1,1,76,91,0.3495915,"\int (c+d x)^4 \sinh (a+b x) \, dx","Integrate[(c + d*x)^4*Sinh[a + b*x],x]","\frac{\cosh (a+b x) \left(b^4 (c+d x)^4+12 b^2 d^2 (c+d x)^2+24 d^4\right)-4 b d (c+d x) \sinh (a+b x) \left(b^2 (c+d x)^2+6 d^2\right)}{b^5}","\frac{24 d^4 \cosh (a+b x)}{b^5}-\frac{24 d^3 (c+d x) \sinh (a+b x)}{b^4}+\frac{12 d^2 (c+d x)^2 \cosh (a+b x)}{b^3}-\frac{4 d (c+d x)^3 \sinh (a+b x)}{b^2}+\frac{(c+d x)^4 \cosh (a+b x)}{b}",1,"((24*d^4 + 12*b^2*d^2*(c + d*x)^2 + b^4*(c + d*x)^4)*Cosh[a + b*x] - 4*b*d*(c + d*x)*(6*d^2 + b^2*(c + d*x)^2)*Sinh[a + b*x])/b^5","A",1
2,1,61,70,0.184927,"\int (c+d x)^3 \sinh (a+b x) \, dx","Integrate[(c + d*x)^3*Sinh[a + b*x],x]","\frac{b (c+d x) \cosh (a+b x) \left(b^2 (c+d x)^2+6 d^2\right)-3 d \sinh (a+b x) \left(b^2 (c+d x)^2+2 d^2\right)}{b^4}","-\frac{6 d^3 \sinh (a+b x)}{b^4}+\frac{6 d^2 (c+d x) \cosh (a+b x)}{b^3}-\frac{3 d (c+d x)^2 \sinh (a+b x)}{b^2}+\frac{(c+d x)^3 \cosh (a+b x)}{b}",1,"(b*(c + d*x)*(6*d^2 + b^2*(c + d*x)^2)*Cosh[a + b*x] - 3*d*(2*d^2 + b^2*(c + d*x)^2)*Sinh[a + b*x])/b^4","A",1
3,1,44,49,0.1326987,"\int (c+d x)^2 \sinh (a+b x) \, dx","Integrate[(c + d*x)^2*Sinh[a + b*x],x]","\frac{\cosh (a+b x) \left(b^2 (c+d x)^2+2 d^2\right)-2 b d (c+d x) \sinh (a+b x)}{b^3}","\frac{2 d^2 \cosh (a+b x)}{b^3}-\frac{2 d (c+d x) \sinh (a+b x)}{b^2}+\frac{(c+d x)^2 \cosh (a+b x)}{b}",1,"((2*d^2 + b^2*(c + d*x)^2)*Cosh[a + b*x] - 2*b*d*(c + d*x)*Sinh[a + b*x])/b^3","A",1
4,1,27,28,0.0527912,"\int (c+d x) \sinh (a+b x) \, dx","Integrate[(c + d*x)*Sinh[a + b*x],x]","\frac{b (c+d x) \cosh (a+b x)-d \sinh (a+b x)}{b^2}","\frac{(c+d x) \cosh (a+b x)}{b}-\frac{d \sinh (a+b x)}{b^2}",1,"(b*(c + d*x)*Cosh[a + b*x] - d*Sinh[a + b*x])/b^2","A",1
5,1,49,51,0.0721756,"\int \frac{\sinh (a+b x)}{c+d x} \, dx","Integrate[Sinh[a + b*x]/(c + d*x),x]","\frac{\sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)+\cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{d}","\frac{\sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{d}+\frac{\cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{d}",1,"(CoshIntegral[(b*c)/d + b*x]*Sinh[a - (b*c)/d] + Cosh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/d","A",1
6,1,65,71,0.1912019,"\int \frac{\sinh (a+b x)}{(c+d x)^2} \, dx","Integrate[Sinh[a + b*x]/(c + d*x)^2,x]","\frac{b \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(b \left(\frac{c}{d}+x\right)\right)+b \sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(b \left(\frac{c}{d}+x\right)\right)-\frac{d \sinh (a+b x)}{c+d x}}{d^2}","\frac{b \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{d^2}+\frac{b \sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{d^2}-\frac{\sinh (a+b x)}{d (c+d x)}",1,"(b*Cosh[a - (b*c)/d]*CoshIntegral[b*(c/d + x)] - (d*Sinh[a + b*x])/(c + d*x) + b*Sinh[a - (b*c)/d]*SinhIntegral[b*(c/d + x)])/d^2","A",1
7,1,88,104,0.4460312,"\int \frac{\sinh (a+b x)}{(c+d x)^3} \, dx","Integrate[Sinh[a + b*x]/(c + d*x)^3,x]","\frac{b^2 \sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(b \left(\frac{c}{d}+x\right)\right)+b^2 \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(b \left(\frac{c}{d}+x\right)\right)-\frac{d (b (c+d x) \cosh (a+b x)+d \sinh (a+b x))}{(c+d x)^2}}{2 d^3}","\frac{b^2 \sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{2 d^3}+\frac{b^2 \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{2 d^3}-\frac{b \cosh (a+b x)}{2 d^2 (c+d x)}-\frac{\sinh (a+b x)}{2 d (c+d x)^2}",1,"(b^2*CoshIntegral[b*(c/d + x)]*Sinh[a - (b*c)/d] - (d*(b*(c + d*x)*Cosh[a + b*x] + d*Sinh[a + b*x]))/(c + d*x)^2 + b^2*Cosh[a - (b*c)/d]*SinhIntegral[b*(c/d + x)])/(2*d^3)","A",1
8,1,132,162,0.5831656,"\int (c+d x)^4 \sinh ^2(a+b x) \, dx","Integrate[(c + d*x)^4*Sinh[a + b*x]^2,x]","\frac{-20 b d (c+d x) \cosh (2 (a+b x)) \left(2 b^2 (c+d x)^2+3 d^2\right)+10 \sinh (2 (a+b x)) \left(2 b^4 (c+d x)^4+6 b^2 d^2 (c+d x)^2+3 d^4\right)-8 b^5 x \left(5 c^4+10 c^3 d x+10 c^2 d^2 x^2+5 c d^3 x^3+d^4 x^4\right)}{80 b^5}","\frac{3 d^4 \sinh (a+b x) \cosh (a+b x)}{4 b^5}-\frac{3 d^3 (c+d x) \sinh ^2(a+b x)}{2 b^4}+\frac{3 d^2 (c+d x)^2 \sinh (a+b x) \cosh (a+b x)}{2 b^3}-\frac{d (c+d x)^3 \sinh ^2(a+b x)}{b^2}+\frac{(c+d x)^4 \sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{3 d^4 x}{4 b^4}-\frac{d (c+d x)^3}{2 b^2}-\frac{(c+d x)^5}{10 d}",1,"(-8*b^5*x*(5*c^4 + 10*c^3*d*x + 10*c^2*d^2*x^2 + 5*c*d^3*x^3 + d^4*x^4) - 20*b*d*(c + d*x)*(3*d^2 + 2*b^2*(c + d*x)^2)*Cosh[2*(a + b*x)] + 10*(3*d^4 + 6*b^2*d^2*(c + d*x)^2 + 2*b^4*(c + d*x)^4)*Sinh[2*(a + b*x)])/(80*b^5)","A",1
9,1,104,134,0.3347969,"\int (c+d x)^3 \sinh ^2(a+b x) \, dx","Integrate[(c + d*x)^3*Sinh[a + b*x]^2,x]","\frac{2 b (c+d x) \sinh (2 (a+b x)) \left(2 b^2 (c+d x)^2+3 d^2\right)-3 d \cosh (2 (a+b x)) \left(2 b^2 (c+d x)^2+d^2\right)-2 b^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)}{16 b^4}","-\frac{3 d^3 \sinh ^2(a+b x)}{8 b^4}+\frac{3 d^2 (c+d x) \sinh (a+b x) \cosh (a+b x)}{4 b^3}-\frac{3 d (c+d x)^2 \sinh ^2(a+b x)}{4 b^2}+\frac{(c+d x)^3 \sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{3 c d^2 x}{4 b^2}-\frac{3 d^3 x^2}{8 b^2}-\frac{(c+d x)^4}{8 d}",1,"(-2*b^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) - 3*d*(d^2 + 2*b^2*(c + d*x)^2)*Cosh[2*(a + b*x)] + 2*b*(c + d*x)*(3*d^2 + 2*b^2*(c + d*x)^2)*Sinh[2*(a + b*x)])/(16*b^4)","A",1
10,1,75,95,0.2450272,"\int (c+d x)^2 \sinh ^2(a+b x) \, dx","Integrate[(c + d*x)^2*Sinh[a + b*x]^2,x]","\frac{3 \sinh (2 (a+b x)) \left(2 b^2 (c+d x)^2+d^2\right)-6 b d (c+d x) \cosh (2 (a+b x))-4 b^3 x \left(3 c^2+3 c d x+d^2 x^2\right)}{24 b^3}","\frac{d^2 \sinh (a+b x) \cosh (a+b x)}{4 b^3}-\frac{d (c+d x) \sinh ^2(a+b x)}{2 b^2}+\frac{(c+d x)^2 \sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{d^2 x}{4 b^2}-\frac{(c+d x)^3}{6 d}",1,"(-4*b^3*x*(3*c^2 + 3*c*d*x + d^2*x^2) - 6*b*d*(c + d*x)*Cosh[2*(a + b*x)] + 3*(d^2 + 2*b^2*(c + d*x)^2)*Sinh[2*(a + b*x)])/(24*b^3)","A",1
11,1,52,55,0.1372574,"\int (c+d x) \sinh ^2(a+b x) \, dx","Integrate[(c + d*x)*Sinh[a + b*x]^2,x]","\frac{2 b ((c+d x) \sinh (2 (a+b x))-2 a c-b x (2 c+d x))-d \cosh (2 (a+b x))}{8 b^2}","-\frac{d \sinh ^2(a+b x)}{4 b^2}+\frac{(c+d x) \sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{c x}{2}-\frac{d x^2}{4}",1,"(-(d*Cosh[2*(a + b*x)]) + 2*b*(-2*a*c - b*x*(2*c + d*x) + (c + d*x)*Sinh[2*(a + b*x)]))/(8*b^2)","A",1
12,1,66,78,0.106353,"\int \frac{\sinh ^2(a+b x)}{c+d x} \, dx","Integrate[Sinh[a + b*x]^2/(c + d*x),x]","\frac{\cosh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b (c+d x)}{d}\right)+\sinh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b (c+d x)}{d}\right)-\log (c+d x)}{2 d}","\frac{\cosh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\sinh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}-\frac{\log (c+d x)}{2 d}",1,"(Cosh[2*a - (2*b*c)/d]*CoshIntegral[(2*b*(c + d*x))/d] - Log[c + d*x] + Sinh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*(c + d*x))/d])/(2*d)","A",1
13,1,75,81,0.358669,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^2} \, dx","Integrate[Sinh[a + b*x]^2/(c + d*x)^2,x]","\frac{b \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b (c+d x)}{d}\right)+b \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b (c+d x)}{d}\right)-\frac{d \sinh ^2(a+b x)}{c+d x}}{d^2}","\frac{b \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}+\frac{b \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}-\frac{\sinh ^2(a+b x)}{d (c+d x)}",1,"(b*CoshIntegral[(2*b*(c + d*x))/d]*Sinh[2*a - (2*b*c)/d] - (d*Sinh[a + b*x]^2)/(c + d*x) + b*Cosh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*(c + d*x))/d])/d^2","A",1
14,1,102,112,0.7668649,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^3} \, dx","Integrate[Sinh[a + b*x]^2/(c + d*x)^3,x]","\frac{2 b^2 \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b (c+d x)}{d}\right)+2 b^2 \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b (c+d x)}{d}\right)-\frac{d \left(b (c+d x) \sinh (2 (a+b x))+d \sinh ^2(a+b x)\right)}{(c+d x)^2}}{2 d^3}","\frac{b^2 \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}+\frac{b^2 \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}-\frac{b \sinh (a+b x) \cosh (a+b x)}{d^2 (c+d x)}-\frac{\sinh ^2(a+b x)}{2 d (c+d x)^2}",1,"(2*b^2*Cosh[2*a - (2*b*c)/d]*CoshIntegral[(2*b*(c + d*x))/d] - (d*(d*Sinh[a + b*x]^2 + b*(c + d*x)*Sinh[2*(a + b*x)]))/(c + d*x)^2 + 2*b^2*Sinh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*(c + d*x))/d])/(2*d^3)","A",1
15,1,123,162,0.7555878,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^4} \, dx","Integrate[Sinh[a + b*x]^2/(c + d*x)^4,x]","\frac{4 b^3 \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b (c+d x)}{d}\right)+4 b^3 \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b (c+d x)}{d}\right)-\frac{d \left(\cosh (2 (a+b x)) \left(2 b^2 (c+d x)^2+d^2\right)+d (b (c+d x) \sinh (2 (a+b x))-d)\right)}{(c+d x)^3}}{6 d^4}","\frac{2 b^3 \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b c}{d}+2 b x\right)}{3 d^4}+\frac{2 b^3 \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b c}{d}+2 b x\right)}{3 d^4}-\frac{2 b^2 \sinh ^2(a+b x)}{3 d^3 (c+d x)}-\frac{b \sinh (a+b x) \cosh (a+b x)}{3 d^2 (c+d x)^2}-\frac{\sinh ^2(a+b x)}{3 d (c+d x)^3}-\frac{b^2}{3 d^3 (c+d x)}",1,"(4*b^3*CoshIntegral[(2*b*(c + d*x))/d]*Sinh[2*a - (2*b*c)/d] - (d*((d^2 + 2*b^2*(c + d*x)^2)*Cosh[2*(a + b*x)] + d*(-d + b*(c + d*x)*Sinh[2*(a + b*x)])))/(c + d*x)^3 + 4*b^3*Cosh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*(c + d*x))/d])/(6*d^4)","A",1
16,1,150,225,0.8724814,"\int (c+d x)^4 \sinh ^3(a+b x) \, dx","Integrate[(c + d*x)^4*Sinh[a + b*x]^3,x]","\frac{-24 b d (c+d x) \sinh (a+b x) \left(\cosh (2 (a+b x)) \left(3 b^2 (c+d x)^2+2 d^2\right)-39 b^2 (c+d x)^2-242 d^2\right)-243 \cosh (a+b x) \left(b^4 (c+d x)^4+12 b^2 d^2 (c+d x)^2+24 d^4\right)+\cosh (3 (a+b x)) \left(27 b^4 (c+d x)^4+36 b^2 d^2 (c+d x)^2+8 d^4\right)}{324 b^5}","\frac{8 d^4 \cosh ^3(a+b x)}{81 b^5}-\frac{488 d^4 \cosh (a+b x)}{27 b^5}-\frac{8 d^3 (c+d x) \sinh ^3(a+b x)}{27 b^4}+\frac{160 d^3 (c+d x) \sinh (a+b x)}{9 b^4}-\frac{80 d^2 (c+d x)^2 \cosh (a+b x)}{9 b^3}+\frac{4 d^2 (c+d x)^2 \sinh ^2(a+b x) \cosh (a+b x)}{9 b^3}-\frac{4 d (c+d x)^3 \sinh ^3(a+b x)}{9 b^2}+\frac{8 d (c+d x)^3 \sinh (a+b x)}{3 b^2}-\frac{2 (c+d x)^4 \cosh (a+b x)}{3 b}+\frac{(c+d x)^4 \sinh ^2(a+b x) \cosh (a+b x)}{3 b}",1,"(-243*(24*d^4 + 12*b^2*d^2*(c + d*x)^2 + b^4*(c + d*x)^4)*Cosh[a + b*x] + (8*d^4 + 36*b^2*d^2*(c + d*x)^2 + 27*b^4*(c + d*x)^4)*Cosh[3*(a + b*x)] - 24*b*d*(c + d*x)*(-242*d^2 - 39*b^2*(c + d*x)^2 + (2*d^2 + 3*b^2*(c + d*x)^2)*Cosh[2*(a + b*x)])*Sinh[a + b*x])/(324*b^5)","A",1
17,1,127,175,0.8355102,"\int (c+d x)^3 \sinh ^3(a+b x) \, dx","Integrate[(c + d*x)^3*Sinh[a + b*x]^3,x]","\frac{-162 b (c+d x) \cosh (a+b x) \left(b^2 (c+d x)^2+6 d^2\right)+6 b (c+d x) \cosh (3 (a+b x)) \left(3 b^2 (c+d x)^2+2 d^2\right)-4 d \sinh (a+b x) \left(\cosh (2 (a+b x)) \left(9 b^2 (c+d x)^2+2 d^2\right)-117 b^2 (c+d x)^2-242 d^2\right)}{216 b^4}","-\frac{2 d^3 \sinh ^3(a+b x)}{27 b^4}+\frac{40 d^3 \sinh (a+b x)}{9 b^4}-\frac{40 d^2 (c+d x) \cosh (a+b x)}{9 b^3}+\frac{2 d^2 (c+d x) \sinh ^2(a+b x) \cosh (a+b x)}{9 b^3}-\frac{d (c+d x)^2 \sinh ^3(a+b x)}{3 b^2}+\frac{2 d (c+d x)^2 \sinh (a+b x)}{b^2}-\frac{2 (c+d x)^3 \cosh (a+b x)}{3 b}+\frac{(c+d x)^3 \sinh ^2(a+b x) \cosh (a+b x)}{3 b}",1,"(-162*b*(c + d*x)*(6*d^2 + b^2*(c + d*x)^2)*Cosh[a + b*x] + 6*b*(c + d*x)*(2*d^2 + 3*b^2*(c + d*x)^2)*Cosh[3*(a + b*x)] - 4*d*(-242*d^2 - 117*b^2*(c + d*x)^2 + (2*d^2 + 9*b^2*(c + d*x)^2)*Cosh[2*(a + b*x)])*Sinh[a + b*x])/(216*b^4)","A",1
18,1,86,123,0.3286466,"\int (c+d x)^2 \sinh ^3(a+b x) \, dx","Integrate[(c + d*x)^2*Sinh[a + b*x]^3,x]","\frac{-81 \cosh (a+b x) \left(b^2 (c+d x)^2+2 d^2\right)+\cosh (3 (a+b x)) \left(9 b^2 (c+d x)^2+2 d^2\right)-6 b d (c+d x) (\sinh (3 (a+b x))-27 \sinh (a+b x))}{108 b^3}","\frac{2 d^2 \cosh ^3(a+b x)}{27 b^3}-\frac{14 d^2 \cosh (a+b x)}{9 b^3}-\frac{2 d (c+d x) \sinh ^3(a+b x)}{9 b^2}+\frac{4 d (c+d x) \sinh (a+b x)}{3 b^2}-\frac{2 (c+d x)^2 \cosh (a+b x)}{3 b}+\frac{(c+d x)^2 \sinh ^2(a+b x) \cosh (a+b x)}{3 b}",1,"(-81*(2*d^2 + b^2*(c + d*x)^2)*Cosh[a + b*x] + (2*d^2 + 9*b^2*(c + d*x)^2)*Cosh[3*(a + b*x)] - 6*b*d*(c + d*x)*(-27*Sinh[a + b*x] + Sinh[3*(a + b*x)]))/(108*b^3)","A",1
19,1,59,75,0.1614493,"\int (c+d x) \sinh ^3(a+b x) \, dx","Integrate[(c + d*x)*Sinh[a + b*x]^3,x]","\frac{-27 b (c+d x) \cosh (a+b x)+3 b (c+d x) \cosh (3 (a+b x))+d (27 \sinh (a+b x)-\sinh (3 (a+b x)))}{36 b^2}","-\frac{d \sinh ^3(a+b x)}{9 b^2}+\frac{2 d \sinh (a+b x)}{3 b^2}-\frac{2 (c+d x) \cosh (a+b x)}{3 b}+\frac{(c+d x) \sinh ^2(a+b x) \cosh (a+b x)}{3 b}",1,"(-27*b*(c + d*x)*Cosh[a + b*x] + 3*b*(c + d*x)*Cosh[3*(a + b*x)] + d*(27*Sinh[a + b*x] - Sinh[3*(a + b*x)]))/(36*b^2)","A",1
20,1,102,121,0.18841,"\int \frac{\sinh ^3(a+b x)}{c+d x} \, dx","Integrate[Sinh[a + b*x]^3/(c + d*x),x]","\frac{\sinh \left(3 a-\frac{3 b c}{d}\right) \text{Chi}\left(\frac{3 b (c+d x)}{d}\right)-3 \sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(b \left(\frac{c}{d}+x\right)\right)-3 \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(b \left(\frac{c}{d}+x\right)\right)+\cosh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b (c+d x)}{d}\right)}{4 d}","\frac{\sinh \left(3 a-\frac{3 b c}{d}\right) \text{Chi}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}-\frac{3 \sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{4 d}-\frac{3 \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{\cosh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}",1,"(CoshIntegral[(3*b*(c + d*x))/d]*Sinh[3*a - (3*b*c)/d] - 3*CoshIntegral[b*(c/d + x)]*Sinh[a - (b*c)/d] - 3*Cosh[a - (b*c)/d]*SinhIntegral[b*(c/d + x)] + Cosh[3*a - (3*b*c)/d]*SinhIntegral[(3*b*(c + d*x))/d])/(4*d)","A",1
21,1,160,145,0.9678622,"\int \frac{\sinh ^3(a+b x)}{(c+d x)^2} \, dx","Integrate[Sinh[a + b*x]^3/(c + d*x)^2,x]","\frac{6 b (c+d x) \left(-\cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(b \left(\frac{c}{d}+x\right)\right)+\cosh \left(3 a-\frac{3 b c}{d}\right) \text{Chi}\left(\frac{3 b (c+d x)}{d}\right)-\sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(b \left(\frac{c}{d}+x\right)\right)+\sinh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b (c+d x)}{d}\right)\right)+6 d \sinh (a) \cosh (b x)-2 d \sinh (3 a) \cosh (3 b x)+6 d \cosh (a) \sinh (b x)-2 d \cosh (3 a) \sinh (3 b x)}{8 d^2 (c+d x)}","-\frac{3 b \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{4 d^2}+\frac{3 b \cosh \left(3 a-\frac{3 b c}{d}\right) \text{Chi}\left(\frac{3 b c}{d}+3 b x\right)}{4 d^2}-\frac{3 b \sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{4 d^2}+\frac{3 b \sinh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b c}{d}+3 b x\right)}{4 d^2}-\frac{\sinh ^3(a+b x)}{d (c+d x)}",1,"(6*d*Cosh[b*x]*Sinh[a] - 2*d*Cosh[3*b*x]*Sinh[3*a] + 6*d*Cosh[a]*Sinh[b*x] - 2*d*Cosh[3*a]*Sinh[3*b*x] + 6*b*(c + d*x)*(-(Cosh[a - (b*c)/d]*CoshIntegral[b*(c/d + x)]) + Cosh[3*a - (3*b*c)/d]*CoshIntegral[(3*b*(c + d*x))/d] - Sinh[a - (b*c)/d]*SinhIntegral[b*(c/d + x)] + Sinh[3*a - (3*b*c)/d]*SinhIntegral[(3*b*(c + d*x))/d]))/(8*d^2*(c + d*x))","A",1
22,1,220,184,0.6902823,"\int \frac{\sinh ^3(a+b x)}{(c+d x)^3} \, dx","Integrate[Sinh[a + b*x]^3/(c + d*x)^3,x]","\frac{6 b^2 (c+d x)^2 \left(3 \sinh \left(3 a-\frac{3 b c}{d}\right) \text{Chi}\left(\frac{3 b (c+d x)}{d}\right)-\sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(b \left(\frac{c}{d}+x\right)\right)-\cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(b \left(\frac{c}{d}+x\right)\right)+3 \cosh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b (c+d x)}{d}\right)\right)+6 d \cosh (b x) (b \cosh (a) (c+d x)+d \sinh (a))-2 d \cosh (3 b x) (3 b \cosh (3 a) (c+d x)+d \sinh (3 a))+6 d \sinh (b x) (b \sinh (a) (c+d x)+d \cosh (a))-2 d \sinh (3 b x) (3 b \sinh (3 a) (c+d x)+d \cosh (3 a))}{16 d^3 (c+d x)^2}","\frac{9 b^2 \sinh \left(3 a-\frac{3 b c}{d}\right) \text{Chi}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^3}-\frac{3 b^2 \sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{8 d^3}-\frac{3 b^2 \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{8 d^3}+\frac{9 b^2 \cosh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b c}{d}+3 b x\right)}{8 d^3}-\frac{3 b \sinh ^2(a+b x) \cosh (a+b x)}{2 d^2 (c+d x)}-\frac{\sinh ^3(a+b x)}{2 d (c+d x)^2}",1,"(6*d*Cosh[b*x]*(b*(c + d*x)*Cosh[a] + d*Sinh[a]) - 2*d*Cosh[3*b*x]*(3*b*(c + d*x)*Cosh[3*a] + d*Sinh[3*a]) + 6*d*(d*Cosh[a] + b*(c + d*x)*Sinh[a])*Sinh[b*x] - 2*d*(d*Cosh[3*a] + 3*b*(c + d*x)*Sinh[3*a])*Sinh[3*b*x] + 6*b^2*(c + d*x)^2*(3*CoshIntegral[(3*b*(c + d*x))/d]*Sinh[3*a - (3*b*c)/d] - CoshIntegral[b*(c/d + x)]*Sinh[a - (b*c)/d] - Cosh[a - (b*c)/d]*SinhIntegral[b*(c/d + x)] + 3*Cosh[3*a - (3*b*c)/d]*SinhIntegral[(3*b*(c + d*x))/d]))/(16*d^3*(c + d*x)^2)","A",1
23,1,191,149,2.6480744,"\int (c+d x)^3 \text{csch}(a+b x) \, dx","Integrate[(c + d*x)^3*Csch[a + b*x],x]","\frac{-2 b^3 (c+d x)^3 \tanh ^{-1}(\sinh (a+b x)+\cosh (a+b x))-3 d \left(b^2 (c+d x)^2 \text{Li}_2(-\cosh (a+b x)-\sinh (a+b x))-2 b d (c+d x) \text{Li}_3(-\cosh (a+b x)-\sinh (a+b x))+2 d^2 \text{Li}_4(-\cosh (a+b x)-\sinh (a+b x))\right)+3 d \left(b^2 (c+d x)^2 \text{Li}_2(\cosh (a+b x)+\sinh (a+b x))-2 b d (c+d x) \text{Li}_3(\cosh (a+b x)+\sinh (a+b x))+2 d^2 \text{Li}_4(\cosh (a+b x)+\sinh (a+b x))\right)}{b^4}","-\frac{6 d^3 \text{Li}_4\left(-e^{a+b x}\right)}{b^4}+\frac{6 d^3 \text{Li}_4\left(e^{a+b x}\right)}{b^4}+\frac{6 d^2 (c+d x) \text{Li}_3\left(-e^{a+b x}\right)}{b^3}-\frac{6 d^2 (c+d x) \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{3 d (c+d x)^2 \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{3 d (c+d x)^2 \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(-2*b^3*(c + d*x)^3*ArcTanh[Cosh[a + b*x] + Sinh[a + b*x]] - 3*d*(b^2*(c + d*x)^2*PolyLog[2, -Cosh[a + b*x] - Sinh[a + b*x]] - 2*b*d*(c + d*x)*PolyLog[3, -Cosh[a + b*x] - Sinh[a + b*x]] + 2*d^2*PolyLog[4, -Cosh[a + b*x] - Sinh[a + b*x]]) + 3*d*(b^2*(c + d*x)^2*PolyLog[2, Cosh[a + b*x] + Sinh[a + b*x]] - 2*b*d*(c + d*x)*PolyLog[3, Cosh[a + b*x] + Sinh[a + b*x]] + 2*d^2*PolyLog[4, Cosh[a + b*x] + Sinh[a + b*x]]))/b^4","A",0
24,1,118,99,1.9635002,"\int (c+d x)^2 \text{csch}(a+b x) \, dx","Integrate[(c + d*x)^2*Csch[a + b*x],x]","\frac{-\frac{2 d \left(b (c+d x) \text{Li}_2\left(-e^{a+b x}\right)-d \text{Li}_3\left(-e^{a+b x}\right)\right)}{b^2}+\frac{2 d \left(b (c+d x) \text{Li}_2\left(e^{a+b x}\right)-d \text{Li}_3\left(e^{a+b x}\right)\right)}{b^2}+(c+d x)^2 \log \left(1-e^{a+b x}\right)-(c+d x)^2 \log \left(e^{a+b x}+1\right)}{b}","\frac{2 d^2 \text{Li}_3\left(-e^{a+b x}\right)}{b^3}-\frac{2 d^2 \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{2 d (c+d x) \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{2 d (c+d x) \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"((c + d*x)^2*Log[1 - E^(a + b*x)] - (c + d*x)^2*Log[1 + E^(a + b*x)] - (2*d*(b*(c + d*x)*PolyLog[2, -E^(a + b*x)] - d*PolyLog[3, -E^(a + b*x)]))/b^2 + (2*d*(b*(c + d*x)*PolyLog[2, E^(a + b*x)] - d*PolyLog[3, E^(a + b*x)]))/b^2)/b","A",1
25,1,174,50,0.0560537,"\int (c+d x) \text{csch}(a+b x) \, dx","Integrate[(c + d*x)*Csch[a + b*x],x]","\frac{d \left(-a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)-i \left(i \left(\text{Li}_2\left(-e^{i (i a+i b x)}\right)-\text{Li}_2\left(e^{i (i a+i b x)}\right)\right)+(i a+i b x) \left(\log \left(1-e^{i (i a+i b x)}\right)-\log \left(1+e^{i (i a+i b x)}\right)\right)\right)\right)}{b^2}+\frac{c \log \left(\sinh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}-\frac{c \log \left(\cosh \left(\frac{a}{2}+\frac{b x}{2}\right)\right)}{b}","-\frac{d \text{Li}_2\left(-e^{a+b x}\right)}{b^2}+\frac{d \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{2 (c+d x) \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"-((c*Log[Cosh[a/2 + (b*x)/2]])/b) + (c*Log[Sinh[a/2 + (b*x)/2]])/b + (d*(-(a*Log[Tanh[(a + b*x)/2]]) - I*((I*a + I*b*x)*(Log[1 - E^(I*(I*a + I*b*x))] - Log[1 + E^(I*(I*a + I*b*x))]) + I*(PolyLog[2, -E^(I*(I*a + I*b*x))] - PolyLog[2, E^(I*(I*a + I*b*x))]))))/b^2","C",1
26,0,0,17,10.7083222,"\int \frac{\text{csch}(a+b x)}{c+d x} \, dx","Integrate[Csch[a + b*x]/(c + d*x),x]","\int \frac{\text{csch}(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{csch}(a+b x)}{c+d x},x\right)",0,"Integrate[Csch[a + b*x]/(c + d*x), x]","A",-1
27,0,0,17,10.5230221,"\int \frac{\text{csch}(a+b x)}{(c+d x)^2} \, dx","Integrate[Csch[a + b*x]/(c + d*x)^2,x]","\int \frac{\text{csch}(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{csch}(a+b x)}{(c+d x)^2},x\right)",0,"Integrate[Csch[a + b*x]/(c + d*x)^2, x]","A",-1
28,1,185,103,1.9716095,"\int (c+d x)^3 \text{csch}^2(a+b x) \, dx","Integrate[(c + d*x)^3*Csch[a + b*x]^2,x]","\frac{-\frac{2 b^3 (c+d x)^3}{e^{2 a}-1}+b^3 \text{csch}(a) \sinh (b x) (c+d x)^3 \text{csch}(a+b x)+3 b^2 d (c+d x)^2 \log \left(1-e^{-a-b x}\right)+3 b^2 d (c+d x)^2 \log \left(e^{-a-b x}+1\right)-6 d^2 \left(b (c+d x) \text{Li}_2\left(-e^{-a-b x}\right)+d \text{Li}_3\left(-e^{-a-b x}\right)\right)-6 d^2 \left(b (c+d x) \text{Li}_2\left(e^{-a-b x}\right)+d \text{Li}_3\left(e^{-a-b x}\right)\right)}{b^4}","-\frac{3 d^3 \text{Li}_3\left(e^{2 (a+b x)}\right)}{2 b^4}+\frac{3 d^2 (c+d x) \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^3}+\frac{3 d (c+d x)^2 \log \left(1-e^{2 (a+b x)}\right)}{b^2}-\frac{(c+d x)^3 \coth (a+b x)}{b}-\frac{(c+d x)^3}{b}",1,"((-2*b^3*(c + d*x)^3)/(-1 + E^(2*a)) + 3*b^2*d*(c + d*x)^2*Log[1 - E^(-a - b*x)] + 3*b^2*d*(c + d*x)^2*Log[1 + E^(-a - b*x)] - 6*d^2*(b*(c + d*x)*PolyLog[2, -E^(-a - b*x)] + d*PolyLog[3, -E^(-a - b*x)]) - 6*d^2*(b*(c + d*x)*PolyLog[2, E^(-a - b*x)] + d*PolyLog[3, E^(-a - b*x)]) + b^3*(c + d*x)^3*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b^4","A",1
29,1,198,74,4.7975994,"\int (c+d x)^2 \text{csch}^2(a+b x) \, dx","Integrate[(c + d*x)^2*Csch[a + b*x]^2,x]","\frac{\text{csch}(a) \left(b^2 \sinh (b x) (c+d x)^2 \text{csch}(a+b x)+d^2 \left(-b^2 x^2 \cosh (a) e^{-\tanh ^{-1}(\tanh (a))} \sqrt{\text{sech}^2(a)}-\sinh (a) \text{Li}_2\left(e^{-2 \left(b x+\tanh ^{-1}(\tanh (a))\right)}\right)+i \pi  b x \sinh (a)-i \pi  \sinh (a) \log \left(e^{2 b x}+1\right)+2 b x \sinh (a) \log \left(1-e^{-2 \left(\tanh ^{-1}(\tanh (a))+b x\right)}\right)+2 \sinh (a) \tanh ^{-1}(\tanh (a)) \left(\log \left(1-e^{-2 \left(\tanh ^{-1}(\tanh (a))+b x\right)}\right)-\log \left(i \sinh \left(\tanh ^{-1}(\tanh (a))+b x\right)\right)+b x\right)+i \pi  \sinh (a) \log (\cosh (b x))\right)-2 b c d (b x \cosh (a)-\sinh (a) \log (\sinh (a+b x)))\right)}{b^3}","\frac{d^2 \text{Li}_2\left(e^{2 (a+b x)}\right)}{b^3}+\frac{2 d (c+d x) \log \left(1-e^{2 (a+b x)}\right)}{b^2}-\frac{(c+d x)^2 \coth (a+b x)}{b}-\frac{(c+d x)^2}{b}",1,"(Csch[a]*(-2*b*c*d*(b*x*Cosh[a] - Log[Sinh[a + b*x]]*Sinh[a]) + d^2*(-((b^2*x^2*Cosh[a]*Sqrt[Sech[a]^2])/E^ArcTanh[Tanh[a]]) + I*b*Pi*x*Sinh[a] - I*Pi*Log[1 + E^(2*b*x)]*Sinh[a] + 2*b*x*Log[1 - E^(-2*(b*x + ArcTanh[Tanh[a]]))]*Sinh[a] + I*Pi*Log[Cosh[b*x]]*Sinh[a] + 2*ArcTanh[Tanh[a]]*(b*x + Log[1 - E^(-2*(b*x + ArcTanh[Tanh[a]]))] - Log[I*Sinh[b*x + ArcTanh[Tanh[a]]]])*Sinh[a] - PolyLog[2, E^(-2*(b*x + ArcTanh[Tanh[a]]))]*Sinh[a]) + b^2*(c + d*x)^2*Csch[a + b*x]*Sinh[b*x]))/b^3","C",0
30,1,52,29,0.0765318,"\int (c+d x) \text{csch}^2(a+b x) \, dx","Integrate[(c + d*x)*Csch[a + b*x]^2,x]","\frac{d \log (\sinh (a+b x))}{b^2}-\frac{c \coth (a+b x)}{b}-\frac{d x \coth (a)}{b}+\frac{d x \text{csch}(a) \sinh (b x) \text{csch}(a+b x)}{b}","\frac{d \log (\sinh (a+b x))}{b^2}-\frac{(c+d x) \coth (a+b x)}{b}",1,"-((d*x*Coth[a])/b) - (c*Coth[a + b*x])/b + (d*Log[Sinh[a + b*x]])/b^2 + (d*x*Csch[a]*Csch[a + b*x]*Sinh[b*x])/b","A",1
31,0,0,19,16.9978308,"\int \frac{\text{csch}^2(a+b x)}{c+d x} \, dx","Integrate[Csch[a + b*x]^2/(c + d*x),x]","\int \frac{\text{csch}^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{csch}^2(a+b x)}{c+d x},x\right)",0,"Integrate[Csch[a + b*x]^2/(c + d*x), x]","A",-1
32,0,0,19,17.6224861,"\int \frac{\text{csch}^2(a+b x)}{(c+d x)^2} \, dx","Integrate[Csch[a + b*x]^2/(c + d*x)^2,x]","\int \frac{\text{csch}^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{csch}^2(a+b x)}{(c+d x)^2},x\right)",0,"Integrate[Csch[a + b*x]^2/(c + d*x)^2, x]","A",-1
33,1,440,256,8.918671,"\int (c+d x)^3 \text{csch}^3(a+b x) \, dx","Integrate[(c + d*x)^3*Csch[a + b*x]^3,x]","-\frac{b^3 c^3 \log \left(1-e^{a+b x}\right)-b^3 c^3 \log \left(e^{a+b x}+1\right)+3 b^3 c^2 d x \log \left(1-e^{a+b x}\right)-3 b^3 c^2 d x \log \left(e^{a+b x}+1\right)+3 b^3 c d^2 x^2 \log \left(1-e^{a+b x}\right)-3 b^3 c d^2 x^2 \log \left(e^{a+b x}+1\right)+b^3 d^3 x^3 \log \left(1-e^{a+b x}\right)-b^3 d^3 x^3 \log \left(e^{a+b x}+1\right)-3 d \text{Li}_2\left(-e^{a+b x}\right) \left(b^2 (c+d x)^2-2 d^2\right)+3 d \text{Li}_2\left(e^{a+b x}\right) \left(b^2 (c+d x)^2-2 d^2\right)+b^2 (c+d x)^2 \text{csch}(a+b x) (b (c+d x) \coth (a+b x)+3 d)+6 b c d^2 \text{Li}_3\left(-e^{a+b x}\right)-6 b c d^2 \text{Li}_3\left(e^{a+b x}\right)-6 b c d^2 \log \left(1-e^{a+b x}\right)+6 b c d^2 \log \left(e^{a+b x}+1\right)+6 b d^3 x \text{Li}_3\left(-e^{a+b x}\right)-6 b d^3 x \text{Li}_3\left(e^{a+b x}\right)-6 d^3 \text{Li}_4\left(-e^{a+b x}\right)+6 d^3 \text{Li}_4\left(e^{a+b x}\right)-6 b d^3 x \log \left(1-e^{a+b x}\right)+6 b d^3 x \log \left(e^{a+b x}+1\right)}{2 b^4}","-\frac{3 d^3 \text{Li}_2\left(-e^{a+b x}\right)}{b^4}+\frac{3 d^3 \text{Li}_2\left(e^{a+b x}\right)}{b^4}+\frac{3 d^3 \text{Li}_4\left(-e^{a+b x}\right)}{b^4}-\frac{3 d^3 \text{Li}_4\left(e^{a+b x}\right)}{b^4}-\frac{3 d^2 (c+d x) \text{Li}_3\left(-e^{a+b x}\right)}{b^3}+\frac{3 d^2 (c+d x) \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{6 d^2 (c+d x) \tanh ^{-1}\left(e^{a+b x}\right)}{b^3}+\frac{3 d (c+d x)^2 \text{Li}_2\left(-e^{a+b x}\right)}{2 b^2}-\frac{3 d (c+d x)^2 \text{Li}_2\left(e^{a+b x}\right)}{2 b^2}-\frac{3 d (c+d x)^2 \text{csch}(a+b x)}{2 b^2}+\frac{(c+d x)^3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{(c+d x)^3 \coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-1/2*(b^2*(c + d*x)^2*(3*d + b*(c + d*x)*Coth[a + b*x])*Csch[a + b*x] + b^3*c^3*Log[1 - E^(a + b*x)] - 6*b*c*d^2*Log[1 - E^(a + b*x)] + 3*b^3*c^2*d*x*Log[1 - E^(a + b*x)] - 6*b*d^3*x*Log[1 - E^(a + b*x)] + 3*b^3*c*d^2*x^2*Log[1 - E^(a + b*x)] + b^3*d^3*x^3*Log[1 - E^(a + b*x)] - b^3*c^3*Log[1 + E^(a + b*x)] + 6*b*c*d^2*Log[1 + E^(a + b*x)] - 3*b^3*c^2*d*x*Log[1 + E^(a + b*x)] + 6*b*d^3*x*Log[1 + E^(a + b*x)] - 3*b^3*c*d^2*x^2*Log[1 + E^(a + b*x)] - b^3*d^3*x^3*Log[1 + E^(a + b*x)] - 3*d*(-2*d^2 + b^2*(c + d*x)^2)*PolyLog[2, -E^(a + b*x)] + 3*d*(-2*d^2 + b^2*(c + d*x)^2)*PolyLog[2, E^(a + b*x)] + 6*b*c*d^2*PolyLog[3, -E^(a + b*x)] + 6*b*d^3*x*PolyLog[3, -E^(a + b*x)] - 6*b*c*d^2*PolyLog[3, E^(a + b*x)] - 6*b*d^3*x*PolyLog[3, E^(a + b*x)] - 6*d^3*PolyLog[4, -E^(a + b*x)] + 6*d^3*PolyLog[4, E^(a + b*x)])/b^4","A",1
34,1,420,154,10.2734322,"\int (c+d x)^2 \text{csch}^3(a+b x) \, dx","Integrate[(c + d*x)^2*Csch[a + b*x]^3,x]","\frac{\text{csch}\left(\frac{a}{2}\right) \text{csch}\left(\frac{a}{2}+\frac{b x}{2}\right) \left(c d \sinh \left(\frac{b x}{2}\right)+d^2 x \sinh \left(\frac{b x}{2}\right)\right)}{2 b^2}+\frac{\text{sech}\left(\frac{a}{2}\right) \text{sech}\left(\frac{a}{2}+\frac{b x}{2}\right) \left(c d \sinh \left(\frac{b x}{2}\right)+d^2 x \sinh \left(\frac{b x}{2}\right)\right)}{2 b^2}-\frac{d \text{csch}(a) (c+d x)}{b^2}+\frac{b^2 \left(-c^2\right) \log \left(1-e^{a+b x}\right)+b^2 c^2 \log \left(e^{a+b x}+1\right)-2 b^2 c d x \log \left(1-e^{a+b x}\right)+2 b^2 c d x \log \left(e^{a+b x}+1\right)-b^2 d^2 x^2 \log \left(1-e^{a+b x}\right)+b^2 d^2 x^2 \log \left(e^{a+b x}+1\right)+2 b d (c+d x) \text{Li}_2\left(-e^{a+b x}\right)-2 b d (c+d x) \text{Li}_2\left(e^{a+b x}\right)-2 d^2 \text{Li}_3\left(-e^{a+b x}\right)+2 d^2 \text{Li}_3\left(e^{a+b x}\right)+2 d^2 \log \left(1-e^{a+b x}\right)-2 d^2 \log \left(e^{a+b x}+1\right)}{2 b^3}+\frac{\left(-c^2-2 c d x-d^2 x^2\right) \text{csch}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}+\frac{\left(-c^2-2 c d x-d^2 x^2\right) \text{sech}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}","-\frac{d^2 \text{Li}_3\left(-e^{a+b x}\right)}{b^3}+\frac{d^2 \text{Li}_3\left(e^{a+b x}\right)}{b^3}-\frac{d^2 \tanh ^{-1}(\cosh (a+b x))}{b^3}+\frac{d (c+d x) \text{Li}_2\left(-e^{a+b x}\right)}{b^2}-\frac{d (c+d x) \text{Li}_2\left(e^{a+b x}\right)}{b^2}-\frac{d (c+d x) \text{csch}(a+b x)}{b^2}+\frac{(c+d x)^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{(c+d x)^2 \coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-((d*(c + d*x)*Csch[a])/b^2) + ((-c^2 - 2*c*d*x - d^2*x^2)*Csch[a/2 + (b*x)/2]^2)/(8*b) + (-(b^2*c^2*Log[1 - E^(a + b*x)]) + 2*d^2*Log[1 - E^(a + b*x)] - 2*b^2*c*d*x*Log[1 - E^(a + b*x)] - b^2*d^2*x^2*Log[1 - E^(a + b*x)] + b^2*c^2*Log[1 + E^(a + b*x)] - 2*d^2*Log[1 + E^(a + b*x)] + 2*b^2*c*d*x*Log[1 + E^(a + b*x)] + b^2*d^2*x^2*Log[1 + E^(a + b*x)] + 2*b*d*(c + d*x)*PolyLog[2, -E^(a + b*x)] - 2*b*d*(c + d*x)*PolyLog[2, E^(a + b*x)] - 2*d^2*PolyLog[3, -E^(a + b*x)] + 2*d^2*PolyLog[3, E^(a + b*x)])/(2*b^3) + ((-c^2 - 2*c*d*x - d^2*x^2)*Sech[a/2 + (b*x)/2]^2)/(8*b) + (Csch[a/2]*Csch[a/2 + (b*x)/2]*(c*d*Sinh[(b*x)/2] + d^2*x*Sinh[(b*x)/2]))/(2*b^2) + (Sech[a/2]*Sech[a/2 + (b*x)/2]*(c*d*Sinh[(b*x)/2] + d^2*x*Sinh[(b*x)/2]))/(2*b^2)","B",1
35,1,313,92,2.311046,"\int (c+d x) \text{csch}^3(a+b x) \, dx","Integrate[(c + d*x)*Csch[a + b*x]^3,x]","-\frac{d \left(-a \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)-i \left(i \left(\text{Li}_2\left(-e^{i (i a+i b x)}\right)-\text{Li}_2\left(e^{i (i a+i b x)}\right)\right)+(i a+i b x) \left(\log \left(1-e^{i (i a+i b x)}\right)-\log \left(1+e^{i (i a+i b x)}\right)\right)\right)\right)}{2 b^2}+\frac{d \text{csch}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{csch}\left(\frac{a}{2}+\frac{b x}{2}\right)}{4 b^2}+\frac{d \text{sech}\left(\frac{a}{2}\right) \sinh \left(\frac{b x}{2}\right) \text{sech}\left(\frac{a}{2}+\frac{b x}{2}\right)}{4 b^2}-\frac{c \text{csch}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{c \text{sech}^2\left(\frac{1}{2} (a+b x)\right)}{8 b}-\frac{c \log \left(\tanh \left(\frac{1}{2} (a+b x)\right)\right)}{2 b}-\frac{d x \text{csch}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}-\frac{d x \text{sech}^2\left(\frac{a}{2}+\frac{b x}{2}\right)}{8 b}","\frac{d \text{Li}_2\left(-e^{a+b x}\right)}{2 b^2}-\frac{d \text{Li}_2\left(e^{a+b x}\right)}{2 b^2}-\frac{d \text{csch}(a+b x)}{2 b^2}+\frac{(c+d x) \tanh ^{-1}\left(e^{a+b x}\right)}{b}-\frac{(c+d x) \coth (a+b x) \text{csch}(a+b x)}{2 b}",1,"-1/8*(d*x*Csch[a/2 + (b*x)/2]^2)/b - (c*Csch[(a + b*x)/2]^2)/(8*b) - (c*Log[Tanh[(a + b*x)/2]])/(2*b) - (d*(-(a*Log[Tanh[(a + b*x)/2]]) - I*((I*a + I*b*x)*(Log[1 - E^(I*(I*a + I*b*x))] - Log[1 + E^(I*(I*a + I*b*x))]) + I*(PolyLog[2, -E^(I*(I*a + I*b*x))] - PolyLog[2, E^(I*(I*a + I*b*x))]))))/(2*b^2) - (d*x*Sech[a/2 + (b*x)/2]^2)/(8*b) - (c*Sech[(a + b*x)/2]^2)/(8*b) + (d*Csch[a/2]*Csch[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(4*b^2) + (d*Sech[a/2]*Sech[a/2 + (b*x)/2]*Sinh[(b*x)/2])/(4*b^2)","C",1
36,0,0,19,68.9033626,"\int \frac{\text{csch}^3(a+b x)}{c+d x} \, dx","Integrate[Csch[a + b*x]^3/(c + d*x),x]","\int \frac{\text{csch}^3(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{csch}^3(a+b x)}{c+d x},x\right)",0,"Integrate[Csch[a + b*x]^3/(c + d*x), x]","A",-1
37,0,0,19,74.3722221,"\int \frac{\text{csch}^3(a+b x)}{(c+d x)^2} \, dx","Integrate[Csch[a + b*x]^3/(c + d*x)^2,x]","\int \frac{\text{csch}^3(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{csch}^3(a+b x)}{(c+d x)^2},x\right)",0,"Integrate[Csch[a + b*x]^3/(c + d*x)^2, x]","A",-1
38,1,108,171,0.0564377,"\int (c+d x)^{5/2} \sinh (a+b x) \, dx","Integrate[(c + d*x)^(5/2)*Sinh[a + b*x],x]","\frac{d^3 e^{-a-\frac{b c}{d}} \left(e^{\frac{2 b c}{d}} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{7}{2},\frac{b (c+d x)}{d}\right)-e^{2 a} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{7}{2},-\frac{b (c+d x)}{d}\right)\right)}{2 b^4 \sqrt{c+d x}}","-\frac{15 \sqrt{\pi } d^{5/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \cosh (a+b x)}{4 b^3}-\frac{5 d (c+d x)^{3/2} \sinh (a+b x)}{2 b^2}+\frac{(c+d x)^{5/2} \cosh (a+b x)}{b}",1,"(d^3*E^(-a - (b*c)/d)*(-(E^(2*a)*Sqrt[-((b*(c + d*x))/d)]*Gamma[7/2, -((b*(c + d*x))/d)]) + E^((2*b*c)/d)*Sqrt[(b*(c + d*x))/d]*Gamma[7/2, (b*(c + d*x))/d]))/(2*b^4*Sqrt[c + d*x])","A",1
39,1,106,146,0.0862094,"\int (c+d x)^{3/2} \sinh (a+b x) \, dx","Integrate[(c + d*x)^(3/2)*Sinh[a + b*x],x]","\frac{d \sqrt{c+d x} e^{-a-\frac{b c}{d}} \left(\frac{e^{\frac{2 b c}{d}} \Gamma \left(\frac{5}{2},\frac{b (c+d x)}{d}\right)}{\sqrt{\frac{b (c+d x)}{d}}}-\frac{e^{2 a} \Gamma \left(\frac{5}{2},-\frac{b (c+d x)}{d}\right)}{\sqrt{-\frac{b (c+d x)}{d}}}\right)}{2 b^2}","-\frac{3 \sqrt{\pi } d^{3/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}+\frac{3 \sqrt{\pi } d^{3/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}-\frac{3 d \sqrt{c+d x} \sinh (a+b x)}{2 b^2}+\frac{(c+d x)^{3/2} \cosh (a+b x)}{b}",1,"(d*E^(-a - (b*c)/d)*Sqrt[c + d*x]*(-((E^(2*a)*Gamma[5/2, -((b*(c + d*x))/d)])/Sqrt[-((b*(c + d*x))/d)]) + (E^((2*b*c)/d)*Gamma[5/2, (b*(c + d*x))/d])/Sqrt[(b*(c + d*x))/d]))/(2*b^2)","A",1
