1,1,138,104,0.0987557,"\int x^5 \left(a+b \text{csch}\left(c+d x^2\right)\right) \, dx","Integrate[x^5*(a + b*Csch[c + d*x^2]),x]","\frac{a x^6}{6}-\frac{b \left(d^2 x^4 \tanh ^{-1}\left(\sinh \left(c+d x^2\right)+\cosh \left(c+d x^2\right)\right)+d x^2 \text{Li}_2\left(-\cosh \left(d x^2+c\right)-\sinh \left(d x^2+c\right)\right)-d x^2 \text{Li}_2\left(\cosh \left(d x^2+c\right)+\sinh \left(d x^2+c\right)\right)-\text{Li}_3\left(-\cosh \left(d x^2+c\right)-\sinh \left(d x^2+c\right)\right)+\text{Li}_3\left(\cosh \left(d x^2+c\right)+\sinh \left(d x^2+c\right)\right)\right)}{d^3}","\frac{a x^6}{6}+\frac{b \text{Li}_3\left(-e^{d x^2+c}\right)}{d^3}-\frac{b \text{Li}_3\left(e^{d x^2+c}\right)}{d^3}-\frac{b x^2 \text{Li}_2\left(-e^{d x^2+c}\right)}{d^2}+\frac{b x^2 \text{Li}_2\left(e^{d x^2+c}\right)}{d^2}-\frac{b x^4 \tanh ^{-1}\left(e^{c+d x^2}\right)}{d}",1,"(a*x^6)/6 - (b*(d^2*x^4*ArcTanh[Cosh[c + d*x^2] + Sinh[c + d*x^2]] + d*x^2*PolyLog[2, -Cosh[c + d*x^2] - Sinh[c + d*x^2]] - d*x^2*PolyLog[2, Cosh[c + d*x^2] + Sinh[c + d*x^2]] - PolyLog[3, -Cosh[c + d*x^2] - Sinh[c + d*x^2]] + PolyLog[3, Cosh[c + d*x^2] + Sinh[c + d*x^2]]))/d^3","A",0
2,0,0,26,12.8796384,"\int x^4 \left(a+b \text{csch}\left(c+d x^2\right)\right) \, dx","Integrate[x^4*(a + b*Csch[c + d*x^2]),x]","\int x^4 \left(a+b \text{csch}\left(c+d x^2\right)\right) \, dx","b \text{Int}\left(x^4 \text{csch}\left(c+d x^2\right),x\right)+\frac{a x^5}{5}",0,"Integrate[x^4*(a + b*Csch[c + d*x^2]), x]","A",-1
3,1,108,68,0.1426252,"\int x^3 \left(a+b \text{csch}\left(c+d x^2\right)\right) \, dx","Integrate[x^3*(a + b*Csch[c + d*x^2]),x]","\frac{1}{4} \left(a x^4+\frac{2 b \left(\text{Li}_2\left(-e^{-d x^2-c}\right)-\text{Li}_2\left(e^{-d x^2-c}\right)+\left(c+d x^2\right) \left(\log \left(1-e^{-c-d x^2}\right)-\log \left(e^{-c-d x^2}+1\right)\right)-c \log \left(\tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)\right)\right)}{d^2}\right)","\frac{a x^4}{4}-\frac{b \text{Li}_2\left(-e^{d x^2+c}\right)}{2 d^2}+\frac{b \text{Li}_2\left(e^{d x^2+c}\right)}{2 d^2}-\frac{b x^2 \tanh ^{-1}\left(e^{c+d x^2}\right)}{d}",1,"(a*x^4 + (2*b*((c + d*x^2)*(Log[1 - E^(-c - d*x^2)] - Log[1 + E^(-c - d*x^2)]) - c*Log[Tanh[(c + d*x^2)/2]] + PolyLog[2, -E^(-c - d*x^2)] - PolyLog[2, E^(-c - d*x^2)]))/d^2)/4","A",1
4,0,0,26,10.5418737,"\int x^2 \left(a+b \text{csch}\left(c+d x^2\right)\right) \, dx","Integrate[x^2*(a + b*Csch[c + d*x^2]),x]","\int x^2 \left(a+b \text{csch}\left(c+d x^2\right)\right) \, dx","b \text{Int}\left(x^2 \text{csch}\left(c+d x^2\right),x\right)+\frac{a x^3}{3}",0,"Integrate[x^2*(a + b*Csch[c + d*x^2]), x]","A",-1
5,1,57,26,0.0344598,"\int x \left(a+b \text{csch}\left(c+d x^2\right)\right) \, dx","Integrate[x*(a + b*Csch[c + d*x^2]),x]","\frac{a x^2}{2}+\frac{b \log \left(\sinh \left(\frac{c}{2}+\frac{d x^2}{2}\right)\right)}{2 d}-\frac{b \log \left(\cosh \left(\frac{c}{2}+\frac{d x^2}{2}\right)\right)}{2 d}","\frac{a x^2}{2}-\frac{b \tanh ^{-1}\left(\cosh \left(c+d x^2\right)\right)}{2 d}",1,"(a*x^2)/2 - (b*Log[Cosh[c/2 + (d*x^2)/2]])/(2*d) + (b*Log[Sinh[c/2 + (d*x^2)/2]])/(2*d)","B",1
6,0,0,22,9.6526341,"\int \frac{a+b \text{csch}\left(c+d x^2\right)}{x} \, dx","Integrate[(a + b*Csch[c + d*x^2])/x,x]","\int \frac{a+b \text{csch}\left(c+d x^2\right)}{x} \, dx","b \text{Int}\left(\frac{\text{csch}\left(c+d x^2\right)}{x},x\right)+a \log (x)",0,"Integrate[(a + b*Csch[c + d*x^2])/x, x]","A",-1
7,0,0,24,11.215623,"\int \frac{a+b \text{csch}\left(c+d x^2\right)}{x^2} \, dx","Integrate[(a + b*Csch[c + d*x^2])/x^2,x]","\int \frac{a+b \text{csch}\left(c+d x^2\right)}{x^2} \, dx","b \text{Int}\left(\frac{\text{csch}\left(c+d x^2\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Csch[c + d*x^2])/x^2, x]","A",-1
8,1,595,196,6.2661595,"\int x^5 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2 \, dx","Integrate[x^5*(a + b*Csch[c + d*x^2])^2,x]","-\frac{-2 a^2 e^{2 c} d^3 x^6+2 a^2 d^3 x^6-12 a b e^{2 c} d^2 x^4 \log \left(1-e^{-c-d x^2}\right)+12 a b d^2 x^4 \log \left(1-e^{-c-d x^2}\right)+12 a b e^{2 c} d^2 x^4 \log \left(e^{-c-d x^2}+1\right)-12 a b d^2 x^4 \log \left(e^{-c-d x^2}+1\right)+12 b \left(e^{2 c}-1\right) \left(b-2 a d x^2\right) \text{Li}_2\left(-e^{-d x^2-c}\right)+12 b \left(e^{2 c}-1\right) \left(2 a d x^2+b\right) \text{Li}_2\left(e^{-d x^2-c}\right)-24 a b e^{2 c} \text{Li}_3\left(-e^{-d x^2-c}\right)+24 a b \text{Li}_3\left(-e^{-d x^2-c}\right)+24 a b e^{2 c} \text{Li}_3\left(e^{-d x^2-c}\right)-24 a b \text{Li}_3\left(e^{-d x^2-c}\right)-3 b^2 e^{2 c} d^2 x^4 \text{csch}\left(\frac{c}{2}\right) \sinh \left(\frac{d x^2}{2}\right) \text{csch}\left(\frac{1}{2} \left(c+d x^2\right)\right)+3 b^2 d^2 x^4 \text{csch}\left(\frac{c}{2}\right) \sinh \left(\frac{d x^2}{2}\right) \text{csch}\left(\frac{1}{2} \left(c+d x^2\right)\right)+3 b^2 e^{2 c} d^2 x^4 \text{sech}\left(\frac{c}{2}\right) \sinh \left(\frac{d x^2}{2}\right) \text{sech}\left(\frac{1}{2} \left(c+d x^2\right)\right)-3 b^2 d^2 x^4 \text{sech}\left(\frac{c}{2}\right) \sinh \left(\frac{d x^2}{2}\right) \text{sech}\left(\frac{1}{2} \left(c+d x^2\right)\right)-12 b^2 e^{2 c} d x^2 \log \left(1-e^{-c-d x^2}\right)+12 b^2 d x^2 \log \left(1-e^{-c-d x^2}\right)-12 b^2 e^{2 c} d x^2 \log \left(e^{-c-d x^2}+1\right)+12 b^2 d x^2 \log \left(e^{-c-d x^2}+1\right)+12 b^2 d^2 x^4}{12 \left(e^{2 c}-1\right) d^3}","\frac{a^2 x^6}{6}+\frac{2 a b \text{Li}_3\left(-e^{d x^2+c}\right)}{d^3}-\frac{2 a b \text{Li}_3\left(e^{d x^2+c}\right)}{d^3}-\frac{2 a b x^2 \text{Li}_2\left(-e^{d x^2+c}\right)}{d^2}+\frac{2 a b x^2 \text{Li}_2\left(e^{d x^2+c}\right)}{d^2}-\frac{2 a b x^4 \tanh ^{-1}\left(e^{c+d x^2}\right)}{d}+\frac{b^2 \text{Li}_2\left(e^{2 \left(d x^2+c\right)}\right)}{2 d^3}+\frac{b^2 x^2 \log \left(1-e^{2 \left(c+d x^2\right)}\right)}{d^2}-\frac{b^2 x^4 \coth \left(c+d x^2\right)}{2 d}-\frac{b^2 x^4}{2 d}",1,"-1/12*(12*b^2*d^2*x^4 + 2*a^2*d^3*x^6 - 2*a^2*d^3*E^(2*c)*x^6 + 12*b^2*d*x^2*Log[1 - E^(-c - d*x^2)] - 12*b^2*d*E^(2*c)*x^2*Log[1 - E^(-c - d*x^2)] + 12*a*b*d^2*x^4*Log[1 - E^(-c - d*x^2)] - 12*a*b*d^2*E^(2*c)*x^4*Log[1 - E^(-c - d*x^2)] + 12*b^2*d*x^2*Log[1 + E^(-c - d*x^2)] - 12*b^2*d*E^(2*c)*x^2*Log[1 + E^(-c - d*x^2)] - 12*a*b*d^2*x^4*Log[1 + E^(-c - d*x^2)] + 12*a*b*d^2*E^(2*c)*x^4*Log[1 + E^(-c - d*x^2)] + 12*b*(-1 + E^(2*c))*(b - 2*a*d*x^2)*PolyLog[2, -E^(-c - d*x^2)] + 12*b*(-1 + E^(2*c))*(b + 2*a*d*x^2)*PolyLog[2, E^(-c - d*x^2)] + 24*a*b*PolyLog[3, -E^(-c - d*x^2)] - 24*a*b*E^(2*c)*PolyLog[3, -E^(-c - d*x^2)] - 24*a*b*PolyLog[3, E^(-c - d*x^2)] + 24*a*b*E^(2*c)*PolyLog[3, E^(-c - d*x^2)] + 3*b^2*d^2*x^4*Csch[c/2]*Csch[(c + d*x^2)/2]*Sinh[(d*x^2)/2] - 3*b^2*d^2*E^(2*c)*x^4*Csch[c/2]*Csch[(c + d*x^2)/2]*Sinh[(d*x^2)/2] - 3*b^2*d^2*x^4*Sech[c/2]*Sech[(c + d*x^2)/2]*Sinh[(d*x^2)/2] + 3*b^2*d^2*E^(2*c)*x^4*Sech[c/2]*Sech[(c + d*x^2)/2]*Sinh[(d*x^2)/2])/(d^3*(-1 + E^(2*c)))","B",1
9,0,0,21,34.7125618,"\int x^4 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2 \, dx","Integrate[x^4*(a + b*Csch[c + d*x^2])^2,x]","\int x^4 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2 \, dx","\text{Int}\left(x^4 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2,x\right)",0,"Integrate[x^4*(a + b*Csch[c + d*x^2])^2, x]","A",-1
10,1,260,108,4.4960729,"\int x^3 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2 \, dx","Integrate[x^3*(a + b*Csch[c + d*x^2])^2,x]","\frac{2 d x^2 \left(a^2 d x^2-2 b^2 \coth (c)\right)+8 a b \left(\frac{\text{sech}(c) \left(\text{Li}_2\left(-e^{-d x^2-\tanh ^{-1}(\tanh (c))}\right)-\text{Li}_2\left(e^{-d x^2-\tanh ^{-1}(\tanh (c))}\right)+\left(\tanh ^{-1}(\tanh (c))+d x^2\right) \left(\log \left(1-e^{-\tanh ^{-1}(\tanh (c))-d x^2}\right)-\log \left(e^{-\tanh ^{-1}(\tanh (c))-d x^2}+1\right)\right)\right)}{\sqrt{\text{sech}^2(c)}}+2 \tanh ^{-1}(\tanh (c)) \tanh ^{-1}\left(\sinh (c) \tanh \left(\frac{d x^2}{2}\right)+\cosh (c)\right)\right)+4 b^2 d x^2 \coth (c)+2 b^2 d x^2 \text{csch}\left(\frac{c}{2}\right) \sinh \left(\frac{d x^2}{2}\right) \text{csch}\left(\frac{1}{2} \left(c+d x^2\right)\right)-2 b^2 d x^2 \text{sech}\left(\frac{c}{2}\right) \sinh \left(\frac{d x^2}{2}\right) \text{sech}\left(\frac{1}{2} \left(c+d x^2\right)\right)-4 b^2 \left(d x^2 \coth (c)-\log \left(\sinh \left(c+d x^2\right)\right)\right)}{8 d^2}","\frac{a^2 x^4}{4}-\frac{a b \text{Li}_2\left(-e^{d x^2+c}\right)}{d^2}+\frac{a b \text{Li}_2\left(e^{d x^2+c}\right)}{d^2}-\frac{2 a b x^2 \tanh ^{-1}\left(e^{c+d x^2}\right)}{d}+\frac{b^2 \log \left(\sinh \left(c+d x^2\right)\right)}{2 d^2}-\frac{b^2 x^2 \coth \left(c+d x^2\right)}{2 d}",1,"(4*b^2*d*x^2*Coth[c] + 2*d*x^2*(a^2*d*x^2 - 2*b^2*Coth[c]) - 4*b^2*(d*x^2*Coth[c] - Log[Sinh[c + d*x^2]]) + 8*a*b*(2*ArcTanh[Tanh[c]]*ArcTanh[Cosh[c] + Sinh[c]*Tanh[(d*x^2)/2]] + (((d*x^2 + ArcTanh[Tanh[c]])*(Log[1 - E^(-(d*x^2) - ArcTanh[Tanh[c]])] - Log[1 + E^(-(d*x^2) - ArcTanh[Tanh[c]])]) + PolyLog[2, -E^(-(d*x^2) - ArcTanh[Tanh[c]])] - PolyLog[2, E^(-(d*x^2) - ArcTanh[Tanh[c]])])*Sech[c])/Sqrt[Sech[c]^2]) + 2*b^2*d*x^2*Csch[c/2]*Csch[(c + d*x^2)/2]*Sinh[(d*x^2)/2] - 2*b^2*d*x^2*Sech[c/2]*Sech[(c + d*x^2)/2]*Sinh[(d*x^2)/2])/(8*d^2)","B",0
11,0,0,21,31.3965483,"\int x^2 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2 \, dx","Integrate[x^2*(a + b*Csch[c + d*x^2])^2,x]","\int x^2 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2 \, dx","\text{Int}\left(x^2 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2,x\right)",0,"Integrate[x^2*(a + b*Csch[c + d*x^2])^2, x]","A",-1
12,1,69,45,0.2768035,"\int x \left(a+b \text{csch}\left(c+d x^2\right)\right)^2 \, dx","Integrate[x*(a + b*Csch[c + d*x^2])^2,x]","-\frac{-2 a \left(a c+a d x^2+2 b \log \left(\tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)\right)\right)+b^2 \tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)+b^2 \coth \left(\frac{1}{2} \left(c+d x^2\right)\right)}{4 d}","\frac{a^2 x^2}{2}-\frac{a b \tanh ^{-1}\left(\cosh \left(c+d x^2\right)\right)}{d}-\frac{b^2 \coth \left(c+d x^2\right)}{2 d}",1,"-1/4*(b^2*Coth[(c + d*x^2)/2] - 2*a*(a*c + a*d*x^2 + 2*b*Log[Tanh[(c + d*x^2)/2]]) + b^2*Tanh[(c + d*x^2)/2])/d","A",1
13,0,0,21,66.8984947,"\int \frac{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2}{x} \, dx","Integrate[(a + b*Csch[c + d*x^2])^2/x,x]","\int \frac{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2}{x},x\right)",0,"Integrate[(a + b*Csch[c + d*x^2])^2/x, x]","A",-1
14,0,0,21,43.9133425,"\int \frac{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Csch[c + d*x^2])^2/x^2,x]","\int \frac{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2}{x^2},x\right)",0,"Integrate[(a + b*Csch[c + d*x^2])^2/x^2, x]","A",-1
15,1,147,90,0.0921646,"\int x \text{csch}^7\left(a+b x^2\right) \, dx","Integrate[x*Csch[a + b*x^2]^7,x]","-\frac{\text{csch}^6\left(\frac{1}{2} \left(a+b x^2\right)\right)}{768 b}+\frac{\text{csch}^4\left(\frac{1}{2} \left(a+b x^2\right)\right)}{128 b}-\frac{5 \text{csch}^2\left(\frac{1}{2} \left(a+b x^2\right)\right)}{128 b}-\frac{\text{sech}^6\left(\frac{1}{2} \left(a+b x^2\right)\right)}{768 b}-\frac{\text{sech}^4\left(\frac{1}{2} \left(a+b x^2\right)\right)}{128 b}-\frac{5 \text{sech}^2\left(\frac{1}{2} \left(a+b x^2\right)\right)}{128 b}-\frac{5 \log \left(\tanh \left(\frac{1}{2} \left(a+b x^2\right)\right)\right)}{32 b}","\frac{5 \tanh ^{-1}\left(\cosh \left(a+b x^2\right)\right)}{32 b}-\frac{\coth \left(a+b x^2\right) \text{csch}^5\left(a+b x^2\right)}{12 b}+\frac{5 \coth \left(a+b x^2\right) \text{csch}^3\left(a+b x^2\right)}{48 b}-\frac{5 \coth \left(a+b x^2\right) \text{csch}\left(a+b x^2\right)}{32 b}",1,"(-5*Csch[(a + b*x^2)/2]^2)/(128*b) + Csch[(a + b*x^2)/2]^4/(128*b) - Csch[(a + b*x^2)/2]^6/(768*b) - (5*Log[Tanh[(a + b*x^2)/2]])/(32*b) - (5*Sech[(a + b*x^2)/2]^2)/(128*b) - Sech[(a + b*x^2)/2]^4/(128*b) - Sech[(a + b*x^2)/2]^6/(768*b)","A",1
16,1,256,325,0.2047531,"\int \frac{x^5}{a+b \text{csch}\left(c+d x^2\right)} \, dx","Integrate[x^5/(a + b*Csch[c + d*x^2]),x]","\frac{-3 b d^2 x^4 \log \left(\frac{a e^{c+d x^2}}{b-\sqrt{a^2+b^2}}+1\right)+3 b d^2 x^4 \log \left(\frac{a e^{c+d x^2}}{\sqrt{a^2+b^2}+b}+1\right)-6 b d x^2 \text{Li}_2\left(\frac{a e^{d x^2+c}}{\sqrt{a^2+b^2}-b}\right)+6 b d x^2 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)+6 b \text{Li}_3\left(\frac{a e^{d x^2+c}}{\sqrt{a^2+b^2}-b}\right)-6 b \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)+d^3 x^6 \sqrt{a^2+b^2}}{6 a d^3 \sqrt{a^2+b^2}}","\frac{b \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b-\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{b \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{b x^2 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}+\frac{b x^2 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{b x^4 \log \left(\frac{a e^{c+d x^2}}{b-\sqrt{a^2+b^2}}+1\right)}{2 a d \sqrt{a^2+b^2}}+\frac{b x^4 \log \left(\frac{a e^{c+d x^2}}{\sqrt{a^2+b^2}+b}+1\right)}{2 a d \sqrt{a^2+b^2}}+\frac{x^6}{6 a}",1,"(Sqrt[a^2 + b^2]*d^3*x^6 - 3*b*d^2*x^4*Log[1 + (a*E^(c + d*x^2))/(b - Sqrt[a^2 + b^2])] + 3*b*d^2*x^4*Log[1 + (a*E^(c + d*x^2))/(b + Sqrt[a^2 + b^2])] - 6*b*d*x^2*PolyLog[2, (a*E^(c + d*x^2))/(-b + Sqrt[a^2 + b^2])] + 6*b*d*x^2*PolyLog[2, -((a*E^(c + d*x^2))/(b + Sqrt[a^2 + b^2]))] + 6*b*PolyLog[3, (a*E^(c + d*x^2))/(-b + Sqrt[a^2 + b^2])] - 6*b*PolyLog[3, -((a*E^(c + d*x^2))/(b + Sqrt[a^2 + b^2]))])/(6*a*Sqrt[a^2 + b^2]*d^3)","A",1
17,0,0,21,9.8170369,"\int \frac{x^4}{a+b \text{csch}\left(c+d x^2\right)} \, dx","Integrate[x^4/(a + b*Csch[c + d*x^2]),x]","\int \frac{x^4}{a+b \text{csch}\left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{x^4}{a+b \text{csch}\left(c+d x^2\right)},x\right)",0,"Integrate[x^4/(a + b*Csch[c + d*x^2]), x]","A",-1
18,1,1166,225,3.213777,"\int \frac{x^3}{a+b \text{csch}\left(c+d x^2\right)} \, dx","Integrate[x^3/(a + b*Csch[c + d*x^2]),x]","\frac{\text{csch}\left(d x^2+c\right) \left(x^4+\frac{2 i b \pi  \tanh ^{-1}\left(\frac{b \tanh \left(\frac{1}{2} \left(d x^2+c\right)\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} \left(2 i d x^2+2 i c+\pi \right)\right)}{\sqrt{-a^2-b^2}}\right)+\left(-2 i d x^2-2 i c+\pi \right) \tanh ^{-1}\left(\frac{(b-i a) \tan \left(\frac{1}{4} \left(2 i d x^2+2 i c+\pi \right)\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} \left(2 i d x^2+2 i c+\pi \right)\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} \left(2 i d x^2+2 i c+\pi \right)\right)+1\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} \left(2 i d x^2+2 i c+\pi \right)\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} \left(2 i d x^2+2 i c+\pi \right)\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} \left(2 i d x^2+2 i c+\pi \right)\right)+i\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} \left(2 i d x^2+2 i c+\pi \right)\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} \left(2 i d x^2+2 i c+\pi \right)\right)}{\sqrt{-a^2-b^2}}\right)-2 i \tanh ^{-1}\left(\frac{(b-i a) \tan \left(\frac{1}{4} \left(2 i d x^2+2 i c+\pi \right)\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(-\frac{(-1)^{3/4} \sqrt{-a^2-b^2} e^{-\frac{d x^2}{2}-\frac{c}{2}}}{\sqrt{2} \sqrt{-i a} \sqrt{b+a \sinh \left(d x^2+c\right)}}\right)+\left(\cos ^{-1}\left(-\frac{i b}{a}\right)-2 \tan ^{-1}\left(\frac{(a-i b) \cot \left(\frac{1}{4} \left(2 i d x^2+2 i c+\pi \right)\right)}{\sqrt{-a^2-b^2}}\right)+2 i \tanh ^{-1}\left(\frac{(b-i a) \tan \left(\frac{1}{4} \left(2 i d x^2+2 i c+\pi \right)\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(\frac{\sqrt[4]{-1} \sqrt{-a^2-b^2} e^{\frac{1}{2} \left(d x^2+c\right)}}{\sqrt{2} \sqrt{-i a} \sqrt{b+a \sinh \left(d x^2+c\right)}}\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} \left(2 i d x^2+2 i c+\pi \right)\right)\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} \left(2 i d x^2+2 i c+\pi \right)\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} \left(2 i d x^2+2 i c+\pi \right)\right)\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} \left(2 i d x^2+2 i c+\pi \right)\right)\right)}\right)\right)\right)}{\sqrt{-a^2-b^2} d^2}\right) \left(b+a \sinh \left(d x^2+c\right)\right)}{4 a \left(a+b \text{csch}\left(d x^2+c\right)\right)}","-\frac{b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{a^2+b^2}}\right)}{2 a d^2 \sqrt{a^2+b^2}}+\frac{b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)}{2 a d^2 \sqrt{a^2+b^2}}-\frac{b x^2 \log \left(\frac{a e^{c+d x^2}}{b-\sqrt{a^2+b^2}}+1\right)}{2 a d \sqrt{a^2+b^2}}+\frac{b x^2 \log \left(\frac{a e^{c+d x^2}}{\sqrt{a^2+b^2}+b}+1\right)}{2 a d \sqrt{a^2+b^2}}+\frac{x^4}{4 a}",1,"(Csch[c + d*x^2]*(x^4 + ((2*I)*b*Pi*ArcTanh[(-a + b*Tanh[(c + d*x^2)/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^2)/4])/Sqrt[-a^2 - b^2]] + ((-2*I)*c + Pi - (2*I)*d*x^2)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x^2)/4])/Sqrt[-a^2 - b^2]] - (ArcCos[((-I)*b)/a] - 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x^2)/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^2)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x^2)/4]))] - (ArcCos[((-I)*b)/a] + 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x^2)/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^2)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x^2)/4]))] + (ArcCos[((-I)*b)/a] + 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x^2)/4])/Sqrt[-a^2 - b^2]] - (2*I)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x^2)/4])/Sqrt[-a^2 - b^2]])*Log[-(((-1)^(3/4)*Sqrt[-a^2 - b^2]*E^(-1/2*c - (d*x^2)/2))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x^2]]))] + (ArcCos[((-I)*b)/a] - 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x^2)/4])/Sqrt[-a^2 - b^2]] + (2*I)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x^2)/4])/Sqrt[-a^2 - b^2]])*Log[((-1)^(1/4)*Sqrt[-a^2 - b^2]*E^((c + d*x^2)/2))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x^2]])] + 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^2)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x^2)/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^2)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x^2)/4]))])))/(Sqrt[-a^2 - b^2]*d^2))*(b + a*Sinh[c + d*x^2]))/(4*a*(a + b*Csch[c + d*x^2]))","C",1
