1,1,156,117,1.7330873,"\int (c+d x)^3 \tanh (e+f x) \, dx","Integrate[(c + d*x)^3*Tanh[e + f*x],x]","\frac{1}{4} x \tanh (e) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)-\frac{3 d \left(2 f^2 (c+d x)^2 \text{Li}_2\left(-e^{-2 (e+f x)}\right)+d \left(2 f (c+d x) \text{Li}_3\left(-e^{-2 (e+f x)}\right)+d \text{Li}_4\left(-e^{-2 (e+f x)}\right)\right)\right)}{4 f^4}+\frac{(c+d x)^3 \log \left(e^{-2 (e+f x)}+1\right)}{f}+\frac{(c+d x)^4}{2 d \left(e^{2 e}+1\right)}","-\frac{3 d^2 (c+d x) \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 d (c+d x)^2 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^2}+\frac{(c+d x)^3 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{(c+d x)^4}{4 d}+\frac{3 d^3 \text{Li}_4\left(-e^{2 (e+f x)}\right)}{4 f^4}",1,"(c + d*x)^4/(2*d*(1 + E^(2*e))) + ((c + d*x)^3*Log[1 + E^(-2*(e + f*x))])/f - (3*d*(2*f^2*(c + d*x)^2*PolyLog[2, -E^(-2*(e + f*x))] + d*(2*f*(c + d*x)*PolyLog[3, -E^(-2*(e + f*x))] + d*PolyLog[4, -E^(-2*(e + f*x))])))/(4*f^4) + (x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Tanh[e])/4","A",1
2,1,143,84,1.4641967,"\int (c+d x)^2 \tanh (e+f x) \, dx","Integrate[(c + d*x)^2*Tanh[e + f*x],x]","\frac{1}{3} x \tanh (e) \left(3 c^2+3 c d x+d^2 x^2\right)+\frac{e^{2 e} \left(-\frac{3 d \left(e^{-2 e}+1\right) \left(2 f (c+d x) \text{Li}_2\left(-e^{-2 (e+f x)}\right)+d \text{Li}_3\left(-e^{-2 (e+f x)}\right)\right)}{f^3}+\frac{6 \left(e^{-2 e}+1\right) (c+d x)^2 \log \left(e^{-2 (e+f x)}+1\right)}{f}+\frac{4 e^{-2 e} (c+d x)^3}{d}\right)}{6 \left(e^{2 e}+1\right)}","\frac{d (c+d x) \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^2}+\frac{(c+d x)^2 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{(c+d x)^3}{3 d}-\frac{d^2 \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^3}",1,"(E^(2*e)*((4*(c + d*x)^3)/(d*E^(2*e)) + (6*(1 + E^(-2*e))*(c + d*x)^2*Log[1 + E^(-2*(e + f*x))])/f - (3*d*(1 + E^(-2*e))*(2*f*(c + d*x)*PolyLog[2, -E^(-2*(e + f*x))] + d*PolyLog[3, -E^(-2*(e + f*x))]))/f^3))/(6*(1 + E^(2*e))) + (x*(3*c^2 + 3*c*d*x + d^2*x^2)*Tanh[e])/3","A",1
3,1,210,57,4.4175026,"\int (c+d x) \tanh (e+f x) \, dx","Integrate[(c + d*x)*Tanh[e + f*x],x]","\frac{c \log (\cosh (e+f x))}{f}+\frac{d \text{csch}(e) \text{sech}(e) \left(f^2 x^2 e^{-\tanh ^{-1}(\coth (e))}-\frac{i \coth (e) \left(i \text{Li}_2\left(e^{2 i \left(i f x+i \tanh ^{-1}(\coth (e))\right)}\right)-f x \left(-\pi +2 i \tanh ^{-1}(\coth (e))\right)-2 \left(i \tanh ^{-1}(\coth (e))+i f x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\coth (e))+i f x\right)}\right)+2 i \tanh ^{-1}(\coth (e)) \log \left(i \sinh \left(\tanh ^{-1}(\coth (e))+f x\right)\right)-\pi  \log \left(e^{2 f x}+1\right)+\pi  \log (\cosh (f x))\right)}{\sqrt{1-\coth ^2(e)}}\right)}{2 f^2 \sqrt{\text{csch}^2(e) \left(\sinh ^2(e)-\cosh ^2(e)\right)}}+\frac{1}{2} d x^2 \tanh (e)","\frac{(c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{(c+d x)^2}{2 d}+\frac{d \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^2}",1,"(c*Log[Cosh[e + f*x]])/f + (d*Csch[e]*((f^2*x^2)/E^ArcTanh[Coth[e]] - (I*Coth[e]*(-(f*x*(-Pi + (2*I)*ArcTanh[Coth[e]])) - Pi*Log[1 + E^(2*f*x)] - 2*(I*f*x + I*ArcTanh[Coth[e]])*Log[1 - E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))] + Pi*Log[Cosh[f*x]] + (2*I)*ArcTanh[Coth[e]]*Log[I*Sinh[f*x + ArcTanh[Coth[e]]]] + I*PolyLog[2, E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))]))/Sqrt[1 - Coth[e]^2])*Sech[e])/(2*f^2*Sqrt[Csch[e]^2*(-Cosh[e]^2 + Sinh[e]^2)]) + (d*x^2*Tanh[e])/2","C",0
4,0,0,17,9.5989869,"\int \frac{\tanh (e+f x)}{c+d x} \, dx","Integrate[Tanh[e + f*x]/(c + d*x),x]","\int \frac{\tanh (e+f x)}{c+d x} \, dx","\text{Int}\left(\frac{\tanh (e+f x)}{c+d x},x\right)",0,"Integrate[Tanh[e + f*x]/(c + d*x), x]","A",-1
5,0,0,17,16.8053107,"\int \frac{\tanh (e+f x)}{(c+d x)^2} \, dx","Integrate[Tanh[e + f*x]/(c + d*x)^2,x]","\int \frac{\tanh (e+f x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\tanh (e+f x)}{(c+d x)^2},x\right)",0,"Integrate[Tanh[e + f*x]/(c + d*x)^2, x]","A",-1
6,1,179,119,2.1000656,"\int (c+d x)^3 \tanh ^2(e+f x) \, dx","Integrate[(c + d*x)^3*Tanh[e + f*x]^2,x]","\frac{1}{4} \left(x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)+\frac{2 d e^{2 e} \left(-\frac{3 d \left(e^{-2 e}+1\right) \left(2 f (c+d x) \text{Li}_2\left(-e^{-2 (e+f x)}\right)+d \text{Li}_3\left(-e^{-2 (e+f x)}\right)\right)}{f^3}+\frac{6 \left(e^{-2 e}+1\right) (c+d x)^2 \log \left(e^{-2 (e+f x)}+1\right)}{f}+\frac{4 e^{-2 e} (c+d x)^3}{d}\right)}{\left(e^{2 e}+1\right) f}-\frac{4 \text{sech}(e) (c+d x)^3 \sinh (f x) \text{sech}(e+f x)}{f}\right)","\frac{3 d^2 (c+d x) \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^3}+\frac{3 d (c+d x)^2 \log \left(e^{2 (e+f x)}+1\right)}{f^2}-\frac{(c+d x)^3 \tanh (e+f x)}{f}-\frac{(c+d x)^3}{f}+\frac{(c+d x)^4}{4 d}-\frac{3 d^3 \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^4}",1,"(x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) + (2*d*E^(2*e)*((4*(c + d*x)^3)/(d*E^(2*e)) + (6*(1 + E^(-2*e))*(c + d*x)^2*Log[1 + E^(-2*(e + f*x))])/f - (3*d*(1 + E^(-2*e))*(2*f*(c + d*x)*PolyLog[2, -E^(-2*(e + f*x))] + d*PolyLog[3, -E^(-2*(e + f*x))]))/f^3))/((1 + E^(2*e))*f) - (4*(c + d*x)^3*Sech[e]*Sech[e + f*x]*Sinh[f*x])/f)/4","A",1
7,1,301,88,6.3448046,"\int (c+d x)^2 \tanh ^2(e+f x) \, dx","Integrate[(c + d*x)^2*Tanh[e + f*x]^2,x]","\frac{\text{sech}(e) \text{sech}(e+f x) \left(c^2 (-\sinh (f x))-2 c d x \sinh (f x)-d^2 x^2 \sinh (f x)\right)}{f}+\frac{1}{3} x \left(3 c^2+3 c d x+d^2 x^2\right)+\frac{2 c d \text{sech}(e) (\cosh (e) \log (\sinh (e) \sinh (f x)+\cosh (e) \cosh (f x))-f x \sinh (e))}{f^2 \left(\cosh ^2(e)-\sinh ^2(e)\right)}+\frac{d^2 \text{csch}(e) \text{sech}(e) \left(f^2 x^2 e^{-\tanh ^{-1}(\coth (e))}-\frac{i \coth (e) \left(i \text{Li}_2\left(e^{2 i \left(i f x+i \tanh ^{-1}(\coth (e))\right)}\right)-f x \left(-\pi +2 i \tanh ^{-1}(\coth (e))\right)-2 \left(i \tanh ^{-1}(\coth (e))+i f x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\coth (e))+i f x\right)}\right)+2 i \tanh ^{-1}(\coth (e)) \log \left(i \sinh \left(\tanh ^{-1}(\coth (e))+f x\right)\right)-\pi  \log \left(e^{2 f x}+1\right)+\pi  \log (\cosh (f x))\right)}{\sqrt{1-\coth ^2(e)}}\right)}{f^3 \sqrt{\text{csch}^2(e) \left(\sinh ^2(e)-\cosh ^2(e)\right)}}","\frac{2 d (c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f^2}-\frac{(c+d x)^2 \tanh (e+f x)}{f}-\frac{(c+d x)^2}{f}+\frac{(c+d x)^3}{3 d}+\frac{d^2 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^3}",1,"(x*(3*c^2 + 3*c*d*x + d^2*x^2))/3 + (2*c*d*Sech[e]*(Cosh[e]*Log[Cosh[e]*Cosh[f*x] + Sinh[e]*Sinh[f*x]] - f*x*Sinh[e]))/(f^2*(Cosh[e]^2 - Sinh[e]^2)) + (d^2*Csch[e]*((f^2*x^2)/E^ArcTanh[Coth[e]] - (I*Coth[e]*(-(f*x*(-Pi + (2*I)*ArcTanh[Coth[e]])) - Pi*Log[1 + E^(2*f*x)] - 2*(I*f*x + I*ArcTanh[Coth[e]])*Log[1 - E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))] + Pi*Log[Cosh[f*x]] + (2*I)*ArcTanh[Coth[e]]*Log[I*Sinh[f*x + ArcTanh[Coth[e]]]] + I*PolyLog[2, E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))]))/Sqrt[1 - Coth[e]^2])*Sech[e])/(f^3*Sqrt[Csch[e]^2*(-Cosh[e]^2 + Sinh[e]^2)]) + (Sech[e]*Sech[e + f*x]*(-(c^2*Sinh[f*x]) - 2*c*d*x*Sinh[f*x] - d^2*x^2*Sinh[f*x]))/f","C",0
8,1,77,40,0.246978,"\int (c+d x) \tanh ^2(e+f x) \, dx","Integrate[(c + d*x)*Tanh[e + f*x]^2,x]","\frac{c \tanh ^{-1}(\tanh (e+f x))}{f}-\frac{c \tanh (e+f x)}{f}+\frac{d \log (\cosh (e+f x))}{f^2}-\frac{d x \text{sech}(e) \sinh (f x) \text{sech}(e+f x)}{f}+\frac{d x \text{sech}(e) (f x \cosh (e)-2 \sinh (e))}{2 f}","-\frac{(c+d x) \tanh (e+f x)}{f}+c x+\frac{d \log (\cosh (e+f x))}{f^2}+\frac{d x^2}{2}",1,"(c*ArcTanh[Tanh[e + f*x]])/f + (d*Log[Cosh[e + f*x]])/f^2 + (d*x*Sech[e]*(f*x*Cosh[e] - 2*Sinh[e]))/(2*f) - (d*x*Sech[e]*Sech[e + f*x]*Sinh[f*x])/f - (c*Tanh[e + f*x])/f","A",1
9,0,0,19,19.3350904,"\int \frac{\tanh ^2(e+f x)}{c+d x} \, dx","Integrate[Tanh[e + f*x]^2/(c + d*x),x]","\int \frac{\tanh ^2(e+f x)}{c+d x} \, dx","\text{Int}\left(\frac{\tanh ^2(e+f x)}{c+d x},x\right)",0,"Integrate[Tanh[e + f*x]^2/(c + d*x), x]","A",-1
10,0,0,19,19.6141532,"\int \frac{\tanh ^2(e+f x)}{(c+d x)^2} \, dx","Integrate[Tanh[e + f*x]^2/(c + d*x)^2,x]","\int \frac{\tanh ^2(e+f x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\tanh ^2(e+f x)}{(c+d x)^2},x\right)",0,"Integrate[Tanh[e + f*x]^2/(c + d*x)^2, x]","A",-1
11,1,801,237,12.7501949,"\int (c+d x)^3 \tanh ^3(e+f x) \, dx","Integrate[(c + d*x)^3*Tanh[e + f*x]^3,x]","\frac{\text{sech}(e) (\cosh (e) \log (\cosh (e) \cosh (f x)+\sinh (e) \sinh (f x))-f x \sinh (e)) c^3}{f \left(\cosh ^2(e)-\sinh ^2(e)\right)}+\frac{3 d \text{csch}(e) \left(e^{-\tanh ^{-1}(\coth (e))} f^2 x^2-\frac{i \coth (e) \left(-f x \left(2 i \tanh ^{-1}(\coth (e))-\pi \right)-\pi  \log \left(1+e^{2 f x}\right)-2 \left(i f x+i \tanh ^{-1}(\coth (e))\right) \log \left(1-e^{2 i \left(i f x+i \tanh ^{-1}(\coth (e))\right)}\right)+\pi  \log (\cosh (f x))+2 i \tanh ^{-1}(\coth (e)) \log \left(i \sinh \left(f x+\tanh ^{-1}(\coth (e))\right)\right)+i \text{Li}_2\left(e^{2 i \left(i f x+i \tanh ^{-1}(\coth (e))\right)}\right)\right)}{\sqrt{1-\coth ^2(e)}}\right) \text{sech}(e) c^2}{2 f^2 \sqrt{\text{csch}^2(e) \left(\sinh ^2(e)-\cosh ^2(e)\right)}}+\frac{d^2 e^{-e} \left(2 f^2 \left(2 f x+3 \left(1+e^{2 e}\right) \log \left(1+e^{-2 (e+f x)}\right)\right) x^2-6 \left(1+e^{2 e}\right) f \text{Li}_2\left(-e^{-2 (e+f x)}\right) x-3 \left(1+e^{2 e}\right) \text{Li}_3\left(-e^{-2 (e+f x)}\right)\right) \text{sech}(e) c}{4 f^3}+\frac{3 d^2 \text{sech}(e) (\cosh (e) \log (\cosh (e) \cosh (f x)+\sinh (e) \sinh (f x))-f x \sinh (e)) c}{f^3 \left(\cosh ^2(e)-\sinh ^2(e)\right)}+\frac{(c+d x)^3 \text{sech}^2(e+f x)}{2 f}+\frac{1}{8} d^3 e^e \left(2 e^{-2 e} x^4+\frac{4 \left(1+e^{-2 e}\right) \log \left(1+e^{-2 (e+f x)}\right) x^3}{f}-\frac{3 e^{-2 e} \left(1+e^{2 e}\right) \left(2 f^2 \text{Li}_2\left(-e^{-2 (e+f x)}\right) x^2+2 f \text{Li}_3\left(-e^{-2 (e+f x)}\right) x+\text{Li}_4\left(-e^{-2 (e+f x)}\right)\right)}{f^4}\right) \text{sech}(e)-\frac{3 \text{sech}(e) \text{sech}(e+f x) \left(x^2 \sinh (f x) d^3+2 c x \sinh (f x) d^2+c^2 \sinh (f x) d\right)}{2 f^2}+\frac{1}{4} x \left(4 c^3+6 d x c^2+4 d^2 x^2 c+d^3 x^3\right) \tanh (e)+\frac{3 d^3 \text{csch}(e) \left(e^{-\tanh ^{-1}(\coth (e))} f^2 x^2-\frac{i \coth (e) \left(-f x \left(2 i \tanh ^{-1}(\coth (e))-\pi \right)-\pi  \log \left(1+e^{2 f x}\right)-2 \left(i f x+i \tanh ^{-1}(\coth (e))\right) \log \left(1-e^{2 i \left(i f x+i \tanh ^{-1}(\coth (e))\right)}\right)+\pi  \log (\cosh (f x))+2 i \tanh ^{-1}(\coth (e)) \log \left(i \sinh \left(f x+\tanh ^{-1}(\coth (e))\right)\right)+i \text{Li}_2\left(e^{2 i \left(i f x+i \tanh ^{-1}(\coth (e))\right)}\right)\right)}{\sqrt{1-\coth ^2(e)}}\right) \text{sech}(e)}{2 f^4 \sqrt{\text{csch}^2(e) \left(\sinh ^2(e)-\cosh ^2(e)\right)}}","-\frac{3 d^2 (c+d x) \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 d^2 (c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f^3}+\frac{3 d (c+d x)^2 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^2}-\frac{3 d (c+d x)^2 \tanh (e+f x)}{2 f^2}+\frac{(c+d x)^3 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{(c+d x)^3 \tanh ^2(e+f x)}{2 f}-\frac{3 d (c+d x)^2}{2 f^2}+\frac{(c+d x)^3}{2 f}-\frac{(c+d x)^4}{4 d}+\frac{3 d^3 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^4}+\frac{3 d^3 \text{Li}_4\left(-e^{2 (e+f x)}\right)}{4 f^4}",1,"(c*d^2*(2*f^2*x^2*(2*f*x + 3*(1 + E^(2*e))*Log[1 + E^(-2*(e + f*x))]) - 6*(1 + E^(2*e))*f*x*PolyLog[2, -E^(-2*(e + f*x))] - 3*(1 + E^(2*e))*PolyLog[3, -E^(-2*(e + f*x))])*Sech[e])/(4*E^e*f^3) + (d^3*E^e*((2*x^4)/E^(2*e) + (4*(1 + E^(-2*e))*x^3*Log[1 + E^(-2*(e + f*x))])/f - (3*(1 + E^(2*e))*(2*f^2*x^2*PolyLog[2, -E^(-2*(e + f*x))] + 2*f*x*PolyLog[3, -E^(-2*(e + f*x))] + PolyLog[4, -E^(-2*(e + f*x))]))/(E^(2*e)*f^4))*Sech[e])/8 + ((c + d*x)^3*Sech[e + f*x]^2)/(2*f) + (3*c*d^2*Sech[e]*(Cosh[e]*Log[Cosh[e]*Cosh[f*x] + Sinh[e]*Sinh[f*x]] - f*x*Sinh[e]))/(f^3*(Cosh[e]^2 - Sinh[e]^2)) + (c^3*Sech[e]*(Cosh[e]*Log[Cosh[e]*Cosh[f*x] + Sinh[e]*Sinh[f*x]] - f*x*Sinh[e]))/(f*(Cosh[e]^2 - Sinh[e]^2)) + (3*d^3*Csch[e]*((f^2*x^2)/E^ArcTanh[Coth[e]] - (I*Coth[e]*(-(f*x*(-Pi + (2*I)*ArcTanh[Coth[e]])) - Pi*Log[1 + E^(2*f*x)] - 2*(I*f*x + I*ArcTanh[Coth[e]])*Log[1 - E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))] + Pi*Log[Cosh[f*x]] + (2*I)*ArcTanh[Coth[e]]*Log[I*Sinh[f*x + ArcTanh[Coth[e]]]] + I*PolyLog[2, E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))]))/Sqrt[1 - Coth[e]^2])*Sech[e])/(2*f^4*Sqrt[Csch[e]^2*(-Cosh[e]^2 + Sinh[e]^2)]) + (3*c^2*d*Csch[e]*((f^2*x^2)/E^ArcTanh[Coth[e]] - (I*Coth[e]*(-(f*x*(-Pi + (2*I)*ArcTanh[Coth[e]])) - Pi*Log[1 + E^(2*f*x)] - 2*(I*f*x + I*ArcTanh[Coth[e]])*Log[1 - E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))] + Pi*Log[Cosh[f*x]] + (2*I)*ArcTanh[Coth[e]]*Log[I*Sinh[f*x + ArcTanh[Coth[e]]]] + I*PolyLog[2, E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))]))/Sqrt[1 - Coth[e]^2])*Sech[e])/(2*f^2*Sqrt[Csch[e]^2*(-Cosh[e]^2 + Sinh[e]^2)]) - (3*Sech[e]*Sech[e + f*x]*(c^2*d*Sinh[f*x] + 2*c*d^2*x*Sinh[f*x] + d^3*x^2*Sinh[f*x]))/(2*f^2) + (x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Tanh[e])/4","C",0
12,1,458,157,7.9399958,"\int (c+d x)^2 \tanh ^3(e+f x) \, dx","Integrate[(c + d*x)^2*Tanh[e + f*x]^3,x]","\frac{1}{3} x \tanh (e) \left(3 c^2+3 c d x+d^2 x^2\right)+\frac{c^2 \text{sech}(e) (\cosh (e) \log (\sinh (e) \sinh (f x)+\cosh (e) \cosh (f x))-f x \sinh (e))}{f \left(\cosh ^2(e)-\sinh ^2(e)\right)}+\frac{\text{sech}(e) \text{sech}(e+f x) \left(d^2 (-x) \sinh (f x)-c d \sinh (f x)\right)}{f^2}+\frac{c d \text{csch}(e) \text{sech}(e) \left(f^2 x^2 e^{-\tanh ^{-1}(\coth (e))}-\frac{i \coth (e) \left(i \text{Li}_2\left(e^{2 i \left(i f x+i \tanh ^{-1}(\coth (e))\right)}\right)-f x \left(-\pi +2 i \tanh ^{-1}(\coth (e))\right)-2 \left(i \tanh ^{-1}(\coth (e))+i f x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\coth (e))+i f x\right)}\right)+2 i \tanh ^{-1}(\coth (e)) \log \left(i \sinh \left(\tanh ^{-1}(\coth (e))+f x\right)\right)-\pi  \log \left(e^{2 f x}+1\right)+\pi  \log (\cosh (f x))\right)}{\sqrt{1-\coth ^2(e)}}\right)}{f^2 \sqrt{\text{csch}^2(e) \left(\sinh ^2(e)-\cosh ^2(e)\right)}}+\frac{(c+d x)^2 \text{sech}^2(e+f x)}{2 f}+\frac{d^2 \text{sech}(e) (\cosh (e) \log (\sinh (e) \sinh (f x)+\cosh (e) \cosh (f x))-f x \sinh (e))}{f^3 \left(\cosh ^2(e)-\sinh ^2(e)\right)}+\frac{d^2 e^{-e} \text{sech}(e) \left(2 f^2 x^2 \left(3 \left(e^{2 e}+1\right) \log \left(e^{-2 (e+f x)}+1\right)+2 f x\right)-6 \left(e^{2 e}+1\right) f x \text{Li}_2\left(-e^{-2 (e+f x)}\right)-3 \left(e^{2 e}+1\right) \text{Li}_3\left(-e^{-2 (e+f x)}\right)\right)}{12 f^3}","\frac{d (c+d x) \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^2}-\frac{d (c+d x) \tanh (e+f x)}{f^2}+\frac{(c+d x)^2 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{(c+d x)^2 \tanh ^2(e+f x)}{2 f}+\frac{c d x}{f}-\frac{(c+d x)^3}{3 d}-\frac{d^2 \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^3}+\frac{d^2 \log (\cosh (e+f x))}{f^3}+\frac{d^2 x^2}{2 f}",1,"(d^2*(2*f^2*x^2*(2*f*x + 3*(1 + E^(2*e))*Log[1 + E^(-2*(e + f*x))]) - 6*(1 + E^(2*e))*f*x*PolyLog[2, -E^(-2*(e + f*x))] - 3*(1 + E^(2*e))*PolyLog[3, -E^(-2*(e + f*x))])*Sech[e])/(12*E^e*f^3) + ((c + d*x)^2*Sech[e + f*x]^2)/(2*f) + (d^2*Sech[e]*(Cosh[e]*Log[Cosh[e]*Cosh[f*x] + Sinh[e]*Sinh[f*x]] - f*x*Sinh[e]))/(f^3*(Cosh[e]^2 - Sinh[e]^2)) + (c^2*Sech[e]*(Cosh[e]*Log[Cosh[e]*Cosh[f*x] + Sinh[e]*Sinh[f*x]] - f*x*Sinh[e]))/(f*(Cosh[e]^2 - Sinh[e]^2)) + (c*d*Csch[e]*((f^2*x^2)/E^ArcTanh[Coth[e]] - (I*Coth[e]*(-(f*x*(-Pi + (2*I)*ArcTanh[Coth[e]])) - Pi*Log[1 + E^(2*f*x)] - 2*(I*f*x + I*ArcTanh[Coth[e]])*Log[1 - E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))] + Pi*Log[Cosh[f*x]] + (2*I)*ArcTanh[Coth[e]]*Log[I*Sinh[f*x + ArcTanh[Coth[e]]]] + I*PolyLog[2, E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))]))/Sqrt[1 - Coth[e]^2])*Sech[e])/(f^2*Sqrt[Csch[e]^2*(-Cosh[e]^2 + Sinh[e]^2)]) + (Sech[e]*Sech[e + f*x]*(-(c*d*Sinh[f*x]) - d^2*x*Sinh[f*x]))/f^2 + (x*(3*c^2 + 3*c*d*x + d^2*x^2)*Tanh[e])/3","C",0