40,1,104,123,0.073631,"\int \sqrt{c+d x} \sinh (a+b x) \, dx","Integrate[Sqrt[c + d*x]*Sinh[a + b*x],x]","\frac{\sqrt{c+d x} e^{-a-\frac{b c}{d}} \left(\frac{e^{2 a} \Gamma \left(\frac{3}{2},-\frac{b (c+d x)}{d}\right)}{\sqrt{-\frac{b (c+d x)}{d}}}+\frac{e^{\frac{2 b c}{d}} \Gamma \left(\frac{3}{2},\frac{b (c+d x)}{d}\right)}{\sqrt{\frac{b (c+d x)}{d}}}\right)}{2 b}","-\frac{\sqrt{\pi } \sqrt{d} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{3/2}}+\frac{\sqrt{c+d x} \cosh (a+b x)}{b}",1,"(E^(-a - (b*c)/d)*Sqrt[c + d*x]*((E^(2*a)*Gamma[3/2, -((b*(c + d*x))/d)])/Sqrt[-((b*(c + d*x))/d)] + (E^((2*b*c)/d)*Gamma[3/2, (b*(c + d*x))/d])/Sqrt[(b*(c + d*x))/d]))/(2*b)","A",1
41,1,104,104,0.0341415,"\int \frac{\sinh (a+b x)}{\sqrt{c+d x}} \, dx","Integrate[Sinh[a + b*x]/Sqrt[c + d*x],x]","\frac{e^{-a-\frac{b c}{d}} \left(e^{2 a} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)+e^{\frac{2 b c}{d}} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)\right)}{2 b \sqrt{c+d x}}","\frac{\sqrt{\pi } e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}-\frac{\sqrt{\pi } e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}",1,"(E^(-a - (b*c)/d)*(E^(2*a)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)] + E^((2*b*c)/d)*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (b*(c + d*x))/d]))/(2*b*Sqrt[c + d*x])","A",1
42,1,120,118,0.1383606,"\int \frac{\sinh (a+b x)}{(c+d x)^{3/2}} \, dx","Integrate[Sinh[a + b*x]/(c + d*x)^(3/2),x]","\frac{e^{-a-\frac{b c}{d}} \left(-2 e^{a+\frac{b c}{d}} \sinh (a+b x)+e^{2 a} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)-e^{\frac{2 b c}{d}} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)\right)}{d \sqrt{c+d x}}","\frac{\sqrt{\pi } \sqrt{b} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{\sqrt{\pi } \sqrt{b} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sinh (a+b x)}{d \sqrt{c+d x}}",1,"(E^(-a - (b*c)/d)*(E^(2*a)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)] - E^((2*b*c)/d)*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (b*(c + d*x))/d] - 2*E^(a + (b*c)/d)*Sinh[a + b*x]))/(d*Sqrt[c + d*x])","A",1
43,1,161,149,0.7249961,"\int \frac{\sinh (a+b x)}{(c+d x)^{5/2}} \, dx","Integrate[Sinh[a + b*x]/(c + d*x)^(5/2),x]","\frac{2 b \left(\frac{e^a \left(e^{-\frac{b c}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)-e^{b x}\right)}{d \sqrt{c+d x}}+\frac{e^{-a-b x} \left(e^{b \left(\frac{c}{d}+x\right)} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)-1\right)}{d \sqrt{c+d x}}\right)}{3 d}-\frac{2 \sinh (a+b x)}{3 d (c+d x)^{3/2}}","-\frac{2 \sqrt{\pi } b^{3/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{3 d^{5/2}}+\frac{2 \sqrt{\pi } b^{3/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 b \cosh (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \sinh (a+b x)}{3 d (c+d x)^{3/2}}",1,"(2*b*((E^a*(-E^(b*x) + (Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)])/E^((b*c)/d)))/(d*Sqrt[c + d*x]) + (E^(-a - b*x)*(-1 + E^(b*(c/d + x))*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (b*(c + d*x))/d]))/(d*Sqrt[c + d*x])))/(3*d) - (2*Sinh[a + b*x])/(3*d*(c + d*x)^(3/2))","A",1
44,1,168,174,0.5357918,"\int \frac{\sinh (a+b x)}{(c+d x)^{7/2}} \, dx","Integrate[Sinh[a + b*x]/(c + d*x)^(7/2),x]","\frac{2 \left(-b (c+d x) \left(e^{a-\frac{b c}{d}} \left(e^{b \left(\frac{c}{d}+x\right)} (2 b (c+d x)+d)+2 d \left(-\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)\right)+e^{-a-b x} \left(-2 b (c+d x)+2 d e^{b \left(\frac{c}{d}+x\right)} \left(\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)+d\right)\right)-3 d^2 \sinh (a+b x)\right)}{15 d^3 (c+d x)^{5/2}}","\frac{4 \sqrt{\pi } b^{5/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}+\frac{4 \sqrt{\pi } b^{5/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}-\frac{8 b^2 \sinh (a+b x)}{15 d^3 \sqrt{c+d x}}-\frac{4 b \cosh (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \sinh (a+b x)}{5 d (c+d x)^{5/2}}",1,"(2*(-(b*(c + d*x)*(E^(a - (b*c)/d)*(E^(b*(c/d + x))*(d + 2*b*(c + d*x)) + 2*d*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, -((b*(c + d*x))/d)]) + E^(-a - b*x)*(d - 2*b*(c + d*x) + 2*d*E^(b*(c/d + x))*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d]))) - 3*d^2*Sinh[a + b*x]))/(15*d^3*(c + d*x)^(5/2))","A",1
45,1,190,239,6.2935047,"\int (c+d x)^{5/2} \sinh ^2(a+b x) \, dx","Integrate[(c + d*x)^(5/2)*Sinh[a + b*x]^2,x]","\frac{\sqrt{c+d x} \left(-b (c+d x) \left(7 \sqrt{2} d^3 \Gamma \left(\frac{7}{2},\frac{2 b (c+d x)}{d}\right) \left(\cosh \left(2 a-\frac{2 b c}{d}\right)-\sinh \left(2 a-\frac{2 b c}{d}\right)\right)+64 b^3 (c+d x)^3 \sqrt{\frac{b (c+d x)}{d}}\right)-7 \sqrt{2} d^4 \sqrt{-\frac{b^2 (c+d x)^2}{d^2}} \Gamma \left(\frac{7}{2},-\frac{2 b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)+\cosh \left(2 a-\frac{2 b c}{d}\right)\right)\right)}{448 b^3 d^2 \left(\frac{b (c+d x)}{d}\right)^{3/2}}","\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{256 b^{7/2}}-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{256 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \sinh (2 a+2 b x)}{64 b^3}-\frac{5 d (c+d x)^{3/2} \sinh ^2(a+b x)}{8 b^2}+\frac{(c+d x)^{5/2} \sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{5 d (c+d x)^{3/2}}{16 b^2}-\frac{(c+d x)^{7/2}}{7 d}",1,"(Sqrt[c + d*x]*(-(b*(c + d*x)*(64*b^3*(c + d*x)^3*Sqrt[(b*(c + d*x))/d] + 7*Sqrt[2]*d^3*Gamma[7/2, (2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] - Sinh[2*a - (2*b*c)/d]))) - 7*Sqrt[2]*d^4*Sqrt[-((b^2*(c + d*x)^2)/d^2)]*Gamma[7/2, (-2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d])))/(448*b^3*d^2*((b*(c + d*x))/d)^(3/2))","A",0
46,1,163,211,2.1220834,"\int (c+d x)^{3/2} \sinh ^2(a+b x) \, dx","Integrate[(c + d*x)^(3/2)*Sinh[a + b*x]^2,x]","\frac{5 \sqrt{2} d^3 \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{5}{2},\frac{2 b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)-\cosh \left(2 a-\frac{2 b c}{d}\right)\right)+5 \sqrt{2} d^3 \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{5}{2},-\frac{2 b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)+\cosh \left(2 a-\frac{2 b c}{d}\right)\right)-32 b^3 (c+d x)^3}{160 b^3 d \sqrt{c+d x}}","\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{5/2}}-\frac{3 d \sqrt{c+d x} \sinh ^2(a+b x)}{8 b^2}+\frac{(c+d x)^{3/2} \sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{3 d \sqrt{c+d x}}{16 b^2}-\frac{(c+d x)^{5/2}}{5 d}",1,"(-32*b^3*(c + d*x)^3 + 5*Sqrt[2]*d^3*Sqrt[(b*(c + d*x))/d]*Gamma[5/2, (2*b*(c + d*x))/d]*(-Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]) + 5*Sqrt[2]*d^3*Sqrt[-((b*(c + d*x))/d)]*Gamma[5/2, (-2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]))/(160*b^3*d*Sqrt[c + d*x])","A",1
47,1,129,166,0.5590766,"\int \sqrt{c+d x} \sinh ^2(a+b x) \, dx","Integrate[Sqrt[c + d*x]*Sinh[a + b*x]^2,x]","\frac{1}{48} \sqrt{c+d x} \left(\frac{3 \sqrt{2} e^{2 a-\frac{2 b c}{d}} \Gamma \left(\frac{3}{2},-\frac{2 b (c+d x)}{d}\right)}{b \sqrt{-\frac{b (c+d x)}{d}}}-\frac{3 \sqrt{2} e^{\frac{2 b c}{d}-2 a} \Gamma \left(\frac{3}{2},\frac{2 b (c+d x)}{d}\right)}{b \sqrt{\frac{b (c+d x)}{d}}}-\frac{16 (c+d x)}{d}\right)","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{3/2}}+\frac{\sqrt{c+d x} \sinh (2 a+2 b x)}{4 b}-\frac{(c+d x)^{3/2}}{3 d}",1,"(Sqrt[c + d*x]*((-16*(c + d*x))/d + (3*Sqrt[2]*E^(2*a - (2*b*c)/d)*Gamma[3/2, (-2*b*(c + d*x))/d])/(b*Sqrt[-((b*(c + d*x))/d)]) - (3*Sqrt[2]*E^(-2*a + (2*b*c)/d)*Gamma[3/2, (2*b*(c + d*x))/d])/(b*Sqrt[(b*(c + d*x))/d])))/48","A",1
48,1,142,139,0.11609,"\int \frac{\sinh ^2(a+b x)}{\sqrt{c+d x}} \, dx","Integrate[Sinh[a + b*x]^2/Sqrt[c + d*x],x]","\frac{e^{2 a-\frac{2 b c}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{2 b (c+d x)}{d}\right)}{4 \sqrt{2} b \sqrt{c+d x}}-\frac{e^{\frac{2 b c}{d}-2 a} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},\frac{2 b (c+d x)}{d}\right)}{4 \sqrt{2} b \sqrt{c+d x}}-\frac{\sqrt{c+d x}}{d}","\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 \sqrt{b} \sqrt{d}}+\frac{\sqrt{\frac{\pi }{2}} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 \sqrt{b} \sqrt{d}}-\frac{\sqrt{c+d x}}{d}",1,"-(Sqrt[c + d*x]/d) + (E^(2*a - (2*b*c)/d)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-2*b*(c + d*x))/d])/(4*Sqrt[2]*b*Sqrt[c + d*x]) - (E^(-2*a + (2*b*c)/d)*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (2*b*(c + d*x))/d])/(4*Sqrt[2]*b*Sqrt[c + d*x])","A",1
49,1,570,142,4.5842227,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^{3/2}} \, dx","Integrate[Sinh[a + b*x]^2/(c + d*x)^(3/2),x]","\frac{e^{-\frac{2 b (c+d x)}{d}} \left(-\sqrt{2 \pi } \sqrt{b} \cosh (2 a) \sqrt{c+d x} e^{\frac{2 b (c+d x)}{d}} \sinh \left(\frac{2 b c}{d}\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)-\sqrt{2 \pi } \sqrt{b} \cosh (2 a) \sqrt{c+d x} e^{\frac{2 b (c+d x)}{d}} \sinh \left(\frac{2 b c}{d}\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)+\sqrt{d} \sinh (2 a) e^{\frac{4 b (c+d x)}{d}} \sinh \left(\frac{2 b c}{d}\right)-\sqrt{d} \cosh (2 a) e^{\frac{4 b (c+d x)}{d}} \cosh \left(\frac{2 b c}{d}\right)-\sqrt{d} \sinh (2 a) e^{\frac{4 b (c+d x)}{d}} \cosh \left(\frac{2 b c}{d}\right)+\sqrt{d} \cosh (2 a) e^{\frac{4 b (c+d x)}{d}} \sinh \left(\frac{2 b c}{d}\right)+\sqrt{2} \sqrt{d} e^{\frac{2 b (c+d x)}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{2 b (c+d x)}{d}\right) \left(\cosh \left(2 a-\frac{2 b c}{d}\right)+\sinh (2 a) \cosh \left(\frac{2 b c}{d}\right)\right)+\sqrt{2} \sqrt{d} e^{\frac{2 b (c+d x)}{d}} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},\frac{2 b (c+d x)}{d}\right) \left(\cosh (2 a) \cosh \left(\frac{2 b c}{d}\right)-\sinh (2 a) \left(\sinh \left(\frac{2 b c}{d}\right)+\cosh \left(\frac{2 b c}{d}\right)\right)\right)+\sqrt{d} \sinh (2 a) \sinh \left(\frac{2 b c}{d}\right)-\sqrt{d} \cosh (2 a) \cosh \left(\frac{2 b c}{d}\right)+\sqrt{d} \sinh (2 a) \cosh \left(\frac{2 b c}{d}\right)-\sqrt{d} \cosh (2 a) \sinh \left(\frac{2 b c}{d}\right)+2 \sqrt{d} e^{\frac{2 b (c+d x)}{d}}\right)}{2 d^{3/2} \sqrt{c+d x}}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sinh ^2(a+b x)}{d \sqrt{c+d x}}",1,"(2*Sqrt[d]*E^((2*b*(c + d*x))/d) - Sqrt[d]*Cosh[2*a]*Cosh[(2*b*c)/d] - Sqrt[d]*E^((4*b*(c + d*x))/d)*Cosh[2*a]*Cosh[(2*b*c)/d] + Sqrt[d]*Cosh[(2*b*c)/d]*Sinh[2*a] - Sqrt[d]*E^((4*b*(c + d*x))/d)*Cosh[(2*b*c)/d]*Sinh[2*a] + Sqrt[2]*Sqrt[d]*E^((2*b*(c + d*x))/d)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] + Cosh[(2*b*c)/d]*Sinh[2*a]) - Sqrt[d]*Cosh[2*a]*Sinh[(2*b*c)/d] + Sqrt[d]*E^((4*b*(c + d*x))/d)*Cosh[2*a]*Sinh[(2*b*c)/d] - Sqrt[b]*E^((2*b*(c + d*x))/d)*Sqrt[2*Pi]*Sqrt[c + d*x]*Cosh[2*a]*Erf[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]*Sinh[(2*b*c)/d] - Sqrt[b]*E^((2*b*(c + d*x))/d)*Sqrt[2*Pi]*Sqrt[c + d*x]*Cosh[2*a]*Erfi[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]*Sinh[(2*b*c)/d] + Sqrt[d]*Sinh[2*a]*Sinh[(2*b*c)/d] + Sqrt[d]*E^((4*b*(c + d*x))/d)*Sinh[2*a]*Sinh[(2*b*c)/d] + Sqrt[2]*Sqrt[d]*E^((2*b*(c + d*x))/d)*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (2*b*(c + d*x))/d]*(Cosh[2*a]*Cosh[(2*b*c)/d] - Sinh[2*a]*(Cosh[(2*b*c)/d] + Sinh[(2*b*c)/d])))/(2*d^(3/2)*E^((2*b*(c + d*x))/d)*Sqrt[c + d*x])","B",1
50,1,156,174,1.1226704,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^{5/2}} \, dx","Integrate[Sinh[a + b*x]^2/(c + d*x)^(5/2),x]","-\frac{2 e^{-2 \left(a+\frac{b c}{d}\right)} \left(e^{2 \left(a+\frac{b c}{d}\right)} \left(2 b (c+d x) \sinh (2 (a+b x))+d \sinh ^2(a+b x)\right)+\sqrt{2} e^{4 a} d \left(-\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{2 b (c+d x)}{d}\right)+\sqrt{2} d e^{\frac{4 b c}{d}} \left(\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{2 b (c+d x)}{d}\right)\right)}{3 d^2 (c+d x)^{3/2}}","\frac{2 \sqrt{2 \pi } b^{3/2} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{3 d^{5/2}}+\frac{2 \sqrt{2 \pi } b^{3/2} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{8 b \sinh (a+b x) \cosh (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \sinh ^2(a+b x)}{3 d (c+d x)^{3/2}}",1,"(-2*(Sqrt[2]*d*E^(4*a)*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, (-2*b*(c + d*x))/d] + Sqrt[2]*d*E^((4*b*c)/d)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (2*b*(c + d*x))/d] + E^(2*(a + (b*c)/d))*(d*Sinh[a + b*x]^2 + 2*b*(c + d*x)*Sinh[2*(a + b*x)])))/(3*d^2*E^(2*(a + (b*c)/d))*(c + d*x)^(3/2))","A",1
51,1,825,220,8.5826999,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^{7/2}} \, dx","Integrate[Sinh[a + b*x]^2/(c + d*x)^(7/2),x]","\frac{e^{-\frac{2 b (c+d x)}{d}} \left(16 \sqrt{2} d^2 e^{\frac{2 b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{2 b (c+d x)}{d}\right) \left(\cosh \left(2 a-\frac{2 b c}{d}\right)+\sinh \left(2 a-\frac{2 b c}{d}\right)\right) \left(-\frac{b (c+d x)}{d}\right)^{5/2}+6 d^2 e^{\frac{2 b (c+d x)}{d}}-16 b^2 c^2 e^{\frac{4 b (c+d x)}{d}} \cosh \left(2 a-\frac{2 b c}{d}\right)-3 d^2 e^{\frac{4 b (c+d x)}{d}} \cosh \left(2 a-\frac{2 b c}{d}\right)-4 b c d e^{\frac{4 b (c+d x)}{d}} \cosh \left(2 a-\frac{2 b c}{d}\right)-16 b^2 c^2 \cosh \left(2 a-\frac{2 b c}{d}\right)-3 d^2 \cosh \left(2 a-\frac{2 b c}{d}\right)-16 b^2 d^2 e^{\frac{4 b (c+d x)}{d}} x^2 \cosh \left(2 a-\frac{2 b c}{d}\right)-16 b^2 d^2 x^2 \cosh \left(2 a-\frac{2 b c}{d}\right)+4 b c d \cosh \left(2 a-\frac{2 b c}{d}\right)-4 b d^2 e^{\frac{4 b (c+d x)}{d}} x \cosh \left(2 a-\frac{2 b c}{d}\right)-32 b^2 c d e^{\frac{4 b (c+d x)}{d}} x \cosh \left(2 a-\frac{2 b c}{d}\right)+4 b d^2 x \cosh \left(2 a-\frac{2 b c}{d}\right)-32 b^2 c d x \cosh \left(2 a-\frac{2 b c}{d}\right)+16 \sqrt{2} d^2 e^{\frac{2 b (c+d x)}{d}} \left(\frac{b (c+d x)}{d}\right)^{5/2} \Gamma \left(\frac{1}{2},\frac{2 b (c+d x)}{d}\right) \left(\cosh \left(2 a-\frac{2 b c}{d}\right)-\sinh \left(2 a-\frac{2 b c}{d}\right)\right)-16 b^2 c^2 e^{\frac{4 b (c+d x)}{d}} \sinh \left(2 a-\frac{2 b c}{d}\right)-3 d^2 e^{\frac{4 b (c+d x)}{d}} \sinh \left(2 a-\frac{2 b c}{d}\right)-4 b c d e^{\frac{4 b (c+d x)}{d}} \sinh \left(2 a-\frac{2 b c}{d}\right)+16 b^2 c^2 \sinh \left(2 a-\frac{2 b c}{d}\right)+3 d^2 \sinh \left(2 a-\frac{2 b c}{d}\right)-16 b^2 d^2 e^{\frac{4 b (c+d x)}{d}} x^2 \sinh \left(2 a-\frac{2 b c}{d}\right)+16 b^2 d^2 x^2 \sinh \left(2 a-\frac{2 b c}{d}\right)-4 b c d \sinh \left(2 a-\frac{2 b c}{d}\right)-4 b d^2 e^{\frac{4 b (c+d x)}{d}} x \sinh \left(2 a-\frac{2 b c}{d}\right)-32 b^2 c d e^{\frac{4 b (c+d x)}{d}} x \sinh \left(2 a-\frac{2 b c}{d}\right)-4 b d^2 x \sinh \left(2 a-\frac{2 b c}{d}\right)+32 b^2 c d x \sinh \left(2 a-\frac{2 b c}{d}\right)\right)}{30 d^3 (c+d x)^{5/2}}","-\frac{8 \sqrt{2 \pi } b^{5/2} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}+\frac{8 \sqrt{2 \pi } b^{5/2} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}-\frac{32 b^2 \sinh ^2(a+b x)}{15 d^3 \sqrt{c+d x}}-\frac{8 b \sinh (a+b x) \cosh (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \sinh ^2(a+b x)}{5 d (c+d x)^{5/2}}-\frac{16 b^2}{15 d^3 \sqrt{c+d x}}",1,"(6*d^2*E^((2*b*(c + d*x))/d) - 16*b^2*c^2*Cosh[2*a - (2*b*c)/d] + 4*b*c*d*Cosh[2*a - (2*b*c)/d] - 3*d^2*Cosh[2*a - (2*b*c)/d] - 16*b^2*c^2*E^((4*b*(c + d*x))/d)*Cosh[2*a - (2*b*c)/d] - 4*b*c*d*E^((4*b*(c + d*x))/d)*Cosh[2*a - (2*b*c)/d] - 3*d^2*E^((4*b*(c + d*x))/d)*Cosh[2*a - (2*b*c)/d] - 32*b^2*c*d*x*Cosh[2*a - (2*b*c)/d] + 4*b*d^2*x*Cosh[2*a - (2*b*c)/d] - 32*b^2*c*d*E^((4*b*(c + d*x))/d)*x*Cosh[2*a - (2*b*c)/d] - 4*b*d^2*E^((4*b*(c + d*x))/d)*x*Cosh[2*a - (2*b*c)/d] - 16*b^2*d^2*x^2*Cosh[2*a - (2*b*c)/d] - 16*b^2*d^2*E^((4*b*(c + d*x))/d)*x^2*Cosh[2*a - (2*b*c)/d] + 16*Sqrt[2]*d^2*E^((2*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] - Sinh[2*a - (2*b*c)/d]) + 16*b^2*c^2*Sinh[2*a - (2*b*c)/d] - 4*b*c*d*Sinh[2*a - (2*b*c)/d] + 3*d^2*Sinh[2*a - (2*b*c)/d] - 16*b^2*c^2*E^((4*b*(c + d*x))/d)*Sinh[2*a - (2*b*c)/d] - 4*b*c*d*E^((4*b*(c + d*x))/d)*Sinh[2*a - (2*b*c)/d] - 3*d^2*E^((4*b*(c + d*x))/d)*Sinh[2*a - (2*b*c)/d] + 32*b^2*c*d*x*Sinh[2*a - (2*b*c)/d] - 4*b*d^2*x*Sinh[2*a - (2*b*c)/d] - 32*b^2*c*d*E^((4*b*(c + d*x))/d)*x*Sinh[2*a - (2*b*c)/d] - 4*b*d^2*E^((4*b*(c + d*x))/d)*x*Sinh[2*a - (2*b*c)/d] + 16*b^2*d^2*x^2*Sinh[2*a - (2*b*c)/d] - 16*b^2*d^2*E^((4*b*(c + d*x))/d)*x^2*Sinh[2*a - (2*b*c)/d] + 16*Sqrt[2]*d^2*E^((2*b*(c + d*x))/d)*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]))/(30*d^3*E^((2*b*(c + d*x))/d)*(c + d*x)^(5/2))","B",1
52,1,222,251,0.539107,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^{9/2}} \, dx","Integrate[Sinh[a + b*x]^2/(c + d*x)^(9/2),x]","\frac{2 \left(-32 b^3 (c+d x)^3 \sinh (2 (a+b x))+16 \sqrt{2} b^3 (c+d x)^3 e^{2 a-\frac{2 b c}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{2 b (c+d x)}{d}\right)-16 \sqrt{2} b^3 (c+d x)^3 e^{\frac{2 b c}{d}-2 a} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},\frac{2 b (c+d x)}{d}\right)-16 b^2 d (c+d x)^2 \sinh ^2(a+b x)-6 b d^2 (c+d x) \sinh (2 (a+b x))-15 d^3 \sinh ^2(a+b x)-8 b^2 d (c+d x)^2\right)}{105 d^4 (c+d x)^{7/2}}","\frac{32 \sqrt{2 \pi } b^{7/2} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{105 d^{9/2}}+\frac{32 \sqrt{2 \pi } b^{7/2} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{105 d^{9/2}}-\frac{128 b^3 \sinh (a+b x) \cosh (a+b x)}{105 d^4 \sqrt{c+d x}}-\frac{32 b^2 \sinh ^2(a+b x)}{105 d^3 (c+d x)^{3/2}}-\frac{8 b \sinh (a+b x) \cosh (a+b x)}{35 d^2 (c+d x)^{5/2}}-\frac{2 \sinh ^2(a+b x)}{7 d (c+d x)^{7/2}}-\frac{16 b^2}{105 d^3 (c+d x)^{3/2}}",1,"(2*(-8*b^2*d*(c + d*x)^2 + 16*Sqrt[2]*b^3*E^(2*a - (2*b*c)/d)*(c + d*x)^3*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-2*b*(c + d*x))/d] - 16*Sqrt[2]*b^3*E^(-2*a + (2*b*c)/d)*(c + d*x)^3*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (2*b*(c + d*x))/d] - 15*d^3*Sinh[a + b*x]^2 - 16*b^2*d*(c + d*x)^2*Sinh[a + b*x]^2 - 6*b*d^2*(c + d*x)*Sinh[2*(a + b*x)] - 32*b^3*(c + d*x)^3*Sinh[2*(a + b*x)]))/(105*d^4*(c + d*x)^(7/2))","A",1
53,1,243,381,9.0447101,"\int (c+d x)^{5/2} \sinh ^3(a+b x) \, dx","Integrate[(c + d*x)^(5/2)*Sinh[a + b*x]^3,x]","-\frac{d^3 \left(\sqrt{3} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{7}{2},-\frac{3 b (c+d x)}{d}\right) \left(\sinh \left(3 a-\frac{3 b c}{d}\right)+\cosh \left(3 a-\frac{3 b c}{d}\right)\right)+\left(\sinh \left(a-\frac{b c}{d}\right)-\cosh \left(a-\frac{b c}{d}\right)\right) \left(\sqrt{\frac{b (c+d x)}{d}} \left(\sqrt{3} \Gamma \left(\frac{7}{2},\frac{3 b (c+d x)}{d}\right) \left(\cosh \left(2 a-\frac{2 b c}{d}\right)-\sinh \left(2 a-\frac{2 b c}{d}\right)\right)-243 \Gamma \left(\frac{7}{2},\frac{b (c+d x)}{d}\right)\right)+243 \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{7}{2},-\frac{b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)+\cosh \left(2 a-\frac{2 b c}{d}\right)\right)\right)\right)}{648 b^4 \sqrt{c+d x}}","\frac{45 \sqrt{\pi } d^{5/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{576 b^{7/2}}+\frac{45 \sqrt{\pi } d^{5/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{576 b^{7/2}}-\frac{45 d^2 \sqrt{c+d x} \cosh (a+b x)}{16 b^3}+\frac{5 d^2 \sqrt{c+d x} \cosh (3 a+3 b x)}{144 b^3}-\frac{5 d (c+d x)^{3/2} \sinh ^3(a+b x)}{18 b^2}+\frac{5 d (c+d x)^{3/2} \sinh (a+b x)}{3 b^2}-\frac{2 (c+d x)^{5/2} \cosh (a+b x)}{3 b}+\frac{(c+d x)^{5/2} \sinh ^2(a+b x) \cosh (a+b x)}{3 b}",1,"-1/648*(d^3*(Sqrt[3]*Sqrt[-((b*(c + d*x))/d)]*Gamma[7/2, (-3*b*(c + d*x))/d]*(Cosh[3*a - (3*b*c)/d] + Sinh[3*a - (3*b*c)/d]) + (Sqrt[(b*(c + d*x))/d]*(-243*Gamma[7/2, (b*(c + d*x))/d] + Sqrt[3]*Gamma[7/2, (3*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] - Sinh[2*a - (2*b*c)/d])) + 243*Sqrt[-((b*(c + d*x))/d)]*Gamma[7/2, -((b*(c + d*x))/d)]*(Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]))*(-Cosh[a - (b*c)/d] + Sinh[a - (b*c)/d])))/(b^4*Sqrt[c + d*x])","A",1
54,1,243,325,3.7174941,"\int (c+d x)^{3/2} \sinh ^3(a+b x) \, dx","Integrate[(c + d*x)^(3/2)*Sinh[a + b*x]^3,x]","\frac{d^2 \left(\sqrt{3} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{5}{2},-\frac{3 b (c+d x)}{d}\right) \left(\sinh \left(3 a-\frac{3 b c}{d}\right)+\cosh \left(3 a-\frac{3 b c}{d}\right)\right)+\left(\sinh \left(a-\frac{b c}{d}\right)-\cosh \left(a-\frac{b c}{d}\right)\right) \left(81 \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{5}{2},-\frac{b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)+\cosh \left(2 a-\frac{2 b c}{d}\right)\right)+\sqrt{\frac{b (c+d x)}{d}} \left(\sqrt{3} \Gamma \left(\frac{5}{2},\frac{3 b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)-\cosh \left(2 a-\frac{2 b c}{d}\right)\right)+81 \Gamma \left(\frac{5}{2},\frac{b (c+d x)}{d}\right)\right)\right)\right)}{216 b^3 \sqrt{c+d x}}","\frac{9 \sqrt{\pi } d^{3/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{32 b^{5/2}}-\frac{\sqrt{\frac{\pi }{3}} d^{3/2} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{96 b^{5/2}}-\frac{9 \sqrt{\pi } d^{3/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{32 b^{5/2}}+\frac{\sqrt{\frac{\pi }{3}} d^{3/2} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{96 b^{5/2}}-\frac{d \sqrt{c+d x} \sinh ^3(a+b x)}{6 b^2}+\frac{d \sqrt{c+d x} \sinh (a+b x)}{b^2}-\frac{2 (c+d x)^{3/2} \cosh (a+b x)}{3 b}+\frac{(c+d x)^{3/2} \sinh ^2(a+b x) \cosh (a+b x)}{3 b}",1,"(d^2*(Sqrt[3]*Sqrt[-((b*(c + d*x))/d)]*Gamma[5/2, (-3*b*(c + d*x))/d]*(Cosh[3*a - (3*b*c)/d] + Sinh[3*a - (3*b*c)/d]) + (81*Sqrt[-((b*(c + d*x))/d)]*Gamma[5/2, -((b*(c + d*x))/d)]*(Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]) + Sqrt[(b*(c + d*x))/d]*(81*Gamma[5/2, (b*(c + d*x))/d] + Sqrt[3]*Gamma[5/2, (3*b*(c + d*x))/d]*(-Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d])))*(-Cosh[a - (b*c)/d] + Sinh[a - (b*c)/d])))/(216*b^3*Sqrt[c + d*x])","A",1
55,1,209,275,0.2782015,"\int \sqrt{c+d x} \sinh ^3(a+b x) \, dx","Integrate[Sqrt[c + d*x]*Sinh[a + b*x]^3,x]","\frac{\sqrt{c+d x} e^{-3 \left(a+\frac{b c}{d}\right)} \left(\sqrt{3} e^{6 a} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{3}{2},-\frac{3 b (c+d x)}{d}\right)-27 e^{4 a+\frac{2 b c}{d}} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{3}{2},-\frac{b (c+d x)}{d}\right)+e^{\frac{4 b c}{d}} \sqrt{-\frac{b (c+d x)}{d}} \left(\sqrt{3} e^{\frac{2 b c}{d}} \Gamma \left(\frac{3}{2},\frac{3 b (c+d x)}{d}\right)-27 e^{2 a} \Gamma \left(\frac{3}{2},\frac{b (c+d x)}{d}\right)\right)\right)}{72 b \sqrt{-\frac{b^2 (c+d x)^2}{d^2}}}","\frac{3 \sqrt{\pi } \sqrt{d} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{3/2}}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{48 b^{3/2}}+\frac{3 \sqrt{\pi } \sqrt{d} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{3/2}}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{48 b^{3/2}}-\frac{3 \sqrt{c+d x} \cosh (a+b x)}{4 b}+\frac{\sqrt{c+d x} \cosh (3 a+3 b x)}{12 b}",1,"(Sqrt[c + d*x]*(Sqrt[3]*E^(6*a)*Sqrt[(b*(c + d*x))/d]*Gamma[3/2, (-3*b*(c + d*x))/d] - 27*E^(4*a + (2*b*c)/d)*Sqrt[(b*(c + d*x))/d]*Gamma[3/2, -((b*(c + d*x))/d)] + E^((4*b*c)/d)*Sqrt[-((b*(c + d*x))/d)]*(-27*E^(2*a)*Gamma[3/2, (b*(c + d*x))/d] + Sqrt[3]*E^((2*b*c)/d)*Gamma[3/2, (3*b*(c + d*x))/d])))/(72*b*E^(3*(a + (b*c)/d))*Sqrt[-((b^2*(c + d*x)^2)/d^2)])","A",1
56,1,191,228,0.1733792,"\int \frac{\sinh ^3(a+b x)}{\sqrt{c+d x}} \, dx","Integrate[Sinh[a + b*x]^3/Sqrt[c + d*x],x]","\frac{e^{-3 \left(a+\frac{b c}{d}\right)} \left(\sqrt{3} e^{6 a} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{3 b (c+d x)}{d}\right)-9 e^{4 a+\frac{2 b c}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)+e^{\frac{4 b c}{d}} \sqrt{\frac{b (c+d x)}{d}} \left(\sqrt{3} e^{\frac{2 b c}{d}} \Gamma \left(\frac{1}{2},\frac{3 b (c+d x)}{d}\right)-9 e^{2 a} \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)\right)\right)}{24 b \sqrt{c+d x}}","\frac{3 \sqrt{\pi } e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 \sqrt{b} \sqrt{d}}-\frac{\sqrt{\frac{\pi }{3}} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 \sqrt{b} \sqrt{d}}-\frac{3 \sqrt{\pi } e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 \sqrt{b} \sqrt{d}}+\frac{\sqrt{\frac{\pi }{3}} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 \sqrt{b} \sqrt{d}}",1,"(Sqrt[3]*E^(6*a)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-3*b*(c + d*x))/d] - 9*E^(4*a + (2*b*c)/d)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)] + E^((4*b*c)/d)*Sqrt[(b*(c + d*x))/d]*(-9*E^(2*a)*Gamma[1/2, (b*(c + d*x))/d] + Sqrt[3]*E^((2*b*c)/d)*Gamma[1/2, (3*b*(c + d*x))/d]))/(24*b*E^(3*(a + (b*c)/d))*Sqrt[c + d*x])","A",1
57,1,2058,246,10.110318,"\int \frac{\sinh ^3(a+b x)}{(c+d x)^{3/2}} \, dx","Integrate[Sinh[a + b*x]^3/(c + d*x)^(3/2),x]","\text{Result too large to show}","-\frac{3 \sqrt{\pi } \sqrt{b} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 d^{3/2}}+\frac{\sqrt{3 \pi } \sqrt{b} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 d^{3/2}}-\frac{3 \sqrt{\pi } \sqrt{b} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 d^{3/2}}+\frac{\sqrt{3 \pi } \sqrt{b} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 d^{3/2}}-\frac{2 \sinh ^3(a+b x)}{d \sqrt{c+d x}}",1,"(-3*(Cosh[a]*(-(((-((1 + E^((2*b*(c + d*x))/d))/E^((b*(c + d*x))/d)) + Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)] + Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (b*(c + d*x))/d])*Sinh[(b*c)/d])/(d*Sqrt[c + d*x])) + (Cosh[(b*c)/d]*(Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)] - Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (b*(c + d*x))/d] - 2*Sinh[(b*(c + d*x))/d]))/(d*Sqrt[c + d*x])) + Sinh[a]*((Cosh[(b*c)/d]*(-((1 + E^((2*b*(c + d*x))/d))/E^((b*(c + d*x))/d)) + Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)] + Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (b*(c + d*x))/d]))/(d*Sqrt[c + d*x]) + (Sinh[(b*c)/d]*(-(Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)]) + Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (b*(c + d*x))/d] + 2*Sinh[(b*(c + d*x))/d]))/(d*Sqrt[c + d*x]))))/4 + (-(Sinh[3*a]*(-(((1 + 2*Cosh[(2*b*c)/d])*(-((1 + E^((6*b*(c + d*x))/d))/E^((3*b*(c + d*x))/d)) + Sqrt[3]*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-3*b*(c + d*x))/d] + Sqrt[3]*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (3*b*(c + d*x))/d])*Sinh[(b*c)/d])/(d*Sqrt[c + d*x])) + (Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*((Sqrt[b]*Sqrt[6*Pi]*(Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]))/Sqrt[d] - (2*Sqrt[2]*Sinh[(3*b*(c + d*x))/d])/Sqrt[c + d*x]))/(Sqrt[2]*d))) - Cosh[3*a]*((Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-((1 + E^((6*b*(c + d*x))/d))/E^((3*b*(c + d*x))/d)) + Sqrt[3]*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-3*b*(c + d*x))/d] + Sqrt[3]*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (3*b*(c + d*x))/d]))/(d*Sqrt[c + d*x]) - ((1 + 2*Cosh[(2*b*c)/d])*Sinh[(b*c)/d]*((Sqrt[b]*Sqrt[6*Pi]*(Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]))/Sqrt[d] - (2*Sqrt[2]*Sinh[(3*b*(c + d*x))/d])/Sqrt[c + d*x]))/(Sqrt[2]*d)))/8 + (Sinh[3*a]*(-(((1 + 2*Cosh[(2*b*c)/d])*(-((1 + E^((6*b*(c + d*x))/d))/E^((3*b*(c + d*x))/d)) + Sqrt[3]*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-3*b*(c + d*x))/d] + Sqrt[3]*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (3*b*(c + d*x))/d])*Sinh[(b*c)/d])/(d*Sqrt[c + d*x])) + (Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*((Sqrt[b]*Sqrt[6*Pi]*(Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]))/Sqrt[d] - (2*Sqrt[2]*Sinh[(3*b*(c + d*x))/d])/Sqrt[c + d*x]))/(Sqrt[2]*d)) + Cosh[3*a]*((Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-((1 + E^((6*b*(c + d*x))/d))/E^((3*b*(c + d*x))/d)) + Sqrt[3]*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-3*b*(c + d*x))/d] + Sqrt[3]*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (3*b*(c + d*x))/d]))/(d*Sqrt[c + d*x]) - ((1 + 2*Cosh[(2*b*c)/d])*Sinh[(b*c)/d]*((Sqrt[b]*Sqrt[6*Pi]*(Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]))/Sqrt[d] - (2*Sqrt[2]*Sinh[(3*b*(c + d*x))/d])/Sqrt[c + d*x]))/(Sqrt[2]*d)))/8 + (Cosh[3*a]*(-(((1 + 2*Cosh[(2*b*c)/d])*(-((1 + E^((6*b*(c + d*x))/d))/E^((3*b*(c + d*x))/d)) + Sqrt[3]*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-3*b*(c + d*x))/d] + Sqrt[3]*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (3*b*(c + d*x))/d])*Sinh[(b*c)/d])/(d*Sqrt[c + d*x])) + (Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*((Sqrt[b]*Sqrt[6*Pi]*(Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]))/Sqrt[d] - (2*Sqrt[2]*Sinh[(3*b*(c + d*x))/d])/Sqrt[c + d*x]))/(Sqrt[2]*d)) + Sinh[3*a]*((Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-((1 + E^((6*b*(c + d*x))/d))/E^((3*b*(c + d*x))/d)) + Sqrt[3]*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-3*b*(c + d*x))/d] + Sqrt[3]*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (3*b*(c + d*x))/d]))/(d*Sqrt[c + d*x]) - ((1 + 2*Cosh[(2*b*c)/d])*Sinh[(b*c)/d]*((Sqrt[b]*Sqrt[6*Pi]*(Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]))/Sqrt[d] - (2*Sqrt[2]*Sinh[(3*b*(c + d*x))/d])/Sqrt[c + d*x]))/(Sqrt[2]*d)))/4","B",1
58,1,253,277,2.9122031,"\int \frac{\sinh ^3(a+b x)}{(c+d x)^{5/2}} \, dx","Integrate[Sinh[a + b*x]^3/(c + d*x)^(5/2),x]","\frac{e^{-3 \left(a+\frac{b c}{d}\right)} \left(-3 \sqrt{3} e^{6 a} d \left(-\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 b (c+d x)}{d}\right)+3 d e^{4 a+\frac{2 b c}{d}} \left(-\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)-3 d e^{2 a+\frac{4 b c}{d}} \left(\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)-4 e^{3 \left(a+\frac{b c}{d}\right)} \sinh ^2(a+b x) (6 b (c+d x) \cosh (a+b x)+d \sinh (a+b x))+3 \sqrt{3} d e^{\frac{6 b c}{d}} \left(\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{3 b (c+d x)}{d}\right)\right)}{6 d^2 (c+d x)^{3/2}}","\frac{\sqrt{\pi } b^{3/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 d^{5/2}}-\frac{\sqrt{3 \pi } b^{3/2} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 d^{5/2}}-\frac{\sqrt{\pi } b^{3/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 d^{5/2}}+\frac{\sqrt{3 \pi } b^{3/2} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 d^{5/2}}-\frac{4 b \sinh ^2(a+b x) \cosh (a+b x)}{d^2 \sqrt{c+d x}}-\frac{2 \sinh ^3(a+b x)}{3 d (c+d x)^{3/2}}",1,"(-3*Sqrt[3]*d*E^(6*a)*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + 3*d*E^(4*a + (2*b*c)/d)*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, -((b*(c + d*x))/d)] - 3*d*E^(2*a + (4*b*c)/d)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d] + 3*Sqrt[3]*d*E^((6*b*c)/d)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (3*b*(c + d*x))/d] - 4*E^(3*(a + (b*c)/d))*Sinh[a + b*x]^2*(6*b*(c + d*x)*Cosh[a + b*x] + d*Sinh[a + b*x]))/(6*d^2*E^(3*(a + (b*c)/d))*(c + d*x)^(3/2))","A",1
59,1,3211,331,17.8074255,"\int \frac{\sinh ^3(a+b x)}{(c+d x)^{7/2}} \, dx","Integrate[Sinh[a + b*x]^3/(c + d*x)^(7/2),x]","\text{Result too large to show}","-\frac{\sqrt{\pi } b^{5/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{3 \sqrt{3 \pi } b^{5/2} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{\sqrt{\pi } b^{5/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{3 \sqrt{3 \pi } b^{5/2} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{24 b^2 \sinh ^3(a+b x)}{5 d^3 \sqrt{c+d x}}-\frac{16 b^2 \sinh (a+b x)}{5 d^3 \sqrt{c+d x}}-\frac{4 b \sinh ^2(a+b x) \cosh (a+b x)}{5 d^2 (c+d x)^{3/2}}-\frac{2 \sinh ^3(a+b x)}{5 d (c+d x)^{5/2}}",1,"(-3*(Cosh[a]*(-1/30*((-2*E^((b*(c + d*x))/d)*(3*d^2 + 2*b*d*(c + d*x) + 4*b^2*(c + d*x)^2) + 8*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, -((b*(c + d*x))/d)] + (-6*d^2 + 4*b*d*(c + d*x) - 8*b^2*(c + d*x)^2 + 8*b*d*E^((b*(c + d*x))/d)*(c + d*x)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d])/E^((b*(c + d*x))/d))*Sinh[(b*c)/d])/(d^3*(c + d*x)^(5/2)) + (2*Cosh[(b*c)/d]*(-1/2*(b*(c + d*x)*(2*E^((b*(c + d*x))/d)*(d + 2*b*(c + d*x)) + 4*d*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, -((b*(c + d*x))/d)] + (2*(d - 2*b*(c + d*x) + 2*d*E^((b*(c + d*x))/d)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d]))/E^((b*(c + d*x))/d))) - 3*d^2*Sinh[(b*(c + d*x))/d]))/(15*d^3*(c + d*x)^(5/2))) + Sinh[a]*((Cosh[(b*c)/d]*(-2*E^((b*(c + d*x))/d)*(3*d^2 + 2*b*d*(c + d*x) + 4*b^2*(c + d*x)^2) + 8*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, -((b*(c + d*x))/d)] + (-6*d^2 + 4*b*d*(c + d*x) - 8*b^2*(c + d*x)^2 + 8*b*d*E^((b*(c + d*x))/d)*(c + d*x)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d])/E^((b*(c + d*x))/d)))/(30*d^3*(c + d*x)^(5/2)) - (2*Sinh[(b*c)/d]*(-1/2*(b*(c + d*x)*(2*E^((b*(c + d*x))/d)*(d + 2*b*(c + d*x)) + 4*d*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, -((b*(c + d*x))/d)] + (2*(d - 2*b*(c + d*x) + 2*d*E^((b*(c + d*x))/d)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d]))/E^((b*(c + d*x))/d))) - 3*d^2*Sinh[(b*(c + d*x))/d]))/(15*d^3*(c + d*x)^(5/2)))))/4 + (-(Sinh[3*a]*(-1/10*((1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d))*Sinh[(b*c)/d])/(d^3*(c + d*x)^(5/2)) - (2*Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2)))) - Cosh[3*a]*((Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d)))/(10*d^3*(c + d*x)^(5/2)) + (2*(1 + 2*Cosh[(2*b*c)/d])*Sinh[(b*c)/d]*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2))))/8 + (Sinh[3*a]*(-1/10*((1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d))*Sinh[(b*c)/d])/(d^3*(c + d*x)^(5/2)) - (2*Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2))) + Cosh[3*a]*((Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d)))/(10*d^3*(c + d*x)^(5/2)) + (2*(1 + 2*Cosh[(2*b*c)/d])*Sinh[(b*c)/d]*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2))))/8 + (Cosh[3*a]*(-1/10*((1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d))*Sinh[(b*c)/d])/(d^3*(c + d*x)^(5/2)) - (2*Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2))) + Sinh[3*a]*((Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d)))/(10*d^3*(c + d*x)^(5/2)) + (2*(1 + 2*Cosh[(2*b*c)/d])*Sinh[(b*c)/d]*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2))))/4","B",1
