x + 2 i \, a^{3} d e f - 2 \, a^{2} b d e f + {\left(-2 i \, a^{3} d f^{2} x + 2 \, a^{2} b d f^{2} x - 2 i \, a^{3} d e f + 2 \, a^{2} b d e f\right)} \cosh\left(d x + c\right)^{2} + {\left(-4 i \, a^{3} d f^{2} x + 4 \, a^{2} b d f^{2} x - 4 i \, a^{3} d e f + 4 \, a^{2} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-2 i \, a^{3} d f^{2} x + 2 \, a^{2} b d f^{2} x - 2 i \, a^{3} d e f + 2 \, a^{2} b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(-2 i \, a^{3} d f^{2} x - 2 \, a^{2} b d f^{2} x - 2 i \, a^{3} d e f - 2 \, a^{2} b d e f + {\left(2 i \, a^{3} d f^{2} x + 2 \, a^{2} b d f^{2} x + 2 i \, a^{3} d e f + 2 \, a^{2} b d e f\right)} \cosh\left(d x + c\right)^{2} + {\left(4 i \, a^{3} d f^{2} x + 4 \, a^{2} b d f^{2} x + 4 i \, a^{3} d e f + 4 \, a^{2} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(2 i \, a^{3} d f^{2} x + 2 \, a^{2} b d f^{2} x + 2 i \, a^{3} d e f + 2 \, a^{2} b d e f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f + {\left(a^{3} + a b^{2}\right)} f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f + {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f + {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f^{2} x + {\left(a^{2} b + b^{3}\right)} d e f + {\left(a^{3} + a b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2} - {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2} - {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} e^{2} - 2 \, b^{3} c d e f + b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2} - {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2} - {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d^{2} f^{2} x^{2} + 2 \, b^{3} d^{2} e f x + 2 \, b^{3} c d e f - b^{3} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} b + b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d e f + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f + {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(i \, a^{3} d^{2} e^{2} - a^{2} b d^{2} e^{2} - 2 i \, a^{3} c d e f + 2 \, a^{2} b c d e f + i \, a^{3} c^{2} f^{2} - a^{2} b c^{2} f^{2} + {\left(-i \, a^{3} d^{2} e^{2} + a^{2} b d^{2} e^{2} + 2 i \, a^{3} c d e f - 2 \, a^{2} b c d e f - i \, a^{3} c^{2} f^{2} + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-2 i \, a^{3} d^{2} e^{2} + 2 \, a^{2} b d^{2} e^{2} + 4 i \, a^{3} c d e f - 4 \, a^{2} b c d e f - 2 i \, a^{3} c^{2} f^{2} + 2 \, a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-i \, a^{3} d^{2} e^{2} + a^{2} b d^{2} e^{2} + 2 i \, a^{3} c d e f - 2 \, a^{2} b c d e f - i \, a^{3} c^{2} f^{2} + a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(-i \, a^{3} d^{2} e^{2} - a^{2} b d^{2} e^{2} + 2 i \, a^{3} c d e f + 2 \, a^{2} b c d e f - i \, a^{3} c^{2} f^{2} - a^{2} b c^{2} f^{2} + {\left(i \, a^{3} d^{2} e^{2} + a^{2} b d^{2} e^{2} - 2 i \, a^{3} c d e f - 2 \, a^{2} b c d e f + i \, a^{3} c^{2} f^{2} + a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 i \, a^{3} d^{2} e^{2} + 2 \, a^{2} b d^{2} e^{2} - 4 i \, a^{3} c d e f - 4 \, a^{2} b c d e f + 2 i \, a^{3} c^{2} f^{2} + 2 \, a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(i \, a^{3} d^{2} e^{2} + a^{2} b d^{2} e^{2} - 2 i \, a^{3} c d e f - 2 \, a^{2} b c d e f + i \, a^{3} c^{2} f^{2} + a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d e f + {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d e f + {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d e f + {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} d e f + {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(-i \, a^{3} d^{2} f^{2} x^{2} - a^{2} b d^{2} f^{2} x^{2} - 2 i \, a^{3} d^{2} e f x - 2 \, a^{2} b d^{2} e f x - 2 i \, a^{3} c d e f - 2 \, a^{2} b c d e f + i \, a^{3} c^{2} f^{2} + a^{2} b c^{2} f^{2} + {\left(i \, a^{3} d^{2} f^{2} x^{2} + a^{2} b d^{2} f^{2} x^{2} + 2 i \, a^{3} d^{2} e f x + 2 \, a^{2} b d^{2} e f x + 2 i \, a^{3} c d e f + 2 \, a^{2} b c d e f - i \, a^{3} c^{2} f^{2} - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 i \, a^{3} d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} f^{2} x^{2} + 4 i \, a^{3} d^{2} e f x + 4 \, a^{2} b d^{2} e f x + 4 i \, a^{3} c d e f + 4 \, a^{2} b c d e f - 2 i \, a^{3} c^{2} f^{2} - 2 \, a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(i \, a^{3} d^{2} f^{2} x^{2} + a^{2} b d^{2} f^{2} x^{2} + 2 i \, a^{3} d^{2} e f x + 2 \, a^{2} b d^{2} e f x + 2 i \, a^{3} c d e f + 2 \, a^{2} b c d e f - i \, a^{3} c^{2} f^{2} - a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(i \, a^{3} d^{2} f^{2} x^{2} - a^{2} b d^{2} f^{2} x^{2} + 2 i \, a^{3} d^{2} e f x - 2 \, a^{2} b d^{2} e f x + 2 i \, a^{3} c d e f - 2 \, a^{2} b c d e f - i \, a^{3} c^{2} f^{2} + a^{2} b c^{2} f^{2} + {\left(-i \, a^{3} d^{2} f^{2} x^{2} + a^{2} b d^{2} f^{2} x^{2} - 2 i \, a^{3} d^{2} e f x + 2 \, a^{2} b d^{2} e f x - 2 i \, a^{3} c d e f + 2 \, a^{2} b c d e f + i \, a^{3} c^{2} f^{2} - a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(-2 i \, a^{3} d^{2} f^{2} x^{2} + 2 \, a^{2} b d^{2} f^{2} x^{2} - 4 i \, a^{3} d^{2} e f x + 4 \, a^{2} b d^{2} e f x - 4 i \, a^{3} c d e f + 4 \, a^{2} b c d e f + 2 i \, a^{3} c^{2} f^{2} - 2 \, a^{2} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-i \, a^{3} d^{2} f^{2} x^{2} + a^{2} b d^{2} f^{2} x^{2} - 2 i \, a^{3} d^{2} e f x + 2 \, a^{2} b d^{2} e f x - 2 i \, a^{3} c d e f + 2 \, a^{2} b c d e f + i \, a^{3} c^{2} f^{2} - a^{2} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2} - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} c d e f - {\left({\left(a^{2} b + b^{3}\right)} c^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b + b^{3}\right)} d^{2} e f - {\left(a^{3} + a b^{2}\right)} d f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(b^{3} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{2} \sinh\left(d x + c\right)^{2} - b^{3} f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(b^{3} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f^{2} \sinh\left(d x + c\right)^{2} - b^{3} f^{2}\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f^{2} \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(-2 i \, a^{3} f^{2} + 2 \, a^{2} b f^{2} - 2 \, {\left(-i \, a^{3} f^{2} + a^{2} b f^{2}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(-i \, a^{3} f^{2} + a^{2} b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - 2 \, {\left(-i \, a^{3} f^{2} + a^{2} b f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + 2 \, {\left(-i \, a^{3} f^{2} - a^{2} b f^{2} + {\left(i \, a^{3} f^{2} + a^{2} b f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(i \, a^{3} f^{2} + a^{2} b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(i \, a^{3} f^{2} + a^{2} b f^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{2} b + b^{3}\right)} f^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f^{2} \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} + a b^{2}\right)} d^{2} e f x + {\left(a^{3} + a b^{2}\right)} d^{2} e^{2}\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + a^{2} b^{2}\right)} d^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{2} b^{2}\right)} d^{3} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d^{3}}"," ",0,"-(2*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + (a^3 + a*b^2)*d^2*e^2)*cosh(d*x + c) + 2*(b^3*d*f^2*x + b^3*d*e*f - (b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^2 - 2*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f^2*x + b^3*d*e*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^3*d*f^2*x + b^3*d*e*f - (b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)^2 - 2*(b^3*d*f^2*x + b^3*d*e*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f^2*x + b^3*d*e*f)*sinh(d*x + c)^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f - (a^3 + a*b^2)*f^2 - ((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f - (a^3 + a*b^2)*f^2)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f - (a^3 + a*b^2)*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f - (a^3 + a*b^2)*f^2)*sinh(d*x + c)^2)*dilog(cosh(d*x + c) + sinh(d*x + c)) - (2*I*a^3*d*f^2*x - 2*a^2*b*d*f^2*x + 2*I*a^3*d*e*f - 2*a^2*b*d*e*f + (-2*I*a^3*d*f^2*x + 2*a^2*b*d*f^2*x - 2*I*a^3*d*e*f + 2*a^2*b*d*e*f)*cosh(d*x + c)^2 + (-4*I*a^3*d*f^2*x + 4*a^2*b*d*f^2*x - 4*I*a^3*d*e*f + 4*a^2*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (-2*I*a^3*d*f^2*x + 2*a^2*b*d*f^2*x - 2*I*a^3*d*e*f + 2*a^2*b*d*e*f)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (-2*I*a^3*d*f^2*x - 2*a^2*b*d*f^2*x - 2*I*a^3*d*e*f - 2*a^2*b*d*e*f + (2*I*a^3*d*f^2*x + 2*a^2*b*d*f^2*x + 2*I*a^3*d*e*f + 2*a^2*b*d*e*f)*cosh(d*x + c)^2 + (4*I*a^3*d*f^2*x + 4*a^2*b*d*f^2*x + 4*I*a^3*d*e*f + 4*a^2*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c) + (2*I*a^3*d*f^2*x + 2*a^2*b*d*f^2*x + 2*I*a^3*d*e*f + 2*a^2*b*d*e*f)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f + (a^3 + a*b^2)*f^2 - ((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f + (a^3 + a*b^2)*f^2)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f + (a^3 + a*b^2)*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f^2*x + (a^2*b + b^3)*d*e*f + (a^3 + a*b^2)*f^2)*sinh(d*x + c)^2)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2 - (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2 - (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*e^2 - 2*b^3*c*d*e*f + b^3*c^2*f^2)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2 - (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2 - (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d^2*f^2*x^2 + 2*b^3*d^2*e*f*x + 2*b^3*c*d*e*f - b^3*c^2*f^2)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - ((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f - ((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^2*f^2*x^2 + (a^2*b + b^3)*d^2*e^2 + 2*(a^3 + a*b^2)*d*e*f + 2*((a^2*b + b^3)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^2*b + b^3)*d^2*e*f + (a^3 + a*b^2)*d*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (I*a^3*d^2*e^2 - a^2*b*d^2*e^2 - 2*I*a^3*c*d*e*f + 2*a^2*b*c*d*e*f + I*a^3*c^2*f^2 - a^2*b*c^2*f^2 + (-I*a^3*d^2*e^2 + a^2*b*d^2*e^2 + 2*I*a^3*c*d*e*f - 2*a^2*b*c*d*e*f - I*a^3*c^2*f^2 + a^2*b*c^2*f^2)*cosh(d*x + c)^2 + (-2*I*a^3*d^2*e^2 + 2*a^2*b*d^2*e^2 + 4*I*a^3*c*d*e*f - 4*a^2*b*c*d*e*f - 2*I*a^3*c^2*f^2 + 2*a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-I*a^3*d^2*e^2 + a^2*b*d^2*e^2 + 2*I*a^3*c*d*e*f - 2*a^2*b*c*d*e*f - I*a^3*c^2*f^2 + a^2*b*c^2*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (-I*a^3*d^2*e^2 - a^2*b*d^2*e^2 + 2*I*a^3*c*d*e*f + 2*a^2*b*c*d*e*f - I*a^3*c^2*f^2 - a^2*b*c^2*f^2 + (I*a^3*d^2*e^2 + a^2*b*d^2*e^2 - 2*I*a^3*c*d*e*f - 2*a^2*b*c*d*e*f + I*a^3*c^2*f^2 + a^2*b*c^2*f^2)*cosh(d*x + c)^2 + (2*I*a^3*d^2*e^2 + 2*a^2*b*d^2*e^2 - 4*I*a^3*c*d*e*f - 4*a^2*b*c*d*e*f + 2*I*a^3*c^2*f^2 + 2*a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (I*a^3*d^2*e^2 + a^2*b*d^2*e^2 - 2*I*a^3*c*d*e*f - 2*a^2*b*c*d*e*f + I*a^3*c^2*f^2 + a^2*b*c^2*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) - ((a^2*b + b^3)*d^2*e^2 - 2*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d*e*f + ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2 - ((a^2*b + b^3)*d^2*e^2 - 2*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d*e*f + ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*e^2 - 2*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d*e*f + ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^2*e^2 - 2*(a^3 + a*b^2 + (a^2*b + b^3)*c)*d*e*f + ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (-I*a^3*d^2*f^2*x^2 - a^2*b*d^2*f^2*x^2 - 2*I*a^3*d^2*e*f*x - 2*a^2*b*d^2*e*f*x - 2*I*a^3*c*d*e*f - 2*a^2*b*c*d*e*f + I*a^3*c^2*f^2 + a^2*b*c^2*f^2 + (I*a^3*d^2*f^2*x^2 + a^2*b*d^2*f^2*x^2 + 2*I*a^3*d^2*e*f*x + 2*a^2*b*d^2*e*f*x + 2*I*a^3*c*d*e*f + 2*a^2*b*c*d*e*f - I*a^3*c^2*f^2 - a^2*b*c^2*f^2)*cosh(d*x + c)^2 + (2*I*a^3*d^2*f^2*x^2 + 2*a^2*b*d^2*f^2*x^2 + 4*I*a^3*d^2*e*f*x + 4*a^2*b*d^2*e*f*x + 4*I*a^3*c*d*e*f + 4*a^2*b*c*d*e*f - 2*I*a^3*c^2*f^2 - 2*a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (I*a^3*d^2*f^2*x^2 + a^2*b*d^2*f^2*x^2 + 2*I*a^3*d^2*e*f*x + 2*a^2*b*d^2*e*f*x + 2*I*a^3*c*d*e*f + 2*a^2*b*c*d*e*f - I*a^3*c^2*f^2 - a^2*b*c^2*f^2)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (I*a^3*d^2*f^2*x^2 - a^2*b*d^2*f^2*x^2 + 2*I*a^3*d^2*e*f*x - 2*a^2*b*d^2*e*f*x + 2*I*a^3*c*d*e*f - 2*a^2*b*c*d*e*f - I*a^3*c^2*f^2 + a^2*b*c^2*f^2 + (-I*a^3*d^2*f^2*x^2 + a^2*b*d^2*f^2*x^2 - 2*I*a^3*d^2*e*f*x + 2*a^2*b*d^2*e*f*x - 2*I*a^3*c*d*e*f + 2*a^2*b*c*d*e*f + I*a^3*c^2*f^2 - a^2*b*c^2*f^2)*cosh(d*x + c)^2 + (-2*I*a^3*d^2*f^2*x^2 + 2*a^2*b*d^2*f^2*x^2 - 4*I*a^3*d^2*e*f*x + 4*a^2*b*d^2*e*f*x - 4*I*a^3*c*d*e*f + 4*a^2*b*c*d*e*f + 2*I*a^3*c^2*f^2 - 2*a^2*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c) + (-I*a^3*d^2*f^2*x^2 + a^2*b*d^2*f^2*x^2 - 2*I*a^3*d^2*e*f*x + 2*a^2*b*d^2*e*f*x - 2*I*a^3*c*d*e*f + 2*a^2*b*c*d*e*f + I*a^3*c^2*f^2 - a^2*b*c^2*f^2)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - ((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*e*f - ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2 - ((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*e*f - ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*e*f - ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d^2*f^2*x^2 + 2*(a^2*b + b^3)*c*d*e*f - ((a^2*b + b^3)*c^2 + 2*(a^3 + a*b^2)*c)*f^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^2*b + b^3)*d^2*e*f - (a^3 + a*b^2)*d*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 2*(b^3*f^2*cosh(d*x + c)^2 + 2*b^3*f^2*cosh(d*x + c)*sinh(d*x + c) + b^3*f^2*sinh(d*x + c)^2 - b^3*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*(b^3*f^2*cosh(d*x + c)^2 + 2*b^3*f^2*cosh(d*x + c)*sinh(d*x + c) + b^3*f^2*sinh(d*x + c)^2 - b^3*f^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*((a^2*b + b^3)*f^2*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f^2*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f^2*sinh(d*x + c)^2 - (a^2*b + b^3)*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - (-2*I*a^3*f^2 + 2*a^2*b*f^2 - 2*(-I*a^3*f^2 + a^2*b*f^2)*cosh(d*x + c)^2 - 4*(-I*a^3*f^2 + a^2*b*f^2)*cosh(d*x + c)*sinh(d*x + c) - 2*(-I*a^3*f^2 + a^2*b*f^2)*sinh(d*x + c)^2)*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + 2*(-I*a^3*f^2 - a^2*b*f^2 + (I*a^3*f^2 + a^2*b*f^2)*cosh(d*x + c)^2 + 2*(I*a^3*f^2 + a^2*b*f^2)*cosh(d*x + c)*sinh(d*x + c) + (I*a^3*f^2 + a^2*b*f^2)*sinh(d*x + c)^2)*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*((a^2*b + b^3)*f^2*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f^2*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f^2*sinh(d*x + c)^2 - (a^2*b + b^3)*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) + 2*((a^3 + a*b^2)*d^2*f^2*x^2 + 2*(a^3 + a*b^2)*d^2*e*f*x + (a^3 + a*b^2)*d^2*e^2)*sinh(d*x + c))/((a^4 + a^2*b^2)*d^3*cosh(d*x + c)^2 + 2*(a^4 + a^2*b^2)*d^3*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^2*b^2)*d^3*sinh(d*x + c)^2 - (a^4 + a^2*b^2)*d^3)","C",0
466,1,2591,0,0.670928," ","integrate((f*x+e)*csch(d*x+c)^2*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e\right)} \cosh\left(d x + c\right) - {\left(b^{3} f \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f \sinh\left(d x + c\right)^{2} - b^{3} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{3} f \cosh\left(d x + c\right)^{2} + 2 \, b^{3} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} f \sinh\left(d x + c\right)^{2} - b^{3} f\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left({\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(i \, a^{3} f - a^{2} b f + {\left(-i \, a^{3} f + a^{2} b f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(i \, a^{3} f - a^{2} b f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-i \, a^{3} f + a^{2} b f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(-i \, a^{3} f - a^{2} b f + {\left(i \, a^{3} f + a^{2} b f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(-i \, a^{3} f - a^{2} b f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(i \, a^{3} f + a^{2} b f\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + {\left({\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b + b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} b + b^{3}\right)} f \sinh\left(d x + c\right)^{2} - {\left(a^{2} b + b^{3}\right)} f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(b^{3} d e - b^{3} c f - {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d e - b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d e - b^{3} c f - {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d e - b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d e - b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{3} d f x + b^{3} c f - {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f x + b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{3} d f x + b^{3} c f - {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{3} d f x + b^{3} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(b^{3} d f x + b^{3} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} d e + {\left(a^{3} + a b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a b^{2}\right)} f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(i \, a^{3} d e - a^{2} b d e - i \, a^{3} c f + a^{2} b c f + {\left(-i \, a^{3} d e + a^{2} b d e + i \, a^{3} c f - a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + {\left(-2 i \, a^{3} d e + 2 \, a^{2} b d e + 2 i \, a^{3} c f - 2 \, a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-i \, a^{3} d e + a^{2} b d e + i \, a^{3} c f - a^{2} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(-i \, a^{3} d e - a^{2} b d e + i \, a^{3} c f + a^{2} b c f + {\left(i \, a^{3} d e + a^{2} b d e - i \, a^{3} c f - a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + {\left(2 i \, a^{3} d e + 2 \, a^{2} b d e - 2 i \, a^{3} c f - 2 \, a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(i \, a^{3} d e + a^{2} b d e - i \, a^{3} c f - a^{2} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left({\left(a^{2} b + b^{3}\right)} d e - {\left({\left(a^{2} b + b^{3}\right)} d e - {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d e - {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d e - {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} + a b^{2} + {\left(a^{2} b + b^{3}\right)} c\right)} f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(-i \, a^{3} d f x - a^{2} b d f x - i \, a^{3} c f - a^{2} b c f + {\left(i \, a^{3} d f x + a^{2} b d f x + i \, a^{3} c f + a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + {\left(2 i \, a^{3} d f x + 2 \, a^{2} b d f x + 2 i \, a^{3} c f + 2 \, a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(i \, a^{3} d f x + a^{2} b d f x + i \, a^{3} c f + a^{2} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(i \, a^{3} d f x - a^{2} b d f x + i \, a^{3} c f - a^{2} b c f + {\left(-i \, a^{3} d f x + a^{2} b d f x - i \, a^{3} c f + a^{2} b c f\right)} \cosh\left(d x + c\right)^{2} + {\left(-2 i \, a^{3} d f x + 2 \, a^{2} b d f x - 2 i \, a^{3} c f + 2 \, a^{2} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(-i \, a^{3} d f x + a^{2} b d f x - i \, a^{3} c f + a^{2} b c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} c f - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left({\left(a^{2} b + b^{3}\right)} d f x + {\left(a^{2} b + b^{3}\right)} c f\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 2 \, {\left({\left(a^{3} + a b^{2}\right)} d f x + {\left(a^{3} + a b^{2}\right)} d e\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + a^{2} b^{2}\right)} d^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d^{2}}"," ",0,"-(2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e)*cosh(d*x + c) - (b^3*f*cosh(d*x + c)^2 + 2*b^3*f*cosh(d*x + c)*sinh(d*x + c) + b^3*f*sinh(d*x + c)^2 - b^3*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^3*f*cosh(d*x + c)^2 + 2*b^3*f*cosh(d*x + c)*sinh(d*x + c) + b^3*f*sinh(d*x + c)^2 - b^3*f)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + ((a^2*b + b^3)*f*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f*sinh(d*x + c)^2 - (a^2*b + b^3)*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) - (I*a^3*f - a^2*b*f + (-I*a^3*f + a^2*b*f)*cosh(d*x + c)^2 - 2*(I*a^3*f - a^2*b*f)*cosh(d*x + c)*sinh(d*x + c) + (-I*a^3*f + a^2*b*f)*sinh(d*x + c)^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (-I*a^3*f - a^2*b*f + (I*a^3*f + a^2*b*f)*cosh(d*x + c)^2 - 2*(-I*a^3*f - a^2*b*f)*cosh(d*x + c)*sinh(d*x + c) + (I*a^3*f + a^2*b*f)*sinh(d*x + c)^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + ((a^2*b + b^3)*f*cosh(d*x + c)^2 + 2*(a^2*b + b^3)*f*cosh(d*x + c)*sinh(d*x + c) + (a^2*b + b^3)*f*sinh(d*x + c)^2 - (a^2*b + b^3)*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (b^3*d*e - b^3*c*f - (b^3*d*e - b^3*c*f)*cosh(d*x + c)^2 - 2*(b^3*d*e - b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*e - b^3*c*f)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d*e - b^3*c*f - (b^3*d*e - b^3*c*f)*cosh(d*x + c)^2 - 2*(b^3*d*e - b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*e - b^3*c*f)*sinh(d*x + c)^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^3*d*f*x + b^3*c*f - (b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^2 - 2*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f*x + b^3*c*f)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^3*d*f*x + b^3*c*f - (b^3*d*f*x + b^3*c*f)*cosh(d*x + c)^2 - 2*(b^3*d*f*x + b^3*c*f)*cosh(d*x + c)*sinh(d*x + c) - (b^3*d*f*x + b^3*c*f)*sinh(d*x + c)^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^3 + a*b^2)*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*d*e + (a^3 + a*b^2)*f)*sinh(d*x + c)^2 + (a^3 + a*b^2)*f)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (I*a^3*d*e - a^2*b*d*e - I*a^3*c*f + a^2*b*c*f + (-I*a^3*d*e + a^2*b*d*e + I*a^3*c*f - a^2*b*c*f)*cosh(d*x + c)^2 + (-2*I*a^3*d*e + 2*a^2*b*d*e + 2*I*a^3*c*f - 2*a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (-I*a^3*d*e + a^2*b*d*e + I*a^3*c*f - a^2*b*c*f)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) - (-I*a^3*d*e - a^2*b*d*e + I*a^3*c*f + a^2*b*c*f + (I*a^3*d*e + a^2*b*d*e - I*a^3*c*f - a^2*b*c*f)*cosh(d*x + c)^2 + (2*I*a^3*d*e + 2*a^2*b*d*e - 2*I*a^3*c*f - 2*a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (I*a^3*d*e + a^2*b*d*e - I*a^3*c*f - a^2*b*c*f)*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) - ((a^2*b + b^3)*d*e - ((a^2*b + b^3)*d*e - (a^3 + a*b^2 + (a^2*b + b^3)*c)*f)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*e - (a^3 + a*b^2 + (a^2*b + b^3)*c)*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*e - (a^3 + a*b^2 + (a^2*b + b^3)*c)*f)*sinh(d*x + c)^2 - (a^3 + a*b^2 + (a^2*b + b^3)*c)*f)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (-I*a^3*d*f*x - a^2*b*d*f*x - I*a^3*c*f - a^2*b*c*f + (I*a^3*d*f*x + a^2*b*d*f*x + I*a^3*c*f + a^2*b*c*f)*cosh(d*x + c)^2 + (2*I*a^3*d*f*x + 2*a^2*b*d*f*x + 2*I*a^3*c*f + 2*a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (I*a^3*d*f*x + a^2*b*d*f*x + I*a^3*c*f + a^2*b*c*f)*sinh(d*x + c)^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (I*a^3*d*f*x - a^2*b*d*f*x + I*a^3*c*f - a^2*b*c*f + (-I*a^3*d*f*x + a^2*b*d*f*x - I*a^3*c*f + a^2*b*c*f)*cosh(d*x + c)^2 + (-2*I*a^3*d*f*x + 2*a^2*b*d*f*x - 2*I*a^3*c*f + 2*a^2*b*c*f)*cosh(d*x + c)*sinh(d*x + c) + (-I*a^3*d*f*x + a^2*b*d*f*x - I*a^3*c*f + a^2*b*c*f)*sinh(d*x + c)^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*c*f - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*c*f)*cosh(d*x + c)^2 - 2*((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*c*f)*cosh(d*x + c)*sinh(d*x + c) - ((a^2*b + b^3)*d*f*x + (a^2*b + b^3)*c*f)*sinh(d*x + c)^2)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 2*((a^3 + a*b^2)*d*f*x + (a^3 + a*b^2)*d*e)*sinh(d*x + c))/((a^4 + a^2*b^2)*d^2*cosh(d*x + c)^2 + 2*(a^4 + a^2*b^2)*d^2*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^2*b^2)*d^2*sinh(d*x + c)^2 - (a^4 + a^2*b^2)*d^2)","B",0
467,1,441,0,0.698388," ","integrate(csch(d*x+c)^2*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} \sinh\left(d x + c\right)^{2} - a^{3}\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left(a^{3} + a b^{2}\right)} \cosh\left(d x + c\right) - {\left(b^{3} \cosh\left(d x + c\right)^{2} + 2 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{3} \sinh\left(d x + c\right)^{2} - b^{3}\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{2} b \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} b \sinh\left(d x + c\right)^{2} - a^{2} b\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{2} b + b^{3} - {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(a^{3} + a b^{2}\right)} \sinh\left(d x + c\right)}{{\left(a^{4} + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{2} b^{2}\right)} d}"," ",0,"-(2*(a^3*cosh(d*x + c)^2 + 2*a^3*cosh(d*x + c)*sinh(d*x + c) + a^3*sinh(d*x + c)^2 - a^3)*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(a^3 + a*b^2)*cosh(d*x + c) - (b^3*cosh(d*x + c)^2 + 2*b^3*cosh(d*x + c)*sinh(d*x + c) + b^3*sinh(d*x + c)^2 - b^3)*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) - (a^2*b*cosh(d*x + c)^2 + 2*a^2*b*cosh(d*x + c)*sinh(d*x + c) + a^2*b*sinh(d*x + c)^2 - a^2*b)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (a^2*b + b^3 - (a^2*b + b^3)*cosh(d*x + c)^2 - 2*(a^2*b + b^3)*cosh(d*x + c)*sinh(d*x + c) - (a^2*b + b^3)*sinh(d*x + c)^2)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(a^3 + a*b^2)*sinh(d*x + c))/((a^4 + a^2*b^2)*d*cosh(d*x + c)^2 + 2*(a^4 + a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^2*b^2)*d*sinh(d*x + c)^2 - (a^4 + a^2*b^2)*d)","B",0
468,0,0,0,12.186247," ","integrate(csch(d*x+c)^2*sech(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(d x + c\right)^{2} \operatorname{sech}\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(csch(d*x + c)^2*sech(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
469,1,10467,0,1.325191," ","integrate((f*x+e)^2*csch(d*x+c)^2*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} - 8 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c d e f + 4 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c^{2} f^{2} + 4 \, {\left({\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f x + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c d e f - {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f x + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c d e f - {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e f x + {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e f x + {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e^{2} + 4 \, {\left({\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f x + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c d e f - {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d^{2} e f x + {\left(a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d^{2} e f x + {\left(a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2} + 6 \, {\left({\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f x + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c d e f - {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e f x + {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{5} d f^{2} x + b^{5} d e f - {\left(b^{5} d f^{2} x + b^{5} d e f\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(b^{5} d f^{2} x + b^{5} d e f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(b^{5} d f^{2} x + b^{5} d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{5} d f^{2} x + b^{5} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(b^{5} d f^{2} x + b^{5} d e f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left(b^{5} d f^{2} x + b^{5} d e f - {\left(b^{5} d f^{2} x + b^{5} d e f\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(b^{5} d f^{2} x + b^{5} d e f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(b^{5} d f^{2} x + b^{5} d e f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{5} d f^{2} x + b^{5} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(b^{5} d f^{2} x + b^{5} d e f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2} - {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2} - {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(b^{5} d^{2} e^{2} - 2 \, b^{5} c d e f + b^{5} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2} - {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2} - {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(b^{5} d^{2} f^{2} x^{2} + 2 \, b^{5} d^{2} e f x + 2 \, b^{5} c d e f - b^{5} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left(b^{5} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{5} f^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} f^{2} \sinh\left(d x + c\right)^{4} - b^{5} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left(b^{5} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{5} f^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} f^{2} \sinh\left(d x + c\right)^{4} - b^{5} f^{2}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 4 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e f x + {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left({\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} + 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + {\left(24 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} + 24 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} + 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left({\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} - 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + {\left(24 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} - 24 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} - 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{5} + a^{3} b^{2}\right)} f^{2} + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} f^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f^{2} x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d e f + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d e f + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d e f + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d e f + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d e f + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d e f + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f - 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f + 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f - 16 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + {\left(24 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f + 24 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f - 24 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 24 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f + 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f - 16 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f - 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left({\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f - 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f - 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f - 16 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + {\left(24 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f - 24 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f - 24 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 24 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f - 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f - 16 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f - 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{5} + a^{3} b^{2}\right)} d e f + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d e f + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} d e f + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} d e f + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} d e f + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} d e f + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e^{2} - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} d e f + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} d e f + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x - {\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} - {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x - 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x + 16 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - {\left(24 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x - 24 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x + 24 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 24 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x - 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x + 16 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} - 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x - {\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} - {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x + 16 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - {\left(24 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + 24 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x + 24 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 24 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - {\left(16 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x + 16 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 16 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(4 \, {\left(a^{5} + a^{3} b^{2}\right)} d f^{2} x + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} d f^{2} x + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} c f^{2} + 4 i \, {\left(a^{4} b + a^{2} b^{3}\right)} c f^{2}\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c d e f - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c d e f - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c d e f - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c d e f - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c d e f - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c d e f - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d^{2} e f - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} d f^{2}\right)} x\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \sinh\left(d x + c\right)^{4} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2}\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \sinh\left(d x + c\right)^{4} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f^{2}\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 4 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e f x + {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e^{2} - 4 \, {\left({\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d^{2} e f x + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c d e f - {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e f x + {\left(a^{4} b + a^{2} b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} d^{2} e f x + {\left(a^{3} b^{2} + a b^{4}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{3} \sinh\left(d x + c\right)^{4} - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{3}\right)}}"," ",0,"-1/2*(4*(2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*e^2 - 8*(2*a^5 + 3*a^3*b^2 + a*b^4)*c*d*e*f + 4*(2*a^5 + 3*a^3*b^2 + a*b^4)*c^2*f^2 + 4*((2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*e*f*x + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*c*d*e*f - (2*a^5 + 3*a^3*b^2 + a*b^4)*c^2*f^2)*cosh(d*x + c)^4 + 4*((2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*e*f*x + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*c*d*e*f - (2*a^5 + 3*a^3*b^2 + a*b^4)*c^2*f^2)*sinh(d*x + c)^4 + 4*((a^4*b + a^2*b^3)*d^2*f^2*x^2 + 2*(a^4*b + a^2*b^3)*d^2*e*f*x + (a^4*b + a^2*b^3)*d^2*e^2)*cosh(d*x + c)^3 + 4*((a^4*b + a^2*b^3)*d^2*f^2*x^2 + 2*(a^4*b + a^2*b^3)*d^2*e*f*x + (a^4*b + a^2*b^3)*d^2*e^2 + 4*((2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*e*f*x + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*c*d*e*f - (2*a^5 + 3*a^3*b^2 + a*b^4)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*((a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(a^3*b^2 + a*b^4)*d^2*e*f*x + (a^3*b^2 + a*b^4)*d^2*e^2)*cosh(d*x + c)^2 + 4*((a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(a^3*b^2 + a*b^4)*d^2*e*f*x + (a^3*b^2 + a*b^4)*d^2*e^2 + 6*((2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*e*f*x + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*c*d*e*f - (2*a^5 + 3*a^3*b^2 + a*b^4)*c^2*f^2)*cosh(d*x + c)^2 + 3*((a^4*b + a^2*b^3)*d^2*f^2*x^2 + 2*(a^4*b + a^2*b^3)*d^2*e*f*x + (a^4*b + a^2*b^3)*d^2*e^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 4*(b^5*d*f^2*x + b^5*d*e*f - (b^5*d*f^2*x + b^5*d*e*f)*cosh(d*x + c)^4 - 4*(b^5*d*f^2*x + b^5*d*e*f)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(b^5*d*f^2*x + b^5*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(b^5*d*f^2*x + b^5*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 - (b^5*d*f^2*x + b^5*d*e*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 4*(b^5*d*f^2*x + b^5*d*e*f - (b^5*d*f^2*x + b^5*d*e*f)*cosh(d*x + c)^4 - 4*(b^5*d*f^2*x + b^5*d*e*f)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(b^5*d*f^2*x + b^5*d*e*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(b^5*d*f^2*x + b^5*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 - (b^5*d*f^2*x + b^5*d*e*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2 - (b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2)*cosh(d*x + c)^4 - 4*(b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 - (b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2 - (b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2)*cosh(d*x + c)^4 - 4*(b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 - (b^5*d^2*e^2 - 2*b^5*c*d*e*f + b^5*c^2*f^2)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2 - (b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2)*cosh(d*x + c)^4 - 4*(b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 - (b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2 - (b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2)*cosh(d*x + c)^4 - 4*(b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 - (b^5*d^2*f^2*x^2 + 2*b^5*d^2*e*f*x + 2*b^5*c*d*e*f - b^5*c^2*f^2)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*(b^5*f^2*cosh(d*x + c)^4 + 4*b^5*f^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*f^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*f^2*sinh(d*x + c)^4 - b^5*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 4*(b^5*f^2*cosh(d*x + c)^4 + 4*b^5*f^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*f^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*f^2*sinh(d*x + c)^4 - b^5*f^2)*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 4*((a^4*b + a^2*b^3)*d^2*f^2*x^2 + 2*(a^4*b + a^2*b^3)*d^2*e*f*x + (a^4*b + a^2*b^3)*d^2*e^2)*cosh(d*x + c) - 4*((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x - ((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*cosh(d*x + c)^4 - 4*((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*cosh(d*x + c)^3*sinh(d*x + c) - 6*((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 - ((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*sinh(d*x + c)^4 + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*dilog(cosh(d*x + c) + sinh(d*x + c)) - ((4*(a^5 + a^3*b^2)*f^2 + 4*I*(a^4*b + a^2*b^3)*f^2)*cosh(d*x + c)^4 + (16*(a^5 + a^3*b^2)*f^2 + 16*I*(a^4*b + a^2*b^3)*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + (24*(a^5 + a^3*b^2)*f^2 + 24*I*(a^4*b + a^2*b^3)*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + (16*(a^5 + a^3*b^2)*f^2 + 16*I*(a^4*b + a^2*b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*(a^5 + a^3*b^2)*f^2 + 4*I*(a^4*b + a^2*b^3)*f^2)*sinh(d*x + c)^4 - 4*(a^5 + a^3*b^2)*f^2 - 4*I*(a^4*b + a^2*b^3)*f^2)*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - ((4*(a^5 + a^3*b^2)*f^2 - 4*I*(a^4*b + a^2*b^3)*f^2)*cosh(d*x + c)^4 + (16*(a^5 + a^3*b^2)*f^2 - 16*I*(a^4*b + a^2*b^3)*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + (24*(a^5 + a^3*b^2)*f^2 - 24*I*(a^4*b + a^2*b^3)*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + (16*(a^5 + a^3*b^2)*f^2 - 16*I*(a^4*b + a^2*b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*(a^5 + a^3*b^2)*f^2 - 4*I*(a^4*b + a^2*b^3)*f^2)*sinh(d*x + c)^4 - 4*(a^5 + a^3*b^2)*f^2 + 4*I*(a^4*b + a^2*b^3)*f^2)*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + 4*((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x - ((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*cosh(d*x + c)^4 - 4*((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*cosh(d*x + c)^3*sinh(d*x + c) - 6*((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 - ((a^4*b + 2*a^2*b^3 + b^5)*d*f^2*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*sinh(d*x + c)^4 + (a^4*b + 2*a^2*b^3 + b^5)*d*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*f^2)*dilog(-cosh(d*x + c) - sinh(d*x + c)) + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + (a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 - ((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + (a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d*e*f + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^4 - 4*((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + (a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d*e*f + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^3*sinh(d*x + c) - 6*((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + (a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d*e*f + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + (a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d*e*f + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 - ((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + (a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d*e*f + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*sinh(d*x + c)^4 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*d*e*f + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f + (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((4*(a^5 + a^3*b^2)*d*e*f + 4*I*(a^4*b + a^2*b^3)*d*e*f - 4*(a^5 + a^3*b^2)*c*f^2 - 4*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^4 + (16*(a^5 + a^3*b^2)*d*e*f + 16*I*(a^4*b + a^2*b^3)*d*e*f - 16*(a^5 + a^3*b^2)*c*f^2 - 16*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + (24*(a^5 + a^3*b^2)*d*e*f + 24*I*(a^4*b + a^2*b^3)*d*e*f - 24*(a^5 + a^3*b^2)*c*f^2 - 24*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + (16*(a^5 + a^3*b^2)*d*e*f + 16*I*(a^4*b + a^2*b^3)*d*e*f - 16*(a^5 + a^3*b^2)*c*f^2 - 16*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*(a^5 + a^3*b^2)*d*e*f + 4*I*(a^4*b + a^2*b^3)*d*e*f - 4*(a^5 + a^3*b^2)*c*f^2 - 4*I*(a^4*b + a^2*b^3)*c*f^2)*sinh(d*x + c)^4 - 4*(a^5 + a^3*b^2)*d*e*f - 4*I*(a^4*b + a^2*b^3)*d*e*f + 4*(a^5 + a^3*b^2)*c*f^2 + 4*I*(a^4*b + a^2*b^3)*c*f^2)*log(cosh(d*x + c) + sinh(d*x + c) + I) - ((4*(a^5 + a^3*b^2)*d*e*f - 4*I*(a^4*b + a^2*b^3)*d*e*f - 4*(a^5 + a^3*b^2)*c*f^2 + 4*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^4 + (16*(a^5 + a^3*b^2)*d*e*f - 16*I*(a^4*b + a^2*b^3)*d*e*f - 16*(a^5 + a^3*b^2)*c*f^2 + 16*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^3*sinh(d*x + c) + (24*(a^5 + a^3*b^2)*d*e*f - 24*I*(a^4*b + a^2*b^3)*d*e*f - 24*(a^5 + a^3*b^2)*c*f^2 + 24*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + (16*(a^5 + a^3*b^2)*d*e*f - 16*I*(a^4*b + a^2*b^3)*d*e*f - 16*(a^5 + a^3*b^2)*c*f^2 + 16*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*(a^5 + a^3*b^2)*d*e*f - 4*I*(a^4*b + a^2*b^3)*d*e*f - 4*(a^5 + a^3*b^2)*c*f^2 + 4*I*(a^4*b + a^2*b^3)*c*f^2)*sinh(d*x + c)^4 - 4*(a^5 + a^3*b^2)*d*e*f + 4*I*(a^4*b + a^2*b^3)*d*e*f + 4*(a^5 + a^3*b^2)*c*f^2 - 4*I*(a^4*b + a^2*b^3)*c*f^2)*log(cosh(d*x + c) + sinh(d*x + c) - I) - 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 - ((a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 - 2*(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*d*e*f + ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2)*cosh(d*x + c)^4 - 4*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 - 2*(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*d*e*f + ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2)*cosh(d*x + c)^3*sinh(d*x + c) - 6*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 - 2*(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*d*e*f + ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 - 2*(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*d*e*f + ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 - ((a^4*b + 2*a^2*b^3 + b^5)*d^2*e^2 - 2*(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*d*e*f + ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2)*sinh(d*x + c)^4 - 2*(a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*d*e*f + ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (4*(a^5 + a^3*b^2)*d*f^2*x - 4*I*(a^4*b + a^2*b^3)*d*f^2*x - (4*(a^5 + a^3*b^2)*d*f^2*x - 4*I*(a^4*b + a^2*b^3)*d*f^2*x + 4*(a^5 + a^3*b^2)*c*f^2 - 4*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^4 - (16*(a^5 + a^3*b^2)*d*f^2*x - 16*I*(a^4*b + a^2*b^3)*d*f^2*x + 16*(a^5 + a^3*b^2)*c*f^2 - 16*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^3*sinh(d*x + c) - (24*(a^5 + a^3*b^2)*d*f^2*x - 24*I*(a^4*b + a^2*b^3)*d*f^2*x + 24*(a^5 + a^3*b^2)*c*f^2 - 24*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 - (16*(a^5 + a^3*b^2)*d*f^2*x - 16*I*(a^4*b + a^2*b^3)*d*f^2*x + 16*(a^5 + a^3*b^2)*c*f^2 - 16*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 - (4*(a^5 + a^3*b^2)*d*f^2*x - 4*I*(a^4*b + a^2*b^3)*d*f^2*x + 4*(a^5 + a^3*b^2)*c*f^2 - 4*I*(a^4*b + a^2*b^3)*c*f^2)*sinh(d*x + c)^4 + 4*(a^5 + a^3*b^2)*c*f^2 - 4*I*(a^4*b + a^2*b^3)*c*f^2)*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (4*(a^5 + a^3*b^2)*d*f^2*x + 4*I*(a^4*b + a^2*b^3)*d*f^2*x - (4*(a^5 + a^3*b^2)*d*f^2*x + 4*I*(a^4*b + a^2*b^3)*d*f^2*x + 4*(a^5 + a^3*b^2)*c*f^2 + 4*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^4 - (16*(a^5 + a^3*b^2)*d*f^2*x + 16*I*(a^4*b + a^2*b^3)*d*f^2*x + 16*(a^5 + a^3*b^2)*c*f^2 + 16*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^3*sinh(d*x + c) - (24*(a^5 + a^3*b^2)*d*f^2*x + 24*I*(a^4*b + a^2*b^3)*d*f^2*x + 24*(a^5 + a^3*b^2)*c*f^2 + 24*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 - (16*(a^5 + a^3*b^2)*d*f^2*x + 16*I*(a^4*b + a^2*b^3)*d*f^2*x + 16*(a^5 + a^3*b^2)*c*f^2 + 16*I*(a^4*b + a^2*b^3)*c*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 - (4*(a^5 + a^3*b^2)*d*f^2*x + 4*I*(a^4*b + a^2*b^3)*d*f^2*x + 4*(a^5 + a^3*b^2)*c*f^2 + 4*I*(a^4*b + a^2*b^3)*c*f^2)*sinh(d*x + c)^4 + 4*(a^5 + a^3*b^2)*c*f^2 + 4*I*(a^4*b + a^2*b^3)*c*f^2)*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*c*d*e*f - ((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*c*d*e*f - ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2 + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^4 - 4*((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*c*d*e*f - ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2 + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^3*sinh(d*x + c) - 6*((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*c*d*e*f - ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2 + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*c*d*e*f - ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2 + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 - ((a^4*b + 2*a^2*b^3 + b^5)*d^2*f^2*x^2 + 2*(a^4*b + 2*a^2*b^3 + b^5)*c*d*e*f - ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2 + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*sinh(d*x + c)^4 - ((a^4*b + 2*a^2*b^3 + b^5)*c^2 + 2*(a^5 + 2*a^3*b^2 + a*b^4)*c)*f^2 + 2*((a^4*b + 2*a^2*b^3 + b^5)*d^2*e*f - (a^5 + 2*a^3*b^2 + a*b^4)*d*f^2)*x)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 4*((a^4*b + 2*a^2*b^3 + b^5)*f^2*cosh(d*x + c)^4 + 4*(a^4*b + 2*a^2*b^3 + b^5)*f^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4*b + 2*a^2*b^3 + b^5)*f^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4*b + 2*a^2*b^3 + b^5)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*b + 2*a^2*b^3 + b^5)*f^2*sinh(d*x + c)^4 - (a^4*b + 2*a^2*b^3 + b^5)*f^2)*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + 4*((a^4*b + 2*a^2*b^3 + b^5)*f^2*cosh(d*x + c)^4 + 4*(a^4*b + 2*a^2*b^3 + b^5)*f^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4*b + 2*a^2*b^3 + b^5)*f^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4*b + 2*a^2*b^3 + b^5)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*b + 2*a^2*b^3 + b^5)*f^2*sinh(d*x + c)^4 - (a^4*b + 2*a^2*b^3 + b^5)*f^2)*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 4*((a^4*b + a^2*b^3)*d^2*f^2*x^2 + 2*(a^4*b + a^2*b^3)*d^2*e*f*x + (a^4*b + a^2*b^3)*d^2*e^2 - 4*((2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*d^2*e*f*x + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*c*d*e*f - (2*a^5 + 3*a^3*b^2 + a*b^4)*c^2*f^2)*cosh(d*x + c)^3 - 3*((a^4*b + a^2*b^3)*d^2*f^2*x^2 + 2*(a^4*b + a^2*b^3)*d^2*e*f*x + (a^4*b + a^2*b^3)*d^2*e^2)*cosh(d*x + c)^2 - 2*((a^3*b^2 + a*b^4)*d^2*f^2*x^2 + 2*(a^3*b^2 + a*b^4)*d^2*e*f*x + (a^3*b^2 + a*b^4)*d^2*e^2)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 2*a^4*b^2 + a^2*b^4)*d^3*cosh(d*x + c)^4 + 4*(a^6 + 2*a^4*b^2 + a^2*b^4)*d^3*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^6 + 2*a^4*b^2 + a^2*b^4)*d^3*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^6 + 2*a^4*b^2 + a^2*b^4)*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^6 + 2*a^4*b^2 + a^2*b^4)*d^3*sinh(d*x + c)^4 - (a^6 + 2*a^4*b^2 + a^2*b^4)*d^3)","C",0
470,1,4086,0,0.596271," ","integrate((f*x+e)*csch(d*x+c)^2*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d f x + {\left(a^{4} b + a^{2} b^{3}\right)} d e\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d f x + {\left(a^{4} b + a^{2} b^{3}\right)} d e + 4 \, {\left({\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d e - 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c f + 2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{3} b^{2} + a b^{4}\right)} d e\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{3} b^{2} + a b^{4}\right)} d e + 6 \, {\left({\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d f x + {\left(a^{4} b + a^{2} b^{3}\right)} d e\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left(b^{5} f \cosh\left(d x + c\right)^{4} + 4 \, b^{5} f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} f \sinh\left(d x + c\right)^{4} - b^{5} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b^{5} f \cosh\left(d x + c\right)^{4} + 4 \, b^{5} f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{5} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{5} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{5} f \sinh\left(d x + c\right)^{4} - b^{5} f\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{5} d e - b^{5} c f - {\left(b^{5} d e - b^{5} c f\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(b^{5} d e - b^{5} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(b^{5} d e - b^{5} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{5} d e - b^{5} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(b^{5} d e - b^{5} c f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{5} d e - b^{5} c f - {\left(b^{5} d e - b^{5} c f\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(b^{5} d e - b^{5} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(b^{5} d e - b^{5} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{5} d e - b^{5} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(b^{5} d e - b^{5} c f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{5} d f x + b^{5} c f - {\left(b^{5} d f x + b^{5} c f\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(b^{5} d f x + b^{5} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(b^{5} d f x + b^{5} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{5} d f x + b^{5} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(b^{5} d f x + b^{5} c f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{5} d f x + b^{5} c f - {\left(b^{5} d f x + b^{5} c f\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(b^{5} d f x + b^{5} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(b^{5} d f x + b^{5} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{5} d f x + b^{5} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(b^{5} d f x + b^{5} c f\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} b + a^{2} b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} b + a^{2} b^{3}\right)} f \sinh\left(d x + c\right)^{4} - {\left(a^{4} b + a^{2} b^{3}\right)} f\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d f x + {\left(a^{4} b + a^{2} b^{3}\right)} d e\right)} \cosh\left(d x + c\right) + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \sinh\left(d x + c\right)^{4} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f \sinh\left(d x + c\right)^{4} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} f\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left({\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + a^{3} b^{2}\right)} f \sinh\left(d x + c\right)^{4} - {\left(a^{5} + a^{3} b^{2}\right)} f\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left({\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e - {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d e + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c\right)} f\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left({\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} d f x - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} c f\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d f x - 4 \, {\left({\left(2 \, a^{5} + 3 \, a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{5} + 2 \, a^{3} b^{2} + a b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} b + a^{2} b^{3}\right)} d e - 3 \, {\left({\left(a^{4} b + a^{2} b^{3}\right)} d f x + {\left(a^{4} b + a^{2} b^{3}\right)} d e\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{3} b^{2} + a b^{4}\right)} d f x + {\left(a^{3} b^{2} + a b^{4}\right)} d e\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{4} - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d^{2}}"," ",0,"-(2*((2*a^5 + 3*a^3*b^2 + a*b^4)*d*f*x + (a^5 + 2*a^3*b^2 + a*b^4)*c*f)*cosh(d*x + c)^4 + 2*((2*a^5 + 3*a^3*b^2 + a*b^4)*d*f*x + (a^5 + 2*a^3*b^2 + a*b^4)*c*f)*sinh(d*x + c)^4 + 2*((a^4*b + a^2*b^3)*d*f*x + (a^4*b + a^2*b^3)*d*e)*cosh(d*x + c)^3 + 2*((a^4*b + a^2*b^3)*d*f*x + (a^4*b + a^2*b^3)*d*e + 4*((2*a^5 + 3*a^3*b^2 + a*b^4)*d*f*x + (a^5 + 2*a^3*b^2 + a*b^4)*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(2*a^5 + 3*a^3*b^2 + a*b^4)*d*e - 2*(a^5 + 2*a^3*b^2 + a*b^4)*c*f + 2*((a^3*b^2 + a*b^4)*d*f*x + (a^3*b^2 + a*b^4)*d*e)*cosh(d*x + c)^2 + 2*((a^3*b^2 + a*b^4)*d*f*x + (a^3*b^2 + a*b^4)*d*e + 6*((2*a^5 + 3*a^3*b^2 + a*b^4)*d*f*x + (a^5 + 2*a^3*b^2 + a*b^4)*c*f)*cosh(d*x + c)^2 + 3*((a^4*b + a^2*b^3)*d*f*x + (a^4*b + a^2*b^3)*d*e)*cosh(d*x + c))*sinh(d*x + c)^2 - (b^5*f*cosh(d*x + c)^4 + 4*b^5*f*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*f*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*f*sinh(d*x + c)^4 - b^5*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (b^5*f*cosh(d*x + c)^4 + 4*b^5*f*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^5*f*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^5*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^5*f*sinh(d*x + c)^4 - b^5*f)*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^5*d*e - b^5*c*f - (b^5*d*e - b^5*c*f)*cosh(d*x + c)^4 - 4*(b^5*d*e - b^5*c*f)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(b^5*d*e - b^5*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(b^5*d*e - b^5*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 - (b^5*d*e - b^5*c*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^5*d*e - b^5*c*f - (b^5*d*e - b^5*c*f)*cosh(d*x + c)^4 - 4*(b^5*d*e - b^5*c*f)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(b^5*d*e - b^5*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(b^5*d*e - b^5*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 - (b^5*d*e - b^5*c*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^5*d*f*x + b^5*c*f - (b^5*d*f*x + b^5*c*f)*cosh(d*x + c)^4 - 4*(b^5*d*f*x + b^5*c*f)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(b^5*d*f*x + b^5*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(b^5*d*f*x + b^5*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 - (b^5*d*f*x + b^5*c*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^5*d*f*x + b^5*c*f - (b^5*d*f*x + b^5*c*f)*cosh(d*x + c)^4 - 4*(b^5*d*f*x + b^5*c*f)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(b^5*d*f*x + b^5*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(b^5*d*f*x + b^5*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 - (b^5*d*f*x + b^5*c*f)*sinh(d*x + c)^4)*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*((a^4*b + a^2*b^3)*f*cosh(d*x + c)^4 + 4*(a^4*b + a^2*b^3)*f*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4*b + a^2*b^3)*f*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4*b + a^2*b^3)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*b + a^2*b^3)*f*sinh(d*x + c)^4 - (a^4*b + a^2*b^3)*f)*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*((a^4*b + a^2*b^3)*d*f*x + (a^4*b + a^2*b^3)*d*e)*cosh(d*x + c) + ((a^4*b + 2*a^2*b^3 + b^5)*f*cosh(d*x + c)^4 + 4*(a^4*b + 2*a^2*b^3 + b^5)*f*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4*b + 2*a^2*b^3 + b^5)*f*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4*b + 2*a^2*b^3 + b^5)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*b + 2*a^2*b^3 + b^5)*f*sinh(d*x + c)^4 - (a^4*b + 2*a^2*b^3 + b^5)*f)*dilog(cosh(d*x + c) + sinh(d*x + c)) - ((a^4*b + 2*a^2*b^3 + b^5)*f*cosh(d*x + c)^4 + 4*(a^4*b + 2*a^2*b^3 + b^5)*f*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^4*b + 2*a^2*b^3 + b^5)*f*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^4*b + 2*a^2*b^3 + b^5)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*b + 2*a^2*b^3 + b^5)*f*sinh(d*x + c)^4 - (a^4*b + 2*a^2*b^3 + b^5)*f)*dilog(-cosh(d*x + c) - sinh(d*x + c)) - ((a^5 + a^3*b^2)*f*cosh(d*x + c)^4 + 4*(a^5 + a^3*b^2)*f*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^5 + a^3*b^2)*f*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^5 + a^3*b^2)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + a^3*b^2)*f*sinh(d*x + c)^4 - (a^5 + a^3*b^2)*f)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (((a^4*b + 2*a^2*b^3 + b^5)*d*f*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e + (a^5 + 2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^4 + 4*((a^4*b + 2*a^2*b^3 + b^5)*d*f*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e + (a^5 + 2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4*b + 2*a^2*b^3 + b^5)*d*f*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e + (a^5 + 2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4*b + 2*a^2*b^3 + b^5)*d*f*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e + (a^5 + 2*a^3*b^2 + a*b^4)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4*b + 2*a^2*b^3 + b^5)*d*f*x + (a^4*b + 2*a^2*b^3 + b^5)*d*e + (a^5 + 2*a^3*b^2 + a*b^4)*f)*sinh(d*x + c)^4 - (a^4*b + 2*a^2*b^3 + b^5)*d*f*x - (a^4*b + 2*a^2*b^3 + b^5)*d*e - (a^5 + 2*a^3*b^2 + a*b^4)*f)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (((a^4*b + 2*a^2*b^3 + b^5)*d*e - (a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*f)*cosh(d*x + c)^4 + 4*((a^4*b + 2*a^2*b^3 + b^5)*d*e - (a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4*b + 2*a^2*b^3 + b^5)*d*e - (a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4*b + 2*a^2*b^3 + b^5)*d*e - (a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4*b + 2*a^2*b^3 + b^5)*d*e - (a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*f)*sinh(d*x + c)^4 - (a^4*b + 2*a^2*b^3 + b^5)*d*e + (a^5 + 2*a^3*b^2 + a*b^4 + (a^4*b + 2*a^2*b^3 + b^5)*c)*f)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (((a^4*b + 2*a^2*b^3 + b^5)*d*f*x + (a^4*b + 2*a^2*b^3 + b^5)*c*f)*cosh(d*x + c)^4 + 4*((a^4*b + 2*a^2*b^3 + b^5)*d*f*x + (a^4*b + 2*a^2*b^3 + b^5)*c*f)*cosh(d*x + c)^3*sinh(d*x + c) + 6*((a^4*b + 2*a^2*b^3 + b^5)*d*f*x + (a^4*b + 2*a^2*b^3 + b^5)*c*f)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*((a^4*b + 2*a^2*b^3 + b^5)*d*f*x + (a^4*b + 2*a^2*b^3 + b^5)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4*b + 2*a^2*b^3 + b^5)*d*f*x + (a^4*b + 2*a^2*b^3 + b^5)*c*f)*sinh(d*x + c)^4 - (a^4*b + 2*a^2*b^3 + b^5)*d*f*x - (a^4*b + 2*a^2*b^3 + b^5)*c*f)*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*((a^4*b + a^2*b^3)*d*f*x - 4*((2*a^5 + 3*a^3*b^2 + a*b^4)*d*f*x + (a^5 + 2*a^3*b^2 + a*b^4)*c*f)*cosh(d*x + c)^3 + (a^4*b + a^2*b^3)*d*e - 3*((a^4*b + a^2*b^3)*d*f*x + (a^4*b + a^2*b^3)*d*e)*cosh(d*x + c)^2 - 2*((a^3*b^2 + a*b^4)*d*f*x + (a^3*b^2 + a*b^4)*d*e)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 2*a^4*b^2 + a^2*b^4)*d^2*cosh(d*x + c)^4 + 4*(a^6 + 2*a^4*b^2 + a^2*b^4)*d^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^6 + 2*a^4*b^2 + a^2*b^4)*d^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^6 + 2*a^4*b^2 + a^2*b^4)*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^6 + 2*a^4*b^2 + a^2*b^4)*d^2*sinh(d*x + c)^4 - (a^6 + 2*a^4*b^2 + a^2*b^4)*d^2)","B",0
471,1,1040,0,0.606370," ","integrate(csch(d*x+c)^2*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a^{5} + 6 \, a^{3} b^{2} + 2 \, a b^{4} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{2} + a b^{4} + 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left(b^{4} \cosh\left(d x + c\right)^{4} + 4 \, b^{4} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{4} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} \sinh\left(d x + c\right)^{4} - b^{4}\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) - 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) - 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x + c\right) + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) - 6 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - 2 \, {\left(a^{4} b + a^{2} b^{3} - 3 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{2} + a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \sinh\left(d x + c\right)^{4} - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d}"," ",0,"-(4*a^5 + 6*a^3*b^2 + 2*a*b^4 + 2*(a^4*b + a^2*b^3)*cosh(d*x + c)^3 + 2*(a^4*b + a^2*b^3)*sinh(d*x + c)^3 + 2*(a^3*b^2 + a*b^4)*cosh(d*x + c)^2 + 2*(a^3*b^2 + a*b^4 + 3*(a^4*b + a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - (b^4*cosh(d*x + c)^4 + 4*b^4*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^4*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^4*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*sinh(d*x + c)^4 - b^4)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) - 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) - 2*(a^4*b + a^2*b^3)*cosh(d*x + c) + (a^4*b + 2*a^2*b^3 + b^5 - (a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^4 - 4*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)*sinh(d*x + c)^3 - (a^4*b + 2*a^2*b^3 + b^5)*sinh(d*x + c)^4)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (a^4*b + 2*a^2*b^3 + b^5 - (a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^4 - 4*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^3*sinh(d*x + c) - 6*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^2*sinh(d*x + c)^2 - 4*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)*sinh(d*x + c)^3 - (a^4*b + 2*a^2*b^3 + b^5)*sinh(d*x + c)^4)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - 2*(a^4*b + a^2*b^3 - 3*(a^4*b + a^2*b^3)*cosh(d*x + c)^2 - 2*(a^3*b^2 + a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^4 + 4*(a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^6 + 2*a^4*b^2 + a^2*b^4)*d*sinh(d*x + c)^4 - (a^6 + 2*a^4*b^2 + a^2*b^4)*d)","B",0
472,0,0,0,1.635279," ","integrate(csch(d*x+c)^2*sech(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(d x + c\right)^{2} \operatorname{sech}\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(csch(d*x + c)^2*sech(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
473,-1,0,0,0.000000," ","integrate((f*x+e)*csch(d*x+c)^2*sech(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,1,2568,0,2.045904," ","integrate(csch(d*x+c)^2*sech(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{5} + 5 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} + 5 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(2 \, a^{4} b + 2 \, a^{2} b^{3} + 5 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{5} + 3 \, a^{3} b^{2} + 2 \, a b^{4} + 5 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{4} b + a^{2} b^{3} - 5 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a^{5} + 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \sinh\left(d x + c\right)^{6} - 3 \, a^{5} - 5 \, a^{3} b^{2} + {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(3 \, a^{5} + 5 \, a^{3} b^{2} + 15 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{5} + 5 \, a^{3} b^{2} - 15 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{5} + 5 \, a^{3} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(3 \, a^{5} + 5 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right) - {\left(b^{5} \cosh\left(d x + c\right)^{6} + 6 \, b^{5} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{5} \sinh\left(d x + c\right)^{6} + b^{5} \cosh\left(d x + c\right)^{4} - b^{5} \cosh\left(d x + c\right)^{2} - b^{5} + {\left(15 \, b^{5} \cosh\left(d x + c\right)^{2} + b^{5}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{5} \cosh\left(d x + c\right)^{3} + b^{5} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, b^{5} \cosh\left(d x + c\right)^{4} + 6 \, b^{5} \cosh\left(d x + c\right)^{2} - b^{5}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{5} \cosh\left(d x + c\right)^{5} + 2 \, b^{5} \cosh\left(d x + c\right)^{3} - b^{5} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left({\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{6} - a^{4} b - 2 \, a^{2} b^{3} + {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + 15 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{4} b + 2 \, a^{2} b^{3} - 15 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} b + 2 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left({\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \sinh\left(d x + c\right)^{6} - a^{4} b - 2 \, a^{2} b^{3} - b^{5} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} + 15 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5} - 15 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} b + 2 \, a^{2} b^{3} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left(3 \, a^{5} + 5 \, a^{3} b^{2} + 2 \, a b^{4} + 5 \, {\left(3 \, a^{5} + 5 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{5} + 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a^{4} b + a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \sinh\left(d x + c\right)^{6} + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d + 2 \, {\left(3 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"-((3*a^5 + 5*a^3*b^2 + 2*a*b^4)*cosh(d*x + c)^5 + (3*a^5 + 5*a^3*b^2 + 2*a*b^4)*sinh(d*x + c)^5 + 2*(a^4*b + a^2*b^3)*cosh(d*x + c)^4 + (2*a^4*b + 2*a^2*b^3 + 5*(3*a^5 + 5*a^3*b^2 + 2*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(a^5 + 3*a^3*b^2 + 2*a*b^4)*cosh(d*x + c)^3 + 2*(a^5 + 3*a^3*b^2 + 2*a*b^4 + 5*(3*a^5 + 5*a^3*b^2 + 2*a*b^4)*cosh(d*x + c)^2 + 4*(a^4*b + a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(a^4*b + a^2*b^3)*cosh(d*x + c)^2 - 2*(a^4*b + a^2*b^3 - 5*(3*a^5 + 5*a^3*b^2 + 2*a*b^4)*cosh(d*x + c)^3 - 6*(a^4*b + a^2*b^3)*cosh(d*x + c)^2 - 3*(a^5 + 3*a^3*b^2 + 2*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + ((3*a^5 + 5*a^3*b^2)*cosh(d*x + c)^6 + 6*(3*a^5 + 5*a^3*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^5 + 5*a^3*b^2)*sinh(d*x + c)^6 - 3*a^5 - 5*a^3*b^2 + (3*a^5 + 5*a^3*b^2)*cosh(d*x + c)^4 + (3*a^5 + 5*a^3*b^2 + 15*(3*a^5 + 5*a^3*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(3*a^5 + 5*a^3*b^2)*cosh(d*x + c)^3 + (3*a^5 + 5*a^3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (3*a^5 + 5*a^3*b^2)*cosh(d*x + c)^2 - (3*a^5 + 5*a^3*b^2 - 15*(3*a^5 + 5*a^3*b^2)*cosh(d*x + c)^4 - 6*(3*a^5 + 5*a^3*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(3*a^5 + 5*a^3*b^2)*cosh(d*x + c)^5 + 2*(3*a^5 + 5*a^3*b^2)*cosh(d*x + c)^3 - (3*a^5 + 5*a^3*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + (3*a^5 + 5*a^3*b^2 + 2*a*b^4)*cosh(d*x + c) - (b^5*cosh(d*x + c)^6 + 6*b^5*cosh(d*x + c)*sinh(d*x + c)^5 + b^5*sinh(d*x + c)^6 + b^5*cosh(d*x + c)^4 - b^5*cosh(d*x + c)^2 - b^5 + (15*b^5*cosh(d*x + c)^2 + b^5)*sinh(d*x + c)^4 + 4*(5*b^5*cosh(d*x + c)^3 + b^5*cosh(d*x + c))*sinh(d*x + c)^3 + (15*b^5*cosh(d*x + c)^4 + 6*b^5*cosh(d*x + c)^2 - b^5)*sinh(d*x + c)^2 + 2*(3*b^5*cosh(d*x + c)^5 + 2*b^5*cosh(d*x + c)^3 - b^5*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) - ((a^4*b + 2*a^2*b^3)*cosh(d*x + c)^6 + 6*(a^4*b + 2*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4*b + 2*a^2*b^3)*sinh(d*x + c)^6 - a^4*b - 2*a^2*b^3 + (a^4*b + 2*a^2*b^3)*cosh(d*x + c)^4 + (a^4*b + 2*a^2*b^3 + 15*(a^4*b + 2*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(a^4*b + 2*a^2*b^3)*cosh(d*x + c)^3 + (a^4*b + 2*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - (a^4*b + 2*a^2*b^3)*cosh(d*x + c)^2 - (a^4*b + 2*a^2*b^3 - 15*(a^4*b + 2*a^2*b^3)*cosh(d*x + c)^4 - 6*(a^4*b + 2*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(a^4*b + 2*a^2*b^3)*cosh(d*x + c)^5 + 2*(a^4*b + 2*a^2*b^3)*cosh(d*x + c)^3 - (a^4*b + 2*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + ((a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^6 + 6*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4*b + 2*a^2*b^3 + b^5)*sinh(d*x + c)^6 - a^4*b - 2*a^2*b^3 - b^5 + (a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^4 + (a^4*b + 2*a^2*b^3 + b^5 + 15*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^3 + (a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - (a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^2 - (a^4*b + 2*a^2*b^3 + b^5 - 15*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^4 - 6*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^5 + 2*(a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c)^3 - (a^4*b + 2*a^2*b^3 + b^5)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + (3*a^5 + 5*a^3*b^2 + 2*a*b^4 + 5*(3*a^5 + 5*a^3*b^2 + 2*a*b^4)*cosh(d*x + c)^4 + 8*(a^4*b + a^2*b^3)*cosh(d*x + c)^3 + 6*(a^5 + 3*a^3*b^2 + 2*a*b^4)*cosh(d*x + c)^2 - 4*(a^4*b + a^2*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^6 + 6*(a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^6 + 2*a^4*b^2 + a^2*b^4)*d*sinh(d*x + c)^6 + (a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^4 + (15*(a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^2 + (a^6 + 2*a^4*b^2 + a^2*b^4)*d)*sinh(d*x + c)^4 - (a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^2 + 4*(5*(a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^3 + (a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^4 + 6*(a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^2 - (a^6 + 2*a^4*b^2 + a^2*b^4)*d)*sinh(d*x + c)^2 - (a^6 + 2*a^4*b^2 + a^2*b^4)*d + 2*(3*(a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^5 + 2*(a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c)^3 - (a^6 + 2*a^4*b^2 + a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