19,0,0,21,8.6074834,"\int \frac{x^2}{a+b \text{csch}\left(c+d x^2\right)} \, dx","Integrate[x^2/(a + b*Csch[c + d*x^2]),x]","\int \frac{x^2}{a+b \text{csch}\left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{x^2}{a+b \text{csch}\left(c+d x^2\right)},x\right)",0,"Integrate[x^2/(a + b*Csch[c + d*x^2]), x]","A",-1
20,1,71,60,0.1332538,"\int \frac{x}{a+b \text{csch}\left(c+d x^2\right)} \, dx","Integrate[x/(a + b*Csch[c + d*x^2]),x]","\frac{-\frac{2 b \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{-a^2-b^2}}\right)}{d \sqrt{-a^2-b^2}}+\frac{c}{d}+x^2}{2 a}","\frac{b \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{a^2+b^2}}\right)}{a d \sqrt{a^2+b^2}}+\frac{x^2}{2 a}",1,"(c/d + x^2 - (2*b*ArcTan[(a - b*Tanh[(c + d*x^2)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d))/(2*a)","A",1
21,0,0,21,5.3584673,"\int \frac{1}{x \left(a+b \text{csch}\left(c+d x^2\right)\right)} \, dx","Integrate[1/(x*(a + b*Csch[c + d*x^2])),x]","\int \frac{1}{x \left(a+b \text{csch}\left(c+d x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{csch}\left(c+d x^2\right)\right)},x\right)",0,"Integrate[1/(x*(a + b*Csch[c + d*x^2])), x]","A",-1
22,0,0,24,0.2219492,"\int \frac{a+b \text{csch}\left(c+d x^2\right)}{x^2} \, dx","Integrate[(a + b*Csch[c + d*x^2])/x^2,x]","\int \frac{a+b \text{csch}\left(c+d x^2\right)}{x^2} \, dx","b \text{Int}\left(\frac{\text{csch}\left(c+d x^2\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Csch[c + d*x^2])/x^2, x]","A",-1
23,1,1502,922,14.0966783,"\int \frac{x^5}{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2} \, dx","Integrate[x^5/(a + b*Csch[c + d*x^2])^2,x]","\frac{\text{csch}^2\left(d x^2+c\right) \left(b+a \sinh \left(d x^2+c\right)\right) \left(2 \left(b+a \sinh \left(d x^2+c\right)\right) x^6+\frac{6 b^2 \text{csch}(c) \left(b \cosh (c)+a \sinh \left(d x^2\right)\right) x^4}{\left(a^2+b^2\right) d}-\frac{6 b e^{2 c} \left(-2 a^2 d^2 e^c \log \left(\frac{e^{d x^2+2 c} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^4-b^2 d^2 e^c \log \left(\frac{e^{d x^2+2 c} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^4+2 a^2 d^2 e^{3 c} \log \left(\frac{e^{d x^2+2 c} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^4+b^2 d^2 e^{3 c} \log \left(\frac{e^{d x^2+2 c} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^4+2 a^2 d^2 e^c \log \left(\frac{e^{d x^2+2 c} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^4+b^2 d^2 e^c \log \left(\frac{e^{d x^2+2 c} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^4-2 a^2 d^2 e^{3 c} \log \left(\frac{e^{d x^2+2 c} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^4-b^2 d^2 e^{3 c} \log \left(\frac{e^{d x^2+2 c} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^4+2 b d^2 e^{2 c} \sqrt{\left(a^2+b^2\right) e^{2 c}} x^4-2 b d e^{2 c} \sqrt{\left(a^2+b^2\right) e^{2 c}} \log \left(\frac{e^{d x^2+2 c} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2+2 b d \sqrt{\left(a^2+b^2\right) e^{2 c}} \log \left(\frac{e^{d x^2+2 c} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2-2 b d e^{2 c} \sqrt{\left(a^2+b^2\right) e^{2 c}} \log \left(\frac{e^{d x^2+2 c} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2+2 b d \sqrt{\left(a^2+b^2\right) e^{2 c}} \log \left(\frac{e^{d x^2+2 c} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2+2 \left(-1+e^{2 c}\right) \left(2 a^2 d e^c x^2+b^2 d e^c x^2-b \sqrt{\left(a^2+b^2\right) e^{2 c}}\right) \text{Li}_2\left(-\frac{a e^{d x^2+2 c}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-2 \left(-1+e^{2 c}\right) \left(2 a^2 d e^c x^2+b^2 d e^c x^2+b \sqrt{\left(a^2+b^2\right) e^{2 c}}\right) \text{Li}_2\left(-\frac{a e^{d x^2+2 c}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+4 a^2 e^c \text{Li}_3\left(-\frac{a e^{d x^2+2 c}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+2 b^2 e^c \text{Li}_3\left(-\frac{a e^{d x^2+2 c}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-4 a^2 e^{3 c} \text{Li}_3\left(-\frac{a e^{d x^2+2 c}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-2 b^2 e^{3 c} \text{Li}_3\left(-\frac{a e^{d x^2+2 c}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-4 a^2 e^c \text{Li}_3\left(-\frac{a e^{d x^2+2 c}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-2 b^2 e^c \text{Li}_3\left(-\frac{a e^{d x^2+2 c}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+4 a^2 e^{3 c} \text{Li}_3\left(-\frac{a e^{d x^2+2 c}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+2 b^2 e^{3 c} \text{Li}_3\left(-\frac{a e^{d x^2+2 c}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right) \left(b+a \sinh \left(d x^2+c\right)\right)}{d^3 \left(\left(a^2+b^2\right) e^{2 c}\right)^{3/2} \left(-1+e^{2 c}\right)}\right)}{12 a^2 \left(a+b \text{csch}\left(d x^2+c\right)\right)^2}","\frac{x^6}{6 a^2}-\frac{b \log \left(\frac{e^{d x^2+c} a}{b-\sqrt{a^2+b^2}}+1\right) x^4}{a^2 \sqrt{a^2+b^2} d}+\frac{b^3 \log \left(\frac{e^{d x^2+c} a}{b-\sqrt{a^2+b^2}}+1\right) x^4}{2 a^2 \left(a^2+b^2\right)^{3/2} d}+\frac{b \log \left(\frac{e^{d x^2+c} a}{b+\sqrt{a^2+b^2}}+1\right) x^4}{a^2 \sqrt{a^2+b^2} d}-\frac{b^3 \log \left(\frac{e^{d x^2+c} a}{b+\sqrt{a^2+b^2}}+1\right) x^4}{2 a^2 \left(a^2+b^2\right)^{3/2} d}-\frac{b^2 x^4}{2 a^2 \left(a^2+b^2\right) d}-\frac{b^2 \cosh \left(d x^2+c\right) x^4}{2 a \left(a^2+b^2\right) d \left(b+a \sinh \left(d x^2+c\right)\right)}+\frac{b^2 \log \left(\frac{e^{d x^2+c} a}{b-\sqrt{a^2+b^2}}+1\right) x^2}{a^2 \left(a^2+b^2\right) d^2}+\frac{b^2 \log \left(\frac{e^{d x^2+c} a}{b+\sqrt{a^2+b^2}}+1\right) x^2}{a^2 \left(a^2+b^2\right) d^2}-\frac{2 b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{a^2+b^2}}\right) x^2}{a^2 \sqrt{a^2+b^2} d^2}+\frac{b^3 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{a^2+b^2}}\right) x^2}{a^2 \left(a^2+b^2\right)^{3/2} d^2}+\frac{2 b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right) x^2}{a^2 \sqrt{a^2+b^2} d^2}-\frac{b^3 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right) x^2}{a^2 \left(a^2+b^2\right)^{3/2} d^2}+\frac{b^2 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{a^2+b^2}}\right)}{a^2 \left(a^2+b^2\right) d^3}+\frac{b^2 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)}{a^2 \left(a^2+b^2\right) d^3}+\frac{2 b \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b-\sqrt{a^2+b^2}}\right)}{a^2 \sqrt{a^2+b^2} d^3}-\frac{b^3 \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b-\sqrt{a^2+b^2}}\right)}{a^2 \left(a^2+b^2\right)^{3/2} d^3}-\frac{2 b \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)}{a^2 \sqrt{a^2+b^2} d^3}+\frac{b^3 \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)}{a^2 \left(a^2+b^2\right)^{3/2} d^3}",1,"(Csch[c + d*x^2]^2*(b + a*Sinh[c + d*x^2])*((6*b^2*x^4*Csch[c]*(b*Cosh[c] + a*Sinh[d*x^2]))/((a^2 + b^2)*d) + 2*x^6*(b + a*Sinh[c + d*x^2]) - (6*b*E^(2*c)*(2*b*d^2*E^(2*c)*Sqrt[(a^2 + b^2)*E^(2*c)]*x^4 + 2*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*x^2*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 2*b*d*E^(2*c)*Sqrt[(a^2 + b^2)*E^(2*c)]*x^2*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 2*a^2*d^2*E^c*x^4*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - b^2*d^2*E^c*x^4*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*a^2*d^2*E^(3*c)*x^4*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + b^2*d^2*E^(3*c)*x^4*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*x^2*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 2*b*d*E^(2*c)*Sqrt[(a^2 + b^2)*E^(2*c)]*x^2*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*a^2*d^2*E^c*x^4*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + b^2*d^2*E^c*x^4*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 2*a^2*d^2*E^(3*c)*x^4*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - b^2*d^2*E^(3*c)*x^4*Log[1 + (a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*(-1 + E^(2*c))*(-(b*Sqrt[(a^2 + b^2)*E^(2*c)]) + 2*a^2*d*E^c*x^2 + b^2*d*E^c*x^2)*PolyLog[2, -((a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 2*(-1 + E^(2*c))*(b*Sqrt[(a^2 + b^2)*E^(2*c)] + 2*a^2*d*E^c*x^2 + b^2*d*E^c*x^2)*PolyLog[2, -((a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 4*a^2*E^c*PolyLog[3, -((a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 2*b^2*E^c*PolyLog[3, -((a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 4*a^2*E^(3*c)*PolyLog[3, -((a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 2*b^2*E^(3*c)*PolyLog[3, -((a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 4*a^2*E^c*PolyLog[3, -((a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 2*b^2*E^c*PolyLog[3, -((a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 4*a^2*E^(3*c)*PolyLog[3, -((a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 2*b^2*E^(3*c)*PolyLog[3, -((a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])*(b + a*Sinh[c + d*x^2]))/(d^3*((a^2 + b^2)*E^(2*c))^(3/2)*(-1 + E^(2*c)))))/(12*a^2*(a + b*Csch[c + d*x^2])^2)","A",1
24,-1,0,21,180.0010615,"\int \frac{x^4}{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2} \, dx","Integrate[x^4/(a + b*Csch[c + d*x^2])^2,x]","\text{\$Aborted}","\text{Int}\left(\frac{x^4}{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2},x\right)",0,"$Aborted","F",-1
25,1,747,519,6.4375306,"\int \frac{x^3}{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2} \, dx","Integrate[x^3/(a + b*Csch[c + d*x^2])^2,x]","\frac{\text{csch}^2\left(c+d x^2\right) \left(a \sinh \left(c+d x^2\right)+b\right) \left(-\frac{2 b \left(a^2+b^2\right) \left(a \sinh \left(c+d x^2\right)+b\right) \left(-\sqrt{-a^2-b^2} \left(2 a^2+b^2\right) \text{Li}_2\left(\frac{a e^{d x^2+c}}{\sqrt{a^2+b^2}-b}\right)+\sqrt{-a^2-b^2} \left(2 a^2+b^2\right) \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)-b \sqrt{-\left(a^2+b^2\right)^2} \left(c+d x^2\right)-2 a^2 \sqrt{-a^2-b^2} \left(c+d x^2\right) \log \left(\frac{a e^{c+d x^2}}{b-\sqrt{a^2+b^2}}+1\right)+2 a^2 \sqrt{-a^2-b^2} \left(c+d x^2\right) \log \left(\frac{a e^{c+d x^2}}{\sqrt{a^2+b^2}+b}+1\right)-b^2 \sqrt{-a^2-b^2} \left(c+d x^2\right) \log \left(\frac{a e^{c+d x^2}}{b-\sqrt{a^2+b^2}}+1\right)+b^2 \sqrt{-a^2-b^2} \left(c+d x^2\right) \log \left(\frac{a e^{c+d x^2}}{\sqrt{a^2+b^2}+b}+1\right)+b \sqrt{-\left(a^2+b^2\right)^2} \log \left(a \left(e^{2 \left(c+d x^2\right)}-1\right)+2 b e^{c+d x^2}\right)-4 a^2 c \sqrt{a^2+b^2} \tan ^{-1}\left(\frac{b-a e^{-c-d x^2}}{\sqrt{-a^2-b^2}}\right)-2 b^2 c \sqrt{a^2+b^2} \tan ^{-1}\left(\frac{b-a e^{-c-d x^2}}{\sqrt{-a^2-b^2}}\right)+2 b^2 \sqrt{a^2+b^2} \tan ^{-1}\left(\frac{b-a e^{-c-d x^2}}{\sqrt{-a^2-b^2}}\right)+2 b^2 \sqrt{a^2+b^2} \tan ^{-1}\left(\frac{a e^{c+d x^2}+b}{\sqrt{-a^2-b^2}}\right)\right)}{\left(-\left(a^2+b^2\right)^2\right)^{3/2}}-\frac{2 a b^2 d x^2 \cosh \left(c+d x^2\right)}{a^2+b^2}+\left(d x^2-c\right) \left(c+d x^2\right) \left(a \sinh \left(c+d x^2\right)+b\right)\right)}{4 a^2 d^2 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2}","-\frac{b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{a^2+b^2}}\right)}{a^2 d^2 \sqrt{a^2+b^2}}+\frac{b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)}{a^2 d^2 \sqrt{a^2+b^2}}+\frac{b^2 \log \left(a \sinh \left(c+d x^2\right)+b\right)}{2 a^2 d^2 \left(a^2+b^2\right)}-\frac{b x^2 \log \left(\frac{a e^{c+d x^2}}{b-\sqrt{a^2+b^2}}+1\right)}{a^2 d \sqrt{a^2+b^2}}+\frac{b x^2 \log \left(\frac{a e^{c+d x^2}}{\sqrt{a^2+b^2}+b}+1\right)}{a^2 d \sqrt{a^2+b^2}}-\frac{b^2 x^2 \cosh \left(c+d x^2\right)}{2 a d \left(a^2+b^2\right) \left(a \sinh \left(c+d x^2\right)+b\right)}+\frac{b^3 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{a^2+b^2}}\right)}{2 a^2 d^2 \left(a^2+b^2\right)^{3/2}}-\frac{b^3 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{a^2+b^2}}\right)}{2 a^2 d^2 \left(a^2+b^2\right)^{3/2}}+\frac{b^3 x^2 \log \left(\frac{a e^{c+d x^2}}{b-\sqrt{a^2+b^2}}+1\right)}{2 a^2 d \left(a^2+b^2\right)^{3/2}}-\frac{b^3 x^2 \log \left(\frac{a e^{c+d x^2}}{\sqrt{a^2+b^2}+b}+1\right)}{2 a^2 d \left(a^2+b^2\right)^{3/2}}+\frac{x^4}{4 a^2}",1,"(Csch[c + d*x^2]^2*(b + a*Sinh[c + d*x^2])*((-2*a*b^2*d*x^2*Cosh[c + d*x^2])/(a^2 + b^2) + (-c + d*x^2)*(c + d*x^2)*(b + a*Sinh[c + d*x^2]) - (2*b*(a^2 + b^2)*(-(b*Sqrt[-(a^2 + b^2)^2]*(c + d*x^2)) + 2*b^2*Sqrt[a^2 + b^2]*ArcTan[(b - a*E^(-c - d*x^2))/Sqrt[-a^2 - b^2]] - 4*a^2*Sqrt[a^2 + b^2]*c*ArcTan[(b - a*E^(-c - d*x^2))/Sqrt[-a^2 - b^2]] - 2*b^2*Sqrt[a^2 + b^2]*c*ArcTan[(b - a*E^(-c - d*x^2))/Sqrt[-a^2 - b^2]] + 2*b^2*Sqrt[a^2 + b^2]*ArcTan[(b + a*E^(c + d*x^2))/Sqrt[-a^2 - b^2]] - 2*a^2*Sqrt[-a^2 - b^2]*(c + d*x^2)*Log[1 + (a*E^(c + d*x^2))/(b - Sqrt[a^2 + b^2])] - b^2*Sqrt[-a^2 - b^2]*(c + d*x^2)*Log[1 + (a*E^(c + d*x^2))/(b - Sqrt[a^2 + b^2])] + 2*a^2*Sqrt[-a^2 - b^2]*(c + d*x^2)*Log[1 + (a*E^(c + d*x^2))/(b + Sqrt[a^2 + b^2])] + b^2*Sqrt[-a^2 - b^2]*(c + d*x^2)*Log[1 + (a*E^(c + d*x^2))/(b + Sqrt[a^2 + b^2])] + b*Sqrt[-(a^2 + b^2)^2]*Log[2*b*E^(c + d*x^2) + a*(-1 + E^(2*(c + d*x^2)))] - Sqrt[-a^2 - b^2]*(2*a^2 + b^2)*PolyLog[2, (a*E^(c + d*x^2))/(-b + Sqrt[a^2 + b^2])] + Sqrt[-a^2 - b^2]*(2*a^2 + b^2)*PolyLog[2, -((a*E^(c + d*x^2))/(b + Sqrt[a^2 + b^2]))])*(b + a*Sinh[c + d*x^2]))/(-(a^2 + b^2)^2)^(3/2)))/(4*a^2*d^2*(a + b*Csch[c + d*x^2])^2)","A",0
26,-1,0,21,180.0010631,"\int \frac{x^2}{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2} \, dx","Integrate[x^2/(a + b*Csch[c + d*x^2])^2,x]","\text{\$Aborted}","\text{Int}\left(\frac{x^2}{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2},x\right)",0,"$Aborted","F",-1
27,1,161,113,0.4798771,"\int \frac{x}{\left(a+b \text{csch}\left(c+d x^2\right)\right)^2} \, dx","Integrate[x/(a + b*Csch[c + d*x^2])^2,x]","\frac{\text{csch}\left(c+d x^2\right) \left(a \sinh \left(c+d x^2\right)+b\right) \left(-\frac{a b^2 \coth \left(c+d x^2\right)}{a^2+b^2}+\frac{2 b \left(2 a^2+b^2\right) \left(a+b \text{csch}\left(c+d x^2\right)\right) \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+\left(c+d x^2\right) \left(a+b \text{csch}\left(c+d x^2\right)\right)\right)}{2 a^2 d \left(a+b \text{csch}\left(c+d x^2\right)\right)^2}","\frac{b \left(2 a^2+b^2\right) \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{a^2+b^2}}\right)}{a^2 d \left(a^2+b^2\right)^{3/2}}-\frac{b^2 \coth \left(c+d x^2\right)}{2 a d \left(a^2+b^2\right) \left(a+b \text{csch}\left(c+d x^2\right)\right)}+\frac{x^2}{2 a^2}",1,"(Csch[c + d*x^2]*(-((a*b^2*Coth[c + d*x^2])/(a^2 + b^2)) + (c + d*x^2)*(a + b*Csch[c + d*x^2]) + (2*b*(2*a^2 + b^2)*ArcTan[(a - b*Tanh[(c + d*x^2)/2])/Sqrt[-a^2 - b^2]]*(a + b*Csch[c + d*x^2]))/(-a^2 - b^2)^(3/2))*(b + a*Sinh[c + d*x^2]))/(2*a^2*d*(a + b*Csch[c + d*x^2])^2)","A",1
28,-1,0,21,180.0030216,"\int \frac{1}{x \left(a+b \text{csch}\left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Csch[c + d*x^2])^2),x]","\text{\$Aborted}","\text{Int}\left(\frac{1}{x \left(a+b \text{csch}\left(c+d x^2\right)\right)^2},x\right)",0,"$Aborted","F",-1
29,-1,0,21,180.0017055,"\int \frac{1}{x^2 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Csch[c + d*x^2])^2),x]","\text{\$Aborted}","\text{Int}\left(\frac{1}{x^2 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2},x\right)",0,"$Aborted","F",-1
30,-1,0,21,180.0049122,"\int \frac{1}{x^3 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x^3*(a + b*Csch[c + d*x^2])^2),x]","\text{\$Aborted}","\text{Int}\left(\frac{1}{x^3 \left(a+b \text{csch}\left(c+d x^2\right)\right)^2},x\right)",0,"$Aborted","F",-1
31,1,365,356,2.9008694,"\int x^3 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x^3*(a + b*Csch[c + d*Sqrt[x]]),x]","\frac{a x^4}{4}+\frac{2 b \left(d^7 x^{7/2} \log \left(1-e^{c+d \sqrt{x}}\right)-d^7 x^{7/2} \log \left(e^{c+d \sqrt{x}}+1\right)-7 d^6 x^3 \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)+7 d^6 x^3 \text{Li}_2\left(e^{c+d \sqrt{x}}\right)+42 d^5 x^{5/2} \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)-42 d^5 x^{5/2} \text{Li}_3\left(e^{c+d \sqrt{x}}\right)-210 d^4 x^2 \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)+210 d^4 x^2 \text{Li}_4\left(e^{c+d \sqrt{x}}\right)+840 d^3 x^{3/2} \text{Li}_5\left(-e^{c+d \sqrt{x}}\right)-840 d^3 x^{3/2} \text{Li}_5\left(e^{c+d \sqrt{x}}\right)-2520 d^2 x \text{Li}_6\left(-e^{c+d \sqrt{x}}\right)+2520 d^2 x \text{Li}_6\left(e^{c+d \sqrt{x}}\right)+5040 d \sqrt{x} \text{Li}_7\left(-e^{c+d \sqrt{x}}\right)-5040 d \sqrt{x} \text{Li}_7\left(e^{c+d \sqrt{x}}\right)-5040 \text{Li}_8\left(-e^{c+d \sqrt{x}}\right)+5040 \text{Li}_8\left(e^{c+d \sqrt{x}}\right)\right)}{d^8}","\frac{a x^4}{4}-\frac{10080 b \text{Li}_8\left(-e^{c+d \sqrt{x}}\right)}{d^8}+\frac{10080 b \text{Li}_8\left(e^{c+d \sqrt{x}}\right)}{d^8}+\frac{10080 b \sqrt{x} \text{Li}_7\left(-e^{c+d \sqrt{x}}\right)}{d^7}-\frac{10080 b \sqrt{x} \text{Li}_7\left(e^{c+d \sqrt{x}}\right)}{d^7}-\frac{5040 b x \text{Li}_6\left(-e^{c+d \sqrt{x}}\right)}{d^6}+\frac{5040 b x \text{Li}_6\left(e^{c+d \sqrt{x}}\right)}{d^6}+\frac{1680 b x^{3/2} \text{Li}_5\left(-e^{c+d \sqrt{x}}\right)}{d^5}-\frac{1680 b x^{3/2} \text{Li}_5\left(e^{c+d \sqrt{x}}\right)}{d^5}-\frac{420 b x^2 \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)}{d^4}+\frac{420 b x^2 \text{Li}_4\left(e^{c+d \sqrt{x}}\right)}{d^4}+\frac{84 b x^{5/2} \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)}{d^3}-\frac{84 b x^{5/2} \text{Li}_3\left(e^{c+d \sqrt{x}}\right)}{d^3}-\frac{14 b x^3 \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)}{d^2}+\frac{14 b x^3 \text{Li}_2\left(e^{c+d \sqrt{x}}\right)}{d^2}-\frac{4 b x^{7/2} \tanh ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}",1,"(a*x^4)/4 + (2*b*(d^7*x^(7/2)*Log[1 - E^(c + d*Sqrt[x])] - d^7*x^(7/2)*Log[1 + E^(c + d*Sqrt[x])] - 7*d^6*x^3*PolyLog[2, -E^(c + d*Sqrt[x])] + 7*d^6*x^3*PolyLog[2, E^(c + d*Sqrt[x])] + 42*d^5*x^(5/2)*PolyLog[3, -E^(c + d*Sqrt[x])] - 42*d^5*x^(5/2)*PolyLog[3, E^(c + d*Sqrt[x])] - 210*d^4*x^2*PolyLog[4, -E^(c + d*Sqrt[x])] + 210*d^4*x^2*PolyLog[4, E^(c + d*Sqrt[x])] + 840*d^3*x^(3/2)*PolyLog[5, -E^(c + d*Sqrt[x])] - 840*d^3*x^(3/2)*PolyLog[5, E^(c + d*Sqrt[x])] - 2520*d^2*x*PolyLog[6, -E^(c + d*Sqrt[x])] + 2520*d^2*x*PolyLog[6, E^(c + d*Sqrt[x])] + 5040*d*Sqrt[x]*PolyLog[7, -E^(c + d*Sqrt[x])] - 5040*d*Sqrt[x]*PolyLog[7, E^(c + d*Sqrt[x])] - 5040*PolyLog[8, -E^(c + d*Sqrt[x])] + 5040*PolyLog[8, E^(c + d*Sqrt[x])]))/d^8","A",1