60,1,50,111,0.0134788,"\int (d x)^{3/2} \sinh (f x) \, dx","Integrate[(d*x)^(3/2)*Sinh[f*x],x]","\frac{d^2 \left(\sqrt{-f x} \Gamma \left(\frac{5}{2},-f x\right)+\sqrt{f x} \Gamma \left(\frac{5}{2},f x\right)\right)}{2 f^3 \sqrt{d x}}","-\frac{3 \sqrt{\pi } d^{3/2} \text{erf}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{8 f^{5/2}}+\frac{3 \sqrt{\pi } d^{3/2} \text{erfi}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{8 f^{5/2}}-\frac{3 d \sqrt{d x} \sinh (f x)}{2 f^2}+\frac{(d x)^{3/2} \cosh (f x)}{f}",1,"(d^2*(Sqrt[-(f*x)]*Gamma[5/2, -(f*x)] + Sqrt[f*x]*Gamma[5/2, f*x]))/(2*f^3*Sqrt[d*x])","A",1
61,1,49,92,0.0148148,"\int \sqrt{d x} \sinh (f x) \, dx","Integrate[Sqrt[d*x]*Sinh[f*x],x]","\frac{d \left(\sqrt{f x} \Gamma \left(\frac{3}{2},f x\right)-\sqrt{-f x} \Gamma \left(\frac{3}{2},-f x\right)\right)}{2 f^2 \sqrt{d x}}","-\frac{\sqrt{\pi } \sqrt{d} \text{erf}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{4 f^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \text{erfi}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{4 f^{3/2}}+\frac{\sqrt{d x} \cosh (f x)}{f}",1,"(d*(-(Sqrt[-(f*x)]*Gamma[3/2, -(f*x)]) + Sqrt[f*x]*Gamma[3/2, f*x]))/(2*f^2*Sqrt[d*x])","A",1
62,1,47,77,0.0078257,"\int \frac{\sinh (f x)}{\sqrt{d x}} \, dx","Integrate[Sinh[f*x]/Sqrt[d*x],x]","\frac{\sqrt{-f x} \Gamma \left(\frac{1}{2},-f x\right)+\sqrt{f x} \Gamma \left(\frac{1}{2},f x\right)}{2 f \sqrt{d x}}","\frac{\sqrt{\pi } \text{erfi}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{2 \sqrt{d} \sqrt{f}}-\frac{\sqrt{\pi } \text{erf}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{2 \sqrt{d} \sqrt{f}}",1,"(Sqrt[-(f*x)]*Gamma[1/2, -(f*x)] + Sqrt[f*x]*Gamma[1/2, f*x])/(2*f*Sqrt[d*x])","A",1
63,1,49,87,0.0194379,"\int \frac{\sinh (f x)}{(d x)^{3/2}} \, dx","Integrate[Sinh[f*x]/(d*x)^(3/2),x]","\frac{x \left(-2 \sinh (f x)+\sqrt{-f x} \Gamma \left(\frac{1}{2},-f x\right)-\sqrt{f x} \Gamma \left(\frac{1}{2},f x\right)\right)}{(d x)^{3/2}}","\frac{\sqrt{\pi } \sqrt{f} \text{erf}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{\sqrt{\pi } \sqrt{f} \text{erfi}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \sinh (f x)}{d \sqrt{d x}}",1,"(x*(Sqrt[-(f*x)]*Gamma[1/2, -(f*x)] - Sqrt[f*x]*Gamma[1/2, f*x] - 2*Sinh[f*x]))/(d*x)^(3/2)","A",1
64,1,84,114,0.0782414,"\int \frac{\sinh (f x)}{(d x)^{5/2}} \, dx","Integrate[Sinh[f*x]/(d*x)^(5/2),x]","-\frac{x e^{-f x} \left(e^{2 f x}+2 f x e^{2 f x}+2 f x+2 e^{f x} (-f x)^{3/2} \Gamma \left(\frac{1}{2},-f x\right)-2 e^{f x} (f x)^{3/2} \Gamma \left(\frac{1}{2},f x\right)-1\right)}{3 (d x)^{5/2}}","-\frac{2 \sqrt{\pi } f^{3/2} \text{erf}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}+\frac{2 \sqrt{\pi } f^{3/2} \text{erfi}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 f \cosh (f x)}{3 d^2 \sqrt{d x}}-\frac{2 \sinh (f x)}{3 d (d x)^{3/2}}",1,"-1/3*(x*(-1 + E^(2*f*x) + 2*f*x + 2*E^(2*f*x)*f*x + 2*E^(f*x)*(-(f*x))^(3/2)*Gamma[1/2, -(f*x)] - 2*E^(f*x)*(f*x)^(3/2)*Gamma[1/2, f*x]))/(E^(f*x)*(d*x)^(5/2))","A",1
65,0,0,19,22.6585969,"\int \sqrt{c+d x} \text{csch}(a+b x) \, dx","Integrate[Sqrt[c + d*x]*Csch[a + b*x],x]","\int \sqrt{c+d x} \text{csch}(a+b x) \, dx","\text{Int}\left(\sqrt{c+d x} \text{csch}(a+b x),x\right)",0,"Integrate[Sqrt[c + d*x]*Csch[a + b*x], x]","A",-1
66,0,0,19,21.0345774,"\int \frac{\text{csch}(a+b x)}{\sqrt{c+d x}} \, dx","Integrate[Csch[a + b*x]/Sqrt[c + d*x],x]","\int \frac{\text{csch}(a+b x)}{\sqrt{c+d x}} \, dx","\text{Int}\left(\frac{\text{csch}(a+b x)}{\sqrt{c+d x}},x\right)",0,"Integrate[Csch[a + b*x]/Sqrt[c + d*x], x]","A",-1
67,0,0,63,6.0365897,"\int \frac{\sinh ^{\frac{3}{2}}(x)}{x^3} \, dx","Integrate[Sinh[x]^(3/2)/x^3,x]","\int \frac{\sinh ^{\frac{3}{2}}(x)}{x^3} \, dx","\frac{9}{8} \text{Int}\left(\frac{\sinh ^{\frac{3}{2}}(x)}{x},x\right)+\frac{3}{8} \text{Int}\left(\frac{1}{x \sqrt{\sinh (x)}},x\right)-\frac{\sinh ^{\frac{3}{2}}(x)}{2 x^2}-\frac{3 \sqrt{\sinh (x)} \cosh (x)}{4 x}",0,"Integrate[Sinh[x]^(3/2)/x^3, x]","A",-1
68,1,17,20,0.1175046,"\int \left(\frac{x}{\sinh ^{\frac{3}{2}}(x)}-x \sqrt{\sinh (x)}\right) \, dx","Integrate[x/Sinh[x]^(3/2) - x*Sqrt[Sinh[x]],x]","\frac{4 \sinh (x)-2 x \cosh (x)}{\sqrt{\sinh (x)}}","4 \sqrt{\sinh (x)}-\frac{2 x \cosh (x)}{\sqrt{\sinh (x)}}",1,"(-2*x*Cosh[x] + 4*Sinh[x])/Sqrt[Sinh[x]]","A",1
69,1,22,24,0.0708143,"\int \left(\frac{x}{\sinh ^{\frac{5}{2}}(x)}+\frac{x}{3 \sqrt{\sinh (x)}}\right) \, dx","Integrate[x/Sinh[x]^(5/2) + x/(3*Sqrt[Sinh[x]]),x]","\frac{1}{6} \sqrt{\sinh (x)} (-8 \text{csch}(x)-4 x \coth (x) \text{csch}(x))","-\frac{4}{3 \sqrt{\sinh (x)}}-\frac{2 x \cosh (x)}{3 \sinh ^{\frac{3}{2}}(x)}",1,"((-8*Csch[x] - 4*x*Coth[x]*Csch[x])*Sqrt[Sinh[x]])/6","A",1
70,1,33,47,0.1225384,"\int \left(\frac{x}{\sinh ^{\frac{7}{2}}(x)}+\frac{3}{5} x \sqrt{\sinh (x)}\right) \, dx","Integrate[x/Sinh[x]^(7/2) + (3*x*Sqrt[Sinh[x]])/5,x]","\frac{46 \sinh (x)-18 \sinh (3 x)-21 x \cosh (x)+9 x \cosh (3 x)}{30 \sinh ^{\frac{5}{2}}(x)}","-\frac{4}{15 \sinh ^{\frac{3}{2}}(x)}-\frac{12 \sqrt{\sinh (x)}}{5}-\frac{2 x \cosh (x)}{5 \sinh ^{\frac{5}{2}}(x)}+\frac{6 x \cosh (x)}{5 \sqrt{\sinh (x)}}",1,"(-21*x*Cosh[x] + 9*x*Cosh[3*x] + 46*Sinh[x] - 18*Sinh[3*x])/(30*Sinh[x]^(5/2))","A",1
71,1,68,58,1.2346174,"\int \left(\frac{x^2}{\sinh ^{\frac{3}{2}}(x)}-x^2 \sqrt{\sinh (x)}\right) \, dx","Integrate[x^2/Sinh[x]^(3/2) - x^2*Sqrt[Sinh[x]],x]","-\frac{2 \left(-8 \sqrt{2} (\sinh (x)-\cosh (x)) \sqrt{-\sinh (x) (\sinh (x)+\cosh (x))} \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};\cosh (2 x)+\sinh (2 x)\right)+x^2 \cosh (x)-4 (x-2) \sinh (x)\right)}{\sqrt{\sinh (x)}}","-\frac{2 x^2 \cosh (x)}{\sqrt{\sinh (x)}}+8 x \sqrt{\sinh (x)}-\frac{16 i \sqrt{\sinh (x)} E\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right)}{\sqrt{i \sinh (x)}}",1,"(-2*(x^2*Cosh[x] - 4*(-2 + x)*Sinh[x] - 8*Sqrt[2]*Hypergeometric2F1[-1/4, 1/2, 3/4, Cosh[2*x] + Sinh[2*x]]*(-Cosh[x] + Sinh[x])*Sqrt[-(Sinh[x]*(Cosh[x] + Sinh[x]))]))/Sqrt[Sinh[x]]","C",1
72,0,0,21,3.0699793,"\int (c+d x)^m (b \sinh (e+f x))^n \, dx","Integrate[(c + d*x)^m*(b*Sinh[e + f*x])^n,x]","\int (c+d x)^m (b \sinh (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (b \sinh (e+f x))^n,x\right)",0,"Integrate[(c + d*x)^m*(b*Sinh[e + f*x])^n, x]","A",-1
73,1,206,237,0.1909085,"\int (c+d x)^m \sinh ^3(a+b x) \, dx","Integrate[(c + d*x)^m*Sinh[a + b*x]^3,x]","\frac{3^{-m-1} e^{-3 \left(a+\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{b^2 (c+d x)^2}{d^2}\right)^{-m} \left(e^{6 a} \left(b \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{3 b (c+d x)}{d}\right)-3^{m+2} e^{4 a+\frac{2 b c}{d}} \left(b \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{b (c+d x)}{d}\right)+e^{\frac{4 b c}{d}} \left(-\frac{b (c+d x)}{d}\right)^m \left(e^{\frac{2 b c}{d}} \Gamma \left(m+1,\frac{3 b (c+d x)}{d}\right)-e^{2 a} 3^{m+2} \Gamma \left(m+1,\frac{b (c+d x)}{d}\right)\right)\right)}{8 b}","\frac{3^{-m-1} e^{3 a-\frac{3 b c}{d}} (c+d x)^m \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{3 b (c+d x)}{d}\right)}{8 b}-\frac{3 e^{a-\frac{b c}{d}} (c+d x)^m \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{b (c+d x)}{d}\right)}{8 b}-\frac{3 e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{b (c+d x)}{d}\right)}{8 b}+\frac{3^{-m-1} e^{\frac{3 b c}{d}-3 a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{3 b (c+d x)}{d}\right)}{8 b}",1,"(3^(-1 - m)*(c + d*x)^m*(E^(6*a)*(b*(c/d + x))^m*Gamma[1 + m, (-3*b*(c + d*x))/d] - 3^(2 + m)*E^(4*a + (2*b*c)/d)*(b*(c/d + x))^m*Gamma[1 + m, -((b*(c + d*x))/d)] + E^((4*b*c)/d)*(-((b*(c + d*x))/d))^m*(-(3^(2 + m)*E^(2*a)*Gamma[1 + m, (b*(c + d*x))/d]) + E^((2*b*c)/d)*Gamma[1 + m, (3*b*(c + d*x))/d])))/(8*b*E^(3*(a + (b*c)/d))*(-((b^2*(c + d*x)^2)/d^2))^m)","A",1
74,1,131,144,0.1578403,"\int (c+d x)^m \sinh ^2(a+b x) \, dx","Integrate[(c + d*x)^m*Sinh[a + b*x]^2,x]","\frac{1}{8} (c+d x)^m \left(\frac{2^{-m} e^{2 a-\frac{2 b c}{d}} \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 b (c+d x)}{d}\right)}{b}-\frac{2^{-m} e^{\frac{2 b c}{d}-2 a} \left(\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 b (c+d x)}{d}\right)}{b}-\frac{4 (c+d x)}{d (m+1)}\right)","\frac{2^{-m-3} e^{2 a-\frac{2 b c}{d}} (c+d x)^m \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 b (c+d x)}{d}\right)}{b}-\frac{2^{-m-3} e^{\frac{2 b c}{d}-2 a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 b (c+d x)}{d}\right)}{b}-\frac{(c+d x)^{m+1}}{2 d (m+1)}",1,"((c + d*x)^m*((-4*(c + d*x))/(d*(1 + m)) + (E^(2*a - (2*b*c)/d)*Gamma[1 + m, (-2*b*(c + d*x))/d])/(2^m*b*(-((b*(c + d*x))/d))^m) - (E^(-2*a + (2*b*c)/d)*Gamma[1 + m, (2*b*(c + d*x))/d])/(2^m*b*((b*(c + d*x))/d)^m)))/8","A",1
75,1,101,110,0.0541359,"\int (c+d x)^m \sinh (a+b x) \, dx","Integrate[(c + d*x)^m*Sinh[a + b*x],x]","\frac{e^{-a-\frac{b c}{d}} (c+d x)^m \left(e^{2 a} \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{b (c+d x)}{d}\right)+e^{\frac{2 b c}{d}} \left(b \left(\frac{c}{d}+x\right)\right)^{-m} \Gamma \left(m+1,\frac{b (c+d x)}{d}\right)\right)}{2 b}","\frac{e^{a-\frac{b c}{d}} (c+d x)^m \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{b (c+d x)}{d}\right)}{2 b}+\frac{e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{b (c+d x)}{d}\right)}{2 b}",1,"(E^(-a - (b*c)/d)*(c + d*x)^m*((E^(2*a)*Gamma[1 + m, -((b*(c + d*x))/d)])/(-((b*(c + d*x))/d))^m + (E^((2*b*c)/d)*Gamma[1 + m, (b*(c + d*x))/d])/(b*(c/d + x))^m))/(2*b)","A",1
76,0,0,17,6.3683952,"\int (c+d x)^m \text{csch}(a+b x) \, dx","Integrate[(c + d*x)^m*Csch[a + b*x],x]","\int (c+d x)^m \text{csch}(a+b x) \, dx","\text{Int}\left(\text{csch}(a+b x) (c+d x)^m,x\right)",0,"Integrate[(c + d*x)^m*Csch[a + b*x], x]","A",-1
77,0,0,19,3.6747663,"\int (c+d x)^m \text{csch}^2(a+b x) \, dx","Integrate[(c + d*x)^m*Csch[a + b*x]^2,x]","\int (c+d x)^m \text{csch}^2(a+b x) \, dx","\text{Int}\left(\text{csch}^2(a+b x) (c+d x)^m,x\right)",0,"Integrate[(c + d*x)^m*Csch[a + b*x]^2, x]","A",-1
78,1,54,59,0.0257298,"\int x^{3+m} \sinh (a+b x) \, dx","Integrate[x^(3 + m)*Sinh[a + b*x],x]","\frac{e^{-a} x^m \left((b x)^{-m} \Gamma (m+4,b x)-e^{2 a} (-b x)^{-m} \Gamma (m+4,-b x)\right)}{2 b^4}","\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+4,b x)}{2 b^4}-\frac{e^a x^m (-b x)^{-m} \Gamma (m+4,-b x)}{2 b^4}",1,"(x^m*(-((E^(2*a)*Gamma[4 + m, -(b*x)])/(-(b*x))^m) + Gamma[4 + m, b*x]/(b*x)^m))/(2*b^4*E^a)","A",1
79,1,53,59,0.0192766,"\int x^{2+m} \sinh (a+b x) \, dx","Integrate[x^(2 + m)*Sinh[a + b*x],x]","\frac{e^{-a} x^m \left(e^{2 a} (-b x)^{-m} \Gamma (m+3,-b x)+(b x)^{-m} \Gamma (m+3,b x)\right)}{2 b^3}","\frac{e^a x^m (-b x)^{-m} \Gamma (m+3,-b x)}{2 b^3}+\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+3,b x)}{2 b^3}",1,"(x^m*((E^(2*a)*Gamma[3 + m, -(b*x)])/(-(b*x))^m + Gamma[3 + m, b*x]/(b*x)^m))/(2*b^3*E^a)","A",1
80,1,54,59,0.0216961,"\int x^{1+m} \sinh (a+b x) \, dx","Integrate[x^(1 + m)*Sinh[a + b*x],x]","\frac{e^{-a} x^m \left((b x)^{-m} \Gamma (m+2,b x)-e^{2 a} (-b x)^{-m} \Gamma (m+2,-b x)\right)}{2 b^2}","\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+2,b x)}{2 b^2}-\frac{e^a x^m (-b x)^{-m} \Gamma (m+2,-b x)}{2 b^2}",1,"(x^m*(-((E^(2*a)*Gamma[2 + m, -(b*x)])/(-(b*x))^m) + Gamma[2 + m, b*x]/(b*x)^m))/(2*b^2*E^a)","A",1
81,1,53,59,0.0169045,"\int x^m \sinh (a+b x) \, dx","Integrate[x^m*Sinh[a + b*x],x]","\frac{e^{-a} x^m \left(e^{2 a} (-b x)^{-m} \Gamma (m+1,-b x)+(b x)^{-m} \Gamma (m+1,b x)\right)}{2 b}","\frac{e^a x^m (-b x)^{-m} \Gamma (m+1,-b x)}{2 b}+\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{2 b}",1,"(x^m*((E^(2*a)*Gamma[1 + m, -(b*x)])/(-(b*x))^m + Gamma[1 + m, b*x]/(b*x)^m))/(2*b*E^a)","A",1
82,1,49,49,0.0218436,"\int x^{-1+m} \sinh (a+b x) \, dx","Integrate[x^(-1 + m)*Sinh[a + b*x],x]","\frac{1}{2} e^{-a} x^m (b x)^{-m} \Gamma (m,b x)-\frac{1}{2} e^a x^m (-b x)^{-m} \Gamma (m,-b x)","\frac{1}{2} e^{-a} x^m (b x)^{-m} \Gamma (m,b x)-\frac{1}{2} e^a x^m (-b x)^{-m} \Gamma (m,-b x)",1,"-1/2*(E^a*x^m*Gamma[m, -(b*x)])/(-(b*x))^m + (x^m*Gamma[m, b*x])/(2*E^a*(b*x)^m)","A",1
83,1,51,55,0.0181087,"\int x^{-2+m} \sinh (a+b x) \, dx","Integrate[x^(-2 + m)*Sinh[a + b*x],x]","\frac{1}{2} e^{-a} b x^m \left(e^{2 a} (-b x)^{-m} \Gamma (m-1,-b x)+(b x)^{-m} \Gamma (m-1,b x)\right)","\frac{1}{2} e^a b x^m (-b x)^{-m} \Gamma (m-1,-b x)+\frac{1}{2} e^{-a} b x^m (b x)^{-m} \Gamma (m-1,b x)",1,"(b*x^m*((E^(2*a)*Gamma[-1 + m, -(b*x)])/(-(b*x))^m + Gamma[-1 + m, b*x]/(b*x)^m))/(2*E^a)","A",1
84,1,54,59,0.0216289,"\int x^{-3+m} \sinh (a+b x) \, dx","Integrate[x^(-3 + m)*Sinh[a + b*x],x]","\frac{1}{2} e^{-a} b^2 x^m \left((b x)^{-m} \Gamma (m-2,b x)-e^{2 a} (-b x)^{-m} \Gamma (m-2,-b x)\right)","\frac{1}{2} e^{-a} b^2 x^m (b x)^{-m} \Gamma (m-2,b x)-\frac{1}{2} e^a b^2 x^m (-b x)^{-m} \Gamma (m-2,-b x)",1,"(b^2*x^m*(-((E^(2*a)*Gamma[-2 + m, -(b*x)])/(-(b*x))^m) + Gamma[-2 + m, b*x]/(b*x)^m))/(2*E^a)","A",1
85,1,79,86,0.123196,"\int x^{3+m} \sinh ^2(a+b x) \, dx","Integrate[x^(3 + m)*Sinh[a + b*x]^2,x]","\frac{1}{64} x^m \left(-\frac{e^{2 a} 2^{-m} (-b x)^{-m} \Gamma (m+4,-2 b x)}{b^4}-\frac{e^{-2 a} 2^{-m} (b x)^{-m} \Gamma (m+4,2 b x)}{b^4}-\frac{32 x^4}{m+4}\right)","-\frac{e^{2 a} 2^{-m-6} x^m (-b x)^{-m} \Gamma (m+4,-2 b x)}{b^4}-\frac{e^{-2 a} 2^{-m-6} x^m (b x)^{-m} \Gamma (m+4,2 b x)}{b^4}-\frac{x^{m+4}}{2 (m+4)}",1,"(x^m*((-32*x^4)/(4 + m) - (E^(2*a)*Gamma[4 + m, -2*b*x])/(2^m*b^4*(-(b*x))^m) - Gamma[4 + m, 2*b*x]/(2^m*b^4*E^(2*a)*(b*x)^m)))/64","A",1
86,1,78,85,0.1206856,"\int x^{2+m} \sinh ^2(a+b x) \, dx","Integrate[x^(2 + m)*Sinh[a + b*x]^2,x]","\frac{1}{32} x^m \left(\frac{e^{2 a} 2^{-m} (-b x)^{-m} \Gamma (m+3,-2 b x)}{b^3}-\frac{e^{-2 a} 2^{-m} (b x)^{-m} \Gamma (m+3,2 b x)}{b^3}-\frac{16 x^3}{m+3}\right)","\frac{e^{2 a} 2^{-m-5} x^m (-b x)^{-m} \Gamma (m+3,-2 b x)}{b^3}-\frac{e^{-2 a} 2^{-m-5} x^m (b x)^{-m} \Gamma (m+3,2 b x)}{b^3}-\frac{x^{m+3}}{2 (m+3)}",1,"(x^m*((-16*x^3)/(3 + m) + (E^(2*a)*Gamma[3 + m, -2*b*x])/(2^m*b^3*(-(b*x))^m) - Gamma[3 + m, 2*b*x]/(2^m*b^3*E^(2*a)*(b*x)^m)))/32","A",1
87,1,79,86,0.1285356,"\int x^{1+m} \sinh ^2(a+b x) \, dx","Integrate[x^(1 + m)*Sinh[a + b*x]^2,x]","\frac{1}{16} x^m \left(-\frac{e^{2 a} 2^{-m} (-b x)^{-m} \Gamma (m+2,-2 b x)}{b^2}-\frac{e^{-2 a} 2^{-m} (b x)^{-m} \Gamma (m+2,2 b x)}{b^2}-\frac{8 x^2}{m+2}\right)","-\frac{e^{2 a} 2^{-m-4} x^m (-b x)^{-m} \Gamma (m+2,-2 b x)}{b^2}-\frac{e^{-2 a} 2^{-m-4} x^m (b x)^{-m} \Gamma (m+2,2 b x)}{b^2}-\frac{x^{m+2}}{2 (m+2)}",1,"(x^m*((-8*x^2)/(2 + m) - (E^(2*a)*Gamma[2 + m, -2*b*x])/(2^m*b^2*(-(b*x))^m) - Gamma[2 + m, 2*b*x]/(2^m*b^2*E^(2*a)*(b*x)^m)))/16","A",1
88,1,76,85,0.1056348,"\int x^m \sinh ^2(a+b x) \, dx","Integrate[x^m*Sinh[a + b*x]^2,x]","\frac{1}{8} x^m \left(\frac{e^{2 a} 2^{-m} (-b x)^{-m} \Gamma (m+1,-2 b x)}{b}-\frac{e^{-2 a} 2^{-m} (b x)^{-m} \Gamma (m+1,2 b x)}{b}-\frac{4 x}{m+1}\right)","\frac{e^{2 a} 2^{-m-3} x^m (-b x)^{-m} \Gamma (m+1,-2 b x)}{b}-\frac{e^{-2 a} 2^{-m-3} x^m (b x)^{-m} \Gamma (m+1,2 b x)}{b}-\frac{x^{m+1}}{2 (m+1)}",1,"(x^m*((-4*x)/(1 + m) + (E^(2*a)*Gamma[1 + m, -2*b*x])/(2^m*b*(-(b*x))^m) - Gamma[1 + m, 2*b*x]/(2^m*b*E^(2*a)*(b*x)^m)))/8","A",1
89,1,63,72,0.0745713,"\int x^{-1+m} \sinh ^2(a+b x) \, dx","Integrate[x^(-1 + m)*Sinh[a + b*x]^2,x]","-\frac{x^m \left(e^{2 a} 2^{-m} m (-b x)^{-m} \Gamma (m,-2 b x)+e^{-2 a} 2^{-m} m (b x)^{-m} \Gamma (m,2 b x)+2\right)}{4 m}","e^{2 a} \left(-2^{-m-2}\right) x^m (-b x)^{-m} \Gamma (m,-2 b x)-e^{-2 a} 2^{-m-2} x^m (b x)^{-m} \Gamma (m,2 b x)-\frac{x^m}{2 m}",1,"-1/4*(x^m*(2 + (E^(2*a)*m*Gamma[m, -2*b*x])/(2^m*(-(b*x))^m) + (m*Gamma[m, 2*b*x])/(2^m*E^(2*a)*(b*x)^m)))/m","A",1
90,1,72,83,0.0985777,"\int x^{-2+m} \sinh ^2(a+b x) \, dx","Integrate[x^(-2 + m)*Sinh[a + b*x]^2,x]","\frac{1}{2} x^m \left(e^{2 a} b 2^{-m} (-b x)^{-m} \Gamma (m-1,-2 b x)-e^{-2 a} b 2^{-m} (b x)^{-m} \Gamma (m-1,2 b x)+\frac{1}{x-m x}\right)","e^{2 a} b 2^{-m-1} x^m (-b x)^{-m} \Gamma (m-1,-2 b x)-e^{-2 a} b 2^{-m-1} x^m (b x)^{-m} \Gamma (m-1,2 b x)+\frac{x^{m-1}}{2 (1-m)}",1,"(x^m*((x - m*x)^(-1) + (b*E^(2*a)*Gamma[-1 + m, -2*b*x])/(2^m*(-(b*x))^m) - (b*Gamma[-1 + m, 2*b*x])/(2^m*E^(2*a)*(b*x)^m)))/2","A",1
91,1,77,84,0.1135226,"\int x^{-3+m} \sinh ^2(a+b x) \, dx","Integrate[x^(-3 + m)*Sinh[a + b*x]^2,x]","x^m \left(e^{2 a} b^2 \left(-2^{-m}\right) (-b x)^{-m} \Gamma (m-2,-2 b x)-e^{-2 a} b^2 2^{-m} (b x)^{-m} \Gamma (m-2,2 b x)+\frac{1}{(4-2 m) x^2}\right)","-e^{2 a} b^2 2^{-m} x^m (-b x)^{-m} \Gamma (m-2,-2 b x)-e^{-2 a} b^2 2^{-m} x^m (b x)^{-m} \Gamma (m-2,2 b x)+\frac{x^{m-2}}{2 (2-m)}",1,"x^m*(1/((4 - 2*m)*x^2) - (b^2*E^(2*a)*Gamma[-2 + m, -2*b*x])/(2^m*(-(b*x))^m) - (b^2*Gamma[-2 + m, 2*b*x])/(2^m*E^(2*a)*(b*x)^m))","A",1
92,1,17,24,0.0981975,"\int \left(\frac{x}{\text{csch}^{\frac{3}{2}}(x)}+\frac{1}{3} x \sqrt{\text{csch}(x)}\right) \, dx","Integrate[x/Csch[x]^(3/2) + (x*Sqrt[Csch[x]])/3,x]","\frac{2 (3 x \coth (x)-2)}{9 \text{csch}^{\frac{3}{2}}(x)}","\frac{2 x \cosh (x)}{3 \sqrt{\text{csch}(x)}}-\frac{4}{9 \text{csch}^{\frac{3}{2}}(x)}",1,"(2*(-2 + 3*x*Coth[x]))/(9*Csch[x]^(3/2))","A",1
93,1,17,24,0.1284718,"\int \left(\frac{x}{\text{csch}^{\frac{5}{2}}(x)}+\frac{3 x}{5 \sqrt{\text{csch}(x)}}\right) \, dx","Integrate[x/Csch[x]^(5/2) + (3*x)/(5*Sqrt[Csch[x]]),x]","\frac{2 (5 x \coth (x)-2)}{25 \text{csch}^{\frac{5}{2}}(x)}","\frac{2 x \cosh (x)}{5 \text{csch}^{\frac{3}{2}}(x)}-\frac{4}{25 \text{csch}^{\frac{5}{2}}(x)}",1,"(2*(-2 + 5*x*Coth[x]))/(25*Csch[x]^(5/2))","A",1
94,1,45,47,0.109725,"\int \left(\frac{x}{\text{csch}^{\frac{7}{2}}(x)}-\frac{5}{21} x \sqrt{\text{csch}(x)}\right) \, dx","Integrate[x/Csch[x]^(7/2) - (5*x*Sqrt[Csch[x]])/21,x]","\sqrt{\text{csch}(x)} \left(-\frac{13}{42} x \sinh (2 x)+\frac{1}{28} x \sinh (4 x)+\frac{88}{441} \cosh (2 x)-\frac{1}{98} \cosh (4 x)-\frac{167}{882}\right)","\frac{20}{63 \text{csch}^{\frac{3}{2}}(x)}-\frac{4}{49 \text{csch}^{\frac{7}{2}}(x)}+\frac{2 x \cosh (x)}{7 \text{csch}^{\frac{5}{2}}(x)}-\frac{10 x \cosh (x)}{21 \sqrt{\text{csch}(x)}}",1,"Sqrt[Csch[x]]*(-167/882 + (88*Cosh[2*x])/441 - Cosh[4*x]/98 - (13*x*Sinh[2*x])/42 + (x*Sinh[4*x])/28)","A",1
95,1,63,76,0.1480355,"\int \left(\frac{x^2}{\text{csch}^{\frac{3}{2}}(x)}+\frac{1}{3} x^2 \sqrt{\text{csch}(x)}\right) \, dx","Integrate[x^2/Csch[x]^(3/2) + (x^2*Sqrt[Csch[x]])/3,x]","\frac{1}{27} \sqrt{\text{csch}(x)} \left(9 x^2 \sinh (2 x)+12 x+8 \sinh (2 x)-12 x \cosh (2 x)-16 i \sqrt{i \sinh (x)} F\left(\left.\frac{1}{4} (\pi -2 i x)\right|2\right)\right)","\frac{2 x^2 \cosh (x)}{3 \sqrt{\text{csch}(x)}}-\frac{8 x}{9 \text{csch}^{\frac{3}{2}}(x)}+\frac{16 \cosh (x)}{27 \sqrt{\text{csch}(x)}}-\frac{16}{27} i \sqrt{i \sinh (x)} \sqrt{\text{csch}(x)} F\left(\left.\frac{\pi }{4}-\frac{i x}{2}\right|2\right)",1,"(Sqrt[Csch[x]]*(12*x - 12*x*Cosh[2*x] - (16*I)*EllipticF[(Pi - (2*I)*x)/4, 2]*Sqrt[I*Sinh[x]] + 8*Sinh[2*x] + 9*x^2*Sinh[2*x]))/27","A",1
96,1,128,98,0.8209876,"\int (c+d x)^3 (a+i a \sinh (e+f x)) \, dx","Integrate[(c + d*x)^3*(a + I*a*Sinh[e + f*x]),x]","\frac{a \left(-12 i d \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \sinh (e+f x)+4 i f (c+d x) \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+6\right)\right) \cosh (e+f x)+f^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right)}{4 f^4}","\frac{6 i a d^2 (c+d x) \cosh (e+f x)}{f^3}-\frac{3 i a d (c+d x)^2 \sinh (e+f x)}{f^2}+\frac{i a (c+d x)^3 \cosh (e+f x)}{f}+\frac{a (c+d x)^4}{4 d}-\frac{6 i a d^3 \sinh (e+f x)}{f^4}",1,"(a*(f^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) + (4*I)*f*(c + d*x)*(c^2*f^2 + 2*c*d*f^2*x + d^2*(6 + f^2*x^2))*Cosh[e + f*x] - (12*I)*d*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Sinh[e + f*x]))/(4*f^4)","A",1
97,1,88,74,0.4290756,"\int (c+d x)^2 (a+i a \sinh (e+f x)) \, dx","Integrate[(c + d*x)^2*(a + I*a*Sinh[e + f*x]),x]","\frac{a \left(3 i \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \cosh (e+f x)+f^3 x \left(3 c^2+3 c d x+d^2 x^2\right)-6 i d f (c+d x) \sinh (e+f x)\right)}{3 f^3}","-\frac{2 i a d (c+d x) \sinh (e+f x)}{f^2}+\frac{i a (c+d x)^2 \cosh (e+f x)}{f}+\frac{a (c+d x)^3}{3 d}+\frac{2 i a d^2 \cosh (e+f x)}{f^3}",1,"(a*(f^3*x*(3*c^2 + 3*c*d*x + d^2*x^2) + (3*I)*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Cosh[e + f*x] - (6*I)*d*f*(c + d*x)*Sinh[e + f*x]))/(3*f^3)","A",1
98,1,48,50,0.0863024,"\int (c+d x) (a+i a \sinh (e+f x)) \, dx","Integrate[(c + d*x)*(a + I*a*Sinh[e + f*x]),x]","\frac{a \left(2 i f (c+d x) \cosh (e+f x)+f^2 x (2 c+d x)-2 i d \sinh (e+f x)\right)}{2 f^2}","\frac{i a (c+d x) \cosh (e+f x)}{f}+\frac{a (c+d x)^2}{2 d}-\frac{i a d \sinh (e+f x)}{f^2}",1,"(a*(f^2*x*(2*c + d*x) + (2*I)*f*(c + d*x)*Cosh[e + f*x] - (2*I)*d*Sinh[e + f*x]))/(2*f^2)","A",1
99,1,60,70,0.2856284,"\int \frac{a+i a \sinh (e+f x)}{c+d x} \, dx","Integrate[(a + I*a*Sinh[e + f*x])/(c + d*x),x]","\frac{a \left(i \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+i \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+\log (c+d x)\right)}{d}","\frac{i a \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{d}+\frac{i a \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d}+\frac{a \log (c+d x)}{d}",1,"(a*(Log[c + d*x] + I*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] + I*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)]))/d","A",1
100,1,83,95,0.4807488,"\int \frac{a+i a \sinh (e+f x)}{(c+d x)^2} \, dx","Integrate[(a + I*a*Sinh[e + f*x])/(c + d*x)^2,x]","\frac{i a \left(f (c+d x) \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+f (c+d x) \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-d (\sinh (e+f x)-i)\right)}{d^2 (c+d x)}","\frac{i a f \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{i a f \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{i a \sinh (e+f x)}{d (c+d x)}-\frac{a}{d (c+d x)}",1,"(I*a*(f*(c + d*x)*Cosh[e - (c*f)/d]*CoshIntegral[f*(c/d + x)] - d*(-I + Sinh[e + f*x]) + f*(c + d*x)*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)]))/(d^2*(c + d*x))","A",1
101,1,109,131,0.6502715,"\int \frac{a+i a \sinh (e+f x)}{(c+d x)^3} \, dx","Integrate[(a + I*a*Sinh[e + f*x])/(c + d*x)^3,x]","\frac{i a \left(f^2 (c+d x)^2 \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+f^2 (c+d x)^2 \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-d (f (c+d x) \cosh (e+f x)+d (\sinh (e+f x)-i))\right)}{2 d^3 (c+d x)^2}","\frac{i a f^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{2 d^3}+\frac{i a f^2 \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{2 d^3}-\frac{i a f \cosh (e+f x)}{2 d^2 (c+d x)}-\frac{i a \sinh (e+f x)}{2 d (c+d x)^2}-\frac{a}{2 d (c+d x)^2}",1,"((I/2)*a*(f^2*(c + d*x)^2*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] - d*(f*(c + d*x)*Cosh[e + f*x] + d*(-I + Sinh[e + f*x])) + f^2*(c + d*x)^2*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)]))/(d^3*(c + d*x)^2)","A",1
102,1,220,245,1.4140699,"\int (c+d x)^3 (a+i a \sinh (e+f x))^2 \, dx","Integrate[(c + d*x)^3*(a + I*a*Sinh[e + f*x])^2,x]","\frac{a^2 \left(-2 f (c+d x) \left(2 c^2 f^2+4 c d f^2 x+d^2 \left(2 f^2 x^2+3\right)\right) \sinh (2 (e+f x))-96 i d \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \sinh (e+f x)+32 i f (c+d x) \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+6\right)\right) \cosh (e+f x)+3 d \left(2 c^2 f^2+4 c d f^2 x+d^2 \left(2 f^2 x^2+1\right)\right) \cosh (2 (e+f x))+6 f^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right)}{16 f^4}","\frac{12 i a^2 d^2 (c+d x) \cosh (e+f x)}{f^3}-\frac{3 a^2 d^2 (c+d x) \sinh (e+f x) \cosh (e+f x)}{4 f^3}+\frac{3 a^2 c d^2 x}{4 f^2}+\frac{3 a^2 d (c+d x)^2 \sinh ^2(e+f x)}{4 f^2}-\frac{6 i a^2 d (c+d x)^2 \sinh (e+f x)}{f^2}+\frac{2 i a^2 (c+d x)^3 \cosh (e+f x)}{f}-\frac{a^2 (c+d x)^3 \sinh (e+f x) \cosh (e+f x)}{2 f}+\frac{3 a^2 (c+d x)^4}{8 d}+\frac{3 a^2 d^3 \sinh ^2(e+f x)}{8 f^4}-\frac{12 i a^2 d^3 \sinh (e+f x)}{f^4}+\frac{3 a^2 d^3 x^2}{8 f^2}",1,"(a^2*(6*f^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) + (32*I)*f*(c + d*x)*(c^2*f^2 + 2*c*d*f^2*x + d^2*(6 + f^2*x^2))*Cosh[e + f*x] + 3*d*(2*c^2*f^2 + 4*c*d*f^2*x + d^2*(1 + 2*f^2*x^2))*Cosh[2*(e + f*x)] - (96*I)*d*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Sinh[e + f*x] - 2*f*(c + d*x)*(2*c^2*f^2 + 4*c*d*f^2*x + d^2*(3 + 2*f^2*x^2))*Sinh[2*(e + f*x)]))/(16*f^4)","A",1
103,1,189,174,0.6881078,"\int (c+d x)^2 (a+i a \sinh (e+f x))^2 \, dx","Integrate[(c + d*x)^2*(a + I*a*Sinh[e + f*x])^2,x]","\frac{a^2 \left(16 i \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \cosh (e+f x)-2 c^2 f^2 \sinh (2 (e+f x))+12 c^2 f^3 x-4 c d f^2 x \sinh (2 (e+f x))-32 i c d f \sinh (e+f x)+2 d f (c+d x) \cosh (2 (e+f x))+12 c d f^3 x^2-2 d^2 f^2 x^2 \sinh (2 (e+f x))-32 i d^2 f x \sinh (e+f x)-d^2 \sinh (2 (e+f x))+4 d^2 f^3 x^3\right)}{8 f^3}","\frac{a^2 d (c+d x) \sinh ^2(e+f x)}{2 f^2}-\frac{4 i a^2 d (c+d x) \sinh (e+f x)}{f^2}+\frac{2 i a^2 (c+d x)^2 \cosh (e+f x)}{f}-\frac{a^2 (c+d x)^2 \sinh (e+f x) \cosh (e+f x)}{2 f}+\frac{a^2 (c+d x)^3}{2 d}+\frac{4 i a^2 d^2 \cosh (e+f x)}{f^3}-\frac{a^2 d^2 \sinh (e+f x) \cosh (e+f x)}{4 f^3}+\frac{a^2 d^2 x}{4 f^2}",1,"(a^2*(12*c^2*f^3*x + 12*c*d*f^3*x^2 + 4*d^2*f^3*x^3 + (16*I)*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Cosh[e + f*x] + 2*d*f*(c + d*x)*Cosh[2*(e + f*x)] - (32*I)*c*d*f*Sinh[e + f*x] - (32*I)*d^2*f*x*Sinh[e + f*x] - d^2*Sinh[2*(e + f*x)] - 2*c^2*f^2*Sinh[2*(e + f*x)] - 4*c*d*f^2*x*Sinh[2*(e + f*x)] - 2*d^2*f^2*x^2*Sinh[2*(e + f*x)]))/(8*f^3)","A",1
104,1,86,122,1.1767089,"\int (c+d x) (a+i a \sinh (e+f x))^2 \, dx","Integrate[(c + d*x)*(a + I*a*Sinh[e + f*x])^2,x]","\frac{a^2 (-2 (3 (e+f x) (-2 c f+d e-d f x)+f (c+d x) \sinh (2 (e+f x))+8 i d \sinh (e+f x))+16 i f (c+d x) \cosh (e+f x)+d \cosh (2 (e+f x)))}{8 f^2}","\frac{2 i a^2 (c+d x) \cosh (e+f x)}{f}-\frac{a^2 (c+d x) \sinh (e+f x) \cosh (e+f x)}{2 f}+\frac{a^2 (c+d x)^2}{2 d}+\frac{1}{2} a^2 c x+\frac{a^2 d \sinh ^2(e+f x)}{4 f^2}-\frac{2 i a^2 d \sinh (e+f x)}{f^2}+\frac{1}{4} a^2 d x^2",1,"(a^2*((16*I)*f*(c + d*x)*Cosh[e + f*x] + d*Cosh[2*(e + f*x)] - 2*(3*(e + f*x)*(d*e - 2*c*f - d*f*x) + (8*I)*d*Sinh[e + f*x] + f*(c + d*x)*Sinh[2*(e + f*x)])))/(8*f^2)","A",1
105,1,117,149,0.3605124,"\int \frac{(a+i a \sinh (e+f x))^2}{c+d x} \, dx","Integrate[(a + I*a*Sinh[e + f*x])^2/(c + d*x),x]","-\frac{a^2 \left(-4 i \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+\text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)+\sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-4 i \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-3 \log (c+d x)\right)}{2 d}","\frac{2 i a^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{d}-\frac{a^2 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{2 d}-\frac{a^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{2 d}+\frac{2 i a^2 \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d}+\frac{3 a^2 \log (c+d x)}{2 d}",1,"-1/2*(a^2*(Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*f*(c + d*x))/d] - 3*Log[c + d*x] - (4*I)*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] - (4*I)*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d]))/d","A",1
106,1,214,170,0.6430991,"\int \frac{(a+i a \sinh (e+f x))^2}{(c+d x)^2} \, dx","Integrate[(a + I*a*Sinh[e + f*x])^2/(c + d*x)^2,x]","\frac{a^2 \left(-2 f (c+d x) \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)+4 i f (c+d x) \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+4 i d f x \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+4 i c f \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-2 d f x \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-2 c f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-4 i d \sinh (e+f x)+d \cosh (2 (e+f x))-3 d\right)}{2 d^2 (c+d x)}","-\frac{a^2 f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{d^2}+\frac{2 i a^2 f \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{2 i a^2 f \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{a^2 f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{d^2}-\frac{4 a^2 \cosh ^4\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{d (c+d x)}",1,"(a^2*(-3*d + d*Cosh[2*(e + f*x)] + (4*I)*f*(c + d*x)*Cosh[e - (c*f)/d]*CoshIntegral[f*(c/d + x)] - 2*f*(c + d*x)*CoshIntegral[(2*f*(c + d*x))/d]*Sinh[2*e - (2*c*f)/d] - (4*I)*d*Sinh[e + f*x] + (4*I)*c*f*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + (4*I)*d*f*x*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] - 2*c*f*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] - 2*d*f*x*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d]))/(2*d^2*(c + d*x))","A",1
107,1,198,236,2.2052526,"\int \frac{(a+i a \sinh (e+f x))^2}{(c+d x)^3} \, dx","Integrate[(a + I*a*Sinh[e + f*x])^2/(c + d*x)^3,x]","\frac{a^2 \left(4 i f^2 \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)-4 f^2 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)-4 f^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+4 i f^2 \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+\frac{d (-4 i f (c+d x) \cosh (e+f x)+2 c f \sinh (2 (e+f x))-4 i d \sinh (e+f x)+2 d f x \sinh (2 (e+f x))+d \cosh (2 (e+f x))-3 d)}{(c+d x)^2}\right)}{4 d^3}","\frac{i a^2 f^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{d^3}-\frac{a^2 f^2 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{d^3}-\frac{a^2 f^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{d^3}+\frac{i a^2 f^2 \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^3}-\frac{4 a^2 f \sinh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \cosh ^3\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{d^2 (c+d x)}-\frac{2 a^2 \cosh ^4\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{d (c+d x)^2}",1,"(a^2*(-4*f^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*f*(c + d*x))/d] + (4*I)*f^2*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] + (d*(-3*d - (4*I)*f*(c + d*x)*Cosh[e + f*x] + d*Cosh[2*(e + f*x)] - (4*I)*d*Sinh[e + f*x] + 2*c*f*Sinh[2*(e + f*x)] + 2*d*f*x*Sinh[2*(e + f*x)]))/(c + d*x)^2 + (4*I)*f^2*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] - 4*f^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d]))/(4*d^3)","A",1
108,1,206,132,2.9315291,"\int \frac{(c+d x)^3}{a+i a \sinh (e+f x)} \, dx","Integrate[(c + d*x)^3/(a + I*a*Sinh[e + f*x]),x]","\frac{2 \left(\frac{3 d e^e \left(-\frac{2 i d e^{-e} \left(e^e-i\right) \left(f (c+d x) \text{Li}_2\left(i e^{-e-f x}\right)+d \text{Li}_3\left(i e^{-e-f x}\right)\right)}{f^3}+\frac{\left(e^{-e}+i\right) (c+d x)^2 \log \left(1-i e^{-e-f x}\right)}{f}+\frac{e^{-e} (c+d x)^3}{3 d}\right)}{-1-i e^e}+\frac{(c+d x)^3 \sinh \left(\frac{f x}{2}\right)}{\left(\cosh \left(\frac{e}{2}\right)+i \sinh \left(\frac{e}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)}\right)}{a f}","-\frac{12 d^2 (c+d x) \text{Li}_2\left(-i e^{e+f x}\right)}{a f^3}-\frac{6 d (c+d x)^2 \log \left(1+i e^{e+f x}\right)}{a f^2}+\frac{(c+d x)^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{a f}+\frac{(c+d x)^3}{a f}+\frac{12 d^3 \text{Li}_3\left(-i e^{e+f x}\right)}{a f^4}",1,"(2*((3*d*E^e*((c + d*x)^3/(3*d*E^e) + ((I + E^(-e))*(c + d*x)^2*Log[1 - I*E^(-e - f*x)])/f - ((2*I)*d*(-I + E^e)*(f*(c + d*x)*PolyLog[2, I*E^(-e - f*x)] + d*PolyLog[3, I*E^(-e - f*x)]))/(E^e*f^3)))/(-1 - I*E^e) + ((c + d*x)^3*Sinh[(f*x)/2])/((Cosh[e/2] + I*Sinh[e/2])*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))))/(a*f)","A",1
109,1,150,101,2.2286265,"\int \frac{(c+d x)^2}{a+i a \sinh (e+f x)} \, dx","Integrate[(c + d*x)^2/(a + I*a*Sinh[e + f*x]),x]","\frac{2 \left(\frac{f^2 (c+d x)^2 \sinh \left(\frac{f x}{2}\right)}{\left(\cosh \left(\frac{e}{2}\right)+i \sinh \left(\frac{e}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)}+\frac{i f (c+d x) \left(f (c+d x)+2 d \left(1+i e^e\right) \log \left(1-i e^{-e-f x}\right)\right)}{e^e-i}+2 d^2 \text{Li}_2\left(i e^{-e-f x}\right)\right)}{a f^3}","-\frac{4 d (c+d x) \log \left(1+i e^{e+f x}\right)}{a f^2}+\frac{(c+d x)^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{a f}+\frac{(c+d x)^2}{a f}-\frac{4 d^2 \text{Li}_2\left(-i e^{e+f x}\right)}{a f^3}",1,"(2*((I*f*(c + d*x)*(f*(c + d*x) + 2*d*(1 + I*E^e)*Log[1 - I*E^(-e - f*x)]))/(-I + E^e) + 2*d^2*PolyLog[2, I*E^(-e - f*x)] + (f^2*(c + d*x)^2*Sinh[(f*x)/2])/((Cosh[e/2] + I*Sinh[e/2])*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))))/(a*f^3)","A",1
110,1,185,63,0.4585459,"\int \frac{c+d x}{a+i a \sinh (e+f x)} \, dx","Integrate[(c + d*x)/(a + I*a*Sinh[e + f*x]),x]","\frac{2 c f \sinh \left(\frac{f x}{2}\right)+i d f x \cosh \left(e+\frac{f x}{2}\right)-i d \sinh \left(e+\frac{f x}{2}\right) \log (\cosh (e+f x))+2 d \sinh \left(e+\frac{f x}{2}\right) \tan ^{-1}\left(\sinh \left(\frac{f x}{2}\right) \text{sech}\left(e+\frac{f x}{2}\right)\right)+\cosh \left(\frac{f x}{2}\right) \left(-d \log (\cosh (e+f x))-2 i d \tan ^{-1}\left(\sinh \left(\frac{f x}{2}\right) \text{sech}\left(e+\frac{f x}{2}\right)\right)\right)+d f x \sinh \left(\frac{f x}{2}\right)}{a f^2 \left(\cosh \left(\frac{e}{2}\right)+i \sinh \left(\frac{e}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)}","\frac{(c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{a f}-\frac{2 d \log \left(\cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)\right)}{a f^2}",1,"(I*d*f*x*Cosh[e + (f*x)/2] + Cosh[(f*x)/2]*((-2*I)*d*ArcTan[Sech[e + (f*x)/2]*Sinh[(f*x)/2]] - d*Log[Cosh[e + f*x]]) + 2*c*f*Sinh[(f*x)/2] + d*f*x*Sinh[(f*x)/2] + 2*d*ArcTan[Sech[e + (f*x)/2]*Sinh[(f*x)/2]]*Sinh[e + (f*x)/2] - I*d*Log[Cosh[e + f*x]]*Sinh[e + (f*x)/2])/(a*f^2*(Cosh[e/2] + I*Sinh[e/2])*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))","B",1