475,-1,0,0,0.000000," ","integrate(csch(d*x+c)^2*sech(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,1,11595,0,1.185323," ","integrate((f*x+e)^3*coth(d*x+c)*csch(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a^{2} d^{2} e^{2} f - 6 \, a^{2} c d e f^{2} + 3 \, a^{2} c^{2} f^{3} - 3 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + 2 \, a^{2} c d e f^{2} - a^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + 2 \, a^{2} c d e f^{2} - a^{2} c^{2} f^{3}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + a b d^{3} e^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + a b d^{3} e^{3} - 6 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + 2 \, a^{2} c d e f^{2} - a^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(2 \, a^{2} d^{3} f^{3} x^{3} + 2 \, a^{2} d^{3} e^{3} + 3 \, a^{2} d^{2} e^{2} f - 12 \, a^{2} c d e f^{2} + 6 \, a^{2} c^{2} f^{3} + 3 \, {\left(2 \, a^{2} d^{3} e f^{2} - a^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(a^{2} d^{3} e^{2} f - a^{2} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{2} d^{3} f^{3} x^{3} + 2 \, a^{2} d^{3} e^{3} + 3 \, a^{2} d^{2} e^{2} f - 12 \, a^{2} c d e f^{2} + 6 \, a^{2} c^{2} f^{3} + 3 \, {\left(2 \, a^{2} d^{3} e f^{2} - a^{2} d^{2} f^{3}\right)} x^{2} + 18 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + 2 \, a^{2} c d e f^{2} - a^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} d^{3} e^{2} f - a^{2} d^{2} e f^{2}\right)} x - 6 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + a b d^{3} e^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + a b d^{3} e^{3}\right)} \cosh\left(d x + c\right) - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + a^{2} f^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + a^{2} f^{3} - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x + 4 \, {\left({\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f - 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} - a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + a^{2} f^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + a^{2} f^{3} - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x + 4 \, {\left({\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{3} x^{2} + b^{2} d^{2} e^{2} f + 2 \, a b d e f^{2} + a^{2} f^{3} + 2 \, {\left(b^{2} d^{2} e f^{2} + a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3} + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3} - 3 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3} + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3} - 3 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3} + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3} - 3 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3} + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3} - 3 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, a^{2} d e f^{2} + {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, a^{2} d e f^{2} + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, a^{2} d e f^{2} + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, a^{2} d e f^{2} + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, a^{2} d e f^{2} + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, a^{2} d e f^{2} + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} - 3 \, {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, a^{2} d e f^{2} + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x + 4 \, {\left({\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, a^{2} d e f^{2} + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} f^{3} x^{3} + b^{2} d^{3} e^{3} + 3 \, a b d^{2} e^{2} f + 3 \, a^{2} d e f^{2} + 3 \, {\left(b^{2} d^{3} e f^{2} + a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f + 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} d e f^{2} + {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3}\right)} \sinh\left(d x + c\right)^{4} - {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} - 3 \, {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} e^{3} - 3 \, {\left(b^{2} c + a b\right)} d^{2} e^{2} f + 3 \, {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} d e f^{2} - {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} + {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} - 3 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x + 4 \, {\left({\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} c d^{2} e^{2} f - 3 \, {\left(b^{2} c^{2} + 2 \, a b c\right)} d e f^{2} + {\left(b^{2} c^{3} + 3 \, a b c^{2} + 3 \, a^{2} c\right)} f^{3} + 3 \, {\left(b^{2} d^{3} e f^{2} - a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left(b^{2} d^{3} e^{2} f - 2 \, a b d^{2} e f^{2} + a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 6 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} + b^{2} f^{3} + 2 \, {\left(3 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} - b^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{3} - b^{2} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} + b^{2} f^{3} + 2 \, {\left(3 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} - b^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{3} - b^{2} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} + b^{2} f^{3} + 2 \, {\left(3 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} - b^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{3} - b^{2} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} + b^{2} f^{3} + 2 \, {\left(3 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} - b^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{3} - b^{2} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - 3 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - 3 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3} - 3 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - a b f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 6 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3} - 3 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + a b f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + a b d^{3} e^{3} + 6 \, {\left(a^{2} d^{2} f^{3} x^{2} + 2 \, a^{2} d^{2} e f^{2} x + 2 \, a^{2} c d e f^{2} - a^{2} c^{2} f^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + a b d^{3} e^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} d^{3} f^{3} x^{3} + 2 \, a^{2} d^{3} e^{3} + 3 \, a^{2} d^{2} e^{2} f - 12 \, a^{2} c d e f^{2} + 6 \, a^{2} c^{2} f^{3} + 3 \, {\left(2 \, a^{2} d^{3} e f^{2} - a^{2} d^{2} f^{3}\right)} x^{2} + 6 \, {\left(a^{2} d^{3} e^{2} f - a^{2} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{a^{3} d^{4} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d^{4} \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d^{4} \cosh\left(d x + c\right)^{2} + a^{3} d^{4} + 2 \, {\left(3 \, a^{3} d^{4} \cosh\left(d x + c\right)^{2} - a^{3} d^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d^{4} \cosh\left(d x + c\right)^{3} - a^{3} d^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"(3*a^2*d^2*e^2*f - 6*a^2*c*d*e*f^2 + 3*a^2*c^2*f^3 - 3*(a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + 2*a^2*c*d*e*f^2 - a^2*c^2*f^3)*cosh(d*x + c)^4 - 3*(a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + 2*a^2*c*d*e*f^2 - a^2*c^2*f^3)*sinh(d*x + c)^4 + 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + a*b*d^3*e^3)*cosh(d*x + c)^3 + 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + a*b*d^3*e^3 - 6*(a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + 2*a^2*c*d*e*f^2 - a^2*c^2*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 - (2*a^2*d^3*f^3*x^3 + 2*a^2*d^3*e^3 + 3*a^2*d^2*e^2*f - 12*a^2*c*d*e*f^2 + 6*a^2*c^2*f^3 + 3*(2*a^2*d^3*e*f^2 - a^2*d^2*f^3)*x^2 + 6*(a^2*d^3*e^2*f - a^2*d^2*e*f^2)*x)*cosh(d*x + c)^2 - (2*a^2*d^3*f^3*x^3 + 2*a^2*d^3*e^3 + 3*a^2*d^2*e^2*f - 12*a^2*c*d*e*f^2 + 6*a^2*c^2*f^3 + 3*(2*a^2*d^3*e*f^2 - a^2*d^2*f^3)*x^2 + 18*(a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + 2*a^2*c*d*e*f^2 - a^2*c^2*f^3)*cosh(d*x + c)^2 + 6*(a^2*d^3*e^2*f - a^2*d^2*e*f^2)*x - 6*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + a*b*d^3*e^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + a*b*d^3*e^3)*cosh(d*x + c) - 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*sinh(d*x + c)^4 - 2*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f - 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^3 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*sinh(d*x + c)^4 - 2*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f - 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^3 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 3*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + a^2*f^3 + (b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*sinh(d*x + c)^4 - 2*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + a^2*f^3 - 3*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*cosh(d*x + c)^2 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*sinh(d*x + c)^2 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x + 4*((b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*cosh(d*x + c)^3 - (b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f - 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 - a*b*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + 3*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + a^2*f^3 + (b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*sinh(d*x + c)^4 - 2*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + a^2*f^3 - 3*(b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*cosh(d*x + c)^2 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*sinh(d*x + c)^2 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x + 4*((b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*cosh(d*x + c)^3 - (b^2*d^2*f^3*x^2 + b^2*d^2*e^2*f + 2*a*b*d*e*f^2 + a^2*f^3 + 2*(b^2*d^2*e*f^2 + a*b*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) - (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3 + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^4 + 4*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sinh(d*x + c)^4 - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3 - 3*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^3 - (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3 + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^4 + 4*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sinh(d*x + c)^4 - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3 - 3*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^3 - (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3 + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^4 + 4*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sinh(d*x + c)^4 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3 - 3*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^3 - (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3 + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^4 + 4*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sinh(d*x + c)^4 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3 - 3*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^3 - (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*a^2*d*e*f^2 + (b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*a^2*d*e*f^2 + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c)^4 + 4*(b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*a^2*d*e*f^2 + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*a^2*d*e*f^2 + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*sinh(d*x + c)^4 + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 - 2*(b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*a^2*d*e*f^2 + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*a^2*d*e*f^2 + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 - 3*(b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*a^2*d*e*f^2 + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c)^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*sinh(d*x + c)^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x + 4*((b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*a^2*d*e*f^2 + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c)^3 - (b^2*d^3*f^3*x^3 + b^2*d^3*e^3 + 3*a*b*d^2*e^2*f + 3*a^2*d*e*f^2 + 3*(b^2*d^3*e*f^2 + a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f + 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c + a^2)*d*e*f^2 + (b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c + a^2)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3)*cosh(d*x + c)^4 + 4*(b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c + a^2)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c + a^2)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3)*sinh(d*x + c)^4 - (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 - 2*(b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c + a^2)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3)*cosh(d*x + c)^2 - 2*(b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c + a^2)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 - 3*(b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c + a^2)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c + a^2)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3)*cosh(d*x + c)^3 - (b^2*d^3*e^3 - 3*(b^2*c + a*b)*d^2*e^2*f + 3*(b^2*c^2 + 2*a*b*c + a^2)*d*e*f^2 - (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c)^4 + 4*(b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*sinh(d*x + c)^4 + (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c)^2 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 - 3*(b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c)^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*sinh(d*x + c)^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x + 4*((b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c)^3 - (b^2*d^3*f^3*x^3 + 3*b^2*c*d^2*e^2*f - 3*(b^2*c^2 + 2*a*b*c)*d*e*f^2 + (b^2*c^3 + 3*a*b*c^2 + 3*a^2*c)*f^3 + 3*(b^2*d^3*e*f^2 - a*b*d^2*f^3)*x^2 + 3*(b^2*d^3*e^2*f - 2*a*b*d^2*e*f^2 + a^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 6*(b^2*f^3*cosh(d*x + c)^4 + 4*b^2*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^3*sinh(d*x + c)^4 - 2*b^2*f^3*cosh(d*x + c)^2 + b^2*f^3 + 2*(3*b^2*f^3*cosh(d*x + c)^2 - b^2*f^3)*sinh(d*x + c)^2 + 4*(b^2*f^3*cosh(d*x + c)^3 - b^2*f^3*cosh(d*x + c))*sinh(d*x + c))*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b^2*f^3*cosh(d*x + c)^4 + 4*b^2*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^3*sinh(d*x + c)^4 - 2*b^2*f^3*cosh(d*x + c)^2 + b^2*f^3 + 2*(3*b^2*f^3*cosh(d*x + c)^2 - b^2*f^3)*sinh(d*x + c)^2 + 4*(b^2*f^3*cosh(d*x + c)^3 - b^2*f^3*cosh(d*x + c))*sinh(d*x + c))*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b^2*f^3*cosh(d*x + c)^4 + 4*b^2*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^3*sinh(d*x + c)^4 - 2*b^2*f^3*cosh(d*x + c)^2 + b^2*f^3 + 2*(3*b^2*f^3*cosh(d*x + c)^2 - b^2*f^3)*sinh(d*x + c)^2 + 4*(b^2*f^3*cosh(d*x + c)^3 - b^2*f^3*cosh(d*x + c))*sinh(d*x + c))*polylog(4, cosh(d*x + c) + sinh(d*x + c)) + 6*(b^2*f^3*cosh(d*x + c)^4 + 4*b^2*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^3*sinh(d*x + c)^4 - 2*b^2*f^3*cosh(d*x + c)^2 + b^2*f^3 + 2*(3*b^2*f^3*cosh(d*x + c)^2 - b^2*f^3)*sinh(d*x + c)^2 + 4*(b^2*f^3*cosh(d*x + c)^3 - b^2*f^3*cosh(d*x + c))*sinh(d*x + c))*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) + 6*(b^2*d*f^3*x + b^2*d*e*f^2 + (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^4 + 4*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^3*x + b^2*d*e*f^2)*sinh(d*x + c)^4 - 2*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2 - 2*(b^2*d*f^3*x + b^2*d*e*f^2 - 3*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^3 - (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 6*(b^2*d*f^3*x + b^2*d*e*f^2 + (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^4 + 4*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^3*x + b^2*d*e*f^2)*sinh(d*x + c)^4 - 2*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2 - 2*(b^2*d*f^3*x + b^2*d*e*f^2 - 3*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^3 - (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 6*(b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3 + (b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*cosh(d*x + c)^4 + 4*(b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*sinh(d*x + c)^4 - 2*(b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*cosh(d*x + c)^2 - 2*(b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3 - 3*(b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*cosh(d*x + c)^3 - (b^2*d*f^3*x + b^2*d*e*f^2 - a*b*f^3)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 6*(b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3 + (b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*cosh(d*x + c)^4 + 4*(b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*sinh(d*x + c)^4 - 2*(b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*cosh(d*x + c)^2 - 2*(b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3 - 3*(b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*cosh(d*x + c)^3 - (b^2*d*f^3*x + b^2*d*e*f^2 + a*b*f^3)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 2*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + a*b*d^3*e^3 + 6*(a^2*d^2*f^3*x^2 + 2*a^2*d^2*e*f^2*x + 2*a^2*c*d*e*f^2 - a^2*c^2*f^3)*cosh(d*x + c)^3 - 3*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + a*b*d^3*e^3)*cosh(d*x + c)^2 + (2*a^2*d^3*f^3*x^3 + 2*a^2*d^3*e^3 + 3*a^2*d^2*e^2*f - 12*a^2*c*d*e*f^2 + 6*a^2*c^2*f^3 + 3*(2*a^2*d^3*e*f^2 - a^2*d^2*f^3)*x^2 + 6*(a^2*d^3*e^2*f - a^2*d^2*e*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(a^3*d^4*cosh(d*x + c)^4 + 4*a^3*d^4*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d^4*sinh(d*x + c)^4 - 2*a^3*d^4*cosh(d*x + c)^2 + a^3*d^4 + 2*(3*a^3*d^4*cosh(d*x + c)^2 - a^3*d^4)*sinh(d*x + c)^2 + 4*(a^3*d^4*cosh(d*x + c)^3 - a^3*d^4*cosh(d*x + c))*sinh(d*x + c))","C",0
477,1,6479,0,1.025072," ","integrate((f*x+e)^2*coth(d*x+c)*csch(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a^{2} d e f - 2 \, a^{2} c f^{2} - 2 \, {\left(a^{2} d f^{2} x + a^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} d f^{2} x + a^{2} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2} - 4 \, {\left(a^{2} d f^{2} x + a^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} + a^{2} d e f - 2 \, a^{2} c f^{2} + {\left(2 \, a^{2} d^{2} e f - a^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} + a^{2} d e f - 2 \, a^{2} c f^{2} + 6 \, {\left(a^{2} d f^{2} x + a^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} d^{2} e f - a^{2} d f^{2}\right)} x - 3 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f - 3 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f - 3 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f + {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2}\right)} \sinh\left(d x + c\right)^{4} - a b f^{2} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2} - 3 \, {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{2} x + b^{2} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f + {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2}\right)} \sinh\left(d x + c\right)^{4} + a b f^{2} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2} - 3 \, {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{2} x + b^{2} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2} - 3 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2} - 3 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2} + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2} - 3 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2} + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2} - 3 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} + a^{2} f^{2} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} - 3 \, {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x + 4 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{2} x^{2} + b^{2} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left(b^{2} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left(b^{2} d^{2} e^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} f^{2} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} f^{2} - 3 \, {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} e^{2} - 2 \, {\left(b^{2} c + a b\right)} d e f + {\left(b^{2} c^{2} + 2 \, a b c + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} - 3 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x + 4 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d e f - {\left(b^{2} c^{2} + 2 \, a b c\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} + b^{2} f^{2} + 2 \, {\left(3 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} - b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{3} - b^{2} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} + b^{2} f^{2} + 2 \, {\left(3 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} - b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{3} - b^{2} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} + b^{2} f^{2} + 2 \, {\left(3 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} - b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{3} - b^{2} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} + b^{2} f^{2} + 2 \, {\left(3 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} - b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{3} - b^{2} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2} + 4 \, {\left(a^{2} d f^{2} x + a^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} + a^{2} d e f - 2 \, a^{2} c f^{2} + {\left(2 \, a^{2} d^{2} e f - a^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{a^{3} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d^{3} \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d^{3} \cosh\left(d x + c\right)^{2} + a^{3} d^{3} + 2 \, {\left(3 \, a^{3} d^{3} \cosh\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d^{3} \cosh\left(d x + c\right)^{3} - a^{3} d^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"(2*a^2*d*e*f - 2*a^2*c*f^2 - 2*(a^2*d*f^2*x + a^2*c*f^2)*cosh(d*x + c)^4 - 2*(a^2*d*f^2*x + a^2*c*f^2)*sinh(d*x + c)^4 + 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2)*cosh(d*x + c)^3 + 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2 - 4*(a^2*d*f^2*x + a^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 + a^2*d*e*f - 2*a^2*c*f^2 + (2*a^2*d^2*e*f - a^2*d*f^2)*x)*cosh(d*x + c)^2 - 2*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 + a^2*d*e*f - 2*a^2*c*f^2 + 6*(a^2*d*f^2*x + a^2*c*f^2)*cosh(d*x + c)^2 + (2*a^2*d^2*e*f - a^2*d*f^2)*x - 3*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2)*cosh(d*x + c) - 2*(b^2*d*f^2*x + b^2*d*e*f + (b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^4 + 4*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^2*x + b^2*d*e*f)*sinh(d*x + c)^4 - 2*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^2 - 2*(b^2*d*f^2*x + b^2*d*e*f - 3*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^3 - (b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b^2*d*f^2*x + b^2*d*e*f + (b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^4 + 4*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^2*x + b^2*d*e*f)*sinh(d*x + c)^4 - 2*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^2 - 2*(b^2*d*f^2*x + b^2*d*e*f - 3*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^3 - (b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^2*d*f^2*x + b^2*d*e*f + (b^2*d*f^2*x + b^2*d*e*f - a*b*f^2)*cosh(d*x + c)^4 + 4*(b^2*d*f^2*x + b^2*d*e*f - a*b*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^2*x + b^2*d*e*f - a*b*f^2)*sinh(d*x + c)^4 - a*b*f^2 - 2*(b^2*d*f^2*x + b^2*d*e*f - a*b*f^2)*cosh(d*x + c)^2 - 2*(b^2*d*f^2*x + b^2*d*e*f - a*b*f^2 - 3*(b^2*d*f^2*x + b^2*d*e*f - a*b*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^2*x + b^2*d*e*f - a*b*f^2)*cosh(d*x + c)^3 - (b^2*d*f^2*x + b^2*d*e*f - a*b*f^2)*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + 2*(b^2*d*f^2*x + b^2*d*e*f + (b^2*d*f^2*x + b^2*d*e*f + a*b*f^2)*cosh(d*x + c)^4 + 4*(b^2*d*f^2*x + b^2*d*e*f + a*b*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^2*x + b^2*d*e*f + a*b*f^2)*sinh(d*x + c)^4 + a*b*f^2 - 2*(b^2*d*f^2*x + b^2*d*e*f + a*b*f^2)*cosh(d*x + c)^2 - 2*(b^2*d*f^2*x + b^2*d*e*f + a*b*f^2 - 3*(b^2*d*f^2*x + b^2*d*e*f + a*b*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^2*x + b^2*d*e*f + a*b*f^2)*cosh(d*x + c)^3 - (b^2*d*f^2*x + b^2*d*e*f + a*b*f^2)*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) - (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2 + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2 - 3*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^3 - (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2 + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2 - 3*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^3 - (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2 + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2 - 3*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^3 - (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2 + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2 - 3*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^3 - (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + (b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*sinh(d*x + c)^4 + a^2*f^2 - 2*(b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 - 3*(b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)^2 + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*sinh(d*x + c)^2 + 2*(b^2*d^2*e*f + a*b*d*f^2)*x + 4*((b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)^3 - (b^2*d^2*f^2*x^2 + b^2*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*(b^2*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (b^2*d^2*e^2 + (b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c + a^2)*f^2)*cosh(d*x + c)^4 + 4*(b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c + a^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c + a^2)*f^2)*sinh(d*x + c)^4 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c + a^2)*f^2 - 2*(b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c + a^2)*f^2)*cosh(d*x + c)^2 - 2*(b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c + a^2)*f^2 - 3*(b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c + a^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c + a^2)*f^2)*cosh(d*x + c)^3 - (b^2*d^2*e^2 - 2*(b^2*c + a*b)*d*e*f + (b^2*c^2 + 2*a*b*c + a^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f + (b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*sinh(d*x + c)^4 - (b^2*c^2 + 2*a*b*c)*f^2 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 - 3*(b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*sinh(d*x + c)^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x + 4*((b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^3 - (b^2*d^2*f^2*x^2 + 2*b^2*c*d*e*f - (b^2*c^2 + 2*a*b*c)*f^2 + 2*(b^2*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 2*(b^2*f^2*cosh(d*x + c)^4 + 4*b^2*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^2*sinh(d*x + c)^4 - 2*b^2*f^2*cosh(d*x + c)^2 + b^2*f^2 + 2*(3*b^2*f^2*cosh(d*x + c)^2 - b^2*f^2)*sinh(d*x + c)^2 + 4*(b^2*f^2*cosh(d*x + c)^3 - b^2*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*(b^2*f^2*cosh(d*x + c)^4 + 4*b^2*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^2*sinh(d*x + c)^4 - 2*b^2*f^2*cosh(d*x + c)^2 + b^2*f^2 + 2*(3*b^2*f^2*cosh(d*x + c)^2 - b^2*f^2)*sinh(d*x + c)^2 + 4*(b^2*f^2*cosh(d*x + c)^3 - b^2*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(b^2*f^2*cosh(d*x + c)^4 + 4*b^2*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^2*sinh(d*x + c)^4 - 2*b^2*f^2*cosh(d*x + c)^2 + b^2*f^2 + 2*(3*b^2*f^2*cosh(d*x + c)^2 - b^2*f^2)*sinh(d*x + c)^2 + 4*(b^2*f^2*cosh(d*x + c)^3 - b^2*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 2*(b^2*f^2*cosh(d*x + c)^4 + 4*b^2*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^2*sinh(d*x + c)^4 - 2*b^2*f^2*cosh(d*x + c)^2 + b^2*f^2 + 2*(3*b^2*f^2*cosh(d*x + c)^2 - b^2*f^2)*sinh(d*x + c)^2 + 4*(b^2*f^2*cosh(d*x + c)^3 - b^2*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2 + 4*(a^2*d*f^2*x + a^2*c*f^2)*cosh(d*x + c)^3 - 3*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2)*cosh(d*x + c)^2 + 2*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 + a^2*d*e*f - 2*a^2*c*f^2 + (2*a^2*d^2*e*f - a^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(a^3*d^3*cosh(d*x + c)^4 + 4*a^3*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d^3*sinh(d*x + c)^4 - 2*a^3*d^3*cosh(d*x + c)^2 + a^3*d^3 + 2*(3*a^3*d^3*cosh(d*x + c)^2 - a^3*d^3)*sinh(d*x + c)^2 + 4*(a^3*d^3*cosh(d*x + c)^3 - a^3*d^3*cosh(d*x + c))*sinh(d*x + c))","C",0
478,1,2899,0,0.741206," ","integrate((f*x+e)*coth(d*x+c)*csch(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a b d f x + a b d e\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a b d f x + a b d e\right)} \sinh\left(d x + c\right)^{3} + a^{2} f - {\left(2 \, a^{2} d f x + 2 \, a^{2} d e + a^{2} f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{2} d f x + 2 \, a^{2} d e + a^{2} f - 6 \, {\left(a b d f x + a b d e\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d f x + a b d e\right)} \cosh\left(d x + c\right) - {\left(b^{2} f \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f \cosh\left(d x + c\right)^{2} + b^{2} f + 2 \, {\left(3 \, b^{2} f \cosh\left(d x + c\right)^{2} - b^{2} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f \cosh\left(d x + c\right)^{3} - b^{2} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{2} f \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f \cosh\left(d x + c\right)^{2} + b^{2} f + 2 \, {\left(3 \, b^{2} f \cosh\left(d x + c\right)^{2} - b^{2} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f \cosh\left(d x + c\right)^{3} - b^{2} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left(b^{2} f \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f \cosh\left(d x + c\right)^{2} + b^{2} f + 2 \, {\left(3 \, b^{2} f \cosh\left(d x + c\right)^{2} - b^{2} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f \cosh\left(d x + c\right)^{3} - b^{2} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(b^{2} f \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f \cosh\left(d x + c\right)^{2} + b^{2} f + 2 \, {\left(3 \, b^{2} f \cosh\left(d x + c\right)^{2} - b^{2} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f \cosh\left(d x + c\right)^{3} - b^{2} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left({\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d e - b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + b^{2} d e - b^{2} c f - 2 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d e - b^{2} c f - 3 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left({\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d e - b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + b^{2} d e - b^{2} c f - 2 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d e - b^{2} c f - 3 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{2} d f x + {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f x + b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + b^{2} c f - 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f x + b^{2} c f - 3 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{2} d f x + {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f x + b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + b^{2} c f - 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f x + b^{2} c f - 3 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{2} d f x + {\left(b^{2} d f x + b^{2} d e + a b f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f x + b^{2} d e + a b f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f x + b^{2} d e + a b f\right)} \sinh\left(d x + c\right)^{4} + b^{2} d e + a b f - 2 \, {\left(b^{2} d f x + b^{2} d e + a b f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f x + b^{2} d e + a b f - 3 \, {\left(b^{2} d f x + b^{2} d e + a b f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f x + b^{2} d e + a b f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f x + b^{2} d e + a b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \sinh\left(d x + c\right)^{4} + b^{2} d e - 2 \, {\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d e - 3 \, {\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} c + a b\right)} f\right)} \sinh\left(d x + c\right)^{2} - {\left(b^{2} c + a b\right)} f + 4 \, {\left({\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d e - {\left(b^{2} c + a b\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(b^{2} d f x + {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f x + b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + b^{2} c f - 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f x + b^{2} c f - 3 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left(a b d f x + a b d e - 3 \, {\left(a b d f x + a b d e\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} d f x + 2 \, a^{2} d e + a^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{a^{3} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d^{2} \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d^{2} \cosh\left(d x + c\right)^{2} + a^{3} d^{2} + 2 \, {\left(3 \, a^{3} d^{2} \cosh\left(d x + c\right)^{2} - a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d^{2} \cosh\left(d x + c\right)^{3} - a^{3} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"(2*(a*b*d*f*x + a*b*d*e)*cosh(d*x + c)^3 + 2*(a*b*d*f*x + a*b*d*e)*sinh(d*x + c)^3 + a^2*f - (2*a^2*d*f*x + 2*a^2*d*e + a^2*f)*cosh(d*x + c)^2 - (2*a^2*d*f*x + 2*a^2*d*e + a^2*f - 6*(a*b*d*f*x + a*b*d*e)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(a*b*d*f*x + a*b*d*e)*cosh(d*x + c) - (b^2*f*cosh(d*x + c)^4 + 4*b^2*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f*sinh(d*x + c)^4 - 2*b^2*f*cosh(d*x + c)^2 + b^2*f + 2*(3*b^2*f*cosh(d*x + c)^2 - b^2*f)*sinh(d*x + c)^2 + 4*(b^2*f*cosh(d*x + c)^3 - b^2*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^2*f*cosh(d*x + c)^4 + 4*b^2*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f*sinh(d*x + c)^4 - 2*b^2*f*cosh(d*x + c)^2 + b^2*f + 2*(3*b^2*f*cosh(d*x + c)^2 - b^2*f)*sinh(d*x + c)^2 + 4*(b^2*f*cosh(d*x + c)^3 - b^2*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + (b^2*f*cosh(d*x + c)^4 + 4*b^2*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f*sinh(d*x + c)^4 - 2*b^2*f*cosh(d*x + c)^2 + b^2*f + 2*(3*b^2*f*cosh(d*x + c)^2 - b^2*f)*sinh(d*x + c)^2 + 4*(b^2*f*cosh(d*x + c)^3 - b^2*f*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + (b^2*f*cosh(d*x + c)^4 + 4*b^2*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f*sinh(d*x + c)^4 - 2*b^2*f*cosh(d*x + c)^2 + b^2*f + 2*(3*b^2*f*cosh(d*x + c)^2 - b^2*f)*sinh(d*x + c)^2 + 4*(b^2*f*cosh(d*x + c)^3 - b^2*f*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) - ((b^2*d*e - b^2*c*f)*cosh(d*x + c)^4 + 4*(b^2*d*e - b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*e - b^2*c*f)*sinh(d*x + c)^4 + b^2*d*e - b^2*c*f - 2*(b^2*d*e - b^2*c*f)*cosh(d*x + c)^2 - 2*(b^2*d*e - b^2*c*f - 3*(b^2*d*e - b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*e - b^2*c*f)*cosh(d*x + c)^3 - (b^2*d*e - b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - ((b^2*d*e - b^2*c*f)*cosh(d*x + c)^4 + 4*(b^2*d*e - b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*e - b^2*c*f)*sinh(d*x + c)^4 + b^2*d*e - b^2*c*f - 2*(b^2*d*e - b^2*c*f)*cosh(d*x + c)^2 - 2*(b^2*d*e - b^2*c*f - 3*(b^2*d*e - b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*e - b^2*c*f)*cosh(d*x + c)^3 - (b^2*d*e - b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^2*d*f*x + (b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^4 + 4*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f*x + b^2*c*f)*sinh(d*x + c)^4 + b^2*c*f - 2*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2 - 2*(b^2*d*f*x + b^2*c*f - 3*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^3 - (b^2*d*f*x + b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^2*d*f*x + (b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^4 + 4*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f*x + b^2*c*f)*sinh(d*x + c)^4 + b^2*c*f - 2*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2 - 2*(b^2*d*f*x + b^2*c*f - 3*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^3 - (b^2*d*f*x + b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^2*d*f*x + (b^2*d*f*x + b^2*d*e + a*b*f)*cosh(d*x + c)^4 + 4*(b^2*d*f*x + b^2*d*e + a*b*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f*x + b^2*d*e + a*b*f)*sinh(d*x + c)^4 + b^2*d*e + a*b*f - 2*(b^2*d*f*x + b^2*d*e + a*b*f)*cosh(d*x + c)^2 - 2*(b^2*d*f*x + b^2*d*e + a*b*f - 3*(b^2*d*f*x + b^2*d*e + a*b*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f*x + b^2*d*e + a*b*f)*cosh(d*x + c)^3 - (b^2*d*f*x + b^2*d*e + a*b*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((b^2*d*e - (b^2*c + a*b)*f)*cosh(d*x + c)^4 + 4*(b^2*d*e - (b^2*c + a*b)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*e - (b^2*c + a*b)*f)*sinh(d*x + c)^4 + b^2*d*e - 2*(b^2*d*e - (b^2*c + a*b)*f)*cosh(d*x + c)^2 - 2*(b^2*d*e - 3*(b^2*d*e - (b^2*c + a*b)*f)*cosh(d*x + c)^2 - (b^2*c + a*b)*f)*sinh(d*x + c)^2 - (b^2*c + a*b)*f + 4*((b^2*d*e - (b^2*c + a*b)*f)*cosh(d*x + c)^3 - (b^2*d*e - (b^2*c + a*b)*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (b^2*d*f*x + (b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^4 + 4*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f*x + b^2*c*f)*sinh(d*x + c)^4 + b^2*c*f - 2*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2 - 2*(b^2*d*f*x + b^2*c*f - 3*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^3 - (b^2*d*f*x + b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*(a*b*d*f*x + a*b*d*e - 3*(a*b*d*f*x + a*b*d*e)*cosh(d*x + c)^2 + (2*a^2*d*f*x + 2*a^2*d*e + a^2*f)*cosh(d*x + c))*sinh(d*x + c))/(a^3*d^2*cosh(d*x + c)^4 + 4*a^3*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d^2*sinh(d*x + c)^4 - 2*a^3*d^2*cosh(d*x + c)^2 + a^3*d^2 + 2*(3*a^3*d^2*cosh(d*x + c)^2 - a^3*d^2)*sinh(d*x + c)^2 + 4*(a^3*d^2*cosh(d*x + c)^3 - a^3*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
479,1,545,0,1.542179," ","integrate(coth(d*x+c)*csch(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a b \cosh\left(d x + c\right)^{3} + 2 \, a b \sinh\left(d x + c\right)^{3} - 2 \, a^{2} \cosh\left(d x + c\right)^{2} - 2 \, a b \cosh\left(d x + c\right) + 2 \, {\left(3 \, a b \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} - b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} - b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(3 \, a b \cosh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) - a b\right)} \sinh\left(d x + c\right)}{a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d \cosh\left(d x + c\right)^{2} + a^{3} d + 2 \, {\left(3 \, a^{3} d \cosh\left(d x + c\right)^{2} - a^{3} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d \cosh\left(d x + c\right)^{3} - a^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"(2*a*b*cosh(d*x + c)^3 + 2*a*b*sinh(d*x + c)^3 - 2*a^2*cosh(d*x + c)^2 - 2*a*b*cosh(d*x + c) + 2*(3*a*b*cosh(d*x + c) - a^2)*sinh(d*x + c)^2 - (b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 - 2*b^2*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^2 + b^2 + 4*(b^2*cosh(d*x + c)^3 - b^2*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + (b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 - 2*b^2*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^2 + b^2 + 4*(b^2*cosh(d*x + c)^3 - b^2*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(3*a*b*cosh(d*x + c)^2 - 2*a^2*cosh(d*x + c) - a*b)*sinh(d*x + c))/(a^3*d*cosh(d*x + c)^4 + 4*a^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d*sinh(d*x + c)^4 - 2*a^3*d*cosh(d*x + c)^2 + a^3*d + 2*(3*a^3*d*cosh(d*x + c)^2 - a^3*d)*sinh(d*x + c)^2 + 4*(a^3*d*cosh(d*x + c)^3 - a^3*d*cosh(d*x + c))*sinh(d*x + c))","B",0
480,0,0,0,2.590846," ","integrate(coth(d*x+c)*csch(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(d x + c\right) \operatorname{csch}\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(coth(d*x + c)*csch(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