32,1,273,260,2.8362513,"\int x^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x^2*(a + b*Csch[c + d*Sqrt[x]]),x]","\frac{a x^3}{3}+\frac{2 b \left(d^5 x^{5/2} \log \left(1-e^{c+d \sqrt{x}}\right)-d^5 x^{5/2} \log \left(e^{c+d \sqrt{x}}+1\right)-5 d^4 x^2 \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)+5 d^4 x^2 \text{Li}_2\left(e^{c+d \sqrt{x}}\right)+20 d^3 x^{3/2} \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)-20 d^3 x^{3/2} \text{Li}_3\left(e^{c+d \sqrt{x}}\right)-60 d^2 x \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)+60 d^2 x \text{Li}_4\left(e^{c+d \sqrt{x}}\right)+120 d \sqrt{x} \text{Li}_5\left(-e^{c+d \sqrt{x}}\right)-120 d \sqrt{x} \text{Li}_5\left(e^{c+d \sqrt{x}}\right)-120 \text{Li}_6\left(-e^{c+d \sqrt{x}}\right)+120 \text{Li}_6\left(e^{c+d \sqrt{x}}\right)\right)}{d^6}","\frac{a x^3}{3}-\frac{240 b \text{Li}_6\left(-e^{c+d \sqrt{x}}\right)}{d^6}+\frac{240 b \text{Li}_6\left(e^{c+d \sqrt{x}}\right)}{d^6}+\frac{240 b \sqrt{x} \text{Li}_5\left(-e^{c+d \sqrt{x}}\right)}{d^5}-\frac{240 b \sqrt{x} \text{Li}_5\left(e^{c+d \sqrt{x}}\right)}{d^5}-\frac{120 b x \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)}{d^4}+\frac{120 b x \text{Li}_4\left(e^{c+d \sqrt{x}}\right)}{d^4}+\frac{40 b x^{3/2} \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)}{d^3}-\frac{40 b x^{3/2} \text{Li}_3\left(e^{c+d \sqrt{x}}\right)}{d^3}-\frac{10 b x^2 \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)}{d^2}+\frac{10 b x^2 \text{Li}_2\left(e^{c+d \sqrt{x}}\right)}{d^2}-\frac{4 b x^{5/2} \tanh ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}",1,"(a*x^3)/3 + (2*b*(d^5*x^(5/2)*Log[1 - E^(c + d*Sqrt[x])] - d^5*x^(5/2)*Log[1 + E^(c + d*Sqrt[x])] - 5*d^4*x^2*PolyLog[2, -E^(c + d*Sqrt[x])] + 5*d^4*x^2*PolyLog[2, E^(c + d*Sqrt[x])] + 20*d^3*x^(3/2)*PolyLog[3, -E^(c + d*Sqrt[x])] - 20*d^3*x^(3/2)*PolyLog[3, E^(c + d*Sqrt[x])] - 60*d^2*x*PolyLog[4, -E^(c + d*Sqrt[x])] + 60*d^2*x*PolyLog[4, E^(c + d*Sqrt[x])] + 120*d*Sqrt[x]*PolyLog[5, -E^(c + d*Sqrt[x])] - 120*d*Sqrt[x]*PolyLog[5, E^(c + d*Sqrt[x])] - 120*PolyLog[6, -E^(c + d*Sqrt[x])] + 120*PolyLog[6, E^(c + d*Sqrt[x])]))/d^6","A",1
33,1,181,164,2.7685552,"\int x \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x*(a + b*Csch[c + d*Sqrt[x]]),x]","\frac{a x^2}{2}+\frac{2 b \left(d^3 x^{3/2} \log \left(1-e^{c+d \sqrt{x}}\right)-d^3 x^{3/2} \log \left(e^{c+d \sqrt{x}}+1\right)-3 d^2 x \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)+3 d^2 x \text{Li}_2\left(e^{c+d \sqrt{x}}\right)+6 d \sqrt{x} \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)-6 d \sqrt{x} \text{Li}_3\left(e^{c+d \sqrt{x}}\right)-6 \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)+6 \text{Li}_4\left(e^{c+d \sqrt{x}}\right)\right)}{d^4}","\frac{a x^2}{2}-\frac{12 b \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)}{d^4}+\frac{12 b \text{Li}_4\left(e^{c+d \sqrt{x}}\right)}{d^4}+\frac{12 b \sqrt{x} \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)}{d^3}-\frac{12 b \sqrt{x} \text{Li}_3\left(e^{c+d \sqrt{x}}\right)}{d^3}-\frac{6 b x \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)}{d^2}+\frac{6 b x \text{Li}_2\left(e^{c+d \sqrt{x}}\right)}{d^2}-\frac{4 b x^{3/2} \tanh ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}",1,"(a*x^2)/2 + (2*b*(d^3*x^(3/2)*Log[1 - E^(c + d*Sqrt[x])] - d^3*x^(3/2)*Log[1 + E^(c + d*Sqrt[x])] - 3*d^2*x*PolyLog[2, -E^(c + d*Sqrt[x])] + 3*d^2*x*PolyLog[2, E^(c + d*Sqrt[x])] + 6*d*Sqrt[x]*PolyLog[3, -E^(c + d*Sqrt[x])] - 6*d*Sqrt[x]*PolyLog[3, E^(c + d*Sqrt[x])] - 6*PolyLog[4, -E^(c + d*Sqrt[x])] + 6*PolyLog[4, E^(c + d*Sqrt[x])]))/d^4","A",1
34,0,0,24,18.2685604,"\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{x} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])/x,x]","\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{x} \, dx","b \text{Int}\left(\frac{\text{csch}\left(c+d \sqrt{x}\right)}{x},x\right)+a \log (x)",0,"Integrate[(a + b*Csch[c + d*Sqrt[x]])/x, x]","A",-1
35,0,0,26,20.992184,"\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{x^2} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])/x^2,x]","\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{x^2} \, dx","b \text{Int}\left(\frac{\text{csch}\left(c+d \sqrt{x}\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Csch[c + d*Sqrt[x]])/x^2, x]","A",-1
36,1,1077,597,12.6288092,"\int x^3 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[x^3*(a + b*Csch[c + d*Sqrt[x]])^2,x]","\frac{a^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \sinh ^2\left(c+d \sqrt{x}\right) x^4}{4 \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)^2}+\frac{b^2 \text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \sinh ^2\left(c+d \sqrt{x}\right) \sinh \left(\frac{d \sqrt{x}}{2}\right) x^{7/2}}{d \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)^2}-\frac{b^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right) \sinh ^2\left(c+d \sqrt{x}\right) \sinh \left(\frac{d \sqrt{x}}{2}\right) x^{7/2}}{d \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)^2}+\frac{2 b \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \left(-\frac{2 b x^{7/2} d^7}{-1+e^{2 c}}+2 a x^{7/2} \log \left(1-e^{-c-d \sqrt{x}}\right) d^7-2 a x^{7/2} \log \left(1+e^{-c-d \sqrt{x}}\right) d^7+7 b x^3 \log \left(1-e^{-c-d \sqrt{x}}\right) d^6+7 b x^3 \log \left(1+e^{-c-d \sqrt{x}}\right) d^6-42 b \left(x^{5/2} \text{Li}_2\left(-e^{-c-d \sqrt{x}}\right) d^5+5 x^2 \text{Li}_3\left(-e^{-c-d \sqrt{x}}\right) d^4+20 \left(x^{3/2} \text{Li}_4\left(-e^{-c-d \sqrt{x}}\right) d^3+3 x \text{Li}_5\left(-e^{-c-d \sqrt{x}}\right) d^2+6 \left(d \sqrt{x} \text{Li}_6\left(-e^{-c-d \sqrt{x}}\right)+\text{Li}_7\left(-e^{-c-d \sqrt{x}}\right)\right)\right)\right)-42 b \left(x^{5/2} \text{Li}_2\left(e^{-c-d \sqrt{x}}\right) d^5+5 x^2 \text{Li}_3\left(e^{-c-d \sqrt{x}}\right) d^4+20 \left(x^{3/2} \text{Li}_4\left(e^{-c-d \sqrt{x}}\right) d^3+3 x \text{Li}_5\left(e^{-c-d \sqrt{x}}\right) d^2+6 \left(d \sqrt{x} \text{Li}_6\left(e^{-c-d \sqrt{x}}\right)+\text{Li}_7\left(e^{-c-d \sqrt{x}}\right)\right)\right)\right)+14 a \left(x^3 \text{Li}_2\left(-e^{-c-d \sqrt{x}}\right) d^6+6 \left(x^{5/2} \text{Li}_3\left(-e^{-c-d \sqrt{x}}\right) d^5+5 x^2 \text{Li}_4\left(-e^{-c-d \sqrt{x}}\right) d^4+20 \left(x^{3/2} \text{Li}_5\left(-e^{-c-d \sqrt{x}}\right) d^3+3 x \text{Li}_6\left(-e^{-c-d \sqrt{x}}\right) d^2+6 \sqrt{x} \text{Li}_7\left(-e^{-c-d \sqrt{x}}\right) d+6 \text{Li}_8\left(-e^{-c-d \sqrt{x}}\right)\right)\right)\right)-14 a \left(x^3 \text{Li}_2\left(e^{-c-d \sqrt{x}}\right) d^6+6 \left(x^{5/2} \text{Li}_3\left(e^{-c-d \sqrt{x}}\right) d^5+5 x^2 \text{Li}_4\left(e^{-c-d \sqrt{x}}\right) d^4+20 \left(x^{3/2} \text{Li}_5\left(e^{-c-d \sqrt{x}}\right) d^3+3 x \text{Li}_6\left(e^{-c-d \sqrt{x}}\right) d^2+6 \sqrt{x} \text{Li}_7\left(e^{-c-d \sqrt{x}}\right) d+6 \text{Li}_8\left(e^{-c-d \sqrt{x}}\right)\right)\right)\right)\right) \sinh ^2\left(c+d \sqrt{x}\right)}{d^8 \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)^2}","\frac{a^2 x^4}{4}-\frac{20160 a b \text{Li}_8\left(-e^{c+d \sqrt{x}}\right)}{d^8}+\frac{20160 a b \text{Li}_8\left(e^{c+d \sqrt{x}}\right)}{d^8}+\frac{20160 a b \sqrt{x} \text{Li}_7\left(-e^{c+d \sqrt{x}}\right)}{d^7}-\frac{20160 a b \sqrt{x} \text{Li}_7\left(e^{c+d \sqrt{x}}\right)}{d^7}-\frac{10080 a b x \text{Li}_6\left(-e^{c+d \sqrt{x}}\right)}{d^6}+\frac{10080 a b x \text{Li}_6\left(e^{c+d \sqrt{x}}\right)}{d^6}+\frac{3360 a b x^{3/2} \text{Li}_5\left(-e^{c+d \sqrt{x}}\right)}{d^5}-\frac{3360 a b x^{3/2} \text{Li}_5\left(e^{c+d \sqrt{x}}\right)}{d^5}-\frac{840 a b x^2 \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)}{d^4}+\frac{840 a b x^2 \text{Li}_4\left(e^{c+d \sqrt{x}}\right)}{d^4}+\frac{168 a b x^{5/2} \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)}{d^3}-\frac{168 a b x^{5/2} \text{Li}_3\left(e^{c+d \sqrt{x}}\right)}{d^3}-\frac{28 a b x^3 \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)}{d^2}+\frac{28 a b x^3 \text{Li}_2\left(e^{c+d \sqrt{x}}\right)}{d^2}-\frac{8 a b x^{7/2} \tanh ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}-\frac{315 b^2 \text{Li}_7\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{2 d^8}+\frac{315 b^2 \sqrt{x} \text{Li}_6\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^7}-\frac{315 b^2 x \text{Li}_5\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^6}+\frac{210 b^2 x^{3/2} \text{Li}_4\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{105 b^2 x^2 \text{Li}_3\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{42 b^2 x^{5/2} \text{Li}_2\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{14 b^2 x^3 \log \left(1-e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b^2 x^{7/2} \coth \left(c+d \sqrt{x}\right)}{d}-\frac{2 b^2 x^{7/2}}{d}",1,"(a^2*x^4*(a + b*Csch[c + d*Sqrt[x]])^2*Sinh[c + d*Sqrt[x]]^2)/(4*(b + a*Sinh[c + d*Sqrt[x]])^2) + (2*b*(a + b*Csch[c + d*Sqrt[x]])^2*((-2*b*d^7*x^(7/2))/(-1 + E^(2*c)) + 7*b*d^6*x^3*Log[1 - E^(-c - d*Sqrt[x])] + 2*a*d^7*x^(7/2)*Log[1 - E^(-c - d*Sqrt[x])] + 7*b*d^6*x^3*Log[1 + E^(-c - d*Sqrt[x])] - 2*a*d^7*x^(7/2)*Log[1 + E^(-c - d*Sqrt[x])] - 42*b*(d^5*x^(5/2)*PolyLog[2, -E^(-c - d*Sqrt[x])] + 5*d^4*x^2*PolyLog[3, -E^(-c - d*Sqrt[x])] + 20*(d^3*x^(3/2)*PolyLog[4, -E^(-c - d*Sqrt[x])] + 3*d^2*x*PolyLog[5, -E^(-c - d*Sqrt[x])] + 6*(d*Sqrt[x]*PolyLog[6, -E^(-c - d*Sqrt[x])] + PolyLog[7, -E^(-c - d*Sqrt[x])]))) - 42*b*(d^5*x^(5/2)*PolyLog[2, E^(-c - d*Sqrt[x])] + 5*d^4*x^2*PolyLog[3, E^(-c - d*Sqrt[x])] + 20*(d^3*x^(3/2)*PolyLog[4, E^(-c - d*Sqrt[x])] + 3*d^2*x*PolyLog[5, E^(-c - d*Sqrt[x])] + 6*(d*Sqrt[x]*PolyLog[6, E^(-c - d*Sqrt[x])] + PolyLog[7, E^(-c - d*Sqrt[x])]))) + 14*a*(d^6*x^3*PolyLog[2, -E^(-c - d*Sqrt[x])] + 6*(d^5*x^(5/2)*PolyLog[3, -E^(-c - d*Sqrt[x])] + 5*d^4*x^2*PolyLog[4, -E^(-c - d*Sqrt[x])] + 20*(d^3*x^(3/2)*PolyLog[5, -E^(-c - d*Sqrt[x])] + 3*d^2*x*PolyLog[6, -E^(-c - d*Sqrt[x])] + 6*d*Sqrt[x]*PolyLog[7, -E^(-c - d*Sqrt[x])] + 6*PolyLog[8, -E^(-c - d*Sqrt[x])]))) - 14*a*(d^6*x^3*PolyLog[2, E^(-c - d*Sqrt[x])] + 6*(d^5*x^(5/2)*PolyLog[3, E^(-c - d*Sqrt[x])] + 5*d^4*x^2*PolyLog[4, E^(-c - d*Sqrt[x])] + 20*(d^3*x^(3/2)*PolyLog[5, E^(-c - d*Sqrt[x])] + 3*d^2*x*PolyLog[6, E^(-c - d*Sqrt[x])] + 6*d*Sqrt[x]*PolyLog[7, E^(-c - d*Sqrt[x])] + 6*PolyLog[8, E^(-c - d*Sqrt[x])]))))*Sinh[c + d*Sqrt[x]]^2)/(d^8*(b + a*Sinh[c + d*Sqrt[x]])^2) + (b^2*x^(7/2)*Csch[c/2]*Csch[c/2 + (d*Sqrt[x])/2]*(a + b*Csch[c + d*Sqrt[x]])^2*Sinh[c + d*Sqrt[x]]^2*Sinh[(d*Sqrt[x])/2])/(d*(b + a*Sinh[c + d*Sqrt[x]])^2) - (b^2*x^(7/2)*(a + b*Csch[c + d*Sqrt[x]])^2*Sech[c/2]*Sech[c/2 + (d*Sqrt[x])/2]*Sinh[c + d*Sqrt[x]]^2*Sinh[(d*Sqrt[x])/2])/(d*(b + a*Sinh[c + d*Sqrt[x]])^2)","A",1
37,1,833,441,12.0699919,"\int x^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[x^2*(a + b*Csch[c + d*Sqrt[x]])^2,x]","\frac{a^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \sinh ^2\left(c+d \sqrt{x}\right) x^3}{3 \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)^2}+\frac{b^2 \text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \sinh ^2\left(c+d \sqrt{x}\right) \sinh \left(\frac{d \sqrt{x}}{2}\right) x^{5/2}}{d \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)^2}-\frac{b^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right) \sinh ^2\left(c+d \sqrt{x}\right) \sinh \left(\frac{d \sqrt{x}}{2}\right) x^{5/2}}{d \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)^2}+\frac{2 b \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \left(-\frac{2 b x^{5/2} d^5}{-1+e^{2 c}}+2 a x^{5/2} \log \left(1-e^{-c-d \sqrt{x}}\right) d^5-2 a x^{5/2} \log \left(1+e^{-c-d \sqrt{x}}\right) d^5+5 b x^2 \log \left(1-e^{-c-d \sqrt{x}}\right) d^4+5 b x^2 \log \left(1+e^{-c-d \sqrt{x}}\right) d^4+40 a x^{3/2} \text{Li}_3\left(-e^{-c-d \sqrt{x}}\right) d^3-40 a x^{3/2} \text{Li}_3\left(e^{-c-d \sqrt{x}}\right) d^3-60 b x \text{Li}_3\left(-e^{-c-d \sqrt{x}}\right) d^2-60 b x \text{Li}_3\left(e^{-c-d \sqrt{x}}\right) d^2+120 a x \text{Li}_4\left(-e^{-c-d \sqrt{x}}\right) d^2-120 a x \text{Li}_4\left(e^{-c-d \sqrt{x}}\right) d^2-120 b \sqrt{x} \text{Li}_4\left(-e^{-c-d \sqrt{x}}\right) d-120 b \sqrt{x} \text{Li}_4\left(e^{-c-d \sqrt{x}}\right) d+240 a \sqrt{x} \text{Li}_5\left(-e^{-c-d \sqrt{x}}\right) d-240 a \sqrt{x} \text{Li}_5\left(e^{-c-d \sqrt{x}}\right) d+10 \left(a d^4 x^2-2 b d^3 x^{3/2}\right) \text{Li}_2\left(-e^{-c-d \sqrt{x}}\right)-10 \left(a x^2 d^4+2 b x^{3/2} d^3\right) \text{Li}_2\left(e^{-c-d \sqrt{x}}\right)-120 b \text{Li}_5\left(-e^{-c-d \sqrt{x}}\right)-120 b \text{Li}_5\left(e^{-c-d \sqrt{x}}\right)+240 a \text{Li}_6\left(-e^{-c-d \sqrt{x}}\right)-240 a \text{Li}_6\left(e^{-c-d \sqrt{x}}\right)\right) \sinh ^2\left(c+d \sqrt{x}\right)}{d^6 \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)^2}","\frac{a^2 x^3}{3}-\frac{480 a b \text{Li}_6\left(-e^{c+d \sqrt{x}}\right)}{d^6}+\frac{480 a b \text{Li}_6\left(e^{c+d \sqrt{x}}\right)}{d^6}+\frac{480 a b \sqrt{x} \text{Li}_5\left(-e^{c+d \sqrt{x}}\right)}{d^5}-\frac{480 a b \sqrt{x} \text{Li}_5\left(e^{c+d \sqrt{x}}\right)}{d^5}-\frac{240 a b x \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)}{d^4}+\frac{240 a b x \text{Li}_4\left(e^{c+d \sqrt{x}}\right)}{d^4}+\frac{80 a b x^{3/2} \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)}{d^3}-\frac{80 a b x^{3/2} \text{Li}_3\left(e^{c+d \sqrt{x}}\right)}{d^3}-\frac{20 a b x^2 \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)}{d^2}+\frac{20 a b x^2 \text{Li}_2\left(e^{c+d \sqrt{x}}\right)}{d^2}-\frac{8 a b x^{5/2} \tanh ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}-\frac{15 b^2 \text{Li}_5\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^6}+\frac{30 b^2 \sqrt{x} \text{Li}_4\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{30 b^2 x \text{Li}_3\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{20 b^2 x^{3/2} \text{Li}_2\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{10 b^2 x^2 \log \left(1-e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b^2 x^{5/2} \coth \left(c+d \sqrt{x}\right)}{d}-\frac{2 b^2 x^{5/2}}{d}",1,"(a^2*x^3*(a + b*Csch[c + d*Sqrt[x]])^2*Sinh[c + d*Sqrt[x]]^2)/(3*(b + a*Sinh[c + d*Sqrt[x]])^2) + (2*b*(a + b*Csch[c + d*Sqrt[x]])^2*((-2*b*d^5*x^(5/2))/(-1 + E^(2*c)) + 5*b*d^4*x^2*Log[1 - E^(-c - d*Sqrt[x])] + 2*a*d^5*x^(5/2)*Log[1 - E^(-c - d*Sqrt[x])] + 5*b*d^4*x^2*Log[1 + E^(-c - d*Sqrt[x])] - 2*a*d^5*x^(5/2)*Log[1 + E^(-c - d*Sqrt[x])] + 10*(-2*b*d^3*x^(3/2) + a*d^4*x^2)*PolyLog[2, -E^(-c - d*Sqrt[x])] - 10*(2*b*d^3*x^(3/2) + a*d^4*x^2)*PolyLog[2, E^(-c - d*Sqrt[x])] - 60*b*d^2*x*PolyLog[3, -E^(-c - d*Sqrt[x])] + 40*a*d^3*x^(3/2)*PolyLog[3, -E^(-c - d*Sqrt[x])] - 60*b*d^2*x*PolyLog[3, E^(-c - d*Sqrt[x])] - 40*a*d^3*x^(3/2)*PolyLog[3, E^(-c - d*Sqrt[x])] - 120*b*d*Sqrt[x]*PolyLog[4, -E^(-c - d*Sqrt[x])] + 120*a*d^2*x*PolyLog[4, -E^(-c - d*Sqrt[x])] - 120*b*d*Sqrt[x]*PolyLog[4, E^(-c - d*Sqrt[x])] - 120*a*d^2*x*PolyLog[4, E^(-c - d*Sqrt[x])] - 120*b*PolyLog[5, -E^(-c - d*Sqrt[x])] + 240*a*d*Sqrt[x]*PolyLog[5, -E^(-c - d*Sqrt[x])] - 120*b*PolyLog[5, E^(-c - d*Sqrt[x])] - 240*a*d*Sqrt[x]*PolyLog[5, E^(-c - d*Sqrt[x])] + 240*a*PolyLog[6, -E^(-c - d*Sqrt[x])] - 240*a*PolyLog[6, E^(-c - d*Sqrt[x])])*Sinh[c + d*Sqrt[x]]^2)/(d^6*(b + a*Sinh[c + d*Sqrt[x]])^2) + (b^2*x^(5/2)*Csch[c/2]*Csch[c/2 + (d*Sqrt[x])/2]*(a + b*Csch[c + d*Sqrt[x]])^2*Sinh[c + d*Sqrt[x]]^2*Sinh[(d*Sqrt[x])/2])/(d*(b + a*Sinh[c + d*Sqrt[x]])^2) - (b^2*x^(5/2)*(a + b*Csch[c + d*Sqrt[x]])^2*Sech[c/2]*Sech[c/2 + (d*Sqrt[x])/2]*Sinh[c + d*Sqrt[x]]^2*Sinh[(d*Sqrt[x])/2])/(d*(b + a*Sinh[c + d*Sqrt[x]])^2)","A",1