111,0,0,26,20.6632264,"\int \frac{1}{(c+d x) (a+i a \sinh (e+f x))} \, dx","Integrate[1/((c + d*x)*(a + I*a*Sinh[e + f*x])),x]","\int \frac{1}{(c+d x) (a+i a \sinh (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+i a \sinh (e+f x))},x\right)",0,"Integrate[1/((c + d*x)*(a + I*a*Sinh[e + f*x])), x]","A",-1
112,0,0,26,21.0714346,"\int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))} \, dx","Integrate[1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))},x\right)",0,"Integrate[1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])), x]","A",-1
113,1,443,305,6.1929581,"\int \frac{(c+d x)^3}{(a+i a \sinh (e+f x))^2} \, dx","Integrate[(c + d*x)^3/(a + I*a*Sinh[e + f*x])^2,x]","\frac{\frac{2 d \left(\frac{3 \left(1+i e^e\right) \left(2 d^2-c^2 f^2\right) \left(f x-\log \left(-e^{e+f x}+i\right)\right)}{f}+3 c^2 f^2 x-6 c d \left(1+i e^e\right) \text{Li}_2\left(i e^{-e-f x}\right)+6 c d \left(1+i e^e\right) f x \log \left(1-i e^{-e-f x}\right)+3 c d f^2 x^2-6 d^2 \left(1+i e^e\right) \left(x \text{Li}_2\left(i e^{-e-f x}\right)+\frac{\text{Li}_3\left(i e^{-e-f x}\right)}{f}\right)+3 d^2 \left(1+i e^e\right) f x^2 \log \left(1-i e^{-e-f x}\right)+d^2 f^2 x^3-6 d^2 x\right)}{-1-i e^e}+\frac{(c+d x) \left(i \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2-6\right)\right) \cosh \left(e+\frac{3 f x}{2}\right)+3 \sinh \left(\frac{f x}{2}\right) \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2-4\right)\right)+3 i d f (c+d x) \sinh \left(e+\frac{f x}{2}\right)+3 d f (c+d x) \cosh \left(\frac{f x}{2}\right)+6 i d^2 \cosh \left(e+\frac{f x}{2}\right)\right)}{\left(\cosh \left(\frac{e}{2}\right)+i \sinh \left(\frac{e}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^3}}{3 a^2 f^3}","-\frac{4 d^2 (c+d x) \text{Li}_2\left(-i e^{e+f x}\right)}{a^2 f^3}-\frac{2 d^2 (c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{a^2 f^3}-\frac{2 d (c+d x)^2 \log \left(1+i e^{e+f x}\right)}{a^2 f^2}+\frac{d (c+d x)^2 \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{2 a^2 f^2}+\frac{(c+d x)^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{3 a^2 f}+\frac{(c+d x)^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{6 a^2 f}+\frac{(c+d x)^3}{3 a^2 f}+\frac{4 d^3 \text{Li}_3\left(-i e^{e+f x}\right)}{a^2 f^4}+\frac{4 d^3 \log \left(\cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)\right)}{a^2 f^4}",1,"((2*d*(-6*d^2*x + 3*c^2*f^2*x + 3*c*d*f^2*x^2 + d^2*f^2*x^3 + 6*c*d*(1 + I*E^e)*f*x*Log[1 - I*E^(-e - f*x)] + 3*d^2*(1 + I*E^e)*f*x^2*Log[1 - I*E^(-e - f*x)] + (3*(1 + I*E^e)*(2*d^2 - c^2*f^2)*(f*x - Log[I - E^(e + f*x)]))/f - 6*c*d*(1 + I*E^e)*PolyLog[2, I*E^(-e - f*x)] - 6*d^2*(1 + I*E^e)*(x*PolyLog[2, I*E^(-e - f*x)] + PolyLog[3, I*E^(-e - f*x)]/f)))/(-1 - I*E^e) + ((c + d*x)*(3*d*f*(c + d*x)*Cosh[(f*x)/2] + (6*I)*d^2*Cosh[e + (f*x)/2] + I*(c^2*f^2 + 2*c*d*f^2*x + d^2*(-6 + f^2*x^2))*Cosh[e + (3*f*x)/2] + 3*(c^2*f^2 + 2*c*d*f^2*x + d^2*(-4 + f^2*x^2))*Sinh[(f*x)/2] + (3*I)*d*f*(c + d*x)*Sinh[e + (f*x)/2]))/((Cosh[e/2] + I*Sinh[e/2])*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^3))/(3*a^2*f^3)","A",1
114,1,269,241,3.6146326,"\int \frac{(c+d x)^2}{(a+i a \sinh (e+f x))^2} \, dx","Integrate[(c + d*x)^2/(a + I*a*Sinh[e + f*x])^2,x]","\frac{\frac{i \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2-2\right)\right) \cosh \left(e+\frac{3 f x}{2}\right)+\sinh \left(\frac{f x}{2}\right) \left(3 c^2 f^2+6 c d f^2 x+d^2 \left(3 f^2 x^2-4\right)\right)+2 i d f (c+d x) \sinh \left(e+\frac{f x}{2}\right)+2 d f (c+d x) \cosh \left(\frac{f x}{2}\right)+2 i d^2 \cosh \left(e+\frac{f x}{2}\right)}{\left(\cosh \left(\frac{e}{2}\right)+i \sinh \left(\frac{e}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^3}+\frac{2 i f (c+d x) \left(f (c+d x)+2 d \left(1+i e^e\right) \log \left(1-i e^{-e-f x}\right)\right)}{e^e-i}+4 d^2 \text{Li}_2\left(i e^{-e-f x}\right)}{3 a^2 f^3}","-\frac{4 d (c+d x) \log \left(1+i e^{e+f x}\right)}{3 a^2 f^2}+\frac{d (c+d x) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{3 a^2 f^2}+\frac{(c+d x)^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{3 a^2 f}+\frac{(c+d x)^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{6 a^2 f}+\frac{(c+d x)^2}{3 a^2 f}-\frac{4 d^2 \text{Li}_2\left(-i e^{e+f x}\right)}{3 a^2 f^3}-\frac{2 d^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{3 a^2 f^3}",1,"(((2*I)*f*(c + d*x)*(f*(c + d*x) + 2*d*(1 + I*E^e)*Log[1 - I*E^(-e - f*x)]))/(-I + E^e) + 4*d^2*PolyLog[2, I*E^(-e - f*x)] + (2*d*f*(c + d*x)*Cosh[(f*x)/2] + (2*I)*d^2*Cosh[e + (f*x)/2] + I*(c^2*f^2 + 2*c*d*f^2*x + d^2*(-2 + f^2*x^2))*Cosh[e + (3*f*x)/2] + (3*c^2*f^2 + 6*c*d*f^2*x + d^2*(-4 + 3*f^2*x^2))*Sinh[(f*x)/2] + (2*I)*d*f*(c + d*x)*Sinh[e + (f*x)/2])/((Cosh[e/2] + I*Sinh[e/2])*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^3))/(3*a^2*f^3)","A",1
115,1,241,158,1.0452812,"\int \frac{c+d x}{(a+i a \sinh (e+f x))^2} \, dx","Integrate[(c + d*x)/(a + I*a*Sinh[e + f*x])^2,x]","\frac{\left(\sinh \left(\frac{1}{2} (e+f x)\right)-i \cosh \left(\frac{1}{2} (e+f x)\right)\right) \left(\cosh \left(\frac{3}{2} (e+f x)\right) \left(2 c f+2 d \tan ^{-1}\left(\tanh \left(\frac{1}{2} (e+f x)\right)\right)-i d \log (\cosh (e+f x))-d e+d f x\right)+2 i \sinh \left(\frac{1}{2} (e+f x)\right) \left(-3 c f-4 d \tan ^{-1}\left(\tanh \left(\frac{1}{2} (e+f x)\right)\right)+2 i d \log (\cosh (e+f x))+d \cosh (e+f x) \left(-2 \tan ^{-1}\left(\tanh \left(\frac{1}{2} (e+f x)\right)\right)+i \log (\cosh (e+f x))+e+f x\right)+2 d e-d f x-i d\right)+d \cosh \left(\frac{1}{2} (e+f x)\right) \left(-6 \tan ^{-1}\left(\tanh \left(\frac{1}{2} (e+f x)\right)\right)+3 i \log (\cosh (e+f x))+3 e+3 f x-2 i\right)\right)}{6 a^2 f^2 (\sinh (e+f x)-i)^2}","\frac{(c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{3 a^2 f}+\frac{(c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{6 a^2 f}+\frac{d \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{6 a^2 f^2}-\frac{2 d \log \left(\cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)\right)}{3 a^2 f^2}",1,"(((-I)*Cosh[(e + f*x)/2] + Sinh[(e + f*x)/2])*(d*Cosh[(e + f*x)/2]*(-2*I + 3*e + 3*f*x - 6*ArcTan[Tanh[(e + f*x)/2]] + (3*I)*Log[Cosh[e + f*x]]) + Cosh[(3*(e + f*x))/2]*(-(d*e) + 2*c*f + d*f*x + 2*d*ArcTan[Tanh[(e + f*x)/2]] - I*d*Log[Cosh[e + f*x]]) + (2*I)*((-I)*d + 2*d*e - 3*c*f - d*f*x - 4*d*ArcTan[Tanh[(e + f*x)/2]] + d*Cosh[e + f*x]*(e + f*x - 2*ArcTan[Tanh[(e + f*x)/2]] + I*Log[Cosh[e + f*x]]) + (2*I)*d*Log[Cosh[e + f*x]])*Sinh[(e + f*x)/2]))/(6*a^2*f^2*(-I + Sinh[e + f*x])^2)","A",1
116,0,0,26,35.2464356,"\int \frac{1}{(c+d x) (a+i a \sinh (e+f x))^2} \, dx","Integrate[1/((c + d*x)*(a + I*a*Sinh[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+i a \sinh (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+i a \sinh (e+f x))^2},x\right)",0,"Integrate[1/((c + d*x)*(a + I*a*Sinh[e + f*x])^2), x]","A",-1
117,0,0,26,37.7159923,"\int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))^2} \, dx","Integrate[1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))^2},x\right)",0,"Integrate[1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])^2), x]","A",-1
118,1,141,181,0.2158718,"\int x^4 \sqrt{a+i a \sinh (e+f x)} \, dx","Integrate[x^4*Sqrt[a + I*a*Sinh[e + f*x]],x]","\frac{2 \sqrt{a+i a \sinh (e+f x)} \left(\left(f^4 x^4-8 i f^3 x^3+48 f^2 x^2-192 i f x+384\right) \sinh \left(\frac{1}{2} (e+f x)\right)+i \left(f^4 x^4+8 i f^3 x^3+48 f^2 x^2+192 i f x+384\right) \cosh \left(\frac{1}{2} (e+f x)\right)\right)}{f^5 \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)}","\frac{768 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{f^5}-\frac{384 x \sqrt{a+i a \sinh (e+f x)}}{f^4}+\frac{96 x^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{f^3}-\frac{16 x^3 \sqrt{a+i a \sinh (e+f x)}}{f^2}+\frac{2 x^4 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{f}",1,"(2*(I*(384 + (192*I)*f*x + 48*f^2*x^2 + (8*I)*f^3*x^3 + f^4*x^4)*Cosh[(e + f*x)/2] + (384 - (192*I)*f*x + 48*f^2*x^2 - (8*I)*f^3*x^3 + f^4*x^4)*Sinh[(e + f*x)/2])*Sqrt[a + I*a*Sinh[e + f*x]])/(f^5*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))","A",1
119,1,125,136,0.2927633,"\int x^3 \sqrt{a+i a \sinh (e+f x)} \, dx","Integrate[x^3*Sqrt[a + I*a*Sinh[e + f*x]],x]","\frac{2 \sqrt{a+i a \sinh (e+f x)} \left(\left(f^3 x^3-6 i f^2 x^2+24 f x-48 i\right) \sinh \left(\frac{1}{2} (e+f x)\right)+i \left(f^3 x^3+6 i f^2 x^2+24 f x+48 i\right) \cosh \left(\frac{1}{2} (e+f x)\right)\right)}{f^4 \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)}","-\frac{96 \sqrt{a+i a \sinh (e+f x)}}{f^4}+\frac{48 x \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{f^3}-\frac{12 x^2 \sqrt{a+i a \sinh (e+f x)}}{f^2}+\frac{2 x^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{f}",1,"(2*(I*(48*I + 24*f*x + (6*I)*f^2*x^2 + f^3*x^3)*Cosh[(e + f*x)/2] + (-48*I + 24*f*x - (6*I)*f^2*x^2 + f^3*x^3)*Sinh[(e + f*x)/2])*Sqrt[a + I*a*Sinh[e + f*x]])/(f^4*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))","A",1
120,1,105,111,0.2209153,"\int x^2 \sqrt{a+i a \sinh (e+f x)} \, dx","Integrate[x^2*Sqrt[a + I*a*Sinh[e + f*x]],x]","\frac{2 \sqrt{a+i a \sinh (e+f x)} \left(\left(f^2 x^2-4 i f x+8\right) \sinh \left(\frac{1}{2} (e+f x)\right)+i \left(f^2 x^2+4 i f x+8\right) \cosh \left(\frac{1}{2} (e+f x)\right)\right)}{f^3 \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)}","\frac{16 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{f^3}-\frac{8 x \sqrt{a+i a \sinh (e+f x)}}{f^2}+\frac{2 x^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{f}",1,"(2*(I*(8 + (4*I)*f*x + f^2*x^2)*Cosh[(e + f*x)/2] + (8 - (4*I)*f*x + f^2*x^2)*Sinh[(e + f*x)/2])*Sqrt[a + I*a*Sinh[e + f*x]])/(f^3*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))","A",1
121,1,87,66,0.1623762,"\int x \sqrt{a+i a \sinh (e+f x)} \, dx","Integrate[x*Sqrt[a + I*a*Sinh[e + f*x]],x]","\frac{2 \sqrt{a+i a \sinh (e+f x)} \left((f x-2 i) \sinh \left(\frac{1}{2} (e+f x)\right)+(-2+i f x) \cosh \left(\frac{1}{2} (e+f x)\right)\right)}{f^2 \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)}","\frac{2 x \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{f}-\frac{4 \sqrt{a+i a \sinh (e+f x)}}{f^2}",1,"(2*((-2 + I*f*x)*Cosh[(e + f*x)/2] + (-2*I + f*x)*Sinh[(e + f*x)/2])*Sqrt[a + I*a*Sinh[e + f*x]])/(f^2*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))","A",1
122,1,96,125,0.1553322,"\int \frac{\sqrt{a+i a \sinh (e+f x)}}{x} \, dx","Integrate[Sqrt[a + I*a*Sinh[e + f*x]]/x,x]","\frac{\sqrt{a+i a \sinh (e+f x)} \left(\text{Chi}\left(\frac{f x}{2}\right) \left(\cosh \left(\frac{e}{2}\right)+i \sinh \left(\frac{e}{2}\right)\right)+\left(\sinh \left(\frac{e}{2}\right)+i \cosh \left(\frac{e}{2}\right)\right) \text{Shi}\left(\frac{f x}{2}\right)\right)}{\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)}","i \sinh \left(\frac{1}{4} (2 e-i \pi )\right) \text{Chi}\left(\frac{f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}+i \cosh \left(\frac{1}{4} (2 e-i \pi )\right) \text{Shi}\left(\frac{f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}",1,"(Sqrt[a + I*a*Sinh[e + f*x]]*(CoshIntegral[(f*x)/2]*(Cosh[e/2] + I*Sinh[e/2]) + (I*Cosh[e/2] + Sinh[e/2])*SinhIntegral[(f*x)/2]))/(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])","A",1
123,1,133,149,0.2552553,"\int \frac{\sqrt{a+i a \sinh (e+f x)}}{x^2} \, dx","Integrate[Sqrt[a + I*a*Sinh[e + f*x]]/x^2,x]","\frac{\sqrt{a+i a \sinh (e+f x)} \left(f x \text{Chi}\left(\frac{f x}{2}\right) \left(\sinh \left(\frac{e}{2}\right)+i \cosh \left(\frac{e}{2}\right)\right)+f x \left(\cosh \left(\frac{e}{2}\right)+i \sinh \left(\frac{e}{2}\right)\right) \text{Shi}\left(\frac{f x}{2}\right)-2 \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)\right)}{2 x \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)}","\frac{1}{2} f \sinh \left(\frac{1}{4} (2 e+i \pi )\right) \text{Chi}\left(\frac{f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}+\frac{1}{2} f \cosh \left(\frac{1}{4} (2 e+i \pi )\right) \text{Shi}\left(\frac{f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}-\frac{\sqrt{a+i a \sinh (e+f x)}}{x}",1,"(Sqrt[a + I*a*Sinh[e + f*x]]*(f*x*CoshIntegral[(f*x)/2]*(I*Cosh[e/2] + Sinh[e/2]) - 2*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]) + f*x*(Cosh[e/2] + I*Sinh[e/2])*SinhIntegral[(f*x)/2]))/(2*x*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))","A",1
124,1,170,204,0.3499971,"\int \frac{\sqrt{a+i a \sinh (e+f x)}}{x^3} \, dx","Integrate[Sqrt[a + I*a*Sinh[e + f*x]]/x^3,x]","\frac{\sqrt{a+i a \sinh (e+f x)} \left(f^2 x^2 \text{Chi}\left(\frac{f x}{2}\right) \left(\cosh \left(\frac{e}{2}\right)+i \sinh \left(\frac{e}{2}\right)\right)+f^2 x^2 \left(\sinh \left(\frac{e}{2}\right)+i \cosh \left(\frac{e}{2}\right)\right) \text{Shi}\left(\frac{f x}{2}\right)-2 f x \sinh \left(\frac{1}{2} (e+f x)\right)-4 i \sinh \left(\frac{1}{2} (e+f x)\right)-2 i f x \cosh \left(\frac{1}{2} (e+f x)\right)-4 \cosh \left(\frac{1}{2} (e+f x)\right)\right)}{8 x^2 \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)}","\frac{1}{8} i f^2 \sinh \left(\frac{1}{4} (2 e-i \pi )\right) \text{Chi}\left(\frac{f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}+\frac{1}{8} i f^2 \cosh \left(\frac{1}{4} (2 e-i \pi )\right) \text{Shi}\left(\frac{f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}-\frac{\sqrt{a+i a \sinh (e+f x)}}{2 x^2}-\frac{f \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{4 x}",1,"(Sqrt[a + I*a*Sinh[e + f*x]]*(-4*Cosh[(e + f*x)/2] - (2*I)*f*x*Cosh[(e + f*x)/2] + f^2*x^2*CoshIntegral[(f*x)/2]*(Cosh[e/2] + I*Sinh[e/2]) - (4*I)*Sinh[(e + f*x)/2] - 2*f*x*Sinh[(e + f*x)/2] + f^2*x^2*(I*Cosh[e/2] + Sinh[e/2])*SinhIntegral[(f*x)/2]))/(8*x^2*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))","A",1
125,1,269,377,1.3815739,"\int x^3 (a+i a \sinh (e+f x))^{3/2} \, dx","Integrate[x^3*(a + I*a*Sinh[e + f*x])^(3/2),x]","-\frac{a (\sinh (e+f x)-i) \sqrt{a+i a \sinh (e+f x)} \left(-81 i f^3 x^3 \sinh \left(\frac{1}{2} (e+f x)\right)+9 i f^3 x^3 \sinh \left(\frac{3}{2} (e+f x)\right)-486 f^2 x^2 \sinh \left(\frac{1}{2} (e+f x)\right)-18 f^2 x^2 \sinh \left(\frac{3}{2} (e+f x)\right)+81 \left(f^3 x^3+6 i f^2 x^2+24 f x+48 i\right) \cosh \left(\frac{1}{2} (e+f x)\right)+\left(9 f^3 x^3-18 i f^2 x^2+24 f x-16 i\right) \cosh \left(\frac{3}{2} (e+f x)\right)-1944 i f x \sinh \left(\frac{1}{2} (e+f x)\right)+24 i f x \sinh \left(\frac{3}{2} (e+f x)\right)-3888 \sinh \left(\frac{1}{2} (e+f x)\right)-16 \sinh \left(\frac{3}{2} (e+f x)\right)\right)}{27 f^4 \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^3}","-\frac{1280 a \sqrt{a+i a \sinh (e+f x)}}{9 f^4}-\frac{64 a \cosh ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{27 f^4}+\frac{640 a x \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{9 f^3}+\frac{32 a x \sinh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{9 f^3}-\frac{16 a x^2 \sqrt{a+i a \sinh (e+f x)}}{f^2}-\frac{8 a x^2 \cosh ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{3 f^2}+\frac{8 a x^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{3 f}+\frac{4 a x^3 \sinh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{3 f}",1,"-1/27*(a*(-I + Sinh[e + f*x])*Sqrt[a + I*a*Sinh[e + f*x]]*(81*(48*I + 24*f*x + (6*I)*f^2*x^2 + f^3*x^3)*Cosh[(e + f*x)/2] + (-16*I + 24*f*x - (18*I)*f^2*x^2 + 9*f^3*x^3)*Cosh[(3*(e + f*x))/2] - 3888*Sinh[(e + f*x)/2] - (1944*I)*f*x*Sinh[(e + f*x)/2] - 486*f^2*x^2*Sinh[(e + f*x)/2] - (81*I)*f^3*x^3*Sinh[(e + f*x)/2] - 16*Sinh[(3*(e + f*x))/2] + (24*I)*f*x*Sinh[(3*(e + f*x))/2] - 18*f^2*x^2*Sinh[(3*(e + f*x))/2] + (9*I)*f^3*x^3*Sinh[(3*(e + f*x))/2]))/(f^4*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^3)","A",1
126,1,173,303,1.0563637,"\int x^2 (a+i a \sinh (e+f x))^{3/2} \, dx","Integrate[x^2*(a + I*a*Sinh[e + f*x])^(3/2),x]","-\frac{a (\sinh (e+f x)-i) \sqrt{a+i a \sinh (e+f x)} \left(81 \left(f^2 x^2+4 i f x+8\right) \cosh \left(\frac{1}{2} (e+f x)\right)+\left(9 f^2 x^2-12 i f x+8\right) \cosh \left(\frac{3}{2} (e+f x)\right)+2 i \sinh \left(\frac{1}{2} (e+f x)\right) \left(\left(9 f^2 x^2+12 i f x+8\right) \cosh (e+f x)-4 \left(9 f^2 x^2-42 i f x+80\right)\right)\right)}{27 f^3 \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^3}","\frac{32 a \sinh ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{27 f^3}+\frac{224 a \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{9 f^3}-\frac{32 a x \sqrt{a+i a \sinh (e+f x)}}{3 f^2}-\frac{16 a x \cosh ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{9 f^2}+\frac{8 a x^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{3 f}+\frac{4 a x^2 \sinh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{3 f}",1,"-1/27*(a*(81*(8 + (4*I)*f*x + f^2*x^2)*Cosh[(e + f*x)/2] + (8 - (12*I)*f*x + 9*f^2*x^2)*Cosh[(3*(e + f*x))/2] + (2*I)*(-4*(80 - (42*I)*f*x + 9*f^2*x^2) + (8 + (12*I)*f*x + 9*f^2*x^2)*Cosh[e + f*x])*Sinh[(e + f*x)/2])*(-I + Sinh[e + f*x])*Sqrt[a + I*a*Sinh[e + f*x]])/(f^3*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^3)","A",1
127,1,138,185,0.7205777,"\int x (a+i a \sinh (e+f x))^{3/2} \, dx","Integrate[x*(a + I*a*Sinh[e + f*x])^(3/2),x]","-\frac{a (\sinh (e+f x)-i) \sqrt{a+i a \sinh (e+f x)} \left(27 (f x+2 i) \cosh \left(\frac{1}{2} (e+f x)\right)+(3 f x-2 i) \cosh \left(\frac{3}{2} (e+f x)\right)+2 i \sinh \left(\frac{1}{2} (e+f x)\right) ((3 f x+2 i) \cosh (e+f x)-12 f x+28 i)\right)}{9 f^2 \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^3}","-\frac{16 a \sqrt{a+i a \sinh (e+f x)}}{3 f^2}-\frac{8 a \cosh ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{9 f^2}+\frac{8 a x \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{3 f}+\frac{4 a x \sinh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{3 f}",1,"-1/9*(a*(27*(2*I + f*x)*Cosh[(e + f*x)/2] + (-2*I + 3*f*x)*Cosh[(3*(e + f*x))/2] + (2*I)*(28*I - 12*f*x + (2*I + 3*f*x)*Cosh[e + f*x])*Sinh[(e + f*x)/2])*(-I + Sinh[e + f*x])*Sqrt[a + I*a*Sinh[e + f*x]])/(f^2*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^3)","A",1
128,1,146,261,0.7384887,"\int \frac{(a+i a \sinh (e+f x))^{3/2}}{x} \, dx","Integrate[(a + I*a*Sinh[e + f*x])^(3/2)/x,x]","\frac{a \sqrt{a+i a \sinh (e+f x)} \left(3 \text{Chi}\left(\frac{f x}{2}\right) \left(\cosh \left(\frac{e}{2}\right)+i \sinh \left(\frac{e}{2}\right)\right)-\text{Chi}\left(\frac{3 f x}{2}\right) \left(\cosh \left(\frac{3 e}{2}\right)-i \sinh \left(\frac{3 e}{2}\right)\right)+\left(\sinh \left(\frac{e}{2}\right)+i \cosh \left(\frac{e}{2}\right)\right) \left(3 \text{Shi}\left(\frac{f x}{2}\right)+(1+2 i \sinh (e)) \text{Shi}\left(\frac{3 f x}{2}\right)\right)\right)}{2 \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)}","\frac{3}{2} i a \sinh \left(\frac{1}{4} (2 e-i \pi )\right) \text{Chi}\left(\frac{f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}+\frac{1}{2} i a \sinh \left(\frac{1}{4} (6 e+i \pi )\right) \text{Chi}\left(\frac{3 f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}+\frac{3}{2} i a \cosh \left(\frac{1}{4} (2 e-i \pi )\right) \text{Shi}\left(\frac{f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}+\frac{1}{2} i a \cosh \left(\frac{1}{4} (6 e+i \pi )\right) \text{Shi}\left(\frac{3 f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}",1,"(a*Sqrt[a + I*a*Sinh[e + f*x]]*(3*CoshIntegral[(f*x)/2]*(Cosh[e/2] + I*Sinh[e/2]) - CoshIntegral[(3*f*x)/2]*(Cosh[(3*e)/2] - I*Sinh[(3*e)/2]) + (I*Cosh[e/2] + Sinh[e/2])*(3*SinhIntegral[(f*x)/2] + (1 + (2*I)*Sinh[e])*SinhIntegral[(3*f*x)/2])))/(2*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))","A",1
129,1,243,302,0.8547856,"\int \frac{(a+i a \sinh (e+f x))^{3/2}}{x^2} \, dx","Integrate[(a + I*a*Sinh[e + f*x])^(3/2)/x^2,x]","\frac{a (\sinh (e+f x)-i) \sqrt{a+i a \sinh (e+f x)} \left(-3 f x \text{Chi}\left(\frac{f x}{2}\right) \left(\cosh \left(\frac{e}{2}\right)-i \sinh \left(\frac{e}{2}\right)\right)-3 f x \text{Chi}\left(\frac{3 f x}{2}\right) \left(\cosh \left(\frac{3 e}{2}\right)+i \sinh \left(\frac{3 e}{2}\right)\right)-3 f x \sinh \left(\frac{e}{2}\right) \text{Shi}\left(\frac{f x}{2}\right)-3 f x \sinh \left(\frac{3 e}{2}\right) \text{Shi}\left(\frac{3 f x}{2}\right)+3 i f x \cosh \left(\frac{e}{2}\right) \text{Shi}\left(\frac{f x}{2}\right)-3 i f x \cosh \left(\frac{3 e}{2}\right) \text{Shi}\left(\frac{3 f x}{2}\right)+6 \sinh \left(\frac{1}{2} (e+f x)\right)+2 \sinh \left(\frac{3}{2} (e+f x)\right)-6 i \cosh \left(\frac{1}{2} (e+f x)\right)+2 i \cosh \left(\frac{3}{2} (e+f x)\right)\right)}{4 x \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^3}","-\frac{3}{4} a f \sinh \left(\frac{1}{4} (6 e-i \pi )\right) \text{Chi}\left(\frac{3 f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}+\frac{3}{4} a f \sinh \left(\frac{1}{4} (2 e+i \pi )\right) \text{Chi}\left(\frac{f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}+\frac{3}{4} a f \cosh \left(\frac{1}{4} (2 e+i \pi )\right) \text{Shi}\left(\frac{f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}-\frac{3}{4} a f \cosh \left(\frac{1}{4} (6 e-i \pi )\right) \text{Shi}\left(\frac{3 f x}{2}\right) \text{sech}\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}-\frac{2 a \cosh ^2\left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (e+f x)}}{x}",1,"(a*(-I + Sinh[e + f*x])*Sqrt[a + I*a*Sinh[e + f*x]]*((-6*I)*Cosh[(e + f*x)/2] + (2*I)*Cosh[(3*(e + f*x))/2] - 3*f*x*CoshIntegral[(f*x)/2]*(Cosh[e/2] - I*Sinh[e/2]) - 3*f*x*CoshIntegral[(3*f*x)/2]*(Cosh[(3*e)/2] + I*Sinh[(3*e)/2]) + 6*Sinh[(e + f*x)/2] + 2*Sinh[(3*(e + f*x))/2] + (3*I)*f*x*Cosh[e/2]*SinhIntegral[(f*x)/2] - 3*f*x*Sinh[e/2]*SinhIntegral[(f*x)/2] - (3*I)*f*x*Cosh[(3*e)/2]*SinhIntegral[(3*f*x)/2] - 3*f*x*Sinh[(3*e)/2]*SinhIntegral[(3*f*x)/2]))/(4*x*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^3)","A",1
130,1,2918,638,7.4096633,"\int x^3 (a+i a \sinh (c+d x))^{5/2} \, dx","Integrate[x^3*(a + I*a*Sinh[c + d*x])^(5/2),x]","\text{Result too large to show}","-\frac{265216 a^2 \sqrt{a+i a \sinh (c+d x)}}{1125 d^4}-\frac{384 a^2 \cosh ^4\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{625 d^4}-\frac{17408 a^2 \cosh ^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{3375 d^4}+\frac{132608 a^2 x \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{1125 d^3}+\frac{192 a^2 x \sinh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \cosh ^3\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{125 d^3}+\frac{8704 a^2 x \sinh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{1125 d^3}-\frac{128 a^2 x^2 \sqrt{a+i a \sinh (c+d x)}}{5 d^2}-\frac{48 a^2 x^2 \cosh ^4\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{25 d^2}-\frac{64 a^2 x^2 \cosh ^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{15 d^2}+\frac{64 a^2 x^3 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{15 d}+\frac{8 a^2 x^3 \sinh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \cosh ^3\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{5 d}+\frac{32 a^2 x^3 \sinh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{15 d}",1,"(2*(((-1/135000 - I/135000)*Cosh[5*(c/2 + (d*x)/2)])/d^3 + ((1/135000 + I/135000)*Sinh[5*(c/2 + (d*x)/2)])/d^3)*(1296*I - (3240*I)*c + (4050*I)*c^2 - (3375*I)*c^3 + (6480*I)*(c/2 + (d*x)/2) - (16200*I)*c*(c/2 + (d*x)/2) + (20250*I)*c^2*(c/2 + (d*x)/2) + (16200*I)*(c/2 + (d*x)/2)^2 - (40500*I)*c*(c/2 + (d*x)/2)^2 + (27000*I)*(c/2 + (d*x)/2)^3 - 50000*Cosh[2*(c/2 + (d*x)/2)] + 75000*c*Cosh[2*(c/2 + (d*x)/2)] - 56250*c^2*Cosh[2*(c/2 + (d*x)/2)] + 28125*c^3*Cosh[2*(c/2 + (d*x)/2)] - 150000*(c/2 + (d*x)/2)*Cosh[2*(c/2 + (d*x)/2)] + 225000*c*(c/2 + (d*x)/2)*Cosh[2*(c/2 + (d*x)/2)] - 168750*c^2*(c/2 + (d*x)/2)*Cosh[2*(c/2 + (d*x)/2)] - 225000*(c/2 + (d*x)/2)^2*Cosh[2*(c/2 + (d*x)/2)] + 337500*c*(c/2 + (d*x)/2)^2*Cosh[2*(c/2 + (d*x)/2)] - 225000*(c/2 + (d*x)/2)^3*Cosh[2*(c/2 + (d*x)/2)] - (8100000*I)*Cosh[4*(c/2 + (d*x)/2)] + (4050000*I)*c*Cosh[4*(c/2 + (d*x)/2)] - (1012500*I)*c^2*Cosh[4*(c/2 + (d*x)/2)] + (168750*I)*c^3*Cosh[4*(c/2 + (d*x)/2)] - (8100000*I)*(c/2 + (d*x)/2)*Cosh[4*(c/2 + (d*x)/2)] + (4050000*I)*c*(c/2 + (d*x)/2)*Cosh[4*(c/2 + (d*x)/2)] - (1012500*I)*c^2*(c/2 + (d*x)/2)*Cosh[4*(c/2 + (d*x)/2)] - (4050000*I)*(c/2 + (d*x)/2)^2*Cosh[4*(c/2 + (d*x)/2)] + (2025000*I)*c*(c/2 + (d*x)/2)^2*Cosh[4*(c/2 + (d*x)/2)] - (1350000*I)*(c/2 + (d*x)/2)^3*Cosh[4*(c/2 + (d*x)/2)] + 8100000*Cosh[6*(c/2 + (d*x)/2)] + 4050000*c*Cosh[6*(c/2 + (d*x)/2)] + 1012500*c^2*Cosh[6*(c/2 + (d*x)/2)] + 168750*c^3*Cosh[6*(c/2 + (d*x)/2)] - 8100000*(c/2 + (d*x)/2)*Cosh[6*(c/2 + (d*x)/2)] - 4050000*c*(c/2 + (d*x)/2)*Cosh[6*(c/2 + (d*x)/2)] - 1012500*c^2*(c/2 + (d*x)/2)*Cosh[6*(c/2 + (d*x)/2)] + 4050000*(c/2 + (d*x)/2)^2*Cosh[6*(c/2 + (d*x)/2)] + 2025000*c*(c/2 + (d*x)/2)^2*Cosh[6*(c/2 + (d*x)/2)] - 1350000*(c/2 + (d*x)/2)^3*Cosh[6*(c/2 + (d*x)/2)] + (50000*I)*Cosh[8*(c/2 + (d*x)/2)] + (75000*I)*c*Cosh[8*(c/2 + (d*x)/2)] + (56250*I)*c^2*Cosh[8*(c/2 + (d*x)/2)] + (28125*I)*c^3*Cosh[8*(c/2 + (d*x)/2)] - (150000*I)*(c/2 + (d*x)/2)*Cosh[8*(c/2 + (d*x)/2)] - (225000*I)*c*(c/2 + (d*x)/2)*Cosh[8*(c/2 + (d*x)/2)] - (168750*I)*c^2*(c/2 + (d*x)/2)*Cosh[8*(c/2 + (d*x)/2)] + (225000*I)*(c/2 + (d*x)/2)^2*Cosh[8*(c/2 + (d*x)/2)] + (337500*I)*c*(c/2 + (d*x)/2)^2*Cosh[8*(c/2 + (d*x)/2)] - (225000*I)*(c/2 + (d*x)/2)^3*Cosh[8*(c/2 + (d*x)/2)] - 1296*Cosh[10*(c/2 + (d*x)/2)] - 3240*c*Cosh[10*(c/2 + (d*x)/2)] - 4050*c^2*Cosh[10*(c/2 + (d*x)/2)] - 3375*c^3*Cosh[10*(c/2 + (d*x)/2)] + 6480*(c/2 + (d*x)/2)*Cosh[10*(c/2 + (d*x)/2)] + 16200*c*(c/2 + (d*x)/2)*Cosh[10*(c/2 + (d*x)/2)] + 20250*c^2*(c/2 + (d*x)/2)*Cosh[10*(c/2 + (d*x)/2)] - 16200*(c/2 + (d*x)/2)^2*Cosh[10*(c/2 + (d*x)/2)] - 40500*c*(c/2 + (d*x)/2)^2*Cosh[10*(c/2 + (d*x)/2)] + 27000*(c/2 + (d*x)/2)^3*Cosh[10*(c/2 + (d*x)/2)] - 50000*Sinh[2*(c/2 + (d*x)/2)] + 75000*c*Sinh[2*(c/2 + (d*x)/2)] - 56250*c^2*Sinh[2*(c/2 + (d*x)/2)] + 28125*c^3*Sinh[2*(c/2 + (d*x)/2)] - 150000*(c/2 + (d*x)/2)*Sinh[2*(c/2 + (d*x)/2)] + 225000*c*(c/2 + (d*x)/2)*Sinh[2*(c/2 + (d*x)/2)] - 168750*c^2*(c/2 + (d*x)/2)*Sinh[2*(c/2 + (d*x)/2)] - 225000*(c/2 + (d*x)/2)^2*Sinh[2*(c/2 + (d*x)/2)] + 337500*c*(c/2 + (d*x)/2)^2*Sinh[2*(c/2 + (d*x)/2)] - 225000*(c/2 + (d*x)/2)^3*Sinh[2*(c/2 + (d*x)/2)] - (8100000*I)*Sinh[4*(c/2 + (d*x)/2)] + (4050000*I)*c*Sinh[4*(c/2 + (d*x)/2)] - (1012500*I)*c^2*Sinh[4*(c/2 + (d*x)/2)] + (168750*I)*c^3*Sinh[4*(c/2 + (d*x)/2)] - (8100000*I)*(c/2 + (d*x)/2)*Sinh[4*(c/2 + (d*x)/2)] + (4050000*I)*c*(c/2 + (d*x)/2)*Sinh[4*(c/2 + (d*x)/2)] - (1012500*I)*c^2*(c/2 + (d*x)/2)*Sinh[4*(c/2 + (d*x)/2)] - (4050000*I)*(c/2 + (d*x)/2)^2*Sinh[4*(c/2 + (d*x)/2)] + (2025000*I)*c*(c/2 + (d*x)/2)^2*Sinh[4*(c/2 + (d*x)/2)] - (1350000*I)*(c/2 + (d*x)/2)^3*Sinh[4*(c/2 + (d*x)/2)] + 8100000*Sinh[6*(c/2 + (d*x)/2)] + 4050000*c*Sinh[6*(c/2 + (d*x)/2)] + 1012500*c^2*Sinh[6*(c/2 + (d*x)/2)] + 168750*c^3*Sinh[6*(c/2 + (d*x)/2)] - 8100000*(c/2 + (d*x)/2)*Sinh[6*(c/2 + (d*x)/2)] - 4050000*c*(c/2 + (d*x)/2)*Sinh[6*(c/2 + (d*x)/2)] - 1012500*c^2*(c/2 + (d*x)/2)*Sinh[6*(c/2 + (d*x)/2)] + 4050000*(c/2 + (d*x)/2)^2*Sinh[6*(c/2 + (d*x)/2)] + 2025000*c*(c/2 + (d*x)/2)^2*Sinh[6*(c/2 + (d*x)/2)] - 1350000*(c/2 + (d*x)/2)^3*Sinh[6*(c/2 + (d*x)/2)] + (50000*I)*Sinh[8*(c/2 + (d*x)/2)] + (75000*I)*c*Sinh[8*(c/2 + (d*x)/2)] + (56250*I)*c^2*Sinh[8*(c/2 + (d*x)/2)] + (28125*I)*c^3*Sinh[8*(c/2 + (d*x)/2)] - (150000*I)*(c/2 + (d*x)/2)*Sinh[8*(c/2 + (d*x)/2)] - (225000*I)*c*(c/2 + (d*x)/2)*Sinh[8*(c/2 + (d*x)/2)] - (168750*I)*c^2*(c/2 + (d*x)/2)*Sinh[8*(c/2 + (d*x)/2)] + (225000*I)*(c/2 + (d*x)/2)^2*Sinh[8*(c/2 + (d*x)/2)] + (337500*I)*c*(c/2 + (d*x)/2)^2*Sinh[8*(c/2 + (d*x)/2)] - (225000*I)*(c/2 + (d*x)/2)^3*Sinh[8*(c/2 + (d*x)/2)] - 1296*Sinh[10*(c/2 + (d*x)/2)] - 3240*c*Sinh[10*(c/2 + (d*x)/2)] - 4050*c^2*Sinh[10*(c/2 + (d*x)/2)] - 3375*c^3*Sinh[10*(c/2 + (d*x)/2)] + 6480*(c/2 + (d*x)/2)*Sinh[10*(c/2 + (d*x)/2)] + 16200*c*(c/2 + (d*x)/2)*Sinh[10*(c/2 + (d*x)/2)] + 20250*c^2*(c/2 + (d*x)/2)*Sinh[10*(c/2 + (d*x)/2)] - 16200*(c/2 + (d*x)/2)^2*Sinh[10*(c/2 + (d*x)/2)] - 40500*c*(c/2 + (d*x)/2)^2*Sinh[10*(c/2 + (d*x)/2)] + 27000*(c/2 + (d*x)/2)^3*Sinh[10*(c/2 + (d*x)/2)])*(a + I*a*Sinh[c + d*x])^(5/2))/(d*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^5)","B",1
131,1,300,506,1.6325106,"\int x^2 (a+i a \sinh (c+d x))^{5/2} \, dx","Integrate[x^2*(a + I*a*Sinh[c + d*x])^(5/2),x]","\frac{a^2 \sqrt{a+i a \sinh (c+d x)} \left(33750 d^2 x^2 \sinh \left(\frac{1}{2} (c+d x)\right)-5625 d^2 x^2 \sinh \left(\frac{3}{2} (c+d x)\right)-675 d^2 x^2 \sinh \left(\frac{5}{2} (c+d x)\right)-675 i d^2 x^2 \cosh \left(\frac{5}{2} (c+d x)\right)+33750 i \left(d^2 x^2+4 i d x+8\right) \cosh \left(\frac{1}{2} (c+d x)\right)+625 \left(9 i d^2 x^2+12 d x+8 i\right) \cosh \left(\frac{3}{2} (c+d x)\right)-135000 i d x \sinh \left(\frac{1}{2} (c+d x)\right)-7500 i d x \sinh \left(\frac{3}{2} (c+d x)\right)+540 i d x \sinh \left(\frac{5}{2} (c+d x)\right)+270000 \sinh \left(\frac{1}{2} (c+d x)\right)-5000 \sinh \left(\frac{3}{2} (c+d x)\right)-216 \sinh \left(\frac{5}{2} (c+d x)\right)+540 d x \cosh \left(\frac{5}{2} (c+d x)\right)-216 i \cosh \left(\frac{5}{2} (c+d x)\right)\right)}{6750 d^3 \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}","\frac{64 a^2 \sinh ^4\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{125 d^3}+\frac{2432 a^2 \sinh ^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{675 d^3}+\frac{9536 a^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{225 d^3}-\frac{256 a^2 x \sqrt{a+i a \sinh (c+d x)}}{15 d^2}-\frac{32 a^2 x \cosh ^4\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{25 d^2}-\frac{128 a^2 x \cosh ^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{45 d^2}+\frac{64 a^2 x^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{15 d}+\frac{8 a^2 x^2 \sinh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \cosh ^3\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{5 d}+\frac{32 a^2 x^2 \sinh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{15 d}",1,"(a^2*Sqrt[a + I*a*Sinh[c + d*x]]*((33750*I)*(8 + (4*I)*d*x + d^2*x^2)*Cosh[(c + d*x)/2] + 625*(8*I + 12*d*x + (9*I)*d^2*x^2)*Cosh[(3*(c + d*x))/2] - (216*I)*Cosh[(5*(c + d*x))/2] + 540*d*x*Cosh[(5*(c + d*x))/2] - (675*I)*d^2*x^2*Cosh[(5*(c + d*x))/2] + 270000*Sinh[(c + d*x)/2] - (135000*I)*d*x*Sinh[(c + d*x)/2] + 33750*d^2*x^2*Sinh[(c + d*x)/2] - 5000*Sinh[(3*(c + d*x))/2] - (7500*I)*d*x*Sinh[(3*(c + d*x))/2] - 5625*d^2*x^2*Sinh[(3*(c + d*x))/2] - 216*Sinh[(5*(c + d*x))/2] + (540*I)*d*x*Sinh[(5*(c + d*x))/2] - 675*d^2*x^2*Sinh[(5*(c + d*x))/2]))/(6750*d^3*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]))","A",1
132,1,218,312,1.2684384,"\int x (a+i a \sinh (c+d x))^{5/2} \, dx","Integrate[x*(a + I*a*Sinh[c + d*x])^(5/2),x]","\frac{a^2 (\sinh (c+d x)-i)^2 \sqrt{a+i a \sinh (c+d x)} \left(-2250 d x \sinh \left(\frac{1}{2} (c+d x)\right)+4500 i \sinh \left(\frac{1}{2} (c+d x)\right)+375 d x \sinh \left(\frac{3}{2} (c+d x)\right)+250 i \sinh \left(\frac{3}{2} (c+d x)\right)+45 d x \sinh \left(\frac{5}{2} (c+d x)\right)-18 i \sinh \left(\frac{5}{2} (c+d x)\right)+2250 (2-i d x) \cosh \left(\frac{1}{2} (c+d x)\right)+(-250-375 i d x) \cosh \left(\frac{3}{2} (c+d x)\right)+45 i d x \cosh \left(\frac{5}{2} (c+d x)\right)-18 \cosh \left(\frac{5}{2} (c+d x)\right)\right)}{450 d^2 \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^5}","-\frac{128 a^2 \sqrt{a+i a \sinh (c+d x)}}{15 d^2}-\frac{16 a^2 \cosh ^4\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{25 d^2}-\frac{64 a^2 \cosh ^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{45 d^2}+\frac{64 a^2 x \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{15 d}+\frac{8 a^2 x \sinh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \cosh ^3\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{5 d}+\frac{32 a^2 x \sinh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{15 d}",1,"(a^2*(-I + Sinh[c + d*x])^2*Sqrt[a + I*a*Sinh[c + d*x]]*(2250*(2 - I*d*x)*Cosh[(c + d*x)/2] + (-250 - (375*I)*d*x)*Cosh[(3*(c + d*x))/2] - 18*Cosh[(5*(c + d*x))/2] + (45*I)*d*x*Cosh[(5*(c + d*x))/2] + (4500*I)*Sinh[(c + d*x)/2] - 2250*d*x*Sinh[(c + d*x)/2] + (250*I)*Sinh[(3*(c + d*x))/2] + 375*d*x*Sinh[(3*(c + d*x))/2] - (18*I)*Sinh[(5*(c + d*x))/2] + 45*d*x*Sinh[(5*(c + d*x))/2]))/(450*d^2*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^5)","A",1
