1,1,85,0,0.431298," ","integrate(x^3*(b*x+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(4 \, b d^{3} x^{3} + 3 \, a d^{3} x^{2} + 24 \, b d x + 6 \, a d\right)} \cosh\left(d x + c\right) - {\left(b d^{4} x^{4} + a d^{4} x^{3} + 12 \, b d^{2} x^{2} + 6 \, a d^{2} x + 24 \, b\right)} \sinh\left(d x + c\right)}{d^{5}}"," ",0,"-((4*b*d^3*x^3 + 3*a*d^3*x^2 + 24*b*d*x + 6*a*d)*cosh(d*x + c) - (b*d^4*x^4 + a*d^4*x^3 + 12*b*d^2*x^2 + 6*a*d^2*x + 24*b)*sinh(d*x + c))/d^5","A",0
2,1,67,0,0.998690," ","integrate(x^2*(b*x+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(3 \, b d^{2} x^{2} + 2 \, a d^{2} x + 6 \, b\right)} \cosh\left(d x + c\right) - {\left(b d^{3} x^{3} + a d^{3} x^{2} + 6 \, b d x + 2 \, a d\right)} \sinh\left(d x + c\right)}{d^{4}}"," ",0,"-((3*b*d^2*x^2 + 2*a*d^2*x + 6*b)*cosh(d*x + c) - (b*d^3*x^3 + a*d^3*x^2 + 6*b*d*x + 2*a*d)*sinh(d*x + c))/d^4","A",0
3,1,48,0,0.654376," ","integrate(x*(b*x+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(2 \, b d x + a d\right)} \cosh\left(d x + c\right) - {\left(b d^{2} x^{2} + a d^{2} x + 2 \, b\right)} \sinh\left(d x + c\right)}{d^{3}}"," ",0,"-((2*b*d*x + a*d)*cosh(d*x + c) - (b*d^2*x^2 + a*d^2*x + 2*b)*sinh(d*x + c))/d^3","A",0
4,1,30,0,0.439563," ","integrate((b*x+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{b \cosh\left(d x + c\right) - {\left(b d x + a d\right)} \sinh\left(d x + c\right)}{d^{2}}"," ",0,"-(b*cosh(d*x + c) - (b*d*x + a*d)*sinh(d*x + c))/d^2","A",0
5,1,54,0,0.761693," ","integrate((b*x+a)*cosh(d*x+c)/x,x, algorithm=""fricas"")","\frac{{\left(a d {\rm Ei}\left(d x\right) + a d {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, b \sinh\left(d x + c\right) + {\left(a d {\rm Ei}\left(d x\right) - a d {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d}"," ",0,"1/2*((a*d*Ei(d*x) + a*d*Ei(-d*x))*cosh(c) + 2*b*sinh(d*x + c) + (a*d*Ei(d*x) - a*d*Ei(-d*x))*sinh(c))/d","A",0
6,1,76,0,0.544204," ","integrate((b*x+a)*cosh(d*x+c)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a \cosh\left(d x + c\right) - {\left({\left(a d + b\right)} x {\rm Ei}\left(d x\right) - {\left(a d - b\right)} x {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(a d + b\right)} x {\rm Ei}\left(d x\right) + {\left(a d - b\right)} x {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, x}"," ",0,"-1/2*(2*a*cosh(d*x + c) - ((a*d + b)*x*Ei(d*x) - (a*d - b)*x*Ei(-d*x))*cosh(c) - ((a*d + b)*x*Ei(d*x) + (a*d - b)*x*Ei(-d*x))*sinh(c))/x","A",0
7,1,116,0,0.520713," ","integrate((b*x+a)*cosh(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a d x \sinh\left(d x + c\right) + 2 \, {\left(2 \, b x + a\right)} \cosh\left(d x + c\right) - {\left({\left(a d^{2} + 2 \, b d\right)} x^{2} {\rm Ei}\left(d x\right) + {\left(a d^{2} - 2 \, b d\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(a d^{2} + 2 \, b d\right)} x^{2} {\rm Ei}\left(d x\right) - {\left(a d^{2} - 2 \, b d\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{4 \, x^{2}}"," ",0,"-1/4*(2*a*d*x*sinh(d*x + c) + 2*(2*b*x + a)*cosh(d*x + c) - ((a*d^2 + 2*b*d)*x^2*Ei(d*x) + (a*d^2 - 2*b*d)*x^2*Ei(-d*x))*cosh(c) - ((a*d^2 + 2*b*d)*x^2*Ei(d*x) - (a*d^2 - 2*b*d)*x^2*Ei(-d*x))*sinh(c))/x^2","A",0
8,1,143,0,0.492547," ","integrate((b*x+a)*cosh(d*x+c)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(a d^{2} x^{2} + 3 \, b x + 2 \, a\right)} \cosh\left(d x + c\right) - {\left({\left(a d^{3} + 3 \, b d^{2}\right)} x^{3} {\rm Ei}\left(d x\right) - {\left(a d^{3} - 3 \, b d^{2}\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left(3 \, b d x^{2} + a d x\right)} \sinh\left(d x + c\right) - {\left({\left(a d^{3} + 3 \, b d^{2}\right)} x^{3} {\rm Ei}\left(d x\right) + {\left(a d^{3} - 3 \, b d^{2}\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{12 \, x^{3}}"," ",0,"-1/12*(2*(a*d^2*x^2 + 3*b*x + 2*a)*cosh(d*x + c) - ((a*d^3 + 3*b*d^2)*x^3*Ei(d*x) - (a*d^3 - 3*b*d^2)*x^3*Ei(-d*x))*cosh(c) + 2*(3*b*d*x^2 + a*d*x)*sinh(d*x + c) - ((a*d^3 + 3*b*d^2)*x^3*Ei(d*x) + (a*d^3 - 3*b*d^2)*x^3*Ei(-d*x))*sinh(c))/x^3","A",0
9,1,161,0,0.554043," ","integrate((b*x+a)*cosh(d*x+c)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, b d^{2} x^{3} + a d^{2} x^{2} + 8 \, b x + 6 \, a\right)} \cosh\left(d x + c\right) - {\left({\left(a d^{4} + 4 \, b d^{3}\right)} x^{4} {\rm Ei}\left(d x\right) + {\left(a d^{4} - 4 \, b d^{3}\right)} x^{4} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left(a d^{3} x^{3} + 4 \, b d x^{2} + 2 \, a d x\right)} \sinh\left(d x + c\right) - {\left({\left(a d^{4} + 4 \, b d^{3}\right)} x^{4} {\rm Ei}\left(d x\right) - {\left(a d^{4} - 4 \, b d^{3}\right)} x^{4} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{48 \, x^{4}}"," ",0,"-1/48*(2*(4*b*d^2*x^3 + a*d^2*x^2 + 8*b*x + 6*a)*cosh(d*x + c) - ((a*d^4 + 4*b*d^3)*x^4*Ei(d*x) + (a*d^4 - 4*b*d^3)*x^4*Ei(-d*x))*cosh(c) + 2*(a*d^3*x^3 + 4*b*d*x^2 + 2*a*d*x)*sinh(d*x + c) - ((a*d^4 + 4*b*d^3)*x^4*Ei(d*x) - (a*d^4 - 4*b*d^3)*x^4*Ei(-d*x))*sinh(c))/x^4","A",0
10,1,127,0,0.492842," ","integrate(x^2*(b*x+a)^2*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, b^{2} d^{3} x^{3} + 3 \, a b d^{3} x^{2} + 6 \, a b d + {\left(a^{2} d^{3} + 12 \, b^{2} d\right)} x\right)} \cosh\left(d x + c\right) - {\left(b^{2} d^{4} x^{4} + 2 \, a b d^{4} x^{3} + 12 \, a b d^{2} x + 2 \, a^{2} d^{2} + {\left(a^{2} d^{4} + 12 \, b^{2} d^{2}\right)} x^{2} + 24 \, b^{2}\right)} \sinh\left(d x + c\right)}{d^{5}}"," ",0,"-(2*(2*b^2*d^3*x^3 + 3*a*b*d^3*x^2 + 6*a*b*d + (a^2*d^3 + 12*b^2*d)*x)*cosh(d*x + c) - (b^2*d^4*x^4 + 2*a*b*d^4*x^3 + 12*a*b*d^2*x + 2*a^2*d^2 + (a^2*d^4 + 12*b^2*d^2)*x^2 + 24*b^2)*sinh(d*x + c))/d^5","A",0
11,1,95,0,0.534506," ","integrate(x*(b*x+a)^2*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(3 \, b^{2} d^{2} x^{2} + 4 \, a b d^{2} x + a^{2} d^{2} + 6 \, b^{2}\right)} \cosh\left(d x + c\right) - {\left(b^{2} d^{3} x^{3} + 2 \, a b d^{3} x^{2} + 4 \, a b d + {\left(a^{2} d^{3} + 6 \, b^{2} d\right)} x\right)} \sinh\left(d x + c\right)}{d^{4}}"," ",0,"-((3*b^2*d^2*x^2 + 4*a*b*d^2*x + a^2*d^2 + 6*b^2)*cosh(d*x + c) - (b^2*d^3*x^3 + 2*a*b*d^3*x^2 + 4*a*b*d + (a^2*d^3 + 6*b^2*d)*x)*sinh(d*x + c))/d^4","A",0
12,1,64,0,0.395614," ","integrate((b*x+a)^2*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{2} d x + a b d\right)} \cosh\left(d x + c\right) - {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2} + 2 \, b^{2}\right)} \sinh\left(d x + c\right)}{d^{3}}"," ",0,"-(2*(b^2*d*x + a*b*d)*cosh(d*x + c) - (b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2 + 2*b^2)*sinh(d*x + c))/d^3","A",0
13,1,94,0,0.621923," ","integrate((b*x+a)^2*cosh(d*x+c)/x,x, algorithm=""fricas"")","-\frac{2 \, b^{2} \cosh\left(d x + c\right) - {\left(a^{2} d^{2} {\rm Ei}\left(d x\right) + a^{2} d^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 2 \, {\left(b^{2} d x + 2 \, a b d\right)} \sinh\left(d x + c\right) - {\left(a^{2} d^{2} {\rm Ei}\left(d x\right) - a^{2} d^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d^{2}}"," ",0,"-1/2*(2*b^2*cosh(d*x + c) - (a^2*d^2*Ei(d*x) + a^2*d^2*Ei(-d*x))*cosh(c) - 2*(b^2*d*x + 2*a*b*d)*sinh(d*x + c) - (a^2*d^2*Ei(d*x) - a^2*d^2*Ei(-d*x))*sinh(c))/d^2","A",0
14,1,122,0,0.536707," ","integrate((b*x+a)^2*cosh(d*x+c)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} d \cosh\left(d x + c\right) - 2 \, b^{2} x \sinh\left(d x + c\right) - {\left({\left(a^{2} d^{2} + 2 \, a b d\right)} x {\rm Ei}\left(d x\right) - {\left(a^{2} d^{2} - 2 \, a b d\right)} x {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(a^{2} d^{2} + 2 \, a b d\right)} x {\rm Ei}\left(d x\right) + {\left(a^{2} d^{2} - 2 \, a b d\right)} x {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d x}"," ",0,"-1/2*(2*a^2*d*cosh(d*x + c) - 2*b^2*x*sinh(d*x + c) - ((a^2*d^2 + 2*a*b*d)*x*Ei(d*x) - (a^2*d^2 - 2*a*b*d)*x*Ei(-d*x))*cosh(c) - ((a^2*d^2 + 2*a*b*d)*x*Ei(d*x) + (a^2*d^2 - 2*a*b*d)*x*Ei(-d*x))*sinh(c))/(d*x)","A",0
15,1,153,0,0.627038," ","integrate((b*x+a)^2*cosh(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a^{2} d x \sinh\left(d x + c\right) + 2 \, {\left(4 \, a b x + a^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} d^{2} + 4 \, a b d + 2 \, b^{2}\right)} x^{2} {\rm Ei}\left(d x\right) + {\left(a^{2} d^{2} - 4 \, a b d + 2 \, b^{2}\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(a^{2} d^{2} + 4 \, a b d + 2 \, b^{2}\right)} x^{2} {\rm Ei}\left(d x\right) - {\left(a^{2} d^{2} - 4 \, a b d + 2 \, b^{2}\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{4 \, x^{2}}"," ",0,"-1/4*(2*a^2*d*x*sinh(d*x + c) + 2*(4*a*b*x + a^2)*cosh(d*x + c) - ((a^2*d^2 + 4*a*b*d + 2*b^2)*x^2*Ei(d*x) + (a^2*d^2 - 4*a*b*d + 2*b^2)*x^2*Ei(-d*x))*cosh(c) - ((a^2*d^2 + 4*a*b*d + 2*b^2)*x^2*Ei(d*x) - (a^2*d^2 - 4*a*b*d + 2*b^2)*x^2*Ei(-d*x))*sinh(c))/x^2","A",0
16,1,194,0,0.474828," ","integrate((b*x+a)^2*cosh(d*x+c)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(6 \, a b x + {\left(a^{2} d^{2} + 6 \, b^{2}\right)} x^{2} + 2 \, a^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} d^{3} + 6 \, a b d^{2} + 6 \, b^{2} d\right)} x^{3} {\rm Ei}\left(d x\right) - {\left(a^{2} d^{3} - 6 \, a b d^{2} + 6 \, b^{2} d\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left(6 \, a b d x^{2} + a^{2} d x\right)} \sinh\left(d x + c\right) - {\left({\left(a^{2} d^{3} + 6 \, a b d^{2} + 6 \, b^{2} d\right)} x^{3} {\rm Ei}\left(d x\right) + {\left(a^{2} d^{3} - 6 \, a b d^{2} + 6 \, b^{2} d\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{12 \, x^{3}}"," ",0,"-1/12*(2*(6*a*b*x + (a^2*d^2 + 6*b^2)*x^2 + 2*a^2)*cosh(d*x + c) - ((a^2*d^3 + 6*a*b*d^2 + 6*b^2*d)*x^3*Ei(d*x) - (a^2*d^3 - 6*a*b*d^2 + 6*b^2*d)*x^3*Ei(-d*x))*cosh(c) + 2*(6*a*b*d*x^2 + a^2*d*x)*sinh(d*x + c) - ((a^2*d^3 + 6*a*b*d^2 + 6*b^2*d)*x^3*Ei(d*x) + (a^2*d^3 - 6*a*b*d^2 + 6*b^2*d)*x^3*Ei(-d*x))*sinh(c))/x^3","A",0
17,1,231,0,0.471105," ","integrate((b*x+a)^2*cosh(d*x+c)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(8 \, a b d^{2} x^{3} + 16 \, a b x + {\left(a^{2} d^{2} + 12 \, b^{2}\right)} x^{2} + 6 \, a^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} d^{4} + 8 \, a b d^{3} + 12 \, b^{2} d^{2}\right)} x^{4} {\rm Ei}\left(d x\right) + {\left(a^{2} d^{4} - 8 \, a b d^{3} + 12 \, b^{2} d^{2}\right)} x^{4} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left(8 \, a b d x^{2} + 2 \, a^{2} d x + {\left(a^{2} d^{3} + 12 \, b^{2} d\right)} x^{3}\right)} \sinh\left(d x + c\right) - {\left({\left(a^{2} d^{4} + 8 \, a b d^{3} + 12 \, b^{2} d^{2}\right)} x^{4} {\rm Ei}\left(d x\right) - {\left(a^{2} d^{4} - 8 \, a b d^{3} + 12 \, b^{2} d^{2}\right)} x^{4} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{48 \, x^{4}}"," ",0,"-1/48*(2*(8*a*b*d^2*x^3 + 16*a*b*x + (a^2*d^2 + 12*b^2)*x^2 + 6*a^2)*cosh(d*x + c) - ((a^2*d^4 + 8*a*b*d^3 + 12*b^2*d^2)*x^4*Ei(d*x) + (a^2*d^4 - 8*a*b*d^3 + 12*b^2*d^2)*x^4*Ei(-d*x))*cosh(c) + 2*(8*a*b*d*x^2 + 2*a^2*d*x + (a^2*d^3 + 12*b^2*d)*x^3)*sinh(d*x + c) - ((a^2*d^4 + 8*a*b*d^3 + 12*b^2*d^2)*x^4*Ei(d*x) - (a^2*d^4 - 8*a*b*d^3 + 12*b^2*d^2)*x^4*Ei(-d*x))*sinh(c))/x^4","A",0
18,1,236,0,0.446488," ","integrate(x^4*cosh(d*x+c)/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{4} d^{2} x^{2} - 2 \, a b^{3} d^{2} x + a^{2} b^{2} d^{2} + 6 \, b^{4}\right)} \cosh\left(d x + c\right) - {\left(a^{4} d^{4} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + a^{4} d^{4} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(b^{4} d^{3} x^{3} - a b^{3} d^{3} x^{2} - a^{3} b d^{3} - 2 \, a b^{3} d + {\left(a^{2} b^{2} d^{3} + 6 \, b^{4} d\right)} x\right)} \sinh\left(d x + c\right) + {\left(a^{4} d^{4} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - a^{4} d^{4} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, b^{5} d^{4}}"," ",0,"-1/2*(2*(3*b^4*d^2*x^2 - 2*a*b^3*d^2*x + a^2*b^2*d^2 + 6*b^4)*cosh(d*x + c) - (a^4*d^4*Ei((b*d*x + a*d)/b) + a^4*d^4*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - 2*(b^4*d^3*x^3 - a*b^3*d^3*x^2 - a^3*b*d^3 - 2*a*b^3*d + (a^2*b^2*d^3 + 6*b^4*d)*x)*sinh(d*x + c) + (a^4*d^4*Ei((b*d*x + a*d)/b) - a^4*d^4*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^5*d^4)","A",0
19,1,190,0,0.911350," ","integrate(x^3*cosh(d*x+c)/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, b^{3} d x - a b^{2} d\right)} \cosh\left(d x + c\right) + {\left(a^{3} d^{3} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + a^{3} d^{3} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(b^{3} d^{2} x^{2} - a b^{2} d^{2} x + a^{2} b d^{2} + 2 \, b^{3}\right)} \sinh\left(d x + c\right) - {\left(a^{3} d^{3} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - a^{3} d^{3} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, b^{4} d^{3}}"," ",0,"-1/2*(2*(2*b^3*d*x - a*b^2*d)*cosh(d*x + c) + (a^3*d^3*Ei((b*d*x + a*d)/b) + a^3*d^3*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - 2*(b^3*d^2*x^2 - a*b^2*d^2*x + a^2*b*d^2 + 2*b^3)*sinh(d*x + c) - (a^3*d^3*Ei((b*d*x + a*d)/b) - a^3*d^3*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^4*d^3)","A",0
20,1,156,0,0.564033," ","integrate(x^2*cosh(d*x+c)/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, b^{2} \cosh\left(d x + c\right) - {\left(a^{2} d^{2} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + a^{2} d^{2} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(b^{2} d x - a b d\right)} \sinh\left(d x + c\right) + {\left(a^{2} d^{2} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - a^{2} d^{2} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, b^{3} d^{2}}"," ",0,"-1/2*(2*b^2*cosh(d*x + c) - (a^2*d^2*Ei((b*d*x + a*d)/b) + a^2*d^2*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - 2*(b^2*d*x - a*b*d)*sinh(d*x + c) + (a^2*d^2*Ei((b*d*x + a*d)/b) - a^2*d^2*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^3*d^2)","A",0
21,1,118,0,0.450595," ","integrate(x*cosh(d*x+c)/(b*x+a),x, algorithm=""fricas"")","-\frac{{\left(a d {\rm Ei}\left(\frac{b d x + a d}{b}\right) + a d {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - 2 \, b \sinh\left(d x + c\right) - {\left(a d {\rm Ei}\left(\frac{b d x + a d}{b}\right) - a d {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, b^{2} d}"," ",0,"-1/2*((a*d*Ei((b*d*x + a*d)/b) + a*d*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - 2*b*sinh(d*x + c) - (a*d*Ei((b*d*x + a*d)/b) - a*d*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^2*d)","A",0
22,1,95,0,0.508250," ","integrate(cosh(d*x+c)/(b*x+a),x, algorithm=""fricas"")","\frac{{\left({\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - {\left({\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, b}"," ",0,"1/2*((Ei((b*d*x + a*d)/b) + Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - (Ei((b*d*x + a*d)/b) - Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/b","A",0
23,1,123,0,0.638493," ","integrate(cosh(d*x+c)/x/(b*x+a),x, algorithm=""fricas"")","\frac{{\left({\rm Ei}\left(d x\right) + {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) + {\left({\rm Ei}\left(d x\right) - {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left({\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, a}"," ",0,"1/2*((Ei(d*x) + Ei(-d*x))*cosh(c) - (Ei((b*d*x + a*d)/b) + Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) + (Ei(d*x) - Ei(-d*x))*sinh(c) + (Ei((b*d*x + a*d)/b) - Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/a","A",0
24,1,179,0,0.484414," ","integrate(cosh(d*x+c)/x^2/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a \cosh\left(d x + c\right) - {\left({\left(a d - b\right)} x {\rm Ei}\left(d x\right) - {\left(a d + b\right)} x {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left(b x {\rm Ei}\left(\frac{b d x + a d}{b}\right) + b x {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - {\left({\left(a d - b\right)} x {\rm Ei}\left(d x\right) + {\left(a d + b\right)} x {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left(b x {\rm Ei}\left(\frac{b d x + a d}{b}\right) - b x {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, a^{2} x}"," ",0,"-1/2*(2*a*cosh(d*x + c) - ((a*d - b)*x*Ei(d*x) - (a*d + b)*x*Ei(-d*x))*cosh(c) - (b*x*Ei((b*d*x + a*d)/b) + b*x*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - ((a*d - b)*x*Ei(d*x) + (a*d + b)*x*Ei(-d*x))*sinh(c) + (b*x*Ei((b*d*x + a*d)/b) - b*x*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(a^2*x)","A",0
25,1,275,0,0.516288," ","integrate(cosh(d*x+c)/x^3/(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, a^{2} d x \sinh\left(d x + c\right) - 2 \, {\left(2 \, a b x - a^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} d^{2} - 2 \, a b d + 2 \, b^{2}\right)} x^{2} {\rm Ei}\left(d x\right) + {\left(a^{2} d^{2} + 2 \, a b d + 2 \, b^{2}\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left(b^{2} x^{2} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + b^{2} x^{2} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - {\left({\left(a^{2} d^{2} - 2 \, a b d + 2 \, b^{2}\right)} x^{2} {\rm Ei}\left(d x\right) - {\left(a^{2} d^{2} + 2 \, a b d + 2 \, b^{2}\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) - 2 \, {\left(b^{2} x^{2} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - b^{2} x^{2} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{4 \, a^{3} x^{2}}"," ",0,"-1/4*(2*a^2*d*x*sinh(d*x + c) - 2*(2*a*b*x - a^2)*cosh(d*x + c) - ((a^2*d^2 - 2*a*b*d + 2*b^2)*x^2*Ei(d*x) + (a^2*d^2 + 2*a*b*d + 2*b^2)*x^2*Ei(-d*x))*cosh(c) + 2*(b^2*x^2*Ei((b*d*x + a*d)/b) + b^2*x^2*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - ((a^2*d^2 - 2*a*b*d + 2*b^2)*x^2*Ei(d*x) - (a^2*d^2 + 2*a*b*d + 2*b^2)*x^2*Ei(-d*x))*sinh(c) - 2*(b^2*x^2*Ei((b*d*x + a*d)/b) - b^2*x^2*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(a^3*x^2)","A",0
26,1,371,0,0.468467," ","integrate(x^4*cosh(d*x+c)/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{4} b d^{3} + 2 \, b^{5} d x^{2} - 2 \, a^{2} b^{3} d\right)} \cosh\left(d x + c\right) - {\left({\left(a^{5} d^{4} - 4 \, a^{4} b d^{3} + {\left(a^{4} b d^{4} - 4 \, a^{3} b^{2} d^{3}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(a^{5} d^{4} + 4 \, a^{4} b d^{3} + {\left(a^{4} b d^{4} + 4 \, a^{3} b^{2} d^{3}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(b^{5} d^{2} x^{3} - a b^{4} d^{2} x^{2} + 3 \, a^{3} b^{2} d^{2} + 2 \, a b^{4} + {\left(a^{2} b^{3} d^{2} + 2 \, b^{5}\right)} x\right)} \sinh\left(d x + c\right) + {\left({\left(a^{5} d^{4} - 4 \, a^{4} b d^{3} + {\left(a^{4} b d^{4} - 4 \, a^{3} b^{2} d^{3}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(a^{5} d^{4} + 4 \, a^{4} b d^{3} + {\left(a^{4} b d^{4} + 4 \, a^{3} b^{2} d^{3}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(b^{7} d^{3} x + a b^{6} d^{3}\right)}}"," ",0,"-1/2*(2*(a^4*b*d^3 + 2*b^5*d*x^2 - 2*a^2*b^3*d)*cosh(d*x + c) - ((a^5*d^4 - 4*a^4*b*d^3 + (a^4*b*d^4 - 4*a^3*b^2*d^3)*x)*Ei((b*d*x + a*d)/b) - (a^5*d^4 + 4*a^4*b*d^3 + (a^4*b*d^4 + 4*a^3*b^2*d^3)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - 2*(b^5*d^2*x^3 - a*b^4*d^2*x^2 + 3*a^3*b^2*d^2 + 2*a*b^4 + (a^2*b^3*d^2 + 2*b^5)*x)*sinh(d*x + c) + ((a^5*d^4 - 4*a^4*b*d^3 + (a^4*b*d^4 - 4*a^3*b^2*d^3)*x)*Ei((b*d*x + a*d)/b) + (a^5*d^4 + 4*a^4*b*d^3 + (a^4*b*d^4 + 4*a^3*b^2*d^3)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^7*d^3*x + a*b^6*d^3)","A",0