13,1,263,100,6.1444158,"\int (c+d x) \tanh ^3(e+f x) \, dx","Integrate[(c + d*x)*Tanh[e + f*x]^3,x]","-\frac{c \tanh ^2(e+f x)}{2 f}+\frac{c \log (\cosh (e+f x))}{f}+\frac{d \text{csch}(e) \text{sech}(e) \left(f^2 x^2 e^{-\tanh ^{-1}(\coth (e))}-\frac{i \coth (e) \left(i \text{Li}_2\left(e^{2 i \left(i f x+i \tanh ^{-1}(\coth (e))\right)}\right)-f x \left(-\pi +2 i \tanh ^{-1}(\coth (e))\right)-2 \left(i \tanh ^{-1}(\coth (e))+i f x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\coth (e))+i f x\right)}\right)+2 i \tanh ^{-1}(\coth (e)) \log \left(i \sinh \left(\tanh ^{-1}(\coth (e))+f x\right)\right)-\pi  \log \left(e^{2 f x}+1\right)+\pi  \log (\cosh (f x))\right)}{\sqrt{1-\coth ^2(e)}}\right)}{2 f^2 \sqrt{\text{csch}^2(e) \left(\sinh ^2(e)-\cosh ^2(e)\right)}}-\frac{d \text{sech}(e) \sinh (f x) \text{sech}(e+f x)}{2 f^2}+\frac{d x \text{sech}^2(e+f x)}{2 f}+\frac{1}{2} d x^2 \tanh (e)","\frac{(c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{(c+d x) \tanh ^2(e+f x)}{2 f}-\frac{(c+d x)^2}{2 d}+\frac{d \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^2}-\frac{d \tanh (e+f x)}{2 f^2}+\frac{d x}{2 f}",1,"(c*Log[Cosh[e + f*x]])/f + (d*x*Sech[e + f*x]^2)/(2*f) + (d*Csch[e]*((f^2*x^2)/E^ArcTanh[Coth[e]] - (I*Coth[e]*(-(f*x*(-Pi + (2*I)*ArcTanh[Coth[e]])) - Pi*Log[1 + E^(2*f*x)] - 2*(I*f*x + I*ArcTanh[Coth[e]])*Log[1 - E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))] + Pi*Log[Cosh[f*x]] + (2*I)*ArcTanh[Coth[e]]*Log[I*Sinh[f*x + ArcTanh[Coth[e]]]] + I*PolyLog[2, E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))]))/Sqrt[1 - Coth[e]^2])*Sech[e])/(2*f^2*Sqrt[Csch[e]^2*(-Cosh[e]^2 + Sinh[e]^2)]) - (d*Sech[e]*Sech[e + f*x]*Sinh[f*x])/(2*f^2) + (d*x^2*Tanh[e])/2 - (c*Tanh[e + f*x]^2)/(2*f)","C",0
14,0,0,19,31.0723602,"\int \frac{\tanh ^3(e+f x)}{c+d x} \, dx","Integrate[Tanh[e + f*x]^3/(c + d*x),x]","\int \frac{\tanh ^3(e+f x)}{c+d x} \, dx","\text{Int}\left(\frac{\tanh ^3(e+f x)}{c+d x},x\right)",0,"Integrate[Tanh[e + f*x]^3/(c + d*x), x]","A",-1
15,0,0,19,23.1470716,"\int \frac{\tanh ^3(e+f x)}{(c+d x)^2} \, dx","Integrate[Tanh[e + f*x]^3/(c + d*x)^2,x]","\int \frac{\tanh ^3(e+f x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\tanh ^3(e+f x)}{(c+d x)^2},x\right)",0,"Integrate[Tanh[e + f*x]^3/(c + d*x)^2, x]","A",-1
16,0,0,1392,39.8543934,"\int (c+d x) (b \tanh (e+f x))^{5/2} \, dx","Integrate[(c + d*x)*(b*Tanh[e + f*x])^(5/2),x]","\int (c+d x) (b \tanh (e+f x))^{5/2} \, dx","-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)^2 (-b)^{5/2}}{2 f^2}-\frac{(c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) (-b)^{5/2}}{f}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right) (-b)^{5/2}}{f^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) (-b)^{5/2}}{2 f^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(-\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) (-b)^{5/2}}{2 f^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right) (-b)^{5/2}}{f^2}+\frac{d \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right) (-b)^{5/2}}{2 f^2}-\frac{d \text{Li}_2\left(1-\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) (-b)^{5/2}}{4 f^2}-\frac{d \text{Li}_2\left(\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}+1\right) (-b)^{5/2}}{4 f^2}+\frac{d \text{Li}_2\left(1-\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right) (-b)^{5/2}}{2 f^2}+\frac{b^{5/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)^2}{2 f^2}-\frac{2 b (c+d x) (b \tanh (e+f x))^{3/2}}{3 f}+\frac{2 b^{5/2} d \tan ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{3 f^2}+\frac{b^{5/2} (c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{f}+\frac{2 b^{5/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{3 f^2}-\frac{b^{5/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right)}{f^2}+\frac{b^{5/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right)}{f^2}-\frac{b^{5/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{2 f^2}-\frac{b^{5/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{2 f^2}-\frac{b^{5/2} d \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right)}{2 f^2}-\frac{b^{5/2} d \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right)}{2 f^2}+\frac{b^{5/2} d \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{4 f^2}+\frac{b^{5/2} d \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{4 f^2}-\frac{4 b^2 d \sqrt{b \tanh (e+f x)}}{3 f^2}",1,"Integrate[(c + d*x)*(b*Tanh[e + f*x])^(5/2), x]","F",-1
17,0,0,1363,29.4176417,"\int (c+d x) (b \tanh (e+f x))^{3/2} \, dx","Integrate[(c + d*x)*(b*Tanh[e + f*x])^(3/2),x]","\int (c+d x) (b \tanh (e+f x))^{3/2} \, dx","-\frac{(-b)^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)^2}{2 f^2}-\frac{(-b)^{3/2} (c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{f}+\frac{(-b)^{3/2} d \log \left(\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{f^2}-\frac{(-b)^{3/2} d \log \left(\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{2 f^2}-\frac{(-b)^{3/2} d \log \left(-\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{2 f^2}-\frac{(-b)^{3/2} d \log \left(\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{f^2}+\frac{b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)^2}{2 f^2}-\frac{2 b^{3/2} d \tan ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{f^2}+\frac{b^{3/2} (c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{f}+\frac{2 b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{f^2}-\frac{b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right)}{f^2}+\frac{b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right)}{f^2}-\frac{b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{2 f^2}-\frac{b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{2 f^2}-\frac{b^{3/2} d \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right)}{2 f^2}-\frac{b^{3/2} d \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right)}{2 f^2}+\frac{b^{3/2} d \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{4 f^2}+\frac{b^{3/2} d \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{4 f^2}+\frac{(-b)^{3/2} d \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right)}{2 f^2}-\frac{(-b)^{3/2} d \text{Li}_2\left(1-\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right)}{4 f^2}-\frac{(-b)^{3/2} d \text{Li}_2\left(\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}+1\right)}{4 f^2}+\frac{(-b)^{3/2} d \text{Li}_2\left(1-\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right)}{2 f^2}-\frac{2 b (c+d x) \sqrt{b \tanh (e+f x)}}{f}",1,"Integrate[(c + d*x)*(b*Tanh[e + f*x])^(3/2), x]","F",-1
18,1,556,1280,5.3198833,"\int (c+d x) \sqrt{b \tanh (e+f x)} \, dx","Integrate[(c + d*x)*Sqrt[b*Tanh[e + f*x]],x]","\frac{\sqrt{b \tanh (e+f x)} \left(-4 f (c+d x) \left(\log \left(1-\sqrt{\tanh (e+f x)}\right)-\log \left(\sqrt{\tanh (e+f x)}+1\right)+2 \tan ^{-1}\left(\sqrt{\tanh (e+f x)}\right)\right)+d \left(-2 \text{Li}_2\left(\frac{1}{2} \left(1-\sqrt{\tanh (e+f x)}\right)\right)+2 \text{Li}_2\left(\left(-\frac{1}{2}-\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}-1\right)\right)+2 \text{Li}_2\left(\left(-\frac{1}{2}+\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}-1\right)\right)+2 \text{Li}_2\left(\frac{1}{2} \left(\sqrt{\tanh (e+f x)}+1\right)\right)-2 \text{Li}_2\left(\left(\frac{1}{2}-\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}+1\right)\right)-2 \text{Li}_2\left(\left(\frac{1}{2}+\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}+1\right)\right)+i \text{Li}_2\left(-e^{4 i \tan ^{-1}\left(\sqrt{\tanh (e+f x)}\right)}\right)-\log ^2\left(1-\sqrt{\tanh (e+f x)}\right)+\log ^2\left(\sqrt{\tanh (e+f x)}+1\right)+2 \log \left(1-\sqrt{\tanh (e+f x)}\right) \log \left(\left(\frac{1}{2}+\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}-i\right)\right)+2 \log \left(1-\sqrt{\tanh (e+f x)}\right) \log \left(\left(\frac{1}{2}-\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}+i\right)\right)-2 \log \left(1-\sqrt{\tanh (e+f x)}\right) \log \left(\frac{1}{2} \left(\sqrt{\tanh (e+f x)}+1\right)\right)-2 \log \left(1-\left(\frac{1}{2}-\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}+1\right)\right) \log \left(\sqrt{\tanh (e+f x)}+1\right)+2 \log \left(\frac{1}{2} \left(1-\sqrt{\tanh (e+f x)}\right)\right) \log \left(\sqrt{\tanh (e+f x)}+1\right)-2 \log \left(\left(-\frac{1}{2}-\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}+i\right)\right) \log \left(\sqrt{\tanh (e+f x)}+1\right)+4 i \tan ^{-1}\left(\sqrt{\tanh (e+f x)}\right)^2-4 \tan ^{-1}\left(\sqrt{\tanh (e+f x)}\right) \log \left(1+e^{4 i \tan ^{-1}\left(\sqrt{\tanh (e+f x)}\right)}\right)\right)\right)}{8 f^2 \sqrt{\tanh (e+f x)}}","-\frac{\sqrt{-b} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)^2}{2 f^2}-\frac{\sqrt{-b} (c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{f}+\frac{\sqrt{-b} d \log \left(\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{f^2}-\frac{\sqrt{-b} d \log \left(\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{2 f^2}-\frac{\sqrt{-b} d \log \left(-\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{2 f^2}-\frac{\sqrt{-b} d \log \left(\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{f^2}+\frac{\sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)^2}{2 f^2}+\frac{\sqrt{b} (c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{f}-\frac{\sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right)}{f^2}+\frac{\sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right)}{f^2}-\frac{\sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{2 f^2}-\frac{\sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{2 f^2}-\frac{\sqrt{b} d \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right)}{2 f^2}-\frac{\sqrt{b} d \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right)}{2 f^2}+\frac{\sqrt{b} d \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{4 f^2}+\frac{\sqrt{b} d \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{4 f^2}+\frac{\sqrt{-b} d \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right)}{2 f^2}-\frac{\sqrt{-b} d \text{Li}_2\left(1-\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right)}{4 f^2}-\frac{\sqrt{-b} d \text{Li}_2\left(\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}+1\right)}{4 f^2}+\frac{\sqrt{-b} d \text{Li}_2\left(1-\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right)}{2 f^2}",1,"((-4*f*(c + d*x)*(2*ArcTan[Sqrt[Tanh[e + f*x]]] + Log[1 - Sqrt[Tanh[e + f*x]]] - Log[1 + Sqrt[Tanh[e + f*x]]]) + d*((4*I)*ArcTan[Sqrt[Tanh[e + f*x]]]^2 - 4*ArcTan[Sqrt[Tanh[e + f*x]]]*Log[1 + E^((4*I)*ArcTan[Sqrt[Tanh[e + f*x]]])] - Log[1 - Sqrt[Tanh[e + f*x]]]^2 + 2*Log[1 - Sqrt[Tanh[e + f*x]]]*Log[(1/2 + I/2)*(-I + Sqrt[Tanh[e + f*x]])] + 2*Log[1 - Sqrt[Tanh[e + f*x]]]*Log[(1/2 - I/2)*(I + Sqrt[Tanh[e + f*x]])] - 2*Log[1 - Sqrt[Tanh[e + f*x]]]*Log[(1 + Sqrt[Tanh[e + f*x]])/2] - 2*Log[1 - (1/2 - I/2)*(1 + Sqrt[Tanh[e + f*x]])]*Log[1 + Sqrt[Tanh[e + f*x]]] + 2*Log[(1 - Sqrt[Tanh[e + f*x]])/2]*Log[1 + Sqrt[Tanh[e + f*x]]] - 2*Log[(-1/2 - I/2)*(I + Sqrt[Tanh[e + f*x]])]*Log[1 + Sqrt[Tanh[e + f*x]]] + Log[1 + Sqrt[Tanh[e + f*x]]]^2 + I*PolyLog[2, -E^((4*I)*ArcTan[Sqrt[Tanh[e + f*x]]])] - 2*PolyLog[2, (1 - Sqrt[Tanh[e + f*x]])/2] + 2*PolyLog[2, (-1/2 - I/2)*(-1 + Sqrt[Tanh[e + f*x]])] + 2*PolyLog[2, (-1/2 + I/2)*(-1 + Sqrt[Tanh[e + f*x]])] + 2*PolyLog[2, (1 + Sqrt[Tanh[e + f*x]])/2] - 2*PolyLog[2, (1/2 - I/2)*(1 + Sqrt[Tanh[e + f*x]])] - 2*PolyLog[2, (1/2 + I/2)*(1 + Sqrt[Tanh[e + f*x]])]))*Sqrt[b*Tanh[e + f*x]])/(8*f^2*Sqrt[Tanh[e + f*x]])","C",0
