1,1,171,0,0.445232," ","integrate((d*x+c)^4*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{4 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + b^{3} c^{3} d + 6 \, b c d^{3} + 3 \, {\left(b^{3} c^{2} d^{2} + 2 \, b d^{4}\right)} x\right)} \cosh\left(b x + a\right) - {\left(b^{4} d^{4} x^{4} + 4 \, b^{4} c d^{3} x^{3} + b^{4} c^{4} + 12 \, b^{2} c^{2} d^{2} + 24 \, d^{4} + 6 \, {\left(b^{4} c^{2} d^{2} + 2 \, b^{2} d^{4}\right)} x^{2} + 4 \, {\left(b^{4} c^{3} d + 6 \, b^{2} c d^{3}\right)} x\right)} \sinh\left(b x + a\right)}{b^{5}}"," ",0,"-(4*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + b^3*c^3*d + 6*b*c*d^3 + 3*(b^3*c^2*d^2 + 2*b*d^4)*x)*cosh(b*x + a) - (b^4*d^4*x^4 + 4*b^4*c*d^3*x^3 + b^4*c^4 + 12*b^2*c^2*d^2 + 24*d^4 + 6*(b^4*c^2*d^2 + 2*b^2*d^4)*x^2 + 4*(b^4*c^3*d + 6*b^2*c*d^3)*x)*sinh(b*x + a))/b^5","A",0
2,1,111,0,0.660241," ","integrate((d*x+c)^3*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d + 2 \, d^{3}\right)} \cosh\left(b x + a\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + b^{3} c^{3} + 6 \, b c d^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)}{b^{4}}"," ",0,"-(3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d + 2*d^3)*cosh(b*x + a) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + b^3*c^3 + 6*b*c*d^2 + 3*(b^3*c^2*d + 2*b*d^3)*x)*sinh(b*x + a))/b^4","A",0
3,1,64,0,0.656071," ","integrate((d*x+c)^2*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{2 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2} + 2 \, d^{2}\right)} \sinh\left(b x + a\right)}{b^{3}}"," ",0,"-(2*(b*d^2*x + b*c*d)*cosh(b*x + a) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2 + 2*d^2)*sinh(b*x + a))/b^3","A",0
4,1,30,0,0.629947," ","integrate((d*x+c)*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{d \cosh\left(b x + a\right) - {\left(b d x + b c\right)} \sinh\left(b x + a\right)}{b^{2}}"," ",0,"-(d*cosh(b*x + a) - (b*d*x + b*c)*sinh(b*x + a))/b^2","A",0
5,1,94,0,0.481316," ","integrate(cosh(b*x+a)/(d*x+c),x, algorithm=""fricas"")","\frac{{\left({\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left({\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right)}{2 \, d}"," ",0,"1/2*((Ei((b*d*x + b*c)/d) + Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) + (Ei((b*d*x + b*c)/d) - Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d))/d","A",0
6,1,150,0,0.742660," ","integrate(cosh(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, d \cosh\left(b x + a\right) - {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(2*d*cosh(b*x + a) - ((b*d*x + b*c)*Ei((b*d*x + b*c)/d) - (b*d*x + b*c)*Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) - ((b*d*x + b*c)*Ei((b*d*x + b*c)/d) + (b*d*x + b*c)*Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d))/(d^3*x + c*d^2)","B",0
7,1,254,0,0.533458," ","integrate(cosh(b*x+a)/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, d^{2} \cosh\left(b x + a\right) - {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) + 2 \, {\left(b d^{2} x + b c d\right)} \sinh\left(b x + a\right) - {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(2*d^2*cosh(b*x + a) - ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei((b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) + 2*(b*d^2*x + b*c*d)*sinh(b*x + a) - ((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei((b*d*x + b*c)/d) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
8,1,312,0,0.430879," ","integrate((d*x+c)^4*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{5} d^{4} x^{5} + 10 \, b^{5} c d^{3} x^{4} + 20 \, b^{5} c^{2} d^{2} x^{3} + 20 \, b^{5} c^{3} d x^{2} + 10 \, b^{5} c^{4} x - 5 \, {\left(2 \, b^{3} d^{4} x^{3} + 6 \, b^{3} c d^{3} x^{2} + 2 \, b^{3} c^{3} d + 3 \, b c d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} + b d^{4}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 5 \, {\left(2 \, b^{4} d^{4} x^{4} + 8 \, b^{4} c d^{3} x^{3} + 2 \, b^{4} c^{4} + 6 \, b^{2} c^{2} d^{2} + 3 \, d^{4} + 6 \, {\left(2 \, b^{4} c^{2} d^{2} + b^{2} d^{4}\right)} x^{2} + 4 \, {\left(2 \, b^{4} c^{3} d + 3 \, b^{2} c d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - 5 \, {\left(2 \, b^{3} d^{4} x^{3} + 6 \, b^{3} c d^{3} x^{2} + 2 \, b^{3} c^{3} d + 3 \, b c d^{3} + 3 \, {\left(2 \, b^{3} c^{2} d^{2} + b d^{4}\right)} x\right)} \sinh\left(b x + a\right)^{2}}{20 \, b^{5}}"," ",0,"1/20*(2*b^5*d^4*x^5 + 10*b^5*c*d^3*x^4 + 20*b^5*c^2*d^2*x^3 + 20*b^5*c^3*d*x^2 + 10*b^5*c^4*x - 5*(2*b^3*d^4*x^3 + 6*b^3*c*d^3*x^2 + 2*b^3*c^3*d + 3*b*c*d^3 + 3*(2*b^3*c^2*d^2 + b*d^4)*x)*cosh(b*x + a)^2 + 5*(2*b^4*d^4*x^4 + 8*b^4*c*d^3*x^3 + 2*b^4*c^4 + 6*b^2*c^2*d^2 + 3*d^4 + 6*(2*b^4*c^2*d^2 + b^2*d^4)*x^2 + 4*(2*b^4*c^3*d + 3*b^2*c*d^3)*x)*cosh(b*x + a)*sinh(b*x + a) - 5*(2*b^3*d^4*x^3 + 6*b^3*c*d^3*x^2 + 2*b^3*c^3*d + 3*b*c*d^3 + 3*(2*b^3*c^2*d^2 + b*d^4)*x)*sinh(b*x + a)^2)/b^5","B",0
9,1,209,0,0.498428," ","integrate((d*x+c)^3*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{4} d^{3} x^{4} + 8 \, b^{4} c d^{2} x^{3} + 12 \, b^{4} c^{2} d x^{2} + 8 \, b^{4} c^{3} x - 3 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d + d^{3}\right)} \cosh\left(b x + a\right)^{2} + 4 \, {\left(2 \, b^{3} d^{3} x^{3} + 6 \, b^{3} c d^{2} x^{2} + 2 \, b^{3} c^{3} + 3 \, b c d^{2} + 3 \, {\left(2 \, b^{3} c^{2} d + b d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - 3 \, {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d + d^{3}\right)} \sinh\left(b x + a\right)^{2}}{16 \, b^{4}}"," ",0,"1/16*(2*b^4*d^3*x^4 + 8*b^4*c*d^2*x^3 + 12*b^4*c^2*d*x^2 + 8*b^4*c^3*x - 3*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d + d^3)*cosh(b*x + a)^2 + 4*(2*b^3*d^3*x^3 + 6*b^3*c*d^2*x^2 + 2*b^3*c^3 + 3*b*c*d^2 + 3*(2*b^3*c^2*d + b*d^3)*x)*cosh(b*x + a)*sinh(b*x + a) - 3*(2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d + d^3)*sinh(b*x + a)^2)/b^4","A",0
10,1,123,0,0.719429," ","integrate((d*x+c)^2*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{3} d^{2} x^{3} + 6 \, b^{3} c d x^{2} + 6 \, b^{3} c^{2} x - 3 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{2} + 3 \, {\left(2 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c d x + 2 \, b^{2} c^{2} + d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - 3 \, {\left(b d^{2} x + b c d\right)} \sinh\left(b x + a\right)^{2}}{12 \, b^{3}}"," ",0,"1/12*(2*b^3*d^2*x^3 + 6*b^3*c*d*x^2 + 6*b^3*c^2*x - 3*(b*d^2*x + b*c*d)*cosh(b*x + a)^2 + 3*(2*b^2*d^2*x^2 + 4*b^2*c*d*x + 2*b^2*c^2 + d^2)*cosh(b*x + a)*sinh(b*x + a) - 3*(b*d^2*x + b*c*d)*sinh(b*x + a)^2)/b^3","A",0
11,1,66,0,0.544941," ","integrate((d*x+c)*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b^{2} d x^{2} + 4 \, b^{2} c x - d \cosh\left(b x + a\right)^{2} + 4 \, {\left(b d x + b c\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - d \sinh\left(b x + a\right)^{2}}{8 \, b^{2}}"," ",0,"1/8*(2*b^2*d*x^2 + 4*b^2*c*x - d*cosh(b*x + a)^2 + 4*(b*d*x + b*c)*cosh(b*x + a)*sinh(b*x + a) - d*sinh(b*x + a)^2)/b^2","A",0
12,1,104,0,0.467823," ","integrate(cosh(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","\frac{{\left({\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + 2 \, \log\left(d x + c\right)}{4 \, d}"," ",0,"1/4*((Ei(2*(b*d*x + b*c)/d) + Ei(-2*(b*d*x + b*c)/d))*cosh(-2*(b*c - a*d)/d) + (Ei(2*(b*d*x + b*c)/d) - Ei(-2*(b*d*x + b*c)/d))*sinh(-2*(b*c - a*d)/d) + 2*log(d*x + c))/d","A",0
13,1,164,0,0.447308," ","integrate(cosh(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{d \cosh\left(b x + a\right)^{2} + d \sinh\left(b x + a\right)^{2} - {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(d*cosh(b*x + a)^2 + d*sinh(b*x + a)^2 - ((b*d*x + b*c)*Ei(2*(b*d*x + b*c)/d) - (b*d*x + b*c)*Ei(-2*(b*d*x + b*c)/d))*cosh(-2*(b*c - a*d)/d) - ((b*d*x + b*c)*Ei(2*(b*d*x + b*c)/d) + (b*d*x + b*c)*Ei(-2*(b*d*x + b*c)/d))*sinh(-2*(b*c - a*d)/d) + d)/(d^3*x + c*d^2)","B",0
14,1,278,0,0.539645," ","integrate(cosh(b*x+a)^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{d^{2} \cosh\left(b x + a\right)^{2} + d^{2} \sinh\left(b x + a\right)^{2} + 4 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d^{2} - 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(d^2*cosh(b*x + a)^2 + d^2*sinh(b*x + a)^2 + 4*(b*d^2*x + b*c*d)*cosh(b*x + a)*sinh(b*x + a) + d^2 - 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(2*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-2*(b*d*x + b*c)/d))*cosh(-2*(b*c - a*d)/d) - 2*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(2*(b*d*x + b*c)/d) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-2*(b*d*x + b*c)/d))*sinh(-2*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
15,1,409,0,0.837941," ","integrate(cosh(b*x+a)^2/(d*x+c)^4,x, algorithm=""fricas"")","-\frac{d^{3} + {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d + d^{3}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(2 \, b^{2} d^{3} x^{2} + 4 \, b^{2} c d^{2} x + 2 \, b^{2} c^{2} d + d^{3}\right)} \sinh\left(b x + a\right)^{2} - 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - 2 \, {\left({\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} {\rm Ei}\left(\frac{2 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + b^{3} c^{3}\right)} {\rm Ei}\left(-\frac{2 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)}{6 \, {\left(d^{7} x^{3} + 3 \, c d^{6} x^{2} + 3 \, c^{2} d^{5} x + c^{3} d^{4}\right)}}"," ",0,"-1/6*(d^3 + (2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d + d^3)*cosh(b*x + a)^2 + 2*(b*d^3*x + b*c*d^2)*cosh(b*x + a)*sinh(b*x + a) + (2*b^2*d^3*x^2 + 4*b^2*c*d^2*x + 2*b^2*c^2*d + d^3)*sinh(b*x + a)^2 - 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*Ei(2*(b*d*x + b*c)/d) - (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*Ei(-2*(b*d*x + b*c)/d))*cosh(-2*(b*c - a*d)/d) - 2*((b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*Ei(2*(b*d*x + b*c)/d) + (b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + b^3*c^3)*Ei(-2*(b*d*x + b*c)/d))*sinh(-2*(b*c - a*d)/d))/(d^7*x^3 + 3*c*d^6*x^2 + 3*c^2*d^5*x + c^3*d^4)","B",0
16,1,528,0,0.515912," ","integrate((d*x+c)^4*cosh(b*x+a)^3,x, algorithm=""fricas"")","-\frac{12 \, {\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{3} d + 2 \, b c d^{3} + {\left(9 \, b^{3} c^{2} d^{2} + 2 \, b d^{4}\right)} x\right)} \cosh\left(b x + a\right)^{3} + 36 \, {\left(3 \, b^{3} d^{4} x^{3} + 9 \, b^{3} c d^{3} x^{2} + 3 \, b^{3} c^{3} d + 2 \, b c d^{3} + {\left(9 \, b^{3} c^{2} d^{2} + 2 \, b d^{4}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} - {\left(27 \, b^{4} d^{4} x^{4} + 108 \, b^{4} c d^{3} x^{3} + 27 \, b^{4} c^{4} + 36 \, b^{2} c^{2} d^{2} + 8 \, d^{4} + 18 \, {\left(9 \, b^{4} c^{2} d^{2} + 2 \, b^{2} d^{4}\right)} x^{2} + 36 \, {\left(3 \, b^{4} c^{3} d + 2 \, b^{2} c d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{3} + 972 \, {\left(b^{3} d^{4} x^{3} + 3 \, b^{3} c d^{3} x^{2} + b^{3} c^{3} d + 6 \, b c d^{3} + 3 \, {\left(b^{3} c^{2} d^{2} + 2 \, b d^{4}\right)} x\right)} \cosh\left(b x + a\right) - 3 \, {\left(81 \, b^{4} d^{4} x^{4} + 324 \, b^{4} c d^{3} x^{3} + 81 \, b^{4} c^{4} + 972 \, b^{2} c^{2} d^{2} + 1944 \, d^{4} + 486 \, {\left(b^{4} c^{2} d^{2} + 2 \, b^{2} d^{4}\right)} x^{2} + {\left(27 \, b^{4} d^{4} x^{4} + 108 \, b^{4} c d^{3} x^{3} + 27 \, b^{4} c^{4} + 36 \, b^{2} c^{2} d^{2} + 8 \, d^{4} + 18 \, {\left(9 \, b^{4} c^{2} d^{2} + 2 \, b^{2} d^{4}\right)} x^{2} + 36 \, {\left(3 \, b^{4} c^{3} d + 2 \, b^{2} c d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 324 \, {\left(b^{4} c^{3} d + 6 \, b^{2} c d^{3}\right)} x\right)} \sinh\left(b x + a\right)}{324 \, b^{5}}"," ",0,"-1/324*(12*(3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 3*b^3*c^3*d + 2*b*c*d^3 + (9*b^3*c^2*d^2 + 2*b*d^4)*x)*cosh(b*x + a)^3 + 36*(3*b^3*d^4*x^3 + 9*b^3*c*d^3*x^2 + 3*b^3*c^3*d + 2*b*c*d^3 + (9*b^3*c^2*d^2 + 2*b*d^4)*x)*cosh(b*x + a)*sinh(b*x + a)^2 - (27*b^4*d^4*x^4 + 108*b^4*c*d^3*x^3 + 27*b^4*c^4 + 36*b^2*c^2*d^2 + 8*d^4 + 18*(9*b^4*c^2*d^2 + 2*b^2*d^4)*x^2 + 36*(3*b^4*c^3*d + 2*b^2*c*d^3)*x)*sinh(b*x + a)^3 + 972*(b^3*d^4*x^3 + 3*b^3*c*d^3*x^2 + b^3*c^3*d + 6*b*c*d^3 + 3*(b^3*c^2*d^2 + 2*b*d^4)*x)*cosh(b*x + a) - 3*(81*b^4*d^4*x^4 + 324*b^4*c*d^3*x^3 + 81*b^4*c^4 + 972*b^2*c^2*d^2 + 1944*d^4 + 486*(b^4*c^2*d^2 + 2*b^2*d^4)*x^2 + (27*b^4*d^4*x^4 + 108*b^4*c*d^3*x^3 + 27*b^4*c^4 + 36*b^2*c^2*d^2 + 8*d^4 + 18*(9*b^4*c^2*d^2 + 2*b^2*d^4)*x^2 + 36*(3*b^4*c^3*d + 2*b^2*c*d^3)*x)*cosh(b*x + a)^2 + 324*(b^4*c^3*d + 6*b^2*c*d^3)*x)*sinh(b*x + a))/b^5","B",0
17,1,343,0,0.568183," ","integrate((d*x+c)^3*cosh(b*x+a)^3,x, algorithm=""fricas"")","-\frac{{\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d + 2 \, d^{3}\right)} \cosh\left(b x + a\right)^{3} + 3 \, {\left(9 \, b^{2} d^{3} x^{2} + 18 \, b^{2} c d^{2} x + 9 \, b^{2} c^{2} d + 2 \, d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} - 3 \, {\left(3 \, b^{3} d^{3} x^{3} + 9 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{3} + 2 \, b c d^{2} + {\left(9 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{3} + 243 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + b^{2} c^{2} d + 2 \, d^{3}\right)} \cosh\left(b x + a\right) - 9 \, {\left(9 \, b^{3} d^{3} x^{3} + 27 \, b^{3} c d^{2} x^{2} + 9 \, b^{3} c^{3} + 54 \, b c d^{2} + {\left(3 \, b^{3} d^{3} x^{3} + 9 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{3} + 2 \, b c d^{2} + {\left(9 \, b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 27 \, {\left(b^{3} c^{2} d + 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)}{108 \, b^{4}}"," ",0,"-1/108*((9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d + 2*d^3)*cosh(b*x + a)^3 + 3*(9*b^2*d^3*x^2 + 18*b^2*c*d^2*x + 9*b^2*c^2*d + 2*d^3)*cosh(b*x + a)*sinh(b*x + a)^2 - 3*(3*b^3*d^3*x^3 + 9*b^3*c*d^2*x^2 + 3*b^3*c^3 + 2*b*c*d^2 + (9*b^3*c^2*d + 2*b*d^3)*x)*sinh(b*x + a)^3 + 243*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + b^2*c^2*d + 2*d^3)*cosh(b*x + a) - 9*(9*b^3*d^3*x^3 + 27*b^3*c*d^2*x^2 + 9*b^3*c^3 + 54*b*c*d^2 + (3*b^3*d^3*x^3 + 9*b^3*c*d^2*x^2 + 3*b^3*c^3 + 2*b*c*d^2 + (9*b^3*c^2*d + 2*b*d^3)*x)*cosh(b*x + a)^2 + 27*(b^3*c^2*d + 2*b*d^3)*x)*sinh(b*x + a))/b^4","B",0
18,1,199,0,0.535530," ","integrate((d*x+c)^2*cosh(b*x+a)^3,x, algorithm=""fricas"")","-\frac{6 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{3} + 18 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} - {\left(9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x + 9 \, b^{2} c^{2} + 2 \, d^{2}\right)} \sinh\left(b x + a\right)^{3} + 162 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right) - 3 \, {\left(27 \, b^{2} d^{2} x^{2} + 54 \, b^{2} c d x + 27 \, b^{2} c^{2} + {\left(9 \, b^{2} d^{2} x^{2} + 18 \, b^{2} c d x + 9 \, b^{2} c^{2} + 2 \, d^{2}\right)} \cosh\left(b x + a\right)^{2} + 54 \, d^{2}\right)} \sinh\left(b x + a\right)}{108 \, b^{3}}"," ",0,"-1/108*(6*(b*d^2*x + b*c*d)*cosh(b*x + a)^3 + 18*(b*d^2*x + b*c*d)*cosh(b*x + a)*sinh(b*x + a)^2 - (9*b^2*d^2*x^2 + 18*b^2*c*d*x + 9*b^2*c^2 + 2*d^2)*sinh(b*x + a)^3 + 162*(b*d^2*x + b*c*d)*cosh(b*x + a) - 3*(27*b^2*d^2*x^2 + 54*b^2*c*d*x + 27*b^2*c^2 + (9*b^2*d^2*x^2 + 18*b^2*c*d*x + 9*b^2*c^2 + 2*d^2)*cosh(b*x + a)^2 + 54*d^2)*sinh(b*x + a))/b^3","A",0
19,1,95,0,0.471031," ","integrate((d*x+c)*cosh(b*x+a)^3,x, algorithm=""fricas"")","-\frac{d \cosh\left(b x + a\right)^{3} + 3 \, d \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} - 3 \, {\left(b d x + b c\right)} \sinh\left(b x + a\right)^{3} + 27 \, d \cosh\left(b x + a\right) - 9 \, {\left(3 \, b d x + {\left(b d x + b c\right)} \cosh\left(b x + a\right)^{2} + 3 \, b c\right)} \sinh\left(b x + a\right)}{36 \, b^{2}}"," ",0,"-1/36*(d*cosh(b*x + a)^3 + 3*d*cosh(b*x + a)*sinh(b*x + a)^2 - 3*(b*d*x + b*c)*sinh(b*x + a)^3 + 27*d*cosh(b*x + a) - 9*(3*b*d*x + (b*d*x + b*c)*cosh(b*x + a)^2 + 3*b*c)*sinh(b*x + a))/b^2","A",0
20,1,186,0,0.797381," ","integrate(cosh(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","\frac{3 \, {\left({\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left({\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 3 \, {\left({\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, d}"," ",0,"1/8*(3*(Ei((b*d*x + b*c)/d) + Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) + (Ei(3*(b*d*x + b*c)/d) + Ei(-3*(b*d*x + b*c)/d))*cosh(-3*(b*c - a*d)/d) + 3*(Ei((b*d*x + b*c)/d) - Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d) + (Ei(3*(b*d*x + b*c)/d) - Ei(-3*(b*d*x + b*c)/d))*sinh(-3*(b*c - a*d)/d))/d","A",0
21,1,305,0,0.530360," ","integrate(cosh(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, d \cosh\left(b x + a\right)^{3} + 6 \, d \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + 6 \, d \cosh\left(b x + a\right) - 3 \, {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) - 3 \, {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - 3 \, {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right) - 3 \, {\left({\left(b d x + b c\right)} {\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b d x + b c\right)} {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{8 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/8*(2*d*cosh(b*x + a)^3 + 6*d*cosh(b*x + a)*sinh(b*x + a)^2 + 6*d*cosh(b*x + a) - 3*((b*d*x + b*c)*Ei((b*d*x + b*c)/d) - (b*d*x + b*c)*Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) - 3*((b*d*x + b*c)*Ei(3*(b*d*x + b*c)/d) - (b*d*x + b*c)*Ei(-3*(b*d*x + b*c)/d))*cosh(-3*(b*c - a*d)/d) - 3*((b*d*x + b*c)*Ei((b*d*x + b*c)/d) + (b*d*x + b*c)*Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d) - 3*((b*d*x + b*c)*Ei(3*(b*d*x + b*c)/d) + (b*d*x + b*c)*Ei(-3*(b*d*x + b*c)/d))*sinh(-3*(b*c - a*d)/d))/(d^3*x + c*d^2)","B",0
22,1,527,0,0.553399," ","integrate(cosh(b*x+a)^3/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, d^{2} \cosh\left(b x + a\right)^{3} + 6 \, d^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + 6 \, {\left(b d^{2} x + b c d\right)} \sinh\left(b x + a\right)^{3} + 6 \, d^{2} \cosh\left(b x + a\right) - 3 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \cosh\left(-\frac{b c - a d}{d}\right) - 9 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + 6 \, {\left(b d^{2} x + b c d + 3 \, {\left(b d^{2} x + b c d\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right) - 3 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{b d x + b c}{d}\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{b d x + b c}{d}\right)\right)} \sinh\left(-\frac{b c - a d}{d}\right) - 9 \, {\left({\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\rm Ei}\left(-\frac{3 \, {\left(b d x + b c\right)}}{d}\right)\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)}{16 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/16*(2*d^2*cosh(b*x + a)^3 + 6*d^2*cosh(b*x + a)*sinh(b*x + a)^2 + 6*(b*d^2*x + b*c*d)*sinh(b*x + a)^3 + 6*d^2*cosh(b*x + a) - 3*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei((b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-(b*d*x + b*c)/d))*cosh(-(b*c - a*d)/d) - 9*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(3*(b*d*x + b*c)/d) + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-3*(b*d*x + b*c)/d))*cosh(-3*(b*c - a*d)/d) + 6*(b*d^2*x + b*c*d + 3*(b*d^2*x + b*c*d)*cosh(b*x + a)^2)*sinh(b*x + a) - 3*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei((b*d*x + b*c)/d) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-(b*d*x + b*c)/d))*sinh(-(b*c - a*d)/d) - 9*((b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(3*(b*d*x + b*c)/d) - (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*Ei(-3*(b*d*x + b*c)/d))*sinh(-3*(b*c - a*d)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
23,1,195,0,0.562412," ","integrate(x^3*cosh(b*x+a)^4,x, algorithm=""fricas"")","\frac{96 \, b^{4} x^{4} - 3 \, {\left(8 \, b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{4} + 16 \, {\left(8 \, b^{3} x^{3} + 3 \, b x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - 3 \, {\left(8 \, b^{2} x^{2} + 1\right)} \sinh\left(b x + a\right)^{4} - 192 \, {\left(2 \, b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{2} - 6 \, {\left(64 \, b^{2} x^{2} + 3 \, {\left(8 \, b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{2} + 32\right)} \sinh\left(b x + a\right)^{2} + 16 \, {\left({\left(8 \, b^{3} x^{3} + 3 \, b x\right)} \cosh\left(b x + a\right)^{3} + 16 \, {\left(2 \, b^{3} x^{3} + 3 \, b x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)}{1024 \, b^{4}}"," ",0,"1/1024*(96*b^4*x^4 - 3*(8*b^2*x^2 + 1)*cosh(b*x + a)^4 + 16*(8*b^3*x^3 + 3*b*x)*cosh(b*x + a)*sinh(b*x + a)^3 - 3*(8*b^2*x^2 + 1)*sinh(b*x + a)^4 - 192*(2*b^2*x^2 + 1)*cosh(b*x + a)^2 - 6*(64*b^2*x^2 + 3*(8*b^2*x^2 + 1)*cosh(b*x + a)^2 + 32)*sinh(b*x + a)^2 + 16*((8*b^3*x^3 + 3*b*x)*cosh(b*x + a)^3 + 16*(2*b^3*x^3 + 3*b*x)*cosh(b*x + a))*sinh(b*x + a))/b^4","A",0
24,1,147,0,0.787127," ","integrate(x^2*cosh(b*x+a)^4,x, algorithm=""fricas"")","\frac{8 \, b^{3} x^{3} - b x \cosh\left(b x + a\right)^{4} - b x \sinh\left(b x + a\right)^{4} + {\left(8 \, b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - 16 \, b x \cosh\left(b x + a\right)^{2} - 2 \, {\left(3 \, b x \cosh\left(b x + a\right)^{2} + 8 \, b x\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(8 \, b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)^{3} + 16 \, {\left(2 \, b^{2} x^{2} + 1\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)}{64 \, b^{3}}"," ",0,"1/64*(8*b^3*x^3 - b*x*cosh(b*x + a)^4 - b*x*sinh(b*x + a)^4 + (8*b^2*x^2 + 1)*cosh(b*x + a)*sinh(b*x + a)^3 - 16*b*x*cosh(b*x + a)^2 - 2*(3*b*x*cosh(b*x + a)^2 + 8*b*x)*sinh(b*x + a)^2 + ((8*b^2*x^2 + 1)*cosh(b*x + a)^3 + 16*(2*b^2*x^2 + 1)*cosh(b*x + a))*sinh(b*x + a))/b^3","A",0
25,1,114,0,1.187512," ","integrate(x*cosh(b*x+a)^4,x, algorithm=""fricas"")","\frac{16 \, b x \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + 24 \, b^{2} x^{2} - \cosh\left(b x + a\right)^{4} - \sinh\left(b x + a\right)^{4} - 2 \, {\left(3 \, \cosh\left(b x + a\right)^{2} + 8\right)} \sinh\left(b x + a\right)^{2} - 16 \, \cosh\left(b x + a\right)^{2} + 16 \, {\left(b x \cosh\left(b x + a\right)^{3} + 4 \, b x \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)}{128 \, b^{2}}"," ",0,"1/128*(16*b*x*cosh(b*x + a)*sinh(b*x + a)^3 + 24*b^2*x^2 - cosh(b*x + a)^4 - sinh(b*x + a)^4 - 2*(3*cosh(b*x + a)^2 + 8)*sinh(b*x + a)^2 - 16*cosh(b*x + a)^2 + 16*(b*x*cosh(b*x + a)^3 + 4*b*x*cosh(b*x + a))*sinh(b*x + a))/b^2","A",0
26,1,493,0,0.652746," ","integrate((d*x+c)^3*sech(b*x+a),x, algorithm=""fricas"")","\frac{6 i \, d^{3} {\rm polylog}\left(4, i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) - 6 i \, d^{3} {\rm polylog}\left(4, -i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d\right)} {\rm Li}_2\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + {\left(i \, b^{3} c^{3} - 3 i \, a b^{2} c^{2} d + 3 i \, a^{2} b c d^{2} - i \, a^{3} d^{3}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + i\right) + {\left(-i \, b^{3} c^{3} + 3 i \, a b^{2} c^{2} d - 3 i \, a^{2} b c d^{2} + i \, a^{3} d^{3}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - i\right) + {\left(-i \, b^{3} d^{3} x^{3} - 3 i \, b^{3} c d^{2} x^{2} - 3 i \, b^{3} c^{2} d x - 3 i \, a b^{2} c^{2} d + 3 i \, a^{2} b c d^{2} - i \, a^{3} d^{3}\right)} \log\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right) + 1\right) + {\left(i \, b^{3} d^{3} x^{3} + 3 i \, b^{3} c d^{2} x^{2} + 3 i \, b^{3} c^{2} d x + 3 i \, a b^{2} c^{2} d - 3 i \, a^{2} b c d^{2} + i \, a^{3} d^{3}\right)} \log\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right) + 1\right) + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} {\rm polylog}\left(3, i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} {\rm polylog}\left(3, -i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right)}{b^{4}}"," ",0,"(6*I*d^3*polylog(4, I*cosh(b*x + a) + I*sinh(b*x + a)) - 6*I*d^3*polylog(4, -I*cosh(b*x + a) - I*sinh(b*x + a)) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d)*dilog(I*cosh(b*x + a) + I*sinh(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d)*dilog(-I*cosh(b*x + a) - I*sinh(b*x + a)) + (I*b^3*c^3 - 3*I*a*b^2*c^2*d + 3*I*a^2*b*c*d^2 - I*a^3*d^3)*log(cosh(b*x + a) + sinh(b*x + a) + I) + (-I*b^3*c^3 + 3*I*a*b^2*c^2*d - 3*I*a^2*b*c*d^2 + I*a^3*d^3)*log(cosh(b*x + a) + sinh(b*x + a) - I) + (-I*b^3*d^3*x^3 - 3*I*b^3*c*d^2*x^2 - 3*I*b^3*c^2*d*x - 3*I*a*b^2*c^2*d + 3*I*a^2*b*c*d^2 - I*a^3*d^3)*log(I*cosh(b*x + a) + I*sinh(b*x + a) + 1) + (I*b^3*d^3*x^3 + 3*I*b^3*c*d^2*x^2 + 3*I*b^3*c^2*d*x + 3*I*a*b^2*c^2*d - 3*I*a^2*b*c*d^2 + I*a^3*d^3)*log(-I*cosh(b*x + a) - I*sinh(b*x + a) + 1) + (-6*I*b*d^3*x - 6*I*b*c*d^2)*polylog(3, I*cosh(b*x + a) + I*sinh(b*x + a)) + (6*I*b*d^3*x + 6*I*b*c*d^2)*polylog(3, -I*cosh(b*x + a) - I*sinh(b*x + a)))/b^4","C",0
27,1,303,0,0.976184," ","integrate((d*x+c)^2*sech(b*x+a),x, algorithm=""fricas"")","\frac{-2 i \, d^{2} {\rm polylog}\left(3, i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + 2 i \, d^{2} {\rm polylog}\left(3, -i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} {\rm Li}_2\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} {\rm Li}_2\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + {\left(i \, b^{2} c^{2} - 2 i \, a b c d + i \, a^{2} d^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + i\right) + {\left(-i \, b^{2} c^{2} + 2 i \, a b c d - i \, a^{2} d^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - i\right) + {\left(-i \, b^{2} d^{2} x^{2} - 2 i \, b^{2} c d x - 2 i \, a b c d + i \, a^{2} d^{2}\right)} \log\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right) + 1\right) + {\left(i \, b^{2} d^{2} x^{2} + 2 i \, b^{2} c d x + 2 i \, a b c d - i \, a^{2} d^{2}\right)} \log\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right) + 1\right)}{b^{3}}"," ",0,"(-2*I*d^2*polylog(3, I*cosh(b*x + a) + I*sinh(b*x + a)) + 2*I*d^2*polylog(3, -I*cosh(b*x + a) - I*sinh(b*x + a)) + (2*I*b*d^2*x + 2*I*b*c*d)*dilog(I*cosh(b*x + a) + I*sinh(b*x + a)) + (-2*I*b*d^2*x - 2*I*b*c*d)*dilog(-I*cosh(b*x + a) - I*sinh(b*x + a)) + (I*b^2*c^2 - 2*I*a*b*c*d + I*a^2*d^2)*log(cosh(b*x + a) + sinh(b*x + a) + I) + (-I*b^2*c^2 + 2*I*a*b*c*d - I*a^2*d^2)*log(cosh(b*x + a) + sinh(b*x + a) - I) + (-I*b^2*d^2*x^2 - 2*I*b^2*c*d*x - 2*I*a*b*c*d + I*a^2*d^2)*log(I*cosh(b*x + a) + I*sinh(b*x + a) + 1) + (I*b^2*d^2*x^2 + 2*I*b^2*c*d*x + 2*I*a*b*c*d - I*a^2*d^2)*log(-I*cosh(b*x + a) - I*sinh(b*x + a) + 1))/b^3","C",0
28,1,157,0,0.670401," ","integrate((d*x+c)*sech(b*x+a),x, algorithm=""fricas"")","\frac{i \, d {\rm Li}_2\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) - i \, d {\rm Li}_2\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + {\left(i \, b c - i \, a d\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + i\right) + {\left(-i \, b c + i \, a d\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - i\right) + {\left(-i \, b d x - i \, a d\right)} \log\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right) + 1\right) + {\left(i \, b d x + i \, a d\right)} \log\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right) + 1\right)}{b^{2}}"," ",0,"(I*d*dilog(I*cosh(b*x + a) + I*sinh(b*x + a)) - I*d*dilog(-I*cosh(b*x + a) - I*sinh(b*x + a)) + (I*b*c - I*a*d)*log(cosh(b*x + a) + sinh(b*x + a) + I) + (-I*b*c + I*a*d)*log(cosh(b*x + a) + sinh(b*x + a) - I) + (-I*b*d*x - I*a*d)*log(I*cosh(b*x + a) + I*sinh(b*x + a) + 1) + (I*b*d*x + I*a*d)*log(-I*cosh(b*x + a) - I*sinh(b*x + a) + 1))/b^2","B",0
29,0,0,0,0.592353," ","integrate(sech(b*x+a)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(b x + a\right)}{d x + c}, x\right)"," ",0,"integral(sech(b*x + a)/(d*x + c), x)","F",0
30,0,0,0,0.680367," ","integrate(sech(b*x+a)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(b x + a\right)}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(sech(b*x + a)/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
31,1,1332,0,0.755812," ","integrate((d*x+c)^3*sech(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, b^{3} c^{3} - 6 \, a b^{2} c^{2} d + 6 \, a^{2} b c d^{2} - 2 \, a^{3} d^{3} - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cosh\left(b x + a\right)^{2} - 4 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - 2 \, {\left(b^{3} d^{3} x^{3} + 3 \, b^{3} c d^{2} x^{2} + 3 \, b^{3} c^{2} d x + 3 \, a b^{2} c^{2} d - 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \sinh\left(b x + a\right)^{2} + 6 \, {\left(b d^{3} x + b c d^{2} + {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b d^{3} x + b c d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + 6 \, {\left(b d^{3} x + b c d^{2} + {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b d^{3} x + b c d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b d^{3} x + b c d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + i\right) + 3 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3} + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b^{2} c^{2} d - 2 \, a b c d^{2} + a^{2} d^{3}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - i\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3} + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right) + 1\right) + 3 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3} + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b^{2} d^{3} x^{2} + 2 \, b^{2} c d^{2} x + 2 \, a b c d^{2} - a^{2} d^{3}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right) + 1\right) - 6 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} + 2 \, d^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d^{3} \sinh\left(b x + a\right)^{2} + d^{3}\right)} {\rm polylog}\left(3, i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) - 6 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} + 2 \, d^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d^{3} \sinh\left(b x + a\right)^{2} + d^{3}\right)} {\rm polylog}\left(3, -i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right)}{b^{4} \cosh\left(b x + a\right)^{2} + 2 \, b^{4} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{4} \sinh\left(b x + a\right)^{2} + b^{4}}"," ",0,"-(2*b^3*c^3 - 6*a*b^2*c^2*d + 6*a^2*b*c*d^2 - 2*a^3*d^3 - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cosh(b*x + a)^2 - 4*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*cosh(b*x + a)*sinh(b*x + a) - 2*(b^3*d^3*x^3 + 3*b^3*c*d^2*x^2 + 3*b^3*c^2*d*x + 3*a*b^2*c^2*d - 3*a^2*b*c*d^2 + a^3*d^3)*sinh(b*x + a)^2 + 6*(b*d^3*x + b*c*d^2 + (b*d^3*x + b*c*d^2)*cosh(b*x + a)^2 + 2*(b*d^3*x + b*c*d^2)*cosh(b*x + a)*sinh(b*x + a) + (b*d^3*x + b*c*d^2)*sinh(b*x + a)^2)*dilog(I*cosh(b*x + a) + I*sinh(b*x + a)) + 6*(b*d^3*x + b*c*d^2 + (b*d^3*x + b*c*d^2)*cosh(b*x + a)^2 + 2*(b*d^3*x + b*c*d^2)*cosh(b*x + a)*sinh(b*x + a) + (b*d^3*x + b*c*d^2)*sinh(b*x + a)^2)*dilog(-I*cosh(b*x + a) - I*sinh(b*x + a)) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cosh(b*x + a)^2 + 2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cosh(b*x + a)*sinh(b*x + a) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sinh(b*x + a)^2)*log(cosh(b*x + a) + sinh(b*x + a) + I) + 3*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3 + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cosh(b*x + a)^2 + 2*(b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*cosh(b*x + a)*sinh(b*x + a) + (b^2*c^2*d - 2*a*b*c*d^2 + a^2*d^3)*sinh(b*x + a)^2)*log(cosh(b*x + a) + sinh(b*x + a) - I) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3 + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cosh(b*x + a)^2 + 2*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cosh(b*x + a)*sinh(b*x + a) + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*sinh(b*x + a)^2)*log(I*cosh(b*x + a) + I*sinh(b*x + a) + 1) + 3*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3 + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cosh(b*x + a)^2 + 2*(b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*cosh(b*x + a)*sinh(b*x + a) + (b^2*d^3*x^2 + 2*b^2*c*d^2*x + 2*a*b*c*d^2 - a^2*d^3)*sinh(b*x + a)^2)*log(-I*cosh(b*x + a) - I*sinh(b*x + a) + 1) - 6*(d^3*cosh(b*x + a)^2 + 2*d^3*cosh(b*x + a)*sinh(b*x + a) + d^3*sinh(b*x + a)^2 + d^3)*polylog(3, I*cosh(b*x + a) + I*sinh(b*x + a)) - 6*(d^3*cosh(b*x + a)^2 + 2*d^3*cosh(b*x + a)*sinh(b*x + a) + d^3*sinh(b*x + a)^2 + d^3)*polylog(3, -I*cosh(b*x + a) - I*sinh(b*x + a)))/(b^4*cosh(b*x + a)^2 + 2*b^4*cosh(b*x + a)*sinh(b*x + a) + b^4*sinh(b*x + a)^2 + b^4)","C",0