27,1,333,0,0.536442," ","integrate(x^3*cosh(d*x+c)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} b d^{2} - b^{4} x - a b^{3}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{4} d^{3} - 3 \, a^{3} b d^{2} + {\left(a^{3} b d^{3} - 3 \, a^{2} b^{2} d^{2}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(a^{4} d^{3} + 3 \, a^{3} b d^{2} + {\left(a^{3} b d^{3} + 3 \, a^{2} b^{2} d^{2}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) + 2 \, {\left(b^{4} d x^{2} - a b^{3} d x - 2 \, a^{2} b^{2} d\right)} \sinh\left(d x + c\right) + {\left({\left(a^{4} d^{3} - 3 \, a^{3} b d^{2} + {\left(a^{3} b d^{3} - 3 \, a^{2} b^{2} d^{2}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(a^{4} d^{3} + 3 \, a^{3} b d^{2} + {\left(a^{3} b d^{3} + 3 \, a^{2} b^{2} d^{2}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(b^{6} d^{2} x + a b^{5} d^{2}\right)}}"," ",0,"1/2*(2*(a^3*b*d^2 - b^4*x - a*b^3)*cosh(d*x + c) - ((a^4*d^3 - 3*a^3*b*d^2 + (a^3*b*d^3 - 3*a^2*b^2*d^2)*x)*Ei((b*d*x + a*d)/b) - (a^4*d^3 + 3*a^3*b*d^2 + (a^3*b*d^3 + 3*a^2*b^2*d^2)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) + 2*(b^4*d*x^2 - a*b^3*d*x - 2*a^2*b^2*d)*sinh(d*x + c) + ((a^4*d^3 - 3*a^3*b*d^2 + (a^3*b*d^3 - 3*a^2*b^2*d^2)*x)*Ei((b*d*x + a*d)/b) + (a^4*d^3 + 3*a^3*b*d^2 + (a^3*b*d^3 + 3*a^2*b^2*d^2)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^6*d^2*x + a*b^5*d^2)","A",0
28,1,274,0,0.473419," ","integrate(x^2*cosh(d*x+c)/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} b d \cosh\left(d x + c\right) - {\left({\left(a^{3} d^{2} - 2 \, a^{2} b d + {\left(a^{2} b d^{2} - 2 \, a b^{2} d\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(a^{3} d^{2} + 2 \, a^{2} b d + {\left(a^{2} b d^{2} + 2 \, a b^{2} d\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(b^{3} x + a b^{2}\right)} \sinh\left(d x + c\right) + {\left({\left(a^{3} d^{2} - 2 \, a^{2} b d + {\left(a^{2} b d^{2} - 2 \, a b^{2} d\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(a^{3} d^{2} + 2 \, a^{2} b d + {\left(a^{2} b d^{2} + 2 \, a b^{2} d\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(b^{5} d x + a b^{4} d\right)}}"," ",0,"-1/2*(2*a^2*b*d*cosh(d*x + c) - ((a^3*d^2 - 2*a^2*b*d + (a^2*b*d^2 - 2*a*b^2*d)*x)*Ei((b*d*x + a*d)/b) - (a^3*d^2 + 2*a^2*b*d + (a^2*b*d^2 + 2*a*b^2*d)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - 2*(b^3*x + a*b^2)*sinh(d*x + c) + ((a^3*d^2 - 2*a^2*b*d + (a^2*b*d^2 - 2*a*b^2*d)*x)*Ei((b*d*x + a*d)/b) + (a^3*d^2 + 2*a^2*b*d + (a^2*b*d^2 + 2*a*b^2*d)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^5*d*x + a*b^4*d)","A",0
29,1,200,0,0.384796," ","integrate(x*cosh(d*x+c)/(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, a b \cosh\left(d x + c\right) - {\left({\left(a^{2} d - a b + {\left(a b d - b^{2}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(a^{2} d + a b + {\left(a b d + b^{2}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) + {\left({\left(a^{2} d - a b + {\left(a b d - b^{2}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(a^{2} d + a b + {\left(a b d + b^{2}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(b^{4} x + a b^{3}\right)}}"," ",0,"1/2*(2*a*b*cosh(d*x + c) - ((a^2*d - a*b + (a*b*d - b^2)*x)*Ei((b*d*x + a*d)/b) - (a^2*d + a*b + (a*b*d + b^2)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) + ((a^2*d - a*b + (a*b*d - b^2)*x)*Ei((b*d*x + a*d)/b) + (a^2*d + a*b + (a*b*d + b^2)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^4*x + a*b^3)","A",0
30,1,149,0,0.566472," ","integrate(cosh(d*x+c)/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b \cosh\left(d x + c\right) - {\left({\left(b d x + a d\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(b d x + a d\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) + {\left({\left(b d x + a d\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(b d x + a d\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(b^{3} x + a b^{2}\right)}}"," ",0,"-1/2*(2*b*cosh(d*x + c) - ((b*d*x + a*d)*Ei((b*d*x + a*d)/b) - (b*d*x + a*d)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) + ((b*d*x + a*d)*Ei((b*d*x + a*d)/b) + (b*d*x + a*d)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^3*x + a*b^2)","B",0
31,1,270,0,0.612391," ","integrate(cosh(d*x+c)/x/(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, a b \cosh\left(d x + c\right) + {\left({\left(b^{2} x + a b\right)} {\rm Ei}\left(d x\right) + {\left(b^{2} x + a b\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(a^{2} d + a b + {\left(a b d + b^{2}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(a^{2} d - a b + {\left(a b d - b^{2}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) + {\left({\left(b^{2} x + a b\right)} {\rm Ei}\left(d x\right) - {\left(b^{2} x + a b\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left({\left(a^{2} d + a b + {\left(a b d + b^{2}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(a^{2} d - a b + {\left(a b d - b^{2}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(a^{2} b^{2} x + a^{3} b\right)}}"," ",0,"1/2*(2*a*b*cosh(d*x + c) + ((b^2*x + a*b)*Ei(d*x) + (b^2*x + a*b)*Ei(-d*x))*cosh(c) - ((a^2*d + a*b + (a*b*d + b^2)*x)*Ei((b*d*x + a*d)/b) - (a^2*d - a*b + (a*b*d - b^2)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) + ((b^2*x + a*b)*Ei(d*x) - (b^2*x + a*b)*Ei(-d*x))*sinh(c) + ((a^2*d + a*b + (a*b*d + b^2)*x)*Ei((b*d*x + a*d)/b) + (a^2*d - a*b + (a*b*d - b^2)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(a^2*b^2*x + a^3*b)","A",0
32,1,377,0,0.503070," ","integrate(cosh(d*x+c)/x^2/(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a b x + a^{2}\right)} \cosh\left(d x + c\right) - {\left({\left({\left(a b d - 2 \, b^{2}\right)} x^{2} + {\left(a^{2} d - 2 \, a b\right)} x\right)} {\rm Ei}\left(d x\right) - {\left({\left(a b d + 2 \, b^{2}\right)} x^{2} + {\left(a^{2} d + 2 \, a b\right)} x\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left({\left(a b d + 2 \, b^{2}\right)} x^{2} + {\left(a^{2} d + 2 \, a b\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left({\left(a b d - 2 \, b^{2}\right)} x^{2} + {\left(a^{2} d - 2 \, a b\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - {\left({\left({\left(a b d - 2 \, b^{2}\right)} x^{2} + {\left(a^{2} d - 2 \, a b\right)} x\right)} {\rm Ei}\left(d x\right) + {\left({\left(a b d + 2 \, b^{2}\right)} x^{2} + {\left(a^{2} d + 2 \, a b\right)} x\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left({\left({\left(a b d + 2 \, b^{2}\right)} x^{2} + {\left(a^{2} d + 2 \, a b\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left({\left(a b d - 2 \, b^{2}\right)} x^{2} + {\left(a^{2} d - 2 \, a b\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{2 \, {\left(a^{3} b x^{2} + a^{4} x\right)}}"," ",0,"-1/2*(2*(2*a*b*x + a^2)*cosh(d*x + c) - (((a*b*d - 2*b^2)*x^2 + (a^2*d - 2*a*b)*x)*Ei(d*x) - ((a*b*d + 2*b^2)*x^2 + (a^2*d + 2*a*b)*x)*Ei(-d*x))*cosh(c) - (((a*b*d + 2*b^2)*x^2 + (a^2*d + 2*a*b)*x)*Ei((b*d*x + a*d)/b) - ((a*b*d - 2*b^2)*x^2 + (a^2*d - 2*a*b)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - (((a*b*d - 2*b^2)*x^2 + (a^2*d - 2*a*b)*x)*Ei(d*x) + ((a*b*d + 2*b^2)*x^2 + (a^2*d + 2*a*b)*x)*Ei(-d*x))*sinh(c) + (((a*b*d + 2*b^2)*x^2 + (a^2*d + 2*a*b)*x)*Ei((b*d*x + a*d)/b) + ((a*b*d - 2*b^2)*x^2 + (a^2*d - 2*a*b)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(a^3*b*x^2 + a^4*x)","A",0
33,1,566,0,0.870036," ","integrate(x^3*cosh(d*x+c)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(6 \, a^{2} b^{3} d x + 5 \, a^{3} b^{2} d\right)} \cosh\left(d x + c\right) + {\left({\left(a^{5} d^{3} - 6 \, a^{4} b d^{2} + 6 \, a^{3} b^{2} d + {\left(a^{3} b^{2} d^{3} - 6 \, a^{2} b^{3} d^{2} + 6 \, a b^{4} d\right)} x^{2} + 2 \, {\left(a^{4} b d^{3} - 6 \, a^{3} b^{2} d^{2} + 6 \, a^{2} b^{3} d\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(a^{5} d^{3} + 6 \, a^{4} b d^{2} + 6 \, a^{3} b^{2} d + {\left(a^{3} b^{2} d^{3} + 6 \, a^{2} b^{3} d^{2} + 6 \, a b^{4} d\right)} x^{2} + 2 \, {\left(a^{4} b d^{3} + 6 \, a^{3} b^{2} d^{2} + 6 \, a^{2} b^{3} d\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(a^{4} b d^{2} + 2 \, b^{5} x^{2} + 2 \, a^{2} b^{3} + {\left(a^{3} b^{2} d^{2} + 4 \, a b^{4}\right)} x\right)} \sinh\left(d x + c\right) - {\left({\left(a^{5} d^{3} - 6 \, a^{4} b d^{2} + 6 \, a^{3} b^{2} d + {\left(a^{3} b^{2} d^{3} - 6 \, a^{2} b^{3} d^{2} + 6 \, a b^{4} d\right)} x^{2} + 2 \, {\left(a^{4} b d^{3} - 6 \, a^{3} b^{2} d^{2} + 6 \, a^{2} b^{3} d\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(a^{5} d^{3} + 6 \, a^{4} b d^{2} + 6 \, a^{3} b^{2} d + {\left(a^{3} b^{2} d^{3} + 6 \, a^{2} b^{3} d^{2} + 6 \, a b^{4} d\right)} x^{2} + 2 \, {\left(a^{4} b d^{3} + 6 \, a^{3} b^{2} d^{2} + 6 \, a^{2} b^{3} d\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(b^{8} d x^{2} + 2 \, a b^{7} d x + a^{2} b^{6} d\right)}}"," ",0,"-1/4*(2*(6*a^2*b^3*d*x + 5*a^3*b^2*d)*cosh(d*x + c) + ((a^5*d^3 - 6*a^4*b*d^2 + 6*a^3*b^2*d + (a^3*b^2*d^3 - 6*a^2*b^3*d^2 + 6*a*b^4*d)*x^2 + 2*(a^4*b*d^3 - 6*a^3*b^2*d^2 + 6*a^2*b^3*d)*x)*Ei((b*d*x + a*d)/b) + (a^5*d^3 + 6*a^4*b*d^2 + 6*a^3*b^2*d + (a^3*b^2*d^3 + 6*a^2*b^3*d^2 + 6*a*b^4*d)*x^2 + 2*(a^4*b*d^3 + 6*a^3*b^2*d^2 + 6*a^2*b^3*d)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - 2*(a^4*b*d^2 + 2*b^5*x^2 + 2*a^2*b^3 + (a^3*b^2*d^2 + 4*a*b^4)*x)*sinh(d*x + c) - ((a^5*d^3 - 6*a^4*b*d^2 + 6*a^3*b^2*d + (a^3*b^2*d^3 - 6*a^2*b^3*d^2 + 6*a*b^4*d)*x^2 + 2*(a^4*b*d^3 - 6*a^3*b^2*d^2 + 6*a^2*b^3*d)*x)*Ei((b*d*x + a*d)/b) - (a^5*d^3 + 6*a^4*b*d^2 + 6*a^3*b^2*d + (a^3*b^2*d^3 + 6*a^2*b^3*d^2 + 6*a*b^4*d)*x^2 + 2*(a^4*b*d^3 + 6*a^3*b^2*d^2 + 6*a^2*b^3*d)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^8*d*x^2 + 2*a*b^7*d*x + a^2*b^6*d)","B",0
34,1,475,0,0.614849," ","integrate(x^2*cosh(d*x+c)/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, a b^{3} x + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{4} d^{2} - 4 \, a^{3} b d + 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} - 4 \, a b^{3} d + 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} - 4 \, a^{2} b^{2} d + 2 \, a b^{3}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(a^{4} d^{2} + 4 \, a^{3} b d + 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} + 4 \, a b^{3} d + 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} + 4 \, a^{2} b^{2} d + 2 \, a b^{3}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(a^{2} b^{2} d x + a^{3} b d\right)} \sinh\left(d x + c\right) - {\left({\left(a^{4} d^{2} - 4 \, a^{3} b d + 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} - 4 \, a b^{3} d + 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} - 4 \, a^{2} b^{2} d + 2 \, a b^{3}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(a^{4} d^{2} + 4 \, a^{3} b d + 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} + 4 \, a b^{3} d + 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} + 4 \, a^{2} b^{2} d + 2 \, a b^{3}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(b^{7} x^{2} + 2 \, a b^{6} x + a^{2} b^{5}\right)}}"," ",0,"1/4*(2*(4*a*b^3*x + 3*a^2*b^2)*cosh(d*x + c) + ((a^4*d^2 - 4*a^3*b*d + 2*a^2*b^2 + (a^2*b^2*d^2 - 4*a*b^3*d + 2*b^4)*x^2 + 2*(a^3*b*d^2 - 4*a^2*b^2*d + 2*a*b^3)*x)*Ei((b*d*x + a*d)/b) + (a^4*d^2 + 4*a^3*b*d + 2*a^2*b^2 + (a^2*b^2*d^2 + 4*a*b^3*d + 2*b^4)*x^2 + 2*(a^3*b*d^2 + 4*a^2*b^2*d + 2*a*b^3)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - 2*(a^2*b^2*d*x + a^3*b*d)*sinh(d*x + c) - ((a^4*d^2 - 4*a^3*b*d + 2*a^2*b^2 + (a^2*b^2*d^2 - 4*a*b^3*d + 2*b^4)*x^2 + 2*(a^3*b*d^2 - 4*a^2*b^2*d + 2*a*b^3)*x)*Ei((b*d*x + a*d)/b) - (a^4*d^2 + 4*a^3*b*d + 2*a^2*b^2 + (a^2*b^2*d^2 + 4*a*b^3*d + 2*b^4)*x^2 + 2*(a^3*b*d^2 + 4*a^2*b^2*d + 2*a*b^3)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^7*x^2 + 2*a*b^6*x + a^2*b^5)","A",0
35,1,373,0,0.532980," ","integrate(x*cosh(d*x+c)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, b^{3} x + a b^{2}\right)} \cosh\left(d x + c\right) + {\left({\left(a^{3} d^{2} - 2 \, a^{2} b d + {\left(a b^{2} d^{2} - 2 \, b^{3} d\right)} x^{2} + 2 \, {\left(a^{2} b d^{2} - 2 \, a b^{2} d\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(a^{3} d^{2} + 2 \, a^{2} b d + {\left(a b^{2} d^{2} + 2 \, b^{3} d\right)} x^{2} + 2 \, {\left(a^{2} b d^{2} + 2 \, a b^{2} d\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(a b^{2} d x + a^{2} b d\right)} \sinh\left(d x + c\right) - {\left({\left(a^{3} d^{2} - 2 \, a^{2} b d + {\left(a b^{2} d^{2} - 2 \, b^{3} d\right)} x^{2} + 2 \, {\left(a^{2} b d^{2} - 2 \, a b^{2} d\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(a^{3} d^{2} + 2 \, a^{2} b d + {\left(a b^{2} d^{2} + 2 \, b^{3} d\right)} x^{2} + 2 \, {\left(a^{2} b d^{2} + 2 \, a b^{2} d\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(b^{6} x^{2} + 2 \, a b^{5} x + a^{2} b^{4}\right)}}"," ",0,"-1/4*(2*(2*b^3*x + a*b^2)*cosh(d*x + c) + ((a^3*d^2 - 2*a^2*b*d + (a*b^2*d^2 - 2*b^3*d)*x^2 + 2*(a^2*b*d^2 - 2*a*b^2*d)*x)*Ei((b*d*x + a*d)/b) + (a^3*d^2 + 2*a^2*b*d + (a*b^2*d^2 + 2*b^3*d)*x^2 + 2*(a^2*b*d^2 + 2*a*b^2*d)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - 2*(a*b^2*d*x + a^2*b*d)*sinh(d*x + c) - ((a^3*d^2 - 2*a^2*b*d + (a*b^2*d^2 - 2*b^3*d)*x^2 + 2*(a^2*b*d^2 - 2*a*b^2*d)*x)*Ei((b*d*x + a*d)/b) - (a^3*d^2 + 2*a^2*b*d + (a*b^2*d^2 + 2*b^3*d)*x^2 + 2*(a^2*b*d^2 + 2*a*b^2*d)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^6*x^2 + 2*a*b^5*x + a^2*b^4)","B",0
36,1,253,0,0.484160," ","integrate(cosh(d*x+c)/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, b^{2} \cosh\left(d x + c\right) - {\left({\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) + 2 \, {\left(b^{2} d x + a b d\right)} \sinh\left(d x + c\right) + {\left({\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(b^{2} d^{2} x^{2} + 2 \, a b d^{2} x + a^{2} d^{2}\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(b^{5} x^{2} + 2 \, a b^{4} x + a^{2} b^{3}\right)}}"," ",0,"-1/4*(2*b^2*cosh(d*x + c) - ((b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*Ei((b*d*x + a*d)/b) + (b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) + 2*(b^2*d*x + a*b*d)*sinh(d*x + c) + ((b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*Ei((b*d*x + a*d)/b) - (b^2*d^2*x^2 + 2*a*b*d^2*x + a^2*d^2)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(b^5*x^2 + 2*a*b^4*x + a^2*b^3)","B",0
37,1,601,0,0.479100," ","integrate(cosh(d*x+c)/x/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a b^{3} x + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left({\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)} {\rm Ei}\left(d x\right) + {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(a^{4} d^{2} + 2 \, a^{3} b d + 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} + 2 \, a b^{3} d + 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} + 2 \, a^{2} b^{2} d + 2 \, a b^{3}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left(a^{4} d^{2} - 2 \, a^{3} b d + 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} - 2 \, a b^{3} d + 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} - 2 \, a^{2} b^{2} d + 2 \, a b^{3}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) + 2 \, {\left(a^{2} b^{2} d x + a^{3} b d\right)} \sinh\left(d x + c\right) + 2 \, {\left({\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)} {\rm Ei}\left(d x\right) - {\left(b^{4} x^{2} + 2 \, a b^{3} x + a^{2} b^{2}\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left({\left(a^{4} d^{2} + 2 \, a^{3} b d + 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} + 2 \, a b^{3} d + 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} + 2 \, a^{2} b^{2} d + 2 \, a b^{3}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left(a^{4} d^{2} - 2 \, a^{3} b d + 2 \, a^{2} b^{2} + {\left(a^{2} b^{2} d^{2} - 2 \, a b^{3} d + 2 \, b^{4}\right)} x^{2} + 2 \, {\left(a^{3} b d^{2} - 2 \, a^{2} b^{2} d + 2 \, a b^{3}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(a^{3} b^{4} x^{2} + 2 \, a^{4} b^{3} x + a^{5} b^{2}\right)}}"," ",0,"1/4*(2*(2*a*b^3*x + 3*a^2*b^2)*cosh(d*x + c) + 2*((b^4*x^2 + 2*a*b^3*x + a^2*b^2)*Ei(d*x) + (b^4*x^2 + 2*a*b^3*x + a^2*b^2)*Ei(-d*x))*cosh(c) - ((a^4*d^2 + 2*a^3*b*d + 2*a^2*b^2 + (a^2*b^2*d^2 + 2*a*b^3*d + 2*b^4)*x^2 + 2*(a^3*b*d^2 + 2*a^2*b^2*d + 2*a*b^3)*x)*Ei((b*d*x + a*d)/b) + (a^4*d^2 - 2*a^3*b*d + 2*a^2*b^2 + (a^2*b^2*d^2 - 2*a*b^3*d + 2*b^4)*x^2 + 2*(a^3*b*d^2 - 2*a^2*b^2*d + 2*a*b^3)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) + 2*(a^2*b^2*d*x + a^3*b*d)*sinh(d*x + c) + 2*((b^4*x^2 + 2*a*b^3*x + a^2*b^2)*Ei(d*x) - (b^4*x^2 + 2*a*b^3*x + a^2*b^2)*Ei(-d*x))*sinh(c) + ((a^4*d^2 + 2*a^3*b*d + 2*a^2*b^2 + (a^2*b^2*d^2 + 2*a*b^3*d + 2*b^4)*x^2 + 2*(a^3*b*d^2 + 2*a^2*b^2*d + 2*a*b^3)*x)*Ei((b*d*x + a*d)/b) - (a^4*d^2 - 2*a^3*b*d + 2*a^2*b^2 + (a^2*b^2*d^2 - 2*a*b^3*d + 2*b^4)*x^2 + 2*(a^3*b*d^2 - 2*a^2*b^2*d + 2*a*b^3)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(a^3*b^4*x^2 + 2*a^4*b^3*x + a^5*b^2)","B",0
