1,1,143,125,1.4118704,"\int x^5 \left(a+b \text{sech}\left(c+d x^2\right)\right) \, dx","Integrate[x^5*(a + b*Sech[c + d*x^2]),x]","\frac{a x^6}{6}+\frac{i b \left(d^2 x^4 \log \left(1-i e^{c+d x^2}\right)-d^2 x^4 \log \left(1+i e^{c+d x^2}\right)-2 d x^2 \text{Li}_2\left(-i e^{d x^2+c}\right)+2 d x^2 \text{Li}_2\left(i e^{d x^2+c}\right)+2 \text{Li}_3\left(-i e^{d x^2+c}\right)-2 \text{Li}_3\left(i e^{d x^2+c}\right)\right)}{2 d^3}","\frac{a x^6}{6}+\frac{i b \text{Li}_3\left(-i e^{d x^2+c}\right)}{d^3}-\frac{i b \text{Li}_3\left(i e^{d x^2+c}\right)}{d^3}-\frac{i b x^2 \text{Li}_2\left(-i e^{d x^2+c}\right)}{d^2}+\frac{i b x^2 \text{Li}_2\left(i e^{d x^2+c}\right)}{d^2}+\frac{b x^4 \tan ^{-1}\left(e^{c+d x^2}\right)}{d}",1,"(a*x^6)/6 + ((I/2)*b*(d^2*x^4*Log[1 - I*E^(c + d*x^2)] - d^2*x^4*Log[1 + I*E^(c + d*x^2)] - 2*d*x^2*PolyLog[2, (-I)*E^(c + d*x^2)] + 2*d*x^2*PolyLog[2, I*E^(c + d*x^2)] + 2*PolyLog[3, (-I)*E^(c + d*x^2)] - 2*PolyLog[3, I*E^(c + d*x^2)]))/d^3","A",1
2,0,0,26,3.8954544,"\int x^4 \left(a+b \text{sech}\left(c+d x^2\right)\right) \, dx","Integrate[x^4*(a + b*Sech[c + d*x^2]),x]","\int x^4 \left(a+b \text{sech}\left(c+d x^2\right)\right) \, dx","b \text{Int}\left(x^4 \text{sech}\left(c+d x^2\right),x\right)+\frac{a x^5}{5}",0,"Integrate[x^4*(a + b*Sech[c + d*x^2]), x]","A",-1
3,1,134,77,0.1769401,"\int x^3 \left(a+b \text{sech}\left(c+d x^2\right)\right) \, dx","Integrate[x^3*(a + b*Sech[c + d*x^2]),x]","\frac{1}{4} \left(a x^4+\frac{b \left(-2 i \left(\text{Li}_2\left(-i e^{d x^2+c}\right)-\text{Li}_2\left(i e^{d x^2+c}\right)\right)-\left(\left(-2 i c-2 i d x^2+\pi \right) \left(\log \left(1-i e^{c+d x^2}\right)-\log \left(1+i e^{c+d x^2}\right)\right)\right)+(\pi -2 i c) \log \left(\cot \left(\frac{1}{4} \left(2 i c+2 i d x^2+\pi \right)\right)\right)\right)}{d^2}\right)","\frac{a x^4}{4}-\frac{i b \text{Li}_2\left(-i e^{d x^2+c}\right)}{2 d^2}+\frac{i b \text{Li}_2\left(i e^{d x^2+c}\right)}{2 d^2}+\frac{b x^2 \tan ^{-1}\left(e^{c+d x^2}\right)}{d}",1,"(a*x^4 + (b*(-(((-2*I)*c + Pi - (2*I)*d*x^2)*(Log[1 - I*E^(c + d*x^2)] - Log[1 + I*E^(c + d*x^2)])) + ((-2*I)*c + Pi)*Log[Cot[((2*I)*c + Pi + (2*I)*d*x^2)/4]] - (2*I)*(PolyLog[2, (-I)*E^(c + d*x^2)] - PolyLog[2, I*E^(c + d*x^2)])))/d^2)/4","A",1
4,0,0,26,3.3325666,"\int x^2 \left(a+b \text{sech}\left(c+d x^2\right)\right) \, dx","Integrate[x^2*(a + b*Sech[c + d*x^2]),x]","\int x^2 \left(a+b \text{sech}\left(c+d x^2\right)\right) \, dx","b \text{Int}\left(x^2 \text{sech}\left(c+d x^2\right),x\right)+\frac{a x^3}{3}",0,"Integrate[x^2*(a + b*Sech[c + d*x^2]), x]","A",-1
5,1,26,26,0.0213507,"\int x \left(a+b \text{sech}\left(c+d x^2\right)\right) \, dx","Integrate[x*(a + b*Sech[c + d*x^2]),x]","\frac{a x^2}{2}+\frac{b \tan ^{-1}\left(\sinh \left(c+d x^2\right)\right)}{2 d}","\frac{a x^2}{2}+\frac{b \tan ^{-1}\left(\sinh \left(c+d x^2\right)\right)}{2 d}",1,"(a*x^2)/2 + (b*ArcTan[Sinh[c + d*x^2]])/(2*d)","A",1
6,0,0,22,2.6771332,"\int \frac{a+b \text{sech}\left(c+d x^2\right)}{x} \, dx","Integrate[(a + b*Sech[c + d*x^2])/x,x]","\int \frac{a+b \text{sech}\left(c+d x^2\right)}{x} \, dx","b \text{Int}\left(\frac{\text{sech}\left(c+d x^2\right)}{x},x\right)+a \log (x)",0,"Integrate[(a + b*Sech[c + d*x^2])/x, x]","A",-1
7,0,0,24,3.4901538,"\int \frac{a+b \text{sech}\left(c+d x^2\right)}{x^2} \, dx","Integrate[(a + b*Sech[c + d*x^2])/x^2,x]","\int \frac{a+b \text{sech}\left(c+d x^2\right)}{x^2} \, dx","b \text{Int}\left(\frac{\text{sech}\left(c+d x^2\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Sech[c + d*x^2])/x^2, x]","A",-1
8,1,294,217,4.800862,"\int x^5 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2 \, dx","Integrate[x^5*(a + b*Sech[c + d*x^2])^2,x]","\frac{\cosh \left(c+d x^2\right) \left(a+b \text{sech}\left(c+d x^2\right)\right)^2 \left(a^2 x^6 \cosh \left(c+d x^2\right)+\frac{3 b \cosh \left(c+d x^2\right) \left(2 i a d^2 x^4 \log \left(1-i e^{c+d x^2}\right)-2 i a d^2 x^4 \log \left(1+i e^{c+d x^2}\right)-4 i a d x^2 \text{Li}_2\left(-i e^{d x^2+c}\right)+4 i a d x^2 \text{Li}_2\left(i e^{d x^2+c}\right)+4 i a \text{Li}_3\left(-i e^{d x^2+c}\right)-4 i a \text{Li}_3\left(i e^{d x^2+c}\right)+\frac{2 b e^{2 c} d^2 x^4}{e^{2 c}+1}-b \text{Li}_2\left(-e^{2 \left(d x^2+c\right)}\right)-2 b d x^2 \log \left(e^{2 \left(c+d x^2\right)}+1\right)\right)}{d^3}+\frac{3 b^2 x^4 \text{sech}(c) \sinh \left(d x^2\right)}{d}\right)}{6 \left(a \cosh \left(c+d x^2\right)+b\right)^2}","\frac{a^2 x^6}{6}+\frac{2 i a b \text{Li}_3\left(-i e^{d x^2+c}\right)}{d^3}-\frac{2 i a b \text{Li}_3\left(i e^{d x^2+c}\right)}{d^3}-\frac{2 i a b x^2 \text{Li}_2\left(-i e^{d x^2+c}\right)}{d^2}+\frac{2 i a b x^2 \text{Li}_2\left(i e^{d x^2+c}\right)}{d^2}+\frac{2 a b x^4 \tan ^{-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(e^{2 \left(c+d x^2\right)}+1\right)}{d^2}+\frac{b^2 x^4 \tanh \left(c+d x^2\right)}{2 d}+\frac{b^2 x^4}{2 d}",1,"(Cosh[c + d*x^2]*(a + b*Sech[c + d*x^2])^2*(a^2*x^6*Cosh[c + d*x^2] + (3*b*Cosh[c + d*x^2]*((2*b*d^2*E^(2*c)*x^4)/(1 + E^(2*c)) + (2*I)*a*d^2*x^4*Log[1 - I*E^(c + d*x^2)] - (2*I)*a*d^2*x^4*Log[1 + I*E^(c + d*x^2)] - 2*b*d*x^2*Log[1 + E^(2*(c + d*x^2))] - (4*I)*a*d*x^2*PolyLog[2, (-I)*E^(c + d*x^2)] + (4*I)*a*d*x^2*PolyLog[2, I*E^(c + d*x^2)] - b*PolyLog[2, -E^(2*(c + d*x^2))] + (4*I)*a*PolyLog[3, (-I)*E^(c + d*x^2)] - (4*I)*a*PolyLog[3, I*E^(c + d*x^2)]))/d^3 + (3*b^2*x^4*Sech[c]*Sinh[d*x^2])/d))/(6*(b + a*Cosh[c + d*x^2])^2)","A",1
9,0,0,21,8.9123718,"\int x^4 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2 \, dx","Integrate[x^4*(a + b*Sech[c + d*x^2])^2,x]","\int x^4 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2 \, dx","\text{Int}\left(x^4 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2,x\right)",0,"Integrate[x^4*(a + b*Sech[c + d*x^2])^2, x]","A",-1
10,1,273,119,3.1978995,"\int x^3 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2 \, dx","Integrate[x^3*(a + b*Sech[c + d*x^2])^2,x]","\frac{\cosh \left(c+d x^2\right) \left(a+b \text{sech}\left(c+d x^2\right)\right)^2 \left(d x^2 \cosh \left(c+d x^2\right) \left(a^2 d x^2+2 b^2 \tanh (c)\right)+4 a b \cosh \left(c+d x^2\right) \left(\frac{\text{csch}(c) \left(\text{Li}_2\left(-e^{-d x^2-\tanh ^{-1}(\coth (c))}\right)-\text{Li}_2\left(e^{-d x^2-\tanh ^{-1}(\coth (c))}\right)+\left(\tanh ^{-1}(\coth (c))+d x^2\right) \left(\log \left(1-e^{-\tanh ^{-1}(\coth (c))-d x^2}\right)-\log \left(e^{-\tanh ^{-1}(\coth (c))-d x^2}+1\right)\right)\right)}{\sqrt{-\text{csch}^2(c)}}-2 \tanh ^{-1}(\coth (c)) \tan ^{-1}\left(\cosh (c) \tanh \left(\frac{d x^2}{2}\right)+\sinh (c)\right)\right)-2 b^2 d x^2 \tanh (c) \cosh \left(c+d x^2\right)+2 b^2 d x^2 \text{sech}(c) \sinh \left(d x^2\right)-2 b^2 \cosh \left(c+d x^2\right) \left(\log \left(\cosh \left(c+d x^2\right)\right)-d x^2 \tanh (c)\right)\right)}{4 d^2 \left(a \cosh \left(c+d x^2\right)+b\right)^2}","\frac{a^2 x^4}{4}-\frac{i a b \text{Li}_2\left(-i e^{d x^2+c}\right)}{d^2}+\frac{i a b \text{Li}_2\left(i e^{d x^2+c}\right)}{d^2}+\frac{2 a b x^2 \tan ^{-1}\left(e^{c+d x^2}\right)}{d}-\frac{b^2 \log \left(\cosh \left(c+d x^2\right)\right)}{2 d^2}+\frac{b^2 x^2 \tanh \left(c+d x^2\right)}{2 d}",1,"(Cosh[c + d*x^2]*(a + b*Sech[c + d*x^2])^2*(4*a*b*Cosh[c + d*x^2]*(-2*ArcTan[Sinh[c] + Cosh[c]*Tanh[(d*x^2)/2]]*ArcTanh[Coth[c]] + (Csch[c]*((d*x^2 + ArcTanh[Coth[c]])*(Log[1 - E^(-(d*x^2) - ArcTanh[Coth[c]])] - Log[1 + E^(-(d*x^2) - ArcTanh[Coth[c]])]) + PolyLog[2, -E^(-(d*x^2) - ArcTanh[Coth[c]])] - PolyLog[2, E^(-(d*x^2) - ArcTanh[Coth[c]])]))/Sqrt[-Csch[c]^2]) + 2*b^2*d*x^2*Sech[c]*Sinh[d*x^2] - 2*b^2*d*x^2*Cosh[c + d*x^2]*Tanh[c] + d*x^2*Cosh[c + d*x^2]*(a^2*d*x^2 + 2*b^2*Tanh[c]) - 2*b^2*Cosh[c + d*x^2]*(Log[Cosh[c + d*x^2]] - d*x^2*Tanh[c])))/(4*d^2*(b + a*Cosh[c + d*x^2])^2)","B",0
11,0,0,21,7.9490239,"\int x^2 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2 \, dx","Integrate[x^2*(a + b*Sech[c + d*x^2])^2,x]","\int x^2 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2 \, dx","\text{Int}\left(x^2 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2,x\right)",0,"Integrate[x^2*(a + b*Sech[c + d*x^2])^2, x]","A",-1
12,1,44,44,0.0992343,"\int x \left(a+b \text{sech}\left(c+d x^2\right)\right)^2 \, dx","Integrate[x*(a + b*Sech[c + d*x^2])^2,x]","\frac{a \left(a \left(c+d x^2\right)+2 b \tan ^{-1}\left(\sinh \left(c+d x^2\right)\right)\right)+b^2 \tanh \left(c+d x^2\right)}{2 d}","\frac{a^2 x^2}{2}+\frac{a b \tan ^{-1}\left(\sinh \left(c+d x^2\right)\right)}{d}+\frac{b^2 \tanh \left(c+d x^2\right)}{2 d}",1,"(a*(a*(c + d*x^2) + 2*b*ArcTan[Sinh[c + d*x^2]]) + b^2*Tanh[c + d*x^2])/(2*d)","A",1
13,0,0,21,20.6808288,"\int \frac{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2}{x} \, dx","Integrate[(a + b*Sech[c + d*x^2])^2/x,x]","\int \frac{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2}{x},x\right)",0,"Integrate[(a + b*Sech[c + d*x^2])^2/x, x]","A",-1
14,0,0,21,9.8541099,"\int \frac{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Sech[c + d*x^2])^2/x^2,x]","\int \frac{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2}{x^2},x\right)",0,"Integrate[(a + b*Sech[c + d*x^2])^2/x^2, x]","A",-1
15,1,77,90,0.1456356,"\int x \text{sech}^7\left(a+b x^2\right) \, dx","Integrate[x*Sech[a + b*x^2]^7,x]","\frac{15 \tan ^{-1}\left(\sinh \left(a+b x^2\right)\right)+8 \tanh \left(a+b x^2\right) \text{sech}^5\left(a+b x^2\right)+10 \tanh \left(a+b x^2\right) \text{sech}^3\left(a+b x^2\right)+15 \tanh \left(a+b x^2\right) \text{sech}\left(a+b x^2\right)}{96 b}","\frac{5 \tan ^{-1}\left(\sinh \left(a+b x^2\right)\right)}{32 b}+\frac{\tanh \left(a+b x^2\right) \text{sech}^5\left(a+b x^2\right)}{12 b}+\frac{5 \tanh \left(a+b x^2\right) \text{sech}^3\left(a+b x^2\right)}{48 b}+\frac{5 \tanh \left(a+b x^2\right) \text{sech}\left(a+b x^2\right)}{32 b}",1,"(15*ArcTan[Sinh[a + b*x^2]] + 15*Sech[a + b*x^2]*Tanh[a + b*x^2] + 10*Sech[a + b*x^2]^3*Tanh[a + b*x^2] + 8*Sech[a + b*x^2]^5*Tanh[a + b*x^2])/(96*b)","A",1
16,1,376,349,1.5662943,"\int \frac{x^5}{a+b \text{sech}\left(c+d x^2\right)} \, dx","Integrate[x^5/(a + b*Sech[c + d*x^2]),x]","\frac{d^3 x^6 \sqrt{e^{2 c} \left(b^2-a^2\right)}-3 b e^c d^2 x^4 \log \left(\frac{a e^{2 c+d x^2}}{b e^c-\sqrt{e^{2 c} \left(b^2-a^2\right)}}+1\right)+3 b e^c d^2 x^4 \log \left(\frac{a e^{2 c+d x^2}}{\sqrt{e^{2 c} \left(b^2-a^2\right)}+b e^c}+1\right)-6 b e^c d x^2 \text{Li}_2\left(-\frac{a e^{d x^2+2 c}}{b e^c-\sqrt{\left(b^2-a^2\right) e^{2 c}}}\right)+6 b e^c d x^2 \text{Li}_2\left(-\frac{a e^{d x^2+2 c}}{e^c b+\sqrt{\left(b^2-a^2\right) e^{2 c}}}\right)+6 b e^c \text{Li}_3\left(-\frac{a e^{d x^2+2 c}}{b e^c-\sqrt{\left(b^2-a^2\right) e^{2 c}}}\right)-6 b e^c \text{Li}_3\left(-\frac{a e^{d x^2+2 c}}{e^c b+\sqrt{\left(b^2-a^2\right) e^{2 c}}}\right)}{6 a d^3 \sqrt{e^{2 c} \left(b^2-a^2\right)}}","\frac{b \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{b \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b+\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{b x^2 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{b x^2 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{b x^4 \log \left(\frac{a e^{c+d x^2}}{b-\sqrt{b^2-a^2}}+1\right)}{2 a d \sqrt{b^2-a^2}}+\frac{b x^4 \log \left(\frac{a e^{c+d x^2}}{\sqrt{b^2-a^2}+b}+1\right)}{2 a d \sqrt{b^2-a^2}}+\frac{x^6}{6 a}",1,"(d^3*Sqrt[(-a^2 + b^2)*E^(2*c)]*x^6 - 3*b*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)])] + 3*b*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)])] - 6*b*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)]))] + 6*b*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)]))] + 6*b*E^c*PolyLog[3, -((a*E^(2*c + d*x^2))/(b*E^c - Sqrt[(-a^2 + b^2)*E^(2*c)]))] - 6*b*E^c*PolyLog[3, -((a*E^(2*c + d*x^2))/(b*E^c + Sqrt[(-a^2 + b^2)*E^(2*c)]))])/(6*a*d^3*Sqrt[(-a^2 + b^2)*E^(2*c)])","A",1
17,0,0,21,8.7341079,"\int \frac{x^4}{a+b \text{sech}\left(c+d x^2\right)} \, dx","Integrate[x^4/(a + b*Sech[c + d*x^2]),x]","\int \frac{x^4}{a+b \text{sech}\left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{x^4}{a+b \text{sech}\left(c+d x^2\right)},x\right)",0,"Integrate[x^4/(a + b*Sech[c + d*x^2]), x]","A",-1