32,1,715,0,0.613807," ","integrate((d*x+c)^2*sech(b*x+a)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2} - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + 2 \, a b c d - a^{2} d^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left(d^{2} \cosh\left(b x + a\right)^{2} + 2 \, d^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d^{2} \sinh\left(b x + a\right)^{2} + d^{2}\right)} {\rm Li}_2\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + {\left(d^{2} \cosh\left(b x + a\right)^{2} + 2 \, d^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d^{2} \sinh\left(b x + a\right)^{2} + d^{2}\right)} {\rm Li}_2\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + {\left(b c d - a d^{2} + {\left(b c d - a d^{2}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b c d - a d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b c d - a d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + i\right) + {\left(b c d - a d^{2} + {\left(b c d - a d^{2}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b c d - a d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b c d - a d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - i\right) + {\left(b d^{2} x + a d^{2} + {\left(b d^{2} x + a d^{2}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b d^{2} x + a d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b d^{2} x + a d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right) + 1\right) + {\left(b d^{2} x + a d^{2} + {\left(b d^{2} x + a d^{2}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b d^{2} x + a d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(b d^{2} x + a d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)} \log\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right) + 1\right)\right)}}{b^{3} \cosh\left(b x + a\right)^{2} + 2 \, b^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{3} \sinh\left(b x + a\right)^{2} + b^{3}}"," ",0,"-2*(b^2*c^2 - 2*a*b*c*d + a^2*d^2 - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cosh(b*x + a)^2 - 2*(b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*cosh(b*x + a)*sinh(b*x + a) - (b^2*d^2*x^2 + 2*b^2*c*d*x + 2*a*b*c*d - a^2*d^2)*sinh(b*x + a)^2 + (d^2*cosh(b*x + a)^2 + 2*d^2*cosh(b*x + a)*sinh(b*x + a) + d^2*sinh(b*x + a)^2 + d^2)*dilog(I*cosh(b*x + a) + I*sinh(b*x + a)) + (d^2*cosh(b*x + a)^2 + 2*d^2*cosh(b*x + a)*sinh(b*x + a) + d^2*sinh(b*x + a)^2 + d^2)*dilog(-I*cosh(b*x + a) - I*sinh(b*x + a)) + (b*c*d - a*d^2 + (b*c*d - a*d^2)*cosh(b*x + a)^2 + 2*(b*c*d - a*d^2)*cosh(b*x + a)*sinh(b*x + a) + (b*c*d - a*d^2)*sinh(b*x + a)^2)*log(cosh(b*x + a) + sinh(b*x + a) + I) + (b*c*d - a*d^2 + (b*c*d - a*d^2)*cosh(b*x + a)^2 + 2*(b*c*d - a*d^2)*cosh(b*x + a)*sinh(b*x + a) + (b*c*d - a*d^2)*sinh(b*x + a)^2)*log(cosh(b*x + a) + sinh(b*x + a) - I) + (b*d^2*x + a*d^2 + (b*d^2*x + a*d^2)*cosh(b*x + a)^2 + 2*(b*d^2*x + a*d^2)*cosh(b*x + a)*sinh(b*x + a) + (b*d^2*x + a*d^2)*sinh(b*x + a)^2)*log(I*cosh(b*x + a) + I*sinh(b*x + a) + 1) + (b*d^2*x + a*d^2 + (b*d^2*x + a*d^2)*cosh(b*x + a)^2 + 2*(b*d^2*x + a*d^2)*cosh(b*x + a)*sinh(b*x + a) + (b*d^2*x + a*d^2)*sinh(b*x + a)^2)*log(-I*cosh(b*x + a) - I*sinh(b*x + a) + 1))/(b^3*cosh(b*x + a)^2 + 2*b^3*cosh(b*x + a)*sinh(b*x + a) + b^3*sinh(b*x + a)^2 + b^3)","C",0
33,1,161,0,0.763586," ","integrate((d*x+c)*sech(b*x+a)^2,x, algorithm=""fricas"")","\frac{2 \, b d x \cosh\left(b x + a\right)^{2} + 4 \, b d x \cosh\left(b x + a\right) \sinh\left(b x + a\right) + 2 \, b d x \sinh\left(b x + a\right)^{2} - 2 \, b c - {\left(d \cosh\left(b x + a\right)^{2} + 2 \, d \cosh\left(b x + a\right) \sinh\left(b x + a\right) + d \sinh\left(b x + a\right)^{2} + d\right)} \log\left(\frac{2 \, \cosh\left(b x + a\right)}{\cosh\left(b x + a\right) - \sinh\left(b x + a\right)}\right)}{b^{2} \cosh\left(b x + a\right)^{2} + 2 \, b^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{2} \sinh\left(b x + a\right)^{2} + b^{2}}"," ",0,"(2*b*d*x*cosh(b*x + a)^2 + 4*b*d*x*cosh(b*x + a)*sinh(b*x + a) + 2*b*d*x*sinh(b*x + a)^2 - 2*b*c - (d*cosh(b*x + a)^2 + 2*d*cosh(b*x + a)*sinh(b*x + a) + d*sinh(b*x + a)^2 + d)*log(2*cosh(b*x + a)/(cosh(b*x + a) - sinh(b*x + a))))/(b^2*cosh(b*x + a)^2 + 2*b^2*cosh(b*x + a)*sinh(b*x + a) + b^2*sinh(b*x + a)^2 + b^2)","B",0
34,0,0,0,0.692374," ","integrate(sech(b*x+a)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(b x + a\right)^{2}}{d x + c}, x\right)"," ",0,"integral(sech(b*x + a)^2/(d*x + c), x)","F",0
35,0,0,0,2.443055," ","integrate(sech(b*x+a)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(b x + a\right)^{2}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(sech(b*x + a)^2/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
36,1,4735,0,1.215859," ","integrate((d*x+c)^3*sech(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} + 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b^{2} c d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} + 6 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} + 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b^{2} c d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + 2 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} + 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b^{2} c d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{3} - 2 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} - 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} - b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b^{2} c d^{2}\right)} x\right)} \cosh\left(b x + a\right) + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \cosh\left(b x + a\right)^{4} + {\left(12 i \, b^{2} d^{3} x^{2} + 24 i \, b^{2} c d^{2} x + 12 i \, b^{2} c^{2} d - 24 i \, d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(3 i \, b^{2} d^{3} x^{2} + 6 i \, b^{2} c d^{2} x + 3 i \, b^{2} c^{2} d - 6 i \, d^{3}\right)} \sinh\left(b x + a\right)^{4} - 6 i \, d^{3} + {\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d - 12 i \, d^{3}\right)} \cosh\left(b x + a\right)^{2} + {\left(6 i \, b^{2} d^{3} x^{2} + 12 i \, b^{2} c d^{2} x + 6 i \, b^{2} c^{2} d - 12 i \, d^{3} + {\left(18 i \, b^{2} d^{3} x^{2} + 36 i \, b^{2} c d^{2} x + 18 i \, b^{2} c^{2} d - 36 i \, d^{3}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(12 i \, b^{2} d^{3} x^{2} + 24 i \, b^{2} c d^{2} x + 12 i \, b^{2} c^{2} d - 24 i \, d^{3}\right)} \cosh\left(b x + a\right)^{3} + {\left(12 i \, b^{2} d^{3} x^{2} + 24 i \, b^{2} c d^{2} x + 12 i \, b^{2} c^{2} d - 24 i \, d^{3}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm Li}_2\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \cosh\left(b x + a\right)^{4} + {\left(-12 i \, b^{2} d^{3} x^{2} - 24 i \, b^{2} c d^{2} x - 12 i \, b^{2} c^{2} d + 24 i \, d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(-3 i \, b^{2} d^{3} x^{2} - 6 i \, b^{2} c d^{2} x - 3 i \, b^{2} c^{2} d + 6 i \, d^{3}\right)} \sinh\left(b x + a\right)^{4} + 6 i \, d^{3} + {\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d + 12 i \, d^{3}\right)} \cosh\left(b x + a\right)^{2} + {\left(-6 i \, b^{2} d^{3} x^{2} - 12 i \, b^{2} c d^{2} x - 6 i \, b^{2} c^{2} d + 12 i \, d^{3} + {\left(-18 i \, b^{2} d^{3} x^{2} - 36 i \, b^{2} c d^{2} x - 18 i \, b^{2} c^{2} d + 36 i \, d^{3}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(-12 i \, b^{2} d^{3} x^{2} - 24 i \, b^{2} c d^{2} x - 12 i \, b^{2} c^{2} d + 24 i \, d^{3}\right)} \cosh\left(b x + a\right)^{3} + {\left(-12 i \, b^{2} d^{3} x^{2} - 24 i \, b^{2} c d^{2} x - 12 i \, b^{2} c^{2} d + 24 i \, d^{3}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + {\left(i \, b^{3} c^{3} - 3 i \, a b^{2} c^{2} d + 3 i \, {\left(a^{2} - 2\right)} b c d^{2} + {\left(i \, b^{3} c^{3} - 3 i \, a b^{2} c^{2} d + 3 i \, {\left(a^{2} - 2\right)} b c d^{2} - i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{4} + {\left(4 i \, b^{3} c^{3} - 12 i \, a b^{2} c^{2} d + 12 i \, {\left(a^{2} - 2\right)} b c d^{2} - 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(i \, b^{3} c^{3} - 3 i \, a b^{2} c^{2} d + 3 i \, {\left(a^{2} - 2\right)} b c d^{2} - i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \sinh\left(b x + a\right)^{4} - i \, {\left(a^{3} - 6 \, a\right)} d^{3} + {\left(2 i \, b^{3} c^{3} - 6 i \, a b^{2} c^{2} d + 6 i \, {\left(a^{2} - 2\right)} b c d^{2} - 2 i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{2} + {\left(2 i \, b^{3} c^{3} - 6 i \, a b^{2} c^{2} d + 6 i \, {\left(a^{2} - 2\right)} b c d^{2} - 2 i \, {\left(a^{3} - 6 \, a\right)} d^{3} + {\left(6 i \, b^{3} c^{3} - 18 i \, a b^{2} c^{2} d + 18 i \, {\left(a^{2} - 2\right)} b c d^{2} - 6 i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(4 i \, b^{3} c^{3} - 12 i \, a b^{2} c^{2} d + 12 i \, {\left(a^{2} - 2\right)} b c d^{2} - 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{3} + {\left(4 i \, b^{3} c^{3} - 12 i \, a b^{2} c^{2} d + 12 i \, {\left(a^{2} - 2\right)} b c d^{2} - 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + i\right) + {\left(-i \, b^{3} c^{3} + 3 i \, a b^{2} c^{2} d - 3 i \, {\left(a^{2} - 2\right)} b c d^{2} + {\left(-i \, b^{3} c^{3} + 3 i \, a b^{2} c^{2} d - 3 i \, {\left(a^{2} - 2\right)} b c d^{2} + i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{4} + {\left(-4 i \, b^{3} c^{3} + 12 i \, a b^{2} c^{2} d - 12 i \, {\left(a^{2} - 2\right)} b c d^{2} + 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(-i \, b^{3} c^{3} + 3 i \, a b^{2} c^{2} d - 3 i \, {\left(a^{2} - 2\right)} b c d^{2} + i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \sinh\left(b x + a\right)^{4} + i \, {\left(a^{3} - 6 \, a\right)} d^{3} + {\left(-2 i \, b^{3} c^{3} + 6 i \, a b^{2} c^{2} d - 6 i \, {\left(a^{2} - 2\right)} b c d^{2} + 2 i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{2} + {\left(-2 i \, b^{3} c^{3} + 6 i \, a b^{2} c^{2} d - 6 i \, {\left(a^{2} - 2\right)} b c d^{2} + 2 i \, {\left(a^{3} - 6 \, a\right)} d^{3} + {\left(-6 i \, b^{3} c^{3} + 18 i \, a b^{2} c^{2} d - 18 i \, {\left(a^{2} - 2\right)} b c d^{2} + 6 i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(-4 i \, b^{3} c^{3} + 12 i \, a b^{2} c^{2} d - 12 i \, {\left(a^{2} - 2\right)} b c d^{2} + 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)^{3} + {\left(-4 i \, b^{3} c^{3} + 12 i \, a b^{2} c^{2} d - 12 i \, {\left(a^{2} - 2\right)} b c d^{2} + 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - i\right) + {\left(-i \, b^{3} d^{3} x^{3} - 3 i \, b^{3} c d^{2} x^{2} - 3 i \, a b^{2} c^{2} d + 3 i \, a^{2} b c d^{2} + {\left(-i \, b^{3} d^{3} x^{3} - 3 i \, b^{3} c d^{2} x^{2} - 3 i \, a b^{2} c^{2} d + 3 i \, a^{2} b c d^{2} - i \, {\left(a^{3} - 6 \, a\right)} d^{3} - 3 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{4} + {\left(-4 i \, b^{3} d^{3} x^{3} - 12 i \, b^{3} c d^{2} x^{2} - 12 i \, a b^{2} c^{2} d + 12 i \, a^{2} b c d^{2} - 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3} - 12 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(-i \, b^{3} d^{3} x^{3} - 3 i \, b^{3} c d^{2} x^{2} - 3 i \, a b^{2} c^{2} d + 3 i \, a^{2} b c d^{2} - i \, {\left(a^{3} - 6 \, a\right)} d^{3} - 3 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{4} - i \, {\left(a^{3} - 6 \, a\right)} d^{3} + {\left(-2 i \, b^{3} d^{3} x^{3} - 6 i \, b^{3} c d^{2} x^{2} - 6 i \, a b^{2} c^{2} d + 6 i \, a^{2} b c d^{2} - 2 i \, {\left(a^{3} - 6 \, a\right)} d^{3} - 6 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2} + {\left(-2 i \, b^{3} d^{3} x^{3} - 6 i \, b^{3} c d^{2} x^{2} - 6 i \, a b^{2} c^{2} d + 6 i \, a^{2} b c d^{2} - 2 i \, {\left(a^{3} - 6 \, a\right)} d^{3} + {\left(-6 i \, b^{3} d^{3} x^{3} - 18 i \, b^{3} c d^{2} x^{2} - 18 i \, a b^{2} c^{2} d + 18 i \, a^{2} b c d^{2} - 6 i \, {\left(a^{3} - 6 \, a\right)} d^{3} - 18 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2} - 6 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{2} - 3 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x + {\left({\left(-4 i \, b^{3} d^{3} x^{3} - 12 i \, b^{3} c d^{2} x^{2} - 12 i \, a b^{2} c^{2} d + 12 i \, a^{2} b c d^{2} - 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3} - 12 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{3} + {\left(-4 i \, b^{3} d^{3} x^{3} - 12 i \, b^{3} c d^{2} x^{2} - 12 i \, a b^{2} c^{2} d + 12 i \, a^{2} b c d^{2} - 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3} - 12 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right) + 1\right) + {\left(i \, b^{3} d^{3} x^{3} + 3 i \, b^{3} c d^{2} x^{2} + 3 i \, a b^{2} c^{2} d - 3 i \, a^{2} b c d^{2} + {\left(i \, b^{3} d^{3} x^{3} + 3 i \, b^{3} c d^{2} x^{2} + 3 i \, a b^{2} c^{2} d - 3 i \, a^{2} b c d^{2} + i \, {\left(a^{3} - 6 \, a\right)} d^{3} + 3 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{4} + {\left(4 i \, b^{3} d^{3} x^{3} + 12 i \, b^{3} c d^{2} x^{2} + 12 i \, a b^{2} c^{2} d - 12 i \, a^{2} b c d^{2} + 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3} + 12 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(i \, b^{3} d^{3} x^{3} + 3 i \, b^{3} c d^{2} x^{2} + 3 i \, a b^{2} c^{2} d - 3 i \, a^{2} b c d^{2} + i \, {\left(a^{3} - 6 \, a\right)} d^{3} + 3 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{4} + i \, {\left(a^{3} - 6 \, a\right)} d^{3} + {\left(2 i \, b^{3} d^{3} x^{3} + 6 i \, b^{3} c d^{2} x^{2} + 6 i \, a b^{2} c^{2} d - 6 i \, a^{2} b c d^{2} + 2 i \, {\left(a^{3} - 6 \, a\right)} d^{3} + 6 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2} + {\left(2 i \, b^{3} d^{3} x^{3} + 6 i \, b^{3} c d^{2} x^{2} + 6 i \, a b^{2} c^{2} d - 6 i \, a^{2} b c d^{2} + 2 i \, {\left(a^{3} - 6 \, a\right)} d^{3} + {\left(6 i \, b^{3} d^{3} x^{3} + 18 i \, b^{3} c d^{2} x^{2} + 18 i \, a b^{2} c^{2} d - 18 i \, a^{2} b c d^{2} + 6 i \, {\left(a^{3} - 6 \, a\right)} d^{3} + 18 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 6 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{2} + 3 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x + {\left({\left(4 i \, b^{3} d^{3} x^{3} + 12 i \, b^{3} c d^{2} x^{2} + 12 i \, a b^{2} c^{2} d - 12 i \, a^{2} b c d^{2} + 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3} + 12 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{3} + {\left(4 i \, b^{3} d^{3} x^{3} + 12 i \, b^{3} c d^{2} x^{2} + 12 i \, a b^{2} c^{2} d - 12 i \, a^{2} b c d^{2} + 4 i \, {\left(a^{3} - 6 \, a\right)} d^{3} + 12 i \, {\left(b^{3} c^{2} d - 2 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right) + 1\right) + {\left(6 i \, d^{3} \cosh\left(b x + a\right)^{4} + 24 i \, d^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + 6 i \, d^{3} \sinh\left(b x + a\right)^{4} + 12 i \, d^{3} \cosh\left(b x + a\right)^{2} + 6 i \, d^{3} + {\left(36 i \, d^{3} \cosh\left(b x + a\right)^{2} + 12 i \, d^{3}\right)} \sinh\left(b x + a\right)^{2} + {\left(24 i \, d^{3} \cosh\left(b x + a\right)^{3} + 24 i \, d^{3} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm polylog}\left(4, i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + {\left(-6 i \, d^{3} \cosh\left(b x + a\right)^{4} - 24 i \, d^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - 6 i \, d^{3} \sinh\left(b x + a\right)^{4} - 12 i \, d^{3} \cosh\left(b x + a\right)^{2} - 6 i \, d^{3} + {\left(-36 i \, d^{3} \cosh\left(b x + a\right)^{2} - 12 i \, d^{3}\right)} \sinh\left(b x + a\right)^{2} + {\left(-24 i \, d^{3} \cosh\left(b x + a\right)^{3} - 24 i \, d^{3} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm polylog}\left(4, -i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + {\left(-6 i \, b d^{3} x + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \cosh\left(b x + a\right)^{4} + {\left(-24 i \, b d^{3} x - 24 i \, b c d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(-6 i \, b d^{3} x - 6 i \, b c d^{2}\right)} \sinh\left(b x + a\right)^{4} - 6 i \, b c d^{2} + {\left(-12 i \, b d^{3} x - 12 i \, b c d^{2}\right)} \cosh\left(b x + a\right)^{2} + {\left(-12 i \, b d^{3} x - 12 i \, b c d^{2} + {\left(-36 i \, b d^{3} x - 36 i \, b c d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(-24 i \, b d^{3} x - 24 i \, b c d^{2}\right)} \cosh\left(b x + a\right)^{3} + {\left(-24 i \, b d^{3} x - 24 i \, b c d^{2}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + {\left(6 i \, b d^{3} x + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \cosh\left(b x + a\right)^{4} + {\left(24 i \, b d^{3} x + 24 i \, b c d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(6 i \, b d^{3} x + 6 i \, b c d^{2}\right)} \sinh\left(b x + a\right)^{4} + 6 i \, b c d^{2} + {\left(12 i \, b d^{3} x + 12 i \, b c d^{2}\right)} \cosh\left(b x + a\right)^{2} + {\left(12 i \, b d^{3} x + 12 i \, b c d^{2} + {\left(36 i \, b d^{3} x + 36 i \, b c d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(24 i \, b d^{3} x + 24 i \, b c d^{2}\right)} \cosh\left(b x + a\right)^{3} + {\left(24 i \, b d^{3} x + 24 i \, b c d^{2}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) - 2 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} - 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} - b^{2} d^{3}\right)} x^{2} - 3 \, {\left(b^{3} d^{3} x^{3} + b^{3} c^{3} + 3 \, b^{2} c^{2} d + 3 \, {\left(b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 3 \, {\left(b^{3} c^{2} d + 2 \, b^{2} c d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 3 \, {\left(b^{3} c^{2} d - 2 \, b^{2} c d^{2}\right)} x\right)} \sinh\left(b x + a\right)}{2 \, {\left(b^{4} \cosh\left(b x + a\right)^{4} + 4 \, b^{4} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b^{4} \sinh\left(b x + a\right)^{4} + 2 \, b^{4} \cosh\left(b x + a\right)^{2} + b^{4} + 2 \, {\left(3 \, b^{4} \cosh\left(b x + a\right)^{2} + b^{4}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(b^{4} \cosh\left(b x + a\right)^{3} + b^{4} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"1/2*(2*(b^3*d^3*x^3 + b^3*c^3 + 3*b^2*c^2*d + 3*(b^3*c*d^2 + b^2*d^3)*x^2 + 3*(b^3*c^2*d + 2*b^2*c*d^2)*x)*cosh(b*x + a)^3 + 6*(b^3*d^3*x^3 + b^3*c^3 + 3*b^2*c^2*d + 3*(b^3*c*d^2 + b^2*d^3)*x^2 + 3*(b^3*c^2*d + 2*b^2*c*d^2)*x)*cosh(b*x + a)*sinh(b*x + a)^2 + 2*(b^3*d^3*x^3 + b^3*c^3 + 3*b^2*c^2*d + 3*(b^3*c*d^2 + b^2*d^3)*x^2 + 3*(b^3*c^2*d + 2*b^2*c*d^2)*x)*sinh(b*x + a)^3 - 2*(b^3*d^3*x^3 + b^3*c^3 - 3*b^2*c^2*d + 3*(b^3*c*d^2 - b^2*d^3)*x^2 + 3*(b^3*c^2*d - 2*b^2*c*d^2)*x)*cosh(b*x + a) + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d - 6*I*d^3)*cosh(b*x + a)^4 + (12*I*b^2*d^3*x^2 + 24*I*b^2*c*d^2*x + 12*I*b^2*c^2*d - 24*I*d^3)*cosh(b*x + a)*sinh(b*x + a)^3 + (3*I*b^2*d^3*x^2 + 6*I*b^2*c*d^2*x + 3*I*b^2*c^2*d - 6*I*d^3)*sinh(b*x + a)^4 - 6*I*d^3 + (6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d - 12*I*d^3)*cosh(b*x + a)^2 + (6*I*b^2*d^3*x^2 + 12*I*b^2*c*d^2*x + 6*I*b^2*c^2*d - 12*I*d^3 + (18*I*b^2*d^3*x^2 + 36*I*b^2*c*d^2*x + 18*I*b^2*c^2*d - 36*I*d^3)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((12*I*b^2*d^3*x^2 + 24*I*b^2*c*d^2*x + 12*I*b^2*c^2*d - 24*I*d^3)*cosh(b*x + a)^3 + (12*I*b^2*d^3*x^2 + 24*I*b^2*c*d^2*x + 12*I*b^2*c^2*d - 24*I*d^3)*cosh(b*x + a))*sinh(b*x + a))*dilog(I*cosh(b*x + a) + I*sinh(b*x + a)) + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + 6*I*d^3)*cosh(b*x + a)^4 + (-12*I*b^2*d^3*x^2 - 24*I*b^2*c*d^2*x - 12*I*b^2*c^2*d + 24*I*d^3)*cosh(b*x + a)*sinh(b*x + a)^3 + (-3*I*b^2*d^3*x^2 - 6*I*b^2*c*d^2*x - 3*I*b^2*c^2*d + 6*I*d^3)*sinh(b*x + a)^4 + 6*I*d^3 + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d + 12*I*d^3)*cosh(b*x + a)^2 + (-6*I*b^2*d^3*x^2 - 12*I*b^2*c*d^2*x - 6*I*b^2*c^2*d + 12*I*d^3 + (-18*I*b^2*d^3*x^2 - 36*I*b^2*c*d^2*x - 18*I*b^2*c^2*d + 36*I*d^3)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((-12*I*b^2*d^3*x^2 - 24*I*b^2*c*d^2*x - 12*I*b^2*c^2*d + 24*I*d^3)*cosh(b*x + a)^3 + (-12*I*b^2*d^3*x^2 - 24*I*b^2*c*d^2*x - 12*I*b^2*c^2*d + 24*I*d^3)*cosh(b*x + a))*sinh(b*x + a))*dilog(-I*cosh(b*x + a) - I*sinh(b*x + a)) + (I*b^3*c^3 - 3*I*a*b^2*c^2*d + 3*I*(a^2 - 2)*b*c*d^2 + (I*b^3*c^3 - 3*I*a*b^2*c^2*d + 3*I*(a^2 - 2)*b*c*d^2 - I*(a^3 - 6*a)*d^3)*cosh(b*x + a)^4 + (4*I*b^3*c^3 - 12*I*a*b^2*c^2*d + 12*I*(a^2 - 2)*b*c*d^2 - 4*I*(a^3 - 6*a)*d^3)*cosh(b*x + a)*sinh(b*x + a)^3 + (I*b^3*c^3 - 3*I*a*b^2*c^2*d + 3*I*(a^2 - 2)*b*c*d^2 - I*(a^3 - 6*a)*d^3)*sinh(b*x + a)^4 - I*(a^3 - 6*a)*d^3 + (2*I*b^3*c^3 - 6*I*a*b^2*c^2*d + 6*I*(a^2 - 2)*b*c*d^2 - 2*I*(a^3 - 6*a)*d^3)*cosh(b*x + a)^2 + (2*I*b^3*c^3 - 6*I*a*b^2*c^2*d + 6*I*(a^2 - 2)*b*c*d^2 - 2*I*(a^3 - 6*a)*d^3 + (6*I*b^3*c^3 - 18*I*a*b^2*c^2*d + 18*I*(a^2 - 2)*b*c*d^2 - 6*I*(a^3 - 6*a)*d^3)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((4*I*b^3*c^3 - 12*I*a*b^2*c^2*d + 12*I*(a^2 - 2)*b*c*d^2 - 4*I*(a^3 - 6*a)*d^3)*cosh(b*x + a)^3 + (4*I*b^3*c^3 - 12*I*a*b^2*c^2*d + 12*I*(a^2 - 2)*b*c*d^2 - 4*I*(a^3 - 6*a)*d^3)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) + I) + (-I*b^3*c^3 + 3*I*a*b^2*c^2*d - 3*I*(a^2 - 2)*b*c*d^2 + (-I*b^3*c^3 + 3*I*a*b^2*c^2*d - 3*I*(a^2 - 2)*b*c*d^2 + I*(a^3 - 6*a)*d^3)*cosh(b*x + a)^4 + (-4*I*b^3*c^3 + 12*I*a*b^2*c^2*d - 12*I*(a^2 - 2)*b*c*d^2 + 4*I*(a^3 - 6*a)*d^3)*cosh(b*x + a)*sinh(b*x + a)^3 + (-I*b^3*c^3 + 3*I*a*b^2*c^2*d - 3*I*(a^2 - 2)*b*c*d^2 + I*(a^3 - 6*a)*d^3)*sinh(b*x + a)^4 + I*(a^3 - 6*a)*d^3 + (-2*I*b^3*c^3 + 6*I*a*b^2*c^2*d - 6*I*(a^2 - 2)*b*c*d^2 + 2*I*(a^3 - 6*a)*d^3)*cosh(b*x + a)^2 + (-2*I*b^3*c^3 + 6*I*a*b^2*c^2*d - 6*I*(a^2 - 2)*b*c*d^2 + 2*I*(a^3 - 6*a)*d^3 + (-6*I*b^3*c^3 + 18*I*a*b^2*c^2*d - 18*I*(a^2 - 2)*b*c*d^2 + 6*I*(a^3 - 6*a)*d^3)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((-4*I*b^3*c^3 + 12*I*a*b^2*c^2*d - 12*I*(a^2 - 2)*b*c*d^2 + 4*I*(a^3 - 6*a)*d^3)*cosh(b*x + a)^3 + (-4*I*b^3*c^3 + 12*I*a*b^2*c^2*d - 12*I*(a^2 - 2)*b*c*d^2 + 4*I*(a^3 - 6*a)*d^3)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) - I) + (-I*b^3*d^3*x^3 - 3*I*b^3*c*d^2*x^2 - 3*I*a*b^2*c^2*d + 3*I*a^2*b*c*d^2 + (-I*b^3*d^3*x^3 - 3*I*b^3*c*d^2*x^2 - 3*I*a*b^2*c^2*d + 3*I*a^2*b*c*d^2 - I*(a^3 - 6*a)*d^3 - 3*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^4 + (-4*I*b^3*d^3*x^3 - 12*I*b^3*c*d^2*x^2 - 12*I*a*b^2*c^2*d + 12*I*a^2*b*c*d^2 - 4*I*(a^3 - 6*a)*d^3 - 12*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)*sinh(b*x + a)^3 + (-I*b^3*d^3*x^3 - 3*I*b^3*c*d^2*x^2 - 3*I*a*b^2*c^2*d + 3*I*a^2*b*c*d^2 - I*(a^3 - 6*a)*d^3 - 3*I*(b^3*c^2*d - 2*b*d^3)*x)*sinh(b*x + a)^4 - I*(a^3 - 6*a)*d^3 + (-2*I*b^3*d^3*x^3 - 6*I*b^3*c*d^2*x^2 - 6*I*a*b^2*c^2*d + 6*I*a^2*b*c*d^2 - 2*I*(a^3 - 6*a)*d^3 - 6*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^2 + (-2*I*b^3*d^3*x^3 - 6*I*b^3*c*d^2*x^2 - 6*I*a*b^2*c^2*d + 6*I*a^2*b*c*d^2 - 2*I*(a^3 - 6*a)*d^3 + (-6*I*b^3*d^3*x^3 - 18*I*b^3*c*d^2*x^2 - 18*I*a*b^2*c^2*d + 18*I*a^2*b*c*d^2 - 6*I*(a^3 - 6*a)*d^3 - 18*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^2 - 6*I*(b^3*c^2*d - 2*b*d^3)*x)*sinh(b*x + a)^2 - 3*I*(b^3*c^2*d - 2*b*d^3)*x + ((-4*I*b^3*d^3*x^3 - 12*I*b^3*c*d^2*x^2 - 12*I*a*b^2*c^2*d + 12*I*a^2*b*c*d^2 - 4*I*(a^3 - 6*a)*d^3 - 12*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^3 + (-4*I*b^3*d^3*x^3 - 12*I*b^3*c*d^2*x^2 - 12*I*a*b^2*c^2*d + 12*I*a^2*b*c*d^2 - 4*I*(a^3 - 6*a)*d^3 - 12*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a))*sinh(b*x + a))*log(I*cosh(b*x + a) + I*sinh(b*x + a) + 1) + (I*b^3*d^3*x^3 + 3*I*b^3*c*d^2*x^2 + 3*I*a*b^2*c^2*d - 3*I*a^2*b*c*d^2 + (I*b^3*d^3*x^3 + 3*I*b^3*c*d^2*x^2 + 3*I*a*b^2*c^2*d - 3*I*a^2*b*c*d^2 + I*(a^3 - 6*a)*d^3 + 3*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^4 + (4*I*b^3*d^3*x^3 + 12*I*b^3*c*d^2*x^2 + 12*I*a*b^2*c^2*d - 12*I*a^2*b*c*d^2 + 4*I*(a^3 - 6*a)*d^3 + 12*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)*sinh(b*x + a)^3 + (I*b^3*d^3*x^3 + 3*I*b^3*c*d^2*x^2 + 3*I*a*b^2*c^2*d - 3*I*a^2*b*c*d^2 + I*(a^3 - 6*a)*d^3 + 3*I*(b^3*c^2*d - 2*b*d^3)*x)*sinh(b*x + a)^4 + I*(a^3 - 6*a)*d^3 + (2*I*b^3*d^3*x^3 + 6*I*b^3*c*d^2*x^2 + 6*I*a*b^2*c^2*d - 6*I*a^2*b*c*d^2 + 2*I*(a^3 - 6*a)*d^3 + 6*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^2 + (2*I*b^3*d^3*x^3 + 6*I*b^3*c*d^2*x^2 + 6*I*a*b^2*c^2*d - 6*I*a^2*b*c*d^2 + 2*I*(a^3 - 6*a)*d^3 + (6*I*b^3*d^3*x^3 + 18*I*b^3*c*d^2*x^2 + 18*I*a*b^2*c^2*d - 18*I*a^2*b*c*d^2 + 6*I*(a^3 - 6*a)*d^3 + 18*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^2 + 6*I*(b^3*c^2*d - 2*b*d^3)*x)*sinh(b*x + a)^2 + 3*I*(b^3*c^2*d - 2*b*d^3)*x + ((4*I*b^3*d^3*x^3 + 12*I*b^3*c*d^2*x^2 + 12*I*a*b^2*c^2*d - 12*I*a^2*b*c*d^2 + 4*I*(a^3 - 6*a)*d^3 + 12*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a)^3 + (4*I*b^3*d^3*x^3 + 12*I*b^3*c*d^2*x^2 + 12*I*a*b^2*c^2*d - 12*I*a^2*b*c*d^2 + 4*I*(a^3 - 6*a)*d^3 + 12*I*(b^3*c^2*d - 2*b*d^3)*x)*cosh(b*x + a))*sinh(b*x + a))*log(-I*cosh(b*x + a) - I*sinh(b*x + a) + 1) + (6*I*d^3*cosh(b*x + a)^4 + 24*I*d^3*cosh(b*x + a)*sinh(b*x + a)^3 + 6*I*d^3*sinh(b*x + a)^4 + 12*I*d^3*cosh(b*x + a)^2 + 6*I*d^3 + (36*I*d^3*cosh(b*x + a)^2 + 12*I*d^3)*sinh(b*x + a)^2 + (24*I*d^3*cosh(b*x + a)^3 + 24*I*d^3*cosh(b*x + a))*sinh(b*x + a))*polylog(4, I*cosh(b*x + a) + I*sinh(b*x + a)) + (-6*I*d^3*cosh(b*x + a)^4 - 24*I*d^3*cosh(b*x + a)*sinh(b*x + a)^3 - 6*I*d^3*sinh(b*x + a)^4 - 12*I*d^3*cosh(b*x + a)^2 - 6*I*d^3 + (-36*I*d^3*cosh(b*x + a)^2 - 12*I*d^3)*sinh(b*x + a)^2 + (-24*I*d^3*cosh(b*x + a)^3 - 24*I*d^3*cosh(b*x + a))*sinh(b*x + a))*polylog(4, -I*cosh(b*x + a) - I*sinh(b*x + a)) + (-6*I*b*d^3*x + (-6*I*b*d^3*x - 6*I*b*c*d^2)*cosh(b*x + a)^4 + (-24*I*b*d^3*x - 24*I*b*c*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (-6*I*b*d^3*x - 6*I*b*c*d^2)*sinh(b*x + a)^4 - 6*I*b*c*d^2 + (-12*I*b*d^3*x - 12*I*b*c*d^2)*cosh(b*x + a)^2 + (-12*I*b*d^3*x - 12*I*b*c*d^2 + (-36*I*b*d^3*x - 36*I*b*c*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((-24*I*b*d^3*x - 24*I*b*c*d^2)*cosh(b*x + a)^3 + (-24*I*b*d^3*x - 24*I*b*c*d^2)*cosh(b*x + a))*sinh(b*x + a))*polylog(3, I*cosh(b*x + a) + I*sinh(b*x + a)) + (6*I*b*d^3*x + (6*I*b*d^3*x + 6*I*b*c*d^2)*cosh(b*x + a)^4 + (24*I*b*d^3*x + 24*I*b*c*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (6*I*b*d^3*x + 6*I*b*c*d^2)*sinh(b*x + a)^4 + 6*I*b*c*d^2 + (12*I*b*d^3*x + 12*I*b*c*d^2)*cosh(b*x + a)^2 + (12*I*b*d^3*x + 12*I*b*c*d^2 + (36*I*b*d^3*x + 36*I*b*c*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((24*I*b*d^3*x + 24*I*b*c*d^2)*cosh(b*x + a)^3 + (24*I*b*d^3*x + 24*I*b*c*d^2)*cosh(b*x + a))*sinh(b*x + a))*polylog(3, -I*cosh(b*x + a) - I*sinh(b*x + a)) - 2*(b^3*d^3*x^3 + b^3*c^3 - 3*b^2*c^2*d + 3*(b^3*c*d^2 - b^2*d^3)*x^2 - 3*(b^3*d^3*x^3 + b^3*c^3 + 3*b^2*c^2*d + 3*(b^3*c*d^2 + b^2*d^3)*x^2 + 3*(b^3*c^2*d + 2*b^2*c*d^2)*x)*cosh(b*x + a)^2 + 3*(b^3*c^2*d - 2*b^2*c*d^2)*x)*sinh(b*x + a))/(b^4*cosh(b*x + a)^4 + 4*b^4*cosh(b*x + a)*sinh(b*x + a)^3 + b^4*sinh(b*x + a)^4 + 2*b^4*cosh(b*x + a)^2 + b^4 + 2*(3*b^4*cosh(b*x + a)^2 + b^4)*sinh(b*x + a)^2 + 4*(b^4*cosh(b*x + a)^3 + b^4*cosh(b*x + a))*sinh(b*x + a))","C",0
37,1,2613,0,1.267058," ","integrate((d*x+c)^2*sech(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 \, b c d + 2 \, {\left(b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} + 6 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 \, b c d + 2 \, {\left(b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + 2 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 \, b c d + 2 \, {\left(b^{2} c d + b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{3} - 2 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} - 2 \, b c d + 2 \, {\left(b^{2} c d - b d^{2}\right)} x\right)} \cosh\left(b x + a\right) + {\left({\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \cosh\left(b x + a\right)^{4} + {\left(8 i \, b d^{2} x + 8 i \, b c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(2 i \, b d^{2} x + 2 i \, b c d\right)} \sinh\left(b x + a\right)^{4} + 2 i \, b d^{2} x + 2 i \, b c d + {\left(4 i \, b d^{2} x + 4 i \, b c d\right)} \cosh\left(b x + a\right)^{2} + {\left(4 i \, b d^{2} x + 4 i \, b c d + {\left(12 i \, b d^{2} x + 12 i \, b c d\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(8 i \, b d^{2} x + 8 i \, b c d\right)} \cosh\left(b x + a\right)^{3} + {\left(8 i \, b d^{2} x + 8 i \, b c d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm Li}_2\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + {\left({\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \cosh\left(b x + a\right)^{4} + {\left(-8 i \, b d^{2} x - 8 i \, b c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(-2 i \, b d^{2} x - 2 i \, b c d\right)} \sinh\left(b x + a\right)^{4} - 2 i \, b d^{2} x - 2 i \, b c d + {\left(-4 i \, b d^{2} x - 4 i \, b c d\right)} \cosh\left(b x + a\right)^{2} + {\left(-4 i \, b d^{2} x - 4 i \, b c d + {\left(-12 i \, b d^{2} x - 12 i \, b c d\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(-8 i \, b d^{2} x - 8 i \, b c d\right)} \cosh\left(b x + a\right)^{3} + {\left(-8 i \, b d^{2} x - 8 i \, b c d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm Li}_2\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + {\left({\left(i \, b^{2} c^{2} - 2 i \, a b c d + i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{4} + {\left(4 i \, b^{2} c^{2} - 8 i \, a b c d + 4 i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(i \, b^{2} c^{2} - 2 i \, a b c d + i \, {\left(a^{2} - 2\right)} d^{2}\right)} \sinh\left(b x + a\right)^{4} + i \, b^{2} c^{2} - 2 i \, a b c d + i \, {\left(a^{2} - 2\right)} d^{2} + {\left(2 i \, b^{2} c^{2} - 4 i \, a b c d + 2 i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{2} + {\left(2 i \, b^{2} c^{2} - 4 i \, a b c d + 2 i \, {\left(a^{2} - 2\right)} d^{2} + {\left(6 i \, b^{2} c^{2} - 12 i \, a b c d + 6 i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(4 i \, b^{2} c^{2} - 8 i \, a b c d + 4 i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{3} + {\left(4 i \, b^{2} c^{2} - 8 i \, a b c d + 4 i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + i\right) + {\left({\left(-i \, b^{2} c^{2} + 2 i \, a b c d - i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{4} + {\left(-4 i \, b^{2} c^{2} + 8 i \, a b c d - 4 i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(-i \, b^{2} c^{2} + 2 i \, a b c d - i \, {\left(a^{2} - 2\right)} d^{2}\right)} \sinh\left(b x + a\right)^{4} - i \, b^{2} c^{2} + 2 i \, a b c d - i \, {\left(a^{2} - 2\right)} d^{2} + {\left(-2 i \, b^{2} c^{2} + 4 i \, a b c d - 2 i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{2} + {\left(-2 i \, b^{2} c^{2} + 4 i \, a b c d - 2 i \, {\left(a^{2} - 2\right)} d^{2} + {\left(-6 i \, b^{2} c^{2} + 12 i \, a b c d - 6 i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(-4 i \, b^{2} c^{2} + 8 i \, a b c d - 4 i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)^{3} + {\left(-4 i \, b^{2} c^{2} + 8 i \, a b c d - 4 i \, {\left(a^{2} - 2\right)} d^{2}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - i\right) + {\left(-i \, b^{2} d^{2} x^{2} - 2 i \, b^{2} c d x + {\left(-i \, b^{2} d^{2} x^{2} - 2 i \, b^{2} c d x - 2 i \, a b c d + i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{4} + {\left(-4 i \, b^{2} d^{2} x^{2} - 8 i \, b^{2} c d x - 8 i \, a b c d + 4 i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(-i \, b^{2} d^{2} x^{2} - 2 i \, b^{2} c d x - 2 i \, a b c d + i \, a^{2} d^{2}\right)} \sinh\left(b x + a\right)^{4} - 2 i \, a b c d + i \, a^{2} d^{2} + {\left(-2 i \, b^{2} d^{2} x^{2} - 4 i \, b^{2} c d x - 4 i \, a b c d + 2 i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2} + {\left(-2 i \, b^{2} d^{2} x^{2} - 4 i \, b^{2} c d x - 4 i \, a b c d + 2 i \, a^{2} d^{2} + {\left(-6 i \, b^{2} d^{2} x^{2} - 12 i \, b^{2} c d x - 12 i \, a b c d + 6 i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(-4 i \, b^{2} d^{2} x^{2} - 8 i \, b^{2} c d x - 8 i \, a b c d + 4 i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{3} + {\left(-4 i \, b^{2} d^{2} x^{2} - 8 i \, b^{2} c d x - 8 i \, a b c d + 4 i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right) + 1\right) + {\left(i \, b^{2} d^{2} x^{2} + 2 i \, b^{2} c d x + {\left(i \, b^{2} d^{2} x^{2} + 2 i \, b^{2} c d x + 2 i \, a b c d - i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{4} + {\left(4 i \, b^{2} d^{2} x^{2} + 8 i \, b^{2} c d x + 8 i \, a b c d - 4 i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(i \, b^{2} d^{2} x^{2} + 2 i \, b^{2} c d x + 2 i \, a b c d - i \, a^{2} d^{2}\right)} \sinh\left(b x + a\right)^{4} + 2 i \, a b c d - i \, a^{2} d^{2} + {\left(2 i \, b^{2} d^{2} x^{2} + 4 i \, b^{2} c d x + 4 i \, a b c d - 2 i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2} + {\left(2 i \, b^{2} d^{2} x^{2} + 4 i \, b^{2} c d x + 4 i \, a b c d - 2 i \, a^{2} d^{2} + {\left(6 i \, b^{2} d^{2} x^{2} + 12 i \, b^{2} c d x + 12 i \, a b c d - 6 i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + {\left({\left(4 i \, b^{2} d^{2} x^{2} + 8 i \, b^{2} c d x + 8 i \, a b c d - 4 i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right)^{3} + {\left(4 i \, b^{2} d^{2} x^{2} + 8 i \, b^{2} c d x + 8 i \, a b c d - 4 i \, a^{2} d^{2}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right) + 1\right) + {\left(-2 i \, d^{2} \cosh\left(b x + a\right)^{4} - 8 i \, d^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - 2 i \, d^{2} \sinh\left(b x + a\right)^{4} - 4 i \, d^{2} \cosh\left(b x + a\right)^{2} + {\left(-12 i \, d^{2} \cosh\left(b x + a\right)^{2} - 4 i \, d^{2}\right)} \sinh\left(b x + a\right)^{2} - 2 i \, d^{2} + {\left(-8 i \, d^{2} \cosh\left(b x + a\right)^{3} - 8 i \, d^{2} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm polylog}\left(3, i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + {\left(2 i \, d^{2} \cosh\left(b x + a\right)^{4} + 8 i \, d^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + 2 i \, d^{2} \sinh\left(b x + a\right)^{4} + 4 i \, d^{2} \cosh\left(b x + a\right)^{2} + {\left(12 i \, d^{2} \cosh\left(b x + a\right)^{2} + 4 i \, d^{2}\right)} \sinh\left(b x + a\right)^{2} + 2 i \, d^{2} + {\left(8 i \, d^{2} \cosh\left(b x + a\right)^{3} + 8 i \, d^{2} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} {\rm polylog}\left(3, -i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) - 2 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} - 2 \, b c d - 3 \, {\left(b^{2} d^{2} x^{2} + b^{2} c^{2} + 2 \, b c d + 2 \, {\left(b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(b^{2} c d - b d^{2}\right)} x\right)} \sinh\left(b x + a\right)}{2 \, {\left(b^{3} \cosh\left(b x + a\right)^{4} + 4 \, b^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b^{3} \sinh\left(b x + a\right)^{4} + 2 \, b^{3} \cosh\left(b x + a\right)^{2} + b^{3} + 2 \, {\left(3 \, b^{3} \cosh\left(b x + a\right)^{2} + b^{3}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(b^{3} \cosh\left(b x + a\right)^{3} + b^{3} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"1/2*(2*(b^2*d^2*x^2 + b^2*c^2 + 2*b*c*d + 2*(b^2*c*d + b*d^2)*x)*cosh(b*x + a)^3 + 6*(b^2*d^2*x^2 + b^2*c^2 + 2*b*c*d + 2*(b^2*c*d + b*d^2)*x)*cosh(b*x + a)*sinh(b*x + a)^2 + 2*(b^2*d^2*x^2 + b^2*c^2 + 2*b*c*d + 2*(b^2*c*d + b*d^2)*x)*sinh(b*x + a)^3 - 2*(b^2*d^2*x^2 + b^2*c^2 - 2*b*c*d + 2*(b^2*c*d - b*d^2)*x)*cosh(b*x + a) + ((2*I*b*d^2*x + 2*I*b*c*d)*cosh(b*x + a)^4 + (8*I*b*d^2*x + 8*I*b*c*d)*cosh(b*x + a)*sinh(b*x + a)^3 + (2*I*b*d^2*x + 2*I*b*c*d)*sinh(b*x + a)^4 + 2*I*b*d^2*x + 2*I*b*c*d + (4*I*b*d^2*x + 4*I*b*c*d)*cosh(b*x + a)^2 + (4*I*b*d^2*x + 4*I*b*c*d + (12*I*b*d^2*x + 12*I*b*c*d)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((8*I*b*d^2*x + 8*I*b*c*d)*cosh(b*x + a)^3 + (8*I*b*d^2*x + 8*I*b*c*d)*cosh(b*x + a))*sinh(b*x + a))*dilog(I*cosh(b*x + a) + I*sinh(b*x + a)) + ((-2*I*b*d^2*x - 2*I*b*c*d)*cosh(b*x + a)^4 + (-8*I*b*d^2*x - 8*I*b*c*d)*cosh(b*x + a)*sinh(b*x + a)^3 + (-2*I*b*d^2*x - 2*I*b*c*d)*sinh(b*x + a)^4 - 2*I*b*d^2*x - 2*I*b*c*d + (-4*I*b*d^2*x - 4*I*b*c*d)*cosh(b*x + a)^2 + (-4*I*b*d^2*x - 4*I*b*c*d + (-12*I*b*d^2*x - 12*I*b*c*d)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((-8*I*b*d^2*x - 8*I*b*c*d)*cosh(b*x + a)^3 + (-8*I*b*d^2*x - 8*I*b*c*d)*cosh(b*x + a))*sinh(b*x + a))*dilog(-I*cosh(b*x + a) - I*sinh(b*x + a)) + ((I*b^2*c^2 - 2*I*a*b*c*d + I*(a^2 - 2)*d^2)*cosh(b*x + a)^4 + (4*I*b^2*c^2 - 8*I*a*b*c*d + 4*I*(a^2 - 2)*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (I*b^2*c^2 - 2*I*a*b*c*d + I*(a^2 - 2)*d^2)*sinh(b*x + a)^4 + I*b^2*c^2 - 2*I*a*b*c*d + I*(a^2 - 2)*d^2 + (2*I*b^2*c^2 - 4*I*a*b*c*d + 2*I*(a^2 - 2)*d^2)*cosh(b*x + a)^2 + (2*I*b^2*c^2 - 4*I*a*b*c*d + 2*I*(a^2 - 2)*d^2 + (6*I*b^2*c^2 - 12*I*a*b*c*d + 6*I*(a^2 - 2)*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((4*I*b^2*c^2 - 8*I*a*b*c*d + 4*I*(a^2 - 2)*d^2)*cosh(b*x + a)^3 + (4*I*b^2*c^2 - 8*I*a*b*c*d + 4*I*(a^2 - 2)*d^2)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) + I) + ((-I*b^2*c^2 + 2*I*a*b*c*d - I*(a^2 - 2)*d^2)*cosh(b*x + a)^4 + (-4*I*b^2*c^2 + 8*I*a*b*c*d - 4*I*(a^2 - 2)*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (-I*b^2*c^2 + 2*I*a*b*c*d - I*(a^2 - 2)*d^2)*sinh(b*x + a)^4 - I*b^2*c^2 + 2*I*a*b*c*d - I*(a^2 - 2)*d^2 + (-2*I*b^2*c^2 + 4*I*a*b*c*d - 2*I*(a^2 - 2)*d^2)*cosh(b*x + a)^2 + (-2*I*b^2*c^2 + 4*I*a*b*c*d - 2*I*(a^2 - 2)*d^2 + (-6*I*b^2*c^2 + 12*I*a*b*c*d - 6*I*(a^2 - 2)*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((-4*I*b^2*c^2 + 8*I*a*b*c*d - 4*I*(a^2 - 2)*d^2)*cosh(b*x + a)^3 + (-4*I*b^2*c^2 + 8*I*a*b*c*d - 4*I*(a^2 - 2)*d^2)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) - I) + (-I*b^2*d^2*x^2 - 2*I*b^2*c*d*x + (-I*b^2*d^2*x^2 - 2*I*b^2*c*d*x - 2*I*a*b*c*d + I*a^2*d^2)*cosh(b*x + a)^4 + (-4*I*b^2*d^2*x^2 - 8*I*b^2*c*d*x - 8*I*a*b*c*d + 4*I*a^2*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (-I*b^2*d^2*x^2 - 2*I*b^2*c*d*x - 2*I*a*b*c*d + I*a^2*d^2)*sinh(b*x + a)^4 - 2*I*a*b*c*d + I*a^2*d^2 + (-2*I*b^2*d^2*x^2 - 4*I*b^2*c*d*x - 4*I*a*b*c*d + 2*I*a^2*d^2)*cosh(b*x + a)^2 + (-2*I*b^2*d^2*x^2 - 4*I*b^2*c*d*x - 4*I*a*b*c*d + 2*I*a^2*d^2 + (-6*I*b^2*d^2*x^2 - 12*I*b^2*c*d*x - 12*I*a*b*c*d + 6*I*a^2*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((-4*I*b^2*d^2*x^2 - 8*I*b^2*c*d*x - 8*I*a*b*c*d + 4*I*a^2*d^2)*cosh(b*x + a)^3 + (-4*I*b^2*d^2*x^2 - 8*I*b^2*c*d*x - 8*I*a*b*c*d + 4*I*a^2*d^2)*cosh(b*x + a))*sinh(b*x + a))*log(I*cosh(b*x + a) + I*sinh(b*x + a) + 1) + (I*b^2*d^2*x^2 + 2*I*b^2*c*d*x + (I*b^2*d^2*x^2 + 2*I*b^2*c*d*x + 2*I*a*b*c*d - I*a^2*d^2)*cosh(b*x + a)^4 + (4*I*b^2*d^2*x^2 + 8*I*b^2*c*d*x + 8*I*a*b*c*d - 4*I*a^2*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 + (I*b^2*d^2*x^2 + 2*I*b^2*c*d*x + 2*I*a*b*c*d - I*a^2*d^2)*sinh(b*x + a)^4 + 2*I*a*b*c*d - I*a^2*d^2 + (2*I*b^2*d^2*x^2 + 4*I*b^2*c*d*x + 4*I*a*b*c*d - 2*I*a^2*d^2)*cosh(b*x + a)^2 + (2*I*b^2*d^2*x^2 + 4*I*b^2*c*d*x + 4*I*a*b*c*d - 2*I*a^2*d^2 + (6*I*b^2*d^2*x^2 + 12*I*b^2*c*d*x + 12*I*a*b*c*d - 6*I*a^2*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + ((4*I*b^2*d^2*x^2 + 8*I*b^2*c*d*x + 8*I*a*b*c*d - 4*I*a^2*d^2)*cosh(b*x + a)^3 + (4*I*b^2*d^2*x^2 + 8*I*b^2*c*d*x + 8*I*a*b*c*d - 4*I*a^2*d^2)*cosh(b*x + a))*sinh(b*x + a))*log(-I*cosh(b*x + a) - I*sinh(b*x + a) + 1) + (-2*I*d^2*cosh(b*x + a)^4 - 8*I*d^2*cosh(b*x + a)*sinh(b*x + a)^3 - 2*I*d^2*sinh(b*x + a)^4 - 4*I*d^2*cosh(b*x + a)^2 + (-12*I*d^2*cosh(b*x + a)^2 - 4*I*d^2)*sinh(b*x + a)^2 - 2*I*d^2 + (-8*I*d^2*cosh(b*x + a)^3 - 8*I*d^2*cosh(b*x + a))*sinh(b*x + a))*polylog(3, I*cosh(b*x + a) + I*sinh(b*x + a)) + (2*I*d^2*cosh(b*x + a)^4 + 8*I*d^2*cosh(b*x + a)*sinh(b*x + a)^3 + 2*I*d^2*sinh(b*x + a)^4 + 4*I*d^2*cosh(b*x + a)^2 + (12*I*d^2*cosh(b*x + a)^2 + 4*I*d^2)*sinh(b*x + a)^2 + 2*I*d^2 + (8*I*d^2*cosh(b*x + a)^3 + 8*I*d^2*cosh(b*x + a))*sinh(b*x + a))*polylog(3, -I*cosh(b*x + a) - I*sinh(b*x + a)) - 2*(b^2*d^2*x^2 + b^2*c^2 - 2*b*c*d - 3*(b^2*d^2*x^2 + b^2*c^2 + 2*b*c*d + 2*(b^2*c*d + b*d^2)*x)*cosh(b*x + a)^2 + 2*(b^2*c*d - b*d^2)*x)*sinh(b*x + a))/(b^3*cosh(b*x + a)^4 + 4*b^3*cosh(b*x + a)*sinh(b*x + a)^3 + b^3*sinh(b*x + a)^4 + 2*b^3*cosh(b*x + a)^2 + b^3 + 2*(3*b^3*cosh(b*x + a)^2 + b^3)*sinh(b*x + a)^2 + 4*(b^3*cosh(b*x + a)^3 + b^3*cosh(b*x + a))*sinh(b*x + a))","C",0
38,1,1243,0,1.205318," ","integrate((d*x+c)*sech(b*x+a)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(b d x + b c + d\right)} \cosh\left(b x + a\right)^{3} + 6 \, {\left(b d x + b c + d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + 2 \, {\left(b d x + b c + d\right)} \sinh\left(b x + a\right)^{3} - 2 \, {\left(b d x + b c - d\right)} \cosh\left(b x + a\right) + {\left(i \, d \cosh\left(b x + a\right)^{4} + 4 i \, d \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + i \, d \sinh\left(b x + a\right)^{4} + 2 i \, d \cosh\left(b x + a\right)^{2} + {\left(6 i \, d \cosh\left(b x + a\right)^{2} + 2 i \, d\right)} \sinh\left(b x + a\right)^{2} + {\left(4 i \, d \cosh\left(b x + a\right)^{3} + 4 i \, d \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + i \, d\right)} {\rm Li}_2\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right)\right) + {\left(-i \, d \cosh\left(b x + a\right)^{4} - 4 i \, d \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - i \, d \sinh\left(b x + a\right)^{4} - 2 i \, d \cosh\left(b x + a\right)^{2} + {\left(-6 i \, d \cosh\left(b x + a\right)^{2} - 2 i \, d\right)} \sinh\left(b x + a\right)^{2} + {\left(-4 i \, d \cosh\left(b x + a\right)^{3} - 4 i \, d \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) - i \, d\right)} {\rm Li}_2\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right)\right) + {\left({\left(i \, b c - i \, a d\right)} \cosh\left(b x + a\right)^{4} + {\left(4 i \, b c - 4 i \, a d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(i \, b c - i \, a d\right)} \sinh\left(b x + a\right)^{4} + {\left(2 i \, b c - 2 i \, a d\right)} \cosh\left(b x + a\right)^{2} + {\left({\left(6 i \, b c - 6 i \, a d\right)} \cosh\left(b x + a\right)^{2} + 2 i \, b c - 2 i \, a d\right)} \sinh\left(b x + a\right)^{2} + i \, b c - i \, a d + {\left({\left(4 i \, b c - 4 i \, a d\right)} \cosh\left(b x + a\right)^{3} + {\left(4 i \, b c - 4 i \, a d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) + i\right) + {\left({\left(-i \, b c + i \, a d\right)} \cosh\left(b x + a\right)^{4} + {\left(-4 i \, b c + 4 i \, a d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(-i \, b c + i \, a d\right)} \sinh\left(b x + a\right)^{4} + {\left(-2 i \, b c + 2 i \, a d\right)} \cosh\left(b x + a\right)^{2} + {\left({\left(-6 i \, b c + 6 i \, a d\right)} \cosh\left(b x + a\right)^{2} - 2 i \, b c + 2 i \, a d\right)} \sinh\left(b x + a\right)^{2} - i \, b c + i \, a d + {\left({\left(-4 i \, b c + 4 i \, a d\right)} \cosh\left(b x + a\right)^{3} + {\left(-4 i \, b c + 4 i \, a d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(\cosh\left(b x + a\right) + \sinh\left(b x + a\right) - i\right) + {\left({\left(-i \, b d x - i \, a d\right)} \cosh\left(b x + a\right)^{4} + {\left(-4 i \, b d x - 4 i \, a d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(-i \, b d x - i \, a d\right)} \sinh\left(b x + a\right)^{4} - i \, b d x + {\left(-2 i \, b d x - 2 i \, a d\right)} \cosh\left(b x + a\right)^{2} + {\left(-2 i \, b d x + {\left(-6 i \, b d x - 6 i \, a d\right)} \cosh\left(b x + a\right)^{2} - 2 i \, a d\right)} \sinh\left(b x + a\right)^{2} - i \, a d + {\left({\left(-4 i \, b d x - 4 i \, a d\right)} \cosh\left(b x + a\right)^{3} + {\left(-4 i \, b d x - 4 i \, a d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(i \, \cosh\left(b x + a\right) + i \, \sinh\left(b x + a\right) + 1\right) + {\left({\left(i \, b d x + i \, a d\right)} \cosh\left(b x + a\right)^{4} + {\left(4 i \, b d x + 4 i \, a d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(i \, b d x + i \, a d\right)} \sinh\left(b x + a\right)^{4} + i \, b d x + {\left(2 i \, b d x + 2 i \, a d\right)} \cosh\left(b x + a\right)^{2} + {\left(2 i \, b d x + {\left(6 i \, b d x + 6 i \, a d\right)} \cosh\left(b x + a\right)^{2} + 2 i \, a d\right)} \sinh\left(b x + a\right)^{2} + i \, a d + {\left({\left(4 i \, b d x + 4 i \, a d\right)} \cosh\left(b x + a\right)^{3} + {\left(4 i \, b d x + 4 i \, a d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \log\left(-i \, \cosh\left(b x + a\right) - i \, \sinh\left(b x + a\right) + 1\right) - 2 \, {\left(b d x - 3 \, {\left(b d x + b c + d\right)} \cosh\left(b x + a\right)^{2} + b c - d\right)} \sinh\left(b x + a\right)}{2 \, {\left(b^{2} \cosh\left(b x + a\right)^{4} + 4 \, b^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + b^{2} \sinh\left(b x + a\right)^{4} + 2 \, b^{2} \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(b x + a\right)^{2} + b^{2}\right)} \sinh\left(b x + a\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(b x + a\right)^{3} + b^{2} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"1/2*(2*(b*d*x + b*c + d)*cosh(b*x + a)^3 + 6*(b*d*x + b*c + d)*cosh(b*x + a)*sinh(b*x + a)^2 + 2*(b*d*x + b*c + d)*sinh(b*x + a)^3 - 2*(b*d*x + b*c - d)*cosh(b*x + a) + (I*d*cosh(b*x + a)^4 + 4*I*d*cosh(b*x + a)*sinh(b*x + a)^3 + I*d*sinh(b*x + a)^4 + 2*I*d*cosh(b*x + a)^2 + (6*I*d*cosh(b*x + a)^2 + 2*I*d)*sinh(b*x + a)^2 + (4*I*d*cosh(b*x + a)^3 + 4*I*d*cosh(b*x + a))*sinh(b*x + a) + I*d)*dilog(I*cosh(b*x + a) + I*sinh(b*x + a)) + (-I*d*cosh(b*x + a)^4 - 4*I*d*cosh(b*x + a)*sinh(b*x + a)^3 - I*d*sinh(b*x + a)^4 - 2*I*d*cosh(b*x + a)^2 + (-6*I*d*cosh(b*x + a)^2 - 2*I*d)*sinh(b*x + a)^2 + (-4*I*d*cosh(b*x + a)^3 - 4*I*d*cosh(b*x + a))*sinh(b*x + a) - I*d)*dilog(-I*cosh(b*x + a) - I*sinh(b*x + a)) + ((I*b*c - I*a*d)*cosh(b*x + a)^4 + (4*I*b*c - 4*I*a*d)*cosh(b*x + a)*sinh(b*x + a)^3 + (I*b*c - I*a*d)*sinh(b*x + a)^4 + (2*I*b*c - 2*I*a*d)*cosh(b*x + a)^2 + ((6*I*b*c - 6*I*a*d)*cosh(b*x + a)^2 + 2*I*b*c - 2*I*a*d)*sinh(b*x + a)^2 + I*b*c - I*a*d + ((4*I*b*c - 4*I*a*d)*cosh(b*x + a)^3 + (4*I*b*c - 4*I*a*d)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) + I) + ((-I*b*c + I*a*d)*cosh(b*x + a)^4 + (-4*I*b*c + 4*I*a*d)*cosh(b*x + a)*sinh(b*x + a)^3 + (-I*b*c + I*a*d)*sinh(b*x + a)^4 + (-2*I*b*c + 2*I*a*d)*cosh(b*x + a)^2 + ((-6*I*b*c + 6*I*a*d)*cosh(b*x + a)^2 - 2*I*b*c + 2*I*a*d)*sinh(b*x + a)^2 - I*b*c + I*a*d + ((-4*I*b*c + 4*I*a*d)*cosh(b*x + a)^3 + (-4*I*b*c + 4*I*a*d)*cosh(b*x + a))*sinh(b*x + a))*log(cosh(b*x + a) + sinh(b*x + a) - I) + ((-I*b*d*x - I*a*d)*cosh(b*x + a)^4 + (-4*I*b*d*x - 4*I*a*d)*cosh(b*x + a)*sinh(b*x + a)^3 + (-I*b*d*x - I*a*d)*sinh(b*x + a)^4 - I*b*d*x + (-2*I*b*d*x - 2*I*a*d)*cosh(b*x + a)^2 + (-2*I*b*d*x + (-6*I*b*d*x - 6*I*a*d)*cosh(b*x + a)^2 - 2*I*a*d)*sinh(b*x + a)^2 - I*a*d + ((-4*I*b*d*x - 4*I*a*d)*cosh(b*x + a)^3 + (-4*I*b*d*x - 4*I*a*d)*cosh(b*x + a))*sinh(b*x + a))*log(I*cosh(b*x + a) + I*sinh(b*x + a) + 1) + ((I*b*d*x + I*a*d)*cosh(b*x + a)^4 + (4*I*b*d*x + 4*I*a*d)*cosh(b*x + a)*sinh(b*x + a)^3 + (I*b*d*x + I*a*d)*sinh(b*x + a)^4 + I*b*d*x + (2*I*b*d*x + 2*I*a*d)*cosh(b*x + a)^2 + (2*I*b*d*x + (6*I*b*d*x + 6*I*a*d)*cosh(b*x + a)^2 + 2*I*a*d)*sinh(b*x + a)^2 + I*a*d + ((4*I*b*d*x + 4*I*a*d)*cosh(b*x + a)^3 + (4*I*b*d*x + 4*I*a*d)*cosh(b*x + a))*sinh(b*x + a))*log(-I*cosh(b*x + a) - I*sinh(b*x + a) + 1) - 2*(b*d*x - 3*(b*d*x + b*c + d)*cosh(b*x + a)^2 + b*c - d)*sinh(b*x + a))/(b^2*cosh(b*x + a)^4 + 4*b^2*cosh(b*x + a)*sinh(b*x + a)^3 + b^2*sinh(b*x + a)^4 + 2*b^2*cosh(b*x + a)^2 + 2*(3*b^2*cosh(b*x + a)^2 + b^2)*sinh(b*x + a)^2 + b^2 + 4*(b^2*cosh(b*x + a)^3 + b^2*cosh(b*x + a))*sinh(b*x + a))","B",0
39,0,0,0,0.857730," ","integrate(sech(b*x+a)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(b x + a\right)^{3}}{d x + c}, x\right)"," ",0,"integral(sech(b*x + a)^3/(d*x + c), x)","F",0
40,0,0,0,2.020109," ","integrate(sech(b*x+a)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(b x + a\right)^{3}}{d^{2} x^{2} + 2 \, c d x + c^{2}}, x\right)"," ",0,"integral(sech(b*x + a)^3/(d^2*x^2 + 2*c*d*x + c^2), x)","F",0
41,1,523,0,0.910221," ","integrate((d*x+c)^(5/2)*cosh(b*x+a),x, algorithm=""fricas"")","\frac{15 \, \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{3} \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 15 \, \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{3} \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 2 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} + 10 \, b^{2} c d + 15 \, b d^{2} - {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(4 \, b^{3} c d + 5 \, b^{2} d^{2}\right)} x\right)} \sqrt{d x + c}}{16 \, {\left(b^{4} \cosh\left(b x + a\right) + b^{4} \sinh\left(b x + a\right)\right)}}"," ",0,"1/16*(15*sqrt(pi)*(d^3*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d^3*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d^3*cosh(-(b*c - a*d)/d) - d^3*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 15*sqrt(pi)*(d^3*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d^3*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d^3*cosh(-(b*c - a*d)/d) + d^3*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - 2*(4*b^3*d^2*x^2 + 4*b^3*c^2 + 10*b^2*c*d + 15*b*d^2 - (4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^2 - 2*(4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)*sinh(b*x + a) - (4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*sinh(b*x + a)^2 + 2*(4*b^3*c*d + 5*b^2*d^2)*x)*sqrt(d*x + c))/(b^4*cosh(b*x + a) + b^4*sinh(b*x + a))","B",0
42,1,387,0,2.983043," ","integrate((d*x+c)^(3/2)*cosh(b*x+a),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{2} \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 3 \, \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{2} \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 2 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \sinh\left(b x + a\right)^{2} + 3 \, b d\right)} \sqrt{d x + c}}{8 \, {\left(b^{3} \cosh\left(b x + a\right) + b^{3} \sinh\left(b x + a\right)\right)}}"," ",0,"1/8*(3*sqrt(pi)*(d^2*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d^2*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d^2*cosh(-(b*c - a*d)/d) - d^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) - 3*sqrt(pi)*(d^2*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d^2*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d^2*cosh(-(b*c - a*d)/d) + d^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - 2*(2*b^2*d*x + 2*b^2*c - (2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a)^2 - 2*(2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a)*sinh(b*x + a) - (2*b^2*d*x + 2*b^2*c - 3*b*d)*sinh(b*x + a)^2 + 3*b*d)*sqrt(d*x + c))/(b^3*cosh(b*x + a) + b^3*sinh(b*x + a))","B",0
43,1,302,0,1.019407," ","integrate(cosh(b*x+a)*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d \cosh\left(-\frac{b c - a d}{d}\right) - d \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + \sqrt{\pi} {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d \cosh\left(-\frac{b c - a d}{d}\right) + d \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 2 \, {\left(b \cosh\left(b x + a\right)^{2} + 2 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b \sinh\left(b x + a\right)^{2} - b\right)} \sqrt{d x + c}}{4 \, {\left(b^{2} \cosh\left(b x + a\right) + b^{2} \sinh\left(b x + a\right)\right)}}"," ",0,"1/4*(sqrt(pi)*(d*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d*cosh(-(b*c - a*d)/d) - d*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + sqrt(pi)*(d*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + (d*cosh(-(b*c - a*d)/d) + d*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + 2*(b*cosh(b*x + a)^2 + 2*b*cosh(b*x + a)*sinh(b*x + a) + b*sinh(b*x + a)^2 - b)*sqrt(d*x + c))/(b^2*cosh(b*x + a) + b^2*sinh(b*x + a))","B",0
44,1,123,0,0.557915," ","integrate(cosh(b*x+a)/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\pi} \sqrt{\frac{b}{d}} {\left(\cosh\left(-\frac{b c - a d}{d}\right) - \sinh\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - \sqrt{\pi} \sqrt{-\frac{b}{d}} {\left(\cosh\left(-\frac{b c - a d}{d}\right) + \sinh\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right)}{2 \, b}"," ",0,"1/2*(sqrt(pi)*sqrt(b/d)*(cosh(-(b*c - a*d)/d) - sinh(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(b/d)) - sqrt(pi)*sqrt(-b/d)*(cosh(-(b*c - a*d)/d) + sinh(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-b/d)))/b","A",0
45,1,338,0,1.047044," ","integrate(cosh(b*x+a)/(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + \sqrt{d x + c} {\left(\cosh\left(b x + a\right)^{2} + 2 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right) + \sinh\left(b x + a\right)^{2} + 1\right)}}{{\left(d^{2} x + c d\right)} \cosh\left(b x + a\right) + {\left(d^{2} x + c d\right)} \sinh\left(b x + a\right)}"," ",0,"-(sqrt(pi)*((d*x + c)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((d*x + c)*cosh(-(b*c - a*d)/d) - (d*x + c)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + sqrt(pi)*((d*x + c)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((d*x + c)*cosh(-(b*c - a*d)/d) + (d*x + c)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + sqrt(d*x + c)*(cosh(b*x + a)^2 + 2*cosh(b*x + a)*sinh(b*x + a) + sinh(b*x + a)^2 + 1))/((d^2*x + c*d)*cosh(b*x + a) + (d^2*x + c*d)*sinh(b*x + a))","B",0
46,1,534,0,0.908183," ","integrate(cosh(b*x+a)/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 2 \, \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left(2 \, b d x - {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) - {\left(2 \, b d x + 2 \, b c + d\right)} \sinh\left(b x + a\right)^{2} + 2 \, b c - d\right)} \sqrt{d x + c}}{3 \, {\left({\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right) + {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"1/3*(2*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) - 2*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + (2*b*d*x - (2*b*d*x + 2*b*c + d)*cosh(b*x + a)^2 - 2*(2*b*d*x + 2*b*c + d)*cosh(b*x + a)*sinh(b*x + a) - (2*b*d*x + 2*b*c + d)*sinh(b*x + a)^2 + 2*b*c - d)*sqrt(d*x + c))/((d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a) + (d^4*x^2 + 2*c*d^3*x + c^2*d^2)*sinh(b*x + a))","B",0
47,1,853,0,0.511325," ","integrate(cosh(b*x+a)/(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 4 \, \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} - 2 \, b c d + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{2} + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d - b d^{2}\right)} x\right)} \sqrt{d x + c}}{15 \, {\left({\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right) + {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \sinh\left(b x + a\right)\right)}}"," ",0,"-1/15*(4*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 4*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + (4*b^2*d^2*x^2 + 4*b^2*c^2 - 2*b*c*d + (4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^2 + 2*(4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a)*sinh(b*x + a) + (4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*sinh(b*x + a)^2 + 3*d^2 + 2*(4*b^2*c*d - b*d^2)*x)*sqrt(d*x + c))/((d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a) + (d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*sinh(b*x + a))","B",0
48,1,1001,0,0.464556," ","integrate((d*x+c)^(5/2)*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} \sqrt{\pi} {\left(d^{4} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{4} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{4} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{4} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{4} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{4} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 105 \, \sqrt{2} \sqrt{\pi} {\left(d^{4} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{4} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{4} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{4} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{4} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{4} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 4 \, {\left(112 \, b^{3} d^{3} x^{2} + 112 \, b^{3} c^{2} d + 140 \, b^{2} c d^{2} - 7 \, {\left(16 \, b^{3} d^{3} x^{2} + 16 \, b^{3} c^{2} d - 20 \, b^{2} c d^{2} + 15 \, b d^{3} + 4 \, {\left(8 \, b^{3} c d^{2} - 5 \, b^{2} d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{4} - 28 \, {\left(16 \, b^{3} d^{3} x^{2} + 16 \, b^{3} c^{2} d - 20 \, b^{2} c d^{2} + 15 \, b d^{3} + 4 \, {\left(8 \, b^{3} c d^{2} - 5 \, b^{2} d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - 7 \, {\left(16 \, b^{3} d^{3} x^{2} + 16 \, b^{3} c^{2} d - 20 \, b^{2} c d^{2} + 15 \, b d^{3} + 4 \, {\left(8 \, b^{3} c d^{2} - 5 \, b^{2} d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{4} + 105 \, b d^{3} - 128 \, {\left(b^{4} d^{3} x^{3} + 3 \, b^{4} c d^{2} x^{2} + 3 \, b^{4} c^{2} d x + b^{4} c^{3}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(64 \, b^{4} d^{3} x^{3} + 192 \, b^{4} c d^{2} x^{2} + 192 \, b^{4} c^{2} d x + 64 \, b^{4} c^{3} + 21 \, {\left(16 \, b^{3} d^{3} x^{2} + 16 \, b^{3} c^{2} d - 20 \, b^{2} c d^{2} + 15 \, b d^{3} + 4 \, {\left(8 \, b^{3} c d^{2} - 5 \, b^{2} d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 28 \, {\left(8 \, b^{3} c d^{2} + 5 \, b^{2} d^{3}\right)} x - 4 \, {\left(7 \, {\left(16 \, b^{3} d^{3} x^{2} + 16 \, b^{3} c^{2} d - 20 \, b^{2} c d^{2} + 15 \, b d^{3} + 4 \, {\left(8 \, b^{3} c d^{2} - 5 \, b^{2} d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{3} + 64 \, {\left(b^{4} d^{3} x^{3} + 3 \, b^{4} c d^{2} x^{2} + 3 \, b^{4} c^{2} d x + b^{4} c^{3}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{3584 \, {\left(b^{4} d \cosh\left(b x + a\right)^{2} + 2 \, b^{4} d \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{4} d \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"1/3584*(105*sqrt(2)*sqrt(pi)*(d^4*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - d^4*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^4*cosh(-2*(b*c - a*d)/d) - d^4*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^4*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - d^4*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) + 105*sqrt(2)*sqrt(pi)*(d^4*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + d^4*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^4*cosh(-2*(b*c - a*d)/d) + d^4*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^4*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + d^4*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) - 4*(112*b^3*d^3*x^2 + 112*b^3*c^2*d + 140*b^2*c*d^2 - 7*(16*b^3*d^3*x^2 + 16*b^3*c^2*d - 20*b^2*c*d^2 + 15*b*d^3 + 4*(8*b^3*c*d^2 - 5*b^2*d^3)*x)*cosh(b*x + a)^4 - 28*(16*b^3*d^3*x^2 + 16*b^3*c^2*d - 20*b^2*c*d^2 + 15*b*d^3 + 4*(8*b^3*c*d^2 - 5*b^2*d^3)*x)*cosh(b*x + a)*sinh(b*x + a)^3 - 7*(16*b^3*d^3*x^2 + 16*b^3*c^2*d - 20*b^2*c*d^2 + 15*b*d^3 + 4*(8*b^3*c*d^2 - 5*b^2*d^3)*x)*sinh(b*x + a)^4 + 105*b*d^3 - 128*(b^4*d^3*x^3 + 3*b^4*c*d^2*x^2 + 3*b^4*c^2*d*x + b^4*c^3)*cosh(b*x + a)^2 - 2*(64*b^4*d^3*x^3 + 192*b^4*c*d^2*x^2 + 192*b^4*c^2*d*x + 64*b^4*c^3 + 21*(16*b^3*d^3*x^2 + 16*b^3*c^2*d - 20*b^2*c*d^2 + 15*b*d^3 + 4*(8*b^3*c*d^2 - 5*b^2*d^3)*x)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 28*(8*b^3*c*d^2 + 5*b^2*d^3)*x - 4*(7*(16*b^3*d^3*x^2 + 16*b^3*c^2*d - 20*b^2*c*d^2 + 15*b*d^3 + 4*(8*b^3*c*d^2 - 5*b^2*d^3)*x)*cosh(b*x + a)^3 + 64*(b^4*d^3*x^3 + 3*b^4*c*d^2*x^2 + 3*b^4*c^2*d*x + b^4*c^3)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/(b^4*d*cosh(b*x + a)^2 + 2*b^4*d*cosh(b*x + a)*sinh(b*x + a) + b^4*d*sinh(b*x + a)^2)","B",0
49,1,755,0,0.490786," ","integrate((d*x+c)^(3/2)*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{3} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 15 \, \sqrt{2} \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{3} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 4 \, {\left(20 \, b^{2} d^{2} x - 5 \, {\left(4 \, b^{2} d^{2} x + 4 \, b^{2} c d - 3 \, b d^{2}\right)} \cosh\left(b x + a\right)^{4} - 20 \, {\left(4 \, b^{2} d^{2} x + 4 \, b^{2} c d - 3 \, b d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - 5 \, {\left(4 \, b^{2} d^{2} x + 4 \, b^{2} c d - 3 \, b d^{2}\right)} \sinh\left(b x + a\right)^{4} + 20 \, b^{2} c d + 15 \, b d^{2} - 32 \, {\left(b^{3} d^{2} x^{2} + 2 \, b^{3} c d x + b^{3} c^{2}\right)} \cosh\left(b x + a\right)^{2} - 2 \, {\left(16 \, b^{3} d^{2} x^{2} + 32 \, b^{3} c d x + 16 \, b^{3} c^{2} + 15 \, {\left(4 \, b^{2} d^{2} x + 4 \, b^{2} c d - 3 \, b d^{2}\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} - 4 \, {\left(5 \, {\left(4 \, b^{2} d^{2} x + 4 \, b^{2} c d - 3 \, b d^{2}\right)} \cosh\left(b x + a\right)^{3} + 16 \, {\left(b^{3} d^{2} x^{2} + 2 \, b^{3} c d x + b^{3} c^{2}\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{640 \, {\left(b^{3} d \cosh\left(b x + a\right)^{2} + 2 \, b^{3} d \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{3} d \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"1/640*(15*sqrt(2)*sqrt(pi)*(d^3*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - d^3*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^3*cosh(-2*(b*c - a*d)/d) - d^3*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^3*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - d^3*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) - 15*sqrt(2)*sqrt(pi)*(d^3*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + d^3*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^3*cosh(-2*(b*c - a*d)/d) + d^3*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^3*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + d^3*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) - 4*(20*b^2*d^2*x - 5*(4*b^2*d^2*x + 4*b^2*c*d - 3*b*d^2)*cosh(b*x + a)^4 - 20*(4*b^2*d^2*x + 4*b^2*c*d - 3*b*d^2)*cosh(b*x + a)*sinh(b*x + a)^3 - 5*(4*b^2*d^2*x + 4*b^2*c*d - 3*b*d^2)*sinh(b*x + a)^4 + 20*b^2*c*d + 15*b*d^2 - 32*(b^3*d^2*x^2 + 2*b^3*c*d*x + b^3*c^2)*cosh(b*x + a)^2 - 2*(16*b^3*d^2*x^2 + 32*b^3*c*d*x + 16*b^3*c^2 + 15*(4*b^2*d^2*x + 4*b^2*c*d - 3*b*d^2)*cosh(b*x + a)^2)*sinh(b*x + a)^2 - 4*(5*(4*b^2*d^2*x + 4*b^2*c*d - 3*b*d^2)*cosh(b*x + a)^3 + 16*(b^3*d^2*x^2 + 2*b^3*c*d*x + b^3*c^2)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/(b^3*d*cosh(b*x + a)^2 + 2*b^3*d*cosh(b*x + a)*sinh(b*x + a) + b^3*d*sinh(b*x + a)^2)","B",0
50,1,590,0,0.538158," ","integrate(cosh(b*x+a)^2*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 3 \, \sqrt{2} \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 4 \, {\left(3 \, b d \cosh\left(b x + a\right)^{4} + 12 \, b d \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + 3 \, b d \sinh\left(b x + a\right)^{4} + 8 \, {\left(b^{2} d x + b^{2} c\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(4 \, b^{2} d x + 9 \, b d \cosh\left(b x + a\right)^{2} + 4 \, b^{2} c\right)} \sinh\left(b x + a\right)^{2} - 3 \, b d + 4 \, {\left(3 \, b d \cosh\left(b x + a\right)^{3} + 4 \, {\left(b^{2} d x + b^{2} c\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{96 \, {\left(b^{2} d \cosh\left(b x + a\right)^{2} + 2 \, b^{2} d \cosh\left(b x + a\right) \sinh\left(b x + a\right) + b^{2} d \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"1/96*(3*sqrt(2)*sqrt(pi)*(d^2*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - d^2*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^2*cosh(-2*(b*c - a*d)/d) - d^2*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^2*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - d^2*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) + 3*sqrt(2)*sqrt(pi)*(d^2*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + d^2*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + (d^2*cosh(-2*(b*c - a*d)/d) + d^2*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*(d^2*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + d^2*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) + 4*(3*b*d*cosh(b*x + a)^4 + 12*b*d*cosh(b*x + a)*sinh(b*x + a)^3 + 3*b*d*sinh(b*x + a)^4 + 8*(b^2*d*x + b^2*c)*cosh(b*x + a)^2 + 2*(4*b^2*d*x + 9*b*d*cosh(b*x + a)^2 + 4*b^2*c)*sinh(b*x + a)^2 - 3*b*d + 4*(3*b*d*cosh(b*x + a)^3 + 4*(b^2*d*x + b^2*c)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/(b^2*d*cosh(b*x + a)^2 + 2*b^2*d*cosh(b*x + a)*sinh(b*x + a) + b^2*d*sinh(b*x + a)^2)","B",0
51,1,155,0,0.511214," ","integrate(cosh(b*x+a)^2/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{\pi} {\left(d \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - d \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - \sqrt{2} \sqrt{\pi} {\left(d \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + d \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 8 \, \sqrt{d x + c} b}{8 \, b d}"," ",0,"1/8*(sqrt(2)*sqrt(pi)*(d*cosh(-2*(b*c - a*d)/d) - d*sinh(-2*(b*c - a*d)/d))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) - sqrt(2)*sqrt(pi)*(d*cosh(-2*(b*c - a*d)/d) + d*sinh(-2*(b*c - a*d)/d))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) + 8*sqrt(d*x + c)*b)/(b*d)","A",0
52,1,569,0,0.537925," ","integrate(cosh(b*x+a)^2/(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + \sqrt{2} \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left(\cosh\left(b x + a\right)^{4} + 4 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + \sinh\left(b x + a\right)^{4} + 2 \, {\left(3 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 2 \, \cosh\left(b x + a\right)^{2} + 4 \, {\left(\cosh\left(b x + a\right)^{3} + \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} \sqrt{d x + c}}{2 \, {\left({\left(d^{2} x + c d\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(d^{2} x + c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(d^{2} x + c d\right)} \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"-1/2*(sqrt(2)*sqrt(pi)*((d*x + c)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((d*x + c)*cosh(-2*(b*c - a*d)/d) - (d*x + c)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((d*x + c)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) + sqrt(2)*sqrt(pi)*((d*x + c)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((d*x + c)*cosh(-2*(b*c - a*d)/d) + (d*x + c)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((d*x + c)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) + (cosh(b*x + a)^4 + 4*cosh(b*x + a)*sinh(b*x + a)^3 + sinh(b*x + a)^4 + 2*(3*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 2*cosh(b*x + a)^2 + 4*(cosh(b*x + a)^3 + cosh(b*x + a))*sinh(b*x + a) + 1)*sqrt(d*x + c))/((d^2*x + c*d)*cosh(b*x + a)^2 + 2*(d^2*x + c*d)*cosh(b*x + a)*sinh(b*x + a) + (d^2*x + c*d)*sinh(b*x + a)^2)","B",0
53,1,861,0,0.551192," ","integrate(cosh(b*x+a)^2/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{4 \, \sqrt{2} \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 4 \, \sqrt{2} \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - {\left({\left(4 \, b d x + 4 \, b c + d\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(4 \, b d x + 4 \, b c + d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(4 \, b d x + 4 \, b c + d\right)} \sinh\left(b x + a\right)^{4} - 4 \, b d x + 2 \, d \cosh\left(b x + a\right)^{2} + 2 \, {\left(3 \, {\left(4 \, b d x + 4 \, b c + d\right)} \cosh\left(b x + a\right)^{2} + d\right)} \sinh\left(b x + a\right)^{2} - 4 \, b c + 4 \, {\left({\left(4 \, b d x + 4 \, b c + d\right)} \cosh\left(b x + a\right)^{3} + d \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + d\right)} \sqrt{d x + c}}{6 \, {\left({\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"1/6*(4*sqrt(2)*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-2*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) - 4*sqrt(2)*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-2*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) - ((4*b*d*x + 4*b*c + d)*cosh(b*x + a)^4 + 4*(4*b*d*x + 4*b*c + d)*cosh(b*x + a)*sinh(b*x + a)^3 + (4*b*d*x + 4*b*c + d)*sinh(b*x + a)^4 - 4*b*d*x + 2*d*cosh(b*x + a)^2 + 2*(3*(4*b*d*x + 4*b*c + d)*cosh(b*x + a)^2 + d)*sinh(b*x + a)^2 - 4*b*c + 4*((4*b*d*x + 4*b*c + d)*cosh(b*x + a)^3 + d*cosh(b*x + a))*sinh(b*x + a) + d)*sqrt(d*x + c))/((d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a)^2 + 2*(d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a)*sinh(b*x + a) + (d^4*x^2 + 2*c*d^3*x + c^2*d^2)*sinh(b*x + a)^2)","B",0