38,1,762,0,0.536520," ","integrate(cosh(d*x+c)/x^2/(b*x+a)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(6 \, a b^{3} x^{2} + 9 \, a^{2} b^{2} x + 2 \, a^{3} b\right)} \cosh\left(d x + c\right) - 2 \, {\left({\left({\left(a b^{3} d - 3 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{2} b^{2} d - 3 \, a b^{3}\right)} x^{2} + {\left(a^{3} b d - 3 \, a^{2} b^{2}\right)} x\right)} {\rm Ei}\left(d x\right) - {\left({\left(a b^{3} d + 3 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{2} b^{2} d + 3 \, a b^{3}\right)} x^{2} + {\left(a^{3} b d + 3 \, a^{2} b^{2}\right)} x\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left({\left(a^{2} b^{2} d^{2} + 4 \, a b^{3} d + 6 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{3} b d^{2} + 4 \, a^{2} b^{2} d + 6 \, a b^{3}\right)} x^{2} + {\left(a^{4} d^{2} + 4 \, a^{3} b d + 6 \, a^{2} b^{2}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left({\left(a^{2} b^{2} d^{2} - 4 \, a b^{3} d + 6 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{3} b d^{2} - 4 \, a^{2} b^{2} d + 6 \, a b^{3}\right)} x^{2} + {\left(a^{4} d^{2} - 4 \, a^{3} b d + 6 \, a^{2} b^{2}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) + 2 \, {\left(a^{2} b^{2} d x^{2} + a^{3} b d x\right)} \sinh\left(d x + c\right) - 2 \, {\left({\left({\left(a b^{3} d - 3 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{2} b^{2} d - 3 \, a b^{3}\right)} x^{2} + {\left(a^{3} b d - 3 \, a^{2} b^{2}\right)} x\right)} {\rm Ei}\left(d x\right) + {\left({\left(a b^{3} d + 3 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{2} b^{2} d + 3 \, a b^{3}\right)} x^{2} + {\left(a^{3} b d + 3 \, a^{2} b^{2}\right)} x\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left({\left({\left(a^{2} b^{2} d^{2} + 4 \, a b^{3} d + 6 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{3} b d^{2} + 4 \, a^{2} b^{2} d + 6 \, a b^{3}\right)} x^{2} + {\left(a^{4} d^{2} + 4 \, a^{3} b d + 6 \, a^{2} b^{2}\right)} x\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left({\left(a^{2} b^{2} d^{2} - 4 \, a b^{3} d + 6 \, b^{4}\right)} x^{3} + 2 \, {\left(a^{3} b d^{2} - 4 \, a^{2} b^{2} d + 6 \, a b^{3}\right)} x^{2} + {\left(a^{4} d^{2} - 4 \, a^{3} b d + 6 \, a^{2} b^{2}\right)} x\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(a^{4} b^{3} x^{3} + 2 \, a^{5} b^{2} x^{2} + a^{6} b x\right)}}"," ",0,"-1/4*(2*(6*a*b^3*x^2 + 9*a^2*b^2*x + 2*a^3*b)*cosh(d*x + c) - 2*(((a*b^3*d - 3*b^4)*x^3 + 2*(a^2*b^2*d - 3*a*b^3)*x^2 + (a^3*b*d - 3*a^2*b^2)*x)*Ei(d*x) - ((a*b^3*d + 3*b^4)*x^3 + 2*(a^2*b^2*d + 3*a*b^3)*x^2 + (a^3*b*d + 3*a^2*b^2)*x)*Ei(-d*x))*cosh(c) - (((a^2*b^2*d^2 + 4*a*b^3*d + 6*b^4)*x^3 + 2*(a^3*b*d^2 + 4*a^2*b^2*d + 6*a*b^3)*x^2 + (a^4*d^2 + 4*a^3*b*d + 6*a^2*b^2)*x)*Ei((b*d*x + a*d)/b) + ((a^2*b^2*d^2 - 4*a*b^3*d + 6*b^4)*x^3 + 2*(a^3*b*d^2 - 4*a^2*b^2*d + 6*a*b^3)*x^2 + (a^4*d^2 - 4*a^3*b*d + 6*a^2*b^2)*x)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) + 2*(a^2*b^2*d*x^2 + a^3*b*d*x)*sinh(d*x + c) - 2*(((a*b^3*d - 3*b^4)*x^3 + 2*(a^2*b^2*d - 3*a*b^3)*x^2 + (a^3*b*d - 3*a^2*b^2)*x)*Ei(d*x) + ((a*b^3*d + 3*b^4)*x^3 + 2*(a^2*b^2*d + 3*a*b^3)*x^2 + (a^3*b*d + 3*a^2*b^2)*x)*Ei(-d*x))*sinh(c) + (((a^2*b^2*d^2 + 4*a*b^3*d + 6*b^4)*x^3 + 2*(a^3*b*d^2 + 4*a^2*b^2*d + 6*a*b^3)*x^2 + (a^4*d^2 + 4*a^3*b*d + 6*a^2*b^2)*x)*Ei((b*d*x + a*d)/b) - ((a^2*b^2*d^2 - 4*a*b^3*d + 6*b^4)*x^3 + 2*(a^3*b*d^2 - 4*a^2*b^2*d + 6*a*b^3)*x^2 + (a^4*d^2 - 4*a^3*b*d + 6*a^2*b^2)*x)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(a^4*b^3*x^3 + 2*a^5*b^2*x^2 + a^6*b*x)","B",0
39,1,892,0,0.560833," ","integrate(cosh(d*x+c)/x^3/(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(12 \, a b^{3} x^{3} + 18 \, a^{2} b^{2} x^{2} + 4 \, a^{3} b x - a^{4}\right)} \cosh\left(d x + c\right) + {\left({\left({\left(a^{2} b^{2} d^{2} - 6 \, a b^{3} d + 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} - 6 \, a^{2} b^{2} d + 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} - 6 \, a^{3} b d + 12 \, a^{2} b^{2}\right)} x^{2}\right)} {\rm Ei}\left(d x\right) + {\left({\left(a^{2} b^{2} d^{2} + 6 \, a b^{3} d + 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} + 6 \, a^{2} b^{2} d + 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} + 6 \, a^{3} b d + 12 \, a^{2} b^{2}\right)} x^{2}\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left({\left(a^{2} b^{2} d^{2} + 6 \, a b^{3} d + 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} + 6 \, a^{2} b^{2} d + 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} + 6 \, a^{3} b d + 12 \, a^{2} b^{2}\right)} x^{2}\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) + {\left({\left(a^{2} b^{2} d^{2} - 6 \, a b^{3} d + 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} - 6 \, a^{2} b^{2} d + 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} - 6 \, a^{3} b d + 12 \, a^{2} b^{2}\right)} x^{2}\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \cosh\left(-\frac{b c - a d}{b}\right) - 2 \, {\left(a^{3} b d x^{2} + a^{4} d x\right)} \sinh\left(d x + c\right) + {\left({\left({\left(a^{2} b^{2} d^{2} - 6 \, a b^{3} d + 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} - 6 \, a^{2} b^{2} d + 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} - 6 \, a^{3} b d + 12 \, a^{2} b^{2}\right)} x^{2}\right)} {\rm Ei}\left(d x\right) - {\left({\left(a^{2} b^{2} d^{2} + 6 \, a b^{3} d + 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} + 6 \, a^{2} b^{2} d + 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} + 6 \, a^{3} b d + 12 \, a^{2} b^{2}\right)} x^{2}\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left({\left({\left(a^{2} b^{2} d^{2} + 6 \, a b^{3} d + 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} + 6 \, a^{2} b^{2} d + 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} + 6 \, a^{3} b d + 12 \, a^{2} b^{2}\right)} x^{2}\right)} {\rm Ei}\left(\frac{b d x + a d}{b}\right) - {\left({\left(a^{2} b^{2} d^{2} - 6 \, a b^{3} d + 12 \, b^{4}\right)} x^{4} + 2 \, {\left(a^{3} b d^{2} - 6 \, a^{2} b^{2} d + 12 \, a b^{3}\right)} x^{3} + {\left(a^{4} d^{2} - 6 \, a^{3} b d + 12 \, a^{2} b^{2}\right)} x^{2}\right)} {\rm Ei}\left(-\frac{b d x + a d}{b}\right)\right)} \sinh\left(-\frac{b c - a d}{b}\right)}{4 \, {\left(a^{5} b^{2} x^{4} + 2 \, a^{6} b x^{3} + a^{7} x^{2}\right)}}"," ",0,"1/4*(2*(12*a*b^3*x^3 + 18*a^2*b^2*x^2 + 4*a^3*b*x - a^4)*cosh(d*x + c) + (((a^2*b^2*d^2 - 6*a*b^3*d + 12*b^4)*x^4 + 2*(a^3*b*d^2 - 6*a^2*b^2*d + 12*a*b^3)*x^3 + (a^4*d^2 - 6*a^3*b*d + 12*a^2*b^2)*x^2)*Ei(d*x) + ((a^2*b^2*d^2 + 6*a*b^3*d + 12*b^4)*x^4 + 2*(a^3*b*d^2 + 6*a^2*b^2*d + 12*a*b^3)*x^3 + (a^4*d^2 + 6*a^3*b*d + 12*a^2*b^2)*x^2)*Ei(-d*x))*cosh(c) - (((a^2*b^2*d^2 + 6*a*b^3*d + 12*b^4)*x^4 + 2*(a^3*b*d^2 + 6*a^2*b^2*d + 12*a*b^3)*x^3 + (a^4*d^2 + 6*a^3*b*d + 12*a^2*b^2)*x^2)*Ei((b*d*x + a*d)/b) + ((a^2*b^2*d^2 - 6*a*b^3*d + 12*b^4)*x^4 + 2*(a^3*b*d^2 - 6*a^2*b^2*d + 12*a*b^3)*x^3 + (a^4*d^2 - 6*a^3*b*d + 12*a^2*b^2)*x^2)*Ei(-(b*d*x + a*d)/b))*cosh(-(b*c - a*d)/b) - 2*(a^3*b*d*x^2 + a^4*d*x)*sinh(d*x + c) + (((a^2*b^2*d^2 - 6*a*b^3*d + 12*b^4)*x^4 + 2*(a^3*b*d^2 - 6*a^2*b^2*d + 12*a*b^3)*x^3 + (a^4*d^2 - 6*a^3*b*d + 12*a^2*b^2)*x^2)*Ei(d*x) - ((a^2*b^2*d^2 + 6*a*b^3*d + 12*b^4)*x^4 + 2*(a^3*b*d^2 + 6*a^2*b^2*d + 12*a*b^3)*x^3 + (a^4*d^2 + 6*a^3*b*d + 12*a^2*b^2)*x^2)*Ei(-d*x))*sinh(c) + (((a^2*b^2*d^2 + 6*a*b^3*d + 12*b^4)*x^4 + 2*(a^3*b*d^2 + 6*a^2*b^2*d + 12*a*b^3)*x^3 + (a^4*d^2 + 6*a^3*b*d + 12*a^2*b^2)*x^2)*Ei((b*d*x + a*d)/b) - ((a^2*b^2*d^2 - 6*a*b^3*d + 12*b^4)*x^4 + 2*(a^3*b*d^2 - 6*a^2*b^2*d + 12*a*b^3)*x^3 + (a^4*d^2 - 6*a^3*b*d + 12*a^2*b^2)*x^2)*Ei(-(b*d*x + a*d)/b))*sinh(-(b*c - a*d)/b))/(a^5*b^2*x^4 + 2*a^6*b*x^3 + a^7*x^2)","B",0
40,1,95,0,0.527855," ","integrate(x^3*(b*x^2+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(5 \, b d^{4} x^{4} + 6 \, a d^{2} + 3 \, {\left(a d^{4} + 20 \, b d^{2}\right)} x^{2} + 120 \, b\right)} \cosh\left(d x + c\right) - {\left(b d^{5} x^{5} + {\left(a d^{5} + 20 \, b d^{3}\right)} x^{3} + 6 \, {\left(a d^{3} + 20 \, b d\right)} x\right)} \sinh\left(d x + c\right)}{d^{6}}"," ",0,"-((5*b*d^4*x^4 + 6*a*d^2 + 3*(a*d^4 + 20*b*d^2)*x^2 + 120*b)*cosh(d*x + c) - (b*d^5*x^5 + (a*d^5 + 20*b*d^3)*x^3 + 6*(a*d^3 + 20*b*d)*x)*sinh(d*x + c))/d^6","A",0
41,1,78,0,0.465856," ","integrate(x^2*(b*x^2+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, b d^{3} x^{3} + {\left(a d^{3} + 12 \, b d\right)} x\right)} \cosh\left(d x + c\right) - {\left(b d^{4} x^{4} + 2 \, a d^{2} + {\left(a d^{4} + 12 \, b d^{2}\right)} x^{2} + 24 \, b\right)} \sinh\left(d x + c\right)}{d^{5}}"," ",0,"-(2*(2*b*d^3*x^3 + (a*d^3 + 12*b*d)*x)*cosh(d*x + c) - (b*d^4*x^4 + 2*a*d^2 + (a*d^4 + 12*b*d^2)*x^2 + 24*b)*sinh(d*x + c))/d^5","A",0
42,1,60,0,0.423181," ","integrate(x*(b*x^2+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(3 \, b d^{2} x^{2} + a d^{2} + 6 \, b\right)} \cosh\left(d x + c\right) - {\left(b d^{3} x^{3} + {\left(a d^{3} + 6 \, b d\right)} x\right)} \sinh\left(d x + c\right)}{d^{4}}"," ",0,"-((3*b*d^2*x^2 + a*d^2 + 6*b)*cosh(d*x + c) - (b*d^3*x^3 + (a*d^3 + 6*b*d)*x)*sinh(d*x + c))/d^4","A",0
43,1,42,0,0.441454," ","integrate((b*x^2+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, b d x \cosh\left(d x + c\right) - {\left(b d^{2} x^{2} + a d^{2} + 2 \, b\right)} \sinh\left(d x + c\right)}{d^{3}}"," ",0,"-(2*b*d*x*cosh(d*x + c) - (b*d^2*x^2 + a*d^2 + 2*b)*sinh(d*x + c))/d^3","A",0
44,1,73,0,0.539758," ","integrate((b*x^2+a)*cosh(d*x+c)/x,x, algorithm=""fricas"")","\frac{2 \, b d x \sinh\left(d x + c\right) - 2 \, b \cosh\left(d x + c\right) + {\left(a d^{2} {\rm Ei}\left(d x\right) + a d^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + {\left(a d^{2} {\rm Ei}\left(d x\right) - a d^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d^{2}}"," ",0,"1/2*(2*b*d*x*sinh(d*x + c) - 2*b*cosh(d*x + c) + (a*d^2*Ei(d*x) + a*d^2*Ei(-d*x))*cosh(c) + (a*d^2*Ei(d*x) - a*d^2*Ei(-d*x))*sinh(c))/d^2","A",0
45,1,82,0,0.575140," ","integrate((b*x^2+a)*cosh(d*x+c)/x^2,x, algorithm=""fricas"")","-\frac{2 \, a d \cosh\left(d x + c\right) - 2 \, b x \sinh\left(d x + c\right) - {\left(a d^{2} x {\rm Ei}\left(d x\right) - a d^{2} x {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left(a d^{2} x {\rm Ei}\left(d x\right) + a d^{2} x {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d x}"," ",0,"-1/2*(2*a*d*cosh(d*x + c) - 2*b*x*sinh(d*x + c) - (a*d^2*x*Ei(d*x) - a*d^2*x*Ei(-d*x))*cosh(c) - (a*d^2*x*Ei(d*x) + a*d^2*x*Ei(-d*x))*sinh(c))/(d*x)","A",0
46,1,107,0,0.498508," ","integrate((b*x^2+a)*cosh(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a d x \sinh\left(d x + c\right) + 2 \, a \cosh\left(d x + c\right) - {\left({\left(a d^{2} + 2 \, b\right)} x^{2} {\rm Ei}\left(d x\right) + {\left(a d^{2} + 2 \, b\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(a d^{2} + 2 \, b\right)} x^{2} {\rm Ei}\left(d x\right) - {\left(a d^{2} + 2 \, b\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{4 \, x^{2}}"," ",0,"-1/4*(2*a*d*x*sinh(d*x + c) + 2*a*cosh(d*x + c) - ((a*d^2 + 2*b)*x^2*Ei(d*x) + (a*d^2 + 2*b)*x^2*Ei(-d*x))*cosh(c) - ((a*d^2 + 2*b)*x^2*Ei(d*x) - (a*d^2 + 2*b)*x^2*Ei(-d*x))*sinh(c))/x^2","A",0
47,1,127,0,0.506579," ","integrate((b*x^2+a)*cosh(d*x+c)/x^4,x, algorithm=""fricas"")","-\frac{2 \, a d x \sinh\left(d x + c\right) + 2 \, {\left({\left(a d^{2} + 6 \, b\right)} x^{2} + 2 \, a\right)} \cosh\left(d x + c\right) - {\left({\left(a d^{3} + 6 \, b d\right)} x^{3} {\rm Ei}\left(d x\right) - {\left(a d^{3} + 6 \, b d\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(a d^{3} + 6 \, b d\right)} x^{3} {\rm Ei}\left(d x\right) + {\left(a d^{3} + 6 \, b d\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{12 \, x^{3}}"," ",0,"-1/12*(2*a*d*x*sinh(d*x + c) + 2*((a*d^2 + 6*b)*x^2 + 2*a)*cosh(d*x + c) - ((a*d^3 + 6*b*d)*x^3*Ei(d*x) - (a*d^3 + 6*b*d)*x^3*Ei(-d*x))*cosh(c) - ((a*d^3 + 6*b*d)*x^3*Ei(d*x) + (a*d^3 + 6*b*d)*x^3*Ei(-d*x))*sinh(c))/x^3","A",0
48,1,152,0,0.482504," ","integrate((b*x^2+a)*cosh(d*x+c)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a d^{2} + 12 \, b\right)} x^{2} + 6 \, a\right)} \cosh\left(d x + c\right) - {\left({\left(a d^{4} + 12 \, b d^{2}\right)} x^{4} {\rm Ei}\left(d x\right) + {\left(a d^{4} + 12 \, b d^{2}\right)} x^{4} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left({\left(a d^{3} + 12 \, b d\right)} x^{3} + 2 \, a d x\right)} \sinh\left(d x + c\right) - {\left({\left(a d^{4} + 12 \, b d^{2}\right)} x^{4} {\rm Ei}\left(d x\right) - {\left(a d^{4} + 12 \, b d^{2}\right)} x^{4} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{48 \, x^{4}}"," ",0,"-1/48*(2*((a*d^2 + 12*b)*x^2 + 6*a)*cosh(d*x + c) - ((a*d^4 + 12*b*d^2)*x^4*Ei(d*x) + (a*d^4 + 12*b*d^2)*x^4*Ei(-d*x))*cosh(c) + 2*((a*d^3 + 12*b*d)*x^3 + 2*a*d*x)*sinh(d*x + c) - ((a*d^4 + 12*b*d^2)*x^4*Ei(d*x) - (a*d^4 + 12*b*d^2)*x^4*Ei(-d*x))*sinh(c))/x^4","A",0
49,1,155,0,0.623466," ","integrate(x^2*(b*x^2+a)^2*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{2} d^{5} x^{5} + 4 \, {\left(a b d^{5} + 15 \, b^{2} d^{3}\right)} x^{3} + {\left(a^{2} d^{5} + 24 \, a b d^{3} + 360 \, b^{2} d\right)} x\right)} \cosh\left(d x + c\right) - {\left(b^{2} d^{6} x^{6} + 2 \, a^{2} d^{4} + 2 \, {\left(a b d^{6} + 15 \, b^{2} d^{4}\right)} x^{4} + 48 \, a b d^{2} + {\left(a^{2} d^{6} + 24 \, a b d^{4} + 360 \, b^{2} d^{2}\right)} x^{2} + 720 \, b^{2}\right)} \sinh\left(d x + c\right)}{d^{7}}"," ",0,"-(2*(3*b^2*d^5*x^5 + 4*(a*b*d^5 + 15*b^2*d^3)*x^3 + (a^2*d^5 + 24*a*b*d^3 + 360*b^2*d)*x)*cosh(d*x + c) - (b^2*d^6*x^6 + 2*a^2*d^4 + 2*(a*b*d^6 + 15*b^2*d^4)*x^4 + 48*a*b*d^2 + (a^2*d^6 + 24*a*b*d^4 + 360*b^2*d^2)*x^2 + 720*b^2)*sinh(d*x + c))/d^7","A",0
50,1,126,0,0.614588," ","integrate(x*(b*x^2+a)^2*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(5 \, b^{2} d^{4} x^{4} + a^{2} d^{4} + 12 \, a b d^{2} + 6 \, {\left(a b d^{4} + 10 \, b^{2} d^{2}\right)} x^{2} + 120 \, b^{2}\right)} \cosh\left(d x + c\right) - {\left(b^{2} d^{5} x^{5} + 2 \, {\left(a b d^{5} + 10 \, b^{2} d^{3}\right)} x^{3} + {\left(a^{2} d^{5} + 12 \, a b d^{3} + 120 \, b^{2} d\right)} x\right)} \sinh\left(d x + c\right)}{d^{6}}"," ",0,"-((5*b^2*d^4*x^4 + a^2*d^4 + 12*a*b*d^2 + 6*(a*b*d^4 + 10*b^2*d^2)*x^2 + 120*b^2)*cosh(d*x + c) - (b^2*d^5*x^5 + 2*(a*b*d^5 + 10*b^2*d^3)*x^3 + (a^2*d^5 + 12*a*b*d^3 + 120*b^2*d)*x)*sinh(d*x + c))/d^6","A",0
51,1,98,0,0.436563," ","integrate((b*x^2+a)^2*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{4 \, {\left(b^{2} d^{3} x^{3} + {\left(a b d^{3} + 6 \, b^{2} d\right)} x\right)} \cosh\left(d x + c\right) - {\left(b^{2} d^{4} x^{4} + a^{2} d^{4} + 4 \, a b d^{2} + 2 \, {\left(a b d^{4} + 6 \, b^{2} d^{2}\right)} x^{2} + 24 \, b^{2}\right)} \sinh\left(d x + c\right)}{d^{5}}"," ",0,"-(4*(b^2*d^3*x^3 + (a*b*d^3 + 6*b^2*d)*x)*cosh(d*x + c) - (b^2*d^4*x^4 + a^2*d^4 + 4*a*b*d^2 + 2*(a*b*d^4 + 6*b^2*d^2)*x^2 + 24*b^2)*sinh(d*x + c))/d^5","A",0
52,1,130,0,0.587928," ","integrate((b*x^2+a)^2*cosh(d*x+c)/x,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, b^{2} d^{2} x^{2} + 2 \, a b d^{2} + 6 \, b^{2}\right)} \cosh\left(d x + c\right) - {\left(a^{2} d^{4} {\rm Ei}\left(d x\right) + a^{2} d^{4} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 2 \, {\left(b^{2} d^{3} x^{3} + 2 \, {\left(a b d^{3} + 3 \, b^{2} d\right)} x\right)} \sinh\left(d x + c\right) - {\left(a^{2} d^{4} {\rm Ei}\left(d x\right) - a^{2} d^{4} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d^{4}}"," ",0,"-1/2*(2*(3*b^2*d^2*x^2 + 2*a*b*d^2 + 6*b^2)*cosh(d*x + c) - (a^2*d^4*Ei(d*x) + a^2*d^4*Ei(-d*x))*cosh(c) - 2*(b^2*d^3*x^3 + 2*(a*b*d^3 + 3*b^2*d)*x)*sinh(d*x + c) - (a^2*d^4*Ei(d*x) - a^2*d^4*Ei(-d*x))*sinh(c))/d^4","A",0
53,1,127,0,0.763407," ","integrate((b*x^2+a)^2*cosh(d*x+c)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} d^{3} + 2 \, b^{2} d x^{2}\right)} \cosh\left(d x + c\right) - {\left(a^{2} d^{4} x {\rm Ei}\left(d x\right) - a^{2} d^{4} x {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 2 \, {\left(b^{2} d^{2} x^{3} + 2 \, {\left(a b d^{2} + b^{2}\right)} x\right)} \sinh\left(d x + c\right) - {\left(a^{2} d^{4} x {\rm Ei}\left(d x\right) + a^{2} d^{4} x {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d^{3} x}"," ",0,"-1/2*(2*(a^2*d^3 + 2*b^2*d*x^2)*cosh(d*x + c) - (a^2*d^4*x*Ei(d*x) - a^2*d^4*x*Ei(-d*x))*cosh(c) - 2*(b^2*d^2*x^3 + 2*(a*b*d^2 + b^2)*x)*sinh(d*x + c) - (a^2*d^4*x*Ei(d*x) + a^2*d^4*x*Ei(-d*x))*sinh(c))/(d^3*x)","A",0
54,1,164,0,0.894683," ","integrate((b*x^2+a)^2*cosh(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} d^{2} + 2 \, b^{2} x^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} d^{4} + 4 \, a b d^{2}\right)} x^{2} {\rm Ei}\left(d x\right) + {\left(a^{2} d^{4} + 4 \, a b d^{2}\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left(a^{2} d^{3} x - 2 \, b^{2} d x^{3}\right)} \sinh\left(d x + c\right) - {\left({\left(a^{2} d^{4} + 4 \, a b d^{2}\right)} x^{2} {\rm Ei}\left(d x\right) - {\left(a^{2} d^{4} + 4 \, a b d^{2}\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{4 \, d^{2} x^{2}}"," ",0,"-1/4*(2*(a^2*d^2 + 2*b^2*x^2)*cosh(d*x + c) - ((a^2*d^4 + 4*a*b*d^2)*x^2*Ei(d*x) + (a^2*d^4 + 4*a*b*d^2)*x^2*Ei(-d*x))*cosh(c) + 2*(a^2*d^3*x - 2*b^2*d*x^3)*sinh(d*x + c) - ((a^2*d^4 + 4*a*b*d^2)*x^2*Ei(d*x) - (a^2*d^4 + 4*a*b*d^2)*x^2*Ei(-d*x))*sinh(c))/(d^2*x^2)","A",0
55,1,171,0,0.481637," ","integrate((b*x^2+a)^2*cosh(d*x+c)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a^{2} d + {\left(a^{2} d^{3} + 12 \, a b d\right)} x^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} d^{4} + 12 \, a b d^{2}\right)} x^{3} {\rm Ei}\left(d x\right) - {\left(a^{2} d^{4} + 12 \, a b d^{2}\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left(a^{2} d^{2} x - 6 \, b^{2} x^{3}\right)} \sinh\left(d x + c\right) - {\left({\left(a^{2} d^{4} + 12 \, a b d^{2}\right)} x^{3} {\rm Ei}\left(d x\right) + {\left(a^{2} d^{4} + 12 \, a b d^{2}\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{12 \, d x^{3}}"," ",0,"-1/12*(2*(2*a^2*d + (a^2*d^3 + 12*a*b*d)*x^2)*cosh(d*x + c) - ((a^2*d^4 + 12*a*b*d^2)*x^3*Ei(d*x) - (a^2*d^4 + 12*a*b*d^2)*x^3*Ei(-d*x))*cosh(c) + 2*(a^2*d^2*x - 6*b^2*x^3)*sinh(d*x + c) - ((a^2*d^4 + 12*a*b*d^2)*x^3*Ei(d*x) + (a^2*d^4 + 12*a*b*d^2)*x^3*Ei(-d*x))*sinh(c))/(d*x^3)","A",0
56,1,194,0,0.546437," ","integrate((b*x^2+a)^2*cosh(d*x+c)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(a^{2} d^{2} + 24 \, a b\right)} x^{2} + 6 \, a^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} d^{4} + 24 \, a b d^{2} + 24 \, b^{2}\right)} x^{4} {\rm Ei}\left(d x\right) + {\left(a^{2} d^{4} + 24 \, a b d^{2} + 24 \, b^{2}\right)} x^{4} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left(2 \, a^{2} d x + {\left(a^{2} d^{3} + 24 \, a b d\right)} x^{3}\right)} \sinh\left(d x + c\right) - {\left({\left(a^{2} d^{4} + 24 \, a b d^{2} + 24 \, b^{2}\right)} x^{4} {\rm Ei}\left(d x\right) - {\left(a^{2} d^{4} + 24 \, a b d^{2} + 24 \, b^{2}\right)} x^{4} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{48 \, x^{4}}"," ",0,"-1/48*(2*((a^2*d^2 + 24*a*b)*x^2 + 6*a^2)*cosh(d*x + c) - ((a^2*d^4 + 24*a*b*d^2 + 24*b^2)*x^4*Ei(d*x) + (a^2*d^4 + 24*a*b*d^2 + 24*b^2)*x^4*Ei(-d*x))*cosh(c) + 2*(2*a^2*d*x + (a^2*d^3 + 24*a*b*d)*x^3)*sinh(d*x + c) - ((a^2*d^4 + 24*a*b*d^2 + 24*b^2)*x^4*Ei(d*x) - (a^2*d^4 + 24*a*b*d^2 + 24*b^2)*x^4*Ei(-d*x))*sinh(c))/x^4","A",0
57,1,605,0,0.800462," ","integrate(x^4*cosh(d*x+c)/(b*x^2+a),x, algorithm=""fricas"")","-\frac{8 \, b d x \cosh\left(d x + c\right) + {\left({\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - 4 \, {\left(b d^{2} x^{2} - a d^{2} + 2 \, b\right)} \sinh\left(d x + c\right) + {\left({\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{4 \, {\left(b^{2} d^{3} \cosh\left(d x + c\right)^{2} - b^{2} d^{3} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/4*(8*b*d*x*cosh(d*x + c) + ((a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x - sqrt(-a*d^2/b)) + (a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - ((a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x + sqrt(-a*d^2/b)) + (a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - 4*(b*d^2*x^2 - a*d^2 + 2*b)*sinh(d*x + c) + ((a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x - sqrt(-a*d^2/b)) - (a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + ((a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x + sqrt(-a*d^2/b)) - (a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/(b^2*d^3*cosh(d*x + c)^2 - b^2*d^3*sinh(d*x + c)^2)","B",0