133,1,242,403,1.3678269,"\int \frac{(a+i a \sinh (c+d x))^{5/2}}{x} \, dx","Integrate[(a + I*a*Sinh[c + d*x])^(5/2)/x,x]","\frac{a^2 (\sinh (c+d x)-i)^2 \sqrt{a+i a \sinh (c+d x)} \left(i \sinh \left(\frac{5 c}{2}\right) \text{Chi}\left(\frac{5 d x}{2}\right)+\cosh \left(\frac{5 c}{2}\right) \text{Chi}\left(\frac{5 d x}{2}\right)-10 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \text{Chi}\left(\frac{d x}{2}\right)+5 \left(\cosh \left(\frac{3 c}{2}\right)-i \sinh \left(\frac{3 c}{2}\right)\right) \text{Chi}\left(\frac{3 d x}{2}\right)-10 \sinh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right)+5 \sinh \left(\frac{3 c}{2}\right) \text{Shi}\left(\frac{3 d x}{2}\right)+\sinh \left(\frac{5 c}{2}\right) \text{Shi}\left(\frac{5 d x}{2}\right)-10 i \cosh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right)-5 i \cosh \left(\frac{3 c}{2}\right) \text{Shi}\left(\frac{3 d x}{2}\right)+i \cosh \left(\frac{5 c}{2}\right) \text{Shi}\left(\frac{5 d x}{2}\right)\right)}{4 \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^5}","-\frac{1}{4} i a^2 \sinh \left(\frac{5 c}{2}-\frac{i \pi }{4}\right) \text{Chi}\left(\frac{5 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}+\frac{5}{2} i a^2 \sinh \left(\frac{1}{4} (2 c-i \pi )\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}+\frac{5}{4} i a^2 \sinh \left(\frac{1}{4} (6 c+i \pi )\right) \text{Chi}\left(\frac{3 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}+\frac{5}{2} i a^2 \cosh \left(\frac{1}{4} (2 c-i \pi )\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}+\frac{5}{4} i a^2 \cosh \left(\frac{1}{4} (6 c+i \pi )\right) \text{Shi}\left(\frac{3 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}-\frac{1}{4} i a^2 \cosh \left(\frac{5 c}{2}-\frac{i \pi }{4}\right) \text{Shi}\left(\frac{5 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}",1,"(a^2*(-I + Sinh[c + d*x])^2*Sqrt[a + I*a*Sinh[c + d*x]]*(Cosh[(5*c)/2]*CoshIntegral[(5*d*x)/2] - 10*CoshIntegral[(d*x)/2]*(Cosh[c/2] + I*Sinh[c/2]) + 5*CoshIntegral[(3*d*x)/2]*(Cosh[(3*c)/2] - I*Sinh[(3*c)/2]) + I*CoshIntegral[(5*d*x)/2]*Sinh[(5*c)/2] - (10*I)*Cosh[c/2]*SinhIntegral[(d*x)/2] - 10*Sinh[c/2]*SinhIntegral[(d*x)/2] - (5*I)*Cosh[(3*c)/2]*SinhIntegral[(3*d*x)/2] + 5*Sinh[(3*c)/2]*SinhIntegral[(3*d*x)/2] + I*Cosh[(5*c)/2]*SinhIntegral[(5*d*x)/2] + Sinh[(5*c)/2]*SinhIntegral[(5*d*x)/2]))/(4*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^5)","A",1
134,1,347,444,2.2135312,"\int \frac{(a+i a \sinh (c+d x))^{5/2}}{x^2} \, dx","Integrate[(a + I*a*Sinh[c + d*x])^(5/2)/x^2,x]","\frac{a^2 (\sinh (c+d x)-i)^2 \sqrt{a+i a \sinh (c+d x)} \left(5 d x \sinh \left(\frac{5 c}{2}\right) \text{Chi}\left(\frac{5 d x}{2}\right)+5 i d x \cosh \left(\frac{5 c}{2}\right) \text{Chi}\left(\frac{5 d x}{2}\right)-10 i d x \left(\cosh \left(\frac{c}{2}\right)-i \sinh \left(\frac{c}{2}\right)\right) \text{Chi}\left(\frac{d x}{2}\right)+15 d x \left(\sinh \left(\frac{3 c}{2}\right)-i \cosh \left(\frac{3 c}{2}\right)\right) \text{Chi}\left(\frac{3 d x}{2}\right)-10 i d x \sinh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right)-15 i d x \sinh \left(\frac{3 c}{2}\right) \text{Shi}\left(\frac{3 d x}{2}\right)+5 i d x \sinh \left(\frac{5 c}{2}\right) \text{Shi}\left(\frac{5 d x}{2}\right)-10 d x \cosh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right)+15 d x \cosh \left(\frac{3 c}{2}\right) \text{Shi}\left(\frac{3 d x}{2}\right)+5 d x \cosh \left(\frac{5 c}{2}\right) \text{Shi}\left(\frac{5 d x}{2}\right)+20 i \sinh \left(\frac{1}{2} (c+d x)\right)+10 i \sinh \left(\frac{3}{2} (c+d x)\right)-2 i \sinh \left(\frac{5}{2} (c+d x)\right)+20 \cosh \left(\frac{1}{2} (c+d x)\right)-10 \cosh \left(\frac{3}{2} (c+d x)\right)-2 \cosh \left(\frac{5}{2} (c+d x)\right)\right)}{8 x \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^5}","-\frac{5}{8} a^2 d \sinh \left(\frac{5 c}{2}+\frac{i \pi }{4}\right) \text{Chi}\left(\frac{5 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}-\frac{15}{8} a^2 d \sinh \left(\frac{1}{4} (6 c-i \pi )\right) \text{Chi}\left(\frac{3 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}+\frac{5}{4} a^2 d \sinh \left(\frac{1}{4} (2 c+i \pi )\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}+\frac{5}{4} a^2 d \cosh \left(\frac{1}{4} (2 c+i \pi )\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}-\frac{15}{8} a^2 d \cosh \left(\frac{1}{4} (6 c-i \pi )\right) \text{Shi}\left(\frac{3 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}-\frac{5}{8} a^2 d \cosh \left(\frac{5 c}{2}+\frac{i \pi }{4}\right) \text{Shi}\left(\frac{5 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}-\frac{4 a^2 \cosh ^4\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{x}",1,"(a^2*(-I + Sinh[c + d*x])^2*Sqrt[a + I*a*Sinh[c + d*x]]*(20*Cosh[(c + d*x)/2] - 10*Cosh[(3*(c + d*x))/2] - 2*Cosh[(5*(c + d*x))/2] + (5*I)*d*x*Cosh[(5*c)/2]*CoshIntegral[(5*d*x)/2] - (10*I)*d*x*CoshIntegral[(d*x)/2]*(Cosh[c/2] - I*Sinh[c/2]) + 15*d*x*CoshIntegral[(3*d*x)/2]*((-I)*Cosh[(3*c)/2] + Sinh[(3*c)/2]) + 5*d*x*CoshIntegral[(5*d*x)/2]*Sinh[(5*c)/2] + (20*I)*Sinh[(c + d*x)/2] + (10*I)*Sinh[(3*(c + d*x))/2] - (2*I)*Sinh[(5*(c + d*x))/2] - 10*d*x*Cosh[c/2]*SinhIntegral[(d*x)/2] - (10*I)*d*x*Sinh[c/2]*SinhIntegral[(d*x)/2] + 15*d*x*Cosh[(3*c)/2]*SinhIntegral[(3*d*x)/2] - (15*I)*d*x*Sinh[(3*c)/2]*SinhIntegral[(3*d*x)/2] + 5*d*x*Cosh[(5*c)/2]*SinhIntegral[(5*d*x)/2] + (5*I)*d*x*Sinh[(5*c)/2]*SinhIntegral[(5*d*x)/2]))/(8*x*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^5)","A",1
135,1,4751,536,7.4754476,"\int \frac{(a+i a \sinh (c+d x))^{5/2}}{x^3} \, dx","Integrate[(a + I*a*Sinh[c + d*x])^(5/2)/x^3,x]","\text{Result too large to show}","-\frac{25}{32} i a^2 d^2 \sinh \left(\frac{5 c}{2}-\frac{i \pi }{4}\right) \text{Chi}\left(\frac{5 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}+\frac{5}{16} i a^2 d^2 \sinh \left(\frac{1}{4} (2 c-i \pi )\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}+\frac{45}{32} i a^2 d^2 \sinh \left(\frac{1}{4} (6 c+i \pi )\right) \text{Chi}\left(\frac{3 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}+\frac{5}{16} i a^2 d^2 \cosh \left(\frac{1}{4} (2 c-i \pi )\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}+\frac{45}{32} i a^2 d^2 \cosh \left(\frac{1}{4} (6 c+i \pi )\right) \text{Shi}\left(\frac{3 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}-\frac{25}{32} i a^2 d^2 \cosh \left(\frac{5 c}{2}-\frac{i \pi }{4}\right) \text{Shi}\left(\frac{5 d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}-\frac{2 a^2 \cosh ^4\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{x^2}-\frac{5 a^2 d \sinh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \cosh ^3\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \sqrt{a+i a \sinh (c+d x)}}{x}",1,"(2*((1/128 + I/128)*Cosh[5*(c/2 + (d*x)/2)] - (1/128 + I/128)*Sinh[5*(c/2 + (d*x)/2)])*(a + I*a*Sinh[c + d*x])^(5/2)*((-4*I)*d^3 - (10*I)*c*d^3 + (20*I)*d^3*(c/2 + (d*x)/2) + 20*d^3*Cosh[2*(c/2 + (d*x)/2)] + 30*c*d^3*Cosh[2*(c/2 + (d*x)/2)] - 60*d^3*(c/2 + (d*x)/2)*Cosh[2*(c/2 + (d*x)/2)] + (40*I)*d^3*Cosh[4*(c/2 + (d*x)/2)] + (20*I)*c*d^3*Cosh[4*(c/2 + (d*x)/2)] - (40*I)*d^3*(c/2 + (d*x)/2)*Cosh[4*(c/2 + (d*x)/2)] - 40*d^3*Cosh[6*(c/2 + (d*x)/2)] + 20*c*d^3*Cosh[6*(c/2 + (d*x)/2)] - 40*d^3*(c/2 + (d*x)/2)*Cosh[6*(c/2 + (d*x)/2)] - (20*I)*d^3*Cosh[8*(c/2 + (d*x)/2)] + (30*I)*c*d^3*Cosh[8*(c/2 + (d*x)/2)] - (60*I)*d^3*(c/2 + (d*x)/2)*Cosh[8*(c/2 + (d*x)/2)] + 4*d^3*Cosh[10*(c/2 + (d*x)/2)] - 10*c*d^3*Cosh[10*(c/2 + (d*x)/2)] + 20*d^3*(c/2 + (d*x)/2)*Cosh[10*(c/2 + (d*x)/2)] - (10*I)*c^2*d^3*Cosh[c/2 - 5*(c/2 + (d*x)/2)]*CoshIntegral[(d*x)/2] + (40*I)*c*d^3*(c/2 + (d*x)/2)*Cosh[c/2 - 5*(c/2 + (d*x)/2)]*CoshIntegral[(d*x)/2] - (40*I)*d^3*(c/2 + (d*x)/2)^2*Cosh[c/2 - 5*(c/2 + (d*x)/2)]*CoshIntegral[(d*x)/2] + 10*c^2*d^3*Cosh[c/2 + 5*(c/2 + (d*x)/2)]*CoshIntegral[(d*x)/2] - 40*c*d^3*(c/2 + (d*x)/2)*Cosh[c/2 + 5*(c/2 + (d*x)/2)]*CoshIntegral[(d*x)/2] + 40*d^3*(c/2 + (d*x)/2)^2*Cosh[c/2 + 5*(c/2 + (d*x)/2)]*CoshIntegral[(d*x)/2] - 45*c^2*d^3*Cosh[(3*c)/2 - 5*(c/2 + (d*x)/2)]*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)] + 180*c*d^3*(c/2 + (d*x)/2)*Cosh[(3*c)/2 - 5*(c/2 + (d*x)/2)]*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)] - 180*d^3*(c/2 + (d*x)/2)^2*Cosh[(3*c)/2 - 5*(c/2 + (d*x)/2)]*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)] + (45*I)*c^2*d^3*Cosh[(3*c)/2 + 5*(c/2 + (d*x)/2)]*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)] - (180*I)*c*d^3*(c/2 + (d*x)/2)*Cosh[(3*c)/2 + 5*(c/2 + (d*x)/2)]*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)] + (180*I)*d^3*(c/2 + (d*x)/2)^2*Cosh[(3*c)/2 + 5*(c/2 + (d*x)/2)]*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)] + (25*I)*c^2*d^3*Cosh[(5*c)/2 - 5*(c/2 + (d*x)/2)]*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)] - (100*I)*c*d^3*(c/2 + (d*x)/2)*Cosh[(5*c)/2 - 5*(c/2 + (d*x)/2)]*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)] + (100*I)*d^3*(c/2 + (d*x)/2)^2*Cosh[(5*c)/2 - 5*(c/2 + (d*x)/2)]*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)] - 25*c^2*d^3*Cosh[(5*c)/2 + 5*(c/2 + (d*x)/2)]*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)] + 100*c*d^3*(c/2 + (d*x)/2)*Cosh[(5*c)/2 + 5*(c/2 + (d*x)/2)]*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)] - 100*d^3*(c/2 + (d*x)/2)^2*Cosh[(5*c)/2 + 5*(c/2 + (d*x)/2)]*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)] + 20*d^3*Sinh[2*(c/2 + (d*x)/2)] + 30*c*d^3*Sinh[2*(c/2 + (d*x)/2)] - 60*d^3*(c/2 + (d*x)/2)*Sinh[2*(c/2 + (d*x)/2)] + (40*I)*d^3*Sinh[4*(c/2 + (d*x)/2)] + (20*I)*c*d^3*Sinh[4*(c/2 + (d*x)/2)] - (40*I)*d^3*(c/2 + (d*x)/2)*Sinh[4*(c/2 + (d*x)/2)] - 40*d^3*Sinh[6*(c/2 + (d*x)/2)] + 20*c*d^3*Sinh[6*(c/2 + (d*x)/2)] - 40*d^3*(c/2 + (d*x)/2)*Sinh[6*(c/2 + (d*x)/2)] - (20*I)*d^3*Sinh[8*(c/2 + (d*x)/2)] + (30*I)*c*d^3*Sinh[8*(c/2 + (d*x)/2)] - (60*I)*d^3*(c/2 + (d*x)/2)*Sinh[8*(c/2 + (d*x)/2)] + 4*d^3*Sinh[10*(c/2 + (d*x)/2)] - 10*c*d^3*Sinh[10*(c/2 + (d*x)/2)] + 20*d^3*(c/2 + (d*x)/2)*Sinh[10*(c/2 + (d*x)/2)] + (10*I)*c^2*d^3*CoshIntegral[(d*x)/2]*Sinh[c/2 - 5*(c/2 + (d*x)/2)] - (40*I)*c*d^3*(c/2 + (d*x)/2)*CoshIntegral[(d*x)/2]*Sinh[c/2 - 5*(c/2 + (d*x)/2)] + (40*I)*d^3*(c/2 + (d*x)/2)^2*CoshIntegral[(d*x)/2]*Sinh[c/2 - 5*(c/2 + (d*x)/2)] + 45*c^2*d^3*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)]*Sinh[(3*c)/2 - 5*(c/2 + (d*x)/2)] - 180*c*d^3*(c/2 + (d*x)/2)*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)]*Sinh[(3*c)/2 - 5*(c/2 + (d*x)/2)] + 180*d^3*(c/2 + (d*x)/2)^2*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)]*Sinh[(3*c)/2 - 5*(c/2 + (d*x)/2)] - (25*I)*c^2*d^3*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)]*Sinh[(5*c)/2 - 5*(c/2 + (d*x)/2)] + (100*I)*c*d^3*(c/2 + (d*x)/2)*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)]*Sinh[(5*c)/2 - 5*(c/2 + (d*x)/2)] - (100*I)*d^3*(c/2 + (d*x)/2)^2*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)]*Sinh[(5*c)/2 - 5*(c/2 + (d*x)/2)] + 10*c^2*d^3*CoshIntegral[(d*x)/2]*Sinh[c/2 + 5*(c/2 + (d*x)/2)] - 40*c*d^3*(c/2 + (d*x)/2)*CoshIntegral[(d*x)/2]*Sinh[c/2 + 5*(c/2 + (d*x)/2)] + 40*d^3*(c/2 + (d*x)/2)^2*CoshIntegral[(d*x)/2]*Sinh[c/2 + 5*(c/2 + (d*x)/2)] + (45*I)*c^2*d^3*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)]*Sinh[(3*c)/2 + 5*(c/2 + (d*x)/2)] - (180*I)*c*d^3*(c/2 + (d*x)/2)*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)]*Sinh[(3*c)/2 + 5*(c/2 + (d*x)/2)] + (180*I)*d^3*(c/2 + (d*x)/2)^2*CoshIntegral[(-3*c)/2 + 3*(c/2 + (d*x)/2)]*Sinh[(3*c)/2 + 5*(c/2 + (d*x)/2)] - 25*c^2*d^3*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)]*Sinh[(5*c)/2 + 5*(c/2 + (d*x)/2)] + 100*c*d^3*(c/2 + (d*x)/2)*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)]*Sinh[(5*c)/2 + 5*(c/2 + (d*x)/2)] - 100*d^3*(c/2 + (d*x)/2)^2*CoshIntegral[(-5*c)/2 + 5*(c/2 + (d*x)/2)]*Sinh[(5*c)/2 + 5*(c/2 + (d*x)/2)] + (10*I)*c^2*d^3*Cosh[c/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] - (40*I)*c*d^3*(c/2 + (d*x)/2)*Cosh[c/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] + (40*I)*d^3*(c/2 + (d*x)/2)^2*Cosh[c/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] + 10*c^2*d^3*Cosh[c/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] - 40*c*d^3*(c/2 + (d*x)/2)*Cosh[c/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] + 40*d^3*(c/2 + (d*x)/2)^2*Cosh[c/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] - (10*I)*c^2*d^3*Sinh[c/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] + (40*I)*c*d^3*(c/2 + (d*x)/2)*Sinh[c/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] - (40*I)*d^3*(c/2 + (d*x)/2)^2*Sinh[c/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] + 10*c^2*d^3*Sinh[c/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] - 40*c*d^3*(c/2 + (d*x)/2)*Sinh[c/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] + 40*d^3*(c/2 + (d*x)/2)^2*Sinh[c/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(d*x)/2] + (25*I)*c^2*d^3*Cosh[(5*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] - (100*I)*c*d^3*(c/2 + (d*x)/2)*Cosh[(5*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] + (100*I)*d^3*(c/2 + (d*x)/2)^2*Cosh[(5*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] + 25*c^2*d^3*Cosh[(5*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] - 100*c*d^3*(c/2 + (d*x)/2)*Cosh[(5*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] + 100*d^3*(c/2 + (d*x)/2)^2*Cosh[(5*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] - (25*I)*c^2*d^3*Sinh[(5*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] + (100*I)*c*d^3*(c/2 + (d*x)/2)*Sinh[(5*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] - (100*I)*d^3*(c/2 + (d*x)/2)^2*Sinh[(5*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] + 25*c^2*d^3*Sinh[(5*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] - 100*c*d^3*(c/2 + (d*x)/2)*Sinh[(5*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] + 100*d^3*(c/2 + (d*x)/2)^2*Sinh[(5*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(5*c)/2 - 5*(c/2 + (d*x)/2)] - 45*c^2*d^3*Cosh[(3*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] + 180*c*d^3*(c/2 + (d*x)/2)*Cosh[(3*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] - 180*d^3*(c/2 + (d*x)/2)^2*Cosh[(3*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] - (45*I)*c^2*d^3*Cosh[(3*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] + (180*I)*c*d^3*(c/2 + (d*x)/2)*Cosh[(3*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] - (180*I)*d^3*(c/2 + (d*x)/2)^2*Cosh[(3*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] + 45*c^2*d^3*Sinh[(3*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] - 180*c*d^3*(c/2 + (d*x)/2)*Sinh[(3*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] + 180*d^3*(c/2 + (d*x)/2)^2*Sinh[(3*c)/2 - 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] - (45*I)*c^2*d^3*Sinh[(3*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] + (180*I)*c*d^3*(c/2 + (d*x)/2)*Sinh[(3*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)] - (180*I)*d^3*(c/2 + (d*x)/2)^2*Sinh[(3*c)/2 + 5*(c/2 + (d*x)/2)]*SinhIntegral[(3*c)/2 - 3*(c/2 + (d*x)/2)]))/(d*(-c + 2*(c/2 + (d*x)/2))^2*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^5)","B",1
136,1,331,493,1.2208294,"\int \frac{x^3}{\sqrt{a+i a \sinh (e+f x)}} \, dx","Integrate[x^3/Sqrt[a + I*a*Sinh[e + f*x]],x]","\frac{(1-i) (-1)^{3/4} \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right) \left(e^3 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-e^3 \log \left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}+1\right)+2 i e^3 \tan ^{-1}\left(\sqrt[4]{-1} e^{\frac{1}{2} (e+f x)}\right)+f^3 x^3 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-f^3 x^3 \log \left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}+1\right)-6 f^2 x^2 \text{Li}_2\left(-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+6 f^2 x^2 \text{Li}_2\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+24 f x \text{Li}_3\left(-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-24 f x \text{Li}_3\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-48 \text{Li}_4\left(-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+48 \text{Li}_4\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)\right)}{f^4 \sqrt{a+i a \sinh (e+f x)}}","\frac{96 i \text{Li}_4\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^4 \sqrt{a+i a \sinh (e+f x)}}-\frac{96 i \text{Li}_4\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^4 \sqrt{a+i a \sinh (e+f x)}}-\frac{48 i x \text{Li}_3\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{48 i x \text{Li}_3\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{12 i x^2 \text{Li}_2\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{12 i x^2 \text{Li}_2\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}+\frac{4 i x^3 \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \tanh ^{-1}\left(e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f \sqrt{a+i a \sinh (e+f x)}}",1,"((1 - I)*(-1)^(3/4)*((2*I)*e^3*ArcTan[(-1)^(1/4)*E^((e + f*x)/2)] + e^3*Log[1 - (-1)^(3/4)*E^((e + f*x)/2)] + f^3*x^3*Log[1 - (-1)^(3/4)*E^((e + f*x)/2)] - e^3*Log[1 + (-1)^(3/4)*E^((e + f*x)/2)] - f^3*x^3*Log[1 + (-1)^(3/4)*E^((e + f*x)/2)] - 6*f^2*x^2*PolyLog[2, -((-1)^(3/4)*E^((e + f*x)/2))] + 6*f^2*x^2*PolyLog[2, (-1)^(3/4)*E^((e + f*x)/2)] + 24*f*x*PolyLog[3, -((-1)^(3/4)*E^((e + f*x)/2))] - 24*f*x*PolyLog[3, (-1)^(3/4)*E^((e + f*x)/2)] - 48*PolyLog[4, -((-1)^(3/4)*E^((e + f*x)/2))] + 48*PolyLog[4, (-1)^(3/4)*E^((e + f*x)/2)])*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))/(f^4*Sqrt[a + I*a*Sinh[e + f*x]])","A",1
137,1,276,349,0.9266986,"\int \frac{x^2}{\sqrt{a+i a \sinh (e+f x)}} \, dx","Integrate[x^2/Sqrt[a + I*a*Sinh[e + f*x]],x]","\frac{(1+i) (-1)^{3/4} \left(\sinh \left(\frac{1}{2} (e+f x)\right)-i \cosh \left(\frac{1}{2} (e+f x)\right)\right) \left(-e^2 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+e^2 \log \left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}+1\right)-2 i e^2 \tan ^{-1}\left(\sqrt[4]{-1} e^{\frac{1}{2} (e+f x)}\right)+f^2 x^2 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-f^2 x^2 \log \left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}+1\right)-4 f x \text{Li}_2\left(-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+4 f x \text{Li}_2\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+8 \text{Li}_3\left(-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-8 \text{Li}_3\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}","-\frac{16 i \text{Li}_3\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{16 i \text{Li}_3\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{8 i x \text{Li}_2\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{8 i x \text{Li}_2\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}+\frac{4 i x^2 \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \tanh ^{-1}\left(e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f \sqrt{a+i a \sinh (e+f x)}}",1,"((1 + I)*(-1)^(3/4)*((-2*I)*e^2*ArcTan[(-1)^(1/4)*E^((e + f*x)/2)] - e^2*Log[1 - (-1)^(3/4)*E^((e + f*x)/2)] + f^2*x^2*Log[1 - (-1)^(3/4)*E^((e + f*x)/2)] + e^2*Log[1 + (-1)^(3/4)*E^((e + f*x)/2)] - f^2*x^2*Log[1 + (-1)^(3/4)*E^((e + f*x)/2)] - 4*f*x*PolyLog[2, -((-1)^(3/4)*E^((e + f*x)/2))] + 4*f*x*PolyLog[2, (-1)^(3/4)*E^((e + f*x)/2)] + 8*PolyLog[3, -((-1)^(3/4)*E^((e + f*x)/2))] - 8*PolyLog[3, (-1)^(3/4)*E^((e + f*x)/2)])*((-I)*Cosh[(e + f*x)/2] + Sinh[(e + f*x)/2]))/(f^3*Sqrt[a + I*a*Sinh[e + f*x]])","A",1
138,1,221,207,0.4590292,"\int \frac{x}{\sqrt{a+i a \sinh (e+f x)}} \, dx","Integrate[x/Sqrt[a + I*a*Sinh[e + f*x]],x]","\frac{\sqrt{2} \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right) \left(-2 i \left(\text{Li}_2\left(-\sqrt[4]{-1} e^{-\frac{e}{2}-\frac{f x}{2}}\right)-\text{Li}_2\left(\sqrt[4]{-1} e^{-\frac{e}{2}-\frac{f x}{2}}\right)\right)-\frac{1}{2} (2 i e+2 i f x+\pi ) \left(\log \left(1-\sqrt[4]{-1} e^{-\frac{e}{2}-\frac{f x}{2}}\right)-\log \left(\sqrt[4]{-1} e^{-\frac{e}{2}-\frac{f x}{2}}+1\right)\right)-2 e \tan ^{-1}\left(\frac{\tanh \left(\frac{1}{4} (e+f x)\right)+i}{\sqrt{2}}\right)+i \pi  \tan ^{-1}\left(\frac{\tanh \left(\frac{1}{4} (e+f x)\right)+i}{\sqrt{2}}\right)\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}","\frac{4 i \text{Li}_2\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{4 i \text{Li}_2\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}+\frac{4 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \tanh ^{-1}\left(e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f \sqrt{a+i a \sinh (e+f x)}}",1,"(Sqrt[2]*(-2*e*ArcTan[(I + Tanh[(e + f*x)/4])/Sqrt[2]] + I*Pi*ArcTan[(I + Tanh[(e + f*x)/4])/Sqrt[2]] - (((2*I)*e + Pi + (2*I)*f*x)*(Log[1 - (-1)^(1/4)*E^(-1/2*e - (f*x)/2)] - Log[1 + (-1)^(1/4)*E^(-1/2*e - (f*x)/2)]))/2 - (2*I)*(PolyLog[2, -((-1)^(1/4)*E^(-1/2*e - (f*x)/2))] - PolyLog[2, (-1)^(1/4)*E^(-1/2*e - (f*x)/2)]))*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]))/(f^2*Sqrt[a + I*a*Sinh[e + f*x]])","A",1
139,0,0,24,3.7955648,"\int \frac{1}{x \sqrt{a+i a \sinh (e+f x)}} \, dx","Integrate[1/(x*Sqrt[a + I*a*Sinh[e + f*x]]),x]","\int \frac{1}{x \sqrt{a+i a \sinh (e+f x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{a+i a \sinh (e+f x)}},x\right)",0,"Integrate[1/(x*Sqrt[a + I*a*Sinh[e + f*x]]), x]","A",-1
140,0,0,24,3.8459362,"\int \frac{1}{x^2 \sqrt{a+i a \sinh (e+f x)}} \, dx","Integrate[1/(x^2*Sqrt[a + I*a*Sinh[e + f*x]]),x]","\int \frac{1}{x^2 \sqrt{a+i a \sinh (e+f x)}} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{a+i a \sinh (e+f x)}},x\right)",0,"Integrate[1/(x^2*Sqrt[a + I*a*Sinh[e + f*x]]), x]","A",-1
141,1,546,807,3.1502627,"\int \frac{x^3}{(a+i a \sinh (e+f x))^{3/2}} \, dx","Integrate[x^3/(a + I*a*Sinh[e + f*x])^(3/2),x]","\frac{\left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right) \left(\left(\frac{1}{2}-\frac{i}{2}\right) (-1)^{3/4} \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^2 \left(e^3 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-e^3 \log \left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}+1\right)+2 e^3 \tanh ^{-1}\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+f^3 x^3 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-f^3 x^3 \log \left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}+1\right)-6 \left(f^2 x^2-8\right) \text{Li}_2\left(-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+6 \left(f^2 x^2-8\right) \text{Li}_2\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+24 f x \text{Li}_3\left(-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-24 f x \text{Li}_3\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-48 \text{Li}_4\left(-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+48 \text{Li}_4\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-24 e \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+24 e \log \left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}+1\right)-24 f x \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+24 f x \log \left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}+1\right)-48 e \tanh ^{-1}\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)\right)+2 f^3 x^3 \sinh \left(\frac{1}{2} (e+f x)\right)+f^2 x^2 (6+i f x) \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)\right)}{2 f^4 (a+i a \sinh (e+f x))^{3/2}}","\frac{\tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) x^3}{2 a f \sqrt{i \sinh (e+f x) a+a}}+\frac{i \tanh ^{-1}\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) x^3}{a f \sqrt{i \sinh (e+f x) a+a}}+\frac{3 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{Li}_2\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) x^2}{a f^2 \sqrt{i \sinh (e+f x) a+a}}-\frac{3 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{Li}_2\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) x^2}{a f^2 \sqrt{i \sinh (e+f x) a+a}}+\frac{3 x^2}{a f^2 \sqrt{i \sinh (e+f x) a+a}}-\frac{24 i \tanh ^{-1}\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) x}{a f^3 \sqrt{i \sinh (e+f x) a+a}}-\frac{12 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{Li}_3\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) x}{a f^3 \sqrt{i \sinh (e+f x) a+a}}+\frac{12 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{Li}_3\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) x}{a f^3 \sqrt{i \sinh (e+f x) a+a}}-\frac{24 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{Li}_2\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right)}{a f^4 \sqrt{i \sinh (e+f x) a+a}}+\frac{24 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{Li}_2\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right)}{a f^4 \sqrt{i \sinh (e+f x) a+a}}+\frac{24 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{Li}_4\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right)}{a f^4 \sqrt{i \sinh (e+f x) a+a}}-\frac{24 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{Li}_4\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right)}{a f^4 \sqrt{i \sinh (e+f x) a+a}}",1,"((Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])*(f^2*x^2*(6 + I*f*x)*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]) + (1/2 - I/2)*(-1)^(3/4)*(-48*e*ArcTanh[(-1)^(3/4)*E^((e + f*x)/2)] + 2*e^3*ArcTanh[(-1)^(3/4)*E^((e + f*x)/2)] - 24*e*Log[1 - (-1)^(3/4)*E^((e + f*x)/2)] + e^3*Log[1 - (-1)^(3/4)*E^((e + f*x)/2)] - 24*f*x*Log[1 - (-1)^(3/4)*E^((e + f*x)/2)] + f^3*x^3*Log[1 - (-1)^(3/4)*E^((e + f*x)/2)] + 24*e*Log[1 + (-1)^(3/4)*E^((e + f*x)/2)] - e^3*Log[1 + (-1)^(3/4)*E^((e + f*x)/2)] + 24*f*x*Log[1 + (-1)^(3/4)*E^((e + f*x)/2)] - f^3*x^3*Log[1 + (-1)^(3/4)*E^((e + f*x)/2)] - 6*(-8 + f^2*x^2)*PolyLog[2, -((-1)^(3/4)*E^((e + f*x)/2))] + 6*(-8 + f^2*x^2)*PolyLog[2, (-1)^(3/4)*E^((e + f*x)/2)] + 24*f*x*PolyLog[3, -((-1)^(3/4)*E^((e + f*x)/2))] - 24*f*x*PolyLog[3, (-1)^(3/4)*E^((e + f*x)/2)] - 48*PolyLog[4, -((-1)^(3/4)*E^((e + f*x)/2))] + 48*PolyLog[4, (-1)^(3/4)*E^((e + f*x)/2)])*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^2 + 2*f^3*x^3*Sinh[(e + f*x)/2]))/(2*f^4*(a + I*a*Sinh[e + f*x])^(3/2))","A",1
142,1,384,506,1.6842061,"\int \frac{x^2}{(a+i a \sinh (e+f x))^{3/2}} \, dx","Integrate[x^2/(a + I*a*Sinh[e + f*x])^(3/2),x]","\frac{\left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right) \left(-\left(\frac{1}{2}-\frac{i}{2}\right) (-1)^{3/4} \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^2 \left(e^2 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-e^2 \log \left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}+1\right)+2 e^2 \tanh ^{-1}\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-f^2 x^2 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+f^2 x^2 \log \left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}+1\right)+4 f x \text{Li}_2\left(-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-4 f x \text{Li}_2\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-8 \text{Li}_3\left(-(-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)+8 \text{Li}_3\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)-16 \tanh ^{-1}\left((-1)^{3/4} e^{\frac{1}{2} (e+f x)}\right)\right)+2 f^2 x^2 \sinh \left(\frac{1}{2} (e+f x)\right)+f x (4+i f x) \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)\right)}{2 f^3 (a+i a \sinh (e+f x))^{3/2}}","-\frac{4 i \text{Li}_3\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{a f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{4 i \text{Li}_3\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{a f^3 \sqrt{a+i a \sinh (e+f x)}}-\frac{4 \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \tan ^{-1}\left(\sinh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)\right)}{a f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{2 i x \text{Li}_2\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{a f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{2 i x \text{Li}_2\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{a f^2 \sqrt{a+i a \sinh (e+f x)}}+\frac{2 x}{a f^2 \sqrt{a+i a \sinh (e+f x)}}+\frac{x^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{2 a f \sqrt{a+i a \sinh (e+f x)}}+\frac{i x^2 \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \tanh ^{-1}\left(e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f \sqrt{a+i a \sinh (e+f x)}}",1,"((Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])*(f*x*(4 + I*f*x)*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]) - (1/2 - I/2)*(-1)^(3/4)*(-16*ArcTanh[(-1)^(3/4)*E^((e + f*x)/2)] + 2*e^2*ArcTanh[(-1)^(3/4)*E^((e + f*x)/2)] + e^2*Log[1 - (-1)^(3/4)*E^((e + f*x)/2)] - f^2*x^2*Log[1 - (-1)^(3/4)*E^((e + f*x)/2)] - e^2*Log[1 + (-1)^(3/4)*E^((e + f*x)/2)] + f^2*x^2*Log[1 + (-1)^(3/4)*E^((e + f*x)/2)] + 4*f*x*PolyLog[2, -((-1)^(3/4)*E^((e + f*x)/2))] - 4*f*x*PolyLog[2, (-1)^(3/4)*E^((e + f*x)/2)] - 8*PolyLog[3, -((-1)^(3/4)*E^((e + f*x)/2))] + 8*PolyLog[3, (-1)^(3/4)*E^((e + f*x)/2)])*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^2 + 2*f^2*x^2*Sinh[(e + f*x)/2]))/(2*f^3*(a + I*a*Sinh[e + f*x])^(3/2))","A",1
143,1,332,288,0.7595771,"\int \frac{x}{(a+i a \sinh (e+f x))^{3/2}} \, dx","Integrate[x/(a + I*a*Sinh[e + f*x])^(3/2),x]","\frac{\left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right) \left(\frac{i \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^2 \left(-2 \text{Li}_2\left(-\sqrt[4]{-1} e^{-\frac{e}{2}-\frac{f x}{2}}\right)+2 \text{Li}_2\left(\sqrt[4]{-1} e^{-\frac{e}{2}-\frac{f x}{2}}\right)+\frac{1}{2} i (2 i e+2 i f x+\pi ) \left(\log \left(1-\sqrt[4]{-1} e^{-\frac{e}{2}-\frac{f x}{2}}\right)-\log \left(\sqrt[4]{-1} e^{-\frac{e}{2}-\frac{f x}{2}}+1\right)\right)+\pi  \tan ^{-1}\left(\frac{\tanh \left(\frac{1}{4} (e+f x)\right)+i}{\sqrt{2}}\right)\right)}{\sqrt{2}}+2 f x \sinh \left(\frac{1}{2} (e+f x)\right)+(2+i f x) \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)-\sqrt{2} e \tan ^{-1}\left(\frac{\tanh \left(\frac{1}{4} (e+f x)\right)+i}{\sqrt{2}}\right) \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^2\right)}{2 f^2 (a+i a \sinh (e+f x))^{3/2}}","\frac{i \text{Li}_2\left(-e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{a f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{i \text{Li}_2\left(e^{\frac{1}{4} (2 e-i \pi )+\frac{f x}{2}}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{a f^2 \sqrt{a+i a \sinh (e+f x)}}+\frac{1}{a f^2 \sqrt{a+i a \sinh (e+f x)}}+\frac{x \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{2 a f \sqrt{a+i a \sinh (e+f x)}}+\frac{i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \tanh ^{-1}\left(e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f \sqrt{a+i a \sinh (e+f x)}}",1,"((Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])*((2 + I*f*x)*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2]) - Sqrt[2]*e*ArcTan[(I + Tanh[(e + f*x)/4])/Sqrt[2]]*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^2 + (I*(Pi*ArcTan[(I + Tanh[(e + f*x)/4])/Sqrt[2]] + (I/2)*((2*I)*e + Pi + (2*I)*f*x)*(Log[1 - (-1)^(1/4)*E^(-1/2*e - (f*x)/2)] - Log[1 + (-1)^(1/4)*E^(-1/2*e - (f*x)/2)]) - 2*PolyLog[2, -((-1)^(1/4)*E^(-1/2*e - (f*x)/2))] + 2*PolyLog[2, (-1)^(1/4)*E^(-1/2*e - (f*x)/2)])*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^2)/Sqrt[2] + 2*f*x*Sinh[(e + f*x)/2]))/(2*f^2*(a + I*a*Sinh[e + f*x])^(3/2))","A",1
144,0,0,24,21.0998284,"\int \frac{1}{x (a+i a \sinh (e+f x))^{3/2}} \, dx","Integrate[1/(x*(a + I*a*Sinh[e + f*x])^(3/2)),x]","\int \frac{1}{x (a+i a \sinh (e+f x))^{3/2}} \, dx","\text{Int}\left(\frac{1}{x (a+i a \sinh (e+f x))^{3/2}},x\right)",0,"Integrate[1/(x*(a + I*a*Sinh[e + f*x])^(3/2)), x]","A",-1
145,0,0,24,24.0910834,"\int \frac{1}{x^2 (a+i a \sinh (e+f x))^{3/2}} \, dx","Integrate[1/(x^2*(a + I*a*Sinh[e + f*x])^(3/2)),x]","\int \frac{1}{x^2 (a+i a \sinh (e+f x))^{3/2}} \, dx","\text{Int}\left(\frac{1}{x^2 (a+i a \sinh (e+f x))^{3/2}},x\right)",0,"Integrate[1/(x^2*(a + I*a*Sinh[e + f*x])^(3/2)), x]","A",-1