38,1,616,287,11.5131529,"\int x \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[x*(a + b*Csch[c + d*Sqrt[x]])^2,x]","\frac{a^2 x^2 \sinh ^2\left(c+d \sqrt{x}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{2 \left(a \sinh \left(c+d \sqrt{x}\right)+b\right)^2}+\frac{b^2 x^{3/2} \text{csch}\left(\frac{c}{2}\right) \sinh \left(\frac{d \sqrt{x}}{2}\right) \sinh ^2\left(c+d \sqrt{x}\right) \text{csch}\left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{d \left(a \sinh \left(c+d \sqrt{x}\right)+b\right)^2}-\frac{b^2 x^{3/2} \text{sech}\left(\frac{c}{2}\right) \sinh \left(\frac{d \sqrt{x}}{2}\right) \sinh ^2\left(c+d \sqrt{x}\right) \text{sech}\left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{d \left(a \sinh \left(c+d \sqrt{x}\right)+b\right)^2}+\frac{2 b \sinh ^2\left(c+d \sqrt{x}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \left(6 \left(a d^2 x-b d \sqrt{x}\right) \text{Li}_2\left(-e^{-c-d \sqrt{x}}\right)-6 \left(a d^2 x+b d \sqrt{x}\right) \text{Li}_2\left(e^{-c-d \sqrt{x}}\right)+2 a d^3 x^{3/2} \log \left(1-e^{-c-d \sqrt{x}}\right)-2 a d^3 x^{3/2} \log \left(e^{-c-d \sqrt{x}}+1\right)+12 a d \sqrt{x} \text{Li}_3\left(-e^{-c-d \sqrt{x}}\right)-12 a d \sqrt{x} \text{Li}_3\left(e^{-c-d \sqrt{x}}\right)+12 a \text{Li}_4\left(-e^{-c-d \sqrt{x}}\right)-12 a \text{Li}_4\left(e^{-c-d \sqrt{x}}\right)-\frac{2 b d^3 x^{3/2}}{e^{2 c}-1}+3 b d^2 x \log \left(1-e^{-c-d \sqrt{x}}\right)+3 b d^2 x \log \left(e^{-c-d \sqrt{x}}+1\right)-6 b \text{Li}_3\left(-e^{-c-d \sqrt{x}}\right)-6 b \text{Li}_3\left(e^{-c-d \sqrt{x}}\right)\right)}{d^4 \left(a \sinh \left(c+d \sqrt{x}\right)+b\right)^2}","\frac{a^2 x^2}{2}-\frac{24 a b \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)}{d^4}+\frac{24 a b \text{Li}_4\left(e^{c+d \sqrt{x}}\right)}{d^4}+\frac{24 a b \sqrt{x} \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)}{d^3}-\frac{24 a b \sqrt{x} \text{Li}_3\left(e^{c+d \sqrt{x}}\right)}{d^3}-\frac{12 a b x \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)}{d^2}+\frac{12 a b x \text{Li}_2\left(e^{c+d \sqrt{x}}\right)}{d^2}-\frac{8 a b x^{3/2} \tanh ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}-\frac{3 b^2 \text{Li}_3\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{6 b^2 \sqrt{x} \text{Li}_2\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{6 b^2 x \log \left(1-e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b^2 x^{3/2} \coth \left(c+d \sqrt{x}\right)}{d}-\frac{2 b^2 x^{3/2}}{d}",1,"(a^2*x^2*(a + b*Csch[c + d*Sqrt[x]])^2*Sinh[c + d*Sqrt[x]]^2)/(2*(b + a*Sinh[c + d*Sqrt[x]])^2) + (2*b*(a + b*Csch[c + d*Sqrt[x]])^2*((-2*b*d^3*x^(3/2))/(-1 + E^(2*c)) + 3*b*d^2*x*Log[1 - E^(-c - d*Sqrt[x])] + 2*a*d^3*x^(3/2)*Log[1 - E^(-c - d*Sqrt[x])] + 3*b*d^2*x*Log[1 + E^(-c - d*Sqrt[x])] - 2*a*d^3*x^(3/2)*Log[1 + E^(-c - d*Sqrt[x])] + 6*(-(b*d*Sqrt[x]) + a*d^2*x)*PolyLog[2, -E^(-c - d*Sqrt[x])] - 6*(b*d*Sqrt[x] + a*d^2*x)*PolyLog[2, E^(-c - d*Sqrt[x])] - 6*b*PolyLog[3, -E^(-c - d*Sqrt[x])] + 12*a*d*Sqrt[x]*PolyLog[3, -E^(-c - d*Sqrt[x])] - 6*b*PolyLog[3, E^(-c - d*Sqrt[x])] - 12*a*d*Sqrt[x]*PolyLog[3, E^(-c - d*Sqrt[x])] + 12*a*PolyLog[4, -E^(-c - d*Sqrt[x])] - 12*a*PolyLog[4, E^(-c - d*Sqrt[x])])*Sinh[c + d*Sqrt[x]]^2)/(d^4*(b + a*Sinh[c + d*Sqrt[x]])^2) + (b^2*x^(3/2)*Csch[c/2]*Csch[c/2 + (d*Sqrt[x])/2]*(a + b*Csch[c + d*Sqrt[x]])^2*Sinh[c + d*Sqrt[x]]^2*Sinh[(d*Sqrt[x])/2])/(d*(b + a*Sinh[c + d*Sqrt[x]])^2) - (b^2*x^(3/2)*(a + b*Csch[c + d*Sqrt[x]])^2*Sech[c/2]*Sech[c/2 + (d*Sqrt[x])/2]*Sinh[c + d*Sqrt[x]]^2*Sinh[(d*Sqrt[x])/2])/(d*(b + a*Sinh[c + d*Sqrt[x]])^2)","B",1
39,0,0,23,130.8482261,"\int \frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])^2/x,x]","\int \frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x},x\right)",0,"Integrate[(a + b*Csch[c + d*Sqrt[x]])^2/x, x]","A",-1
40,0,0,23,62.4553267,"\int \frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])^2/x^2,x]","\int \frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x^2},x\right)",0,"Integrate[(a + b*Csch[c + d*Sqrt[x]])^2/x^2, x]","A",-1
41,1,905,897,2.6214317,"\int \frac{x^3}{a+b \text{csch}\left(c+d \sqrt{x}\right)} \, dx","Integrate[x^3/(a + b*Csch[c + d*Sqrt[x]]),x]","\frac{\text{csch}\left(c+d \sqrt{x}\right) \left(x^4-\frac{8 b e^c \left(x^{7/2} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^7-x^{7/2} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^7+7 x^3 \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^6-7 x^3 \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^6-42 x^{5/2} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^5+42 x^{5/2} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^5+210 x^2 \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^4-210 x^2 \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^4-840 x^{3/2} \text{Li}_5\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^3+840 x^{3/2} \text{Li}_5\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^3+2520 x \text{Li}_6\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^2-2520 x \text{Li}_6\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^2-5040 \sqrt{x} \text{Li}_7\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+5040 \sqrt{x} \text{Li}_7\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+5040 \text{Li}_8\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-5040 \text{Li}_8\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right)}{d^8 \sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)}{4 a \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)}","\frac{x^4}{4 a}-\frac{2 b \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) x^{7/2}}{a \sqrt{a^2+b^2} d}+\frac{2 b \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) x^{7/2}}{a \sqrt{a^2+b^2} d}-\frac{14 b \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^3}{a \sqrt{a^2+b^2} d^2}+\frac{14 b \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^3}{a \sqrt{a^2+b^2} d^2}+\frac{84 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^{5/2}}{a \sqrt{a^2+b^2} d^3}-\frac{84 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^{5/2}}{a \sqrt{a^2+b^2} d^3}-\frac{420 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^2}{a \sqrt{a^2+b^2} d^4}+\frac{420 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^2}{a \sqrt{a^2+b^2} d^4}+\frac{1680 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^{3/2}}{a \sqrt{a^2+b^2} d^5}-\frac{1680 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^{3/2}}{a \sqrt{a^2+b^2} d^5}-\frac{5040 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x}{a \sqrt{a^2+b^2} d^6}+\frac{5040 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x}{a \sqrt{a^2+b^2} d^6}+\frac{10080 b \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) \sqrt{x}}{a \sqrt{a^2+b^2} d^7}-\frac{10080 b \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) \sqrt{x}}{a \sqrt{a^2+b^2} d^7}-\frac{10080 b \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a \sqrt{a^2+b^2} d^8}+\frac{10080 b \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a \sqrt{a^2+b^2} d^8}",1,"(Csch[c + d*Sqrt[x]]*(x^4 - (8*b*E^c*(d^7*x^(7/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - d^7*x^(7/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 7*d^6*x^3*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 7*d^6*x^3*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 42*d^5*x^(5/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 42*d^5*x^(5/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 210*d^4*x^2*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 210*d^4*x^2*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 840*d^3*x^(3/2)*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 840*d^3*x^(3/2)*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 2520*d^2*x*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 2520*d^2*x*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 5040*d*Sqrt[x]*PolyLog[7, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 5040*d*Sqrt[x]*PolyLog[7, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 5040*PolyLog[8, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 5040*PolyLog[8, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(d^8*Sqrt[(a^2 + b^2)*E^(2*c)]))*(b + a*Sinh[c + d*Sqrt[x]]))/(4*a*(a + b*Csch[c + d*Sqrt[x]]))","A",1
42,1,716,673,2.0253645,"\int \frac{x^2}{a+b \text{csch}\left(c+d \sqrt{x}\right)} \, dx","Integrate[x^2/(a + b*Csch[c + d*Sqrt[x]]),x]","\frac{d^6 x^3 \sqrt{e^{2 c} \left(a^2+b^2\right)}-6 b e^c d^5 x^{5/2} \log \left(\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{e^{2 c} \left(a^2+b^2\right)}}+1\right)+6 b e^c d^5 x^{5/2} \log \left(\frac{a e^{2 c+d \sqrt{x}}}{\sqrt{e^{2 c} \left(a^2+b^2\right)}+b e^c}+1\right)-30 b e^c d^4 x^2 \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+30 b e^c d^4 x^2 \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+120 b e^c d^3 x^{3/2} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-120 b e^c d^3 x^{3/2} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-360 b e^c d^2 x \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+360 b e^c d^2 x \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+720 b e^c d \sqrt{x} \text{Li}_5\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-720 b e^c d \sqrt{x} \text{Li}_5\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-720 b e^c \text{Li}_6\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+720 b e^c \text{Li}_6\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{3 a d^6 \sqrt{e^{2 c} \left(a^2+b^2\right)}}","-\frac{240 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^6 \sqrt{a^2+b^2}}+\frac{240 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^6 \sqrt{a^2+b^2}}+\frac{240 b \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^5 \sqrt{a^2+b^2}}-\frac{240 b \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^5 \sqrt{a^2+b^2}}-\frac{120 b x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^4 \sqrt{a^2+b^2}}+\frac{120 b x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^4 \sqrt{a^2+b^2}}+\frac{40 b x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{40 b x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{10 b x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}+\frac{10 b x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{2 b x^{5/2} \log \left(\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{2 b x^{5/2} \log \left(\frac{a e^{c+d \sqrt{x}}}{\sqrt{a^2+b^2}+b}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{x^3}{3 a}",1,"(d^6*Sqrt[(a^2 + b^2)*E^(2*c)]*x^3 - 6*b*d^5*E^c*x^(5/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*b*d^5*E^c*x^(5/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 30*b*d^4*E^c*x^2*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 30*b*d^4*E^c*x^2*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 120*b*d^3*E^c*x^(3/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 120*b*d^3*E^c*x^(3/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 360*b*d^2*E^c*x*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 360*b*d^2*E^c*x*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 720*b*d*E^c*Sqrt[x]*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 720*b*d*E^c*Sqrt[x]*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 720*b*E^c*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 720*b*E^c*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/(3*a*d^6*Sqrt[(a^2 + b^2)*E^(2*c)])","A",1
43,1,488,449,2.0422477,"\int \frac{x}{a+b \text{csch}\left(c+d \sqrt{x}\right)} \, dx","Integrate[x/(a + b*Csch[c + d*Sqrt[x]]),x]","\frac{d^4 x^2 \sqrt{e^{2 c} \left(a^2+b^2\right)}-4 b e^c d^3 x^{3/2} \log \left(\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{e^{2 c} \left(a^2+b^2\right)}}+1\right)+4 b e^c d^3 x^{3/2} \log \left(\frac{a e^{2 c+d \sqrt{x}}}{\sqrt{e^{2 c} \left(a^2+b^2\right)}+b e^c}+1\right)-12 b e^c d^2 x \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+12 b e^c d^2 x \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+24 b e^c d \sqrt{x} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-24 b e^c d \sqrt{x} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-24 b e^c \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+24 b e^c \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{2 a d^4 \sqrt{e^{2 c} \left(a^2+b^2\right)}}","-\frac{12 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^4 \sqrt{a^2+b^2}}+\frac{12 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^4 \sqrt{a^2+b^2}}+\frac{12 b \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{12 b \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{6 b x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}+\frac{6 b x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{2 b x^{3/2} \log \left(\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{2 b x^{3/2} \log \left(\frac{a e^{c+d \sqrt{x}}}{\sqrt{a^2+b^2}+b}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{x^2}{2 a}",1,"(d^4*Sqrt[(a^2 + b^2)*E^(2*c)]*x^2 - 4*b*d^3*E^c*x^(3/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 4*b*d^3*E^c*x^(3/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 12*b*d^2*E^c*x*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 12*b*d^2*E^c*x*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 24*b*d*E^c*Sqrt[x]*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 24*b*d*E^c*Sqrt[x]*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 24*b*E^c*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 24*b*E^c*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/(2*a*d^4*Sqrt[(a^2 + b^2)*E^(2*c)])","A",1
44,0,0,23,5.3221352,"\int \frac{1}{x \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)} \, dx","Integrate[1/(x*(a + b*Csch[c + d*Sqrt[x]])),x]","\int \frac{1}{x \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)},x\right)",0,"Integrate[1/(x*(a + b*Csch[c + d*Sqrt[x]])), x]","A",-1
45,0,0,26,1.5892173,"\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{x^2} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])/x^2,x]","\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{x^2} \, dx","b \text{Int}\left(\frac{\text{csch}\left(c+d \sqrt{x}\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Csch[c + d*Sqrt[x]])/x^2, x]","A",-1
46,1,2923,2663,21.0755529,"\int \frac{x^3}{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[x^3/(a + b*Csch[c + d*Sqrt[x]])^2,x]","\text{Result too large to show}","\frac{x^4}{4 a^2}-\frac{4 b \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) x^{7/2}}{a^2 \sqrt{a^2+b^2} d}+\frac{2 b^3 \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) x^{7/2}}{a^2 \left(a^2+b^2\right)^{3/2} d}+\frac{4 b \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) x^{7/2}}{a^2 \sqrt{a^2+b^2} d}-\frac{2 b^3 \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) x^{7/2}}{a^2 \left(a^2+b^2\right)^{3/2} d}-\frac{2 b^2 x^{7/2}}{a^2 \left(a^2+b^2\right) d}-\frac{2 b^2 \cosh \left(c+d \sqrt{x}\right) x^{7/2}}{a \left(a^2+b^2\right) d \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)}+\frac{14 b^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) x^3}{a^2 \left(a^2+b^2\right) d^2}+\frac{14 b^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) x^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{28 b \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^3}{a^2 \sqrt{a^2+b^2} d^2}+\frac{14 b^3 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^3}{a^2 \left(a^2+b^2\right)^{3/2} d^2}+\frac{28 b \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^3}{a^2 \sqrt{a^2+b^2} d^2}-\frac{14 b^3 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^3}{a^2 \left(a^2+b^2\right)^{3/2} d^2}+\frac{84 b^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^{5/2}}{a^2 \left(a^2+b^2\right) d^3}+\frac{84 b^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^{5/2}}{a^2 \left(a^2+b^2\right) d^3}+\frac{168 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^{5/2}}{a^2 \sqrt{a^2+b^2} d^3}-\frac{84 b^3 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^{5/2}}{a^2 \left(a^2+b^2\right)^{3/2} d^3}-\frac{168 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^{5/2}}{a^2 \sqrt{a^2+b^2} d^3}+\frac{84 b^3 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^{5/2}}{a^2 \left(a^2+b^2\right)^{3/2} d^3}-\frac{420 b^2 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^2}{a^2 \left(a^2+b^2\right) d^4}-\frac{420 b^2 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^2}{a^2 \left(a^2+b^2\right) d^4}-\frac{840 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^2}{a^2 \sqrt{a^2+b^2} d^4}+\frac{420 b^3 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^2}{a^2 \left(a^2+b^2\right)^{3/2} d^4}+\frac{840 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^2}{a^2 \sqrt{a^2+b^2} d^4}-\frac{420 b^3 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^2}{a^2 \left(a^2+b^2\right)^{3/2} d^4}+\frac{1680 b^2 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^{3/2}}{a^2 \left(a^2+b^2\right) d^5}+\frac{1680 b^2 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^{3/2}}{a^2 \left(a^2+b^2\right) d^5}+\frac{3360 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^{3/2}}{a^2 \sqrt{a^2+b^2} d^5}-\frac{1680 b^3 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x^{3/2}}{a^2 \left(a^2+b^2\right)^{3/2} d^5}-\frac{3360 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^{3/2}}{a^2 \sqrt{a^2+b^2} d^5}+\frac{1680 b^3 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x^{3/2}}{a^2 \left(a^2+b^2\right)^{3/2} d^5}-\frac{5040 b^2 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x}{a^2 \left(a^2+b^2\right) d^6}-\frac{5040 b^2 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x}{a^2 \left(a^2+b^2\right) d^6}-\frac{10080 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x}{a^2 \sqrt{a^2+b^2} d^6}+\frac{5040 b^3 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) x}{a^2 \left(a^2+b^2\right)^{3/2} d^6}+\frac{10080 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x}{a^2 \sqrt{a^2+b^2} d^6}-\frac{5040 b^3 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) x}{a^2 \left(a^2+b^2\right)^{3/2} d^6}+\frac{10080 b^2 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) \sqrt{x}}{a^2 \left(a^2+b^2\right) d^7}+\frac{10080 b^2 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) \sqrt{x}}{a^2 \left(a^2+b^2\right) d^7}+\frac{20160 b \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) \sqrt{x}}{a^2 \sqrt{a^2+b^2} d^7}-\frac{10080 b^3 \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) \sqrt{x}}{a^2 \left(a^2+b^2\right)^{3/2} d^7}-\frac{20160 b \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) \sqrt{x}}{a^2 \sqrt{a^2+b^2} d^7}+\frac{10080 b^3 \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) \sqrt{x}}{a^2 \left(a^2+b^2\right)^{3/2} d^7}-\frac{10080 b^2 \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a^2 \left(a^2+b^2\right) d^8}-\frac{10080 b^2 \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a^2 \left(a^2+b^2\right) d^8}-\frac{20160 b \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a^2 \sqrt{a^2+b^2} d^8}+\frac{10080 b^3 \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a^2 \left(a^2+b^2\right)^{3/2} d^8}+\frac{20160 b \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a^2 \sqrt{a^2+b^2} d^8}-\frac{10080 b^3 \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a^2 \left(a^2+b^2\right)^{3/2} d^8}",1,"(x^4*Csch[c + d*Sqrt[x]]^2*(b + a*Sinh[c + d*Sqrt[x]])^2)/(4*a^2*(a + b*Csch[c + d*Sqrt[x]])^2) - (2*b*E^c*Csch[c + d*Sqrt[x]]^2*(2*b*E^c*x^(7/2) - ((-1 + E^(2*c))*(7*b*d^6*Sqrt[(a^2 + b^2)*E^(2*c)]*x^3*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 