54,1,1350,0,0.633304," ","integrate(cosh(b*x+a)^2/(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{16 \, \sqrt{2} \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 16 \, \sqrt{2} \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left(16 \, b^{2} d^{2} x^{2} + {\left(16 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c^{2} + 4 \, b c d + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{4} + 4 \, {\left(16 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c^{2} + 4 \, b c d + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} + {\left(16 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c^{2} + 4 \, b c d + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d + b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{4} + 16 \, b^{2} c^{2} + 6 \, d^{2} \cosh\left(b x + a\right)^{2} - 4 \, b c d + 6 \, {\left({\left(16 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c^{2} + 4 \, b c d + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + d^{2}\right)} \sinh\left(b x + a\right)^{2} + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d - b d^{2}\right)} x + 4 \, {\left({\left(16 \, b^{2} d^{2} x^{2} + 16 \, b^{2} c^{2} + 4 \, b c d + 3 \, d^{2} + 4 \, {\left(8 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} + 3 \, d^{2} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{30 \, {\left({\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"-1/30*(16*sqrt(2)*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-2*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) + 16*sqrt(2)*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-2*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) + (16*b^2*d^2*x^2 + (16*b^2*d^2*x^2 + 16*b^2*c^2 + 4*b*c*d + 3*d^2 + 4*(8*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^4 + 4*(16*b^2*d^2*x^2 + 16*b^2*c^2 + 4*b*c*d + 3*d^2 + 4*(8*b^2*c*d + b*d^2)*x)*cosh(b*x + a)*sinh(b*x + a)^3 + (16*b^2*d^2*x^2 + 16*b^2*c^2 + 4*b*c*d + 3*d^2 + 4*(8*b^2*c*d + b*d^2)*x)*sinh(b*x + a)^4 + 16*b^2*c^2 + 6*d^2*cosh(b*x + a)^2 - 4*b*c*d + 6*((16*b^2*d^2*x^2 + 16*b^2*c^2 + 4*b*c*d + 3*d^2 + 4*(8*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^2 + d^2)*sinh(b*x + a)^2 + 3*d^2 + 4*(8*b^2*c*d - b*d^2)*x + 4*((16*b^2*d^2*x^2 + 16*b^2*c^2 + 4*b*c*d + 3*d^2 + 4*(8*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^3 + 3*d^2*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/((d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a)^2 + 2*(d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a)*sinh(b*x + a) + (d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*sinh(b*x + a)^2)","B",0
55,1,1825,0,0.715402," ","integrate(cosh(b*x+a)^2/(d*x+c)^(9/2),x, algorithm=""fricas"")","\frac{64 \, \sqrt{2} \sqrt{\pi} {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 64 \, \sqrt{2} \sqrt{\pi} {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left({\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{3} d^{4} x^{4} + 4 \, b^{3} c d^{3} x^{3} + 6 \, b^{3} c^{2} d^{2} x^{2} + 4 \, b^{3} c^{3} d x + b^{3} c^{4}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{2 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} - 16 \, b^{2} c^{2} d - 30 \, d^{3} \cosh\left(b x + a\right)^{2} - {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} + 16 \, b^{2} c^{2} d + 12 \, b c d^{2} + 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 4 \, {\left(48 \, b^{3} c^{2} d + 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{4} - 4 \, {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} + 16 \, b^{2} c^{2} d + 12 \, b c d^{2} + 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 4 \, {\left(48 \, b^{3} c^{2} d + 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{3} - {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} + 16 \, b^{2} c^{2} d + 12 \, b c d^{2} + 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 4 \, {\left(48 \, b^{3} c^{2} d + 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x\right)} \sinh\left(b x + a\right)^{4} + 12 \, b c d^{2} - 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} - b^{2} d^{3}\right)} x^{2} - 6 \, {\left(5 \, d^{3} + {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} + 16 \, b^{2} c^{2} d + 12 \, b c d^{2} + 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 4 \, {\left(48 \, b^{3} c^{2} d + 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{2}\right)} \sinh\left(b x + a\right)^{2} + 4 \, {\left(48 \, b^{3} c^{2} d - 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x - 4 \, {\left(15 \, d^{3} \cosh\left(b x + a\right) + {\left(64 \, b^{3} d^{3} x^{3} + 64 \, b^{3} c^{3} + 16 \, b^{2} c^{2} d + 12 \, b c d^{2} + 15 \, d^{3} + 16 \, {\left(12 \, b^{3} c d^{2} + b^{2} d^{3}\right)} x^{2} + 4 \, {\left(48 \, b^{3} c^{2} d + 8 \, b^{2} c d^{2} + 3 \, b d^{3}\right)} x\right)} \cosh\left(b x + a\right)^{3}\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{210 \, {\left({\left(d^{8} x^{4} + 4 \, c d^{7} x^{3} + 6 \, c^{2} d^{6} x^{2} + 4 \, c^{3} d^{5} x + c^{4} d^{4}\right)} \cosh\left(b x + a\right)^{2} + 2 \, {\left(d^{8} x^{4} + 4 \, c d^{7} x^{3} + 6 \, c^{2} d^{6} x^{2} + 4 \, c^{3} d^{5} x + c^{4} d^{4}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right) + {\left(d^{8} x^{4} + 4 \, c d^{7} x^{3} + 6 \, c^{2} d^{6} x^{2} + 4 \, c^{3} d^{5} x + c^{4} d^{4}\right)} \sinh\left(b x + a\right)^{2}\right)}}"," ",0,"1/210*(64*sqrt(2)*sqrt(pi)*((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) - (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(-2*(b*c - a*d)/d) - (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) - (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(b/d)) - 64*sqrt(2)*sqrt(pi)*((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)^2*cosh(-2*(b*c - a*d)/d) + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)^2*sinh(-2*(b*c - a*d)/d) + ((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(-2*(b*c - a*d)/d) + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a)^2 + 2*((b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)*cosh(-2*(b*c - a*d)/d) + (b^3*d^4*x^4 + 4*b^3*c*d^3*x^3 + 6*b^3*c^2*d^2*x^2 + 4*b^3*c^3*d*x + b^3*c^4)*cosh(b*x + a)*sinh(-2*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-b/d)) + (64*b^3*d^3*x^3 + 64*b^3*c^3 - 16*b^2*c^2*d - 30*d^3*cosh(b*x + a)^2 - (64*b^3*d^3*x^3 + 64*b^3*c^3 + 16*b^2*c^2*d + 12*b*c*d^2 + 15*d^3 + 16*(12*b^3*c*d^2 + b^2*d^3)*x^2 + 4*(48*b^3*c^2*d + 8*b^2*c*d^2 + 3*b*d^3)*x)*cosh(b*x + a)^4 - 4*(64*b^3*d^3*x^3 + 64*b^3*c^3 + 16*b^2*c^2*d + 12*b*c*d^2 + 15*d^3 + 16*(12*b^3*c*d^2 + b^2*d^3)*x^2 + 4*(48*b^3*c^2*d + 8*b^2*c*d^2 + 3*b*d^3)*x)*cosh(b*x + a)*sinh(b*x + a)^3 - (64*b^3*d^3*x^3 + 64*b^3*c^3 + 16*b^2*c^2*d + 12*b*c*d^2 + 15*d^3 + 16*(12*b^3*c*d^2 + b^2*d^3)*x^2 + 4*(48*b^3*c^2*d + 8*b^2*c*d^2 + 3*b*d^3)*x)*sinh(b*x + a)^4 + 12*b*c*d^2 - 15*d^3 + 16*(12*b^3*c*d^2 - b^2*d^3)*x^2 - 6*(5*d^3 + (64*b^3*d^3*x^3 + 64*b^3*c^3 + 16*b^2*c^2*d + 12*b*c*d^2 + 15*d^3 + 16*(12*b^3*c*d^2 + b^2*d^3)*x^2 + 4*(48*b^3*c^2*d + 8*b^2*c*d^2 + 3*b*d^3)*x)*cosh(b*x + a)^2)*sinh(b*x + a)^2 + 4*(48*b^3*c^2*d - 8*b^2*c*d^2 + 3*b*d^3)*x - 4*(15*d^3*cosh(b*x + a) + (64*b^3*d^3*x^3 + 64*b^3*c^3 + 16*b^2*c^2*d + 12*b*c*d^2 + 15*d^3 + 16*(12*b^3*c*d^2 + b^2*d^3)*x^2 + 4*(48*b^3*c^2*d + 8*b^2*c*d^2 + 3*b*d^3)*x)*cosh(b*x + a)^3)*sinh(b*x + a))*sqrt(d*x + c))/((d^8*x^4 + 4*c*d^7*x^3 + 6*c^2*d^6*x^2 + 4*c^3*d^5*x + c^4*d^4)*cosh(b*x + a)^2 + 2*(d^8*x^4 + 4*c*d^7*x^3 + 6*c^2*d^6*x^2 + 4*c^3*d^5*x + c^4*d^4)*cosh(b*x + a)*sinh(b*x + a) + (d^8*x^4 + 4*c*d^7*x^3 + 6*c^2*d^6*x^2 + 4*c^3*d^5*x + c^4*d^4)*sinh(b*x + a)^2)","B",0
56,1,2092,0,0.644843," ","integrate((d*x+c)^(5/2)*cosh(b*x+a)^3,x, algorithm=""fricas"")","\frac{5 \, \sqrt{3} \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 5 \, \sqrt{3} \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 1215 \, \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{3} \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 1215 \, \sqrt{\pi} {\left(d^{3} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{3} \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{3} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{3} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + d^{3} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - 6 \, {\left(12 \, b^{3} d^{2} x^{2} - {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{6} - 6 \, {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} - {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{6} + 12 \, b^{3} c^{2} - 27 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{4} - 3 \, {\left(36 \, b^{3} d^{2} x^{2} + 36 \, b^{3} c^{2} - 90 \, b^{2} c d + 135 \, b d^{2} + 5 \, {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 18 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{4} + 10 \, b^{2} c d - 4 \, {\left(5 \, {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} + 27 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 5 \, b d^{2} + 27 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} + 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d + 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 3 \, {\left(36 \, b^{3} d^{2} x^{2} + 36 \, b^{3} c^{2} - 5 \, {\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{4} + 90 \, b^{2} c d + 135 \, b d^{2} - 54 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 18 \, {\left(4 \, b^{3} c d + 5 \, b^{2} d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{2} + 2 \, {\left(12 \, b^{3} c d + 5 \, b^{2} d^{2}\right)} x - 6 \, {\left({\left(12 \, b^{3} d^{2} x^{2} + 12 \, b^{3} c^{2} - 10 \, b^{2} c d + 5 \, b d^{2} + 2 \, {\left(12 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{5} + 18 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} - 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d - 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} - 9 \, {\left(4 \, b^{3} d^{2} x^{2} + 4 \, b^{3} c^{2} + 10 \, b^{2} c d + 15 \, b d^{2} + 2 \, {\left(4 \, b^{3} c d + 5 \, b^{2} d^{2}\right)} x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{1728 \, {\left(b^{4} \cosh\left(b x + a\right)^{3} + 3 \, b^{4} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, b^{4} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + b^{4} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"1/1728*(5*sqrt(3)*sqrt(pi)*(d^3*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - d^3*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d^3*cosh(-3*(b*c - a*d)/d) - d^3*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^3*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - d^3*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^3*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - d^3*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) + 5*sqrt(3)*sqrt(pi)*(d^3*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + d^3*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d^3*cosh(-3*(b*c - a*d)/d) + d^3*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^3*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + d^3*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^3*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + d^3*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) + 1215*sqrt(pi)*(d^3*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - d^3*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d^3*cosh(-(b*c - a*d)/d) - d^3*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^3*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d^3*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^3*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - d^3*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 1215*sqrt(pi)*(d^3*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + d^3*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d^3*cosh(-(b*c - a*d)/d) + d^3*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^3*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d^3*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^3*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + d^3*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - 6*(12*b^3*d^2*x^2 - (12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^6 - 6*(12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)*sinh(b*x + a)^5 - (12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*sinh(b*x + a)^6 + 12*b^3*c^2 - 27*(4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^4 - 3*(36*b^3*d^2*x^2 + 36*b^3*c^2 - 90*b^2*c*d + 135*b*d^2 + 5*(12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^2 + 18*(4*b^3*c*d - 5*b^2*d^2)*x)*sinh(b*x + a)^4 + 10*b^2*c*d - 4*(5*(12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^3 + 27*(4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a))*sinh(b*x + a)^3 + 5*b*d^2 + 27*(4*b^3*d^2*x^2 + 4*b^3*c^2 + 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d + 5*b^2*d^2)*x)*cosh(b*x + a)^2 + 3*(36*b^3*d^2*x^2 + 36*b^3*c^2 - 5*(12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^4 + 90*b^2*c*d + 135*b*d^2 - 54*(4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^2 + 18*(4*b^3*c*d + 5*b^2*d^2)*x)*sinh(b*x + a)^2 + 2*(12*b^3*c*d + 5*b^2*d^2)*x - 6*((12*b^3*d^2*x^2 + 12*b^3*c^2 - 10*b^2*c*d + 5*b*d^2 + 2*(12*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^5 + 18*(4*b^3*d^2*x^2 + 4*b^3*c^2 - 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d - 5*b^2*d^2)*x)*cosh(b*x + a)^3 - 9*(4*b^3*d^2*x^2 + 4*b^3*c^2 + 10*b^2*c*d + 15*b*d^2 + 2*(4*b^3*c*d + 5*b^2*d^2)*x)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/(b^4*cosh(b*x + a)^3 + 3*b^4*cosh(b*x + a)^2*sinh(b*x + a) + 3*b^4*cosh(b*x + a)*sinh(b*x + a)^2 + b^4*sinh(b*x + a)^3)","B",0
57,1,1545,0,0.671812," ","integrate((d*x+c)^(3/2)*cosh(b*x+a)^3,x, algorithm=""fricas"")","\frac{\sqrt{3} \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - \sqrt{3} \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 81 \, \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{2} \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 81 \, \sqrt{\pi} {\left(d^{2} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d^{2} \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d^{2} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d^{2} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + d^{2} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 6 \, {\left({\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right)^{6} + 6 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + {\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \sinh\left(b x + a\right)^{6} + 9 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right)^{4} + 3 \, {\left(6 \, b^{2} d x + 6 \, b^{2} c + 5 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right)^{2} - 9 \, b d\right)} \sinh\left(b x + a\right)^{4} - 2 \, b^{2} d x + 4 \, {\left(5 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right)^{3} + 9 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} - 2 \, b^{2} c - 9 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c + 3 \, b d\right)} \cosh\left(b x + a\right)^{2} + 3 \, {\left(5 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right)^{4} - 6 \, b^{2} d x - 6 \, b^{2} c + 18 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right)^{2} - 9 \, b d\right)} \sinh\left(b x + a\right)^{2} - b d + 6 \, {\left({\left(2 \, b^{2} d x + 2 \, b^{2} c - b d\right)} \cosh\left(b x + a\right)^{5} + 6 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c - 3 \, b d\right)} \cosh\left(b x + a\right)^{3} - 3 \, {\left(2 \, b^{2} d x + 2 \, b^{2} c + 3 \, b d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{288 \, {\left(b^{3} \cosh\left(b x + a\right)^{3} + 3 \, b^{3} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, b^{3} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + b^{3} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"1/288*(sqrt(3)*sqrt(pi)*(d^2*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - d^2*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d^2*cosh(-3*(b*c - a*d)/d) - d^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^2*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - d^2*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^2*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - d^2*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) - sqrt(3)*sqrt(pi)*(d^2*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + d^2*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d^2*cosh(-3*(b*c - a*d)/d) + d^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^2*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + d^2*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^2*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + d^2*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) + 81*sqrt(pi)*(d^2*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - d^2*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d^2*cosh(-(b*c - a*d)/d) - d^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^2*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d^2*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^2*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - d^2*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) - 81*sqrt(pi)*(d^2*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + d^2*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d^2*cosh(-(b*c - a*d)/d) + d^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d^2*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d^2*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d^2*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + d^2*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + 6*((2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)^6 + 6*(2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)*sinh(b*x + a)^5 + (2*b^2*d*x + 2*b^2*c - b*d)*sinh(b*x + a)^6 + 9*(2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a)^4 + 3*(6*b^2*d*x + 6*b^2*c + 5*(2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)^2 - 9*b*d)*sinh(b*x + a)^4 - 2*b^2*d*x + 4*(5*(2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)^3 + 9*(2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a))*sinh(b*x + a)^3 - 2*b^2*c - 9*(2*b^2*d*x + 2*b^2*c + 3*b*d)*cosh(b*x + a)^2 + 3*(5*(2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)^4 - 6*b^2*d*x - 6*b^2*c + 18*(2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a)^2 - 9*b*d)*sinh(b*x + a)^2 - b*d + 6*((2*b^2*d*x + 2*b^2*c - b*d)*cosh(b*x + a)^5 + 6*(2*b^2*d*x + 2*b^2*c - 3*b*d)*cosh(b*x + a)^3 - 3*(2*b^2*d*x + 2*b^2*c + 3*b*d)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/(b^3*cosh(b*x + a)^3 + 3*b^3*cosh(b*x + a)^2*sinh(b*x + a) + 3*b^3*cosh(b*x + a)*sinh(b*x + a)^2 + b^3*sinh(b*x + a)^3)","B",0
58,1,1217,0,0.508055," ","integrate(cosh(b*x+a)^3*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{3} \sqrt{\pi} {\left(d \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - d \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + \sqrt{3} \sqrt{\pi} {\left(d \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + d \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 27 \, \sqrt{\pi} {\left(d \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - d \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d \cosh\left(-\frac{b c - a d}{d}\right) - d \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - d \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - d \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 27 \, \sqrt{\pi} {\left(d \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + d \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left(d \cosh\left(-\frac{b c - a d}{d}\right) + d \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(d \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + d \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left(d \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + d \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 6 \, {\left(b \cosh\left(b x + a\right)^{6} + 6 \, b \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + b \sinh\left(b x + a\right)^{6} + 9 \, b \cosh\left(b x + a\right)^{4} + 3 \, {\left(5 \, b \cosh\left(b x + a\right)^{2} + 3 \, b\right)} \sinh\left(b x + a\right)^{4} + 4 \, {\left(5 \, b \cosh\left(b x + a\right)^{3} + 9 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} - 9 \, b \cosh\left(b x + a\right)^{2} + 3 \, {\left(5 \, b \cosh\left(b x + a\right)^{4} + 18 \, b \cosh\left(b x + a\right)^{2} - 3 \, b\right)} \sinh\left(b x + a\right)^{2} + 6 \, {\left(b \cosh\left(b x + a\right)^{5} + 6 \, b \cosh\left(b x + a\right)^{3} - 3 \, b \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) - b\right)} \sqrt{d x + c}}{144 \, {\left(b^{2} \cosh\left(b x + a\right)^{3} + 3 \, b^{2} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, b^{2} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + b^{2} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"1/144*(sqrt(3)*sqrt(pi)*(d*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - d*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d*cosh(-3*(b*c - a*d)/d) - d*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - d*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - d*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) + sqrt(3)*sqrt(pi)*(d*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + d*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + (d*cosh(-3*(b*c - a*d)/d) + d*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + d*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + d*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) + 27*sqrt(pi)*(d*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - d*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d*cosh(-(b*c - a*d)/d) - d*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - d*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - d*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 27*sqrt(pi)*(d*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + d*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + (d*cosh(-(b*c - a*d)/d) + d*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*(d*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + d*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*(d*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + d*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + 6*(b*cosh(b*x + a)^6 + 6*b*cosh(b*x + a)*sinh(b*x + a)^5 + b*sinh(b*x + a)^6 + 9*b*cosh(b*x + a)^4 + 3*(5*b*cosh(b*x + a)^2 + 3*b)*sinh(b*x + a)^4 + 4*(5*b*cosh(b*x + a)^3 + 9*b*cosh(b*x + a))*sinh(b*x + a)^3 - 9*b*cosh(b*x + a)^2 + 3*(5*b*cosh(b*x + a)^4 + 18*b*cosh(b*x + a)^2 - 3*b)*sinh(b*x + a)^2 + 6*(b*cosh(b*x + a)^5 + 6*b*cosh(b*x + a)^3 - 3*b*cosh(b*x + a))*sinh(b*x + a) - b)*sqrt(d*x + c))/(b^2*cosh(b*x + a)^3 + 3*b^2*cosh(b*x + a)^2*sinh(b*x + a) + 3*b^2*cosh(b*x + a)*sinh(b*x + a)^2 + b^2*sinh(b*x + a)^3)","B",0
59,1,253,0,0.556395," ","integrate(cosh(b*x+a)^3/(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{3} \sqrt{\pi} \sqrt{\frac{b}{d}} {\left(\cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - \sqrt{3} \sqrt{\pi} \sqrt{-\frac{b}{d}} {\left(\cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 9 \, \sqrt{\pi} \sqrt{\frac{b}{d}} {\left(\cosh\left(-\frac{b c - a d}{d}\right) - \sinh\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 9 \, \sqrt{\pi} \sqrt{-\frac{b}{d}} {\left(\cosh\left(-\frac{b c - a d}{d}\right) + \sinh\left(-\frac{b c - a d}{d}\right)\right)} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right)}{24 \, b}"," ",0,"1/24*(sqrt(3)*sqrt(pi)*sqrt(b/d)*(cosh(-3*(b*c - a*d)/d) - sinh(-3*(b*c - a*d)/d))*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) - sqrt(3)*sqrt(pi)*sqrt(-b/d)*(cosh(-3*(b*c - a*d)/d) + sinh(-3*(b*c - a*d)/d))*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) + 9*sqrt(pi)*sqrt(b/d)*(cosh(-(b*c - a*d)/d) - sinh(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(b/d)) - 9*sqrt(pi)*sqrt(-b/d)*(cosh(-(b*c - a*d)/d) + sinh(-(b*c - a*d)/d))*erf(sqrt(d*x + c)*sqrt(-b/d)))/b","A",0
60,1,1344,0,0.549374," ","integrate(cosh(b*x+a)^3/(d*x+c)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{3} \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + \sqrt{3} \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 3 \, \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 3 \, \sqrt{\pi} {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(d x + c\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(d x + c\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left(\cosh\left(b x + a\right)^{6} + 6 \, \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + \sinh\left(b x + a\right)^{6} + 3 \, {\left(5 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{4} + 3 \, \cosh\left(b x + a\right)^{4} + 4 \, {\left(5 \, \cosh\left(b x + a\right)^{3} + 3 \, \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left(5 \, \cosh\left(b x + a\right)^{4} + 6 \, \cosh\left(b x + a\right)^{2} + 1\right)} \sinh\left(b x + a\right)^{2} + 3 \, \cosh\left(b x + a\right)^{2} + 6 \, {\left(\cosh\left(b x + a\right)^{5} + 2 \, \cosh\left(b x + a\right)^{3} + \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + 1\right)} \sqrt{d x + c}}{4 \, {\left({\left(d^{2} x + c d\right)} \cosh\left(b x + a\right)^{3} + 3 \, {\left(d^{2} x + c d\right)} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, {\left(d^{2} x + c d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + {\left(d^{2} x + c d\right)} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"-1/4*(sqrt(3)*sqrt(pi)*((d*x + c)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((d*x + c)*cosh(-3*(b*c - a*d)/d) - (d*x + c)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((d*x + c)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((d*x + c)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) + sqrt(3)*sqrt(pi)*((d*x + c)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((d*x + c)*cosh(-3*(b*c - a*d)/d) + (d*x + c)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((d*x + c)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((d*x + c)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) + 3*sqrt(pi)*((d*x + c)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((d*x + c)*cosh(-(b*c - a*d)/d) - (d*x + c)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((d*x + c)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((d*x + c)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - (d*x + c)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 3*sqrt(pi)*((d*x + c)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((d*x + c)*cosh(-(b*c - a*d)/d) + (d*x + c)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((d*x + c)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((d*x + c)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + (d*x + c)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + (cosh(b*x + a)^6 + 6*cosh(b*x + a)*sinh(b*x + a)^5 + sinh(b*x + a)^6 + 3*(5*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^4 + 3*cosh(b*x + a)^4 + 4*(5*cosh(b*x + a)^3 + 3*cosh(b*x + a))*sinh(b*x + a)^3 + 3*(5*cosh(b*x + a)^4 + 6*cosh(b*x + a)^2 + 1)*sinh(b*x + a)^2 + 3*cosh(b*x + a)^2 + 6*(cosh(b*x + a)^5 + 2*cosh(b*x + a)^3 + cosh(b*x + a))*sinh(b*x + a) + 1)*sqrt(d*x + c))/((d^2*x + c*d)*cosh(b*x + a)^3 + 3*(d^2*x + c*d)*cosh(b*x + a)^2*sinh(b*x + a) + 3*(d^2*x + c*d)*cosh(b*x + a)*sinh(b*x + a)^2 + (d^2*x + c*d)*sinh(b*x + a)^3)","B",0
61,1,2058,0,0.713425," ","integrate(cosh(b*x+a)^3/(d*x+c)^(5/2),x, algorithm=""fricas"")","\frac{6 \, \sqrt{3} \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 6 \, \sqrt{3} \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 6 \, \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) - 6 \, \sqrt{\pi} {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) - {\left({\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right)^{6} + 6 \, {\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + {\left(6 \, b d x + 6 \, b c + d\right)} \sinh\left(b x + a\right)^{6} + 3 \, {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right)^{4} + 3 \, {\left(2 \, b d x + 5 \, {\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right)^{2} + 2 \, b c + d\right)} \sinh\left(b x + a\right)^{4} + 4 \, {\left(5 \, {\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right)^{3} + 3 \, {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} - 6 \, b d x - 3 \, {\left(2 \, b d x + 2 \, b c - d\right)} \cosh\left(b x + a\right)^{2} + 3 \, {\left(5 \, {\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right)^{4} - 2 \, b d x + 6 \, {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right)^{2} - 2 \, b c + d\right)} \sinh\left(b x + a\right)^{2} - 6 \, b c + 6 \, {\left({\left(6 \, b d x + 6 \, b c + d\right)} \cosh\left(b x + a\right)^{5} + 2 \, {\left(2 \, b d x + 2 \, b c + d\right)} \cosh\left(b x + a\right)^{3} - {\left(2 \, b d x + 2 \, b c - d\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right) + d\right)} \sqrt{d x + c}}{12 \, {\left({\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right)^{3} + 3 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + {\left(d^{4} x^{2} + 2 \, c d^{3} x + c^{2} d^{2}\right)} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"1/12*(6*sqrt(3)*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-3*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) - 6*sqrt(3)*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-3*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) + 6*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) - 6*sqrt(pi)*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) - ((6*b*d*x + 6*b*c + d)*cosh(b*x + a)^6 + 6*(6*b*d*x + 6*b*c + d)*cosh(b*x + a)*sinh(b*x + a)^5 + (6*b*d*x + 6*b*c + d)*sinh(b*x + a)^6 + 3*(2*b*d*x + 2*b*c + d)*cosh(b*x + a)^4 + 3*(2*b*d*x + 5*(6*b*d*x + 6*b*c + d)*cosh(b*x + a)^2 + 2*b*c + d)*sinh(b*x + a)^4 + 4*(5*(6*b*d*x + 6*b*c + d)*cosh(b*x + a)^3 + 3*(2*b*d*x + 2*b*c + d)*cosh(b*x + a))*sinh(b*x + a)^3 - 6*b*d*x - 3*(2*b*d*x + 2*b*c - d)*cosh(b*x + a)^2 + 3*(5*(6*b*d*x + 6*b*c + d)*cosh(b*x + a)^4 - 2*b*d*x + 6*(2*b*d*x + 2*b*c + d)*cosh(b*x + a)^2 - 2*b*c + d)*sinh(b*x + a)^2 - 6*b*c + 6*((6*b*d*x + 6*b*c + d)*cosh(b*x + a)^5 + 2*(2*b*d*x + 2*b*c + d)*cosh(b*x + a)^3 - (2*b*d*x + 2*b*c - d)*cosh(b*x + a))*sinh(b*x + a) + d)*sqrt(d*x + c))/((d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a)^3 + 3*(d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a)^2*sinh(b*x + a) + 3*(d^4*x^2 + 2*c*d^3*x + c^2*d^2)*cosh(b*x + a)*sinh(b*x + a)^2 + (d^4*x^2 + 2*c*d^3*x + c^2*d^2)*sinh(b*x + a)^3)","B",0
62,1,3280,0,0.624748," ","integrate(cosh(b*x+a)^3/(d*x+c)^(7/2),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{3} \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 12 \, \sqrt{3} \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{3 \, {\left(b c - a d\right)}}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + 4 \, \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) - {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{\frac{b}{d}}\right) + 4 \, \sqrt{\pi} {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{3} \sinh\left(-\frac{b c - a d}{d}\right) + {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{3} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right) \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)^{2} + 3 \, {\left({\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \cosh\left(-\frac{b c - a d}{d}\right) + {\left(b^{2} d^{3} x^{3} + 3 \, b^{2} c d^{2} x^{2} + 3 \, b^{2} c^{2} d x + b^{2} c^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(-\frac{b c - a d}{d}\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{-\frac{b}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{b}{d}}\right) + {\left({\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{6} + 6 \, {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{5} + {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{6} + 12 \, b^{2} d^{2} x^{2} + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{4} + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 15 \, {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{4} + 12 \, b^{2} c^{2} + 4 \, {\left(5 \, {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)^{3} - 2 \, b c d + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} - 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d - b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + {\left(4 \, b^{2} d^{2} x^{2} + 15 \, {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{4} + 4 \, b^{2} c^{2} - 2 \, b c d + 6 \, {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{2} + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d - b d^{2}\right)} x\right)} \sinh\left(b x + a\right)^{2} + d^{2} + 2 \, {\left(12 \, b^{2} c d - b d^{2}\right)} x + 2 \, {\left(3 \, {\left(12 \, b^{2} d^{2} x^{2} + 12 \, b^{2} c^{2} + 2 \, b c d + d^{2} + 2 \, {\left(12 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{5} + 2 \, {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} + 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d + b d^{2}\right)} x\right)} \cosh\left(b x + a\right)^{3} + {\left(4 \, b^{2} d^{2} x^{2} + 4 \, b^{2} c^{2} - 2 \, b c d + 3 \, d^{2} + 2 \, {\left(4 \, b^{2} c d - b d^{2}\right)} x\right)} \cosh\left(b x + a\right)\right)} \sinh\left(b x + a\right)\right)} \sqrt{d x + c}}{20 \, {\left({\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right)^{3} + 3 \, {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right)^{2} \sinh\left(b x + a\right) + 3 \, {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \cosh\left(b x + a\right) \sinh\left(b x + a\right)^{2} + {\left(d^{6} x^{3} + 3 \, c d^{5} x^{2} + 3 \, c^{2} d^{4} x + c^{3} d^{3}\right)} \sinh\left(b x + a\right)^{3}\right)}}"," ",0,"-1/20*(12*sqrt(3)*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-3*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(b/d)) + 12*sqrt(3)*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*cosh(-3*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*sinh(-3*(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-3*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-3*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-3*(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-3*(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-b/d)) + 4*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) - (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(b/d)*erf(sqrt(d*x + c)*sqrt(b/d)) + 4*sqrt(pi)*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^3*sinh(-(b*c - a*d)/d) + ((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^3 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)*sinh(-(b*c - a*d)/d))*sinh(b*x + a)^2 + 3*((b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*cosh(-(b*c - a*d)/d) + (b^2*d^3*x^3 + 3*b^2*c*d^2*x^2 + 3*b^2*c^2*d*x + b^2*c^3)*cosh(b*x + a)^2*sinh(-(b*c - a*d)/d))*sinh(b*x + a))*sqrt(-b/d)*erf(sqrt(d*x + c)*sqrt(-b/d)) + ((12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^6 + 6*(12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)*sinh(b*x + a)^5 + (12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*sinh(b*x + a)^6 + 12*b^2*d^2*x^2 + (4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^4 + (4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 15*(12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^2 + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*sinh(b*x + a)^4 + 12*b^2*c^2 + 4*(5*(12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^3 + (4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a))*sinh(b*x + a)^3 - 2*b*c*d + (4*b^2*d^2*x^2 + 4*b^2*c^2 - 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d - b*d^2)*x)*cosh(b*x + a)^2 + (4*b^2*d^2*x^2 + 15*(12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^4 + 4*b^2*c^2 - 2*b*c*d + 6*(4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^2 + 3*d^2 + 2*(4*b^2*c*d - b*d^2)*x)*sinh(b*x + a)^2 + d^2 + 2*(12*b^2*c*d - b*d^2)*x + 2*(3*(12*b^2*d^2*x^2 + 12*b^2*c^2 + 2*b*c*d + d^2 + 2*(12*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^5 + 2*(4*b^2*d^2*x^2 + 4*b^2*c^2 + 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d + b*d^2)*x)*cosh(b*x + a)^3 + (4*b^2*d^2*x^2 + 4*b^2*c^2 - 2*b*c*d + 3*d^2 + 2*(4*b^2*c*d - b*d^2)*x)*cosh(b*x + a))*sinh(b*x + a))*sqrt(d*x + c))/((d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a)^3 + 3*(d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a)^2*sinh(b*x + a) + 3*(d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*cosh(b*x + a)*sinh(b*x + a)^2 + (d^6*x^3 + 3*c*d^5*x^2 + 3*c^2*d^4*x + c^3*d^3)*sinh(b*x + a)^3)","B",0