146,1,1200,1016,4.3735248,"\int \frac{x^3}{(a+i a \sinh (c+d x))^{5/2}} \, dx","Integrate[x^3/(a + I*a*Sinh[c + d*x])^(5/2),x]","\frac{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left((1-i) (-1)^{3/4} \left(6 \tanh ^{-1}\left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right) c^3+3 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right) c^3-3 \log \left(1+(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right) c^3-160 \tanh ^{-1}\left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right) c-80 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right) c+80 \log \left(1+(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right) c+3 d^3 x^3 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)-80 d x \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)-3 d^3 x^3 \log \left(1+(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)+80 d x \log \left(1+(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)-2 \left(9 d^2 x^2-80\right) \text{Li}_2\left(-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)+2 \left(9 d^2 x^2-80\right) \text{Li}_2\left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)+72 d x \text{Li}_3\left(-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)-72 d x \text{Li}_3\left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)-144 \text{Li}_4\left(-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)+144 \text{Li}_4\left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^4-11 i c^3 \cosh \left(\frac{1}{2} (c+d x)\right)+11 i (c+d x)^3 \cosh \left(\frac{1}{2} (c+d x)\right)+70 c^2 \cosh \left(\frac{1}{2} (c+d x)\right)-33 i c (c+d x)^2 \cosh \left(\frac{1}{2} (c+d x)\right)+70 (c+d x)^2 \cosh \left(\frac{1}{2} (c+d x)\right)+8 i c \cosh \left(\frac{1}{2} (c+d x)\right)+33 i c^2 (c+d x) \cosh \left(\frac{1}{2} (c+d x)\right)-140 c (c+d x) \cosh \left(\frac{1}{2} (c+d x)\right)-8 i (c+d x) \cosh \left(\frac{1}{2} (c+d x)\right)-48 \cosh \left(\frac{1}{2} (c+d x)\right)-3 i c^3 \cosh \left(\frac{3}{2} (c+d x)\right)+3 i (c+d x)^3 \cosh \left(\frac{3}{2} (c+d x)\right)-18 c^2 \cosh \left(\frac{3}{2} (c+d x)\right)-9 i c (c+d x)^2 \cosh \left(\frac{3}{2} (c+d x)\right)-18 (c+d x)^2 \cosh \left(\frac{3}{2} (c+d x)\right)+8 i c \cosh \left(\frac{3}{2} (c+d x)\right)+9 i c^2 (c+d x) \cosh \left(\frac{3}{2} (c+d x)\right)+36 c (c+d x) \cosh \left(\frac{3}{2} (c+d x)\right)-8 i (c+d x) \cosh \left(\frac{3}{2} (c+d x)\right)+16 \cosh \left(\frac{3}{2} (c+d x)\right)-11 c^3 \sinh \left(\frac{1}{2} (c+d x)\right)+11 (c+d x)^3 \sinh \left(\frac{1}{2} (c+d x)\right)+70 i c^2 \sinh \left(\frac{1}{2} (c+d x)\right)-33 c (c+d x)^2 \sinh \left(\frac{1}{2} (c+d x)\right)+70 i (c+d x)^2 \sinh \left(\frac{1}{2} (c+d x)\right)+8 c \sinh \left(\frac{1}{2} (c+d x)\right)+33 c^2 (c+d x) \sinh \left(\frac{1}{2} (c+d x)\right)-140 i c (c+d x) \sinh \left(\frac{1}{2} (c+d x)\right)-8 (c+d x) \sinh \left(\frac{1}{2} (c+d x)\right)-48 i \sinh \left(\frac{1}{2} (c+d x)\right)+3 c^3 \sinh \left(\frac{3}{2} (c+d x)\right)-3 (c+d x)^3 \sinh \left(\frac{3}{2} (c+d x)\right)+18 i c^2 \sinh \left(\frac{3}{2} (c+d x)\right)+9 c (c+d x)^2 \sinh \left(\frac{3}{2} (c+d x)\right)+18 i (c+d x)^2 \sinh \left(\frac{3}{2} (c+d x)\right)-8 c \sinh \left(\frac{3}{2} (c+d x)\right)-9 c^2 (c+d x) \sinh \left(\frac{3}{2} (c+d x)\right)-36 i c (c+d x) \sinh \left(\frac{3}{2} (c+d x)\right)+8 (c+d x) \sinh \left(\frac{3}{2} (c+d x)\right)-16 i \sinh \left(\frac{3}{2} (c+d x)\right)\right)}{32 d^4 (i \sinh (c+d x) a+a)^{5/2}}","\frac{\text{sech}^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) x^3}{8 a^2 d \sqrt{i \sinh (c+d x) a+a}}+\frac{3 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) x^3}{16 a^2 d \sqrt{i \sinh (c+d x) a+a}}+\frac{3 i \tanh ^{-1}\left(e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) x^3}{8 a^2 d \sqrt{i \sinh (c+d x) a+a}}+\frac{\text{sech}^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) x^2}{4 a^2 d^2 \sqrt{i \sinh (c+d x) a+a}}+\frac{9 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{Li}_2\left(-e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) x^2}{8 a^2 d^2 \sqrt{i \sinh (c+d x) a+a}}-\frac{9 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{Li}_2\left(e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) x^2}{8 a^2 d^2 \sqrt{i \sinh (c+d x) a+a}}+\frac{9 x^2}{8 a^2 d^2 \sqrt{i \sinh (c+d x) a+a}}-\frac{\tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) x}{2 a^2 d^3 \sqrt{i \sinh (c+d x) a+a}}-\frac{10 i \tanh ^{-1}\left(e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) x}{a^2 d^3 \sqrt{i \sinh (c+d x) a+a}}-\frac{9 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{Li}_3\left(-e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) x}{2 a^2 d^3 \sqrt{i \sinh (c+d x) a+a}}+\frac{9 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{Li}_3\left(e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) x}{2 a^2 d^3 \sqrt{i \sinh (c+d x) a+a}}-\frac{10 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{Li}_2\left(-e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right)}{a^2 d^4 \sqrt{i \sinh (c+d x) a+a}}+\frac{10 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{Li}_2\left(e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right)}{a^2 d^4 \sqrt{i \sinh (c+d x) a+a}}+\frac{9 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{Li}_4\left(-e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right)}{a^2 d^4 \sqrt{i \sinh (c+d x) a+a}}-\frac{9 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{Li}_4\left(e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right)}{a^2 d^4 \sqrt{i \sinh (c+d x) a+a}}-\frac{1}{a^2 d^4 \sqrt{i \sinh (c+d x) a+a}}",1,"((Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*(-48*Cosh[(c + d*x)/2] + (8*I)*c*Cosh[(c + d*x)/2] + 70*c^2*Cosh[(c + d*x)/2] - (11*I)*c^3*Cosh[(c + d*x)/2] - (8*I)*(c + d*x)*Cosh[(c + d*x)/2] - 140*c*(c + d*x)*Cosh[(c + d*x)/2] + (33*I)*c^2*(c + d*x)*Cosh[(c + d*x)/2] + 70*(c + d*x)^2*Cosh[(c + d*x)/2] - (33*I)*c*(c + d*x)^2*Cosh[(c + d*x)/2] + (11*I)*(c + d*x)^3*Cosh[(c + d*x)/2] + 16*Cosh[(3*(c + d*x))/2] + (8*I)*c*Cosh[(3*(c + d*x))/2] - 18*c^2*Cosh[(3*(c + d*x))/2] - (3*I)*c^3*Cosh[(3*(c + d*x))/2] - (8*I)*(c + d*x)*Cosh[(3*(c + d*x))/2] + 36*c*(c + d*x)*Cosh[(3*(c + d*x))/2] + (9*I)*c^2*(c + d*x)*Cosh[(3*(c + d*x))/2] - 18*(c + d*x)^2*Cosh[(3*(c + d*x))/2] - (9*I)*c*(c + d*x)^2*Cosh[(3*(c + d*x))/2] + (3*I)*(c + d*x)^3*Cosh[(3*(c + d*x))/2] + (1 - I)*(-1)^(3/4)*(-160*c*ArcTanh[(-1)^(3/4)*E^((c + d*x)/2)] + 6*c^3*ArcTanh[(-1)^(3/4)*E^((c + d*x)/2)] - 80*c*Log[1 - (-1)^(3/4)*E^((c + d*x)/2)] + 3*c^3*Log[1 - (-1)^(3/4)*E^((c + d*x)/2)] - 80*d*x*Log[1 - (-1)^(3/4)*E^((c + d*x)/2)] + 3*d^3*x^3*Log[1 - (-1)^(3/4)*E^((c + d*x)/2)] + 80*c*Log[1 + (-1)^(3/4)*E^((c + d*x)/2)] - 3*c^3*Log[1 + (-1)^(3/4)*E^((c + d*x)/2)] + 80*d*x*Log[1 + (-1)^(3/4)*E^((c + d*x)/2)] - 3*d^3*x^3*Log[1 + (-1)^(3/4)*E^((c + d*x)/2)] - 2*(-80 + 9*d^2*x^2)*PolyLog[2, -((-1)^(3/4)*E^((c + d*x)/2))] + 2*(-80 + 9*d^2*x^2)*PolyLog[2, (-1)^(3/4)*E^((c + d*x)/2)] + 72*d*x*PolyLog[3, -((-1)^(3/4)*E^((c + d*x)/2))] - 72*d*x*PolyLog[3, (-1)^(3/4)*E^((c + d*x)/2)] - 144*PolyLog[4, -((-1)^(3/4)*E^((c + d*x)/2))] + 144*PolyLog[4, (-1)^(3/4)*E^((c + d*x)/2)])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^4 - (48*I)*Sinh[(c + d*x)/2] + 8*c*Sinh[(c + d*x)/2] + (70*I)*c^2*Sinh[(c + d*x)/2] - 11*c^3*Sinh[(c + d*x)/2] - 8*(c + d*x)*Sinh[(c + d*x)/2] - (140*I)*c*(c + d*x)*Sinh[(c + d*x)/2] + 33*c^2*(c + d*x)*Sinh[(c + d*x)/2] + (70*I)*(c + d*x)^2*Sinh[(c + d*x)/2] - 33*c*(c + d*x)^2*Sinh[(c + d*x)/2] + 11*(c + d*x)^3*Sinh[(c + d*x)/2] - (16*I)*Sinh[(3*(c + d*x))/2] - 8*c*Sinh[(3*(c + d*x))/2] + (18*I)*c^2*Sinh[(3*(c + d*x))/2] + 3*c^3*Sinh[(3*(c + d*x))/2] + 8*(c + d*x)*Sinh[(3*(c + d*x))/2] - (36*I)*c*(c + d*x)*Sinh[(3*(c + d*x))/2] - 9*c^2*(c + d*x)*Sinh[(3*(c + d*x))/2] + (18*I)*(c + d*x)^2*Sinh[(3*(c + d*x))/2] + 9*c*(c + d*x)^2*Sinh[(3*(c + d*x))/2] - 3*(c + d*x)^3*Sinh[(3*(c + d*x))/2]))/(32*d^4*(a + I*a*Sinh[c + d*x])^(5/2))","A",1
147,1,482,689,2.287205,"\int \frac{x^2}{(a+i a \sinh (c+d x))^{5/2}} \, dx","Integrate[x^2/(a + I*a*Sinh[c + d*x])^(5/2),x]","\frac{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(\left(-\frac{1}{2}+\frac{i}{2}\right) (-1)^{3/4} \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^4 \left(9 c^2 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)-9 c^2 \log \left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}+1\right)+18 c^2 \tanh ^{-1}\left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)-9 d^2 x^2 \log \left(1-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)+9 d^2 x^2 \log \left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}+1\right)+36 d x \text{Li}_2\left(-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)-36 d x \text{Li}_2\left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)-72 \text{Li}_3\left(-(-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)+72 \text{Li}_3\left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)-160 \tanh ^{-1}\left((-1)^{3/4} e^{\frac{1}{2} (c+d x)}\right)\right)+24 d^2 x^2 \sinh \left(\frac{1}{2} (c+d x)\right)+\left(9 i d^2 x^2+36 d x-8 i\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^3+2 \left(9 d^2 x^2-8\right) \sinh \left(\frac{1}{2} (c+d x)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2+4 d x (4+3 i d x) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)\right)}{48 d^3 (a+i a \sinh (c+d x))^{5/2}}","-\frac{3 i \text{Li}_3\left(-e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{2 a^2 d^3 \sqrt{a+i a \sinh (c+d x)}}+\frac{3 i \text{Li}_3\left(e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{2 a^2 d^3 \sqrt{a+i a \sinh (c+d x)}}-\frac{\tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{6 a^2 d^3 \sqrt{a+i a \sinh (c+d x)}}-\frac{5 \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \tan ^{-1}\left(\sinh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)\right)}{3 a^2 d^3 \sqrt{a+i a \sinh (c+d x)}}+\frac{3 i x \text{Li}_2\left(-e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{4 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}-\frac{3 i x \text{Li}_2\left(e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{4 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}+\frac{3 x}{4 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}+\frac{x \text{sech}^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{6 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}+\frac{3 x^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{16 a^2 d \sqrt{a+i a \sinh (c+d x)}}+\frac{3 i x^2 \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \tanh ^{-1}\left(e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{8 a^2 d \sqrt{a+i a \sinh (c+d x)}}+\frac{x^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{sech}^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{8 a^2 d \sqrt{a+i a \sinh (c+d x)}}",1,"((Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*(4*d*x*(4 + (3*I)*d*x)*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + (-8*I + 36*d*x + (9*I)*d^2*x^2)*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^3 - (1/2 - I/2)*(-1)^(3/4)*(-160*ArcTanh[(-1)^(3/4)*E^((c + d*x)/2)] + 18*c^2*ArcTanh[(-1)^(3/4)*E^((c + d*x)/2)] + 9*c^2*Log[1 - (-1)^(3/4)*E^((c + d*x)/2)] - 9*d^2*x^2*Log[1 - (-1)^(3/4)*E^((c + d*x)/2)] - 9*c^2*Log[1 + (-1)^(3/4)*E^((c + d*x)/2)] + 9*d^2*x^2*Log[1 + (-1)^(3/4)*E^((c + d*x)/2)] + 36*d*x*PolyLog[2, -((-1)^(3/4)*E^((c + d*x)/2))] - 36*d*x*PolyLog[2, (-1)^(3/4)*E^((c + d*x)/2)] - 72*PolyLog[3, -((-1)^(3/4)*E^((c + d*x)/2))] + 72*PolyLog[3, (-1)^(3/4)*E^((c + d*x)/2)])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^4 + 24*d^2*x^2*Sinh[(c + d*x)/2] + 2*(-8 + 9*d^2*x^2)*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2*Sinh[(c + d*x)/2]))/(48*d^3*(a + I*a*Sinh[c + d*x])^(5/2))","A",1
148,1,411,416,1.5232753,"\int \frac{x}{(a+i a \sinh (c+d x))^{5/2}} \, dx","Integrate[x/(a + I*a*Sinh[c + d*x])^(5/2),x]","\frac{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(\frac{9 i \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^4 \left(-2 \text{Li}_2\left(-\sqrt[4]{-1} e^{-\frac{c}{2}-\frac{d x}{2}}\right)+2 \text{Li}_2\left(\sqrt[4]{-1} e^{-\frac{c}{2}-\frac{d x}{2}}\right)+\frac{1}{2} i (2 i c+2 i d x+\pi ) \left(\log \left(1-\sqrt[4]{-1} e^{-\frac{c}{2}-\frac{d x}{2}}\right)-\log \left(\sqrt[4]{-1} e^{-\frac{c}{2}-\frac{d x}{2}}+1\right)\right)+\pi  \tan ^{-1}\left(\frac{\tanh \left(\frac{1}{4} (c+d x)\right)+i}{\sqrt{2}}\right)\right)}{\sqrt{2}}+24 d x \sinh \left(\frac{1}{2} (c+d x)\right)+9 (2+i d x) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^3+18 d x \sinh \left(\frac{1}{2} (c+d x)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2+4 (2+3 i d x) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)-9 \sqrt{2} c \tan ^{-1}\left(\frac{\tanh \left(\frac{1}{4} (c+d x)\right)+i}{\sqrt{2}}\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^4\right)}{48 d^2 (a+i a \sinh (c+d x))^{5/2}}","\frac{3 i \text{Li}_2\left(-e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{8 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}-\frac{3 i \text{Li}_2\left(e^{\frac{1}{4} (2 c-i \pi )+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{8 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}+\frac{3}{8 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}+\frac{\text{sech}^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{12 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}+\frac{3 x \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{16 a^2 d \sqrt{a+i a \sinh (c+d x)}}+\frac{3 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \tanh ^{-1}\left(e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{8 a^2 d \sqrt{a+i a \sinh (c+d x)}}+\frac{x \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{sech}^2\left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{8 a^2 d \sqrt{a+i a \sinh (c+d x)}}",1,"((Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*(4*(2 + (3*I)*d*x)*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + 9*(2 + I*d*x)*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^3 - 9*Sqrt[2]*c*ArcTan[(I + Tanh[(c + d*x)/4])/Sqrt[2]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^4 + ((9*I)*(Pi*ArcTan[(I + Tanh[(c + d*x)/4])/Sqrt[2]] + (I/2)*((2*I)*c + Pi + (2*I)*d*x)*(Log[1 - (-1)^(1/4)*E^(-1/2*c - (d*x)/2)] - Log[1 + (-1)^(1/4)*E^(-1/2*c - (d*x)/2)]) - 2*PolyLog[2, -((-1)^(1/4)*E^(-1/2*c - (d*x)/2))] + 2*PolyLog[2, (-1)^(1/4)*E^(-1/2*c - (d*x)/2)])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^4)/Sqrt[2] + 24*d*x*Sinh[(c + d*x)/2] + 18*d*x*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2*Sinh[(c + d*x)/2]))/(48*d^2*(a + I*a*Sinh[c + d*x])^(5/2))","A",1
149,0,0,24,34.8044631,"\int \frac{1}{x (a+i a \sinh (c+d x))^{5/2}} \, dx","Integrate[1/(x*(a + I*a*Sinh[c + d*x])^(5/2)),x]","\int \frac{1}{x (a+i a \sinh (c+d x))^{5/2}} \, dx","\text{Int}\left(\frac{1}{x (a+i a \sinh (c+d x))^{5/2}},x\right)",0,"Integrate[1/(x*(a + I*a*Sinh[c + d*x])^(5/2)), x]","A",-1
150,0,0,24,3.9607966,"\int \frac{\sqrt[3]{a+i a \sinh (e+f x)}}{x} \, dx","Integrate[(a + I*a*Sinh[e + f*x])^(1/3)/x,x]","\int \frac{\sqrt[3]{a+i a \sinh (e+f x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt[3]{a+i a \sinh (e+f x)}}{x},x\right)",0,"Integrate[(a + I*a*Sinh[e + f*x])^(1/3)/x, x]","A",-1
151,0,0,26,4.3010562,"\int (c+d x)^m (a+i a \sinh (e+f x))^n \, dx","Integrate[(c + d*x)^m*(a + I*a*Sinh[e + f*x])^n,x]","\int (c+d x)^m (a+i a \sinh (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (a+i a \sinh (e+f x))^n,x\right)",0,"Integrate[(c + d*x)^m*(a + I*a*Sinh[e + f*x])^n, x]","A",-1
152,1,339,410,1.5528918,"\int (c+d x)^m (a+i a \sinh (e+f x))^3 \, dx","Integrate[(c + d*x)^m*(a + I*a*Sinh[e + f*x])^3,x]","\frac{1}{24} a^3 (c+d x)^m \left(-\frac{i 3^{-m} e^{3 e-\frac{3 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{3 f (c+d x)}{d}\right)}{f}-\frac{9\ 2^{-m} e^{2 e-\frac{2 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)}{f}+\frac{45 i e^{e-\frac{c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{f}+\frac{45 i e^{\frac{c f}{d}-e} \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{f}+\frac{9\ 2^{-m} e^{\frac{2 c f}{d}-2 e} \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}-\frac{i 3^{-m} e^{\frac{3 c f}{d}-3 e} \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{3 f (c+d x)}{d}\right)}{f}+\frac{60 (c+d x)}{d (m+1)}\right)","-\frac{i a^3 3^{-m-1} e^{3 e-\frac{3 c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{3 f (c+d x)}{d}\right)}{8 f}-\frac{3 a^3 2^{-m-3} e^{2 e-\frac{2 c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)}{f}+\frac{15 i a^3 e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{8 f}+\frac{15 i a^3 e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{8 f}+\frac{3 a^3 2^{-m-3} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}-\frac{i a^3 3^{-m-1} e^{\frac{3 c f}{d}-3 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{3 f (c+d x)}{d}\right)}{8 f}+\frac{5 a^3 (c+d x)^{m+1}}{2 d (m+1)}",1,"(a^3*(c + d*x)^m*((60*(c + d*x))/(d*(1 + m)) - (I*E^(3*e - (3*c*f)/d)*Gamma[1 + m, (-3*f*(c + d*x))/d])/(3^m*f*(-((f*(c + d*x))/d))^m) - (9*E^(2*e - (2*c*f)/d)*Gamma[1 + m, (-2*f*(c + d*x))/d])/(2^m*f*(-((f*(c + d*x))/d))^m) + ((45*I)*E^(e - (c*f)/d)*Gamma[1 + m, -((f*(c + d*x))/d)])/(f*(-((f*(c + d*x))/d))^m) + ((45*I)*E^(-e + (c*f)/d)*Gamma[1 + m, (f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m) + (9*E^(-2*e + (2*c*f)/d)*Gamma[1 + m, (2*f*(c + d*x))/d])/(2^m*f*((f*(c + d*x))/d)^m) - (I*E^(-3*e + (3*c*f)/d)*Gamma[1 + m, (3*f*(c + d*x))/d])/(3^m*f*((f*(c + d*x))/d)^m)))/24","A",1
153,1,229,268,0.7494648,"\int (c+d x)^m (a+i a \sinh (e+f x))^2 \, dx","Integrate[(c + d*x)^m*(a + I*a*Sinh[e + f*x])^2,x]","\frac{1}{8} a^2 (c+d x)^m \left(-\frac{2^{-m} e^{2 e-\frac{2 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)}{f}+\frac{8 i e^{e-\frac{c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{f}+\frac{8 i e^{\frac{c f}{d}-e} \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{f}+\frac{2^{-m} e^{\frac{2 c f}{d}-2 e} \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}+\frac{12 (c+d x)}{d (m+1)}\right)","-\frac{a^2 2^{-m-3} e^{2 e-\frac{2 c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)}{f}+\frac{i a^2 e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{f}+\frac{i a^2 e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{f}+\frac{a^2 2^{-m-3} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}+\frac{3 a^2 (c+d x)^{m+1}}{2 d (m+1)}",1,"(a^2*(c + d*x)^m*((12*(c + d*x))/(d*(1 + m)) - (E^(2*e - (2*c*f)/d)*Gamma[1 + m, (-2*f*(c + d*x))/d])/(2^m*f*(-((f*(c + d*x))/d))^m) + ((8*I)*E^(e - (c*f)/d)*Gamma[1 + m, -((f*(c + d*x))/d)])/(f*(-((f*(c + d*x))/d))^m) + ((8*I)*E^(-e + (c*f)/d)*Gamma[1 + m, (f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m) + (E^(-2*e + (2*c*f)/d)*Gamma[1 + m, (2*f*(c + d*x))/d])/(2^m*f*((f*(c + d*x))/d)^m)))/8","A",1
154,1,207,135,0.5057733,"\int (c+d x)^m (a+i a \sinh (e+f x)) \, dx","Integrate[(c + d*x)^m*(a + I*a*Sinh[e + f*x]),x]","-\frac{a e^{-\frac{c f}{d}-e} (c+d x)^m (\sinh (e+f x)-i) \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(-2 i f (c+d x) e^{\frac{c f}{d}+e} \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^m+d e^{2 e} (m+1) \left(f \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)+d (m+1) e^{\frac{2 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)\right)}{2 d f (m+1) \left(\cosh \left(\frac{1}{2} (e+f x)\right)+i \sinh \left(\frac{1}{2} (e+f x)\right)\right)^2}","\frac{i a e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{2 f}+\frac{i a e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{2 f}+\frac{a (c+d x)^{m+1}}{d (m+1)}",1,"-1/2*(a*E^(-e - (c*f)/d)*(c + d*x)^m*((-2*I)*E^(e + (c*f)/d)*f*(c + d*x)*(-((f^2*(c + d*x)^2)/d^2))^m + d*E^(2*e)*(1 + m)*(f*(c/d + x))^m*Gamma[1 + m, -((f*(c + d*x))/d)] + d*E^((2*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (f*(c + d*x))/d])*(-I + Sinh[e + f*x]))/(d*f*(1 + m)*(-((f^2*(c + d*x)^2)/d^2))^m*(Cosh[(e + f*x)/2] + I*Sinh[(e + f*x)/2])^2)","A",1
155,0,0,26,4.1822092,"\int \frac{(c+d x)^m}{a+i a \sinh (e+f x)} \, dx","Integrate[(c + d*x)^m/(a + I*a*Sinh[e + f*x]),x]","\int \frac{(c+d x)^m}{a+i a \sinh (e+f x)} \, dx","\text{Int}\left(\frac{(c+d x)^m}{a+i a \sinh (e+f x)},x\right)",0,"Integrate[(c + d*x)^m/(a + I*a*Sinh[e + f*x]), x]","A",-1
156,0,0,26,16.9308947,"\int \frac{(c+d x)^m}{(a+i a \sinh (e+f x))^2} \, dx","Integrate[(c + d*x)^m/(a + I*a*Sinh[e + f*x])^2,x]","\int \frac{(c+d x)^m}{(a+i a \sinh (e+f x))^2} \, dx","\text{Int}\left(\frac{(c+d x)^m}{(a+i a \sinh (e+f x))^2},x\right)",0,"Integrate[(c + d*x)^m/(a + I*a*Sinh[e + f*x])^2, x]","A",-1
157,1,123,89,0.4577522,"\int (c+d x)^3 (a+b \sinh (e+f x)) \, dx","Integrate[(c + d*x)^3*(a + b*Sinh[e + f*x]),x]","\frac{1}{4} a x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)-\frac{3 b d \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \sinh (e+f x)}{f^4}+\frac{b (c+d x) \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+6\right)\right) \cosh (e+f x)}{f^3}","\frac{a (c+d x)^4}{4 d}+\frac{6 b d^2 (c+d x) \cosh (e+f x)}{f^3}-\frac{3 b d (c+d x)^2 \sinh (e+f x)}{f^2}+\frac{b (c+d x)^3 \cosh (e+f x)}{f}-\frac{6 b d^3 \sinh (e+f x)}{f^4}",1,"(a*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3))/4 + (b*(c + d*x)*(c^2*f^2 + 2*c*d*f^2*x + d^2*(6 + f^2*x^2))*Cosh[e + f*x])/f^3 - (3*b*d*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Sinh[e + f*x])/f^4","A",1
158,1,83,67,0.3166935,"\int (c+d x)^2 (a+b \sinh (e+f x)) \, dx","Integrate[(c + d*x)^2*(a + b*Sinh[e + f*x]),x]","\frac{1}{3} a x \left(3 c^2+3 c d x+d^2 x^2\right)+\frac{b \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \cosh (e+f x)}{f^3}-\frac{2 b d (c+d x) \sinh (e+f x)}{f^2}","\frac{a (c+d x)^3}{3 d}-\frac{2 b d (c+d x) \sinh (e+f x)}{f^2}+\frac{b (c+d x)^2 \cosh (e+f x)}{f}+\frac{2 b d^2 \cosh (e+f x)}{f^3}",1,"(a*x*(3*c^2 + 3*c*d*x + d^2*x^2))/3 + (b*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Cosh[e + f*x])/f^3 - (2*b*d*(c + d*x)*Sinh[e + f*x])/f^2","A",1
159,1,43,45,0.1180365,"\int (c+d x) (a+b \sinh (e+f x)) \, dx","Integrate[(c + d*x)*(a + b*Sinh[e + f*x]),x]","\frac{1}{2} a x (2 c+d x)+\frac{b (c+d x) \cosh (e+f x)}{f}-\frac{b d \sinh (e+f x)}{f^2}","\frac{a (c+d x)^2}{2 d}+\frac{b (c+d x) \cosh (e+f x)}{f}-\frac{b d \sinh (e+f x)}{f^2}",1,"(a*x*(2*c + d*x))/2 + (b*(c + d*x)*Cosh[e + f*x])/f - (b*d*Sinh[e + f*x])/f^2","A",1
160,1,57,64,0.1410796,"\int \frac{a+b \sinh (e+f x)}{c+d x} \, dx","Integrate[(a + b*Sinh[e + f*x])/(c + d*x),x]","\frac{a \log (c+d x)+b \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+b \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)}{d}","\frac{a \log (c+d x)}{d}+\frac{b \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{d}+\frac{b \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d}",1,"(a*Log[c + d*x] + b*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] + b*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)])/d","A",1
161,1,71,87,0.3491852,"\int \frac{a+b \sinh (e+f x)}{(c+d x)^2} \, dx","Integrate[(a + b*Sinh[e + f*x])/(c + d*x)^2,x]","\frac{-\frac{d (a+b \sinh (e+f x))}{c+d x}+b f \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+b f \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)}{d^2}","-\frac{a}{d (c+d x)}+\frac{b f \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{b f \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{b \sinh (e+f x)}{d (c+d x)}",1,"(b*f*Cosh[e - (c*f)/d]*CoshIntegral[f*(c/d + x)] - (d*(a + b*Sinh[e + f*x]))/(c + d*x) + b*f*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)])/d^2","A",1
162,1,95,123,0.6181858,"\int \frac{a+b \sinh (e+f x)}{(c+d x)^3} \, dx","Integrate[(a + b*Sinh[e + f*x])/(c + d*x)^3,x]","\frac{-\frac{d (d (a+b \sinh (e+f x))+b f (c+d x) \cosh (e+f x))}{(c+d x)^2}+b f^2 \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+b f^2 \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)}{2 d^3}","-\frac{a}{2 d (c+d x)^2}+\frac{b f^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{2 d^3}+\frac{b f^2 \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{2 d^3}-\frac{b f \cosh (e+f x)}{2 d^2 (c+d x)}-\frac{b \sinh (e+f x)}{2 d (c+d x)^2}",1,"(b*f^2*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] - (d*(b*f*(c + d*x)*Cosh[e + f*x] + d*(a + b*Sinh[e + f*x])))/(c + d*x)^2 + b*f^2*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)])/(2*d^3)","A",1
163,1,235,250,1.3618229,"\int (c+d x)^3 (a+b \sinh (e+f x))^2 \, dx","Integrate[(c + d*x)^3*(a + b*Sinh[e + f*x])^2,x]","\frac{2 \left(f^4 x \left(2 a^2-b^2\right) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)-48 a b d \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \sinh (e+f x)+b^2 f (c+d x) \left(2 c^2 f^2+4 c d f^2 x+d^2 \left(2 f^2 x^2+3\right)\right) \sinh (2 (e+f x))\right)+32 a b f (c+d x) \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+6\right)\right) \cosh (e+f x)-3 b^2 d \left(2 c^2 f^2+4 c d f^2 x+d^2 \left(2 f^2 x^2+1\right)\right) \cosh (2 (e+f x))}{16 f^4}","\frac{a^2 (c+d x)^4}{4 d}+\frac{12 a b d^2 (c+d x) \cosh (e+f x)}{f^3}-\frac{6 a b d (c+d x)^2 \sinh (e+f x)}{f^2}+\frac{2 a b (c+d x)^3 \cosh (e+f x)}{f}-\frac{12 a b d^3 \sinh (e+f x)}{f^4}+\frac{3 b^2 d^2 (c+d x) \sinh (e+f x) \cosh (e+f x)}{4 f^3}-\frac{3 b^2 c d^2 x}{4 f^2}-\frac{3 b^2 d (c+d x)^2 \sinh ^2(e+f x)}{4 f^2}+\frac{b^2 (c+d x)^3 \sinh (e+f x) \cosh (e+f x)}{2 f}-\frac{b^2 (c+d x)^4}{8 d}-\frac{3 b^2 d^3 \sinh ^2(e+f x)}{8 f^4}-\frac{3 b^2 d^3 x^2}{8 f^2}",1,"(32*a*b*f*(c + d*x)*(c^2*f^2 + 2*c*d*f^2*x + d^2*(6 + f^2*x^2))*Cosh[e + f*x] - 3*b^2*d*(2*c^2*f^2 + 4*c*d*f^2*x + d^2*(1 + 2*f^2*x^2))*Cosh[2*(e + f*x)] + 2*((2*a^2 - b^2)*f^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) - 48*a*b*d*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Sinh[e + f*x] + b^2*f*(c + d*x)*(2*c^2*f^2 + 4*c*d*f^2*x + d^2*(3 + 2*f^2*x^2))*Sinh[2*(e + f*x)]))/(16*f^4)","A",1
164,1,249,182,0.7260693,"\int (c+d x)^2 (a+b \sinh (e+f x))^2 \, dx","Integrate[(c + d*x)^2*(a + b*Sinh[e + f*x])^2,x]","\frac{24 a^2 c^2 f^3 x+24 a^2 c d f^3 x^2+8 a^2 d^2 f^3 x^3+48 a b \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \cosh (e+f x)-96 a b c d f \sinh (e+f x)-96 a b d^2 f x \sinh (e+f x)+6 b^2 c^2 f^2 \sinh (2 (e+f x))-12 b^2 c^2 f^3 x+12 b^2 c d f^2 x \sinh (2 (e+f x))-6 b^2 d f (c+d x) \cosh (2 (e+f x))-12 b^2 c d f^3 x^2+6 b^2 d^2 f^2 x^2 \sinh (2 (e+f x))+3 b^2 d^2 \sinh (2 (e+f x))-4 b^2 d^2 f^3 x^3}{24 f^3}","\frac{a^2 (c+d x)^3}{3 d}-\frac{4 a b d (c+d x) \sinh (e+f x)}{f^2}+\frac{2 a b (c+d x)^2 \cosh (e+f x)}{f}+\frac{4 a b d^2 \cosh (e+f x)}{f^3}-\frac{b^2 d (c+d x) \sinh ^2(e+f x)}{2 f^2}+\frac{b^2 (c+d x)^2 \sinh (e+f x) \cosh (e+f x)}{2 f}-\frac{b^2 (c+d x)^3}{6 d}+\frac{b^2 d^2 \sinh (e+f x) \cosh (e+f x)}{4 f^3}-\frac{b^2 d^2 x}{4 f^2}",1,"(24*a^2*c^2*f^3*x - 12*b^2*c^2*f^3*x + 24*a^2*c*d*f^3*x^2 - 12*b^2*c*d*f^3*x^2 + 8*a^2*d^2*f^3*x^3 - 4*b^2*d^2*f^3*x^3 + 48*a*b*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Cosh[e + f*x] - 6*b^2*d*f*(c + d*x)*Cosh[2*(e + f*x)] - 96*a*b*c*d*f*Sinh[e + f*x] - 96*a*b*d^2*f*x*Sinh[e + f*x] + 3*b^2*d^2*Sinh[2*(e + f*x)] + 6*b^2*c^2*f^2*Sinh[2*(e + f*x)] + 12*b^2*c*d*f^2*x*Sinh[2*(e + f*x)] + 6*b^2*d^2*f^2*x^2*Sinh[2*(e + f*x)])/(24*f^3)","A",1
165,1,98,116,0.7224021,"\int (c+d x) (a+b \sinh (e+f x))^2 \, dx","Integrate[(c + d*x)*(a + b*Sinh[e + f*x])^2,x]","-\frac{2 \left(2 a^2-b^2\right) (e+f x) (d (e-f x)-2 c f)-16 a b f (c+d x) \cosh (e+f x)+16 a b d \sinh (e+f x)-2 b^2 f (c+d x) \sinh (2 (e+f x))+b^2 d \cosh (2 (e+f x))}{8 f^2}","\frac{a^2 (c+d x)^2}{2 d}+\frac{2 a b (c+d x) \cosh (e+f x)}{f}-\frac{2 a b d \sinh (e+f x)}{f^2}+\frac{b^2 (c+d x) \sinh (e+f x) \cosh (e+f x)}{2 f}-\frac{1}{2} b^2 c x-\frac{b^2 d \sinh ^2(e+f x)}{4 f^2}-\frac{1}{4} b^2 d x^2",1,"-1/8*(2*(2*a^2 - b^2)*(e + f*x)*(-2*c*f + d*(e - f*x)) - 16*a*b*f*(c + d*x)*Cosh[e + f*x] + b^2*d*Cosh[2*(e + f*x)] + 16*a*b*d*Sinh[e + f*x] - 2*b^2*f*(c + d*x)*Sinh[2*(e + f*x)])/f^2","A",1
166,1,134,156,0.2946467,"\int \frac{(a+b \sinh (e+f x))^2}{c+d x} \, dx","Integrate[(a + b*Sinh[e + f*x])^2/(c + d*x),x]","\frac{2 a^2 \log (c+d x)+4 a b \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+4 a b \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+b^2 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)+b^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-b^2 \log (c+d x)}{2 d}","\frac{a^2 \log (c+d x)}{d}+\frac{2 a b \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{d}+\frac{2 a b \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d}+\frac{b^2 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{2 d}+\frac{b^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{2 d}-\frac{b^2 \log (c+d x)}{2 d}",1,"(b^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*f*(c + d*x))/d] + 2*a^2*Log[c + d*x] - b^2*Log[c + d*x] + 4*a*b*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] + 4*a*b*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + b^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d])/(2*d)","A",1
167,1,232,183,0.5962474,"\int \frac{(a+b \sinh (e+f x))^2}{(c+d x)^2} \, dx","Integrate[(a + b*Sinh[e + f*x])^2/(c + d*x)^2,x]","\frac{-2 a^2 d+4 a b f (c+d x) \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+4 a b c f \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+4 a b d f x \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-4 a b d \sinh (e+f x)+2 b^2 f (c+d x) \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)+2 b^2 c f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+2 b^2 d f x \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-b^2 d \cosh (2 (e+f x))+b^2 d}{2 d^2 (c+d x)}","-\frac{a^2}{d (c+d x)}+\frac{2 a b f \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{2 a b f \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{2 a b \sinh (e+f x)}{d (c+d x)}+\frac{b^2 f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{d^2}+\frac{b^2 f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{d^2}-\frac{b^2 \sinh ^2(e+f x)}{d (c+d x)}",1,"(-2*a^2*d + b^2*d - b^2*d*Cosh[2*(e + f*x)] + 4*a*b*f*(c + d*x)*Cosh[e - (c*f)/d]*CoshIntegral[f*(c/d + x)] + 2*b^2*f*(c + d*x)*CoshIntegral[(2*f*(c + d*x))/d]*Sinh[2*e - (2*c*f)/d] - 4*a*b*d*Sinh[e + f*x] + 4*a*b*c*f*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 4*a*b*d*f*x*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 2*b^2*c*f*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] + 2*b^2*d*f*x*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d])/(2*d^2*(c + d*x))","A",1
168,1,395,242,0.9001399,"\int \frac{(a+b \sinh (e+f x))^2}{(c+d x)^3} \, dx","Integrate[(a + b*Sinh[e + f*x])^2/(c + d*x)^3,x]","\frac{-2 a^2 d^2+4 a b c^2 f^2 \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+4 a b f^2 (c+d x)^2 \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+4 a b d^2 f^2 x^2 \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+8 a b c d f^2 x \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-4 a b c d f \cosh (e+f x)-4 a b d^2 \sinh (e+f x)-4 a b d^2 f x \cosh (e+f x)+4 b^2 c^2 f^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+4 b^2 f^2 (c+d x)^2 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)+4 b^2 d^2 f^2 x^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+8 b^2 c d f^2 x \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-2 b^2 c d f \sinh (2 (e+f x))-2 b^2 d^2 f x \sinh (2 (e+f x))-b^2 d^2 \cosh (2 (e+f x))+b^2 d^2}{4 d^3 (c+d x)^2}","-\frac{a^2}{2 d (c+d x)^2}+\frac{a b f^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{d^3}+\frac{a b f^2 \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^3}-\frac{a b f \cosh (e+f x)}{d^2 (c+d x)}-\frac{a b \sinh (e+f x)}{d (c+d x)^2}+\frac{b^2 f^2 \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)}{d^3}+\frac{b^2 f^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(2 x f+\frac{2 c f}{d}\right)}{d^3}-\frac{b^2 f \sinh (e+f x) \cosh (e+f x)}{d^2 (c+d x)}-\frac{b^2 \sinh ^2(e+f x)}{2 d (c+d x)^2}",1,"(-2*a^2*d^2 + b^2*d^2 - 4*a*b*c*d*f*Cosh[e + f*x] - 4*a*b*d^2*f*x*Cosh[e + f*x] - b^2*d^2*Cosh[2*(e + f*x)] + 4*b^2*f^2*(c + d*x)^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*f*(c + d*x))/d] + 4*a*b*f^2*(c + d*x)^2*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] - 4*a*b*d^2*Sinh[e + f*x] - 2*b^2*c*d*f*Sinh[2*(e + f*x)] - 2*b^2*d^2*f*x*Sinh[2*(e + f*x)] + 4*a*b*c^2*f^2*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 8*a*b*c*d*f^2*x*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 4*a*b*d^2*f^2*x^2*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 4*b^2*c^2*f^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] + 8*b^2*c*d*f^2*x*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] + 4*b^2*d^2*f^2*x^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d])/(4*d^3*(c + d*x)^2)","A",1
169,1,318,404,0.2510936,"\int \frac{(c+d x)^3}{a+b \sinh (e+f x)} \, dx","Integrate[(c + d*x)^3/(a + b*Sinh[e + f*x]),x]","\frac{\frac{3 d \left(f^2 (c+d x)^2 \text{Li}_2\left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}-a}\right)-2 d f (c+d x) \text{Li}_3\left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}-a}\right)+2 d^2 \text{Li}_4\left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}-a}\right)\right)}{f^3}-\frac{3 d \left(f^2 (c+d x)^2 \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)-2 d f (c+d x) \text{Li}_3\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)+2 d^2 \text{Li}_4\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)\right)}{f^3}+(c+d x)^3 \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)-(c+d x)^3 \log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)}{f \sqrt{a^2+b^2}}","-\frac{6 d^2 (c+d x) \text{Li}_3\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^3 \sqrt{a^2+b^2}}+\frac{6 d^2 (c+d x) \text{Li}_3\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^3 \sqrt{a^2+b^2}}+\frac{3 d (c+d x)^2 \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^2 \sqrt{a^2+b^2}}-\frac{3 d (c+d x)^2 \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^2 \sqrt{a^2+b^2}}+\frac{(c+d x)^3 \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)}{f \sqrt{a^2+b^2}}-\frac{(c+d x)^3 \log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)}{f \sqrt{a^2+b^2}}+\frac{6 d^3 \text{Li}_4\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^4 \sqrt{a^2+b^2}}-\frac{6 d^3 \text{Li}_4\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^4 \sqrt{a^2+b^2}}",1,"((c + d*x)^3*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])] - (c + d*x)^3*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])] + (3*d*(f^2*(c + d*x)^2*PolyLog[2, (b*E^(e + f*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*f*(c + d*x)*PolyLog[3, (b*E^(e + f*x))/(-a + Sqrt[a^2 + b^2])] + 2*d^2*PolyLog[4, (b*E^(e + f*x))/(-a + Sqrt[a^2 + b^2])]))/f^3 - (3*d*(f^2*(c + d*x)^2*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))] - 2*d*f*(c + d*x)*PolyLog[3, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))] + 2*d^2*PolyLog[4, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))]))/f^3)/(Sqrt[a^2 + b^2]*f)","A",1