18,1,843,241,1.762568,"\int \frac{x^3}{a+b \text{sech}\left(c+d x^2\right)} \, dx","Integrate[x^3/(a + b*Sech[c + d*x^2]),x]","\frac{\left(b+a \cosh \left(d x^2+c\right)\right) \left(x^4+\frac{2 b \left(2 \left(d x^2+c\right) \tan ^{-1}\left(\frac{(a+b) \coth \left(\frac{1}{2} \left(d x^2+c\right)\right)}{\sqrt{a^2-b^2}}\right)+2 \left(c-i \cos ^{-1}\left(-\frac{b}{a}\right)\right) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)}{\sqrt{a^2-b^2}}\right)+\left(\cos ^{-1}\left(-\frac{b}{a}\right)+2 \left(\tan ^{-1}\left(\frac{(a+b) \coth \left(\frac{1}{2} \left(d x^2+c\right)\right)}{\sqrt{a^2-b^2}}\right)+\tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)}{\sqrt{a^2-b^2}}\right)\right)\right) \log \left(\frac{\sqrt{a^2-b^2} e^{-\frac{d x^2}{2}-\frac{c}{2}}}{\sqrt{2} \sqrt{a} \sqrt{b+a \cosh \left(d x^2+c\right)}}\right)+\left(\cos ^{-1}\left(-\frac{b}{a}\right)-2 \left(\tan ^{-1}\left(\frac{(a+b) \coth \left(\frac{1}{2} \left(d x^2+c\right)\right)}{\sqrt{a^2-b^2}}\right)+\tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)}{\sqrt{a^2-b^2}}\right)\right)\right) \log \left(\frac{\sqrt{a^2-b^2} e^{\frac{1}{2} \left(d x^2+c\right)}}{\sqrt{2} \sqrt{a} \sqrt{b+a \cosh \left(d x^2+c\right)}}\right)-\left(\cos ^{-1}\left(-\frac{b}{a}\right)+2 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)}{\sqrt{a^2-b^2}}\right)\right) \log \left(\frac{(a+b) \left(-a+b+i \sqrt{a^2-b^2}\right) \left(\tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)-1\right)}{a \left(a+b+i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{b}{a}\right)-2 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)}{\sqrt{a^2-b^2}}\right)\right) \log \left(\frac{(a+b) \left(a-b+i \sqrt{a^2-b^2}\right) \left(\tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)+1\right)}{a \left(a+b+i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(b-i \sqrt{a^2-b^2}\right) \left(a+b-i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)\right)}{a \left(a+b+i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(b+i \sqrt{a^2-b^2}\right) \left(a+b-i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)\right)}{a \left(a+b+i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^2+c\right)\right)\right)}\right)\right)\right)}{\sqrt{a^2-b^2} d^2}\right) \text{sech}\left(d x^2+c\right)}{4 a \left(a+b \text{sech}\left(d x^2+c\right)\right)}","-\frac{b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{b^2-a^2}}\right)}{2 a d^2 \sqrt{b^2-a^2}}+\frac{b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{b^2-a^2}}\right)}{2 a d^2 \sqrt{b^2-a^2}}-\frac{b x^2 \log \left(\frac{a e^{c+d x^2}}{b-\sqrt{b^2-a^2}}+1\right)}{2 a d \sqrt{b^2-a^2}}+\frac{b x^2 \log \left(\frac{a e^{c+d x^2}}{\sqrt{b^2-a^2}+b}+1\right)}{2 a d \sqrt{b^2-a^2}}+\frac{x^4}{4 a}",1,"((b + a*Cosh[c + d*x^2])*(x^4 + (2*b*(2*(c + d*x^2)*ArcTan[((a + b)*Coth[(c + d*x^2)/2])/Sqrt[a^2 - b^2]] + 2*(c - I*ArcCos[-(b/a)])*ArcTan[((a - b)*Tanh[(c + d*x^2)/2])/Sqrt[a^2 - b^2]] + (ArcCos[-(b/a)] + 2*(ArcTan[((a + b)*Coth[(c + d*x^2)/2])/Sqrt[a^2 - b^2]] + ArcTan[((a - b)*Tanh[(c + d*x^2)/2])/Sqrt[a^2 - b^2]]))*Log[(Sqrt[a^2 - b^2]*E^(-1/2*c - (d*x^2)/2))/(Sqrt[2]*Sqrt[a]*Sqrt[b + a*Cosh[c + d*x^2]])] + (ArcCos[-(b/a)] - 2*(ArcTan[((a + b)*Coth[(c + d*x^2)/2])/Sqrt[a^2 - b^2]] + ArcTan[((a - b)*Tanh[(c + d*x^2)/2])/Sqrt[a^2 - b^2]]))*Log[(Sqrt[a^2 - b^2]*E^((c + d*x^2)/2))/(Sqrt[2]*Sqrt[a]*Sqrt[b + a*Cosh[c + d*x^2]])] - (ArcCos[-(b/a)] + 2*ArcTan[((a - b)*Tanh[(c + d*x^2)/2])/Sqrt[a^2 - b^2]])*Log[((a + b)*(-a + b + I*Sqrt[a^2 - b^2])*(-1 + Tanh[(c + d*x^2)/2]))/(a*(a + b + I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^2)/2]))] - (ArcCos[-(b/a)] - 2*ArcTan[((a - b)*Tanh[(c + d*x^2)/2])/Sqrt[a^2 - b^2]])*Log[((a + b)*(a - b + I*Sqrt[a^2 - b^2])*(1 + Tanh[(c + d*x^2)/2]))/(a*(a + b + I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^2)/2]))] + I*(PolyLog[2, ((b - I*Sqrt[a^2 - b^2])*(a + b - I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^2)/2]))/(a*(a + b + I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^2)/2]))] - PolyLog[2, ((b + I*Sqrt[a^2 - b^2])*(a + b - I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^2)/2]))/(a*(a + b + I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^2)/2]))])))/(Sqrt[a^2 - b^2]*d^2))*Sech[c + d*x^2])/(4*a*(a + b*Sech[c + d*x^2]))","C",1
19,0,0,21,7.8105076,"\int \frac{x^2}{a+b \text{sech}\left(c+d x^2\right)} \, dx","Integrate[x^2/(a + b*Sech[c + d*x^2]),x]","\int \frac{x^2}{a+b \text{sech}\left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{x^2}{a+b \text{sech}\left(c+d x^2\right)},x\right)",0,"Integrate[x^2/(a + b*Sech[c + d*x^2]), x]","A",-1
20,1,67,66,0.1237604,"\int \frac{x}{a+b \text{sech}\left(c+d x^2\right)} \, dx","Integrate[x/(a + b*Sech[c + d*x^2]),x]","\frac{\frac{2 b \tan ^{-1}\left(\frac{(b-a) \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{x^2}{2 a}-\frac{b \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{a+b}}\right)}{a d \sqrt{a-b} \sqrt{a+b}}",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
21,0,0,21,5.1789047,"\int \frac{1}{x \left(a+b \text{sech}\left(c+d x^2\right)\right)} \, dx","Integrate[1/(x*(a + b*Sech[c + d*x^2])),x]","\int \frac{1}{x \left(a+b \text{sech}\left(c+d x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{sech}\left(c+d x^2\right)\right)},x\right)",0,"Integrate[1/(x*(a + b*Sech[c + d*x^2])), x]","A",-1
22,0,0,24,0.1031264,"\int \frac{a+b \text{sech}\left(c+d x^2\right)}{x^2} \, dx","Integrate[(a + b*Sech[c + d*x^2])/x^2,x]","\int \frac{a+b \text{sech}\left(c+d x^2\right)}{x^2} \, dx","b \text{Int}\left(\frac{\text{sech}\left(c+d x^2\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Sech[c + d*x^2])/x^2, x]","A",-1
23,1,1565,994,12.8905045,"\int \frac{x^5}{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","Integrate[x^5/(a + b*Sech[c + d*x^2])^2,x]","\frac{\left(b+a \cosh \left(d x^2+c\right)\right) \text{sech}^2\left(d x^2+c\right) \left(\left(b+a \cosh \left(d x^2+c\right)\right) x^6+\frac{3 b^2 \text{sech}(c) \left(a \sinh \left(d x^2\right)-b \sinh (c)\right) x^4}{(a-b) (a+b) d}-\frac{3 b e^{2 c} \left(b+a \cosh \left(d x^2+c\right)\right) \left(-2 a^2 d^2 e^c \log \left(\frac{e^{d x^2+2 c} a}{b e^c-\sqrt{\left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}+1\right) x^4+2 b d^2 e^{2 c} \sqrt{\left(b^2-a^2\right) e^{2 c}} x^4-2 b d e^{2 c} \sqrt{\left(b^2-a^2\right) e^{2 c}} \log \left(\frac{e^{d x^2+2 c} a}{b e^c-\sqrt{\left(b^2-a^2\right) e^{2 c}}}+1\right) x^2-2 b d \sqrt{\left(b^2-a^2\right) e^{2 c}} \log \left(\frac{e^{d x^2+2 c} a}{b e^c-\sqrt{\left(b^2-a^2\right) e^{2 c}}}+1\right) x^2-2 b d e^{2 c} \sqrt{\left(b^2-a^2\right) e^{2 c}} \log \left(\frac{e^{d x^2+2 c} a}{e^c b+\sqrt{\left(b^2-a^2\right) e^{2 c}}}+1\right) x^2-2 b d \sqrt{\left(b^2-a^2\right) e^{2 c}} \log \left(\frac{e^{d x^2+2 c} a}{e^c b+\sqrt{\left(b^2-a^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(b^2-a^2\right) e^{2 c}}\right) \text{Li}_2\left(-\frac{a e^{d x^2+2 c}}{b e^c-\sqrt{\left(b^2-a^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(b^2-a^2\right) e^{2 c}}\right) \text{Li}_2\left(-\frac{a e^{d x^2+2 c}}{e^c b+\sqrt{\left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right)\right)}{d^3 \left(\left(b^2-a^2\right) e^{2 c}\right)^{3/2} \left(1+e^{2 c}\right)}\right)}{6 a^2 \left(a+b \text{sech}\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{b^2-a^2}}+1\right) x^4}{a^2 \sqrt{b^2-a^2} d}+\frac{b^3 \log \left(\frac{e^{d x^2+c} a}{b-\sqrt{b^2-a^2}}+1\right) x^4}{2 a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{b \log \left(\frac{e^{d x^2+c} a}{b+\sqrt{b^2-a^2}}+1\right) x^4}{a^2 \sqrt{b^2-a^2} d}-\frac{b^3 \log \left(\frac{e^{d x^2+c} a}{b+\sqrt{b^2-a^2}}+1\right) x^4}{2 a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{b^2 \sinh \left(d x^2+c\right) x^4}{2 a \left(a^2-b^2\right) d \left(b+a \cosh \left(d x^2+c\right)\right)}+\frac{b^2 x^4}{2 a^2 \left(a^2-b^2\right) d}-\frac{b^2 \log \left(\frac{e^{d x^2+c} a}{b-\sqrt{b^2-a^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{b^2-a^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{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^2}+\frac{b^3 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^2}+\frac{2 b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^2}-\frac{b^3 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{b^2 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{b^2-a^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{b^2-a^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{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^3}-\frac{b^3 \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^3}-\frac{2 b \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^3}+\frac{b^3 \text{Li}_3\left(-\frac{a e^{d x^2+c}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^3}",1,"((b + a*Cosh[c + d*x^2])*Sech[c + d*x^2]^2*(x^6*(b + a*Cosh[c + d*x^2]) - (3*b*E^(2*c)*(b + a*Cosh[c + d*x^2])*(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)]))]))/(d^3*((-a^2 + b^2)*E^(2*c))^(3/2)*(1 + E^(2*c))) + (3*b^2*x^4*Sech[c]*(-(b*Sinh[c]) + a*Sinh[d*x^2]))/((a - b)*(a + b)*d)))/(6*a^2*(a + b*Sech[c + d*x^2])^2)","A",1
24,0,0,21,59.2552494,"\int \frac{x^4}{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","Integrate[x^4/(a + b*Sech[c + d*x^2])^2,x]","\int \frac{x^4}{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{x^4}{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[x^4/(a + b*Sech[c + d*x^2])^2, x]","A",-1
25,1,755,555,6.3080188,"\int \frac{x^3}{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","Integrate[x^3/(a + b*Sech[c + d*x^2])^2,x]","\frac{\text{sech}^2\left(c+d x^2\right) \left(a \cosh \left(c+d x^2\right)+b\right) \left(-\frac{2 b \left(a^2-b^2\right) \left(a \cosh \left(c+d x^2\right)+b\right) \left(\sqrt{a^2-b^2} \left(b^2-2 a^2\right) \text{Li}_2\left(\frac{a e^{d x^2+c}}{\sqrt{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^2}+b}+1\right)-b \sqrt{-\left(a^2-b^2\right)^2} \log \left(a e^{2 \left(c+d x^2\right)}+a+2 b e^{c+d x^2}\right)-4 a^2 c \sqrt{b^2-a^2} \tan ^{-1}\left(\frac{a e^{-c-d x^2}+b}{\sqrt{a^2-b^2}}\right)+2 b^2 c \sqrt{b^2-a^2} \tan ^{-1}\left(\frac{a e^{-c-d x^2}+b}{\sqrt{a^2-b^2}}\right)-2 b^2 \sqrt{b^2-a^2} \tan ^{-1}\left(\frac{a e^{-c-d x^2}+b}{\sqrt{a^2-b^2}}\right)-2 b^2 \sqrt{b^2-a^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 \sinh \left(c+d x^2\right)}{(a-b) (a+b)}+\left(d x^2-c\right) \left(c+d x^2\right) \left(a \cosh \left(c+d x^2\right)+b\right)\right)}{4 a^2 d^2 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2}","-\frac{b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d^2 \sqrt{b^2-a^2}}+\frac{b \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{b^2-a^2}}\right)}{a^2 d^2 \sqrt{b^2-a^2}}-\frac{b^2 \log \left(a \cosh \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{b^2-a^2}}+1\right)}{a^2 d \sqrt{b^2-a^2}}+\frac{b x^2 \log \left(\frac{a e^{c+d x^2}}{\sqrt{b^2-a^2}+b}+1\right)}{a^2 d \sqrt{b^2-a^2}}+\frac{b^2 x^2 \sinh \left(c+d x^2\right)}{2 a d \left(a^2-b^2\right) \left(a \cosh \left(c+d x^2\right)+b\right)}+\frac{b^3 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b-\sqrt{b^2-a^2}}\right)}{2 a^2 d^2 \left(b^2-a^2\right)^{3/2}}-\frac{b^3 \text{Li}_2\left(-\frac{a e^{d x^2+c}}{b+\sqrt{b^2-a^2}}\right)}{2 a^2 d^2 \left(b^2-a^2\right)^{3/2}}+\frac{b^3 x^2 \log \left(\frac{a e^{c+d x^2}}{b-\sqrt{b^2-a^2}}+1\right)}{2 a^2 d \left(b^2-a^2\right)^{3/2}}-\frac{b^3 x^2 \log \left(\frac{a e^{c+d x^2}}{\sqrt{b^2-a^2}+b}+1\right)}{2 a^2 d \left(b^2-a^2\right)^{3/2}}+\frac{x^4}{4 a^2}",1,"((b + a*Cosh[c + d*x^2])*Sech[c + d*x^2]^2*((-c + d*x^2)*(c + d*x^2)*(b + a*Cosh[c + d*x^2]) - (2*b*(a^2 - b^2)*(b + a*Cosh[c + d*x^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[a + 2*b*E^(c + d*x^2) + a*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]))]))/(-(a^2 - b^2)^2)^(3/2) + (2*a*b^2*d*x^2*Sinh[c + d*x^2])/((a - b)*(a + b))))/(4*a^2*d^2*(a + b*Sech[c + d*x^2])^2)","A",0
26,0,0,21,52.9715086,"\int \frac{x^2}{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","Integrate[x^2/(a + b*Sech[c + d*x^2])^2,x]","\int \frac{x^2}{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{x^2}{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[x^2/(a + b*Sech[c + d*x^2])^2, x]","A",-1
27,1,220,123,0.4598869,"\int \frac{x}{\left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","Integrate[x/(a + b*Sech[c + d*x^2])^2,x]","\frac{b \left(\left(a^2-b^2\right)^{3/2} \left(c+d x^2\right)+a b \sqrt{a^2-b^2} \sinh \left(c+d x^2\right)+\left(4 a^2 b-2 b^3\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{a^2-b^2}}\right)\right)+a \cosh \left(c+d x^2\right) \left(\left(a^2-b^2\right)^{3/2} \left(c+d x^2\right)+\left(4 a^2 b-2 b^3\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{a^2-b^2}}\right)\right)}{2 a^2 d (a-b) (a+b) \sqrt{a^2-b^2} \left(a \cosh \left(c+d x^2\right)+b\right)}","-\frac{b \left(2 a^2-b^2\right) \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} \left(c+d x^2\right)\right)}{\sqrt{a+b}}\right)}{a^2 d (a-b)^{3/2} (a+b)^{3/2}}+\frac{b^2 \tanh \left(c+d x^2\right)}{2 a d \left(a^2-b^2\right) \left(a+b \text{sech}\left(c+d x^2\right)\right)}+\frac{x^2}{2 a^2}",1,"(a*((a^2 - b^2)^(3/2)*(c + d*x^2) + (4*a^2*b - 2*b^3)*ArcTan[((-a + b)*Tanh[(c + d*x^2)/2])/Sqrt[a^2 - b^2]])*Cosh[c + d*x^2] + b*((a^2 - b^2)^(3/2)*(c + d*x^2) + (4*a^2*b - 2*b^3)*ArcTan[((-a + b)*Tanh[(c + d*x^2)/2])/Sqrt[a^2 - b^2]] + a*b*Sqrt[a^2 - b^2]*Sinh[c + d*x^2]))/(2*a^2*(a - b)*(a + b)*Sqrt[a^2 - b^2]*d*(b + a*Cosh[c + d*x^2]))","A",1
28,0,0,21,104.6954118,"\int \frac{1}{x \left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Sech[c + d*x^2])^2),x]","\int \frac{1}{x \left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{sech}\left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[1/(x*(a + b*Sech[c + d*x^2])^2), x]","A",-1
29,0,0,21,67.3973659,"\int \frac{1}{x^2 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Sech[c + d*x^2])^2),x]","\int \frac{1}{x^2 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[1/(x^2*(a + b*Sech[c + d*x^2])^2), x]","A",-1