63,1,191,0,0.452575," ","integrate((d*x)^(3/2)*cosh(f*x),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\pi} {\left(d^{2} \cosh\left(f x\right) + d^{2} \sinh\left(f x\right)\right)} \sqrt{\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{f}{d}}\right) - 3 \, \sqrt{\pi} {\left(d^{2} \cosh\left(f x\right) + d^{2} \sinh\left(f x\right)\right)} \sqrt{-\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{f}{d}}\right) - 2 \, {\left(2 \, d f^{2} x - {\left(2 \, d f^{2} x - 3 \, d f\right)} \cosh\left(f x\right)^{2} - 2 \, {\left(2 \, d f^{2} x - 3 \, d f\right)} \cosh\left(f x\right) \sinh\left(f x\right) - {\left(2 \, d f^{2} x - 3 \, d f\right)} \sinh\left(f x\right)^{2} + 3 \, d f\right)} \sqrt{d x}}{8 \, {\left(f^{3} \cosh\left(f x\right) + f^{3} \sinh\left(f x\right)\right)}}"," ",0,"1/8*(3*sqrt(pi)*(d^2*cosh(f*x) + d^2*sinh(f*x))*sqrt(f/d)*erf(sqrt(d*x)*sqrt(f/d)) - 3*sqrt(pi)*(d^2*cosh(f*x) + d^2*sinh(f*x))*sqrt(-f/d)*erf(sqrt(d*x)*sqrt(-f/d)) - 2*(2*d*f^2*x - (2*d*f^2*x - 3*d*f)*cosh(f*x)^2 - 2*(2*d*f^2*x - 3*d*f)*cosh(f*x)*sinh(f*x) - (2*d*f^2*x - 3*d*f)*sinh(f*x)^2 + 3*d*f)*sqrt(d*x))/(f^3*cosh(f*x) + f^3*sinh(f*x))","B",0
64,1,138,0,0.628228," ","integrate(cosh(f*x)*(d*x)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\pi} {\left(d \cosh\left(f x\right) + d \sinh\left(f x\right)\right)} \sqrt{\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{f}{d}}\right) + \sqrt{\pi} {\left(d \cosh\left(f x\right) + d \sinh\left(f x\right)\right)} \sqrt{-\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{f}{d}}\right) + 2 \, {\left(f \cosh\left(f x\right)^{2} + 2 \, f \cosh\left(f x\right) \sinh\left(f x\right) + f \sinh\left(f x\right)^{2} - f\right)} \sqrt{d x}}{4 \, {\left(f^{2} \cosh\left(f x\right) + f^{2} \sinh\left(f x\right)\right)}}"," ",0,"1/4*(sqrt(pi)*(d*cosh(f*x) + d*sinh(f*x))*sqrt(f/d)*erf(sqrt(d*x)*sqrt(f/d)) + sqrt(pi)*(d*cosh(f*x) + d*sinh(f*x))*sqrt(-f/d)*erf(sqrt(d*x)*sqrt(-f/d)) + 2*(f*cosh(f*x)^2 + 2*f*cosh(f*x)*sinh(f*x) + f*sinh(f*x)^2 - f)*sqrt(d*x))/(f^2*cosh(f*x) + f^2*sinh(f*x))","B",0
65,1,59,0,0.457579," ","integrate(cosh(f*x)/(d*x)^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{\pi} \sqrt{\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{f}{d}}\right) - \sqrt{\pi} \sqrt{-\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{f}{d}}\right)}{2 \, f}"," ",0,"1/2*(sqrt(pi)*sqrt(f/d)*erf(sqrt(d*x)*sqrt(f/d)) - sqrt(pi)*sqrt(-f/d)*erf(sqrt(d*x)*sqrt(-f/d)))/f","A",0
66,1,136,0,0.480249," ","integrate(cosh(f*x)/(d*x)^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{\pi} {\left(d x \cosh\left(f x\right) + d x \sinh\left(f x\right)\right)} \sqrt{\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{f}{d}}\right) + \sqrt{\pi} {\left(d x \cosh\left(f x\right) + d x \sinh\left(f x\right)\right)} \sqrt{-\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{f}{d}}\right) + \sqrt{d x} {\left(\cosh\left(f x\right)^{2} + 2 \, \cosh\left(f x\right) \sinh\left(f x\right) + \sinh\left(f x\right)^{2} + 1\right)}}{d^{2} x \cosh\left(f x\right) + d^{2} x \sinh\left(f x\right)}"," ",0,"-(sqrt(pi)*(d*x*cosh(f*x) + d*x*sinh(f*x))*sqrt(f/d)*erf(sqrt(d*x)*sqrt(f/d)) + sqrt(pi)*(d*x*cosh(f*x) + d*x*sinh(f*x))*sqrt(-f/d)*erf(sqrt(d*x)*sqrt(-f/d)) + sqrt(d*x)*(cosh(f*x)^2 + 2*cosh(f*x)*sinh(f*x) + sinh(f*x)^2 + 1))/(d^2*x*cosh(f*x) + d^2*x*sinh(f*x))","B",0
67,1,179,0,0.540222," ","integrate(cosh(f*x)/(d*x)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{\pi} {\left(d f x^{2} \cosh\left(f x\right) + d f x^{2} \sinh\left(f x\right)\right)} \sqrt{\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{\frac{f}{d}}\right) - 2 \, \sqrt{\pi} {\left(d f x^{2} \cosh\left(f x\right) + d f x^{2} \sinh\left(f x\right)\right)} \sqrt{-\frac{f}{d}} \operatorname{erf}\left(\sqrt{d x} \sqrt{-\frac{f}{d}}\right) - {\left({\left(2 \, f x + 1\right)} \cosh\left(f x\right)^{2} + 2 \, {\left(2 \, f x + 1\right)} \cosh\left(f x\right) \sinh\left(f x\right) + {\left(2 \, f x + 1\right)} \sinh\left(f x\right)^{2} - 2 \, f x + 1\right)} \sqrt{d x}}{3 \, {\left(d^{3} x^{2} \cosh\left(f x\right) + d^{3} x^{2} \sinh\left(f x\right)\right)}}"," ",0,"1/3*(2*sqrt(pi)*(d*f*x^2*cosh(f*x) + d*f*x^2*sinh(f*x))*sqrt(f/d)*erf(sqrt(d*x)*sqrt(f/d)) - 2*sqrt(pi)*(d*f*x^2*cosh(f*x) + d*f*x^2*sinh(f*x))*sqrt(-f/d)*erf(sqrt(d*x)*sqrt(-f/d)) - ((2*f*x + 1)*cosh(f*x)^2 + 2*(2*f*x + 1)*cosh(f*x)*sinh(f*x) + (2*f*x + 1)*sinh(f*x)^2 - 2*f*x + 1)*sqrt(d*x))/(d^3*x^2*cosh(f*x) + d^3*x^2*sinh(f*x))","B",0
68,0,0,0,0.450619," ","integrate(sech(b*x+a)*(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{d x + c} \operatorname{sech}\left(b x + a\right), x\right)"," ",0,"integral(sqrt(d*x + c)*sech(b*x + a), x)","F",0
69,0,0,0,0.458674," ","integrate(sech(b*x+a)/(d*x+c)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(b x + a\right)}{\sqrt{d x + c}}, x\right)"," ",0,"integral(sech(b*x + a)/sqrt(d*x + c), x)","F",0
70,-2,0,0,0.000000," ","integrate(cosh(x)^(3/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
71,-2,0,0,0.000000," ","integrate(x/cosh(x)^(3/2)+x*cosh(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
72,1,109,0,0.525797," ","integrate(x/cosh(x)^(5/2)-1/3*x/cosh(x)^(1/2),x, algorithm=""fricas"")","\frac{4 \, {\left({\left(x + 2\right)} \cosh\left(x\right)^{3} + 3 \, {\left(x + 2\right)} \cosh\left(x\right) \sinh\left(x\right)^{2} + {\left(x + 2\right)} \sinh\left(x\right)^{3} - {\left(x - 2\right)} \cosh\left(x\right) + {\left(3 \, {\left(x + 2\right)} \cosh\left(x\right)^{2} - x + 2\right)} \sinh\left(x\right)\right)} \sqrt{\cosh\left(x\right)}}{3 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"4/3*((x + 2)*cosh(x)^3 + 3*(x + 2)*cosh(x)*sinh(x)^2 + (x + 2)*sinh(x)^3 - (x - 2)*cosh(x) + (3*(x + 2)*cosh(x)^2 - x + 2)*sinh(x))*sqrt(cosh(x))/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)","B",0
73,-2,0,0,0.000000," ","integrate(x/cosh(x)^(7/2)+3/5*x*cosh(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
74,-2,0,0,0.000000," ","integrate(x^2/cosh(x)^(3/2)+x^2*cosh(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
75,0,0,0,0.525129," ","integrate((d*x+c)^m*(b*cosh(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \left(b \cosh\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((d*x + c)^m*(b*cosh(f*x + e))^n, x)","F",0
76,1,340,0,0.554604," ","integrate((d*x+c)^m*cosh(b*x+a)^3,x, algorithm=""fricas"")","-\frac{\cosh\left(\frac{d m \log\left(\frac{3 \, b}{d}\right) - 3 \, b c + 3 \, a d}{d}\right) \Gamma\left(m + 1, \frac{3 \, {\left(b d x + b c\right)}}{d}\right) + 9 \, \cosh\left(\frac{d m \log\left(\frac{b}{d}\right) - b c + a d}{d}\right) \Gamma\left(m + 1, \frac{b d x + b c}{d}\right) - 9 \, \cosh\left(\frac{d m \log\left(-\frac{b}{d}\right) + b c - a d}{d}\right) \Gamma\left(m + 1, -\frac{b d x + b c}{d}\right) - \cosh\left(\frac{d m \log\left(-\frac{3 \, b}{d}\right) + 3 \, b c - 3 \, a d}{d}\right) \Gamma\left(m + 1, -\frac{3 \, {\left(b d x + b c\right)}}{d}\right) - \Gamma\left(m + 1, \frac{3 \, {\left(b d x + b c\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{3 \, b}{d}\right) - 3 \, b c + 3 \, a d}{d}\right) - 9 \, \Gamma\left(m + 1, \frac{b d x + b c}{d}\right) \sinh\left(\frac{d m \log\left(\frac{b}{d}\right) - b c + a d}{d}\right) + 9 \, \Gamma\left(m + 1, -\frac{b d x + b c}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{b}{d}\right) + b c - a d}{d}\right) + \Gamma\left(m + 1, -\frac{3 \, {\left(b d x + b c\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{3 \, b}{d}\right) + 3 \, b c - 3 \, a d}{d}\right)}{24 \, b}"," ",0,"-1/24*(cosh((d*m*log(3*b/d) - 3*b*c + 3*a*d)/d)*gamma(m + 1, 3*(b*d*x + b*c)/d) + 9*cosh((d*m*log(b/d) - b*c + a*d)/d)*gamma(m + 1, (b*d*x + b*c)/d) - 9*cosh((d*m*log(-b/d) + b*c - a*d)/d)*gamma(m + 1, -(b*d*x + b*c)/d) - cosh((d*m*log(-3*b/d) + 3*b*c - 3*a*d)/d)*gamma(m + 1, -3*(b*d*x + b*c)/d) - gamma(m + 1, 3*(b*d*x + b*c)/d)*sinh((d*m*log(3*b/d) - 3*b*c + 3*a*d)/d) - 9*gamma(m + 1, (b*d*x + b*c)/d)*sinh((d*m*log(b/d) - b*c + a*d)/d) + 9*gamma(m + 1, -(b*d*x + b*c)/d)*sinh((d*m*log(-b/d) + b*c - a*d)/d) + gamma(m + 1, -3*(b*d*x + b*c)/d)*sinh((d*m*log(-3*b/d) + 3*b*c - 3*a*d)/d))/b","A",0
77,1,241,0,0.548398," ","integrate((d*x+c)^m*cosh(b*x+a)^2,x, algorithm=""fricas"")","-\frac{{\left(d m + d\right)} \cosh\left(\frac{d m \log\left(\frac{2 \, b}{d}\right) - 2 \, b c + 2 \, a d}{d}\right) \Gamma\left(m + 1, \frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left(d m + d\right)} \cosh\left(\frac{d m \log\left(-\frac{2 \, b}{d}\right) + 2 \, b c - 2 \, a d}{d}\right) \Gamma\left(m + 1, -\frac{2 \, {\left(b d x + b c\right)}}{d}\right) - {\left(d m + d\right)} \Gamma\left(m + 1, \frac{2 \, {\left(b d x + b c\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{2 \, b}{d}\right) - 2 \, b c + 2 \, a d}{d}\right) + {\left(d m + d\right)} \Gamma\left(m + 1, -\frac{2 \, {\left(b d x + b c\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{2 \, b}{d}\right) + 2 \, b c - 2 \, a d}{d}\right) - 4 \, {\left(b d x + b c\right)} \cosh\left(m \log\left(d x + c\right)\right) - 4 \, {\left(b d x + b c\right)} \sinh\left(m \log\left(d x + c\right)\right)}{8 \, {\left(b d m + b d\right)}}"," ",0,"-1/8*((d*m + d)*cosh((d*m*log(2*b/d) - 2*b*c + 2*a*d)/d)*gamma(m + 1, 2*(b*d*x + b*c)/d) - (d*m + d)*cosh((d*m*log(-2*b/d) + 2*b*c - 2*a*d)/d)*gamma(m + 1, -2*(b*d*x + b*c)/d) - (d*m + d)*gamma(m + 1, 2*(b*d*x + b*c)/d)*sinh((d*m*log(2*b/d) - 2*b*c + 2*a*d)/d) + (d*m + d)*gamma(m + 1, -2*(b*d*x + b*c)/d)*sinh((d*m*log(-2*b/d) + 2*b*c - 2*a*d)/d) - 4*(b*d*x + b*c)*cosh(m*log(d*x + c)) - 4*(b*d*x + b*c)*sinh(m*log(d*x + c)))/(b*d*m + b*d)","A",0
78,1,168,0,0.455457," ","integrate((d*x+c)^m*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{\cosh\left(\frac{d m \log\left(\frac{b}{d}\right) - b c + a d}{d}\right) \Gamma\left(m + 1, \frac{b d x + b c}{d}\right) - \cosh\left(\frac{d m \log\left(-\frac{b}{d}\right) + b c - a d}{d}\right) \Gamma\left(m + 1, -\frac{b d x + b c}{d}\right) - \Gamma\left(m + 1, \frac{b d x + b c}{d}\right) \sinh\left(\frac{d m \log\left(\frac{b}{d}\right) - b c + a d}{d}\right) + \Gamma\left(m + 1, -\frac{b d x + b c}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{b}{d}\right) + b c - a d}{d}\right)}{2 \, b}"," ",0,"-1/2*(cosh((d*m*log(b/d) - b*c + a*d)/d)*gamma(m + 1, (b*d*x + b*c)/d) - cosh((d*m*log(-b/d) + b*c - a*d)/d)*gamma(m + 1, -(b*d*x + b*c)/d) - gamma(m + 1, (b*d*x + b*c)/d)*sinh((d*m*log(b/d) - b*c + a*d)/d) + gamma(m + 1, -(b*d*x + b*c)/d)*sinh((d*m*log(-b/d) + b*c - a*d)/d))/b","A",0
79,0,0,0,0.627050," ","integrate((d*x+c)^m*sech(b*x+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \operatorname{sech}\left(b x + a\right), x\right)"," ",0,"integral((d*x + c)^m*sech(b*x + a), x)","F",0
80,0,0,0,0.500470," ","integrate((d*x+c)^m*sech(b*x+a)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} \operatorname{sech}\left(b x + a\right)^{2}, x\right)"," ",0,"integral((d*x + c)^m*sech(b*x + a)^2, x)","F",0
81,1,86,0,0.456022," ","integrate(x^(3+m)*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{\cosh\left({\left(m + 3\right)} \log\left(b\right) + a\right) \Gamma\left(m + 4, b x\right) - \cosh\left({\left(m + 3\right)} \log\left(-b\right) - a\right) \Gamma\left(m + 4, -b x\right) + \Gamma\left(m + 4, -b x\right) \sinh\left({\left(m + 3\right)} \log\left(-b\right) - a\right) - \Gamma\left(m + 4, b x\right) \sinh\left({\left(m + 3\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"-1/2*(cosh((m + 3)*log(b) + a)*gamma(m + 4, b*x) - cosh((m + 3)*log(-b) - a)*gamma(m + 4, -b*x) + gamma(m + 4, -b*x)*sinh((m + 3)*log(-b) - a) - gamma(m + 4, b*x)*sinh((m + 3)*log(b) + a))/b","A",0
82,1,86,0,0.448515," ","integrate(x^(2+m)*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{\cosh\left({\left(m + 2\right)} \log\left(b\right) + a\right) \Gamma\left(m + 3, b x\right) - \cosh\left({\left(m + 2\right)} \log\left(-b\right) - a\right) \Gamma\left(m + 3, -b x\right) + \Gamma\left(m + 3, -b x\right) \sinh\left({\left(m + 2\right)} \log\left(-b\right) - a\right) - \Gamma\left(m + 3, b x\right) \sinh\left({\left(m + 2\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"-1/2*(cosh((m + 2)*log(b) + a)*gamma(m + 3, b*x) - cosh((m + 2)*log(-b) - a)*gamma(m + 3, -b*x) + gamma(m + 3, -b*x)*sinh((m + 2)*log(-b) - a) - gamma(m + 3, b*x)*sinh((m + 2)*log(b) + a))/b","A",0
83,1,86,0,0.438130," ","integrate(x^(1+m)*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{\cosh\left({\left(m + 1\right)} \log\left(b\right) + a\right) \Gamma\left(m + 2, b x\right) - \cosh\left({\left(m + 1\right)} \log\left(-b\right) - a\right) \Gamma\left(m + 2, -b x\right) + \Gamma\left(m + 2, -b x\right) \sinh\left({\left(m + 1\right)} \log\left(-b\right) - a\right) - \Gamma\left(m + 2, b x\right) \sinh\left({\left(m + 1\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"-1/2*(cosh((m + 1)*log(b) + a)*gamma(m + 2, b*x) - cosh((m + 1)*log(-b) - a)*gamma(m + 2, -b*x) + gamma(m + 2, -b*x)*sinh((m + 1)*log(-b) - a) - gamma(m + 2, b*x)*sinh((m + 1)*log(b) + a))/b","A",0
84,1,78,0,0.458677," ","integrate(x^m*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{\cosh\left(m \log\left(b\right) + a\right) \Gamma\left(m + 1, b x\right) - \cosh\left(m \log\left(-b\right) - a\right) \Gamma\left(m + 1, -b x\right) + \Gamma\left(m + 1, -b x\right) \sinh\left(m \log\left(-b\right) - a\right) - \Gamma\left(m + 1, b x\right) \sinh\left(m \log\left(b\right) + a\right)}{2 \, b}"," ",0,"-1/2*(cosh(m*log(b) + a)*gamma(m + 1, b*x) - cosh(m*log(-b) - a)*gamma(m + 1, -b*x) + gamma(m + 1, -b*x)*sinh(m*log(-b) - a) - gamma(m + 1, b*x)*sinh(m*log(b) + a))/b","A",0
85,1,78,0,0.438570," ","integrate(x^(-1+m)*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{\cosh\left({\left(m - 1\right)} \log\left(b\right) + a\right) \Gamma\left(m, b x\right) - \cosh\left({\left(m - 1\right)} \log\left(-b\right) - a\right) \Gamma\left(m, -b x\right) + \Gamma\left(m, -b x\right) \sinh\left({\left(m - 1\right)} \log\left(-b\right) - a\right) - \Gamma\left(m, b x\right) \sinh\left({\left(m - 1\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"-1/2*(cosh((m - 1)*log(b) + a)*gamma(m, b*x) - cosh((m - 1)*log(-b) - a)*gamma(m, -b*x) + gamma(m, -b*x)*sinh((m - 1)*log(-b) - a) - gamma(m, b*x)*sinh((m - 1)*log(b) + a))/b","A",0
86,1,86,0,0.506233," ","integrate(x^(-2+m)*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{\cosh\left({\left(m - 2\right)} \log\left(b\right) + a\right) \Gamma\left(m - 1, b x\right) - \cosh\left({\left(m - 2\right)} \log\left(-b\right) - a\right) \Gamma\left(m - 1, -b x\right) + \Gamma\left(m - 1, -b x\right) \sinh\left({\left(m - 2\right)} \log\left(-b\right) - a\right) - \Gamma\left(m - 1, b x\right) \sinh\left({\left(m - 2\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"-1/2*(cosh((m - 2)*log(b) + a)*gamma(m - 1, b*x) - cosh((m - 2)*log(-b) - a)*gamma(m - 1, -b*x) + gamma(m - 1, -b*x)*sinh((m - 2)*log(-b) - a) - gamma(m - 1, b*x)*sinh((m - 2)*log(b) + a))/b","A",0
87,1,86,0,0.423089," ","integrate(x^(-3+m)*cosh(b*x+a),x, algorithm=""fricas"")","-\frac{\cosh\left({\left(m - 3\right)} \log\left(b\right) + a\right) \Gamma\left(m - 2, b x\right) - \cosh\left({\left(m - 3\right)} \log\left(-b\right) - a\right) \Gamma\left(m - 2, -b x\right) + \Gamma\left(m - 2, -b x\right) \sinh\left({\left(m - 3\right)} \log\left(-b\right) - a\right) - \Gamma\left(m - 2, b x\right) \sinh\left({\left(m - 3\right)} \log\left(b\right) + a\right)}{2 \, b}"," ",0,"-1/2*(cosh((m - 3)*log(b) + a)*gamma(m - 2, b*x) - cosh((m - 3)*log(-b) - a)*gamma(m - 2, -b*x) + gamma(m - 2, -b*x)*sinh((m - 3)*log(-b) - a) - gamma(m - 2, b*x)*sinh((m - 3)*log(b) + a))/b","A",0
88,1,136,0,0.505110," ","integrate(x^(3+m)*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x \cosh\left({\left(m + 3\right)} \log\left(x\right)\right) - {\left(m + 4\right)} \cosh\left({\left(m + 3\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m + 4, 2 \, b x\right) + {\left(m + 4\right)} \cosh\left({\left(m + 3\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m + 4, -2 \, b x\right) + {\left(m + 4\right)} \Gamma\left(m + 4, 2 \, b x\right) \sinh\left({\left(m + 3\right)} \log\left(2 \, b\right) + 2 \, a\right) - {\left(m + 4\right)} \Gamma\left(m + 4, -2 \, b x\right) \sinh\left({\left(m + 3\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m + 3\right)} \log\left(x\right)\right)}{8 \, {\left(b m + 4 \, b\right)}}"," ",0,"1/8*(4*b*x*cosh((m + 3)*log(x)) - (m + 4)*cosh((m + 3)*log(2*b) + 2*a)*gamma(m + 4, 2*b*x) + (m + 4)*cosh((m + 3)*log(-2*b) - 2*a)*gamma(m + 4, -2*b*x) + (m + 4)*gamma(m + 4, 2*b*x)*sinh((m + 3)*log(2*b) + 2*a) - (m + 4)*gamma(m + 4, -2*b*x)*sinh((m + 3)*log(-2*b) - 2*a) + 4*b*x*sinh((m + 3)*log(x)))/(b*m + 4*b)","A",0
89,1,136,0,0.514863," ","integrate(x^(2+m)*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x \cosh\left({\left(m + 2\right)} \log\left(x\right)\right) - {\left(m + 3\right)} \cosh\left({\left(m + 2\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m + 3, 2 \, b x\right) + {\left(m + 3\right)} \cosh\left({\left(m + 2\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m + 3, -2 \, b x\right) + {\left(m + 3\right)} \Gamma\left(m + 3, 2 \, b x\right) \sinh\left({\left(m + 2\right)} \log\left(2 \, b\right) + 2 \, a\right) - {\left(m + 3\right)} \Gamma\left(m + 3, -2 \, b x\right) \sinh\left({\left(m + 2\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m + 2\right)} \log\left(x\right)\right)}{8 \, {\left(b m + 3 \, b\right)}}"," ",0,"1/8*(4*b*x*cosh((m + 2)*log(x)) - (m + 3)*cosh((m + 2)*log(2*b) + 2*a)*gamma(m + 3, 2*b*x) + (m + 3)*cosh((m + 2)*log(-2*b) - 2*a)*gamma(m + 3, -2*b*x) + (m + 3)*gamma(m + 3, 2*b*x)*sinh((m + 2)*log(2*b) + 2*a) - (m + 3)*gamma(m + 3, -2*b*x)*sinh((m + 2)*log(-2*b) - 2*a) + 4*b*x*sinh((m + 2)*log(x)))/(b*m + 3*b)","A",0
90,1,136,0,0.541800," ","integrate(x^(1+m)*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x \cosh\left({\left(m + 1\right)} \log\left(x\right)\right) - {\left(m + 2\right)} \cosh\left({\left(m + 1\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m + 2, 2 \, b x\right) + {\left(m + 2\right)} \cosh\left({\left(m + 1\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m + 2, -2 \, b x\right) + {\left(m + 2\right)} \Gamma\left(m + 2, 2 \, b x\right) \sinh\left({\left(m + 1\right)} \log\left(2 \, b\right) + 2 \, a\right) - {\left(m + 2\right)} \Gamma\left(m + 2, -2 \, b x\right) \sinh\left({\left(m + 1\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m + 1\right)} \log\left(x\right)\right)}{8 \, {\left(b m + 2 \, b\right)}}"," ",0,"1/8*(4*b*x*cosh((m + 1)*log(x)) - (m + 2)*cosh((m + 1)*log(2*b) + 2*a)*gamma(m + 2, 2*b*x) + (m + 2)*cosh((m + 1)*log(-2*b) - 2*a)*gamma(m + 2, -2*b*x) + (m + 2)*gamma(m + 2, 2*b*x)*sinh((m + 1)*log(2*b) + 2*a) - (m + 2)*gamma(m + 2, -2*b*x)*sinh((m + 1)*log(-2*b) - 2*a) + 4*b*x*sinh((m + 1)*log(x)))/(b*m + 2*b)","A",0
91,1,122,0,0.489120," ","integrate(x^m*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x \cosh\left(m \log\left(x\right)\right) - {\left(m + 1\right)} \cosh\left(m \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m + 1, 2 \, b x\right) + {\left(m + 1\right)} \cosh\left(m \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m + 1, -2 \, b x\right) + {\left(m + 1\right)} \Gamma\left(m + 1, 2 \, b x\right) \sinh\left(m \log\left(2 \, b\right) + 2 \, a\right) - {\left(m + 1\right)} \Gamma\left(m + 1, -2 \, b x\right) \sinh\left(m \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left(m \log\left(x\right)\right)}{8 \, {\left(b m + b\right)}}"," ",0,"1/8*(4*b*x*cosh(m*log(x)) - (m + 1)*cosh(m*log(2*b) + 2*a)*gamma(m + 1, 2*b*x) + (m + 1)*cosh(m*log(-2*b) - 2*a)*gamma(m + 1, -2*b*x) + (m + 1)*gamma(m + 1, 2*b*x)*sinh(m*log(2*b) + 2*a) - (m + 1)*gamma(m + 1, -2*b*x)*sinh(m*log(-2*b) - 2*a) + 4*b*x*sinh(m*log(x)))/(b*m + b)","A",0
92,1,117,0,0.479323," ","integrate(x^(-1+m)*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x \cosh\left({\left(m - 1\right)} \log\left(x\right)\right) - m \cosh\left({\left(m - 1\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m, 2 \, b x\right) + m \cosh\left({\left(m - 1\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m, -2 \, b x\right) + m \Gamma\left(m, 2 \, b x\right) \sinh\left({\left(m - 1\right)} \log\left(2 \, b\right) + 2 \, a\right) - m \Gamma\left(m, -2 \, b x\right) \sinh\left({\left(m - 1\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m - 1\right)} \log\left(x\right)\right)}{8 \, b m}"," ",0,"1/8*(4*b*x*cosh((m - 1)*log(x)) - m*cosh((m - 1)*log(2*b) + 2*a)*gamma(m, 2*b*x) + m*cosh((m - 1)*log(-2*b) - 2*a)*gamma(m, -2*b*x) + m*gamma(m, 2*b*x)*sinh((m - 1)*log(2*b) + 2*a) - m*gamma(m, -2*b*x)*sinh((m - 1)*log(-2*b) - 2*a) + 4*b*x*sinh((m - 1)*log(x)))/(b*m)","A",0
93,1,136,0,0.456707," ","integrate(x^(-2+m)*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x \cosh\left({\left(m - 2\right)} \log\left(x\right)\right) - {\left(m - 1\right)} \cosh\left({\left(m - 2\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m - 1, 2 \, b x\right) + {\left(m - 1\right)} \cosh\left({\left(m - 2\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m - 1, -2 \, b x\right) + {\left(m - 1\right)} \Gamma\left(m - 1, 2 \, b x\right) \sinh\left({\left(m - 2\right)} \log\left(2 \, b\right) + 2 \, a\right) - {\left(m - 1\right)} \Gamma\left(m - 1, -2 \, b x\right) \sinh\left({\left(m - 2\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m - 2\right)} \log\left(x\right)\right)}{8 \, {\left(b m - b\right)}}"," ",0,"1/8*(4*b*x*cosh((m - 2)*log(x)) - (m - 1)*cosh((m - 2)*log(2*b) + 2*a)*gamma(m - 1, 2*b*x) + (m - 1)*cosh((m - 2)*log(-2*b) - 2*a)*gamma(m - 1, -2*b*x) + (m - 1)*gamma(m - 1, 2*b*x)*sinh((m - 2)*log(2*b) + 2*a) - (m - 1)*gamma(m - 1, -2*b*x)*sinh((m - 2)*log(-2*b) - 2*a) + 4*b*x*sinh((m - 2)*log(x)))/(b*m - b)","A",0
94,1,136,0,0.444064," ","integrate(x^(-3+m)*cosh(b*x+a)^2,x, algorithm=""fricas"")","\frac{4 \, b x \cosh\left({\left(m - 3\right)} \log\left(x\right)\right) - {\left(m - 2\right)} \cosh\left({\left(m - 3\right)} \log\left(2 \, b\right) + 2 \, a\right) \Gamma\left(m - 2, 2 \, b x\right) + {\left(m - 2\right)} \cosh\left({\left(m - 3\right)} \log\left(-2 \, b\right) - 2 \, a\right) \Gamma\left(m - 2, -2 \, b x\right) + {\left(m - 2\right)} \Gamma\left(m - 2, 2 \, b x\right) \sinh\left({\left(m - 3\right)} \log\left(2 \, b\right) + 2 \, a\right) - {\left(m - 2\right)} \Gamma\left(m - 2, -2 \, b x\right) \sinh\left({\left(m - 3\right)} \log\left(-2 \, b\right) - 2 \, a\right) + 4 \, b x \sinh\left({\left(m - 3\right)} \log\left(x\right)\right)}{8 \, {\left(b m - 2 \, b\right)}}"," ",0,"1/8*(4*b*x*cosh((m - 3)*log(x)) - (m - 2)*cosh((m - 3)*log(2*b) + 2*a)*gamma(m - 2, 2*b*x) + (m - 2)*cosh((m - 3)*log(-2*b) - 2*a)*gamma(m - 2, -2*b*x) + (m - 2)*gamma(m - 2, 2*b*x)*sinh((m - 3)*log(2*b) + 2*a) - (m - 2)*gamma(m - 2, -2*b*x)*sinh((m - 3)*log(-2*b) - 2*a) + 4*b*x*sinh((m - 3)*log(x)))/(b*m - 2*b)","A",0
95,-2,0,0,0.000000," ","integrate(x/sech(x)^(3/2)-1/3*x*sech(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
96,-2,0,0,0.000000," ","integrate(x/sech(x)^(5/2)-3/5*x/sech(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
97,-2,0,0,0.000000," ","integrate(x/sech(x)^(7/2)-5/21*x*sech(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
98,-2,0,0,0.000000," ","integrate(x^2/sech(x)^(3/2)-1/3*x^2*sech(x)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
99,1,168,0,0.645201," ","integrate((d*x+c)^3*(a+a*cosh(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{3} f^{4} x^{4} + 4 \, a c d^{2} f^{4} x^{3} + 6 \, a c^{2} d f^{4} x^{2} + 4 \, a c^{3} f^{4} x - 12 \, {\left(a d^{3} f^{2} x^{2} + 2 \, a c d^{2} f^{2} x + a c^{2} d f^{2} + 2 \, a d^{3}\right)} \cosh\left(f x + e\right) + 4 \, {\left(a d^{3} f^{3} x^{3} + 3 \, a c d^{2} f^{3} x^{2} + a c^{3} f^{3} + 6 \, a c d^{2} f + 3 \, {\left(a c^{2} d f^{3} + 2 \, a d^{3} f\right)} x\right)} \sinh\left(f x + e\right)}{4 \, f^{4}}"," ",0,"1/4*(a*d^3*f^4*x^4 + 4*a*c*d^2*f^4*x^3 + 6*a*c^2*d*f^4*x^2 + 4*a*c^3*f^4*x - 12*(a*d^3*f^2*x^2 + 2*a*c*d^2*f^2*x + a*c^2*d*f^2 + 2*a*d^3)*cosh(f*x + e) + 4*(a*d^3*f^3*x^3 + 3*a*c*d^2*f^3*x^2 + a*c^3*f^3 + 6*a*c*d^2*f + 3*(a*c^2*d*f^3 + 2*a*d^3*f)*x)*sinh(f*x + e))/f^4","A",0
100,1,102,0,0.614745," ","integrate((d*x+c)^2*(a+a*cosh(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{2} f^{3} x^{3} + 3 \, a c d f^{3} x^{2} + 3 \, a c^{2} f^{3} x - 6 \, {\left(a d^{2} f x + a c d f\right)} \cosh\left(f x + e\right) + 3 \, {\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x + a c^{2} f^{2} + 2 \, a d^{2}\right)} \sinh\left(f x + e\right)}{3 \, f^{3}}"," ",0,"1/3*(a*d^2*f^3*x^3 + 3*a*c*d*f^3*x^2 + 3*a*c^2*f^3*x - 6*(a*d^2*f*x + a*c*d*f)*cosh(f*x + e) + 3*(a*d^2*f^2*x^2 + 2*a*c*d*f^2*x + a*c^2*f^2 + 2*a*d^2)*sinh(f*x + e))/f^3","A",0
101,1,51,0,0.520477," ","integrate((d*x+c)*(a+a*cosh(f*x+e)),x, algorithm=""fricas"")","\frac{a d f^{2} x^{2} + 2 \, a c f^{2} x - 2 \, a d \cosh\left(f x + e\right) + 2 \, {\left(a d f x + a c f\right)} \sinh\left(f x + e\right)}{2 \, f^{2}}"," ",0,"1/2*(a*d*f^2*x^2 + 2*a*c*f^2*x - 2*a*d*cosh(f*x + e) + 2*(a*d*f*x + a*c*f)*sinh(f*x + e))/f^2","A",0
102,1,111,0,0.441990," ","integrate((a+a*cosh(f*x+e))/(d*x+c),x, algorithm=""fricas"")","\frac{{\left(a {\rm Ei}\left(\frac{d f x + c f}{d}\right) + a {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + 2 \, a \log\left(d x + c\right) - {\left(a {\rm Ei}\left(\frac{d f x + c f}{d}\right) - a {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right)}{2 \, d}"," ",0,"1/2*((a*Ei((d*f*x + c*f)/d) + a*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + 2*a*log(d*x + c) - (a*Ei((d*f*x + c*f)/d) - a*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d))/d","A",0
103,1,162,0,0.589041," ","integrate((a+a*cosh(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, a d \cosh\left(f x + e\right) + 2 \, a d - {\left({\left(a d f x + a c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(a d f x + a c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + {\left({\left(a d f x + a c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(a d f x + a c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(2*a*d*cosh(f*x + e) + 2*a*d - ((a*d*f*x + a*c*f)*Ei((d*f*x + c*f)/d) - (a*d*f*x + a*c*f)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + ((a*d*f*x + a*c*f)*Ei((d*f*x + c*f)/d) + (a*d*f*x + a*c*f)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d))/(d^3*x + c*d^2)","A",0
104,1,274,0,0.562228," ","integrate((a+a*cosh(f*x+e))/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, a d^{2} \cosh\left(f x + e\right) + 2 \, a d^{2} - {\left({\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x + a c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x + a c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + 2 \, {\left(a d^{2} f x + a c d f\right)} \sinh\left(f x + e\right) + {\left({\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x + a c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(a d^{2} f^{2} x^{2} + 2 \, a c d f^{2} x + a c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(2*a*d^2*cosh(f*x + e) + 2*a*d^2 - ((a*d^2*f^2*x^2 + 2*a*c*d*f^2*x + a*c^2*f^2)*Ei((d*f*x + c*f)/d) + (a*d^2*f^2*x^2 + 2*a*c*d*f^2*x + a*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + 2*(a*d^2*f*x + a*c*d*f)*sinh(f*x + e) + ((a*d^2*f^2*x^2 + 2*a*c*d*f^2*x + a*c^2*f^2)*Ei((d*f*x + c*f)/d) - (a*d^2*f^2*x^2 + 2*a*c*d*f^2*x + a*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
105,1,395,0,0.533089," ","integrate((d*x+c)^3*(a+a*cosh(f*x+e))^2,x, algorithm=""fricas"")","\frac{6 \, a^{2} d^{3} f^{4} x^{4} + 24 \, a^{2} c d^{2} f^{4} x^{3} + 36 \, a^{2} c^{2} d f^{4} x^{2} + 24 \, a^{2} c^{3} f^{4} x - 3 \, {\left(2 \, a^{2} d^{3} f^{2} x^{2} + 4 \, a^{2} c d^{2} f^{2} x + 2 \, a^{2} c^{2} d f^{2} + a^{2} d^{3}\right)} \cosh\left(f x + e\right)^{2} - 3 \, {\left(2 \, a^{2} d^{3} f^{2} x^{2} + 4 \, a^{2} c d^{2} f^{2} x + 2 \, a^{2} c^{2} d f^{2} + a^{2} d^{3}\right)} \sinh\left(f x + e\right)^{2} - 96 \, {\left(a^{2} d^{3} f^{2} x^{2} + 2 \, a^{2} c d^{2} f^{2} x + a^{2} c^{2} d f^{2} + 2 \, a^{2} d^{3}\right)} \cosh\left(f x + e\right) + 4 \, {\left(8 \, a^{2} d^{3} f^{3} x^{3} + 24 \, a^{2} c d^{2} f^{3} x^{2} + 8 \, a^{2} c^{3} f^{3} + 48 \, a^{2} c d^{2} f + 24 \, {\left(a^{2} c^{2} d f^{3} + 2 \, a^{2} d^{3} f\right)} x + {\left(2 \, a^{2} d^{3} f^{3} x^{3} + 6 \, a^{2} c d^{2} f^{3} x^{2} + 2 \, a^{2} c^{3} f^{3} + 3 \, a^{2} c d^{2} f + 3 \, {\left(2 \, a^{2} c^{2} d f^{3} + a^{2} d^{3} f\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{16 \, f^{4}}"," ",0,"1/16*(6*a^2*d^3*f^4*x^4 + 24*a^2*c*d^2*f^4*x^3 + 36*a^2*c^2*d*f^4*x^2 + 24*a^2*c^3*f^4*x - 3*(2*a^2*d^3*f^2*x^2 + 4*a^2*c*d^2*f^2*x + 2*a^2*c^2*d*f^2 + a^2*d^3)*cosh(f*x + e)^2 - 3*(2*a^2*d^3*f^2*x^2 + 4*a^2*c*d^2*f^2*x + 2*a^2*c^2*d*f^2 + a^2*d^3)*sinh(f*x + e)^2 - 96*(a^2*d^3*f^2*x^2 + 2*a^2*c*d^2*f^2*x + a^2*c^2*d*f^2 + 2*a^2*d^3)*cosh(f*x + e) + 4*(8*a^2*d^3*f^3*x^3 + 24*a^2*c*d^2*f^3*x^2 + 8*a^2*c^3*f^3 + 48*a^2*c*d^2*f + 24*(a^2*c^2*d*f^3 + 2*a^2*d^3*f)*x + (2*a^2*d^3*f^3*x^3 + 6*a^2*c*d^2*f^3*x^2 + 2*a^2*c^3*f^3 + 3*a^2*c*d^2*f + 3*(2*a^2*c^2*d*f^3 + a^2*d^3*f)*x)*cosh(f*x + e))*sinh(f*x + e))/f^4","A",0
106,1,227,0,0.510962," ","integrate((d*x+c)^2*(a+a*cosh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} d^{2} f^{3} x^{3} + 6 \, a^{2} c d f^{3} x^{2} + 6 \, a^{2} c^{2} f^{3} x - {\left(a^{2} d^{2} f x + a^{2} c d f\right)} \cosh\left(f x + e\right)^{2} - {\left(a^{2} d^{2} f x + a^{2} c d f\right)} \sinh\left(f x + e\right)^{2} - 16 \, {\left(a^{2} d^{2} f x + a^{2} c d f\right)} \cosh\left(f x + e\right) + {\left(8 \, a^{2} d^{2} f^{2} x^{2} + 16 \, a^{2} c d f^{2} x + 8 \, a^{2} c^{2} f^{2} + 16 \, a^{2} d^{2} + {\left(2 \, a^{2} d^{2} f^{2} x^{2} + 4 \, a^{2} c d f^{2} x + 2 \, a^{2} c^{2} f^{2} + a^{2} d^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{4 \, f^{3}}"," ",0,"1/4*(2*a^2*d^2*f^3*x^3 + 6*a^2*c*d*f^3*x^2 + 6*a^2*c^2*f^3*x - (a^2*d^2*f*x + a^2*c*d*f)*cosh(f*x + e)^2 - (a^2*d^2*f*x + a^2*c*d*f)*sinh(f*x + e)^2 - 16*(a^2*d^2*f*x + a^2*c*d*f)*cosh(f*x + e) + (8*a^2*d^2*f^2*x^2 + 16*a^2*c*d*f^2*x + 8*a^2*c^2*f^2 + 16*a^2*d^2 + (2*a^2*d^2*f^2*x^2 + 4*a^2*c*d*f^2*x + 2*a^2*c^2*f^2 + a^2*d^2)*cosh(f*x + e))*sinh(f*x + e))/f^3","A",0
107,1,113,0,0.608386," ","integrate((d*x+c)*(a+a*cosh(f*x+e))^2,x, algorithm=""fricas"")","\frac{6 \, a^{2} d f^{2} x^{2} + 12 \, a^{2} c f^{2} x - a^{2} d \cosh\left(f x + e\right)^{2} - a^{2} d \sinh\left(f x + e\right)^{2} - 16 \, a^{2} d \cosh\left(f x + e\right) + 4 \, {\left(4 \, a^{2} d f x + 4 \, a^{2} c f + {\left(a^{2} d f x + a^{2} c f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{8 \, f^{2}}"," ",0,"1/8*(6*a^2*d*f^2*x^2 + 12*a^2*c*f^2*x - a^2*d*cosh(f*x + e)^2 - a^2*d*sinh(f*x + e)^2 - 16*a^2*d*cosh(f*x + e) + 4*(4*a^2*d*f*x + 4*a^2*c*f + (a^2*d*f*x + a^2*c*f)*cosh(f*x + e))*sinh(f*x + e))/f^2","A",0
