1,1,191,149,0.1723596,"\int (c+d x)^3 \text{csch}(a+b x) \, dx","Integrate[(c + d*x)^3*Csch[a + b*x],x]","\frac{-2 b^3 (c+d x)^3 \tanh ^{-1}(\sinh (a+b x)+\cosh (a+b x))-3 d \left(b^2 (c+d x)^2 \text{Li}_2(-\cosh (a+b x)-\sinh (a+b x))-2 b d (c+d x) \text{Li}_3(-\cosh (a+b x)-\sinh (a+b x))+2 d^2 \text{Li}_4(-\cosh (a+b x)-\sinh (a+b x))\right)+3 d \left(b^2 (c+d x)^2 \text{Li}_2(\cosh (a+b x)+\sinh (a+b x))-2 b d (c+d x) \text{Li}_3(\cosh (a+b x)+\sinh (a+b x))+2 d^2 \text{Li}_4(\cosh (a+b x)+\sinh (a+b x))\right)}{b^4}","-\frac{6 d^3 \text{Li}_4\left(-e^{a+b x}\right)}{b^4}+\frac{6 d^3 \text{Li}_4\left(e^{a+b x}\right)}{b^4}+\frac{6 d^2 (c+d x) \text{Li}_3\left(-e^{a+b x}\right)}{b^3}-\frac{6 d^2 (c+d x) \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{3 d (c+d x)^2 \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{3 d (c+d x)^2 \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(-2*b^3*(c + d*x)^3*ArcTanh[Cosh[a + b*x] + Sinh[a + b*x]] - 3*d*(b^2*(c + d*x)^2*PolyLog[2, -Cosh[a + b*x] - Sinh[a + b*x]] - 2*b*d*(c + d*x)*PolyLog[3, -Cosh[a + b*x] - Sinh[a + b*x]] + 2*d^2*PolyLog[4, -Cosh[a + b*x] - Sinh[a + b*x]]) + 3*d*(b^2*(c + d*x)^2*PolyLog[2, Cosh[a + b*x] + Sinh[a + b*x]] - 2*b*d*(c + d*x)*PolyLog[3, Cosh[a + b*x] + Sinh[a + b*x]] + 2*d^2*PolyLog[4, Cosh[a + b*x] + Sinh[a + b*x]]))/b^4","A",0
2,1,118,99,0.116359,"\int (c+d x)^2 \text{csch}(a+b x) \, dx","Integrate[(c + d*x)^2*Csch[a + b*x],x]","\frac{-\frac{2 d \left(b (c+d x) \text{Li}_2\left(-e^{a+b x}\right)-d \text{Li}_3\left(-e^{a+b x}\right)\right)}{b^2}+\frac{2 d \left(b (c+d x) \text{Li}_2\left(e^{a+b x}\right)-d \text{Li}_3\left(e^{a+b x}\right)\right)}{b^2}+(c+d x)^2 \log \left(1-e^{a+b x}\right)-(c+d x)^2 \log \left(e^{a+b x}+1\right)}{b}","\frac{2 d^2 \text{Li}_3\left(-e^{a+b x}\right)}{b^3}-\frac{2 d^2 \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{2 d (c+d x) \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{2 d (c+d x) \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"((c + d*x)^2*Log[1 - E^(a + b*x)] - (c + d*x)^2*Log[1 + E^(a + b*x)] - (2*d*(b*(c + d*x)*PolyLog[2, -E^(a + b*x)] - d*PolyLog[3, -E^(a + b*x)]))/b^2 + (2*d*(b*(c + d*x)*PolyLog[2, E^(a + b*x)] - d*PolyLog[3, E^(a + b*x)]))/b^2)/b","A",1
3,1,174,50,0.0721991,"\int (c+d x) \text{csch}(a+b x) \, dx","Integrate[(c + d*x)*Csch[a + b*x],x]","\frac{d \left(-a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)-i \left(i \left(\text{Li}_2\left(-e^{i (i a+i b x)}\right)-\text{Li}_2\left(e^{i (i a+i b x)}\right)\right)+(i a+i b x) \left(\log \left(1-e^{i (i a+i b x)}\right)-\log \left(1+e^{i (i a+i b x)}\right)\right)\right)\right)}{b^2}+\frac{c \log \left(\sinh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}-\frac{c \log \left(\cosh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}","-\frac{d \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{d \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{2 (c+d x) \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"-((c*Log[Cosh[a/2 + (b*x)/2]])/b) + (c*Log[Sinh[a/2 + (b*x)/2]])/b + (d*(-(a*Log[Tanh[(a + b*x)/2]]) - I*((I*a + I*b*x)*(Log[1 - E^(I*(I*a + I*b*x))] - Log[1 + E^(I*(I*a + I*b*x))]) + I*(PolyLog[2, -E^(I*(I*a + I*b*x))] - PolyLog[2, E^(I*(I*a + I*b*x))]))))/b^2","C",1
4,0,0,13,18.4512729,"\int \frac{\text{csch}(a+b x)}{x} \, dx","Integrate[Csch[a + b*x]/x,x]","\int \frac{\text{csch}(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}(a+b x)}{x},x\right)",0,"Integrate[Csch[a + b*x]/x, x]","A",-1
5,1,185,103,0.8626373,"\int (c+d x)^3 \text{csch}^2(a+b x) \, dx","Integrate[(c + d*x)^3*Csch[a + b*x]^2,x]","\frac{-\frac{2 b^3 (c+d x)^3}{e^{2 a}-1}+b^3 \text{csch}(a) \sinh (b x) (c+d x)^3 \text{csch}(a+b x)+3 b^2 d (c+d x)^2 \log \left(1-e^{-a-b x}\right)+3 b^2 d (c+d x)^2 \log \left(e^{-a-b x}+1\right)-6 d^2 \left(b (c+d x) \text{Li}_2\left(-e^{-a-b x}\right)+d \text{Li}_3\left(-e^{-a-b x}\right)\right)-6 d^2 \left(b (c+d x) \text{Li}_2\left(e^{-a-b x}\right)+d \text{Li}_3\left(e^{-a-b x}\right)\right)}{b^4}","-\frac{3 d^3 \text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 d^2 (c+d x) \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^3}+\frac{3 d (c+d x)^2 \log \left(1-e^{2 (a+b x)}\right)}{b^2}-\frac{(c+d x)^3 \coth (a+b x)}{b}-\frac{(c+d x)^3}{b}",1,"((-2*b^3*(c + d*x)^3)/(-1 + E^(2*a)) + 3*b^2*d*(c + d*x)^2*Log[1 - E^(-a - b*x)] + 3*b^2*d*(c + d*x)^2*Log[1 + E^(-a - b*x)] - 6*d^2*(b*(c + d*x)*PolyLog[2, -E^(-a - b*x)] + d*PolyLog[3, -E^(-a - b*x)]) - 6*d^2*(b*(c + d*x)*PolyLog[2, E^(-a - b*x)] + d*PolyLog[3, E^(-a - b*x)]) + b^3*(c + d*x)^3*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b^4","A",1
6,1,198,74,5.45213,"\int (c+d x)^2 \text{csch}^2(a+b x) \, dx","Integrate[(c + d*x)^2*Csch[a + b*x]^2,x]","\frac{\text{csch}(a) \left(b^2 \sinh (b x) (c+d x)^2 \text{csch}(a+b x)+d^2 \left(-b^2 x^2 \cosh (a) e^{-\tanh ^{-1}(\tanh (a))} \sqrt{\text{sech}^2(a)}-\sinh (a) \text{Li}_2\left(e^{-2 \left(b x+\tanh ^{-1}(\tanh (a))\right)}\right)+i \pi  b x \sinh (a)-i \pi  \sinh (a) \log \left(e^{2 b x}+1\right)+2 b x \sinh (a) \log \left(1-e^{-2 \left(\tanh ^{-1}(\tanh (a))+b x\right)}\right)+2 \sinh (a) \tanh ^{-1}(\tanh (a)) \left(\log \left(1-e^{-2 \left(\tanh ^{-1}(\tanh (a))+b x\right)}\right)-\log \left(i \sinh \left(\tanh ^{-1}(\tanh (a))+b x\right)\right)+b x\right)+i \pi  \sinh (a) \log (\cosh (b x))\right)-2 b c d (b x \cosh (a)-\sinh (a) \log (\sinh (a+b x)))\right)}{b^3}","\frac{d^2 \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^3}+\frac{2 d (c+d x) \log \left(1-e^{2 (a+b x)}\right)}{b^2}-\frac{(c+d x)^2 \coth (a+b x)}{b}-\frac{(c+d x)^2}{b}",1,"(Csch[a]*(-2*b*c*d*(b*x*Cosh[a] - Log[Sinh[a + b*x]]*Sinh[a]) + d^2*(-((b^2*x^2*Cosh[a]*Sqrt[Sech[a]^2])/E^ArcTanh[Tanh[a]]) + I*b*Pi*x*Sinh[a] - I*Pi*Log[1 + E^(2*b*x)]*Sinh[a] + 2*b*x*Log[1 - E^(-2*(b*x + ArcTanh[Tanh[a]]))]*Sinh[a] + I*Pi*Log[Cosh[b*x]]*Sinh[a] + 2*ArcTanh[Tanh[a]]*(b*x + Log[1 - E^(-2*(b*x + ArcTanh[Tanh[a]]))] - Log[I*Sinh[b*x + ArcTanh[Tanh[a]]]])*Sinh[a] - PolyLog[2, E^(-2*(b*x + ArcTanh[Tanh[a]]))]*Sinh[a]) + b^2*(c + d*x)^2*Csch[a + b*x]*Sinh[b*x]))/b^3","C",0
7,1,52,29,0.0984328,"\int (c+d x) \text{csch}^2(a+b x) \, dx","Integrate[(c + d*x)*Csch[a + b*x]^2,x]","\frac{d \log (\sinh (a+b x))}{b^2}-\frac{c \coth (a+b x)}{b}-\frac{d x \coth (a)}{b}+\frac{d x \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b}","\frac{d \log (\sinh (a+b x))}{b^2}-\frac{(c+d x) \coth (a+b x)}{b}",1,"-((d*x*Coth[a])/b) - (c*Coth[a + b*x])/b + (d*Log[Sinh[a + b*x]])/b^2 + (d*x*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b","A",1
8,0,0,15,6.8501526,"\int \frac{\text{csch}^2(a+b x)}{x} \, dx","Integrate[Csch[a + b*x]^2/x,x]","\int \frac{\text{csch}^2(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}^2(a+b x)}{x},x\right)",0,"Integrate[Csch[a + b*x]^2/x, x]","A",-1