30,0,0,21,68.2432641,"\int \frac{1}{x^3 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x^3*(a + b*Sech[c + d*x^2])^2),x]","\int \frac{1}{x^3 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^3 \left(a+b \text{sech}\left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[1/(x^3*(a + b*Sech[c + d*x^2])^2), x]","A",-1
31,1,6,6,0.0185353,"\int \frac{\text{sech}^2\left(\frac{1}{x}\right)}{x^2} \, dx","Integrate[Sech[x^(-1)]^2/x^2,x]","-\tanh \left(\frac{1}{x}\right)","-\tanh \left(\frac{1}{x}\right)",1,"-Tanh[x^(-1)]","A",1
32,1,415,426,1.945876,"\int x^3 \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x^3*(a + b*Sech[c + d*Sqrt[x]]),x]","\frac{a x^4}{4}+\frac{2 i b \left(d^7 x^{7/2} \log \left(1-i e^{c+d \sqrt{x}}\right)-d^7 x^{7/2} \log \left(1+i e^{c+d \sqrt{x}}\right)-7 d^6 x^3 \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)+7 d^6 x^3 \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)+42 d^5 x^{5/2} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)-42 d^5 x^{5/2} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)-210 d^4 x^2 \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)+210 d^4 x^2 \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)+840 d^3 x^{3/2} \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)-840 d^3 x^{3/2} \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)-2520 d^2 x \text{Li}_6\left(-i e^{c+d \sqrt{x}}\right)+2520 d^2 x \text{Li}_6\left(i e^{c+d \sqrt{x}}\right)+5040 d \sqrt{x} \text{Li}_7\left(-i e^{c+d \sqrt{x}}\right)-5040 d \sqrt{x} \text{Li}_7\left(i e^{c+d \sqrt{x}}\right)-5040 \text{Li}_8\left(-i e^{c+d \sqrt{x}}\right)+5040 \text{Li}_8\left(i e^{c+d \sqrt{x}}\right)\right)}{d^8}","\frac{a x^4}{4}-\frac{10080 i b \text{Li}_8\left(-i e^{c+d \sqrt{x}}\right)}{d^8}+\frac{10080 i b \text{Li}_8\left(i e^{c+d \sqrt{x}}\right)}{d^8}+\frac{10080 i b \sqrt{x} \text{Li}_7\left(-i e^{c+d \sqrt{x}}\right)}{d^7}-\frac{10080 i b \sqrt{x} \text{Li}_7\left(i e^{c+d \sqrt{x}}\right)}{d^7}-\frac{5040 i b x \text{Li}_6\left(-i e^{c+d \sqrt{x}}\right)}{d^6}+\frac{5040 i b x \text{Li}_6\left(i e^{c+d \sqrt{x}}\right)}{d^6}+\frac{1680 i b x^{3/2} \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{1680 i b x^{3/2} \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{420 i b x^2 \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{420 i b x^2 \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{84 i b x^{5/2} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{84 i b x^{5/2} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{14 i b x^3 \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{14 i b x^3 \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{4 b x^{7/2} \tan ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}",1,"(a*x^4)/4 + ((2*I)*b*(d^7*x^(7/2)*Log[1 - I*E^(c + d*Sqrt[x])] - d^7*x^(7/2)*Log[1 + I*E^(c + d*Sqrt[x])] - 7*d^6*x^3*PolyLog[2, (-I)*E^(c + d*Sqrt[x])] + 7*d^6*x^3*PolyLog[2, I*E^(c + d*Sqrt[x])] + 42*d^5*x^(5/2)*PolyLog[3, (-I)*E^(c + d*Sqrt[x])] - 42*d^5*x^(5/2)*PolyLog[3, I*E^(c + d*Sqrt[x])] - 210*d^4*x^2*PolyLog[4, (-I)*E^(c + d*Sqrt[x])] + 210*d^4*x^2*PolyLog[4, I*E^(c + d*Sqrt[x])] + 840*d^3*x^(3/2)*PolyLog[5, (-I)*E^(c + d*Sqrt[x])] - 840*d^3*x^(3/2)*PolyLog[5, I*E^(c + d*Sqrt[x])] - 2520*d^2*x*PolyLog[6, (-I)*E^(c + d*Sqrt[x])] + 2520*d^2*x*PolyLog[6, I*E^(c + d*Sqrt[x])] + 5040*d*Sqrt[x]*PolyLog[7, (-I)*E^(c + d*Sqrt[x])] - 5040*d*Sqrt[x]*PolyLog[7, I*E^(c + d*Sqrt[x])] - 5040*PolyLog[8, (-I)*E^(c + d*Sqrt[x])] + 5040*PolyLog[8, I*E^(c + d*Sqrt[x])]))/d^8","A",1
33,1,311,310,1.8125175,"\int x^2 \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x^2*(a + b*Sech[c + d*Sqrt[x]]),x]","\frac{a x^3}{3}+\frac{2 i b \left(d^5 x^{5/2} \log \left(1-i e^{c+d \sqrt{x}}\right)-d^5 x^{5/2} \log \left(1+i e^{c+d \sqrt{x}}\right)-5 d^4 x^2 \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)+5 d^4 x^2 \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)+20 d^3 x^{3/2} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)-20 d^3 x^{3/2} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)-60 d^2 x \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)+60 d^2 x \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)+120 d \sqrt{x} \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)-120 d \sqrt{x} \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)-120 \text{Li}_6\left(-i e^{c+d \sqrt{x}}\right)+120 \text{Li}_6\left(i e^{c+d \sqrt{x}}\right)\right)}{d^6}","\frac{a x^3}{3}-\frac{240 i b \text{Li}_6\left(-i e^{c+d \sqrt{x}}\right)}{d^6}+\frac{240 i b \text{Li}_6\left(i e^{c+d \sqrt{x}}\right)}{d^6}+\frac{240 i b \sqrt{x} \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{240 i b \sqrt{x} \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{120 i b x \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{120 i b x \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{40 i b x^{3/2} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{40 i b x^{3/2} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{10 i b x^2 \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{10 i b x^2 \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{4 b x^{5/2} \tan ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}",1,"(a*x^3)/3 + ((2*I)*b*(d^5*x^(5/2)*Log[1 - I*E^(c + d*Sqrt[x])] - d^5*x^(5/2)*Log[1 + I*E^(c + d*Sqrt[x])] - 5*d^4*x^2*PolyLog[2, (-I)*E^(c + d*Sqrt[x])] + 5*d^4*x^2*PolyLog[2, I*E^(c + d*Sqrt[x])] + 20*d^3*x^(3/2)*PolyLog[3, (-I)*E^(c + d*Sqrt[x])] - 20*d^3*x^(3/2)*PolyLog[3, I*E^(c + d*Sqrt[x])] - 60*d^2*x*PolyLog[4, (-I)*E^(c + d*Sqrt[x])] + 60*d^2*x*PolyLog[4, I*E^(c + d*Sqrt[x])] + 120*d*Sqrt[x]*PolyLog[5, (-I)*E^(c + d*Sqrt[x])] - 120*d*Sqrt[x]*PolyLog[5, I*E^(c + d*Sqrt[x])] - 120*PolyLog[6, (-I)*E^(c + d*Sqrt[x])] + 120*PolyLog[6, I*E^(c + d*Sqrt[x])]))/d^6","A",1
34,1,207,194,1.8056129,"\int x \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x*(a + b*Sech[c + d*Sqrt[x]]),x]","\frac{a x^2}{2}+\frac{2 i b \left(d^3 x^{3/2} \log \left(1-i e^{c+d \sqrt{x}}\right)-d^3 x^{3/2} \log \left(1+i e^{c+d \sqrt{x}}\right)-3 d^2 x \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)+3 d^2 x \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)+6 d \sqrt{x} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)-6 d \sqrt{x} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)-6 \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)+6 \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)\right)}{d^4}","\frac{a x^2}{2}-\frac{12 i b \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{12 i b \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{12 i b \sqrt{x} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{12 i b \sqrt{x} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{6 i b x \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{6 i b x \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{4 b x^{3/2} \tan ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}",1,"(a*x^2)/2 + ((2*I)*b*(d^3*x^(3/2)*Log[1 - I*E^(c + d*Sqrt[x])] - d^3*x^(3/2)*Log[1 + I*E^(c + d*Sqrt[x])] - 3*d^2*x*PolyLog[2, (-I)*E^(c + d*Sqrt[x])] + 3*d^2*x*PolyLog[2, I*E^(c + d*Sqrt[x])] + 6*d*Sqrt[x]*PolyLog[3, (-I)*E^(c + d*Sqrt[x])] - 6*d*Sqrt[x]*PolyLog[3, I*E^(c + d*Sqrt[x])] - 6*PolyLog[4, (-I)*E^(c + d*Sqrt[x])] + 6*PolyLog[4, I*E^(c + d*Sqrt[x])]))/d^4","A",1
35,0,0,24,6.2246361,"\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{x} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])/x,x]","\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{x} \, dx","b \text{Int}\left(\frac{\text{sech}\left(c+d \sqrt{x}\right)}{x},x\right)+a \log (x)",0,"Integrate[(a + b*Sech[c + d*Sqrt[x]])/x, x]","A",-1
36,0,0,26,7.3742246,"\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{x^2} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])/x^2,x]","\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{x^2} \, dx","b \text{Int}\left(\frac{\text{sech}\left(c+d \sqrt{x}\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Sech[c + d*Sqrt[x]])/x^2, x]","A",-1
37,1,739,677,8.9928009,"\int x^3 \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[x^3*(a + b*Sech[c + d*Sqrt[x]])^2,x]","\frac{\cosh \left(c+d \sqrt{x}\right) \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2 \left(a^2 x^4 \cosh \left(c+d \sqrt{x}\right)+\frac{2 b \cosh \left(c+d \sqrt{x}\right) \left(\frac{8 b e^{2 c} d^7 x^{7/2}}{e^{2 c}+1}+i \left(8 a d^7 x^{7/2} \log \left(1-i e^{c+d \sqrt{x}}\right)-8 a d^7 x^{7/2} \log \left(1+i e^{c+d \sqrt{x}}\right)-56 a d^6 x^3 \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)+56 a d^6 x^3 \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)+336 a d^5 x^{5/2} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)-336 a d^5 x^{5/2} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)-1680 a d^4 x^2 \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)+1680 a d^4 x^2 \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)+6720 a d^3 x^{3/2} \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)-6720 a d^3 x^{3/2} \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)-20160 a d^2 x \text{Li}_6\left(-i e^{c+d \sqrt{x}}\right)+20160 a d^2 x \text{Li}_6\left(i e^{c+d \sqrt{x}}\right)+40320 a d \sqrt{x} \text{Li}_7\left(-i e^{c+d \sqrt{x}}\right)-40320 a d \sqrt{x} \text{Li}_7\left(i e^{c+d \sqrt{x}}\right)-40320 a \text{Li}_8\left(-i e^{c+d \sqrt{x}}\right)+40320 a \text{Li}_8\left(i e^{c+d \sqrt{x}}\right)+28 i b d^6 x^3 \log \left(e^{2 \left(c+d \sqrt{x}\right)}+1\right)+84 i b d^5 x^{5/2} \text{Li}_2\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)-210 i b d^4 x^2 \text{Li}_3\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)+420 i b d^3 x^{3/2} \text{Li}_4\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)-630 i b d^2 x \text{Li}_5\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)+630 i b d \sqrt{x} \text{Li}_6\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)-315 i b \text{Li}_7\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)\right)\right)}{d^8}+\frac{8 b^2 x^{7/2} \text{sech}(c) \sinh \left(d \sqrt{x}\right)}{d}\right)}{4 \left(a \cosh \left(c+d \sqrt{x}\right)+b\right)^2}","\frac{a^2 x^4}{4}-\frac{20160 i a b \text{Li}_8\left(-i e^{c+d \sqrt{x}}\right)}{d^8}+\frac{20160 i a b \text{Li}_8\left(i e^{c+d \sqrt{x}}\right)}{d^8}+\frac{20160 i a b \sqrt{x} \text{Li}_7\left(-i e^{c+d \sqrt{x}}\right)}{d^7}-\frac{20160 i a b \sqrt{x} \text{Li}_7\left(i e^{c+d \sqrt{x}}\right)}{d^7}-\frac{10080 i a b x \text{Li}_6\left(-i e^{c+d \sqrt{x}}\right)}{d^6}+\frac{10080 i a b x \text{Li}_6\left(i e^{c+d \sqrt{x}}\right)}{d^6}+\frac{3360 i a b x^{3/2} \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{3360 i a b x^{3/2} \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{840 i a b x^2 \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{840 i a b x^2 \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{168 i a b x^{5/2} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{168 i a b x^{5/2} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{28 i a b x^3 \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{28 i a b x^3 \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{8 a b x^{7/2} \tan ^{-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(e^{2 \left(c+d \sqrt{x}\right)}+1\right)}{d^2}+\frac{2 b^2 x^{7/2} \tanh \left(c+d \sqrt{x}\right)}{d}+\frac{2 b^2 x^{7/2}}{d}",1,"(Cosh[c + d*Sqrt[x]]*(a + b*Sech[c + d*Sqrt[x]])^2*(a^2*x^4*Cosh[c + d*Sqrt[x]] + (2*b*Cosh[c + d*Sqrt[x]]*((8*b*d^7*E^(2*c)*x^(7/2))/(1 + E^(2*c)) + I*(8*a*d^7*x^(7/2)*Log[1 - I*E^(c + d*Sqrt[x])] - 8*a*d^7*x^(7/2)*Log[1 + I*E^(c + d*Sqrt[x])] + (28*I)*b*d^6*x^3*Log[1 + E^(2*(c + d*Sqrt[x]))] - 56*a*d^6*x^3*PolyLog[2, (-I)*E^(c + d*Sqrt[x])] + 56*a*d^6*x^3*PolyLog[2, I*E^(c + d*Sqrt[x])] + (84*I)*b*d^5*x^(5/2)*PolyLog[2, -E^(2*(c + d*Sqrt[x]))] + 336*a*d^5*x^(5/2)*PolyLog[3, (-I)*E^(c + d*Sqrt[x])] - 336*a*d^5*x^(5/2)*PolyLog[3, I*E^(c + d*Sqrt[x])] - (210*I)*b*d^4*x^2*PolyLog[3, -E^(2*(c + d*Sqrt[x]))] - 1680*a*d^4*x^2*PolyLog[4, (-I)*E^(c + d*Sqrt[x])] + 1680*a*d^4*x^2*PolyLog[4, I*E^(c + d*Sqrt[x])] + (420*I)*b*d^3*x^(3/2)*PolyLog[4, -E^(2*(c + d*Sqrt[x]))] + 6720*a*d^3*x^(3/2)*PolyLog[5, (-I)*E^(c + d*Sqrt[x])] - 6720*a*d^3*x^(3/2)*PolyLog[5, I*E^(c + d*Sqrt[x])] - (630*I)*b*d^2*x*PolyLog[5, -E^(2*(c + d*Sqrt[x]))] - 20160*a*d^2*x*PolyLog[6, (-I)*E^(c + d*Sqrt[x])] + 20160*a*d^2*x*PolyLog[6, I*E^(c + d*Sqrt[x])] + (630*I)*b*d*Sqrt[x]*PolyLog[6, -E^(2*(c + d*Sqrt[x]))] + 40320*a*d*Sqrt[x]*PolyLog[7, (-I)*E^(c + d*Sqrt[x])] - 40320*a*d*Sqrt[x]*PolyLog[7, I*E^(c + d*Sqrt[x])] - (315*I)*b*PolyLog[7, -E^(2*(c + d*Sqrt[x]))] - 40320*a*PolyLog[8, (-I)*E^(c + d*Sqrt[x])] + 40320*a*PolyLog[8, I*E^(c + d*Sqrt[x])])))/d^8 + (8*b^2*x^(7/2)*Sech[c]*Sinh[d*Sqrt[x]])/d))/(4*(b + a*Cosh[c + d*Sqrt[x]])^2)","A",1