108,1,228,0,0.431815," ","integrate((a+a*cosh(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","\frac{6 \, a^{2} \log\left(d x + c\right) + 4 \, {\left(a^{2} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + a^{2} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + {\left(a^{2} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + a^{2} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) - 4 \, {\left(a^{2} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - a^{2} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right) - {\left(a^{2} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - a^{2} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{4 \, d}"," ",0,"1/4*(6*a^2*log(d*x + c) + 4*(a^2*Ei((d*f*x + c*f)/d) + a^2*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + (a^2*Ei(2*(d*f*x + c*f)/d) + a^2*Ei(-2*(d*f*x + c*f)/d))*cosh(-2*(d*e - c*f)/d) - 4*(a^2*Ei((d*f*x + c*f)/d) - a^2*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d) - (a^2*Ei(2*(d*f*x + c*f)/d) - a^2*Ei(-2*(d*f*x + c*f)/d))*sinh(-2*(d*e - c*f)/d))/d","A",0
109,1,359,0,0.568425," ","integrate((a+a*cosh(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{a^{2} d \cosh\left(f x + e\right)^{2} + a^{2} d \sinh\left(f x + e\right)^{2} + 4 \, a^{2} d \cosh\left(f x + e\right) + 3 \, a^{2} d - 2 \, {\left({\left(a^{2} d f x + a^{2} c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(a^{2} d f x + a^{2} c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) - {\left({\left(a^{2} d f x + a^{2} c f\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(a^{2} d f x + a^{2} c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 2 \, {\left({\left(a^{2} d f x + a^{2} c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(a^{2} d f x + a^{2} c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right) + {\left({\left(a^{2} d f x + a^{2} c f\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + {\left(a^{2} d f x + a^{2} c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(a^2*d*cosh(f*x + e)^2 + a^2*d*sinh(f*x + e)^2 + 4*a^2*d*cosh(f*x + e) + 3*a^2*d - 2*((a^2*d*f*x + a^2*c*f)*Ei((d*f*x + c*f)/d) - (a^2*d*f*x + a^2*c*f)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) - ((a^2*d*f*x + a^2*c*f)*Ei(2*(d*f*x + c*f)/d) - (a^2*d*f*x + a^2*c*f)*Ei(-2*(d*f*x + c*f)/d))*cosh(-2*(d*e - c*f)/d) + 2*((a^2*d*f*x + a^2*c*f)*Ei((d*f*x + c*f)/d) + (a^2*d*f*x + a^2*c*f)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d) + ((a^2*d*f*x + a^2*c*f)*Ei(2*(d*f*x + c*f)/d) + (a^2*d*f*x + a^2*c*f)*Ei(-2*(d*f*x + c*f)/d))*sinh(-2*(d*e - c*f)/d))/(d^3*x + c*d^2)","B",0
110,1,596,0,0.500412," ","integrate((a+a*cosh(f*x+e))^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{a^{2} d^{2} \cosh\left(f x + e\right)^{2} + a^{2} d^{2} \sinh\left(f x + e\right)^{2} + 4 \, a^{2} d^{2} \cosh\left(f x + e\right) + 3 \, a^{2} d^{2} - 2 \, {\left({\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) - 2 \, {\left({\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 4 \, {\left(a^{2} d^{2} f x + a^{2} c d f + {\left(a^{2} d^{2} f x + a^{2} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 2 \, {\left({\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right) + 2 \, {\left({\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(a^{2} d^{2} f^{2} x^{2} + 2 \, a^{2} c d f^{2} x + a^{2} c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(a^2*d^2*cosh(f*x + e)^2 + a^2*d^2*sinh(f*x + e)^2 + 4*a^2*d^2*cosh(f*x + e) + 3*a^2*d^2 - 2*((a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*Ei((d*f*x + c*f)/d) + (a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) - 2*((a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*Ei(2*(d*f*x + c*f)/d) + (a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*Ei(-2*(d*f*x + c*f)/d))*cosh(-2*(d*e - c*f)/d) + 4*(a^2*d^2*f*x + a^2*c*d*f + (a^2*d^2*f*x + a^2*c*d*f)*cosh(f*x + e))*sinh(f*x + e) + 2*((a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*Ei((d*f*x + c*f)/d) - (a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d) + 2*((a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*Ei(2*(d*f*x + c*f)/d) - (a^2*d^2*f^2*x^2 + 2*a^2*c*d*f^2*x + a^2*c^2*f^2)*Ei(-2*(d*f*x + c*f)/d))*sinh(-2*(d*e - c*f)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
111,1,438,0,0.642304," ","integrate((d*x+c)^3/(a+a*cosh(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + 3 \, c^{2} d f^{3} x + d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2}\right)} \cosh\left(f x + e\right) - 6 \, {\left(d^{3} f x + c d^{2} f + {\left(d^{3} f x + c d^{2} f\right)} \cosh\left(f x + e\right) + {\left(d^{3} f x + c d^{2} f\right)} \sinh\left(f x + e\right)\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) - 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \cosh\left(f x + e\right) + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2}\right)} \sinh\left(f x + e\right)\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) + 6 \, {\left(d^{3} \cosh\left(f x + e\right) + d^{3} \sinh\left(f x + e\right) + d^{3}\right)} {\rm polylog}\left(3, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + 3 \, c^{2} d f^{3} x + d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2}\right)} \sinh\left(f x + e\right)\right)}}{a f^{4} \cosh\left(f x + e\right) + a f^{4} \sinh\left(f x + e\right) + a f^{4}}"," ",0,"2*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3 + (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + 3*c^2*d*f^3*x + d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2)*cosh(f*x + e) - 6*(d^3*f*x + c*d^2*f + (d^3*f*x + c*d^2*f)*cosh(f*x + e) + (d^3*f*x + c*d^2*f)*sinh(f*x + e))*dilog(-cosh(f*x + e) - sinh(f*x + e)) - 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*cosh(f*x + e) + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2)*sinh(f*x + e))*log(cosh(f*x + e) + sinh(f*x + e) + 1) + 6*(d^3*cosh(f*x + e) + d^3*sinh(f*x + e) + d^3)*polylog(3, -cosh(f*x + e) - sinh(f*x + e)) + (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + 3*c^2*d*f^3*x + d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2)*sinh(f*x + e))/(a*f^4*cosh(f*x + e) + a*f^4*sinh(f*x + e) + a*f^4)","C",0
112,1,243,0,0.405887," ","integrate((d*x+c)^2/(a+a*cosh(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2} - {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x - d^{2} e^{2} + 2 \, c d e f\right)} \cosh\left(f x + e\right) + 2 \, {\left(d^{2} \cosh\left(f x + e\right) + d^{2} \sinh\left(f x + e\right) + d^{2}\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 2 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cosh\left(f x + e\right) + {\left(d^{2} f x + c d f\right)} \sinh\left(f x + e\right)\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) - {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x - d^{2} e^{2} + 2 \, c d e f\right)} \sinh\left(f x + e\right)\right)}}{a f^{3} \cosh\left(f x + e\right) + a f^{3} \sinh\left(f x + e\right) + a f^{3}}"," ",0,"-2*(d^2*e^2 - 2*c*d*e*f + c^2*f^2 - (d^2*f^2*x^2 + 2*c*d*f^2*x - d^2*e^2 + 2*c*d*e*f)*cosh(f*x + e) + 2*(d^2*cosh(f*x + e) + d^2*sinh(f*x + e) + d^2)*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 2*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cosh(f*x + e) + (d^2*f*x + c*d*f)*sinh(f*x + e))*log(cosh(f*x + e) + sinh(f*x + e) + 1) - (d^2*f^2*x^2 + 2*c*d*f^2*x - d^2*e^2 + 2*c*d*e*f)*sinh(f*x + e))/(a*f^3*cosh(f*x + e) + a*f^3*sinh(f*x + e) + a*f^3)","B",0
113,1,92,0,0.540619," ","integrate((d*x+c)/(a+a*cosh(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(d f x \cosh\left(f x + e\right) + d f x \sinh\left(f x + e\right) - c f - {\left(d \cosh\left(f x + e\right) + d \sinh\left(f x + e\right) + d\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right)\right)}}{a f^{2} \cosh\left(f x + e\right) + a f^{2} \sinh\left(f x + e\right) + a f^{2}}"," ",0,"2*(d*f*x*cosh(f*x + e) + d*f*x*sinh(f*x + e) - c*f - (d*cosh(f*x + e) + d*sinh(f*x + e) + d)*log(cosh(f*x + e) + sinh(f*x + e) + 1))/(a*f^2*cosh(f*x + e) + a*f^2*sinh(f*x + e) + a*f^2)","B",0
114,0,0,0,0.540288," ","integrate(1/(d*x+c)/(a+a*cosh(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(a d x + a c\right)} \cosh\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (a*d*x + a*c)*cosh(f*x + e)), x)","F",0
115,0,0,0,1.190691," ","integrate(1/(d*x+c)^2/(a+a*cosh(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + {\left(a d^{2} x^{2} + 2 \, a c d x + a c^{2}\right)} \cosh\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 + (a*d^2*x^2 + 2*a*c*d*x + a*c^2)*cosh(f*x + e)), x)","F",0
116,1,1863,0,0.582890," ","integrate((d*x+c)^3/(a+a*cosh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(d^{3} e^{3} + 3 \, c^{2} d e f^{2} - c^{3} f^{3} - 6 \, d^{3} e + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - 6 \, d^{3} e + 3 \, {\left(c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} \cosh\left(f x + e\right)^{3} + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - 6 \, d^{3} e + 3 \, {\left(c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} - 6 \, d^{3} e + {\left(3 \, c^{2} d e + c^{2} d\right)} f^{2} + {\left(3 \, c d^{2} f^{3} + d^{3} f^{2}\right)} x^{2} - {\left(3 \, c d^{2} e^{2} - 2 \, c d^{2}\right)} f + {\left(3 \, c^{2} d f^{3} + 2 \, c d^{2} f^{2} - 4 \, d^{3} f\right)} x\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} - 6 \, d^{3} e + {\left(3 \, c^{2} d e + c^{2} d\right)} f^{2} + {\left(3 \, c d^{2} f^{3} + d^{3} f^{2}\right)} x^{2} - {\left(3 \, c d^{2} e^{2} - 2 \, c d^{2}\right)} f + {\left(3 \, c^{2} d f^{3} + 2 \, c d^{2} f^{2} - 4 \, d^{3} f\right)} x + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - 6 \, d^{3} e + 3 \, {\left(c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} - 3 \, {\left(c d^{2} e^{2} - 2 \, c d^{2}\right)} f + 3 \, {\left(d^{3} f^{2} x^{2} + d^{3} e^{3} - c^{3} f^{3} - 6 \, d^{3} e + {\left(3 \, c^{2} d e + c^{2} d\right)} f^{2} - {\left(3 \, c d^{2} e^{2} - 4 \, c d^{2}\right)} f + 2 \, {\left(c d^{2} f^{2} - d^{3} f\right)} x\right)} \cosh\left(f x + e\right) - 6 \, {\left(d^{3} f x + c d^{2} f + {\left(d^{3} f x + c d^{2} f\right)} \cosh\left(f x + e\right)^{3} + {\left(d^{3} f x + c d^{2} f\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(d^{3} f x + c d^{2} f\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(d^{3} f x + c d^{2} f + {\left(d^{3} f x + c d^{2} f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(d^{3} f x + c d^{2} f\right)} \cosh\left(f x + e\right) + 3 \, {\left(d^{3} f x + c d^{2} f + {\left(d^{3} f x + c d^{2} f\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(d^{3} f x + c d^{2} f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) - 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3}\right)} \sinh\left(f x + e\right)^{3} - 2 \, d^{3} + 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3}\right)} \cosh\left(f x + e\right) + 3 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3} + {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(d^{3} f^{2} x^{2} + 2 \, c d^{2} f^{2} x + c^{2} d f^{2} - 2 \, d^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) + 6 \, {\left(d^{3} \cosh\left(f x + e\right)^{3} + d^{3} \sinh\left(f x + e\right)^{3} + 3 \, d^{3} \cosh\left(f x + e\right)^{2} + 3 \, d^{3} \cosh\left(f x + e\right) + d^{3} + 3 \, {\left(d^{3} \cosh\left(f x + e\right) + d^{3}\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(d^{3} \cosh\left(f x + e\right)^{2} + 2 \, d^{3} \cosh\left(f x + e\right) + d^{3}\right)} \sinh\left(f x + e\right)\right)} {\rm polylog}\left(3, -\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 3 \, {\left(d^{3} f^{2} x^{2} + d^{3} e^{3} - c^{3} f^{3} - 6 \, d^{3} e + {\left(3 \, c^{2} d e + c^{2} d\right)} f^{2} + {\left(d^{3} f^{3} x^{3} + 3 \, c d^{2} f^{3} x^{2} + d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - 6 \, d^{3} e + 3 \, {\left(c^{2} d f^{3} - 2 \, d^{3} f\right)} x\right)} \cosh\left(f x + e\right)^{2} - {\left(3 \, c d^{2} e^{2} - 4 \, c d^{2}\right)} f + 2 \, {\left(c d^{2} f^{2} - d^{3} f\right)} x + 2 \, {\left(d^{3} f^{3} x^{3} + d^{3} e^{3} - 6 \, d^{3} e + {\left(3 \, c^{2} d e + c^{2} d\right)} f^{2} + {\left(3 \, c d^{2} f^{3} + d^{3} f^{2}\right)} x^{2} - {\left(3 \, c d^{2} e^{2} - 2 \, c d^{2}\right)} f + {\left(3 \, c^{2} d f^{3} + 2 \, c d^{2} f^{2} - 4 \, d^{3} f\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}{3 \, {\left(a^{2} f^{4} \cosh\left(f x + e\right)^{3} + a^{2} f^{4} \sinh\left(f x + e\right)^{3} + 3 \, a^{2} f^{4} \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f^{4} \cosh\left(f x + e\right) + a^{2} f^{4} + 3 \, {\left(a^{2} f^{4} \cosh\left(f x + e\right) + a^{2} f^{4}\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(a^{2} f^{4} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} f^{4} \cosh\left(f x + e\right) + a^{2} f^{4}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"2/3*(d^3*e^3 + 3*c^2*d*e*f^2 - c^3*f^3 - 6*d^3*e + (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - 6*d^3*e + 3*(c^2*d*f^3 - 2*d^3*f)*x)*cosh(f*x + e)^3 + (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - 6*d^3*e + 3*(c^2*d*f^3 - 2*d^3*f)*x)*sinh(f*x + e)^3 + 3*(d^3*f^3*x^3 + d^3*e^3 - 6*d^3*e + (3*c^2*d*e + c^2*d)*f^2 + (3*c*d^2*f^3 + d^3*f^2)*x^2 - (3*c*d^2*e^2 - 2*c*d^2)*f + (3*c^2*d*f^3 + 2*c*d^2*f^2 - 4*d^3*f)*x)*cosh(f*x + e)^2 + 3*(d^3*f^3*x^3 + d^3*e^3 - 6*d^3*e + (3*c^2*d*e + c^2*d)*f^2 + (3*c*d^2*f^3 + d^3*f^2)*x^2 - (3*c*d^2*e^2 - 2*c*d^2)*f + (3*c^2*d*f^3 + 2*c*d^2*f^2 - 4*d^3*f)*x + (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - 6*d^3*e + 3*(c^2*d*f^3 - 2*d^3*f)*x)*cosh(f*x + e))*sinh(f*x + e)^2 - 3*(c*d^2*e^2 - 2*c*d^2)*f + 3*(d^3*f^2*x^2 + d^3*e^3 - c^3*f^3 - 6*d^3*e + (3*c^2*d*e + c^2*d)*f^2 - (3*c*d^2*e^2 - 4*c*d^2)*f + 2*(c*d^2*f^2 - d^3*f)*x)*cosh(f*x + e) - 6*(d^3*f*x + c*d^2*f + (d^3*f*x + c*d^2*f)*cosh(f*x + e)^3 + (d^3*f*x + c*d^2*f)*sinh(f*x + e)^3 + 3*(d^3*f*x + c*d^2*f)*cosh(f*x + e)^2 + 3*(d^3*f*x + c*d^2*f + (d^3*f*x + c*d^2*f)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(d^3*f*x + c*d^2*f)*cosh(f*x + e) + 3*(d^3*f*x + c*d^2*f + (d^3*f*x + c*d^2*f)*cosh(f*x + e)^2 + 2*(d^3*f*x + c*d^2*f)*cosh(f*x + e))*sinh(f*x + e))*dilog(-cosh(f*x + e) - sinh(f*x + e)) - 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3)*cosh(f*x + e)^3 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3)*sinh(f*x + e)^3 - 2*d^3 + 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3)*cosh(f*x + e)^2 + 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3)*cosh(f*x + e) + 3*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3 + (d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3)*cosh(f*x + e)^2 + 2*(d^3*f^2*x^2 + 2*c*d^2*f^2*x + c^2*d*f^2 - 2*d^3)*cosh(f*x + e))*sinh(f*x + e))*log(cosh(f*x + e) + sinh(f*x + e) + 1) + 6*(d^3*cosh(f*x + e)^3 + d^3*sinh(f*x + e)^3 + 3*d^3*cosh(f*x + e)^2 + 3*d^3*cosh(f*x + e) + d^3 + 3*(d^3*cosh(f*x + e) + d^3)*sinh(f*x + e)^2 + 3*(d^3*cosh(f*x + e)^2 + 2*d^3*cosh(f*x + e) + d^3)*sinh(f*x + e))*polylog(3, -cosh(f*x + e) - sinh(f*x + e)) + 3*(d^3*f^2*x^2 + d^3*e^3 - c^3*f^3 - 6*d^3*e + (3*c^2*d*e + c^2*d)*f^2 + (d^3*f^3*x^3 + 3*c*d^2*f^3*x^2 + d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - 6*d^3*e + 3*(c^2*d*f^3 - 2*d^3*f)*x)*cosh(f*x + e)^2 - (3*c*d^2*e^2 - 4*c*d^2)*f + 2*(c*d^2*f^2 - d^3*f)*x + 2*(d^3*f^3*x^3 + d^3*e^3 - 6*d^3*e + (3*c^2*d*e + c^2*d)*f^2 + (3*c*d^2*f^3 + d^3*f^2)*x^2 - (3*c*d^2*e^2 - 2*c*d^2)*f + (3*c^2*d*f^3 + 2*c*d^2*f^2 - 4*d^3*f)*x)*cosh(f*x + e))*sinh(f*x + e))/(a^2*f^4*cosh(f*x + e)^3 + a^2*f^4*sinh(f*x + e)^3 + 3*a^2*f^4*cosh(f*x + e)^2 + 3*a^2*f^4*cosh(f*x + e) + a^2*f^4 + 3*(a^2*f^4*cosh(f*x + e) + a^2*f^4)*sinh(f*x + e)^2 + 3*(a^2*f^4*cosh(f*x + e)^2 + 2*a^2*f^4*cosh(f*x + e) + a^2*f^4)*sinh(f*x + e))","C",0
117,1,963,0,0.689646," ","integrate((d*x+c)^2/(a+a*cosh(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2} - {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x - d^{2} e^{2} + 2 \, c d e f\right)} \cosh\left(f x + e\right)^{3} - {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x - d^{2} e^{2} + 2 \, c d e f\right)} \sinh\left(f x + e\right)^{3} - {\left(3 \, d^{2} f^{2} x^{2} - 3 \, d^{2} e^{2} + 2 \, d^{2} + 2 \, {\left(3 \, c d e + c d\right)} f + 2 \, {\left(3 \, c d f^{2} + d^{2} f\right)} x\right)} \cosh\left(f x + e\right)^{2} - {\left(3 \, d^{2} f^{2} x^{2} - 3 \, d^{2} e^{2} + 2 \, d^{2} + 2 \, {\left(3 \, c d e + c d\right)} f + 2 \, {\left(3 \, c d f^{2} + d^{2} f\right)} x + 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x - d^{2} e^{2} + 2 \, c d e f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} - 2 \, d^{2} + {\left(3 \, d^{2} e^{2} + 3 \, c^{2} f^{2} - 2 \, d^{2} f x - 4 \, d^{2} - 2 \, {\left(3 \, c d e + c d\right)} f\right)} \cosh\left(f x + e\right) + 2 \, {\left(d^{2} \cosh\left(f x + e\right)^{3} + d^{2} \sinh\left(f x + e\right)^{3} + 3 \, d^{2} \cosh\left(f x + e\right)^{2} + 3 \, d^{2} \cosh\left(f x + e\right) + 3 \, {\left(d^{2} \cosh\left(f x + e\right) + d^{2}\right)} \sinh\left(f x + e\right)^{2} + d^{2} + 3 \, {\left(d^{2} \cosh\left(f x + e\right)^{2} + 2 \, d^{2} \cosh\left(f x + e\right) + d^{2}\right)} \sinh\left(f x + e\right)\right)} {\rm Li}_2\left(-\cosh\left(f x + e\right) - \sinh\left(f x + e\right)\right) + 2 \, {\left(d^{2} f x + {\left(d^{2} f x + c d f\right)} \cosh\left(f x + e\right)^{3} + {\left(d^{2} f x + c d f\right)} \sinh\left(f x + e\right)^{3} + c d f + 3 \, {\left(d^{2} f x + c d f\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(d^{2} f x + c d f\right)} \cosh\left(f x + e\right) + 3 \, {\left(d^{2} f x + c d f + {\left(d^{2} f x + c d f\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(d^{2} f x + c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) + {\left(3 \, d^{2} e^{2} + 3 \, c^{2} f^{2} - 2 \, d^{2} f x - 3 \, {\left(d^{2} f^{2} x^{2} + 2 \, c d f^{2} x - d^{2} e^{2} + 2 \, c d e f\right)} \cosh\left(f x + e\right)^{2} - 4 \, d^{2} - 2 \, {\left(3 \, c d e + c d\right)} f - 2 \, {\left(3 \, d^{2} f^{2} x^{2} - 3 \, d^{2} e^{2} + 2 \, d^{2} + 2 \, {\left(3 \, c d e + c d\right)} f + 2 \, {\left(3 \, c d f^{2} + d^{2} f\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}{3 \, {\left(a^{2} f^{3} \cosh\left(f x + e\right)^{3} + a^{2} f^{3} \sinh\left(f x + e\right)^{3} + 3 \, a^{2} f^{3} \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f^{3} \cosh\left(f x + e\right) + a^{2} f^{3} + 3 \, {\left(a^{2} f^{3} \cosh\left(f x + e\right) + a^{2} f^{3}\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(a^{2} f^{3} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} f^{3} \cosh\left(f x + e\right) + a^{2} f^{3}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-2/3*(d^2*e^2 - 2*c*d*e*f + c^2*f^2 - (d^2*f^2*x^2 + 2*c*d*f^2*x - d^2*e^2 + 2*c*d*e*f)*cosh(f*x + e)^3 - (d^2*f^2*x^2 + 2*c*d*f^2*x - d^2*e^2 + 2*c*d*e*f)*sinh(f*x + e)^3 - (3*d^2*f^2*x^2 - 3*d^2*e^2 + 2*d^2 + 2*(3*c*d*e + c*d)*f + 2*(3*c*d*f^2 + d^2*f)*x)*cosh(f*x + e)^2 - (3*d^2*f^2*x^2 - 3*d^2*e^2 + 2*d^2 + 2*(3*c*d*e + c*d)*f + 2*(3*c*d*f^2 + d^2*f)*x + 3*(d^2*f^2*x^2 + 2*c*d*f^2*x - d^2*e^2 + 2*c*d*e*f)*cosh(f*x + e))*sinh(f*x + e)^2 - 2*d^2 + (3*d^2*e^2 + 3*c^2*f^2 - 2*d^2*f*x - 4*d^2 - 2*(3*c*d*e + c*d)*f)*cosh(f*x + e) + 2*(d^2*cosh(f*x + e)^3 + d^2*sinh(f*x + e)^3 + 3*d^2*cosh(f*x + e)^2 + 3*d^2*cosh(f*x + e) + 3*(d^2*cosh(f*x + e) + d^2)*sinh(f*x + e)^2 + d^2 + 3*(d^2*cosh(f*x + e)^2 + 2*d^2*cosh(f*x + e) + d^2)*sinh(f*x + e))*dilog(-cosh(f*x + e) - sinh(f*x + e)) + 2*(d^2*f*x + (d^2*f*x + c*d*f)*cosh(f*x + e)^3 + (d^2*f*x + c*d*f)*sinh(f*x + e)^3 + c*d*f + 3*(d^2*f*x + c*d*f)*cosh(f*x + e)^2 + 3*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(d^2*f*x + c*d*f)*cosh(f*x + e) + 3*(d^2*f*x + c*d*f + (d^2*f*x + c*d*f)*cosh(f*x + e)^2 + 2*(d^2*f*x + c*d*f)*cosh(f*x + e))*sinh(f*x + e))*log(cosh(f*x + e) + sinh(f*x + e) + 1) + (3*d^2*e^2 + 3*c^2*f^2 - 2*d^2*f*x - 3*(d^2*f^2*x^2 + 2*c*d*f^2*x - d^2*e^2 + 2*c*d*e*f)*cosh(f*x + e)^2 - 4*d^2 - 2*(3*c*d*e + c*d)*f - 2*(3*d^2*f^2*x^2 - 3*d^2*e^2 + 2*d^2 + 2*(3*c*d*e + c*d)*f + 2*(3*c*d*f^2 + d^2*f)*x)*cosh(f*x + e))*sinh(f*x + e))/(a^2*f^3*cosh(f*x + e)^3 + a^2*f^3*sinh(f*x + e)^3 + 3*a^2*f^3*cosh(f*x + e)^2 + 3*a^2*f^3*cosh(f*x + e) + a^2*f^3 + 3*(a^2*f^3*cosh(f*x + e) + a^2*f^3)*sinh(f*x + e)^2 + 3*(a^2*f^3*cosh(f*x + e)^2 + 2*a^2*f^3*cosh(f*x + e) + a^2*f^3)*sinh(f*x + e))","B",0
118,1,385,0,0.532197," ","integrate((d*x+c)/(a+a*cosh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(d f x \cosh\left(f x + e\right)^{3} + d f x \sinh\left(f x + e\right)^{3} + {\left(3 \, d f x + d\right)} \cosh\left(f x + e\right)^{2} + {\left(3 \, d f x \cosh\left(f x + e\right) + 3 \, d f x + d\right)} \sinh\left(f x + e\right)^{2} - c f - {\left(3 \, c f - d\right)} \cosh\left(f x + e\right) - {\left(d \cosh\left(f x + e\right)^{3} + d \sinh\left(f x + e\right)^{3} + 3 \, d \cosh\left(f x + e\right)^{2} + 3 \, {\left(d \cosh\left(f x + e\right) + d\right)} \sinh\left(f x + e\right)^{2} + 3 \, d \cosh\left(f x + e\right) + 3 \, {\left(d \cosh\left(f x + e\right)^{2} + 2 \, d \cosh\left(f x + e\right) + d\right)} \sinh\left(f x + e\right) + d\right)} \log\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1\right) + {\left(3 \, d f x \cosh\left(f x + e\right)^{2} - 3 \, c f + 2 \, {\left(3 \, d f x + d\right)} \cosh\left(f x + e\right) + d\right)} \sinh\left(f x + e\right)\right)}}{3 \, {\left(a^{2} f^{2} \cosh\left(f x + e\right)^{3} + a^{2} f^{2} \sinh\left(f x + e\right)^{3} + 3 \, a^{2} f^{2} \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f^{2} \cosh\left(f x + e\right) + a^{2} f^{2} + 3 \, {\left(a^{2} f^{2} \cosh\left(f x + e\right) + a^{2} f^{2}\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(a^{2} f^{2} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} f^{2} \cosh\left(f x + e\right) + a^{2} f^{2}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"2/3*(d*f*x*cosh(f*x + e)^3 + d*f*x*sinh(f*x + e)^3 + (3*d*f*x + d)*cosh(f*x + e)^2 + (3*d*f*x*cosh(f*x + e) + 3*d*f*x + d)*sinh(f*x + e)^2 - c*f - (3*c*f - d)*cosh(f*x + e) - (d*cosh(f*x + e)^3 + d*sinh(f*x + e)^3 + 3*d*cosh(f*x + e)^2 + 3*(d*cosh(f*x + e) + d)*sinh(f*x + e)^2 + 3*d*cosh(f*x + e) + 3*(d*cosh(f*x + e)^2 + 2*d*cosh(f*x + e) + d)*sinh(f*x + e) + d)*log(cosh(f*x + e) + sinh(f*x + e) + 1) + (3*d*f*x*cosh(f*x + e)^2 - 3*c*f + 2*(3*d*f*x + d)*cosh(f*x + e) + d)*sinh(f*x + e))/(a^2*f^2*cosh(f*x + e)^3 + a^2*f^2*sinh(f*x + e)^3 + 3*a^2*f^2*cosh(f*x + e)^2 + 3*a^2*f^2*cosh(f*x + e) + a^2*f^2 + 3*(a^2*f^2*cosh(f*x + e) + a^2*f^2)*sinh(f*x + e)^2 + 3*(a^2*f^2*cosh(f*x + e)^2 + 2*a^2*f^2*cosh(f*x + e) + a^2*f^2)*sinh(f*x + e))","B",0
119,0,0,0,0.506468," ","integrate(1/(d*x+c)/(a+a*cosh(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d x + a^{2} c + {\left(a^{2} d x + a^{2} c\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d x + a^{2} c\right)} \cosh\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d*x + a^2*c + (a^2*d*x + a^2*c)*cosh(f*x + e)^2 + 2*(a^2*d*x + a^2*c)*cosh(f*x + e)), x)","F",0
120,0,0,0,1.129816," ","integrate(1/(d*x+c)^2/(a+a*cosh(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2} + {\left(a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2}\right)} \cosh\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2 + (a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2)*cosh(f*x + e)^2 + 2*(a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2)*cosh(f*x + e)), x)","F",0
121,-2,0,0,0.000000," ","integrate(x^3*(a+a*cosh(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
122,-2,0,0,0.000000," ","integrate(x^2*(a+a*cosh(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
123,-2,0,0,0.000000," ","integrate(x*(a+a*cosh(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
124,-2,0,0,0.000000," ","integrate((a+a*cosh(d*x+c))^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
125,-2,0,0,0.000000," ","integrate((a+a*cosh(d*x+c))^(1/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
126,-2,0,0,0.000000," ","integrate((a+a*cosh(d*x+c))^(1/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
127,-2,0,0,0.000000," ","integrate(x^3*(a+a*cosh(x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
128,-2,0,0,0.000000," ","integrate(x^2*(a+a*cosh(x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
129,-2,0,0,0.000000," ","integrate(x*(a+a*cosh(x))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
130,-2,0,0,0.000000," ","integrate((a+a*cosh(x))^(1/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
131,-2,0,0,0.000000," ","integrate((a+a*cosh(x))^(1/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
132,-2,0,0,0.000000," ","integrate((a+a*cosh(x))^(1/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
133,-2,0,0,0.000000," ","integrate(x^3*(a+a*cosh(x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
134,-2,0,0,0.000000," ","integrate(x^2*(a+a*cosh(x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
135,-2,0,0,0.000000," ","integrate(x*(a+a*cosh(x))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
136,-2,0,0,0.000000," ","integrate((a+a*cosh(x))^(3/2)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
137,-2,0,0,0.000000," ","integrate((a+a*cosh(x))^(3/2)/x^2,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
138,-2,0,0,0.000000," ","integrate((a+a*cosh(x))^(3/2)/x^3,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
139,0,0,0,0.830974," ","integrate(x^3/(a+a*cosh(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{3}}{\sqrt{a \cosh\left(d x + c\right) + a}}, x\right)"," ",0,"integral(x^3/sqrt(a*cosh(d*x + c) + a), x)","F",0
140,0,0,0,0.644302," ","integrate(x^2/(a+a*cosh(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2}}{\sqrt{a \cosh\left(d x + c\right) + a}}, x\right)"," ",0,"integral(x^2/sqrt(a*cosh(d*x + c) + a), x)","F",0
141,0,0,0,0.505781," ","integrate(x/(a+a*cosh(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x}{\sqrt{a \cosh\left(d x + c\right) + a}}, x\right)"," ",0,"integral(x/sqrt(a*cosh(d*x + c) + a), x)","F",0
142,0,0,0,0.426570," ","integrate(1/x/(a+a*cosh(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cosh\left(d x + c\right) + a}}{a x \cosh\left(d x + c\right) + a x}, x\right)"," ",0,"integral(sqrt(a*cosh(d*x + c) + a)/(a*x*cosh(d*x + c) + a*x), x)","F",0
143,0,0,0,0.627551," ","integrate(1/x^2/(a+a*cosh(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cosh\left(d x + c\right) + a}}{a x^{2} \cosh\left(d x + c\right) + a x^{2}}, x\right)"," ",0,"integral(sqrt(a*cosh(d*x + c) + a)/(a*x^2*cosh(d*x + c) + a*x^2), x)","F",0
144,0,0,0,0.498454," ","integrate(x^3/(a+a*cosh(x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cosh\left(x\right) + a} x^{3}}{a^{2} \cosh\left(x\right)^{2} + 2 \, a^{2} \cosh\left(x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*cosh(x) + a)*x^3/(a^2*cosh(x)^2 + 2*a^2*cosh(x) + a^2), x)","F",0
145,0,0,0,0.435655," ","integrate(x^2/(a+a*cosh(x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cosh\left(x\right) + a} x^{2}}{a^{2} \cosh\left(x\right)^{2} + 2 \, a^{2} \cosh\left(x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*cosh(x) + a)*x^2/(a^2*cosh(x)^2 + 2*a^2*cosh(x) + a^2), x)","F",0
146,0,0,0,0.945455," ","integrate(x/(a+a*cosh(x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cosh\left(x\right) + a} x}{a^{2} \cosh\left(x\right)^{2} + 2 \, a^{2} \cosh\left(x\right) + a^{2}}, x\right)"," ",0,"integral(sqrt(a*cosh(x) + a)*x/(a^2*cosh(x)^2 + 2*a^2*cosh(x) + a^2), x)","F",0
147,0,0,0,0.933934," ","integrate(1/x/(a+a*cosh(x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cosh\left(x\right) + a}}{a^{2} x \cosh\left(x\right)^{2} + 2 \, a^{2} x \cosh\left(x\right) + a^{2} x}, x\right)"," ",0,"integral(sqrt(a*cosh(x) + a)/(a^2*x*cosh(x)^2 + 2*a^2*x*cosh(x) + a^2*x), x)","F",0
148,0,0,0,0.480353," ","integrate(1/x^2/(a+a*cosh(x))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \cosh\left(x\right) + a}}{a^{2} x^{2} \cosh\left(x\right)^{2} + 2 \, a^{2} x^{2} \cosh\left(x\right) + a^{2} x^{2}}, x\right)"," ",0,"integral(sqrt(a*cosh(x) + a)/(a^2*x^2*cosh(x)^2 + 2*a^2*x^2*cosh(x) + a^2*x^2), x)","F",0
149,-2,0,0,0.000000," ","integrate((a+a*cosh(d*x+c))^(1/3)/x,x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
150,0,0,0,0.808304," ","integrate((d*x+c)^m*(a+a*cosh(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} {\left(a \cosh\left(f x + e\right) + a\right)}^{n}, x\right)"," ",0,"integral((d*x + c)^m*(a*cosh(f*x + e) + a)^n, x)","F",0
151,1,713,0,0.707679," ","integrate((d*x+c)^m*(a+a*cosh(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(a^{3} d m + a^{3} d\right)} \cosh\left(\frac{d m \log\left(\frac{3 \, f}{d}\right) + 3 \, d e - 3 \, c f}{d}\right) \Gamma\left(m + 1, \frac{3 \, {\left(d f x + c f\right)}}{d}\right) + 9 \, {\left(a^{3} d m + a^{3} d\right)} \cosh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 45 \, {\left(a^{3} d m + a^{3} d\right)} \cosh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) - 45 \, {\left(a^{3} d m + a^{3} d\right)} \cosh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) - 9 \, {\left(a^{3} d m + a^{3} d\right)} \cosh\left(\frac{d m \log\left(-\frac{2 \, f}{d}\right) - 2 \, d e + 2 \, c f}{d}\right) \Gamma\left(m + 1, -\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(a^{3} d m + a^{3} d\right)} \cosh\left(\frac{d m \log\left(-\frac{3 \, f}{d}\right) - 3 \, d e + 3 \, c f}{d}\right) \Gamma\left(m + 1, -\frac{3 \, {\left(d f x + c f\right)}}{d}\right) - {\left(a^{3} d m + a^{3} d\right)} \Gamma\left(m + 1, \frac{3 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{3 \, f}{d}\right) + 3 \, d e - 3 \, c f}{d}\right) - 9 \, {\left(a^{3} d m + a^{3} d\right)} \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) - 45 \, {\left(a^{3} d m + a^{3} d\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) + 45 \, {\left(a^{3} d m + a^{3} d\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) + 9 \, {\left(a^{3} d m + a^{3} d\right)} \Gamma\left(m + 1, -\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{2 \, f}{d}\right) - 2 \, d e + 2 \, c f}{d}\right) + {\left(a^{3} d m + a^{3} d\right)} \Gamma\left(m + 1, -\frac{3 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{3 \, f}{d}\right) - 3 \, d e + 3 \, c f}{d}\right) - 60 \, {\left(a^{3} d f x + a^{3} c f\right)} \cosh\left(m \log\left(d x + c\right)\right) - 60 \, {\left(a^{3} d f x + a^{3} c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{24 \, {\left(d f m + d f\right)}}"," ",0,"-1/24*((a^3*d*m + a^3*d)*cosh((d*m*log(3*f/d) + 3*d*e - 3*c*f)/d)*gamma(m + 1, 3*(d*f*x + c*f)/d) + 9*(a^3*d*m + a^3*d)*cosh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d)*gamma(m + 1, 2*(d*f*x + c*f)/d) + 45*(a^3*d*m + a^3*d)*cosh((d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) - 45*(a^3*d*m + a^3*d)*cosh((d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) - 9*(a^3*d*m + a^3*d)*cosh((d*m*log(-2*f/d) - 2*d*e + 2*c*f)/d)*gamma(m + 1, -2*(d*f*x + c*f)/d) - (a^3*d*m + a^3*d)*cosh((d*m*log(-3*f/d) - 3*d*e + 3*c*f)/d)*gamma(m + 1, -3*(d*f*x + c*f)/d) - (a^3*d*m + a^3*d)*gamma(m + 1, 3*(d*f*x + c*f)/d)*sinh((d*m*log(3*f/d) + 3*d*e - 3*c*f)/d) - 9*(a^3*d*m + a^3*d)*gamma(m + 1, 2*(d*f*x + c*f)/d)*sinh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d) - 45*(a^3*d*m + a^3*d)*gamma(m + 1, (d*f*x + c*f)/d)*sinh((d*m*log(f/d) + d*e - c*f)/d) + 45*(a^3*d*m + a^3*d)*gamma(m + 1, -(d*f*x + c*f)/d)*sinh((d*m*log(-f/d) - d*e + c*f)/d) + 9*(a^3*d*m + a^3*d)*gamma(m + 1, -2*(d*f*x + c*f)/d)*sinh((d*m*log(-2*f/d) - 2*d*e + 2*c*f)/d) + (a^3*d*m + a^3*d)*gamma(m + 1, -3*(d*f*x + c*f)/d)*sinh((d*m*log(-3*f/d) - 3*d*e + 3*c*f)/d) - 60*(a^3*d*f*x + a^3*c*f)*cosh(m*log(d*x + c)) - 60*(a^3*d*f*x + a^3*c*f)*sinh(m*log(d*x + c)))/(d*f*m + d*f)","A",0
152,1,493,0,0.796447," ","integrate((d*x+c)^m*(a+a*cosh(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} d m + a^{2} d\right)} \cosh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 8 \, {\left(a^{2} d m + a^{2} d\right)} \cosh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) - 8 \, {\left(a^{2} d m + a^{2} d\right)} \cosh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) - {\left(a^{2} d m + a^{2} d\right)} \cosh\left(\frac{d m \log\left(-\frac{2 \, f}{d}\right) - 2 \, d e + 2 \, c f}{d}\right) \Gamma\left(m + 1, -\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(a^{2} d m + a^{2} d\right)} \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) - 8 \, {\left(a^{2} d m + a^{2} d\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) + 8 \, {\left(a^{2} d m + a^{2} d\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) + {\left(a^{2} d m + a^{2} d\right)} \Gamma\left(m + 1, -\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{2 \, f}{d}\right) - 2 \, d e + 2 \, c f}{d}\right) - 12 \, {\left(a^{2} d f x + a^{2} c f\right)} \cosh\left(m \log\left(d x + c\right)\right) - 12 \, {\left(a^{2} d f x + a^{2} c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{8 \, {\left(d f m + d f\right)}}"," ",0,"-1/8*((a^2*d*m + a^2*d)*cosh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d)*gamma(m + 1, 2*(d*f*x + c*f)/d) + 8*(a^2*d*m + a^2*d)*cosh((d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) - 8*(a^2*d*m + a^2*d)*cosh((d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) - (a^2*d*m + a^2*d)*cosh((d*m*log(-2*f/d) - 2*d*e + 2*c*f)/d)*gamma(m + 1, -2*(d*f*x + c*f)/d) - (a^2*d*m + a^2*d)*gamma(m + 1, 2*(d*f*x + c*f)/d)*sinh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d) - 8*(a^2*d*m + a^2*d)*gamma(m + 1, (d*f*x + c*f)/d)*sinh((d*m*log(f/d) + d*e - c*f)/d) + 8*(a^2*d*m + a^2*d)*gamma(m + 1, -(d*f*x + c*f)/d)*sinh((d*m*log(-f/d) - d*e + c*f)/d) + (a^2*d*m + a^2*d)*gamma(m + 1, -2*(d*f*x + c*f)/d)*sinh((d*m*log(-2*f/d) - 2*d*e + 2*c*f)/d) - 12*(a^2*d*f*x + a^2*c*f)*cosh(m*log(d*x + c)) - 12*(a^2*d*f*x + a^2*c*f)*sinh(m*log(d*x + c)))/(d*f*m + d*f)","A",0