19,1,556,1280,4.3863751,"\int \frac{c+d x}{\sqrt{b \tanh (e+f x)}} \, dx","Integrate[(c + d*x)/Sqrt[b*Tanh[e + f*x]],x]","\frac{\sqrt{\tanh (e+f x)} \left(4 f (c+d x) \left(-\log \left(1-\sqrt{\tanh (e+f x)}\right)+\log \left(\sqrt{\tanh (e+f x)}+1\right)+2 \tan ^{-1}\left(\sqrt{\tanh (e+f x)}\right)\right)+d \left(-2 \text{Li}_2\left(\frac{1}{2} \left(1-\sqrt{\tanh (e+f x)}\right)\right)+2 \text{Li}_2\left(\left(-\frac{1}{2}-\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}-1\right)\right)+2 \text{Li}_2\left(\left(-\frac{1}{2}+\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}-1\right)\right)+2 \text{Li}_2\left(\frac{1}{2} \left(\sqrt{\tanh (e+f x)}+1\right)\right)-2 \text{Li}_2\left(\left(\frac{1}{2}-\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}+1\right)\right)-2 \text{Li}_2\left(\left(\frac{1}{2}+\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}+1\right)\right)-i \text{Li}_2\left(-e^{4 i \tan ^{-1}\left(\sqrt{\tanh (e+f x)}\right)}\right)-\log ^2\left(1-\sqrt{\tanh (e+f x)}\right)+\log ^2\left(\sqrt{\tanh (e+f x)}+1\right)+2 \log \left(1-\sqrt{\tanh (e+f x)}\right) \log \left(\left(\frac{1}{2}+\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}-i\right)\right)+2 \log \left(1-\sqrt{\tanh (e+f x)}\right) \log \left(\left(\frac{1}{2}-\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}+i\right)\right)-2 \log \left(1-\sqrt{\tanh (e+f x)}\right) \log \left(\frac{1}{2} \left(\sqrt{\tanh (e+f x)}+1\right)\right)-2 \log \left(1-\left(\frac{1}{2}-\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}+1\right)\right) \log \left(\sqrt{\tanh (e+f x)}+1\right)+2 \log \left(\frac{1}{2} \left(1-\sqrt{\tanh (e+f x)}\right)\right) \log \left(\sqrt{\tanh (e+f x)}+1\right)-2 \log \left(\left(-\frac{1}{2}-\frac{i}{2}\right) \left(\sqrt{\tanh (e+f x)}+i\right)\right) \log \left(\sqrt{\tanh (e+f x)}+1\right)-4 i \tan ^{-1}\left(\sqrt{\tanh (e+f x)}\right)^2+4 \tan ^{-1}\left(\sqrt{\tanh (e+f x)}\right) \log \left(1+e^{4 i \tan ^{-1}\left(\sqrt{\tanh (e+f x)}\right)}\right)\right)\right)}{8 f^2 \sqrt{b \tanh (e+f x)}}","-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)^2}{2 \sqrt{-b} f^2}-\frac{(c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{\sqrt{-b} f}+\frac{d \log \left(\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{\sqrt{-b} f^2}-\frac{d \log \left(\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{2 \sqrt{-b} f^2}-\frac{d \log \left(-\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{2 \sqrt{-b} f^2}-\frac{d \log \left(\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{\sqrt{-b} f^2}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)^2}{2 \sqrt{b} f^2}+\frac{(c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{\sqrt{b} f}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right)}{\sqrt{b} f^2}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right)}{\sqrt{b} f^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{2 \sqrt{b} f^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{2 \sqrt{b} f^2}-\frac{d \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right)}{2 \sqrt{b} f^2}-\frac{d \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right)}{2 \sqrt{b} f^2}+\frac{d \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{4 \sqrt{b} f^2}+\frac{d \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{4 \sqrt{b} f^2}+\frac{d \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right)}{2 \sqrt{-b} f^2}-\frac{d \text{Li}_2\left(1-\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right)}{4 \sqrt{-b} f^2}-\frac{d \text{Li}_2\left(\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}+1\right)}{4 \sqrt{-b} f^2}+\frac{d \text{Li}_2\left(1-\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right)}{2 \sqrt{-b} f^2}",1,"((4*f*(c + d*x)*(2*ArcTan[Sqrt[Tanh[e + f*x]]] - Log[1 - Sqrt[Tanh[e + f*x]]] + Log[1 + Sqrt[Tanh[e + f*x]]]) + d*((-4*I)*ArcTan[Sqrt[Tanh[e + f*x]]]^2 + 4*ArcTan[Sqrt[Tanh[e + f*x]]]*Log[1 + E^((4*I)*ArcTan[Sqrt[Tanh[e + f*x]]])] - Log[1 - Sqrt[Tanh[e + f*x]]]^2 + 2*Log[1 - Sqrt[Tanh[e + f*x]]]*Log[(1/2 + I/2)*(-I + Sqrt[Tanh[e + f*x]])] + 2*Log[1 - Sqrt[Tanh[e + f*x]]]*Log[(1/2 - I/2)*(I + Sqrt[Tanh[e + f*x]])] - 2*Log[1 - Sqrt[Tanh[e + f*x]]]*Log[(1 + Sqrt[Tanh[e + f*x]])/2] - 2*Log[1 - (1/2 - I/2)*(1 + Sqrt[Tanh[e + f*x]])]*Log[1 + Sqrt[Tanh[e + f*x]]] + 2*Log[(1 - Sqrt[Tanh[e + f*x]])/2]*Log[1 + Sqrt[Tanh[e + f*x]]] - 2*Log[(-1/2 - I/2)*(I + Sqrt[Tanh[e + f*x]])]*Log[1 + Sqrt[Tanh[e + f*x]]] + Log[1 + Sqrt[Tanh[e + f*x]]]^2 - I*PolyLog[2, -E^((4*I)*ArcTan[Sqrt[Tanh[e + f*x]]])] - 2*PolyLog[2, (1 - Sqrt[Tanh[e + f*x]])/2] + 2*PolyLog[2, (-1/2 - I/2)*(-1 + Sqrt[Tanh[e + f*x]])] + 2*PolyLog[2, (-1/2 + I/2)*(-1 + Sqrt[Tanh[e + f*x]])] + 2*PolyLog[2, (1 + Sqrt[Tanh[e + f*x]])/2] - 2*PolyLog[2, (1/2 - I/2)*(1 + Sqrt[Tanh[e + f*x]])] - 2*PolyLog[2, (1/2 + I/2)*(1 + Sqrt[Tanh[e + f*x]])]))*Sqrt[Tanh[e + f*x]])/(8*f^2*Sqrt[b*Tanh[e + f*x]])","C",0
20,0,0,1365,27.752278,"\int \frac{c+d x}{(b \tanh (e+f x))^{3/2}} \, dx","Integrate[(c + d*x)/(b*Tanh[e + f*x])^(3/2),x]","\int \frac{c+d x}{(b \tanh (e+f x))^{3/2}} \, dx","-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)^2}{2 (-b)^{3/2} f^2}-\frac{(c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{(-b)^{3/2} f}+\frac{d \log \left(\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{(-b)^{3/2} f^2}-\frac{d \log \left(\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{2 (-b)^{3/2} f^2}-\frac{d \log \left(-\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{2 (-b)^{3/2} f^2}-\frac{d \log \left(\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{(-b)^{3/2} f^2}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)^2}{2 b^{3/2} f^2}+\frac{2 d \tan ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f^2}+\frac{(c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f}+\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)}{b^{3/2} f^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right)}{b^{3/2} f^2}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right)}{b^{3/2} f^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{2 b^{3/2} f^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{2 b^{3/2} f^2}-\frac{d \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right)}{2 b^{3/2} f^2}-\frac{d \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right)}{2 b^{3/2} f^2}+\frac{d \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{4 b^{3/2} f^2}+\frac{d \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right)}{4 b^{3/2} f^2}+\frac{d \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right)}{2 (-b)^{3/2} f^2}-\frac{d \text{Li}_2\left(1-\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right)}{4 (-b)^{3/2} f^2}-\frac{d \text{Li}_2\left(\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}+1\right)}{4 (-b)^{3/2} f^2}+\frac{d \text{Li}_2\left(1-\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right)}{2 (-b)^{3/2} f^2}-\frac{2 (c+d x)}{b f \sqrt{b \tanh (e+f x)}}",1,"Integrate[(c + d*x)/(b*Tanh[e + f*x])^(3/2), x]","F",-1
21,0,0,1341,28.7240295,"\int (c+d x)^2 (b \tanh (e+f x))^{3/2} \, dx","Integrate[(c + d*x)^2*(b*Tanh[e + f*x])^(3/2),x]","\int (c+d x)^2 (b \tanh (e+f x))^{3/2} \, dx","\text{Int}\left(\frac{(c+d x)^2}{\sqrt{b \tanh (e+f x)}},x\right) b^2+\frac{2 d^2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)^2 b^{3/2}}{f^3}+\frac{4 d (c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) b^{3/2}}{f^2}-\frac{4 d^2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right) b^{3/2}}{f^3}+\frac{4 d^2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right) b^{3/2}}{f^3}-\frac{2 d^2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right) b^{3/2}}{f^3}-\frac{2 d^2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right) b^{3/2}}{f^3}-\frac{2 d^2 \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right) b^{3/2}}{f^3}-\frac{2 d^2 \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right) b^{3/2}}{f^3}+\frac{d^2 \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right) b^{3/2}}{f^3}+\frac{d^2 \text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right) b^{3/2}}{f^3}-\frac{2 (c+d x)^2 \sqrt{b \tanh (e+f x)} b}{f}+\frac{2 (-b)^{3/2} d^2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)^2}{f^3}+\frac{4 (-b)^{3/2} d (c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}{f^2}-\frac{4 (-b)^{3/2} d^2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right)}{f^3}+\frac{2 (-b)^{3/2} d^2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right)}{f^3}+\frac{2 (-b)^{3/2} d^2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(-\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right)}{f^3}+\frac{4 (-b)^{3/2} d^2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right)}{f^3}-\frac{2 (-b)^{3/2} d^2 \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right)}{f^3}+\frac{(-b)^{3/2} d^2 \text{Li}_2\left(1-\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right)}{f^3}+\frac{(-b)^{3/2} d^2 \text{Li}_2\left(\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}+1\right)}{f^3}-\frac{2 (-b)^{3/2} d^2 \text{Li}_2\left(1-\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right)}{f^3}",0,"Integrate[(c + d*x)^2*(b*Tanh[e + f*x])^(3/2), x]","A",-1
22,-1,0,23,180.0015876,"\int (c+d x)^2 \sqrt{b \tanh (e+f x)} \, dx","Integrate[(c + d*x)^2*Sqrt[b*Tanh[e + f*x]],x]","\text{\$Aborted}","\text{Int}\left((c+d x)^2 \sqrt{b \tanh (e+f x)},x\right)",0,"$Aborted","F",-1
23,-1,0,23,180.0030203,"\int \frac{(c+d x)^2}{\sqrt{b \tanh (e+f x)}} \, dx","Integrate[(c + d*x)^2/Sqrt[b*Tanh[e + f*x]],x]","\text{\$Aborted}","\text{Int}\left(\frac{(c+d x)^2}{\sqrt{b \tanh (e+f x)}},x\right)",0,"$Aborted","F",-1
24,0,0,1343,35.5926163,"\int \frac{(c+d x)^2}{(b \tanh (e+f x))^{3/2}} \, dx","Integrate[(c + d*x)^2/(b*Tanh[e + f*x])^(3/2),x]","\int \frac{(c+d x)^2}{(b \tanh (e+f x))^{3/2}} \, dx","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)^2 d^2}{(-b)^{3/2} f^3}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right)^2 d^2}{b^{3/2} f^3}-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right) d^2}{b^{3/2} f^3}+\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right) d^2}{b^{3/2} f^3}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right) d^2}{b^{3/2} f^3}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) \log \left(\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right) d^2}{b^{3/2} f^3}-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right) d^2}{(-b)^{3/2} f^3}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) d^2}{(-b)^{3/2} f^3}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(-\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) d^2}{(-b)^{3/2} f^3}+\frac{4 \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) \log \left(\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right) d^2}{(-b)^{3/2} f^3}-\frac{2 \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}-\sqrt{b \tanh (e+f x)}}\right) d^2}{b^{3/2} f^3}-\frac{2 \text{Li}_2\left(1-\frac{2 \sqrt{b}}{\sqrt{b}+\sqrt{b \tanh (e+f x)}}\right) d^2}{b^{3/2} f^3}+\frac{\text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right) d^2}{b^{3/2} f^3}+\frac{\text{Li}_2\left(1-\frac{2 \sqrt{b} \left(\sqrt{-b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}\right) d^2}{b^{3/2} f^3}-\frac{2 \text{Li}_2\left(1-\frac{2}{1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}}\right) d^2}{(-b)^{3/2} f^3}+\frac{\text{Li}_2\left(1-\frac{2 \left(\sqrt{b}-\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}+\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}\right) d^2}{(-b)^{3/2} f^3}+\frac{\text{Li}_2\left(\frac{2 \left(\sqrt{b}+\sqrt{b \tanh (e+f x)}\right)}{\left(\sqrt{-b}-\sqrt{b}\right) \left(1-\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right)}+1\right) d^2}{(-b)^{3/2} f^3}-\frac{2 \text{Li}_2\left(1-\frac{2}{\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}+1}\right) d^2}{(-b)^{3/2} f^3}+\frac{4 (c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{-b}}\right) d}{(-b)^{3/2} f^2}+\frac{4 (c+d x) \tanh ^{-1}\left(\frac{\sqrt{b \tanh (e+f x)}}{\sqrt{b}}\right) d}{b^{3/2} f^2}+\frac{\text{Int}\left((c+d x)^2 \sqrt{b \tanh (e+f x)},x\right)}{b^2}-\frac{2 (c+d x)^2}{b f \sqrt{b \tanh (e+f x)}}",0,"Integrate[(c + d*x)^2/(b*Tanh[e + f*x])^(3/2), x]","A",-1
25,0,0,23,28.753934,"\int \frac{(b \tanh (e+f x))^{3/2}}{c+d x} \, dx","Integrate[(b*Tanh[e + f*x])^(3/2)/(c + d*x),x]","\int \frac{(b \tanh (e+f x))^{3/2}}{c+d x} \, dx","\text{Int}\left(\frac{(b \tanh (e+f x))^{3/2}}{c+d x},x\right)",0,"Integrate[(b*Tanh[e + f*x])^(3/2)/(c + d*x), x]","A",-1
26,0,0,23,2.0926051,"\int \frac{\sqrt{b \tanh (e+f x)}}{c+d x} \, dx","Integrate[Sqrt[b*Tanh[e + f*x]]/(c + d*x),x]","\int \frac{\sqrt{b \tanh (e+f x)}}{c+d x} \, dx","\text{Int}\left(\frac{\sqrt{b \tanh (e+f x)}}{c+d x},x\right)",0,"Integrate[Sqrt[b*Tanh[e + f*x]]/(c + d*x), x]","A",-1
27,0,0,23,2.4553219,"\int \frac{1}{(c+d x) \sqrt{b \tanh (e+f x)}} \, dx","Integrate[1/((c + d*x)*Sqrt[b*Tanh[e + f*x]]),x]","\int \frac{1}{(c+d x) \sqrt{b \tanh (e+f x)}} \, dx","\text{Int}\left(\frac{1}{(c+d x) \sqrt{b \tanh (e+f x)}},x\right)",0,"Integrate[1/((c + d*x)*Sqrt[b*Tanh[e + f*x]]), x]","A",-1
28,0,0,23,26.2653458,"\int \frac{1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx","Integrate[1/((c + d*x)*(b*Tanh[e + f*x])^(3/2)),x]","\int \frac{1}{(c+d x) (b \tanh (e+f x))^{3/2}} \, dx","\text{Int}\left(\frac{1}{(c+d x) (b \tanh (e+f x))^{3/2}},x\right)",0,"Integrate[1/((c + d*x)*(b*Tanh[e + f*x])^(3/2)), x]","A",-1
29,0,0,15,146.5395461,"\int x^m \tanh ^3(a+b x) \, dx","Integrate[x^m*Tanh[a + b*x]^3,x]","\int x^m \tanh ^3(a+b x) \, dx","\text{Int}\left(x^m \tanh ^3(a+b x),x\right)",0,"Integrate[x^m*Tanh[a + b*x]^3, x]","A",-1
30,0,0,15,9.9196967,"\int x^m \tanh ^2(a+b x) \, dx","Integrate[x^m*Tanh[a + b*x]^2,x]","\int x^m \tanh ^2(a+b x) \, dx","\text{Int}\left(x^m \tanh ^2(a+b x),x\right)",0,"Integrate[x^m*Tanh[a + b*x]^2, x]","A",-1
31,0,0,13,7.6243376,"\int x^m \tanh (a+b x) \, dx","Integrate[x^m*Tanh[a + b*x],x]","\int x^m \tanh (a+b x) \, dx","\text{Int}\left(x^m \tanh (a+b x),x\right)",0,"Integrate[x^m*Tanh[a + b*x], x]","A",-1
32,1,244,169,0.4402839,"\int \frac{(c+d x)^3}{a+a \tanh (e+f x)} \, dx","Integrate[(c + d*x)^3/(a + a*Tanh[e + f*x]),x]","\frac{\text{sech}(e+f x) (\sinh (f x)+\cosh (f x)) \left(2 f^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) (\sinh (e)+\cosh (e))+(\sinh (e)-\cosh (e)) \cosh (2 f x) \left(4 c^3 f^3+6 c^2 d f^2 (2 f x+1)+6 c d^2 f \left(2 f^2 x^2+2 f x+1\right)+d^3 \left(4 f^3 x^3+6 f^2 x^2+6 f x+3\right)\right)+(\cosh (e)-\sinh (e)) \sinh (2 f x) \left(4 c^3 f^3+6 c^2 d f^2 (2 f x+1)+6 c d^2 f \left(2 f^2 x^2+2 f x+1\right)+d^3 \left(4 f^3 x^3+6 f^2 x^2+6 f x+3\right)\right)\right)}{16 a f^4 (\tanh (e+f x)+1)}","-\frac{3 d^2 (c+d x)}{4 f^3 (a \tanh (e+f x)+a)}-\frac{3 d (c+d x)^2}{4 f^2 (a \tanh (e+f x)+a)}-\frac{(c+d x)^3}{2 f (a \tanh (e+f x)+a)}+\frac{3 d (c+d x)^2}{8 a f^2}+\frac{(c+d x)^3}{4 a f}+\frac{(c+d x)^4}{8 a d}-\frac{3 d^3}{8 f^4 (a \tanh (e+f x)+a)}+\frac{3 d^3 x}{8 a f^3}",1,"(Sech[e + f*x]*(Cosh[f*x] + Sinh[f*x])*((4*c^3*f^3 + 6*c^2*d*f^2*(1 + 2*f*x) + 6*c*d^2*f*(1 + 2*f*x + 2*f^2*x^2) + d^3*(3 + 6*f*x + 6*f^2*x^2 + 4*f^3*x^3))*Cosh[2*f*x]*(-Cosh[e] + Sinh[e]) + 2*f^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*(Cosh[e] + Sinh[e]) + (4*c^3*f^3 + 6*c^2*d*f^2*(1 + 2*f*x) + 6*c*d^2*f*(1 + 2*f*x + 2*f^2*x^2) + d^3*(3 + 6*f*x + 6*f^2*x^2 + 4*f^3*x^3))*(Cosh[e] - Sinh[e])*Sinh[2*f*x]))/(16*a*f^4*(1 + Tanh[e + f*x]))","A",1
33,1,169,122,0.293475,"\int \frac{(c+d x)^2}{a+a \tanh (e+f x)} \, dx","Integrate[(c + d*x)^2/(a + a*Tanh[e + f*x]),x]","\frac{\text{sech}(e+f x) (\sinh (f x)+\cosh (f x)) \left(\frac{4}{3} f^3 x \left(3 c^2+3 c d x+d^2 x^2\right) (\sinh (e)+\cosh (e))+(\sinh (e)-\cosh (e)) \cosh (2 f x) \left(2 c^2 f^2+2 c d f (2 f x+1)+d^2 \left(2 f^2 x^2+2 f x+1\right)\right)+(\cosh (e)-\sinh (e)) \sinh (2 f x) \left(2 c^2 f^2+2 c d f (2 f x+1)+d^2 \left(2 f^2 x^2+2 f x+1\right)\right)\right)}{8 a f^3 (\tanh (e+f x)+1)}","-\frac{d (c+d x)}{2 f^2 (a \tanh (e+f x)+a)}-\frac{(c+d x)^2}{2 f (a \tanh (e+f x)+a)}+\frac{(c+d x)^2}{4 a f}+\frac{(c+d x)^3}{6 a d}-\frac{d^2}{4 f^3 (a \tanh (e+f x)+a)}+\frac{d^2 x}{4 a f^2}",1,"(Sech[e + f*x]*(Cosh[f*x] + Sinh[f*x])*((2*c^2*f^2 + 2*c*d*f*(1 + 2*f*x) + d^2*(1 + 2*f*x + 2*f^2*x^2))*Cosh[2*f*x]*(-Cosh[e] + Sinh[e]) + (4*f^3*x*(3*c^2 + 3*c*d*x + d^2*x^2)*(Cosh[e] + Sinh[e]))/3 + (2*c^2*f^2 + 2*c*d*f*(1 + 2*f*x) + d^2*(1 + 2*f*x + 2*f^2*x^2))*(Cosh[e] - Sinh[e])*Sinh[2*f*x]))/(8*a*f^3*(1 + Tanh[e + f*x]))","A",1