170,1,233,296,0.1298867,"\int \frac{(c+d x)^2}{a+b \sinh (e+f x)} \, dx","Integrate[(c + d*x)^2/(a + b*Sinh[e + f*x]),x]","\frac{\frac{2 d \left(f (c+d x) \text{Li}_2\left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}-a}\right)-d \text{Li}_3\left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}-a}\right)\right)}{f^2}-\frac{2 d \left(f (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)-d \text{Li}_3\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)\right)}{f^2}+(c+d x)^2 \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)-(c+d x)^2 \log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)}{f \sqrt{a^2+b^2}}","\frac{2 d (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^2 \sqrt{a^2+b^2}}-\frac{2 d (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^2 \sqrt{a^2+b^2}}+\frac{(c+d x)^2 \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)}{f \sqrt{a^2+b^2}}-\frac{(c+d x)^2 \log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)}{f \sqrt{a^2+b^2}}-\frac{2 d^2 \text{Li}_3\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^3 \sqrt{a^2+b^2}}+\frac{2 d^2 \text{Li}_3\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^3 \sqrt{a^2+b^2}}",1,"((c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])] - (c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])] + (2*d*(f*(c + d*x)*PolyLog[2, (b*E^(e + f*x))/(-a + Sqrt[a^2 + b^2])] - d*PolyLog[3, (b*E^(e + f*x))/(-a + Sqrt[a^2 + b^2])]))/f^2 - (2*d*(f*(c + d*x)*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))] - d*PolyLog[3, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))]))/f^2)/(Sqrt[a^2 + b^2]*f)","A",1
171,1,142,187,0.0351114,"\int \frac{c+d x}{a+b \sinh (e+f x)} \, dx","Integrate[(c + d*x)/(a + b*Sinh[e + f*x]),x]","\frac{f (c+d x) \left(\log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)-\log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)\right)+d \text{Li}_2\left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}-a}\right)-d \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^2 \sqrt{a^2+b^2}}","\frac{(c+d x) \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)}{f \sqrt{a^2+b^2}}-\frac{(c+d x) \log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)}{f \sqrt{a^2+b^2}}+\frac{d \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^2 \sqrt{a^2+b^2}}-\frac{d \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^2 \sqrt{a^2+b^2}}",1,"(f*(c + d*x)*(Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])] - Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])]) + d*PolyLog[2, (b*E^(e + f*x))/(-a + Sqrt[a^2 + b^2])] - d*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^2)","A",1
172,0,0,23,0.9896293,"\int \frac{1}{(c+d x) (a+b \sinh (e+f x))} \, dx","Integrate[1/((c + d*x)*(a + b*Sinh[e + f*x])),x]","\int \frac{1}{(c+d x) (a+b \sinh (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \sinh (e+f x))},x\right)",0,"Integrate[1/((c + d*x)*(a + b*Sinh[e + f*x])), x]","A",-1
173,0,0,23,0.921907,"\int \frac{1}{(c+d x)^2 (a+b \sinh (e+f x))} \, dx","Integrate[1/((c + d*x)^2*(a + b*Sinh[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+b \sinh (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \sinh (e+f x))},x\right)",0,"Integrate[1/((c + d*x)^2*(a + b*Sinh[e + f*x])), x]","A",-1
174,1,428,549,1.7362973,"\int \frac{(c+d x)^2}{(a+b \sinh (e+f x))^2} \, dx","Integrate[(c + d*x)^2/(a + b*Sinh[e + f*x])^2,x]","\frac{-\frac{a \left(-f^2 (c+d x)^2 \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)+f^2 (c+d x)^2 \log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)-2 d f (c+d x) \text{Li}_2\left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}-a}\right)+2 d f (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)+2 d^2 \text{Li}_3\left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}-a}\right)-2 d^2 \text{Li}_3\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2}}+2 d f (c+d x) \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)+2 d f (c+d x) \log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)+2 d^2 \text{Li}_2\left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}-a}\right)+2 d^2 \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)-\frac{b f^2 (c+d x)^2 \cosh (e+f x)}{a+b \sinh (e+f x)}-f^2 (c+d x)^2}{f^3 \left(a^2+b^2\right)}","\frac{2 a d (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^2 \left(a^2+b^2\right)^{3/2}}-\frac{2 a d (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^2 \left(a^2+b^2\right)^{3/2}}+\frac{2 d (c+d x) \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)}{f^2 \left(a^2+b^2\right)}+\frac{2 d (c+d x) \log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)}{f^2 \left(a^2+b^2\right)}+\frac{a (c+d x)^2 \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)}{f \left(a^2+b^2\right)^{3/2}}-\frac{a (c+d x)^2 \log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)}{f \left(a^2+b^2\right)^{3/2}}-\frac{b (c+d x)^2 \cosh (e+f x)}{f \left(a^2+b^2\right) (a+b \sinh (e+f x))}-\frac{(c+d x)^2}{f \left(a^2+b^2\right)}+\frac{2 d^2 \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^3 \left(a^2+b^2\right)}+\frac{2 d^2 \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^3 \left(a^2+b^2\right)}-\frac{2 a d^2 \text{Li}_3\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^3 \left(a^2+b^2\right)^{3/2}}+\frac{2 a d^2 \text{Li}_3\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^3 \left(a^2+b^2\right)^{3/2}}",1,"(-(f^2*(c + d*x)^2) + 2*d*f*(c + d*x)*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])] + 2*d*f*(c + d*x)*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])] + 2*d^2*PolyLog[2, (b*E^(e + f*x))/(-a + Sqrt[a^2 + b^2])] + 2*d^2*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))] - (a*(-(f^2*(c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])]) + f^2*(c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(c + d*x)*PolyLog[2, (b*E^(e + f*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(c + d*x)*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))] + 2*d^2*PolyLog[3, (b*E^(e + f*x))/(-a + Sqrt[a^2 + b^2])] - 2*d^2*PolyLog[3, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] - (b*f^2*(c + d*x)^2*Cosh[e + f*x])/(a + b*Sinh[e + f*x]))/((a^2 + b^2)*f^3)","A",1
175,1,194,254,1.0267675,"\int \frac{c+d x}{(a+b \sinh (e+f x))^2} \, dx","Integrate[(c + d*x)/(a + b*Sinh[e + f*x])^2,x]","\frac{\frac{a \left(f (c+d x) \left(\log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)-\log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)\right)+d \text{Li}_2\left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}-a}\right)-d \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2}}-\frac{b f (c+d x) \cosh (e+f x)}{a+b \sinh (e+f x)}+d \log (a+b \sinh (e+f x))}{f^2 \left(a^2+b^2\right)}","\frac{a (c+d x) \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}+1\right)}{f \left(a^2+b^2\right)^{3/2}}-\frac{a (c+d x) \log \left(\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}+1\right)}{f \left(a^2+b^2\right)^{3/2}}-\frac{b (c+d x) \cosh (e+f x)}{f \left(a^2+b^2\right) (a+b \sinh (e+f x))}+\frac{a d \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^2 \left(a^2+b^2\right)^{3/2}}-\frac{a d \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2+b^2}}\right)}{f^2 \left(a^2+b^2\right)^{3/2}}+\frac{d \log (a+b \sinh (e+f x))}{f^2 \left(a^2+b^2\right)}",1,"(d*Log[a + b*Sinh[e + f*x]] + (a*(f*(c + d*x)*(Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])] - Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])]) + d*PolyLog[2, (b*E^(e + f*x))/(-a + Sqrt[a^2 + b^2])] - d*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] - (b*f*(c + d*x)*Cosh[e + f*x])/(a + b*Sinh[e + f*x]))/((a^2 + b^2)*f^2)","A",1
176,0,0,23,50.2326831,"\int \frac{1}{(c+d x) (a+b \sinh (e+f x))^2} \, dx","Integrate[1/((c + d*x)*(a + b*Sinh[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+b \sinh (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \sinh (e+f x))^2},x\right)",0,"Integrate[1/((c + d*x)*(a + b*Sinh[e + f*x])^2), x]","A",-1
177,0,0,23,52.7399442,"\int \frac{1}{(c+d x)^2 (a+b \sinh (e+f x))^2} \, dx","Integrate[1/((c + d*x)^2*(a + b*Sinh[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+b \sinh (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \sinh (e+f x))^2},x\right)",0,"Integrate[1/((c + d*x)^2*(a + b*Sinh[e + f*x])^2), x]","A",-1
178,1,836,544,9.7592091,"\int \frac{e+f x}{(a+b \sinh (c+d x))^3} \, dx","Integrate[(e + f*x)/(a + b*Sinh[c + d*x])^3,x]","\frac{-b d e \cosh (c+d x)+b c f \cosh (c+d x)-b f (c+d x) \cosh (c+d x)}{2 \left(a^2+b^2\right) d^2 (a+b \sinh (c+d x))^2}-\frac{6 \sqrt{a^2+b^2} f \tan ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{-a^2-b^2}}\right) a^2-4 \sqrt{-a^2-b^2} d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) a^2+4 \sqrt{-a^2-b^2} c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) a^2+6 \sqrt{-a^2-b^2} f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) a^2+2 \sqrt{-a^2-b^2} f (c+d x) \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^2-2 \sqrt{-a^2-b^2} f (c+d x) \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^2-3 \sqrt{-\left(a^2+b^2\right)^2} f (c+d x) a+3 \sqrt{-\left(a^2+b^2\right)^2} f \log \left(2 e^{c+d x} a+b \left(-1+e^{2 (c+d x)}\right)\right) a+2 b^2 \sqrt{-a^2-b^2} d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-2 b^2 \sqrt{-a^2-b^2} c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-b^2 \sqrt{-a^2-b^2} f (c+d x) \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right)+b^2 \sqrt{-a^2-b^2} f (c+d x) \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right)+\sqrt{-a^2-b^2} \left(2 a^2-b^2\right) f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+\sqrt{-a^2-b^2} \left(b^2-2 a^2\right) f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{2 \left(-\left(a^2+b^2\right)^2\right)^{3/2} d^2}+\frac{-f a^2-3 b d e \cosh (c+d x) a+3 b c f \cosh (c+d x) a-3 b f (c+d x) \cosh (c+d x) a-b^2 f}{2 \left(a^2+b^2\right)^2 d^2 (a+b \sinh (c+d x))}","\frac{3 a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{2 d^2 \left(a^2+b^2\right)^{5/2}}-\frac{3 a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{2 d^2 \left(a^2+b^2\right)^{5/2}}-\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{2 d^2 \left(a^2+b^2\right)^{3/2}}+\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{2 d^2 \left(a^2+b^2\right)^{3/2}}-\frac{f}{2 d^2 \left(a^2+b^2\right) (a+b \sinh (c+d x))}+\frac{3 a f \log (a+b \sinh (c+d x))}{2 d^2 \left(a^2+b^2\right)^2}+\frac{3 a^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{2 d \left(a^2+b^2\right)^{5/2}}-\frac{3 a^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{2 d \left(a^2+b^2\right)^{5/2}}-\frac{(e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{2 d \left(a^2+b^2\right)^{3/2}}+\frac{(e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{2 d \left(a^2+b^2\right)^{3/2}}-\frac{3 a b (e+f x) \cosh (c+d x)}{2 d \left(a^2+b^2\right)^2 (a+b \sinh (c+d x))}-\frac{b (e+f x) \cosh (c+d x)}{2 d \left(a^2+b^2\right) (a+b \sinh (c+d x))^2}",1,"-1/2*(-3*a*Sqrt[-(a^2 + b^2)^2]*f*(c + d*x) + 6*a^2*Sqrt[a^2 + b^2]*f*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]] - 4*a^2*Sqrt[-a^2 - b^2]*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*b^2*Sqrt[-a^2 - b^2]*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 6*a^2*Sqrt[-a^2 - b^2]*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 4*a^2*Sqrt[-a^2 - b^2]*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*b^2*Sqrt[-a^2 - b^2]*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*a^2*Sqrt[-a^2 - b^2]*f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - b^2*Sqrt[-a^2 - b^2]*f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*a^2*Sqrt[-a^2 - b^2]*f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + b^2*Sqrt[-a^2 - b^2]*f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*a*Sqrt[-(a^2 + b^2)^2]*f*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))] + Sqrt[-a^2 - b^2]*(2*a^2 - b^2)*f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + Sqrt[-a^2 - b^2]*(-2*a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((-(a^2 + b^2)^2)^(3/2)*d^2) + (-(b*d*e*Cosh[c + d*x]) + b*c*f*Cosh[c + d*x] - b*f*(c + d*x)*Cosh[c + d*x])/(2*(a^2 + b^2)*d^2*(a + b*Sinh[c + d*x])^2) + (-(a^2*f) - b^2*f - 3*a*b*d*e*Cosh[c + d*x] + 3*a*b*c*f*Cosh[c + d*x] - 3*a*b*f*(c + d*x)*Cosh[c + d*x])/(2*(a^2 + b^2)^2*d^2*(a + b*Sinh[c + d*x]))","A",1
179,0,0,23,100.7622383,"\int \frac{1}{(e+f x) (a+b \sinh (c+d x))^3} \, dx","Integrate[1/((e + f*x)*(a + b*Sinh[c + d*x])^3),x]","\int \frac{1}{(e+f x) (a+b \sinh (c+d x))^3} \, dx","\text{Int}\left(\frac{1}{(e+f x) (a+b \sinh (c+d x))^3},x\right)",0,"Integrate[1/((e + f*x)*(a + b*Sinh[c + d*x])^3), x]","A",-1
180,0,0,23,93.7685261,"\int \frac{1}{(e+f x)^2 (a+b \sinh (c+d x))^3} \, dx","Integrate[1/((e + f*x)^2*(a + b*Sinh[c + d*x])^3),x]","\int \frac{1}{(e+f x)^2 (a+b \sinh (c+d x))^3} \, dx","\text{Int}\left(\frac{1}{(e+f x)^2 (a+b \sinh (c+d x))^3},x\right)",0,"Integrate[1/((e + f*x)^2*(a + b*Sinh[c + d*x])^3), x]","A",-1
181,0,0,23,4.3744519,"\int (c+d x)^m (a+b \sinh (e+f x))^n \, dx","Integrate[(c + d*x)^m*(a + b*Sinh[e + f*x])^n,x]","\int (c+d x)^m (a+b \sinh (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (a+b \sinh (e+f x))^n,x\right)",0,"Integrate[(c + d*x)^m*(a + b*Sinh[e + f*x])^n, x]","A",-1
182,1,448,543,1.6400926,"\int (c+d x)^m (a+b \sinh (e+f x))^3 \, dx","Integrate[(c + d*x)^m*(a + b*Sinh[e + f*x])^3,x]","\frac{2^{-m-3} 3^{-m-1} e^{-3 \left(\frac{c f}{d}+e\right)} (c+d x)^m \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(-b d 2^m 3^{m+2} (m+1) \left(b^2-4 a^2\right) e^{\frac{2 c f}{d}+4 e} \left(\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)-b d 2^m 3^{m+2} (m+1) \left(b^2-4 a^2\right) e^{\frac{4 c f}{d}+2 e} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)+2^m e^{\frac{3 c f}{d}} \left(4 a e^{3 e} f 3^{m+1} \left(2 a^2-3 b^2\right) (c+d x) \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^m+b^3 d (m+1) e^{\frac{3 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{3 f (c+d x)}{d}\right)\right)+a b^2 d 3^{m+2} (m+1) e^{\frac{c f}{d}+5 e} \left(f \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)-a b^2 d 3^{m+2} (m+1) e^{\frac{5 c f}{d}+e} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)+b^3 d e^{6 e} 2^m (m+1) \left(\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,-\frac{3 f (c+d x)}{d}\right)\right)}{d f (m+1)}","\frac{a^3 (c+d x)^{m+1}}{d (m+1)}+\frac{3 a^2 b e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{2 f}+\frac{3 a^2 b e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{2 f}+\frac{3 a b^2 2^{-m-3} e^{2 e-\frac{2 c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)}{f}-\frac{3 a b^2 2^{-m-3} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}-\frac{3 a b^2 (c+d x)^{m+1}}{2 d (m+1)}+\frac{b^3 3^{-m-1} e^{3 e-\frac{3 c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{3 f (c+d x)}{d}\right)}{8 f}-\frac{3 b^3 e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{8 f}-\frac{3 b^3 e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{8 f}+\frac{b^3 3^{-m-1} e^{\frac{3 c f}{d}-3 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{3 f (c+d x)}{d}\right)}{8 f}",1,"(2^(-3 - m)*3^(-1 - m)*(c + d*x)^m*(2^m*b^3*d*E^(6*e)*(1 + m)*((f*(c + d*x))/d)^m*Gamma[1 + m, (-3*f*(c + d*x))/d] + 3^(2 + m)*a*b^2*d*E^(5*e + (c*f)/d)*(1 + m)*(f*(c/d + x))^m*Gamma[1 + m, (-2*f*(c + d*x))/d] - 2^m*3^(2 + m)*b*(-4*a^2 + b^2)*d*E^(4*e + (2*c*f)/d)*(1 + m)*((f*(c + d*x))/d)^m*Gamma[1 + m, -((f*(c + d*x))/d)] - 2^m*3^(2 + m)*b*(-4*a^2 + b^2)*d*E^(2*e + (4*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (f*(c + d*x))/d] - 3^(2 + m)*a*b^2*d*E^(e + (5*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (2*f*(c + d*x))/d] + 2^m*E^((3*c*f)/d)*(4*3^(1 + m)*a*(2*a^2 - 3*b^2)*E^(3*e)*f*(c + d*x)*(-((f^2*(c + d*x)^2)/d^2))^m + b^3*d*E^((3*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (3*f*(c + d*x))/d])))/(d*E^(3*(e + (c*f)/d))*f*(1 + m)*(-((f^2*(c + d*x)^2)/d^2))^m)","A",1
183,1,254,281,0.7232019,"\int (c+d x)^m (a+b \sinh (e+f x))^2 \, dx","Integrate[(c + d*x)^m*(a + b*Sinh[e + f*x])^2,x]","\frac{(c+d x)^m \left(8 a^2 f (c+d x)+8 a b d (m+1) e^{e-\frac{c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)+8 a b d (m+1) e^{\frac{c f}{d}-e} \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)+b^2 d 2^{-m} (m+1) e^{2 e-\frac{2 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)-b^2 d 2^{-m} (m+1) e^{\frac{2 c f}{d}-2 e} \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)-4 b^2 f (c+d x)\right)}{8 d f (m+1)}","\frac{a^2 (c+d x)^{m+1}}{d (m+1)}+\frac{a b e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{f}+\frac{a b e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{f}+\frac{b^2 2^{-m-3} e^{2 e-\frac{2 c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)}{f}-\frac{b^2 2^{-m-3} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}-\frac{b^2 (c+d x)^{m+1}}{2 d (m+1)}",1,"((c + d*x)^m*(8*a^2*f*(c + d*x) - 4*b^2*f*(c + d*x) + (b^2*d*E^(2*e - (2*c*f)/d)*(1 + m)*Gamma[1 + m, (-2*f*(c + d*x))/d])/(2^m*(-((f*(c + d*x))/d))^m) + (8*a*b*d*E^(e - (c*f)/d)*(1 + m)*Gamma[1 + m, -((f*(c + d*x))/d)])/(-((f*(c + d*x))/d))^m + (8*a*b*d*E^(-e + (c*f)/d)*(1 + m)*Gamma[1 + m, (f*(c + d*x))/d])/((f*(c + d*x))/d)^m - (b^2*d*E^(-2*e + (2*c*f)/d)*(1 + m)*Gamma[1 + m, (2*f*(c + d*x))/d])/(2^m*((f*(c + d*x))/d)^m)))/(8*d*f*(1 + m))","A",1
184,1,118,131,0.1729544,"\int (c+d x)^m (a+b \sinh (e+f x)) \, dx","Integrate[(c + d*x)^m*(a + b*Sinh[e + f*x]),x]","\frac{1}{2} (c+d x)^m \left(\frac{2 a (c+d x)}{d (m+1)}+\frac{b e^{\frac{c f}{d}-e} \left(f \left(\frac{c}{d}+x\right)\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{f}+\frac{b e^{e-\frac{c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{f}\right)","\frac{a (c+d x)^{m+1}}{d (m+1)}+\frac{b e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{2 f}+\frac{b e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{2 f}",1,"((c + d*x)^m*((2*a*(c + d*x))/(d*(1 + m)) + (b*E^(e - (c*f)/d)*Gamma[1 + m, -((f*(c + d*x))/d)])/(f*(-((f*(c + d*x))/d))^m) + (b*E^(-e + (c*f)/d)*Gamma[1 + m, (f*(c + d*x))/d])/(f*(f*(c/d + x))^m)))/2","A",1
185,0,0,23,1.1163716,"\int \frac{(c+d x)^m}{a+b \sinh (e+f x)} \, dx","Integrate[(c + d*x)^m/(a + b*Sinh[e + f*x]),x]","\int \frac{(c+d x)^m}{a+b \sinh (e+f x)} \, dx","\text{Int}\left(\frac{(c+d x)^m}{a+b \sinh (e+f x)},x\right)",0,"Integrate[(c + d*x)^m/(a + b*Sinh[e + f*x]), x]","A",-1
186,0,0,23,5.3833456,"\int \frac{(c+d x)^m}{(a+b \sinh (e+f x))^2} \, dx","Integrate[(c + d*x)^m/(a + b*Sinh[e + f*x])^2,x]","\int \frac{(c+d x)^m}{(a+b \sinh (e+f x))^2} \, dx","\text{Int}\left(\frac{(c+d x)^m}{(a+b \sinh (e+f x))^2},x\right)",0,"Integrate[(c + d*x)^m/(a + b*Sinh[e + f*x])^2, x]","A",-1
187,1,232,163,3.2107585,"\int \frac{(e+f x)^3 \sinh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sinh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{-\frac{8 \left(3 \left(1+i e^c\right) d^2 f (e+f x)^2 \log \left(1-i e^{-c-d x}\right)+6 i \left(-e^c+i\right) f^2 \left(d (e+f x) \text{Li}_2\left(i e^{-c-d x}\right)+f \text{Li}_3\left(i e^{-c-d x}\right)\right)+d^3 (e+f x)^3\right)}{\left(e^c-i\right) d^4}+\frac{8 i \sinh \left(\frac{d x}{2}\right) (e+f x)^3}{d \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}-i x \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right)}{4 a}","\frac{12 i f^3 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^4}-\frac{12 i f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}-\frac{6 i f (e+f x)^2 \log \left(1+i e^{c+d x}\right)}{a d^2}+\frac{i (e+f x)^3 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}+\frac{i (e+f x)^3}{a d}-\frac{i (e+f x)^4}{4 a f}",1,"((-I)*x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3) - (8*(d^3*(e + f*x)^3 + 3*d^2*(1 + I*E^c)*f*(e + f*x)^2*Log[1 - I*E^(-c - d*x)] + (6*I)*(I - E^c)*f^2*(d*(e + f*x)*PolyLog[2, I*E^(-c - d*x)] + f*PolyLog[3, I*E^(-c - d*x)])))/(d^4*(-I + E^c)) + ((8*I)*(e + f*x)^3*Sinh[(d*x)/2])/(d*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])))/(4*a)","A",1
188,1,188,130,2.4013557,"\int \frac{(e+f x)^2 \sinh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sinh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{\frac{3 \left(4 \left(1+i e^c\right) f^2 \text{Li}_2\left(i e^{-c-d x}\right)-2 d (e+f x) \left(d (e+f x)+2 \left(1+i e^c\right) f \log \left(1-i e^{-c-d x}\right)\right)\right)}{\left(e^c-i\right) d^3}+\frac{6 i \sinh \left(\frac{d x}{2}\right) (e+f x)^2}{d \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}-i x \left(3 e^2+3 e f x+f^2 x^2\right)}{3 a}","-\frac{4 i f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}-\frac{4 i f (e+f x) \log \left(1+i e^{c+d x}\right)}{a d^2}+\frac{i (e+f x)^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}+\frac{i (e+f x)^2}{a d}-\frac{i (e+f x)^3}{3 a f}",1,"((-I)*x*(3*e^2 + 3*e*f*x + f^2*x^2) + (3*(-2*d*(e + f*x)*(d*(e + f*x) + 2*(1 + I*E^c)*f*Log[1 - I*E^(-c - d*x)]) + 4*(1 + I*E^c)*f^2*PolyLog[2, I*E^(-c - d*x)]))/(d^3*(-I + E^c)) + ((6*I)*(e + f*x)^2*Sinh[(d*x)/2])/(d*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])))/(3*a)","A",1
189,1,239,90,0.6258783,"\int \frac{(e+f x) \sinh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sinh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{-i \cosh \left(\frac{d x}{2}\right) \left(2 f \log (\cosh (c+d x))+4 i f \tan ^{-1}\left(\sinh \left(\frac{d x}{2}\right) \text{sech}\left(c+\frac{d x}{2}\right)\right)+d^2 x (2 e+f x)\right)+2 d^2 e x \sinh \left(c+\frac{d x}{2}\right)+d^2 f x^2 \sinh \left(c+\frac{d x}{2}\right)-2 d f x \cosh \left(c+\frac{d x}{2}\right)+2 f \sinh \left(c+\frac{d x}{2}\right) \log (\cosh (c+d x))+4 i f \sinh \left(c+\frac{d x}{2}\right) \tan ^{-1}\left(\sinh \left(\frac{d x}{2}\right) \text{sech}\left(c+\frac{d x}{2}\right)\right)+4 i d e \sinh \left(\frac{d x}{2}\right)+2 i d f x \sinh \left(\frac{d x}{2}\right)}{2 a d^2 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}","-\frac{2 i f \log \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)\right)}{a d^2}+\frac{i (e+f x) \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{i e x}{a}-\frac{i f x^2}{2 a}",1,"(-2*d*f*x*Cosh[c + (d*x)/2] - I*Cosh[(d*x)/2]*(d^2*x*(2*e + f*x) + (4*I)*f*ArcTan[Sech[c + (d*x)/2]*Sinh[(d*x)/2]] + 2*f*Log[Cosh[c + d*x]]) + (4*I)*d*e*Sinh[(d*x)/2] + (2*I)*d*f*x*Sinh[(d*x)/2] + 2*d^2*e*x*Sinh[c + (d*x)/2] + d^2*f*x^2*Sinh[c + (d*x)/2] + (4*I)*f*ArcTan[Sech[c + (d*x)/2]*Sinh[(d*x)/2]]*Sinh[c + (d*x)/2] + 2*f*Log[Cosh[c + d*x]]*Sinh[c + (d*x)/2])/(2*a*d^2*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]))","B",1
190,1,61,35,0.2054957,"\int \frac{\sinh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Sinh[c + d*x]/(a + I*a*Sinh[c + d*x]),x]","\frac{i \cosh (c+d x) \left(1-\frac{\sinh ^{-1}(\sinh (c+d x)) (\sinh (c+d x)-i)}{\sqrt{\cosh ^2(c+d x)}}\right)}{a d (\sinh (c+d x)-i)}","-\frac{\cosh (c+d x)}{d (a+i a \sinh (c+d x))}-\frac{i x}{a}",1,"(I*Cosh[c + d*x]*(1 - (ArcSinh[Sinh[c + d*x]]*(-I + Sinh[c + d*x]))/Sqrt[Cosh[c + d*x]^2]))/(a*d*(-I + Sinh[c + d*x]))","A",1
191,0,0,32,48.5737442,"\int \frac{\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Sinh[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"Integrate[Sinh[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",-1
192,0,0,32,41.7513932,"\int \frac{\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Sinh[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"Integrate[Sinh[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",-1
193,1,857,241,6.5338984,"\int \frac{(e+f x)^3 \sinh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sinh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{\frac{i f^3 x^4 \sinh \left(c+\frac{d x}{2}\right) d^4+4 i e f^2 x^3 \sinh \left(c+\frac{d x}{2}\right) d^4+6 i e^2 f x^2 \sinh \left(c+\frac{d x}{2}\right) d^4+4 i e^3 x \sinh \left(c+\frac{d x}{2}\right) d^4-10 e^3 \sinh \left(\frac{d x}{2}\right) d^3-10 f^3 x^3 \sinh \left(\frac{d x}{2}\right) d^3-30 e f^2 x^2 \sinh \left(\frac{d x}{2}\right) d^3-30 e^2 f x \sinh \left(\frac{d x}{2}\right) d^3+2 e^3 \sinh \left(2 c+\frac{3 d x}{2}\right) d^3+2 f^3 x^3 \sinh \left(2 c+\frac{3 d x}{2}\right) d^3+6 e f^2 x^2 \sinh \left(2 c+\frac{3 d x}{2}\right) d^3+6 e^2 f x \sinh \left(2 c+\frac{3 d x}{2}\right) d^3-6 f^3 x^2 \cosh \left(2 c+\frac{3 d x}{2}\right) d^2-6 e^2 f \cosh \left(2 c+\frac{3 d x}{2}\right) d^2-12 e f^2 x \cosh \left(2 c+\frac{3 d x}{2}\right) d^2+6 i f^3 x^2 \sinh \left(c+\frac{d x}{2}\right) d^2+6 i e^2 f \sinh \left(c+\frac{d x}{2}\right) d^2+12 i e f^2 x \sinh \left(c+\frac{d x}{2}\right) d^2+6 i f^3 x^2 \sinh \left(c+\frac{3 d x}{2}\right) d^2+6 i e^2 f \sinh \left(c+\frac{3 d x}{2}\right) d^2+12 i e f^2 x \sinh \left(c+\frac{3 d x}{2}\right) d^2-2 i (e+f x) \left(6 f^2+d^2 (e+f x)^2\right) \cosh \left(c+\frac{d x}{2}\right) d-2 i (e+f x) \left(6 f^2+d^2 (e+f x)^2\right) \cosh \left(c+\frac{3 d x}{2}\right) d-12 e f^2 \sinh \left(\frac{d x}{2}\right) d-12 f^3 x \sinh \left(\frac{d x}{2}\right) d+12 e f^2 \sinh \left(2 c+\frac{3 d x}{2}\right) d+12 f^3 x \sinh \left(2 c+\frac{3 d x}{2}\right) d+\left(x \left(4 e^3+6 f x e^2+4 f^2 x^2 e+f^3 x^3\right) d^4+6 f (e+f x)^2 d^2+12 f^3\right) \cosh \left(\frac{d x}{2}\right)-12 f^3 \cosh \left(2 c+\frac{3 d x}{2}\right)+12 i f^3 \sinh \left(c+\frac{d x}{2}\right)+12 i f^3 \sinh \left(c+\frac{3 d x}{2}\right)}{\left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}-\frac{8 i \left(d^3 (e+f x)^3+3 d^2 \left(1+i e^c\right) f \log \left(1-i e^{-c-d x}\right) (e+f x)^2+6 i \left(i-e^c\right) f^2 \left(d (e+f x) \text{Li}_2\left(i e^{-c-d x}\right)+f \text{Li}_3\left(i e^{-c-d x}\right)\right)\right)}{-i+e^c}}{4 a d^4}","-\frac{12 f^3 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^4}+\frac{6 i f^3 \sinh (c+d x)}{a d^4}+\frac{12 f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}-\frac{6 i f^2 (e+f x) \cosh (c+d x)}{a d^3}+\frac{6 f (e+f x)^2 \log \left(1+i e^{c+d x}\right)}{a d^2}+\frac{3 i f (e+f x)^2 \sinh (c+d x)}{a d^2}-\frac{i (e+f x)^3 \cosh (c+d x)}{a d}-\frac{(e+f x)^3 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{(e+f x)^3}{a d}+\frac{(e+f x)^4}{4 a f}",1,"(((-8*I)*(d^3*(e + f*x)^3 + 3*d^2*(1 + I*E^c)*f*(e + f*x)^2*Log[1 - I*E^(-c - d*x)] + (6*I)*(I - E^c)*f^2*(d*(e + f*x)*PolyLog[2, I*E^(-c - d*x)] + f*PolyLog[3, I*E^(-c - d*x)])))/(-I + E^c) + ((12*f^3 + 6*d^2*f*(e + f*x)^2 + d^4*x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3))*Cosh[(d*x)/2] - (2*I)*d*(e + f*x)*(6*f^2 + d^2*(e + f*x)^2)*Cosh[c + (d*x)/2] - (2*I)*d*(e + f*x)*(6*f^2 + d^2*(e + f*x)^2)*Cosh[c + (3*d*x)/2] - 6*d^2*e^2*f*Cosh[2*c + (3*d*x)/2] - 12*f^3*Cosh[2*c + (3*d*x)/2] - 12*d^2*e*f^2*x*Cosh[2*c + (3*d*x)/2] - 6*d^2*f^3*x^2*Cosh[2*c + (3*d*x)/2] - 10*d^3*e^3*Sinh[(d*x)/2] - 12*d*e*f^2*Sinh[(d*x)/2] - 30*d^3*e^2*f*x*Sinh[(d*x)/2] - 12*d*f^3*x*Sinh[(d*x)/2] - 30*d^3*e*f^2*x^2*Sinh[(d*x)/2] - 10*d^3*f^3*x^3*Sinh[(d*x)/2] + (6*I)*d^2*e^2*f*Sinh[c + (d*x)/2] + (12*I)*f^3*Sinh[c + (d*x)/2] + (4*I)*d^4*e^3*x*Sinh[c + (d*x)/2] + (12*I)*d^2*e*f^2*x*Sinh[c + (d*x)/2] + (6*I)*d^4*e^2*f*x^2*Sinh[c + (d*x)/2] + (6*I)*d^2*f^3*x^2*Sinh[c + (d*x)/2] + (4*I)*d^4*e*f^2*x^3*Sinh[c + (d*x)/2] + I*d^4*f^3*x^4*Sinh[c + (d*x)/2] + (6*I)*d^2*e^2*f*Sinh[c + (3*d*x)/2] + (12*I)*f^3*Sinh[c + (3*d*x)/2] + (12*I)*d^2*e*f^2*x*Sinh[c + (3*d*x)/2] + (6*I)*d^2*f^3*x^2*Sinh[c + (3*d*x)/2] + 2*d^3*e^3*Sinh[2*c + (3*d*x)/2] + 12*d*e*f^2*Sinh[2*c + (3*d*x)/2] + 6*d^3*e^2*f*x*Sinh[2*c + (3*d*x)/2] + 12*d*f^3*x*Sinh[2*c + (3*d*x)/2] + 6*d^3*e*f^2*x^2*Sinh[2*c + (3*d*x)/2] + 2*d^3*f^3*x^3*Sinh[2*c + (3*d*x)/2])/((Cosh[c/2] + I*Sinh[c/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])))/(4*a*d^4)","B",1
194,1,260,184,3.4634792,"\int \frac{(e+f x)^2 \sinh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sinh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{\frac{6 \left(\frac{d (e+f x) \left(2 \left(e^c-i\right) f \log \left(1-i e^{-c-d x}\right)-i d (e+f x)\right)}{e^c-i}-2 f^2 \text{Li}_2\left(i e^{-c-d x}\right)\right)}{d^3}-\frac{3 i \cosh (d x) \left(\cosh (c) \left(d^2 (e+f x)^2+2 f^2\right)-2 d f \sinh (c) (e+f x)\right)}{d^3}-\frac{3 i \sinh (d x) \left(\sinh (c) \left(d^2 (e+f x)^2+2 f^2\right)-2 d f \cosh (c) (e+f x)\right)}{d^3}-\frac{6 \sinh \left(\frac{d x}{2}\right) (e+f x)^2}{d \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}+x \left(3 e^2+3 e f x+f^2 x^2\right)}{3 a}","\frac{4 f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}-\frac{2 i f^2 \cosh (c+d x)}{a d^3}+\frac{4 f (e+f x) \log \left(1+i e^{c+d x}\right)}{a d^2}+\frac{2 i f (e+f x) \sinh (c+d x)}{a d^2}-\frac{i (e+f x)^2 \cosh (c+d x)}{a d}-\frac{(e+f x)^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{(e+f x)^2}{a d}+\frac{(e+f x)^3}{3 a f}",1,"(x*(3*e^2 + 3*e*f*x + f^2*x^2) + (6*((d*(e + f*x)*((-I)*d*(e + f*x) + 2*(-I + E^c)*f*Log[1 - I*E^(-c - d*x)]))/(-I + E^c) - 2*f^2*PolyLog[2, I*E^(-c - d*x)]))/d^3 - ((3*I)*Cosh[d*x]*((2*f^2 + d^2*(e + f*x)^2)*Cosh[c] - 2*d*f*(e + f*x)*Sinh[c]))/d^3 - ((3*I)*(-2*d*f*(e + f*x)*Cosh[c] + (2*f^2 + d^2*(e + f*x)^2)*Sinh[c])*Sinh[d*x])/d^3 - (6*(e + f*x)^2*Sinh[(d*x)/2])/(d*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])))/(3*a)","A",1
195,1,238,119,1.0214801,"\int \frac{(e+f x) \sinh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sinh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{\left(\sinh \left(\frac{1}{2} (c+d x)\right)-i \cosh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right) \left(c^2 (-f)-2 i d (e+f x) \cosh (c+d x)+2 c d e+2 i f \sinh (c+d x)+4 i f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+2 f \log (\cosh (c+d x))-2 i c f+2 d^2 e x+d^2 f x^2-2 i d f x\right)+\sinh \left(\frac{1}{2} (c+d x)\right) \left(i (c+d x+2 i) (-c f+2 d e+d f x)+2 d (e+f x) \cosh (c+d x)-2 f \sinh (c+d x)-4 f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+2 i f \log (\cosh (c+d x))\right)\right)}{2 a d^2 (\sinh (c+d x)-i)}","\frac{i f \sinh (c+d x)}{a d^2}+\frac{2 f \log \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)\right)}{a d^2}-\frac{i (e+f x) \cosh (c+d x)}{a d}-\frac{(e+f x) \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}+\frac{e x}{a}+\frac{f x^2}{2 a}",1,"(((-I)*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2])*(Sinh[(c + d*x)/2]*(I*(2*I + c + d*x)*(2*d*e - c*f + d*f*x) - 4*f*ArcTan[Tanh[(c + d*x)/2]] + 2*d*(e + f*x)*Cosh[c + d*x] + (2*I)*f*Log[Cosh[c + d*x]] - 2*f*Sinh[c + d*x]) + Cosh[(c + d*x)/2]*(2*c*d*e - (2*I)*c*f - c^2*f + 2*d^2*e*x - (2*I)*d*f*x + d^2*f*x^2 + (4*I)*f*ArcTan[Tanh[(c + d*x)/2]] - (2*I)*d*(e + f*x)*Cosh[c + d*x] + 2*f*Log[Cosh[c + d*x]] + (2*I)*f*Sinh[c + d*x])))/(2*a*d^2*(-I + Sinh[c + d*x]))","A",1
196,1,59,52,0.2238548,"\int \frac{\sinh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Sinh[c + d*x]^2/(a + I*a*Sinh[c + d*x]),x]","\frac{\cosh (c+d x) \left(\frac{\sinh ^{-1}(\sinh (c+d x))}{\sqrt{\cosh ^2(c+d x)}}+\frac{-2-i \sinh (c+d x)}{\sinh (c+d x)-i}\right)}{a d}","-\frac{i \cosh (c+d x)}{a d}-\frac{i \cosh (c+d x)}{a d (1+i \sinh (c+d x))}+\frac{x}{a}",1,"(Cosh[c + d*x]*(ArcSinh[Sinh[c + d*x]]/Sqrt[Cosh[c + d*x]^2] + (-2 - I*Sinh[c + d*x])/(-I + Sinh[c + d*x])))/(a*d)","A",1
197,-1,0,34,180.0023657,"\int \frac{\sinh ^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Sinh[c + d*x]^2/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
198,-1,0,34,180.0005232,"\int \frac{\sinh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Sinh[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
199,1,376,393,7.3190829,"\int \frac{(e+f x)^3 \sinh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sinh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{-\frac{192 i f^2 \left(d (e+f x) \text{Li}_2\left(i e^{-c-d x}\right)+f \text{Li}_3\left(i e^{-c-d x}\right)\right)}{d^4}-\frac{96 f^3 \sinh (c+d x)}{d^4}+\frac{3 i f^3 \cosh (2 (c+d x))}{d^4}-\frac{6 i f^2 (e+f x) \sinh (2 (c+d x))}{d^3}+\frac{96 f^2 (e+f x) \cosh (c+d x)}{d^3}+\frac{96 i f (e+f x)^2 \log \left(1-i e^{-c-d x}\right)}{d^2}-\frac{48 f (e+f x)^2 \sinh (c+d x)}{d^2}+\frac{6 i f (e+f x)^2 \cosh (2 (c+d x))}{d^2}+\frac{32 (e+f x)^3}{\left(e^c-i\right) d}-\frac{4 i (e+f x)^3 \sinh (2 (c+d x))}{d}+\frac{16 (e+f x)^3 \cosh (c+d x)}{d}-\frac{32 i \sinh \left(\frac{d x}{2}\right) (e+f x)^3}{d \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}+24 i e^3 x+36 i e^2 f x^2+24 i e f^2 x^3+6 i f^3 x^4}{16 a}","-\frac{12 i f^3 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^4}+\frac{3 i f^3 \sinh ^2(c+d x)}{8 a d^4}-\frac{6 f^3 \sinh (c+d x)}{a d^4}+\frac{12 i f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}+\frac{6 f^2 (e+f x) \cosh (c+d x)}{a d^3}-\frac{3 i f^2 (e+f x) \sinh (c+d x) \cosh (c+d x)}{4 a d^3}+\frac{6 i f (e+f x)^2 \log \left(1+i e^{c+d x}\right)}{a d^2}+\frac{3 i f (e+f x)^2 \sinh ^2(c+d x)}{4 a d^2}-\frac{3 f (e+f x)^2 \sinh (c+d x)}{a d^2}+\frac{(e+f x)^3 \cosh (c+d x)}{a d}-\frac{i (e+f x)^3 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{i (e+f x)^3 \sinh (c+d x) \cosh (c+d x)}{2 a d}+\frac{3 i e f^2 x}{4 a d^2}+\frac{3 i f^3 x^2}{8 a d^2}-\frac{i (e+f x)^3}{a d}+\frac{3 i (e+f x)^4}{8 a f}",1,"((24*I)*e^3*x + (36*I)*e^2*f*x^2 + (24*I)*e*f^2*x^3 + (6*I)*f^3*x^4 + (32*(e + f*x)^3)/(d*(-I + E^c)) + (96*f^2*(e + f*x)*Cosh[c + d*x])/d^3 + (16*(e + f*x)^3*Cosh[c + d*x])/d + ((3*I)*f^3*Cosh[2*(c + d*x)])/d^4 + ((6*I)*f*(e + f*x)^2*Cosh[2*(c + d*x)])/d^2 + ((96*I)*f*(e + f*x)^2*Log[1 - I*E^(-c - d*x)])/d^2 - ((192*I)*f^2*(d*(e + f*x)*PolyLog[2, I*E^(-c - d*x)] + f*PolyLog[3, I*E^(-c - d*x)]))/d^4 - ((32*I)*(e + f*x)^3*Sinh[(d*x)/2])/(d*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])) - (96*f^3*Sinh[c + d*x])/d^4 - (48*f*(e + f*x)^2*Sinh[c + d*x])/d^2 - ((6*I)*f^2*(e + f*x)*Sinh[2*(c + d*x)])/d^3 - ((4*I)*(e + f*x)^3*Sinh[2*(c + d*x)])/d)/(16*a)","A",1