481,1,13504,0,1.497971," ","integrate((f*x+e)^3*coth(d*x+c)^2*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a b d^{3} e^{3} - 12 \, a b c d^{2} e^{2} f + 12 \, a b c^{2} d e f^{2} - 4 \, a b c^{3} f^{3} - 4 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + a^{2} d^{3} e^{3} + 3 \, a^{2} d^{2} e^{2} f + 3 \, {\left(a^{2} d^{3} e f^{2} + a^{2} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a^{2} d^{3} e^{2} f + 2 \, a^{2} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + a^{2} d^{3} e^{3} + 3 \, a^{2} d^{2} e^{2} f + 3 \, {\left(a^{2} d^{3} e f^{2} + a^{2} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a^{2} d^{3} e^{2} f + 2 \, a^{2} d^{2} e f^{2}\right)} x - 8 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x - a b d^{3} e^{3} + 6 \, a b c d^{2} e^{2} f - 6 \, a b c^{2} d e f^{2} + 2 \, a b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a b d^{3} f^{3} x^{3} + 6 \, a b d^{3} e f^{2} x^{2} + 6 \, a b d^{3} e^{2} f x - 2 \, a b d^{3} e^{3} + 12 \, a b c d^{2} e^{2} f - 12 \, a b c^{2} d e f^{2} + 4 \, a b c^{3} f^{3} - 12 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + a^{2} d^{3} e^{3} + 3 \, a^{2} d^{2} e^{2} f + 3 \, {\left(a^{2} d^{3} e f^{2} + a^{2} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a^{2} d^{3} e^{2} f + 2 \, a^{2} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 6 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f - 3 \, {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{3} x^{2} + 2 \, b^{2} d^{2} e f^{2} x + b^{2} d^{2} e^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3} + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3} - 3 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3} + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3} - 3 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3} + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3} - 3 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3} + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3} - 3 \, {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{3} f^{3} x^{3} + 3 \, b^{2} d^{3} e f^{2} x^{2} + 3 \, b^{2} d^{3} e^{2} f x + 3 \, b^{2} c d^{2} e^{2} f - 3 \, b^{2} c^{2} d e f^{2} + b^{2} c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 12 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} + b^{2} f^{3} + 2 \, {\left(3 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} - b^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{3} - b^{2} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{3} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} + b^{2} f^{3} + 2 \, {\left(3 \, b^{2} f^{3} \cosh\left(d x + c\right)^{2} - b^{2} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{3} \cosh\left(d x + c\right)^{3} - b^{2} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(4, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 12 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - 3 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 12 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2} - 3 \, {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{3} x + b^{2} d e f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + a^{2} d^{3} e^{3} - 3 \, a^{2} d^{2} e^{2} f + 3 \, {\left(a^{2} d^{3} e f^{2} - a^{2} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a^{2} d^{3} e^{2} f - 2 \, a^{2} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right) - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f - 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f - 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} - 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f - 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} - 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f - 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} - 2 \, a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f - 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} - 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f - 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f - 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} - 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} - 2 \, a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} - 2 \, a b d f^{3}\right)} x + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f - 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} - 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f - 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} - 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f + 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f + 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f + 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f + 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f + 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f + 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f + 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f + 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{3} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} f + 4 \, a b d e f^{2} + 2 \, a^{2} f^{3} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f^{2} + 2 \, a b d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} + 6 \, a b d^{2} e^{2} f + 6 \, a^{2} d e f^{2} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} + 6 \, a b d^{2} e^{2} f + 6 \, a^{2} d e f^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} + 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f + 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} + 6 \, a b d^{2} e^{2} f + 6 \, a^{2} d e f^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} + 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f + 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} + 6 \, a b d^{2} e^{2} f + 6 \, a^{2} d e f^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} + 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f + 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} + 2 \, a b d^{2} f^{3}\right)} x^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} + 6 \, a b d^{2} e^{2} f + 6 \, a^{2} d e f^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} + 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f + 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} + 6 \, a b d^{2} e^{2} f + 6 \, a^{2} d e f^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} + 2 \, a b d^{2} f^{3}\right)} x^{2} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} + 6 \, a b d^{2} e^{2} f + 6 \, a^{2} d e f^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} + 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f + 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f + 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f + 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} + 6 \, a b d^{2} e^{2} f + 6 \, a^{2} d e f^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} + 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f + 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + {\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} + 6 \, a b d^{2} e^{2} f + 6 \, a^{2} d e f^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} + 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f + 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} d e f^{2} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} d e f^{2} - {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} d e f^{2} - {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} d e f^{2} - {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3}\right)} \sinh\left(d x + c\right)^{4} - {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} d e f^{2} - {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} d e f^{2} - {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} d e f^{2} - {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} d e f^{2} - {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{3} - 3 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d^{2} e^{2} f + 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} d e f^{2} - {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} d e f^{2} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} d e f^{2} + {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} - 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f - 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} d e f^{2} + {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} - 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f - 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} d e f^{2} + {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} - 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f - 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{4} + {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} - 2 \, a b d^{2} f^{3}\right)} x^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} d e f^{2} + {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} - 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f - 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} d e f^{2} + {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} - 2 \, a b d^{2} f^{3}\right)} x^{2} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} d e f^{2} + {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} - 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f - 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f - 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f - 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} d e f^{2} + {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} - 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f - 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} c d^{2} e^{2} f - 3 \, {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} d e f^{2} + {\left(6 \, a b c^{2} + {\left(a^{2} + 2 \, b^{2}\right)} c^{3} + 6 \, a^{2} c\right)} f^{3} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e f^{2} - 2 \, a b d^{2} f^{3}\right)} x^{2} + 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{3} e^{2} f - 4 \, a b d^{2} e f^{2} + 2 \, a^{2} d f^{3}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 6 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, b^{2}\right)} f^{3} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, b^{2}\right)} f^{3} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, b^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, b^{2}\right)} f^{3} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, b^{2}\right)} f^{3} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, b^{2}\right)} f^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} f^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(4, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 6 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} - 2 \, a b f^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} - 2 \, a b f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} - 2 \, a b f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} - 2 \, a b f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} - 2 \, a b f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} - 2 \, a b f^{3} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} - 2 \, a b f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} - 2 \, a b f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} - 2 \, a b f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 6 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} + 2 \, a b f^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} + 2 \, a b f^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} + 2 \, a b f^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} + 2 \, a b f^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} + 2 \, a b f^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} + 2 \, a b f^{3} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} + 2 \, a b f^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} + 2 \, a b f^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{3} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f^{2} + 2 \, a b f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left(a^{2} d^{3} f^{3} x^{3} + a^{2} d^{3} e^{3} - 3 \, a^{2} d^{2} e^{2} f - 8 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x + 3 \, a b c d^{2} e^{2} f - 3 \, a b c^{2} d e f^{2} + a b c^{3} f^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} d^{3} e f^{2} - a^{2} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a^{2} d^{3} f^{3} x^{3} + a^{2} d^{3} e^{3} + 3 \, a^{2} d^{2} e^{2} f + 3 \, {\left(a^{2} d^{3} e f^{2} + a^{2} d^{2} f^{3}\right)} x^{2} + 3 \, {\left(a^{2} d^{3} e^{2} f + 2 \, a^{2} d^{2} e f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(a^{2} d^{3} e^{2} f - 2 \, a^{2} d^{2} e f^{2}\right)} x + 4 \, {\left(a b d^{3} f^{3} x^{3} + 3 \, a b d^{3} e f^{2} x^{2} + 3 \, a b d^{3} e^{2} f x - a b d^{3} e^{3} + 6 \, a b c d^{2} e^{2} f - 6 \, a b c^{2} d e f^{2} + 2 \, a b c^{3} f^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{3} d^{4} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d^{4} \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d^{4} \cosh\left(d x + c\right)^{2} + a^{3} d^{4} + 2 \, {\left(3 \, a^{3} d^{4} \cosh\left(d x + c\right)^{2} - a^{3} d^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d^{4} \cosh\left(d x + c\right)^{3} - a^{3} d^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(4*a*b*d^3*e^3 - 12*a*b*c*d^2*e^2*f + 12*a*b*c^2*d*e*f^2 - 4*a*b*c^3*f^3 - 4*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*cosh(d*x + c)^4 - 4*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*sinh(d*x + c)^4 + 2*(a^2*d^3*f^3*x^3 + a^2*d^3*e^3 + 3*a^2*d^2*e^2*f + 3*(a^2*d^3*e*f^2 + a^2*d^2*f^3)*x^2 + 3*(a^2*d^3*e^2*f + 2*a^2*d^2*e*f^2)*x)*cosh(d*x + c)^3 + 2*(a^2*d^3*f^3*x^3 + a^2*d^3*e^3 + 3*a^2*d^2*e^2*f + 3*(a^2*d^3*e*f^2 + a^2*d^2*f^3)*x^2 + 3*(a^2*d^3*e^2*f + 2*a^2*d^2*e*f^2)*x - 8*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x - a*b*d^3*e^3 + 6*a*b*c*d^2*e^2*f - 6*a*b*c^2*d*e*f^2 + 2*a*b*c^3*f^3)*cosh(d*x + c)^2 + 2*(2*a*b*d^3*f^3*x^3 + 6*a*b*d^3*e*f^2*x^2 + 6*a*b*d^3*e^2*f*x - 2*a*b*d^3*e^3 + 12*a*b*c*d^2*e^2*f - 12*a*b*c^2*d*e*f^2 + 4*a*b*c^3*f^3 - 12*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*cosh(d*x + c)^2 + 3*(a^2*d^3*f^3*x^3 + a^2*d^3*e^3 + 3*a^2*d^2*e^2*f + 3*(a^2*d^3*e*f^2 + a^2*d^2*f^3)*x^2 + 3*(a^2*d^3*e^2*f + 2*a^2*d^2*e*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 6*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*sinh(d*x + c)^4 - 2*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f - 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^3 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 6*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*sinh(d*x + c)^4 - 2*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f - 3*(b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c)^3 - (b^2*d^2*f^3*x^2 + 2*b^2*d^2*e*f^2*x + b^2*d^2*e^2*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3 + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^4 + 4*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sinh(d*x + c)^4 - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3 - 3*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^3 - (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3 + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^4 + 4*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*sinh(d*x + c)^4 - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3 - 3*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c)^3 - (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3 + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^4 + 4*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sinh(d*x + c)^4 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3 - 3*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^3 - (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3 + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^4 + 4*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*sinh(d*x + c)^4 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^2 - 2*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3 - 3*(b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c)^3 - (b^2*d^3*f^3*x^3 + 3*b^2*d^3*e*f^2*x^2 + 3*b^2*d^3*e^2*f*x + 3*b^2*c*d^2*e^2*f - 3*b^2*c^2*d*e*f^2 + b^2*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 12*(b^2*f^3*cosh(d*x + c)^4 + 4*b^2*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^3*sinh(d*x + c)^4 - 2*b^2*f^3*cosh(d*x + c)^2 + b^2*f^3 + 2*(3*b^2*f^3*cosh(d*x + c)^2 - b^2*f^3)*sinh(d*x + c)^2 + 4*(b^2*f^3*cosh(d*x + c)^3 - b^2*f^3*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(b^2*f^3*cosh(d*x + c)^4 + 4*b^2*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^3*sinh(d*x + c)^4 - 2*b^2*f^3*cosh(d*x + c)^2 + b^2*f^3 + 2*(3*b^2*f^3*cosh(d*x + c)^2 - b^2*f^3)*sinh(d*x + c)^2 + 4*(b^2*f^3*cosh(d*x + c)^3 - b^2*f^3*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(4, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 12*(b^2*d*f^3*x + b^2*d*e*f^2 + (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^4 + 4*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^3*x + b^2*d*e*f^2)*sinh(d*x + c)^4 - 2*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2 - 2*(b^2*d*f^3*x + b^2*d*e*f^2 - 3*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^3 - (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 12*(b^2*d*f^3*x + b^2*d*e*f^2 + (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^4 + 4*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^3*x + b^2*d*e*f^2)*sinh(d*x + c)^4 - 2*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2 - 2*(b^2*d*f^3*x + b^2*d*e*f^2 - 3*(b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c)^3 - (b^2*d*f^3*x + b^2*d*e*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*(a^2*d^3*f^3*x^3 + a^2*d^3*e^3 - 3*a^2*d^2*e^2*f + 3*(a^2*d^3*e*f^2 - a^2*d^2*f^3)*x^2 + 3*(a^2*d^3*e^2*f - 2*a^2*d^2*e*f^2)*x)*cosh(d*x + c) - 3*((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f - 4*a*b*d*e*f^2 + 2*a^2*f^3 + ((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f - 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 - 2*a*b*d*f^3)*x)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f - 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 - 2*a*b*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f - 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 - 2*a*b*d*f^3)*x)*sinh(d*x + c)^4 - 2*((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f - 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 - 2*a*b*d*f^3)*x)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f - 4*a*b*d*e*f^2 + 2*a^2*f^3 - 3*((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f - 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 - 2*a*b*d*f^3)*x)*cosh(d*x + c)^2 + 2*((a^2 + 2*b^2)*d^2*e*f^2 - 2*a*b*d*f^3)*x)*sinh(d*x + c)^2 + 2*((a^2 + 2*b^2)*d^2*e*f^2 - 2*a*b*d*f^3)*x + 4*(((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f - 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 - 2*a*b*d*f^3)*x)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f - 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 - 2*a*b*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + 3*((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f + 4*a*b*d*e*f^2 + 2*a^2*f^3 + ((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f + 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f + 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f + 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 + 2*a*b*d*f^3)*x)*sinh(d*x + c)^4 - 2*((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f + 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f + 4*a*b*d*e*f^2 + 2*a^2*f^3 - 3*((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f + 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^2 + 2*((a^2 + 2*b^2)*d^2*e*f^2 + 2*a*b*d*f^3)*x)*sinh(d*x + c)^2 + 2*((a^2 + 2*b^2)*d^2*e*f^2 + 2*a*b*d*f^3)*x + 4*(((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f + 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d^2*f^3*x^2 + (a^2 + 2*b^2)*d^2*e^2*f + 4*a*b*d*e*f^2 + 2*a^2*f^3 + 2*((a^2 + 2*b^2)*d^2*e*f^2 + 2*a*b*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) + ((a^2 + 2*b^2)*d^3*f^3*x^3 + (a^2 + 2*b^2)*d^3*e^3 + 6*a*b*d^2*e^2*f + 6*a^2*d*e*f^2 + ((a^2 + 2*b^2)*d^3*f^3*x^3 + (a^2 + 2*b^2)*d^3*e^3 + 6*a*b*d^2*e^2*f + 6*a^2*d*e*f^2 + 3*((a^2 + 2*b^2)*d^3*e*f^2 + 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f + 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d^3*f^3*x^3 + (a^2 + 2*b^2)*d^3*e^3 + 6*a*b*d^2*e^2*f + 6*a^2*d*e*f^2 + 3*((a^2 + 2*b^2)*d^3*e*f^2 + 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f + 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d^3*f^3*x^3 + (a^2 + 2*b^2)*d^3*e^3 + 6*a*b*d^2*e^2*f + 6*a^2*d*e*f^2 + 3*((a^2 + 2*b^2)*d^3*e*f^2 + 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f + 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*sinh(d*x + c)^4 + 3*((a^2 + 2*b^2)*d^3*e*f^2 + 2*a*b*d^2*f^3)*x^2 - 2*((a^2 + 2*b^2)*d^3*f^3*x^3 + (a^2 + 2*b^2)*d^3*e^3 + 6*a*b*d^2*e^2*f + 6*a^2*d*e*f^2 + 3*((a^2 + 2*b^2)*d^3*e*f^2 + 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f + 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d^3*f^3*x^3 + (a^2 + 2*b^2)*d^3*e^3 + 6*a*b*d^2*e^2*f + 6*a^2*d*e*f^2 + 3*((a^2 + 2*b^2)*d^3*e*f^2 + 2*a*b*d^2*f^3)*x^2 - 3*((a^2 + 2*b^2)*d^3*f^3*x^3 + (a^2 + 2*b^2)*d^3*e^3 + 6*a*b*d^2*e^2*f + 6*a^2*d*e*f^2 + 3*((a^2 + 2*b^2)*d^3*e*f^2 + 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f + 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c)^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f + 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*sinh(d*x + c)^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f + 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x + 4*(((a^2 + 2*b^2)*d^3*f^3*x^3 + (a^2 + 2*b^2)*d^3*e^3 + 6*a*b*d^2*e^2*f + 6*a^2*d*e*f^2 + 3*((a^2 + 2*b^2)*d^3*e*f^2 + 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f + 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d^3*f^3*x^3 + (a^2 + 2*b^2)*d^3*e^3 + 6*a*b*d^2*e^2*f + 6*a^2*d*e*f^2 + 3*((a^2 + 2*b^2)*d^3*e*f^2 + 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f + 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((a^2 + 2*b^2)*d^3*e^3 - 3*(2*a*b + (a^2 + 2*b^2)*c)*d^2*e^2*f + 3*(4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*d*e*f^2 + ((a^2 + 2*b^2)*d^3*e^3 - 3*(2*a*b + (a^2 + 2*b^2)*c)*d^2*e^2*f + 3*(4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*d*e*f^2 - (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d^3*e^3 - 3*(2*a*b + (a^2 + 2*b^2)*c)*d^2*e^2*f + 3*(4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*d*e*f^2 - (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d^3*e^3 - 3*(2*a*b + (a^2 + 2*b^2)*c)*d^2*e^2*f + 3*(4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*d*e*f^2 - (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3)*sinh(d*x + c)^4 - (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 - 2*((a^2 + 2*b^2)*d^3*e^3 - 3*(2*a*b + (a^2 + 2*b^2)*c)*d^2*e^2*f + 3*(4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*d*e*f^2 - (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d^3*e^3 - 3*(2*a*b + (a^2 + 2*b^2)*c)*d^2*e^2*f + 3*(4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*d*e*f^2 - (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 - 3*((a^2 + 2*b^2)*d^3*e^3 - 3*(2*a*b + (a^2 + 2*b^2)*c)*d^2*e^2*f + 3*(4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*d*e*f^2 - (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + 2*b^2)*d^3*e^3 - 3*(2*a*b + (a^2 + 2*b^2)*c)*d^2*e^2*f + 3*(4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*d*e*f^2 - (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d^3*e^3 - 3*(2*a*b + (a^2 + 2*b^2)*c)*d^2*e^2*f + 3*(4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*d*e*f^2 - (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) - ((a^2 + 2*b^2)*d^3*f^3*x^3 + 3*(a^2 + 2*b^2)*c*d^2*e^2*f - 3*(4*a*b*c + (a^2 + 2*b^2)*c^2)*d*e*f^2 + ((a^2 + 2*b^2)*d^3*f^3*x^3 + 3*(a^2 + 2*b^2)*c*d^2*e^2*f - 3*(4*a*b*c + (a^2 + 2*b^2)*c^2)*d*e*f^2 + (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 + 3*((a^2 + 2*b^2)*d^3*e*f^2 - 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f - 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d^3*f^3*x^3 + 3*(a^2 + 2*b^2)*c*d^2*e^2*f - 3*(4*a*b*c + (a^2 + 2*b^2)*c^2)*d*e*f^2 + (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 + 3*((a^2 + 2*b^2)*d^3*e*f^2 - 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f - 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d^3*f^3*x^3 + 3*(a^2 + 2*b^2)*c*d^2*e^2*f - 3*(4*a*b*c + (a^2 + 2*b^2)*c^2)*d*e*f^2 + (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 + 3*((a^2 + 2*b^2)*d^3*e*f^2 - 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f - 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*sinh(d*x + c)^4 + (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 + 3*((a^2 + 2*b^2)*d^3*e*f^2 - 2*a*b*d^2*f^3)*x^2 - 2*((a^2 + 2*b^2)*d^3*f^3*x^3 + 3*(a^2 + 2*b^2)*c*d^2*e^2*f - 3*(4*a*b*c + (a^2 + 2*b^2)*c^2)*d*e*f^2 + (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 + 3*((a^2 + 2*b^2)*d^3*e*f^2 - 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f - 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d^3*f^3*x^3 + 3*(a^2 + 2*b^2)*c*d^2*e^2*f - 3*(4*a*b*c + (a^2 + 2*b^2)*c^2)*d*e*f^2 + (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 + 3*((a^2 + 2*b^2)*d^3*e*f^2 - 2*a*b*d^2*f^3)*x^2 - 3*((a^2 + 2*b^2)*d^3*f^3*x^3 + 3*(a^2 + 2*b^2)*c*d^2*e^2*f - 3*(4*a*b*c + (a^2 + 2*b^2)*c^2)*d*e*f^2 + (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 + 3*((a^2 + 2*b^2)*d^3*e*f^2 - 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f - 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c)^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f - 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*sinh(d*x + c)^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f - 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x + 4*(((a^2 + 2*b^2)*d^3*f^3*x^3 + 3*(a^2 + 2*b^2)*c*d^2*e^2*f - 3*(4*a*b*c + (a^2 + 2*b^2)*c^2)*d*e*f^2 + (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 + 3*((a^2 + 2*b^2)*d^3*e*f^2 - 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f - 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d^3*f^3*x^3 + 3*(a^2 + 2*b^2)*c*d^2*e^2*f - 3*(4*a*b*c + (a^2 + 2*b^2)*c^2)*d*e*f^2 + (6*a*b*c^2 + (a^2 + 2*b^2)*c^3 + 6*a^2*c)*f^3 + 3*((a^2 + 2*b^2)*d^3*e*f^2 - 2*a*b*d^2*f^3)*x^2 + 3*((a^2 + 2*b^2)*d^3*e^2*f - 4*a*b*d^2*e*f^2 + 2*a^2*d*f^3)*x)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 6*((a^2 + 2*b^2)*f^3*cosh(d*x + c)^4 + 4*(a^2 + 2*b^2)*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*b^2)*f^3*sinh(d*x + c)^4 - 2*(a^2 + 2*b^2)*f^3*cosh(d*x + c)^2 + (a^2 + 2*b^2)*f^3 + 2*(3*(a^2 + 2*b^2)*f^3*cosh(d*x + c)^2 - (a^2 + 2*b^2)*f^3)*sinh(d*x + c)^2 + 4*((a^2 + 2*b^2)*f^3*cosh(d*x + c)^3 - (a^2 + 2*b^2)*f^3*cosh(d*x + c))*sinh(d*x + c))*polylog(4, cosh(d*x + c) + sinh(d*x + c)) + 6*((a^2 + 2*b^2)*f^3*cosh(d*x + c)^4 + 4*(a^2 + 2*b^2)*f^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*b^2)*f^3*sinh(d*x + c)^4 - 2*(a^2 + 2*b^2)*f^3*cosh(d*x + c)^2 + (a^2 + 2*b^2)*f^3 + 2*(3*(a^2 + 2*b^2)*f^3*cosh(d*x + c)^2 - (a^2 + 2*b^2)*f^3)*sinh(d*x + c)^2 + 4*((a^2 + 2*b^2)*f^3*cosh(d*x + c)^3 - (a^2 + 2*b^2)*f^3*cosh(d*x + c))*sinh(d*x + c))*polylog(4, -cosh(d*x + c) - sinh(d*x + c)) + 6*((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 - 2*a*b*f^3 + ((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 - 2*a*b*f^3)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 - 2*a*b*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 - 2*a*b*f^3)*sinh(d*x + c)^4 - 2*((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 - 2*a*b*f^3)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 - 2*a*b*f^3 - 3*((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 - 2*a*b*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 - 2*a*b*f^3)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 - 2*a*b*f^3)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 6*((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 + 2*a*b*f^3 + ((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 + 2*a*b*f^3)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 + 2*a*b*f^3)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 + 2*a*b*f^3)*sinh(d*x + c)^4 - 2*((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 + 2*a*b*f^3)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 + 2*a*b*f^3 - 3*((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 + 2*a*b*f^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 + 2*a*b*f^3)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d*f^3*x + (a^2 + 2*b^2)*d*e*f^2 + 2*a*b*f^3)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) + 2*(a^2*d^3*f^3*x^3 + a^2*d^3*e^3 - 3*a^2*d^2*e^2*f - 8*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x + 3*a*b*c*d^2*e^2*f - 3*a*b*c^2*d*e*f^2 + a*b*c^3*f^3)*cosh(d*x + c)^3 + 3*(a^2*d^3*e*f^2 - a^2*d^2*f^3)*x^2 + 3*(a^2*d^3*f^3*x^3 + a^2*d^3*e^3 + 3*a^2*d^2*e^2*f + 3*(a^2*d^3*e*f^2 + a^2*d^2*f^3)*x^2 + 3*(a^2*d^3*e^2*f + 2*a^2*d^2*e*f^2)*x)*cosh(d*x + c)^2 + 3*(a^2*d^3*e^2*f - 2*a^2*d^2*e*f^2)*x + 4*(a*b*d^3*f^3*x^3 + 3*a*b*d^3*e*f^2*x^2 + 3*a*b*d^3*e^2*f*x - a*b*d^3*e^3 + 6*a*b*c*d^2*e^2*f - 6*a*b*c^2*d*e*f^2 + 2*a*b*c^3*f^3)*cosh(d*x + c))*sinh(d*x + c))/(a^3*d^4*cosh(d*x + c)^4 + 4*a^3*d^4*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d^4*sinh(d*x + c)^4 - 2*a^3*d^4*cosh(d*x + c)^2 + a^3*d^4 + 2*(3*a^3*d^4*cosh(d*x + c)^2 - a^3*d^4)*sinh(d*x + c)^2 + 4*(a^3*d^4*cosh(d*x + c)^3 - a^3*d^4*cosh(d*x + c))*sinh(d*x + c))","C",0
482,1,7726,0,0.685749," ","integrate((f*x+e)^2*coth(d*x+c)^2*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a b d^{2} e^{2} - 8 \, a b c d e f + 4 \, a b c^{2} f^{2} - 4 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} + 2 \, a^{2} d e f + 2 \, {\left(a^{2} d^{2} e f + a^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} + 2 \, a^{2} d e f + 2 \, {\left(a^{2} d^{2} e f + a^{2} d f^{2}\right)} x - 8 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x - a b d^{2} e^{2} + 4 \, a b c d e f - 2 \, a b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a b d^{2} f^{2} x^{2} + 4 \, a b d^{2} e f x - 2 \, a b d^{2} e^{2} + 8 \, a b c d e f - 4 \, a b c^{2} f^{2} - 12 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} + 2 \, a^{2} d e f + 2 \, {\left(a^{2} d^{2} e f + a^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} d f^{2} x + b^{2} d e f + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f - 3 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 4 \, {\left(b^{2} d f^{2} x + b^{2} d e f + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f^{2} x + b^{2} d e f - 3 \, {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f^{2} x + b^{2} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2} - 3 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2} + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2} - 3 \, {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2} + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2} - 3 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2} + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2} - 3 \, {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} d^{2} e f x + 2 \, b^{2} c d e f - b^{2} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 4 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} + b^{2} f^{2} + 2 \, {\left(3 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} - b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{3} - b^{2} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 4 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} + b^{2} f^{2} + 2 \, {\left(3 \, b^{2} f^{2} \cosh\left(d x + c\right)^{2} - b^{2} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f^{2} \cosh\left(d x + c\right)^{3} - b^{2} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} - 2 \, a^{2} d e f + 2 \, {\left(a^{2} d^{2} e f - a^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f - 2 \, a b f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f - 2 \, a b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f - 2 \, a b f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, b^{2}\right)} d e f - 2 \, a b f^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f - 2 \, a b f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f - 2 \, a b f^{2} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f - 2 \, a b f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f - 2 \, a b f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f - 2 \, a b f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f + 2 \, a b f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f + 2 \, a b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f + 2 \, a b f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, b^{2}\right)} d e f + 2 \, a b f^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f + 2 \, a b f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f + 2 \, a b f^{2} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f + 2 \, a b f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f + 2 \, a b f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d f^{2} x + {\left(a^{2} + 2 \, b^{2}\right)} d e f + 2 \, a b f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} + 4 \, a b d e f + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} + 4 \, a b d e f + 2 \, a^{2} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f + 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} + 4 \, a b d e f + 2 \, a^{2} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f + 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} + 4 \, a b d e f + 2 \, a^{2} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f + 2 \, a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{2} f^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} + 4 \, a b d e f + 2 \, a^{2} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f + 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} + 4 \, a b d e f + 2 \, a^{2} f^{2} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} + 4 \, a b d e f + 2 \, a^{2} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f + 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f + 2 \, a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f + 2 \, a b d f^{2}\right)} x + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} + 4 \, a b d e f + 2 \, a^{2} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f + 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} + 4 \, a b d e f + 2 \, a^{2} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f + 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d e f + {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d e f + {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d e f + {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d e f + {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} f^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d e f + {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d e f + {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} f^{2} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d e f + {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d e f + {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} d e f + {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2} + 2 \, a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} c d e f + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} c d e f - {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f - 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} c d e f - {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f - 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} c d e f - {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f - 2 \, a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} f^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} c d e f - {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f - 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} c d e f - {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} f^{2} - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} c d e f - {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f - 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f - 2 \, a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f - 2 \, a b d f^{2}\right)} x + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} c d e f - {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f - 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} c d e f - {\left(4 \, a b c + {\left(a^{2} + 2 \, b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d^{2} e f - 2 \, a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, b^{2}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, b^{2}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} - 2 \, a^{2} d e f - 8 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + 2 \, a b c d e f - a b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} + 2 \, a^{2} d e f + 2 \, {\left(a^{2} d^{2} e f + a^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{2} e f - a^{2} d f^{2}\right)} x + 4 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x - a b d^{2} e^{2} + 4 \, a b c d e f - 2 \, a b c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{3} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d^{3} \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d^{3} \cosh\left(d x + c\right)^{2} + a^{3} d^{3} + 2 \, {\left(3 \, a^{3} d^{3} \cosh\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d^{3} \cosh\left(d x + c\right)^{3} - a^{3} d^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(4*a*b*d^2*e^2 - 8*a*b*c*d*e*f + 4*a*b*c^2*f^2 - 4*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*cosh(d*x + c)^4 - 4*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*sinh(d*x + c)^4 + 2*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 + 2*a^2*d*e*f + 2*(a^2*d^2*e*f + a^2*d*f^2)*x)*cosh(d*x + c)^3 + 2*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 + 2*a^2*d*e*f + 2*(a^2*d^2*e*f + a^2*d*f^2)*x - 8*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x - a*b*d^2*e^2 + 4*a*b*c*d*e*f - 2*a*b*c^2*f^2)*cosh(d*x + c)^2 + 2*(2*a*b*d^2*f^2*x^2 + 4*a*b*d^2*e*f*x - 2*a*b*d^2*e^2 + 8*a*b*c*d*e*f - 4*a*b*c^2*f^2 - 12*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*cosh(d*x + c)^2 + 3*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 + 2*a^2*d*e*f + 2*(a^2*d^2*e*f + a^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 4*(b^2*d*f^2*x + b^2*d*e*f + (b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^4 + 4*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^2*x + b^2*d*e*f)*sinh(d*x + c)^4 - 2*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^2 - 2*(b^2*d*f^2*x + b^2*d*e*f - 3*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^3 - (b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 4*(b^2*d*f^2*x + b^2*d*e*f + (b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^4 + 4*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f^2*x + b^2*d*e*f)*sinh(d*x + c)^4 - 2*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^2 - 2*(b^2*d*f^2*x + b^2*d*e*f - 3*(b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c)^3 - (b^2*d*f^2*x + b^2*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2 + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2 - 3*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^3 - (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2 + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2 - 3*(b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c)^3 - (b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2 + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2 - 3*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^3 - (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2 + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2 - 3*(b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c)^3 - (b^2*d^2*f^2*x^2 + 2*b^2*d^2*e*f*x + 2*b^2*c*d*e*f - b^2*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 4*(b^2*f^2*cosh(d*x + c)^4 + 4*b^2*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^2*sinh(d*x + c)^4 - 2*b^2*f^2*cosh(d*x + c)^2 + b^2*f^2 + 2*(3*b^2*f^2*cosh(d*x + c)^2 - b^2*f^2)*sinh(d*x + c)^2 + 4*(b^2*f^2*cosh(d*x + c)^3 - b^2*f^2*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 4*(b^2*f^2*cosh(d*x + c)^4 + 4*b^2*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f^2*sinh(d*x + c)^4 - 2*b^2*f^2*cosh(d*x + c)^2 + b^2*f^2 + 2*(3*b^2*f^2*cosh(d*x + c)^2 - b^2*f^2)*sinh(d*x + c)^2 + 4*(b^2*f^2*cosh(d*x + c)^3 - b^2*f^2*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 - 2*a^2*d*e*f + 2*(a^2*d^2*e*f - a^2*d*f^2)*x)*cosh(d*x + c) - 2*((a^2 + 2*b^2)*d*f^2*x + ((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f - 2*a*b*f^2)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f - 2*a*b*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f - 2*a*b*f^2)*sinh(d*x + c)^4 + (a^2 + 2*b^2)*d*e*f - 2*a*b*f^2 - 2*((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f - 2*a*b*f^2)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f - 2*a*b*f^2 - 3*((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f - 2*a*b*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f - 2*a*b*f^2)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f - 2*a*b*f^2)*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + 2*((a^2 + 2*b^2)*d*f^2*x + ((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f + 2*a*b*f^2)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f + 2*a*b*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f + 2*a*b*f^2)*sinh(d*x + c)^4 + (a^2 + 2*b^2)*d*e*f + 2*a*b*f^2 - 2*((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f + 2*a*b*f^2)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f + 2*a*b*f^2 - 3*((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f + 2*a*b*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f + 2*a*b*f^2)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d*f^2*x + (a^2 + 2*b^2)*d*e*f + 2*a*b*f^2)*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) + ((a^2 + 2*b^2)*d^2*f^2*x^2 + (a^2 + 2*b^2)*d^2*e^2 + 4*a*b*d*e*f + ((a^2 + 2*b^2)*d^2*f^2*x^2 + (a^2 + 2*b^2)*d^2*e^2 + 4*a*b*d*e*f + 2*a^2*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f + 2*a*b*d*f^2)*x)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d^2*f^2*x^2 + (a^2 + 2*b^2)*d^2*e^2 + 4*a*b*d*e*f + 2*a^2*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f + 2*a*b*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d^2*f^2*x^2 + (a^2 + 2*b^2)*d^2*e^2 + 4*a*b*d*e*f + 2*a^2*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f + 2*a*b*d*f^2)*x)*sinh(d*x + c)^4 + 2*a^2*f^2 - 2*((a^2 + 2*b^2)*d^2*f^2*x^2 + (a^2 + 2*b^2)*d^2*e^2 + 4*a*b*d*e*f + 2*a^2*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f + 2*a*b*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d^2*f^2*x^2 + (a^2 + 2*b^2)*d^2*e^2 + 4*a*b*d*e*f + 2*a^2*f^2 - 3*((a^2 + 2*b^2)*d^2*f^2*x^2 + (a^2 + 2*b^2)*d^2*e^2 + 4*a*b*d*e*f + 2*a^2*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f + 2*a*b*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^2 + 2*b^2)*d^2*e*f + 2*a*b*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^2 + 2*b^2)*d^2*e*f + 2*a*b*d*f^2)*x + 4*(((a^2 + 2*b^2)*d^2*f^2*x^2 + (a^2 + 2*b^2)*d^2*e^2 + 4*a*b*d*e*f + 2*a^2*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f + 2*a*b*d*f^2)*x)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d^2*f^2*x^2 + (a^2 + 2*b^2)*d^2*e^2 + 4*a*b*d*e*f + 2*a^2*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f + 2*a*b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((a^2 + 2*b^2)*d^2*e^2 + ((a^2 + 2*b^2)*d^2*e^2 - 2*(2*a*b + (a^2 + 2*b^2)*c)*d*e*f + (4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*f^2)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d^2*e^2 - 2*(2*a*b + (a^2 + 2*b^2)*c)*d*e*f + (4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d^2*e^2 - 2*(2*a*b + (a^2 + 2*b^2)*c)*d*e*f + (4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*f^2)*sinh(d*x + c)^4 - 2*(2*a*b + (a^2 + 2*b^2)*c)*d*e*f + (4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*f^2 - 2*((a^2 + 2*b^2)*d^2*e^2 - 2*(2*a*b + (a^2 + 2*b^2)*c)*d*e*f + (4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*f^2)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d^2*e^2 - 2*(2*a*b + (a^2 + 2*b^2)*c)*d*e*f + (4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*f^2 - 3*((a^2 + 2*b^2)*d^2*e^2 - 2*(2*a*b + (a^2 + 2*b^2)*c)*d*e*f + (4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + 2*b^2)*d^2*e^2 - 2*(2*a*b + (a^2 + 2*b^2)*c)*d*e*f + (4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*f^2)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d^2*e^2 - 2*(2*a*b + (a^2 + 2*b^2)*c)*d*e*f + (4*a*b*c + (a^2 + 2*b^2)*c^2 + 2*a^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) - ((a^2 + 2*b^2)*d^2*f^2*x^2 + 2*(a^2 + 2*b^2)*c*d*e*f + ((a^2 + 2*b^2)*d^2*f^2*x^2 + 2*(a^2 + 2*b^2)*c*d*e*f - (4*a*b*c + (a^2 + 2*b^2)*c^2)*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f - 2*a*b*d*f^2)*x)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d^2*f^2*x^2 + 2*(a^2 + 2*b^2)*c*d*e*f - (4*a*b*c + (a^2 + 2*b^2)*c^2)*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f - 2*a*b*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d^2*f^2*x^2 + 2*(a^2 + 2*b^2)*c*d*e*f - (4*a*b*c + (a^2 + 2*b^2)*c^2)*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f - 2*a*b*d*f^2)*x)*sinh(d*x + c)^4 - (4*a*b*c + (a^2 + 2*b^2)*c^2)*f^2 - 2*((a^2 + 2*b^2)*d^2*f^2*x^2 + 2*(a^2 + 2*b^2)*c*d*e*f - (4*a*b*c + (a^2 + 2*b^2)*c^2)*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f - 2*a*b*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d^2*f^2*x^2 + 2*(a^2 + 2*b^2)*c*d*e*f - (4*a*b*c + (a^2 + 2*b^2)*c^2)*f^2 - 3*((a^2 + 2*b^2)*d^2*f^2*x^2 + 2*(a^2 + 2*b^2)*c*d*e*f - (4*a*b*c + (a^2 + 2*b^2)*c^2)*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f - 2*a*b*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^2 + 2*b^2)*d^2*e*f - 2*a*b*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^2 + 2*b^2)*d^2*e*f - 2*a*b*d*f^2)*x + 4*(((a^2 + 2*b^2)*d^2*f^2*x^2 + 2*(a^2 + 2*b^2)*c*d*e*f - (4*a*b*c + (a^2 + 2*b^2)*c^2)*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f - 2*a*b*d*f^2)*x)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d^2*f^2*x^2 + 2*(a^2 + 2*b^2)*c*d*e*f - (4*a*b*c + (a^2 + 2*b^2)*c^2)*f^2 + 2*((a^2 + 2*b^2)*d^2*e*f - 2*a*b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 2*((a^2 + 2*b^2)*f^2*cosh(d*x + c)^4 + 4*(a^2 + 2*b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*b^2)*f^2*sinh(d*x + c)^4 - 2*(a^2 + 2*b^2)*f^2*cosh(d*x + c)^2 + (a^2 + 2*b^2)*f^2 + 2*(3*(a^2 + 2*b^2)*f^2*cosh(d*x + c)^2 - (a^2 + 2*b^2)*f^2)*sinh(d*x + c)^2 + 4*((a^2 + 2*b^2)*f^2*cosh(d*x + c)^3 - (a^2 + 2*b^2)*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 2*((a^2 + 2*b^2)*f^2*cosh(d*x + c)^4 + 4*(a^2 + 2*b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*b^2)*f^2*sinh(d*x + c)^4 - 2*(a^2 + 2*b^2)*f^2*cosh(d*x + c)^2 + (a^2 + 2*b^2)*f^2 + 2*(3*(a^2 + 2*b^2)*f^2*cosh(d*x + c)^2 - (a^2 + 2*b^2)*f^2)*sinh(d*x + c)^2 + 4*((a^2 + 2*b^2)*f^2*cosh(d*x + c)^3 - (a^2 + 2*b^2)*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) + 2*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 - 2*a^2*d*e*f - 8*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + 2*a*b*c*d*e*f - a*b*c^2*f^2)*cosh(d*x + c)^3 + 3*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 + 2*a^2*d*e*f + 2*(a^2*d^2*e*f + a^2*d*f^2)*x)*cosh(d*x + c)^2 + 2*(a^2*d^2*e*f - a^2*d*f^2)*x + 4*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x - a*b*d^2*e^2 + 4*a*b*c*d*e*f - 2*a*b*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))/(a^3*d^3*cosh(d*x + c)^4 + 4*a^3*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d^3*sinh(d*x + c)^4 - 2*a^3*d^3*cosh(d*x + c)^2 + a^3*d^3 + 2*(3*a^3*d^3*cosh(d*x + c)^2 - a^3*d^3)*sinh(d*x + c)^2 + 4*(a^3*d^3*cosh(d*x + c)^3 - a^3*d^3*cosh(d*x + c))*sinh(d*x + c))","C",0
483,1,3585,0,0.788399," ","integrate((f*x+e)*coth(d*x+c)^2*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left(a b d f x + a b c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b d f x + a b c f\right)} \sinh\left(d x + c\right)^{4} - 4 \, a b d e + 4 \, a b c f - 2 \, {\left(a^{2} d f x + a^{2} d e + a^{2} f\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(a^{2} d f x + a^{2} d e + a^{2} f - 8 \, {\left(a b d f x + a b c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a b d f x - a b d e + 2 \, a b c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(2 \, a b d f x - 2 \, a b d e + 4 \, a b c f - 12 \, {\left(a b d f x + a b c f\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(a^{2} d f x + a^{2} d e + a^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} f \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f \cosh\left(d x + c\right)^{2} + b^{2} f + 2 \, {\left(3 \, b^{2} f \cosh\left(d x + c\right)^{2} - b^{2} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f \cosh\left(d x + c\right)^{3} - b^{2} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{2} f \cosh\left(d x + c\right)^{4} + 4 \, b^{2} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} f \sinh\left(d x + c\right)^{4} - 2 \, b^{2} f \cosh\left(d x + c\right)^{2} + b^{2} f + 2 \, {\left(3 \, b^{2} f \cosh\left(d x + c\right)^{2} - b^{2} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} f \cosh\left(d x + c\right)^{3} - b^{2} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left({\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d e - b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + b^{2} d e - b^{2} c f - 2 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d e - b^{2} c f - 3 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left({\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d e - b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + b^{2} d e - b^{2} c f - 2 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d e - b^{2} c f - 3 \, {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d e - b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{2} d f x + {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f x + b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + b^{2} c f - 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f x + b^{2} c f - 3 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{2} d f x + {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{2} d f x + b^{2} c f\right)} \sinh\left(d x + c\right)^{4} + b^{2} c f - 2 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} d f x + b^{2} c f - 3 \, {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - 2 \, {\left(a^{2} d f x + a^{2} d e - a^{2} f\right)} \cosh\left(d x + c\right) + {\left({\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, b^{2}\right)} f \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, b^{2}\right)} f + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left({\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, b^{2}\right)} f \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, b^{2}\right)} f + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} d e + 2 \, a b f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} d e + 2 \, a b f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} d e + 2 \, a b f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} d e + 2 \, a b f - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} d e + 2 \, a b f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} d e + 2 \, a b f - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} d e + 2 \, a b f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} d e + 2 \, a b f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} d e + 2 \, a b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d e - {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d e - {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d e - {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, b^{2}\right)} d e - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d e - {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d e - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d e - {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{2} - {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} f + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d e - {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d e - {\left(2 \, a b + {\left(a^{2} + 2 \, b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} c f - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} c f - 3 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, b^{2}\right)} d f x + {\left(a^{2} + 2 \, b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left(a^{2} d f x + a^{2} d e - 8 \, {\left(a b d f x + a b c f\right)} \cosh\left(d x + c\right)^{3} - a^{2} f + 3 \, {\left(a^{2} d f x + a^{2} d e + a^{2} f\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a b d f x - a b d e + 2 \, a b c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{3} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d^{2} \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d^{2} \cosh\left(d x + c\right)^{2} + a^{3} d^{2} + 2 \, {\left(3 \, a^{3} d^{2} \cosh\left(d x + c\right)^{2} - a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d^{2} \cosh\left(d x + c\right)^{3} - a^{3} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(4*(a*b*d*f*x + a*b*c*f)*cosh(d*x + c)^4 + 4*(a*b*d*f*x + a*b*c*f)*sinh(d*x + c)^4 - 4*a*b*d*e + 4*a*b*c*f - 2*(a^2*d*f*x + a^2*d*e + a^2*f)*cosh(d*x + c)^3 - 2*(a^2*d*f*x + a^2*d*e + a^2*f - 8*(a*b*d*f*x + a*b*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a*b*d*f*x - a*b*d*e + 2*a*b*c*f)*cosh(d*x + c)^2 - 2*(2*a*b*d*f*x - 2*a*b*d*e + 4*a*b*c*f - 12*(a*b*d*f*x + a*b*c*f)*cosh(d*x + c)^2 + 3*(a^2*d*f*x + a^2*d*e + a^2*f)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(b^2*f*cosh(d*x + c)^4 + 4*b^2*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f*sinh(d*x + c)^4 - 2*b^2*f*cosh(d*x + c)^2 + b^2*f + 2*(3*b^2*f*cosh(d*x + c)^2 - b^2*f)*sinh(d*x + c)^2 + 4*(b^2*f*cosh(d*x + c)^3 - b^2*f*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^2*f*cosh(d*x + c)^4 + 4*b^2*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*f*sinh(d*x + c)^4 - 2*b^2*f*cosh(d*x + c)^2 + b^2*f + 2*(3*b^2*f*cosh(d*x + c)^2 - b^2*f)*sinh(d*x + c)^2 + 4*(b^2*f*cosh(d*x + c)^3 - b^2*f*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*((b^2*d*e - b^2*c*f)*cosh(d*x + c)^4 + 4*(b^2*d*e - b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*e - b^2*c*f)*sinh(d*x + c)^4 + b^2*d*e - b^2*c*f - 2*(b^2*d*e - b^2*c*f)*cosh(d*x + c)^2 - 2*(b^2*d*e - b^2*c*f - 3*(b^2*d*e - b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*e - b^2*c*f)*cosh(d*x + c)^3 - (b^2*d*e - b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*((b^2*d*e - b^2*c*f)*cosh(d*x + c)^4 + 4*(b^2*d*e - b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*e - b^2*c*f)*sinh(d*x + c)^4 + b^2*d*e - b^2*c*f - 2*(b^2*d*e - b^2*c*f)*cosh(d*x + c)^2 - 2*(b^2*d*e - b^2*c*f - 3*(b^2*d*e - b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*e - b^2*c*f)*cosh(d*x + c)^3 - (b^2*d*e - b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^2*d*f*x + (b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^4 + 4*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f*x + b^2*c*f)*sinh(d*x + c)^4 + b^2*c*f - 2*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2 - 2*(b^2*d*f*x + b^2*c*f - 3*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^3 - (b^2*d*f*x + b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^2*d*f*x + (b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^4 + 4*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^2*d*f*x + b^2*c*f)*sinh(d*x + c)^4 + b^2*c*f - 2*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2 - 2*(b^2*d*f*x + b^2*c*f - 3*(b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^2*d*f*x + b^2*c*f)*cosh(d*x + c)^3 - (b^2*d*f*x + b^2*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - 2*(a^2*d*f*x + a^2*d*e - a^2*f)*cosh(d*x + c) + ((a^2 + 2*b^2)*f*cosh(d*x + c)^4 + 4*(a^2 + 2*b^2)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*b^2)*f*sinh(d*x + c)^4 - 2*(a^2 + 2*b^2)*f*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*b^2)*f*cosh(d*x + c)^2 - (a^2 + 2*b^2)*f)*sinh(d*x + c)^2 + (a^2 + 2*b^2)*f + 4*((a^2 + 2*b^2)*f*cosh(d*x + c)^3 - (a^2 + 2*b^2)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) - ((a^2 + 2*b^2)*f*cosh(d*x + c)^4 + 4*(a^2 + 2*b^2)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*b^2)*f*sinh(d*x + c)^4 - 2*(a^2 + 2*b^2)*f*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*b^2)*f*cosh(d*x + c)^2 - (a^2 + 2*b^2)*f)*sinh(d*x + c)^2 + (a^2 + 2*b^2)*f + 4*((a^2 + 2*b^2)*f*cosh(d*x + c)^3 - (a^2 + 2*b^2)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) - (((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*d*e + 2*a*b*f)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*d*e + 2*a*b*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*d*e + 2*a*b*f)*sinh(d*x + c)^4 + (a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*d*e + 2*a*b*f - 2*((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*d*e + 2*a*b*f)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*d*e + 2*a*b*f - 3*((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*d*e + 2*a*b*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*d*e + 2*a*b*f)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*d*e + 2*a*b*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (((a^2 + 2*b^2)*d*e - (2*a*b + (a^2 + 2*b^2)*c)*f)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d*e - (2*a*b + (a^2 + 2*b^2)*c)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d*e - (2*a*b + (a^2 + 2*b^2)*c)*f)*sinh(d*x + c)^4 + (a^2 + 2*b^2)*d*e - 2*((a^2 + 2*b^2)*d*e - (2*a*b + (a^2 + 2*b^2)*c)*f)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d*e - 3*((a^2 + 2*b^2)*d*e - (2*a*b + (a^2 + 2*b^2)*c)*f)*cosh(d*x + c)^2 - (2*a*b + (a^2 + 2*b^2)*c)*f)*sinh(d*x + c)^2 - (2*a*b + (a^2 + 2*b^2)*c)*f + 4*(((a^2 + 2*b^2)*d*e - (2*a*b + (a^2 + 2*b^2)*c)*f)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d*e - (2*a*b + (a^2 + 2*b^2)*c)*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*c*f)*cosh(d*x + c)^4 + 4*((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*c*f)*sinh(d*x + c)^4 + (a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*c*f - 2*((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*c*f)*cosh(d*x + c)^2 - 2*((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*c*f - 3*((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*c*f)*cosh(d*x + c)^3 - ((a^2 + 2*b^2)*d*f*x + (a^2 + 2*b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*(a^2*d*f*x + a^2*d*e - 8*(a*b*d*f*x + a*b*c*f)*cosh(d*x + c)^3 - a^2*f + 3*(a^2*d*f*x + a^2*d*e + a^2*f)*cosh(d*x + c)^2 + 4*(a*b*d*f*x - a*b*d*e + 2*a*b*c*f)*cosh(d*x + c))*sinh(d*x + c))/(a^3*d^2*cosh(d*x + c)^4 + 4*a^3*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d^2*sinh(d*x + c)^4 - 2*a^3*d^2*cosh(d*x + c)^2 + a^3*d^2 + 2*(3*a^3*d^2*cosh(d*x + c)^2 - a^3*d^2)*sinh(d*x + c)^2 + 4*(a^3*d^2*cosh(d*x + c)^3 - a^3*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
484,1,892,0,0.550156," ","integrate(coth(d*x+c)^2*csch(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a^{2} \cosh\left(d x + c\right)^{3} + 2 \, a^{2} \sinh\left(d x + c\right)^{3} - 4 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right) - 2 \, a b\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 4 \, a b + {\left({\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, b^{2} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, b^{2} + 4 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} - 4 \, a b \cosh\left(d x + c\right) + a^{2}\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d \cosh\left(d x + c\right)^{2} + a^{3} d + 2 \, {\left(3 \, a^{3} d \cosh\left(d x + c\right)^{2} - a^{3} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d \cosh\left(d x + c\right)^{3} - a^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*a^2*cosh(d*x + c)^3 + 2*a^2*sinh(d*x + c)^3 - 4*a*b*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c) + 2*(3*a^2*cosh(d*x + c) - 2*a*b)*sinh(d*x + c)^2 - 2*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 4*a*b + ((a^2 + 2*b^2)*cosh(d*x + c)^4 + 4*(a^2 + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*b^2)*sinh(d*x + c)^4 - 2*(a^2 + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*b^2)*cosh(d*x + c)^2 - a^2 - 2*b^2)*sinh(d*x + c)^2 + a^2 + 2*b^2 + 4*((a^2 + 2*b^2)*cosh(d*x + c)^3 - (a^2 + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((a^2 + 2*b^2)*cosh(d*x + c)^4 + 4*(a^2 + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*b^2)*sinh(d*x + c)^4 - 2*(a^2 + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*b^2)*cosh(d*x + c)^2 - a^2 - 2*b^2)*sinh(d*x + c)^2 + a^2 + 2*b^2 + 4*((a^2 + 2*b^2)*cosh(d*x + c)^3 - (a^2 + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(3*a^2*cosh(d*x + c)^2 - 4*a*b*cosh(d*x + c) + a^2)*sinh(d*x + c))/(a^3*d*cosh(d*x + c)^4 + 4*a^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d*sinh(d*x + c)^4 - 2*a^3*d*cosh(d*x + c)^2 + a^3*d + 2*(3*a^3*d*cosh(d*x + c)^2 - a^3*d)*sinh(d*x + c)^2 + 4*(a^3*d*cosh(d*x + c)^3 - a^3*d*cosh(d*x + c))*sinh(d*x + c))","B",0
485,0,0,0,1.041979," ","integrate(coth(d*x+c)^2*csch(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(d x + c\right)^{2} \operatorname{csch}\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(coth(d*x + c)^2*csch(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
486,-1,0,0,0.000000," ","integrate((f*x+e)^3*coth(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,1,7775,0,1.306802," ","integrate((f*x+e)^2*coth(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a^{2} d e f - 2 \, a^{2} c f^{2} - 2 \, {\left(a^{2} d f^{2} x + a^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} d f^{2} x + a^{2} c f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2} - 4 \, {\left(a^{2} d f^{2} x + a^{2} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} + a^{2} d e f - 2 \, a^{2} c f^{2} + {\left(2 \, a^{2} d^{2} e f - a^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} + a^{2} d e f - 2 \, a^{2} c f^{2} + 6 \, {\left(a^{2} d f^{2} x + a^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} d^{2} e f - a^{2} d f^{2}\right)} x - 3 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d e f - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - 3 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d e f - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - 3 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - a b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - a b f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d e f - a b f^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - a b f^{2} - 3 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f - a b f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f + a b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f + a b f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d e f + a b f^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f + a b f^{2} - 3 \, {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d f^{2} x + {\left(a^{2} + b^{2}\right)} d e f + a b f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2} + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2} - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2} + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2} - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2} + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2} - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2} + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2} - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} d^{2} e f x + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(a^{2} + b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} + 2 \, a b d e f + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f + a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} + a^{2} f^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f + a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f + a b d f^{2}\right)} x + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{2} + b^{2}\right)} d^{2} e^{2} + 2 \, a b d e f + a^{2} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f + a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} d e f + {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2} + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} d e f + {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2} + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} d e f + {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2} + a^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} d e f + {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2} + a^{2}\right)} f^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} d e f + {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2} + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} d e f + {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2} + a^{2}\right)} f^{2} - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} d e f + {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2} + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} d e f + {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2} + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{2} e^{2} - 2 \, {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} d e f + {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2} + a^{2}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} c d e f + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f - a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2}\right)} f^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2}\right)} f^{2} - 3 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f - a b d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f - a b d f^{2}\right)} x + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} + b^{2}\right)} c d e f - {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} c^{2}\right)} f^{2} + 2 \, {\left({\left(a^{2} + b^{2}\right)} d^{2} e f - a b d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{2} + b^{2}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{2} + b^{2}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{2} + b^{2}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{2} + b^{2}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + b^{2}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2} + 4 \, {\left(a^{2} d f^{2} x + a^{2} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b d^{2} f^{2} x^{2} + 2 \, a b d^{2} e f x + a b d^{2} e^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d^{2} f^{2} x^{2} + a^{2} d^{2} e^{2} + a^{2} d e f - 2 \, a^{2} c f^{2} + {\left(2 \, a^{2} d^{2} e f - a^{2} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{a^{3} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d^{3} \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d^{3} \cosh\left(d x + c\right)^{2} + a^{3} d^{3} + 2 \, {\left(3 \, a^{3} d^{3} \cosh\left(d x + c\right)^{2} - a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d^{3} \cosh\left(d x + c\right)^{3} - a^{3} d^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"(2*a^2*d*e*f - 2*a^2*c*f^2 - 2*(a^2*d*f^2*x + a^2*c*f^2)*cosh(d*x + c)^4 - 2*(a^2*d*f^2*x + a^2*c*f^2)*sinh(d*x + c)^4 + 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2)*cosh(d*x + c)^3 + 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2 - 4*(a^2*d*f^2*x + a^2*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 + a^2*d*e*f - 2*a^2*c*f^2 + (2*a^2*d^2*e*f - a^2*d*f^2)*x)*cosh(d*x + c)^2 - 2*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 + a^2*d*e*f - 2*a^2*c*f^2 + 6*(a^2*d*f^2*x + a^2*c*f^2)*cosh(d*x + c)^2 + (2*a^2*d^2*e*f - a^2*d*f^2)*x - 3*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2)*cosh(d*x + c) - 2*((a^2 + b^2)*d*f^2*x + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*sinh(d*x + c)^4 + (a^2 + b^2)*d*e*f - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - 3*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - 2*((a^2 + b^2)*d*f^2*x + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*sinh(d*x + c)^4 + (a^2 + b^2)*d*e*f - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - 3*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*((a^2 + b^2)*d*f^2*x + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - a*b*f^2)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - a*b*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - a*b*f^2)*sinh(d*x + c)^4 + (a^2 + b^2)*d*e*f - a*b*f^2 - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - a*b*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - a*b*f^2 - 3*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - a*b*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - a*b*f^2)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f - a*b*f^2)*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + 2*((a^2 + b^2)*d*f^2*x + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f + a*b*f^2)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f + a*b*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f + a*b*f^2)*sinh(d*x + c)^4 + (a^2 + b^2)*d*e*f + a*b*f^2 - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f + a*b*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f + a*b*f^2 - 3*((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f + a*b*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f + a*b*f^2)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*f^2*x + (a^2 + b^2)*d*e*f + a*b*f^2)*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) - ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2 + ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^4 - 2*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2 - 3*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^3 - ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2 + ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^4 - 2*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2 - 3*((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^3 - ((a^2 + b^2)*d^2*e^2 - 2*(a^2 + b^2)*c*d*e*f + (a^2 + b^2)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2 + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^4 - 2*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2 - 3*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^3 - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2 + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*sinh(d*x + c)^4 - 2*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2 - 3*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c)^3 - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*d^2*e*f*x + 2*(a^2 + b^2)*c*d*e*f - (a^2 + b^2)*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + ((a^2 + b^2)*d^2*f^2*x^2 + (a^2 + b^2)*d^2*e^2 + 2*a*b*d*e*f + ((a^2 + b^2)*d^2*f^2*x^2 + (a^2 + b^2)*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*((a^2 + b^2)*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d^2*f^2*x^2 + (a^2 + b^2)*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*((a^2 + b^2)*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d^2*f^2*x^2 + (a^2 + b^2)*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*((a^2 + b^2)*d^2*e*f + a*b*d*f^2)*x)*sinh(d*x + c)^4 + a^2*f^2 - 2*((a^2 + b^2)*d^2*f^2*x^2 + (a^2 + b^2)*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*((a^2 + b^2)*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*f^2*x^2 + (a^2 + b^2)*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 - 3*((a^2 + b^2)*d^2*f^2*x^2 + (a^2 + b^2)*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*((a^2 + b^2)*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^2*e*f + a*b*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^2 + b^2)*d^2*e*f + a*b*d*f^2)*x + 4*(((a^2 + b^2)*d^2*f^2*x^2 + (a^2 + b^2)*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*((a^2 + b^2)*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c)^3 - ((a^2 + b^2)*d^2*f^2*x^2 + (a^2 + b^2)*d^2*e^2 + 2*a*b*d*e*f + a^2*f^2 + 2*((a^2 + b^2)*d^2*e*f + a*b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a^2 + b^2)*d^2*e^2 + ((a^2 + b^2)*d^2*e^2 - 2*(a*b + (a^2 + b^2)*c)*d*e*f + (2*a*b*c + (a^2 + b^2)*c^2 + a^2)*f^2)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d^2*e^2 - 2*(a*b + (a^2 + b^2)*c)*d*e*f + (2*a*b*c + (a^2 + b^2)*c^2 + a^2)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d^2*e^2 - 2*(a*b + (a^2 + b^2)*c)*d*e*f + (2*a*b*c + (a^2 + b^2)*c^2 + a^2)*f^2)*sinh(d*x + c)^4 - 2*(a*b + (a^2 + b^2)*c)*d*e*f + (2*a*b*c + (a^2 + b^2)*c^2 + a^2)*f^2 - 2*((a^2 + b^2)*d^2*e^2 - 2*(a*b + (a^2 + b^2)*c)*d*e*f + (2*a*b*c + (a^2 + b^2)*c^2 + a^2)*f^2)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*e^2 - 2*(a*b + (a^2 + b^2)*c)*d*e*f + (2*a*b*c + (a^2 + b^2)*c^2 + a^2)*f^2 - 3*((a^2 + b^2)*d^2*e^2 - 2*(a*b + (a^2 + b^2)*c)*d*e*f + (2*a*b*c + (a^2 + b^2)*c^2 + a^2)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d^2*e^2 - 2*(a*b + (a^2 + b^2)*c)*d*e*f + (2*a*b*c + (a^2 + b^2)*c^2 + a^2)*f^2)*cosh(d*x + c)^3 - ((a^2 + b^2)*d^2*e^2 - 2*(a*b + (a^2 + b^2)*c)*d*e*f + (2*a*b*c + (a^2 + b^2)*c^2 + a^2)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*c*d*e*f + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*c*d*e*f - (2*a*b*c + (a^2 + b^2)*c^2)*f^2 + 2*((a^2 + b^2)*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*c*d*e*f - (2*a*b*c + (a^2 + b^2)*c^2)*f^2 + 2*((a^2 + b^2)*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*c*d*e*f - (2*a*b*c + (a^2 + b^2)*c^2)*f^2 + 2*((a^2 + b^2)*d^2*e*f - a*b*d*f^2)*x)*sinh(d*x + c)^4 - (2*a*b*c + (a^2 + b^2)*c^2)*f^2 - 2*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*c*d*e*f - (2*a*b*c + (a^2 + b^2)*c^2)*f^2 + 2*((a^2 + b^2)*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*c*d*e*f - (2*a*b*c + (a^2 + b^2)*c^2)*f^2 - 3*((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*c*d*e*f - (2*a*b*c + (a^2 + b^2)*c^2)*f^2 + 2*((a^2 + b^2)*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^2 + b^2)*d^2*e*f - a*b*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^2 + b^2)*d^2*e*f - a*b*d*f^2)*x + 4*(((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*c*d*e*f - (2*a*b*c + (a^2 + b^2)*c^2)*f^2 + 2*((a^2 + b^2)*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c)^3 - ((a^2 + b^2)*d^2*f^2*x^2 + 2*(a^2 + b^2)*c*d*e*f - (2*a*b*c + (a^2 + b^2)*c^2)*f^2 + 2*((a^2 + b^2)*d^2*e*f - a*b*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 2*((a^2 + b^2)*f^2*cosh(d*x + c)^4 + 4*(a^2 + b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + b^2)*f^2*sinh(d*x + c)^4 - 2*(a^2 + b^2)*f^2*cosh(d*x + c)^2 + (a^2 + b^2)*f^2 + 2*(3*(a^2 + b^2)*f^2*cosh(d*x + c)^2 - (a^2 + b^2)*f^2)*sinh(d*x + c)^2 + 4*((a^2 + b^2)*f^2*cosh(d*x + c)^3 - (a^2 + b^2)*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) + 2*((a^2 + b^2)*f^2*cosh(d*x + c)^4 + 4*(a^2 + b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + b^2)*f^2*sinh(d*x + c)^4 - 2*(a^2 + b^2)*f^2*cosh(d*x + c)^2 + (a^2 + b^2)*f^2 + 2*(3*(a^2 + b^2)*f^2*cosh(d*x + c)^2 - (a^2 + b^2)*f^2)*sinh(d*x + c)^2 + 4*((a^2 + b^2)*f^2*cosh(d*x + c)^3 - (a^2 + b^2)*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*((a^2 + b^2)*f^2*cosh(d*x + c)^4 + 4*(a^2 + b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + b^2)*f^2*sinh(d*x + c)^4 - 2*(a^2 + b^2)*f^2*cosh(d*x + c)^2 + (a^2 + b^2)*f^2 + 2*(3*(a^2 + b^2)*f^2*cosh(d*x + c)^2 - (a^2 + b^2)*f^2)*sinh(d*x + c)^2 + 4*((a^2 + b^2)*f^2*cosh(d*x + c)^3 - (a^2 + b^2)*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, cosh(d*x + c) + sinh(d*x + c)) - 2*((a^2 + b^2)*f^2*cosh(d*x + c)^4 + 4*(a^2 + b^2)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + b^2)*f^2*sinh(d*x + c)^4 - 2*(a^2 + b^2)*f^2*cosh(d*x + c)^2 + (a^2 + b^2)*f^2 + 2*(3*(a^2 + b^2)*f^2*cosh(d*x + c)^2 - (a^2 + b^2)*f^2)*sinh(d*x + c)^2 + 4*((a^2 + b^2)*f^2*cosh(d*x + c)^3 - (a^2 + b^2)*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) - 2*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2 + 4*(a^2*d*f^2*x + a^2*c*f^2)*cosh(d*x + c)^3 - 3*(a*b*d^2*f^2*x^2 + 2*a*b*d^2*e*f*x + a*b*d^2*e^2)*cosh(d*x + c)^2 + 2*(a^2*d^2*f^2*x^2 + a^2*d^2*e^2 + a^2*d*e*f - 2*a^2*c*f^2 + (2*a^2*d^2*e*f - a^2*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/(a^3*d^3*cosh(d*x + c)^4 + 4*a^3*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d^3*sinh(d*x + c)^4 - 2*a^3*d^3*cosh(d*x + c)^2 + a^3*d^3 + 2*(3*a^3*d^3*cosh(d*x + c)^2 - a^3*d^3)*sinh(d*x + c)^2 + 4*(a^3*d^3*cosh(d*x + c)^3 - a^3*d^3*cosh(d*x + c))*sinh(d*x + c))","C",0