9,1,440,256,3.3081724,"\int (c+d x)^3 \text{csch}^3(a+b x) \, dx","Integrate[(c + d*x)^3*Csch[a + b*x]^3,x]","-\frac{b^3 c^3 \log \left(1-e^{a+b x}\right)-b^3 c^3 \log \left(e^{a+b x}+1\right)+3 b^3 c^2 d x \log \left(1-e^{a+b x}\right)-3 b^3 c^2 d x \log \left(e^{a+b x}+1\right)+3 b^3 c d^2 x^2 \log \left(1-e^{a+b x}\right)-3 b^3 c d^2 x^2 \log \left(e^{a+b x}+1\right)+b^3 d^3 x^3 \log \left(1-e^{a+b x}\right)-b^3 d^3 x^3 \log \left(e^{a+b x}+1\right)-3 d \text{Li}_2\left(-e^{a+b x}\right) \left(b^2 (c+d x)^2-2 d^2\right)+3 d \text{Li}_2\left(e^{a+b x}\right) \left(b^2 (c+d x)^2-2 d^2\right)+b^2 (c+d x)^2 \text{csch}(a+b x) (b (c+d x) \coth (a+b x)+3 d)+6 b c d^2 \text{Li}_3\left(-e^{a+b x}\right)-6 b c d^2 \text{Li}_3\left(e^{a+b x}\right)-6 b c d^2 \log \left(1-e^{a+b x}\right)+6 b c d^2 \log \left(e^{a+b x}+1\right)+6 b d^3 x \text{Li}_3\left(-e^{a+b x}\right)-6 b d^3 x \text{Li}_3\left(e^{a+b x}\right)-6 d^3 \text{Li}_4\left(-e^{a+b x}\right)+6 d^3 \text{Li}_4\left(e^{a+b x}\right)-6 b d^3 x \log \left(1-e^{a+b x}\right)+6 b d^3 x \log \left(e^{a+b x}+1\right)}{2 b^4}","-\frac{3 d^3 \text{Li}_2\left(-e^{a+b x}\right)}{b^4}+\frac{3 d^3 \text{Li}_2\left(e^{a+b x}\right)}{b^4}+\frac{3 d^3 \text{Li}_4\left(-e^{a+b x}\right)}{b^4}-\frac{3 d^3 \text{Li}_4\left(e^{a+b x}\right)}{b^4}-\frac{3 d^2 (c+d x) \text{Li}_3\left(-e^{a+b x}\right)}{b^3}+\frac{3 d^2 (c+d x) \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{6 d^2 (c+d x) \tanh ^{-1}\left(e^{a+b x}\right)}{b^3}+\frac{3 d (c+d x)^2 \text{Li}_2\left(-e^{a+b x}\right)}{2 b^2}-\frac{3 d (c+d x)^2 \text{Li}_2\left(e^{a+b x}\right)}{2 b^2}-\frac{3 d (c+d x)^2 \text{csch}(a+b x)}{2 b^2}+\frac{(c+d x)^3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{(c+d x)^3 \coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-1/2*(b^2*(c + d*x)^2*(3*d + b*(c + d*x)*Coth[a + b*x])*Csch[a + b*x] + b^3*c^3*Log[1 - E^(a + b*x)] - 6*b*c*d^2*Log[1 - E^(a + b*x)] + 3*b^3*c^2*d*x*Log[1 - E^(a + b*x)] - 6*b*d^3*x*Log[1 - E^(a + b*x)] + 3*b^3*c*d^2*x^2*Log[1 - E^(a + b*x)] + b^3*d^3*x^3*Log[1 - E^(a + b*x)] - b^3*c^3*Log[1 + E^(a + b*x)] + 6*b*c*d^2*Log[1 + E^(a + b*x)] - 3*b^3*c^2*d*x*Log[1 + E^(a + b*x)] + 6*b*d^3*x*Log[1 + E^(a + b*x)] - 3*b^3*c*d^2*x^2*Log[1 + E^(a + b*x)] - b^3*d^3*x^3*Log[1 + E^(a + b*x)] - 3*d*(-2*d^2 + b^2*(c + d*x)^2)*PolyLog[2, -E^(a + b*x)] + 3*d*(-2*d^2 + b^2*(c + d*x)^2)*PolyLog[2, E^(a + b*x)] + 6*b*c*d^2*PolyLog[3, -E^(a + b*x)] + 6*b*d^3*x*PolyLog[3, -E^(a + b*x)] - 6*b*c*d^2*PolyLog[3, E^(a + b*x)] - 6*b*d^3*x*PolyLog[3, E^(a + b*x)] - 6*d^3*PolyLog[4, -E^(a + b*x)] + 6*d^3*PolyLog[4, E^(a + b*x)])/b^4","A",1
10,1,420,154,6.4214154,"\int (c+d x)^2 \text{csch}^3(a+b x) \, dx","Integrate[(c + d*x)^2*Csch[a + b*x]^3,x]","\frac{\text{csch}\left(\frac{a}{2}\right) \text{csch}\left(\frac{a}{2}+\frac{b x}{2}\right) \left(c d \sinh \left(\frac{b x}{2}\right)+d^2 x \sinh \left(\frac{b x}{2}\right)\right)}{2 b^2}+\frac{\text{sech}\left(\frac{a}{2}\right) \text{sech}\left(\frac{a}{2}+\frac{b x}{2}\right) \left(c d \sinh \left(\frac{b x}{2}\right)+d^2 x \sinh \left(\frac{b x}{2}\right)\right)}{2 b^2}-\frac{d \text{csch}(a) (c+d x)}{b^2}+\frac{b^2 \left(-c^2\right) \log \left(1-e^{a+b x}\right)+b^2 c^2 \log \left(e^{a+b x}+1\right)-2 b^2 c d x \log \left(1-e^{a+b x}\right)+2 b^2 c d x \log \left(e^{a+b x}+1\right)-b^2 d^2 x^2 \log \left(1-e^{a+b x}\right)+b^2 d^2 x^2 \log \left(e^{a+b x}+1\right)+2 b d (c+d x) \text{Li}_2\left(-e^{a+b x}\right)-2 b d (c+d x) \text{Li}_2\left(e^{a+b x}\right)-2 d^2 \text{Li}_3\left(-e^{a+b x}\right)+2 d^2 \text{Li}_3\left(e^{a+b x}\right)+2 d^2 \log \left(1-e^{a+b x}\right)-2 d^2 \log \left(e^{a+b x}+1\right)}{2 b^3}+\frac{\left(-c^2-2 c d x-d^2 x^2\right) \text{csch}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}+\frac{\left(-c^2-2 c d x-d^2 x^2\right) \text{sech}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}","-\frac{d^2 \text{Li}_3\left(-e^{a+b x}\right)}{b^3}+\frac{d^2 \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{d^2 \tanh ^{-1}(\cosh (a+b x))}{b^3}+\frac{d (c+d x) \text{Li}_2\left(-e^{a+b x}\right)}{b^2}-\frac{d (c+d x) \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{d (c+d x) \text{csch}(a+b x)}{b^2}+\frac{(c+d x)^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{(c+d x)^2 \coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-((d*(c + d*x)*Csch[a])/b^2) + ((-c^2 - 2*c*d*x - d^2*x^2)*Csch[a/2 + (b*x)/2]^2)/(8*b) + (-(b^2*c^2*Log[1 - E^(a + b*x)]) + 2*d^2*Log[1 - E^(a + b*x)] - 2*b^2*c*d*x*Log[1 - E^(a + b*x)] - b^2*d^2*x^2*Log[1 - E^(a + b*x)] + b^2*c^2*Log[1 + E^(a + b*x)] - 2*d^2*Log[1 + E^(a + b*x)] + 2*b^2*c*d*x*Log[1 + E^(a + b*x)] + b^2*d^2*x^2*Log[1 + E^(a + b*x)] + 2*b*d*(c + d*x)*PolyLog[2, -E^(a + b*x)] - 2*b*d*(c + d*x)*PolyLog[2, E^(a + b*x)] - 2*d^2*PolyLog[3, -E^(a + b*x)] + 2*d^2*PolyLog[3, E^(a + b*x)])/(2*b^3) + ((-c^2 - 2*c*d*x - d^2*x^2)*Sech[a/2 + (b*x)/2]^2)/(8*b) + (Csch[a/2]*Csch[a/2 + (b*x)/2]*(c*d*Sinh[(b*x)/2] + d^2*x*Sinh[(b*x)/2]))/(2*b^2) + (Sech[a/2]*Sech[a/2 + (b*x)/2]*(c*d*Sinh[(b*x)/2] + d^2*x*Sinh[(b*x)/2]))/(2*b^2)","B",1
11,1,313,92,2.6483238,"\int (c+d x) \text{csch}^3(a+b x) \, dx","Integrate[(c + d*x)*Csch[a + b*x]^3,x]","-\frac{d \left(-a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)-i \left(i \left(\text{Li}_2\left(-e^{i (i a+i b x)}\right)-\text{Li}_2\left(e^{i (i a+i b x)}\right)\right)+(i a+i b x) \left(\log \left(1-e^{i (i a+i b x)}\right)-\log \left(1+e^{i (i a+i b x)}\right)\right)\right)\right)}{2 b^2}+\frac{d \text{csch}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{csch}\left(\frac{a}{2}+\frac{b x}{2}\right)}{4 b^2}+\frac{d \text{sech}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{sech}\left(\frac{a}{2}+\frac{b x}{2}\right)}{4 b^2}-\frac{c \text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{c \text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{c \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b}-\frac{d x \text{csch}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}-\frac{d x \text{sech}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}","\frac{d \text{Li}_2\left(-e^{a+b x}\right)}{2 b^2}-\frac{d \text{Li}_2\left(e^{a+b x}\right)}{2 b^2}-\frac{d \text{csch}(a+b x)}{2 b^2}+\frac{(c+d x) \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{(c+d x) \coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-1/8*(d*x*Csch[a/2 + (b*x)/2]^2)/b - (c*Csch[(a + b*x)/2]^2)/(8*b) - (c*Log[Tanh[(a + b*x)/2]])/(2*b) - (d*(-(a*Log[Tanh[(a + b*x)/2]]) - I*((I*a + I*b*x)*(Log[1 - E^(I*(I*a + I*b*x))] - Log[1 + E^(I*(I*a + I*b*x))]) + I*(PolyLog[2, -E^(I*(I*a + I*b*x))] - PolyLog[2, E^(I*(I*a + I*b*x))]))))/(2*b^2) - (d*x*Sech[a/2 + (b*x)/2]^2)/(8*b) - (c*Sech[(a + b*x)/2]^2)/(8*b) + (d*Csch[a/2]*Csch[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(4*b^2) + (d*Sech[a/2]*Sech[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(4*b^2)","C",1
12,0,0,15,44.6083082,"\int \frac{\text{csch}^3(a+b x)}{x} \, dx","Integrate[Csch[a + b*x]^3/x,x]","\int \frac{\text{csch}^3(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{csch}^3(a+b x)}{x},x\right)",0,"Integrate[Csch[a + b*x]^3/x, x]","A",-1
13,1,17,24,0.1086258,"\int \left(\frac{x}{\text{csch}^{\frac{3}{2}}(x)}+\frac{1}{3} x \sqrt{\text{csch}(x)}\right) \, dx","Integrate[x/Csch[x]^(3/2) + (x*Sqrt[Csch[x]])/3,x]","\frac{2 (3 x \coth (x)-2)}{9 \text{csch}^{\frac{3}{2}}(x)}","\frac{2 x \cosh (x)}{3 \sqrt{\text{csch}(x)}}-\frac{4}{9 \text{csch}^{\frac{3}{2}}(x)}",1,"(2*(-2 + 3*x*Coth[x]))/(9*Csch[x]^(3/2))","A",1
14,1,17,24,0.1148273,"\int \left(\frac{x}{\text{csch}^{\frac{5}{2}}(x)}+\frac{3 x}{5 \sqrt{\text{csch}(x)}}\right) \, dx","Integrate[x/Csch[x]^(5/2) + (3*x)/(5*Sqrt[Csch[x]]),x]","\frac{2 (5 x \coth (x)-2)}{25 \text{csch}^{\frac{5}{2}}(x)}","\frac{2 x \cosh (x)}{5 \text{csch}^{\frac{3}{2}}(x)}-\frac{4}{25 \text{csch}^{\frac{5}{2}}(x)}",1,"(2*(-2 + 5*x*Coth[x]))/(25*Csch[x]^(5/2))","A",1
15,1,45,47,0.1150885,"\int \left(\frac{x}{\text{csch}^{\frac{7}{2}}(x)}-\frac{5}{21} x \sqrt{\text{csch}(x)}\right) \, dx","Integrate[x/Csch[x]^(7/2) - (5*x*Sqrt[Csch[x]])/21,x]","\sqrt{\text{csch}(x)} \left(-\frac{13}{42} x \sinh (2 x)+\frac{1}{28} x \sinh (4 x)+\frac{88}{441} \cosh (2 x)-\frac{1}{98} \cosh (4 x)-\frac{167}{882}\right)","\frac{20}{63 \text{csch}^{\frac{3}{2}}(x)}-\frac{4}{49 \text{csch}^{\frac{7}{2}}(x)}+\frac{2 x \cosh (x)}{7 \text{csch}^{\frac{5}{2}}(x)}-\frac{10 x \cosh (x)}{21 \sqrt{\text{csch}(x)}}",1,"Sqrt[Csch[x]]*(-167/882 + (88*Cosh[2*x])/441 - Cosh[4*x]/98 - (13*x*Sinh[2*x])/42 + (x*Sinh[4*x])/28)","A",1
16,1,63,76,0.1483841,"\int \left(\frac{x^2}{\text{csch}^{\frac{3}{2}}(x)}+\frac{1}{3} x^2 \sqrt{\text{csch}(x)}\right) \, dx","Integrate[x^2/Csch[x]^(3/2) + (x^2*Sqrt[Csch[x]])/3,x]","\frac{1}{27} \sqrt{\text{csch}(x)} \left(9 x^2 \sinh (2 x)+12 x+8 \sinh (2 x)-12 x \cosh (2 x)-16 i \sqrt{i \sinh (x)} F\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)\right)","\frac{2 x^2 \cosh (x)}{3 \sqrt{\text{csch}(x)}}-\frac{8 x}{9 \text{csch}^{\frac{3}{2}}(x)}+\frac{16 \cosh (x)}{27 \sqrt{\text{csch}(x)}}-\frac{16}{27} i \sqrt{i \sinh (x)} \sqrt{\text{csch}(x)} F\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right)",1,"(Sqrt[Csch[x]]*(12*x - 12*x*Cosh[2*x] - (16*I)*EllipticF[(Pi - (2*I)*x)/4, 2]*Sqrt[I*Sinh[x]] + 8*Sinh[2*x] + 9*x^2*Sinh[2*x]))/27","A",1