34,1,81,74,0.3082498,"\int \frac{c+d x}{a+a \tanh (e+f x)} \, dx","Integrate[(c + d*x)/(a + a*Tanh[e + f*x]),x]","\frac{\left(2 c f (2 f x+1)+d \left(2 f^2 x^2+2 f x+1\right)\right) \tanh (e+f x)+2 c f (2 f x-1)+d \left(2 f^2 x^2-2 f x-1\right)}{8 a f^2 (\tanh (e+f x)+1)}","-\frac{c+d x}{2 f (a \tanh (e+f x)+a)}+\frac{(c+d x)^2}{4 a d}-\frac{d}{4 f^2 (a \tanh (e+f x)+a)}+\frac{d x}{4 a f}",1,"(2*c*f*(-1 + 2*f*x) + d*(-1 - 2*f*x + 2*f^2*x^2) + (2*c*f*(1 + 2*f*x) + d*(1 + 2*f*x + 2*f^2*x^2))*Tanh[e + f*x])/(8*a*f^2*(1 + Tanh[e + f*x]))","A",1
35,1,122,157,0.2723299,"\int \frac{1}{(c+d x) (a+a \tanh (e+f x))} \, dx","Integrate[1/((c + d*x)*(a + a*Tanh[e + f*x])),x]","\frac{\text{sech}(e+f x) (\sinh (f x)+\cosh (f x)) \left(\text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \left(\cosh \left(e-\frac{2 c f}{d}\right)-\sinh \left(e-\frac{2 c f}{d}\right)\right)+\text{Shi}\left(\frac{2 f (c+d x)}{d}\right) \left(\sinh \left(e-\frac{2 c f}{d}\right)-\cosh \left(e-\frac{2 c f}{d}\right)\right)+(\sinh (e)+\cosh (e)) \log (f (c+d x))\right)}{2 a d (\tanh (e+f x)+1)}","-\frac{\text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{2 a d}+\frac{\text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{2 a d}+\frac{\sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{2 a d}-\frac{\cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{2 a d}+\frac{\log (c+d x)}{2 a d}",1,"(Sech[e + f*x]*(Cosh[f*x] + Sinh[f*x])*(Log[f*(c + d*x)]*(Cosh[e] + Sinh[e]) + CoshIntegral[(2*f*(c + d*x))/d]*(Cosh[e - (2*c*f)/d] - Sinh[e - (2*c*f)/d]) + (-Cosh[e - (2*c*f)/d] + Sinh[e - (2*c*f)/d])*SinhIntegral[(2*f*(c + d*x))/d]))/(2*a*d*(1 + Tanh[e + f*x]))","A",1
36,1,206,159,0.8048586,"\int \frac{1}{(c+d x)^2 (a+a \tanh (e+f x))} \, dx","Integrate[1/((c + d*x)^2*(a + a*Tanh[e + f*x])),x]","-\frac{\text{sech}(e+f x) \left(\sinh \left(\frac{c f}{d}\right)+\cosh \left(\frac{c f}{d}\right)\right) \left(2 f (c+d x) \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \left(\cosh \left(e-\frac{f (c+d x)}{d}\right)-\sinh \left(e-\frac{f (c+d x)}{d}\right)\right)+2 f (c+d x) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right) \left(\sinh \left(e-\frac{f (c+d x)}{d}\right)-\cosh \left(e-\frac{f (c+d x)}{d}\right)\right)+d \left(\sinh \left(f \left(x-\frac{c}{d}\right)+e\right)-\sinh \left(f \left(\frac{c}{d}+x\right)+e\right)+\cosh \left(f \left(x-\frac{c}{d}\right)+e\right)+\cosh \left(f \left(\frac{c}{d}+x\right)+e\right)\right)\right)}{2 a d^2 (c+d x) (\tanh (e+f x)+1)}","\frac{f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{a d^2}-\frac{f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{a d^2}-\frac{f \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a d^2}+\frac{f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a d^2}-\frac{1}{d (c+d x) (a \tanh (e+f x)+a)}",1,"-1/2*(Sech[e + f*x]*(Cosh[(c*f)/d] + Sinh[(c*f)/d])*(d*(Cosh[e + f*(-(c/d) + x)] + Cosh[e + f*(c/d + x)] + Sinh[e + f*(-(c/d) + x)] - Sinh[e + f*(c/d + x)]) + 2*f*(c + d*x)*CoshIntegral[(2*f*(c + d*x))/d]*(Cosh[e - (f*(c + d*x))/d] - Sinh[e - (f*(c + d*x))/d]) + 2*f*(c + d*x)*(-Cosh[e - (f*(c + d*x))/d] + Sinh[e - (f*(c + d*x))/d])*SinhIntegral[(2*f*(c + d*x))/d]))/(a*d^2*(c + d*x)*(1 + Tanh[e + f*x]))","A",1
37,1,264,211,1.1516334,"\int \frac{1}{(c+d x)^3 (a+a \tanh (e+f x))} \, dx","Integrate[1/((c + d*x)^3*(a + a*Tanh[e + f*x])),x]","-\frac{\text{sech}(e+f x) \left(\sinh \left(\frac{c f}{d}\right)+\cosh \left(\frac{c f}{d}\right)\right) \left(4 f^2 (c+d x)^2 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \left(\sinh \left(e-\frac{f (c+d x)}{d}\right)-\cosh \left(e-\frac{f (c+d x)}{d}\right)\right)+4 f^2 (c+d x)^2 \text{Shi}\left(\frac{2 f (c+d x)}{d}\right) \left(\cosh \left(e-\frac{f (c+d x)}{d}\right)-\sinh \left(e-\frac{f (c+d x)}{d}\right)\right)+d \left(d \sinh \left(f \left(x-\frac{c}{d}\right)+e\right)-d \sinh \left(f \left(\frac{c}{d}+x\right)+e\right)+2 c f \sinh \left(f \left(\frac{c}{d}+x\right)+e\right)+2 d f x \sinh \left(f \left(\frac{c}{d}+x\right)+e\right)+d \cosh \left(f \left(x-\frac{c}{d}\right)+e\right)+(-2 c f-2 d f x+d) \cosh \left(f \left(\frac{c}{d}+x\right)+e\right)\right)\right)}{4 a d^3 (c+d x)^2 (\tanh (e+f x)+1)}","-\frac{f^2 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{a d^3}+\frac{f^2 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{a d^3}+\frac{f^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a d^3}-\frac{f^2 \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a d^3}+\frac{f}{d^2 (c+d x) (a \tanh (e+f x)+a)}-\frac{f}{2 a d^2 (c+d x)}-\frac{1}{2 d (c+d x)^2 (a \tanh (e+f x)+a)}",1,"-1/4*(Sech[e + f*x]*(Cosh[(c*f)/d] + Sinh[(c*f)/d])*(d*(d*Cosh[e + f*(-(c/d) + x)] + (d - 2*c*f - 2*d*f*x)*Cosh[e + f*(c/d + x)] + d*Sinh[e + f*(-(c/d) + x)] - d*Sinh[e + f*(c/d + x)] + 2*c*f*Sinh[e + f*(c/d + x)] + 2*d*f*x*Sinh[e + f*(c/d + x)]) + 4*f^2*(c + d*x)^2*CoshIntegral[(2*f*(c + d*x))/d]*(-Cosh[e - (f*(c + d*x))/d] + Sinh[e - (f*(c + d*x))/d]) + 4*f^2*(c + d*x)^2*(Cosh[e - (f*(c + d*x))/d] - Sinh[e - (f*(c + d*x))/d])*SinhIntegral[(2*f*(c + d*x))/d]))/(a*d^3*(c + d*x)^2*(1 + Tanh[e + f*x]))","A",1
38,1,420,230,1.1379581,"\int \frac{(c+d x)^3}{(a+a \tanh (e+f x))^2} \, dx","Integrate[(c + d*x)^3/(a + a*Tanh[e + f*x])^2,x]","\frac{\text{sech}^2(e+f x) (\sinh (f x)+\cosh (f x))^2 \left(f^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) (\sinh (2 e)+\cosh (2 e))+\frac{1}{32} (\sinh (2 e)-\cosh (2 e)) \cosh (4 f x) \left(32 c^3 f^3+24 c^2 d f^2 (4 f x+1)+12 c d^2 f \left(8 f^2 x^2+4 f x+1\right)+d^3 \left(32 f^3 x^3+24 f^2 x^2+12 f x+3\right)\right)+\frac{1}{32} (\cosh (2 e)-\sinh (2 e)) \sinh (4 f x) \left(32 c^3 f^3+24 c^2 d f^2 (4 f x+1)+12 c d^2 f \left(8 f^2 x^2+4 f x+1\right)+d^3 \left(32 f^3 x^3+24 f^2 x^2+12 f x+3\right)\right)+\sinh (2 f x) \left(4 c^3 f^3+6 c^2 d f^2 (2 f x+1)+6 c d^2 f \left(2 f^2 x^2+2 f x+1\right)+d^3 \left(4 f^3 x^3+6 f^2 x^2+6 f x+3\right)\right)-\cosh (2 f x) \left(4 c^3 f^3+6 c^2 d f^2 (2 f x+1)+6 c d^2 f \left(2 f^2 x^2+2 f x+1\right)+d^3 \left(4 f^3 x^3+6 f^2 x^2+6 f x+3\right)\right)\right)}{16 a^2 f^4 (\tanh (e+f x)+1)^2}","-\frac{3 d^2 (c+d x) e^{-4 e-4 f x}}{128 a^2 f^3}-\frac{3 d^2 (c+d x) e^{-2 e-2 f x}}{8 a^2 f^3}-\frac{3 d (c+d x)^2 e^{-4 e-4 f x}}{64 a^2 f^2}-\frac{3 d (c+d x)^2 e^{-2 e-2 f x}}{8 a^2 f^2}-\frac{(c+d x)^3 e^{-4 e-4 f x}}{16 a^2 f}-\frac{(c+d x)^3 e^{-2 e-2 f x}}{4 a^2 f}+\frac{(c+d x)^4}{16 a^2 d}-\frac{3 d^3 e^{-4 e-4 f x}}{512 a^2 f^4}-\frac{3 d^3 e^{-2 e-2 f x}}{16 a^2 f^4}",1,"(Sech[e + f*x]^2*(Cosh[f*x] + Sinh[f*x])^2*(-((4*c^3*f^3 + 6*c^2*d*f^2*(1 + 2*f*x) + 6*c*d^2*f*(1 + 2*f*x + 2*f^2*x^2) + d^3*(3 + 6*f*x + 6*f^2*x^2 + 4*f^3*x^3))*Cosh[2*f*x]) + ((32*c^3*f^3 + 24*c^2*d*f^2*(1 + 4*f*x) + 12*c*d^2*f*(1 + 4*f*x + 8*f^2*x^2) + d^3*(3 + 12*f*x + 24*f^2*x^2 + 32*f^3*x^3))*Cosh[4*f*x]*(-Cosh[2*e] + Sinh[2*e]))/32 + f^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*(Cosh[2*e] + Sinh[2*e]) + (4*c^3*f^3 + 6*c^2*d*f^2*(1 + 2*f*x) + 6*c*d^2*f*(1 + 2*f*x + 2*f^2*x^2) + d^3*(3 + 6*f*x + 6*f^2*x^2 + 4*f^3*x^3))*Sinh[2*f*x] + ((32*c^3*f^3 + 24*c^2*d*f^2*(1 + 4*f*x) + 12*c*d^2*f*(1 + 4*f*x + 8*f^2*x^2) + d^3*(3 + 12*f*x + 24*f^2*x^2 + 32*f^3*x^3))*(Cosh[2*e] - Sinh[2*e])*Sinh[4*f*x])/32))/(16*a^2*f^4*(1 + Tanh[e + f*x])^2)","A",1
39,1,207,170,0.9874445,"\int \frac{(c+d x)^2}{(a+a \tanh (e+f x))^2} \, dx","Integrate[(c + d*x)^2/(a + a*Tanh[e + f*x])^2,x]","\frac{\text{sech}^2(e+f x) \left(\left(24 c^2 f^2 (4 f x+1)+12 c d f \left(8 f^2 x^2+4 f x+1\right)+d^2 \left(32 f^3 x^3+24 f^2 x^2+12 f x+3\right)\right) \sinh (2 (e+f x))+\left(24 c^2 f^2 (4 f x-1)+12 c d f \left(8 f^2 x^2-4 f x-1\right)+d^2 \left(32 f^3 x^3-24 f^2 x^2-12 f x-3\right)\right) \cosh (2 (e+f x))-48 \left(2 c^2 f^2+2 c d f (2 f x+1)+d^2 \left(2 f^2 x^2+2 f x+1\right)\right)\right)}{384 a^2 f^3 (\tanh (e+f x)+1)^2}","-\frac{d (c+d x) e^{-4 e-4 f x}}{32 a^2 f^2}-\frac{d (c+d x) e^{-2 e-2 f x}}{4 a^2 f^2}-\frac{(c+d x)^2 e^{-4 e-4 f x}}{16 a^2 f}-\frac{(c+d x)^2 e^{-2 e-2 f x}}{4 a^2 f}+\frac{(c+d x)^3}{12 a^2 d}-\frac{d^2 e^{-4 e-4 f x}}{128 a^2 f^3}-\frac{d^2 e^{-2 e-2 f x}}{8 a^2 f^3}",1,"(Sech[e + f*x]^2*(-48*(2*c^2*f^2 + 2*c*d*f*(1 + 2*f*x) + d^2*(1 + 2*f*x + 2*f^2*x^2)) + (24*c^2*f^2*(-1 + 4*f*x) + 12*c*d*f*(-1 - 4*f*x + 8*f^2*x^2) + d^2*(-3 - 12*f*x - 24*f^2*x^2 + 32*f^3*x^3))*Cosh[2*(e + f*x)] + (24*c^2*f^2*(1 + 4*f*x) + 12*c*d*f*(1 + 4*f*x + 8*f^2*x^2) + d^2*(3 + 12*f*x + 24*f^2*x^2 + 32*f^3*x^3))*Sinh[2*(e + f*x)]))/(384*a^2*f^3*(1 + Tanh[e + f*x])^2)","A",1
40,1,114,133,0.5443971,"\int \frac{c+d x}{(a+a \tanh (e+f x))^2} \, dx","Integrate[(c + d*x)/(a + a*Tanh[e + f*x])^2,x]","\frac{\text{sech}^2(e+f x) \left(\left(4 c f (4 f x+1)+d \left(8 f^2 x^2+4 f x+1\right)\right) \sinh (2 (e+f x))+\left(4 c f (4 f x-1)+d \left(8 f^2 x^2-4 f x-1\right)\right) \cosh (2 (e+f x))-8 (2 c f+2 d f x+d)\right)}{64 a^2 f^2 (\tanh (e+f x)+1)^2}","-\frac{c+d x}{4 f \left(a^2 \tanh (e+f x)+a^2\right)}+\frac{x (c+d x)}{4 a^2}-\frac{3 d}{16 f^2 \left(a^2 \tanh (e+f x)+a^2\right)}+\frac{3 d x}{16 a^2 f}-\frac{d x^2}{8 a^2}-\frac{c+d x}{4 f (a \tanh (e+f x)+a)^2}-\frac{d}{16 f^2 (a \tanh (e+f x)+a)^2}",1,"(Sech[e + f*x]^2*(-8*(d + 2*c*f + 2*d*f*x) + (4*c*f*(-1 + 4*f*x) + d*(-1 - 4*f*x + 8*f^2*x^2))*Cosh[2*(e + f*x)] + (4*c*f*(1 + 4*f*x) + d*(1 + 4*f*x + 8*f^2*x^2))*Sinh[2*(e + f*x)]))/(64*a^2*f^2*(1 + Tanh[e + f*x])^2)","A",1
41,1,199,297,0.4718725,"\int \frac{1}{(c+d x) (a+a \tanh (e+f x))^2} \, dx","Integrate[1/((c + d*x)*(a + a*Tanh[e + f*x])^2),x]","\frac{\left(\cosh \left(2 e-\frac{2 c f}{d}\right)-\sinh \left(2 e-\frac{2 c f}{d}\right)\right) \left(\text{Chi}\left(\frac{4 f (c+d x)}{d}\right) \left(\cosh \left(2 e-\frac{2 c f}{d}\right)-\sinh \left(2 e-\frac{2 c f}{d}\right)\right)+2 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right)+\sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{4 f (c+d x)}{d}\right)-\cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{4 f (c+d x)}{d}\right)+\sinh \left(2 e-\frac{2 c f}{d}\right) \log (f (c+d x))+\cosh \left(2 e-\frac{2 c f}{d}\right) \log (f (c+d x))-2 \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)\right)}{4 a^2 d}","-\frac{\text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{2 a^2 d}-\frac{\text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \sinh \left(4 e-\frac{4 c f}{d}\right)}{4 a^2 d}+\frac{\text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{\text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \cosh \left(4 e-\frac{4 c f}{d}\right)}{4 a^2 d}+\frac{\sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{2 a^2 d}+\frac{\sinh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{4 a^2 d}-\frac{\cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{2 a^2 d}-\frac{\cosh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{4 a^2 d}+\frac{\log (c+d x)}{4 a^2 d}",1,"((Cosh[2*e - (2*c*f)/d] - Sinh[2*e - (2*c*f)/d])*(2*CoshIntegral[(2*f*(c + d*x))/d] + Cosh[2*e - (2*c*f)/d]*Log[f*(c + d*x)] + CoshIntegral[(4*f*(c + d*x))/d]*(Cosh[2*e - (2*c*f)/d] - Sinh[2*e - (2*c*f)/d]) + Log[f*(c + d*x)]*Sinh[2*e - (2*c*f)/d] - 2*SinhIntegral[(2*f*(c + d*x))/d] - Cosh[2*e - (2*c*f)/d]*SinhIntegral[(4*f*(c + d*x))/d] + Sinh[2*e - (2*c*f)/d]*SinhIntegral[(4*f*(c + d*x))/d]))/(4*a^2*d)","A",1
42,1,442,420,1.4157695,"\int \frac{1}{(c+d x)^2 (a+a \tanh (e+f x))^2} \, dx","Integrate[1/((c + d*x)^2*(a + a*Tanh[e + f*x])^2),x]","\frac{\left(\sinh \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)-\cosh \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)\right) \left(4 f (c+d x) \text{Chi}\left(\frac{4 f (c+d x)}{d}\right) \left(\cosh \left(2 e-\frac{2 f (c+d x)}{d}\right)-\sinh \left(2 e-\frac{2 f (c+d x)}{d}\right)\right)+4 f (c+d x) (\sinh (2 f x)+\cosh (2 f x)) \text{Chi}\left(\frac{2 f (c+d x)}{d}\right)+4 c f \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \sinh \left(2 e-\frac{2 f (c+d x)}{d}\right)+4 d f x \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \sinh \left(2 e-\frac{2 f (c+d x)}{d}\right)-4 c f \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 f (c+d x)}{d}\right)-4 d f x \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 f (c+d x)}{d}\right)+d \sinh \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)-d \sinh \left(2 \left(f \left(\frac{c}{d}+x\right)+e\right)\right)+d \cosh \left(2 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)+d \cosh \left(2 \left(f \left(\frac{c}{d}+x\right)+e\right)\right)-4 c f \sinh (2 f x) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-4 d f x \sinh (2 f x) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-4 c f \cosh (2 f x) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-4 d f x \cosh (2 f x) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-2 d \sinh \left(\frac{2 c f}{d}\right)+2 d \cosh \left(\frac{2 c f}{d}\right)\right)}{4 a^2 d^2 (c+d x)}","\frac{f \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \sinh \left(4 e-\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{f \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \cosh \left(4 e-\frac{4 c f}{d}\right)}{a^2 d^2}-\frac{f \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a^2 d^2}-\frac{f \sinh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{a^2 d^2}+\frac{f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{a^2 d^2}+\frac{f \cosh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{a^2 d^2}-\frac{\sinh ^2(2 e+2 f x)}{4 a^2 d (c+d x)}+\frac{\sinh (2 e+2 f x)}{2 a^2 d (c+d x)}+\frac{\sinh (4 e+4 f x)}{4 a^2 d (c+d x)}-\frac{\cosh ^2(2 e+2 f x)}{4 a^2 d (c+d x)}-\frac{\cosh (2 e+2 f x)}{2 a^2 d (c+d x)}-\frac{1}{4 a^2 d (c+d x)}",1,"((-Cosh[2*(e + f*(-(c/d) + x))] + Sinh[2*(e + f*(-(c/d) + x))])*(2*d*Cosh[(2*c*f)/d] + d*Cosh[2*(e + f*(-(c/d) + x))] + d*Cosh[2*(e + f*(c/d + x))] - 2*d*Sinh[(2*c*f)/d] + 4*f*(c + d*x)*CoshIntegral[(2*f*(c + d*x))/d]*(Cosh[2*f*x] + Sinh[2*f*x]) + d*Sinh[2*(e + f*(-(c/d) + x))] - d*Sinh[2*(e + f*(c/d + x))] + 4*f*(c + d*x)*CoshIntegral[(4*f*(c + d*x))/d]*(Cosh[2*e - (2*f*(c + d*x))/d] - Sinh[2*e - (2*f*(c + d*x))/d]) - 4*c*f*Cosh[2*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 4*d*f*x*Cosh[2*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 4*c*f*Sinh[2*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 4*d*f*x*Sinh[2*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 4*c*f*Cosh[2*e - (2*f*(c + d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] - 4*d*f*x*Cosh[2*e - (2*f*(c + d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] + 4*c*f*Sinh[2*e - (2*f*(c + d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] + 4*d*f*x*Sinh[2*e - (2*f*(c + d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d]))/(4*a^2*d^2*(c + d*x))","A",1