488,1,3547,0,0.540289," ","integrate((f*x+e)*coth(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a b d f x + a b d e\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a b d f x + a b d e\right)} \sinh\left(d x + c\right)^{3} + a^{2} f - {\left(2 \, a^{2} d f x + 2 \, a^{2} d e + a^{2} f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{2} d f x + 2 \, a^{2} d e + a^{2} f - 6 \, {\left(a b d f x + a b d e\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d f x + a b d e\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} f \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + b^{2}\right)} f + 4 \, {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} f \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + b^{2}\right)} f + 4 \, {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} f \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + b^{2}\right)} f + 4 \, {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} f \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{2} + b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + b^{2}\right)} f + 4 \, {\left({\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{2} + b^{2}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left({\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f - 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f - 3 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left({\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f - 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f - 3 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f - 3 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f - 3 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e + a b f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e + a b f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e + a b f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e + a b f - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e + a b f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e + a b f - 3 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e + a b f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e + a b f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} d e + a b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left({\left(a^{2} + b^{2}\right)} d e - {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d e - 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d e - 3 \, {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{2} - {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} f + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d e - {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d e - {\left(a b + {\left(a^{2} + b^{2}\right)} c\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f - 3 \, {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + b^{2}\right)} d f x + {\left(a^{2} + b^{2}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left(a b d f x + a b d e - 3 \, {\left(a b d f x + a b d e\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} d f x + 2 \, a^{2} d e + a^{2} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{a^{3} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d^{2} \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d^{2} \cosh\left(d x + c\right)^{2} + a^{3} d^{2} + 2 \, {\left(3 \, a^{3} d^{2} \cosh\left(d x + c\right)^{2} - a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d^{2} \cosh\left(d x + c\right)^{3} - a^{3} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"(2*(a*b*d*f*x + a*b*d*e)*cosh(d*x + c)^3 + 2*(a*b*d*f*x + a*b*d*e)*sinh(d*x + c)^3 + a^2*f - (2*a^2*d*f*x + 2*a^2*d*e + a^2*f)*cosh(d*x + c)^2 - (2*a^2*d*f*x + 2*a^2*d*e + a^2*f - 6*(a*b*d*f*x + a*b*d*e)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(a*b*d*f*x + a*b*d*e)*cosh(d*x + c) - ((a^2 + b^2)*f*cosh(d*x + c)^4 + 4*(a^2 + b^2)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + b^2)*f*sinh(d*x + c)^4 - 2*(a^2 + b^2)*f*cosh(d*x + c)^2 + 2*(3*(a^2 + b^2)*f*cosh(d*x + c)^2 - (a^2 + b^2)*f)*sinh(d*x + c)^2 + (a^2 + b^2)*f + 4*((a^2 + b^2)*f*cosh(d*x + c)^3 - (a^2 + b^2)*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - ((a^2 + b^2)*f*cosh(d*x + c)^4 + 4*(a^2 + b^2)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + b^2)*f*sinh(d*x + c)^4 - 2*(a^2 + b^2)*f*cosh(d*x + c)^2 + 2*(3*(a^2 + b^2)*f*cosh(d*x + c)^2 - (a^2 + b^2)*f)*sinh(d*x + c)^2 + (a^2 + b^2)*f + 4*((a^2 + b^2)*f*cosh(d*x + c)^3 - (a^2 + b^2)*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + ((a^2 + b^2)*f*cosh(d*x + c)^4 + 4*(a^2 + b^2)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + b^2)*f*sinh(d*x + c)^4 - 2*(a^2 + b^2)*f*cosh(d*x + c)^2 + 2*(3*(a^2 + b^2)*f*cosh(d*x + c)^2 - (a^2 + b^2)*f)*sinh(d*x + c)^2 + (a^2 + b^2)*f + 4*((a^2 + b^2)*f*cosh(d*x + c)^3 - (a^2 + b^2)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + ((a^2 + b^2)*f*cosh(d*x + c)^4 + 4*(a^2 + b^2)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + b^2)*f*sinh(d*x + c)^4 - 2*(a^2 + b^2)*f*cosh(d*x + c)^2 + 2*(3*(a^2 + b^2)*f*cosh(d*x + c)^2 - (a^2 + b^2)*f)*sinh(d*x + c)^2 + (a^2 + b^2)*f + 4*((a^2 + b^2)*f*cosh(d*x + c)^3 - (a^2 + b^2)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) - (((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*sinh(d*x + c)^4 + (a^2 + b^2)*d*e - (a^2 + b^2)*c*f - 2*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f - 3*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*sinh(d*x + c)^4 + (a^2 + b^2)*d*e - (a^2 + b^2)*c*f - 2*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f - 3*((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*e - (a^2 + b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*sinh(d*x + c)^4 + (a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f - 3*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*sinh(d*x + c)^4 + (a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f - 3*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e + a*b*f)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e + a*b*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e + a*b*f)*sinh(d*x + c)^4 + (a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e + a*b*f - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e + a*b*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e + a*b*f - 3*((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e + a*b*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e + a*b*f)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*d*e + a*b*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (((a^2 + b^2)*d*e - (a*b + (a^2 + b^2)*c)*f)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*e - (a*b + (a^2 + b^2)*c)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*e - (a*b + (a^2 + b^2)*c)*f)*sinh(d*x + c)^4 + (a^2 + b^2)*d*e - 2*((a^2 + b^2)*d*e - (a*b + (a^2 + b^2)*c)*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*e - 3*((a^2 + b^2)*d*e - (a*b + (a^2 + b^2)*c)*f)*cosh(d*x + c)^2 - (a*b + (a^2 + b^2)*c)*f)*sinh(d*x + c)^2 - (a*b + (a^2 + b^2)*c)*f + 4*(((a^2 + b^2)*d*e - (a*b + (a^2 + b^2)*c)*f)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*e - (a*b + (a^2 + b^2)*c)*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^4 + 4*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*sinh(d*x + c)^4 + (a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^2 - 2*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f - 3*((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c)^3 - ((a^2 + b^2)*d*f*x + (a^2 + b^2)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*(a*b*d*f*x + a*b*d*e - 3*(a*b*d*f*x + a*b*d*e)*cosh(d*x + c)^2 + (2*a^2*d*f*x + 2*a^2*d*e + a^2*f)*cosh(d*x + c))*sinh(d*x + c))/(a^3*d^2*cosh(d*x + c)^4 + 4*a^3*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d^2*sinh(d*x + c)^4 - 2*a^3*d^2*cosh(d*x + c)^2 + a^3*d^2 + 2*(3*a^3*d^2*cosh(d*x + c)^2 - a^3*d^2)*sinh(d*x + c)^2 + 4*(a^3*d^2*cosh(d*x + c)^3 - a^3*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
489,1,617,0,0.558876," ","integrate(coth(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a b \cosh\left(d x + c\right)^{3} + 2 \, a b \sinh\left(d x + c\right)^{3} - 2 \, a^{2} \cosh\left(d x + c\right)^{2} - 2 \, a b \cosh\left(d x + c\right) + 2 \, {\left(3 \, a b \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + b^{2} + 4 \, {\left({\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left({\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + b^{2} + 4 \, {\left({\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(3 \, a b \cosh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) - a b\right)} \sinh\left(d x + c\right)}{a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} d \sinh\left(d x + c\right)^{4} - 2 \, a^{3} d \cosh\left(d x + c\right)^{2} + a^{3} d + 2 \, {\left(3 \, a^{3} d \cosh\left(d x + c\right)^{2} - a^{3} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} d \cosh\left(d x + c\right)^{3} - a^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"(2*a*b*cosh(d*x + c)^3 + 2*a*b*sinh(d*x + c)^3 - 2*a^2*cosh(d*x + c)^2 - 2*a*b*cosh(d*x + c) + 2*(3*a*b*cosh(d*x + c) - a^2)*sinh(d*x + c)^2 - ((a^2 + b^2)*cosh(d*x + c)^4 + 4*(a^2 + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + b^2)*sinh(d*x + c)^4 - 2*(a^2 + b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + b^2)*cosh(d*x + c)^2 - a^2 - b^2)*sinh(d*x + c)^2 + a^2 + b^2 + 4*((a^2 + b^2)*cosh(d*x + c)^3 - (a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + ((a^2 + b^2)*cosh(d*x + c)^4 + 4*(a^2 + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + b^2)*sinh(d*x + c)^4 - 2*(a^2 + b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + b^2)*cosh(d*x + c)^2 - a^2 - b^2)*sinh(d*x + c)^2 + a^2 + b^2 + 4*((a^2 + b^2)*cosh(d*x + c)^3 - (a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(3*a*b*cosh(d*x + c)^2 - 2*a^2*cosh(d*x + c) - a*b)*sinh(d*x + c))/(a^3*d*cosh(d*x + c)^4 + 4*a^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*d*sinh(d*x + c)^4 - 2*a^3*d*cosh(d*x + c)^2 + a^3*d + 2*(3*a^3*d*cosh(d*x + c)^2 - a^3*d)*sinh(d*x + c)^2 + 4*(a^3*d*cosh(d*x + c)^3 - a^3*d*cosh(d*x + c))*sinh(d*x + c))","B",0
490,0,0,0,2.739390," ","integrate(coth(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(d x + c\right)^{3}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(coth(d*x + c)^3/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
491,-1,0,0,0.000000," ","integrate((f*x+e)^3*csch(d*x+c)^3*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,1,13381,0,0.927256," ","integrate((f*x+e)^2*csch(d*x+c)^3*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} c f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e f + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} - 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f - {\left(a^{4} + a^{2} b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + 6 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f - {\left(a^{4} + a^{2} b^{2}\right)} d f^{2}\right)} x - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f - 3 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d f^{2} x + b^{4} d e f - 3 \, {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d f^{2} x + b^{4} d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - b^{4}\right)} d e f + {\left(a^{3} b + a b^{3}\right)} f^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f + {\left(a^{3} b + a b^{3}\right)} f^{2} - 3 \, {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f + {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(2 \, a^{4} d f^{2} x + 2 i \, a^{3} b d f^{2} x + 2 \, a^{4} d e f + 2 i \, a^{3} b d e f + {\left(2 \, a^{4} d f^{2} x + 2 i \, a^{3} b d f^{2} x + 2 \, a^{4} d e f + 2 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{4} d f^{2} x + 8 i \, a^{3} b d f^{2} x + 8 \, a^{4} d e f + 8 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{4} d f^{2} x + 2 i \, a^{3} b d f^{2} x + 2 \, a^{4} d e f + 2 i \, a^{3} b d e f\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a^{4} d f^{2} x + 4 i \, a^{3} b d f^{2} x + 4 \, a^{4} d e f + 4 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{4} d f^{2} x + 4 i \, a^{3} b d f^{2} x + 4 \, a^{4} d e f + 4 i \, a^{3} b d e f - {\left(12 \, a^{4} d f^{2} x + 12 i \, a^{3} b d f^{2} x + 12 \, a^{4} d e f + 12 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{4} d f^{2} x + 8 i \, a^{3} b d f^{2} x + 8 \, a^{4} d e f + 8 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{4} d f^{2} x + 8 i \, a^{3} b d f^{2} x + 8 \, a^{4} d e f + 8 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) - {\left(2 \, a^{4} d f^{2} x - 2 i \, a^{3} b d f^{2} x + 2 \, a^{4} d e f - 2 i \, a^{3} b d e f + {\left(2 \, a^{4} d f^{2} x - 2 i \, a^{3} b d f^{2} x + 2 \, a^{4} d e f - 2 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{4} d f^{2} x - 8 i \, a^{3} b d f^{2} x + 8 \, a^{4} d e f - 8 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{4} d f^{2} x - 2 i \, a^{3} b d f^{2} x + 2 \, a^{4} d e f - 2 i \, a^{3} b d e f\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a^{4} d f^{2} x - 4 i \, a^{3} b d f^{2} x + 4 \, a^{4} d e f - 4 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{4} d f^{2} x - 4 i \, a^{3} b d f^{2} x + 4 \, a^{4} d e f - 4 i \, a^{3} b d e f - {\left(12 \, a^{4} d f^{2} x - 12 i \, a^{3} b d f^{2} x + 12 \, a^{4} d e f - 12 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{4} d f^{2} x - 8 i \, a^{3} b d f^{2} x + 8 \, a^{4} d e f - 8 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{4} d f^{2} x - 8 i \, a^{3} b d f^{2} x + 8 \, a^{4} d e f - 8 i \, a^{3} b d e f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - b^{4}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} f^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} f^{2} - 3 \, {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - b^{4}\right)} d f^{2} x + {\left(a^{4} - b^{4}\right)} d e f - {\left(a^{3} b + a b^{3}\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2} - 3 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2} - 3 \, {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d^{2} e^{2} - 2 \, b^{4} c d e f + b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2} - 3 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2} - 3 \, {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d^{2} f^{2} x^{2} + 2 \, b^{4} d^{2} e f x + 2 \, b^{4} c d e f - b^{4} c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - b^{4}\right)} d^{2} e^{2} + {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{4} + a^{2} b^{2}\right)} f^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{4} + a^{2} b^{2}\right)} f^{2} - 3 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x + 4 \, {\left({\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} - b^{4}\right)} d^{2} e^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} d e f - {\left(a^{4} + a^{2} b^{2}\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f - {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(a^{4} d^{2} e^{2} + i \, a^{3} b d^{2} e^{2} - 2 \, a^{4} c d e f - 2 i \, a^{3} b c d e f + a^{4} c^{2} f^{2} + i \, a^{3} b c^{2} f^{2} + {\left(a^{4} d^{2} e^{2} + i \, a^{3} b d^{2} e^{2} - 2 \, a^{4} c d e f - 2 i \, a^{3} b c d e f + a^{4} c^{2} f^{2} + i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, a^{4} d^{2} e^{2} + 4 i \, a^{3} b d^{2} e^{2} - 8 \, a^{4} c d e f - 8 i \, a^{3} b c d e f + 4 \, a^{4} c^{2} f^{2} + 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} d^{2} e^{2} + i \, a^{3} b d^{2} e^{2} - 2 \, a^{4} c d e f - 2 i \, a^{3} b c d e f + a^{4} c^{2} f^{2} + i \, a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a^{4} d^{2} e^{2} + 2 i \, a^{3} b d^{2} e^{2} - 4 \, a^{4} c d e f - 4 i \, a^{3} b c d e f + 2 \, a^{4} c^{2} f^{2} + 2 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} d^{2} e^{2} + 2 i \, a^{3} b d^{2} e^{2} - 4 \, a^{4} c d e f - 4 i \, a^{3} b c d e f + 2 \, a^{4} c^{2} f^{2} + 2 i \, a^{3} b c^{2} f^{2} - {\left(6 \, a^{4} d^{2} e^{2} + 6 i \, a^{3} b d^{2} e^{2} - 12 \, a^{4} c d e f - 12 i \, a^{3} b c d e f + 6 \, a^{4} c^{2} f^{2} + 6 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} d^{2} e^{2} + 4 i \, a^{3} b d^{2} e^{2} - 8 \, a^{4} c d e f - 8 i \, a^{3} b c d e f + 4 \, a^{4} c^{2} f^{2} + 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} d^{2} e^{2} + 4 i \, a^{3} b d^{2} e^{2} - 8 \, a^{4} c d e f - 8 i \, a^{3} b c d e f + 4 \, a^{4} c^{2} f^{2} + 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) - {\left(a^{4} d^{2} e^{2} - i \, a^{3} b d^{2} e^{2} - 2 \, a^{4} c d e f + 2 i \, a^{3} b c d e f + a^{4} c^{2} f^{2} - i \, a^{3} b c^{2} f^{2} + {\left(a^{4} d^{2} e^{2} - i \, a^{3} b d^{2} e^{2} - 2 \, a^{4} c d e f + 2 i \, a^{3} b c d e f + a^{4} c^{2} f^{2} - i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, a^{4} d^{2} e^{2} - 4 i \, a^{3} b d^{2} e^{2} - 8 \, a^{4} c d e f + 8 i \, a^{3} b c d e f + 4 \, a^{4} c^{2} f^{2} - 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} d^{2} e^{2} - i \, a^{3} b d^{2} e^{2} - 2 \, a^{4} c d e f + 2 i \, a^{3} b c d e f + a^{4} c^{2} f^{2} - i \, a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a^{4} d^{2} e^{2} - 2 i \, a^{3} b d^{2} e^{2} - 4 \, a^{4} c d e f + 4 i \, a^{3} b c d e f + 2 \, a^{4} c^{2} f^{2} - 2 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} d^{2} e^{2} - 2 i \, a^{3} b d^{2} e^{2} - 4 \, a^{4} c d e f + 4 i \, a^{3} b c d e f + 2 \, a^{4} c^{2} f^{2} - 2 i \, a^{3} b c^{2} f^{2} - {\left(6 \, a^{4} d^{2} e^{2} - 6 i \, a^{3} b d^{2} e^{2} - 12 \, a^{4} c d e f + 12 i \, a^{3} b c d e f + 6 \, a^{4} c^{2} f^{2} - 6 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} d^{2} e^{2} - 4 i \, a^{3} b d^{2} e^{2} - 8 \, a^{4} c d e f + 8 i \, a^{3} b c d e f + 4 \, a^{4} c^{2} f^{2} - 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} d^{2} e^{2} - 4 i \, a^{3} b d^{2} e^{2} - 8 \, a^{4} c d e f + 8 i \, a^{3} b c d e f + 4 \, a^{4} c^{2} f^{2} - 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) + {\left({\left(a^{4} - b^{4}\right)} d^{2} e^{2} + {\left({\left(a^{4} - b^{4}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} d e f - {\left(a^{4} + a^{2} b^{2} - {\left(a^{4} - b^{4}\right)} c^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} d e f - {\left(a^{4} + a^{2} b^{2} - {\left(a^{4} - b^{4}\right)} c^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - b^{4}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} d e f - {\left(a^{4} + a^{2} b^{2} - {\left(a^{4} - b^{4}\right)} c^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} d e f - {\left(a^{4} + a^{2} b^{2} - {\left(a^{4} - b^{4}\right)} c^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} d e f - {\left(a^{4} + a^{2} b^{2} - {\left(a^{4} - b^{4}\right)} c^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} d e f - {\left(a^{4} + a^{2} b^{2} - {\left(a^{4} - b^{4}\right)} c^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} - 3 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} d e f - {\left(a^{4} + a^{2} b^{2} - {\left(a^{4} - b^{4}\right)} c^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} - b^{4}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} d e f - {\left(a^{4} + a^{2} b^{2} - {\left(a^{4} - b^{4}\right)} c^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - b^{4}\right)} d^{2} e^{2} + 2 \, {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} d e f - {\left(a^{4} + a^{2} b^{2} - {\left(a^{4} - b^{4}\right)} c^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left(a^{4} d^{2} f^{2} x^{2} - i \, a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{4} d^{2} e f x - 2 i \, a^{3} b d^{2} e f x + 2 \, a^{4} c d e f - 2 i \, a^{3} b c d e f - a^{4} c^{2} f^{2} + i \, a^{3} b c^{2} f^{2} + {\left(a^{4} d^{2} f^{2} x^{2} - i \, a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{4} d^{2} e f x - 2 i \, a^{3} b d^{2} e f x + 2 \, a^{4} c d e f - 2 i \, a^{3} b c d e f - a^{4} c^{2} f^{2} + i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, a^{4} d^{2} f^{2} x^{2} - 4 i \, a^{3} b d^{2} f^{2} x^{2} + 8 \, a^{4} d^{2} e f x - 8 i \, a^{3} b d^{2} e f x + 8 \, a^{4} c d e f - 8 i \, a^{3} b c d e f - 4 \, a^{4} c^{2} f^{2} + 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} d^{2} f^{2} x^{2} - i \, a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{4} d^{2} e f x - 2 i \, a^{3} b d^{2} e f x + 2 \, a^{4} c d e f - 2 i \, a^{3} b c d e f - a^{4} c^{2} f^{2} + i \, a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a^{4} d^{2} f^{2} x^{2} - 2 i \, a^{3} b d^{2} f^{2} x^{2} + 4 \, a^{4} d^{2} e f x - 4 i \, a^{3} b d^{2} e f x + 4 \, a^{4} c d e f - 4 i \, a^{3} b c d e f - 2 \, a^{4} c^{2} f^{2} + 2 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} d^{2} f^{2} x^{2} - 2 i \, a^{3} b d^{2} f^{2} x^{2} + 4 \, a^{4} d^{2} e f x - 4 i \, a^{3} b d^{2} e f x + 4 \, a^{4} c d e f - 4 i \, a^{3} b c d e f - 2 \, a^{4} c^{2} f^{2} + 2 i \, a^{3} b c^{2} f^{2} - {\left(6 \, a^{4} d^{2} f^{2} x^{2} - 6 i \, a^{3} b d^{2} f^{2} x^{2} + 12 \, a^{4} d^{2} e f x - 12 i \, a^{3} b d^{2} e f x + 12 \, a^{4} c d e f - 12 i \, a^{3} b c d e f - 6 \, a^{4} c^{2} f^{2} + 6 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} d^{2} f^{2} x^{2} - 4 i \, a^{3} b d^{2} f^{2} x^{2} + 8 \, a^{4} d^{2} e f x - 8 i \, a^{3} b d^{2} e f x + 8 \, a^{4} c d e f - 8 i \, a^{3} b c d e f - 4 \, a^{4} c^{2} f^{2} + 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} d^{2} f^{2} x^{2} - 4 i \, a^{3} b d^{2} f^{2} x^{2} + 8 \, a^{4} d^{2} e f x - 8 i \, a^{3} b d^{2} e f x + 8 \, a^{4} c d e f - 8 i \, a^{3} b c d e f - 4 \, a^{4} c^{2} f^{2} + 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) - {\left(a^{4} d^{2} f^{2} x^{2} + i \, a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{4} d^{2} e f x + 2 i \, a^{3} b d^{2} e f x + 2 \, a^{4} c d e f + 2 i \, a^{3} b c d e f - a^{4} c^{2} f^{2} - i \, a^{3} b c^{2} f^{2} + {\left(a^{4} d^{2} f^{2} x^{2} + i \, a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{4} d^{2} e f x + 2 i \, a^{3} b d^{2} e f x + 2 \, a^{4} c d e f + 2 i \, a^{3} b c d e f - a^{4} c^{2} f^{2} - i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, a^{4} d^{2} f^{2} x^{2} + 4 i \, a^{3} b d^{2} f^{2} x^{2} + 8 \, a^{4} d^{2} e f x + 8 i \, a^{3} b d^{2} e f x + 8 \, a^{4} c d e f + 8 i \, a^{3} b c d e f - 4 \, a^{4} c^{2} f^{2} - 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} d^{2} f^{2} x^{2} + i \, a^{3} b d^{2} f^{2} x^{2} + 2 \, a^{4} d^{2} e f x + 2 i \, a^{3} b d^{2} e f x + 2 \, a^{4} c d e f + 2 i \, a^{3} b c d e f - a^{4} c^{2} f^{2} - i \, a^{3} b c^{2} f^{2}\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a^{4} d^{2} f^{2} x^{2} + 2 i \, a^{3} b d^{2} f^{2} x^{2} + 4 \, a^{4} d^{2} e f x + 4 i \, a^{3} b d^{2} e f x + 4 \, a^{4} c d e f + 4 i \, a^{3} b c d e f - 2 \, a^{4} c^{2} f^{2} - 2 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} d^{2} f^{2} x^{2} + 2 i \, a^{3} b d^{2} f^{2} x^{2} + 4 \, a^{4} d^{2} e f x + 4 i \, a^{3} b d^{2} e f x + 4 \, a^{4} c d e f + 4 i \, a^{3} b c d e f - 2 \, a^{4} c^{2} f^{2} - 2 i \, a^{3} b c^{2} f^{2} - {\left(6 \, a^{4} d^{2} f^{2} x^{2} + 6 i \, a^{3} b d^{2} f^{2} x^{2} + 12 \, a^{4} d^{2} e f x + 12 i \, a^{3} b d^{2} e f x + 12 \, a^{4} c d e f + 12 i \, a^{3} b c d e f - 6 \, a^{4} c^{2} f^{2} - 6 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} d^{2} f^{2} x^{2} + 4 i \, a^{3} b d^{2} f^{2} x^{2} + 8 \, a^{4} d^{2} e f x + 8 i \, a^{3} b d^{2} e f x + 8 \, a^{4} c d e f + 8 i \, a^{3} b c d e f - 4 \, a^{4} c^{2} f^{2} - 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} d^{2} f^{2} x^{2} + 4 i \, a^{3} b d^{2} f^{2} x^{2} + 8 \, a^{4} d^{2} e f x + 8 i \, a^{3} b d^{2} e f x + 8 \, a^{4} c d e f + 8 i \, a^{3} b c d e f - 4 \, a^{4} c^{2} f^{2} - 4 i \, a^{3} b c^{2} f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) + {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - b^{4}\right)} c d e f + {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - b^{4}\right)} c d e f - {\left({\left(a^{4} - b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - b^{4}\right)} c d e f - {\left({\left(a^{4} - b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - b^{4}\right)} c d e f - {\left({\left(a^{4} - b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{4} - {\left({\left(a^{4} - b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - b^{4}\right)} c d e f - {\left({\left(a^{4} - b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - b^{4}\right)} c d e f - {\left({\left(a^{4} - b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} - 3 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - b^{4}\right)} c d e f - {\left({\left(a^{4} - b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x + 4 \, {\left({\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - b^{4}\right)} c d e f - {\left({\left(a^{4} - b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - b^{4}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{4} - b^{4}\right)} c d e f - {\left({\left(a^{4} - b^{4}\right)} c^{2} - 2 \, {\left(a^{3} b + a b^{3}\right)} c\right)} f^{2} + 2 \, {\left({\left(a^{4} - b^{4}\right)} d^{2} e f + {\left(a^{3} b + a b^{3}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left(b^{4} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{4} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{4} f^{2} \cosh\left(d x + c\right)^{2} + b^{4} f^{2} + 2 \, {\left(3 \, b^{4} f^{2} \cosh\left(d x + c\right)^{2} - b^{4} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} f^{2} \cosh\left(d x + c\right)^{3} - b^{4} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(b^{4} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{4} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, b^{4} f^{2} \cosh\left(d x + c\right)^{2} + b^{4} f^{2} + 2 \, {\left(3 \, b^{4} f^{2} \cosh\left(d x + c\right)^{2} - b^{4} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} f^{2} \cosh\left(d x + c\right)^{3} - b^{4} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left({\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - b^{4}\right)} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} - b^{4}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{4} - b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, \cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(2 \, a^{4} f^{2} + 2 i \, a^{3} b f^{2} + {\left(2 \, a^{4} f^{2} + 2 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{4} f^{2} + 8 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{4} f^{2} + 2 i \, a^{3} b f^{2}\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a^{4} f^{2} + 4 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{4} f^{2} + 4 i \, a^{3} b f^{2} - {\left(12 \, a^{4} f^{2} + 12 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{4} f^{2} + 8 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{4} f^{2} + 8 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(2 \, a^{4} f^{2} - 2 i \, a^{3} b f^{2} + {\left(2 \, a^{4} f^{2} - 2 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(8 \, a^{4} f^{2} - 8 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{4} f^{2} - 2 i \, a^{3} b f^{2}\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a^{4} f^{2} - 4 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{4} f^{2} - 4 i \, a^{3} b f^{2} - {\left(12 \, a^{4} f^{2} - 12 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{4} f^{2} - 8 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{4} f^{2} - 8 i \, a^{3} b f^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - b^{4}\right)} f^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{4} - b^{4}\right)} f^{2} + 2 \, {\left(3 \, {\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{4} - b^{4}\right)} f^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - b^{4}\right)} f^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm polylog}\left(3, -\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) + 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2} + 4 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d f^{2} x + {\left(a^{4} + a^{2} b^{2}\right)} c f^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} b + a b^{3}\right)} d^{2} e f x + {\left(a^{3} b + a b^{3}\right)} d^{2} e^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} + a^{2} b^{2}\right)} d^{2} f^{2} x^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e^{2} + {\left(a^{4} + a^{2} b^{2}\right)} d e f - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} c f^{2} + {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} d^{2} e f - {\left(a^{4} + a^{2} b^{2}\right)} d f^{2}\right)} x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + a^{3} b^{2}\right)} d^{3} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d^{3} + 2 \, {\left(3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right)^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right)^{3} - {\left(a^{5} + a^{3} b^{2}\right)} d^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"-(2*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*c*f^2)*cosh(d*x + c)^4 + 2*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*c*f^2)*sinh(d*x + c)^4 - 2*(a^4 + a^2*b^2)*d*e*f + 2*(a^4 + a^2*b^2)*c*f^2 - 2*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + (a^3*b + a*b^3)*d^2*e^2)*cosh(d*x + c)^3 - 2*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + (a^3*b + a*b^3)*d^2*e^2 - 4*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*c*f^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*((a^4 + a^2*b^2)*d^2*f^2*x^2 + (a^4 + a^2*b^2)*d^2*e^2 + (a^4 + a^2*b^2)*d*e*f - 2*(a^4 + a^2*b^2)*c*f^2 + (2*(a^4 + a^2*b^2)*d^2*e*f - (a^4 + a^2*b^2)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^4 + a^2*b^2)*d^2*f^2*x^2 + (a^4 + a^2*b^2)*d^2*e^2 + (a^4 + a^2*b^2)*d*e*f - 2*(a^4 + a^2*b^2)*c*f^2 + 6*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*c*f^2)*cosh(d*x + c)^2 + (2*(a^4 + a^2*b^2)*d^2*e*f - (a^4 + a^2*b^2)*d*f^2)*x - 3*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + (a^3*b + a*b^3)*d^2*e^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + (a^3*b + a*b^3)*d^2*e^2)*cosh(d*x + c) + 2*(b^4*d*f^2*x + b^4*d*e*f + (b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^4 + 4*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*f^2*x + b^4*d*e*f)*sinh(d*x + c)^4 - 2*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^2 - 2*(b^4*d*f^2*x + b^4*d*e*f - 3*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^3 - (b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^4*d*f^2*x + b^4*d*e*f + (b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^4 + 4*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*f^2*x + b^4*d*e*f)*sinh(d*x + c)^4 - 2*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^2 - 2*(b^4*d*f^2*x + b^4*d*e*f - 3*(b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c)^3 - (b^4*d*f^2*x + b^4*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*((a^4 - b^4)*d*f^2*x + ((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f + (a^3*b + a*b^3)*f^2)*cosh(d*x + c)^4 + 4*((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f + (a^3*b + a*b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f + (a^3*b + a*b^3)*f^2)*sinh(d*x + c)^4 + (a^4 - b^4)*d*e*f + (a^3*b + a*b^3)*f^2 - 2*((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f + (a^3*b + a*b^3)*f^2)*cosh(d*x + c)^2 - 2*((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f + (a^3*b + a*b^3)*f^2 - 3*((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f + (a^3*b + a*b^3)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f + (a^3*b + a*b^3)*f^2)*cosh(d*x + c)^3 - ((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f + (a^3*b + a*b^3)*f^2)*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) - (2*a^4*d*f^2*x + 2*I*a^3*b*d*f^2*x + 2*a^4*d*e*f + 2*I*a^3*b*d*e*f + (2*a^4*d*f^2*x + 2*I*a^3*b*d*f^2*x + 2*a^4*d*e*f + 2*I*a^3*b*d*e*f)*cosh(d*x + c)^4 + (8*a^4*d*f^2*x + 8*I*a^3*b*d*f^2*x + 8*a^4*d*e*f + 8*I*a^3*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^4*d*f^2*x + 2*I*a^3*b*d*f^2*x + 2*a^4*d*e*f + 2*I*a^3*b*d*e*f)*sinh(d*x + c)^4 - (4*a^4*d*f^2*x + 4*I*a^3*b*d*f^2*x + 4*a^4*d*e*f + 4*I*a^3*b*d*e*f)*cosh(d*x + c)^2 - (4*a^4*d*f^2*x + 4*I*a^3*b*d*f^2*x + 4*a^4*d*e*f + 4*I*a^3*b*d*e*f - (12*a^4*d*f^2*x + 12*I*a^3*b*d*f^2*x + 12*a^4*d*e*f + 12*I*a^3*b*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^4*d*f^2*x + 8*I*a^3*b*d*f^2*x + 8*a^4*d*e*f + 8*I*a^3*b*d*e*f)*cosh(d*x + c)^3 - (8*a^4*d*f^2*x + 8*I*a^3*b*d*f^2*x + 8*a^4*d*e*f + 8*I*a^3*b*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) - (2*a^4*d*f^2*x - 2*I*a^3*b*d*f^2*x + 2*a^4*d*e*f - 2*I*a^3*b*d*e*f + (2*a^4*d*f^2*x - 2*I*a^3*b*d*f^2*x + 2*a^4*d*e*f - 2*I*a^3*b*d*e*f)*cosh(d*x + c)^4 + (8*a^4*d*f^2*x - 8*I*a^3*b*d*f^2*x + 8*a^4*d*e*f - 8*I*a^3*b*d*e*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^4*d*f^2*x - 2*I*a^3*b*d*f^2*x + 2*a^4*d*e*f - 2*I*a^3*b*d*e*f)*sinh(d*x + c)^4 - (4*a^4*d*f^2*x - 4*I*a^3*b*d*f^2*x + 4*a^4*d*e*f - 4*I*a^3*b*d*e*f)*cosh(d*x + c)^2 - (4*a^4*d*f^2*x - 4*I*a^3*b*d*f^2*x + 4*a^4*d*e*f - 4*I*a^3*b*d*e*f - (12*a^4*d*f^2*x - 12*I*a^3*b*d*f^2*x + 12*a^4*d*e*f - 12*I*a^3*b*d*e*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^4*d*f^2*x - 8*I*a^3*b*d*f^2*x + 8*a^4*d*e*f - 8*I*a^3*b*d*e*f)*cosh(d*x + c)^3 - (8*a^4*d*f^2*x - 8*I*a^3*b*d*f^2*x + 8*a^4*d*e*f - 8*I*a^3*b*d*e*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) + 2*((a^4 - b^4)*d*f^2*x + ((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f - (a^3*b + a*b^3)*f^2)*cosh(d*x + c)^4 + 4*((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f - (a^3*b + a*b^3)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f - (a^3*b + a*b^3)*f^2)*sinh(d*x + c)^4 + (a^4 - b^4)*d*e*f - (a^3*b + a*b^3)*f^2 - 2*((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f - (a^3*b + a*b^3)*f^2)*cosh(d*x + c)^2 - 2*((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f - (a^3*b + a*b^3)*f^2 - 3*((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f - (a^3*b + a*b^3)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f - (a^3*b + a*b^3)*f^2)*cosh(d*x + c)^3 - ((a^4 - b^4)*d*f^2*x + (a^4 - b^4)*d*e*f - (a^3*b + a*b^3)*f^2)*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2 - 3*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^3 - (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2 - 3*(b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c)^3 - (b^4*d^2*e^2 - 2*b^4*c*d*e*f + b^4*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2 - 3*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^3 - (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^4 + 4*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*sinh(d*x + c)^4 - 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^2 - 2*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2 - 3*(b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c)^3 - (b^4*d^2*f^2*x^2 + 2*b^4*d^2*e*f*x + 2*b^4*c*d*e*f - b^4*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + ((a^4 - b^4)*d^2*f^2*x^2 + (a^4 - b^4)*d^2*e^2 + ((a^4 - b^4)*d^2*f^2*x^2 + (a^4 - b^4)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f - (a^4 + a^2*b^2)*f^2 + 2*((a^4 - b^4)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^4 + 4*((a^4 - b^4)*d^2*f^2*x^2 + (a^4 - b^4)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f - (a^4 + a^2*b^2)*f^2 + 2*((a^4 - b^4)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - b^4)*d^2*f^2*x^2 + (a^4 - b^4)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f - (a^4 + a^2*b^2)*f^2 + 2*((a^4 - b^4)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*sinh(d*x + c)^4 - 2*(a^3*b + a*b^3)*d*e*f - (a^4 + a^2*b^2)*f^2 - 2*((a^4 - b^4)*d^2*f^2*x^2 + (a^4 - b^4)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f - (a^4 + a^2*b^2)*f^2 + 2*((a^4 - b^4)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^4 - b^4)*d^2*f^2*x^2 + (a^4 - b^4)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f - (a^4 + a^2*b^2)*f^2 - 3*((a^4 - b^4)*d^2*f^2*x^2 + (a^4 - b^4)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f - (a^4 + a^2*b^2)*f^2 + 2*((a^4 - b^4)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^4 - b^4)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^4 - b^4)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x + 4*(((a^4 - b^4)*d^2*f^2*x^2 + (a^4 - b^4)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f - (a^4 + a^2*b^2)*f^2 + 2*((a^4 - b^4)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^3 - ((a^4 - b^4)*d^2*f^2*x^2 + (a^4 - b^4)*d^2*e^2 - 2*(a^3*b + a*b^3)*d*e*f - (a^4 + a^2*b^2)*f^2 + 2*((a^4 - b^4)*d^2*e*f - (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (a^4*d^2*e^2 + I*a^3*b*d^2*e^2 - 2*a^4*c*d*e*f - 2*I*a^3*b*c*d*e*f + a^4*c^2*f^2 + I*a^3*b*c^2*f^2 + (a^4*d^2*e^2 + I*a^3*b*d^2*e^2 - 2*a^4*c*d*e*f - 2*I*a^3*b*c*d*e*f + a^4*c^2*f^2 + I*a^3*b*c^2*f^2)*cosh(d*x + c)^4 + (4*a^4*d^2*e^2 + 4*I*a^3*b*d^2*e^2 - 8*a^4*c*d*e*f - 8*I*a^3*b*c*d*e*f + 4*a^4*c^2*f^2 + 4*I*a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*d^2*e^2 + I*a^3*b*d^2*e^2 - 2*a^4*c*d*e*f - 2*I*a^3*b*c*d*e*f + a^4*c^2*f^2 + I*a^3*b*c^2*f^2)*sinh(d*x + c)^4 - (2*a^4*d^2*e^2 + 2*I*a^3*b*d^2*e^2 - 4*a^4*c*d*e*f - 4*I*a^3*b*c*d*e*f + 2*a^4*c^2*f^2 + 2*I*a^3*b*c^2*f^2)*cosh(d*x + c)^2 - (2*a^4*d^2*e^2 + 2*I*a^3*b*d^2*e^2 - 4*a^4*c*d*e*f - 4*I*a^3*b*c*d*e*f + 2*a^4*c^2*f^2 + 2*I*a^3*b*c^2*f^2 - (6*a^4*d^2*e^2 + 6*I*a^3*b*d^2*e^2 - 12*a^4*c*d*e*f - 12*I*a^3*b*c*d*e*f + 6*a^4*c^2*f^2 + 6*I*a^3*b*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^4*d^2*e^2 + 4*I*a^3*b*d^2*e^2 - 8*a^4*c*d*e*f - 8*I*a^3*b*c*d*e*f + 4*a^4*c^2*f^2 + 4*I*a^3*b*c^2*f^2)*cosh(d*x + c)^3 - (4*a^4*d^2*e^2 + 4*I*a^3*b*d^2*e^2 - 8*a^4*c*d*e*f - 8*I*a^3*b*c*d*e*f + 4*a^4*c^2*f^2 + 4*I*a^3*b*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) - (a^4*d^2*e^2 - I*a^3*b*d^2*e^2 - 2*a^4*c*d*e*f + 2*I*a^3*b*c*d*e*f + a^4*c^2*f^2 - I*a^3*b*c^2*f^2 + (a^4*d^2*e^2 - I*a^3*b*d^2*e^2 - 2*a^4*c*d*e*f + 2*I*a^3*b*c*d*e*f + a^4*c^2*f^2 - I*a^3*b*c^2*f^2)*cosh(d*x + c)^4 + (4*a^4*d^2*e^2 - 4*I*a^3*b*d^2*e^2 - 8*a^4*c*d*e*f + 8*I*a^3*b*c*d*e*f + 4*a^4*c^2*f^2 - 4*I*a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*d^2*e^2 - I*a^3*b*d^2*e^2 - 2*a^4*c*d*e*f + 2*I*a^3*b*c*d*e*f + a^4*c^2*f^2 - I*a^3*b*c^2*f^2)*sinh(d*x + c)^4 - (2*a^4*d^2*e^2 - 2*I*a^3*b*d^2*e^2 - 4*a^4*c*d*e*f + 4*I*a^3*b*c*d*e*f + 2*a^4*c^2*f^2 - 2*I*a^3*b*c^2*f^2)*cosh(d*x + c)^2 - (2*a^4*d^2*e^2 - 2*I*a^3*b*d^2*e^2 - 4*a^4*c*d*e*f + 4*I*a^3*b*c*d*e*f + 2*a^4*c^2*f^2 - 2*I*a^3*b*c^2*f^2 - (6*a^4*d^2*e^2 - 6*I*a^3*b*d^2*e^2 - 12*a^4*c*d*e*f + 12*I*a^3*b*c*d*e*f + 6*a^4*c^2*f^2 - 6*I*a^3*b*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^4*d^2*e^2 - 4*I*a^3*b*d^2*e^2 - 8*a^4*c*d*e*f + 8*I*a^3*b*c*d*e*f + 4*a^4*c^2*f^2 - 4*I*a^3*b*c^2*f^2)*cosh(d*x + c)^3 - (4*a^4*d^2*e^2 - 4*I*a^3*b*d^2*e^2 - 8*a^4*c*d*e*f + 8*I*a^3*b*c*d*e*f + 4*a^4*c^2*f^2 - 4*I*a^3*b*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) + ((a^4 - b^4)*d^2*e^2 + ((a^4 - b^4)*d^2*e^2 + 2*(a^3*b + a*b^3 - (a^4 - b^4)*c)*d*e*f - (a^4 + a^2*b^2 - (a^4 - b^4)*c^2 + 2*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c)^4 + 4*((a^4 - b^4)*d^2*e^2 + 2*(a^3*b + a*b^3 - (a^4 - b^4)*c)*d*e*f - (a^4 + a^2*b^2 - (a^4 - b^4)*c^2 + 2*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - b^4)*d^2*e^2 + 2*(a^3*b + a*b^3 - (a^4 - b^4)*c)*d*e*f - (a^4 + a^2*b^2 - (a^4 - b^4)*c^2 + 2*(a^3*b + a*b^3)*c)*f^2)*sinh(d*x + c)^4 + 2*(a^3*b + a*b^3 - (a^4 - b^4)*c)*d*e*f - (a^4 + a^2*b^2 - (a^4 - b^4)*c^2 + 2*(a^3*b + a*b^3)*c)*f^2 - 2*((a^4 - b^4)*d^2*e^2 + 2*(a^3*b + a*b^3 - (a^4 - b^4)*c)*d*e*f - (a^4 + a^2*b^2 - (a^4 - b^4)*c^2 + 2*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c)^2 - 2*((a^4 - b^4)*d^2*e^2 + 2*(a^3*b + a*b^3 - (a^4 - b^4)*c)*d*e*f - (a^4 + a^2*b^2 - (a^4 - b^4)*c^2 + 2*(a^3*b + a*b^3)*c)*f^2 - 3*((a^4 - b^4)*d^2*e^2 + 2*(a^3*b + a*b^3 - (a^4 - b^4)*c)*d*e*f - (a^4 + a^2*b^2 - (a^4 - b^4)*c^2 + 2*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 - b^4)*d^2*e^2 + 2*(a^3*b + a*b^3 - (a^4 - b^4)*c)*d*e*f - (a^4 + a^2*b^2 - (a^4 - b^4)*c^2 + 2*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c)^3 - ((a^4 - b^4)*d^2*e^2 + 2*(a^3*b + a*b^3 - (a^4 - b^4)*c)*d*e*f - (a^4 + a^2*b^2 - (a^4 - b^4)*c^2 + 2*(a^3*b + a*b^3)*c)*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (a^4*d^2*f^2*x^2 - I*a^3*b*d^2*f^2*x^2 + 2*a^4*d^2*e*f*x - 2*I*a^3*b*d^2*e*f*x + 2*a^4*c*d*e*f - 2*I*a^3*b*c*d*e*f - a^4*c^2*f^2 + I*a^3*b*c^2*f^2 + (a^4*d^2*f^2*x^2 - I*a^3*b*d^2*f^2*x^2 + 2*a^4*d^2*e*f*x - 2*I*a^3*b*d^2*e*f*x + 2*a^4*c*d*e*f - 2*I*a^3*b*c*d*e*f - a^4*c^2*f^2 + I*a^3*b*c^2*f^2)*cosh(d*x + c)^4 + (4*a^4*d^2*f^2*x^2 - 4*I*a^3*b*d^2*f^2*x^2 + 8*a^4*d^2*e*f*x - 8*I*a^3*b*d^2*e*f*x + 8*a^4*c*d*e*f - 8*I*a^3*b*c*d*e*f - 4*a^4*c^2*f^2 + 4*I*a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*d^2*f^2*x^2 - I*a^3*b*d^2*f^2*x^2 + 2*a^4*d^2*e*f*x - 2*I*a^3*b*d^2*e*f*x + 2*a^4*c*d*e*f - 2*I*a^3*b*c*d*e*f - a^4*c^2*f^2 + I*a^3*b*c^2*f^2)*sinh(d*x + c)^4 - (2*a^4*d^2*f^2*x^2 - 2*I*a^3*b*d^2*f^2*x^2 + 4*a^4*d^2*e*f*x - 4*I*a^3*b*d^2*e*f*x + 4*a^4*c*d*e*f - 4*I*a^3*b*c*d*e*f - 2*a^4*c^2*f^2 + 2*I*a^3*b*c^2*f^2)*cosh(d*x + c)^2 - (2*a^4*d^2*f^2*x^2 - 2*I*a^3*b*d^2*f^2*x^2 + 4*a^4*d^2*e*f*x - 4*I*a^3*b*d^2*e*f*x + 4*a^4*c*d*e*f - 4*I*a^3*b*c*d*e*f - 2*a^4*c^2*f^2 + 2*I*a^3*b*c^2*f^2 - (6*a^4*d^2*f^2*x^2 - 6*I*a^3*b*d^2*f^2*x^2 + 12*a^4*d^2*e*f*x - 12*I*a^3*b*d^2*e*f*x + 12*a^4*c*d*e*f - 12*I*a^3*b*c*d*e*f - 6*a^4*c^2*f^2 + 6*I*a^3*b*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^4*d^2*f^2*x^2 - 4*I*a^3*b*d^2*f^2*x^2 + 8*a^4*d^2*e*f*x - 8*I*a^3*b*d^2*e*f*x + 8*a^4*c*d*e*f - 8*I*a^3*b*c*d*e*f - 4*a^4*c^2*f^2 + 4*I*a^3*b*c^2*f^2)*cosh(d*x + c)^3 - (4*a^4*d^2*f^2*x^2 - 4*I*a^3*b*d^2*f^2*x^2 + 8*a^4*d^2*e*f*x - 8*I*a^3*b*d^2*e*f*x + 8*a^4*c*d*e*f - 8*I*a^3*b*c*d*e*f - 4*a^4*c^2*f^2 + 4*I*a^3*b*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) - (a^4*d^2*f^2*x^2 + I*a^3*b*d^2*f^2*x^2 + 2*a^4*d^2*e*f*x + 2*I*a^3*b*d^2*e*f*x + 2*a^4*c*d*e*f + 2*I*a^3*b*c*d*e*f - a^4*c^2*f^2 - I*a^3*b*c^2*f^2 + (a^4*d^2*f^2*x^2 + I*a^3*b*d^2*f^2*x^2 + 2*a^4*d^2*e*f*x + 2*I*a^3*b*d^2*e*f*x + 2*a^4*c*d*e*f + 2*I*a^3*b*c*d*e*f - a^4*c^2*f^2 - I*a^3*b*c^2*f^2)*cosh(d*x + c)^4 + (4*a^4*d^2*f^2*x^2 + 4*I*a^3*b*d^2*f^2*x^2 + 8*a^4*d^2*e*f*x + 8*I*a^3*b*d^2*e*f*x + 8*a^4*c*d*e*f + 8*I*a^3*b*c*d*e*f - 4*a^4*c^2*f^2 - 4*I*a^3*b*c^2*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*d^2*f^2*x^2 + I*a^3*b*d^2*f^2*x^2 + 2*a^4*d^2*e*f*x + 2*I*a^3*b*d^2*e*f*x + 2*a^4*c*d*e*f + 2*I*a^3*b*c*d*e*f - a^4*c^2*f^2 - I*a^3*b*c^2*f^2)*sinh(d*x + c)^4 - (2*a^4*d^2*f^2*x^2 + 2*I*a^3*b*d^2*f^2*x^2 + 4*a^4*d^2*e*f*x + 4*I*a^3*b*d^2*e*f*x + 4*a^4*c*d*e*f + 4*I*a^3*b*c*d*e*f - 2*a^4*c^2*f^2 - 2*I*a^3*b*c^2*f^2)*cosh(d*x + c)^2 - (2*a^4*d^2*f^2*x^2 + 2*I*a^3*b*d^2*f^2*x^2 + 4*a^4*d^2*e*f*x + 4*I*a^3*b*d^2*e*f*x + 4*a^4*c*d*e*f + 4*I*a^3*b*c*d*e*f - 2*a^4*c^2*f^2 - 2*I*a^3*b*c^2*f^2 - (6*a^4*d^2*f^2*x^2 + 6*I*a^3*b*d^2*f^2*x^2 + 12*a^4*d^2*e*f*x + 12*I*a^3*b*d^2*e*f*x + 12*a^4*c*d*e*f + 12*I*a^3*b*c*d*e*f - 6*a^4*c^2*f^2 - 6*I*a^3*b*c^2*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^4*d^2*f^2*x^2 + 4*I*a^3*b*d^2*f^2*x^2 + 8*a^4*d^2*e*f*x + 8*I*a^3*b*d^2*e*f*x + 8*a^4*c*d*e*f + 8*I*a^3*b*c*d*e*f - 4*a^4*c^2*f^2 - 4*I*a^3*b*c^2*f^2)*cosh(d*x + c)^3 - (4*a^4*d^2*f^2*x^2 + 4*I*a^3*b*d^2*f^2*x^2 + 8*a^4*d^2*e*f*x + 8*I*a^3*b*d^2*e*f*x + 8*a^4*c*d*e*f + 8*I*a^3*b*c*d*e*f - 4*a^4*c^2*f^2 - 4*I*a^3*b*c^2*f^2)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) + ((a^4 - b^4)*d^2*f^2*x^2 + 2*(a^4 - b^4)*c*d*e*f + ((a^4 - b^4)*d^2*f^2*x^2 + 2*(a^4 - b^4)*c*d*e*f - ((a^4 - b^4)*c^2 - 2*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - b^4)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^4 + 4*((a^4 - b^4)*d^2*f^2*x^2 + 2*(a^4 - b^4)*c*d*e*f - ((a^4 - b^4)*c^2 - 2*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - b^4)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - b^4)*d^2*f^2*x^2 + 2*(a^4 - b^4)*c*d*e*f - ((a^4 - b^4)*c^2 - 2*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - b^4)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x)*sinh(d*x + c)^4 - ((a^4 - b^4)*c^2 - 2*(a^3*b + a*b^3)*c)*f^2 - 2*((a^4 - b^4)*d^2*f^2*x^2 + 2*(a^4 - b^4)*c*d*e*f - ((a^4 - b^4)*c^2 - 2*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - b^4)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 - 2*((a^4 - b^4)*d^2*f^2*x^2 + 2*(a^4 - b^4)*c*d*e*f - ((a^4 - b^4)*c^2 - 2*(a^3*b + a*b^3)*c)*f^2 - 3*((a^4 - b^4)*d^2*f^2*x^2 + 2*(a^4 - b^4)*c*d*e*f - ((a^4 - b^4)*c^2 - 2*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - b^4)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^2 + 2*((a^4 - b^4)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x)*sinh(d*x + c)^2 + 2*((a^4 - b^4)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x + 4*(((a^4 - b^4)*d^2*f^2*x^2 + 2*(a^4 - b^4)*c*d*e*f - ((a^4 - b^4)*c^2 - 2*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - b^4)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c)^3 - ((a^4 - b^4)*d^2*f^2*x^2 + 2*(a^4 - b^4)*c*d*e*f - ((a^4 - b^4)*c^2 - 2*(a^3*b + a*b^3)*c)*f^2 + 2*((a^4 - b^4)*d^2*e*f + (a^3*b + a*b^3)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*(b^4*f^2*cosh(d*x + c)^4 + 4*b^4*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*f^2*sinh(d*x + c)^4 - 2*b^4*f^2*cosh(d*x + c)^2 + b^4*f^2 + 2*(3*b^4*f^2*cosh(d*x + c)^2 - b^4*f^2)*sinh(d*x + c)^2 + 4*(b^4*f^2*cosh(d*x + c)^3 - b^4*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*(b^4*f^2*cosh(d*x + c)^4 + 4*b^4*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*f^2*sinh(d*x + c)^4 - 2*b^4*f^2*cosh(d*x + c)^2 + b^4*f^2 + 2*(3*b^4*f^2*cosh(d*x + c)^2 - b^4*f^2)*sinh(d*x + c)^2 + 4*(b^4*f^2*cosh(d*x + c)^3 - b^4*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, (a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2))/b) - 2*((a^4 - b^4)*f^2*cosh(d*x + c)^4 + 4*(a^4 - b^4)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - b^4)*f^2*sinh(d*x + c)^4 - 2*(a^4 - b^4)*f^2*cosh(d*x + c)^2 + (a^4 - b^4)*f^2 + 2*(3*(a^4 - b^4)*f^2*cosh(d*x + c)^2 - (a^4 - b^4)*f^2)*sinh(d*x + c)^2 + 4*((a^4 - b^4)*f^2*cosh(d*x + c)^3 - (a^4 - b^4)*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, cosh(d*x + c) + sinh(d*x + c)) + (2*a^4*f^2 + 2*I*a^3*b*f^2 + (2*a^4*f^2 + 2*I*a^3*b*f^2)*cosh(d*x + c)^4 + (8*a^4*f^2 + 8*I*a^3*b*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^4*f^2 + 2*I*a^3*b*f^2)*sinh(d*x + c)^4 - (4*a^4*f^2 + 4*I*a^3*b*f^2)*cosh(d*x + c)^2 - (4*a^4*f^2 + 4*I*a^3*b*f^2 - (12*a^4*f^2 + 12*I*a^3*b*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^4*f^2 + 8*I*a^3*b*f^2)*cosh(d*x + c)^3 - (8*a^4*f^2 + 8*I*a^3*b*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, I*cosh(d*x + c) + I*sinh(d*x + c)) + (2*a^4*f^2 - 2*I*a^3*b*f^2 + (2*a^4*f^2 - 2*I*a^3*b*f^2)*cosh(d*x + c)^4 + (8*a^4*f^2 - 8*I*a^3*b*f^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^4*f^2 - 2*I*a^3*b*f^2)*sinh(d*x + c)^4 - (4*a^4*f^2 - 4*I*a^3*b*f^2)*cosh(d*x + c)^2 - (4*a^4*f^2 - 4*I*a^3*b*f^2 - (12*a^4*f^2 - 12*I*a^3*b*f^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^4*f^2 - 8*I*a^3*b*f^2)*cosh(d*x + c)^3 - (8*a^4*f^2 - 8*I*a^3*b*f^2)*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -I*cosh(d*x + c) - I*sinh(d*x + c)) - 2*((a^4 - b^4)*f^2*cosh(d*x + c)^4 + 4*(a^4 - b^4)*f^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - b^4)*f^2*sinh(d*x + c)^4 - 2*(a^4 - b^4)*f^2*cosh(d*x + c)^2 + (a^4 - b^4)*f^2 + 2*(3*(a^4 - b^4)*f^2*cosh(d*x + c)^2 - (a^4 - b^4)*f^2)*sinh(d*x + c)^2 + 4*((a^4 - b^4)*f^2*cosh(d*x + c)^3 - (a^4 - b^4)*f^2*cosh(d*x + c))*sinh(d*x + c))*polylog(3, -cosh(d*x + c) - sinh(d*x + c)) + 2*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + (a^3*b + a*b^3)*d^2*e^2 + 4*((a^4 + a^2*b^2)*d*f^2*x + (a^4 + a^2*b^2)*c*f^2)*cosh(d*x + c)^3 - 3*((a^3*b + a*b^3)*d^2*f^2*x^2 + 2*(a^3*b + a*b^3)*d^2*e*f*x + (a^3*b + a*b^3)*d^2*e^2)*cosh(d*x + c)^2 + 2*((a^4 + a^2*b^2)*d^2*f^2*x^2 + (a^4 + a^2*b^2)*d^2*e^2 + (a^4 + a^2*b^2)*d*e*f - 2*(a^4 + a^2*b^2)*c*f^2 + (2*(a^4 + a^2*b^2)*d^2*e*f - (a^4 + a^2*b^2)*d*f^2)*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + a^3*b^2)*d^3*cosh(d*x + c)^4 + 4*(a^5 + a^3*b^2)*d^3*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + a^3*b^2)*d^3*sinh(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d^3*cosh(d*x + c)^2 + (a^5 + a^3*b^2)*d^3 + 2*(3*(a^5 + a^3*b^2)*d^3*cosh(d*x + c)^2 - (a^5 + a^3*b^2)*d^3)*sinh(d*x + c)^2 + 4*((a^5 + a^3*b^2)*d^3*cosh(d*x + c)^3 - (a^5 + a^3*b^2)*d^3*cosh(d*x + c))*sinh(d*x + c))","C",0
493,1,5767,0,0.728122," ","integrate((f*x+e)*csch(d*x+c)^3*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e\right)} \sinh\left(d x + c\right)^{3} - {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} d f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e + {\left(a^{4} + a^{2} b^{2}\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} d f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e + {\left(a^{4} + a^{2} b^{2}\right)} f - 6 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + a^{2} b^{2}\right)} f - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e\right)} \cosh\left(d x + c\right) - {\left(b^{4} f \cosh\left(d x + c\right)^{4} + 4 \, b^{4} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} f \sinh\left(d x + c\right)^{4} - 2 \, b^{4} f \cosh\left(d x + c\right)^{2} + b^{4} f + 2 \, {\left(3 \, b^{4} f \cosh\left(d x + c\right)^{2} - b^{4} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} f \cosh\left(d x + c\right)^{3} - b^{4} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left(b^{4} f \cosh\left(d x + c\right)^{4} + 4 \, b^{4} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} f \sinh\left(d x + c\right)^{4} - 2 \, b^{4} f \cosh\left(d x + c\right)^{2} + b^{4} f + 2 \, {\left(3 \, b^{4} f \cosh\left(d x + c\right)^{2} - b^{4} f\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} f \cosh\left(d x + c\right)^{3} - b^{4} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) - {\left({\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - b^{4}\right)} f \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{4} - b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} - b^{4}\right)} f + 4 \, {\left({\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left(a^{4} f + i \, a^{3} b f + {\left(a^{4} f + i \, a^{3} b f\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, a^{4} f + 4 i \, a^{3} b f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} f + i \, a^{3} b f\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a^{4} f + 2 i \, a^{3} b f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} f + 2 i \, a^{3} b f - {\left(6 \, a^{4} f + 6 i \, a^{3} b f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} f + 4 i \, a^{3} b f\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} f + 4 i \, a^{3} b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right)\right) + {\left(a^{4} f - i \, a^{3} b f + {\left(a^{4} f - i \, a^{3} b f\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, a^{4} f - 4 i \, a^{3} b f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} f - i \, a^{3} b f\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a^{4} f - 2 i \, a^{3} b f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} f - 2 i \, a^{3} b f - {\left(6 \, a^{4} f - 6 i \, a^{3} b f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} f - 4 i \, a^{3} b f\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} f - 4 i \, a^{3} b f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right)\right) - {\left({\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - b^{4}\right)} f \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{4} - b^{4}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} - b^{4}\right)} f + 4 \, {\left({\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{4} - b^{4}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - {\left(b^{4} d e - b^{4} c f + {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d e - b^{4} c f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d e - b^{4} c f - 3 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{4} d e - b^{4} c f + {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d e - b^{4} c f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d e - b^{4} c f - 3 \, {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d e - b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b^{4} d f x + b^{4} c f + {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d f x + b^{4} c f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d f x + b^{4} c f - 3 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left(b^{4} d f x + b^{4} c f + {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(b^{4} d f x + b^{4} c f\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b^{4} d f x + b^{4} c f - 3 \, {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{4} d f x + b^{4} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) - {\left({\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} d e - 2 \, {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} d e - 3 \, {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} b + a b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} b + a b^{3}\right)} f + 4 \, {\left({\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} d e - {\left(a^{3} b + a b^{3}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left(a^{4} d e + i \, a^{3} b d e - a^{4} c f - i \, a^{3} b c f + {\left(a^{4} d e + i \, a^{3} b d e - a^{4} c f - i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, a^{4} d e + 4 i \, a^{3} b d e - 4 \, a^{4} c f - 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} d e + i \, a^{3} b d e - a^{4} c f - i \, a^{3} b c f\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a^{4} d e + 2 i \, a^{3} b d e - 2 \, a^{4} c f - 2 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} d e + 2 i \, a^{3} b d e - 2 \, a^{4} c f - 2 i \, a^{3} b c f - {\left(6 \, a^{4} d e + 6 i \, a^{3} b d e - 6 \, a^{4} c f - 6 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} d e + 4 i \, a^{3} b d e - 4 \, a^{4} c f - 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} d e + 4 i \, a^{3} b d e - 4 \, a^{4} c f - 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + i\right) + {\left(a^{4} d e - i \, a^{3} b d e - a^{4} c f + i \, a^{3} b c f + {\left(a^{4} d e - i \, a^{3} b d e - a^{4} c f + i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, a^{4} d e - 4 i \, a^{3} b d e - 4 \, a^{4} c f + 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} d e - i \, a^{3} b d e - a^{4} c f + i \, a^{3} b c f\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a^{4} d e - 2 i \, a^{3} b d e - 2 \, a^{4} c f + 2 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} d e - 2 i \, a^{3} b d e - 2 \, a^{4} c f + 2 i \, a^{3} b c f - {\left(6 \, a^{4} d e - 6 i \, a^{3} b d e - 6 \, a^{4} c f + 6 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} d e - 4 i \, a^{3} b d e - 4 \, a^{4} c f + 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} d e - 4 i \, a^{3} b d e - 4 \, a^{4} c f + 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - i\right) - {\left({\left({\left(a^{4} - b^{4}\right)} d e + {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - b^{4}\right)} d e + {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - b^{4}\right)} d e + {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - b^{4}\right)} d e - 2 \, {\left({\left(a^{4} - b^{4}\right)} d e + {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d e - 3 \, {\left({\left(a^{4} - b^{4}\right)} d e + {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} f + 4 \, {\left({\left({\left(a^{4} - b^{4}\right)} d e + {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - b^{4}\right)} d e + {\left(a^{3} b + a b^{3} - {\left(a^{4} - b^{4}\right)} c\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(a^{4} d f x - i \, a^{3} b d f x + a^{4} c f - i \, a^{3} b c f + {\left(a^{4} d f x - i \, a^{3} b d f x + a^{4} c f - i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, a^{4} d f x - 4 i \, a^{3} b d f x + 4 \, a^{4} c f - 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} d f x - i \, a^{3} b d f x + a^{4} c f - i \, a^{3} b c f\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a^{4} d f x - 2 i \, a^{3} b d f x + 2 \, a^{4} c f - 2 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} d f x - 2 i \, a^{3} b d f x + 2 \, a^{4} c f - 2 i \, a^{3} b c f - {\left(6 \, a^{4} d f x - 6 i \, a^{3} b d f x + 6 \, a^{4} c f - 6 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} d f x - 4 i \, a^{3} b d f x + 4 \, a^{4} c f - 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} d f x - 4 i \, a^{3} b d f x + 4 \, a^{4} c f - 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(i \, \cosh\left(d x + c\right) + i \, \sinh\left(d x + c\right) + 1\right) + {\left(a^{4} d f x + i \, a^{3} b d f x + a^{4} c f + i \, a^{3} b c f + {\left(a^{4} d f x + i \, a^{3} b d f x + a^{4} c f + i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{4} + {\left(4 \, a^{4} d f x + 4 i \, a^{3} b d f x + 4 \, a^{4} c f + 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} d f x + i \, a^{3} b d f x + a^{4} c f + i \, a^{3} b c f\right)} \sinh\left(d x + c\right)^{4} - {\left(2 \, a^{4} d f x + 2 i \, a^{3} b d f x + 2 \, a^{4} c f + 2 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{4} d f x + 2 i \, a^{3} b d f x + 2 \, a^{4} c f + 2 i \, a^{3} b c f - {\left(6 \, a^{4} d f x + 6 i \, a^{3} b d f x + 6 \, a^{4} c f + 6 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} d f x + 4 i \, a^{3} b d f x + 4 \, a^{4} c f + 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} d f x + 4 i \, a^{3} b d f x + 4 \, a^{4} c f + 4 i \, a^{3} b c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-i \, \cosh\left(d x + c\right) - i \, \sinh\left(d x + c\right) + 1\right) - {\left({\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} c f\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} c f - 2 \, {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} c f - 3 \, {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{4} - b^{4}\right)} d f x + {\left(a^{4} - b^{4}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e - 3 \, {\left({\left(a^{3} b + a b^{3}\right)} d f x + {\left(a^{3} b + a b^{3}\right)} d e\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, {\left(a^{4} + a^{2} b^{2}\right)} d f x + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} d e + {\left(a^{4} + a^{2} b^{2}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + a^{3} b^{2}\right)} d^{2} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d^{2} + 2 \, {\left(3 \, {\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{5} + a^{3} b^{2}\right)} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"(2*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e)*cosh(d*x + c)^3 + 2*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e)*sinh(d*x + c)^3 - (2*(a^4 + a^2*b^2)*d*f*x + 2*(a^4 + a^2*b^2)*d*e + (a^4 + a^2*b^2)*f)*cosh(d*x + c)^2 - (2*(a^4 + a^2*b^2)*d*f*x + 2*(a^4 + a^2*b^2)*d*e + (a^4 + a^2*b^2)*f - 6*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e)*cosh(d*x + c))*sinh(d*x + c)^2 + (a^4 + a^2*b^2)*f - 2*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e)*cosh(d*x + c) - (b^4*f*cosh(d*x + c)^4 + 4*b^4*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*f*sinh(d*x + c)^4 - 2*b^4*f*cosh(d*x + c)^2 + b^4*f + 2*(3*b^4*f*cosh(d*x + c)^2 - b^4*f)*sinh(d*x + c)^2 + 4*(b^4*f*cosh(d*x + c)^3 - b^4*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - (b^4*f*cosh(d*x + c)^4 + 4*b^4*f*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*f*sinh(d*x + c)^4 - 2*b^4*f*cosh(d*x + c)^2 + b^4*f + 2*(3*b^4*f*cosh(d*x + c)^2 - b^4*f)*sinh(d*x + c)^2 + 4*(b^4*f*cosh(d*x + c)^3 - b^4*f*cosh(d*x + c))*sinh(d*x + c))*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) - ((a^4 - b^4)*f*cosh(d*x + c)^4 + 4*(a^4 - b^4)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - b^4)*f*sinh(d*x + c)^4 - 2*(a^4 - b^4)*f*cosh(d*x + c)^2 + 2*(3*(a^4 - b^4)*f*cosh(d*x + c)^2 - (a^4 - b^4)*f)*sinh(d*x + c)^2 + (a^4 - b^4)*f + 4*((a^4 - b^4)*f*cosh(d*x + c)^3 - (a^4 - b^4)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + (a^4*f + I*a^3*b*f + (a^4*f + I*a^3*b*f)*cosh(d*x + c)^4 + (4*a^4*f + 4*I*a^3*b*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*f + I*a^3*b*f)*sinh(d*x + c)^4 - (2*a^4*f + 2*I*a^3*b*f)*cosh(d*x + c)^2 - (2*a^4*f + 2*I*a^3*b*f - (6*a^4*f + 6*I*a^3*b*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^4*f + 4*I*a^3*b*f)*cosh(d*x + c)^3 - (4*a^4*f + 4*I*a^3*b*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(I*cosh(d*x + c) + I*sinh(d*x + c)) + (a^4*f - I*a^3*b*f + (a^4*f - I*a^3*b*f)*cosh(d*x + c)^4 + (4*a^4*f - 4*I*a^3*b*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*f - I*a^3*b*f)*sinh(d*x + c)^4 - (2*a^4*f - 2*I*a^3*b*f)*cosh(d*x + c)^2 - (2*a^4*f - 2*I*a^3*b*f - (6*a^4*f - 6*I*a^3*b*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^4*f - 4*I*a^3*b*f)*cosh(d*x + c)^3 - (4*a^4*f - 4*I*a^3*b*f)*cosh(d*x + c))*sinh(d*x + c))*dilog(-I*cosh(d*x + c) - I*sinh(d*x + c)) - ((a^4 - b^4)*f*cosh(d*x + c)^4 + 4*(a^4 - b^4)*f*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - b^4)*f*sinh(d*x + c)^4 - 2*(a^4 - b^4)*f*cosh(d*x + c)^2 + 2*(3*(a^4 - b^4)*f*cosh(d*x + c)^2 - (a^4 - b^4)*f)*sinh(d*x + c)^2 + (a^4 - b^4)*f + 4*((a^4 - b^4)*f*cosh(d*x + c)^3 - (a^4 - b^4)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) - (b^4*d*e - b^4*c*f + (b^4*d*e - b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*e - b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*e - b^4*c*f)*sinh(d*x + c)^4 - 2*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2 - 2*(b^4*d*e - b^4*c*f - 3*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*e - b^4*c*f)*cosh(d*x + c)^3 - (b^4*d*e - b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^4*d*e - b^4*c*f + (b^4*d*e - b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*e - b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*e - b^4*c*f)*sinh(d*x + c)^4 - 2*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2 - 2*(b^4*d*e - b^4*c*f - 3*(b^4*d*e - b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*e - b^4*c*f)*cosh(d*x + c)^3 - (b^4*d*e - b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - (b^4*d*f*x + b^4*c*f + (b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*f*x + b^4*c*f)*sinh(d*x + c)^4 - 2*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2 - 2*(b^4*d*f*x + b^4*c*f - 3*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^3 - (b^4*d*f*x + b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (b^4*d*f*x + b^4*c*f + (b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^4 + 4*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (b^4*d*f*x + b^4*c*f)*sinh(d*x + c)^4 - 2*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2 - 2*(b^4*d*f*x + b^4*c*f - 3*(b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((b^4*d*f*x + b^4*c*f)*cosh(d*x + c)^3 - (b^4*d*f*x + b^4*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) - (((a^4 - b^4)*d*f*x + (a^4 - b^4)*d*e - (a^3*b + a*b^3)*f)*cosh(d*x + c)^4 + 4*((a^4 - b^4)*d*f*x + (a^4 - b^4)*d*e - (a^3*b + a*b^3)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - b^4)*d*f*x + (a^4 - b^4)*d*e - (a^3*b + a*b^3)*f)*sinh(d*x + c)^4 + (a^4 - b^4)*d*f*x + (a^4 - b^4)*d*e - 2*((a^4 - b^4)*d*f*x + (a^4 - b^4)*d*e - (a^3*b + a*b^3)*f)*cosh(d*x + c)^2 - 2*((a^4 - b^4)*d*f*x + (a^4 - b^4)*d*e - 3*((a^4 - b^4)*d*f*x + (a^4 - b^4)*d*e - (a^3*b + a*b^3)*f)*cosh(d*x + c)^2 - (a^3*b + a*b^3)*f)*sinh(d*x + c)^2 - (a^3*b + a*b^3)*f + 4*(((a^4 - b^4)*d*f*x + (a^4 - b^4)*d*e - (a^3*b + a*b^3)*f)*cosh(d*x + c)^3 - ((a^4 - b^4)*d*f*x + (a^4 - b^4)*d*e - (a^3*b + a*b^3)*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (a^4*d*e + I*a^3*b*d*e - a^4*c*f - I*a^3*b*c*f + (a^4*d*e + I*a^3*b*d*e - a^4*c*f - I*a^3*b*c*f)*cosh(d*x + c)^4 + (4*a^4*d*e + 4*I*a^3*b*d*e - 4*a^4*c*f - 4*I*a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*d*e + I*a^3*b*d*e - a^4*c*f - I*a^3*b*c*f)*sinh(d*x + c)^4 - (2*a^4*d*e + 2*I*a^3*b*d*e - 2*a^4*c*f - 2*I*a^3*b*c*f)*cosh(d*x + c)^2 - (2*a^4*d*e + 2*I*a^3*b*d*e - 2*a^4*c*f - 2*I*a^3*b*c*f - (6*a^4*d*e + 6*I*a^3*b*d*e - 6*a^4*c*f - 6*I*a^3*b*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^4*d*e + 4*I*a^3*b*d*e - 4*a^4*c*f - 4*I*a^3*b*c*f)*cosh(d*x + c)^3 - (4*a^4*d*e + 4*I*a^3*b*d*e - 4*a^4*c*f - 4*I*a^3*b*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + I) + (a^4*d*e - I*a^3*b*d*e - a^4*c*f + I*a^3*b*c*f + (a^4*d*e - I*a^3*b*d*e - a^4*c*f + I*a^3*b*c*f)*cosh(d*x + c)^4 + (4*a^4*d*e - 4*I*a^3*b*d*e - 4*a^4*c*f + 4*I*a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*d*e - I*a^3*b*d*e - a^4*c*f + I*a^3*b*c*f)*sinh(d*x + c)^4 - (2*a^4*d*e - 2*I*a^3*b*d*e - 2*a^4*c*f + 2*I*a^3*b*c*f)*cosh(d*x + c)^2 - (2*a^4*d*e - 2*I*a^3*b*d*e - 2*a^4*c*f + 2*I*a^3*b*c*f - (6*a^4*d*e - 6*I*a^3*b*d*e - 6*a^4*c*f + 6*I*a^3*b*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^4*d*e - 4*I*a^3*b*d*e - 4*a^4*c*f + 4*I*a^3*b*c*f)*cosh(d*x + c)^3 - (4*a^4*d*e - 4*I*a^3*b*d*e - 4*a^4*c*f + 4*I*a^3*b*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - I) - (((a^4 - b^4)*d*e + (a^3*b + a*b^3 - (a^4 - b^4)*c)*f)*cosh(d*x + c)^4 + 4*((a^4 - b^4)*d*e + (a^3*b + a*b^3 - (a^4 - b^4)*c)*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - b^4)*d*e + (a^3*b + a*b^3 - (a^4 - b^4)*c)*f)*sinh(d*x + c)^4 + (a^4 - b^4)*d*e - 2*((a^4 - b^4)*d*e + (a^3*b + a*b^3 - (a^4 - b^4)*c)*f)*cosh(d*x + c)^2 - 2*((a^4 - b^4)*d*e - 3*((a^4 - b^4)*d*e + (a^3*b + a*b^3 - (a^4 - b^4)*c)*f)*cosh(d*x + c)^2 + (a^3*b + a*b^3 - (a^4 - b^4)*c)*f)*sinh(d*x + c)^2 + (a^3*b + a*b^3 - (a^4 - b^4)*c)*f + 4*(((a^4 - b^4)*d*e + (a^3*b + a*b^3 - (a^4 - b^4)*c)*f)*cosh(d*x + c)^3 - ((a^4 - b^4)*d*e + (a^3*b + a*b^3 - (a^4 - b^4)*c)*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (a^4*d*f*x - I*a^3*b*d*f*x + a^4*c*f - I*a^3*b*c*f + (a^4*d*f*x - I*a^3*b*d*f*x + a^4*c*f - I*a^3*b*c*f)*cosh(d*x + c)^4 + (4*a^4*d*f*x - 4*I*a^3*b*d*f*x + 4*a^4*c*f - 4*I*a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*d*f*x - I*a^3*b*d*f*x + a^4*c*f - I*a^3*b*c*f)*sinh(d*x + c)^4 - (2*a^4*d*f*x - 2*I*a^3*b*d*f*x + 2*a^4*c*f - 2*I*a^3*b*c*f)*cosh(d*x + c)^2 - (2*a^4*d*f*x - 2*I*a^3*b*d*f*x + 2*a^4*c*f - 2*I*a^3*b*c*f - (6*a^4*d*f*x - 6*I*a^3*b*d*f*x + 6*a^4*c*f - 6*I*a^3*b*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^4*d*f*x - 4*I*a^3*b*d*f*x + 4*a^4*c*f - 4*I*a^3*b*c*f)*cosh(d*x + c)^3 - (4*a^4*d*f*x - 4*I*a^3*b*d*f*x + 4*a^4*c*f - 4*I*a^3*b*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(I*cosh(d*x + c) + I*sinh(d*x + c) + 1) + (a^4*d*f*x + I*a^3*b*d*f*x + a^4*c*f + I*a^3*b*c*f + (a^4*d*f*x + I*a^3*b*d*f*x + a^4*c*f + I*a^3*b*c*f)*cosh(d*x + c)^4 + (4*a^4*d*f*x + 4*I*a^3*b*d*f*x + 4*a^4*c*f + 4*I*a^3*b*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*d*f*x + I*a^3*b*d*f*x + a^4*c*f + I*a^3*b*c*f)*sinh(d*x + c)^4 - (2*a^4*d*f*x + 2*I*a^3*b*d*f*x + 2*a^4*c*f + 2*I*a^3*b*c*f)*cosh(d*x + c)^2 - (2*a^4*d*f*x + 2*I*a^3*b*d*f*x + 2*a^4*c*f + 2*I*a^3*b*c*f - (6*a^4*d*f*x + 6*I*a^3*b*d*f*x + 6*a^4*c*f + 6*I*a^3*b*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^4*d*f*x + 4*I*a^3*b*d*f*x + 4*a^4*c*f + 4*I*a^3*b*c*f)*cosh(d*x + c)^3 - (4*a^4*d*f*x + 4*I*a^3*b*d*f*x + 4*a^4*c*f + 4*I*a^3*b*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-I*cosh(d*x + c) - I*sinh(d*x + c) + 1) - (((a^4 - b^4)*d*f*x + (a^4 - b^4)*c*f)*cosh(d*x + c)^4 + 4*((a^4 - b^4)*d*f*x + (a^4 - b^4)*c*f)*cosh(d*x + c)*sinh(d*x + c)^3 + ((a^4 - b^4)*d*f*x + (a^4 - b^4)*c*f)*sinh(d*x + c)^4 + (a^4 - b^4)*d*f*x + (a^4 - b^4)*c*f - 2*((a^4 - b^4)*d*f*x + (a^4 - b^4)*c*f)*cosh(d*x + c)^2 - 2*((a^4 - b^4)*d*f*x + (a^4 - b^4)*c*f - 3*((a^4 - b^4)*d*f*x + (a^4 - b^4)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(((a^4 - b^4)*d*f*x + (a^4 - b^4)*c*f)*cosh(d*x + c)^3 - ((a^4 - b^4)*d*f*x + (a^4 - b^4)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) - 2*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e - 3*((a^3*b + a*b^3)*d*f*x + (a^3*b + a*b^3)*d*e)*cosh(d*x + c)^2 + (2*(a^4 + a^2*b^2)*d*f*x + 2*(a^4 + a^2*b^2)*d*e + (a^4 + a^2*b^2)*f)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + a^3*b^2)*d^2*cosh(d*x + c)^4 + 4*(a^5 + a^3*b^2)*d^2*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + a^3*b^2)*d^2*sinh(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d^2*cosh(d*x + c)^2 + (a^5 + a^3*b^2)*d^2 + 2*(3*(a^5 + a^3*b^2)*d^2*cosh(d*x + c)^2 - (a^5 + a^3*b^2)*d^2)*sinh(d*x + c)^2 + 4*((a^5 + a^3*b^2)*d^2*cosh(d*x + c)^3 - (a^5 + a^3*b^2)*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
494,1,1035,0,0.793405," ","integrate(csch(d*x+c)^3*sech(d*x+c)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{3} b + a b^{3}\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{4} + a^{2} b^{2} - 3 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{3} b \sinh\left(d x + c\right)^{4} - 2 \, a^{3} b \cosh\left(d x + c\right)^{2} + a^{3} b + 2 \, {\left(3 \, a^{3} b \cosh\left(d x + c\right)^{2} - a^{3} b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b \cosh\left(d x + c\right)^{3} - a^{3} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right) - {\left(b^{4} \cosh\left(d x + c\right)^{4} + 4 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{4} \sinh\left(d x + c\right)^{4} - 2 \, b^{4} \cosh\left(d x + c\right)^{2} + b^{4} + 2 \, {\left(3 \, b^{4} \cosh\left(d x + c\right)^{2} - b^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{4} \cosh\left(d x + c\right)^{3} - b^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left(a^{4} \cosh\left(d x + c\right)^{4} + 4 \, a^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{4} \sinh\left(d x + c\right)^{4} - 2 \, a^{4} \cosh\left(d x + c\right)^{2} + a^{4} + 2 \, {\left(3 \, a^{4} \cosh\left(d x + c\right)^{2} - a^{4}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{4} \cosh\left(d x + c\right)^{3} - a^{4} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left({\left(a^{4} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} - b^{4}\right)} \sinh\left(d x + c\right)^{4} + a^{4} - b^{4} - 2 \, {\left(a^{4} - b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{4} - b^{4} - 3 \, {\left(a^{4} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{4} - b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - 2 \, {\left(a^{3} b + a b^{3} - 3 \, {\left(a^{3} b + a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} + a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + a^{3} b^{2}\right)} d + 4 \, {\left({\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}"," ",0,"(2*(a^3*b + a*b^3)*cosh(d*x + c)^3 + 2*(a^3*b + a*b^3)*sinh(d*x + c)^3 - 2*(a^4 + a^2*b^2)*cosh(d*x + c)^2 - 2*(a^4 + a^2*b^2 - 3*(a^3*b + a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*(a^3*b*cosh(d*x + c)^4 + 4*a^3*b*cosh(d*x + c)*sinh(d*x + c)^3 + a^3*b*sinh(d*x + c)^4 - 2*a^3*b*cosh(d*x + c)^2 + a^3*b + 2*(3*a^3*b*cosh(d*x + c)^2 - a^3*b)*sinh(d*x + c)^2 + 4*(a^3*b*cosh(d*x + c)^3 - a^3*b*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*(a^3*b + a*b^3)*cosh(d*x + c) - (b^4*cosh(d*x + c)^4 + 4*b^4*cosh(d*x + c)*sinh(d*x + c)^3 + b^4*sinh(d*x + c)^4 - 2*b^4*cosh(d*x + c)^2 + b^4 + 2*(3*b^4*cosh(d*x + c)^2 - b^4)*sinh(d*x + c)^2 + 4*(b^4*cosh(d*x + c)^3 - b^4*cosh(d*x + c))*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + (a^4*cosh(d*x + c)^4 + 4*a^4*cosh(d*x + c)*sinh(d*x + c)^3 + a^4*sinh(d*x + c)^4 - 2*a^4*cosh(d*x + c)^2 + a^4 + 2*(3*a^4*cosh(d*x + c)^2 - a^4)*sinh(d*x + c)^2 + 4*(a^4*cosh(d*x + c)^3 - a^4*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - ((a^4 - b^4)*cosh(d*x + c)^4 + 4*(a^4 - b^4)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 - b^4)*sinh(d*x + c)^4 + a^4 - b^4 - 2*(a^4 - b^4)*cosh(d*x + c)^2 - 2*(a^4 - b^4 - 3*(a^4 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^4 - b^4)*cosh(d*x + c)^3 - (a^4 - b^4)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - 2*(a^3*b + a*b^3 - 3*(a^3*b + a*b^3)*cosh(d*x + c)^2 + 2*(a^4 + a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + a^3*b^2)*d*cosh(d*x + c)^4 + 4*(a^5 + a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^5 + a^3*b^2)*d*sinh(d*x + c)^4 - 2*(a^5 + a^3*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^5 + a^3*b^2)*d*cosh(d*x + c)^2 - (a^5 + a^3*b^2)*d)*sinh(d*x + c)^2 + (a^5 + a^3*b^2)*d + 4*((a^5 + a^3*b^2)*d*cosh(d*x + c)^3 - (a^5 + a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
495,0,0,0,83.482144," ","integrate(csch(d*x+c)^3*sech(d*x+c)/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(d x + c\right)^{3} \operatorname{sech}\left(d x + c\right)}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(csch(d*x + c)^3*sech(d*x + c)/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
496,-1,0,0,0.000000," ","integrate((f*x+e)^2*csch(d*x+c)^3*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