58,1,502,0,1.113647," ","integrate(x^3*cosh(d*x+c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{4 \, b d x \sinh\left(d x + c\right) - 4 \, b \cosh\left(d x + c\right) - {\left({\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(a d^{2} \cosh\left(d x + c\right)^{2} - a d^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{4 \, {\left(b^{2} d^{2} \cosh\left(d x + c\right)^{2} - b^{2} d^{2} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/4*(4*b*d*x*sinh(d*x + c) - 4*b*cosh(d*x + c) - ((a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*Ei(d*x - sqrt(-a*d^2/b)) + (a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - ((a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*Ei(d*x + sqrt(-a*d^2/b)) + (a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - ((a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*Ei(d*x - sqrt(-a*d^2/b)) - (a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + ((a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*Ei(d*x + sqrt(-a*d^2/b)) - (a*d^2*cosh(d*x + c)^2 - a*d^2*sinh(d*x + c)^2)*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/(b^2*d^2*cosh(d*x + c)^2 - b^2*d^2*sinh(d*x + c)^2)","B",0
59,1,496,0,0.742977," ","integrate(x^2*cosh(d*x+c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{{\left(\sqrt{-\frac{a d^{2}}{b}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + \sqrt{-\frac{a d^{2}}{b}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(\sqrt{-\frac{a d^{2}}{b}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + \sqrt{-\frac{a d^{2}}{b}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(\sqrt{-\frac{a d^{2}}{b}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - \sqrt{-\frac{a d^{2}}{b}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(\sqrt{-\frac{a d^{2}}{b}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - \sqrt{-\frac{a d^{2}}{b}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + 4 \, \sinh\left(d x + c\right)}{4 \, {\left(b d \cosh\left(d x + c\right)^{2} - b d \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/4*((sqrt(-a*d^2/b)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(d*x - sqrt(-a*d^2/b)) + sqrt(-a*d^2/b)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - (sqrt(-a*d^2/b)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(d*x + sqrt(-a*d^2/b)) + sqrt(-a*d^2/b)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + (sqrt(-a*d^2/b)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(d*x - sqrt(-a*d^2/b)) - sqrt(-a*d^2/b)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + (sqrt(-a*d^2/b)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(d*x + sqrt(-a*d^2/b)) - sqrt(-a*d^2/b)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)) + 4*sinh(d*x + c))/(b*d*cosh(d*x + c)^2 - b*d*sinh(d*x + c)^2)","B",0
60,1,219,0,0.659203," ","integrate(x*cosh(d*x+c)/(b*x^2+a),x, algorithm=""fricas"")","\frac{{\left({\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{4 \, b}"," ",0,"1/4*((Ei(d*x - sqrt(-a*d^2/b)) + Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) + (Ei(d*x + sqrt(-a*d^2/b)) + Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + (Ei(d*x - sqrt(-a*d^2/b)) - Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) - (Ei(d*x + sqrt(-a*d^2/b)) - Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/b","A",0
61,1,316,0,0.727668," ","integrate(cosh(d*x+c)/(b*x^2+a),x, algorithm=""fricas"")","-\frac{{\left(\sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(\sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(\sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(\sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{4 \, a d}"," ",0,"-1/4*((sqrt(-a*d^2/b)*Ei(d*x - sqrt(-a*d^2/b)) + sqrt(-a*d^2/b)*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - (sqrt(-a*d^2/b)*Ei(d*x + sqrt(-a*d^2/b)) + sqrt(-a*d^2/b)*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + (sqrt(-a*d^2/b)*Ei(d*x - sqrt(-a*d^2/b)) - sqrt(-a*d^2/b)*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + (sqrt(-a*d^2/b)*Ei(d*x + sqrt(-a*d^2/b)) - sqrt(-a*d^2/b)*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/(a*d)","B",0
62,1,249,0,0.688746," ","integrate(cosh(d*x+c)/x/(b*x^2+a),x, algorithm=""fricas"")","-\frac{{\left({\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - 2 \, {\left({\rm Ei}\left(d x\right) + {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + {\left({\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - 2 \, {\left({\rm Ei}\left(d x\right) - {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) - {\left({\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{4 \, a}"," ",0,"-1/4*((Ei(d*x - sqrt(-a*d^2/b)) + Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - 2*(Ei(d*x) + Ei(-d*x))*cosh(c) + (Ei(d*x + sqrt(-a*d^2/b)) + Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + (Ei(d*x - sqrt(-a*d^2/b)) - Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) - 2*(Ei(d*x) - Ei(-d*x))*sinh(c) - (Ei(d*x + sqrt(-a*d^2/b)) - Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/a","A",0
63,1,599,0,0.511280," ","integrate(cosh(d*x+c)/x^2/(b*x^2+a),x, algorithm=""fricas"")","-\frac{4 \, a d \cosh\left(d x + c\right) - {\left({\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - 2 \, {\left(a d^{2} x {\rm Ei}\left(d x\right) - a d^{2} x {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + {\left({\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - 2 \, {\left(a d^{2} x {\rm Ei}\left(d x\right) + a d^{2} x {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) - {\left({\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{4 \, {\left(a^{2} d x \cosh\left(d x + c\right)^{2} - a^{2} d x \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/4*(4*a*d*cosh(d*x + c) - ((b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x - sqrt(-a*d^2/b)) + (b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - 2*(a*d^2*x*Ei(d*x) - a*d^2*x*Ei(-d*x))*cosh(c) + ((b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x + sqrt(-a*d^2/b)) + (b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - ((b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x - sqrt(-a*d^2/b)) - (b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) - 2*(a*d^2*x*Ei(d*x) + a*d^2*x*Ei(-d*x))*sinh(c) - ((b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x + sqrt(-a*d^2/b)) - (b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/(a^2*d*x*cosh(d*x + c)^2 - a^2*d*x*sinh(d*x + c)^2)","B",0
64,1,583,0,0.490765," ","integrate(cosh(d*x+c)/x^3/(b*x^2+a),x, algorithm=""fricas"")","-\frac{2 \, a d x \sinh\left(d x + c\right) + 2 \, a \cosh\left(d x + c\right) - {\left({\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a d^{2} - 2 \, b\right)} x^{2} {\rm Ei}\left(d x\right) + {\left(a d^{2} - 2 \, b\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a d^{2} - 2 \, b\right)} x^{2} {\rm Ei}\left(d x\right) - {\left(a d^{2} - 2 \, b\right)} x^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left({\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{4 \, {\left(a^{2} x^{2} \cosh\left(d x + c\right)^{2} - a^{2} x^{2} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/4*(2*a*d*x*sinh(d*x + c) + 2*a*cosh(d*x + c) - ((b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*Ei(d*x - sqrt(-a*d^2/b)) + (b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - ((a*d^2 - 2*b)*x^2*Ei(d*x) + (a*d^2 - 2*b)*x^2*Ei(-d*x))*cosh(c) - ((b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*Ei(d*x + sqrt(-a*d^2/b)) + (b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - ((b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*Ei(d*x - sqrt(-a*d^2/b)) - (b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) - ((a*d^2 - 2*b)*x^2*Ei(d*x) - (a*d^2 - 2*b)*x^2*Ei(-d*x))*sinh(c) + ((b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*Ei(d*x + sqrt(-a*d^2/b)) - (b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/(a^2*x^2*cosh(d*x + c)^2 - a^2*x^2*sinh(d*x + c)^2)","B",0
65,1,1179,0,0.638984," ","integrate(x^4*cosh(d*x+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{4 \, a b d x \cosh\left(d x + c\right) - {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + 8 \, {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right) - {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{8 \, {\left({\left(b^{4} d x^{2} + a b^{3} d\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{4} d x^{2} + a b^{3} d\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/8*(4*a*b*d*x*cosh(d*x + c) - (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - 3*((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + 3*((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + 3*((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - 3*((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + 8*(b^2*x^2 + a*b)*sinh(d*x + c) - (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - 3*((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + 3*((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + 3*((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - 3*((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((b^4*d*x^2 + a*b^3*d)*cosh(d*x + c)^2 - (b^4*d*x^2 + a*b^3*d)*sinh(d*x + c)^2)","B",0
66,1,931,0,0.520925," ","integrate(x^3*cosh(d*x+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{4 \, a \cosh\left(d x + c\right) + {\left({\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{8 \, {\left({\left(b^{3} x^{2} + a b^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{2} + a b^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/8*(4*a*cosh(d*x + c) + ((2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 + ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + (2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 - ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) + ((2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 - ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + (2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 + ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + ((2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 + ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - (2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 - ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) - ((2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 - ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - (2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 + ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((b^3*x^2 + a*b^2)*cosh(d*x + c)^2 - (b^3*x^2 + a*b^2)*sinh(d*x + c)^2)","B",0
67,1,1162,0,0.580066," ","integrate(x^2*cosh(d*x+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{4 \, a b d x \cosh\left(d x + c\right) - {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{8 \, {\left({\left(a b^{3} d x^{2} + a^{2} b^{2} d\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{3} d x^{2} + a^{2} b^{2} d\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/8*(4*a*b*d*x*cosh(d*x + c) - (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a*b^3*d*x^2 + a^2*b^2*d)*cosh(d*x + c)^2 - (a*b^3*d*x^2 + a^2*b^2*d)*sinh(d*x + c)^2)","B",0
68,1,641,0,0.572735," ","integrate(x*cosh(d*x+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{4 \, a \cosh\left(d x + c\right) + {\left({\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{8 \, {\left({\left(a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/8*(4*a*cosh(d*x + c) + (((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x - sqrt(-a*d^2/b)) - ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - (((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x + sqrt(-a*d^2/b)) - ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + (((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x - sqrt(-a*d^2/b)) + ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + (((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(d*x + sqrt(-a*d^2/b)) + ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b)*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)","B",0
69,1,1162,0,0.507596," ","integrate(cosh(d*x+c)/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{4 \, a b d x \cosh\left(d x + c\right) - {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{2} + a^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{2} x^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{2} + a b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{8 \, {\left({\left(a^{2} b^{2} d x^{2} + a^{3} b d\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b^{2} d x^{2} + a^{3} b d\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/8*(4*a*b*d*x*cosh(d*x + c) - (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + (((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 - ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + ((a*b*d^2*x^2 + a^2*d^2)*cosh(d*x + c)^2 - (a*b*d^2*x^2 + a^2*d^2)*sinh(d*x + c)^2 + ((b^2*x^2 + a*b)*cosh(d*x + c)^2 - (b^2*x^2 + a*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a^2*b^2*d*x^2 + a^3*b*d)*cosh(d*x + c)^2 - (a^2*b^2*d*x^2 + a^3*b*d)*sinh(d*x + c)^2)","B",0
70,1,992,0,0.673131," ","integrate(cosh(d*x+c)/x/(b*x^2+a)^2,x, algorithm=""fricas"")","\frac{4 \, a \cosh\left(d x + c\right) - {\left({\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + 4 \, {\left({\left(b x^{2} + a\right)} {\rm Ei}\left(d x\right) + {\left(b x^{2} + a\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + 4 \, {\left({\left(b x^{2} + a\right)} {\rm Ei}\left(d x\right) - {\left(b x^{2} + a\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left({\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(2 \, {\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b x^{2} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{2} + a\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{8 \, {\left({\left(a^{2} b x^{2} + a^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b x^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/8*(4*a*cosh(d*x + c) - ((2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 - ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + (2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 + ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) + 4*((b*x^2 + a)*Ei(d*x) + (b*x^2 + a)*Ei(-d*x))*cosh(c) - ((2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 + ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + (2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 - ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - ((2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 - ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - (2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 + ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + 4*((b*x^2 + a)*Ei(d*x) - (b*x^2 + a)*Ei(-d*x))*sinh(c) + ((2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 + ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - (2*(b*x^2 + a)*cosh(d*x + c)^2 - 2*(b*x^2 + a)*sinh(d*x + c)^2 - ((b*x^2 + a)*cosh(d*x + c)^2 - (b*x^2 + a)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a^2*b*x^2 + a^3)*cosh(d*x + c)^2 - (a^2*b*x^2 + a^3)*sinh(d*x + c)^2)","B",0
71,1,1310,0,0.639818," ","integrate(cosh(d*x+c)/x^2/(b*x^2+a)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(3 \, a b d x^{2} + 2 \, a^{2} d\right)} \cosh\left(d x + c\right) - {\left({\left({\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{2} x^{3} + a b x\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{2} x^{3} + a b x\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - 4 \, {\left({\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} {\rm Ei}\left(d x\right) - {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left({\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{2} x^{3} + a b x\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{2} x^{3} + a b x\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{2} x^{3} + a b x\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{2} x^{3} + a b x\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - 4 \, {\left({\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} {\rm Ei}\left(d x\right) + {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left({\left({\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{2} x^{3} + a b x\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{2} x^{3} + a^{2} d^{2} x\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{2} x^{3} + a b x\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{8 \, {\left({\left(a^{3} b d x^{3} + a^{4} d x\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} b d x^{3} + a^{4} d x\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/8*(4*(3*a*b*d*x^2 + 2*a^2*d)*cosh(d*x + c) - (((a*b*d^2*x^3 + a^2*d^2*x)*cosh(d*x + c)^2 - (a*b*d^2*x^3 + a^2*d^2*x)*sinh(d*x + c)^2 + 3*((b^2*x^3 + a*b*x)*cosh(d*x + c)^2 - (b^2*x^3 + a*b*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - ((a*b*d^2*x^3 + a^2*d^2*x)*cosh(d*x + c)^2 - (a*b*d^2*x^3 + a^2*d^2*x)*sinh(d*x + c)^2 - 3*((b^2*x^3 + a*b*x)*cosh(d*x + c)^2 - (b^2*x^3 + a*b*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - 4*((a*b*d^2*x^3 + a^2*d^2*x)*Ei(d*x) - (a*b*d^2*x^3 + a^2*d^2*x)*Ei(-d*x))*cosh(c) - (((a*b*d^2*x^3 + a^2*d^2*x)*cosh(d*x + c)^2 - (a*b*d^2*x^3 + a^2*d^2*x)*sinh(d*x + c)^2 - 3*((b^2*x^3 + a*b*x)*cosh(d*x + c)^2 - (b^2*x^3 + a*b*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - ((a*b*d^2*x^3 + a^2*d^2*x)*cosh(d*x + c)^2 - (a*b*d^2*x^3 + a^2*d^2*x)*sinh(d*x + c)^2 + 3*((b^2*x^3 + a*b*x)*cosh(d*x + c)^2 - (b^2*x^3 + a*b*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - (((a*b*d^2*x^3 + a^2*d^2*x)*cosh(d*x + c)^2 - (a*b*d^2*x^3 + a^2*d^2*x)*sinh(d*x + c)^2 + 3*((b^2*x^3 + a*b*x)*cosh(d*x + c)^2 - (b^2*x^3 + a*b*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + ((a*b*d^2*x^3 + a^2*d^2*x)*cosh(d*x + c)^2 - (a*b*d^2*x^3 + a^2*d^2*x)*sinh(d*x + c)^2 - 3*((b^2*x^3 + a*b*x)*cosh(d*x + c)^2 - (b^2*x^3 + a*b*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) - 4*((a*b*d^2*x^3 + a^2*d^2*x)*Ei(d*x) + (a*b*d^2*x^3 + a^2*d^2*x)*Ei(-d*x))*sinh(c) + (((a*b*d^2*x^3 + a^2*d^2*x)*cosh(d*x + c)^2 - (a*b*d^2*x^3 + a^2*d^2*x)*sinh(d*x + c)^2 - 3*((b^2*x^3 + a*b*x)*cosh(d*x + c)^2 - (b^2*x^3 + a*b*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + ((a*b*d^2*x^3 + a^2*d^2*x)*cosh(d*x + c)^2 - (a*b*d^2*x^3 + a^2*d^2*x)*sinh(d*x + c)^2 + 3*((b^2*x^3 + a*b*x)*cosh(d*x + c)^2 - (b^2*x^3 + a*b*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a^3*b*d*x^3 + a^4*d*x)*cosh(d*x + c)^2 - (a^3*b*d*x^3 + a^4*d*x)*sinh(d*x + c)^2)","B",0