38,1,573,497,8.3068847,"\int x^2 \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[x^2*(a + b*Sech[c + d*Sqrt[x]])^2,x]","\frac{\cosh \left(c+d \sqrt{x}\right) \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2 \left(a^2 x^3 \cosh \left(c+d \sqrt{x}\right)+\frac{3 b \cosh \left(c+d \sqrt{x}\right) \left(\frac{4 b e^{2 c} d^5 x^{5/2}}{e^{2 c}+1}+i \left(4 a d^5 x^{5/2} \log \left(1-i e^{c+d \sqrt{x}}\right)-4 a d^5 x^{5/2} \log \left(1+i e^{c+d \sqrt{x}}\right)-20 a d^4 x^2 \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)+20 a d^4 x^2 \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)+80 a d^3 x^{3/2} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)-80 a d^3 x^{3/2} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)-240 a d^2 x \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)+240 a d^2 x \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)+480 a d \sqrt{x} \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)-480 a d \sqrt{x} \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)-480 a \text{Li}_6\left(-i e^{c+d \sqrt{x}}\right)+480 a \text{Li}_6\left(i e^{c+d \sqrt{x}}\right)+10 i b d^4 x^2 \log \left(e^{2 \left(c+d \sqrt{x}\right)}+1\right)+20 i b d^3 x^{3/2} \text{Li}_2\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)-30 i b d^2 x \text{Li}_3\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)+30 i b d \sqrt{x} \text{Li}_4\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)-15 i b \text{Li}_5\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)\right)\right)}{d^6}+\frac{6 b^2 x^{5/2} \text{sech}(c) \sinh \left(d \sqrt{x}\right)}{d}\right)}{3 \left(a \cosh \left(c+d \sqrt{x}\right)+b\right)^2}","\frac{a^2 x^3}{3}-\frac{480 i a b \text{Li}_6\left(-i e^{c+d \sqrt{x}}\right)}{d^6}+\frac{480 i a b \text{Li}_6\left(i e^{c+d \sqrt{x}}\right)}{d^6}+\frac{480 i a b \sqrt{x} \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{480 i a b \sqrt{x} \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{240 i a b x \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{240 i a b x \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{80 i a b x^{3/2} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{80 i a b x^{3/2} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{20 i a b x^2 \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{20 i a b x^2 \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{8 a b x^{5/2} \tan ^{-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(e^{2 \left(c+d \sqrt{x}\right)}+1\right)}{d^2}+\frac{2 b^2 x^{5/2} \tanh \left(c+d \sqrt{x}\right)}{d}+\frac{2 b^2 x^{5/2}}{d}",1,"(Cosh[c + d*Sqrt[x]]*(a + b*Sech[c + d*Sqrt[x]])^2*(a^2*x^3*Cosh[c + d*Sqrt[x]] + (3*b*Cosh[c + d*Sqrt[x]]*((4*b*d^5*E^(2*c)*x^(5/2))/(1 + E^(2*c)) + I*(4*a*d^5*x^(5/2)*Log[1 - I*E^(c + d*Sqrt[x])] - 4*a*d^5*x^(5/2)*Log[1 + I*E^(c + d*Sqrt[x])] + (10*I)*b*d^4*x^2*Log[1 + E^(2*(c + d*Sqrt[x]))] - 20*a*d^4*x^2*PolyLog[2, (-I)*E^(c + d*Sqrt[x])] + 20*a*d^4*x^2*PolyLog[2, I*E^(c + d*Sqrt[x])] + (20*I)*b*d^3*x^(3/2)*PolyLog[2, -E^(2*(c + d*Sqrt[x]))] + 80*a*d^3*x^(3/2)*PolyLog[3, (-I)*E^(c + d*Sqrt[x])] - 80*a*d^3*x^(3/2)*PolyLog[3, I*E^(c + d*Sqrt[x])] - (30*I)*b*d^2*x*PolyLog[3, -E^(2*(c + d*Sqrt[x]))] - 240*a*d^2*x*PolyLog[4, (-I)*E^(c + d*Sqrt[x])] + 240*a*d^2*x*PolyLog[4, I*E^(c + d*Sqrt[x])] + (30*I)*b*d*Sqrt[x]*PolyLog[4, -E^(2*(c + d*Sqrt[x]))] + 480*a*d*Sqrt[x]*PolyLog[5, (-I)*E^(c + d*Sqrt[x])] - 480*a*d*Sqrt[x]*PolyLog[5, I*E^(c + d*Sqrt[x])] - (15*I)*b*PolyLog[5, -E^(2*(c + d*Sqrt[x]))] - 480*a*PolyLog[6, (-I)*E^(c + d*Sqrt[x])] + 480*a*PolyLog[6, I*E^(c + d*Sqrt[x])])))/d^6 + (6*b^2*x^(5/2)*Sech[c]*Sinh[d*Sqrt[x]])/d))/(3*(b + a*Cosh[c + d*Sqrt[x]])^2)","A",1
39,1,459,319,8.7049842,"\int x \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[x*(a + b*Sech[c + d*Sqrt[x]])^2,x]","\frac{\cosh \left(c+d \sqrt{x}\right) \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2 \left(a^2 x^2 \cosh \left(c+d \sqrt{x}\right)+\frac{2 b \cosh \left(c+d \sqrt{x}\right) \left(\frac{4 b e^{2 c} d^3 x^{3/2}}{e^{2 c}+1}+i \left(-12 \left(a d^2 x-i b d \sqrt{x}\right) \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)+12 \left(a d^2 x+i b d \sqrt{x}\right) \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)+4 a d^3 x^{3/2} \log \left(1-i e^{c+d \sqrt{x}}\right)-4 a d^3 x^{3/2} \log \left(1+i e^{c+d \sqrt{x}}\right)+24 a d \sqrt{x} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)-24 a d \sqrt{x} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)-24 a \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)+24 a \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)+12 i b d^2 x \log \left(1-i e^{c+d \sqrt{x}}\right)+12 i b d^2 x \log \left(1+i e^{c+d \sqrt{x}}\right)-6 i b d^2 x \log \left(e^{2 \left(c+d \sqrt{x}\right)}+1\right)-3 i b \text{Li}_3\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)\right)\right)}{d^4}+\frac{4 b^2 x^{3/2} \text{sech}(c) \sinh \left(d \sqrt{x}\right)}{d}\right)}{2 \left(a \cosh \left(c+d \sqrt{x}\right)+b\right)^2}","\frac{a^2 x^2}{2}-\frac{24 i a b \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{24 i a b \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{24 i a b \sqrt{x} \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{24 i a b \sqrt{x} \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{12 i a b x \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{12 i a b x \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{8 a b x^{3/2} \tan ^{-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(e^{2 \left(c+d \sqrt{x}\right)}+1\right)}{d^2}+\frac{2 b^2 x^{3/2} \tanh \left(c+d \sqrt{x}\right)}{d}+\frac{2 b^2 x^{3/2}}{d}",1,"(Cosh[c + d*Sqrt[x]]*(a + b*Sech[c + d*Sqrt[x]])^2*(a^2*x^2*Cosh[c + d*Sqrt[x]] + (2*b*Cosh[c + d*Sqrt[x]]*((4*b*d^3*E^(2*c)*x^(3/2))/(1 + E^(2*c)) + I*((12*I)*b*d^2*x*Log[1 - I*E^(c + d*Sqrt[x])] + 4*a*d^3*x^(3/2)*Log[1 - I*E^(c + d*Sqrt[x])] + (12*I)*b*d^2*x*Log[1 + I*E^(c + d*Sqrt[x])] - 4*a*d^3*x^(3/2)*Log[1 + I*E^(c + d*Sqrt[x])] - (6*I)*b*d^2*x*Log[1 + E^(2*(c + d*Sqrt[x]))] - 12*((-I)*b*d*Sqrt[x] + a*d^2*x)*PolyLog[2, (-I)*E^(c + d*Sqrt[x])] + 12*(I*b*d*Sqrt[x] + a*d^2*x)*PolyLog[2, I*E^(c + d*Sqrt[x])] + 24*a*d*Sqrt[x]*PolyLog[3, (-I)*E^(c + d*Sqrt[x])] - 24*a*d*Sqrt[x]*PolyLog[3, I*E^(c + d*Sqrt[x])] - (3*I)*b*PolyLog[3, -E^(2*(c + d*Sqrt[x]))] - 24*a*PolyLog[4, (-I)*E^(c + d*Sqrt[x])] + 24*a*PolyLog[4, I*E^(c + d*Sqrt[x])])))/d^4 + (4*b^2*x^(3/2)*Sech[c]*Sinh[d*Sqrt[x]])/d))/(2*(b + a*Cosh[c + d*Sqrt[x]])^2)","A",0
40,0,0,23,62.2250916,"\int \frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])^2/x,x]","\int \frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x},x\right)",0,"Integrate[(a + b*Sech[c + d*Sqrt[x]])^2/x, x]","A",-1
41,0,0,23,28.2952543,"\int \frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])^2/x^2,x]","\int \frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x^2},x\right)",0,"Integrate[(a + b*Sech[c + d*Sqrt[x]])^2/x^2, x]","A",-1
42,1,939,961,3.2500907,"\int \frac{x^3}{a+b \text{sech}\left(c+d \sqrt{x}\right)} \, dx","Integrate[x^3/(a + b*Sech[c + d*Sqrt[x]]),x]","\frac{\left(b+a \cosh \left(c+d \sqrt{x}\right)\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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right)-5040 \text{Li}_8\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(b^2-a^2\right) e^{2 c}}}\right)\right)}{d^8 \sqrt{\left(b^2-a^2\right) e^{2 c}}}\right) \text{sech}\left(c+d \sqrt{x}\right)}{4 a \left(a+b \text{sech}\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{b^2-a^2}}+1\right) x^{7/2}}{a \sqrt{b^2-a^2} d}+\frac{2 b \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a \sqrt{b^2-a^2} d}-\frac{14 b \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) x^3}{a \sqrt{b^2-a^2} d^2}+\frac{14 b \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^3}{a \sqrt{b^2-a^2} d^2}+\frac{84 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) x^{5/2}}{a \sqrt{b^2-a^2} d^3}-\frac{84 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^{5/2}}{a \sqrt{b^2-a^2} d^3}-\frac{420 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) x^2}{a \sqrt{b^2-a^2} d^4}+\frac{420 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^2}{a \sqrt{b^2-a^2} d^4}+\frac{1680 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) x^{3/2}}{a \sqrt{b^2-a^2} d^5}-\frac{1680 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^{3/2}}{a \sqrt{b^2-a^2} d^5}-\frac{5040 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) x}{a \sqrt{b^2-a^2} d^6}+\frac{5040 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x}{a \sqrt{b^2-a^2} d^6}+\frac{10080 b \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) \sqrt{x}}{a \sqrt{b^2-a^2} d^7}-\frac{10080 b \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) \sqrt{x}}{a \sqrt{b^2-a^2} d^7}-\frac{10080 b \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a \sqrt{b^2-a^2} d^8}+\frac{10080 b \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a \sqrt{b^2-a^2} d^8}",1,"((b + a*Cosh[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)]))*Sech[c + d*Sqrt[x]])/(4*a*(a + b*Sech[c + d*Sqrt[x]]))","A",1
43,1,744,721,2.1796221,"\int \frac{x^2}{a+b \text{sech}\left(c+d \sqrt{x}\right)} \, dx","Integrate[x^2/(a + b*Sech[c + d*Sqrt[x]]),x]","\frac{d^6 x^3 \sqrt{e^{2 c} \left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right)}{3 a d^6 \sqrt{e^{2 c} \left(b^2-a^2\right)}}","-\frac{240 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^6 \sqrt{b^2-a^2}}+\frac{240 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^6 \sqrt{b^2-a^2}}+\frac{240 b \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^5 \sqrt{b^2-a^2}}-\frac{240 b \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^5 \sqrt{b^2-a^2}}-\frac{120 b x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{120 b x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{40 b x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{40 b x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{10 b x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{10 b x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{2 b x^{5/2} \log \left(\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}+1\right)}{a d \sqrt{b^2-a^2}}+\frac{2 b x^{5/2} \log \left(\frac{a e^{c+d \sqrt{x}}}{\sqrt{b^2-a^2}+b}+1\right)}{a d \sqrt{b^2-a^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
44,1,508,481,21.4603368,"\int \frac{x}{a+b \text{sech}\left(c+d \sqrt{x}\right)} \, dx","Integrate[x/(a + b*Sech[c + d*Sqrt[x]]),x]","\frac{d^4 x^2 \sqrt{e^{2 c} \left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right)}{2 a d^4 \sqrt{e^{2 c} \left(b^2-a^2\right)}}","-\frac{12 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{12 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{12 b \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{12 b \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{6 b x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{6 b x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{2 b x^{3/2} \log \left(\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}+1\right)}{a d \sqrt{b^2-a^2}}+\frac{2 b x^{3/2} \log \left(\frac{a e^{c+d \sqrt{x}}}{\sqrt{b^2-a^2}+b}+1\right)}{a d \sqrt{b^2-a^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
45,0,0,23,5.5667619,"\int \frac{1}{x \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)} \, dx","Integrate[1/(x*(a + b*Sech[c + d*Sqrt[x]])),x]","\int \frac{1}{x \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)},x\right)",0,"Integrate[1/(x*(a + b*Sech[c + d*Sqrt[x]])), x]","A",-1
46,0,0,26,1.2900805,"\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{x^2} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])/x^2,x]","\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{x^2} \, dx","b \text{Int}\left(\frac{\text{sech}\left(c+d \sqrt{x}\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Sech[c + d*Sqrt[x]])/x^2, x]","A",-1