497,1,11126,0,0.845370," ","integrate((f*x+e)*csch(d*x+c)^3*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, {\left({\left(2 \, a^{5} b + 3 \, a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left({\left(2 \, a^{5} b + 3 \, a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d e + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d e + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} f - 12 \, {\left({\left(2 \, a^{5} b + 3 \, a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d f x - {\left(a^{3} b^{3} + a b^{5}\right)} d e + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(4 \, {\left(a^{5} b + a^{3} b^{3}\right)} d f x - 2 \, {\left(a^{3} b^{3} + a b^{5}\right)} d e + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f - 30 \, {\left({\left(2 \, a^{5} b + 3 \, a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d e + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left({\left(a^{6} - a^{2} b^{4}\right)} d f x + {\left(a^{6} - a^{2} b^{4}\right)} d e\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left({\left(a^{6} - a^{2} b^{4}\right)} d f x + 20 \, {\left({\left(2 \, a^{5} b + 3 \, a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{6} - a^{2} b^{4}\right)} d e - 5 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d e + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d f x - {\left(a^{3} b^{3} + a b^{5}\right)} d e + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a^{5} b + 3 \, a^{3} b^{3} + a b^{5}\right)} d e + 4 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f - 4 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d f x - 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d e + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(15 \, {\left({\left(2 \, a^{5} b + 3 \, a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{4} - {\left(a^{3} b^{3} + a b^{5}\right)} d f x - 5 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d e + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d e - {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f - 6 \, {\left(2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d f x - {\left(a^{3} b^{3} + a b^{5}\right)} d e + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{6} - a^{2} b^{4}\right)} d f x + {\left(a^{6} - a^{2} b^{4}\right)} d e\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(b^{6} f \cosh\left(d x + c\right)^{6} + 6 \, b^{6} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{6} f \sinh\left(d x + c\right)^{6} - b^{6} f \cosh\left(d x + c\right)^{4} - b^{6} f \cosh\left(d x + c\right)^{2} + b^{6} f + {\left(15 \, b^{6} f \cosh\left(d x + c\right)^{2} - b^{6} f\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{6} f \cosh\left(d x + c\right)^{3} - b^{6} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, b^{6} f \cosh\left(d x + c\right)^{4} - 6 \, b^{6} f \cosh\left(d x + c\right)^{2} - b^{6} f\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{6} f \cosh\left(d x + c\right)^{5} - 2 \, b^{6} f \cosh\left(d x + c\right)^{3} - b^{6} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{6} f \cosh\left(d x + c\right)^{6} + 6 \, b^{6} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{6} f \sinh\left(d x + c\right)^{6} - b^{6} f \cosh\left(d x + c\right)^{4} - b^{6} f \cosh\left(d x + c\right)^{2} + b^{6} f + {\left(15 \, b^{6} f \cosh\left(d x + c\right)^{2} - b^{6} f\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{6} f \cosh\left(d x + c\right)^{3} - b^{6} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, b^{6} f \cosh\left(d x + c\right)^{4} - 6 \, b^{6} f \cosh\left(d x + c\right)^{2} - b^{6} f\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{6} f \cosh\left(d x + c\right)^{5} - 2 \, b^{6} f \cosh\left(d x + c\right)^{3} - b^{6} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} {\rm Li}_2\left(\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b} + 1\right) + 2 \, {\left(b^{6} d e - b^{6} c f + {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(b^{6} d e - b^{6} c f\right)} \sinh\left(d x + c\right)^{6} - {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{4} - {\left(b^{6} d e - b^{6} c f - 15 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{6} d e - b^{6} c f - 15 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) + 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{6} d e - b^{6} c f + {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(b^{6} d e - b^{6} c f\right)} \sinh\left(d x + c\right)^{6} - {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{4} - {\left(b^{6} d e - b^{6} c f - 15 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{6} d e - b^{6} c f - 15 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{6} d e - b^{6} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(d x + c\right) + 2 \, b \sinh\left(d x + c\right) - 2 \, b \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} + 2 \, a\right) - 2 \, {\left(b^{6} d f x + b^{6} c f + {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(b^{6} d f x + b^{6} c f\right)} \sinh\left(d x + c\right)^{6} - {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{4} - {\left(b^{6} d f x + b^{6} c f - 15 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{6} d f x + b^{6} c f - 15 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 2 \, {\left(b^{6} d f x + b^{6} c f + {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(b^{6} d f x + b^{6} c f\right)} \sinh\left(d x + c\right)^{6} - {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{4} - {\left(b^{6} d f x + b^{6} c f - 15 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{6} d f x + b^{6} c f - 15 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(b^{6} d f x + b^{6} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} \log\left(-\frac{a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + b^{2}}{b^{2}}} - b}{b}\right) + 4 \, {\left({\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{6} + a^{4} b^{2}\right)} f \sinh\left(d x + c\right)^{6} - {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{6} + a^{4} b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{6} + a^{4} b^{2}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} + a^{4} b^{2}\right)} f + 2 \, {\left(3 \, {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{6} + a^{4} b^{2}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d e - {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} f\right)} \cosh\left(d x + c\right) - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \sinh\left(d x + c\right)^{6} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f\right)} \sinh\left(d x + c\right)^{4} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{4} - 6 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f + 2 \, {\left(3 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \sinh\left(d x + c\right)^{6} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f\right)} \sinh\left(d x + c\right)^{4} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{4} - 6 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f + 2 \, {\left(3 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} {\rm Li}_2\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right)\right) - 2 \, {\left({\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} b + a^{3} b^{3}\right)} f \sinh\left(d x + c\right)^{6} - {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{5} b + a^{3} b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)^{2} - {\left(a^{5} b + a^{3} b^{3}\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b + a^{3} b^{3}\right)} f + 2 \, {\left(3 \, {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)^{3} - {\left(a^{5} b + a^{3} b^{3}\right)} f \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left({\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \sinh\left(d x + c\right)^{6} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{4} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 15 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + 4 \, {\left(5 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{4} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 6 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f + 2 \, {\left(3 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 2 \, {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{6} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{4} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 15 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{4} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e - 6 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{2} - {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \sinh\left(d x + c\right)^{2} + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f + 2 \, {\left(3 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d e + {\left(2 \, a^{5} b + 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c\right)} f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - {\left({\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \sinh\left(d x + c\right)^{6} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)^{4} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f - 15 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + 4 \, {\left(5 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)^{4} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f - 6 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\cosh\left(d x + c\right) - \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(12 \, {\left({\left(2 \, a^{5} b + 3 \, a^{3} b^{3} + a b^{5}\right)} d f x + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d f x + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d e + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} f\right)} \cosh\left(d x + c\right)^{4} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d f x - 8 \, {\left(2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d f x - {\left(a^{3} b^{3} + a b^{5}\right)} d e + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} d e + 6 \, {\left({\left(a^{6} - a^{2} b^{4}\right)} d f x + {\left(a^{6} - a^{2} b^{4}\right)} d e\right)} \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} f - 4 \, {\left({\left(a^{3} b^{3} + a b^{5}\right)} d f x - 2 \, {\left(a^{5} b + a^{3} b^{3}\right)} d e + {\left(a^{5} b + 2 \, a^{3} b^{3} + a b^{5}\right)} c f\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \sinh\left(d x + c\right)^{6} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{4} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} + {\left(15 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)^{3} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(4*((2*a^5*b + 3*a^3*b^3 + a*b^5)*d*f*x + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c)^6 + 4*((2*a^5*b + 3*a^3*b^3 + a*b^5)*d*f*x + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*sinh(d*x + c)^6 - 2*((3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*f*x + (3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*e + (a^6 + 2*a^4*b^2 + a^2*b^4)*f)*cosh(d*x + c)^5 - 2*((3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*f*x + (3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*e + (a^6 + 2*a^4*b^2 + a^2*b^4)*f - 12*((2*a^5*b + 3*a^3*b^3 + a*b^5)*d*f*x + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(2*(a^5*b + a^3*b^3)*d*f*x - (a^3*b^3 + a*b^5)*d*e + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c)^4 - 2*(4*(a^5*b + a^3*b^3)*d*f*x - 2*(a^3*b^3 + a*b^5)*d*e + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*c*f - 30*((2*a^5*b + 3*a^3*b^3 + a*b^5)*d*f*x + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c)^2 + 5*((3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*f*x + (3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*e + (a^6 + 2*a^4*b^2 + a^2*b^4)*f)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*((a^6 - a^2*b^4)*d*f*x + (a^6 - a^2*b^4)*d*e)*cosh(d*x + c)^3 + 4*((a^6 - a^2*b^4)*d*f*x + 20*((2*a^5*b + 3*a^3*b^3 + a*b^5)*d*f*x + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c)^3 + (a^6 - a^2*b^4)*d*e - 5*((3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*f*x + (3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*e + (a^6 + 2*a^4*b^2 + a^2*b^4)*f)*cosh(d*x + c)^2 - 4*(2*(a^5*b + a^3*b^3)*d*f*x - (a^3*b^3 + a*b^5)*d*e + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(2*a^5*b + 3*a^3*b^3 + a*b^5)*d*e + 4*(a^5*b + 2*a^3*b^3 + a*b^5)*c*f - 4*((a^3*b^3 + a*b^5)*d*f*x - 2*(a^5*b + a^3*b^3)*d*e + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c)^2 + 4*(15*((2*a^5*b + 3*a^3*b^3 + a*b^5)*d*f*x + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c)^4 - (a^3*b^3 + a*b^5)*d*f*x - 5*((3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*f*x + (3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*e + (a^6 + 2*a^4*b^2 + a^2*b^4)*f)*cosh(d*x + c)^3 + 2*(a^5*b + a^3*b^3)*d*e - (a^5*b + 2*a^3*b^3 + a*b^5)*c*f - 6*(2*(a^5*b + a^3*b^3)*d*f*x - (a^3*b^3 + a*b^5)*d*e + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c)^2 + 3*((a^6 - a^2*b^4)*d*f*x + (a^6 - a^2*b^4)*d*e)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(b^6*f*cosh(d*x + c)^6 + 6*b^6*f*cosh(d*x + c)*sinh(d*x + c)^5 + b^6*f*sinh(d*x + c)^6 - b^6*f*cosh(d*x + c)^4 - b^6*f*cosh(d*x + c)^2 + b^6*f + (15*b^6*f*cosh(d*x + c)^2 - b^6*f)*sinh(d*x + c)^4 + 4*(5*b^6*f*cosh(d*x + c)^3 - b^6*f*cosh(d*x + c))*sinh(d*x + c)^3 + (15*b^6*f*cosh(d*x + c)^4 - 6*b^6*f*cosh(d*x + c)^2 - b^6*f)*sinh(d*x + c)^2 + 2*(3*b^6*f*cosh(d*x + c)^5 - 2*b^6*f*cosh(d*x + c)^3 - b^6*f*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^6*f*cosh(d*x + c)^6 + 6*b^6*f*cosh(d*x + c)*sinh(d*x + c)^5 + b^6*f*sinh(d*x + c)^6 - b^6*f*cosh(d*x + c)^4 - b^6*f*cosh(d*x + c)^2 + b^6*f + (15*b^6*f*cosh(d*x + c)^2 - b^6*f)*sinh(d*x + c)^4 + 4*(5*b^6*f*cosh(d*x + c)^3 - b^6*f*cosh(d*x + c))*sinh(d*x + c)^3 + (15*b^6*f*cosh(d*x + c)^4 - 6*b^6*f*cosh(d*x + c)^2 - b^6*f)*sinh(d*x + c)^2 + 2*(3*b^6*f*cosh(d*x + c)^5 - 2*b^6*f*cosh(d*x + c)^3 - b^6*f*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*dilog((a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b + 1) + 2*(b^6*d*e - b^6*c*f + (b^6*d*e - b^6*c*f)*cosh(d*x + c)^6 + 6*(b^6*d*e - b^6*c*f)*cosh(d*x + c)*sinh(d*x + c)^5 + (b^6*d*e - b^6*c*f)*sinh(d*x + c)^6 - (b^6*d*e - b^6*c*f)*cosh(d*x + c)^4 - (b^6*d*e - b^6*c*f - 15*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^3 - (b^6*d*e - b^6*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 - (b^6*d*e - b^6*c*f)*cosh(d*x + c)^2 - (b^6*d*e - b^6*c*f - 15*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^4 + 6*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^5 - 2*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^3 - (b^6*d*e - b^6*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) + 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^6*d*e - b^6*c*f + (b^6*d*e - b^6*c*f)*cosh(d*x + c)^6 + 6*(b^6*d*e - b^6*c*f)*cosh(d*x + c)*sinh(d*x + c)^5 + (b^6*d*e - b^6*c*f)*sinh(d*x + c)^6 - (b^6*d*e - b^6*c*f)*cosh(d*x + c)^4 - (b^6*d*e - b^6*c*f - 15*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^3 - (b^6*d*e - b^6*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 - (b^6*d*e - b^6*c*f)*cosh(d*x + c)^2 - (b^6*d*e - b^6*c*f - 15*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^4 + 6*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^5 - 2*(b^6*d*e - b^6*c*f)*cosh(d*x + c)^3 - (b^6*d*e - b^6*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(2*b*cosh(d*x + c) + 2*b*sinh(d*x + c) - 2*b*sqrt((a^2 + b^2)/b^2) + 2*a) - 2*(b^6*d*f*x + b^6*c*f + (b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^6 + 6*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)*sinh(d*x + c)^5 + (b^6*d*f*x + b^6*c*f)*sinh(d*x + c)^6 - (b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^4 - (b^6*d*f*x + b^6*c*f - 15*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^3 - (b^6*d*f*x + b^6*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 - (b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^2 - (b^6*d*f*x + b^6*c*f - 15*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^4 + 6*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^5 - 2*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^3 - (b^6*d*f*x + b^6*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) + (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 2*(b^6*d*f*x + b^6*c*f + (b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^6 + 6*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)*sinh(d*x + c)^5 + (b^6*d*f*x + b^6*c*f)*sinh(d*x + c)^6 - (b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^4 - (b^6*d*f*x + b^6*c*f - 15*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^3 - (b^6*d*f*x + b^6*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 - (b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^2 - (b^6*d*f*x + b^6*c*f - 15*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^4 + 6*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^5 - 2*(b^6*d*f*x + b^6*c*f)*cosh(d*x + c)^3 - (b^6*d*f*x + b^6*c*f)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2)*log(-(a*cosh(d*x + c) + a*sinh(d*x + c) - (b*cosh(d*x + c) + b*sinh(d*x + c))*sqrt((a^2 + b^2)/b^2) - b)/b) + 4*((a^6 + a^4*b^2)*f*cosh(d*x + c)^6 + 6*(a^6 + a^4*b^2)*f*cosh(d*x + c)*sinh(d*x + c)^5 + (a^6 + a^4*b^2)*f*sinh(d*x + c)^6 - (a^6 + a^4*b^2)*f*cosh(d*x + c)^4 + (15*(a^6 + a^4*b^2)*f*cosh(d*x + c)^2 - (a^6 + a^4*b^2)*f)*sinh(d*x + c)^4 - (a^6 + a^4*b^2)*f*cosh(d*x + c)^2 + 4*(5*(a^6 + a^4*b^2)*f*cosh(d*x + c)^3 - (a^6 + a^4*b^2)*f*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^6 + a^4*b^2)*f*cosh(d*x + c)^4 - 6*(a^6 + a^4*b^2)*f*cosh(d*x + c)^2 - (a^6 + a^4*b^2)*f)*sinh(d*x + c)^2 + (a^6 + a^4*b^2)*f + 2*(3*(a^6 + a^4*b^2)*f*cosh(d*x + c)^5 - 2*(a^6 + a^4*b^2)*f*cosh(d*x + c)^3 - (a^6 + a^4*b^2)*f*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*((3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*f*x + (3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*e - (a^6 + 2*a^4*b^2 + a^2*b^4)*f)*cosh(d*x + c) - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^6 + 6*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*sinh(d*x + c)^6 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^4 + (15*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^2 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f)*sinh(d*x + c)^4 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^2 + 4*(5*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^4 - 6*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^2 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f)*sinh(d*x + c)^2 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f + 2*(3*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^5 - 2*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(cosh(d*x + c) + sinh(d*x + c)) + ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^6 + 6*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*sinh(d*x + c)^6 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^4 + (15*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^2 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f)*sinh(d*x + c)^4 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^2 + 4*(5*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^4 - 6*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^2 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f)*sinh(d*x + c)^2 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f + 2*(3*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^5 - 2*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*f*cosh(d*x + c))*sinh(d*x + c))*dilog(-cosh(d*x + c) - sinh(d*x + c)) - 2*((a^5*b + a^3*b^3)*f*cosh(d*x + c)^6 + 6*(a^5*b + a^3*b^3)*f*cosh(d*x + c)*sinh(d*x + c)^5 + (a^5*b + a^3*b^3)*f*sinh(d*x + c)^6 - (a^5*b + a^3*b^3)*f*cosh(d*x + c)^4 + (15*(a^5*b + a^3*b^3)*f*cosh(d*x + c)^2 - (a^5*b + a^3*b^3)*f)*sinh(d*x + c)^4 - (a^5*b + a^3*b^3)*f*cosh(d*x + c)^2 + 4*(5*(a^5*b + a^3*b^3)*f*cosh(d*x + c)^3 - (a^5*b + a^3*b^3)*f*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5*b + a^3*b^3)*f*cosh(d*x + c)^4 - 6*(a^5*b + a^3*b^3)*f*cosh(d*x + c)^2 - (a^5*b + a^3*b^3)*f)*sinh(d*x + c)^2 + (a^5*b + a^3*b^3)*f + 2*(3*(a^5*b + a^3*b^3)*f*cosh(d*x + c)^5 - 2*(a^5*b + a^3*b^3)*f*cosh(d*x + c)^3 - (a^5*b + a^3*b^3)*f*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + (((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c)^6 + 6*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c)*sinh(d*x + c)^5 + ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*sinh(d*x + c)^6 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c)^4 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 15*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c)^2 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*sinh(d*x + c)^4 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + 4*(5*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c)^3 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c)^2 + (15*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c)^4 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 6*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c)^2 + 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*sinh(d*x + c)^2 - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f + 2*(3*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c)^5 - 2*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c)^3 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 2*(a^5*b + 2*a^3*b^3 + a*b^5)*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c)^6 + 6*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c)*sinh(d*x + c)^5 + ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*sinh(d*x + c)^6 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c)^4 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 15*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c)^2 + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*sinh(d*x + c)^4 + 4*(5*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c)^3 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c)^2 + (15*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c)^4 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e - 6*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c)^2 - (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*sinh(d*x + c)^2 + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f + 2*(3*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c)^5 - 2*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c)^3 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*e + (2*a^5*b + 4*a^3*b^3 + 2*a*b^5 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c)*f)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) - (((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c)^6 + 6*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c)*sinh(d*x + c)^5 + ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*sinh(d*x + c)^6 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c)^4 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f - 15*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + 4*(5*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c)^3 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c)^2 + (15*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c)^4 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f - 6*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c)^5 - 2*((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c)^3 - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*d*f*x + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*c*f)*cosh(d*x + c))*sinh(d*x + c))*log(-cosh(d*x + c) - sinh(d*x + c) + 1) + 2*(12*((2*a^5*b + 3*a^3*b^3 + a*b^5)*d*f*x + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c)^5 - 5*((3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*f*x + (3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*e + (a^6 + 2*a^4*b^2 + a^2*b^4)*f)*cosh(d*x + c)^4 - (3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*f*x - 8*(2*(a^5*b + a^3*b^3)*d*f*x - (a^3*b^3 + a*b^5)*d*e + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 + a^2*b^4)*d*e + 6*((a^6 - a^2*b^4)*d*f*x + (a^6 - a^2*b^4)*d*e)*cosh(d*x + c)^2 + (a^6 + 2*a^4*b^2 + a^2*b^4)*f - 4*((a^3*b^3 + a*b^5)*d*f*x - 2*(a^5*b + a^3*b^3)*d*e + (a^5*b + 2*a^3*b^3 + a*b^5)*c*f)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c)^6 + 6*(a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c)*sinh(d*x + c)^5 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*sinh(d*x + c)^6 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c)^4 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c)^2 + (15*(a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c)^2 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2)*sinh(d*x + c)^4 + 4*(5*(a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c)^3 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c))*sinh(d*x + c)^3 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2 + (15*(a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c)^4 - 6*(a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c)^2 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2)*sinh(d*x + c)^2 + 2*(3*(a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c)^5 - 2*(a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c)^3 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d^2*cosh(d*x + c))*sinh(d*x + c))","B",0
498,1,2653,0,1.232257," ","integrate(csch(d*x+c)^3*sech(d*x+c)^2/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, a^{5} b + 12 \, a^{3} b^{3} + 4 \, a b^{5} + 2 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{3} b^{3} + 2 \, a b^{5} - 5 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a^{6} - a^{2} b^{4} - 5 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(a^{5} b + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(2 \, a^{5} b + 2 \, a^{3} b^{3} - 5 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(b^{5} \cosh\left(d x + c\right)^{6} + 6 \, b^{5} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{5} \sinh\left(d x + c\right)^{6} - b^{5} \cosh\left(d x + c\right)^{4} - b^{5} \cosh\left(d x + c\right)^{2} + b^{5} + {\left(15 \, b^{5} \cosh\left(d x + c\right)^{2} - b^{5}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{5} \cosh\left(d x + c\right)^{3} - b^{5} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, b^{5} \cosh\left(d x + c\right)^{4} - 6 \, b^{5} \cosh\left(d x + c\right)^{2} - b^{5}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{5} \cosh\left(d x + c\right)^{5} - 2 \, b^{5} \cosh\left(d x + c\right)^{3} - b^{5} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} + b^{2}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) + 2 \, a^{2} + b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a b\right)} \sinh\left(d x + c\right) + 2 \, \sqrt{a^{2} + b^{2}} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right) + a\right)}}{b \cosh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) + 2 \, {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right) - b}\right) + 2 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right) - {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \sinh\left(d x + c\right)^{6} + 3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6} - 15 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6} - 15 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \sinh\left(d x + c\right)^{6} + 3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6} - 15 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6} - 15 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{6} + 4 \, a^{4} b^{2} - a^{2} b^{4} - 2 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4} + 5 \, {\left(3 \, a^{6} + 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{4} - 8 \, {\left(a^{3} b^{3} + a b^{5}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(a^{6} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(a^{5} b + a^{3} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{6} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d + 2 \, {\left(3 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(8*a^5*b + 12*a^3*b^3 + 4*a*b^5 + 2*(3*a^6 + 4*a^4*b^2 + a^2*b^4)*cosh(d*x + c)^5 + 2*(3*a^6 + 4*a^4*b^2 + a^2*b^4)*sinh(d*x + c)^5 - 4*(a^3*b^3 + a*b^5)*cosh(d*x + c)^4 - 2*(2*a^3*b^3 + 2*a*b^5 - 5*(3*a^6 + 4*a^4*b^2 + a^2*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(a^6 - a^2*b^4)*cosh(d*x + c)^3 - 4*(a^6 - a^2*b^4 - 5*(3*a^6 + 4*a^4*b^2 + a^2*b^4)*cosh(d*x + c)^2 + 4*(a^3*b^3 + a*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*(a^5*b + a^3*b^3)*cosh(d*x + c)^2 - 4*(2*a^5*b + 2*a^3*b^3 - 5*(3*a^6 + 4*a^4*b^2 + a^2*b^4)*cosh(d*x + c)^3 + 6*(a^3*b^3 + a*b^5)*cosh(d*x + c)^2 + 3*(a^6 - a^2*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(b^5*cosh(d*x + c)^6 + 6*b^5*cosh(d*x + c)*sinh(d*x + c)^5 + b^5*sinh(d*x + c)^6 - b^5*cosh(d*x + c)^4 - b^5*cosh(d*x + c)^2 + b^5 + (15*b^5*cosh(d*x + c)^2 - b^5)*sinh(d*x + c)^4 + 4*(5*b^5*cosh(d*x + c)^3 - b^5*cosh(d*x + c))*sinh(d*x + c)^3 + (15*b^5*cosh(d*x + c)^4 - 6*b^5*cosh(d*x + c)^2 - b^5)*sinh(d*x + c)^2 + 2*(3*b^5*cosh(d*x + c)^5 - 2*b^5*cosh(d*x + c)^3 - b^5*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + b^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a*b*cosh(d*x + c) + 2*a^2 + b^2 + 2*(b^2*cosh(d*x + c) + a*b)*sinh(d*x + c) + 2*sqrt(a^2 + b^2)*(b*cosh(d*x + c) + b*sinh(d*x + c) + a))/(b*cosh(d*x + c)^2 + b*sinh(d*x + c)^2 + 2*a*cosh(d*x + c) + 2*(b*cosh(d*x + c) + a)*sinh(d*x + c) - b)) + 2*(3*a^6 + 4*a^4*b^2 + a^2*b^4)*cosh(d*x + c) - ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^6 + 6*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*sinh(d*x + c)^6 + 3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^4 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6 - 15*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c))*sinh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^2 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6 - 15*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^4 + 6*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^5 - 2*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^6 + 6*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*sinh(d*x + c)^6 + 3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^4 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6 - 15*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c))*sinh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^2 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6 - 15*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^4 + 6*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^5 - 2*(3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c)^3 - (3*a^6 + 4*a^4*b^2 - a^2*b^4 - 2*b^6)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(3*a^6 + 4*a^4*b^2 + a^2*b^4 + 5*(3*a^6 + 4*a^4*b^2 + a^2*b^4)*cosh(d*x + c)^4 - 8*(a^3*b^3 + a*b^5)*cosh(d*x + c)^3 - 6*(a^6 - a^2*b^4)*cosh(d*x + c)^2 - 8*(a^5*b + a^3*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^6 + 6*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d*sinh(d*x + c)^6 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^4 + (15*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^2 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d)*sinh(d*x + c)^4 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^2 + 4*(5*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^3 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^4 - 6*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^2 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d)*sinh(d*x + c)^2 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d + 2*(3*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^5 - 2*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^3 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
499,0,0,0,3.954522," ","integrate(csch(d*x+c)^3*sech(d*x+c)^2/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(d x + c\right)^{3} \operatorname{sech}\left(d x + c\right)^{2}}{a f x + a e + {\left(b f x + b e\right)} \sinh\left(d x + c\right)}, x\right)"," ",0,"integral(csch(d*x + c)^3*sech(d*x + c)^2/(a*f*x + a*e + (b*f*x + b*e)*sinh(d*x + c)), x)","F",0
500,-1,0,0,0.000000," ","integrate((f*x+e)*csch(d*x+c)^3*sech(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,1,3148,0,3.113542," ","integrate(csch(d*x+c)^3*sech(d*x+c)^3/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{7} + {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{6} - {\left(4 \, a^{6} + 6 \, a^{4} b^{2} + 2 \, a^{2} b^{4} - 7 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - {\left(a^{5} b - a^{3} b^{3} - 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{5} b - a^{3} b^{3} - 2 \, a b^{5} - 21 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{4} - {\left(4 \, a^{4} b^{2} + 4 \, a^{2} b^{4} - 35 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + 30 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(a^{5} b - a^{3} b^{3} - 2 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{5} b - a^{3} b^{3} - 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{5} b - a^{3} b^{3} - 2 \, a b^{5} + 35 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} - 40 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(a^{5} b - a^{3} b^{3} - 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2} - 16 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{6} + 6 \, a^{4} b^{2} + 2 \, a^{2} b^{4} - 21 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(a^{5} b - a^{3} b^{3} - 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + 24 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a^{5} b - a^{3} b^{3} - 2 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 56 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \sinh\left(d x + c\right)^{8} + 3 \, a^{5} b + 5 \, a^{3} b^{3} - 2 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} - 35 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 3 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{7} - {\left(3 \, a^{5} b + 5 \, a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(d x + c\right) - {\left(b^{6} \cosh\left(d x + c\right)^{8} + 56 \, b^{6} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, b^{6} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, b^{6} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{6} \sinh\left(d x + c\right)^{8} - 2 \, b^{6} \cosh\left(d x + c\right)^{4} + b^{6} + 2 \, {\left(35 \, b^{6} \cosh\left(d x + c\right)^{4} - b^{6}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{6} \cosh\left(d x + c\right)^{5} - b^{6} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, b^{6} \cosh\left(d x + c\right)^{6} - 3 \, b^{6} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{6} \cosh\left(d x + c\right)^{7} - b^{6} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b \sinh\left(d x + c\right) + a\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left({\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 56 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 2 \, a^{6} + 3 \, a^{4} b^{2} - 2 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - 35 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{6} - 3 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{7} - {\left(2 \, a^{6} + 3 \, a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left({\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)^{8} + 56 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \sinh\left(d x + c\right)^{8} + 2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6} - 2 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6} - 35 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)^{5} - {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)^{6} - 3 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)^{7} - {\left(2 \, a^{6} + 3 \, a^{4} b^{2} - b^{6}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + {\left(7 \, {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} - 3 \, a^{5} b - 5 \, a^{3} b^{3} - 2 \, a b^{5} - 12 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{5} b - a^{3} b^{3} - 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} - 16 \, {\left(a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b - a^{3} b^{3} - 2 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{{\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 56 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 3 \, {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d + 8 \, {\left({\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} - {\left(a^{7} + 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)}"," ",0,"((3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*cosh(d*x + c)^7 + (3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*sinh(d*x + c)^7 - 2*(2*a^6 + 3*a^4*b^2 + a^2*b^4)*cosh(d*x + c)^6 - (4*a^6 + 6*a^4*b^2 + 2*a^2*b^4 - 7*(3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^6 - (a^5*b - a^3*b^3 - 2*a*b^5)*cosh(d*x + c)^5 - (a^5*b - a^3*b^3 - 2*a*b^5 - 21*(3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*cosh(d*x + c)^2 + 12*(2*a^6 + 3*a^4*b^2 + a^2*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(a^4*b^2 + a^2*b^4)*cosh(d*x + c)^4 - (4*a^4*b^2 + 4*a^2*b^4 - 35*(3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*cosh(d*x + c)^3 + 30*(2*a^6 + 3*a^4*b^2 + a^2*b^4)*cosh(d*x + c)^2 + 5*(a^5*b - a^3*b^3 - 2*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^4 + (a^5*b - a^3*b^3 - 2*a*b^5)*cosh(d*x + c)^3 + (a^5*b - a^3*b^3 - 2*a*b^5 + 35*(3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*cosh(d*x + c)^4 - 40*(2*a^6 + 3*a^4*b^2 + a^2*b^4)*cosh(d*x + c)^3 - 10*(a^5*b - a^3*b^3 - 2*a*b^5)*cosh(d*x + c)^2 - 16*(a^4*b^2 + a^2*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*a^6 + 3*a^4*b^2 + a^2*b^4)*cosh(d*x + c)^2 - (4*a^6 + 6*a^4*b^2 + 2*a^2*b^4 - 21*(3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*cosh(d*x + c)^5 + 30*(2*a^6 + 3*a^4*b^2 + a^2*b^4)*cosh(d*x + c)^4 + 10*(a^5*b - a^3*b^3 - 2*a*b^5)*cosh(d*x + c)^3 + 24*(a^4*b^2 + a^2*b^4)*cosh(d*x + c)^2 - 3*(a^5*b - a^3*b^3 - 2*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^2 + ((3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)^8 + 56*(3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*(3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*(3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^5*b + 5*a^3*b^3)*sinh(d*x + c)^8 + 3*a^5*b + 5*a^3*b^3 - 2*(3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)^4 - 2*(3*a^5*b + 5*a^3*b^3 - 35*(3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)^4)*sinh(d*x + c)^4 + 8*(7*(3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)^5 - (3*a^5*b + 5*a^3*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)^6 - 3*(3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)^7 - (3*a^5*b + 5*a^3*b^3)*cosh(d*x + c)^3)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - (3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*cosh(d*x + c) - (b^6*cosh(d*x + c)^8 + 56*b^6*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*b^6*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*b^6*cosh(d*x + c)*sinh(d*x + c)^7 + b^6*sinh(d*x + c)^8 - 2*b^6*cosh(d*x + c)^4 + b^6 + 2*(35*b^6*cosh(d*x + c)^4 - b^6)*sinh(d*x + c)^4 + 8*(7*b^6*cosh(d*x + c)^5 - b^6*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^6*cosh(d*x + c)^6 - 3*b^6*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(b^6*cosh(d*x + c)^7 - b^6*cosh(d*x + c)^3)*sinh(d*x + c))*log(2*(b*sinh(d*x + c) + a)/(cosh(d*x + c) - sinh(d*x + c))) + ((2*a^6 + 3*a^4*b^2)*cosh(d*x + c)^8 + 56*(2*a^6 + 3*a^4*b^2)*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*(2*a^6 + 3*a^4*b^2)*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*(2*a^6 + 3*a^4*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (2*a^6 + 3*a^4*b^2)*sinh(d*x + c)^8 + 2*a^6 + 3*a^4*b^2 - 2*(2*a^6 + 3*a^4*b^2)*cosh(d*x + c)^4 - 2*(2*a^6 + 3*a^4*b^2 - 35*(2*a^6 + 3*a^4*b^2)*cosh(d*x + c)^4)*sinh(d*x + c)^4 + 8*(7*(2*a^6 + 3*a^4*b^2)*cosh(d*x + c)^5 - (2*a^6 + 3*a^4*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(2*a^6 + 3*a^4*b^2)*cosh(d*x + c)^6 - 3*(2*a^6 + 3*a^4*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((2*a^6 + 3*a^4*b^2)*cosh(d*x + c)^7 - (2*a^6 + 3*a^4*b^2)*cosh(d*x + c)^3)*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - ((2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)^8 + 56*(2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*(2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*(2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)*sinh(d*x + c)^7 + (2*a^6 + 3*a^4*b^2 - b^6)*sinh(d*x + c)^8 + 2*a^6 + 3*a^4*b^2 - b^6 - 2*(2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)^4 - 2*(2*a^6 + 3*a^4*b^2 - b^6 - 35*(2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)^4)*sinh(d*x + c)^4 + 8*(7*(2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)^5 - (2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)^6 - 3*(2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)^7 - (2*a^6 + 3*a^4*b^2 - b^6)*cosh(d*x + c)^3)*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + (7*(3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*cosh(d*x + c)^6 - 3*a^5*b - 5*a^3*b^3 - 2*a*b^5 - 12*(2*a^6 + 3*a^4*b^2 + a^2*b^4)*cosh(d*x + c)^5 - 5*(a^5*b - a^3*b^3 - 2*a*b^5)*cosh(d*x + c)^4 - 16*(a^4*b^2 + a^2*b^4)*cosh(d*x + c)^3 + 3*(a^5*b - a^3*b^3 - 2*a*b^5)*cosh(d*x + c)^2 - 4*(2*a^6 + 3*a^4*b^2 + a^2*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^8 + 56*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d*sinh(d*x + c)^8 - 2*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^4 + 2*(35*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^4 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d)*sinh(d*x + c)^4 + 8*(7*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^5 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^6 - 3*(a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + (a^7 + 2*a^5*b^2 + a^3*b^4)*d + 8*((a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^7 - (a^7 + 2*a^5*b^2 + a^3*b^4)*d*cosh(d*x + c)^3)*sinh(d*x + c))","B",0
502,-1,0,0,0.000000," ","integrate(csch(d*x+c)^3*sech(d*x+c)^3/(f*x+e)/(a+b*sinh(d*x+c)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