72,1,1620,0,0.508940," ","integrate(x^3*cosh(d*x+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right) - {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + 4 \, {\left(a b^{2} d x^{3} + a^{2} b d x\right)} \sinh\left(d x + c\right) - {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{32 \, {\left({\left(a b^{5} x^{4} + 2 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{5} x^{4} + 2 \, a^{2} b^{4} x^{2} + a^{3} b^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/32*(8*(2*a*b^2*x^2 + a^2*b)*cosh(d*x + c) - (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - 3*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + 3*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + 3*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - 3*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + 4*(a*b^2*d*x^3 + a^2*b*d*x)*sinh(d*x + c) - (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - 3*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + 3*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + 3*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - 3*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a*b^5*x^4 + 2*a^2*b^4*x^2 + a^3*b^3)*cosh(d*x + c)^2 - (a*b^5*x^4 + 2*a^2*b^4*x^2 + a^3*b^3)*sinh(d*x + c)^2)","B",0
73,1,2047,0,0.476184," ","integrate(x^2*cosh(d*x+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(a b^{2} d x^{3} - a^{2} b d x\right)} \cosh\left(d x + c\right) - {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - 4 \, {\left(a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right) - {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} + b^{3}\right)} x^{4} + a^{2} b + 2 \, {\left(a^{2} b d^{2} + a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{32 \, {\left({\left(a^{2} b^{4} d x^{4} + 2 \, a^{3} b^{3} d x^{2} + a^{4} b^{2} d\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b^{4} d x^{4} + 2 \, a^{3} b^{3} d x^{2} + a^{4} b^{2} d\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/32*(4*(a*b^2*d*x^3 - a^2*b*d*x)*cosh(d*x + c) - (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - 4*(a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c) - (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 + b^3)*x^4 + a^2*b + 2*(a^2*b*d^2 + a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a^2*b^4*d*x^4 + 2*a^3*b^3*d*x^2 + a^4*b^2*d)*cosh(d*x + c)^2 - (a^2*b^4*d*x^4 + 2*a^3*b^3*d*x^2 + a^4*b^2*d)*sinh(d*x + c)^2)","B",0
74,1,1607,0,0.587217," ","integrate(x*cosh(d*x+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{8 \, a^{2} b \cosh\left(d x + c\right) + {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - 4 \, {\left(a b^{2} d x^{3} + a^{2} b d x\right)} \sinh\left(d x + c\right) + {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{32 \, {\left({\left(a^{2} b^{4} x^{4} + 2 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b^{4} x^{4} + 2 \, a^{3} b^{3} x^{2} + a^{4} b^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/32*(8*a^2*b*cosh(d*x + c) + (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) + (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - 4*(a*b^2*d*x^3 + a^2*b*d*x)*sinh(d*x + c) + (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) - (((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - ((a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - (a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a^2*b^4*x^4 + 2*a^3*b^3*x^2 + a^4*b^2)*cosh(d*x + c)^2 - (a^2*b^4*x^4 + 2*a^3*b^3*x^2 + a^4*b^2)*sinh(d*x + c)^2)","B",0
75,1,2116,0,0.664996," ","integrate(cosh(d*x+c)/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, a b^{2} d x^{3} + 5 \, a^{2} b d x\right)} \cosh\left(d x + c\right) - {\left({\left(3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + 4 \, {\left(a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right) - {\left({\left(3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(a b^{2} d^{2} x^{4} + 2 \, a^{2} b d^{2} x^{2} + a^{3} d^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 3 \, b^{3}\right)} x^{4} - 3 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 3 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{32 \, {\left({\left(a^{3} b^{3} d x^{4} + 2 \, a^{4} b^{2} d x^{2} + a^{5} b d\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} b^{3} d x^{4} + 2 \, a^{4} b^{2} d x^{2} + a^{5} b d\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/32*(4*(3*a*b^2*d*x^3 + 5*a^2*b*d*x)*cosh(d*x + c) - ((3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - 3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - (3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - 3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - ((3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - 3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - (3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - 3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + 4*(a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c) - ((3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - 3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + (3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - 3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + ((3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - 3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 + ((a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + (3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*cosh(d*x + c)^2 - 3*(a*b^2*d^2*x^4 + 2*a^2*b*d^2*x^2 + a^3*d^2)*sinh(d*x + c)^2 - ((a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 3*b^3)*x^4 - 3*a^2*b + 2*(a^2*b*d^2 - 3*a*b^2)*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a^3*b^3*d*x^4 + 2*a^4*b^2*d*x^2 + a^5*b*d)*cosh(d*x + c)^2 - (a^3*b^3*d*x^4 + 2*a^4*b^2*d*x^2 + a^5*b*d)*sinh(d*x + c)^2)","B",0
76,1,2076,0,0.552797," ","integrate(cosh(d*x+c)/x/(b*x^2+a)^3,x, algorithm=""fricas"")","\frac{8 \, {\left(2 \, a b^{2} x^{2} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right) + {\left({\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} + 5 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} - 5 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + 16 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} {\rm Ei}\left(d x\right) + {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + {\left({\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} - 5 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} + 5 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) - 4 \, {\left(a b^{2} d x^{3} + a^{2} b d x\right)} \sinh\left(d x + c\right) + {\left({\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} + 5 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} - 5 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) + 16 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} {\rm Ei}\left(d x\right) - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) - {\left({\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} - 5 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} d^{2} + {\left(a b^{2} d^{2} - 8 \, b^{3}\right)} x^{4} - 8 \, a^{2} b + 2 \, {\left(a^{2} b d^{2} - 8 \, a b^{2}\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} + 5 \, {\left({\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{4} + 2 \, a b^{2} x^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{32 \, {\left({\left(a^{3} b^{3} x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{5} b\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} b^{3} x^{4} + 2 \, a^{4} b^{2} x^{2} + a^{5} b\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/32*(8*(2*a*b^2*x^2 + 3*a^2*b)*cosh(d*x + c) + (((a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*sinh(d*x + c)^2 + 5*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + ((a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*sinh(d*x + c)^2 - 5*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) + 16*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*Ei(d*x) + (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*Ei(-d*x))*cosh(c) + (((a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*sinh(d*x + c)^2 - 5*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + ((a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*sinh(d*x + c)^2 + 5*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) - 4*(a*b^2*d*x^3 + a^2*b*d*x)*sinh(d*x + c) + (((a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*sinh(d*x + c)^2 + 5*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - ((a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*sinh(d*x + c)^2 - 5*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) + 16*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*Ei(d*x) - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*Ei(-d*x))*sinh(c) - (((a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*sinh(d*x + c)^2 - 5*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - ((a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*cosh(d*x + c)^2 - (a^3*d^2 + (a*b^2*d^2 - 8*b^3)*x^4 - 8*a^2*b + 2*(a^2*b*d^2 - 8*a*b^2)*x^2)*sinh(d*x + c)^2 + 5*((b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^4 + 2*a*b^2*x^2 + a^2*b)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a^3*b^3*x^4 + 2*a^4*b^2*x^2 + a^5*b)*cosh(d*x + c)^2 - (a^3*b^3*x^4 + 2*a^4*b^2*x^2 + a^5*b)*sinh(d*x + c)^2)","B",0
77,1,2346,0,0.608684," ","integrate(cosh(d*x+c)/x^2/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(15 \, a b^{2} d x^{4} + 25 \, a^{2} b d x^{2} + 8 \, a^{3} d\right)} \cosh\left(d x + c\right) - {\left({\left(7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - 7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sinh\left(d x + c\right)^{2} - {\left({\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - 7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sinh\left(d x + c\right)^{2} + {\left({\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - 16 \, {\left({\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} {\rm Ei}\left(d x\right) - {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - 7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sinh\left(d x + c\right)^{2} + {\left({\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left(7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - 7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sinh\left(d x + c\right)^{2} - {\left({\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + 4 \, {\left(a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sinh\left(d x + c\right) - {\left({\left(7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - 7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sinh\left(d x + c\right)^{2} - {\left({\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - 7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sinh\left(d x + c\right)^{2} + {\left({\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - 16 \, {\left({\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} {\rm Ei}\left(d x\right) + {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) + {\left({\left(7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - 7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sinh\left(d x + c\right)^{2} + {\left({\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left(7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \cosh\left(d x + c\right)^{2} - 7 \, {\left(a b^{2} d^{2} x^{5} + 2 \, a^{2} b d^{2} x^{3} + a^{3} d^{2} x\right)} \sinh\left(d x + c\right)^{2} - {\left({\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 15 \, b^{3}\right)} x^{5} + 2 \, {\left(a^{2} b d^{2} - 15 \, a b^{2}\right)} x^{3} + {\left(a^{3} d^{2} - 15 \, a^{2} b\right)} x\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{32 \, {\left({\left(a^{4} b^{2} d x^{5} + 2 \, a^{5} b d x^{3} + a^{6} d x\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{4} b^{2} d x^{5} + 2 \, a^{5} b d x^{3} + a^{6} d x\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/32*(4*(15*a*b^2*d*x^4 + 25*a^2*b*d*x^2 + 8*a^3*d)*cosh(d*x + c) - ((7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*cosh(d*x + c)^2 - 7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*sinh(d*x + c)^2 - (((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - (7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*cosh(d*x + c)^2 - 7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*sinh(d*x + c)^2 + (((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - 16*((a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*Ei(d*x) - (a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*Ei(-d*x))*cosh(c) - ((7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*cosh(d*x + c)^2 - 7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*sinh(d*x + c)^2 + (((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - (7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*cosh(d*x + c)^2 - 7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*sinh(d*x + c)^2 - (((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + 4*(a^2*b*d^2*x^3 + a^3*d^2*x)*sinh(d*x + c) - ((7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*cosh(d*x + c)^2 - 7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*sinh(d*x + c)^2 - (((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + (7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*cosh(d*x + c)^2 - 7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*sinh(d*x + c)^2 + (((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) - 16*((a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*Ei(d*x) + (a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*Ei(-d*x))*sinh(c) + ((7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*cosh(d*x + c)^2 - 7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*sinh(d*x + c)^2 + (((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + (7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*cosh(d*x + c)^2 - 7*(a*b^2*d^2*x^5 + 2*a^2*b*d^2*x^3 + a^3*d^2*x)*sinh(d*x + c)^2 - (((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 15*b^3)*x^5 + 2*(a^2*b*d^2 - 15*a*b^2)*x^3 + (a^3*d^2 - 15*a^2*b)*x)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a^4*b^2*d*x^5 + 2*a^5*b*d*x^3 + a^6*d*x)*cosh(d*x + c)^2 - (a^4*b^2*d*x^5 + 2*a^5*b*d*x^3 + a^6*d*x)*sinh(d*x + c)^2)","B",0
78,1,2363,0,0.528911," ","integrate(cosh(d*x+c)/x^3/(b*x^2+a)^3,x, algorithm=""fricas"")","-\frac{8 \, {\left(6 \, a b^{2} x^{4} + 9 \, a^{2} b x^{2} + 2 \, a^{3}\right)} \cosh\left(d x + c\right) + {\left({\left({\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} + 9 \, {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} - 9 \, {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - 8 \, {\left({\left({\left(a b^{2} d^{2} - 6 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 6 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 6 \, a^{2} b\right)} x^{2}\right)} {\rm Ei}\left(d x\right) + {\left({\left(a b^{2} d^{2} - 6 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 6 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 6 \, a^{2} b\right)} x^{2}\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + {\left({\left({\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} - 9 \, {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) + {\left({\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} + 9 \, {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \cosh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right) + 4 \, {\left(3 \, a b^{2} d x^{5} + 7 \, a^{2} b d x^{3} + 4 \, a^{3} d x\right)} \sinh\left(d x + c\right) + {\left({\left({\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} + 9 \, {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x - \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} - 9 \, {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x + \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(c + \sqrt{-\frac{a d^{2}}{b}}\right) - 8 \, {\left({\left({\left(a b^{2} d^{2} - 6 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 6 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 6 \, a^{2} b\right)} x^{2}\right)} {\rm Ei}\left(d x\right) - {\left({\left(a b^{2} d^{2} - 6 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 6 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 6 \, a^{2} b\right)} x^{2}\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) - {\left({\left({\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} - 9 \, {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(d x + \sqrt{-\frac{a d^{2}}{b}}\right) - {\left({\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left({\left(a b^{2} d^{2} - 24 \, b^{3}\right)} x^{6} + 2 \, {\left(a^{2} b d^{2} - 24 \, a b^{2}\right)} x^{4} + {\left(a^{3} d^{2} - 24 \, a^{2} b\right)} x^{2}\right)} \sinh\left(d x + c\right)^{2} + 9 \, {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{4} + a^{2} b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a d^{2}}{b}}\right)} {\rm Ei}\left(-d x - \sqrt{-\frac{a d^{2}}{b}}\right)\right)} \sinh\left(-c + \sqrt{-\frac{a d^{2}}{b}}\right)}{32 \, {\left({\left(a^{4} b^{2} x^{6} + 2 \, a^{5} b x^{4} + a^{6} x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{4} b^{2} x^{6} + 2 \, a^{5} b x^{4} + a^{6} x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/32*(8*(6*a*b^2*x^4 + 9*a^2*b*x^2 + 2*a^3)*cosh(d*x + c) + ((((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*sinh(d*x + c)^2 + 9*((b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) + (((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*sinh(d*x + c)^2 - 9*((b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*cosh(c + sqrt(-a*d^2/b)) - 8*(((a*b^2*d^2 - 6*b^3)*x^6 + 2*(a^2*b*d^2 - 6*a*b^2)*x^4 + (a^3*d^2 - 6*a^2*b)*x^2)*Ei(d*x) + ((a*b^2*d^2 - 6*b^3)*x^6 + 2*(a^2*b*d^2 - 6*a*b^2)*x^4 + (a^3*d^2 - 6*a^2*b)*x^2)*Ei(-d*x))*cosh(c) + ((((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*sinh(d*x + c)^2 - 9*((b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) + (((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*sinh(d*x + c)^2 + 9*((b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*cosh(-c + sqrt(-a*d^2/b)) + 4*(3*a*b^2*d*x^5 + 7*a^2*b*d*x^3 + 4*a^3*d*x)*sinh(d*x + c) + ((((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*sinh(d*x + c)^2 + 9*((b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x - sqrt(-a*d^2/b)) - (((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*sinh(d*x + c)^2 - 9*((b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x + sqrt(-a*d^2/b)))*sinh(c + sqrt(-a*d^2/b)) - 8*(((a*b^2*d^2 - 6*b^3)*x^6 + 2*(a^2*b*d^2 - 6*a*b^2)*x^4 + (a^3*d^2 - 6*a^2*b)*x^2)*Ei(d*x) - ((a*b^2*d^2 - 6*b^3)*x^6 + 2*(a^2*b*d^2 - 6*a*b^2)*x^4 + (a^3*d^2 - 6*a^2*b)*x^2)*Ei(-d*x))*sinh(c) - ((((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*sinh(d*x + c)^2 - 9*((b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(d*x + sqrt(-a*d^2/b)) - (((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*cosh(d*x + c)^2 - ((a*b^2*d^2 - 24*b^3)*x^6 + 2*(a^2*b*d^2 - 24*a*b^2)*x^4 + (a^3*d^2 - 24*a^2*b)*x^2)*sinh(d*x + c)^2 + 9*((b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^4 + a^2*b*x^2)*sinh(d*x + c)^2)*sqrt(-a*d^2/b))*Ei(-d*x - sqrt(-a*d^2/b)))*sinh(-c + sqrt(-a*d^2/b)))/((a^4*b^2*x^6 + 2*a^5*b*x^4 + a^6*x^2)*cosh(d*x + c)^2 - (a^4*b^2*x^6 + 2*a^5*b*x^4 + a^6*x^2)*sinh(d*x + c)^2)","B",0