47,1,3033,2851,18.740856,"\int \frac{x^3}{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[x^3/(a + b*Sech[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{b^2-a^2}}+1\right) x^{7/2}}{a^2 \sqrt{b^2-a^2} d}+\frac{2 b^3 \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{4 b \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \sqrt{b^2-a^2} d}-\frac{2 b^3 \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) x^{7/2}}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{2 b^2 \sinh \left(c+d \sqrt{x}\right) x^{7/2}}{a \left(a^2-b^2\right) d \left(b+a \cosh \left(c+d \sqrt{x}\right)\right)}+\frac{2 b^2 x^{7/2}}{a^2 \left(a^2-b^2\right) d}-\frac{14 b^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{b^2-a^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{b^2-a^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{b^2-a^2}}\right) x^3}{a^2 \sqrt{b^2-a^2} d^2}+\frac{14 b^3 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) x^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}+\frac{28 b \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^3}{a^2 \sqrt{b^2-a^2} d^2}-\frac{14 b^3 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{84 b^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^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{b^2-a^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{b^2-a^2}}\right) x^{5/2}}{a^2 \sqrt{b^2-a^2} d^3}-\frac{84 b^3 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^3}-\frac{168 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \sqrt{b^2-a^2} d^3}+\frac{84 b^3 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^{5/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{420 b^2 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^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{b^2-a^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{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^4}+\frac{420 b^3 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^4}+\frac{840 b \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \sqrt{b^2-a^2} d^4}-\frac{420 b^3 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^2}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{1680 b^2 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^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{b^2-a^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{b^2-a^2}}\right) x^{3/2}}{a^2 \sqrt{b^2-a^2} d^5}-\frac{1680 b^3 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^5}-\frac{3360 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \sqrt{b^2-a^2} d^5}+\frac{1680 b^3 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x^{3/2}}{a^2 \left(b^2-a^2\right)^{3/2} d^5}+\frac{5040 b^2 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^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{b^2-a^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{b^2-a^2}}\right) x}{a^2 \sqrt{b^2-a^2} d^6}+\frac{5040 b^3 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) x}{a^2 \left(b^2-a^2\right)^{3/2} d^6}+\frac{10080 b \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x}{a^2 \sqrt{b^2-a^2} d^6}-\frac{5040 b^3 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) x}{a^2 \left(b^2-a^2\right)^{3/2} d^6}-\frac{10080 b^2 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^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{b^2-a^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{b^2-a^2}}\right) \sqrt{x}}{a^2 \sqrt{b^2-a^2} d^7}-\frac{10080 b^3 \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \left(b^2-a^2\right)^{3/2} d^7}-\frac{20160 b \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \sqrt{b^2-a^2} d^7}+\frac{10080 b^3 \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) \sqrt{x}}{a^2 \left(b^2-a^2\right)^{3/2} d^7}+\frac{10080 b^2 \text{Li}_7\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^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{b^2-a^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{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^8}+\frac{10080 b^3 \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^8}+\frac{20160 b \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \sqrt{b^2-a^2} d^8}-\frac{10080 b^3 \text{Li}_8\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a^2 \left(b^2-a^2\right)^{3/2} d^8}",1,"(x^4*(b + a*Cosh[c + d*Sqrt[x]])^2*Sech[c + d*Sqrt[x]]^2)/(4*a^2*(a + b*Sech[c + d*Sqrt[x]])^2) + (2*b*E^c*(b + a*Cosh[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)]))*Sech[c + d*Sqrt[x]]^2)/(a^2*(a^2 - b^2)*d*(1 + E^(2*c))*(a + b*Sech[c + d*Sqrt[x]])^2) + (2*(b + a*Cosh[c + d*Sqrt[x]])*Sech[c]*Sech[c + d*Sqrt[x]]^2*(b^3*x^(7/2)*Sinh[c] - a*b^2*x^(7/2)*Sinh[d*Sqrt[x]]))/(a^2*(-a + b)*(a + b)*d*(a + b*Sech[c + d*Sqrt[x]])^2)","A",0
48,1,2245,2123,17.3750189,"\int \frac{x^2}{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[x^2/(a + b*Sech[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{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{2 x^{5/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{10 x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{10 x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{40 x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{40 x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{120 x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{120 x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{240 \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}+\frac{240 \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}+\frac{240 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^6}-\frac{240 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^6}+\frac{2 x^{5/2} \sinh \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cosh \left(c+d \sqrt{x}\right)\right)}-\frac{4 x^{5/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{4 x^{5/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{20 x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{20 x^2 \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{80 x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{80 x^{3/2} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{240 x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{240 x \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{480 \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}-\frac{480 \sqrt{x} \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}-\frac{480 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^6}+\frac{480 \text{Li}_6\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^6}+\frac{x^3}{3 a^2}",1,"(x^3*(b + a*Cosh[c + d*Sqrt[x]])^2*Sech[c + d*Sqrt[x]]^2)/(3*a^2*(a + b*Sech[c + d*Sqrt[x]])^2) + (2*b*E^c*(b + a*Cosh[c + d*Sqrt[x]])^2*(2*b*E^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)]))]))/(d^5*E^c*Sqrt[(-a^2 + b^2)*E^(2*c)]))*Sech[c + d*Sqrt[x]]^2)/(a^2*(a^2 - b^2)*d*(1 + E^(2*c))*(a + b*Sech[c + d*Sqrt[x]])^2) + (2*(b + a*Cosh[c + d*Sqrt[x]])*Sech[c]*Sech[c + d*Sqrt[x]]^2*(b^3*x^(5/2)*Sinh[c] - a*b^2*x^(5/2)*Sinh[d*Sqrt[x]]))/(a^2*(-a + b)*(a + b)*d*(a + b*Sech[c + d*Sqrt[x]])^2)","A",0
49,1,1393,1395,17.0064855,"\int \frac{x}{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[x/(a + b*Sech[c + d*Sqrt[x]])^2,x]","\frac{\left(b+a \cosh \left(c+d \sqrt{x}\right)\right) \text{sech}^2\left(c+d \sqrt{x}\right) \left(\frac{4 x^{3/2} \text{sech}(c) \left(a \sinh \left(d \sqrt{x}\right)-b \sinh (c)\right) b^2}{(a-b) (a+b) d}+\frac{4 e^c \left(b+a \cosh \left(c+d \sqrt{x}\right)\right) \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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}+1\right) d^3-3 b \sqrt{\left(b^2-a^2\right) e^{2 c}} x \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(b^2-a^2\right) e^{2 c}}}+1\right) d^2-3 b \sqrt{\left(b^2-a^2\right) e^{2 c}} x \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(b^2-a^2\right) e^{2 c}}}+1\right) d^2+3 \left(-2 d e^c \sqrt{x} a^2-2 b \sqrt{\left(b^2-a^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}}}{b e^c-\sqrt{\left(b^2-a^2\right) e^{2 c}}}\right) d-3 \left(-2 d e^c \sqrt{x} a^2+2 b \sqrt{\left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right) d+6 b \sqrt{\left(b^2-a^2\right) e^{2 c}} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(b^2-a^2\right) e^{2 c}}}\right)+6 b \sqrt{\left(b^2-a^2\right) e^{2 c}} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right)\right)}{d^3 \sqrt{\left(b^2-a^2\right) e^{2 c}}}\right) b}{\left(a^2-b^2\right) d \left(1+e^{2 c}\right)}+x^2 \left(b+a \cosh \left(c+d \sqrt{x}\right)\right)\right)}{2 a^2 \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}","\frac{2 x^{3/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{2 x^{3/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{6 x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{6 x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{12 \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{12 \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{12 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{12 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^4}+\frac{2 x^{3/2} \sinh \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cosh \left(c+d \sqrt{x}\right)\right)}-\frac{4 x^{3/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{4 x^{3/2} \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{12 x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{12 x \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{24 \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{24 \sqrt{x} \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{24 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{24 \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{x^2}{2 a^2}",1,"((b + a*Cosh[c + d*Sqrt[x]])*Sech[c + d*Sqrt[x]]^2*(x^2*(b + a*Cosh[c + d*Sqrt[x]]) + (4*b*E^c*(b + a*Cosh[c + d*Sqrt[x]])*(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)])] + 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)]))] - 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)])))/((a^2 - b^2)*d*(1 + E^(2*c))) + (4*b^2*x^(3/2)*Sech[c]*(-(b*Sinh[c]) + a*Sinh[d*Sqrt[x]]))/((a - b)*(a + b)*d)))/(2*a^2*(a + b*Sech[c + d*Sqrt[x]])^2)","A",1
50,0,0,23,120.9665299,"\int \frac{1}{x \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Sech[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Integrate[1/(x*(a + b*Sech[c + d*Sqrt[x]])^2), x]","A",-1
51,0,0,23,71.5266795,"\int \frac{1}{x^2 \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Sech[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^2 \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Integrate[1/(x^2*(a + b*Sech[c + d*Sqrt[x]])^2), x]","A",-1
52,1,288,254,2.0516468,"\int x^{3/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right) \, dx","Integrate[x^(3/2)*(a + b*Sech[c + d*Sqrt[x]]),x]","\frac{2 \left(a d^5 x^{5/2}+5 i b d^4 x^2 \log \left(1-i e^{c+d \sqrt{x}}\right)-5 i b d^4 x^2 \log \left(1+i e^{c+d \sqrt{x}}\right)-20 i b d^3 x^{3/2} \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)+20 i b d^3 x^{3/2} \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)+60 i b d^2 x \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)-60 i b d^2 x \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)-120 i b d \sqrt{x} \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)+120 i b d \sqrt{x} \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)+120 i b \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)-120 i b \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)\right)}{5 d^5}","\frac{2}{5} a x^{5/2}+\frac{48 i b \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{48 i b \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{48 i b \sqrt{x} \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{48 i b \sqrt{x} \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{24 i b x \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{24 i b x \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{8 i b x^{3/2} \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{8 i b x^{3/2} \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{4 b x^2 \tan ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}",1,"(2*(a*d^5*x^(5/2) + (5*I)*b*d^4*x^2*Log[1 - I*E^(c + d*Sqrt[x])] - (5*I)*b*d^4*x^2*Log[1 + I*E^(c + d*Sqrt[x])] - (20*I)*b*d^3*x^(3/2)*PolyLog[2, (-I)*E^(c + d*Sqrt[x])] + (20*I)*b*d^3*x^(3/2)*PolyLog[2, I*E^(c + d*Sqrt[x])] + (60*I)*b*d^2*x*PolyLog[3, (-I)*E^(c + d*Sqrt[x])] - (60*I)*b*d^2*x*PolyLog[3, I*E^(c + d*Sqrt[x])] - (120*I)*b*d*Sqrt[x]*PolyLog[4, (-I)*E^(c + d*Sqrt[x])] + (120*I)*b*d*Sqrt[x]*PolyLog[4, I*E^(c + d*Sqrt[x])] + (120*I)*b*PolyLog[5, (-I)*E^(c + d*Sqrt[x])] - (120*I)*b*PolyLog[5, I*E^(c + d*Sqrt[x])]))/(5*d^5)","A",1
53,1,197,140,7.6553162,"\int \sqrt{x} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right) \, dx","Integrate[Sqrt[x]*(a + b*Sech[c + d*Sqrt[x]]),x]","\frac{2 \left(a d^3 x^{3/2}-6 b d^2 x \tan ^{-1}\left(\cosh \left(c+d \sqrt{x}\right)-\sinh \left(c+d \sqrt{x}\right)\right)-6 i b d \sqrt{x} \text{Li}_2\left(-i \left(\cosh \left(c+d \sqrt{x}\right)-\sinh \left(c+d \sqrt{x}\right)\right)\right)+6 i b d \sqrt{x} \text{Li}_2\left(i \left(\cosh \left(c+d \sqrt{x}\right)-\sinh \left(c+d \sqrt{x}\right)\right)\right)-6 i b \text{Li}_3\left(-i \left(\cosh \left(c+d \sqrt{x}\right)-\sinh \left(c+d \sqrt{x}\right)\right)\right)+6 i b \text{Li}_3\left(i \left(\cosh \left(c+d \sqrt{x}\right)-\sinh \left(c+d \sqrt{x}\right)\right)\right)\right)}{3 d^3}","\frac{2}{3} a x^{3/2}+\frac{4 i b \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{4 i b \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{4 i b \sqrt{x} \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{4 i b \sqrt{x} \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{4 b x \tan ^{-1}\left(e^{c+d \sqrt{x}}\right)}{d}",1,"(2*(a*d^3*x^(3/2) - 6*b*d^2*x*ArcTan[Cosh[c + d*Sqrt[x]] - Sinh[c + d*Sqrt[x]]] - (6*I)*b*d*Sqrt[x]*PolyLog[2, (-I)*(Cosh[c + d*Sqrt[x]] - Sinh[c + d*Sqrt[x]])] + (6*I)*b*d*Sqrt[x]*PolyLog[2, I*(Cosh[c + d*Sqrt[x]] - Sinh[c + d*Sqrt[x]])] - (6*I)*b*PolyLog[3, (-I)*(Cosh[c + d*Sqrt[x]] - Sinh[c + d*Sqrt[x]])] + (6*I)*b*PolyLog[3, I*(Cosh[c + d*Sqrt[x]] - Sinh[c + d*Sqrt[x]])]))/(3*d^3)","A",0
54,1,30,26,0.0360304,"\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])/Sqrt[x],x]","\frac{2 \left(a \left(c+d \sqrt{x}\right)+b \tan ^{-1}\left(\sinh \left(c+d \sqrt{x}\right)\right)\right)}{d}","2 a \sqrt{x}+\frac{2 b \tan ^{-1}\left(\sinh \left(c+d \sqrt{x}\right)\right)}{d}",1,"(2*(a*(c + d*Sqrt[x]) + b*ArcTan[Sinh[c + d*Sqrt[x]]]))/d","A",1
55,0,0,30,8.9157258,"\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{x^{3/2}} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])/x^(3/2),x]","\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{x^{3/2}} \, dx","b \text{Int}\left(\frac{\text{sech}\left(c+d \sqrt{x}\right)}{x^{3/2}},x\right)-\frac{2 a}{\sqrt{x}}",0,"Integrate[(a + b*Sech[c + d*Sqrt[x]])/x^(3/2), x]","A",-1