17,1,2122,448,27.5123321,"\int \frac{(e+f x)^3 \cosh (c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x])/(a + b*Csch[c + d*x]),x]","\text{Result too large to show}","-\frac{6 b f^3 \text{Li}_4\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^2 d^4}-\frac{6 b f^3 \text{Li}_4\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^2 d^4}+\frac{6 b f^2 (e+f x) \text{Li}_3\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^2 d^3}+\frac{6 b f^2 (e+f x) \text{Li}_3\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^2 d^3}-\frac{3 b f (e+f x)^2 \text{Li}_2\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^2 d^2}-\frac{3 b f (e+f x)^2 \text{Li}_2\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^2 d^2}-\frac{b (e+f x)^3 \log \left(\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}+1\right)}{a^2 d}-\frac{b (e+f x)^3 \log \left(\frac{a e^{c+d x}}{\sqrt{a^2+b^2}+b}+1\right)}{a^2 d}+\frac{b (e+f x)^4}{4 a^2 f}-\frac{6 f^3 \cosh (c+d x)}{a d^4}+\frac{6 f^2 (e+f x) \sinh (c+d x)}{a d^3}-\frac{3 f (e+f x)^2 \cosh (c+d x)}{a d^2}+\frac{(e+f x)^3 \sinh (c+d x)}{a d}",1,"(e*f^2*Csch[c + d*x]*(2*b*x^3*(-1 + Coth[c]) - 2*b*x^3*Coth[c] - (6*a^2*b*(d^2*x^2*Log[1 + ((b - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*d*x*PolyLog[2, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*PolyLog[3, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a]))/(Sqrt[a^2 + b^2]*(-b + Sqrt[a^2 + b^2])*d^3) - (6*a^2*b*(d^2*x^2*Log[1 + ((b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*d*x*PolyLog[2, ((b + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/a] - 2*PolyLog[3, ((b + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/a]))/(Sqrt[a^2 + b^2]*(b + Sqrt[a^2 + b^2])*d^3) + (6*b^2*(d^2*x^2*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b - Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])] - 2*PolyLog[3, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])]))/(Sqrt[a^2 + b^2]*d^3) - (6*b^2*(d^2*x^2*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) + (6*a*Cosh[d*x]*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c]))/d^3 + (6*a*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c])*Sinh[d*x])/d^3)*(b + a*Sinh[c + d*x]))/(2*a^2*(a + b*Csch[c + d*x])) + (f^3*Csch[c + d*x]*(-1/4*(b*x^4*Cosh[c]*Csch[c/2]*Sech[c/2])/a^2 + (2*Cosh[d*x]*(-6*Cosh[c] - 3*d^2*x^2*Cosh[c] + 6*d*x*Sinh[c] + d^3*x^3*Sinh[c]))/(a*d^4) + (b*(x^4 - (2*a^2*(d^3*x^3*Log[1 + ((b - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 3*d^2*x^2*PolyLog[2, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 6*d*x*PolyLog[3, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 6*PolyLog[4, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(-b + Sqrt[a^2 + b^2])*d^4) - (2*a^2*(d^3*x^3*Log[1 + ((b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 3*d^2*x^2*PolyLog[2, -(((b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a)] - 6*d*x*PolyLog[3, -(((b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a)] - 6*PolyLog[4, -(((b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a)])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(b + Sqrt[a^2 + b^2])*d^4) + (2*b*(d^3*x^3*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b - Sqrt[a^2 + b^2])] + 3*d^2*x^2*PolyLog[2, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])] - 6*d*x*PolyLog[3, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])] + 6*PolyLog[4, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*d^4) - (2*b*(d^3*x^3*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2])] + 3*d^2*x^2*PolyLog[2, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))] - 6*d*x*PolyLog[3, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))] + 6*PolyLog[4, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*d^4)))/(a^2*(-1 + Cosh[2*c] + Sinh[2*c])) + (2*(6*d*x*Cosh[c] + d^3*x^3*Cosh[c] - 6*Sinh[c] - 3*d^2*x^2*Sinh[c])*Sinh[d*x])/(a*d^4))*(b + a*Sinh[c + d*x]))/(2*(a + b*Csch[c + d*x])) - (e^3*Csch[c + d*x]*((b*Log[b + a*Sinh[c + d*x]])/a^2 - Sinh[c + d*x]/a)*(b + a*Sinh[c + d*x]))/(d*(a + b*Csch[c + d*x])) + (3*e^2*f*Csch[c + d*x]*(b + a*Sinh[c + d*x])*(-(a*Cosh[c + d*x]) - b*(c + d*x)*Log[b + a*Sinh[c + d*x]] + b*c*Log[1 + (a*Sinh[c + d*x])/b] + I*b*((-1/8*I)*(2*c + I*Pi + 2*d*x)^2 - (4*I)*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]]*ArcTan[((I*a + b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[a^2 + b^2]] - (((-2*I)*c + Pi - (2*I)*d*x + 4*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]])*Log[1 + ((-b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])/2 - (((-2*I)*c + Pi - (2*I)*d*x - 4*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]])*Log[1 - ((b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])/2 + (Pi/2 - I*(c + d*x))*Log[b + a*Sinh[c + d*x]] + I*(PolyLog[2, ((b - Sqrt[a^2 + b^2])*E^(c + d*x))/a] + PolyLog[2, ((b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])) + a*d*x*Sinh[c + d*x]))/(a^2*d^2*(a + b*Csch[c + d*x]))","C",0
18,1,1167,330,10.2345887,"\int \frac{(e+f x)^2 \cosh (c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x])/(a + b*Csch[c + d*x]),x]","-\frac{\text{csch}(c+d x) \left(\frac{b \log (b+a \sinh (c+d x))}{a^2}-\frac{\sinh (c+d x)}{a}\right) (b+a \sinh (c+d x)) e^2}{d (a+b \text{csch}(c+d x))}+\frac{2 f \text{csch}(c+d x) (b+a \sinh (c+d x)) \left(-a \cosh (c+d x)-b (c+d x) \log (b+a \sinh (c+d x))+b c \log \left(\frac{a \sinh (c+d x)}{b}+1\right)+i b \left(-\frac{1}{8} i (2 c+2 d x+i \pi )^2-4 i \sin ^{-1}\left(\frac{\sqrt{\frac{i b}{a}+1}}{\sqrt{2}}\right) \tan ^{-1}\left(\frac{(i a+b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{a^2+b^2}}\right)-\frac{1}{2} \left(-2 i c-2 i d x+4 \sin ^{-1}\left(\frac{\sqrt{\frac{i b}{a}+1}}{\sqrt{2}}\right)+\pi \right) \log \left(\frac{e^{c+d x} \left(\sqrt{a^2+b^2}-b\right)}{a}+1\right)-\frac{1}{2} \left(-2 i c-2 i d x-4 \sin ^{-1}\left(\frac{\sqrt{\frac{i b}{a}+1}}{\sqrt{2}}\right)+\pi \right) \log \left(1-\frac{\left(b+\sqrt{a^2+b^2}\right) e^{c+d x}}{a}\right)+\left(\frac{\pi }{2}-i (c+d x)\right) \log (b+a \sinh (c+d x))+i \left(\text{Li}_2\left(\frac{\left(b-\sqrt{a^2+b^2}\right) e^{c+d x}}{a}\right)+\text{Li}_2\left(\frac{\left(b+\sqrt{a^2+b^2}\right) e^{c+d x}}{a}\right)\right)\right)+a d x \sinh (c+d x)\right) e}{a^2 d^2 (a+b \text{csch}(c+d x))}+\frac{f^2 \text{csch}(c+d x) \left(2 b (\coth (c)-1) x^3-2 b \coth (c) x^3-\frac{6 a^2 b \left(d^2 \log \left(\frac{\left(b-\sqrt{a^2+b^2}\right) (\cosh (c+d x)-\sinh (c+d x))}{a}+1\right) x^2-2 d \text{Li}_2\left(\frac{\left(\sqrt{a^2+b^2}-b\right) (\cosh (c+d x)-\sinh (c+d x))}{a}\right) x-2 \text{Li}_3\left(\frac{\left(\sqrt{a^2+b^2}-b\right) (\cosh (c+d x)-\sinh (c+d x))}{a}\right)\right)}{\sqrt{a^2+b^2} \left(\sqrt{a^2+b^2}-b\right) d^3}-\frac{6 a^2 b \left(d^2 \log \left(\frac{\left(b+\sqrt{a^2+b^2}\right) (\cosh (c+d x)-\sinh (c+d x))}{a}+1\right) x^2-2 d \text{Li}_2\left(\frac{\left(b+\sqrt{a^2+b^2}\right) (\sinh (c+d x)-\cosh (c+d x))}{a}\right) x-2 \text{Li}_3\left(\frac{\left(b+\sqrt{a^2+b^2}\right) (\sinh (c+d x)-\cosh (c+d x))}{a}\right)\right)}{\sqrt{a^2+b^2} \left(b+\sqrt{a^2+b^2}\right) d^3}+\frac{6 b^2 \left(d^2 \log \left(\frac{a (\cosh (c+d x)+\sinh (c+d x))}{b-\sqrt{a^2+b^2}}+1\right) x^2+2 d \text{Li}_2\left(\frac{a (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-b}\right) x-2 \text{Li}_3\left(\frac{a (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-b}\right)\right)}{\sqrt{a^2+b^2} d^3}-\frac{6 b^2 \left(d^2 \log \left(\frac{a (\cosh (c+d x)+\sinh (c+d x))}{b+\sqrt{a^2+b^2}}+1\right) x^2+2 d \text{Li}_2\left(-\frac{a (\cosh (c+d x)+\sinh (c+d x))}{b+\sqrt{a^2+b^2}}\right) x-2 \text{Li}_3\left(-\frac{a (\cosh (c+d x)+\sinh (c+d x))}{b+\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2} d^3}+\frac{6 a \cosh (d x) \left(\left(d^2 x^2+2\right) \sinh (c)-2 d x \cosh (c)\right)}{d^3}+\frac{6 a \left(\left(d^2 x^2+2\right) \cosh (c)-2 d x \sinh (c)\right) \sinh (d x)}{d^3}\right) (b+a \sinh (c+d x))}{6 a^2 (a+b \text{csch}(c+d x))}","\frac{2 b f^2 \text{Li}_3\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^2 d^3}+\frac{2 b f^2 \text{Li}_3\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^2 d^3}-\frac{2 b f (e+f x) \text{Li}_2\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^2 d^2}-\frac{2 b f (e+f x) \text{Li}_2\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^2 d^2}-\frac{b (e+f x)^2 \log \left(\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}+1\right)}{a^2 d}-\frac{b (e+f x)^2 \log \left(\frac{a e^{c+d x}}{\sqrt{a^2+b^2}+b}+1\right)}{a^2 d}+\frac{b (e+f x)^3}{3 a^2 f}+\frac{2 f^2 \sinh (c+d x)}{a d^3}-\frac{2 f (e+f x) \cosh (c+d x)}{a d^2}+\frac{(e+f x)^2 \sinh (c+d x)}{a d}",1,"(f^2*Csch[c + d*x]*(2*b*x^3*(-1 + Coth[c]) - 2*b*x^3*Coth[c] - (6*a^2*b*(d^2*x^2*Log[1 + ((b - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*d*x*PolyLog[2, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*PolyLog[3, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a]))/(Sqrt[a^2 + b^2]*(-b + Sqrt[a^2 + b^2])*d^3) - (6*a^2*b*(d^2*x^2*Log[1 + ((b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*d*x*PolyLog[2, ((b + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/a] - 2*PolyLog[3, ((b + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/a]))/(Sqrt[a^2 + b^2]*(b + Sqrt[a^2 + b^2])*d^3) + (6*b^2*(d^2*x^2*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b - Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])] - 2*PolyLog[3, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])]))/(Sqrt[a^2 + b^2]*d^3) - (6*b^2*(d^2*x^2*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) + (6*a*Cosh[d*x]*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c]))/d^3 + (6*a*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c])*Sinh[d*x])/d^3)*(b + a*Sinh[c + d*x]))/(6*a^2*(a + b*Csch[c + d*x])) - (e^2*Csch[c + d*x]*((b*Log[b + a*Sinh[c + d*x]])/a^2 - Sinh[c + d*x]/a)*(b + a*Sinh[c + d*x]))/(d*(a + b*Csch[c + d*x])) + (2*e*f*Csch[c + d*x]*(b + a*Sinh[c + d*x])*(-(a*Cosh[c + d*x]) - b*(c + d*x)*Log[b + a*Sinh[c + d*x]] + b*c*Log[1 + (a*Sinh[c + d*x])/b] + I*b*((-1/8*I)*(2*c + I*Pi + 2*d*x)^2 - (4*I)*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]]*ArcTan[((I*a + b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[a^2 + b^2]] - (((-2*I)*c + Pi - (2*I)*d*x + 4*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]])*Log[1 + ((-b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])/2 - (((-2*I)*c + Pi - (2*I)*d*x - 4*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]])*Log[1 - ((b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])/2 + (Pi/2 - I*(c + d*x))*Log[b + a*Sinh[c + d*x]] + I*(PolyLog[2, ((b - Sqrt[a^2 + b^2])*E^(c + d*x))/a] + PolyLog[2, ((b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])) + a*d*x*Sinh[c + d*x]))/(a^2*d^2*(a + b*Csch[c + d*x]))","C",0
19,1,435,212,1.3939423,"\int \frac{(e+f x) \cosh (c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x])/(a + b*Csch[c + d*x]),x]","\frac{\text{csch}(c+d x) (a \sinh (c+d x)+b) \left(i b f \left(i \left(\text{Li}_2\left(\frac{\left(b-\sqrt{a^2+b^2}\right) e^{c+d x}}{a}\right)+\text{Li}_2\left(\frac{\left(b+\sqrt{a^2+b^2}\right) e^{c+d x}}{a}\right)\right)-\frac{1}{2} \log \left(\frac{\left(\sqrt{a^2+b^2}-b\right) e^{c+d x}}{a}+1\right) \left(4 \sin ^{-1}\left(\frac{\sqrt{1+\frac{i b}{a}}}{\sqrt{2}}\right)-2 i c-2 i d x+\pi \right)-\frac{1}{2} \log \left(1-\frac{\left(\sqrt{a^2+b^2}+b\right) e^{c+d x}}{a}\right) \left(-4 \sin ^{-1}\left(\frac{\sqrt{1+\frac{i b}{a}}}{\sqrt{2}}\right)-2 i c-2 i d x+\pi \right)-4 i \sin ^{-1}\left(\frac{\sqrt{1+\frac{i b}{a}}}{\sqrt{2}}\right) \tan ^{-1}\left(\frac{(b+i a) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{a^2+b^2}}\right)+\left(\frac{\pi }{2}-i (c+d x)\right) \log (a \sinh (c+d x)+b)-\frac{1}{8} i (2 c+2 d x+i \pi )^2\right)+d e (a \sinh (c+d x)-b \log (a \sinh (c+d x)+b))-b f (c+d x) \log (a \sinh (c+d x)+b)+b c f \log \left(\frac{a \sinh (c+d x)}{b}+1\right)+a d f x \sinh (c+d x)-a f \cosh (c+d x)\right)}{a^2 d^2 (a+b \text{csch}(c+d x))}","-\frac{b f \text{Li}_2\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^2 d^2}-\frac{b f \text{Li}_2\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^2 d^2}-\frac{b (e+f x) \log \left(\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}+1\right)}{a^2 d}-\frac{b (e+f x) \log \left(\frac{a e^{c+d x}}{\sqrt{a^2+b^2}+b}+1\right)}{a^2 d}+\frac{b (e+f x)^2}{2 a^2 f}-\frac{f \cosh (c+d x)}{a d^2}+\frac{(e+f x) \sinh (c+d x)}{a d}",1,"(Csch[c + d*x]*(b + a*Sinh[c + d*x])*(-(a*f*Cosh[c + d*x]) - b*f*(c + d*x)*Log[b + a*Sinh[c + d*x]] + b*c*f*Log[1 + (a*Sinh[c + d*x])/b] + I*b*f*((-1/8*I)*(2*c + I*Pi + 2*d*x)^2 - (4*I)*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]]*ArcTan[((I*a + b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[a^2 + b^2]] - (((-2*I)*c + Pi - (2*I)*d*x + 4*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]])*Log[1 + ((-b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])/2 - (((-2*I)*c + Pi - (2*I)*d*x - 4*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]])*Log[1 - ((b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])/2 + (Pi/2 - I*(c + d*x))*Log[b + a*Sinh[c + d*x]] + I*(PolyLog[2, ((b - Sqrt[a^2 + b^2])*E^(c + d*x))/a] + PolyLog[2, ((b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])) + a*d*f*x*Sinh[c + d*x] + d*e*(-(b*Log[b + a*Sinh[c + d*x]]) + a*Sinh[c + d*x])))/(a^2*d^2*(a + b*Csch[c + d*x]))","C",1
20,1,30,34,0.0225756,"\int \frac{\cosh (c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[Cosh[c + d*x]/(a + b*Csch[c + d*x]),x]","\frac{a \sinh (c+d x)-b \log (a \sinh (c+d x)+b)}{a^2 d}","\frac{\sinh (c+d x)}{a d}-\frac{b \log (a \sinh (c+d x)+b)}{a^2 d}",1,"(-(b*Log[b + a*Sinh[c + d*x]]) + a*Sinh[c + d*x])/(a^2*d)","A",1
21,0,0,35,95.5761882,"\int \frac{\cosh (c+d x)}{(e+f x) (a+b \text{csch}(c+d x))} \, dx","Integrate[Cosh[c + d*x]/((e + f*x)*(a + b*Csch[c + d*x])),x]","\int \frac{\cosh (c+d x)}{(e+f x) (a+b \text{csch}(c+d x))} \, dx","\text{Int}\left(\frac{\sinh (c+d x) \cosh (c+d x)}{(e+f x) (a \sinh (c+d x)+b)},x\right)",0,"Integrate[Cosh[c + d*x]/((e + f*x)*(a + b*Csch[c + d*x])), x]","A",-1
22,1,3189,696,14.3070107,"\int \frac{(e+f x)^3 \cosh ^2(c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^2)/(a + b*Csch[c + d*x]),x]","\text{Result too large to show}","\frac{b^2 (e+f x)^4}{4 a^3 f}+\frac{6 b f^3 \sinh (c+d x)}{a^2 d^4}-\frac{6 b f^2 (e+f x) \cosh (c+d x)}{a^2 d^3}+\frac{3 b f (e+f x)^2 \sinh (c+d x)}{a^2 d^2}-\frac{b (e+f x)^3 \cosh (c+d x)}{a^2 d}-\frac{6 b f^3 \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^3 d^4}+\frac{6 b f^3 \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^3 d^4}+\frac{6 b f^2 \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^3 d^3}-\frac{6 b f^2 \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^3 d^3}-\frac{3 b f \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^3 d^2}+\frac{3 b f \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b \sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}+1\right)}{a^3 d}+\frac{b \sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{a e^{c+d x}}{\sqrt{a^2+b^2}+b}+1\right)}{a^3 d}-\frac{3 f^3 \cosh ^2(c+d x)}{8 a d^4}+\frac{3 f^2 (e+f x) \sinh (c+d x) \cosh (c+d x)}{4 a d^3}-\frac{3 f (e+f x)^2 \cosh ^2(c+d x)}{4 a d^2}+\frac{(e+f x)^3 \sinh (c+d x) \cosh (c+d x)}{2 a d}+\frac{3 e f^2 x}{4 a d^2}+\frac{3 f^3 x^2}{8 a d^2}+\frac{(e+f x)^4}{8 a f}",1,"(e^3*(c/d + x - (2*b*ArcTan[(a - b*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d))*Csch[c + d*x]*(b + a*Sinh[c + d*x]))/(4*a*(a + b*Csch[c + d*x])) + (3*e^2*f*Csch[c + d*x]*(x^2 + ((2*I)*b*Pi*ArcTanh[(-a + b*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d^2) + (2*b*(2*(c + I*ArcCos[((-I)*b)/a])*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ((-2*I)*c + Pi - (2*I)*d*x)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (ArcCos[((-I)*b)/a] - 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((a + I*b)*(a - I*b + Sqrt[-a^2 - b^2])*(1 + I*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - (ArcCos[((-I)*b)/a] + 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[(I*(a + I*b)*(-a + I*b + Sqrt[-a^2 - b^2])*(I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] + (ArcCos[((-I)*b)/a] + 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (2*I)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[-(((-1)^(3/4)*Sqrt[-a^2 - b^2]*E^(-1/2*c - (d*x)/2))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x]]))] + (ArcCos[((-I)*b)/a] - 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + (2*I)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((-1)^(1/4)*Sqrt[-a^2 - b^2]*E^((c + d*x)/2))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x]])] + I*(PolyLog[2, ((I*b + Sqrt[-a^2 - b^2])*(a + I*b - I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - PolyLog[2, ((b + I*Sqrt[-a^2 - b^2])*(I*a - b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))])))/(Sqrt[-a^2 - b^2]*d^2))*(b + a*Sinh[c + d*x]))/(8*a*(a + b*Csch[c + d*x])) + (e*f^2*Csch[c + d*x]*(x^3 - (3*b*(d^2*x^2*Log[1 + (a*E^(c + d*x))/(b - Sqrt[a^2 + b^2])] - d^2*x^2*Log[1 + (a*E^(c + d*x))/(b + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] - 2*d*x*PolyLog[2, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] + 2*PolyLog[3, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3))*(b + a*Sinh[c + d*x]))/(4*a*(a + b*Csch[c + d*x])) + (f^3*Csch[c + d*x]*(x^4 - (4*b*(d^3*x^3*Log[1 + (a*E^(c + d*x))/(b - Sqrt[a^2 + b^2])] - d^3*x^3*Log[1 + (a*E^(c + d*x))/(b + Sqrt[a^2 + b^2])] + 3*d^2*x^2*PolyLog[2, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] - 3*d^2*x^2*PolyLog[2, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))] - 6*d*x*PolyLog[3, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] + 6*d*x*PolyLog[3, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))] + 6*PolyLog[4, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] - 6*PolyLog[4, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^4))*(b + a*Sinh[c + d*x]))/(16*a*(a + b*Csch[c + d*x])) + (e*f^2*Csch[c + d*x]*(2*(a^2 + 4*b^2)*x^3 - (6*b*(3*a^2 + 4*b^2)*(d^2*x^2*Log[1 + (a*E^(c + d*x))/(b - Sqrt[a^2 + b^2])] - d^2*x^2*Log[1 + (a*E^(c + d*x))/(b + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] - 2*d*x*PolyLog[2, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] + 2*PolyLog[3, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) - (24*a*b*Cosh[d*x]*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c]))/d^3 + (3*a^2*Cosh[2*d*x]*(-2*d*x*Cosh[2*c] + (1 + 2*d^2*x^2)*Sinh[2*c]))/d^3 - (24*a*b*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c])*Sinh[d*x])/d^3 + (3*a^2*((1 + 2*d^2*x^2)*Cosh[2*c] - 2*d*x*Sinh[2*c])*Sinh[2*d*x])/d^3)*(b + a*Sinh[c + d*x]))/(8*a^3*(a + b*Csch[c + d*x])) + (f^3*Csch[c + d*x]*((a^2 + 4*b^2)*x^4 - (4*b*(3*a^2 + 4*b^2)*(d^3*x^3*Log[1 + (a*E^(c + d*x))/(b - Sqrt[a^2 + b^2])] - d^3*x^3*Log[1 + (a*E^(c + d*x))/(b + Sqrt[a^2 + b^2])] + 3*d^2*x^2*PolyLog[2, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] - 3*d^2*x^2*PolyLog[2, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))] - 6*d*x*PolyLog[3, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] + 6*d*x*PolyLog[3, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))] + 6*PolyLog[4, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] - 6*PolyLog[4, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^4) - (16*a*b*Cosh[d*x]*(d*x*(6 + d^2*x^2)*Cosh[c] - 3*(2 + d^2*x^2)*Sinh[c]))/d^4 + (a^2*Cosh[2*d*x]*(-3*(1 + 2*d^2*x^2)*Cosh[2*c] + 2*d*x*(3 + 2*d^2*x^2)*Sinh[2*c]))/d^4 - (16*a*b*(-3*(2 + d^2*x^2)*Cosh[c] + d*x*(6 + d^2*x^2)*Sinh[c])*Sinh[d*x])/d^4 + (a^2*(2*d*x*(3 + 2*d^2*x^2)*Cosh[2*c] - 3*(1 + 2*d^2*x^2)*Sinh[2*c])*Sinh[2*d*x])/d^4)*(b + a*Sinh[c + d*x]))/(16*a^3*(a + b*Csch[c + d*x])) + (e^3*Csch[c + d*x]*(b + a*Sinh[c + d*x])*((a^2 + 4*b^2)*(c + d*x) - (2*b*(3*a^2 + 4*b^2)*ArcTan[(a - b*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[c + d*x] + a^2*Sinh[2*(c + d*x)]))/(4*a^3*d*(a + b*Csch[c + d*x])) + (3*e^2*f*Csch[c + d*x]*(b + a*Sinh[c + d*x])*((a^2 + 4*b^2)*(-c + d*x)*(c + d*x) - 8*a*b*d*x*Cosh[c + d*x] - a^2*Cosh[2*(c + d*x)] - (2*b*(3*a^2 + 4*b^2)*(2*c*ArcTanh[(b + a*Cosh[c + d*x] + a*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + (c + d*x)*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b - Sqrt[a^2 + b^2])] - (c + d*x)*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2])] + PolyLog[2, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])] - PolyLog[2, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] + 8*a*b*Sinh[c + d*x] + 2*a^2*d*x*Sinh[2*(c + d*x)]))/(8*a^3*d^2*(a + b*Csch[c + d*x]))","C",0
23,1,2342,510,10.424724,"\int \frac{(e+f x)^2 \cosh ^2(c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^2)/(a + b*Csch[c + d*x]),x]","\text{Result too large to show}","\frac{b^2 (e+f x)^3}{3 a^3 f}-\frac{2 b f^2 \cosh (c+d x)}{a^2 d^3}+\frac{2 b f (e+f x) \sinh (c+d x)}{a^2 d^2}-\frac{b (e+f x)^2 \cosh (c+d x)}{a^2 d}+\frac{2 b f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^3 d^3}-\frac{2 b f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^3 d^3}-\frac{2 b f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^3 d^2}+\frac{2 b f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b \sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}+1\right)}{a^3 d}+\frac{b \sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{a e^{c+d x}}{\sqrt{a^2+b^2}+b}+1\right)}{a^3 d}+\frac{f^2 \sinh (c+d x) \cosh (c+d x)}{4 a d^3}-\frac{f (e+f x) \cosh ^2(c+d x)}{2 a d^2}+\frac{(e+f x)^2 \sinh (c+d x) \cosh (c+d x)}{2 a d}+\frac{f^2 x}{4 a d^2}+\frac{(e+f x)^3}{6 a f}",1,"(e^2*(c/d + x - (2*b*ArcTan[(a - b*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d))*Csch[c + d*x]*(b + a*Sinh[c + d*x]))/(4*a*(a + b*Csch[c + d*x])) + (e*f*Csch[c + d*x]*(x^2 + ((2*I)*b*Pi*ArcTanh[(-a + b*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d^2) + (2*b*(2*(c + I*ArcCos[((-I)*b)/a])*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ((-2*I)*c + Pi - (2*I)*d*x)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (ArcCos[((-I)*b)/a] - 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((a + I*b)*(a - I*b + Sqrt[-a^2 - b^2])*(1 + I*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - (ArcCos[((-I)*b)/a] + 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[(I*(a + I*b)*(-a + I*b + Sqrt[-a^2 - b^2])*(I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] + (ArcCos[((-I)*b)/a] + 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (2*I)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[-(((-1)^(3/4)*Sqrt[-a^2 - b^2]*E^(-1/2*c - (d*x)/2))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x]]))] + (ArcCos[((-I)*b)/a] - 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + (2*I)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((-1)^(1/4)*Sqrt[-a^2 - b^2]*E^((c + d*x)/2))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x]])] + I*(PolyLog[2, ((I*b + Sqrt[-a^2 - b^2])*(a + I*b - I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - PolyLog[2, ((b + I*Sqrt[-a^2 - b^2])*(I*a - b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))])))/(Sqrt[-a^2 - b^2]*d^2))*(b + a*Sinh[c + d*x]))/(4*a*(a + b*Csch[c + d*x])) + (f^2*Csch[c + d*x]*(x^3 - (3*b*(d^2*x^2*Log[1 + (a*E^(c + d*x))/(b - Sqrt[a^2 + b^2])] - d^2*x^2*Log[1 + (a*E^(c + d*x))/(b + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] - 