79,1,105,0,0.465730," ","integrate(x^3*(b*x^3+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{3 \, {\left(2 \, b d^{5} x^{5} + a d^{5} x^{2} + 40 \, b d^{3} x^{3} + 2 \, a d^{3} + 240 \, b d x\right)} \cosh\left(d x + c\right) - {\left(b d^{6} x^{6} + a d^{6} x^{3} + 30 \, b d^{4} x^{4} + 6 \, a d^{4} x + 360 \, b d^{2} x^{2} + 720 \, b\right)} \sinh\left(d x + c\right)}{d^{7}}"," ",0,"-(3*(2*b*d^5*x^5 + a*d^5*x^2 + 40*b*d^3*x^3 + 2*a*d^3 + 240*b*d*x)*cosh(d*x + c) - (b*d^6*x^6 + a*d^6*x^3 + 30*b*d^4*x^4 + 6*a*d^4*x + 360*b*d^2*x^2 + 720*b)*sinh(d*x + c))/d^7","A",0
80,1,87,0,0.513501," ","integrate(x^2*(b*x^3+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(5 \, b d^{4} x^{4} + 2 \, a d^{4} x + 60 \, b d^{2} x^{2} + 120 \, b\right)} \cosh\left(d x + c\right) - {\left(b d^{5} x^{5} + a d^{5} x^{2} + 20 \, b d^{3} x^{3} + 2 \, a d^{3} + 120 \, b d x\right)} \sinh\left(d x + c\right)}{d^{6}}"," ",0,"-((5*b*d^4*x^4 + 2*a*d^4*x + 60*b*d^2*x^2 + 120*b)*cosh(d*x + c) - (b*d^5*x^5 + a*d^5*x^2 + 20*b*d^3*x^3 + 2*a*d^3 + 120*b*d*x)*sinh(d*x + c))/d^6","A",0
81,1,68,0,0.595374," ","integrate(x*(b*x^3+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(4 \, b d^{3} x^{3} + a d^{3} + 24 \, b d x\right)} \cosh\left(d x + c\right) - {\left(b d^{4} x^{4} + a d^{4} x + 12 \, b d^{2} x^{2} + 24 \, b\right)} \sinh\left(d x + c\right)}{d^{5}}"," ",0,"-((4*b*d^3*x^3 + a*d^3 + 24*b*d*x)*cosh(d*x + c) - (b*d^4*x^4 + a*d^4*x + 12*b*d^2*x^2 + 24*b)*sinh(d*x + c))/d^5","A",0
82,1,53,0,0.572410," ","integrate((b*x^3+a)*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{3 \, {\left(b d^{2} x^{2} + 2 \, b\right)} \cosh\left(d x + c\right) - {\left(b d^{3} x^{3} + a d^{3} + 6 \, b d x\right)} \sinh\left(d x + c\right)}{d^{4}}"," ",0,"-(3*(b*d^2*x^2 + 2*b)*cosh(d*x + c) - (b*d^3*x^3 + a*d^3 + 6*b*d*x)*sinh(d*x + c))/d^4","A",0
83,1,86,0,0.549467," ","integrate((b*x^3+a)*cosh(d*x+c)/x,x, algorithm=""fricas"")","-\frac{4 \, b d x \cosh\left(d x + c\right) - {\left(a d^{3} {\rm Ei}\left(d x\right) + a d^{3} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 2 \, {\left(b d^{2} x^{2} + 2 \, b\right)} \sinh\left(d x + c\right) - {\left(a d^{3} {\rm Ei}\left(d x\right) - a d^{3} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d^{3}}"," ",0,"-1/2*(4*b*d*x*cosh(d*x + c) - (a*d^3*Ei(d*x) + a*d^3*Ei(-d*x))*cosh(c) - 2*(b*d^2*x^2 + 2*b)*sinh(d*x + c) - (a*d^3*Ei(d*x) - a*d^3*Ei(-d*x))*sinh(c))/d^3","A",0
84,1,90,0,0.590902," ","integrate((b*x^3+a)*cosh(d*x+c)/x^2,x, algorithm=""fricas"")","\frac{2 \, b d x^{2} \sinh\left(d x + c\right) - 2 \, {\left(a d^{2} + b x\right)} \cosh\left(d x + c\right) + {\left(a d^{3} x {\rm Ei}\left(d x\right) - a d^{3} x {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + {\left(a d^{3} x {\rm Ei}\left(d x\right) + a d^{3} x {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d^{2} x}"," ",0,"1/2*(2*b*d*x^2*sinh(d*x + c) - 2*(a*d^2 + b*x)*cosh(d*x + c) + (a*d^3*x*Ei(d*x) - a*d^3*x*Ei(-d*x))*cosh(c) + (a*d^3*x*Ei(d*x) + a*d^3*x*Ei(-d*x))*sinh(c))/(d^2*x)","A",0
85,1,101,0,0.445335," ","integrate((b*x^3+a)*cosh(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, a d \cosh\left(d x + c\right) - {\left(a d^{3} x^{2} {\rm Ei}\left(d x\right) + a d^{3} x^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left(a d^{2} x - 2 \, b x^{2}\right)} \sinh\left(d x + c\right) - {\left(a d^{3} x^{2} {\rm Ei}\left(d x\right) - a d^{3} x^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{4 \, d x^{2}}"," ",0,"-1/4*(2*a*d*cosh(d*x + c) - (a*d^3*x^2*Ei(d*x) + a*d^3*x^2*Ei(-d*x))*cosh(c) + 2*(a*d^2*x - 2*b*x^2)*sinh(d*x + c) - (a*d^3*x^2*Ei(d*x) - a*d^3*x^2*Ei(-d*x))*sinh(c))/(d*x^2)","A",0
86,1,118,0,0.482630," ","integrate((b*x^3+a)*cosh(d*x+c)/x^4,x, algorithm=""fricas"")","-\frac{2 \, a d x \sinh\left(d x + c\right) + 2 \, {\left(a d^{2} x^{2} + 2 \, a\right)} \cosh\left(d x + c\right) - {\left({\left(a d^{3} + 6 \, b\right)} x^{3} {\rm Ei}\left(d x\right) - {\left(a d^{3} - 6 \, b\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - {\left({\left(a d^{3} + 6 \, b\right)} x^{3} {\rm Ei}\left(d x\right) + {\left(a d^{3} - 6 \, b\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{12 \, x^{3}}"," ",0,"-1/12*(2*a*d*x*sinh(d*x + c) + 2*(a*d^2*x^2 + 2*a)*cosh(d*x + c) - ((a*d^3 + 6*b)*x^3*Ei(d*x) - (a*d^3 - 6*b)*x^3*Ei(-d*x))*cosh(c) - ((a*d^3 + 6*b)*x^3*Ei(d*x) + (a*d^3 - 6*b)*x^3*Ei(-d*x))*sinh(c))/x^3","A",0
87,1,161,0,0.470056," ","integrate(x*(b*x^3+a)^2*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{{\left(7 \, b^{2} d^{6} x^{6} + 8 \, a b d^{6} x^{3} + 210 \, b^{2} d^{4} x^{4} + a^{2} d^{6} + 48 \, a b d^{4} x + 2520 \, b^{2} d^{2} x^{2} + 5040 \, b^{2}\right)} \cosh\left(d x + c\right) - {\left(b^{2} d^{7} x^{7} + 2 \, a b d^{7} x^{4} + 42 \, b^{2} d^{5} x^{5} + 24 \, a b d^{5} x^{2} + 840 \, b^{2} d^{3} x^{3} + 48 \, a b d^{3} + {\left(a^{2} d^{7} + 5040 \, b^{2} d\right)} x\right)} \sinh\left(d x + c\right)}{d^{8}}"," ",0,"-((7*b^2*d^6*x^6 + 8*a*b*d^6*x^3 + 210*b^2*d^4*x^4 + a^2*d^6 + 48*a*b*d^4*x + 2520*b^2*d^2*x^2 + 5040*b^2)*cosh(d*x + c) - (b^2*d^7*x^7 + 2*a*b*d^7*x^4 + 42*b^2*d^5*x^5 + 24*a*b*d^5*x^2 + 840*b^2*d^3*x^3 + 48*a*b*d^3 + (a^2*d^7 + 5040*b^2*d)*x)*sinh(d*x + c))/d^8","A",0
88,1,130,0,0.653769," ","integrate((b*x^3+a)^2*cosh(d*x+c),x, algorithm=""fricas"")","-\frac{6 \, {\left(b^{2} d^{5} x^{5} + a b d^{5} x^{2} + 20 \, b^{2} d^{3} x^{3} + 2 \, a b d^{3} + 120 \, b^{2} d x\right)} \cosh\left(d x + c\right) - {\left(b^{2} d^{6} x^{6} + 2 \, a b d^{6} x^{3} + 30 \, b^{2} d^{4} x^{4} + a^{2} d^{6} + 12 \, a b d^{4} x + 360 \, b^{2} d^{2} x^{2} + 720 \, b^{2}\right)} \sinh\left(d x + c\right)}{d^{7}}"," ",0,"-(6*(b^2*d^5*x^5 + a*b*d^5*x^2 + 20*b^2*d^3*x^3 + 2*a*b*d^3 + 120*b^2*d*x)*cosh(d*x + c) - (b^2*d^6*x^6 + 2*a*b*d^6*x^3 + 30*b^2*d^4*x^4 + a^2*d^6 + 12*a*b*d^4*x + 360*b^2*d^2*x^2 + 720*b^2)*sinh(d*x + c))/d^7","A",0
89,1,161,0,0.575870," ","integrate((b*x^3+a)^2*cosh(d*x+c)/x,x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, b^{2} d^{4} x^{4} + 4 \, a b d^{4} x + 60 \, b^{2} d^{2} x^{2} + 120 \, b^{2}\right)} \cosh\left(d x + c\right) - {\left(a^{2} d^{6} {\rm Ei}\left(d x\right) + a^{2} d^{6} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 2 \, {\left(b^{2} d^{5} x^{5} + 2 \, a b d^{5} x^{2} + 20 \, b^{2} d^{3} x^{3} + 4 \, a b d^{3} + 120 \, b^{2} d x\right)} \sinh\left(d x + c\right) - {\left(a^{2} d^{6} {\rm Ei}\left(d x\right) - a^{2} d^{6} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d^{6}}"," ",0,"-1/2*(2*(5*b^2*d^4*x^4 + 4*a*b*d^4*x + 60*b^2*d^2*x^2 + 120*b^2)*cosh(d*x + c) - (a^2*d^6*Ei(d*x) + a^2*d^6*Ei(-d*x))*cosh(c) - 2*(b^2*d^5*x^5 + 2*a*b*d^5*x^2 + 20*b^2*d^3*x^3 + 4*a*b*d^3 + 120*b^2*d*x)*sinh(d*x + c) - (a^2*d^6*Ei(d*x) - a^2*d^6*Ei(-d*x))*sinh(c))/d^6","A",0
90,1,160,0,0.552996," ","integrate((b*x^3+a)^2*cosh(d*x+c)/x^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, b^{2} d^{3} x^{4} + a^{2} d^{5} + 2 \, a b d^{3} x + 24 \, b^{2} d x^{2}\right)} \cosh\left(d x + c\right) - {\left(a^{2} d^{6} x {\rm Ei}\left(d x\right) - a^{2} d^{6} x {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 2 \, {\left(b^{2} d^{4} x^{5} + 2 \, a b d^{4} x^{2} + 12 \, b^{2} d^{2} x^{3} + 24 \, b^{2} x\right)} \sinh\left(d x + c\right) - {\left(a^{2} d^{6} x {\rm Ei}\left(d x\right) + a^{2} d^{6} x {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{2 \, d^{5} x}"," ",0,"-1/2*(2*(4*b^2*d^3*x^4 + a^2*d^5 + 2*a*b*d^3*x + 24*b^2*d*x^2)*cosh(d*x + c) - (a^2*d^6*x*Ei(d*x) - a^2*d^6*x*Ei(-d*x))*cosh(c) - 2*(b^2*d^4*x^5 + 2*a*b*d^4*x^2 + 12*b^2*d^2*x^3 + 24*b^2*x)*sinh(d*x + c) - (a^2*d^6*x*Ei(d*x) + a^2*d^6*x*Ei(-d*x))*sinh(c))/(d^5*x)","A",0
91,1,161,0,0.440091," ","integrate((b*x^3+a)^2*cosh(d*x+c)/x^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(6 \, b^{2} d^{2} x^{4} + a^{2} d^{4} + 12 \, b^{2} x^{2}\right)} \cosh\left(d x + c\right) - {\left(a^{2} d^{6} x^{2} {\rm Ei}\left(d x\right) + a^{2} d^{6} x^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 2 \, {\left(2 \, b^{2} d^{3} x^{5} - a^{2} d^{5} x + 4 \, a b d^{3} x^{2} + 12 \, b^{2} d x^{3}\right)} \sinh\left(d x + c\right) - {\left(a^{2} d^{6} x^{2} {\rm Ei}\left(d x\right) - a^{2} d^{6} x^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{4 \, d^{4} x^{2}}"," ",0,"-1/4*(2*(6*b^2*d^2*x^4 + a^2*d^4 + 12*b^2*x^2)*cosh(d*x + c) - (a^2*d^6*x^2*Ei(d*x) + a^2*d^6*x^2*Ei(-d*x))*cosh(c) - 2*(2*b^2*d^3*x^5 - a^2*d^5*x + 4*a*b*d^3*x^2 + 12*b^2*d*x^3)*sinh(d*x + c) - (a^2*d^6*x^2*Ei(d*x) - a^2*d^6*x^2*Ei(-d*x))*sinh(c))/(d^4*x^2)","A",0
92,1,187,0,0.453128," ","integrate((b*x^3+a)^2*cosh(d*x+c)/x^4,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} d^{5} x^{2} + 12 \, b^{2} d x^{4} + 2 \, a^{2} d^{3}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} d^{6} + 12 \, a b d^{3}\right)} x^{3} {\rm Ei}\left(d x\right) - {\left(a^{2} d^{6} - 12 \, a b d^{3}\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 2 \, {\left(6 \, b^{2} d^{2} x^{5} - a^{2} d^{4} x + 12 \, b^{2} x^{3}\right)} \sinh\left(d x + c\right) - {\left({\left(a^{2} d^{6} + 12 \, a b d^{3}\right)} x^{3} {\rm Ei}\left(d x\right) + {\left(a^{2} d^{6} - 12 \, a b d^{3}\right)} x^{3} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{12 \, d^{3} x^{3}}"," ",0,"-1/12*(2*(a^2*d^5*x^2 + 12*b^2*d*x^4 + 2*a^2*d^3)*cosh(d*x + c) - ((a^2*d^6 + 12*a*b*d^3)*x^3*Ei(d*x) - (a^2*d^6 - 12*a*b*d^3)*x^3*Ei(-d*x))*cosh(c) - 2*(6*b^2*d^2*x^5 - a^2*d^4*x + 12*b^2*x^3)*sinh(d*x + c) - ((a^2*d^6 + 12*a*b*d^3)*x^3*Ei(d*x) + (a^2*d^6 - 12*a*b*d^3)*x^3*Ei(-d*x))*sinh(c))/(d^3*x^3)","A",0
93,1,196,0,0.403458," ","integrate((b*x^3+a)^2*cosh(d*x+c)/x^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} d^{4} x^{2} + 48 \, a b d^{2} x^{3} + 24 \, b^{2} x^{4} + 6 \, a^{2} d^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} d^{6} + 48 \, a b d^{3}\right)} x^{4} {\rm Ei}\left(d x\right) + {\left(a^{2} d^{6} - 48 \, a b d^{3}\right)} x^{4} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + 2 \, {\left(a^{2} d^{5} x^{3} - 24 \, b^{2} d x^{5} + 2 \, a^{2} d^{3} x\right)} \sinh\left(d x + c\right) - {\left({\left(a^{2} d^{6} + 48 \, a b d^{3}\right)} x^{4} {\rm Ei}\left(d x\right) - {\left(a^{2} d^{6} - 48 \, a b d^{3}\right)} x^{4} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{48 \, d^{2} x^{4}}"," ",0,"-1/48*(2*(a^2*d^4*x^2 + 48*a*b*d^2*x^3 + 24*b^2*x^4 + 6*a^2*d^2)*cosh(d*x + c) - ((a^2*d^6 + 48*a*b*d^3)*x^4*Ei(d*x) + (a^2*d^6 - 48*a*b*d^3)*x^4*Ei(-d*x))*cosh(c) + 2*(a^2*d^5*x^3 - 24*b^2*d*x^5 + 2*a^2*d^3*x)*sinh(d*x + c) - ((a^2*d^6 + 48*a*b*d^3)*x^4*Ei(d*x) - (a^2*d^6 - 48*a*b*d^3)*x^4*Ei(-d*x))*sinh(c))/(d^2*x^4)","A",0
94,1,989,0,0.534209," ","integrate(x^4*cosh(d*x+c)/(b*x^3+a),x, algorithm=""fricas"")","\frac{\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} - 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} - 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} - 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} - 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} + 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} + 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} + 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} + 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} - 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} - 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} - 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} - 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} + 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} + 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} + 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} + 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 12 \, d x \sinh\left(d x + c\right) - 12 \, \cosh\left(d x + c\right)}{12 \, {\left(b d^{2} \cosh\left(d x + c\right)^{2} - b d^{2} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/12*((a*d^3/b)^(2/3)*((sqrt(-3) - 1)*cosh(d*x + c)^2 - (sqrt(-3) - 1)*sinh(d*x + c)^2)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (-a*d^3/b)^(2/3)*((sqrt(-3) - 1)*cosh(d*x + c)^2 - (sqrt(-3) - 1)*sinh(d*x + c)^2)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (a*d^3/b)^(2/3)*((sqrt(-3) + 1)*cosh(d*x + c)^2 - (sqrt(-3) + 1)*sinh(d*x + c)^2)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (-a*d^3/b)^(2/3)*((sqrt(-3) + 1)*cosh(d*x + c)^2 - (sqrt(-3) + 1)*sinh(d*x + c)^2)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*(-a*d^3/b)^(2/3)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) + 2*(a*d^3/b)^(2/3)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + (a*d^3/b)^(2/3)*((sqrt(-3) - 1)*cosh(d*x + c)^2 - (sqrt(-3) - 1)*sinh(d*x + c)^2)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (-a*d^3/b)^(2/3)*((sqrt(-3) - 1)*cosh(d*x + c)^2 - (sqrt(-3) - 1)*sinh(d*x + c)^2)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (a*d^3/b)^(2/3)*((sqrt(-3) + 1)*cosh(d*x + c)^2 - (sqrt(-3) + 1)*sinh(d*x + c)^2)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (-a*d^3/b)^(2/3)*((sqrt(-3) + 1)*cosh(d*x + c)^2 - (sqrt(-3) + 1)*sinh(d*x + c)^2)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*(-a*d^3/b)^(2/3)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - 2*(a*d^3/b)^(2/3)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) + 12*d*x*sinh(d*x + c) - 12*cosh(d*x + c))/(b*d^2*cosh(d*x + c)^2 - b*d^2*sinh(d*x + c)^2)","B",0
95,1,977,0,0.585246," ","integrate(x^3*cosh(d*x+c)/(b*x^3+a),x, algorithm=""fricas"")","\frac{\left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} + 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} + 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} + 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} + 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} - 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} - 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} - 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} - 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} + 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} + 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} + 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} + 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} - 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} - 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} - 1\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} - 1\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\cosh\left(d x + c\right)^{2} - \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 12 \, \sinh\left(d x + c\right)}{12 \, {\left(b d \cosh\left(d x + c\right)^{2} - b d \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/12*((a*d^3/b)^(1/3)*((sqrt(-3) + 1)*cosh(d*x + c)^2 - (sqrt(-3) + 1)*sinh(d*x + c)^2)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) - (-a*d^3/b)^(1/3)*((sqrt(-3) + 1)*cosh(d*x + c)^2 - (sqrt(-3) + 1)*sinh(d*x + c)^2)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (a*d^3/b)^(1/3)*((sqrt(-3) - 1)*cosh(d*x + c)^2 - (sqrt(-3) - 1)*sinh(d*x + c)^2)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (-a*d^3/b)^(1/3)*((sqrt(-3) - 1)*cosh(d*x + c)^2 - (sqrt(-3) - 1)*sinh(d*x + c)^2)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*(-a*d^3/b)^(1/3)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) - 2*(a*d^3/b)^(1/3)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + (a*d^3/b)^(1/3)*((sqrt(-3) + 1)*cosh(d*x + c)^2 - (sqrt(-3) + 1)*sinh(d*x + c)^2)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) - (-a*d^3/b)^(1/3)*((sqrt(-3) + 1)*cosh(d*x + c)^2 - (sqrt(-3) + 1)*sinh(d*x + c)^2)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (a*d^3/b)^(1/3)*((sqrt(-3) - 1)*cosh(d*x + c)^2 - (sqrt(-3) - 1)*sinh(d*x + c)^2)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (-a*d^3/b)^(1/3)*((sqrt(-3) - 1)*cosh(d*x + c)^2 - (sqrt(-3) - 1)*sinh(d*x + c)^2)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*(-a*d^3/b)^(1/3)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) + 2*(a*d^3/b)^(1/3)*(cosh(d*x + c)^2 - sinh(d*x + c)^2)*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) + 12*sinh(d*x + c))/(b*d*cosh(d*x + c)^2 - b*d*sinh(d*x + c)^2)","B",0
96,1,500,0,0.449932," ","integrate(x^2*cosh(d*x+c)/(b*x^3+a),x, algorithm=""fricas"")","\frac{{\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right)}{6 \, b}"," ",0,"1/6*(Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) + Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)))/b","B",0
97,1,671,0,0.572519," ","integrate(x*cosh(d*x+c)/(b*x^3+a),x, algorithm=""fricas"")","-\frac{\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{-3} - 1\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{-3} - 1\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{-3} + 1\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{-3} + 1\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{-3} - 1\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{-3} - 1\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{-3} + 1\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left(\sqrt{-3} + 1\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right)}{12 \, a d^{2}}"," ",0,"-1/12*((a*d^3/b)^(2/3)*(sqrt(-3) - 1)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (-a*d^3/b)^(2/3)*(sqrt(-3) - 1)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (a*d^3/b)^(2/3)*(sqrt(-3) + 1)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (-a*d^3/b)^(2/3)*(sqrt(-3) + 1)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + (a*d^3/b)^(2/3)*(sqrt(-3) - 1)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (-a*d^3/b)^(2/3)*(sqrt(-3) - 1)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (a*d^3/b)^(2/3)*(sqrt(-3) + 1)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (-a*d^3/b)^(2/3)*(sqrt(-3) + 1)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*(-a*d^3/b)^(2/3)*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) + 2*(a*d^3/b)^(2/3)*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) - 2*(-a*d^3/b)^(2/3)*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - 2*(a*d^3/b)^(2/3)*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)))/(a*d^2)","B",0
98,1,673,0,0.652372," ","integrate(cosh(d*x+c)/(b*x^3+a),x, algorithm=""fricas"")","-\frac{\left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right)}{12 \, a d}"," ",0,"-1/12*((a*d^3/b)^(1/3)*(sqrt(-3) + 1)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) - (-a*d^3/b)^(1/3)*(sqrt(-3) + 1)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (a*d^3/b)^(1/3)*(sqrt(-3) - 1)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (-a*d^3/b)^(1/3)*(sqrt(-3) - 1)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + (a*d^3/b)^(1/3)*(sqrt(-3) + 1)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) - (-a*d^3/b)^(1/3)*(sqrt(-3) + 1)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (a*d^3/b)^(1/3)*(sqrt(-3) - 1)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (-a*d^3/b)^(1/3)*(sqrt(-3) - 1)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*(-a*d^3/b)^(1/3)*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) - 2*(a*d^3/b)^(1/3)*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) - 2*(-a*d^3/b)^(1/3)*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) + 2*(a*d^3/b)^(1/3)*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)))/(a*d)","B",0