56,0,0,32,9.549986,"\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{x^{5/2}} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])/x^(5/2),x]","\int \frac{a+b \text{sech}\left(c+d \sqrt{x}\right)}{x^{5/2}} \, dx","b \text{Int}\left(\frac{\text{sech}\left(c+d \sqrt{x}\right)}{x^{5/2}},x\right)-\frac{2 a}{3 x^{3/2}}",0,"Integrate[(a + b*Sech[c + d*Sqrt[x]])/x^(5/2), x]","A",-1
57,1,487,407,6.340361,"\int x^{3/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[x^(3/2)*(a + b*Sech[c + d*Sqrt[x]])^2,x]","\frac{2 \cosh \left(c+d \sqrt{x}\right) \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2 \left(a^2 x^{5/2} \cosh \left(c+d \sqrt{x}\right)+\frac{5 b \cosh \left(c+d \sqrt{x}\right) \left(\frac{2 b e^{2 c} d^4 x^2}{e^{2 c}+1}+i \left(2 a d^4 x^2 \log \left(1-i e^{c+d \sqrt{x}}\right)-2 a d^4 x^2 \log \left(1+i e^{c+d \sqrt{x}}\right)-8 a d^3 x^{3/2} \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)+8 a d^3 x^{3/2} \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)+24 a d^2 x \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)-24 a d^2 x \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)-48 a d \sqrt{x} \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)+48 a d \sqrt{x} \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)+48 a \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)-48 a \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)+4 i b d^3 x^{3/2} \log \left(e^{2 \left(c+d \sqrt{x}\right)}+1\right)+6 i b d^2 x \text{Li}_2\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)-6 i b d \sqrt{x} \text{Li}_3\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)+3 i b \text{Li}_4\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)\right)\right)}{d^5}+\frac{5 b^2 x^2 \text{sech}(c) \sinh \left(d \sqrt{x}\right)}{d}\right)}{5 \left(a \cosh \left(c+d \sqrt{x}\right)+b\right)^2}","\frac{2}{5} a^2 x^{5/2}+\frac{96 i a b \text{Li}_5\left(-i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{96 i a b \text{Li}_5\left(i e^{c+d \sqrt{x}}\right)}{d^5}-\frac{96 i a b \sqrt{x} \text{Li}_4\left(-i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{96 i a b \sqrt{x} \text{Li}_4\left(i e^{c+d \sqrt{x}}\right)}{d^4}+\frac{48 i a b x \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{48 i a b x \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{16 i a b x^{3/2} \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{16 i a b x^{3/2} \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{8 a b x^2 \tan ^{-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(e^{2 \left(c+d \sqrt{x}\right)}+1\right)}{d^2}+\frac{2 b^2 x^2 \tanh \left(c+d \sqrt{x}\right)}{d}+\frac{2 b^2 x^2}{d}",1,"(2*Cosh[c + d*Sqrt[x]]*(a + b*Sech[c + d*Sqrt[x]])^2*(a^2*x^(5/2)*Cosh[c + d*Sqrt[x]] + (5*b*Cosh[c + d*Sqrt[x]]*((2*b*d^4*E^(2*c)*x^2)/(1 + E^(2*c)) + I*(2*a*d^4*x^2*Log[1 - I*E^(c + d*Sqrt[x])] - 2*a*d^4*x^2*Log[1 + I*E^(c + d*Sqrt[x])] + (4*I)*b*d^3*x^(3/2)*Log[1 + E^(2*(c + d*Sqrt[x]))] - 8*a*d^3*x^(3/2)*PolyLog[2, (-I)*E^(c + d*Sqrt[x])] + 8*a*d^3*x^(3/2)*PolyLog[2, I*E^(c + d*Sqrt[x])] + (6*I)*b*d^2*x*PolyLog[2, -E^(2*(c + d*Sqrt[x]))] + 24*a*d^2*x*PolyLog[3, (-I)*E^(c + d*Sqrt[x])] - 24*a*d^2*x*PolyLog[3, I*E^(c + d*Sqrt[x])] - (6*I)*b*d*Sqrt[x]*PolyLog[3, -E^(2*(c + d*Sqrt[x]))] - 48*a*d*Sqrt[x]*PolyLog[4, (-I)*E^(c + d*Sqrt[x])] + 48*a*d*Sqrt[x]*PolyLog[4, I*E^(c + d*Sqrt[x])] + (3*I)*b*PolyLog[4, -E^(2*(c + d*Sqrt[x]))] + 48*a*PolyLog[5, (-I)*E^(c + d*Sqrt[x])] - 48*a*PolyLog[5, I*E^(c + d*Sqrt[x])])))/d^5 + (5*b^2*x^2*Sech[c]*Sinh[d*Sqrt[x]])/d))/(5*(b + a*Cosh[c + d*Sqrt[x]])^2)","A",1
58,1,309,229,5.9020769,"\int \sqrt{x} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2 \, dx","Integrate[Sqrt[x]*(a + b*Sech[c + d*Sqrt[x]])^2,x]","\frac{2 \cosh \left(c+d \sqrt{x}\right) \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2 \left(a^2 x^{3/2} \cosh \left(c+d \sqrt{x}\right)+\frac{3 b \cosh \left(c+d \sqrt{x}\right) \left(2 i a \left(d^2 x \log \left(1-i e^{c+d \sqrt{x}}\right)-d^2 x \log \left(1+i e^{c+d \sqrt{x}}\right)-2 d \sqrt{x} \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)+2 d \sqrt{x} \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)+2 \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)-2 \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)\right)+\frac{2 b e^{2 c} d^2 x}{e^{2 c}+1}-b \left(\text{Li}_2\left(-e^{2 \left(c+d \sqrt{x}\right)}\right)+2 d \sqrt{x} \log \left(e^{2 \left(c+d \sqrt{x}\right)}+1\right)\right)\right)}{d^3}+\frac{3 b^2 x \text{sech}(c) \sinh \left(d \sqrt{x}\right)}{d}\right)}{3 \left(a \cosh \left(c+d \sqrt{x}\right)+b\right)^2}","\frac{2}{3} a^2 x^{3/2}+\frac{8 i a b \text{Li}_3\left(-i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{8 i a b \text{Li}_3\left(i e^{c+d \sqrt{x}}\right)}{d^3}-\frac{8 i a b \sqrt{x} \text{Li}_2\left(-i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{8 i a b \sqrt{x} \text{Li}_2\left(i e^{c+d \sqrt{x}}\right)}{d^2}+\frac{8 a b x \tan ^{-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(e^{2 \left(c+d \sqrt{x}\right)}+1\right)}{d^2}+\frac{2 b^2 x \tanh \left(c+d \sqrt{x}\right)}{d}+\frac{2 b^2 x}{d}",1,"(2*Cosh[c + d*Sqrt[x]]*(a + b*Sech[c + d*Sqrt[x]])^2*(a^2*x^(3/2)*Cosh[c + d*Sqrt[x]] + (3*b*Cosh[c + d*Sqrt[x]]*((2*b*d^2*E^(2*c)*x)/(1 + E^(2*c)) - b*(2*d*Sqrt[x]*Log[1 + E^(2*(c + d*Sqrt[x]))] + PolyLog[2, -E^(2*(c + d*Sqrt[x]))]) + (2*I)*a*(d^2*x*Log[1 - I*E^(c + d*Sqrt[x])] - d^2*x*Log[1 + I*E^(c + d*Sqrt[x])] - 2*d*Sqrt[x]*PolyLog[2, (-I)*E^(c + d*Sqrt[x])] + 2*d*Sqrt[x]*PolyLog[2, I*E^(c + d*Sqrt[x])] + 2*PolyLog[3, (-I)*E^(c + d*Sqrt[x])] - 2*PolyLog[3, I*E^(c + d*Sqrt[x])])))/d^3 + (3*b^2*x*Sech[c]*Sinh[d*Sqrt[x]])/d))/(3*(b + a*Cosh[c + d*Sqrt[x]])^2)","A",1
59,1,48,47,0.117343,"\int \frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{\sqrt{x}} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])^2/Sqrt[x],x]","\frac{2 \left(a \left(a \left(c+d \sqrt{x}\right)+2 b \tan ^{-1}\left(\sinh \left(c+d \sqrt{x}\right)\right)\right)+b^2 \tanh \left(c+d \sqrt{x}\right)\right)}{d}","2 a^2 \sqrt{x}+\frac{4 a b \tan ^{-1}\left(\sinh \left(c+d \sqrt{x}\right)\right)}{d}+\frac{2 b^2 \tanh \left(c+d \sqrt{x}\right)}{d}",1,"(2*(a*(a*(c + d*Sqrt[x]) + 2*b*ArcTan[Sinh[c + d*Sqrt[x]]]) + b^2*Tanh[c + d*Sqrt[x]]))/d","A",1
60,0,0,25,27.8745972,"\int \frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x^{3/2}} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])^2/x^(3/2),x]","\int \frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x^{3/2}} \, dx","\text{Int}\left(\frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x^{3/2}},x\right)",0,"Integrate[(a + b*Sech[c + d*Sqrt[x]])^2/x^(3/2), x]","A",-1
61,0,0,25,27.8771821,"\int \frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x^{5/2}} \, dx","Integrate[(a + b*Sech[c + d*Sqrt[x]])^2/x^(5/2),x]","\int \frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x^{5/2}} \, dx","\text{Int}\left(\frac{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}{x^{5/2}},x\right)",0,"Integrate[(a + b*Sech[c + d*Sqrt[x]])^2/x^(5/2), x]","A",-1
62,1,626,601,2.3726123,"\int \frac{x^{3/2}}{a+b \text{sech}\left(c+d \sqrt{x}\right)} \, dx","Integrate[x^(3/2)/(a + b*Sech[c + d*Sqrt[x]]),x]","\frac{2 \left(d^5 x^{5/2} \sqrt{e^{2 c} \left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right)\right)}{5 a d^5 \sqrt{e^{2 c} \left(b^2-a^2\right)}}","\frac{48 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^5 \sqrt{b^2-a^2}}-\frac{48 b \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^5 \sqrt{b^2-a^2}}-\frac{48 b \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{48 b \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^4 \sqrt{b^2-a^2}}+\frac{24 b x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{24 b x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{8 b x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{8 b x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{2 b x^2 \log \left(\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}+1\right)}{a d \sqrt{b^2-a^2}}+\frac{2 b x^2 \log \left(\frac{a e^{c+d \sqrt{x}}}{\sqrt{b^2-a^2}+b}+1\right)}{a d \sqrt{b^2-a^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
63,1,390,361,8.0274402,"\int \frac{\sqrt{x}}{a+b \text{sech}\left(c+d \sqrt{x}\right)} \, dx","Integrate[Sqrt[x]/(a + b*Sech[c + d*Sqrt[x]]),x]","\frac{2 \left(d^3 x^{3/2} \sqrt{e^{2 c} \left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right)\right)}{3 a d^3 \sqrt{e^{2 c} \left(b^2-a^2\right)}}","\frac{4 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{4 b \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^3 \sqrt{b^2-a^2}}-\frac{4 b \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}+\frac{4 b \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right)}{a d^2 \sqrt{b^2-a^2}}-\frac{2 b x \log \left(\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}+1\right)}{a d \sqrt{b^2-a^2}}+\frac{2 b x \log \left(\frac{a e^{c+d \sqrt{x}}}{\sqrt{b^2-a^2}+b}+1\right)}{a d \sqrt{b^2-a^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
64,1,69,68,0.1297148,"\int \frac{1}{\sqrt{x} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)} \, dx","Integrate[1/(Sqrt[x]*(a + b*Sech[c + d*Sqrt[x]])),x]","\frac{2 \left(\frac{2 b \tan ^{-1}\left(\frac{(b-a) \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{2 \sqrt{x}}{a}-\frac{4 b \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{a+b}}\right)}{a d \sqrt{a-b} \sqrt{a+b}}",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
65,0,0,25,8.8296805,"\int \frac{1}{x^{3/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)} \, dx","Integrate[1/(x^(3/2)*(a + b*Sech[c + d*Sqrt[x]])),x]","\int \frac{1}{x^{3/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^{3/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)},x\right)",0,"Integrate[1/(x^(3/2)*(a + b*Sech[c + d*Sqrt[x]])), x]","A",-1
66,0,0,25,9.0318681,"\int \frac{1}{x^{5/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)} \, dx","Integrate[1/(x^(5/2)*(a + b*Sech[c + d*Sqrt[x]])),x]","\int \frac{1}{x^{5/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^{5/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)},x\right)",0,"Integrate[1/(x^(5/2)*(a + b*Sech[c + d*Sqrt[x]])), x]","A",-1
67,1,1769,1755,15.4342119,"\int \frac{x^{3/2}}{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[x^(3/2)/(a + b*Sech[c + d*Sqrt[x]])^2,x]","\frac{2 \left(b+a \cosh \left(c+d \sqrt{x}\right)\right) \text{sech}^2\left(c+d \sqrt{x}\right) \left(\left(b+a \cosh \left(c+d \sqrt{x}\right)\right) x^{5/2}+\frac{5 b^2 \text{sech}(c) \left(a \sinh \left(d \sqrt{x}\right)-b \sinh (c)\right) x^2}{(a-b) (a+b) d}+\frac{5 b e^c \left(b+a \cosh \left(c+d \sqrt{x}\right)\right) \left(2 b e^c x^2-\frac{e^{-c} \left(1+e^{2 c}\right) \left(2 a^2 e^c x^2 \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}+1\right) d^4+4 b \sqrt{\left(b^2-a^2\right) e^{2 c}} x^{3/2} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(b^2-a^2\right) e^{2 c}}}+1\right) d^3+4 b \sqrt{\left(b^2-a^2\right) e^{2 c}} x^{3/2} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(b^2-a^2\right) e^{2 c}}}+1\right) d^3+4 \left(2 d e^c \sqrt{x} a^2+3 b \sqrt{\left(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right) d^2+4 \left(-2 d e^c \sqrt{x} a^2+3 b \sqrt{\left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right) d^2-24 b \sqrt{\left(b^2-a^2\right) e^{2 c}} \sqrt{x} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(b^2-a^2\right) e^{2 c}}}\right) d-24 b \sqrt{\left(b^2-a^2\right) e^{2 c}} \sqrt{x} \text{Li}_3\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right) d+24 b \sqrt{\left(b^2-a^2\right) e^{2 c}} \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{b e^c-\sqrt{\left(b^2-a^2\right) e^{2 c}}}\right)+24 b \sqrt{\left(b^2-a^2\right) e^{2 c}} \text{Li}_4\left(-\frac{a e^{2 c+d \sqrt{x}}}{e^c b+\sqrt{\left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right)\right)}{d^4 \sqrt{\left(b^2-a^2\right) e^{2 c}}}\right)}{\left(a^2-b^2\right) d \left(1+e^{2 c}\right)}\right)}{5 a^2 \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}","\frac{2 x^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{2 x^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{8 x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{8 x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{24 x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{24 x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{48 \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{48 \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^4}-\frac{48 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^5}+\frac{48 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^5}+\frac{2 x^2 \sinh \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cosh \left(c+d \sqrt{x}\right)\right)}-\frac{4 x^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{4 x^2 \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{16 x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{16 x^{3/2} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{48 x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{48 x \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{96 \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{96 \sqrt{x} \text{Li}_4\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^4}+\frac{96 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}-\frac{96 \text{Li}_5\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^5}+\frac{2 x^{5/2}}{5 a^2}",1,"(2*(b + a*Cosh[c + d*Sqrt[x]])*Sech[c + d*Sqrt[x]]^2*(x^(5/2)*(b + a*Cosh[c + d*Sqrt[x]]) + (5*b*E^c*(b + a*Cosh[c + d*Sqrt[x]])*(2*b*E^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)]))]))/(d^4*E^c*Sqrt[(-a^2 + b^2)*E^(2*c)])))/((a^2 - b^2)*d*(1 + E^(2*c))) + (5*b^2*x^2*Sech[c]*(-(b*Sinh[c]) + a*Sinh[d*Sqrt[x]]))/((a - b)*(a + b)*d)))/(5*a^2*(a + b*Sech[c + d*Sqrt[x]])^2)","A",1