2*a^2*d^7*E^c*x^(7/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - b^2*d^7*E^c*x^(7/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 7*b*d^6*Sqrt[(a^2 + b^2)*E^(2*c)]*x^3*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*a^2*d^7*E^c*x^(7/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + b^2*d^7*E^c*x^(7/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 7*d^5*(-6*b*Sqrt[(a^2 + b^2)*E^(2*c)] + 2*a^2*d*E^c*Sqrt[x] + b^2*d*E^c*Sqrt[x])*x^(5/2)*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 7*d^5*(6*b*Sqrt[(a^2 + b^2)*E^(2*c)] + 2*a^2*d*E^c*Sqrt[x] + b^2*d*E^c*Sqrt[x])*x^(5/2)*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 210*b*d^4*Sqrt[(a^2 + b^2)*E^(2*c)]*x^2*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 84*a^2*d^5*E^c*x^(5/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 42*b^2*d^5*E^c*x^(5/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 210*b*d^4*Sqrt[(a^2 + b^2)*E^(2*c)]*x^2*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 84*a^2*d^5*E^c*x^(5/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 42*b^2*d^5*E^c*x^(5/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 840*b*d^3*Sqrt[(a^2 + b^2)*E^(2*c)]*x^(3/2)*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 420*a^2*d^4*E^c*x^2*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 210*b^2*d^4*E^c*x^2*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 840*b*d^3*Sqrt[(a^2 + b^2)*E^(2*c)]*x^(3/2)*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 420*a^2*d^4*E^c*x^2*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 210*b^2*d^4*E^c*x^2*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 2520*b*d^2*Sqrt[(a^2 + b^2)*E^(2*c)]*x*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 1680*a^2*d^3*E^c*x^(3/2)*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 840*b^2*d^3*E^c*x^(3/2)*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 2520*b*d^2*Sqrt[(a^2 + b^2)*E^(2*c)]*x*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 1680*a^2*d^3*E^c*x^(3/2)*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 840*b^2*d^3*E^c*x^(3/2)*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 5040*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*Sqrt[x]*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 5040*a^2*d^2*E^c*x*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 2520*b^2*d^2*E^c*x*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 5040*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*Sqrt[x]*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 5040*a^2*d^2*E^c*x*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 2520*b^2*d^2*E^c*x*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 5040*b*Sqrt[(a^2 + b^2)*E^(2*c)]*PolyLog[7, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 10080*a^2*d*E^c*Sqrt[x]*PolyLog[7, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 5040*b^2*d*E^c*Sqrt[x]*PolyLog[7, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 5040*b*Sqrt[(a^2 + b^2)*E^(2*c)]*PolyLog[7, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 10080*a^2*d*E^c*Sqrt[x]*PolyLog[7, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 5040*b^2*d*E^c*Sqrt[x]*PolyLog[7, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 10080*a^2*E^c*PolyLog[8, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 5040*b^2*E^c*PolyLog[8, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 10080*a^2*E^c*PolyLog[8, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 5040*b^2*E^c*PolyLog[8, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(d^7*E^c*Sqrt[(a^2 + b^2)*E^(2*c)]))*(b + a*Sinh[c + d*Sqrt[x]])^2)/(a^2*(a^2 + b^2)*d*(-1 + E^(2*c))*(a + b*Csch[c + d*Sqrt[x]])^2) + (Csch[c/2]*Csch[c + d*Sqrt[x]]^2*Sech[c/2]*(b + a*Sinh[c + d*Sqrt[x]])*(b^3*x^(7/2)*Cosh[c] + a*b^2*x^(7/2)*Sinh[d*Sqrt[x]]))/(a^2*(a^2 + b^2)*d*(a + b*Csch[c + d*Sqrt[x]])^2)","A",0
47,1,2153,1983,19.7926289,"\int \frac{x^2}{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[x^2/(a + b*Csch[c + d*Sqrt[x]])^2,x]","\text{Result too large to show}","\frac{2 x^{5/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d}-\frac{2 x^{5/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d}+\frac{10 x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{10 x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{40 x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^3}+\frac{40 x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^3}+\frac{120 x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^4}-\frac{120 x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^4}-\frac{240 \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^5}+\frac{240 \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^5}+\frac{240 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^6}-\frac{240 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^6}-\frac{2 x^{5/2} b^2}{a^2 \left(a^2+b^2\right) d}+\frac{10 x^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b^2}{a^2 \left(a^2+b^2\right) d^2}+\frac{10 x^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b^2}{a^2 \left(a^2+b^2\right) d^2}+\frac{40 x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^3}+\frac{40 x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^3}-\frac{120 x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^4}-\frac{120 x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^4}+\frac{240 \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^5}+\frac{240 \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^5}-\frac{240 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^6}-\frac{240 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^6}-\frac{2 x^{5/2} \cosh \left(c+d \sqrt{x}\right) b^2}{a \left(a^2+b^2\right) d \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)}-\frac{4 x^{5/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b}{a^2 \sqrt{a^2+b^2} d}+\frac{4 x^{5/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b}{a^2 \sqrt{a^2+b^2} d}-\frac{20 x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^2}+\frac{20 x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^2}+\frac{80 x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^3}-\frac{80 x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^3}-\frac{240 x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^4}+\frac{240 x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^4}+\frac{480 \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^5}-\frac{480 \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^5}-\frac{480 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^6}+\frac{480 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^6}+\frac{x^3}{3 a^2}",1,"(x^3*Csch[c + d*Sqrt[x]]^2*(b + a*Sinh[c + d*Sqrt[x]])^2)/(3*a^2*(a + b*Csch[c + d*Sqrt[x]])^2) + (2*b*Csch[c + d*Sqrt[x]]^2*((-2*b*d^5*E^(2*c)*x^(5/2))/(-1 + E^(2*c)) + (5*b*d^4*Sqrt[(a^2 + b^2)*E^(2*c)]*x^2*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 2*a^2*d^5*E^c*x^(5/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - b^2*d^5*E^c*x^(5/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 5*b*d^4*Sqrt[(a^2 + b^2)*E^(2*c)]*x^2*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*a^2*d^5*E^c*x^(5/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + b^2*d^5*E^c*x^(5/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 5*d^3*(-4*b*Sqrt[(a^2 + b^2)*E^(2*c)] + 2*a^2*d*E^c*Sqrt[x] + b^2*d*E^c*Sqrt[x])*x^(3/2)*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 5*d^3*(4*b*Sqrt[(a^2 + b^2)*E^(2*c)] + 2*a^2*d*E^c*Sqrt[x] + b^2*d*E^c*Sqrt[x])*x^(3/2)*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 60*b*d^2*Sqrt[(a^2 + b^2)*E^(2*c)]*x*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 40*a^2*d^3*E^c*x^(3/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 20*b^2*d^3*E^c*x^(3/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 60*b*d^2*Sqrt[(a^2 + b^2)*E^(2*c)]*x*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 40*a^2*d^3*E^c*x^(3/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 20*b^2*d^3*E^c*x^(3/2)*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 120*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*Sqrt[x]*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 120*a^2*d^2*E^c*x*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 60*b^2*d^2*E^c*x*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 120*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*Sqrt[x]*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 120*a^2*d^2*E^c*x*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 60*b^2*d^2*E^c*x*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 120*b*Sqrt[(a^2 + b^2)*E^(2*c)]*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 240*a^2*d*E^c*Sqrt[x]*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 120*b^2*d*E^c*Sqrt[x]*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 120*b*Sqrt[(a^2 + b^2)*E^(2*c)]*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 240*a^2*d*E^c*Sqrt[x]*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 120*b^2*d*E^c*Sqrt[x]*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 240*a^2*E^c*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 120*b^2*E^c*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 240*a^2*E^c*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 120*b^2*E^c*PolyLog[6, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/Sqrt[(a^2 + b^2)*E^(2*c)])*(b + a*Sinh[c + d*Sqrt[x]])^2)/(a^2*(a^2 + b^2)*d^6*(a + b*Csch[c + d*Sqrt[x]])^2) + (Csch[c/2]*Csch[c + d*Sqrt[x]]^2*Sech[c/2]*(b + a*Sinh[c + d*Sqrt[x]])*(b^3*x^(5/2)*Cosh[c] + a*b^2*x^(5/2)*Sinh[d*Sqrt[x]]))/(a^2*(a^2 + b^2)*d*(a + b*Csch[c + d*Sqrt[x]])^2)","A",0
48,1,1333,1303,16.2379833,"\int \frac{x}{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[x/(a + b*Csch[c + d*Sqrt[x]])^2,x]","\frac{\text{csch}^2\left(c+d \sqrt{x}\right) \left(b+a \sinh \left(c+d \sqrt{x}\right)\right) \left(\frac{4 x^{3/2} \text{csch}(c) \left(b \cosh (c)+a \sinh \left(d \sqrt{x}\right)\right) b^2}{\left(a^2+b^2\right) d}-\frac{4 e^c \left(2 b e^c x^{3/2}+\frac{e^{-c} \left(-1+e^{2 c}\right) \left(2 a^2 e^c x^{3/2} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^3+b^2 e^c x^{3/2} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^3-2 a^2 e^c x^{3/2} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^3-b^2 e^c x^{3/2} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^3-3 b \sqrt{\left(a^2+b^2\right) e^{2 c}} x \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-3 b \sqrt{\left(a^2+b^2\right) e^{2 c}} x \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-3 \left(2 d e^c \sqrt{x} a^2+2 b \sqrt{\left(a^2+b^2\right) e^{2 c}}+b^2 d e^c \sqrt{x}\right) \sqrt{x} \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-12 a^2 e^c \sqrt{x} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-6 b^2 e^c \sqrt{x} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+12 a^2 e^c \sqrt{x} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+6 b^2 e^c \sqrt{x} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+\left(6 a^2 e^c x d^2+3 b^2 e^c x d^2-6 b \sqrt{\left(a^2+b^2\right) e^{2 c}} \sqrt{x} d\right) \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 b \sqrt{\left(a^2+b^2\right) e^{2 c}} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 b \sqrt{\left(a^2+b^2\right) e^{2 c}} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+12 a^2 e^c \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 b^2 e^c \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-12 a^2 e^c \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 b^2 e^c \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right)}{d^3 \sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) \left(b+a \sinh \left(c+d \sqrt{x}\right)\right) b}{\left(a^2+b^2\right) d \left(-1+e^{2 c}\right)}+x^2 \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)\right)}{2 a^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}","\frac{2 x^{3/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d}-\frac{2 x^{3/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d}+\frac{6 x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{6 x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{12 \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^3}+\frac{12 \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^3}+\frac{12 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^4}-\frac{12 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^4}-\frac{2 x^{3/2} b^2}{a^2 \left(a^2+b^2\right) d}+\frac{6 x \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b^2}{a^2 \left(a^2+b^2\right) d^2}+\frac{6 x \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b^2}{a^2 \left(a^2+b^2\right) d^2}+\frac{12 \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^3}+\frac{12 \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^3}-\frac{12 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^4}-\frac{12 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^4}-\frac{2 x^{3/2} \cosh \left(c+d \sqrt{x}\right) b^2}{a \left(a^2+b^2\right) d \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)}-\frac{4 x^{3/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b}{a^2 \sqrt{a^2+b^2} d}+\frac{4 x^{3/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b}{a^2 \sqrt{a^2+b^2} d}-\frac{12 x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^2}+\frac{12 x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^2}+\frac{24 \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^3}-\frac{24 \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^3}-\frac{24 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^4}+\frac{24 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^4}+\frac{x^2}{2 a^2}",1,"(Csch[c + d*Sqrt[x]]^2*(b + a*Sinh[c + d*Sqrt[x]])*(x^2*(b + a*Sinh[c + d*Sqrt[x]]) - (4*b*E^c*(2*b*E^c*x^(3/2) + ((-1 + E^(2*c))*(-3*b*d^2*Sqrt[(a^2 + b^2)*E^(2*c)]*x*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*a^2*d^3*E^c*x^(3/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + b^2*d^3*E^c*x^(3/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*b*d^2*Sqrt[(a^2 + b^2)*E^(2*c)]*x*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 2*a^2*d^3*E^c*x^(3/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - b^2*d^3*E^c*x^(3/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + (-6*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*Sqrt[x] + 6*a^2*d^2*E^c*x + 3*b^2*d^2*E^c*x)*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 3*d*(2*b*Sqrt[(a^2 + b^2)*E^(2*c)] + 2*a^2*d*E^c*Sqrt[x] + b^2*d*E^c*Sqrt[x])*Sqrt[x]*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*b*Sqrt[(a^2 + b^2)*E^(2*c)]*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 12*a^2*d*E^c*Sqrt[x]*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*b^2*d*E^c*Sqrt[x]*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*b*Sqrt[(a^2 + b^2)*E^(2*c)]*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 12*a^2*d*E^c*Sqrt[x]*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*b^2*d*E^c*Sqrt[x]*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 12*a^2*E^c*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*b^2*E^c*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 12*a^2*E^c*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*b^2*E^c*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(d^3*E^c*Sqrt[(a^2 + b^2)*E^(2*c)]))*(b + a*Sinh[c + d*Sqrt[x]]))/((a^2 + b^2)*d*(-1 + E^(2*c))) + (4*b^2*x^(3/2)*Csch[c]*(b*Cosh[c] + a*Sinh[d*Sqrt[x]]))/((a^2 + b^2)*d)))/(2*a^2*(a + b*Csch[c + d*Sqrt[x]])^2)","A",1
49,0,0,23,141.8555283,"\int \frac{1}{x \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Csch[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Integrate[1/(x*(a + b*Csch[c + d*Sqrt[x]])^2), x]","A",-1
50,0,0,23,73.5920853,"\int \frac{1}{x^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Csch[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Integrate[1/(x^2*(a + b*Csch[c + d*Sqrt[x]])^2), x]","A",-1
51,1,238,214,3.283885,"\int x^{3/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x^(3/2)*(a + b*Csch[c + d*Sqrt[x]]),x]","\frac{2 \left(a d^5 x^{5/2}+5 b d^4 x^2 \log \left(1-e^{c+d \sqrt{x}}\right)-5 b d^4 x^2 \log \left(e^{c+d \sqrt{x}}+1\right)-20 b d^3 x^{3/2} \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)+20 b d^3 x^{3/2} \text{Li}_2\left(e^{c+d \sqrt{x}}\right)+60 b d^2 x \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)-60 b d^2 x \text{Li}_3\left(e^{c+d \sqrt{x}}\right)-120 b d \sqrt{x} \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)+120 b d \sqrt{x} \text{Li}_4\left(e^{c+d \sqrt{x}}\right)+120 b \text{Li}_5\left(-e^{c+d \sqrt{x}}\right)-120 b \text{Li}_5\left(e^{c+d \sqrt{x}}\right)\right)}{5 d^5}","\frac{2}{5} a x^{5/2}+\frac{48 b \text{Li}_5\left(-e^{c+d \sqrt{x}}\right)}{d^5}-\frac{48 b \text{Li}_5\left(e^{c+d \sqrt{x}}\right)}{d^5}-\frac{48 b \sqrt{x} \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)}{d^4}+\frac{48 b \sqrt{x} \text{Li}_4\left(e^{c+d \sqrt{x}}\right)}{d^4}+\frac{24 b x \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)}{d^3}-\frac{24 b x \text{Li}_3\left(e^{c+d \sqrt{x}}\right)}{d^3}-\frac{8 b x^{3/2} \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)}{d^2}+\frac{8 b x^{3/2} \text{Li}_2\left(e^{c+d \sqrt{x}}\right)}{d^2}-\frac{4 b x^2 \tanh ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}",1,"(2*(a*d^5*x^(5/2) + 5*b*d^4*x^2*Log[1 - E^(c + d*Sqrt[x])] - 5*b*d^4*x^2*Log[1 + E^(c + d*Sqrt[x])] - 20*b*d^3*x^(3/2)*PolyLog[2, -E^(c + d*Sqrt[x])] + 20*b*d^3*x^(3/2)*PolyLog[2, E^(c + d*Sqrt[x])] + 60*b*d^2*x*PolyLog[3, -E^(c + d*Sqrt[x])] - 60*b*d^2*x*PolyLog[3, E^(c + d*Sqrt[x])] - 120*b*d*Sqrt[x]*PolyLog[4, -E^(c + d*Sqrt[x])] + 120*b*d*Sqrt[x]*PolyLog[4, E^(c + d*Sqrt[x])] + 120*b*PolyLog[5, -E^(c + d*Sqrt[x])] - 120*b*PolyLog[5, E^(c + d*Sqrt[x])]))/(5*d^5)","A",1