99,1,530,0,0.524429," ","integrate(cosh(d*x+c)/x/(b*x^3+a),x, algorithm=""fricas"")","-\frac{{\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 3 \, {\left({\rm Ei}\left(d x\right) + {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) + {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 3 \, {\left({\rm Ei}\left(d x\right) - {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right) - {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right)}{6 \, a}"," ",0,"-1/6*(Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) - 3*(Ei(d*x) + Ei(-d*x))*cosh(c) + Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - 3*(Ei(d*x) - Ei(-d*x))*sinh(c) - Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)))/a","B",0
100,1,1154,0,0.690378," ","integrate(cosh(d*x+c)/x^2/(b*x^3+a),x, algorithm=""fricas"")","-\frac{12 \, a d^{2} \cosh\left(d x + c\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} b x - b x\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x - b x\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} b x - b x\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x - b x\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} b x + b x\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x + b x\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} b x + b x\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x + b x\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, {\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, {\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} b x - b x\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x - b x\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} b x - b x\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x - b x\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} b x + b x\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x + b x\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(\sqrt{-3} b x + b x\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x + b x\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, {\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, {\left(b x \cosh\left(d x + c\right)^{2} - b x \sinh\left(d x + c\right)^{2}\right)} \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 6 \, {\left(a d^{3} x {\rm Ei}\left(d x\right) - a d^{3} x {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 6 \, {\left(a d^{3} x {\rm Ei}\left(d x\right) + a d^{3} x {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{12 \, {\left(a^{2} d^{2} x \cosh\left(d x + c\right)^{2} - a^{2} d^{2} x \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/12*(12*a*d^2*cosh(d*x + c) - (a*d^3/b)^(2/3)*((sqrt(-3)*b*x - b*x)*cosh(d*x + c)^2 - (sqrt(-3)*b*x - b*x)*sinh(d*x + c)^2)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) - (-a*d^3/b)^(2/3)*((sqrt(-3)*b*x - b*x)*cosh(d*x + c)^2 - (sqrt(-3)*b*x - b*x)*sinh(d*x + c)^2)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (a*d^3/b)^(2/3)*((sqrt(-3)*b*x + b*x)*cosh(d*x + c)^2 - (sqrt(-3)*b*x + b*x)*sinh(d*x + c)^2)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (-a*d^3/b)^(2/3)*((sqrt(-3)*b*x + b*x)*cosh(d*x + c)^2 - (sqrt(-3)*b*x + b*x)*sinh(d*x + c)^2)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*(b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*(-a*d^3/b)^(2/3)*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) - 2*(b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*(a*d^3/b)^(2/3)*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) - (a*d^3/b)^(2/3)*((sqrt(-3)*b*x - b*x)*cosh(d*x + c)^2 - (sqrt(-3)*b*x - b*x)*sinh(d*x + c)^2)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) - (-a*d^3/b)^(2/3)*((sqrt(-3)*b*x - b*x)*cosh(d*x + c)^2 - (sqrt(-3)*b*x - b*x)*sinh(d*x + c)^2)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (a*d^3/b)^(2/3)*((sqrt(-3)*b*x + b*x)*cosh(d*x + c)^2 - (sqrt(-3)*b*x + b*x)*sinh(d*x + c)^2)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (-a*d^3/b)^(2/3)*((sqrt(-3)*b*x + b*x)*cosh(d*x + c)^2 - (sqrt(-3)*b*x + b*x)*sinh(d*x + c)^2)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*(b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*(-a*d^3/b)^(2/3)*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) + 2*(b*x*cosh(d*x + c)^2 - b*x*sinh(d*x + c)^2)*(a*d^3/b)^(2/3)*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) - 6*(a*d^3*x*Ei(d*x) - a*d^3*x*Ei(-d*x))*cosh(c) - 6*(a*d^3*x*Ei(d*x) + a*d^3*x*Ei(-d*x))*sinh(c))/(a^2*d^2*x*cosh(d*x + c)^2 - a^2*d^2*x*sinh(d*x + c)^2)","B",0
101,1,1251,0,0.565830," ","integrate(cosh(d*x+c)/x^3/(b*x^3+a),x, algorithm=""fricas"")","-\frac{6 \, a d^{2} x \sinh\left(d x + c\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} b x^{2} + b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x^{2} + b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} b x^{2} + b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x^{2} + b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} b x^{2} - b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x^{2} - b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} b x^{2} - b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x^{2} - b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, {\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, {\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} b x^{2} + b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x^{2} + b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} b x^{2} + b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x^{2} + b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} b x^{2} - b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x^{2} - b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(\sqrt{-3} b x^{2} - b x^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(\sqrt{-3} b x^{2} - b x^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, {\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, {\left(b x^{2} \cosh\left(d x + c\right)^{2} - b x^{2} \sinh\left(d x + c\right)^{2}\right)} \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 6 \, a d \cosh\left(d x + c\right) - 3 \, {\left(a d^{3} x^{2} {\rm Ei}\left(d x\right) + a d^{3} x^{2} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 3 \, {\left(a d^{3} x^{2} {\rm Ei}\left(d x\right) - a d^{3} x^{2} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{12 \, {\left(a^{2} d x^{2} \cosh\left(d x + c\right)^{2} - a^{2} d x^{2} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/12*(6*a*d^2*x*sinh(d*x + c) - (a*d^3/b)^(1/3)*((sqrt(-3)*b*x^2 + b*x^2)*cosh(d*x + c)^2 - (sqrt(-3)*b*x^2 + b*x^2)*sinh(d*x + c)^2)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (-a*d^3/b)^(1/3)*((sqrt(-3)*b*x^2 + b*x^2)*cosh(d*x + c)^2 - (sqrt(-3)*b*x^2 + b*x^2)*sinh(d*x + c)^2)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (a*d^3/b)^(1/3)*((sqrt(-3)*b*x^2 - b*x^2)*cosh(d*x + c)^2 - (sqrt(-3)*b*x^2 - b*x^2)*sinh(d*x + c)^2)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (-a*d^3/b)^(1/3)*((sqrt(-3)*b*x^2 - b*x^2)*cosh(d*x + c)^2 - (sqrt(-3)*b*x^2 - b*x^2)*sinh(d*x + c)^2)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*(b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*(-a*d^3/b)^(1/3)*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) + 2*(b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*(a*d^3/b)^(1/3)*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) - (a*d^3/b)^(1/3)*((sqrt(-3)*b*x^2 + b*x^2)*cosh(d*x + c)^2 - (sqrt(-3)*b*x^2 + b*x^2)*sinh(d*x + c)^2)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (-a*d^3/b)^(1/3)*((sqrt(-3)*b*x^2 + b*x^2)*cosh(d*x + c)^2 - (sqrt(-3)*b*x^2 + b*x^2)*sinh(d*x + c)^2)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (a*d^3/b)^(1/3)*((sqrt(-3)*b*x^2 - b*x^2)*cosh(d*x + c)^2 - (sqrt(-3)*b*x^2 - b*x^2)*sinh(d*x + c)^2)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (-a*d^3/b)^(1/3)*((sqrt(-3)*b*x^2 - b*x^2)*cosh(d*x + c)^2 - (sqrt(-3)*b*x^2 - b*x^2)*sinh(d*x + c)^2)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*(b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*(-a*d^3/b)^(1/3)*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - 2*(b*x^2*cosh(d*x + c)^2 - b*x^2*sinh(d*x + c)^2)*(a*d^3/b)^(1/3)*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) + 6*a*d*cosh(d*x + c) - 3*(a*d^3*x^2*Ei(d*x) + a*d^3*x^2*Ei(-d*x))*cosh(c) - 3*(a*d^3*x^2*Ei(d*x) - a*d^3*x^2*Ei(-d*x))*sinh(c))/(a^2*d*x^2*cosh(d*x + c)^2 - a^2*d*x^2*sinh(d*x + c)^2)","B",0
102,1,2050,0,0.604669," ","integrate(x^3*cosh(d*x+c)/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{12 \, a d x \cosh\left(d x + c\right) - {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right)}{36 \, {\left({\left(a b^{2} d x^{3} + a^{2} b d\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d x^{3} + a^{2} b d\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/36*(12*a*d*x*cosh(d*x + c) - ((a*d^3/b)^(2/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + ((-a*d^3/b)^(2/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - ((a*d^3/b)^(2/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + ((-a*d^3/b)^(2/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*((-a*d^3/b)^(2/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) + 2*((a*d^3/b)^(2/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) - ((a*d^3/b)^(2/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + ((-a*d^3/b)^(2/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + ((a*d^3/b)^(2/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - ((-a*d^3/b)^(2/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*((-a*d^3/b)^(2/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - 2*((a*d^3/b)^(2/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)))/((a*b^2*d*x^3 + a^2*b*d)*cosh(d*x + c)^2 - (a*b^2*d*x^3 + a^2*b*d)*sinh(d*x + c)^2)","B",0
103,1,1276,0,0.469344," ","integrate(x^2*cosh(d*x+c)/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{\left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 12 \, a \cosh\left(d x + c\right)}{36 \, {\left({\left(a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/36*((a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (-a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (-a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*(-a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2)*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) - 2*(a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2)*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + (a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2)*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (-a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2)*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2)*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (-a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2)*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*(-a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2)*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) + 2*(a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2)*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) + 12*a*cosh(d*x + c))/((a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2)","B",0
104,1,2135,0,0.943798," ","integrate(x*cosh(d*x+c)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{12 \, a b d^{2} x^{2} \cosh\left(d x + c\right) - {\left(2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} - \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b - \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b - \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b - \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b - \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\left(2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} - \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b + \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b + \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\left(2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b + \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b + \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, {\left({\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} - \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, {\left({\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} + \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - {\left(2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} - \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b - \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b - \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b - \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b - \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\left(2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} - \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b + \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b + \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\left(2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} + \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b + \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b + \sqrt{-3} {\left(b^{2} x^{3} + a b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, {\left({\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} - \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, {\left({\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b d^{3} x^{3} + a^{2} d^{3}\right)} \sinh\left(d x + c\right)^{2} + \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{3} + a b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{3} + a b\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right)}{36 \, {\left({\left(a^{2} b^{2} d^{2} x^{3} + a^{3} b d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b^{2} d^{2} x^{3} + a^{3} b d^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/36*(12*a*b*d^2*x^2*cosh(d*x + c) - (2*(a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - 2*(a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 - (a*d^3/b)^(2/3)*((b^2*x^3 + a*b - sqrt(-3)*(b^2*x^3 + a*b))*cosh(d*x + c)^2 - (b^2*x^3 + a*b - sqrt(-3)*(b^2*x^3 + a*b))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (2*(a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - 2*(a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 + (-a*d^3/b)^(2/3)*((b^2*x^3 + a*b - sqrt(-3)*(b^2*x^3 + a*b))*cosh(d*x + c)^2 - (b^2*x^3 + a*b - sqrt(-3)*(b^2*x^3 + a*b))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (2*(a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - 2*(a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 - (a*d^3/b)^(2/3)*((b^2*x^3 + a*b + sqrt(-3)*(b^2*x^3 + a*b))*cosh(d*x + c)^2 - (b^2*x^3 + a*b + sqrt(-3)*(b^2*x^3 + a*b))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (2*(a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - 2*(a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 + (-a*d^3/b)^(2/3)*((b^2*x^3 + a*b + sqrt(-3)*(b^2*x^3 + a*b))*cosh(d*x + c)^2 - (b^2*x^3 + a*b + sqrt(-3)*(b^2*x^3 + a*b))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*((a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - (a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 - (-a*d^3/b)^(2/3)*((b^2*x^3 + a*b)*cosh(d*x + c)^2 - (b^2*x^3 + a*b)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) - 2*((a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - (a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 + (a*d^3/b)^(2/3)*((b^2*x^3 + a*b)*cosh(d*x + c)^2 - (b^2*x^3 + a*b)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) - (2*(a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - 2*(a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 - (a*d^3/b)^(2/3)*((b^2*x^3 + a*b - sqrt(-3)*(b^2*x^3 + a*b))*cosh(d*x + c)^2 - (b^2*x^3 + a*b - sqrt(-3)*(b^2*x^3 + a*b))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (2*(a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - 2*(a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 + (-a*d^3/b)^(2/3)*((b^2*x^3 + a*b - sqrt(-3)*(b^2*x^3 + a*b))*cosh(d*x + c)^2 - (b^2*x^3 + a*b - sqrt(-3)*(b^2*x^3 + a*b))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (2*(a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - 2*(a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 - (a*d^3/b)^(2/3)*((b^2*x^3 + a*b + sqrt(-3)*(b^2*x^3 + a*b))*cosh(d*x + c)^2 - (b^2*x^3 + a*b + sqrt(-3)*(b^2*x^3 + a*b))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (2*(a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - 2*(a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 + (-a*d^3/b)^(2/3)*((b^2*x^3 + a*b + sqrt(-3)*(b^2*x^3 + a*b))*cosh(d*x + c)^2 - (b^2*x^3 + a*b + sqrt(-3)*(b^2*x^3 + a*b))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*((a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - (a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 - (-a*d^3/b)^(2/3)*((b^2*x^3 + a*b)*cosh(d*x + c)^2 - (b^2*x^3 + a*b)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) + 2*((a*b*d^3*x^3 + a^2*d^3)*cosh(d*x + c)^2 - (a*b*d^3*x^3 + a^2*d^3)*sinh(d*x + c)^2 + (a*d^3/b)^(2/3)*((b^2*x^3 + a*b)*cosh(d*x + c)^2 - (b^2*x^3 + a*b)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)))/((a^2*b^2*d^2*x^3 + a^3*b*d^2)*cosh(d*x + c)^2 - (a^2*b^2*d^2*x^3 + a^3*b*d^2)*sinh(d*x + c)^2)","B",0
105,1,2048,0,0.720746," ","integrate(cosh(d*x+c)/(b*x^3+a)^2,x, algorithm=""fricas"")","\frac{12 \, a d x \cosh\left(d x + c\right) - {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right)}{36 \, {\left({\left(a^{2} b d x^{3} + a^{3} d\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b d x^{3} + a^{3} d\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/36*(12*a*d*x*cosh(d*x + c) - ((a*d^3/b)^(2/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + ((-a*d^3/b)^(2/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - ((a*d^3/b)^(2/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + ((-a*d^3/b)^(2/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*((-a*d^3/b)^(2/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) + 2*((a*d^3/b)^(2/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) - ((a*d^3/b)^(2/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + ((-a*d^3/b)^(2/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + ((a*d^3/b)^(2/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - ((-a*d^3/b)^(2/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*((-a*d^3/b)^(2/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - 2*((a*d^3/b)^(2/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)))/((a^2*b*d*x^3 + a^3*d)*cosh(d*x + c)^2 - (a^2*b*d*x^3 + a^3*d)*sinh(d*x + c)^2)","B",0