68,1,986,1027,13.4484017,"\int \frac{\sqrt{x}}{\left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[Sqrt[x]/(a + b*Sech[c + d*Sqrt[x]])^2,x]","\frac{2 \left(b+a \cosh \left(c+d \sqrt{x}\right)\right) \text{sech}^2\left(c+d \sqrt{x}\right) \left(\frac{3 x \text{sech}(c) \left(b \sinh (c)-a \sinh \left(d \sqrt{x}\right)\right) b^2}{\left(b^2-a^2\right) d}+\frac{3 e^c \left(b+a \cosh \left(c+d \sqrt{x}\right)\right) \left(2 b e^c x-\frac{e^{-c} \left(1+e^{2 c}\right) \left(2 d^2 e^c x \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}+1\right)+2 b d \sqrt{\left(b^2-a^2\right) e^{2 c}} \sqrt{x} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{b e^c-\sqrt{\left(b^2-a^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(b^2-a^2\right) e^{2 c}}}+1\right)+2 b d \sqrt{\left(b^2-a^2\right) e^{2 c}} \sqrt{x} \log \left(\frac{e^{2 c+d \sqrt{x}} a}{e^c b+\sqrt{\left(b^2-a^2\right) e^{2 c}}}+1\right)+2 \left(2 d e^c \sqrt{x} a^2+b \sqrt{\left(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right)+2 \left(-2 d e^c \sqrt{x} a^2+b \sqrt{\left(b^2-a^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(b^2-a^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(b^2-a^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(b^2-a^2\right) e^{2 c}}}\right)\right)}{d^2 \sqrt{\left(b^2-a^2\right) e^{2 c}}}\right) b}{\left(a^2-b^2\right) d \left(1+e^{2 c}\right)}+x^{3/2} \left(b+a \cosh \left(c+d \sqrt{x}\right)\right)\right)}{3 a^2 \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2}","\frac{2 x \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}-\frac{2 x \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d}+\frac{4 \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{4 \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^2}-\frac{4 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^2\right)^{3/2} d^3}+\frac{4 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b^3}{a^2 \left(b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^2}}\right) b^2}{a^2 \left(a^2-b^2\right) d^3}+\frac{2 x \sinh \left(c+d \sqrt{x}\right) b^2}{a \left(a^2-b^2\right) d \left(b+a \cosh \left(c+d \sqrt{x}\right)\right)}-\frac{4 x \log \left(\frac{e^{c+d \sqrt{x}} a}{b-\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}+\frac{4 x \log \left(\frac{e^{c+d \sqrt{x}} a}{b+\sqrt{b^2-a^2}}+1\right) b}{a^2 \sqrt{b^2-a^2} d}-\frac{8 \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{8 \sqrt{x} \text{Li}_2\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^2}+\frac{8 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b-\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}-\frac{8 \text{Li}_3\left(-\frac{a e^{c+d \sqrt{x}}}{b+\sqrt{b^2-a^2}}\right) b}{a^2 \sqrt{b^2-a^2} d^3}+\frac{2 x^{3/2}}{3 a^2}",1,"(2*(b + a*Cosh[c + d*Sqrt[x]])*Sech[c + d*Sqrt[x]]^2*(x^(3/2)*(b + a*Cosh[c + d*Sqrt[x]]) + (3*b*E^c*(b + a*Cosh[c + d*Sqrt[x]])*(2*b*E^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)]))]))/(d^2*E^c*Sqrt[(-a^2 + b^2)*E^(2*c)])))/((a^2 - b^2)*d*(1 + E^(2*c))) + (3*b^2*x*Sech[c]*(b*Sinh[c] - a*Sinh[d*Sqrt[x]]))/((-a^2 + b^2)*d)))/(3*a^2*(a + b*Sech[c + d*Sqrt[x]])^2)","A",1
69,1,232,127,0.5174396,"\int \frac{1}{\sqrt{x} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(Sqrt[x]*(a + b*Sech[c + d*Sqrt[x]])^2),x]","\frac{2 \left(b \left(\left(a^2-b^2\right)^{3/2} \left(c+d \sqrt{x}\right)+a b \sqrt{a^2-b^2} \sinh \left(c+d \sqrt{x}\right)+\left(4 a^2 b-2 b^3\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{a^2-b^2}}\right)\right)+a \cosh \left(c+d \sqrt{x}\right) \left(\left(a^2-b^2\right)^{3/2} \left(c+d \sqrt{x}\right)+\left(4 a^2 b-2 b^3\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{a^2-b^2}}\right)\right)\right)}{a^2 d (a-b) (a+b) \sqrt{a^2-b^2} \left(a \cosh \left(c+d \sqrt{x}\right)+b\right)}","-\frac{4 b \left(2 a^2-b^2\right) \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} \left(c+d \sqrt{x}\right)\right)}{\sqrt{a+b}}\right)}{a^2 d (a-b)^{3/2} (a+b)^{3/2}}+\frac{2 b^2 \tanh \left(c+d \sqrt{x}\right)}{a d \left(a^2-b^2\right) \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)}+\frac{2 \sqrt{x}}{a^2}",1,"(2*(a*((a^2 - b^2)^(3/2)*(c + d*Sqrt[x]) + (4*a^2*b - 2*b^3)*ArcTan[((-a + b)*Tanh[(c + d*Sqrt[x])/2])/Sqrt[a^2 - b^2]])*Cosh[c + d*Sqrt[x]] + b*((a^2 - b^2)^(3/2)*(c + d*Sqrt[x]) + (4*a^2*b - 2*b^3)*ArcTan[((-a + b)*Tanh[(c + d*Sqrt[x])/2])/Sqrt[a^2 - b^2]] + a*b*Sqrt[a^2 - b^2]*Sinh[c + d*Sqrt[x]])))/(a^2*(a - b)*(a + b)*Sqrt[a^2 - b^2]*d*(b + a*Cosh[c + d*Sqrt[x]]))","A",1
70,0,0,25,66.9268701,"\int \frac{1}{x^{3/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(x^(3/2)*(a + b*Sech[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^{3/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^{3/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Integrate[1/(x^(3/2)*(a + b*Sech[c + d*Sqrt[x]])^2), x]","A",-1
71,0,0,25,67.0600672,"\int \frac{1}{x^{5/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","Integrate[1/(x^(5/2)*(a + b*Sech[c + d*Sqrt[x]])^2),x]","\int \frac{1}{x^{5/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^{5/2} \left(a+b \text{sech}\left(c+d \sqrt{x}\right)\right)^2},x\right)",0,"Integrate[1/(x^(5/2)*(a + b*Sech[c + d*Sqrt[x]])^2), x]","A",-1
72,0,0,32,18.3357206,"\int (e x)^m \left(a+b \text{sech}\left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^m*(a + b*Sech[c + d*x^n])^p,x]","\int (e x)^m \left(a+b \text{sech}\left(c+d x^n\right)\right)^p \, dx","x^{-m} (e x)^m \text{Int}\left(x^m \left(a+b \text{sech}\left(c+d x^n\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(a + b*Sech[c + d*x^n])^p, x]","A",-1
73,1,41,44,0.0621236,"\int (e x)^{-1+n} \left(a+b \text{sech}\left(c+d x^n\right)\right) \, dx","Integrate[(e*x)^(-1 + n)*(a + b*Sech[c + d*x^n]),x]","\frac{x^{-n} (e x)^n \left(a \left(c+d x^n\right)+b \tan ^{-1}\left(\sinh \left(c+d x^n\right)\right)\right)}{d e n}","\frac{a (e x)^n}{e n}+\frac{b x^{-n} (e x)^n \tan ^{-1}\left(\sinh \left(c+d x^n\right)\right)}{d e n}",1,"((e*x)^n*(a*(c + d*x^n) + b*ArcTan[Sinh[c + d*x^n]]))/(d*e*n*x^n)","A",1
74,1,260,135,0.1819215,"\int (e x)^{-1+2 n} \left(a+b \text{sech}\left(c+d x^n\right)\right) \, dx","Integrate[(e*x)^(-1 + 2*n)*(a + b*Sech[c + d*x^n]),x]","\frac{x^{-2 n} (e x)^{2 n} \left(a d^2 x^{2 n}-2 i b \text{Li}_2\left(-i e^{d x^n+c}\right)+2 i b \text{Li}_2\left(i e^{d x^n+c}\right)+2 i b d x^n \log \left(1-i e^{c+d x^n}\right)-2 i b d x^n \log \left(1+i e^{c+d x^n}\right)+2 i b c \log \left(1-i e^{c+d x^n}\right)-\pi  b \log \left(1-i e^{c+d x^n}\right)-2 i b c \log \left(1+i e^{c+d x^n}\right)+\pi  b \log \left(1+i e^{c+d x^n}\right)-2 i b c \log \left(\cot \left(\frac{1}{4} \left(2 i c+2 i d x^n+\pi \right)\right)\right)+\pi  b \log \left(\cot \left(\frac{1}{4} \left(2 i c+2 i d x^n+\pi \right)\right)\right)\right)}{2 d^2 e n}","\frac{a (e x)^{2 n}}{2 e n}-\frac{i b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-i e^{d x^n+c}\right)}{d^2 e n}+\frac{i b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(i e^{d x^n+c}\right)}{d^2 e n}+\frac{2 b x^{-n} (e x)^{2 n} \tan ^{-1}\left(e^{c+d x^n}\right)}{d e n}",1,"((e*x)^(2*n)*(a*d^2*x^(2*n) + (2*I)*b*c*Log[1 - I*E^(c + d*x^n)] - b*Pi*Log[1 - I*E^(c + d*x^n)] + (2*I)*b*d*x^n*Log[1 - I*E^(c + d*x^n)] - (2*I)*b*c*Log[1 + I*E^(c + d*x^n)] + b*Pi*Log[1 + I*E^(c + d*x^n)] - (2*I)*b*d*x^n*Log[1 + I*E^(c + d*x^n)] - (2*I)*b*c*Log[Cot[((2*I)*c + Pi + (2*I)*d*x^n)/4]] + b*Pi*Log[Cot[((2*I)*c + Pi + (2*I)*d*x^n)/4]] - (2*I)*b*PolyLog[2, (-I)*E^(c + d*x^n)] + (2*I)*b*PolyLog[2, I*E^(c + d*x^n)]))/(2*d^2*e*n*x^(2*n))","A",1
75,0,0,217,10.5303446,"\int (e x)^{-1+3 n} \left(a+b \text{sech}\left(c+d x^n\right)\right) \, dx","Integrate[(e*x)^(-1 + 3*n)*(a + b*Sech[c + d*x^n]),x]","\int (e x)^{-1+3 n} \left(a+b \text{sech}\left(c+d x^n\right)\right) \, dx","\frac{a (e x)^{3 n}}{3 e n}+\frac{2 i b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(-i e^{d x^n+c}\right)}{d^3 e n}-\frac{2 i b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(i e^{d x^n+c}\right)}{d^3 e n}-\frac{2 i b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(-i e^{d x^n+c}\right)}{d^2 e n}+\frac{2 i b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(i e^{d x^n+c}\right)}{d^2 e n}+\frac{2 b x^{-n} (e x)^{3 n} \tan ^{-1}\left(e^{c+d x^n}\right)}{d e n}",1,"Integrate[(e*x)^(-1 + 3*n)*(a + b*Sech[c + d*x^n]), x]","F",-1
76,1,57,79,0.2054434,"\int (e x)^{-1+n} \left(a+b \text{sech}\left(c+d x^n\right)\right)^2 \, dx","Integrate[(e*x)^(-1 + n)*(a + b*Sech[c + d*x^n])^2,x]","\frac{x^{-n} (e x)^n \left(a \left(a \left(c+d x^n\right)+2 b \tan ^{-1}\left(\sinh \left(c+d x^n\right)\right)\right)+b^2 \tanh \left(c+d x^n\right)\right)}{d e n}","\frac{a^2 (e x)^n}{e n}+\frac{2 a b x^{-n} (e x)^n \tan ^{-1}\left(\sinh \left(c+d x^n\right)\right)}{d e n}+\frac{b^2 x^{-n} (e x)^n \tanh \left(c+d x^n\right)}{d e n}",1,"((e*x)^n*(a*(a*(c + d*x^n) + 2*b*ArcTan[Sinh[c + d*x^n]]) + b^2*Tanh[c + d*x^n]))/(d*e*n*x^n)","A",1
77,1,501,208,2.8773976,"\int (e x)^{-1+2 n} \left(a+b \text{sech}\left(c+d x^n\right)\right)^2 \, dx","Integrate[(e*x)^(-1 + 2*n)*(a + b*Sech[c + d*x^n])^2,x]","\frac{\text{csch}^5(c) x^{-2 n} (e x)^{2 n} \text{sech}\left(c+d x^n\right) \left(-a^2 d^2 \sqrt{-\text{csch}^2(c)} x^{2 n} \sinh \left(d x^n\right)+a^2 d^2 \sqrt{-\text{csch}^2(c)} x^{2 n} \sinh \left(2 c+d x^n\right)+8 a b \cosh \left(c+d x^n\right) \text{Li}_2\left(-e^{-d x^n-\tanh ^{-1}(\coth (c))}\right)-8 a b \cosh \left(c+d x^n\right) \text{Li}_2\left(e^{-d x^n-\tanh ^{-1}(\coth (c))}\right)+8 a b d x^n \cosh \left(c+d x^n\right) \log \left(1-e^{-\tanh ^{-1}(\coth (c))-d x^n}\right)-8 a b d x^n \cosh \left(c+d x^n\right) \log \left(e^{-\tanh ^{-1}(\coth (c))-d x^n}+1\right)+8 a b \tanh ^{-1}(\coth (c)) \cosh \left(c+d x^n\right) \log \left(1-e^{-\tanh ^{-1}(\coth (c))-d x^n}\right)-8 a b \tanh ^{-1}(\coth (c)) \cosh \left(c+d x^n\right) \log \left(e^{-\tanh ^{-1}(\coth (c))-d x^n}+1\right)+8 a b \sqrt{-\text{csch}^2(c)} \tanh ^{-1}(\coth (c)) \sinh \left(d x^n\right) \tan ^{-1}\left(\cosh (c) \tanh \left(\frac{d x^n}{2}\right)+\sinh (c)\right)-8 a b \sqrt{-\text{csch}^2(c)} \tanh ^{-1}(\coth (c)) \sinh \left(2 c+d x^n\right) \tan ^{-1}\left(\cosh (c) \tanh \left(\frac{d x^n}{2}\right)+\sinh (c)\right)-2 b^2 d \sqrt{-\text{csch}^2(c)} x^n \cosh \left(d x^n\right)+2 b^2 d \sqrt{-\text{csch}^2(c)} x^n \cosh \left(2 c+d x^n\right)+2 b^2 \sqrt{-\text{csch}^2(c)} \sinh \left(d x^n\right) \log \left(\cosh \left(c+d x^n\right)\right)-2 b^2 \sqrt{-\text{csch}^2(c)} \sinh \left(2 c+d x^n\right) \log \left(\cosh \left(c+d x^n\right)\right)\right)}{4 d^2 e n \left(-\text{csch}^2(c)\right)^{5/2}}","\frac{a^2 (e x)^{2 n}}{2 e n}-\frac{2 i a b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-i e^{d x^n+c}\right)}{d^2 e n}+\frac{2 i a b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(i e^{d x^n+c}\right)}{d^2 e n}+\frac{4 a b x^{-n} (e x)^{2 n} \tan ^{-1}\left(e^{c+d x^n}\right)}{d e n}-\frac{b^2 x^{-2 n} (e x)^{2 n} \log \left(\cosh \left(c+d x^n\right)\right)}{d^2 e n}+\frac{b^2 x^{-n} (e x)^{2 n} \tanh \left(c+d x^n\right)}{d e n}",1,"((e*x)^(2*n)*Csch[c]^5*Sech[c + d*x^n]*(-2*b^2*d*x^n*Cosh[d*x^n]*Sqrt[-Csch[c]^2] + 2*b^2*d*x^n*Cosh[2*c + d*x^n]*Sqrt[-Csch[c]^2] + 8*a*b*d*x^n*Cosh[c + d*x^n]*Log[1 - E^(-(d*x^n) - ArcTanh[Coth[c]])] + 8*a*b*ArcTanh[Coth[c]]*Cosh[c + d*x^n]*Log[1 - E^(-(d*x^n) - ArcTanh[Coth[c]])] - 8*a*b*d*x^n*Cosh[c + d*x^n]*Log[1 + E^(-(d*x^n) - ArcTanh[Coth[c]])] - 8*a*b*ArcTanh[Coth[c]]*Cosh[c + d*x^n]*Log[1 + E^(-(d*x^n) - ArcTanh[Coth[c]])] + 8*a*b*Cosh[c + d*x^n]*PolyLog[2, -E^(-(d*x^n) - ArcTanh[Coth[c]])] - 8*a*b*Cosh[c + d*x^n]*PolyLog[2, E^(-(d*x^n) - ArcTanh[Coth[c]])] - a^2*d^2*x^(2*n)*Sqrt[-Csch[c]^2]*Sinh[d*x^n] + 8*a*b*ArcTan[Sinh[c] + Cosh[c]*Tanh[(d*x^n)/2]]*ArcTanh[Coth[c]]*Sqrt[-Csch[c]^2]*Sinh[d*x^n] + 2*b^2*Sqrt[-Csch[c]^2]*Log[Cosh[c + d*x^n]]*Sinh[d*x^n] + a^2*d^2*x^(2*n)*Sqrt[-Csch[c]^2]*Sinh[2*c + d*x^n] - 8*a*b*ArcTan[Sinh[c] + Cosh[c]*Tanh[(d*x^n)/2]]*ArcTanh[Coth[c]]*Sqrt[-Csch[c]^2]*Sinh[2*c + d*x^n] - 2*b^2*Sqrt[-Csch[c]^2]*Log[Cosh[c + d*x^n]]*Sinh[2*c + d*x^n]))/(4*d^2*e*n*x^(2*n)*(-Csch[c]^2)^(5/2))","B",0