43,1,615,336,2.8540801,"\int \frac{(c+d x)^3}{(a+a \tanh (e+f x))^3} \, dx","Integrate[(c + d*x)^3/(a + a*Tanh[e + f*x])^3,x]","\frac{\text{sech}^3(e+f x) \left(3456 c^3 f^4 x \sinh (3 (e+f x))-2592 c^3 f^3 \sinh (e+f x)+576 c^3 f^3 \sinh (3 (e+f x))+5184 c^2 d f^4 x^2 \sinh (3 (e+f x))-7776 c^2 d f^3 x \sinh (e+f x)+1728 c^2 d f^3 x \sinh (3 (e+f x))-5832 c^2 d f^2 \sinh (e+f x)+288 c^2 d f^2 \sinh (3 (e+f x))-243 \left(32 c^3 f^3+8 c^2 d f^2 (12 f x+5)+4 c d^2 f \left(24 f^2 x^2+20 f x+9\right)+d^3 \left(32 f^3 x^3+40 f^2 x^2+36 f x+17\right)\right) \cosh (e+f x)+16 \left(36 c^3 f^3 (6 f x-1)+18 c^2 d f^2 \left(18 f^2 x^2-6 f x-1\right)+6 c d^2 f \left(36 f^3 x^3-18 f^2 x^2-6 f x-1\right)+d^3 \left(54 f^4 x^4-36 f^3 x^3-18 f^2 x^2-6 f x-1\right)\right) \cosh (3 (e+f x))+3456 c d^2 f^4 x^3 \sinh (3 (e+f x))-7776 c d^2 f^3 x^2 \sinh (e+f x)+1728 c d^2 f^3 x^2 \sinh (3 (e+f x))-11664 c d^2 f^2 x \sinh (e+f x)+576 c d^2 f^2 x \sinh (3 (e+f x))-6804 c d^2 f \sinh (e+f x)+96 c d^2 f \sinh (3 (e+f x))+864 d^3 f^4 x^4 \sinh (3 (e+f x))-2592 d^3 f^3 x^3 \sinh (e+f x)+576 d^3 f^3 x^3 \sinh (3 (e+f x))-5832 d^3 f^2 x^2 \sinh (e+f x)+288 d^3 f^2 x^2 \sinh (3 (e+f x))-6804 d^3 f x \sinh (e+f x)+96 d^3 f x \sinh (3 (e+f x))-3645 d^3 \sinh (e+f x)+16 d^3 \sinh (3 (e+f x))\right)}{27648 a^3 f^4 (\tanh (e+f x)+1)^3}","-\frac{d^2 (c+d x) e^{-6 e-6 f x}}{288 a^3 f^3}-\frac{9 d^2 (c+d x) e^{-4 e-4 f x}}{256 a^3 f^3}-\frac{9 d^2 (c+d x) e^{-2 e-2 f x}}{32 a^3 f^3}-\frac{d (c+d x)^2 e^{-6 e-6 f x}}{96 a^3 f^2}-\frac{9 d (c+d x)^2 e^{-4 e-4 f x}}{128 a^3 f^2}-\frac{9 d (c+d x)^2 e^{-2 e-2 f x}}{32 a^3 f^2}-\frac{(c+d x)^3 e^{-6 e-6 f x}}{48 a^3 f}-\frac{3 (c+d x)^3 e^{-4 e-4 f x}}{32 a^3 f}-\frac{3 (c+d x)^3 e^{-2 e-2 f x}}{16 a^3 f}+\frac{(c+d x)^4}{32 a^3 d}-\frac{d^3 e^{-6 e-6 f x}}{1728 a^3 f^4}-\frac{9 d^3 e^{-4 e-4 f x}}{1024 a^3 f^4}-\frac{9 d^3 e^{-2 e-2 f x}}{64 a^3 f^4}",1,"(Sech[e + f*x]^3*(-243*(32*c^3*f^3 + 8*c^2*d*f^2*(5 + 12*f*x) + 4*c*d^2*f*(9 + 20*f*x + 24*f^2*x^2) + d^3*(17 + 36*f*x + 40*f^2*x^2 + 32*f^3*x^3))*Cosh[e + f*x] + 16*(36*c^3*f^3*(-1 + 6*f*x) + 18*c^2*d*f^2*(-1 - 6*f*x + 18*f^2*x^2) + 6*c*d^2*f*(-1 - 6*f*x - 18*f^2*x^2 + 36*f^3*x^3) + d^3*(-1 - 6*f*x - 18*f^2*x^2 - 36*f^3*x^3 + 54*f^4*x^4))*Cosh[3*(e + f*x)] - 3645*d^3*Sinh[e + f*x] - 6804*c*d^2*f*Sinh[e + f*x] - 5832*c^2*d*f^2*Sinh[e + f*x] - 2592*c^3*f^3*Sinh[e + f*x] - 6804*d^3*f*x*Sinh[e + f*x] - 11664*c*d^2*f^2*x*Sinh[e + f*x] - 7776*c^2*d*f^3*x*Sinh[e + f*x] - 5832*d^3*f^2*x^2*Sinh[e + f*x] - 7776*c*d^2*f^3*x^2*Sinh[e + f*x] - 2592*d^3*f^3*x^3*Sinh[e + f*x] + 16*d^3*Sinh[3*(e + f*x)] + 96*c*d^2*f*Sinh[3*(e + f*x)] + 288*c^2*d*f^2*Sinh[3*(e + f*x)] + 576*c^3*f^3*Sinh[3*(e + f*x)] + 96*d^3*f*x*Sinh[3*(e + f*x)] + 576*c*d^2*f^2*x*Sinh[3*(e + f*x)] + 1728*c^2*d*f^3*x*Sinh[3*(e + f*x)] + 3456*c^3*f^4*x*Sinh[3*(e + f*x)] + 288*d^3*f^2*x^2*Sinh[3*(e + f*x)] + 1728*c*d^2*f^3*x^2*Sinh[3*(e + f*x)] + 5184*c^2*d*f^4*x^2*Sinh[3*(e + f*x)] + 576*d^3*f^3*x^3*Sinh[3*(e + f*x)] + 3456*c*d^2*f^4*x^3*Sinh[3*(e + f*x)] + 864*d^3*f^4*x^4*Sinh[3*(e + f*x)]))/(27648*a^3*f^4*(1 + Tanh[e + f*x])^3)","A",1
44,1,371,246,1.5485432,"\int \frac{(c+d x)^2}{(a+a \tanh (e+f x))^3} \, dx","Integrate[(c + d*x)^2/(a + a*Tanh[e + f*x])^3,x]","\frac{\text{sech}^3(e+f x) \left(-81 \left(24 c^2 f^2+4 c d f (12 f x+5)+d^2 \left(24 f^2 x^2+20 f x+9\right)\right) \cosh (e+f x)+8 \left(18 c^2 f^2 (6 f x-1)+6 c d f \left(18 f^2 x^2-6 f x-1\right)+d^2 \left(36 f^3 x^3-18 f^2 x^2-6 f x-1\right)\right) \cosh (3 (e+f x))+864 c^2 f^3 x \sinh (3 (e+f x))-648 c^2 f^2 \sinh (e+f x)+144 c^2 f^2 \sinh (3 (e+f x))+864 c d f^3 x^2 \sinh (3 (e+f x))-1296 c d f^2 x \sinh (e+f x)+288 c d f^2 x \sinh (3 (e+f x))-972 c d f \sinh (e+f x)+48 c d f \sinh (3 (e+f x))+288 d^2 f^3 x^3 \sinh (3 (e+f x))-648 d^2 f^2 x^2 \sinh (e+f x)+144 d^2 f^2 x^2 \sinh (3 (e+f x))-972 d^2 f x \sinh (e+f x)+48 d^2 f x \sinh (3 (e+f x))-567 d^2 \sinh (e+f x)+8 d^2 \sinh (3 (e+f x))\right)}{6912 a^3 f^3 (\tanh (e+f x)+1)^3}","-\frac{d (c+d x) e^{-6 e-6 f x}}{144 a^3 f^2}-\frac{3 d (c+d x) e^{-4 e-4 f x}}{64 a^3 f^2}-\frac{3 d (c+d x) e^{-2 e-2 f x}}{16 a^3 f^2}-\frac{(c+d x)^2 e^{-6 e-6 f x}}{48 a^3 f}-\frac{3 (c+d x)^2 e^{-4 e-4 f x}}{32 a^3 f}-\frac{3 (c+d x)^2 e^{-2 e-2 f x}}{16 a^3 f}+\frac{(c+d x)^3}{24 a^3 d}-\frac{d^2 e^{-6 e-6 f x}}{864 a^3 f^3}-\frac{3 d^2 e^{-4 e-4 f x}}{256 a^3 f^3}-\frac{3 d^2 e^{-2 e-2 f x}}{32 a^3 f^3}",1,"(Sech[e + f*x]^3*(-81*(24*c^2*f^2 + 4*c*d*f*(5 + 12*f*x) + d^2*(9 + 20*f*x + 24*f^2*x^2))*Cosh[e + f*x] + 8*(18*c^2*f^2*(-1 + 6*f*x) + 6*c*d*f*(-1 - 6*f*x + 18*f^2*x^2) + d^2*(-1 - 6*f*x - 18*f^2*x^2 + 36*f^3*x^3))*Cosh[3*(e + f*x)] - 567*d^2*Sinh[e + f*x] - 972*c*d*f*Sinh[e + f*x] - 648*c^2*f^2*Sinh[e + f*x] - 972*d^2*f*x*Sinh[e + f*x] - 1296*c*d*f^2*x*Sinh[e + f*x] - 648*d^2*f^2*x^2*Sinh[e + f*x] + 8*d^2*Sinh[3*(e + f*x)] + 48*c*d*f*Sinh[3*(e + f*x)] + 144*c^2*f^2*Sinh[3*(e + f*x)] + 48*d^2*f*x*Sinh[3*(e + f*x)] + 288*c*d*f^2*x*Sinh[3*(e + f*x)] + 864*c^2*f^3*x*Sinh[3*(e + f*x)] + 144*d^2*f^2*x^2*Sinh[3*(e + f*x)] + 864*c*d*f^3*x^2*Sinh[3*(e + f*x)] + 288*d^2*f^3*x^3*Sinh[3*(e + f*x)]))/(6912*a^3*f^3*(1 + Tanh[e + f*x])^3)","A",1
45,1,185,183,0.7977925,"\int \frac{c+d x}{(a+a \tanh (e+f x))^3} \, dx","Integrate[(c + d*x)/(a + a*Tanh[e + f*x])^3,x]","\frac{\text{sech}^3(e+f x) \left(4 \left(6 c f (6 f x-1)+d \left(18 f^2 x^2-6 f x-1\right)\right) \cosh (3 (e+f x))-27 (12 c f+d (12 f x+5)) \cosh (e+f x)+144 c f^2 x \sinh (3 (e+f x))-108 c f \sinh (e+f x)+24 c f \sinh (3 (e+f x))+72 d f^2 x^2 \sinh (3 (e+f x))-108 d f x \sinh (e+f x)+24 d f x \sinh (3 (e+f x))-81 d \sinh (e+f x)+4 d \sinh (3 (e+f x))\right)}{1152 a^3 f^2 (\tanh (e+f x)+1)^3}","-\frac{c+d x}{8 f \left(a^3 \tanh (e+f x)+a^3\right)}+\frac{x (c+d x)}{8 a^3}-\frac{11 d}{96 f^2 \left(a^3 \tanh (e+f x)+a^3\right)}+\frac{11 d x}{96 a^3 f}-\frac{d x^2}{16 a^3}-\frac{c+d x}{8 a f (a \tanh (e+f x)+a)^2}-\frac{c+d x}{6 f (a \tanh (e+f x)+a)^3}-\frac{5 d}{96 a f^2 (a \tanh (e+f x)+a)^2}-\frac{d}{36 f^2 (a \tanh (e+f x)+a)^3}",1,"(Sech[e + f*x]^3*(-27*(12*c*f + d*(5 + 12*f*x))*Cosh[e + f*x] + 4*(6*c*f*(-1 + 6*f*x) + d*(-1 - 6*f*x + 18*f^2*x^2))*Cosh[3*(e + f*x)] - 81*d*Sinh[e + f*x] - 108*c*f*Sinh[e + f*x] - 108*d*f*x*Sinh[e + f*x] + 4*d*Sinh[3*(e + f*x)] + 24*c*f*Sinh[3*(e + f*x)] + 24*d*f*x*Sinh[3*(e + f*x)] + 144*c*f^2*x*Sinh[3*(e + f*x)] + 72*d*f^2*x^2*Sinh[3*(e + f*x)]))/(1152*a^3*f^2*(1 + Tanh[e + f*x])^3)","A",1
46,1,312,437,0.7199491,"\int \frac{1}{(c+d x) (a+a \tanh (e+f x))^3} \, dx","Integrate[1/((c + d*x)*(a + a*Tanh[e + f*x])^3),x]","\frac{\text{sech}^3(e+f x) (\sinh (f x)+\cosh (f x))^3 \left(\left(\cosh \left(e-\frac{4 c f}{d}\right)-\sinh \left(e-\frac{4 c f}{d}\right)\right) \left(-\text{Chi}\left(\frac{6 f (c+d x)}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)+\text{Chi}\left(\frac{6 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)+3 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \left(\sinh \left(2 e-\frac{2 c f}{d}\right)+\cosh \left(2 e-\frac{2 c f}{d}\right)\right)+3 \text{Chi}\left(\frac{4 f (c+d x)}{d}\right)-3 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+\sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{6 f (c+d x)}{d}\right)-3 \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-\cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{6 f (c+d x)}{d}\right)-3 \text{Shi}\left(\frac{4 f (c+d x)}{d}\right)\right)+\sinh (3 e) \log (f (c+d x))+\cosh (3 e) \log (f (c+d x))\right)}{8 a^3 d (\tanh (e+f x)+1)^3}","-\frac{3 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{8 a^3 d}-\frac{\text{Chi}\left(6 x f+\frac{6 c f}{d}\right) \sinh \left(6 e-\frac{6 c f}{d}\right)}{8 a^3 d}-\frac{3 \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \sinh \left(4 e-\frac{4 c f}{d}\right)}{8 a^3 d}+\frac{3 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{8 a^3 d}+\frac{3 \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \cosh \left(4 e-\frac{4 c f}{d}\right)}{8 a^3 d}+\frac{\text{Chi}\left(6 x f+\frac{6 c f}{d}\right) \cosh \left(6 e-\frac{6 c f}{d}\right)}{8 a^3 d}+\frac{3 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{8 a^3 d}+\frac{3 \sinh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{8 a^3 d}+\frac{\sinh \left(6 e-\frac{6 c f}{d}\right) \text{Shi}\left(6 x f+\frac{6 c f}{d}\right)}{8 a^3 d}-\frac{3 \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{8 a^3 d}-\frac{3 \cosh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{8 a^3 d}-\frac{\cosh \left(6 e-\frac{6 c f}{d}\right) \text{Shi}\left(6 x f+\frac{6 c f}{d}\right)}{8 a^3 d}+\frac{\log (c+d x)}{8 a^3 d}",1,"(Sech[e + f*x]^3*(Cosh[f*x] + Sinh[f*x])^3*(Cosh[3*e]*Log[f*(c + d*x)] + Log[f*(c + d*x)]*Sinh[3*e] + (Cosh[e - (4*c*f)/d] - Sinh[e - (4*c*f)/d])*(3*CoshIntegral[(4*f*(c + d*x))/d] + Cosh[2*e - (2*c*f)/d]*CoshIntegral[(6*f*(c + d*x))/d] - CoshIntegral[(6*f*(c + d*x))/d]*Sinh[2*e - (2*c*f)/d] + 3*CoshIntegral[(2*f*(c + d*x))/d]*(Cosh[2*e - (2*c*f)/d] + Sinh[2*e - (2*c*f)/d]) - 3*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] - 3*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] - 3*SinhIntegral[(4*f*(c + d*x))/d] - Cosh[2*e - (2*c*f)/d]*SinhIntegral[(6*f*(c + d*x))/d] + Sinh[2*e - (2*c*f)/d]*SinhIntegral[(6*f*(c + d*x))/d])))/(8*a^3*d*(1 + Tanh[e + f*x])^3)","A",1
47,1,794,692,3.1311893,"\int \frac{1}{(c+d x)^2 (a+a \tanh (e+f x))^3} \, dx","Integrate[1/((c + d*x)^2*(a + a*Tanh[e + f*x])^3),x]","-\frac{\text{sech}^3(e+f x) \left(\sinh \left(\frac{3 c f}{d}\right)+\cosh \left(\frac{3 c f}{d}\right)\right) \left(-6 c f \text{Chi}\left(\frac{6 f (c+d x)}{d}\right) \sinh \left(3 e-\frac{3 f (c+d x)}{d}\right)-6 d f x \text{Chi}\left(\frac{6 f (c+d x)}{d}\right) \sinh \left(3 e-\frac{3 f (c+d x)}{d}\right)+6 c f \text{Chi}\left(\frac{6 f (c+d x)}{d}\right) \cosh \left(3 e-\frac{3 f (c+d x)}{d}\right)+6 d f x \text{Chi}\left(\frac{6 f (c+d x)}{d}\right) \cosh \left(3 e-\frac{3 f (c+d x)}{d}\right)+6 f (c+d x) \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \left(\sinh \left(-\frac{c f}{d}+e+3 f x\right)+\cosh \left(-\frac{c f}{d}+e+3 f x\right)\right)+12 f (c+d x) \text{Chi}\left(\frac{4 f (c+d x)}{d}\right) \left(\cosh \left(e-\frac{f (c+3 d x)}{d}\right)-\sinh \left(e-\frac{f (c+3 d x)}{d}\right)\right)-6 c f \text{Shi}\left(\frac{2 f (c+d x)}{d}\right) \sinh \left(-\frac{c f}{d}+e+3 f x\right)-6 d f x \text{Shi}\left(\frac{2 f (c+d x)}{d}\right) \sinh \left(-\frac{c f}{d}+e+3 f x\right)+12 c f \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \sinh \left(e-\frac{f (c+3 d x)}{d}\right)+12 d f x \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \sinh \left(e-\frac{f (c+3 d x)}{d}\right)+6 c f \text{Shi}\left(\frac{6 f (c+d x)}{d}\right) \sinh \left(3 e-\frac{3 f (c+d x)}{d}\right)+6 d f x \text{Shi}\left(\frac{6 f (c+d x)}{d}\right) \sinh \left(3 e-\frac{3 f (c+d x)}{d}\right)-6 c f \text{Shi}\left(\frac{2 f (c+d x)}{d}\right) \cosh \left(-\frac{c f}{d}+e+3 f x\right)-6 d f x \text{Shi}\left(\frac{2 f (c+d x)}{d}\right) \cosh \left(-\frac{c f}{d}+e+3 f x\right)-12 c f \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \cosh \left(e-\frac{f (c+3 d x)}{d}\right)-12 d f x \text{Shi}\left(\frac{4 f (c+d x)}{d}\right) \cosh \left(e-\frac{f (c+3 d x)}{d}\right)-6 c f \text{Shi}\left(\frac{6 f (c+d x)}{d}\right) \cosh \left(3 e-\frac{3 f (c+d x)}{d}\right)-6 d f x \text{Shi}\left(\frac{6 f (c+d x)}{d}\right) \cosh \left(3 e-\frac{3 f (c+d x)}{d}\right)+3 d \sinh \left(f \left(x-\frac{3 c}{d}\right)+e\right)+d \sinh \left(3 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)-d \sinh \left(3 \left(f \left(\frac{c}{d}+x\right)+e\right)\right)-3 d \sinh \left(f \left(\frac{3 c}{d}+x\right)+e\right)+3 d \cosh \left(f \left(x-\frac{3 c}{d}\right)+e\right)+d \cosh \left(3 \left(f \left(x-\frac{c}{d}\right)+e\right)\right)+d \cosh \left(3 \left(f \left(\frac{c}{d}+x\right)+e\right)\right)+3 d \cosh \left(f \left(\frac{3 c}{d}+x\right)+e\right)\right)}{8 a^3 d^2 (c+d x) (\tanh (e+f x)+1)^3}","\frac{3 f \text{Chi}\left(6 x f+\frac{6 c f}{d}\right) \sinh \left(6 e-\frac{6 c f}{d}\right)}{4 a^3 d^2}+\frac{3 f \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \sinh \left(4 e-\frac{4 c f}{d}\right)}{2 a^3 d^2}+\frac{3 f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \text{Chi}\left(4 x f+\frac{4 c f}{d}\right) \cosh \left(4 e-\frac{4 c f}{d}\right)}{2 a^3 d^2}-\frac{3 f \text{Chi}\left(6 x f+\frac{6 c f}{d}\right) \cosh \left(6 e-\frac{6 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{4 a^3 d^2}-\frac{3 f \sinh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{2 a^3 d^2}-\frac{3 f \sinh \left(6 e-\frac{6 c f}{d}\right) \text{Shi}\left(6 x f+\frac{6 c f}{d}\right)}{4 a^3 d^2}+\frac{3 f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{4 a^3 d^2}+\frac{3 f \cosh \left(4 e-\frac{4 c f}{d}\right) \text{Shi}\left(4 x f+\frac{4 c f}{d}\right)}{2 a^3 d^2}+\frac{3 f \cosh \left(6 e-\frac{6 c f}{d}\right) \text{Shi}\left(6 x f+\frac{6 c f}{d}\right)}{4 a^3 d^2}+\frac{\sinh ^3(2 e+2 f x)}{8 a^3 d (c+d x)}-\frac{3 \sinh ^2(2 e+2 f x)}{8 a^3 d (c+d x)}+\frac{15 \sinh (2 e+2 f x)}{32 a^3 d (c+d x)}+\frac{3 \sinh (4 e+4 f x)}{8 a^3 d (c+d x)}+\frac{3 \sinh (6 e+6 f x)}{32 a^3 d (c+d x)}-\frac{\cosh ^3(2 e+2 f x)}{8 a^3 d (c+d x)}-\frac{3 \cosh ^2(2 e+2 f x)}{8 a^3 d (c+d x)}-\frac{9 \cosh (2 e+2 f x)}{32 a^3 d (c+d x)}-\frac{3 \cosh (6 e+6 f x)}{32 a^3 d (c+d x)}-\frac{1}{8 a^3 d (c+d x)}",1,"-1/8*(Sech[e + f*x]^3*(Cosh[(3*c*f)/d] + Sinh[(3*c*f)/d])*(3*d*Cosh[e + f*((-3*c)/d + x)] + d*Cosh[3*(e + f*(-(c/d) + x))] + d*Cosh[3*(e + f*(c/d + x))] + 3*d*Cosh[e + f*((3*c)/d + x)] + 6*c*f*Cosh[3*e - (3*f*(c + d*x))/d]*CoshIntegral[(6*f*(c + d*x))/d] + 6*d*f*x*Cosh[3*e - (3*f*(c + d*x))/d]*CoshIntegral[(6*f*(c + d*x))/d] + 6*f*(c + d*x)*CoshIntegral[(2*f*(c + d*x))/d]*(Cosh[e - (c*f)/d + 3*f*x] + Sinh[e - (c*f)/d + 3*f*x]) + 3*d*Sinh[e + f*((-3*c)/d + x)] + d*Sinh[3*(e + f*(-(c/d) + x))] - d*Sinh[3*(e + f*(c/d + x))] - 3*d*Sinh[e + f*((3*c)/d + x)] - 6*c*f*CoshIntegral[(6*f*(c + d*x))/d]*Sinh[3*e - (3*f*(c + d*x))/d] - 6*d*f*x*CoshIntegral[(6*f*(c + d*x))/d]*Sinh[3*e - (3*f*(c + d*x))/d] + 12*f*(c + d*x)*CoshIntegral[(4*f*(c + d*x))/d]*(Cosh[e - (f*(c + 3*d*x))/d] - Sinh[e - (f*(c + 3*d*x))/d]) - 6*c*f*Cosh[e - (c*f)/d + 3*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 6*d*f*x*Cosh[e - (c*f)/d + 3*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 6*c*f*Sinh[e - (c*f)/d + 3*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 6*d*f*x*Sinh[e - (c*f)/d + 3*f*x]*SinhIntegral[(2*f*(c + d*x))/d] - 12*c*f*Cosh[e - (f*(c + 3*d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] - 12*d*f*x*Cosh[e - (f*(c + 3*d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] + 12*c*f*Sinh[e - (f*(c + 3*d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] + 12*d*f*x*Sinh[e - (f*(c + 3*d*x))/d]*SinhIntegral[(4*f*(c + d*x))/d] - 6*c*f*Cosh[3*e - (3*f*(c + d*x))/d]*SinhIntegral[(6*f*(c + d*x))/d] - 6*d*f*x*Cosh[3*e - (3*f*(c + d*x))/d]*SinhIntegral[(6*f*(c + d*x))/d] + 6*c*f*Sinh[3*e - (3*f*(c + d*x))/d]*SinhIntegral[(6*f*(c + d*x))/d] + 6*d*f*x*Sinh[3*e - (3*f*(c + d*x))/d]*SinhIntegral[(6*f*(c + d*x))/d]))/(a^3*d^2*(c + d*x)*(1 + Tanh[e + f*x])^3)","A",0