52,1,142,120,9.6927221,"\int \sqrt{x} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right) \, dx","Integrate[Sqrt[x]*(a + b*Csch[c + d*Sqrt[x]]),x]","\frac{2 \left(a d^3 x^{3/2}+3 b d^2 x \log \left(1-e^{c+d \sqrt{x}}\right)-3 b d^2 x \log \left(e^{c+d \sqrt{x}}+1\right)-6 b d \sqrt{x} \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)+6 b d \sqrt{x} \text{Li}_2\left(e^{c+d \sqrt{x}}\right)+6 b \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)-6 b \text{Li}_3\left(e^{c+d \sqrt{x}}\right)\right)}{3 d^3}","\frac{2}{3} a x^{3/2}+\frac{4 b \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)}{d^3}-\frac{4 b \text{Li}_3\left(e^{c+d \sqrt{x}}\right)}{d^3}-\frac{4 b \sqrt{x} \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)}{d^2}+\frac{4 b \sqrt{x} \text{Li}_2\left(e^{c+d \sqrt{x}}\right)}{d^2}-\frac{4 b x \tanh ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}",1,"(2*(a*d^3*x^(3/2) + 3*b*d^2*x*Log[1 - E^(c + d*Sqrt[x])] - 3*b*d^2*x*Log[1 + E^(c + d*Sqrt[x])] - 6*b*d*Sqrt[x]*PolyLog[2, -E^(c + d*Sqrt[x])] + 6*b*d*Sqrt[x]*PolyLog[2, E^(c + d*Sqrt[x])] + 6*b*PolyLog[3, -E^(c + d*Sqrt[x])] - 6*b*PolyLog[3, E^(c + d*Sqrt[x])]))/(3*d^3)","A",1
53,1,34,26,0.0429258,"\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])/Sqrt[x],x]","\frac{2 \left(a \left(c+d \sqrt{x}\right)+b \log \left(\tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)\right)\right)}{d}","2 a \sqrt{x}-\frac{2 b \tanh ^{-1}\left(\cosh \left(c+d \sqrt{x}\right)\right)}{d}",1,"(2*(a*(c + d*Sqrt[x]) + b*Log[Tanh[(c + d*Sqrt[x])/2]]))/d","A",1
54,0,0,30,24.2337701,"\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{x^{3/2}} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])/x^(3/2),x]","\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{x^{3/2}} \, dx","b \text{Int}\left(\frac{\text{csch}\left(c+d \sqrt{x}\right)}{x^{3/2}},x\right)-\frac{2 a}{\sqrt{x}}",0,"Integrate[(a + b*Csch[c + d*Sqrt[x]])/x^(3/2), x]","A",-1
55,0,0,32,25.7593348,"\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{x^{5/2}} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])/x^(5/2),x]","\int \frac{a+b \text{csch}\left(c+d \sqrt{x}\right)}{x^{5/2}} \, dx","b \text{Int}\left(\frac{\text{csch}\left(c+d \sqrt{x}\right)}{x^{5/2}},x\right)-\frac{2 a}{3 x^{3/2}}",0,"Integrate[(a + b*Csch[c + d*Sqrt[x]])/x^(5/2), x]","A",-1
56,1,718,363,10.9922682,"\int x^{3/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[x^(3/2)*(a + b*Csch[c + d*Sqrt[x]])^2,x]","\frac{2 a^2 x^{5/2} \sinh ^2\left(c+d \sqrt{x}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{5 \left(a \sinh \left(c+d \sqrt{x}\right)+b\right)^2}+\frac{b^2 x^2 \text{csch}\left(\frac{c}{2}\right) \sinh \left(\frac{d \sqrt{x}}{2}\right) \sinh ^2\left(c+d \sqrt{x}\right) \text{csch}\left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{d \left(a \sinh \left(c+d \sqrt{x}\right)+b\right)^2}-\frac{b^2 x^2 \text{sech}\left(\frac{c}{2}\right) \sinh \left(\frac{d \sqrt{x}}{2}\right) \sinh ^2\left(c+d \sqrt{x}\right) \text{sech}\left(\frac{c}{2}+\frac{d \sqrt{x}}{2}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{d \left(a \sinh \left(c+d \sqrt{x}\right)+b\right)^2}+\frac{4 b \sinh ^2\left(c+d \sqrt{x}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \left(2 d^2 x \left(2 a d \sqrt{x}-3 b\right) \text{Li}_2\left(-e^{-c-d \sqrt{x}}\right)-2 d^2 x \left(2 a d \sqrt{x}+3 b\right) \text{Li}_2\left(e^{-c-d \sqrt{x}}\right)+a d^4 x^2 \log \left(1-e^{-c-d \sqrt{x}}\right)-a d^4 x^2 \log \left(e^{-c-d \sqrt{x}}+1\right)+12 a d^2 x \text{Li}_3\left(-e^{-c-d \sqrt{x}}\right)-12 a d^2 x \text{Li}_3\left(e^{-c-d \sqrt{x}}\right)+24 a d \sqrt{x} \text{Li}_4\left(-e^{-c-d \sqrt{x}}\right)-24 a d \sqrt{x} \text{Li}_4\left(e^{-c-d \sqrt{x}}\right)+24 a \text{Li}_5\left(-e^{-c-d \sqrt{x}}\right)-24 a \text{Li}_5\left(e^{-c-d \sqrt{x}}\right)-\frac{b d^4 x^2}{e^{2 c}-1}+2 b d^3 x^{3/2} \log \left(1-e^{-c-d \sqrt{x}}\right)+2 b d^3 x^{3/2} \log \left(e^{-c-d \sqrt{x}}+1\right)-12 b d \sqrt{x} \text{Li}_3\left(-e^{-c-d \sqrt{x}}\right)-12 b d \sqrt{x} \text{Li}_3\left(e^{-c-d \sqrt{x}}\right)-12 b \text{Li}_4\left(-e^{-c-d \sqrt{x}}\right)-12 b \text{Li}_4\left(e^{-c-d \sqrt{x}}\right)\right)}{d^5 \left(a \sinh \left(c+d \sqrt{x}\right)+b\right)^2}","\frac{2}{5} a^2 x^{5/2}+\frac{96 a b \text{Li}_5\left(-e^{c+d \sqrt{x}}\right)}{d^5}-\frac{96 a b \text{Li}_5\left(e^{c+d \sqrt{x}}\right)}{d^5}-\frac{96 a b \sqrt{x} \text{Li}_4\left(-e^{c+d \sqrt{x}}\right)}{d^4}+\frac{96 a b \sqrt{x} \text{Li}_4\left(e^{c+d \sqrt{x}}\right)}{d^4}+\frac{48 a b x \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)}{d^3}-\frac{48 a b x \text{Li}_3\left(e^{c+d \sqrt{x}}\right)}{d^3}-\frac{16 a b x^{3/2} \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)}{d^2}+\frac{16 a b x^{3/2} \text{Li}_2\left(e^{c+d \sqrt{x}}\right)}{d^2}-\frac{8 a b x^2 \tanh ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}+\frac{6 b^2 \text{Li}_4\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^5}-\frac{12 b^2 \sqrt{x} \text{Li}_3\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^4}+\frac{12 b^2 x \text{Li}_2\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{8 b^2 x^{3/2} \log \left(1-e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b^2 x^2 \coth \left(c+d \sqrt{x}\right)}{d}-\frac{2 b^2 x^2}{d}",1,"(2*a^2*x^(5/2)*(a + b*Csch[c + d*Sqrt[x]])^2*Sinh[c + d*Sqrt[x]]^2)/(5*(b + a*Sinh[c + d*Sqrt[x]])^2) + (4*b*(a + b*Csch[c + d*Sqrt[x]])^2*(-((b*d^4*x^2)/(-1 + E^(2*c))) + 2*b*d^3*x^(3/2)*Log[1 - E^(-c - d*Sqrt[x])] + a*d^4*x^2*Log[1 - E^(-c - d*Sqrt[x])] + 2*b*d^3*x^(3/2)*Log[1 + E^(-c - d*Sqrt[x])] - a*d^4*x^2*Log[1 + E^(-c - d*Sqrt[x])] + 2*d^2*(-3*b + 2*a*d*Sqrt[x])*x*PolyLog[2, -E^(-c - d*Sqrt[x])] - 2*d^2*(3*b + 2*a*d*Sqrt[x])*x*PolyLog[2, E^(-c - d*Sqrt[x])] - 12*b*d*Sqrt[x]*PolyLog[3, -E^(-c - d*Sqrt[x])] + 12*a*d^2*x*PolyLog[3, -E^(-c - d*Sqrt[x])] - 12*b*d*Sqrt[x]*PolyLog[3, E^(-c - d*Sqrt[x])] - 12*a*d^2*x*PolyLog[3, E^(-c - d*Sqrt[x])] - 12*b*PolyLog[4, -E^(-c - d*Sqrt[x])] + 24*a*d*Sqrt[x]*PolyLog[4, -E^(-c - d*Sqrt[x])] - 12*b*PolyLog[4, E^(-c - d*Sqrt[x])] - 24*a*d*Sqrt[x]*PolyLog[4, E^(-c - d*Sqrt[x])] + 24*a*PolyLog[5, -E^(-c - d*Sqrt[x])] - 24*a*PolyLog[5, E^(-c - d*Sqrt[x])])*Sinh[c + d*Sqrt[x]]^2)/(d^5*(b + a*Sinh[c + d*Sqrt[x]])^2) + (b^2*x^2*Csch[c/2]*Csch[c/2 + (d*Sqrt[x])/2]*(a + b*Csch[c + d*Sqrt[x]])^2*Sinh[c + d*Sqrt[x]]^2*Sinh[(d*Sqrt[x])/2])/(d*(b + a*Sinh[c + d*Sqrt[x]])^2) - (b^2*x^2*(a + b*Csch[c + d*Sqrt[x]])^2*Sech[c/2]*Sech[c/2 + (d*Sqrt[x])/2]*Sinh[c + d*Sqrt[x]]^2*Sinh[(d*Sqrt[x])/2])/(d*(b + a*Sinh[c + d*Sqrt[x]])^2)","A",1
57,1,316,209,9.2765135,"\int \sqrt{x} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[Sqrt[x]*(a + b*Csch[c + d*Sqrt[x]])^2,x]","\frac{2}{3} a^2 x^{3/2}+\frac{4 b \left(-\left(b-2 a d \sqrt{x}\right) \text{Li}_2\left(-e^{-c-d \sqrt{x}}\right)-\left(2 a d \sqrt{x}+b\right) \text{Li}_2\left(e^{-c-d \sqrt{x}}\right)+a d^2 x \log \left(1-e^{-c-d \sqrt{x}}\right)-a d^2 x \log \left(e^{-c-d \sqrt{x}}+1\right)+2 a \text{Li}_3\left(-e^{-c-d \sqrt{x}}\right)-2 a \text{Li}_3\left(e^{-c-d \sqrt{x}}\right)-\frac{b d^2 x}{e^{2 c}-1}+b d \sqrt{x} \log \left(1-e^{-c-d \sqrt{x}}\right)+b d \sqrt{x} \log \left(e^{-c-d \sqrt{x}}+1\right)\right)}{d^3}+\frac{b^2 x \text{csch}\left(\frac{c}{2}\right) \sinh \left(\frac{d \sqrt{x}}{2}\right) \text{csch}\left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{d}-\frac{b^2 x \text{sech}\left(\frac{c}{2}\right) \sinh \left(\frac{d \sqrt{x}}{2}\right) \text{sech}\left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{d}","\frac{2}{3} a^2 x^{3/2}+\frac{8 a b \text{Li}_3\left(-e^{c+d \sqrt{x}}\right)}{d^3}-\frac{8 a b \text{Li}_3\left(e^{c+d \sqrt{x}}\right)}{d^3}-\frac{8 a b \sqrt{x} \text{Li}_2\left(-e^{c+d \sqrt{x}}\right)}{d^2}+\frac{8 a b \sqrt{x} \text{Li}_2\left(e^{c+d \sqrt{x}}\right)}{d^2}-\frac{8 a b x \tanh ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}+\frac{2 b^2 \text{Li}_2\left(e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^3}+\frac{4 b^2 \sqrt{x} \log \left(1-e^{2 \left(c+d \sqrt{x}\right)}\right)}{d^2}-\frac{2 b^2 x \coth \left(c+d \sqrt{x}\right)}{d}-\frac{2 b^2 x}{d}",1,"(2*a^2*x^(3/2))/3 + (4*b*(-((b*d^2*x)/(-1 + E^(2*c))) + b*d*Sqrt[x]*Log[1 - E^(-c - d*Sqrt[x])] + a*d^2*x*Log[1 - E^(-c - d*Sqrt[x])] + b*d*Sqrt[x]*Log[1 + E^(-c - d*Sqrt[x])] - a*d^2*x*Log[1 + E^(-c - d*Sqrt[x])] - (b - 2*a*d*Sqrt[x])*PolyLog[2, -E^(-c - d*Sqrt[x])] - (b + 2*a*d*Sqrt[x])*PolyLog[2, E^(-c - d*Sqrt[x])] + 2*a*PolyLog[3, -E^(-c - d*Sqrt[x])] - 2*a*PolyLog[3, E^(-c - d*Sqrt[x])]))/d^3 + (b^2*x*Csch[c/2]*Csch[(c + d*Sqrt[x])/2]*Sinh[(d*Sqrt[x])/2])/d - (b^2*x*Sech[c/2]*Sech[(c + d*Sqrt[x])/2]*Sinh[(d*Sqrt[x])/2])/d","A",1
58,1,75,47,0.2755762,"\int \frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{\sqrt{x}} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])^2/Sqrt[x],x]","-\frac{-2 a \left(a c+a d \sqrt{x}+2 b \log \left(\tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)\right)\right)+b^2 \tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)+b^2 \coth \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{d}","2 a^2 \sqrt{x}-\frac{4 a b \tanh ^{-1}\left(\cosh \left(c+d \sqrt{x}\right)\right)}{d}-\frac{2 b^2 \coth \left(c+d \sqrt{x}\right)}{d}",1,"-((b^2*Coth[(c + d*Sqrt[x])/2] - 2*a*(a*c + a*d*Sqrt[x] + 2*b*Log[Tanh[(c + d*Sqrt[x])/2]]) + b^2*Tanh[(c + d*Sqrt[x])/2])/d)","A",1
59,0,0,25,59.5350554,"\int \frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x^{3/2}} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])^2/x^(3/2),x]","\int \frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x^{3/2}} \, dx","\text{Int}\left(\frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x^{3/2}},x\right)",0,"Integrate[(a + b*Csch[c + d*Sqrt[x]])^2/x^(3/2), x]","A",-1
60,0,0,25,60.0946559,"\int \frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x^{5/2}} \, dx","Integrate[(a + b*Csch[c + d*Sqrt[x]])^2/x^(5/2),x]","\int \frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x^{5/2}} \, dx","\text{Int}\left(\frac{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}{x^{5/2}},x\right)",0,"Integrate[(a + b*Csch[c + d*Sqrt[x]])^2/x^(5/2), x]","A",-1
61,1,602,561,2.2297974,"\int \frac{x^{3/2}}{a+b \text{csch}\left(c+d \sqrt{x}\right)} \, dx","Integrate[x^(3/2)/(a + b*Csch[c + d*Sqrt[x]]),x]","\frac{2 \left(d^5 x^{5/2} \sqrt{e^{2 c} \left(a^2+b^2\right)}-5 b e^c d^4 x^2 \log \left(\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{e^{2 c} \left(a^2+b^2\right)}}+1\right)+5 b e^c d^4 x^2 \log \left(\frac{a e^{2 c+d \sqrt{x}}}{\sqrt{e^{2 c} \left(a^2+b^2\right)}+b e^c}+1\right)-20 b e^c d^3 x^{3/2} \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+20 b e^c d^3 x^{3/2} \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+60 b e^c d^2 x \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-60 b e^c d^2 x \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-120 b e^c d \sqrt{x} \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+120 b e^c d \sqrt{x} \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+120 b e^c \text{Li}_5\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-120 b e^c \text{Li}_5\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right)}{5 a d^5 \sqrt{e^{2 c} \left(a^2+b^2\right)}}","\frac{48 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^5 \sqrt{a^2+b^2}}-\frac{48 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^5 \sqrt{a^2+b^2}}-\frac{48 b \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^4 \sqrt{a^2+b^2}}+\frac{48 b \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^4 \sqrt{a^2+b^2}}+\frac{24 b x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{24 b x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{8 b x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}+\frac{8 b x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{2 b x^2 \log \left(\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{2 b x^2 \log \left(\frac{a e^{c+d \sqrt{x}}}{\sqrt{a^2+b^2}+b}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{2 x^{5/2}}{5 a}",1,"(2*(d^5*Sqrt[(a^2 + b^2)*E^(2*c)]*x^(5/2) - 5*b*d^4*E^c*x^2*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 5*b*d^4*E^c*x^2*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 20*b*d^3*E^c*x^(3/2)*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 20*b*d^3*E^c*x^(3/2)*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 60*b*d^2*E^c*x*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 60*b*d^2*E^c*x*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 120*b*d*E^c*Sqrt[x]*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 120*b*d*E^c*Sqrt[x]*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 120*b*E^c*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 120*b*E^c*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(5*a*d^5*Sqrt[(a^2 + b^2)*E^(2*c)])","A",1
62,1,374,337,8.0563905,"\int \frac{\sqrt{x}}{a+b \text{csch}\left(c+d \sqrt{x}\right)} \, dx","Integrate[Sqrt[x]/(a + b*Csch[c + d*Sqrt[x]]),x]","\frac{2 \left(d^3 x^{3/2} \sqrt{e^{2 c} \left(a^2+b^2\right)}-3 b e^c d^2 x \log \left(\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{e^{2 c} \left(a^2+b^2\right)}}+1\right)+3 b e^c d^2 x \log \left(\frac{a e^{2 c+d \sqrt{x}}}{\sqrt{e^{2 c} \left(a^2+b^2\right)}+b e^c}+1\right)-6 b e^c d \sqrt{x} \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 b e^c d \sqrt{x} \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 b e^c \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 b e^c \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right)}{3 a d^3 \sqrt{e^{2 c} \left(a^2+b^2\right)}}","\frac{4 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{4 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{4 b \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}+\frac{4 b \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{2 b x \log \left(\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{2 b x \log \left(\frac{a e^{c+d \sqrt{x}}}{\sqrt{a^2+b^2}+b}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{2 x^{3/2}}{3 a}",1,"(2*(d^3*Sqrt[(a^2 + b^2)*E^(2*c)]*x^(3/2) - 3*b*d^2*E^c*x*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*b*d^2*E^c*x*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*b*d*E^c*Sqrt[x]*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*b*d*E^c*Sqrt[x]*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*b*E^c*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*b*E^c*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*a*d^3*Sqrt[(a^2 + b^2)*E^(2*c)])","A",1
63,1,73,63,0.1491013,"\int \frac{1}{\sqrt{x} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)} \, dx","Integrate[1/(Sqrt[x]*(a + b*Csch[c + d*Sqrt[x]])),x]","\frac{2 \left(-\frac{2 b \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{-a^2-b^2}}\right)}{d \sqrt{-a^2-b^2}}+\frac{c}{d}+\sqrt{x}\right)}{a}","\frac{4 b \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{a^2+b^2}}\right)}{a d \sqrt{a^2+b^2}}+\frac{2 \sqrt{x}}{a}",1,"(2*(c/d + Sqrt[x] - (2*b*ArcTan[(a - b*Tanh[(c + d*Sqrt[x])/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d)))/a","A",1
64,0,0,25,7.6980497,"\int \frac{1}{x^{3/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)} \, dx","Integrate[1/(x^(3/2)*(a + b*Csch[c + d*Sqrt[x]])),x]","\int \frac{1}{x^{3/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^{3/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)},x\right)",0,"Integrate[1/(x^(3/2)*(a + b*Csch[c + d*Sqrt[x]])), x]","A",-1
65,0,0,25,7.6052363,"\int \frac{1}{x^{5/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)} \, dx","Integrate[1/(x^(5/2)*(a + b*Csch[c + d*Sqrt[x]])),x]","\int \frac{1}{x^{5/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^{5/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)},x\right)",0,"Integrate[1/(x^(5/2)*(a + b*Csch[c + d*Sqrt[x]])), x]","A",-1