78,0,0,363,70.761507,"\int (e x)^{-1+3 n} \left(a+b \text{sech}\left(c+d x^n\right)\right)^2 \, dx","Integrate[(e*x)^(-1 + 3*n)*(a + b*Sech[c + d*x^n])^2,x]","\int (e x)^{-1+3 n} \left(a+b \text{sech}\left(c+d x^n\right)\right)^2 \, dx","\frac{a^2 (e x)^{3 n}}{3 e n}+\frac{4 i a b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(-i e^{d x^n+c}\right)}{d^3 e n}-\frac{4 i a b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(i e^{d x^n+c}\right)}{d^3 e n}-\frac{4 i a b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(-i e^{d x^n+c}\right)}{d^2 e n}+\frac{4 i a b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(i e^{d x^n+c}\right)}{d^2 e n}+\frac{4 a b x^{-n} (e x)^{3 n} \tan ^{-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(e^{2 \left(c+d x^n\right)}+1\right)}{d^2 e n}+\frac{b^2 x^{-n} (e x)^{3 n} \tanh \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*Sech[c + d*x^n])^2, x]","F",-1
79,1,80,87,0.1522433,"\int \frac{(e x)^{-1+n}}{a+b \text{sech}\left(c+d x^n\right)} \, dx","Integrate[(e*x)^(-1 + n)/(a + b*Sech[c + d*x^n]),x]","\frac{(e x)^n \left(\frac{2 b x^{-n} \tan ^{-1}\left(\frac{(b-a) \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{(e x)^n}{a e n}-\frac{2 b x^{-n} (e x)^n \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{a+b}}\right)}{a d e n \sqrt{a-b} \sqrt{a+b}}",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
80,1,859,307,2.1004058,"\int \frac{(e x)^{-1+2 n}}{a+b \text{sech}\left(c+d x^n\right)} \, dx","Integrate[(e*x)^(-1 + 2*n)/(a + b*Sech[c + d*x^n]),x]","\frac{(e x)^{2 n} \left(b+a \cosh \left(d x^n+c\right)\right) \left(\frac{2 b \left(2 \left(d x^n+c\right) \tan ^{-1}\left(\frac{(a+b) \coth \left(\frac{1}{2} \left(d x^n+c\right)\right)}{\sqrt{a^2-b^2}}\right)+2 \left(c-i \cos ^{-1}\left(-\frac{b}{a}\right)\right) \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)}{\sqrt{a^2-b^2}}\right)+\left(\cos ^{-1}\left(-\frac{b}{a}\right)+2 \left(\tan ^{-1}\left(\frac{(a+b) \coth \left(\frac{1}{2} \left(d x^n+c\right)\right)}{\sqrt{a^2-b^2}}\right)+\tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)}{\sqrt{a^2-b^2}}\right)\right)\right) \log \left(\frac{\sqrt{a^2-b^2} e^{-\frac{d x^n}{2}-\frac{c}{2}}}{\sqrt{2} \sqrt{a} \sqrt{b+a \cosh \left(d x^n+c\right)}}\right)+\left(\cos ^{-1}\left(-\frac{b}{a}\right)-2 \left(\tan ^{-1}\left(\frac{(a+b) \coth \left(\frac{1}{2} \left(d x^n+c\right)\right)}{\sqrt{a^2-b^2}}\right)+\tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)}{\sqrt{a^2-b^2}}\right)\right)\right) \log \left(\frac{\sqrt{a^2-b^2} e^{\frac{1}{2} \left(d x^n+c\right)}}{\sqrt{2} \sqrt{a} \sqrt{b+a \cosh \left(d x^n+c\right)}}\right)-\left(\cos ^{-1}\left(-\frac{b}{a}\right)+2 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)}{\sqrt{a^2-b^2}}\right)\right) \log \left(\frac{(a+b) \left(-a+b+i \sqrt{a^2-b^2}\right) \left(\tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)-1\right)}{a \left(a+b+i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{b}{a}\right)-2 \tan ^{-1}\left(\frac{(a-b) \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)}{\sqrt{a^2-b^2}}\right)\right) \log \left(\frac{(a+b) \left(a-b+i \sqrt{a^2-b^2}\right) \left(\tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)+1\right)}{a \left(a+b+i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)\right)}\right)+i \left(\text{Li}_2\left(\frac{\left(b-i \sqrt{a^2-b^2}\right) \left(a+b-i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)\right)}{a \left(a+b+i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)\right)}\right)-\text{Li}_2\left(\frac{\left(b+i \sqrt{a^2-b^2}\right) \left(a+b-i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)\right)}{a \left(a+b+i \sqrt{a^2-b^2} \tanh \left(\frac{1}{2} \left(d x^n+c\right)\right)\right)}\right)\right)\right) x^{-2 n}}{\sqrt{a^2-b^2} d^2}+1\right) \text{sech}\left(d x^n+c\right)}{2 a e n \left(a+b \text{sech}\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{b^2-a^2}}\right)}{a d^2 e n \sqrt{b^2-a^2}}+\frac{b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{b^2-a^2}}\right)}{a d^2 e n \sqrt{b^2-a^2}}-\frac{b x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{b-\sqrt{b^2-a^2}}+1\right)}{a d e n \sqrt{b^2-a^2}}+\frac{b x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{\sqrt{b^2-a^2}+b}+1\right)}{a d e n \sqrt{b^2-a^2}}+\frac{(e x)^{2 n}}{2 a e n}",1,"((e*x)^(2*n)*(b + a*Cosh[c + d*x^n])*(1 + (2*b*(2*(c + d*x^n)*ArcTan[((a + b)*Coth[(c + d*x^n)/2])/Sqrt[a^2 - b^2]] + 2*(c - I*ArcCos[-(b/a)])*ArcTan[((a - b)*Tanh[(c + d*x^n)/2])/Sqrt[a^2 - b^2]] + (ArcCos[-(b/a)] + 2*(ArcTan[((a + b)*Coth[(c + d*x^n)/2])/Sqrt[a^2 - b^2]] + ArcTan[((a - b)*Tanh[(c + d*x^n)/2])/Sqrt[a^2 - b^2]]))*Log[(Sqrt[a^2 - b^2]*E^(-1/2*c - (d*x^n)/2))/(Sqrt[2]*Sqrt[a]*Sqrt[b + a*Cosh[c + d*x^n]])] + (ArcCos[-(b/a)] - 2*(ArcTan[((a + b)*Coth[(c + d*x^n)/2])/Sqrt[a^2 - b^2]] + ArcTan[((a - b)*Tanh[(c + d*x^n)/2])/Sqrt[a^2 - b^2]]))*Log[(Sqrt[a^2 - b^2]*E^((c + d*x^n)/2))/(Sqrt[2]*Sqrt[a]*Sqrt[b + a*Cosh[c + d*x^n]])] - (ArcCos[-(b/a)] + 2*ArcTan[((a - b)*Tanh[(c + d*x^n)/2])/Sqrt[a^2 - b^2]])*Log[((a + b)*(-a + b + I*Sqrt[a^2 - b^2])*(-1 + Tanh[(c + d*x^n)/2]))/(a*(a + b + I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^n)/2]))] - (ArcCos[-(b/a)] - 2*ArcTan[((a - b)*Tanh[(c + d*x^n)/2])/Sqrt[a^2 - b^2]])*Log[((a + b)*(a - b + I*Sqrt[a^2 - b^2])*(1 + Tanh[(c + d*x^n)/2]))/(a*(a + b + I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^n)/2]))] + I*(PolyLog[2, ((b - I*Sqrt[a^2 - b^2])*(a + b - I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^n)/2]))/(a*(a + b + I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^n)/2]))] - PolyLog[2, ((b + I*Sqrt[a^2 - b^2])*(a + b - I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^n)/2]))/(a*(a + b + I*Sqrt[a^2 - b^2]*Tanh[(c + d*x^n)/2]))])))/(Sqrt[a^2 - b^2]*d^2*x^(2*n)))*Sech[c + d*x^n])/(2*a*e*n*(a + b*Sech[c + d*x^n]))","C",1
81,0,0,452,7.2195804,"\int \frac{(e x)^{-1+3 n}}{a+b \text{sech}\left(c+d x^n\right)} \, dx","Integrate[(e*x)^(-1 + 3*n)/(a + b*Sech[c + d*x^n]),x]","\int \frac{(e x)^{-1+3 n}}{a+b \text{sech}\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{b^2-a^2}}\right)}{a d^3 e n \sqrt{b^2-a^2}}-\frac{2 b x^{-3 n} (e x)^{3 n} \text{Li}_3\left(-\frac{a e^{d x^n+c}}{b+\sqrt{b^2-a^2}}\right)}{a d^3 e n \sqrt{b^2-a^2}}-\frac{2 b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b-\sqrt{b^2-a^2}}\right)}{a d^2 e n \sqrt{b^2-a^2}}+\frac{2 b x^{-2 n} (e x)^{3 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{b^2-a^2}}\right)}{a d^2 e n \sqrt{b^2-a^2}}-\frac{b x^{-n} (e x)^{3 n} \log \left(\frac{a e^{c+d x^n}}{b-\sqrt{b^2-a^2}}+1\right)}{a d e n \sqrt{b^2-a^2}}+\frac{b x^{-n} (e x)^{3 n} \log \left(\frac{a e^{c+d x^n}}{\sqrt{b^2-a^2}+b}+1\right)}{a d e n \sqrt{b^2-a^2}}+\frac{(e x)^{3 n}}{3 a e n}",1,"Integrate[(e*x)^(-1 + 3*n)/(a + b*Sech[c + d*x^n]), x]","F",-1
82,1,233,157,0.5982643,"\int \frac{(e x)^{-1+n}}{\left(a+b \text{sech}\left(c+d x^n\right)\right)^2} \, dx","Integrate[(e*x)^(-1 + n)/(a + b*Sech[c + d*x^n])^2,x]","\frac{x^{-n} (e x)^n \left(b \left(\left(a^2-b^2\right)^{3/2} \left(c+d x^n\right)+a b \sqrt{a^2-b^2} \sinh \left(c+d x^n\right)+\left(4 a^2 b-2 b^3\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{a^2-b^2}}\right)\right)+a \cosh \left(c+d x^n\right) \left(\left(a^2-b^2\right)^{3/2} \left(c+d x^n\right)+\left(4 a^2 b-2 b^3\right) \tan ^{-1}\left(\frac{(b-a) \tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{a^2-b^2}}\right)\right)\right)}{a^2 d e n (a-b) (a+b) \sqrt{a^2-b^2} \left(a \cosh \left(c+d x^n\right)+b\right)}","-\frac{2 b \left(2 a^2-b^2\right) x^{-n} (e x)^n \tan ^{-1}\left(\frac{\sqrt{a-b} \tanh \left(\frac{1}{2} \left(c+d x^n\right)\right)}{\sqrt{a+b}}\right)}{a^2 d e n (a-b)^{3/2} (a+b)^{3/2}}+\frac{b^2 x^{-n} (e x)^n \tanh \left(c+d x^n\right)}{a d e n \left(a^2-b^2\right) \left(a+b \text{sech}\left(c+d x^n\right)\right)}+\frac{(e x)^n}{a^2 e n}",1,"((e*x)^n*(a*((a^2 - b^2)^(3/2)*(c + d*x^n) + (4*a^2*b - 2*b^3)*ArcTan[((-a + b)*Tanh[(c + d*x^n)/2])/Sqrt[a^2 - b^2]])*Cosh[c + d*x^n] + b*((a^2 - b^2)^(3/2)*(c + d*x^n) + (4*a^2*b - 2*b^3)*ArcTan[((-a + b)*Tanh[(c + d*x^n)/2])/Sqrt[a^2 - b^2]] + a*b*Sqrt[a^2 - b^2]*Sinh[c + d*x^n])))/(a^2*(a - b)*(a + b)*Sqrt[a^2 - b^2]*d*e*n*x^n*(b + a*Cosh[c + d*x^n]))","A",1
83,1,542,717,30.8181385,"\int \frac{(e x)^{-1+2 n}}{\left(a+b \text{sech}\left(c+d x^n\right)\right)^2} \, dx","Integrate[(e*x)^(-1 + 2*n)/(a + b*Sech[c + d*x^n])^2,x]","\frac{x^{-2 n} (e x)^{2 n} \text{sech}^2\left(c+d x^n\right) \left(a \cosh \left(c+d x^n\right)+b\right) \left(\frac{2 b \left(a \cosh \left(c+d x^n\right)+b\right) \left(\frac{2 b e^{2 c} d x^n}{e^{2 c}+1}-\frac{\left(2 a^2-b^2\right) \text{Li}_2\left(\frac{a e^{d x^n+c}}{\sqrt{b^2-a^2}-b}\right)+\left(b^2-2 a^2\right) \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{b^2-a^2}}\right)+2 a^2 d x^n \log \left(\frac{a e^{c+d x^n}}{b-\sqrt{b^2-a^2}}+1\right)-b^2 d x^n \log \left(\frac{a e^{c+d x^n}}{b-\sqrt{b^2-a^2}}+1\right)-2 a^2 d x^n \log \left(\frac{a e^{c+d x^n}}{\sqrt{b^2-a^2}+b}+1\right)+b^2 d x^n \log \left(\frac{a e^{c+d x^n}}{\sqrt{b^2-a^2}+b}+1\right)+b \sqrt{b^2-a^2} \log \left(a e^{2 \left(c+d x^n\right)}+a+2 b e^{c+d x^n}\right)}{\sqrt{b^2-a^2}}\right)}{a^2-b^2}+\frac{2 b^2 d \tanh (c) x^n \left(a \cosh \left(c+d x^n\right)+b\right)}{b^2-a^2}+\frac{d x^n \left(a \cosh \left(c+d x^n\right)+b\right) \left(d \left(a^2-b^2\right) x^n+2 b^2 \tanh (c)\right)}{(a-b) (a+b)}+\frac{2 b^2 d \text{sech}(c) x^n \left(b \sinh (c)-a \sinh \left(d x^n\right)\right)}{(b-a) (a+b)}\right)}{2 a^2 d^2 e n \left(a+b \text{sech}\left(c+d x^n\right)\right)^2}","-\frac{2 b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b-\sqrt{b^2-a^2}}\right)}{a^2 d^2 e n \sqrt{b^2-a^2}}+\frac{2 b x^{-2 n} (e x)^{2 n} \text{Li}_2\left(-\frac{a e^{d x^n+c}}{b+\sqrt{b^2-a^2}}\right)}{a^2 d^2 e n \sqrt{b^2-a^2}}-\frac{b^2 x^{-2 n} (e x)^{2 n} \log \left(a \cosh \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{b^2-a^2}}+1\right)}{a^2 d e n \sqrt{b^2-a^2}}+\frac{2 b x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{\sqrt{b^2-a^2}+b}+1\right)}{a^2 d e n \sqrt{b^2-a^2}}+\frac{b^2 x^{-n} (e x)^{2 n} \sinh \left(c+d x^n\right)}{a d e n \left(a^2-b^2\right) \left(a \cosh \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{b^2-a^2}}\right)}{a^2 d^2 e n \left(b^2-a^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{b^2-a^2}}\right)}{a^2 d^2 e n \left(b^2-a^2\right)^{3/2}}+\frac{b^3 x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{b-\sqrt{b^2-a^2}}+1\right)}{a^2 d e n \left(b^2-a^2\right)^{3/2}}-\frac{b^3 x^{-n} (e x)^{2 n} \log \left(\frac{a e^{c+d x^n}}{\sqrt{b^2-a^2}+b}+1\right)}{a^2 d e n \left(b^2-a^2\right)^{3/2}}+\frac{(e x)^{2 n}}{2 a^2 e n}",1,"((e*x)^(2*n)*(b + a*Cosh[c + d*x^n])*Sech[c + d*x^n]^2*((2*b*(b + a*Cosh[c + d*x^n])*((2*b*d*E^(2*c)*x^n)/(1 + E^(2*c)) - (2*a^2*d*x^n*Log[1 + (a*E^(c + d*x^n))/(b - Sqrt[-a^2 + b^2])] - b^2*d*x^n*Log[1 + (a*E^(c + d*x^n))/(b - Sqrt[-a^2 + b^2])] - 2*a^2*d*x^n*Log[1 + (a*E^(c + d*x^n))/(b + Sqrt[-a^2 + b^2])] + b^2*d*x^n*Log[1 + (a*E^(c + d*x^n))/(b + Sqrt[-a^2 + b^2])] + b*Sqrt[-a^2 + b^2]*Log[a + 2*b*E^(c + d*x^n) + a*E^(2*(c + d*x^n))] + (2*a^2 - b^2)*PolyLog[2, (a*E^(c + d*x^n))/(-b + Sqrt[-a^2 + b^2])] + (-2*a^2 + b^2)*PolyLog[2, -((a*E^(c + d*x^n))/(b + Sqrt[-a^2 + b^2]))])/Sqrt[-a^2 + b^2]))/(a^2 - b^2) + (2*b^2*d*x^n*Sech[c]*(b*Sinh[c] - a*Sinh[d*x^n]))/((-a + b)*(a + b)) + (2*b^2*d*x^n*(b + a*Cosh[c + d*x^n])*Tanh[c])/(-a^2 + b^2) + (d*x^n*(b + a*Cosh[c + d*x^n])*((a^2 - b^2)*d*x^n + 2*b^2*Tanh[c]))/((a - b)*(a + b))))/(2*a^2*d^2*e*n*x^(2*n)*(a + b*Sech[c + d*x^n])^2)","A",1
84,0,0,1284,117.9108759,"\int \frac{(e x)^{-1+3 n}}{\left(a+b \text{sech}\left(c+d x^n\right)\right)^2} \, dx","Integrate[(e*x)^(-1 + 3*n)/(a + b*Sech[c + d*x^n])^2,x]","\int \frac{(e x)^{-1+3 n}}{\left(a+b \text{sech}\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{b^2-a^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{b^2-a^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{b^2-a^2}}\right) x^{-3 n}}{a^2 \sqrt{b^2-a^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{b^2-a^2}}\right) x^{-3 n}}{a^2 \left(b^2-a^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{b^2-a^2}}\right) x^{-3 n}}{a^2 \sqrt{b^2-a^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{b^2-a^2}}\right) x^{-3 n}}{a^2 \left(b^2-a^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{b^2-a^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{b^2-a^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{b^2-a^2}}\right) x^{-2 n}}{a^2 \sqrt{b^2-a^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{b^2-a^2}}\right) x^{-2 n}}{a^2 \left(b^2-a^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{b^2-a^2}}\right) x^{-2 n}}{a^2 \sqrt{b^2-a^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{b^2-a^2}}\right) x^{-2 n}}{a^2 \left(b^2-a^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{b^2-a^2}}+1\right) x^{-n}}{a^2 \sqrt{b^2-a^2} d e n}+\frac{b^3 (e x)^{3 n} \log \left(\frac{e^{d x^n+c} a}{b-\sqrt{b^2-a^2}}+1\right) x^{-n}}{a^2 \left(b^2-a^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{b^2-a^2}}+1\right) x^{-n}}{a^2 \sqrt{b^2-a^2} d e n}-\frac{b^3 (e x)^{3 n} \log \left(\frac{e^{d x^n+c} a}{b+\sqrt{b^2-a^2}}+1\right) x^{-n}}{a^2 \left(b^2-a^2\right)^{3/2} d e n}+\frac{b^2 (e x)^{3 n} \sinh \left(d x^n+c\right) x^{-n}}{a \left(a^2-b^2\right) d e n \left(b+a \cosh \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*Sech[c + d*x^n])^2, x]","F",-1