48,0,0,23,34.6536735,"\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx","Integrate[(c + d*x)^m*(a + a*Tanh[e + f*x])^2,x]","\int (c+d x)^m (a+a \tanh (e+f x))^2 \, dx","\text{Int}\left((c+d x)^m (a \tanh (e+f x)+a)^2,x\right)",0,"Integrate[(c + d*x)^m*(a + a*Tanh[e + f*x])^2, x]","A",-1
49,0,0,21,13.9848227,"\int (c+d x)^m (a+a \tanh (e+f x)) \, dx","Integrate[(c + d*x)^m*(a + a*Tanh[e + f*x]),x]","\int (c+d x)^m (a+a \tanh (e+f x)) \, dx","\text{Int}\left((c+d x)^m (a \tanh (e+f x)+a),x\right)",0,"Integrate[(c + d*x)^m*(a + a*Tanh[e + f*x]), x]","A",-1
50,1,186,89,1.1981678,"\int \frac{(c+d x)^m}{a+a \tanh (e+f x)} \, dx","Integrate[(c + d*x)^m/(a + a*Tanh[e + f*x]),x]","\frac{2^{-m-2} (c+d x)^m \text{sech}(e+f x) \left(-\frac{f (c+d x)}{d}\right)^m \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(\sinh \left(f \left(\frac{c}{d}+x\right)\right)+\cosh \left(f \left(\frac{c}{d}+x\right)\right)\right) \left(f 2^{m+1} (c+d x) \left(f \left(\frac{c}{d}+x\right)\right)^m \left(\sinh \left(e-\frac{c f}{d}\right)+\cosh \left(e-\frac{c f}{d}\right)\right)+d (m+1) \left(\sinh \left(e-\frac{c f}{d}\right)-\cosh \left(e-\frac{c f}{d}\right)\right) \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)\right)}{a d f (m+1) (\tanh (e+f x)+1)}","\frac{(c+d x)^{m+1}}{2 a d (m+1)}-\frac{2^{-m-2} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{a f}",1,"(2^(-2 - m)*(c + d*x)^m*(-((f*(c + d*x))/d))^m*Sech[e + f*x]*(d*(1 + m)*Gamma[1 + m, (2*f*(c + d*x))/d]*(-Cosh[e - (c*f)/d] + Sinh[e - (c*f)/d]) + 2^(1 + m)*f*(f*(c/d + x))^m*(c + d*x)*(Cosh[e - (c*f)/d] + Sinh[e - (c*f)/d]))*(Cosh[f*(c/d + x)] + Sinh[f*(c/d + x)]))/(a*d*f*(1 + m)*(-((f^2*(c + d*x)^2)/d^2))^m*(1 + Tanh[e + f*x]))","B",1
51,1,195,153,11.1728723,"\int \frac{(c+d x)^m}{(a+a \tanh (e+f x))^2} \, dx","Integrate[(c + d*x)^m/(a + a*Tanh[e + f*x])^2,x]","\frac{4^{-m-2} (c+d x)^m \text{sech}^2(e+f x) (\sinh (2 f x)+\cosh (2 f x)) \left(-\frac{f (c+d x)}{d}\right)^m \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(d 4^{m+1} (\sinh (e)+\cosh (e))^2 \left(\frac{f (c+d x)}{d}\right)^{m+1}-d (m+1) e^{\frac{4 c f}{d}} (\cosh (2 e)-\sinh (2 e)) \Gamma \left(m+1,\frac{4 f (c+d x)}{d}\right)-d 2^{m+2} (m+1) e^{\frac{2 c f}{d}} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)\right)}{a^2 d f (m+1) (\tanh (e+f x)+1)^2}","-\frac{2^{-m-2} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{a^2 f}-\frac{4^{-m-2} e^{\frac{4 c f}{d}-4 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{4 f (c+d x)}{d}\right)}{a^2 f}+\frac{(c+d x)^{m+1}}{4 a^2 d (m+1)}",1,"(4^(-2 - m)*(c + d*x)^m*(-((f*(c + d*x))/d))^m*Sech[e + f*x]^2*(-(2^(2 + m)*d*E^((2*c*f)/d)*(1 + m)*Gamma[1 + m, (2*f*(c + d*x))/d]) + 4^(1 + m)*d*((f*(c + d*x))/d)^(1 + m)*(Cosh[e] + Sinh[e])^2 - d*E^((4*c*f)/d)*(1 + m)*Gamma[1 + m, (4*f*(c + d*x))/d]*(Cosh[2*e] - Sinh[2*e]))*(Cosh[2*f*x] + Sinh[2*f*x]))/(a^2*d*f*(1 + m)*(-((f^2*(c + d*x)^2)/d^2))^m*(1 + Tanh[e + f*x])^2)","A",1
52,-1,0,224,180.001988,"\int \frac{(c+d x)^m}{(a+a \tanh (e+f x))^3} \, dx","Integrate[(c + d*x)^m/(a + a*Tanh[e + f*x])^3,x]","\text{\$Aborted}","-\frac{3\ 2^{-m-4} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{a^3 f}-\frac{3\ 2^{-2 m-5} e^{\frac{4 c f}{d}-4 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{4 f (c+d x)}{d}\right)}{a^3 f}-\frac{2^{-m-4} 3^{-m-1} e^{\frac{6 c f}{d}-6 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{6 f (c+d x)}{d}\right)}{a^3 f}+\frac{(c+d x)^{m+1}}{8 a^3 d (m+1)}",1,"$Aborted","F",-1
53,1,161,137,2.1707087,"\int (c+d x)^3 (a+b \tanh (e+f x)) \, dx","Integrate[(c + d*x)^3*(a + b*Tanh[e + f*x]),x]","\frac{1}{4} \left(x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) (a+b \tanh (e))+b \left(-\frac{3 d \left(2 f^2 (c+d x)^2 \text{Li}_2\left(-e^{-2 (e+f x)}\right)+d \left(2 f (c+d x) \text{Li}_3\left(-e^{-2 (e+f x)}\right)+d \text{Li}_4\left(-e^{-2 (e+f x)}\right)\right)\right)}{f^4}+\frac{4 (c+d x)^3 \log \left(e^{-2 (e+f x)}+1\right)}{f}+\frac{2 (c+d x)^4}{d \left(e^{2 e}+1\right)}\right)\right)","\frac{a (c+d x)^4}{4 d}-\frac{3 b d^2 (c+d x) \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 b d (c+d x)^2 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^2}+\frac{b (c+d x)^3 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{b (c+d x)^4}{4 d}+\frac{3 b d^3 \text{Li}_4\left(-e^{2 (e+f x)}\right)}{4 f^4}",1,"(b*((2*(c + d*x)^4)/(d*(1 + E^(2*e))) + (4*(c + d*x)^3*Log[1 + E^(-2*(e + f*x))])/f - (3*d*(2*f^2*(c + d*x)^2*PolyLog[2, -E^(-2*(e + f*x))] + d*(2*f*(c + d*x)*PolyLog[3, -E^(-2*(e + f*x))] + d*PolyLog[4, -E^(-2*(e + f*x))])))/f^4) + x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*(a + b*Tanh[e]))/4","A",1
54,1,147,103,1.7675595,"\int (c+d x)^2 (a+b \tanh (e+f x)) \, dx","Integrate[(c + d*x)^2*(a + b*Tanh[e + f*x]),x]","\frac{1}{6} \left(2 x \left(3 c^2+3 c d x+d^2 x^2\right) (a+b \tanh (e))+\frac{b e^{2 e} \left(-\frac{3 d \left(e^{-2 e}+1\right) \left(2 f (c+d x) \text{Li}_2\left(-e^{-2 (e+f x)}\right)+d \text{Li}_3\left(-e^{-2 (e+f x)}\right)\right)}{f^3}+\frac{6 \left(e^{-2 e}+1\right) (c+d x)^2 \log \left(e^{-2 (e+f x)}+1\right)}{f}+\frac{4 e^{-2 e} (c+d x)^3}{d}\right)}{e^{2 e}+1}\right)","\frac{a (c+d x)^3}{3 d}+\frac{b d (c+d x) \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^2}+\frac{b (c+d x)^2 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{b (c+d x)^3}{3 d}-\frac{b d^2 \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^3}",1,"((b*E^(2*e)*((4*(c + d*x)^3)/(d*E^(2*e)) + (6*(1 + E^(-2*e))*(c + d*x)^2*Log[1 + E^(-2*(e + f*x))])/f - (3*d*(1 + E^(-2*e))*(2*f*(c + d*x)*PolyLog[2, -E^(-2*(e + f*x))] + d*PolyLog[3, -E^(-2*(e + f*x))]))/f^3))/(1 + E^(2*e)) + 2*x*(3*c^2 + 3*c*d*x + d^2*x^2)*(a + b*Tanh[e]))/6","A",1
55,1,226,75,4.2630554,"\int (c+d x) (a+b \tanh (e+f x)) \, dx","Integrate[(c + d*x)*(a + b*Tanh[e + f*x]),x]","a c x+\frac{1}{2} a d x^2+\frac{b c \log (\cosh (e+f x))}{f}+\frac{b d \text{csch}(e) \text{sech}(e) \left(f^2 x^2 e^{-\tanh ^{-1}(\coth (e))}-\frac{i \coth (e) \left(i \text{Li}_2\left(e^{2 i \left(i f x+i \tanh ^{-1}(\coth (e))\right)}\right)-f x \left(-\pi +2 i \tanh ^{-1}(\coth (e))\right)-2 \left(i \tanh ^{-1}(\coth (e))+i f x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\coth (e))+i f x\right)}\right)+2 i \tanh ^{-1}(\coth (e)) \log \left(i \sinh \left(\tanh ^{-1}(\coth (e))+f x\right)\right)-\pi  \log \left(e^{2 f x}+1\right)+\pi  \log (\cosh (f x))\right)}{\sqrt{1-\coth ^2(e)}}\right)}{2 f^2 \sqrt{\text{csch}^2(e) \left(\sinh ^2(e)-\cosh ^2(e)\right)}}+\frac{1}{2} b d x^2 \tanh (e)","\frac{a (c+d x)^2}{2 d}+\frac{b (c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{b (c+d x)^2}{2 d}+\frac{b d \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^2}",1,"a*c*x + (a*d*x^2)/2 + (b*c*Log[Cosh[e + f*x]])/f + (b*d*Csch[e]*((f^2*x^2)/E^ArcTanh[Coth[e]] - (I*Coth[e]*(-(f*x*(-Pi + (2*I)*ArcTanh[Coth[e]])) - Pi*Log[1 + E^(2*f*x)] - 2*(I*f*x + I*ArcTanh[Coth[e]])*Log[1 - E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))] + Pi*Log[Cosh[f*x]] + (2*I)*ArcTanh[Coth[e]]*Log[I*Sinh[f*x + ArcTanh[Coth[e]]]] + I*PolyLog[2, E^((2*I)*(I*f*x + I*ArcTanh[Coth[e]]))]))/Sqrt[1 - Coth[e]^2])*Sech[e])/(2*f^2*Sqrt[Csch[e]^2*(-Cosh[e]^2 + Sinh[e]^2)]) + (b*d*x^2*Tanh[e])/2","C",0
56,0,0,21,4.5546629,"\int \frac{a+b \tanh (e+f x)}{c+d x} \, dx","Integrate[(a + b*Tanh[e + f*x])/(c + d*x),x]","\int \frac{a+b \tanh (e+f x)}{c+d x} \, dx","\text{Int}\left(\frac{a+b \tanh (e+f x)}{c+d x},x\right)",0,"Integrate[(a + b*Tanh[e + f*x])/(c + d*x), x]","A",-1
57,0,0,21,11.398826,"\int \frac{a+b \tanh (e+f x)}{(c+d x)^2} \, dx","Integrate[(a + b*Tanh[e + f*x])/(c + d*x)^2,x]","\int \frac{a+b \tanh (e+f x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{a+b \tanh (e+f x)}{(c+d x)^2},x\right)",0,"Integrate[(a + b*Tanh[e + f*x])/(c + d*x)^2, x]","A",-1
58,1,508,277,7.9013843,"\int (c+d x)^3 (a+b \tanh (e+f x))^2 \, dx","Integrate[(c + d*x)^3*(a + b*Tanh[e + f*x])^2,x]","\frac{1}{8} \left(\frac{\text{sech}(e) \text{sech}(e+f x) \left(f x \left(a^2+b^2\right) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \cosh (2 e+f x)+f x \left(a^2+b^2\right) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \cosh (f x)+2 a b f x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \sinh (2 e+f x)-2 b \sinh (f x) \left(a f x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)+4 b (c+d x)^3\right)\right)}{f}+4 b \left(-\frac{2 c^2 \left(2 f x-\log \left(e^{2 (e+f x)}+1\right)\right) (2 a c f+3 b d)}{f^2}-\frac{3 d^2 \left(2 f x \text{Li}_2\left(-e^{-2 (e+f x)}\right)+\text{Li}_3\left(-e^{-2 (e+f x)}\right)\right) (2 a c f+b d)}{f^4}+\frac{6 d^2 x^2 \log \left(e^{-2 (e+f x)}+1\right) (2 a c f+b d)}{f^2}-\frac{6 c d \text{Li}_2\left(-e^{-2 (e+f x)}\right) (a c f+b d)}{f^3}+\frac{12 c d x \log \left(e^{-2 (e+f x)}+1\right) (a c f+b d)}{f^2}+\frac{2 a (c+d x)^4}{d \left(e^{2 e}+1\right)}-\frac{3 a d^3 \left(2 f^2 x^2 \text{Li}_2\left(-e^{-2 (e+f x)}\right)+2 f x \text{Li}_3\left(-e^{-2 (e+f x)}\right)+\text{Li}_4\left(-e^{-2 (e+f x)}\right)\right)}{f^4}+\frac{4 a d^3 x^3 \log \left(e^{-2 (e+f x)}+1\right)}{f}+\frac{4 b (c+d x)^3}{\left(e^{2 e}+1\right) f}\right)\right)","\frac{a^2 (c+d x)^4}{4 d}-\frac{3 a b d^2 (c+d x) \text{Li}_3\left(-e^{2 (e+f x)}\right)}{f^3}+\frac{3 a b d (c+d x)^2 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^2}+\frac{2 a b (c+d x)^3 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{a b (c+d x)^4}{2 d}+\frac{3 a b d^3 \text{Li}_4\left(-e^{2 (e+f x)}\right)}{2 f^4}+\frac{3 b^2 d^2 (c+d x) \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^3}+\frac{3 b^2 d (c+d x)^2 \log \left(e^{2 (e+f x)}+1\right)}{f^2}-\frac{b^2 (c+d x)^3 \tanh (e+f x)}{f}-\frac{b^2 (c+d x)^3}{f}+\frac{b^2 (c+d x)^4}{4 d}-\frac{3 b^2 d^3 \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^4}",1,"(4*b*((4*b*(c + d*x)^3)/((1 + E^(2*e))*f) + (2*a*(c + d*x)^4)/(d*(1 + E^(2*e))) + (12*c*d*(b*d + a*c*f)*x*Log[1 + E^(-2*(e + f*x))])/f^2 + (6*d^2*(b*d + 2*a*c*f)*x^2*Log[1 + E^(-2*(e + f*x))])/f^2 + (4*a*d^3*x^3*Log[1 + E^(-2*(e + f*x))])/f - (2*c^2*(3*b*d + 2*a*c*f)*(2*f*x - Log[1 + E^(2*(e + f*x))]))/f^2 - (6*c*d*(b*d + a*c*f)*PolyLog[2, -E^(-2*(e + f*x))])/f^3 - (3*d^2*(b*d + 2*a*c*f)*(2*f*x*PolyLog[2, -E^(-2*(e + f*x))] + PolyLog[3, -E^(-2*(e + f*x))]))/f^4 - (3*a*d^3*(2*f^2*x^2*PolyLog[2, -E^(-2*(e + f*x))] + 2*f*x*PolyLog[3, -E^(-2*(e + f*x))] + PolyLog[4, -E^(-2*(e + f*x))]))/f^4) + (Sech[e]*Sech[e + f*x]*((a^2 + b^2)*f*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Cosh[f*x] + (a^2 + b^2)*f*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Cosh[2*e + f*x] - 2*b*(4*b*(c + d*x)^3 + a*f*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3))*Sinh[f*x] + 2*a*b*f*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Sinh[2*e + f*x]))/f)/8","A",1
59,1,232,211,5.7580057,"\int (c+d x)^2 (a+b \tanh (e+f x))^2 \, dx","Integrate[(c + d*x)^2*(a + b*Tanh[e + f*x])^2,x]","\frac{1}{3} \left(x \left(3 c^2+3 c d x+d^2 x^2\right) \left(a^2+2 a b \tanh (e)+b^2\right)+\frac{b \left(2 f \left(\frac{f x \left(2 a f \left(-3 c^2 e^{2 e}+3 c d x+d^2 x^2\right)+3 b d \left(d x-2 c e^{2 e}\right)\right)}{e^{2 e}+1}+3 d x \log \left(e^{-2 (e+f x)}+1\right) (a f (2 c+d x)+b d)+3 c \log \left(e^{2 (e+f x)}+1\right) (a c f+b d)\right)-3 d \text{Li}_2\left(-e^{-2 (e+f x)}\right) (2 a f (c+d x)+b d)-3 a d^2 \text{Li}_3\left(-e^{-2 (e+f x)}\right)\right)}{f^3}-\frac{3 b^2 \text{sech}(e) (c+d x)^2 \sinh (f x) \text{sech}(e+f x)}{f}\right)","\frac{a^2 (c+d x)^3}{3 d}+\frac{2 a b d (c+d x) \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^2}+\frac{2 a b (c+d x)^2 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{2 a b (c+d x)^3}{3 d}-\frac{a b d^2 \text{Li}_3\left(-e^{2 (e+f x)}\right)}{f^3}+\frac{2 b^2 d (c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f^2}-\frac{b^2 (c+d x)^2 \tanh (e+f x)}{f}-\frac{b^2 (c+d x)^2}{f}+\frac{b^2 (c+d x)^3}{3 d}+\frac{b^2 d^2 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^3}",1,"((b*(2*f*((f*x*(3*b*d*(-2*c*E^(2*e) + d*x) + 2*a*f*(-3*c^2*E^(2*e) + 3*c*d*x + d^2*x^2)))/(1 + E^(2*e)) + 3*d*x*(b*d + a*f*(2*c + d*x))*Log[1 + E^(-2*(e + f*x))] + 3*c*(b*d + a*c*f)*Log[1 + E^(2*(e + f*x))]) - 3*d*(b*d + 2*a*f*(c + d*x))*PolyLog[2, -E^(-2*(e + f*x))] - 3*a*d^2*PolyLog[3, -E^(-2*(e + f*x))]))/f^3 - (3*b^2*(c + d*x)^2*Sech[e]*Sech[e + f*x]*Sinh[f*x])/f + x*(3*c^2 + 3*c*d*x + d^2*x^2)*(a^2 + b^2 + 2*a*b*Tanh[e]))/3","A",1
60,1,192,127,2.4497281,"\int (c+d x) (a+b \tanh (e+f x))^2 \, dx","Integrate[(c + d*x)*(a + b*Tanh[e + f*x])^2,x]","\frac{\cosh (e+f x) (a+b \tanh (e+f x))^2 \left(\cosh (e+f x) \left(-\left((e+f x) \left(a^2 (-2 c f+d e-d f x)-2 a b d (e+f x)+b^2 (-2 c f+d e-d f x)\right)\right)+2 b \log (\cosh (e+f x)) (2 a c f-2 a d e+b d)+4 a b d (e+f x) \log \left(e^{-2 (e+f x)}+1\right)\right)-2 a b d \text{Li}_2\left(-e^{-2 (e+f x)}\right) \cosh (e+f x)-2 b^2 f (c+d x) \sinh (e+f x)\right)}{2 f^2 (a \cosh (e+f x)+b \sinh (e+f x))^2}","\frac{a^2 (c+d x)^2}{2 d}+\frac{2 a b (c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{a b (c+d x)^2}{d}+\frac{a b d \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^2}-\frac{b^2 (c+d x) \tanh (e+f x)}{f}+b^2 c x+\frac{b^2 d \log (\cosh (e+f x))}{f^2}+\frac{1}{2} b^2 d x^2",1,"(Cosh[e + f*x]*(Cosh[e + f*x]*(-((e + f*x)*(-2*a*b*d*(e + f*x) + a^2*(d*e - 2*c*f - d*f*x) + b^2*(d*e - 2*c*f - d*f*x))) + 4*a*b*d*(e + f*x)*Log[1 + E^(-2*(e + f*x))] + 2*b*(b*d - 2*a*d*e + 2*a*c*f)*Log[Cosh[e + f*x]]) - 2*a*b*d*Cosh[e + f*x]*PolyLog[2, -E^(-2*(e + f*x))] - 2*b^2*f*(c + d*x)*Sinh[e + f*x])*(a + b*Tanh[e + f*x])^2)/(2*f^2*(a*Cosh[e + f*x] + b*Sinh[e + f*x])^2)","A",1
61,0,0,23,41.5898302,"\int \frac{(a+b \tanh (e+f x))^2}{c+d x} \, dx","Integrate[(a + b*Tanh[e + f*x])^2/(c + d*x),x]","\int \frac{(a+b \tanh (e+f x))^2}{c+d x} \, dx","\text{Int}\left(\frac{(a+b \tanh (e+f x))^2}{c+d x},x\right)",0,"Integrate[(a + b*Tanh[e + f*x])^2/(c + d*x), x]","A",-1
62,0,0,23,27.1741543,"\int \frac{(a+b \tanh (e+f x))^2}{(c+d x)^2} \, dx","Integrate[(a + b*Tanh[e + f*x])^2/(c + d*x)^2,x]","\int \frac{(a+b \tanh (e+f x))^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{(a+b \tanh (e+f x))^2}{(c+d x)^2},x\right)",0,"Integrate[(a + b*Tanh[e + f*x])^2/(c + d*x)^2, x]","A",-1