66,1,1761,1639,18.4127342,"\int \frac{x^{3/2}}{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[x^(3/2)/(a + b*Csch[c + d*Sqrt[x]])^2,x]","\frac{2 \text{csch}^2\left(c+d \sqrt{x}\right) \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)^2 x^{5/2}}{5 a^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}+\frac{2 b \text{csch}^2\left(c+d \sqrt{x}\right) \left(\frac{-2 a^2 e^c x^2 \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^4-b^2 e^c x^2 \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^4+2 a^2 e^c x^2 \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^4+b^2 e^c x^2 \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^4+4 b \sqrt{\left(a^2+b^2\right) e^{2 c}} x^{3/2} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^3+4 b \sqrt{\left(a^2+b^2\right) e^{2 c}} x^{3/2} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^3-4 \left(2 d e^c \sqrt{x} a^2-3 b \sqrt{\left(a^2+b^2\right) e^{2 c}}+b^2 d e^c \sqrt{x}\right) x \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^2+4 \left(2 d e^c \sqrt{x} a^2+3 b \sqrt{\left(a^2+b^2\right) e^{2 c}}+b^2 d e^c \sqrt{x}\right) x \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^2+24 a^2 e^c x \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^2+12 b^2 e^c x \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^2-24 a^2 e^c x \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^2-12 b^2 e^c x \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d^2-24 b \sqrt{\left(a^2+b^2\right) e^{2 c}} \sqrt{x} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-24 b \sqrt{\left(a^2+b^2\right) e^{2 c}} \sqrt{x} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-48 a^2 e^c \sqrt{x} \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-24 b^2 e^c \sqrt{x} \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+48 a^2 e^c \sqrt{x} \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+24 b^2 e^c \sqrt{x} \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+24 b \sqrt{\left(a^2+b^2\right) e^{2 c}} \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+24 b \sqrt{\left(a^2+b^2\right) e^{2 c}} \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+48 a^2 e^c \text{Li}_5\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+24 b^2 e^c \text{Li}_5\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-48 a^2 e^c \text{Li}_5\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-24 b^2 e^c \text{Li}_5\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{\sqrt{\left(a^2+b^2\right) e^{2 c}}}-\frac{2 b d^4 e^{2 c} x^2}{-1+e^{2 c}}\right) \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)^2}{a^2 \left(a^2+b^2\right) d^5 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}^2\left(c+d \sqrt{x}\right) \text{sech}\left(\frac{c}{2}\right) \left(b+a \sinh \left(c+d \sqrt{x}\right)\right) \left(x^2 \cosh (c) b^3+a x^2 \sinh \left(d \sqrt{x}\right) b^2\right)}{a^2 \left(a^2+b^2\right) d \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}","\frac{2 x^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d}-\frac{2 x^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d}+\frac{8 x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{8 x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{24 x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^3}+\frac{24 x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^3}+\frac{48 \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^4}-\frac{48 \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^4}-\frac{48 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^5}+\frac{48 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^5}-\frac{2 x^2 b^2}{a^2 \left(a^2+b^2\right) d}+\frac{8 x^{3/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b^2}{a^2 \left(a^2+b^2\right) d^2}+\frac{8 x^{3/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b^2}{a^2 \left(a^2+b^2\right) d^2}+\frac{24 x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^3}+\frac{24 x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^3}-\frac{48 \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^4}-\frac{48 \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^4}+\frac{48 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^5}+\frac{48 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^5}-\frac{2 x^2 \cosh \left(c+d \sqrt{x}\right) b^2}{a \left(a^2+b^2\right) d \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)}-\frac{4 x^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b}{a^2 \sqrt{a^2+b^2} d}+\frac{4 x^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b}{a^2 \sqrt{a^2+b^2} d}-\frac{16 x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^2}+\frac{16 x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^2}+\frac{48 x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^3}-\frac{48 x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^3}-\frac{96 \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^4}+\frac{96 \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^4}+\frac{96 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^5}-\frac{96 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^5}+\frac{2 x^{5/2}}{5 a^2}",1,"(2*x^(5/2)*Csch[c + d*Sqrt[x]]^2*(b + a*Sinh[c + d*Sqrt[x]])^2)/(5*a^2*(a + b*Csch[c + d*Sqrt[x]])^2) + (2*b*Csch[c + d*Sqrt[x]]^2*((-2*b*d^4*E^(2*c)*x^2)/(-1 + E^(2*c)) + (4*b*d^3*Sqrt[(a^2 + b^2)*E^(2*c)]*x^(3/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 2*a^2*d^4*E^c*x^2*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - b^2*d^4*E^c*x^2*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 4*b*d^3*Sqrt[(a^2 + b^2)*E^(2*c)]*x^(3/2)*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*a^2*d^4*E^c*x^2*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + b^2*d^4*E^c*x^2*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 4*d^2*(-3*b*Sqrt[(a^2 + b^2)*E^(2*c)] + 2*a^2*d*E^c*Sqrt[x] + b^2*d*E^c*Sqrt[x])*x*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 4*d^2*(3*b*Sqrt[(a^2 + b^2)*E^(2*c)] + 2*a^2*d*E^c*Sqrt[x] + b^2*d*E^c*Sqrt[x])*x*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 24*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*Sqrt[x]*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 24*a^2*d^2*E^c*x*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 12*b^2*d^2*E^c*x*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 24*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*Sqrt[x]*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 24*a^2*d^2*E^c*x*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 12*b^2*d^2*E^c*x*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 24*b*Sqrt[(a^2 + b^2)*E^(2*c)]*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 48*a^2*d*E^c*Sqrt[x]*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 24*b^2*d*E^c*Sqrt[x]*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 24*b*Sqrt[(a^2 + b^2)*E^(2*c)]*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 48*a^2*d*E^c*Sqrt[x]*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 24*b^2*d*E^c*Sqrt[x]*PolyLog[4, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 48*a^2*E^c*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 24*b^2*E^c*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 48*a^2*E^c*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 24*b^2*E^c*PolyLog[5, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/Sqrt[(a^2 + b^2)*E^(2*c)])*(b + a*Sinh[c + d*Sqrt[x]])^2)/(a^2*(a^2 + b^2)*d^5*(a + b*Csch[c + d*Sqrt[x]])^2) + (Csch[c/2]*Csch[c + d*Sqrt[x]]^2*Sech[c/2]*(b + a*Sinh[c + d*Sqrt[x]])*(b^3*x^2*Cosh[c] + a*b^2*x^2*Sinh[d*Sqrt[x]]))/(a^2*(a^2 + b^2)*d*(a + b*Csch[c + d*Sqrt[x]])^2)","A",0
67,1,934,959,15.2712625,"\int \frac{\sqrt{x}}{\left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[Sqrt[x]/(a + b*Csch[c + d*Sqrt[x]])^2,x]","\frac{\text{csch}^2\left(c+d \sqrt{x}\right) \left(b+a \sinh \left(c+d \sqrt{x}\right)\right) \left(\frac{6 x \text{csch}(c) \left(b \cosh (c)+a \sinh \left(d \sqrt{x}\right)\right) b^2}{\left(a^2+b^2\right) d}+\frac{6 \left(\frac{-2 d^2 e^c x \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) a^2+2 d^2 e^c x \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) a^2+4 e^c \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) a^2-4 e^c \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) a^2-b^2 d^2 e^c x \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right)+2 b d \sqrt{\left(a^2+b^2\right) e^{2 c}} \sqrt{x} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right)+b^2 d^2 e^c x \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right)+2 b d \sqrt{\left(a^2+b^2\right) e^{2 c}} \sqrt{x} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right)+2 \left(-2 d e^c \sqrt{x} a^2+b \sqrt{\left(a^2+b^2\right) e^{2 c}}-b^2 d e^c \sqrt{x}\right) \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+2 \left(2 d e^c \sqrt{x} a^2+b \sqrt{\left(a^2+b^2\right) e^{2 c}}+b^2 d e^c \sqrt{x}\right) \text{Li}_2\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+2 b^2 e^c \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-2 b^2 e^c \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{\sqrt{\left(a^2+b^2\right) e^{2 c}}}-\frac{2 b d^2 e^{2 c} x}{-1+e^{2 c}}\right) \left(b+a \sinh \left(c+d \sqrt{x}\right)\right) b}{\left(a^2+b^2\right) d^3}+2 x^{3/2} \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)\right)}{3 a^2 \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}","\frac{2 x \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d}-\frac{2 x \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d}+\frac{4 \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{4 \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{4 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^3}+\frac{4 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right)^{3/2} d^3}-\frac{2 x b^2}{a^2 \left(a^2+b^2\right) d}+\frac{4 \sqrt{x} \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b^2}{a^2 \left(a^2+b^2\right) d^2}+\frac{4 \sqrt{x} \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b^2}{a^2 \left(a^2+b^2\right) d^2}+\frac{4 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^3}+\frac{4 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b^2}{a^2 \left(a^2+b^2\right) d^3}-\frac{2 x \cosh \left(c+d \sqrt{x}\right) b^2}{a \left(a^2+b^2\right) d \left(b+a \sinh \left(c+d \sqrt{x}\right)\right)}-\frac{4 x \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{a^2+b^2}}+1\right) b}{a^2 \sqrt{a^2+b^2} d}+\frac{4 x \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{a^2+b^2}}+1\right) b}{a^2 \sqrt{a^2+b^2} d}-\frac{8 \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^2}+\frac{8 \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^2}+\frac{8 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^3}-\frac{8 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{a^2+b^2}}\right) b}{a^2 \sqrt{a^2+b^2} d^3}+\frac{2 x^{3/2}}{3 a^2}",1,"(Csch[c + d*Sqrt[x]]^2*(b + a*Sinh[c + d*Sqrt[x]])*(2*x^(3/2)*(b + a*Sinh[c + d*Sqrt[x]]) + (6*b*((-2*b*d^2*E^(2*c)*x)/(-1 + E^(2*c)) + (2*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*Sqrt[x]*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 2*a^2*d^2*E^c*x*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - b^2*d^2*E^c*x*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*b*d*Sqrt[(a^2 + b^2)*E^(2*c)]*Sqrt[x]*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*a^2*d^2*E^c*x*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + b^2*d^2*E^c*x*Log[1 + (a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*(b*Sqrt[(a^2 + b^2)*E^(2*c)] - 2*a^2*d*E^c*Sqrt[x] - b^2*d*E^c*Sqrt[x])*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 2*(b*Sqrt[(a^2 + b^2)*E^(2*c)] + 2*a^2*d*E^c*Sqrt[x] + b^2*d*E^c*Sqrt[x])*PolyLog[2, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 4*a^2*E^c*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 2*b^2*E^c*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 4*a^2*E^c*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 2*b^2*E^c*PolyLog[3, -((a*E^(2*c + d*Sqrt[x]))/(b*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/Sqrt[(a^2 + b^2)*E^(2*c)])*(b + a*Sinh[c + d*Sqrt[x]]))/((a^2 + b^2)*d^3) + (6*b^2*x*Csch[c]*(b*Cosh[c] + a*Sinh[d*Sqrt[x]]))/((a^2 + b^2)*d)))/(3*a^2*(a + b*Csch[c + d*Sqrt[x]])^2)","A",1
68,1,175,118,0.4421816,"\int \frac{1}{\sqrt{x} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(Sqrt[x]*(a + b*Csch[c + d*Sqrt[x]])^2),x]","\frac{2 \text{csch}\left(c+d \sqrt{x}\right) \left(a \sinh \left(c+d \sqrt{x}\right)+b\right) \left(-\frac{a b^2 \coth \left(c+d \sqrt{x}\right)}{a^2+b^2}+\frac{2 b \left(2 a^2+b^2\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right) \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+\left(c+d \sqrt{x}\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)\right)}{a^2 d \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2}","\frac{4 b \left(2 a^2+b^2\right) \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{a^2+b^2}}\right)}{a^2 d \left(a^2+b^2\right)^{3/2}}-\frac{2 b^2 \coth \left(c+d \sqrt{x}\right)}{a d \left(a^2+b^2\right) \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)}+\frac{2 \sqrt{x}}{a^2}",1,"(2*Csch[c + d*Sqrt[x]]*(-((a*b^2*Coth[c + d*Sqrt[x]])/(a^2 + b^2)) + (c + d*Sqrt[x])*(a + b*Csch[c + d*Sqrt[x]]) + (2*b*(2*a^2 + b^2)*ArcTan[(a - b*Tanh[(c + d*Sqrt[x])/2])/Sqrt[-a^2 - b^2]]*(a + b*Csch[c + d*Sqrt[x]]))/(-a^2 - b^2)^(3/2))*(b + a*Sinh[c + d*Sqrt[x]]))/(a^2*d*(a + b*Csch[c + d*Sqrt[x]])^2)","A",1
69,0,0,25,67.5059376,"\int \frac{1}{x^{3/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(x^(3/2)*(a + b*Csch[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^{3/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^{3/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Integrate[1/(x^(3/2)*(a + b*Csch[c + d*Sqrt[x]])^2), x]","A",-1
70,0,0,25,68.5477984,"\int \frac{1}{x^{5/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(x^(5/2)*(a + b*Csch[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^{5/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^{5/2} \left(a+b \text{csch}\left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Integrate[1/(x^(5/2)*(a + b*Csch[c + d*Sqrt[x]])^2), x]","A",-1
71,0,0,32,17.4491829,"\int (e x)^m \left(a+b \text{csch}\left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^m*(a + b*Csch[c + d*x^n])^p,x]","\int (e x)^m \left(a+b \text{csch}\left(c+d x^n\right)\right)^p \, dx","x^{-m} (e x)^m \text{Int}\left(x^m \left(a+b \text{csch}\left(c+d x^n\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(a + b*Csch[c + d*x^n])^p, x]","A",-1
72,1,45,45,0.0624415,"\int (e x)^{-1+n} \left(a+b \text{csch}\left(c+d x^n\right)\right) \, dx","Integrate[(e*x)^(-1 + n)*(a + b*Csch[c + d*x^n]),x]","\frac{x^{-n} (e x)^n \left(a \left(c+d x^n\right)+b \log \left(\tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)\right)\right)}{d e n}","\frac{a (e x)^n}{e n}-\frac{b x^{-n} (e x)^n \tanh ^{-1}\left(\cosh \left(c+d x^n\right)\right)}{d e n}",1,"((e*x)^n*(a*(c + d*x^n) + b*Log[Tanh[(c + d*x^n)/2]]))/(d*e*n*x^n)","A",1
73,1,175,124,0.1496951,"\int (e x)^{-1+2 n} \left(a+b \text{csch}\left(c+d x^n\right)\right) \, dx","Integrate[(e*x)^(-1 + 2*n)*(a + b*Csch[c + d*x^n]),x]","\frac{x^{-2 n} (e x)^{2 n} \left(a d^2 x^{2 n}+2 b \text{Li}_2\left(-e^{-d x^n-c}\right)-2 b \text{Li}_2\left(e^{-d x^n-c}\right)+2 b d x^n \log \left(1-e^{-c-d x^n}\right)-2 b d x^n \log \left(e^{-c-d x^n}+1\right)+2 b c \log \left(1-e^{-c-d x^n}\right)-2 b c \log \left(e^{-c-d x^n}+1\right)-2 b c \log \left(\tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)\right)\right)}{2 d^2 e n}","\frac{a (e x)^{2 n}}{2 e n}-\frac{b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-e^{d x^n+c}\right)}{d^2 e n}+\frac{b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(e^{d x^n+c}\right)}{d^2 e n}-\frac{2 b x^{-n} (e x)^{2 n} \tanh ^{-1}\left(e^{c+d x^n}\right)}{d e n}",1,"((e*x)^(2*n)*(a*d^2*x^(2*n) + 2*b*c*Log[1 - E^(-c - d*x^n)] + 2*b*d*x^n*Log[1 - E^(-c - d*x^n)] - 2*b*c*Log[1 + E^(-c - d*x^n)] - 2*b*d*x^n*Log[1 + E^(-c - d*x^n)] - 2*b*c*Log[Tanh[(c + d*x^n)/2]] + 2*b*PolyLog[2, -E^(-c - d*x^n)] - 2*b*PolyLog[2, E^(-c - d*x^n)]))/(2*d^2*e*n*x^(2*n))","A",1
74,0,0,197,28.257673,"\int (e x)^{-1+3 n} \left(a+b \text{csch}\left(c+d x^n\right)\right) \, dx","Integrate[(e*x)^(-1 + 3*n)*(a + b*Csch[c + d*x^n]),x]","\int (e x)^{-1+3 n} \left(a+b \text{csch}\left(c+d x^n\right)\right) \, dx","\frac{a (e x)^{3 n}}{3 e n}+\frac{2 b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(-e^{d x^n+c}\right)}{d^3 e n}-\frac{2 b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(e^{d x^n+c}\right)}{d^3 e n}-\frac{2 b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(-e^{d x^n+c}\right)}{d^2 e n}+\frac{2 b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(e^{d x^n+c}\right)}{d^2 e n}-\frac{2 b x^{-n} (e x)^{3 n} \tanh ^{-1}\left(e^{c+d x^n}\right)}{d e n}",1,"Integrate[(e*x)^(-1 + 3*n)*(a + b*Csch[c + d*x^n]), x]","F",-1
75,1,87,80,0.3701522,"\int (e x)^{-1+n} \left(a+b \text{csch}\left(c+d x^n\right)\right)^2 \, dx","Integrate[(e*x)^(-1 + n)*(a + b*Csch[c + d*x^n])^2,x]","\frac{x^{-n} (e x)^n \left(2 a \left(a c+a d x^n+2 b \log \left(\tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)\right)\right)-b^2 \tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)+b^2 \left(-\coth \left(\frac{1}{2} \left(c+d x^n\right)\right)\right)\right)}{2 d e n}","\frac{a^2 (e x)^n}{e n}-\frac{2 a b x^{-n} (e x)^n \tanh ^{-1}\left(\cosh \left(c+d x^n\right)\right)}{d e n}-\frac{b^2 x^{-n} (e x)^n \coth \left(c+d x^n\right)}{d e n}",1,"((e*x)^n*(-(b^2*Coth[(c + d*x^n)/2]) + 2*a*(a*c + a*d*x^n + 2*b*Log[Tanh[(c + d*x^n)/2]]) - b^2*Tanh[(c + d*x^n)/2]))/(2*d*e*n*x^n)","A",1
76,1,278,198,5.4890212,"\int (e x)^{-1+2 n} \left(a+b \text{csch}\left(c+d x^n\right)\right)^2 \, dx","Integrate[(e*x)^(-1 + 2*n)*(a + b*Csch[c + d*x^n])^2,x]","\frac{x^{-2 n} (e x)^{2 n} \left(2 d x^n \left(a^2 d x^n-2 b^2 \coth (c)\right)+8 a b \left(\frac{\text{sech}(c) \left(\text{Li}_2\left(-e^{-d x^n-\tanh ^{-1}(\tanh (c))}\right)-\text{Li}_2\left(e^{-d x^n-\tanh ^{-1}(\tanh (c))}\right)+\left(\tanh ^{-1}(\tanh (c))+d x^n\right) \left(\log \left(1-e^{-\tanh ^{-1}(\tanh (c))-d x^n}\right)-\log \left(e^{-\tanh ^{-1}(\tanh (c))-d x^n}+1\right)\right)\right)}{\sqrt{\text{sech}^2(c)}}+2 \tanh ^{-1}(\tanh (c)) \tanh ^{-1}\left(\sinh (c) \tanh \left(\frac{d x^n}{2}\right)+\cosh (c)\right)\right)+4 b^2 d \coth (c) x^n+2 b^2 d \text{csch}\left(\frac{c}{2}\right) x^n \sinh \left(\frac{d x^n}{2}\right) \text{csch}\left(\frac{1}{2} \left(c+d x^n\right)\right)-2 b^2 d \text{sech}\left(\frac{c}{2}\right) x^n \sinh \left(\frac{d x^n}{2}\right) \text{sech}\left(\frac{1}{2} \left(c+d x^n\right)\right)-4 b^2 \left(d \coth (c) x^n-\log \left(\sinh \left(c+d x^n\right)\right)\right)\right)}{4 d^2 e n}","\frac{a^2 (e x)^{2 n}}{2 e n}-\frac{2 a b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-e^{d x^n+c}\right)}{d^2 e n}+\frac{2 a b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(e^{d x^n+c}\right)}{d^2 e n}-\frac{4 a b x^{-n} (e x)^{2 n} \tanh ^{-1}\left(e^{c+d x^n}\right)}{d e n}+\frac{b^2 x^{-2 n} (e x)^{2 n} \log \left(\sinh \left(c+d x^n\right)\right)}{d^2 e n}-\frac{b^2 x^{-n} (e x)^{2 n} \coth \left(c+d x^n\right)}{d e n}",1,"((e*x)^(2*n)*(4*b^2*d*x^n*Coth[c] + 2*d*x^n*(a^2*d*x^n - 2*b^2*Coth[c]) - 4*b^2*(d*x^n*Coth[c] - Log[Sinh[c + d*x^n]]) + 8*a*b*(2*ArcTanh[Tanh[c]]*ArcTanh[Cosh[c] + Sinh[c]*Tanh[(d*x^n)/2]] + (((d*x^n + ArcTanh[Tanh[c]])*(Log[1 - E^(-(d*x^n) - ArcTanh[Tanh[c]])] - Log[1 + E^(-(d*x^n) - ArcTanh[Tanh[c]])]) + PolyLog[2, -E^(-(d*x^n) - ArcTanh[Tanh[c]])] - PolyLog[2, E^(-(d*x^n) - ArcTanh[Tanh[c]])])*Sech[c])/Sqrt[Sech[c]^2]) + 2*b^2*d*x^n*Csch[c/2]*Csch[(c + d*x^n)/2]*Sinh[(d*x^n)/2] - 2*b^2*d*x^n*Sech[c/2]*Sech[(c + d*x^n)/2]*Sinh[(d*x^n)/2]))/(4*d^2*e*n*x^(2*n))","A",0