153,1,249,0,0.594336," ","integrate((d*x+c)^m*(a+a*cosh(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(a d m + a d\right)} \cosh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) - {\left(a d m + a d\right)} \cosh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) - {\left(a d m + a d\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) + {\left(a d m + a d\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) - 2 \, {\left(a d f x + a c f\right)} \cosh\left(m \log\left(d x + c\right)\right) - 2 \, {\left(a d f x + a c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{2 \, {\left(d f m + d f\right)}}"," ",0,"-1/2*((a*d*m + a*d)*cosh((d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) - (a*d*m + a*d)*cosh((d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) - (a*d*m + a*d)*gamma(m + 1, (d*f*x + c*f)/d)*sinh((d*m*log(f/d) + d*e - c*f)/d) + (a*d*m + a*d)*gamma(m + 1, -(d*f*x + c*f)/d)*sinh((d*m*log(-f/d) - d*e + c*f)/d) - 2*(a*d*f*x + a*c*f)*cosh(m*log(d*x + c)) - 2*(a*d*f*x + a*c*f)*sinh(m*log(d*x + c)))/(d*f*m + d*f)","A",0
154,0,0,0,0.649394," ","integrate((d*x+c)^m/(a+a*cosh(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{a \cosh\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*x + c)^m/(a*cosh(f*x + e) + a), x)","F",0
155,0,0,0,0.585419," ","integrate((d*x+c)^m/(a+a*cosh(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{a^{2} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} \cosh\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((d*x + c)^m/(a^2*cosh(f*x + e)^2 + 2*a^2*cosh(f*x + e) + a^2), x)","F",0
156,1,168,0,0.578990," ","integrate((d*x+c)^3*(a+b*cosh(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{3} f^{4} x^{4} + 4 \, a c d^{2} f^{4} x^{3} + 6 \, a c^{2} d f^{4} x^{2} + 4 \, a c^{3} f^{4} x - 12 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2} + 2 \, b d^{3}\right)} \cosh\left(f x + e\right) + 4 \, {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + b c^{3} f^{3} + 6 \, b c d^{2} f + 3 \, {\left(b c^{2} d f^{3} + 2 \, b d^{3} f\right)} x\right)} \sinh\left(f x + e\right)}{4 \, f^{4}}"," ",0,"1/4*(a*d^3*f^4*x^4 + 4*a*c*d^2*f^4*x^3 + 6*a*c^2*d*f^4*x^2 + 4*a*c^3*f^4*x - 12*(b*d^3*f^2*x^2 + 2*b*c*d^2*f^2*x + b*c^2*d*f^2 + 2*b*d^3)*cosh(f*x + e) + 4*(b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + b*c^3*f^3 + 6*b*c*d^2*f + 3*(b*c^2*d*f^3 + 2*b*d^3*f)*x)*sinh(f*x + e))/f^4","A",0
157,1,102,0,0.587984," ","integrate((d*x+c)^2*(a+b*cosh(f*x+e)),x, algorithm=""fricas"")","\frac{a d^{2} f^{3} x^{3} + 3 \, a c d f^{3} x^{2} + 3 \, a c^{2} f^{3} x - 6 \, {\left(b d^{2} f x + b c d f\right)} \cosh\left(f x + e\right) + 3 \, {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2} + 2 \, b d^{2}\right)} \sinh\left(f x + e\right)}{3 \, f^{3}}"," ",0,"1/3*(a*d^2*f^3*x^3 + 3*a*c*d*f^3*x^2 + 3*a*c^2*f^3*x - 6*(b*d^2*f*x + b*c*d*f)*cosh(f*x + e) + 3*(b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2 + 2*b*d^2)*sinh(f*x + e))/f^3","A",0
158,1,51,0,0.772407," ","integrate((d*x+c)*(a+b*cosh(f*x+e)),x, algorithm=""fricas"")","\frac{a d f^{2} x^{2} + 2 \, a c f^{2} x - 2 \, b d \cosh\left(f x + e\right) + 2 \, {\left(b d f x + b c f\right)} \sinh\left(f x + e\right)}{2 \, f^{2}}"," ",0,"1/2*(a*d*f^2*x^2 + 2*a*c*f^2*x - 2*b*d*cosh(f*x + e) + 2*(b*d*f*x + b*c*f)*sinh(f*x + e))/f^2","A",0
159,1,111,0,0.556489," ","integrate((a+b*cosh(f*x+e))/(d*x+c),x, algorithm=""fricas"")","\frac{{\left(b {\rm Ei}\left(\frac{d f x + c f}{d}\right) + b {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + 2 \, a \log\left(d x + c\right) - {\left(b {\rm Ei}\left(\frac{d f x + c f}{d}\right) - b {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right)}{2 \, d}"," ",0,"1/2*((b*Ei((d*f*x + c*f)/d) + b*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + 2*a*log(d*x + c) - (b*Ei((d*f*x + c*f)/d) - b*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d))/d","A",0
160,1,162,0,0.490115," ","integrate((a+b*cosh(f*x+e))/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, b d \cosh\left(f x + e\right) + 2 \, a d - {\left({\left(b d f x + b c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(b d f x + b c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + {\left({\left(b d f x + b c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(b d f x + b c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(2*b*d*cosh(f*x + e) + 2*a*d - ((b*d*f*x + b*c*f)*Ei((d*f*x + c*f)/d) - (b*d*f*x + b*c*f)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + ((b*d*f*x + b*c*f)*Ei((d*f*x + c*f)/d) + (b*d*f*x + b*c*f)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d))/(d^3*x + c*d^2)","A",0
161,1,274,0,0.543121," ","integrate((a+b*cosh(f*x+e))/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{2 \, b d^{2} \cosh\left(f x + e\right) + 2 \, a d^{2} - {\left({\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + 2 \, {\left(b d^{2} f x + b c d f\right)} \sinh\left(f x + e\right) + {\left({\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x + b c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(2*b*d^2*cosh(f*x + e) + 2*a*d^2 - ((b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*Ei((d*f*x + c*f)/d) + (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + 2*(b*d^2*f*x + b*c*d*f)*sinh(f*x + e) + ((b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*Ei((d*f*x + c*f)/d) - (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x + b*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
162,1,409,0,1.020111," ","integrate((d*x+c)^3*(a+b*cosh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} + b^{2}\right)} d^{3} f^{4} x^{4} + 8 \, {\left(2 \, a^{2} + b^{2}\right)} c d^{2} f^{4} x^{3} + 12 \, {\left(2 \, a^{2} + b^{2}\right)} c^{2} d f^{4} x^{2} + 8 \, {\left(2 \, a^{2} + b^{2}\right)} c^{3} f^{4} x - 3 \, {\left(2 \, b^{2} d^{3} f^{2} x^{2} + 4 \, b^{2} c d^{2} f^{2} x + 2 \, b^{2} c^{2} d f^{2} + b^{2} d^{3}\right)} \cosh\left(f x + e\right)^{2} - 3 \, {\left(2 \, b^{2} d^{3} f^{2} x^{2} + 4 \, b^{2} c d^{2} f^{2} x + 2 \, b^{2} c^{2} d f^{2} + b^{2} d^{3}\right)} \sinh\left(f x + e\right)^{2} - 96 \, {\left(a b d^{3} f^{2} x^{2} + 2 \, a b c d^{2} f^{2} x + a b c^{2} d f^{2} + 2 \, a b d^{3}\right)} \cosh\left(f x + e\right) + 4 \, {\left(8 \, a b d^{3} f^{3} x^{3} + 24 \, a b c d^{2} f^{3} x^{2} + 8 \, a b c^{3} f^{3} + 48 \, a b c d^{2} f + 24 \, {\left(a b c^{2} d f^{3} + 2 \, a b d^{3} f\right)} x + {\left(2 \, b^{2} d^{3} f^{3} x^{3} + 6 \, b^{2} c d^{2} f^{3} x^{2} + 2 \, b^{2} c^{3} f^{3} + 3 \, b^{2} c d^{2} f + 3 \, {\left(2 \, b^{2} c^{2} d f^{3} + b^{2} d^{3} f\right)} x\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{16 \, f^{4}}"," ",0,"1/16*(2*(2*a^2 + b^2)*d^3*f^4*x^4 + 8*(2*a^2 + b^2)*c*d^2*f^4*x^3 + 12*(2*a^2 + b^2)*c^2*d*f^4*x^2 + 8*(2*a^2 + b^2)*c^3*f^4*x - 3*(2*b^2*d^3*f^2*x^2 + 4*b^2*c*d^2*f^2*x + 2*b^2*c^2*d*f^2 + b^2*d^3)*cosh(f*x + e)^2 - 3*(2*b^2*d^3*f^2*x^2 + 4*b^2*c*d^2*f^2*x + 2*b^2*c^2*d*f^2 + b^2*d^3)*sinh(f*x + e)^2 - 96*(a*b*d^3*f^2*x^2 + 2*a*b*c*d^2*f^2*x + a*b*c^2*d*f^2 + 2*a*b*d^3)*cosh(f*x + e) + 4*(8*a*b*d^3*f^3*x^3 + 24*a*b*c*d^2*f^3*x^2 + 8*a*b*c^3*f^3 + 48*a*b*c*d^2*f + 24*(a*b*c^2*d*f^3 + 2*a*b*d^3*f)*x + (2*b^2*d^3*f^3*x^3 + 6*b^2*c*d^2*f^3*x^2 + 2*b^2*c^3*f^3 + 3*b^2*c*d^2*f + 3*(2*b^2*c^2*d*f^3 + b^2*d^3*f)*x)*cosh(f*x + e))*sinh(f*x + e))/f^4","A",0
163,1,240,0,0.526067," ","integrate((d*x+c)^2*(a+b*cosh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} + b^{2}\right)} d^{2} f^{3} x^{3} + 6 \, {\left(2 \, a^{2} + b^{2}\right)} c d f^{3} x^{2} + 6 \, {\left(2 \, a^{2} + b^{2}\right)} c^{2} f^{3} x - 3 \, {\left(b^{2} d^{2} f x + b^{2} c d f\right)} \cosh\left(f x + e\right)^{2} - 3 \, {\left(b^{2} d^{2} f x + b^{2} c d f\right)} \sinh\left(f x + e\right)^{2} - 48 \, {\left(a b d^{2} f x + a b c d f\right)} \cosh\left(f x + e\right) + 3 \, {\left(8 \, a b d^{2} f^{2} x^{2} + 16 \, a b c d f^{2} x + 8 \, a b c^{2} f^{2} + 16 \, a b d^{2} + {\left(2 \, b^{2} d^{2} f^{2} x^{2} + 4 \, b^{2} c d f^{2} x + 2 \, b^{2} c^{2} f^{2} + b^{2} d^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{12 \, f^{3}}"," ",0,"1/12*(2*(2*a^2 + b^2)*d^2*f^3*x^3 + 6*(2*a^2 + b^2)*c*d*f^3*x^2 + 6*(2*a^2 + b^2)*c^2*f^3*x - 3*(b^2*d^2*f*x + b^2*c*d*f)*cosh(f*x + e)^2 - 3*(b^2*d^2*f*x + b^2*c*d*f)*sinh(f*x + e)^2 - 48*(a*b*d^2*f*x + a*b*c*d*f)*cosh(f*x + e) + 3*(8*a*b*d^2*f^2*x^2 + 16*a*b*c*d*f^2*x + 8*a*b*c^2*f^2 + 16*a*b*d^2 + (2*b^2*d^2*f^2*x^2 + 4*b^2*c*d*f^2*x + 2*b^2*c^2*f^2 + b^2*d^2)*cosh(f*x + e))*sinh(f*x + e))/f^3","A",0
164,1,122,0,0.563590," ","integrate((d*x+c)*(a+b*cosh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(2 \, a^{2} + b^{2}\right)} d f^{2} x^{2} + 4 \, {\left(2 \, a^{2} + b^{2}\right)} c f^{2} x - b^{2} d \cosh\left(f x + e\right)^{2} - b^{2} d \sinh\left(f x + e\right)^{2} - 16 \, a b d \cosh\left(f x + e\right) + 4 \, {\left(4 \, a b d f x + 4 \, a b c f + {\left(b^{2} d f x + b^{2} c f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{8 \, f^{2}}"," ",0,"1/8*(2*(2*a^2 + b^2)*d*f^2*x^2 + 4*(2*a^2 + b^2)*c*f^2*x - b^2*d*cosh(f*x + e)^2 - b^2*d*sinh(f*x + e)^2 - 16*a*b*d*cosh(f*x + e) + 4*(4*a*b*d*f*x + 4*a*b*c*f + (b^2*d*f*x + b^2*c*f)*cosh(f*x + e))*sinh(f*x + e))/f^2","A",0
165,1,230,0,0.505643," ","integrate((a+b*cosh(f*x+e))^2/(d*x+c),x, algorithm=""fricas"")","\frac{4 \, {\left(a b {\rm Ei}\left(\frac{d f x + c f}{d}\right) + a b {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) + {\left(b^{2} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + b^{2} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 2 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(d x + c\right) - 4 \, {\left(a b {\rm Ei}\left(\frac{d f x + c f}{d}\right) - a b {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right) - {\left(b^{2} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - b^{2} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{4 \, d}"," ",0,"1/4*(4*(a*b*Ei((d*f*x + c*f)/d) + a*b*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) + (b^2*Ei(2*(d*f*x + c*f)/d) + b^2*Ei(-2*(d*f*x + c*f)/d))*cosh(-2*(d*e - c*f)/d) + 2*(2*a^2 + b^2)*log(d*x + c) - 4*(a*b*Ei((d*f*x + c*f)/d) - a*b*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d) - (b^2*Ei(2*(d*f*x + c*f)/d) - b^2*Ei(-2*(d*f*x + c*f)/d))*sinh(-2*(d*e - c*f)/d))/d","A",0
166,1,355,0,0.496533," ","integrate((a+b*cosh(f*x+e))^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{b^{2} d \cosh\left(f x + e\right)^{2} + b^{2} d \sinh\left(f x + e\right)^{2} + 4 \, a b d \cosh\left(f x + e\right) + {\left(2 \, a^{2} + b^{2}\right)} d - 2 \, {\left({\left(a b d f x + a b c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(a b d f x + a b c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) - {\left({\left(b^{2} d f x + b^{2} c f\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(b^{2} d f x + b^{2} c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 2 \, {\left({\left(a b d f x + a b c f\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(a b d f x + a b c f\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right) + {\left({\left(b^{2} d f x + b^{2} c f\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + {\left(b^{2} d f x + b^{2} c f\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{2 \, {\left(d^{3} x + c d^{2}\right)}}"," ",0,"-1/2*(b^2*d*cosh(f*x + e)^2 + b^2*d*sinh(f*x + e)^2 + 4*a*b*d*cosh(f*x + e) + (2*a^2 + b^2)*d - 2*((a*b*d*f*x + a*b*c*f)*Ei((d*f*x + c*f)/d) - (a*b*d*f*x + a*b*c*f)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) - ((b^2*d*f*x + b^2*c*f)*Ei(2*(d*f*x + c*f)/d) - (b^2*d*f*x + b^2*c*f)*Ei(-2*(d*f*x + c*f)/d))*cosh(-2*(d*e - c*f)/d) + 2*((a*b*d*f*x + a*b*c*f)*Ei((d*f*x + c*f)/d) + (a*b*d*f*x + a*b*c*f)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d) + ((b^2*d*f*x + b^2*c*f)*Ei(2*(d*f*x + c*f)/d) + (b^2*d*f*x + b^2*c*f)*Ei(-2*(d*f*x + c*f)/d))*sinh(-2*(d*e - c*f)/d))/(d^3*x + c*d^2)","A",0
167,1,586,0,0.518646," ","integrate((a+b*cosh(f*x+e))^2/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{b^{2} d^{2} \cosh\left(f x + e\right)^{2} + b^{2} d^{2} \sinh\left(f x + e\right)^{2} + 4 \, a b d^{2} \cosh\left(f x + e\right) + {\left(2 \, a^{2} + b^{2}\right)} d^{2} - 2 \, {\left({\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) + {\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \cosh\left(-\frac{d e - c f}{d}\right) - 2 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) + {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \cosh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right) + 4 \, {\left(a b d^{2} f x + a b c d f + {\left(b^{2} d^{2} f x + b^{2} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 2 \, {\left({\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} {\rm Ei}\left(\frac{d f x + c f}{d}\right) - {\left(a b d^{2} f^{2} x^{2} + 2 \, a b c d f^{2} x + a b c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{d f x + c f}{d}\right)\right)} \sinh\left(-\frac{d e - c f}{d}\right) + 2 \, {\left({\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} {\rm Ei}\left(\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(b^{2} d^{2} f^{2} x^{2} + 2 \, b^{2} c d f^{2} x + b^{2} c^{2} f^{2}\right)} {\rm Ei}\left(-\frac{2 \, {\left(d f x + c f\right)}}{d}\right)\right)} \sinh\left(-\frac{2 \, {\left(d e - c f\right)}}{d}\right)}{4 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/4*(b^2*d^2*cosh(f*x + e)^2 + b^2*d^2*sinh(f*x + e)^2 + 4*a*b*d^2*cosh(f*x + e) + (2*a^2 + b^2)*d^2 - 2*((a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*Ei((d*f*x + c*f)/d) + (a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*cosh(-(d*e - c*f)/d) - 2*((b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*Ei(2*(d*f*x + c*f)/d) + (b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*Ei(-2*(d*f*x + c*f)/d))*cosh(-2*(d*e - c*f)/d) + 4*(a*b*d^2*f*x + a*b*c*d*f + (b^2*d^2*f*x + b^2*c*d*f)*cosh(f*x + e))*sinh(f*x + e) + 2*((a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*Ei((d*f*x + c*f)/d) - (a*b*d^2*f^2*x^2 + 2*a*b*c*d*f^2*x + a*b*c^2*f^2)*Ei(-(d*f*x + c*f)/d))*sinh(-(d*e - c*f)/d) + 2*((b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*Ei(2*(d*f*x + c*f)/d) - (b^2*d^2*f^2*x^2 + 2*b^2*c*d*f^2*x + b^2*c^2*f^2)*Ei(-2*(d*f*x + c*f)/d))*sinh(-2*(d*e - c*f)/d))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","B",0
168,1,1042,0,0.616838," ","integrate((d*x+c)^3/(a+b*cosh(f*x+e)),x, algorithm=""fricas"")","\frac{6 \, b d^{3} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 6 \, b d^{3} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 3 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) - 3 \, {\left(b d^{3} f^{2} x^{2} + 2 \, b c d^{2} f^{2} x + b c^{2} d f^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) + {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right) - {\left(b d^{3} f^{3} x^{3} + 3 \, b c d^{2} f^{3} x^{2} + 3 \, b c^{2} d f^{3} x + b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right) - 6 \, {\left(b d^{3} f x + b c d^{2} f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(b d^{3} f x + b c d^{2} f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right)}{{\left(a^{2} - b^{2}\right)} f^{4}}"," ",0,"(6*b*d^3*sqrt((a^2 - b^2)/b^2)*polylog(4, -(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) - 6*b*d^3*sqrt((a^2 - b^2)/b^2)*polylog(4, -(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) + 3*(b*d^3*f^2*x^2 + 2*b*c*d^2*f^2*x + b*c^2*d*f^2)*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) - 3*(b*d^3*f^2*x^2 + 2*b*c*d^2*f^2*x + b*c^2*d*f^2)*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) + (b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt((a^2 - b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) - (b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*sqrt((a^2 - b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) + (b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*sqrt((a^2 - b^2)/b^2)*log((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b) - (b*d^3*f^3*x^3 + 3*b*c*d^2*f^3*x^2 + 3*b*c^2*d*f^3*x + b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*sqrt((a^2 - b^2)/b^2)*log((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b) - 6*(b*d^3*f*x + b*c*d^2*f)*sqrt((a^2 - b^2)/b^2)*polylog(3, -(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) + 6*(b*d^3*f*x + b*c*d^2*f)*sqrt((a^2 - b^2)/b^2)*polylog(3, -(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b))/((a^2 - b^2)*f^4)","C",0
169,1,736,0,0.494347," ","integrate((d*x+c)^2/(a+b*cosh(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, b d^{2} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 2 \, b d^{2} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left(b d^{2} f x + b c d f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) + 2 \, {\left(b d^{2} f x + b c d f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) + {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right) + {\left(b d^{2} f^{2} x^{2} + 2 \, b c d f^{2} x - b d^{2} e^{2} + 2 \, b c d e f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right)}{{\left(a^{2} - b^{2}\right)} f^{3}}"," ",0,"-(2*b*d^2*sqrt((a^2 - b^2)/b^2)*polylog(3, -(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) - 2*b*d^2*sqrt((a^2 - b^2)/b^2)*polylog(3, -(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) - 2*(b*d^2*f*x + b*c*d*f)*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) + 2*(b*d^2*f*x + b*c*d*f)*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) + (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt((a^2 - b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) - (b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*sqrt((a^2 - b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) - (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*sqrt((a^2 - b^2)/b^2)*log((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b) + (b*d^2*f^2*x^2 + 2*b*c*d*f^2*x - b*d^2*e^2 + 2*b*c*d*e*f)*sqrt((a^2 - b^2)/b^2)*log((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b))/((a^2 - b^2)*f^3)","C",0
170,1,473,0,0.494462," ","integrate((d*x+c)/(a+b*cosh(f*x+e)),x, algorithm=""fricas"")","\frac{b d \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) - b d \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) + {\left(b d e - b c f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) - {\left(b d e - b c f\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) + {\left(b d f x + b d e\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right) - {\left(b d f x + b d e\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right)}{{\left(a^{2} - b^{2}\right)} f^{2}}"," ",0,"(b*d*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) - b*d*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) + (b*d*e - b*c*f)*sqrt((a^2 - b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) - (b*d*e - b*c*f)*sqrt((a^2 - b^2)/b^2)*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) + (b*d*f*x + b*d*e)*sqrt((a^2 - b^2)/b^2)*log((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b) - (b*d*f*x + b*d*e)*sqrt((a^2 - b^2)/b^2)*log((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b))/((a^2 - b^2)*f^2)","B",0
171,0,0,0,1.435711," ","integrate(1/(d*x+c)/(a+b*cosh(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + a c + {\left(b d x + b c\right)} \cosh\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d*x + a*c + (b*d*x + b*c)*cosh(f*x + e)), x)","F",0
172,0,0,0,0.538791," ","integrate(1/(d*x+c)^2/(a+b*cosh(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} \cosh\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*cosh(f*x + e)), x)","F",0
173,1,7116,0,0.771059," ","integrate((d*x+c)^3/(a+b*cosh(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 6 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 6 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c^{3} f^{3} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{3} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{3} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2}\right)} \sinh\left(f x + e\right)^{2} - 6 \, {\left(a b^{2} d^{3} \cosh\left(f x + e\right)^{2} + a b^{2} d^{3} \sinh\left(f x + e\right)^{2} + 2 \, a^{2} b d^{3} \cosh\left(f x + e\right) + a b^{2} d^{3} + 2 \, {\left(a b^{2} d^{3} \cosh\left(f x + e\right) + a^{2} b d^{3}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left(a b^{2} d^{3} \cosh\left(f x + e\right)^{2} + a b^{2} d^{3} \sinh\left(f x + e\right)^{2} + 2 \, a^{2} b d^{3} \cosh\left(f x + e\right) + a b^{2} d^{3} + 2 \, {\left(a b^{2} d^{3} \cosh\left(f x + e\right) + a^{2} b d^{3}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(4, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} c d^{2} f^{3} x^{2} + 3 \, {\left(a^{3} - a b^{2}\right)} c^{2} d f^{3} x + 2 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e^{2} f + 6 \, {\left(a^{3} - a b^{2}\right)} c^{2} d e f^{2} - {\left(a^{3} - a b^{2}\right)} c^{3} f^{3}\right)} \cosh\left(f x + e\right) - 3 \, {\left(2 \, {\left(a^{2} b - b^{3}\right)} d^{3} f x + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f x + {\left(a^{2} b - b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f x + {\left(a^{2} b - b^{3}\right)} c d^{2} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f x + {\left(a^{3} - a b^{2}\right)} c d^{2} f\right)} \cosh\left(f x + e\right) + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f x + {\left(a^{3} - a b^{2}\right)} c d^{2} f + {\left({\left(a^{2} b - b^{3}\right)} d^{3} f x + {\left(a^{2} b - b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d^{3} f^{2} x^{2} + 2 \, a b^{2} c d^{2} f^{2} x + a b^{2} c^{2} d f^{2} + {\left(a b^{2} d^{3} f^{2} x^{2} + 2 \, a b^{2} c d^{2} f^{2} x + a b^{2} c^{2} d f^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{3} f^{2} x^{2} + 2 \, a b^{2} c d^{2} f^{2} x + a b^{2} c^{2} d f^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{3} f^{2} x^{2} + 2 \, a^{2} b c d^{2} f^{2} x + a^{2} b c^{2} d f^{2}\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{3} f^{2} x^{2} + 2 \, a^{2} b c d^{2} f^{2} x + a^{2} b c^{2} d f^{2} + {\left(a b^{2} d^{3} f^{2} x^{2} + 2 \, a b^{2} c d^{2} f^{2} x + a b^{2} c^{2} d f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) - 3 \, {\left(2 \, {\left(a^{2} b - b^{3}\right)} d^{3} f x + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f x + {\left(a^{2} b - b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f x + {\left(a^{2} b - b^{3}\right)} c d^{2} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f x + {\left(a^{3} - a b^{2}\right)} c d^{2} f\right)} \cosh\left(f x + e\right) + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f x + {\left(a^{3} - a b^{2}\right)} c d^{2} f + {\left({\left(a^{2} b - b^{3}\right)} d^{3} f x + {\left(a^{2} b - b^{3}\right)} c d^{2} f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d^{3} f^{2} x^{2} + 2 \, a b^{2} c d^{2} f^{2} x + a b^{2} c^{2} d f^{2} + {\left(a b^{2} d^{3} f^{2} x^{2} + 2 \, a b^{2} c d^{2} f^{2} x + a b^{2} c^{2} d f^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{3} f^{2} x^{2} + 2 \, a b^{2} c d^{2} f^{2} x + a b^{2} c^{2} d f^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{3} f^{2} x^{2} + 2 \, a^{2} b c d^{2} f^{2} x + a^{2} b c^{2} d f^{2}\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{3} f^{2} x^{2} + 2 \, a^{2} b c d^{2} f^{2} x + a^{2} b c^{2} d f^{2} + {\left(a b^{2} d^{3} f^{2} x^{2} + 2 \, a b^{2} c d^{2} f^{2} x + a b^{2} c^{2} d f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) - {\left(3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 6 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2}\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + {\left(a^{3} - a b^{2}\right)} c^{2} d f^{2}\right)} \cosh\left(f x + e\right) + 6 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + {\left(a^{3} - a b^{2}\right)} c^{2} d f^{2} + {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) - {\left(3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 6 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2}\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + {\left(a^{3} - a b^{2}\right)} c^{2} d f^{2}\right)} \cosh\left(f x + e\right) + 6 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} e^{2} - 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + {\left(a^{3} - a b^{2}\right)} c^{2} d f^{2} + {\left({\left(a^{2} b - b^{3}\right)} d^{3} e^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + {\left(a^{2} b - b^{3}\right)} c^{2} d f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3}\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} - a^{2} b c^{3} f^{3} + {\left(a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} - a b^{2} c^{3} f^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) - {\left(3 \, {\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 6 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} f^{2} x - {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f\right)} \cosh\left(f x + e\right) + 6 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} f^{2} x - {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b c d^{2} f^{3} x^{2} + 3 \, a^{2} b c^{2} d f^{3} x + a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2}\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b c d^{2} f^{3} x^{2} + 3 \, a^{2} b c^{2} d f^{3} x + a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right) - {\left(3 \, {\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 6 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - 3 \, {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 6 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} f^{2} x - {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f\right)} \cosh\left(f x + e\right) + 6 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} f^{2} x - {\left(a^{3} - a b^{2}\right)} d^{3} e^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e f + {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{3} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b c d^{2} f^{3} x^{2} + 3 \, a^{2} b c^{2} d f^{3} x + a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2}\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{3} f^{3} x^{3} + 3 \, a^{2} b c d^{2} f^{3} x^{2} + 3 \, a^{2} b c^{2} d f^{3} x + a^{2} b d^{3} e^{3} - 3 \, a^{2} b c d^{2} e^{2} f + 3 \, a^{2} b c^{2} d e f^{2} + {\left(a b^{2} d^{3} f^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} x + a b^{2} d^{3} e^{3} - 3 \, a b^{2} c d^{2} e^{2} f + 3 \, a b^{2} c^{2} d e f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} \cosh\left(f x + e\right)^{2} + {\left(a^{2} b - b^{3}\right)} d^{3} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} d^{3} \cosh\left(f x + e\right) + {\left(a^{2} b - b^{3}\right)} d^{3} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} \cosh\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d^{3}\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{3} f x + a^{2} b c d^{2} f\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{3} f x + a^{2} b c d^{2} f + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 6 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} \cosh\left(f x + e\right)^{2} + {\left(a^{2} b - b^{3}\right)} d^{3} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} d^{3} \cosh\left(f x + e\right) + {\left(a^{2} b - b^{3}\right)} d^{3} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} \cosh\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d^{3}\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{3} f x + a^{2} b c d^{2} f\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{3} f x + a^{2} b c d^{2} f + {\left(a b^{2} d^{3} f x + a b^{2} c d^{2} f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm polylog}\left(3, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left({\left(a^{3} - a b^{2}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} c d^{2} f^{3} x^{2} + 3 \, {\left(a^{3} - a b^{2}\right)} c^{2} d f^{3} x + 2 \, {\left(a^{3} - a b^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} - a b^{2}\right)} c d^{2} e^{2} f + 6 \, {\left(a^{3} - a b^{2}\right)} c^{2} d e f^{2} - {\left(a^{3} - a b^{2}\right)} c^{3} f^{3} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{3} f^{3} x^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} f^{3} x^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d f^{3} x + {\left(a^{2} b - b^{3}\right)} d^{3} e^{3} - 3 \, {\left(a^{2} b - b^{3}\right)} c d^{2} e^{2} f + 3 \, {\left(a^{2} b - b^{3}\right)} c^{2} d e f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{4} \cosh\left(f x + e\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{4} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f^{4} \cosh\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{4} + 2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{4} \cosh\left(f x + e\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f^{4}\right)} \sinh\left(f x + e\right)}"," ",0,"-(2*(a^2*b - b^3)*d^3*e^3 - 6*(a^2*b - b^3)*c*d^2*e^2*f + 6*(a^2*b - b^3)*c^2*d*e*f^2 - 2*(a^2*b - b^3)*c^3*f^3 + 2*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*c*d^2*f^3*x^2 + 3*(a^2*b - b^3)*c^2*d*f^3*x + (a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2)*cosh(f*x + e)^2 + 2*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*c*d^2*f^3*x^2 + 3*(a^2*b - b^3)*c^2*d*f^3*x + (a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2)*sinh(f*x + e)^2 - 6*(a*b^2*d^3*cosh(f*x + e)^2 + a*b^2*d^3*sinh(f*x + e)^2 + 2*a^2*b*d^3*cosh(f*x + e) + a*b^2*d^3 + 2*(a*b^2*d^3*cosh(f*x + e) + a^2*b*d^3)*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2)*polylog(4, -(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) + 6*(a*b^2*d^3*cosh(f*x + e)^2 + a*b^2*d^3*sinh(f*x + e)^2 + 2*a^2*b*d^3*cosh(f*x + e) + a*b^2*d^3 + 2*(a*b^2*d^3*cosh(f*x + e) + a^2*b*d^3)*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2)*polylog(4, -(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) + 2*((a^3 - a*b^2)*d^3*f^3*x^3 + 3*(a^3 - a*b^2)*c*d^2*f^3*x^2 + 3*(a^3 - a*b^2)*c^2*d*f^3*x + 2*(a^3 - a*b^2)*d^3*e^3 - 6*(a^3 - a*b^2)*c*d^2*e^2*f + 6*(a^3 - a*b^2)*c^2*d*e*f^2 - (a^3 - a*b^2)*c^3*f^3)*cosh(f*x + e) - 3*(2*(a^2*b - b^3)*d^3*f*x + 2*(a^2*b - b^3)*c*d^2*f + 2*((a^2*b - b^3)*d^3*f*x + (a^2*b - b^3)*c*d^2*f)*cosh(f*x + e)^2 + 2*((a^2*b - b^3)*d^3*f*x + (a^2*b - b^3)*c*d^2*f)*sinh(f*x + e)^2 + 4*((a^3 - a*b^2)*d^3*f*x + (a^3 - a*b^2)*c*d^2*f)*cosh(f*x + e) + 4*((a^3 - a*b^2)*d^3*f*x + (a^3 - a*b^2)*c*d^2*f + ((a^2*b - b^3)*d^3*f*x + (a^2*b - b^3)*c*d^2*f)*cosh(f*x + e))*sinh(f*x + e) + (a*b^2*d^3*f^2*x^2 + 2*a*b^2*c*d^2*f^2*x + a*b^2*c^2*d*f^2 + (a*b^2*d^3*f^2*x^2 + 2*a*b^2*c*d^2*f^2*x + a*b^2*c^2*d*f^2)*cosh(f*x + e)^2 + (a*b^2*d^3*f^2*x^2 + 2*a*b^2*c*d^2*f^2*x + a*b^2*c^2*d*f^2)*sinh(f*x + e)^2 + 2*(a^2*b*d^3*f^2*x^2 + 2*a^2*b*c*d^2*f^2*x + a^2*b*c^2*d*f^2)*cosh(f*x + e) + 2*(a^2*b*d^3*f^2*x^2 + 2*a^2*b*c*d^2*f^2*x + a^2*b*c^2*d*f^2 + (a*b^2*d^3*f^2*x^2 + 2*a*b^2*c*d^2*f^2*x + a*b^2*c^2*d*f^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) - 3*(2*(a^2*b - b^3)*d^3*f*x + 2*(a^2*b - b^3)*c*d^2*f + 2*((a^2*b - b^3)*d^3*f*x + (a^2*b - b^3)*c*d^2*f)*cosh(f*x + e)^2 + 2*((a^2*b - b^3)*d^3*f*x + (a^2*b - b^3)*c*d^2*f)*sinh(f*x + e)^2 + 4*((a^3 - a*b^2)*d^3*f*x + (a^3 - a*b^2)*c*d^2*f)*cosh(f*x + e) + 4*((a^3 - a*b^2)*d^3*f*x + (a^3 - a*b^2)*c*d^2*f + ((a^2*b - b^3)*d^3*f*x + (a^2*b - b^3)*c*d^2*f)*cosh(f*x + e))*sinh(f*x + e) - (a*b^2*d^3*f^2*x^2 + 2*a*b^2*c*d^2*f^2*x + a*b^2*c^2*d*f^2 + (a*b^2*d^3*f^2*x^2 + 2*a*b^2*c*d^2*f^2*x + a*b^2*c^2*d*f^2)*cosh(f*x + e)^2 + (a*b^2*d^3*f^2*x^2 + 2*a*b^2*c*d^2*f^2*x + a*b^2*c^2*d*f^2)*sinh(f*x + e)^2 + 2*(a^2*b*d^3*f^2*x^2 + 2*a^2*b*c*d^2*f^2*x + a^2*b*c^2*d*f^2)*cosh(f*x + e) + 2*(a^2*b*d^3*f^2*x^2 + 2*a^2*b*c*d^2*f^2*x + a^2*b*c^2*d*f^2 + (a*b^2*d^3*f^2*x^2 + 2*a*b^2*c*d^2*f^2*x + a*b^2*c^2*d*f^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) - (3*(a^2*b - b^3)*d^3*e^2 - 6*(a^2*b - b^3)*c*d^2*e*f + 3*(a^2*b - b^3)*c^2*d*f^2 + 3*((a^2*b - b^3)*d^3*e^2 - 2*(a^2*b - b^3)*c*d^2*e*f + (a^2*b - b^3)*c^2*d*f^2)*cosh(f*x + e)^2 + 3*((a^2*b - b^3)*d^3*e^2 - 2*(a^2*b - b^3)*c*d^2*e*f + (a^2*b - b^3)*c^2*d*f^2)*sinh(f*x + e)^2 + 6*((a^3 - a*b^2)*d^3*e^2 - 2*(a^3 - a*b^2)*c*d^2*e*f + (a^3 - a*b^2)*c^2*d*f^2)*cosh(f*x + e) + 6*((a^3 - a*b^2)*d^3*e^2 - 2*(a^3 - a*b^2)*c*d^2*e*f + (a^3 - a*b^2)*c^2*d*f^2 + ((a^2*b - b^3)*d^3*e^2 - 2*(a^2*b - b^3)*c*d^2*e*f + (a^2*b - b^3)*c^2*d*f^2)*cosh(f*x + e))*sinh(f*x + e) + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*cosh(f*x + e)^2 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*sinh(f*x + e)^2 + 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(f*x + e) + 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) - (3*(a^2*b - b^3)*d^3*e^2 - 6*(a^2*b - b^3)*c*d^2*e*f + 3*(a^2*b - b^3)*c^2*d*f^2 + 3*((a^2*b - b^3)*d^3*e^2 - 2*(a^2*b - b^3)*c*d^2*e*f + (a^2*b - b^3)*c^2*d*f^2)*cosh(f*x + e)^2 + 3*((a^2*b - b^3)*d^3*e^2 - 2*(a^2*b - b^3)*c*d^2*e*f + (a^2*b - b^3)*c^2*d*f^2)*sinh(f*x + e)^2 + 6*((a^3 - a*b^2)*d^3*e^2 - 2*(a^3 - a*b^2)*c*d^2*e*f + (a^3 - a*b^2)*c^2*d*f^2)*cosh(f*x + e) + 6*((a^3 - a*b^2)*d^3*e^2 - 2*(a^3 - a*b^2)*c*d^2*e*f + (a^3 - a*b^2)*c^2*d*f^2 + ((a^2*b - b^3)*d^3*e^2 - 2*(a^2*b - b^3)*c*d^2*e*f + (a^2*b - b^3)*c^2*d*f^2)*cosh(f*x + e))*sinh(f*x + e) - (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*cosh(f*x + e)^2 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*sinh(f*x + e)^2 + 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3)*cosh(f*x + e) + 2*(a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 - a^2*b*c^3*f^3 + (a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 - a*b^2*c^3*f^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) - (3*(a^2*b - b^3)*d^3*f^2*x^2 + 6*(a^2*b - b^3)*c*d^2*f^2*x - 3*(a^2*b - b^3)*d^3*e^2 + 6*(a^2*b - b^3)*c*d^2*e*f + 3*((a^2*b - b^3)*d^3*f^2*x^2 + 2*(a^2*b - b^3)*c*d^2*f^2*x - (a^2*b - b^3)*d^3*e^2 + 2*(a^2*b - b^3)*c*d^2*e*f)*cosh(f*x + e)^2 + 3*((a^2*b - b^3)*d^3*f^2*x^2 + 2*(a^2*b - b^3)*c*d^2*f^2*x - (a^2*b - b^3)*d^3*e^2 + 2*(a^2*b - b^3)*c*d^2*e*f)*sinh(f*x + e)^2 + 6*((a^3 - a*b^2)*d^3*f^2*x^2 + 2*(a^3 - a*b^2)*c*d^2*f^2*x - (a^3 - a*b^2)*d^3*e^2 + 2*(a^3 - a*b^2)*c*d^2*e*f)*cosh(f*x + e) + 6*((a^3 - a*b^2)*d^3*f^2*x^2 + 2*(a^3 - a*b^2)*c*d^2*f^2*x - (a^3 - a*b^2)*d^3*e^2 + 2*(a^3 - a*b^2)*c*d^2*e*f + ((a^2*b - b^3)*d^3*f^2*x^2 + 2*(a^2*b - b^3)*c*d^2*f^2*x - (a^2*b - b^3)*d^3*e^2 + 2*(a^2*b - b^3)*c*d^2*e*f)*cosh(f*x + e))*sinh(f*x + e) + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2)*cosh(f*x + e)^2 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2)*sinh(f*x + e)^2 + 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*c*d^2*f^3*x^2 + 3*a^2*b*c^2*d*f^3*x + a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2)*cosh(f*x + e) + 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*c*d^2*f^3*x^2 + 3*a^2*b*c^2*d*f^3*x + a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*log((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b) - (3*(a^2*b - b^3)*d^3*f^2*x^2 + 6*(a^2*b - b^3)*c*d^2*f^2*x - 3*(a^2*b - b^3)*d^3*e^2 + 6*(a^2*b - b^3)*c*d^2*e*f + 3*((a^2*b - b^3)*d^3*f^2*x^2 + 2*(a^2*b - b^3)*c*d^2*f^2*x - (a^2*b - b^3)*d^3*e^2 + 2*(a^2*b - b^3)*c*d^2*e*f)*cosh(f*x + e)^2 + 3*((a^2*b - b^3)*d^3*f^2*x^2 + 2*(a^2*b - b^3)*c*d^2*f^2*x - (a^2*b - b^3)*d^3*e^2 + 2*(a^2*b - b^3)*c*d^2*e*f)*sinh(f*x + e)^2 + 6*((a^3 - a*b^2)*d^3*f^2*x^2 + 2*(a^3 - a*b^2)*c*d^2*f^2*x - (a^3 - a*b^2)*d^3*e^2 + 2*(a^3 - a*b^2)*c*d^2*e*f)*cosh(f*x + e) + 6*((a^3 - a*b^2)*d^3*f^2*x^2 + 2*(a^3 - a*b^2)*c*d^2*f^2*x - (a^3 - a*b^2)*d^3*e^2 + 2*(a^3 - a*b^2)*c*d^2*e*f + ((a^2*b - b^3)*d^3*f^2*x^2 + 2*(a^2*b - b^3)*c*d^2*f^2*x - (a^2*b - b^3)*d^3*e^2 + 2*(a^2*b - b^3)*c*d^2*e*f)*cosh(f*x + e))*sinh(f*x + e) - (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2)*cosh(f*x + e)^2 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2)*sinh(f*x + e)^2 + 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*c*d^2*f^3*x^2 + 3*a^2*b*c^2*d*f^3*x + a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2)*cosh(f*x + e) + 2*(a^2*b*d^3*f^3*x^3 + 3*a^2*b*c*d^2*f^3*x^2 + 3*a^2*b*c^2*d*f^3*x + a^2*b*d^3*e^3 - 3*a^2*b*c*d^2*e^2*f + 3*a^2*b*c^2*d*e*f^2 + (a*b^2*d^3*f^3*x^3 + 3*a*b^2*c*d^2*f^3*x^2 + 3*a*b^2*c^2*d*f^3*x + a*b^2*d^3*e^3 - 3*a*b^2*c*d^2*e^2*f + 3*a*b^2*c^2*d*e*f^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*log((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b) + 6*((a^2*b - b^3)*d^3*cosh(f*x + e)^2 + (a^2*b - b^3)*d^3*sinh(f*x + e)^2 + 2*(a^3 - a*b^2)*d^3*cosh(f*x + e) + (a^2*b - b^3)*d^3 + 2*((a^2*b - b^3)*d^3*cosh(f*x + e) + (a^3 - a*b^2)*d^3)*sinh(f*x + e) + (a*b^2*d^3*f*x + a*b^2*c*d^2*f + (a*b^2*d^3*f*x + a*b^2*c*d^2*f)*cosh(f*x + e)^2 + (a*b^2*d^3*f*x + a*b^2*c*d^2*f)*sinh(f*x + e)^2 + 2*(a^2*b*d^3*f*x + a^2*b*c*d^2*f)*cosh(f*x + e) + 2*(a^2*b*d^3*f*x + a^2*b*c*d^2*f + (a*b^2*d^3*f*x + a*b^2*c*d^2*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*polylog(3, -(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) + 6*((a^2*b - b^3)*d^3*cosh(f*x + e)^2 + (a^2*b - b^3)*d^3*sinh(f*x + e)^2 + 2*(a^3 - a*b^2)*d^3*cosh(f*x + e) + (a^2*b - b^3)*d^3 + 2*((a^2*b - b^3)*d^3*cosh(f*x + e) + (a^3 - a*b^2)*d^3)*sinh(f*x + e) - (a*b^2*d^3*f*x + a*b^2*c*d^2*f + (a*b^2*d^3*f*x + a*b^2*c*d^2*f)*cosh(f*x + e)^2 + (a*b^2*d^3*f*x + a*b^2*c*d^2*f)*sinh(f*x + e)^2 + 2*(a^2*b*d^3*f*x + a^2*b*c*d^2*f)*cosh(f*x + e) + 2*(a^2*b*d^3*f*x + a^2*b*c*d^2*f + (a*b^2*d^3*f*x + a*b^2*c*d^2*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*polylog(3, -(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) + 2*((a^3 - a*b^2)*d^3*f^3*x^3 + 3*(a^3 - a*b^2)*c*d^2*f^3*x^2 + 3*(a^3 - a*b^2)*c^2*d*f^3*x + 2*(a^3 - a*b^2)*d^3*e^3 - 6*(a^3 - a*b^2)*c*d^2*e^2*f + 6*(a^3 - a*b^2)*c^2*d*e*f^2 - (a^3 - a*b^2)*c^3*f^3 + 2*((a^2*b - b^3)*d^3*f^3*x^3 + 3*(a^2*b - b^3)*c*d^2*f^3*x^2 + 3*(a^2*b - b^3)*c^2*d*f^3*x + (a^2*b - b^3)*d^3*e^3 - 3*(a^2*b - b^3)*c*d^2*e^2*f + 3*(a^2*b - b^3)*c^2*d*e*f^2)*cosh(f*x + e))*sinh(f*x + e))/((a^4*b - 2*a^2*b^3 + b^5)*f^4*cosh(f*x + e)^2 + (a^4*b - 2*a^2*b^3 + b^5)*f^4*sinh(f*x + e)^2 + 2*(a^5 - 2*a^3*b^2 + a*b^4)*f^4*cosh(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*f^4 + 2*((a^4*b - 2*a^2*b^3 + b^5)*f^4*cosh(f*x + e) + (a^5 - 2*a^3*b^2 + a*b^4)*f^4)*sinh(f*x + e))","C",0
174,1,4105,0,0.545406," ","integrate((d*x+c)^2/(a+b*cosh(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} - 4 \, {\left(a^{2} b - b^{3}\right)} c d e f + 2 \, {\left(a^{2} b - b^{3}\right)} c^{2} f^{2} - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f\right)} \cosh\left(f x + e\right)^{2} - 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f\right)} \sinh\left(f x + e\right)^{2} - 2 \, {\left(a b^{2} d^{2} \cosh\left(f x + e\right)^{2} + a b^{2} d^{2} \sinh\left(f x + e\right)^{2} + 2 \, a^{2} b d^{2} \cosh\left(f x + e\right) + a b^{2} d^{2} + 2 \, {\left(a b^{2} d^{2} \cosh\left(f x + e\right) + a^{2} b d^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) + 2 \, {\left(a b^{2} d^{2} \cosh\left(f x + e\right)^{2} + a b^{2} d^{2} \sinh\left(f x + e\right)^{2} + 2 \, a^{2} b d^{2} \cosh\left(f x + e\right) + a b^{2} d^{2} + 2 \, {\left(a b^{2} d^{2} \cosh\left(f x + e\right) + a^{2} b d^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm polylog}\left(3, -\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}}{b}\right) - 2 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c d f^{2} x - 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 4 \, {\left(a^{3} - a b^{2}\right)} c d e f - {\left(a^{3} - a b^{2}\right)} c^{2} f^{2}\right)} \cosh\left(f x + e\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{2} + {\left(a^{2} b - b^{3}\right)} d^{2} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} \cosh\left(f x + e\right) + {\left(a^{2} b - b^{3}\right)} d^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} \cosh\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d^{2}\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d^{2} f x + a b^{2} c d f + {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{2} f x + a^{2} b c d f\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{2} f x + a^{2} b c d f + {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} \cosh\left(f x + e\right)^{2} + {\left(a^{2} b - b^{3}\right)} d^{2} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} \cosh\left(f x + e\right) + {\left(a^{2} b - b^{3}\right)} d^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} \cosh\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d^{2}\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d^{2} f x + a b^{2} c d f + {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{2} f x + a^{2} b c d f\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{2} f x + a^{2} b c d f + {\left(a b^{2} d^{2} f x + a b^{2} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) - {\left(2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e - 2 \, {\left(a^{2} b - b^{3}\right)} c d f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e - {\left(a^{2} b - b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e - {\left(a^{2} b - b^{3}\right)} c d f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} e - {\left(a^{3} - a b^{2}\right)} c d f\right)} \cosh\left(f x + e\right) + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} e - {\left(a^{3} - a b^{2}\right)} c d f + {\left({\left(a^{2} b - b^{3}\right)} d^{2} e - {\left(a^{2} b - b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) - {\left(2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e - 2 \, {\left(a^{2} b - b^{3}\right)} c d f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e - {\left(a^{2} b - b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} e - {\left(a^{2} b - b^{3}\right)} c d f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} e - {\left(a^{3} - a b^{2}\right)} c d f\right)} \cosh\left(f x + e\right) + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} e - {\left(a^{3} - a b^{2}\right)} c d f + {\left({\left(a^{2} b - b^{3}\right)} d^{2} e - {\left(a^{2} b - b^{3}\right)} c d f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2}\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{2} e^{2} - 2 \, a^{2} b c d e f + a^{2} b c^{2} f^{2} + {\left(a b^{2} d^{2} e^{2} - 2 \, a b^{2} c d e f + a b^{2} c^{2} f^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) + {\left(2 \, {\left(a^{2} b - b^{3}\right)} d^{2} f x + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f x + {\left(a^{2} b - b^{3}\right)} d^{2} e\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f x + {\left(a^{2} b - b^{3}\right)} d^{2} e\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} f x + {\left(a^{3} - a b^{2}\right)} d^{2} e\right)} \cosh\left(f x + e\right) + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} f x + {\left(a^{3} - a b^{2}\right)} d^{2} e + {\left({\left(a^{2} b - b^{3}\right)} d^{2} f x + {\left(a^{2} b - b^{3}\right)} d^{2} e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right) + {\left(2 \, {\left(a^{2} b - b^{3}\right)} d^{2} f x + 2 \, {\left(a^{2} b - b^{3}\right)} d^{2} e + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f x + {\left(a^{2} b - b^{3}\right)} d^{2} e\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f x + {\left(a^{2} b - b^{3}\right)} d^{2} e\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} f x + {\left(a^{3} - a b^{2}\right)} d^{2} e\right)} \cosh\left(f x + e\right) + 4 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} f x + {\left(a^{3} - a b^{2}\right)} d^{2} e + {\left({\left(a^{2} b - b^{3}\right)} d^{2} f x + {\left(a^{2} b - b^{3}\right)} d^{2} e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d^{2} f^{2} x^{2} + 2 \, a^{2} b c d f^{2} x - a^{2} b d^{2} e^{2} + 2 \, a^{2} b c d e f + {\left(a b^{2} d^{2} f^{2} x^{2} + 2 \, a b^{2} c d f^{2} x - a b^{2} d^{2} e^{2} + 2 \, a b^{2} c d e f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right) - 2 \, {\left({\left(a^{3} - a b^{2}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} c d f^{2} x - 2 \, {\left(a^{3} - a b^{2}\right)} d^{2} e^{2} + 4 \, {\left(a^{3} - a b^{2}\right)} c d e f - {\left(a^{3} - a b^{2}\right)} c^{2} f^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d^{2} f^{2} x^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d f^{2} x - {\left(a^{2} b - b^{3}\right)} d^{2} e^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} c d e f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} \cosh\left(f x + e\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f^{3} \cosh\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} + 2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{3} \cosh\left(f x + e\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f^{3}\right)} \sinh\left(f x + e\right)}"," ",0,"(2*(a^2*b - b^3)*d^2*e^2 - 4*(a^2*b - b^3)*c*d*e*f + 2*(a^2*b - b^3)*c^2*f^2 - 2*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*c*d*f^2*x - (a^2*b - b^3)*d^2*e^2 + 2*(a^2*b - b^3)*c*d*e*f)*cosh(f*x + e)^2 - 2*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*c*d*f^2*x - (a^2*b - b^3)*d^2*e^2 + 2*(a^2*b - b^3)*c*d*e*f)*sinh(f*x + e)^2 - 2*(a*b^2*d^2*cosh(f*x + e)^2 + a*b^2*d^2*sinh(f*x + e)^2 + 2*a^2*b*d^2*cosh(f*x + e) + a*b^2*d^2 + 2*(a*b^2*d^2*cosh(f*x + e) + a^2*b*d^2)*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2)*polylog(3, -(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) + 2*(a*b^2*d^2*cosh(f*x + e)^2 + a*b^2*d^2*sinh(f*x + e)^2 + 2*a^2*b*d^2*cosh(f*x + e) + a*b^2*d^2 + 2*(a*b^2*d^2*cosh(f*x + e) + a^2*b*d^2)*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2)*polylog(3, -(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))/b) - 2*((a^3 - a*b^2)*d^2*f^2*x^2 + 2*(a^3 - a*b^2)*c*d*f^2*x - 2*(a^3 - a*b^2)*d^2*e^2 + 4*(a^3 - a*b^2)*c*d*e*f - (a^3 - a*b^2)*c^2*f^2)*cosh(f*x + e) + 2*((a^2*b - b^3)*d^2*cosh(f*x + e)^2 + (a^2*b - b^3)*d^2*sinh(f*x + e)^2 + 2*(a^3 - a*b^2)*d^2*cosh(f*x + e) + (a^2*b - b^3)*d^2 + 2*((a^2*b - b^3)*d^2*cosh(f*x + e) + (a^3 - a*b^2)*d^2)*sinh(f*x + e) + (a*b^2*d^2*f*x + a*b^2*c*d*f + (a*b^2*d^2*f*x + a*b^2*c*d*f)*cosh(f*x + e)^2 + (a*b^2*d^2*f*x + a*b^2*c*d*f)*sinh(f*x + e)^2 + 2*(a^2*b*d^2*f*x + a^2*b*c*d*f)*cosh(f*x + e) + 2*(a^2*b*d^2*f*x + a^2*b*c*d*f + (a*b^2*d^2*f*x + a*b^2*c*d*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) + 2*((a^2*b - b^3)*d^2*cosh(f*x + e)^2 + (a^2*b - b^3)*d^2*sinh(f*x + e)^2 + 2*(a^3 - a*b^2)*d^2*cosh(f*x + e) + (a^2*b - b^3)*d^2 + 2*((a^2*b - b^3)*d^2*cosh(f*x + e) + (a^3 - a*b^2)*d^2)*sinh(f*x + e) - (a*b^2*d^2*f*x + a*b^2*c*d*f + (a*b^2*d^2*f*x + a*b^2*c*d*f)*cosh(f*x + e)^2 + (a*b^2*d^2*f*x + a*b^2*c*d*f)*sinh(f*x + e)^2 + 2*(a^2*b*d^2*f*x + a^2*b*c*d*f)*cosh(f*x + e) + 2*(a^2*b*d^2*f*x + a^2*b*c*d*f + (a*b^2*d^2*f*x + a*b^2*c*d*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) - (2*(a^2*b - b^3)*d^2*e - 2*(a^2*b - b^3)*c*d*f + 2*((a^2*b - b^3)*d^2*e - (a^2*b - b^3)*c*d*f)*cosh(f*x + e)^2 + 2*((a^2*b - b^3)*d^2*e - (a^2*b - b^3)*c*d*f)*sinh(f*x + e)^2 + 4*((a^3 - a*b^2)*d^2*e - (a^3 - a*b^2)*c*d*f)*cosh(f*x + e) + 4*((a^3 - a*b^2)*d^2*e - (a^3 - a*b^2)*c*d*f + ((a^2*b - b^3)*d^2*e - (a^2*b - b^3)*c*d*f)*cosh(f*x + e))*sinh(f*x + e) + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(f*x + e)^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sinh(f*x + e)^2 + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(f*x + e) + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) - (2*(a^2*b - b^3)*d^2*e - 2*(a^2*b - b^3)*c*d*f + 2*((a^2*b - b^3)*d^2*e - (a^2*b - b^3)*c*d*f)*cosh(f*x + e)^2 + 2*((a^2*b - b^3)*d^2*e - (a^2*b - b^3)*c*d*f)*sinh(f*x + e)^2 + 4*((a^3 - a*b^2)*d^2*e - (a^3 - a*b^2)*c*d*f)*cosh(f*x + e) + 4*((a^3 - a*b^2)*d^2*e - (a^3 - a*b^2)*c*d*f + ((a^2*b - b^3)*d^2*e - (a^2*b - b^3)*c*d*f)*cosh(f*x + e))*sinh(f*x + e) - (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(f*x + e)^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*sinh(f*x + e)^2 + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2)*cosh(f*x + e) + 2*(a^2*b*d^2*e^2 - 2*a^2*b*c*d*e*f + a^2*b*c^2*f^2 + (a*b^2*d^2*e^2 - 2*a*b^2*c*d*e*f + a*b^2*c^2*f^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) + (2*(a^2*b - b^3)*d^2*f*x + 2*(a^2*b - b^3)*d^2*e + 2*((a^2*b - b^3)*d^2*f*x + (a^2*b - b^3)*d^2*e)*cosh(f*x + e)^2 + 2*((a^2*b - b^3)*d^2*f*x + (a^2*b - b^3)*d^2*e)*sinh(f*x + e)^2 + 4*((a^3 - a*b^2)*d^2*f*x + (a^3 - a*b^2)*d^2*e)*cosh(f*x + e) + 4*((a^3 - a*b^2)*d^2*f*x + (a^3 - a*b^2)*d^2*e + ((a^2*b - b^3)*d^2*f*x + (a^2*b - b^3)*d^2*e)*cosh(f*x + e))*sinh(f*x + e) + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*cosh(f*x + e)^2 + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*sinh(f*x + e)^2 + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f)*cosh(f*x + e) + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*log((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b) + (2*(a^2*b - b^3)*d^2*f*x + 2*(a^2*b - b^3)*d^2*e + 2*((a^2*b - b^3)*d^2*f*x + (a^2*b - b^3)*d^2*e)*cosh(f*x + e)^2 + 2*((a^2*b - b^3)*d^2*f*x + (a^2*b - b^3)*d^2*e)*sinh(f*x + e)^2 + 4*((a^3 - a*b^2)*d^2*f*x + (a^3 - a*b^2)*d^2*e)*cosh(f*x + e) + 4*((a^3 - a*b^2)*d^2*f*x + (a^3 - a*b^2)*d^2*e + ((a^2*b - b^3)*d^2*f*x + (a^2*b - b^3)*d^2*e)*cosh(f*x + e))*sinh(f*x + e) - (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*cosh(f*x + e)^2 + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*sinh(f*x + e)^2 + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f)*cosh(f*x + e) + 2*(a^2*b*d^2*f^2*x^2 + 2*a^2*b*c*d*f^2*x - a^2*b*d^2*e^2 + 2*a^2*b*c*d*e*f + (a*b^2*d^2*f^2*x^2 + 2*a*b^2*c*d*f^2*x - a*b^2*d^2*e^2 + 2*a*b^2*c*d*e*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*log((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b) - 2*((a^3 - a*b^2)*d^2*f^2*x^2 + 2*(a^3 - a*b^2)*c*d*f^2*x - 2*(a^3 - a*b^2)*d^2*e^2 + 4*(a^3 - a*b^2)*c*d*e*f - (a^3 - a*b^2)*c^2*f^2 + 2*((a^2*b - b^3)*d^2*f^2*x^2 + 2*(a^2*b - b^3)*c*d*f^2*x - (a^2*b - b^3)*d^2*e^2 + 2*(a^2*b - b^3)*c*d*e*f)*cosh(f*x + e))*sinh(f*x + e))/((a^4*b - 2*a^2*b^3 + b^5)*f^3*cosh(f*x + e)^2 + (a^4*b - 2*a^2*b^3 + b^5)*f^3*sinh(f*x + e)^2 + 2*(a^5 - 2*a^3*b^2 + a*b^4)*f^3*cosh(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*f^3 + 2*((a^4*b - 2*a^2*b^3 + b^5)*f^3*cosh(f*x + e) + (a^5 - 2*a^3*b^2 + a*b^4)*f^3)*sinh(f*x + e))","C",0
175,1,1765,0,0.861052," ","integrate((d*x+c)/(a+b*cosh(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} b - b^{3}\right)} d e - 2 \, {\left(a^{2} b - b^{3}\right)} c f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} d e\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} d e\right)} \sinh\left(f x + e\right)^{2} - {\left(a b^{2} d \cosh\left(f x + e\right)^{2} + a b^{2} d \sinh\left(f x + e\right)^{2} + 2 \, a^{2} b d \cosh\left(f x + e\right) + a b^{2} d + 2 \, {\left(a b^{2} d \cosh\left(f x + e\right) + a^{2} b d\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) + {\left(a b^{2} d \cosh\left(f x + e\right)^{2} + a b^{2} d \sinh\left(f x + e\right)^{2} + 2 \, a^{2} b d \cosh\left(f x + e\right) + a b^{2} d + 2 \, {\left(a b^{2} d \cosh\left(f x + e\right) + a^{2} b d\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} {\rm Li}_2\left(-\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b} + 1\right) - {\left(a b^{2} d f x + a b^{2} d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d f x + a b^{2} d e\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d f x + a^{2} b d e\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d f x + a^{2} b d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) + {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right) + {\left(a b^{2} d f x + a b^{2} d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d f x + a b^{2} d e\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d f x + a^{2} b d e\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d f x + a^{2} b d e + {\left(a b^{2} d f x + a b^{2} d e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} \log\left(\frac{a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right) - {\left(b \cosh\left(f x + e\right) + b \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + b}{b}\right) + 2 \, {\left({\left(a^{3} - a b^{2}\right)} d f x + 2 \, {\left(a^{3} - a b^{2}\right)} d e - {\left(a^{3} - a b^{2}\right)} c f\right)} \cosh\left(f x + e\right) - {\left({\left(a^{2} b - b^{3}\right)} d \cosh\left(f x + e\right)^{2} + {\left(a^{2} b - b^{3}\right)} d \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} d \cosh\left(f x + e\right) + {\left(a^{2} b - b^{3}\right)} d + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d \cosh\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d\right)} \sinh\left(f x + e\right) + {\left(a b^{2} d e - a b^{2} c f + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d e - a b^{2} c f\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d e - a^{2} b c f + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) + 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) - {\left({\left(a^{2} b - b^{3}\right)} d \cosh\left(f x + e\right)^{2} + {\left(a^{2} b - b^{3}\right)} d \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{3} - a b^{2}\right)} d \cosh\left(f x + e\right) + {\left(a^{2} b - b^{3}\right)} d + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d \cosh\left(f x + e\right) + {\left(a^{3} - a b^{2}\right)} d\right)} \sinh\left(f x + e\right) - {\left(a b^{2} d e - a b^{2} c f + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(f x + e\right)^{2} + {\left(a b^{2} d e - a b^{2} c f\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{2} b d e - a^{2} b c f\right)} \cosh\left(f x + e\right) + 2 \, {\left(a^{2} b d e - a^{2} b c f + {\left(a b^{2} d e - a b^{2} c f\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{a^{2} - b^{2}}{b^{2}}}\right)} \log\left(2 \, b \cosh\left(f x + e\right) + 2 \, b \sinh\left(f x + e\right) - 2 \, b \sqrt{\frac{a^{2} - b^{2}}{b^{2}}} + 2 \, a\right) + 2 \, {\left({\left(a^{3} - a b^{2}\right)} d f x + 2 \, {\left(a^{3} - a b^{2}\right)} d e - {\left(a^{3} - a b^{2}\right)} c f + 2 \, {\left({\left(a^{2} b - b^{3}\right)} d f x + {\left(a^{2} b - b^{3}\right)} d e\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(f x + e\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \sinh\left(f x + e\right)^{2} + 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2} \cosh\left(f x + e\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} + 2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} f^{2} \cosh\left(f x + e\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} f^{2}\right)} \sinh\left(f x + e\right)}"," ",0,"-(2*(a^2*b - b^3)*d*e - 2*(a^2*b - b^3)*c*f + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*d*e)*cosh(f*x + e)^2 + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*d*e)*sinh(f*x + e)^2 - (a*b^2*d*cosh(f*x + e)^2 + a*b^2*d*sinh(f*x + e)^2 + 2*a^2*b*d*cosh(f*x + e) + a*b^2*d + 2*(a*b^2*d*cosh(f*x + e) + a^2*b*d)*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) + (a*b^2*d*cosh(f*x + e)^2 + a*b^2*d*sinh(f*x + e)^2 + 2*a^2*b*d*cosh(f*x + e) + a*b^2*d + 2*(a*b^2*d*cosh(f*x + e) + a^2*b*d)*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2)*dilog(-(a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b + 1) - (a*b^2*d*f*x + a*b^2*d*e + (a*b^2*d*f*x + a*b^2*d*e)*cosh(f*x + e)^2 + (a*b^2*d*f*x + a*b^2*d*e)*sinh(f*x + e)^2 + 2*(a^2*b*d*f*x + a^2*b*d*e)*cosh(f*x + e) + 2*(a^2*b*d*f*x + a^2*b*d*e + (a*b^2*d*f*x + a*b^2*d*e)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2)*log((a*cosh(f*x + e) + a*sinh(f*x + e) + (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b) + (a*b^2*d*f*x + a*b^2*d*e + (a*b^2*d*f*x + a*b^2*d*e)*cosh(f*x + e)^2 + (a*b^2*d*f*x + a*b^2*d*e)*sinh(f*x + e)^2 + 2*(a^2*b*d*f*x + a^2*b*d*e)*cosh(f*x + e) + 2*(a^2*b*d*f*x + a^2*b*d*e + (a*b^2*d*f*x + a*b^2*d*e)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2)*log((a*cosh(f*x + e) + a*sinh(f*x + e) - (b*cosh(f*x + e) + b*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2) + b)/b) + 2*((a^3 - a*b^2)*d*f*x + 2*(a^3 - a*b^2)*d*e - (a^3 - a*b^2)*c*f)*cosh(f*x + e) - ((a^2*b - b^3)*d*cosh(f*x + e)^2 + (a^2*b - b^3)*d*sinh(f*x + e)^2 + 2*(a^3 - a*b^2)*d*cosh(f*x + e) + (a^2*b - b^3)*d + 2*((a^2*b - b^3)*d*cosh(f*x + e) + (a^3 - a*b^2)*d)*sinh(f*x + e) + (a*b^2*d*e - a*b^2*c*f + (a*b^2*d*e - a*b^2*c*f)*cosh(f*x + e)^2 + (a*b^2*d*e - a*b^2*c*f)*sinh(f*x + e)^2 + 2*(a^2*b*d*e - a^2*b*c*f)*cosh(f*x + e) + 2*(a^2*b*d*e - a^2*b*c*f + (a*b^2*d*e - a*b^2*c*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) + 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) - ((a^2*b - b^3)*d*cosh(f*x + e)^2 + (a^2*b - b^3)*d*sinh(f*x + e)^2 + 2*(a^3 - a*b^2)*d*cosh(f*x + e) + (a^2*b - b^3)*d + 2*((a^2*b - b^3)*d*cosh(f*x + e) + (a^3 - a*b^2)*d)*sinh(f*x + e) - (a*b^2*d*e - a*b^2*c*f + (a*b^2*d*e - a*b^2*c*f)*cosh(f*x + e)^2 + (a*b^2*d*e - a*b^2*c*f)*sinh(f*x + e)^2 + 2*(a^2*b*d*e - a^2*b*c*f)*cosh(f*x + e) + 2*(a^2*b*d*e - a^2*b*c*f + (a*b^2*d*e - a*b^2*c*f)*cosh(f*x + e))*sinh(f*x + e))*sqrt((a^2 - b^2)/b^2))*log(2*b*cosh(f*x + e) + 2*b*sinh(f*x + e) - 2*b*sqrt((a^2 - b^2)/b^2) + 2*a) + 2*((a^3 - a*b^2)*d*f*x + 2*(a^3 - a*b^2)*d*e - (a^3 - a*b^2)*c*f + 2*((a^2*b - b^3)*d*f*x + (a^2*b - b^3)*d*e)*cosh(f*x + e))*sinh(f*x + e))/((a^4*b - 2*a^2*b^3 + b^5)*f^2*cosh(f*x + e)^2 + (a^4*b - 2*a^2*b^3 + b^5)*f^2*sinh(f*x + e)^2 + 2*(a^5 - 2*a^3*b^2 + a*b^4)*f^2*cosh(f*x + e) + (a^4*b - 2*a^2*b^3 + b^5)*f^2 + 2*((a^4*b - 2*a^2*b^3 + b^5)*f^2*cosh(f*x + e) + (a^5 - 2*a^3*b^2 + a*b^4)*f^2)*sinh(f*x + e))","B",0
176,0,0,0,0.616439," ","integrate(1/(d*x+c)/(a+b*cosh(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d x + a^{2} c + {\left(b^{2} d x + b^{2} c\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a b d x + a b c\right)} \cosh\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d*x + a^2*c + (b^2*d*x + b^2*c)*cosh(f*x + e)^2 + 2*(a*b*d*x + a*b*c)*cosh(f*x + e)), x)","F",0
177,0,0,0,0.778754," ","integrate(1/(d*x+c)^2/(a+b*cosh(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} \cosh\left(f x + e\right)}, x\right)"," ",0,"integral(1/(a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*cosh(f*x + e)^2 + 2*(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*cosh(f*x + e)), x)","F",0
178,0,0,0,0.591488," ","integrate((d*x+c)^m*(a+b*cosh(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d x + c\right)}^{m} {\left(b \cosh\left(f x + e\right) + a\right)}^{n}, x\right)"," ",0,"integral((d*x + c)^m*(b*cosh(f*x + e) + a)^n, x)","F",0
179,1,813,0,0.623952," ","integrate((d*x+c)^m*(a+b*cosh(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(b^{3} d m + b^{3} d\right)} \cosh\left(\frac{d m \log\left(\frac{3 \, f}{d}\right) + 3 \, d e - 3 \, c f}{d}\right) \Gamma\left(m + 1, \frac{3 \, {\left(d f x + c f\right)}}{d}\right) + 9 \, {\left(a b^{2} d m + a b^{2} d\right)} \cosh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 9 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d m + {\left(4 \, a^{2} b + b^{3}\right)} d\right)} \cosh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) - 9 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d m + {\left(4 \, a^{2} b + b^{3}\right)} d\right)} \cosh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) - 9 \, {\left(a b^{2} d m + a b^{2} d\right)} \cosh\left(\frac{d m \log\left(-\frac{2 \, f}{d}\right) - 2 \, d e + 2 \, c f}{d}\right) \Gamma\left(m + 1, -\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(b^{3} d m + b^{3} d\right)} \cosh\left(\frac{d m \log\left(-\frac{3 \, f}{d}\right) - 3 \, d e + 3 \, c f}{d}\right) \Gamma\left(m + 1, -\frac{3 \, {\left(d f x + c f\right)}}{d}\right) - {\left(b^{3} d m + b^{3} d\right)} \Gamma\left(m + 1, \frac{3 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{3 \, f}{d}\right) + 3 \, d e - 3 \, c f}{d}\right) - 9 \, {\left(a b^{2} d m + a b^{2} d\right)} \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) - 9 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d m + {\left(4 \, a^{2} b + b^{3}\right)} d\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) + 9 \, {\left({\left(4 \, a^{2} b + b^{3}\right)} d m + {\left(4 \, a^{2} b + b^{3}\right)} d\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) + 9 \, {\left(a b^{2} d m + a b^{2} d\right)} \Gamma\left(m + 1, -\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{2 \, f}{d}\right) - 2 \, d e + 2 \, c f}{d}\right) + {\left(b^{3} d m + b^{3} d\right)} \Gamma\left(m + 1, -\frac{3 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{3 \, f}{d}\right) - 3 \, d e + 3 \, c f}{d}\right) - 12 \, {\left({\left(2 \, a^{3} + 3 \, a b^{2}\right)} d f x + {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c f\right)} \cosh\left(m \log\left(d x + c\right)\right) - 12 \, {\left({\left(2 \, a^{3} + 3 \, a b^{2}\right)} d f x + {\left(2 \, a^{3} + 3 \, a b^{2}\right)} c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{24 \, {\left(d f m + d f\right)}}"," ",0,"-1/24*((b^3*d*m + b^3*d)*cosh((d*m*log(3*f/d) + 3*d*e - 3*c*f)/d)*gamma(m + 1, 3*(d*f*x + c*f)/d) + 9*(a*b^2*d*m + a*b^2*d)*cosh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d)*gamma(m + 1, 2*(d*f*x + c*f)/d) + 9*((4*a^2*b + b^3)*d*m + (4*a^2*b + b^3)*d)*cosh((d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) - 9*((4*a^2*b + b^3)*d*m + (4*a^2*b + b^3)*d)*cosh((d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) - 9*(a*b^2*d*m + a*b^2*d)*cosh((d*m*log(-2*f/d) - 2*d*e + 2*c*f)/d)*gamma(m + 1, -2*(d*f*x + c*f)/d) - (b^3*d*m + b^3*d)*cosh((d*m*log(-3*f/d) - 3*d*e + 3*c*f)/d)*gamma(m + 1, -3*(d*f*x + c*f)/d) - (b^3*d*m + b^3*d)*gamma(m + 1, 3*(d*f*x + c*f)/d)*sinh((d*m*log(3*f/d) + 3*d*e - 3*c*f)/d) - 9*(a*b^2*d*m + a*b^2*d)*gamma(m + 1, 2*(d*f*x + c*f)/d)*sinh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d) - 9*((4*a^2*b + b^3)*d*m + (4*a^2*b + b^3)*d)*gamma(m + 1, (d*f*x + c*f)/d)*sinh((d*m*log(f/d) + d*e - c*f)/d) + 9*((4*a^2*b + b^3)*d*m + (4*a^2*b + b^3)*d)*gamma(m + 1, -(d*f*x + c*f)/d)*sinh((d*m*log(-f/d) - d*e + c*f)/d) + 9*(a*b^2*d*m + a*b^2*d)*gamma(m + 1, -2*(d*f*x + c*f)/d)*sinh((d*m*log(-2*f/d) - 2*d*e + 2*c*f)/d) + (b^3*d*m + b^3*d)*gamma(m + 1, -3*(d*f*x + c*f)/d)*sinh((d*m*log(-3*f/d) - 3*d*e + 3*c*f)/d) - 12*((2*a^3 + 3*a*b^2)*d*f*x + (2*a^3 + 3*a*b^2)*c*f)*cosh(m*log(d*x + c)) - 12*((2*a^3 + 3*a*b^2)*d*f*x + (2*a^3 + 3*a*b^2)*c*f)*sinh(m*log(d*x + c)))/(d*f*m + d*f)","A",0
180,1,509,0,0.801907," ","integrate((d*x+c)^m*(a+b*cosh(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(b^{2} d m + b^{2} d\right)} \cosh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) + 8 \, {\left(a b d m + a b d\right)} \cosh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) - 8 \, {\left(a b d m + a b d\right)} \cosh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) - {\left(b^{2} d m + b^{2} d\right)} \cosh\left(\frac{d m \log\left(-\frac{2 \, f}{d}\right) - 2 \, d e + 2 \, c f}{d}\right) \Gamma\left(m + 1, -\frac{2 \, {\left(d f x + c f\right)}}{d}\right) - {\left(b^{2} d m + b^{2} d\right)} \Gamma\left(m + 1, \frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(\frac{2 \, f}{d}\right) + 2 \, d e - 2 \, c f}{d}\right) - 8 \, {\left(a b d m + a b d\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) + 8 \, {\left(a b d m + a b d\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) + {\left(b^{2} d m + b^{2} d\right)} \Gamma\left(m + 1, -\frac{2 \, {\left(d f x + c f\right)}}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{2 \, f}{d}\right) - 2 \, d e + 2 \, c f}{d}\right) - 4 \, {\left({\left(2 \, a^{2} + b^{2}\right)} d f x + {\left(2 \, a^{2} + b^{2}\right)} c f\right)} \cosh\left(m \log\left(d x + c\right)\right) - 4 \, {\left({\left(2 \, a^{2} + b^{2}\right)} d f x + {\left(2 \, a^{2} + b^{2}\right)} c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{8 \, {\left(d f m + d f\right)}}"," ",0,"-1/8*((b^2*d*m + b^2*d)*cosh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d)*gamma(m + 1, 2*(d*f*x + c*f)/d) + 8*(a*b*d*m + a*b*d)*cosh((d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) - 8*(a*b*d*m + a*b*d)*cosh((d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) - (b^2*d*m + b^2*d)*cosh((d*m*log(-2*f/d) - 2*d*e + 2*c*f)/d)*gamma(m + 1, -2*(d*f*x + c*f)/d) - (b^2*d*m + b^2*d)*gamma(m + 1, 2*(d*f*x + c*f)/d)*sinh((d*m*log(2*f/d) + 2*d*e - 2*c*f)/d) - 8*(a*b*d*m + a*b*d)*gamma(m + 1, (d*f*x + c*f)/d)*sinh((d*m*log(f/d) + d*e - c*f)/d) + 8*(a*b*d*m + a*b*d)*gamma(m + 1, -(d*f*x + c*f)/d)*sinh((d*m*log(-f/d) - d*e + c*f)/d) + (b^2*d*m + b^2*d)*gamma(m + 1, -2*(d*f*x + c*f)/d)*sinh((d*m*log(-2*f/d) - 2*d*e + 2*c*f)/d) - 4*((2*a^2 + b^2)*d*f*x + (2*a^2 + b^2)*c*f)*cosh(m*log(d*x + c)) - 4*((2*a^2 + b^2)*d*f*x + (2*a^2 + b^2)*c*f)*sinh(m*log(d*x + c)))/(d*f*m + d*f)","A",0
181,1,249,0,0.557879," ","integrate((d*x+c)^m*(a+b*cosh(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(b d m + b d\right)} \cosh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) - {\left(b d m + b d\right)} \cosh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) - {\left(b d m + b d\right)} \Gamma\left(m + 1, \frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(\frac{f}{d}\right) + d e - c f}{d}\right) + {\left(b d m + b d\right)} \Gamma\left(m + 1, -\frac{d f x + c f}{d}\right) \sinh\left(\frac{d m \log\left(-\frac{f}{d}\right) - d e + c f}{d}\right) - 2 \, {\left(a d f x + a c f\right)} \cosh\left(m \log\left(d x + c\right)\right) - 2 \, {\left(a d f x + a c f\right)} \sinh\left(m \log\left(d x + c\right)\right)}{2 \, {\left(d f m + d f\right)}}"," ",0,"-1/2*((b*d*m + b*d)*cosh((d*m*log(f/d) + d*e - c*f)/d)*gamma(m + 1, (d*f*x + c*f)/d) - (b*d*m + b*d)*cosh((d*m*log(-f/d) - d*e + c*f)/d)*gamma(m + 1, -(d*f*x + c*f)/d) - (b*d*m + b*d)*gamma(m + 1, (d*f*x + c*f)/d)*sinh((d*m*log(f/d) + d*e - c*f)/d) + (b*d*m + b*d)*gamma(m + 1, -(d*f*x + c*f)/d)*sinh((d*m*log(-f/d) - d*e + c*f)/d) - 2*(a*d*f*x + a*c*f)*cosh(m*log(d*x + c)) - 2*(a*d*f*x + a*c*f)*sinh(m*log(d*x + c)))/(d*f*m + d*f)","A",0
182,0,0,0,0.663173," ","integrate((d*x+c)^m/(a+b*cosh(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{b \cosh\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*x + c)^m/(b*cosh(f*x + e) + a), x)","F",0
183,0,0,0,0.474164," ","integrate((d*x+c)^m/(a+b*cosh(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b \cosh\left(f x + e\right) + a^{2}}, x\right)"," ",0,"integral((d*x + c)^m/(b^2*cosh(f*x + e)^2 + 2*a*b*cosh(f*x + e) + a^2), x)","F",0