106,1,1773,0,0.682946," ","integrate(cosh(d*x+c)/x/(b*x^3+a)^2,x, algorithm=""fricas"")","-\frac{{\left(6 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(6 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\left(6 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\left(6 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, {\left(3 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, {\left(3 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + {\left(6 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(6 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\left(6 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\left(6 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} - \sqrt{-3} {\left(b x^{3} + a\right)} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, {\left(3 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, {\left(3 \, {\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - 3 \, {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b x^{3} + a\right)} \cosh\left(d x + c\right)^{2} - {\left(b x^{3} + a\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 12 \, a \cosh\left(d x + c\right) - 18 \, {\left({\left(b x^{3} + a\right)} {\rm Ei}\left(d x\right) + {\left(b x^{3} + a\right)} {\rm Ei}\left(-d x\right)\right)} \cosh\left(c\right) - 18 \, {\left({\left(b x^{3} + a\right)} {\rm Ei}\left(d x\right) - {\left(b x^{3} + a\right)} {\rm Ei}\left(-d x\right)\right)} \sinh\left(c\right)}{36 \, {\left({\left(a^{2} b x^{3} + a^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b x^{3} + a^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/36*((6*(b*x^3 + a)*cosh(d*x + c)^2 - 6*(b*x^3 + a)*sinh(d*x + c)^2 - (a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (6*(b*x^3 + a)*cosh(d*x + c)^2 - 6*(b*x^3 + a)*sinh(d*x + c)^2 - (-a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (6*(b*x^3 + a)*cosh(d*x + c)^2 - 6*(b*x^3 + a)*sinh(d*x + c)^2 - (a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (6*(b*x^3 + a)*cosh(d*x + c)^2 - 6*(b*x^3 + a)*sinh(d*x + c)^2 - (-a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*(3*(b*x^3 + a)*cosh(d*x + c)^2 - 3*(b*x^3 + a)*sinh(d*x + c)^2 + (-a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) + 2*(3*(b*x^3 + a)*cosh(d*x + c)^2 - 3*(b*x^3 + a)*sinh(d*x + c)^2 + (a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + (6*(b*x^3 + a)*cosh(d*x + c)^2 - 6*(b*x^3 + a)*sinh(d*x + c)^2 - (a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + (6*(b*x^3 + a)*cosh(d*x + c)^2 - 6*(b*x^3 + a)*sinh(d*x + c)^2 - (-a*d^3/b)^(1/3)*((b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 + sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (6*(b*x^3 + a)*cosh(d*x + c)^2 - 6*(b*x^3 + a)*sinh(d*x + c)^2 - (a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (6*(b*x^3 + a)*cosh(d*x + c)^2 - 6*(b*x^3 + a)*sinh(d*x + c)^2 - (-a*d^3/b)^(1/3)*((b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*cosh(d*x + c)^2 - (b*x^3 - sqrt(-3)*(b*x^3 + a) + a)*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*(3*(b*x^3 + a)*cosh(d*x + c)^2 - 3*(b*x^3 + a)*sinh(d*x + c)^2 + (-a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - 2*(3*(b*x^3 + a)*cosh(d*x + c)^2 - 3*(b*x^3 + a)*sinh(d*x + c)^2 + (a*d^3/b)^(1/3)*((b*x^3 + a)*cosh(d*x + c)^2 - (b*x^3 + a)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) - 12*a*cosh(d*x + c) - 18*((b*x^3 + a)*Ei(d*x) + (b*x^3 + a)*Ei(-d*x))*cosh(c) - 18*((b*x^3 + a)*Ei(d*x) - (b*x^3 + a)*Ei(-d*x))*sinh(c))/((a^2*b*x^3 + a^3)*cosh(d*x + c)^2 - (a^2*b*x^3 + a^3)*sinh(d*x + c)^2)","B",0
107,1,2980,0,1.004454," ","integrate(x^5*cosh(d*x+c)/(b*x^3+a)^3,x, algorithm=""fricas"")","\frac{{\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} - 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 36 \, {\left(2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right) - 12 \, {\left(a b d x^{4} + a^{2} d x\right)} \sinh\left(d x + c\right)}{216 \, {\left({\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{4} x^{6} + 2 \, a^{2} b^{3} x^{3} + a^{3} b^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/216*(((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) - 4*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + ((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) - 4*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + ((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) - 4*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + ((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) - 4*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2) - 4*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) - 2*((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2) - 4*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + ((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) - 4*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + ((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) - 4*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - ((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) - 4*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - ((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) - 4*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2) - 4*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) + 2*((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2) - 4*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) - 36*(2*a*b*x^3 + a^2)*cosh(d*x + c) - 12*(a*b*d*x^4 + a^2*d*x)*sinh(d*x + c))/((a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2)*cosh(d*x + c)^2 - (a*b^4*x^6 + 2*a^2*b^3*x^3 + a^3*b^2)*sinh(d*x + c)^2)","B",0
108,1,4691,0,0.588919," ","integrate(x^4*cosh(d*x+c)/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{{\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) - {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, {\left(2 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, {\left(2 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) - {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, {\left(2 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, {\left(2 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 12 \, {\left(2 \, a b^{2} d^{2} x^{5} - a^{2} b d^{2} x^{2}\right)} \cosh\left(d x + c\right) + 12 \, {\left(a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)}{216 \, {\left({\left(a^{2} b^{4} d^{2} x^{6} + 2 \, a^{3} b^{3} d^{2} x^{3} + a^{4} b^{2} d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b^{4} d^{2} x^{6} + 2 \, a^{3} b^{3} d^{2} x^{3} + a^{4} b^{2} d^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/216*((4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 2*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) + (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) - (4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 2*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) + (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 2*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) + (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 2*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) + (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*(2*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 2*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 2*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) + 2*(2*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 2*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 2*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + (4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 2*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) + (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) - (4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 2*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) + (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 2*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) + (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 2*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) + (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*(2*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 2*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 2*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - 2*(2*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 2*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 2*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) - 12*(2*a*b^2*d^2*x^5 - a^2*b*d^2*x^2)*cosh(d*x + c) + 12*(a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c))/((a^2*b^4*d^2*x^6 + 2*a^3*b^3*d^2*x^3 + a^4*b^2*d^2)*cosh(d*x + c)^2 - (a^2*b^4*d^2*x^6 + 2*a^3*b^3*d^2*x^3 + a^4*b^2*d^2)*sinh(d*x + c)^2)","B",0
109,1,2962,0,0.647573," ","integrate(x^3*cosh(d*x+c)/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{{\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 6 \, {\left(a b^{2} d x^{4} - 2 \, a^{2} b d x\right)} \cosh\left(d x + c\right) - 6 \, {\left(a b^{2} d^{2} x^{5} + a^{2} b d^{2} x^{2}\right)} \sinh\left(d x + c\right)}{108 \, {\left({\left(a^{2} b^{4} d x^{6} + 2 \, a^{3} b^{3} d x^{3} + a^{4} b^{2} d\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b^{4} d x^{6} + 2 \, a^{3} b^{3} d x^{3} + a^{4} b^{2} d\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/108*(((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + (a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - (-a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + (a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - (-a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 2*(-a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) + ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 2*(a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + (a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - (-a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + (a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - (-a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 2*(-a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - ((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 2*(a*d^3/b)^(1/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) - 6*(a*b^2*d*x^4 - 2*a^2*b*d*x)*cosh(d*x + c) - 6*(a*b^2*d^2*x^5 + a^2*b*d^2*x^2)*sinh(d*x + c))/((a^2*b^4*d*x^6 + 2*a^3*b^3*d*x^3 + a^4*b^2*d)*cosh(d*x + c)^2 - (a^2*b^4*d*x^6 + 2*a^3*b^3*d*x^3 + a^4*b^2*d)*sinh(d*x + c)^2)","B",0
110,1,2972,0,0.692366," ","integrate(x^2*cosh(d*x+c)/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{36 \, a^{2} \cosh\left(d x + c\right) + {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) + {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} + \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2} - \sqrt{-3} {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, {\left(\left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, {\left(\left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)} + 2 \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} x^{6} + 2 \, a b x^{3} + a^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 12 \, {\left(a b d x^{4} + a^{2} d x\right)} \sinh\left(d x + c\right)}{216 \, {\left({\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{2} b^{3} x^{6} + 2 \, a^{3} b^{2} x^{3} + a^{4} b\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/216*(36*a^2*cosh(d*x + c) + ((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + ((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + ((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + ((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) - 2*((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + ((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) + ((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - ((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - ((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 + sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2 - sqrt(-3)*(b^2*x^6 + 2*a*b*x^3 + a^2))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*((-a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2) + 2*(-a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) + 2*((a*d^3/b)^(2/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2) + 2*(a*d^3/b)^(1/3)*((b^2*x^6 + 2*a*b*x^3 + a^2)*cosh(d*x + c)^2 - (b^2*x^6 + 2*a*b*x^3 + a^2)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) - 12*(a*b*d*x^4 + a^2*d*x)*sinh(d*x + c))/((a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*cosh(d*x + c)^2 - (a^2*b^3*x^6 + 2*a^3*b^2*x^3 + a^4*b)*sinh(d*x + c)^2)","B",0
111,1,4691,0,0.683049," ","integrate(x*cosh(d*x+c)/(b*x^3+a)^3,x, algorithm=""fricas"")","-\frac{{\left(8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) - {\left(8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) + {\left(8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) - {\left(8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \cosh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) - 2 \, {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + 2 \, {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \cosh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) + {\left(8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x - \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} + c\right) - {\left(8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b - \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} + \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x - \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} + 1\right)} - c\right) - {\left(8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} - c\right) + {\left(8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b + \sqrt{-3} {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)}\right)} \sinh\left(d x + c\right)^{2}\right)} - \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3} - \sqrt{-3} {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)}\right) \sinh\left(\frac{1}{2} \, \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left(\sqrt{-3} - 1\right)} + c\right) + 2 \, {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} - 4 \, \left(-\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(-d x + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(c + \left(-\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 2 \, {\left(4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, \left(\frac{a d^{3}}{b}\right)^{\frac{2}{3}} {\left({\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{3} x^{6} + 2 \, a b^{2} x^{3} + a^{2} b\right)} \sinh\left(d x + c\right)^{2}\right)} + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}} {\left({\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \cosh\left(d x + c\right)^{2} - {\left(a b^{2} d^{3} x^{6} + 2 \, a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)^{2}\right)}\right)} {\rm Ei}\left(d x + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) \sinh\left(-c + \left(\frac{a d^{3}}{b}\right)^{\frac{1}{3}}\right) - 12 \, {\left(4 \, a b^{2} d^{2} x^{5} + 7 \, a^{2} b d^{2} x^{2}\right)} \cosh\left(d x + c\right) - 12 \, {\left(a^{2} b d^{3} x^{3} + a^{3} d^{3}\right)} \sinh\left(d x + c\right)}{216 \, {\left({\left(a^{3} b^{3} d^{2} x^{6} + 2 \, a^{4} b^{2} d^{2} x^{3} + a^{5} b d^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(a^{3} b^{3} d^{2} x^{6} + 2 \, a^{4} b^{2} d^{2} x^{3} + a^{5} b d^{2}\right)} \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/216*((8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 4*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) - (8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 4*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) + (8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 4*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) - (8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 4*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*cosh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) - 2*(4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 4*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2) + (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*cosh(c + (-a*d^3/b)^(1/3)) + 2*(4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 4*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2) + (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*cosh(-c + (a*d^3/b)^(1/3)) + (8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 4*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(d*x - 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) + 1) + c) - (8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 4*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b - sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 + sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(-d*x - 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) + 1) - c) - (8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 4*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) - (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(d*x + 1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(a*d^3/b)^(1/3)*(sqrt(-3) - 1) - c) + (8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 8*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 4*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b + sqrt(-3)*(b^3*x^6 + 2*a*b^2*x^3 + a^2*b))*sinh(d*x + c)^2) - (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3 - sqrt(-3)*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3))*sinh(d*x + c)^2))*Ei(-d*x + 1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1))*sinh(1/2*(-a*d^3/b)^(1/3)*(sqrt(-3) - 1) + c) + 2*(4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 - 4*(-a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2) + (-a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2))*Ei(-d*x + (-a*d^3/b)^(1/3))*sinh(c + (-a*d^3/b)^(1/3)) - 2*(4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - 4*(a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2 + 4*(a*d^3/b)^(2/3)*((b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*cosh(d*x + c)^2 - (b^3*x^6 + 2*a*b^2*x^3 + a^2*b)*sinh(d*x + c)^2) + (a*d^3/b)^(1/3)*((a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*cosh(d*x + c)^2 - (a*b^2*d^3*x^6 + 2*a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c)^2))*Ei(d*x + (a*d^3/b)^(1/3))*sinh(-c + (a*d^3/b)^(1/3)) - 12*(4*a*b^2*d^2*x^5 + 7*a^2*b*d^2*x^2)*cosh(d*x + c) - 12*(a^2*b*d^3*x^3 + a^3*d^3)*sinh(d*x + c))/((a^3*b^3*d^2*x^6 + 2*a^4*b^2*d^2*x^3 + a^5*b*d^2)*cosh(d*x + c)^2 - (a^3*b^3*d^2*x^6 + 2*a^4*b^2*d^2*x^3 + a^5*b*d^2)*sinh(d*x + c)^2)","B",0