63,1,2010,566,14.6078219,"\int (c+d x)^3 (a+b \tanh (e+f x))^3 \, dx","Integrate[(c + d*x)^3*(a + b*Tanh[e + f*x])^3,x]","\text{Result too large to show}","\frac{a^3 (c+d x)^4}{4 d}-\frac{9 a^2 b d^2 (c+d x) \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^3}+\frac{9 a^2 b d (c+d x)^2 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^2}+\frac{3 a^2 b (c+d x)^3 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{3 a^2 b (c+d x)^4}{4 d}+\frac{9 a^2 b d^3 \text{Li}_4\left(-e^{2 (e+f x)}\right)}{4 f^4}+\frac{9 a b^2 d^2 (c+d x) \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^3}+\frac{9 a b^2 d (c+d x)^2 \log \left(e^{2 (e+f x)}+1\right)}{f^2}-\frac{3 a b^2 (c+d x)^3 \tanh (e+f x)}{f}-\frac{3 a b^2 (c+d x)^3}{f}+\frac{3 a b^2 (c+d x)^4}{4 d}-\frac{9 a b^2 d^3 \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^4}-\frac{3 b^3 d^2 (c+d x) \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^3}+\frac{3 b^3 d^2 (c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f^3}+\frac{3 b^3 d (c+d x)^2 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^2}-\frac{3 b^3 d (c+d x)^2 \tanh (e+f x)}{2 f^2}+\frac{b^3 (c+d x)^3 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{b^3 (c+d x)^3 \tanh ^2(e+f x)}{2 f}-\frac{3 b^3 d (c+d x)^2}{2 f^2}+\frac{b^3 (c+d x)^3}{2 f}-\frac{b^3 (c+d x)^4}{4 d}+\frac{3 b^3 d^3 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^4}+\frac{3 b^3 d^3 \text{Li}_4\left(-e^{2 (e+f x)}\right)}{4 f^4}",1,"(b*E^(2*e)*(-24*b^2*c*d^2*x - 72*a*b*c^2*d*f*x - 24*a^2*c^3*f^2*x - 8*b^2*c^3*f^2*x - 12*b^2*d^3*x^2 - 72*a*b*c*d^2*f*x^2 - 36*a^2*c^2*d*f^2*x^2 - 12*b^2*c^2*d*f^2*x^2 - 24*a*b*d^3*f*x^3 - 24*a^2*c*d^2*f^2*x^3 - 8*b^2*c*d^2*f^2*x^3 - 6*a^2*d^3*f^2*x^4 - 2*b^2*d^3*f^2*x^4 + 36*a*b*c^2*d*Log[1 + E^(2*(e + f*x))] + (36*a*b*c^2*d*Log[1 + E^(2*(e + f*x))])/E^(2*e) + (12*b^2*c*d^2*Log[1 + E^(2*(e + f*x))])/f + (12*b^2*c*d^2*Log[1 + E^(2*(e + f*x))])/(E^(2*e)*f) + 12*a^2*c^3*f*Log[1 + E^(2*(e + f*x))] + 4*b^2*c^3*f*Log[1 + E^(2*(e + f*x))] + (12*a^2*c^3*f*Log[1 + E^(2*(e + f*x))])/E^(2*e) + (4*b^2*c^3*f*Log[1 + E^(2*(e + f*x))])/E^(2*e) + 72*a*b*c*d^2*x*Log[1 + E^(2*(e + f*x))] + (72*a*b*c*d^2*x*Log[1 + E^(2*(e + f*x))])/E^(2*e) + (12*b^2*d^3*x*Log[1 + E^(2*(e + f*x))])/f + (12*b^2*d^3*x*Log[1 + E^(2*(e + f*x))])/(E^(2*e)*f) + 36*a^2*c^2*d*f*x*Log[1 + E^(2*(e + f*x))] + 12*b^2*c^2*d*f*x*Log[1 + E^(2*(e + f*x))] + (36*a^2*c^2*d*f*x*Log[1 + E^(2*(e + f*x))])/E^(2*e) + (12*b^2*c^2*d*f*x*Log[1 + E^(2*(e + f*x))])/E^(2*e) + 36*a*b*d^3*x^2*Log[1 + E^(2*(e + f*x))] + (36*a*b*d^3*x^2*Log[1 + E^(2*(e + f*x))])/E^(2*e) + 36*a^2*c*d^2*f*x^2*Log[1 + E^(2*(e + f*x))] + 12*b^2*c*d^2*f*x^2*Log[1 + E^(2*(e + f*x))] + (36*a^2*c*d^2*f*x^2*Log[1 + E^(2*(e + f*x))])/E^(2*e) + (12*b^2*c*d^2*f*x^2*Log[1 + E^(2*(e + f*x))])/E^(2*e) + 12*a^2*d^3*f*x^3*Log[1 + E^(2*(e + f*x))] + 4*b^2*d^3*f*x^3*Log[1 + E^(2*(e + f*x))] + (12*a^2*d^3*f*x^3*Log[1 + E^(2*(e + f*x))])/E^(2*e) + (4*b^2*d^3*f*x^3*Log[1 + E^(2*(e + f*x))])/E^(2*e) + (6*d*(1 + E^(2*e))*(6*a*b*d*f*(c + d*x) + 3*a^2*f^2*(c + d*x)^2 + b^2*(d^2 + c^2*f^2 + 2*c*d*f^2*x + d^2*f^2*x^2))*PolyLog[2, -E^(2*(e + f*x))])/(E^(2*e)*f^2) - (6*d^2*(1 + E^(2*e))*(3*a*b*d + 3*a^2*f*(c + d*x) + b^2*f*(c + d*x))*PolyLog[3, -E^(2*(e + f*x))])/(E^(2*e)*f^2) + (9*a^2*d^3*PolyLog[4, -E^(2*(e + f*x))])/f^2 + (3*b^2*d^3*PolyLog[4, -E^(2*(e + f*x))])/f^2 + (9*a^2*d^3*PolyLog[4, -E^(2*(e + f*x))])/(E^(2*e)*f^2) + (3*b^2*d^3*PolyLog[4, -E^(2*(e + f*x))])/(E^(2*e)*f^2)))/(4*(1 + E^(2*e))*f^2) + ((b^3*c^3 + 3*b^3*c^2*d*x + 3*b^3*c*d^2*x^2 + b^3*d^3*x^3)*Sech[e + f*x]^2)/(2*f) + (3*x^2*(a^3*c^2*d - 3*a^2*b*c^2*d + 3*a*b^2*c^2*d - b^3*c^2*d + a^3*c^2*d*Cosh[2*e] + 3*a^2*b*c^2*d*Cosh[2*e] + 3*a*b^2*c^2*d*Cosh[2*e] + b^3*c^2*d*Cosh[2*e] + a^3*c^2*d*Sinh[2*e] + 3*a^2*b*c^2*d*Sinh[2*e] + 3*a*b^2*c^2*d*Sinh[2*e] + b^3*c^2*d*Sinh[2*e]))/(2*(1 + Cosh[2*e] + Sinh[2*e])) + (x^3*(a^3*c*d^2 - 3*a^2*b*c*d^2 + 3*a*b^2*c*d^2 - b^3*c*d^2 + a^3*c*d^2*Cosh[2*e] + 3*a^2*b*c*d^2*Cosh[2*e] + 3*a*b^2*c*d^2*Cosh[2*e] + b^3*c*d^2*Cosh[2*e] + a^3*c*d^2*Sinh[2*e] + 3*a^2*b*c*d^2*Sinh[2*e] + 3*a*b^2*c*d^2*Sinh[2*e] + b^3*c*d^2*Sinh[2*e]))/(1 + Cosh[2*e] + Sinh[2*e]) + (x^4*(a^3*d^3 - 3*a^2*b*d^3 + 3*a*b^2*d^3 - b^3*d^3 + a^3*d^3*Cosh[2*e] + 3*a^2*b*d^3*Cosh[2*e] + 3*a*b^2*d^3*Cosh[2*e] + b^3*d^3*Cosh[2*e] + a^3*d^3*Sinh[2*e] + 3*a^2*b*d^3*Sinh[2*e] + 3*a*b^2*d^3*Sinh[2*e] + b^3*d^3*Sinh[2*e]))/(4*(1 + Cosh[2*e] + Sinh[2*e])) + x*(a^3*c^3 + 3*a*b^2*c^3 - (3*a^2*b*c^3)/(1 + Cosh[2*e] + Sinh[2*e]) + (3*a^2*b*c^3*Cosh[2*e] + 3*a^2*b*c^3*Sinh[2*e])/(1 + Cosh[2*e] + Sinh[2*e]) + (2*b^3*c^3*Cosh[2*e] + 2*b^3*c^3*Sinh[2*e])/((1 + Cosh[2*e] + Sinh[2*e])*(1 - Cosh[2*e] + Cosh[4*e] - Sinh[2*e] + Sinh[4*e])) + (-2*b^3*c^3*Cosh[4*e] - 2*b^3*c^3*Sinh[4*e])/((1 + Cosh[2*e] + Sinh[2*e])*(1 - Cosh[2*e] + Cosh[4*e] - Sinh[2*e] + Sinh[4*e])) - (b^3*c^3)/(1 + Cosh[6*e] + Sinh[6*e]) + (b^3*c^3*Cosh[6*e] + b^3*c^3*Sinh[6*e])/(1 + Cosh[6*e] + Sinh[6*e])) - (3*Sech[e]*Sech[e + f*x]*(b^3*c^2*d*Sinh[f*x] + 2*a*b^2*c^3*f*Sinh[f*x] + 2*b^3*c*d^2*x*Sinh[f*x] + 6*a*b^2*c^2*d*f*x*Sinh[f*x] + b^3*d^3*x^2*Sinh[f*x] + 6*a*b^2*c*d^2*f*x^2*Sinh[f*x] + 2*a*b^2*d^3*f*x^3*Sinh[f*x]))/(2*f^2)","B",1
64,1,1142,405,11.8455781,"\int (c+d x)^2 (a+b \tanh (e+f x))^3 \, dx","Integrate[(c + d*x)^2*(a + b*Tanh[e + f*x])^3,x]","\frac{\text{sech}(e) \left(2 d^2 f^2 x^3 \cosh (e) a^3+6 c d f^2 x^2 \cosh (e) a^3+6 c^2 f^2 x \cosh (e) a^3+d^2 f^2 x^3 \cosh (e+2 f x) a^3+3 c d f^2 x^2 \cosh (e+2 f x) a^3+3 c^2 f^2 x \cosh (e+2 f x) a^3+d^2 f^2 x^3 \cosh (3 e+2 f x) a^3+3 c d f^2 x^2 \cosh (3 e+2 f x) a^3+3 c^2 f^2 x \cosh (3 e+2 f x) a^3+6 b d^2 f^2 x^3 \sinh (e) a^2+18 b c d f^2 x^2 \sinh (e) a^2+18 b c^2 f^2 x \sinh (e) a^2-3 b d^2 f^2 x^3 \sinh (e+2 f x) a^2-9 b c d f^2 x^2 \sinh (e+2 f x) a^2-9 b c^2 f^2 x \sinh (e+2 f x) a^2+3 b d^2 f^2 x^3 \sinh (3 e+2 f x) a^2+9 b c d f^2 x^2 \sinh (3 e+2 f x) a^2+9 b c^2 f^2 x \sinh (3 e+2 f x) a^2+6 b^2 d^2 f^2 x^3 \cosh (e) a+18 b^2 c d f^2 x^2 \cosh (e) a+18 b^2 c^2 f^2 x \cosh (e) a+3 b^2 d^2 f^2 x^3 \cosh (e+2 f x) a+9 b^2 c d f^2 x^2 \cosh (e+2 f x) a+9 b^2 c^2 f^2 x \cosh (e+2 f x) a+3 b^2 d^2 f^2 x^3 \cosh (3 e+2 f x) a+9 b^2 c d f^2 x^2 \cosh (3 e+2 f x) a+9 b^2 c^2 f^2 x \cosh (3 e+2 f x) a+18 b^2 d^2 f x^2 \sinh (e) a+18 b^2 c^2 f \sinh (e) a+36 b^2 c d f x \sinh (e) a-18 b^2 d^2 f x^2 \sinh (e+2 f x) a-18 b^2 c^2 f \sinh (e+2 f x) a-36 b^2 c d f x \sinh (e+2 f x) a+6 b^3 d^2 f x^2 \cosh (e)+6 b^3 c^2 f \cosh (e)+12 b^3 c d f x \cosh (e)+2 b^3 d^2 f^2 x^3 \sinh (e)+6 b^3 c d f^2 x^2 \sinh (e)+6 b^3 c d \sinh (e)+6 b^3 d^2 x \sinh (e)+6 b^3 c^2 f^2 x \sinh (e)-b^3 d^2 f^2 x^3 \sinh (e+2 f x)-3 b^3 c d f^2 x^2 \sinh (e+2 f x)-6 b^3 c d \sinh (e+2 f x)-6 b^3 d^2 x \sinh (e+2 f x)-3 b^3 c^2 f^2 x \sinh (e+2 f x)+b^3 d^2 f^2 x^3 \sinh (3 e+2 f x)+3 b^3 c d f^2 x^2 \sinh (3 e+2 f x)+3 b^3 c^2 f^2 x \sinh (3 e+2 f x)\right) \text{sech}^2(e+f x)}{12 f^2}+\frac{b \left(-3 \left(3 a^2+b^2\right) \text{Li}_3\left(-e^{2 (e+f x)}\right) d^2+6 \left(3 f (c+d x) a^2+3 b d a+b^2 f (c+d x)\right) \text{Li}_2\left(-e^{2 (e+f x)}\right) d-\frac{4 e^{2 e} f x \left(\left(\left(f^2 x^2+3\right) d^2+3 c f^2 x d+3 c^2 f^2\right) b^2+9 a d f (2 c+d x) b+3 a^2 f^2 \left(3 c^2+3 d x c+d^2 x^2\right)\right)}{1+e^{2 e}}+6 \left(\left(\left(f^2 x^2+1\right) d^2+2 c f^2 x d+c^2 f^2\right) b^2+6 a d f (c+d x) b+3 a^2 f^2 (c+d x)^2\right) \log \left(1+e^{2 (e+f x)}\right)\right)}{6 f^3}","\frac{a^3 (c+d x)^3}{3 d}+\frac{3 a^2 b d (c+d x) \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^2}+\frac{3 a^2 b (c+d x)^2 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{a^2 b (c+d x)^3}{d}-\frac{3 a^2 b d^2 \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^3}+\frac{6 a b^2 d (c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f^2}-\frac{3 a b^2 (c+d x)^2 \tanh (e+f x)}{f}-\frac{3 a b^2 (c+d x)^2}{f}+\frac{a b^2 (c+d x)^3}{d}+\frac{3 a b^2 d^2 \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^3}+\frac{b^3 d (c+d x) \text{Li}_2\left(-e^{2 (e+f x)}\right)}{f^2}-\frac{b^3 d (c+d x) \tanh (e+f x)}{f^2}+\frac{b^3 (c+d x)^2 \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{b^3 (c+d x)^2 \tanh ^2(e+f x)}{2 f}+\frac{b^3 c d x}{f}-\frac{b^3 (c+d x)^3}{3 d}-\frac{b^3 d^2 \text{Li}_3\left(-e^{2 (e+f x)}\right)}{2 f^3}+\frac{b^3 d^2 \log (\cosh (e+f x))}{f^3}+\frac{b^3 d^2 x^2}{2 f}",1,"(b*((-4*E^(2*e)*f*x*(9*a*b*d*f*(2*c + d*x) + 3*a^2*f^2*(3*c^2 + 3*c*d*x + d^2*x^2) + b^2*(3*c^2*f^2 + 3*c*d*f^2*x + d^2*(3 + f^2*x^2))))/(1 + E^(2*e)) + 6*(6*a*b*d*f*(c + d*x) + 3*a^2*f^2*(c + d*x)^2 + b^2*(c^2*f^2 + 2*c*d*f^2*x + d^2*(1 + f^2*x^2)))*Log[1 + E^(2*(e + f*x))] + 6*d*(3*a*b*d + 3*a^2*f*(c + d*x) + b^2*f*(c + d*x))*PolyLog[2, -E^(2*(e + f*x))] - 3*(3*a^2 + b^2)*d^2*PolyLog[3, -E^(2*(e + f*x))]))/(6*f^3) + (Sech[e]*Sech[e + f*x]^2*(6*b^3*c^2*f*Cosh[e] + 12*b^3*c*d*f*x*Cosh[e] + 6*a^3*c^2*f^2*x*Cosh[e] + 18*a*b^2*c^2*f^2*x*Cosh[e] + 6*b^3*d^2*f*x^2*Cosh[e] + 6*a^3*c*d*f^2*x^2*Cosh[e] + 18*a*b^2*c*d*f^2*x^2*Cosh[e] + 2*a^3*d^2*f^2*x^3*Cosh[e] + 6*a*b^2*d^2*f^2*x^3*Cosh[e] + 3*a^3*c^2*f^2*x*Cosh[e + 2*f*x] + 9*a*b^2*c^2*f^2*x*Cosh[e + 2*f*x] + 3*a^3*c*d*f^2*x^2*Cosh[e + 2*f*x] + 9*a*b^2*c*d*f^2*x^2*Cosh[e + 2*f*x] + a^3*d^2*f^2*x^3*Cosh[e + 2*f*x] + 3*a*b^2*d^2*f^2*x^3*Cosh[e + 2*f*x] + 3*a^3*c^2*f^2*x*Cosh[3*e + 2*f*x] + 9*a*b^2*c^2*f^2*x*Cosh[3*e + 2*f*x] + 3*a^3*c*d*f^2*x^2*Cosh[3*e + 2*f*x] + 9*a*b^2*c*d*f^2*x^2*Cosh[3*e + 2*f*x] + a^3*d^2*f^2*x^3*Cosh[3*e + 2*f*x] + 3*a*b^2*d^2*f^2*x^3*Cosh[3*e + 2*f*x] + 6*b^3*c*d*Sinh[e] + 18*a*b^2*c^2*f*Sinh[e] + 6*b^3*d^2*x*Sinh[e] + 36*a*b^2*c*d*f*x*Sinh[e] + 18*a^2*b*c^2*f^2*x*Sinh[e] + 6*b^3*c^2*f^2*x*Sinh[e] + 18*a*b^2*d^2*f*x^2*Sinh[e] + 18*a^2*b*c*d*f^2*x^2*Sinh[e] + 6*b^3*c*d*f^2*x^2*Sinh[e] + 6*a^2*b*d^2*f^2*x^3*Sinh[e] + 2*b^3*d^2*f^2*x^3*Sinh[e] - 6*b^3*c*d*Sinh[e + 2*f*x] - 18*a*b^2*c^2*f*Sinh[e + 2*f*x] - 6*b^3*d^2*x*Sinh[e + 2*f*x] - 36*a*b^2*c*d*f*x*Sinh[e + 2*f*x] - 9*a^2*b*c^2*f^2*x*Sinh[e + 2*f*x] - 3*b^3*c^2*f^2*x*Sinh[e + 2*f*x] - 18*a*b^2*d^2*f*x^2*Sinh[e + 2*f*x] - 9*a^2*b*c*d*f^2*x^2*Sinh[e + 2*f*x] - 3*b^3*c*d*f^2*x^2*Sinh[e + 2*f*x] - 3*a^2*b*d^2*f^2*x^3*Sinh[e + 2*f*x] - b^3*d^2*f^2*x^3*Sinh[e + 2*f*x] + 9*a^2*b*c^2*f^2*x*Sinh[3*e + 2*f*x] + 3*b^3*c^2*f^2*x*Sinh[3*e + 2*f*x] + 9*a^2*b*c*d*f^2*x^2*Sinh[3*e + 2*f*x] + 3*b^3*c*d*f^2*x^2*Sinh[3*e + 2*f*x] + 3*a^2*b*d^2*f^2*x^3*Sinh[3*e + 2*f*x] + b^3*d^2*f^2*x^3*Sinh[3*e + 2*f*x]))/(12*f^2)","B",1
65,1,265,261,3.6842052,"\int (c+d x) (a+b \tanh (e+f x))^3 \, dx","Integrate[(c + d*x)*(a + b*Tanh[e + f*x])^3,x]","\frac{\cosh (e+f x) (a+b \tanh (e+f x))^3 \left(-b d \left(3 a^2+b^2\right) \text{Li}_2\left(-e^{-2 (e+f x)}\right) \cosh ^2(e+f x)+\cosh ^2(e+f x) \left(-2 b \log (\cosh (e+f x)) \left(3 a^2 (d e-c f)-3 a b d+b^2 (d e-c f)\right)+2 b d \left(3 a^2+b^2\right) (e+f x) \log \left(e^{-2 (e+f x)}+1\right)-\left((e+f x) \left(a^3 (d (e-f x)-2 c f)-3 a^2 b d (e+f x)+3 a b^2 (d (e-f x)-2 c f)-b^3 d (e+f x)\right)\right)\right)-\frac{1}{2} b^2 \sinh (2 (e+f x)) (6 a f (c+d x)+b d)+b^3 f (c+d x)\right)}{2 f^2 (a \cosh (e+f x)+b \sinh (e+f x))^3}","\frac{a^3 (c+d x)^2}{2 d}+\frac{3 a^2 b (c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{3 a^2 b (c+d x)^2}{2 d}+\frac{3 a^2 b d \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^2}-\frac{3 a b^2 (c+d x) \tanh (e+f x)}{f}+3 a b^2 c x+\frac{3 a b^2 d \log (\cosh (e+f x))}{f^2}+\frac{3}{2} a b^2 d x^2+\frac{b^3 (c+d x) \log \left(e^{2 (e+f x)}+1\right)}{f}-\frac{b^3 (c+d x) \tanh ^2(e+f x)}{2 f}-\frac{b^3 (c+d x)^2}{2 d}+\frac{b^3 d \text{Li}_2\left(-e^{2 (e+f x)}\right)}{2 f^2}-\frac{b^3 d \tanh (e+f x)}{2 f^2}+\frac{b^3 d x}{2 f}",1,"(Cosh[e + f*x]*(b^3*f*(c + d*x) + Cosh[e + f*x]^2*(-((e + f*x)*(-3*a^2*b*d*(e + f*x) - b^3*d*(e + f*x) + a^3*(-2*c*f + d*(e - f*x)) + 3*a*b^2*(-2*c*f + d*(e - f*x)))) + 2*b*(3*a^2 + b^2)*d*(e + f*x)*Log[1 + E^(-2*(e + f*x))] - 2*b*(-3*a*b*d + 3*a^2*(d*e - c*f) + b^2*(d*e - c*f))*Log[Cosh[e + f*x]]) - b*(3*a^2 + b^2)*d*Cosh[e + f*x]^2*PolyLog[2, -E^(-2*(e + f*x))] - (b^2*(b*d + 6*a*f*(c + d*x))*Sinh[2*(e + f*x)])/2)*(a + b*Tanh[e + f*x])^3)/(2*f^2*(a*Cosh[e + f*x] + b*Sinh[e + f*x])^3)","A",1
66,0,0,23,63.488285,"\int \frac{(a+b \tanh (e+f x))^3}{c+d x} \, dx","Integrate[(a + b*Tanh[e + f*x])^3/(c + d*x),x]","\int \frac{(a+b \tanh (e+f x))^3}{c+d x} \, dx","\text{Int}\left(\frac{(a+b \tanh (e+f x))^3}{c+d x},x\right)",0,"Integrate[(a + b*Tanh[e + f*x])^3/(c + d*x), x]","A",-1
67,0,0,23,55.4190189,"\int \frac{(a+b \tanh (e+f x))^3}{(c+d x)^2} \, dx","Integrate[(a + b*Tanh[e + f*x])^3/(c + d*x)^2,x]","\int \frac{(a+b \tanh (e+f x))^3}{(c+d x)^2} \, dx","\text{Int}\left(\frac{(a+b \tanh (e+f x))^3}{(c+d x)^2},x\right)",0,"Integrate[(a + b*Tanh[e + f*x])^3/(c + d*x)^2, x]","A",-1
68,1,239,212,3.4869012,"\int \frac{(c+d x)^3}{a+b \tanh (e+f x)} \, dx","Integrate[(c + d*x)^3/(a + b*Tanh[e + f*x]),x]","\frac{x \cosh (e) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)}{4 (a \cosh (e)+b \sinh (e))}+\frac{b \left(\frac{3 d \left(2 f^2 (c+d x)^2 \text{Li}_2\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)+d \left(2 f (c+d x) \text{Li}_3\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)+d \text{Li}_4\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)\right)\right)}{f^4 (a-b)}-\frac{4 (c+d x)^3 \log \left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}+1\right)}{f (a-b)}-\frac{2 (c+d x)^4}{d \left(a \left(e^{2 e}+1\right)+b \left(e^{2 e}-1\right)\right)}\right)}{4 (a+b)}","\frac{3 b d^2 (c+d x) \text{Li}_3\left(-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^3 \left(a^2-b^2\right)}+\frac{3 b d (c+d x)^2 \text{Li}_2\left(-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^2 \left(a^2-b^2\right)}-\frac{b (c+d x)^3 \log \left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}+1\right)}{f \left(a^2-b^2\right)}+\frac{3 b d^3 \text{Li}_4\left(-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{4 f^4 \left(a^2-b^2\right)}+\frac{(c+d x)^4}{4 d (a+b)}",1,"(b*((-2*(c + d*x)^4)/(d*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))) - (4*(c + d*x)^3*Log[1 + (a - b)/((a + b)*E^(2*(e + f*x)))])/((a - b)*f) + (3*d*(2*f^2*(c + d*x)^2*PolyLog[2, (-a + b)/((a + b)*E^(2*(e + f*x)))] + d*(2*f*(c + d*x)*PolyLog[3, (-a + b)/((a + b)*E^(2*(e + f*x)))] + d*PolyLog[4, (-a + b)/((a + b)*E^(2*(e + f*x)))])))/((a - b)*f^4)))/(4*(a + b)) + (x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Cosh[e])/(4*(a*Cosh[e] + b*Sinh[e]))","A",1