2*d*x*PolyLog[2, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] + 2*PolyLog[3, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3))*(b + a*Sinh[c + d*x]))/(12*a*(a + b*Csch[c + d*x])) + (f^2*Csch[c + d*x]*(2*(a^2 + 4*b^2)*x^3 - (6*b*(3*a^2 + 4*b^2)*(d^2*x^2*Log[1 + (a*E^(c + d*x))/(b - Sqrt[a^2 + b^2])] - d^2*x^2*Log[1 + (a*E^(c + d*x))/(b + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] - 2*d*x*PolyLog[2, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] + 2*PolyLog[3, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) - (24*a*b*Cosh[d*x]*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c]))/d^3 + (3*a^2*Cosh[2*d*x]*(-2*d*x*Cosh[2*c] + (1 + 2*d^2*x^2)*Sinh[2*c]))/d^3 - (24*a*b*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c])*Sinh[d*x])/d^3 + (3*a^2*((1 + 2*d^2*x^2)*Cosh[2*c] - 2*d*x*Sinh[2*c])*Sinh[2*d*x])/d^3)*(b + a*Sinh[c + d*x]))/(24*a^3*(a + b*Csch[c + d*x])) + (e^2*Csch[c + d*x]*(b + a*Sinh[c + d*x])*((a^2 + 4*b^2)*(c + d*x) - (2*b*(3*a^2 + 4*b^2)*ArcTan[(a - b*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[c + d*x] + a^2*Sinh[2*(c + d*x)]))/(4*a^3*d*(a + b*Csch[c + d*x])) + (e*f*Csch[c + d*x]*(b + a*Sinh[c + d*x])*((a^2 + 4*b^2)*(-c + d*x)*(c + d*x) - 8*a*b*d*x*Cosh[c + d*x] - a^2*Cosh[2*(c + d*x)] - (2*b*(3*a^2 + 4*b^2)*(2*c*ArcTanh[(b + a*Cosh[c + d*x] + a*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + (c + d*x)*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b - Sqrt[a^2 + b^2])] - (c + d*x)*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2])] + PolyLog[2, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])] - PolyLog[2, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] + 8*a*b*Sinh[c + d*x] + 2*a^2*d*x*Sinh[2*(c + d*x)]))/(4*a^3*d^2*(a + b*Csch[c + d*x]))","C",0
24,1,1581,327,4.3039613,"\int \frac{(e+f x) \cosh ^2(c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^2)/(a + b*Csch[c + d*x]),x]","\frac{\text{csch}(c+d x) (b+a \sinh (c+d x)) \left(2 e \left(\frac{c}{d}+x-\frac{2 b \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2} d}\right) a^2+f \left(x^2+\frac{2 i b \pi  \tanh ^{-1}\left(\frac{b \tanh \left(\frac{1}{2} (c+d x)\right)-a}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2} d^2}+\frac{2 b \left(2 \left(c+i \cos ^{-1}\left(-\frac{i b}{a}\right)\right) \tan ^{-1}\left(\frac{(a-i b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)+(-2 i c-2 i d x+\pi ) \tanh ^{-1}\left(\frac{(b-i a) \tan \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)-\left(\cos ^{-1}\left(-\frac{i b}{a}\right)-2 \tan ^{-1}\left(\frac{(a-i b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(\frac{(a+i b) \left(a-i b+\sqrt{-a^2-b^2}\right) \left(i \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)+1\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{i b}{a}\right)+2 \tan ^{-1}\left(\frac{(a-i b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(\frac{i (a+i b) \left(-a+i b+\sqrt{-a^2-b^2}\right) \left(\cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)+i\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}\right)+\left(\cos ^{-1}\left(-\frac{i b}{a}\right)+2 \tan ^{-1}\left(\frac{(a-i b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)-2 i \tanh ^{-1}\left(\frac{(b-i a) \tan \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(-\frac{(-1)^{3/4} \sqrt{-a^2-b^2} e^{-\frac{c}{2}-\frac{d x}{2}}}{\sqrt{2} \sqrt{-i a} \sqrt{b+a \sinh (c+d x)}}\right)+\left(\cos ^{-1}\left(-\frac{i b}{a}\right)-2 \tan ^{-1}\left(\frac{(a-i b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)+2 i \tanh ^{-1}\left(\frac{(b-i a) \tan \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(\frac{\sqrt[4]{-1} \sqrt{-a^2-b^2} e^{\frac{1}{2} (c+d x)}}{\sqrt{2} \sqrt{-i a} \sqrt{b+a \sinh (c+d x)}}\right)+i \left(\text{Li}_2\left(\frac{\left(i b+\sqrt{-a^2-b^2}\right) \left(a+i b-i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}\right)-\text{Li}_2\left(\frac{\left(b+i \sqrt{-a^2-b^2}\right) \left(i a-b+\sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}\right)\right)\right)}{\sqrt{-a^2-b^2} d^2}\right) a^2+\frac{2 e \left(\sinh (2 (c+d x)) a^2-4 b \cosh (c+d x) a+\left(a^2+4 b^2\right) (c+d x)-\frac{2 b \left(3 a^2+4 b^2\right) \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}\right)}{d}+\frac{f \left(-\cosh (2 (c+d x)) a^2+2 d x \sinh (2 (c+d x)) a^2-8 b d x \cosh (c+d x) a+8 b \sinh (c+d x) a+\left(a^2+4 b^2\right) (d x-c) (c+d x)-\frac{2 b \left(3 a^2+4 b^2\right) \left(2 c \tanh ^{-1}\left(\frac{b+a \cosh (c+d x)+a \sinh (c+d x)}{\sqrt{a^2+b^2}}\right)+(c+d x) \log \left(\frac{a (\cosh (c+d x)+\sinh (c+d x))}{b-\sqrt{a^2+b^2}}+1\right)-(c+d x) \log \left(\frac{a (\cosh (c+d x)+\sinh (c+d x))}{b+\sqrt{a^2+b^2}}+1\right)+\text{Li}_2\left(\frac{a (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-b}\right)-\text{Li}_2\left(-\frac{a (\cosh (c+d x)+\sinh (c+d x))}{b+\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2}}\right)}{d^2}\right)}{8 a^3 (a+b \text{csch}(c+d x))}","\frac{b^2 e x}{a^3}+\frac{b^2 f x^2}{2 a^3}+\frac{b f \sinh (c+d x)}{a^2 d^2}-\frac{b (e+f x) \cosh (c+d x)}{a^2 d}-\frac{b f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^3 d^2}+\frac{b f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b \sqrt{a^2+b^2} (e+f x) \log \left(\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}+1\right)}{a^3 d}+\frac{b \sqrt{a^2+b^2} (e+f x) \log \left(\frac{a e^{c+d x}}{\sqrt{a^2+b^2}+b}+1\right)}{a^3 d}-\frac{f \cosh ^2(c+d x)}{4 a d^2}+\frac{(e+f x) \sinh (c+d x) \cosh (c+d x)}{2 a d}+\frac{e x}{2 a}+\frac{f x^2}{4 a}",1,"(Csch[c + d*x]*(b + a*Sinh[c + d*x])*(2*a^2*e*(c/d + x - (2*b*ArcTan[(a - b*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d)) + a^2*f*(x^2 + ((2*I)*b*Pi*ArcTanh[(-a + b*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d^2) + (2*b*(2*(c + I*ArcCos[((-I)*b)/a])*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ((-2*I)*c + Pi - (2*I)*d*x)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (ArcCos[((-I)*b)/a] - 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((a + I*b)*(a - I*b + Sqrt[-a^2 - b^2])*(1 + I*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - (ArcCos[((-I)*b)/a] + 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[(I*(a + I*b)*(-a + I*b + Sqrt[-a^2 - b^2])*(I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] + (ArcCos[((-I)*b)/a] + 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (2*I)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[-(((-1)^(3/4)*Sqrt[-a^2 - b^2]*E^(-1/2*c - (d*x)/2))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x]]))] + (ArcCos[((-I)*b)/a] - 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + (2*I)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((-1)^(1/4)*Sqrt[-a^2 - b^2]*E^((c + d*x)/2))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x]])] + I*(PolyLog[2, ((I*b + Sqrt[-a^2 - b^2])*(a + I*b - I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - PolyLog[2, ((b + I*Sqrt[-a^2 - b^2])*(I*a - b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))])))/(Sqrt[-a^2 - b^2]*d^2)) + (2*e*((a^2 + 4*b^2)*(c + d*x) - (2*b*(3*a^2 + 4*b^2)*ArcTan[(a - b*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[c + d*x] + a^2*Sinh[2*(c + d*x)]))/d + (f*((a^2 + 4*b^2)*(-c + d*x)*(c + d*x) - 8*a*b*d*x*Cosh[c + d*x] - a^2*Cosh[2*(c + d*x)] - (2*b*(3*a^2 + 4*b^2)*(2*c*ArcTanh[(b + a*Cosh[c + d*x] + a*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + (c + d*x)*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b - Sqrt[a^2 + b^2])] - (c + d*x)*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2])] + PolyLog[2, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])] - PolyLog[2, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] + 8*a*b*Sinh[c + d*x] + 2*a^2*d*x*Sinh[2*(c + d*x)]))/d^2))/(8*a^3*(a + b*Csch[c + d*x]))","C",0