77,0,0,344,101.560817,"\int (e x)^{-1+3 n} \left(a+b \text{csch}\left(c+d x^n\right)\right)^2 \, dx","Integrate[(e*x)^(-1 + 3*n)*(a + b*Csch[c + d*x^n])^2,x]","\int (e x)^{-1+3 n} \left(a+b \text{csch}\left(c+d x^n\right)\right)^2 \, dx","\frac{a^2 (e x)^{3 n}}{3 e n}+\frac{4 a b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(-e^{d x^n+c}\right)}{d^3 e n}-\frac{4 a b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(e^{d x^n+c}\right)}{d^3 e n}-\frac{4 a b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(-e^{d x^n+c}\right)}{d^2 e n}+\frac{4 a b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(e^{d x^n+c}\right)}{d^2 e n}-\frac{4 a b x^{-n} (e x)^{3 n} \tanh ^{-1}\left(e^{c+d x^n}\right)}{d e n}+\frac{b^2 x^{-3 n} (e x)^{3 n} \text{Li}_2\left(e^{2 \left(d x^n+c\right)}\right)}{d^3 e n}+\frac{2 b^2 x^{-2 n} (e x)^{3 n} \log \left(1-e^{2 \left(c+d x^n\right)}\right)}{d^2 e n}-\frac{b^2 x^{-n} (e x)^{3 n} \coth \left(c+d x^n\right)}{d e n}-\frac{b^2 x^{-n} (e x)^{3 n}}{d e n}",1,"Integrate[(e*x)^(-1 + 3*n)*(a + b*Csch[c + d*x^n])^2, x]","F",-1
78,1,84,82,0.1725568,"\int \frac{(e x)^{-1+n}}{a+b \text{csch}\left(c+d x^n\right)} \, dx","Integrate[(e*x)^(-1 + n)/(a + b*Csch[c + d*x^n]),x]","\frac{(e x)^n \left(-\frac{2 b x^{-n} \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+c x^{-n}+d\right)}{a d e n}","\frac{2 b x^{-n} (e x)^n \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{a^2+b^2}}\right)}{a d e n \sqrt{a^2+b^2}}+\frac{(e x)^n}{a e n}",1,"((e*x)^n*(d + c/x^n - (2*b*ArcTan[(a - b*Tanh[(c + d*x^n)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*x^n)))/(a*d*e*n)","A",1
79,1,1181,291,4.5202908,"\int \frac{(e x)^{-1+2 n}}{a+b \text{csch}\left(c+d x^n\right)} \, dx","Integrate[(e*x)^(-1 + 2*n)/(a + b*Csch[c + d*x^n]),x]","\frac{(e x)^{2 n} \text{csch}\left(d x^n+c\right) \left(1-\frac{2 b x^{-2 n} \left(-\frac{i \pi  \tanh ^{-1}\left(\frac{b \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)-a}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}-\frac{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} \left(2 i d x^n+2 i c+\pi \right)\right)}{\sqrt{-a^2-b^2}}\right)+\left(-2 i d x^n-2 i c+\pi \right) \tanh ^{-1}\left(\frac{(b-i a) \tan \left(\frac{1}{4} \left(2 i d x^n+2 i c+\pi \right)\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} \left(2 i d x^n+2 i c+\pi \right)\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} \left(2 i d x^n+2 i c+\pi \right)\right)+1\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} \left(2 i d x^n+2 i c+\pi \right)\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} \left(2 i d x^n+2 i c+\pi \right)\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} \left(2 i d x^n+2 i c+\pi \right)\right)+i\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} \left(2 i d x^n+2 i c+\pi \right)\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} \left(2 i d x^n+2 i c+\pi \right)\right)}{\sqrt{-a^2-b^2}}\right)-2 i \tanh ^{-1}\left(\frac{(b-i a) \tan \left(\frac{1}{4} \left(2 i d x^n+2 i c+\pi \right)\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(-\frac{(-1)^{3/4} \sqrt{-a^2-b^2} e^{-\frac{d x^n}{2}-\frac{c}{2}}}{\sqrt{2} \sqrt{-i a} \sqrt{b+a \sinh \left(d x^n+c\right)}}\right)+\left(\cos ^{-1}\left(-\frac{i b}{a}\right)-2 \tan ^{-1}\left(\frac{(a-i b) \cot \left(\frac{1}{4} \left(2 i d x^n+2 i c+\pi \right)\right)}{\sqrt{-a^2-b^2}}\right)+2 i \tanh ^{-1}\left(\frac{(b-i a) \tan \left(\frac{1}{4} \left(2 i d x^n+2 i c+\pi \right)\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(\frac{\sqrt[4]{-1} \sqrt{-a^2-b^2} e^{\frac{1}{2} \left(d x^n+c\right)}}{\sqrt{2} \sqrt{-i a} \sqrt{b+a \sinh \left(d x^n+c\right)}}\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} \left(2 i d x^n+2 i c+\pi \right)\right)\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} \left(2 i d x^n+2 i c+\pi \right)\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} \left(2 i d x^n+2 i c+\pi \right)\right)\right)}{a \left(a+i b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} \left(2 i d x^n+2 i c+\pi \right)\right)\right)}\right)\right)}{\sqrt{-a^2-b^2}}\right)}{d^2}\right) \left(b+a \sinh \left(d x^n+c\right)\right)}{2 a e n \left(a+b \text{csch}\left(d x^n+c\right)\right)}","-\frac{b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b-\sqrt{a^2+b^2}}\right)}{a d^2 e n \sqrt{a^2+b^2}}+\frac{b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{a^2+b^2}}\right)}{a d^2 e n \sqrt{a^2+b^2}}-\frac{b x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{b-\sqrt{a^2+b^2}}+1\right)}{a d e n \sqrt{a^2+b^2}}+\frac{b x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{\sqrt{a^2+b^2}+b}+1\right)}{a d e n \sqrt{a^2+b^2}}+\frac{(e x)^{2 n}}{2 a e n}",1,"((e*x)^(2*n)*Csch[c + d*x^n]*(1 - (2*b*(((-I)*Pi*ArcTanh[(-a + b*Tanh[(c + d*x^n)/2])/Sqrt[a^2 + b^2]])/Sqrt[a^2 + b^2] - (2*(c + I*ArcCos[((-I)*b)/a])*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x^n)/4])/Sqrt[-a^2 - b^2]] + ((-2*I)*c + Pi - (2*I)*d*x^n)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x^n)/4])/Sqrt[-a^2 - b^2]] - (ArcCos[((-I)*b)/a] - 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x^n)/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^n)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x^n)/4]))] - (ArcCos[((-I)*b)/a] + 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x^n)/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^n)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x^n)/4]))] + (ArcCos[((-I)*b)/a] + 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x^n)/4])/Sqrt[-a^2 - b^2]] - (2*I)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x^n)/4])/Sqrt[-a^2 - b^2]])*Log[-(((-1)^(3/4)*Sqrt[-a^2 - b^2]*E^(-1/2*c - (d*x^n)/2))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x^n]]))] + (ArcCos[((-I)*b)/a] - 2*ArcTan[((a - I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x^n)/4])/Sqrt[-a^2 - b^2]] + (2*I)*ArcTanh[(((-I)*a + b)*Tan[((2*I)*c + Pi + (2*I)*d*x^n)/4])/Sqrt[-a^2 - b^2]])*Log[((-1)^(1/4)*Sqrt[-a^2 - b^2]*E^((c + d*x^n)/2))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x^n]])] + 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^n)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x^n)/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^n)/4]))/(a*(a + I*b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x^n)/4]))]))/Sqrt[-a^2 - b^2]))/(d^2*x^(2*n)))*(b + a*Sinh[c + d*x^n]))/(2*a*e*n*(a + b*Csch[c + d*x^n]))","C",1
80,0,0,428,6.9934922,"\int \frac{(e x)^{-1+3 n}}{a+b \text{csch}\left(c+d x^n\right)} \, dx","Integrate[(e*x)^(-1 + 3*n)/(a + b*Csch[c + d*x^n]),x]","\int \frac{(e x)^{-1+3 n}}{a+b \text{csch}\left(c+d x^n\right)} \, dx","\frac{2 b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(-\frac{a e^{d x^n+c}}{b-\sqrt{a^2+b^2}}\right)}{a d^3 e n \sqrt{a^2+b^2}}-\frac{2 b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(-\frac{a e^{d x^n+c}}{b+\sqrt{a^2+b^2}}\right)}{a d^3 e n \sqrt{a^2+b^2}}-\frac{2 b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b-\sqrt{a^2+b^2}}\right)}{a d^2 e n \sqrt{a^2+b^2}}+\frac{2 b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{a^2+b^2}}\right)}{a d^2 e n \sqrt{a^2+b^2}}-\frac{b x^{-n} (e x)^{3 n} \log \left(\frac{a e^{c+d x^n}}{b-\sqrt{a^2+b^2}}+1\right)}{a d e n \sqrt{a^2+b^2}}+\frac{b x^{-n} (e x)^{3 n} \log \left(\frac{a e^{c+d x^n}}{\sqrt{a^2+b^2}+b}+1\right)}{a d e n \sqrt{a^2+b^2}}+\frac{(e x)^{3 n}}{3 a e n}",1,"Integrate[(e*x)^(-1 + 3*n)/(a + b*Csch[c + d*x^n]), x]","F",-1
81,1,167,149,0.5904287,"\int \frac{(e x)^{-1+n}}{\left(a+b \text{csch}\left(c+d x^n\right)\right)^2} \, dx","Integrate[(e*x)^(-1 + n)/(a + b*Csch[c + d*x^n])^2,x]","-\frac{x^{-n} (e x)^n \left(\left(a+b \text{csch}\left(c+d x^n\right)\right) \left(-\left(\left(-a^2-b^2\right)^{3/2} \left(c+d x^n\right)\right)-2 b \left(2 a^2+b^2\right) \tan ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{-a^2-b^2}}\right)\right)-a b^2 \sqrt{-a^2-b^2} \coth \left(c+d x^n\right)\right)}{a^2 d e n \left(-a^2-b^2\right)^{3/2} \left(a+b \text{csch}\left(c+d x^n\right)\right)}","\frac{2 b \left(2 a^2+b^2\right) x^{-n} (e x)^n \tanh ^{-1}\left(\frac{a-b \tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{a^2+b^2}}\right)}{a^2 d e n \left(a^2+b^2\right)^{3/2}}-\frac{b^2 x^{-n} (e x)^n \coth \left(c+d x^n\right)}{a d e n \left(a^2+b^2\right) \left(a+b \text{csch}\left(c+d x^n\right)\right)}+\frac{(e x)^n}{a^2 e n}",1,"-(((e*x)^n*(-(a*b^2*Sqrt[-a^2 - b^2]*Coth[c + d*x^n]) + (-((-a^2 - b^2)^(3/2)*(c + d*x^n)) - 2*b*(2*a^2 + b^2)*ArcTan[(a - b*Tanh[(c + d*x^n)/2])/Sqrt[-a^2 - b^2]])*(a + b*Csch[c + d*x^n])))/(a^2*(-a^2 - b^2)^(3/2)*d*e*n*x^n*(a + b*Csch[c + d*x^n])))","A",1
82,1,3259,681,33.9903031,"\int \frac{(e x)^{-1+2 n}}{\left(a+b \text{csch}\left(c+d x^n\right)\right)^2} \, dx","Integrate[(e*x)^(-1 + 2*n)/(a + b*Csch[c + d*x^n])^2,x]","\text{Result too large to show}","-\frac{2 b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b-\sqrt{a^2+b^2}}\right)}{a^2 d^2 e n \sqrt{a^2+b^2}}+\frac{2 b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{a^2+b^2}}\right)}{a^2 d^2 e n \sqrt{a^2+b^2}}+\frac{b^2 x^{-2 n} (e x)^{2 n} \log \left(a \sinh \left(c+d x^n\right)+b\right)}{a^2 d^2 e n \left(a^2+b^2\right)}-\frac{2 b x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{b-\sqrt{a^2+b^2}}+1\right)}{a^2 d e n \sqrt{a^2+b^2}}+\frac{2 b x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{\sqrt{a^2+b^2}+b}+1\right)}{a^2 d e n \sqrt{a^2+b^2}}-\frac{b^2 x^{-n} (e x)^{2 n} \cosh \left(c+d x^n\right)}{a d e n \left(a^2+b^2\right) \left(a \sinh \left(c+d x^n\right)+b\right)}+\frac{b^3 x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b-\sqrt{a^2+b^2}}\right)}{a^2 d^2 e n \left(a^2+b^2\right)^{3/2}}-\frac{b^3 x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{a^2+b^2}}\right)}{a^2 d^2 e n \left(a^2+b^2\right)^{3/2}}+\frac{b^3 x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{b-\sqrt{a^2+b^2}}+1\right)}{a^2 d e n \left(a^2+b^2\right)^{3/2}}-\frac{b^3 x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{\sqrt{a^2+b^2}+b}+1\right)}{a^2 d e n \left(a^2+b^2\right)^{3/2}}+\frac{(e x)^{2 n}}{2 a^2 e n}",1,"(b^2*x^(1 - n)*(e*x)^(-1 + 2*n)*Csch[c/2]*Csch[c + d*x^n]^2*Sech[c/2]*(b*Cosh[c] + a*Sinh[d*x^n])*(b + a*Sinh[c + d*x^n]))/(2*a^2*(a^2 + b^2)*d*n*(a + b*Csch[c + d*x^n])^2) + (b^2*x^(1 - n)*(e*x)^(-1 + 2*n)*Coth[c]*Csch[c + d*x^n]^2*(b + a*Sinh[c + d*x^n])^2)/(a^2*(a^2 + b^2)*d*n*(a + b*Csch[c + d*x^n])^2) - (2*b^3*x^(1 - 2*n)*(e*x)^(-1 + 2*n)*ArcTan[(a - b*Tanh[(c + d*x^n)/2])/Sqrt[-a^2 - b^2]]*Coth[c]*Csch[c + d*x^n]^2*(b + a*Sinh[c + d*x^n])^2)/(a^2*Sqrt[-a^2 - b^2]*(a^2 + b^2)*d^2*n*(a + b*Csch[c + d*x^n])^2) - (2*b*x^(1 - 2*n)*(e*x)^(-1 + 2*n)*Csch[c + d*x^n]^2*(((-I)*Pi*ArcTanh[(-a + b*Tanh[(c + d*x^n)/2])/Sqrt[a^2 + b^2]])/Sqrt[a^2 + b^2] - (2*((-I)*c + Pi/2 - I*d*x^n)*ArcTanh[(((-I)*a + b)*Cot[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]] - 2*((-I)*c + ArcCos[((-I)*b)/a])*ArcTanh[(((-I)*a - b)*Tan[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]] + (ArcCos[((-I)*b)/a] - (2*I)*(ArcTanh[(((-I)*a + b)*Cot[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]] - ArcTanh[(((-I)*a - b)*Tan[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]]))*Log[Sqrt[-a^2 - b^2]/(Sqrt[2]*Sqrt[(-I)*a]*E^((I/2)*((-I)*c + Pi/2 - I*d*x^n))*Sqrt[b + a*Sinh[c + d*x^n]])] + (ArcCos[((-I)*b)/a] + (2*I)*(ArcTanh[(((-I)*a + b)*Cot[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]] - ArcTanh[(((-I)*a - b)*Tan[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]]))*Log[(Sqrt[-a^2 - b^2]*E^((I/2)*((-I)*c + Pi/2 - I*d*x^n)))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x^n]])] - (ArcCos[((-I)*b)/a] + (2*I)*ArcTanh[(((-I)*a - b)*Tan[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]])*Log[1 - (I*(b - I*Sqrt[-a^2 - b^2])*((-I)*a + b - Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))/(a*((-I)*a + b + Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))] + (-ArcCos[((-I)*b)/a] + (2*I)*ArcTanh[(((-I)*a - b)*Tan[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]])*Log[1 - (I*(b + I*Sqrt[-a^2 - b^2])*((-I)*a + b - Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))/(a*((-I)*a + b + Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))] + I*(PolyLog[2, (I*(b - I*Sqrt[-a^2 - b^2])*((-I)*a + b - Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))/(a*((-I)*a + b + Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))] - PolyLog[2, (I*(b + I*Sqrt[-a^2 - b^2])*((-I)*a + b - Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))/(a*((-I)*a + b + Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))]))/Sqrt[-a^2 - b^2])*(b + a*Sinh[c + d*x^n])^2)/((a^2 + b^2)*d^2*n*(a + b*Csch[c + d*x^n])^2) - (b^3*x^(1 - 2*n)*(e*x)^(-1 + 2*n)*Csch[c + d*x^n]^2*(((-I)*Pi*ArcTanh[(-a + b*Tanh[(c + d*x^n)/2])/Sqrt[a^2 + b^2]])/Sqrt[a^2 + b^2] - (2*((-I)*c + Pi/2 - I*d*x^n)*ArcTanh[(((-I)*a + b)*Cot[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]] - 2*((-I)*c + ArcCos[((-I)*b)/a])*ArcTanh[(((-I)*a - b)*Tan[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]] + (ArcCos[((-I)*b)/a] - (2*I)*(ArcTanh[(((-I)*a + b)*Cot[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]] - ArcTanh[(((-I)*a - b)*Tan[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]]))*Log[Sqrt[-a^2 - b^2]/(Sqrt[2]*Sqrt[(-I)*a]*E^((I/2)*((-I)*c + Pi/2 - I*d*x^n))*Sqrt[b + a*Sinh[c + d*x^n]])] + (ArcCos[((-I)*b)/a] + (2*I)*(ArcTanh[(((-I)*a + b)*Cot[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]] - ArcTanh[(((-I)*a - b)*Tan[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]]))*Log[(Sqrt[-a^2 - b^2]*E^((I/2)*((-I)*c + Pi/2 - I*d*x^n)))/(Sqrt[2]*Sqrt[(-I)*a]*Sqrt[b + a*Sinh[c + d*x^n]])] - (ArcCos[((-I)*b)/a] + (2*I)*ArcTanh[(((-I)*a - b)*Tan[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]])*Log[1 - (I*(b - I*Sqrt[-a^2 - b^2])*((-I)*a + b - Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))/(a*((-I)*a + b + Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))] + (-ArcCos[((-I)*b)/a] + (2*I)*ArcTanh[(((-I)*a - b)*Tan[((-I)*c + Pi/2 - I*d*x^n)/2])/Sqrt[-a^2 - b^2]])*Log[1 - (I*(b + I*Sqrt[-a^2 - b^2])*((-I)*a + b - Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))/(a*((-I)*a + b + Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))] + I*(PolyLog[2, (I*(b - I*Sqrt[-a^2 - b^2])*((-I)*a + b - Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))/(a*((-I)*a + b + Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))] - PolyLog[2, (I*(b + I*Sqrt[-a^2 - b^2])*((-I)*a + b - Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))/(a*((-I)*a + b + Sqrt[-a^2 - b^2]*Tan[((-I)*c + Pi/2 - I*d*x^n)/2]))]))/Sqrt[-a^2 - b^2])*(b + a*Sinh[c + d*x^n])^2)/(a^2*(a^2 + b^2)*d^2*n*(a + b*Csch[c + d*x^n])^2) + (x^(1 - n)*(e*x)^(-1 + 2*n)*Csch[c/2]*Csch[c + d*x^n]^2*Sech[c/2]*(-2*b^2*Cosh[c] + a^2*d*x^n*Sinh[c] + b^2*d*x^n*Sinh[c])*(b + a*Sinh[c + d*x^n])^2)/(4*a^2*(a^2 + b^2)*d*n*(a + b*Csch[c + d*x^n])^2) - (b^2*x^(1 - 2*n)*(e*x)^(-1 + 2*n)*Csch[c]*Csch[c + d*x^n]^2*(-(a*d*x^n*Cosh[c]) + a*Log[b + a*Cosh[d*x^n]*Sinh[c] + a*Cosh[c]*Sinh[d*x^n]]*Sinh[c] + (2*a*b*ArcTan[(a*Cosh[c] + (-b + a*Sinh[c])*Tanh[(d*x^n)/2])/Sqrt[-b^2 - a^2*Cosh[c]^2 + a^2*Sinh[c]^2]]*Cosh[c])/Sqrt[-b^2 - a^2*Cosh[c]^2 + a^2*Sinh[c]^2])*(b + a*Sinh[c + d*x^n])^2)/(a*(a^2 + b^2)*d^2*n*(a + b*Csch[c + d*x^n])^2*(-(a^2*Cosh[c]^2) + a^2*Sinh[c]^2))","C",0
83,0,0,1218,118.9612951,"\int \frac{(e x)^{-1+3 n}}{\left(a+b \text{csch}\left(c+d x^n\right)\right)^2} \, dx","Integrate[(e*x)^(-1 + 3*n)/(a + b*Csch[c + d*x^n])^2,x]","\int \frac{(e x)^{-1+3 n}}{\left(a+b \text{csch}\left(c+d x^n\right)\right)^2} \, dx","\frac{2 b^2 (e x)^{3 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b-\sqrt{a^2+b^2}}\right) x^{-3 n}}{a^2 \left(a^2+b^2\right) d^3 e n}+\frac{2 b^2 (e x)^{3 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{a^2+b^2}}\right) x^{-3 n}}{a^2 \left(a^2+b^2\right) d^3 e n}+\frac{4 b (e x)^{3 n} \text{Li}_3\left(-\frac{a e^{d x^n+c}}{b-\sqrt{a^2+b^2}}\right) x^{-3 n}}{a^2 \sqrt{a^2+b^2} d^3 e n}-\frac{2 b^3 (e x)^{3 n} \text{Li}_3\left(-\frac{a e^{d x^n+c}}{b-\sqrt{a^2+b^2}}\right) x^{-3 n}}{a^2 \left(a^2+b^2\right)^{3/2} d^3 e n}-\frac{4 b (e x)^{3 n} \text{Li}_3\left(-\frac{a e^{d x^n+c}}{b+\sqrt{a^2+b^2}}\right) x^{-3 n}}{a^2 \sqrt{a^2+b^2} d^3 e n}+\frac{2 b^3 (e x)^{3 n} \text{Li}_3\left(-\frac{a e^{d x^n+c}}{b+\sqrt{a^2+b^2}}\right) x^{-3 n}}{a^2 \left(a^2+b^2\right)^{3/2} d^3 e n}+\frac{2 b^2 (e x)^{3 n} \log \left(\frac{e^{d x^n+c} a}{b-\sqrt{a^2+b^2}}+1\right) x^{-2 n}}{a^2 \left(a^2+b^2\right) d^2 e n}+\frac{2 b^2 (e x)^{3 n} \log \left(\frac{e^{d x^n+c} a}{b+\sqrt{a^2+b^2}}+1\right) x^{-2 n}}{a^2 \left(a^2+b^2\right) d^2 e n}-\frac{4 b (e x)^{3 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b-\sqrt{a^2+b^2}}\right) x^{-2 n}}{a^2 \sqrt{a^2+b^2} d^2 e n}+\frac{2 b^3 (e x)^{3 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b-\sqrt{a^2+b^2}}\right) x^{-2 n}}{a^2 \left(a^2+b^2\right)^{3/2} d^2 e n}+\frac{4 b (e x)^{3 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{a^2+b^2}}\right) x^{-2 n}}{a^2 \sqrt{a^2+b^2} d^2 e n}-\frac{2 b^3 (e x)^{3 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{a^2+b^2}}\right) x^{-2 n}}{a^2 \left(a^2+b^2\right)^{3/2} d^2 e n}-\frac{b^2 (e x)^{3 n} x^{-n}}{a^2 \left(a^2+b^2\right) d e n}-\frac{2 b (e x)^{3 n} \log \left(\frac{e^{d x^n+c} a}{b-\sqrt{a^2+b^2}}+1\right) x^{-n}}{a^2 \sqrt{a^2+b^2} d e n}+\frac{b^3 (e x)^{3 n} \log \left(\frac{e^{d x^n+c} a}{b-\sqrt{a^2+b^2}}+1\right) x^{-n}}{a^2 \left(a^2+b^2\right)^{3/2} d e n}+\frac{2 b (e x)^{3 n} \log \left(\frac{e^{d x^n+c} a}{b+\sqrt{a^2+b^2}}+1\right) x^{-n}}{a^2 \sqrt{a^2+b^2} d e n}-\frac{b^3 (e x)^{3 n} \log \left(\frac{e^{d x^n+c} a}{b+\sqrt{a^2+b^2}}+1\right) x^{-n}}{a^2 \left(a^2+b^2\right)^{3/2} d e n}-\frac{b^2 (e x)^{3 n} \cosh \left(d x^n+c\right) x^{-n}}{a \left(a^2+b^2\right) d e n \left(b+a \sinh \left(d x^n+c\right)\right)}+\frac{(e x)^{3 n}}{3 a^2 e n}",1,"Integrate[(e*x)^(-1 + 3*n)/(a + b*Csch[c + d*x^n])^2, x]","F",-1