69,1,191,157,3.8683308,"\int \frac{(c+d x)^2}{a+b \tanh (e+f x)} \, dx","Integrate[(c + d*x)^2/(a + b*Tanh[e + f*x]),x]","\frac{x \cosh (e) \left(3 c^2+3 c d x+d^2 x^2\right)}{3 (a \cosh (e)+b \sinh (e))}+\frac{b \left(\frac{3 d \left(2 f (c+d x) \text{Li}_2\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)+d \text{Li}_3\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)\right)}{f^3 (a-b)}-\frac{6 (c+d x)^2 \log \left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}+1\right)}{f (a-b)}-\frac{4 (c+d x)^3}{d \left(a \left(e^{2 e}+1\right)+b \left(e^{2 e}-1\right)\right)}\right)}{6 (a+b)}","\frac{b d (c+d x) \text{Li}_2\left(-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f^2 \left(a^2-b^2\right)}-\frac{b (c+d x)^2 \log \left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}+1\right)}{f \left(a^2-b^2\right)}+\frac{b d^2 \text{Li}_3\left(-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^3 \left(a^2-b^2\right)}+\frac{(c+d x)^3}{3 d (a+b)}",1,"(b*((-4*(c + d*x)^3)/(d*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))) - (6*(c + d*x)^2*Log[1 + (a - b)/((a + b)*E^(2*(e + f*x)))])/((a - b)*f) + (3*d*(2*f*(c + d*x)*PolyLog[2, (-a + b)/((a + b)*E^(2*(e + f*x)))] + d*PolyLog[3, (-a + b)/((a + b)*E^(2*(e + f*x)))]))/((a - b)*f^3)))/(6*(a + b)) + (x*(3*c^2 + 3*c*d*x + d^2*x^2)*Cosh[e])/(3*(a*Cosh[e] + b*Sinh[e]))","A",1
70,1,144,108,3.3261443,"\int \frac{c+d x}{a+b \tanh (e+f x)} \, dx","Integrate[(c + d*x)/(a + b*Tanh[e + f*x]),x]","\frac{b \left(-\frac{2 (c+d x) \log \left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}+1\right)}{f (a-b)}-\frac{2 (c+d x)^2}{d \left(a \left(e^{2 e}+1\right)+b \left(e^{2 e}-1\right)\right)}+\frac{d \text{Li}_2\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)}{f^2 (a-b)}\right)}{2 (a+b)}+\frac{x \cosh (e) (2 c+d x)}{2 (a \cosh (e)+b \sinh (e))}","-\frac{b (c+d x) \log \left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}+1\right)}{f \left(a^2-b^2\right)}+\frac{b d \text{Li}_2\left(-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{2 f^2 \left(a^2-b^2\right)}+\frac{(c+d x)^2}{2 d (a+b)}",1,"(b*((-2*(c + d*x)^2)/(d*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))) - (2*(c + d*x)*Log[1 + (a - b)/((a + b)*E^(2*(e + f*x)))])/((a - b)*f) + (d*PolyLog[2, (-a + b)/((a + b)*E^(2*(e + f*x)))])/((a - b)*f^2)))/(2*(a + b)) + (x*(2*c + d*x)*Cosh[e])/(2*(a*Cosh[e] + b*Sinh[e]))","A",1
71,0,0,23,15.5765349,"\int \frac{1}{(c+d x) (a+b \tanh (e+f x))} \, dx","Integrate[1/((c + d*x)*(a + b*Tanh[e + f*x])),x]","\int \frac{1}{(c+d x) (a+b \tanh (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \tanh (e+f x))},x\right)",0,"Integrate[1/((c + d*x)*(a + b*Tanh[e + f*x])), x]","A",-1
72,0,0,23,24.3296605,"\int \frac{1}{(c+d x)^2 (a+b \tanh (e+f x))} \, dx","Integrate[1/((c + d*x)^2*(a + b*Tanh[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+b \tanh (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \tanh (e+f x))},x\right)",0,"Integrate[1/((c + d*x)^2*(a + b*Tanh[e + f*x])), x]","A",-1
73,1,1019,642,13.0783665,"\int \frac{(c+d x)^3}{(a+b \tanh (e+f x))^2} \, dx","Integrate[(c + d*x)^3/(a + b*Tanh[e + f*x])^2,x]","\frac{b \left(-4 a \left(b \left(-1+e^{2 e}\right)+a \left(1+e^{2 e}\right)\right) f^3 x^3 \log \left(\frac{e^{-2 (e+f x)} (a-b)}{a+b}+1\right) d^4+3 a \left(b \left(-1+e^{2 e}\right)+a \left(1+e^{2 e}\right)\right) \left(2 f^2 \text{Li}_2\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right) x^2+2 f \text{Li}_3\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right) x+\text{Li}_4\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)\right) d^4+6 \left(b \left(-1+e^{2 e}\right)+a \left(1+e^{2 e}\right)\right) f^2 (b d-2 a c f) x^2 \log \left(\frac{e^{-2 (e+f x)} (a-b)}{a+b}+1\right) d^3-3 \left(b \left(-1+e^{2 e}\right)+a \left(1+e^{2 e}\right)\right) (b d-2 a c f) \left(2 f x \text{Li}_2\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)+\text{Li}_3\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)\right) d^3-12 c \left(b \left(-1+e^{2 e}\right)+a \left(1+e^{2 e}\right)\right) f^2 (a c f-b d) x \log \left(\frac{e^{-2 (e+f x)} (a-b)}{a+b}+1\right) d^2+6 c \left(b \left(-1+e^{2 e}\right)+a \left(1+e^{2 e}\right)\right) f (a c f-b d) \text{Li}_2\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right) d^2+4 (a-b) b f^3 (c+d x)^3 d+2 c^2 \left(b \left(-1+e^{2 e}\right)+a \left(1+e^{2 e}\right)\right) f^2 (2 a c f-3 b d) \left(2 f x-\log \left(a+(a+b) e^{2 (e+f x)}-b\right)\right) d-2 a (a-b) f^4 (c+d x)^4\right)}{2 (a-b)^2 (a+b)^2 d \left(b \left(-1+e^{2 e}\right)+a \left(1+e^{2 e}\right)\right) f^4}+\frac{a^2 d^3 f \cosh (f x) x^4+b^2 d^3 f \cosh (f x) x^4+a^2 d^3 f \cosh (2 e+f x) x^4-b^2 d^3 f \cosh (2 e+f x) x^4+2 a b d^3 f \sinh (f x) x^4+4 a^2 c d^2 f \cosh (f x) x^3+4 b^2 c d^2 f \cosh (f x) x^3+4 a^2 c d^2 f \cosh (2 e+f x) x^3-4 b^2 c d^2 f \cosh (2 e+f x) x^3-8 b^2 d^3 \sinh (f x) x^3+8 a b c d^2 f \sinh (f x) x^3+6 a^2 c^2 d f \cosh (f x) x^2+6 b^2 c^2 d f \cosh (f x) x^2+6 a^2 c^2 d f \cosh (2 e+f x) x^2-6 b^2 c^2 d f \cosh (2 e+f x) x^2-24 b^2 c d^2 \sinh (f x) x^2+12 a b c^2 d f \sinh (f x) x^2+4 a^2 c^3 f \cosh (f x) x+4 b^2 c^3 f \cosh (f x) x+4 a^2 c^3 f \cosh (2 e+f x) x-4 b^2 c^3 f \cosh (2 e+f x) x-24 b^2 c^2 d \sinh (f x) x+8 a b c^3 f \sinh (f x) x-8 b^2 c^3 \sinh (f x)}{8 (a-b) (a+b) f (a \cosh (e)+b \sinh (e)) (a \cosh (e+f x)+b \sinh (e+f x))}","\frac{3 b^2 d^2 (c+d x) \text{Li}_2\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 \left(a^2-b^2\right)^2}-\frac{3 b^2 d^2 (c+d x) \text{Li}_3\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 \left(a^2-b^2\right)^2}+\frac{3 b^2 d (c+d x)^2 \text{Li}_2\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{3 b^2 d (c+d x)^2 \log \left(\frac{(a+b) e^{2 e+2 f x}}{a-b}+1\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{2 b^2 (c+d x)^3 \log \left(\frac{(a+b) e^{2 e+2 f x}}{a-b}+1\right)}{f \left(a^2-b^2\right)^2}-\frac{2 b^2 (c+d x)^3}{f \left(a^2-b^2\right)^2}-\frac{3 b^2 d^3 \text{Li}_3\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{2 f^4 \left(a^2-b^2\right)^2}+\frac{3 b^2 d^3 \text{Li}_4\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{2 f^4 \left(a^2-b^2\right)^2}+\frac{2 b^2 (c+d x)^3}{f (a-b) (a+b)^2 \left((a+b) e^{2 e+2 f x}+a-b\right)}+\frac{3 b d^2 (c+d x) \text{Li}_3\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 (a-b)^2 (a+b)}-\frac{3 b d (c+d x)^2 \text{Li}_2\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 (a-b)^2 (a+b)}-\frac{2 b (c+d x)^3 \log \left(\frac{(a+b) e^{2 e+2 f x}}{a-b}+1\right)}{f (a-b)^2 (a+b)}+\frac{(c+d x)^4}{4 d (a-b)^2}-\frac{3 b d^3 \text{Li}_4\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{2 f^4 (a-b)^2 (a+b)}",1,"(b*(4*(a - b)*b*d*f^3*(c + d*x)^3 - 2*a*(a - b)*f^4*(c + d*x)^4 - 12*c*d^2*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))*f^2*(-(b*d) + a*c*f)*x*Log[1 + (a - b)/((a + b)*E^(2*(e + f*x)))] + 6*d^3*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))*f^2*(b*d - 2*a*c*f)*x^2*Log[1 + (a - b)/((a + b)*E^(2*(e + f*x)))] - 4*a*d^4*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))*f^3*x^3*Log[1 + (a - b)/((a + b)*E^(2*(e + f*x)))] + 2*c^2*d*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))*f^2*(-3*b*d + 2*a*c*f)*(2*f*x - Log[a - b + (a + b)*E^(2*(e + f*x))]) + 6*c*d^2*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))*f*(-(b*d) + a*c*f)*PolyLog[2, (-a + b)/((a + b)*E^(2*(e + f*x)))] - 3*d^3*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))*(b*d - 2*a*c*f)*(2*f*x*PolyLog[2, (-a + b)/((a + b)*E^(2*(e + f*x)))] + PolyLog[3, (-a + b)/((a + b)*E^(2*(e + f*x)))]) + 3*a*d^4*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))*(2*f^2*x^2*PolyLog[2, (-a + b)/((a + b)*E^(2*(e + f*x)))] + 2*f*x*PolyLog[3, (-a + b)/((a + b)*E^(2*(e + f*x)))] + PolyLog[4, (-a + b)/((a + b)*E^(2*(e + f*x)))])))/(2*(a - b)^2*(a + b)^2*d*(b*(-1 + E^(2*e)) + a*(1 + E^(2*e)))*f^4) + (4*a^2*c^3*f*x*Cosh[f*x] + 4*b^2*c^3*f*x*Cosh[f*x] + 6*a^2*c^2*d*f*x^2*Cosh[f*x] + 6*b^2*c^2*d*f*x^2*Cosh[f*x] + 4*a^2*c*d^2*f*x^3*Cosh[f*x] + 4*b^2*c*d^2*f*x^3*Cosh[f*x] + a^2*d^3*f*x^4*Cosh[f*x] + b^2*d^3*f*x^4*Cosh[f*x] + 4*a^2*c^3*f*x*Cosh[2*e + f*x] - 4*b^2*c^3*f*x*Cosh[2*e + f*x] + 6*a^2*c^2*d*f*x^2*Cosh[2*e + f*x] - 6*b^2*c^2*d*f*x^2*Cosh[2*e + f*x] + 4*a^2*c*d^2*f*x^3*Cosh[2*e + f*x] - 4*b^2*c*d^2*f*x^3*Cosh[2*e + f*x] + a^2*d^3*f*x^4*Cosh[2*e + f*x] - b^2*d^3*f*x^4*Cosh[2*e + f*x] - 8*b^2*c^3*Sinh[f*x] - 24*b^2*c^2*d*x*Sinh[f*x] + 8*a*b*c^3*f*x*Sinh[f*x] - 24*b^2*c*d^2*x^2*Sinh[f*x] + 12*a*b*c^2*d*f*x^2*Sinh[f*x] - 8*b^2*d^3*x^3*Sinh[f*x] + 8*a*b*c*d^2*f*x^3*Sinh[f*x] + 2*a*b*d^3*f*x^4*Sinh[f*x])/(8*(a - b)*(a + b)*f*(a*Cosh[e] + b*Sinh[e])*(a*Cosh[e + f*x] + b*Sinh[e + f*x]))","A",1
74,1,506,476,9.3914017,"\int \frac{(c+d x)^2}{(a+b \tanh (e+f x))^2} \, dx","Integrate[(c + d*x)^2/(a + b*Tanh[e + f*x])^2,x]","\frac{\frac{f^2 (a-b) (a+b) \left(f x \left(a^2-b^2\right) \left(3 c^2+3 c d x+d^2 x^2\right) \cosh (2 e+f x)+f x \left(a^2+b^2\right) \left(3 c^2+3 c d x+d^2 x^2\right) \cosh (f x)+2 b \sinh (f x) \left(a f x \left(3 c^2+3 c d x+d^2 x^2\right)-3 b (c+d x)^2\right)\right)}{(a \cosh (e)+b \sinh (e)) (a \cosh (e+f x)+b \sinh (e+f x))}-\frac{12 b d f^2 x^2 (a-b) (2 a c f-b d)}{a \left(e^{2 e}+1\right)+b \left(e^{2 e}-1\right)}-\frac{24 b c f^2 x (a-b) (a c f-b d)}{a \left(e^{2 e}+1\right)+b \left(e^{2 e}-1\right)}-6 b d (b d-2 a c f) \text{Li}_2\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)+12 b d f x (b d-2 a c f) \log \left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}+1\right)+12 b c f (a c f-b d) \left(2 f x-\log \left((a+b) e^{2 (e+f x)}+a-b\right)\right)-\frac{8 a b d^2 f^3 x^3 (a-b)}{a \left(e^{2 e}+1\right)+b \left(e^{2 e}-1\right)}-12 a b d^2 f^2 x^2 \log \left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}+1\right)+6 a b d^2 \left(2 f x \text{Li}_2\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)+\text{Li}_3\left(\frac{(b-a) e^{-2 (e+f x)}}{a+b}\right)\right)}{6 f^3 (a-b)^2 (a+b)^2}","\frac{2 b^2 d (c+d x) \text{Li}_2\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{2 b^2 d (c+d x) \log \left(\frac{(a+b) e^{2 e+2 f x}}{a-b}+1\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{2 b^2 (c+d x)^2 \log \left(\frac{(a+b) e^{2 e+2 f x}}{a-b}+1\right)}{f \left(a^2-b^2\right)^2}-\frac{2 b^2 (c+d x)^2}{f \left(a^2-b^2\right)^2}+\frac{b^2 d^2 \text{Li}_2\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 \left(a^2-b^2\right)^2}-\frac{b^2 d^2 \text{Li}_3\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 \left(a^2-b^2\right)^2}+\frac{2 b^2 (c+d x)^2}{f (a-b) (a+b)^2 \left((a+b) e^{2 e+2 f x}+a-b\right)}-\frac{2 b d (c+d x) \text{Li}_2\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^2 (a-b)^2 (a+b)}-\frac{2 b (c+d x)^2 \log \left(\frac{(a+b) e^{2 e+2 f x}}{a-b}+1\right)}{f (a-b)^2 (a+b)}+\frac{(c+d x)^3}{3 d (a-b)^2}+\frac{b d^2 \text{Li}_3\left(-\frac{(a+b) e^{2 e+2 f x}}{a-b}\right)}{f^3 (a-b)^2 (a+b)}",1,"((-24*(a - b)*b*c*f^2*(-(b*d) + a*c*f)*x)/(b*(-1 + E^(2*e)) + a*(1 + E^(2*e))) - (12*(a - b)*b*d*f^2*(-(b*d) + 2*a*c*f)*x^2)/(b*(-1 + E^(2*e)) + a*(1 + E^(2*e))) - (8*a*(a - b)*b*d^2*f^3*x^3)/(b*(-1 + E^(2*e)) + a*(1 + E^(2*e))) + 12*b*d*f*(b*d - 2*a*c*f)*x*Log[1 + (a - b)/((a + b)*E^(2*(e + f*x)))] - 12*a*b*d^2*f^2*x^2*Log[1 + (a - b)/((a + b)*E^(2*(e + f*x)))] + 12*b*c*f*(-(b*d) + a*c*f)*(2*f*x - Log[a - b + (a + b)*E^(2*(e + f*x))]) - 6*b*d*(b*d - 2*a*c*f)*PolyLog[2, (-a + b)/((a + b)*E^(2*(e + f*x)))] + 6*a*b*d^2*(2*f*x*PolyLog[2, (-a + b)/((a + b)*E^(2*(e + f*x)))] + PolyLog[3, (-a + b)/((a + b)*E^(2*(e + f*x)))]) + ((a - b)*(a + b)*f^2*((a^2 + b^2)*f*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Cosh[f*x] + (a^2 - b^2)*f*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Cosh[2*e + f*x] + 2*b*(-3*b*(c + d*x)^2 + a*f*x*(3*c^2 + 3*c*d*x + d^2*x^2))*Sinh[f*x]))/((a*Cosh[e] + b*Sinh[e])*(a*Cosh[e + f*x] + b*Sinh[e + f*x])))/(6*(a - b)^2*(a + b)^2*f^3)","A",1
75,1,476,196,7.0635954,"\int \frac{c+d x}{(a+b \tanh (e+f x))^2} \, dx","Integrate[(c + d*x)/(a + b*Tanh[e + f*x])^2,x]","\frac{\text{sech}^2(e+f x) (a \cosh (e+f x)+b \sinh (e+f x)) \left(2 b^2 f \left(b^2-a^2\right) (c+d x) \sinh (e+f x)-a \left(a^2-b^2\right) (e+f x) (d (e-f x)-2 c f) (a \cosh (e+f x)+b \sinh (e+f x))+2 a b d (a \cosh (e+f x)+b \sinh (e+f x)) \left(b \sqrt{1-\frac{a^2}{b^2}} e^{-\tanh ^{-1}\left(\frac{a}{b}\right)} (e+f x)^2+a \text{Li}_2\left(e^{-2 \left(e+f x+\tanh ^{-1}\left(\frac{a}{b}\right)\right)}\right)-i a \left(\pi -2 i \tanh ^{-1}\left(\frac{a}{b}\right)\right) (e+f x)-2 a \left(\tanh ^{-1}\left(\frac{a}{b}\right)+e+f x\right) \log \left(1-e^{-2 \left(\tanh ^{-1}\left(\frac{a}{b}\right)+e+f x\right)}\right)+2 a \tanh ^{-1}\left(\frac{a}{b}\right) \log \left(i \sinh \left(\tanh ^{-1}\left(\frac{a}{b}\right)+e+f x\right)\right)+i \pi  a \log \left(e^{2 (e+f x)}+1\right)-i \pi  a \log (\cosh (e+f x))\right)-2 b^2 d (a \cosh (e+f x)+b \sinh (e+f x)) (b (e+f x)-a \log (a \cosh (e+f x)+b \sinh (e+f x)))+4 a b c f (a \cosh (e+f x)+b \sinh (e+f x)) (b (e+f x)-a \log (a \cosh (e+f x)+b \sinh (e+f x)))-4 a b d e (a \cosh (e+f x)+b \sinh (e+f x)) (b (e+f x)-a \log (a \cosh (e+f x)+b \sinh (e+f x)))\right)}{2 a f^2 \left(a^2-b^2\right)^2 (a+b \tanh (e+f x))^2}","\frac{b (-2 a c f-2 a d f x+b d) \log \left(\frac{(a-b) e^{-2 (e+f x)}}{a+b}+1\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{b (c+d x)}{f \left(a^2-b^2\right) (a+b \tanh (e+f x))}-\frac{(c+d x)^2}{2 d \left(a^2-b^2\right)}+\frac{a b d \text{Li}_2\left(-\frac{(a-b) e^{-2 (e+f x)}}{a+b}\right)}{f^2 \left(a^2-b^2\right)^2}+\frac{(-2 a c f-2 a d f x+b d)^2}{4 a d f^2 (a-b) (a+b)^2}",1,"(Sech[e + f*x]^2*(a*Cosh[e + f*x] + b*Sinh[e + f*x])*(2*b^2*(-a^2 + b^2)*f*(c + d*x)*Sinh[e + f*x] - a*(a^2 - b^2)*(e + f*x)*(-2*c*f + d*(e - f*x))*(a*Cosh[e + f*x] + b*Sinh[e + f*x]) - 2*b^2*d*(b*(e + f*x) - a*Log[a*Cosh[e + f*x] + b*Sinh[e + f*x]])*(a*Cosh[e + f*x] + b*Sinh[e + f*x]) - 4*a*b*d*e*(b*(e + f*x) - a*Log[a*Cosh[e + f*x] + b*Sinh[e + f*x]])*(a*Cosh[e + f*x] + b*Sinh[e + f*x]) + 4*a*b*c*f*(b*(e + f*x) - a*Log[a*Cosh[e + f*x] + b*Sinh[e + f*x]])*(a*Cosh[e + f*x] + b*Sinh[e + f*x]) + 2*a*b*d*((Sqrt[1 - a^2/b^2]*b*(e + f*x)^2)/E^ArcTanh[a/b] - I*a*(e + f*x)*(Pi - (2*I)*ArcTanh[a/b]) + I*a*Pi*Log[1 + E^(2*(e + f*x))] - 2*a*(e + f*x + ArcTanh[a/b])*Log[1 - E^(-2*(e + f*x + ArcTanh[a/b]))] - I*a*Pi*Log[Cosh[e + f*x]] + 2*a*ArcTanh[a/b]*Log[I*Sinh[e + f*x + ArcTanh[a/b]]] + a*PolyLog[2, E^(-2*(e + f*x + ArcTanh[a/b]))])*(a*Cosh[e + f*x] + b*Sinh[e + f*x])))/(2*a*(a^2 - b^2)^2*f^2*(a + b*Tanh[e + f*x])^2)","C",0
76,0,0,23,156.930476,"\int \frac{1}{(c+d x) (a+b \tanh (e+f x))^2} \, dx","Integrate[1/((c + d*x)*(a + b*Tanh[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+b \tanh (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \tanh (e+f x))^2},x\right)",0,"Integrate[1/((c + d*x)*(a + b*Tanh[e + f*x])^2), x]","A",-1
77,0,0,23,128.0167688,"\int \frac{1}{(c+d x)^2 (a+b \tanh (e+f x))^2} \, dx","Integrate[1/((c + d*x)^2*(a + b*Tanh[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+b \tanh (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \tanh (e+f x))^2},x\right)",0,"Integrate[1/((c + d*x)^2*(a + b*Tanh[e + f*x])^2), x]","A",-1