25,1,109,95,0.5358691,"\int \frac{\cosh ^2(c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[Cosh[c + d*x]^2/(a + b*Csch[c + d*x]),x]","\frac{8 b \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)+a^2 \sinh (2 (c+d x))+2 a^2 c+2 a^2 d x-4 a b \cosh (c+d x)+4 b^2 c+4 b^2 d x}{4 a^3 d}","-\frac{\cosh (c+d x) (2 b-a \sinh (c+d x))}{2 a^2 d}+\frac{2 b \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a^3 d}+\frac{x \left(a^2+2 b^2\right)}{2 a^3}",1,"(2*a^2*c + 4*b^2*c + 2*a^2*d*x + 4*b^2*d*x + 8*b*Sqrt[-a^2 - b^2]*ArcTan[(a - b*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] - 4*a*b*Cosh[c + d*x] + a^2*Sinh[2*(c + d*x)])/(4*a^3*d)","A",1
26,1,7866,864,39.7286102,"\int \frac{(e+f x)^3 \cosh ^3(c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^3)/(a + b*Csch[c + d*x]),x]","\text{Result too large to show}","\frac{b \left(a^2+b^2\right) (e+f x)^4}{4 a^4 f}-\frac{b \sinh ^2(c+d x) (e+f x)^3}{2 a^2 d}-\frac{b \left(a^2+b^2\right) \log \left(\frac{e^{c+d x} a}{b-\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{a^4 d}-\frac{b \left(a^2+b^2\right) \log \left(\frac{e^{c+d x} a}{b+\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{a^4 d}+\frac{\cosh ^2(c+d x) \sinh (c+d x) (e+f x)^3}{3 a d}+\frac{b^2 \sinh (c+d x) (e+f x)^3}{a^3 d}+\frac{2 \sinh (c+d x) (e+f x)^3}{3 a d}-\frac{b (e+f x)^3}{4 a^2 d}-\frac{f \cosh ^3(c+d x) (e+f x)^2}{3 a d^2}-\frac{3 b^2 f \cosh (c+d x) (e+f x)^2}{a^3 d^2}-\frac{2 f \cosh (c+d x) (e+f x)^2}{a d^2}-\frac{3 b \left(a^2+b^2\right) f \text{Li}_2\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right) (e+f x)^2}{a^4 d^2}-\frac{3 b \left(a^2+b^2\right) f \text{Li}_2\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right) (e+f x)^2}{a^4 d^2}+\frac{3 b f \cosh (c+d x) \sinh (c+d x) (e+f x)^2}{4 a^2 d^2}-\frac{3 b f^2 \sinh ^2(c+d x) (e+f x)}{4 a^2 d^3}+\frac{6 b \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right) (e+f x)}{a^4 d^3}+\frac{6 b \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right) (e+f x)}{a^4 d^3}+\frac{6 b^2 f^2 \sinh (c+d x) (e+f x)}{a^3 d^3}+\frac{40 f^2 \sinh (c+d x) (e+f x)}{9 a d^3}+\frac{2 f^2 \cosh ^2(c+d x) \sinh (c+d x) (e+f x)}{9 a d^3}-\frac{2 f^3 \cosh ^3(c+d x)}{27 a d^4}-\frac{3 b f^3 x}{8 a^2 d^3}-\frac{6 b^2 f^3 \cosh (c+d x)}{a^3 d^4}-\frac{40 f^3 \cosh (c+d x)}{9 a d^4}-\frac{6 b \left(a^2+b^2\right) f^3 \text{Li}_4\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^4 d^4}-\frac{6 b \left(a^2+b^2\right) f^3 \text{Li}_4\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^4 d^4}+\frac{3 b f^3 \cosh (c+d x) \sinh (c+d x)}{8 a^2 d^4}",1,"Result too large to show","C",0
27,1,3874,636,17.3277566,"\int \frac{(e+f x)^2 \cosh ^3(c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^3)/(a + b*Csch[c + d*x]),x]","\text{Result too large to show}","\frac{2 b^2 f^2 \sinh (c+d x)}{a^3 d^3}-\frac{2 b^2 f (e+f x) \cosh (c+d x)}{a^3 d^2}+\frac{b^2 (e+f x)^2 \sinh (c+d x)}{a^3 d}-\frac{b f^2 \sinh ^2(c+d x)}{4 a^2 d^3}+\frac{b f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 a^2 d^2}-\frac{b (e+f x)^2 \sinh ^2(c+d x)}{2 a^2 d}-\frac{b e f x}{2 a^2 d}-\frac{b f^2 x^2}{4 a^2 d}+\frac{2 b f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^4 d^3}+\frac{2 b f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^4 d^3}-\frac{2 b f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^4 d^2}-\frac{2 b f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^4 d^2}-\frac{b \left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}+1\right)}{a^4 d}-\frac{b \left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{a e^{c+d x}}{\sqrt{a^2+b^2}+b}+1\right)}{a^4 d}+\frac{b \left(a^2+b^2\right) (e+f x)^3}{3 a^4 f}+\frac{2 f^2 \sinh ^3(c+d x)}{27 a d^3}+\frac{14 f^2 \sinh (c+d x)}{9 a d^3}-\frac{2 f (e+f x) \cosh ^3(c+d x)}{9 a d^2}-\frac{4 f (e+f x) \cosh (c+d x)}{3 a d^2}+\frac{2 (e+f x)^2 \sinh (c+d x)}{3 a d}+\frac{(e+f x)^2 \sinh (c+d x) \cosh ^2(c+d x)}{3 a d}",1,"(f^2*Csch[c + d*x]*(2*b*x^3*(-1 + Coth[c]) - 2*b*x^3*Coth[c] - (6*a^2*b*(d^2*x^2*Log[1 + ((b - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*d*x*PolyLog[2, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*PolyLog[3, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a]))/(Sqrt[a^2 + b^2]*(-b + Sqrt[a^2 + b^2])*d^3) - (6*a^2*b*(d^2*x^2*Log[1 + ((b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*d*x*PolyLog[2, ((b + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/a] - 2*PolyLog[3, ((b + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/a]))/(Sqrt[a^2 + b^2]*(b + Sqrt[a^2 + b^2])*d^3) + (6*b^2*(d^2*x^2*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b - Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])] - 2*PolyLog[3, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])]))/(Sqrt[a^2 + b^2]*d^3) - (6*b^2*(d^2*x^2*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) + (6*a*Cosh[d*x]*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c]))/d^3 + (6*a*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c])*Sinh[d*x])/d^3)*(b + a*Sinh[c + d*x]))/(12*a^2*(a + b*Csch[c + d*x])) - (e^2*Csch[c + d*x]*((b*Log[b + a*Sinh[c + d*x]])/a^2 - Sinh[c + d*x]/a)*(b + a*Sinh[c + d*x]))/(2*d*(a + b*Csch[c + d*x])) + (e*f*Csch[c + d*x]*(b + a*Sinh[c + d*x])*(-(a*Cosh[c + d*x]) - b*(c + d*x)*Log[b + a*Sinh[c + d*x]] + b*c*Log[1 + (a*Sinh[c + d*x])/b] + I*b*((-1/8*I)*(2*c + I*Pi + 2*d*x)^2 - (4*I)*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]]*ArcTan[((I*a + b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[a^2 + b^2]] - (((-2*I)*c + Pi - (2*I)*d*x + 4*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]])*Log[1 + ((-b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])/2 - (((-2*I)*c + Pi - (2*I)*d*x - 4*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]])*Log[1 - ((b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])/2 + (Pi/2 - I*(c + d*x))*Log[b + a*Sinh[c + d*x]] + I*(PolyLog[2, ((b - Sqrt[a^2 + b^2])*E^(c + d*x))/a] + PolyLog[2, ((b + Sqrt[a^2 + b^2])*E^(c + d*x))/a])) + a*d*x*Sinh[c + d*x]))/(a^2*d^2*(a + b*Csch[c + d*x])) + (e^2*Csch[c + d*x]*(b + a*Sinh[c + d*x])*(-3*b*(a^2 + 2*b^2)*Log[b + a*Sinh[c + d*x]] + 3*a*(a^2 + 2*b^2)*Sinh[c + d*x] - 3*a^2*b*Sinh[c + d*x]^2 + 2*a^3*Sinh[c + d*x]^3))/(6*a^4*d*(a + b*Csch[c + d*x])) + (e*f*Csch[c + d*x]*(b + a*Sinh[c + d*x])*(-18*a*(a^2 + 4*b^2)*Cosh[c + d*x] - 18*a^2*b*d*x*Cosh[2*(c + d*x)] - 2*a^3*Cosh[3*(c + d*x)] - 36*b*(a^2 + 2*b^2)*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (a*E^(c + d*x))/(b - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (a*E^(c + d*x))/(b + Sqrt[a^2 + b^2])] - c*Log[b + a*Sinh[c + d*x]] + PolyLog[2, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] + PolyLog[2, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))]) + 18*a*(a^2 + 4*b^2)*d*x*Sinh[c + d*x] + 9*a^2*b*Sinh[2*(c + d*x)] + 6*a^3*d*x*Sinh[3*(c + d*x)]))/(36*a^4*d^2*(a + b*Csch[c + d*x])) + (f^2*Csch[c + d*x]*(b + a*Sinh[c + d*x])*((2*b*(a^2 + 2*b^2)*(-1 + Coth[c])*(2*x^3 + (6*b*(d^2*x^2*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b - Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])] - 2*PolyLog[3, (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(-b + Sqrt[a^2 + b^2])])*Sinh[c]*(Cosh[c] + Sinh[c]))/(Sqrt[a^2 + b^2]*d^3) - (3*a^2*(d^2*x^2*Log[1 + ((b - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*d*x*PolyLog[2, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*PolyLog[3, ((-b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(-b + Sqrt[a^2 + b^2])*d^3) - (3*a^2*(d^2*x^2*Log[1 + ((b + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/a] - 2*d*x*PolyLog[2, ((b + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/a] - 2*PolyLog[3, ((b + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/a])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(b + Sqrt[a^2 + b^2])*d^3) - (3*b*(d^2*x^2*Log[1 + (a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, -((a*(Cosh[c + d*x] + Sinh[c + d*x]))/(b + Sqrt[a^2 + b^2]))])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*d^3)))/(3*a^4) + Csch[c]*(Cosh[3*c + 3*d*x]/(108*a^4*d^3) - Sinh[3*c + 3*d*x]/(108*a^4*d^3))*(27*a^2*b*Cosh[d*x] + 54*a^2*b*d*x*Cosh[d*x] + 54*a^2*b*d^2*x^2*Cosh[d*x] - 27*a^2*b*Cosh[2*c + d*x] - 54*a^2*b*d*x*Cosh[2*c + d*x] - 54*a^2*b*d^2*x^2*Cosh[2*c + d*x] + 108*a^3*Cosh[c + 2*d*x] + 432*a*b^2*Cosh[c + 2*d*x] + 108*a^3*d*x*Cosh[c + 2*d*x] + 432*a*b^2*d*x*Cosh[c + 2*d*x] + 54*a^3*d^2*x^2*Cosh[c + 2*d*x] + 216*a*b^2*d^2*x^2*Cosh[c + 2*d*x] - 108*a^3*Cosh[3*c + 2*d*x] - 432*a*b^2*Cosh[3*c + 2*d*x] - 108*a^3*d*x*Cosh[3*c + 2*d*x] - 432*a*b^2*d*x*Cosh[3*c + 2*d*x] - 54*a^3*d^2*x^2*Cosh[3*c + 2*d*x] - 216*a*b^2*d^2*x^2*Cosh[3*c + 2*d*x] - 72*a^2*b*d^3*x^3*Cosh[2*c + 3*d*x] - 144*b^3*d^3*x^3*Cosh[2*c + 3*d*x] - 72*a^2*b*d^3*x^3*Cosh[4*c + 3*d*x] - 144*b^3*d^3*x^3*Cosh[4*c + 3*d*x] - 108*a^3*Cosh[3*c + 4*d*x] - 432*a*b^2*Cosh[3*c + 4*d*x] + 108*a^3*d*x*Cosh[3*c + 4*d*x] + 432*a*b^2*d*x*Cosh[3*c + 4*d*x] - 54*a^3*d^2*x^2*Cosh[3*c + 4*d*x] - 216*a*b^2*d^2*x^2*Cosh[3*c + 4*d*x] + 108*a^3*Cosh[5*c + 4*d*x] + 432*a*b^2*Cosh[5*c + 4*d*x] - 108*a^3*d*x*Cosh[5*c + 4*d*x] - 432*a*b^2*d*x*Cosh[5*c + 4*d*x] + 54*a^3*d^2*x^2*Cosh[5*c + 4*d*x] + 216*a*b^2*d^2*x^2*Cosh[5*c + 4*d*x] + 27*a^2*b*Cosh[4*c + 5*d*x] - 54*a^2*b*d*x*Cosh[4*c + 5*d*x] + 54*a^2*b*d^2*x^2*Cosh[4*c + 5*d*x] - 27*a^2*b*Cosh[6*c + 5*d*x] + 54*a^2*b*d*x*Cosh[6*c + 5*d*x] - 54*a^2*b*d^2*x^2*Cosh[6*c + 5*d*x] - 4*a^3*Cosh[5*c + 6*d*x] + 12*a^3*d*x*Cosh[5*c + 6*d*x] - 18*a^3*d^2*x^2*Cosh[5*c + 6*d*x] + 4*a^3*Cosh[7*c + 6*d*x] - 12*a^3*d*x*Cosh[7*c + 6*d*x] + 18*a^3*d^2*x^2*Cosh[7*c + 6*d*x] - 8*a^3*Sinh[c] - 24*a^3*d*x*Sinh[c] - 36*a^3*d^2*x^2*Sinh[c] + 27*a^2*b*Sinh[d*x] + 54*a^2*b*d*x*Sinh[d*x] + 54*a^2*b*d^2*x^2*Sinh[d*x] - 27*a^2*b*Sinh[2*c + d*x] - 54*a^2*b*d*x*Sinh[2*c + d*x] - 54*a^2*b*d^2*x^2*Sinh[2*c + d*x] + 108*a^3*Sinh[c + 2*d*x] + 432*a*b^2*Sinh[c + 2*d*x] + 108*a^3*d*x*Sinh[c + 2*d*x] + 432*a*b^2*d*x*Sinh[c + 2*d*x] + 54*a^3*d^2*x^2*Sinh[c + 2*d*x] + 216*a*b^2*d^2*x^2*Sinh[c + 2*d*x] - 108*a^3*Sinh[3*c + 2*d*x] - 432*a*b^2*Sinh[3*c + 2*d*x] - 108*a^3*d*x*Sinh[3*c + 2*d*x] - 432*a*b^2*d*x*Sinh[3*c + 2*d*x] - 54*a^3*d^2*x^2*Sinh[3*c + 2*d*x] - 216*a*b^2*d^2*x^2*Sinh[3*c + 2*d*x] - 72*a^2*b*d^3*x^3*Sinh[2*c + 3*d*x] - 144*b^3*d^3*x^3*Sinh[2*c + 3*d*x] - 72*a^2*b*d^3*x^3*Sinh[4*c + 3*d*x] - 144*b^3*d^3*x^3*Sinh[4*c + 3*d*x] - 108*a^3*Sinh[3*c + 4*d*x] - 432*a*b^2*Sinh[3*c + 4*d*x] + 108*a^3*d*x*Sinh[3*c + 4*d*x] + 432*a*b^2*d*x*Sinh[3*c + 4*d*x] - 54*a^3*d^2*x^2*Sinh[3*c + 4*d*x] - 216*a*b^2*d^2*x^2*Sinh[3*c + 4*d*x] + 108*a^3*Sinh[5*c + 4*d*x] + 432*a*b^2*Sinh[5*c + 4*d*x] - 108*a^3*d*x*Sinh[5*c + 4*d*x] - 432*a*b^2*d*x*Sinh[5*c + 4*d*x] + 54*a^3*d^2*x^2*Sinh[5*c + 4*d*x] + 216*a*b^2*d^2*x^2*Sinh[5*c + 4*d*x] + 27*a^2*b*Sinh[4*c + 5*d*x] - 54*a^2*b*d*x*Sinh[4*c + 5*d*x] + 54*a^2*b*d^2*x^2*Sinh[4*c + 5*d*x] - 27*a^2*b*Sinh[6*c + 5*d*x] + 54*a^2*b*d*x*Sinh[6*c + 5*d*x] - 54*a^2*b*d^2*x^2*Sinh[6*c + 5*d*x] - 4*a^3*Sinh[5*c + 6*d*x] + 12*a^3*d*x*Sinh[5*c + 6*d*x] - 18*a^3*d^2*x^2*Sinh[5*c + 6*d*x] + 4*a^3*Sinh[7*c + 6*d*x] - 12*a^3*d*x*Sinh[7*c + 6*d*x] + 18*a^3*d^2*x^2*Sinh[7*c + 6*d*x])))/(8*(a + b*Csch[c + d*x]))","C",0
28,1,743,400,5.9108906,"\int \frac{(e+f x) \cosh ^3(c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^3)/(a + b*Csch[c + d*x]),x]","-\frac{\text{csch}(c+d x) (a \sinh (c+d x)+b) \left(\frac{9}{2} a^2 f \left(8 b \left(\text{Li}_2\left(\frac{\left(b-\sqrt{a^2+b^2}\right) e^{c+d x}}{a}\right)+\text{Li}_2\left(\frac{\left(b+\sqrt{a^2+b^2}\right) e^{c+d x}}{a}\right)\right)+4 b \log \left(\frac{\left(\sqrt{a^2+b^2}-b\right) e^{c+d x}}{a}+1\right) \left(4 i \sin ^{-1}\left(\frac{\sqrt{1+\frac{i b}{a}}}{\sqrt{2}}\right)+2 c+2 d x+i \pi \right)+4 b \log \left(1-\frac{\left(\sqrt{a^2+b^2}+b\right) e^{c+d x}}{a}\right) \left(-4 i \sin ^{-1}\left(\frac{\sqrt{1+\frac{i b}{a}}}{\sqrt{2}}\right)+2 c+2 d x+i \pi \right)-32 b \sin ^{-1}\left(\frac{\sqrt{1+\frac{i b}{a}}}{\sqrt{2}}\right) \tan ^{-1}\left(\frac{(b+i a) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{a^2+b^2}}\right)-4 i \pi  b \log (a \sinh (c+d x)+b)-8 b c \log \left(\frac{a \sinh (c+d x)}{b}+1\right)-8 a d x \sinh (c+d x)+8 a \cosh (c+d x)-b (2 c+2 d x+i \pi )^2\right)-36 a^2 d e (a \sinh (c+d x)-b \log (a \sinh (c+d x)+b))+12 d e \left(-2 a^3 \sinh ^3(c+d x)-3 a \left(a^2+2 b^2\right) \sinh (c+d x)+3 b \left(a^2+2 b^2\right) \log (a \sinh (c+d x)+b)+3 a^2 b \sinh ^2(c+d x)\right)+f \left(-6 a^3 d x \sinh (3 (c+d x))+2 a^3 \cosh (3 (c+d x))+36 b \left(a^2+2 b^2\right) \left(\text{Li}_2\left(\frac{a e^{c+d x}}{\sqrt{a^2+b^2}-b}\right)+\text{Li}_2\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)+(c+d x) \log \left(\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}+1\right)+(c+d x) \log \left(\frac{a e^{c+d x}}{\sqrt{a^2+b^2}+b}+1\right)-c \log (a \sinh (c+d x)+b)-\frac{1}{2} (c+d x)^2\right)-18 a d x \left(a^2+4 b^2\right) \sinh (c+d x)+18 a \left(a^2+4 b^2\right) \cosh (c+d x)-9 a^2 b \sinh (2 (c+d x))+18 a^2 b d x \cosh (2 (c+d x))\right)\right)}{72 a^4 d^2 (a+b \text{csch}(c+d x))}","-\frac{b^2 f \cosh (c+d x)}{a^3 d^2}+\frac{b^2 (e+f x) \sinh (c+d x)}{a^3 d}+\frac{b f \sinh (c+d x) \cosh (c+d x)}{4 a^2 d^2}-\frac{b (e+f x) \sinh ^2(c+d x)}{2 a^2 d}-\frac{b f x}{4 a^2 d}-\frac{b f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}\right)}{a^4 d^2}-\frac{b f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{a e^{c+d x}}{b+\sqrt{a^2+b^2}}\right)}{a^4 d^2}-\frac{b \left(a^2+b^2\right) (e+f x) \log \left(\frac{a e^{c+d x}}{b-\sqrt{a^2+b^2}}+1\right)}{a^4 d}-\frac{b \left(a^2+b^2\right) (e+f x) \log \left(\frac{a e^{c+d x}}{\sqrt{a^2+b^2}+b}+1\right)}{a^4 d}+\frac{b \left(a^2+b^2\right) (e+f x)^2}{2 a^4 f}-\frac{f \cosh ^3(c+d x)}{9 a d^2}-\frac{2 f \cosh (c+d x)}{3 a d^2}+\frac{2 (e+f x) \sinh (c+d x)}{3 a d}+\frac{(e+f x) \sinh (c+d x) \cosh ^2(c+d x)}{3 a d}",1,"-1/72*(Csch[c + d*x]*(b + a*Sinh[c + d*x])*(-36*a^2*d*e*(-(b*Log[b + a*Sinh[c + d*x]]) + a*Sinh[c + d*x]) + (9*a^2*f*(-(b*(2*c + I*Pi + 2*d*x)^2) - 32*b*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]]*ArcTan[((I*a + b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[a^2 + b^2]] + 8*a*Cosh[c + d*x] + 4*b*(2*c + I*Pi + 2*d*x + (4*I)*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]])*Log[1 + ((-b + Sqrt[a^2 + b^2])*E^(c + d*x))/a] + 4*b*(2*c + I*Pi + 2*d*x - (4*I)*ArcSin[Sqrt[1 + (I*b)/a]/Sqrt[2]])*Log[1 - ((b + Sqrt[a^2 + b^2])*E^(c + d*x))/a] - (4*I)*b*Pi*Log[b + a*Sinh[c + d*x]] - 8*b*c*Log[1 + (a*Sinh[c + d*x])/b] + 8*b*(PolyLog[2, ((b - Sqrt[a^2 + b^2])*E^(c + d*x))/a] + PolyLog[2, ((b + Sqrt[a^2 + b^2])*E^(c + d*x))/a]) - 8*a*d*x*Sinh[c + d*x]))/2 + 12*d*e*(3*b*(a^2 + 2*b^2)*Log[b + a*Sinh[c + d*x]] - 3*a*(a^2 + 2*b^2)*Sinh[c + d*x] + 3*a^2*b*Sinh[c + d*x]^2 - 2*a^3*Sinh[c + d*x]^3) + f*(18*a*(a^2 + 4*b^2)*Cosh[c + d*x] + 18*a^2*b*d*x*Cosh[2*(c + d*x)] + 2*a^3*Cosh[3*(c + d*x)] + 36*b*(a^2 + 2*b^2)*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (a*E^(c + d*x))/(b - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (a*E^(c + d*x))/(b + Sqrt[a^2 + b^2])] - c*Log[b + a*Sinh[c + d*x]] + PolyLog[2, (a*E^(c + d*x))/(-b + Sqrt[a^2 + b^2])] + PolyLog[2, -((a*E^(c + d*x))/(b + Sqrt[a^2 + b^2]))]) - 18*a*(a^2 + 4*b^2)*d*x*Sinh[c + d*x] - 9*a^2*b*Sinh[2*(c + d*x)] - 6*a^3*d*x*Sinh[3*(c + d*x)])))/(a^4*d^2*(a + b*Csch[c + d*x]))","C",1
29,1,75,85,0.2386824,"\int \frac{\cosh ^3(c+d x)}{a+b \text{csch}(c+d x)} \, dx","Integrate[Cosh[c + d*x]^3/(a + b*Csch[c + d*x]),x]","\frac{2 a^3 \sinh ^3(c+d x)+6 a \left(a^2+b^2\right) \sinh (c+d x)-6 b \left(a^2+b^2\right) \log (a \sinh (c+d x)+b)-3 a^2 b \sinh ^2(c+d x)}{6 a^4 d}","-\frac{b \sinh ^2(c+d x)}{2 a^2 d}-\frac{b \left(a^2+b^2\right) \log (a \sinh (c+d x)+b)}{a^4 d}+\frac{\left(a^2+b^2\right) \sinh (c+d x)}{a^3 d}+\frac{\sinh ^3(c+d x)}{3 a d}",1,"(-6*b*(a^2 + b^2)*Log[b + a*Sinh[c + d*x]] + 6*a*(a^2 + b^2)*Sinh[c + d*x] - 3*a^2*b*Sinh[c + d*x]^2 + 2*a^3*Sinh[c + d*x]^3)/(6*a^4*d)","A",1