200,1,1661,287,4.9834138,"\int \frac{(e+f x)^2 \sinh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sinh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{e^{-2 c} \left(-8 e^{2 c} f^2 x^3 \sinh \left(\frac{d x}{2}\right) d^3+8 i e^{3 c} f^2 x^3 \sinh \left(\frac{d x}{2}\right) d^3-24 e e^{2 c} f x^2 \sinh \left(\frac{d x}{2}\right) d^3+24 i e e^{3 c} f x^2 \sinh \left(\frac{d x}{2}\right) d^3-24 e^2 e^{2 c} x \sinh \left(\frac{d x}{2}\right) d^3+24 i e^2 e^{3 c} x \sinh \left(\frac{d x}{2}\right) d^3-6 i e^2 e^c \cosh \left(\frac{3 d x}{2}\right) d^2+6 e^2 e^{4 c} \cosh \left(\frac{3 d x}{2}\right) d^2-6 i e^c f^2 x^2 \cosh \left(\frac{3 d x}{2}\right) d^2+6 e^{4 c} f^2 x^2 \cosh \left(\frac{3 d x}{2}\right) d^2-12 i e e^c f x \cosh \left(\frac{3 d x}{2}\right) d^2+12 e e^{4 c} f x \cosh \left(\frac{3 d x}{2}\right) d^2-2 i e^2 e^{5 c} \cosh \left(\frac{5 d x}{2}\right) d^2+2 e^2 \cosh \left(\frac{5 d x}{2}\right) d^2-2 i e^{5 c} f^2 x^2 \cosh \left(\frac{5 d x}{2}\right) d^2+2 f^2 x^2 \cosh \left(\frac{5 d x}{2}\right) d^2-4 i e e^{5 c} f x \cosh \left(\frac{5 d x}{2}\right) d^2+4 e f x \cosh \left(\frac{5 d x}{2}\right) d^2-40 e^2 e^{2 c} \sinh \left(\frac{d x}{2}\right) d^2-8 i e^2 e^{3 c} \sinh \left(\frac{d x}{2}\right) d^2-40 e^{2 c} f^2 x^2 \sinh \left(\frac{d x}{2}\right) d^2-8 i e^{3 c} f^2 x^2 \sinh \left(\frac{d x}{2}\right) d^2-80 e e^{2 c} f x \sinh \left(\frac{d x}{2}\right) d^2-16 i e e^{3 c} f x \sinh \left(\frac{d x}{2}\right) d^2+6 i e^2 e^c \sinh \left(\frac{3 d x}{2}\right) d^2+6 e^2 e^{4 c} \sinh \left(\frac{3 d x}{2}\right) d^2+6 i e^c f^2 x^2 \sinh \left(\frac{3 d x}{2}\right) d^2+6 e^{4 c} f^2 x^2 \sinh \left(\frac{3 d x}{2}\right) d^2+12 i e e^c f x \sinh \left(\frac{3 d x}{2}\right) d^2+12 e e^{4 c} f x \sinh \left(\frac{3 d x}{2}\right) d^2-2 i e^2 e^{5 c} \sinh \left(\frac{5 d x}{2}\right) d^2-2 e^2 \sinh \left(\frac{5 d x}{2}\right) d^2-2 i e^{5 c} f^2 x^2 \sinh \left(\frac{5 d x}{2}\right) d^2-2 f^2 x^2 \sinh \left(\frac{5 d x}{2}\right) d^2-4 i e e^{5 c} f x \sinh \left(\frac{5 d x}{2}\right) d^2-4 e f x \sinh \left(\frac{5 d x}{2}\right) d^2-14 i e e^c f \cosh \left(\frac{3 d x}{2}\right) d-14 e e^{4 c} f \cosh \left(\frac{3 d x}{2}\right) d-14 i e^c f^2 x \cosh \left(\frac{3 d x}{2}\right) d-14 e^{4 c} f^2 x \cosh \left(\frac{3 d x}{2}\right) d+2 i e e^{5 c} f \cosh \left(\frac{5 d x}{2}\right) d+2 e f \cosh \left(\frac{5 d x}{2}\right) d+2 i e^{5 c} f^2 x \cosh \left(\frac{5 d x}{2}\right) d+2 f^2 x \cosh \left(\frac{5 d x}{2}\right) d-16 e e^{2 c} f \sinh \left(\frac{d x}{2}\right) d+16 i e e^{3 c} f \sinh \left(\frac{d x}{2}\right) d-16 e^{2 c} f^2 x \sinh \left(\frac{d x}{2}\right) d+16 i e^{3 c} f^2 x \sinh \left(\frac{d x}{2}\right) d-64 e e^{2 c} f \log \left(1-i e^{-c-d x}\right) \sinh \left(\frac{d x}{2}\right) d+64 i e e^{3 c} f \log \left(1-i e^{-c-d x}\right) \sinh \left(\frac{d x}{2}\right) d-64 e^{2 c} f^2 x \log \left(1-i e^{-c-d x}\right) \sinh \left(\frac{d x}{2}\right) d+64 i e^{3 c} f^2 x \log \left(1-i e^{-c-d x}\right) \sinh \left(\frac{d x}{2}\right) d+14 i e e^c f \sinh \left(\frac{3 d x}{2}\right) d-14 e e^{4 c} f \sinh \left(\frac{3 d x}{2}\right) d+14 i e^c f^2 x \sinh \left(\frac{3 d x}{2}\right) d-14 e^{4 c} f^2 x \sinh \left(\frac{3 d x}{2}\right) d+2 i e e^{5 c} f \sinh \left(\frac{5 d x}{2}\right) d-2 e f \sinh \left(\frac{5 d x}{2}\right) d+2 i e^{5 c} f^2 x \sinh \left(\frac{5 d x}{2}\right) d-2 f^2 x \sinh \left(\frac{5 d x}{2}\right) d-15 i e^c f^2 \cosh \left(\frac{3 d x}{2}\right)+15 e^{4 c} f^2 \cosh \left(\frac{3 d x}{2}\right)-i e^{5 c} f^2 \cosh \left(\frac{5 d x}{2}\right)+f^2 \cosh \left(\frac{5 d x}{2}\right)+8 e^{2 c} \cosh \left(\frac{d x}{2}\right) \left(\left(1+i e^c\right) x \left(3 e^2+3 f x e+f^2 x^2\right) d^3+\left(5-i e^c\right) (e+f x)^2 d^2+2 \left(1+i e^c\right) f (e+f x) d+8 \left(1+i e^c\right) f (e+f x) \log \left(1-i e^{-c-d x}\right) d+2 \left(1-i e^c\right) f^2\right)-16 e^{2 c} f^2 \sinh \left(\frac{d x}{2}\right)-16 i e^{3 c} f^2 \sinh \left(\frac{d x}{2}\right)+64 e^{2 c} f^2 \text{Li}_2\left(i e^{-c-d x}\right) \left(\left(-1-i e^c\right) \cosh \left(\frac{d x}{2}\right)+\left(1-i e^c\right) \sinh \left(\frac{d x}{2}\right)\right)+15 i e^c f^2 \sinh \left(\frac{3 d x}{2}\right)+15 e^{4 c} f^2 \sinh \left(\frac{3 d x}{2}\right)-i e^{5 c} f^2 \sinh \left(\frac{5 d x}{2}\right)-f^2 \sinh \left(\frac{5 d x}{2}\right)\right)}{16 a d^3 \left(\left(-i+e^c\right) \cosh \left(\frac{d x}{2}\right)+\left(i+e^c\right) \sinh \left(\frac{d x}{2}\right)\right)}","\frac{4 i f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}+\frac{2 f^2 \cosh (c+d x)}{a d^3}-\frac{i f^2 \sinh (c+d x) \cosh (c+d x)}{4 a d^3}+\frac{4 i f (e+f x) \log \left(1+i e^{c+d x}\right)}{a d^2}+\frac{i f (e+f x) \sinh ^2(c+d x)}{2 a d^2}-\frac{2 f (e+f x) \sinh (c+d x)}{a d^2}+\frac{(e+f x)^2 \cosh (c+d x)}{a d}-\frac{i (e+f x)^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{i (e+f x)^2 \sinh (c+d x) \cosh (c+d x)}{2 a d}+\frac{i f^2 x}{4 a d^2}-\frac{i (e+f x)^2}{a d}+\frac{i (e+f x)^3}{2 a f}",1,"((-6*I)*d^2*e^2*E^c*Cosh[(3*d*x)/2] + 6*d^2*e^2*E^(4*c)*Cosh[(3*d*x)/2] - (14*I)*d*e*E^c*f*Cosh[(3*d*x)/2] - 14*d*e*E^(4*c)*f*Cosh[(3*d*x)/2] - (15*I)*E^c*f^2*Cosh[(3*d*x)/2] + 15*E^(4*c)*f^2*Cosh[(3*d*x)/2] - (12*I)*d^2*e*E^c*f*x*Cosh[(3*d*x)/2] + 12*d^2*e*E^(4*c)*f*x*Cosh[(3*d*x)/2] - (14*I)*d*E^c*f^2*x*Cosh[(3*d*x)/2] - 14*d*E^(4*c)*f^2*x*Cosh[(3*d*x)/2] - (6*I)*d^2*E^c*f^2*x^2*Cosh[(3*d*x)/2] + 6*d^2*E^(4*c)*f^2*x^2*Cosh[(3*d*x)/2] + 2*d^2*e^2*Cosh[(5*d*x)/2] - (2*I)*d^2*e^2*E^(5*c)*Cosh[(5*d*x)/2] + 2*d*e*f*Cosh[(5*d*x)/2] + (2*I)*d*e*E^(5*c)*f*Cosh[(5*d*x)/2] + f^2*Cosh[(5*d*x)/2] - I*E^(5*c)*f^2*Cosh[(5*d*x)/2] + 4*d^2*e*f*x*Cosh[(5*d*x)/2] - (4*I)*d^2*e*E^(5*c)*f*x*Cosh[(5*d*x)/2] + 2*d*f^2*x*Cosh[(5*d*x)/2] + (2*I)*d*E^(5*c)*f^2*x*Cosh[(5*d*x)/2] + 2*d^2*f^2*x^2*Cosh[(5*d*x)/2] - (2*I)*d^2*E^(5*c)*f^2*x^2*Cosh[(5*d*x)/2] + 8*E^(2*c)*Cosh[(d*x)/2]*(2*(1 - I*E^c)*f^2 + 2*d*(1 + I*E^c)*f*(e + f*x) + d^2*(5 - I*E^c)*(e + f*x)^2 + d^3*(1 + I*E^c)*x*(3*e^2 + 3*e*f*x + f^2*x^2) + 8*d*(1 + I*E^c)*f*(e + f*x)*Log[1 - I*E^(-c - d*x)]) - 40*d^2*e^2*E^(2*c)*Sinh[(d*x)/2] - (8*I)*d^2*e^2*E^(3*c)*Sinh[(d*x)/2] - 16*d*e*E^(2*c)*f*Sinh[(d*x)/2] + (16*I)*d*e*E^(3*c)*f*Sinh[(d*x)/2] - 16*E^(2*c)*f^2*Sinh[(d*x)/2] - (16*I)*E^(3*c)*f^2*Sinh[(d*x)/2] - 24*d^3*e^2*E^(2*c)*x*Sinh[(d*x)/2] + (24*I)*d^3*e^2*E^(3*c)*x*Sinh[(d*x)/2] - 80*d^2*e*E^(2*c)*f*x*Sinh[(d*x)/2] - (16*I)*d^2*e*E^(3*c)*f*x*Sinh[(d*x)/2] - 16*d*E^(2*c)*f^2*x*Sinh[(d*x)/2] + (16*I)*d*E^(3*c)*f^2*x*Sinh[(d*x)/2] - 24*d^3*e*E^(2*c)*f*x^2*Sinh[(d*x)/2] + (24*I)*d^3*e*E^(3*c)*f*x^2*Sinh[(d*x)/2] - 40*d^2*E^(2*c)*f^2*x^2*Sinh[(d*x)/2] - (8*I)*d^2*E^(3*c)*f^2*x^2*Sinh[(d*x)/2] - 8*d^3*E^(2*c)*f^2*x^3*Sinh[(d*x)/2] + (8*I)*d^3*E^(3*c)*f^2*x^3*Sinh[(d*x)/2] - 64*d*e*E^(2*c)*f*Log[1 - I*E^(-c - d*x)]*Sinh[(d*x)/2] + (64*I)*d*e*E^(3*c)*f*Log[1 - I*E^(-c - d*x)]*Sinh[(d*x)/2] - 64*d*E^(2*c)*f^2*x*Log[1 - I*E^(-c - d*x)]*Sinh[(d*x)/2] + (64*I)*d*E^(3*c)*f^2*x*Log[1 - I*E^(-c - d*x)]*Sinh[(d*x)/2] + 64*E^(2*c)*f^2*PolyLog[2, I*E^(-c - d*x)]*((-1 - I*E^c)*Cosh[(d*x)/2] + (1 - I*E^c)*Sinh[(d*x)/2]) + (6*I)*d^2*e^2*E^c*Sinh[(3*d*x)/2] + 6*d^2*e^2*E^(4*c)*Sinh[(3*d*x)/2] + (14*I)*d*e*E^c*f*Sinh[(3*d*x)/2] - 14*d*e*E^(4*c)*f*Sinh[(3*d*x)/2] + (15*I)*E^c*f^2*Sinh[(3*d*x)/2] + 15*E^(4*c)*f^2*Sinh[(3*d*x)/2] + (12*I)*d^2*e*E^c*f*x*Sinh[(3*d*x)/2] + 12*d^2*e*E^(4*c)*f*x*Sinh[(3*d*x)/2] + (14*I)*d*E^c*f^2*x*Sinh[(3*d*x)/2] - 14*d*E^(4*c)*f^2*x*Sinh[(3*d*x)/2] + (6*I)*d^2*E^c*f^2*x^2*Sinh[(3*d*x)/2] + 6*d^2*E^(4*c)*f^2*x^2*Sinh[(3*d*x)/2] - 2*d^2*e^2*Sinh[(5*d*x)/2] - (2*I)*d^2*e^2*E^(5*c)*Sinh[(5*d*x)/2] - 2*d*e*f*Sinh[(5*d*x)/2] + (2*I)*d*e*E^(5*c)*f*Sinh[(5*d*x)/2] - f^2*Sinh[(5*d*x)/2] - I*E^(5*c)*f^2*Sinh[(5*d*x)/2] - 4*d^2*e*f*x*Sinh[(5*d*x)/2] - (4*I)*d^2*e*E^(5*c)*f*x*Sinh[(5*d*x)/2] - 2*d*f^2*x*Sinh[(5*d*x)/2] + (2*I)*d*E^(5*c)*f^2*x*Sinh[(5*d*x)/2] - 2*d^2*f^2*x^2*Sinh[(5*d*x)/2] - (2*I)*d^2*E^(5*c)*f^2*x^2*Sinh[(5*d*x)/2])/(16*a*d^3*E^(2*c)*((-I + E^c)*Cosh[(d*x)/2] + (I + E^c)*Sinh[(d*x)/2]))","B",1
201,1,325,175,1.7861225,"\int \frac{(e+f x) \sinh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sinh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right) \left(2 \left(-3 c^2 f-d (e+f x) \sinh (2 (c+d x))+6 c d e+4 i f \sinh (c+d x)+8 i f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+4 f \log (\cosh (c+d x))-4 i c f+6 d^2 e x+3 d^2 f x^2-4 i d f x\right)-8 i d (e+f x) \cosh (c+d x)+f \cosh (2 (c+d x))\right)+\sinh \left(\frac{1}{2} (c+d x)\right) \left(8 d (e+f x) \cosh (c+d x)+i \left(f \cosh (2 (c+d x))+2 \left(-3 c^2 f-d (e+f x) \sinh (2 (c+d x))+6 c d e+4 i f \sinh (c+d x)+8 i f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+4 f \log (\cosh (c+d x))-4 i c f+6 d^2 e x+3 d^2 f x^2+8 i d e+4 i d f x\right)\right)\right)\right)}{8 a d^2 (\sinh (c+d x)-i)}","\frac{i f \sinh ^2(c+d x)}{4 a d^2}-\frac{f \sinh (c+d x)}{a d^2}+\frac{2 i f \log \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)\right)}{a d^2}+\frac{(e+f x) \cosh (c+d x)}{a d}-\frac{i (e+f x) \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{i (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 a d}+\frac{3 i e x}{2 a}+\frac{3 i f x^2}{4 a}",1,"((Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*(Cosh[(c + d*x)/2]*((-8*I)*d*(e + f*x)*Cosh[c + d*x] + f*Cosh[2*(c + d*x)] + 2*(6*c*d*e - (4*I)*c*f - 3*c^2*f + 6*d^2*e*x - (4*I)*d*f*x + 3*d^2*f*x^2 + (8*I)*f*ArcTan[Tanh[(c + d*x)/2]] + 4*f*Log[Cosh[c + d*x]] + (4*I)*f*Sinh[c + d*x] - d*(e + f*x)*Sinh[2*(c + d*x)])) + Sinh[(c + d*x)/2]*(8*d*(e + f*x)*Cosh[c + d*x] + I*(f*Cosh[2*(c + d*x)] + 2*((8*I)*d*e + 6*c*d*e - (4*I)*c*f - 3*c^2*f + 6*d^2*e*x + (4*I)*d*f*x + 3*d^2*f*x^2 + (8*I)*f*ArcTan[Tanh[(c + d*x)/2]] + 4*f*Log[Cosh[c + d*x]] + (4*I)*f*Sinh[c + d*x] - d*(e + f*x)*Sinh[2*(c + d*x)])))))/(8*a*d^2*(-I + Sinh[c + d*x]))","A",1
202,1,109,83,0.1669289,"\int \frac{\sinh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Sinh[c + d*x]^3/(a + I*a*Sinh[c + d*x]),x]","\frac{\left(3 \sqrt{1+i \sinh (c+d x)} \sinh ^{-1}(\sinh (c+d x))+\sqrt{1-i \sinh (c+d x)} \left(-i \sinh ^2(c+d x)+\sinh (c+d x)-4 i\right)\right) \cosh (c+d x)}{2 a d \sqrt{1-i \sinh (c+d x)} (\sinh (c+d x)-i)}","\frac{2 \cosh (c+d x)}{a d}-\frac{\sinh ^2(c+d x) \cosh (c+d x)}{d (a+i a \sinh (c+d x))}-\frac{3 i \sinh (c+d x) \cosh (c+d x)}{2 a d}+\frac{3 i x}{2 a}",1,"(Cosh[c + d*x]*(3*ArcSinh[Sinh[c + d*x]]*Sqrt[1 + I*Sinh[c + d*x]] + Sqrt[1 - I*Sinh[c + d*x]]*(-4*I + Sinh[c + d*x] - I*Sinh[c + d*x]^2)))/(2*a*d*Sqrt[1 - I*Sinh[c + d*x]]*(-I + Sinh[c + d*x]))","A",1
203,-1,0,34,180.0021664,"\int \frac{\sinh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Sinh[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
204,-1,0,34,180.0015122,"\int \frac{\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Sinh[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
205,1,363,313,5.3680344,"\int \frac{(e+f x)^3 \text{csch}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Csch[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{\frac{2 d^3 (e+f x)^3}{e^c-i}-\frac{2 i d^3 \sinh \left(\frac{d x}{2}\right) (e+f x)^3}{\left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}-2 d^3 (e+f x)^3 \tanh ^{-1}(\sinh (c+d x)+\cosh (c+d x))-3 f \left(d^2 (e+f x)^2 \text{Li}_2(-\cosh (c+d x)-\sinh (c+d x))-2 d f (e+f x) \text{Li}_3(-\cosh (c+d x)-\sinh (c+d x))+2 f^2 \text{Li}_4(-\cosh (c+d x)-\sinh (c+d x))\right)+3 f \left(d^2 (e+f x)^2 \text{Li}_2(\cosh (c+d x)+\sinh (c+d x))-2 d f (e+f x) \text{Li}_3(\cosh (c+d x)+\sinh (c+d x))+2 f^2 \text{Li}_4(\cosh (c+d x)+\sinh (c+d x))\right)+6 i d^2 f (e+f x)^2 \log \left(1-i e^{-c-d x}\right)-12 i f^2 \left(d (e+f x) \text{Li}_2\left(i e^{-c-d x}\right)+f \text{Li}_3\left(i e^{-c-d x}\right)\right)}{a d^4}","-\frac{12 i f^3 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^4}-\frac{6 f^3 \text{Li}_4\left(-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{Li}_4\left(e^{c+d x}\right)}{a d^4}+\frac{12 i f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right)}{a d^2}+\frac{6 i f (e+f x)^2 \log \left(1+i e^{c+d x}\right)}{a d^2}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{i (e+f x)^3 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{i (e+f x)^3}{a d}",1,"((2*d^3*(e + f*x)^3)/(-I + E^c) - 2*d^3*(e + f*x)^3*ArcTanh[Cosh[c + d*x] + Sinh[c + d*x]] + (6*I)*d^2*f*(e + f*x)^2*Log[1 - I*E^(-c - d*x)] - (12*I)*f^2*(d*(e + f*x)*PolyLog[2, I*E^(-c - d*x)] + f*PolyLog[3, I*E^(-c - d*x)]) - 3*f*(d^2*(e + f*x)^2*PolyLog[2, -Cosh[c + d*x] - Sinh[c + d*x]] - 2*d*f*(e + f*x)*PolyLog[3, -Cosh[c + d*x] - Sinh[c + d*x]] + 2*f^2*PolyLog[4, -Cosh[c + d*x] - Sinh[c + d*x]]) + 3*f*(d^2*(e + f*x)^2*PolyLog[2, Cosh[c + d*x] + Sinh[c + d*x]] - 2*d*f*(e + f*x)*PolyLog[3, Cosh[c + d*x] + Sinh[c + d*x]] + 2*f^2*PolyLog[4, Cosh[c + d*x] + Sinh[c + d*x]]) - ((2*I)*d^3*(e + f*x)^3*Sinh[(d*x)/2])/((Cosh[c/2] + I*Sinh[c/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])))/(a*d^4)","A",0
206,1,275,224,4.1297137,"\int \frac{(e+f x)^2 \text{csch}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{d^2 (e+f x)^2 \log \left(1-e^{c+d x}\right)-d^2 (e+f x)^2 \log \left(e^{c+d x}+1\right)-\frac{2 i d^2 \sinh \left(\frac{d x}{2}\right) (e+f x)^2}{\left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}+\frac{2 d (e+f x) \left(2 \left(e^c-i\right) f \log \left(1-i e^{-c-d x}\right)-i d (e+f x)\right)-4 \left(e^c-i\right) f^2 \text{Li}_2\left(i e^{-c-d x}\right)}{-1-i e^c}-2 d f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)+2 d f (e+f x) \text{Li}_2\left(e^{c+d x}\right)+2 f^2 \text{Li}_3\left(-e^{c+d x}\right)-2 f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}","\frac{4 i f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}+\frac{2 f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{2 f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{2 f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^2}+\frac{4 i f (e+f x) \log \left(1+i e^{c+d x}\right)}{a d^2}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{i (e+f x)^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{i (e+f x)^2}{a d}",1,"(d^2*(e + f*x)^2*Log[1 - E^(c + d*x)] - d^2*(e + f*x)^2*Log[1 + E^(c + d*x)] + (2*d*(e + f*x)*((-I)*d*(e + f*x) + 2*(-I + E^c)*f*Log[1 - I*E^(-c - d*x)]) - 4*(-I + E^c)*f^2*PolyLog[2, I*E^(-c - d*x)])/(-1 - I*E^c) - 2*d*f*(e + f*x)*PolyLog[2, -E^(c + d*x)] + 2*d*f*(e + f*x)*PolyLog[2, E^(c + d*x)] + 2*f^2*PolyLog[3, -E^(c + d*x)] - 2*f^2*PolyLog[3, E^(c + d*x)] - ((2*I)*d^2*(e + f*x)^2*Sinh[(d*x)/2])/((Cosh[c/2] + I*Sinh[c/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])))/(a*d^3)","A",1
207,1,345,126,1.2215463,"\int \frac{(e+f x) \text{csch}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(-2 i d (e+f x) \sinh \left(\frac{1}{2} (c+d x)\right)+d e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+f \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)+(c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+f (c+d x) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+i f \log (\cosh (c+d x)) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)-c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)-2 f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)\right)}{d^2 (a+i a \sinh (c+d x))}","-\frac{f \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{f \text{Li}_2\left(e^{c+d x}\right)}{a d^2}+\frac{2 i f \log \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)\right)}{a d^2}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{i (e+f x) \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}",1,"((Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*(f*(c + d*x)*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) - 2*f*ArcTan[Tanh[(c + d*x)/2]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + I*f*Log[Cosh[c + d*x]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + d*e*Log[Tanh[(c + d*x)/2]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) - c*f*Log[Tanh[(c + d*x)/2]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + f*((c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) - (2*I)*d*(e + f*x)*Sinh[(c + d*x)/2]))/(d^2*(a + I*a*Sinh[c + d*x]))","B",1
208,1,52,41,0.0649273,"\int \frac{\text{csch}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Csch[c + d*x]/(a + I*a*Sinh[c + d*x]),x]","-\frac{\text{sech}(c+d x) \left(i \sinh (c+d x)+\sqrt{\cosh ^2(c+d x)} \tanh ^{-1}\left(\sqrt{\cosh ^2(c+d x)}\right)-1\right)}{a d}","-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}+\frac{\cosh (c+d x)}{d (a+i a \sinh (c+d x))}",1,"-((Sech[c + d*x]*(-1 + ArcTanh[Sqrt[Cosh[c + d*x]^2]]*Sqrt[Cosh[c + d*x]^2] + I*Sinh[c + d*x]))/(a*d))","A",1
209,0,0,32,46.5207664,"\int \frac{\text{csch}(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Csch[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{csch}(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"Integrate[Csch[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",-1
210,0,0,32,57.4455964,"\int \frac{\text{csch}(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Csch[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{csch}(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"Integrate[Csch[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",-1
211,1,1042,419,17.1540262,"\int \frac{(e+f x)^3 \text{csch}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Csch[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","-\frac{2 i \left(d^3 (e+f x)^3+3 d^2 \left(1+i e^c\right) f \log \left(1-i e^{-c-d x}\right) (e+f x)^2+6 i \left(i-e^c\right) f^2 \left(d (e+f x) \text{Li}_2\left(i e^{-c-d x}\right)+f \text{Li}_3\left(i e^{-c-d x}\right)\right)\right)}{a d^4 \left(-i+e^c\right)}+\frac{i d^3 x^3 \log (\cosh (c+d x)-\sinh (c+d x)+1) f^3-i d^3 x^3 \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^3+3 i \left(d^2 \text{Li}_2(\cosh (c+d x)-\sinh (c+d x)) x^2+2 (d x \text{Li}_3(\cosh (c+d x)-\sinh (c+d x))+\text{Li}_4(\cosh (c+d x)-\sinh (c+d x)))\right) f^3-3 i \left(d^2 \text{Li}_2(\sinh (c+d x)-\cosh (c+d x)) x^2+2 (d x \text{Li}_3(\sinh (c+d x)-\cosh (c+d x))+\text{Li}_4(\sinh (c+d x)-\cosh (c+d x)))\right) f^3+3 d^2 (i d e+f) x^2 \log (\cosh (c+d x)-\sinh (c+d x)+1) f^2+3 d^2 (f-i d e) x^2 \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^2+6 i (d e+i f) (d x \text{Li}_2(\cosh (c+d x)-\sinh (c+d x))+\text{Li}_3(\cosh (c+d x)-\sinh (c+d x))) f^2-6 (i d e+f) (d x \text{Li}_2(\sinh (c+d x)-\cosh (c+d x))+\text{Li}_3(\sinh (c+d x)-\cosh (c+d x))) f^2+3 d^2 e (i d e+2 f) x \log (\cosh (c+d x)-\sinh (c+d x)+1) f+3 d^2 e (2 f-i d e) x \log (-\cosh (c+d x)+\sinh (c+d x)+1) f+3 i d e (d e+2 i f) \text{Li}_2(\cosh (c+d x)-\sinh (c+d x)) f-3 i d e (d e-2 i f) \text{Li}_2(\sinh (c+d x)-\cosh (c+d x)) f-d^3 (e+f x)^3 (\coth (c)-1)+i d^2 e^2 (d e+3 i f) (d x-\log (-\cosh (c+d x)-\sinh (c+d x)+1))-i d^2 e^2 (d e-3 i f) (d x-\log (\cosh (c+d x)+\sinh (c+d x)+1))}{a d^4}+\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(-\sinh \left(\frac{d x}{2}\right) e^3-3 f x \sinh \left(\frac{d x}{2}\right) e^2-3 f^2 x^2 \sinh \left(\frac{d x}{2}\right) e-f^3 x^3 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(\sinh \left(\frac{d x}{2}\right) e^3+3 f x \sinh \left(\frac{d x}{2}\right) e^2+3 f^2 x^2 \sinh \left(\frac{d x}{2}\right) e+f^3 x^3 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}-\frac{2 \left(\sinh \left(\frac{d x}{2}\right) e^3+3 f x \sinh \left(\frac{d x}{2}\right) e^2+3 f^2 x^2 \sinh \left(\frac{d x}{2}\right) e+f^3 x^3 \sinh \left(\frac{d x}{2}\right)\right)}{a d \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}","-\frac{12 f^3 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^4}-\frac{3 f^3 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a d^4}+\frac{6 i f^3 \text{Li}_4\left(-e^{c+d x}\right)}{a d^4}-\frac{6 i f^3 \text{Li}_4\left(e^{c+d x}\right)}{a d^4}+\frac{12 f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}+\frac{3 f^2 (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^3}-\frac{6 i f^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}+\frac{6 i f^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right)}{a d^2}+\frac{6 f (e+f x)^2 \log \left(1+i e^{c+d x}\right)}{a d^2}+\frac{3 f (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a d^2}+\frac{2 i (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{(e+f x)^3 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{(e+f x)^3 \coth (c+d x)}{a d}-\frac{2 (e+f x)^3}{a d}",1,"((-2*I)*(d^3*(e + f*x)^3 + 3*d^2*(1 + I*E^c)*f*(e + f*x)^2*Log[1 - I*E^(-c - d*x)] + (6*I)*(I - E^c)*f^2*(d*(e + f*x)*PolyLog[2, I*E^(-c - d*x)] + f*PolyLog[3, I*E^(-c - d*x)])))/(a*d^4*(-I + E^c)) + (-(d^3*(e + f*x)^3*(-1 + Coth[c])) + I*d^2*e^2*(d*e + (3*I)*f)*(d*x - Log[1 - Cosh[c + d*x] - Sinh[c + d*x]]) + 3*d^2*e*f*(I*d*e + 2*f)*x*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] + 3*d^2*f^2*(I*d*e + f)*x^2*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] + I*d^3*f^3*x^3*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] + 3*d^2*e*f*((-I)*d*e + 2*f)*x*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] + 3*d^2*f^2*((-I)*d*e + f)*x^2*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] - I*d^3*f^3*x^3*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] - I*d^2*e^2*(d*e - (3*I)*f)*(d*x - Log[1 + Cosh[c + d*x] + Sinh[c + d*x]]) + (3*I)*d*e*(d*e + (2*I)*f)*f*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] - (3*I)*d*e*(d*e - (2*I)*f)*f*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + (6*I)*(d*e + I*f)*f^2*(d*x*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]]) - 6*f^2*(I*d*e + f)*(d*x*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]]) + (3*I)*f^3*(d^2*x^2*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 2*(d*x*PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[4, Cosh[c + d*x] - Sinh[c + d*x]])) - (3*I)*f^3*(d^2*x^2*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 2*(d*x*PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[4, -Cosh[c + d*x] + Sinh[c + d*x]])))/(a*d^4) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(-(e^3*Sinh[(d*x)/2]) - 3*e^2*f*x*Sinh[(d*x)/2] - 3*e*f^2*x^2*Sinh[(d*x)/2] - f^3*x^3*Sinh[(d*x)/2]))/(2*a*d) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2]))/(2*a*d) - (2*(e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2]))/(a*d*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2]))","B",1
212,1,715,296,12.9168192,"\int \frac{(e+f x)^2 \text{csch}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{2 \left(\frac{d (e+f x) \left(2 \left(e^c-i\right) f \log \left(1-i e^{-c-d x}\right)-i d (e+f x)\right)}{e^c-i}-2 f^2 \text{Li}_2\left(i e^{-c-d x}\right)\right)}{a d^3}+\frac{-i \left(e^{2 c}-1\right) d^2 f^2 x^2 \log \left(1-e^{-c-d x}\right)+i \left(e^{2 c}-1\right) d^2 f^2 x^2 \log \left(e^{-c-d x}+1\right)-2 \left(e^{2 c}-1\right) f (f+i d e) \text{Li}_2\left(-e^{-c-d x}\right)+2 i \left(e^{2 c}-1\right) f (d e+i f) \text{Li}_2\left(e^{-c-d x}\right)+2 \left(e^{2 c}-1\right) d f x (f-i d e) \log \left(1-e^{-c-d x}\right)+2 \left(e^{2 c}-1\right) d f x (f+i d e) \log \left(e^{-c-d x}+1\right)+i \left(e^{2 c}-1\right) d e (d e+2 i f) \left(d x-\log \left(1-e^{c+d x}\right)\right)+\left(1-e^{2 c}\right) d e (2 f+i d e) \left(d x-\log \left(e^{c+d x}+1\right)\right)-2 i \left(e^{2 c}-1\right) f^2 \left(d x \text{Li}_2\left(-e^{-c-d x}\right)+\text{Li}_3\left(-e^{-c-d x}\right)\right)+2 i \left(e^{2 c}-1\right) f^2 \left(d x \text{Li}_2\left(e^{-c-d x}\right)+\text{Li}_3\left(e^{-c-d x}\right)\right)-2 d^2 (e+f x)^2}{a \left(e^{2 c}-1\right) d^3}-\frac{2 \left(e^2 \sinh \left(\frac{d x}{2}\right)+2 e f x \sinh \left(\frac{d x}{2}\right)+f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{a d \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(e^2 \sinh \left(\frac{d x}{2}\right)+2 e f x \sinh \left(\frac{d x}{2}\right)+f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}+\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(e^2 \left(-\sinh \left(\frac{d x}{2}\right)\right)-2 e f x \sinh \left(\frac{d x}{2}\right)-f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}","\frac{4 f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}+\frac{f^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^3}-\frac{2 i f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}+\frac{2 i f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}+\frac{2 i f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}-\frac{2 i f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^2}+\frac{4 f (e+f x) \log \left(1+i e^{c+d x}\right)}{a d^2}+\frac{2 f (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d^2}+\frac{2 i (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{(e+f x)^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{(e+f x)^2 \coth (c+d x)}{a d}-\frac{2 (e+f x)^2}{a d}",1,"(2*((d*(e + f*x)*((-I)*d*(e + f*x) + 2*(-I + E^c)*f*Log[1 - I*E^(-c - d*x)]))/(-I + E^c) - 2*f^2*PolyLog[2, I*E^(-c - d*x)]))/(a*d^3) + (-2*d^2*(e + f*x)^2 + 2*d*(-1 + E^(2*c))*f*((-I)*d*e + f)*x*Log[1 - E^(-c - d*x)] - I*d^2*(-1 + E^(2*c))*f^2*x^2*Log[1 - E^(-c - d*x)] + 2*d*(-1 + E^(2*c))*f*(I*d*e + f)*x*Log[1 + E^(-c - d*x)] + I*d^2*(-1 + E^(2*c))*f^2*x^2*Log[1 + E^(-c - d*x)] + I*d*e*(-1 + E^(2*c))*(d*e + (2*I)*f)*(d*x - Log[1 - E^(c + d*x)]) + d*e*(1 - E^(2*c))*(I*d*e + 2*f)*(d*x - Log[1 + E^(c + d*x)]) - 2*(-1 + E^(2*c))*f*(I*d*e + f)*PolyLog[2, -E^(-c - d*x)] + (2*I)*(-1 + E^(2*c))*(d*e + I*f)*f*PolyLog[2, E^(-c - d*x)] - (2*I)*(-1 + E^(2*c))*f^2*(d*x*PolyLog[2, -E^(-c - d*x)] + PolyLog[3, -E^(-c - d*x)]) + (2*I)*(-1 + E^(2*c))*f^2*(d*x*PolyLog[2, E^(-c - d*x)] + PolyLog[3, E^(-c - d*x)]))/(a*d^3*(-1 + E^(2*c))) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(-(e^2*Sinh[(d*x)/2]) - 2*e*f*x*Sinh[(d*x)/2] - f^2*x^2*Sinh[(d*x)/2]))/(2*a*d) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^2*Sinh[(d*x)/2] + 2*e*f*x*Sinh[(d*x)/2] + f^2*x^2*Sinh[(d*x)/2]))/(2*a*d) - (2*(e^2*Sinh[(d*x)/2] + 2*e*f*x*Sinh[(d*x)/2] + f^2*x^2*Sinh[(d*x)/2]))/(a*d*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2]))","B",1
213,1,454,163,5.220037,"\int \frac{(e+f x) \text{csch}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(-4 d (e+f x) \sinh \left(\frac{1}{2} (c+d x)\right)-i d (e+f x) \sinh \left(\frac{1}{2} (c+d x)\right) \left(\tanh \left(\frac{1}{2} (c+d x)\right)-i\right)-d (e+f x) \cosh \left(\frac{1}{2} (c+d x)\right) \left(\coth \left(\frac{1}{2} (c+d x)\right)+i\right)+2 d e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) \left(\sinh \left(\frac{1}{2} (c+d x)\right)-i \cosh \left(\frac{1}{2} (c+d x)\right)\right)-2 i f \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)+(c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+2 f (c+d x) \left(\sinh \left(\frac{1}{2} (c+d x)\right)-i \cosh \left(\frac{1}{2} (c+d x)\right)\right)+2 f \log (\cosh (c+d x)) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+2 f \log (\sinh (c+d x)) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+2 i c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+4 i f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)\right)}{2 d^2 (a+i a \sinh (c+d x))}","\frac{i f \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}-\frac{i f \text{Li}_2\left(e^{c+d x}\right)}{a d^2}+\frac{f \log (\sinh (c+d x))}{a d^2}+\frac{2 f \log \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)\right)}{a d^2}+\frac{2 i (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{(e+f x) \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}-\frac{(e+f x) \coth (c+d x)}{a d}",1,"((Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*(-(d*(e + f*x)*Cosh[(c + d*x)/2]*(I + Coth[(c + d*x)/2])) + (4*I)*f*ArcTan[Tanh[(c + d*x)/2]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + 2*f*Log[Cosh[c + d*x]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + 2*f*Log[Sinh[c + d*x]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + (2*I)*c*f*Log[Tanh[(c + d*x)/2]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) - (2*I)*f*((c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) - 4*d*(e + f*x)*Sinh[(c + d*x)/2] + 2*f*(c + d*x)*((-I)*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2]) + 2*d*e*Log[Tanh[(c + d*x)/2]]*((-I)*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2]) - I*d*(e + f*x)*Sinh[(c + d*x)/2]*(-I + Tanh[(c + d*x)/2])))/(2*d^2*(a + I*a*Sinh[c + d*x]))","B",1
214,1,61,57,0.2004619,"\int \frac{\text{csch}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Csch[c + d*x]^2/(a + I*a*Sinh[c + d*x]),x]","-\frac{\text{sech}(c+d x) \left(2 \sinh (c+d x)+\text{csch}(c+d x)-i \sqrt{\cosh ^2(c+d x)} \tanh ^{-1}\left(\sqrt{\cosh ^2(c+d x)}\right)+i\right)}{a d}","-\frac{2 \coth (c+d x)}{a d}+\frac{i \tanh ^{-1}(\cosh (c+d x))}{a d}+\frac{\coth (c+d x)}{d (a+i a \sinh (c+d x))}",1,"-((Sech[c + d*x]*(I - I*ArcTanh[Sqrt[Cosh[c + d*x]^2]]*Sqrt[Cosh[c + d*x]^2] + Csch[c + d*x] + 2*Sinh[c + d*x]))/(a*d))","A",1
215,0,0,34,133.4378573,"\int \frac{\text{csch}^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Csch[c + d*x]^2/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{csch}^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"Integrate[Csch[c + d*x]^2/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",-1
216,-1,0,34,180.00008,"\int \frac{\text{csch}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Csch[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{csch}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
217,1,2478,546,69.6770347,"\int \frac{(e+f x)^3 \text{csch}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Csch[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{3 f^3 \text{Li}_2\left(-e^{c+d x}\right)}{a d^4}+\frac{3 f^3 \text{Li}_2\left(e^{c+d x}\right)}{a d^4}+\frac{12 i f^3 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^4}+\frac{3 i f^3 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a d^4}+\frac{9 f^3 \text{Li}_4\left(-e^{c+d x}\right)}{a d^4}-\frac{9 f^3 \text{Li}_4\left(e^{c+d x}\right)}{a d^4}-\frac{12 i f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}-\frac{3 i f^2 (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^3}-\frac{9 f^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}+\frac{9 f^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{6 f^2 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d^3}+\frac{9 f (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right)}{2 a d^2}-\frac{9 f (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right)}{2 a d^2}-\frac{6 i f (e+f x)^2 \log \left(1+i e^{c+d x}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a d^2}-\frac{3 f (e+f x)^2 \text{csch}(c+d x)}{2 a d^2}+\frac{3 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{i (e+f x)^3 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}+\frac{i (e+f x)^3 \coth (c+d x)}{a d}-\frac{(e+f x)^3 \coth (c+d x) \text{csch}(c+d x)}{2 a d}+\frac{2 i (e+f x)^3}{a d}",1,"(-3*e^3*Log[Tanh[(c + d*x)/2]])/(2*a*d) + (3*e*f^2*Log[Tanh[(c + d*x)/2]])/(a*d^3) - (9*e^2*f*(-(c*Log[Tanh[(c + d*x)/2]]) - I*((I*c + I*d*x)*(Log[1 - E^(I*(I*c + I*d*x))] - Log[1 + E^(I*(I*c + I*d*x))]) + I*(PolyLog[2, -E^(I*(I*c + I*d*x))] - PolyLog[2, E^(I*(I*c + I*d*x))]))))/(2*a*d^2) + (3*f^3*(-(c*Log[Tanh[(c + d*x)/2]]) - I*((I*c + I*d*x)*(Log[1 - E^(I*(I*c + I*d*x))] - Log[1 + E^(I*(I*c + I*d*x))]) + I*(PolyLog[2, -E^(I*(I*c + I*d*x))] - PolyLog[2, E^(I*(I*c + I*d*x))]))))/(a*d^4) - (2*(d^3*(e + f*x)^3 + 3*d^2*(1 + I*E^c)*f*(e + f*x)^2*Log[1 - I*E^(-c - d*x)] + (6*I)*(I - E^c)*f^2*(d*(e + f*x)*PolyLog[2, I*E^(-c - d*x)] + f*PolyLog[3, I*E^(-c - d*x)])))/(a*d^4*(-I + E^c)) + ((I/2)*E^c*f^3*Csch[c]*((2*d^3*x^3)/E^(2*c) - 3*d^2*(1 - E^(-2*c))*x^2*Log[1 - E^(-c - d*x)] - 3*d^2*(1 - E^(-2*c))*x^2*Log[1 + E^(-c - d*x)] + 6*(1 - E^(-2*c))*(d*x*PolyLog[2, -E^(-c - d*x)] + PolyLog[3, -E^(-c - d*x)]) + 6*(1 - E^(-2*c))*(d*x*PolyLog[2, E^(-c - d*x)] + PolyLog[3, E^(-c - d*x)])))/(a*d^4) + (9*e*f^2*(d^2*x^2*ArcTanh[Cosh[c + d*x] + Sinh[c + d*x]] + d*x*PolyLog[2, -Cosh[c + d*x] - Sinh[c + d*x]] - d*x*PolyLog[2, Cosh[c + d*x] + Sinh[c + d*x]] - PolyLog[3, -Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] + Sinh[c + d*x]]))/(a*d^3) - (3*f^3*(-2*d^3*x^3*ArcTanh[Cosh[c + d*x] + Sinh[c + d*x]] - 3*d^2*x^2*PolyLog[2, -Cosh[c + d*x] - Sinh[c + d*x]] + 3*d^2*x^2*PolyLog[2, Cosh[c + d*x] + Sinh[c + d*x]] + 6*d*x*PolyLog[3, -Cosh[c + d*x] - Sinh[c + d*x]] - 6*d*x*PolyLog[3, Cosh[c + d*x] + Sinh[c + d*x]] - 6*PolyLog[4, -Cosh[c + d*x] - Sinh[c + d*x]] + 6*PolyLog[4, Cosh[c + d*x] + Sinh[c + d*x]]))/(2*a*d^4) + ((3*I)*e^2*f*Csch[c]*(-(d*x*Cosh[c]) + Log[Cosh[d*x]*Sinh[c] + Cosh[c]*Sinh[d*x]]*Sinh[c]))/(a*d^2*(-Cosh[c]^2 + Sinh[c]^2)) + (Csch[c]*Csch[c + d*x]^2*(3*e^2*f*Cosh[(d*x)/2] + 6*e*f^2*x*Cosh[(d*x)/2] + 3*f^3*x^2*Cosh[(d*x)/2] + 3*e^2*f*Cosh[(3*d*x)/2] + 6*e*f^2*x*Cosh[(3*d*x)/2] + 3*f^3*x^2*Cosh[(3*d*x)/2] + (5*I)*d*e^3*Cosh[c - (d*x)/2] + (15*I)*d*e^2*f*x*Cosh[c - (d*x)/2] + (15*I)*d*e*f^2*x^2*Cosh[c - (d*x)/2] + (5*I)*d*f^3*x^3*Cosh[c - (d*x)/2] - I*d*e^3*Cosh[c + (d*x)/2] - (3*I)*d*e^2*f*x*Cosh[c + (d*x)/2] - (3*I)*d*e*f^2*x^2*Cosh[c + (d*x)/2] - I*d*f^3*x^3*Cosh[c + (d*x)/2] - 3*e^2*f*Cosh[2*c + (d*x)/2] - 6*e*f^2*x*Cosh[2*c + (d*x)/2] - 3*f^3*x^2*Cosh[2*c + (d*x)/2] + I*d*e^3*Cosh[c + (3*d*x)/2] + (3*I)*d*e^2*f*x*Cosh[c + (3*d*x)/2] + (3*I)*d*e*f^2*x^2*Cosh[c + (3*d*x)/2] + I*d*f^3*x^3*Cosh[c + (3*d*x)/2] - 3*e^2*f*Cosh[2*c + (3*d*x)/2] - 6*e*f^2*x*Cosh[2*c + (3*d*x)/2] - 3*f^3*x^2*Cosh[2*c + (3*d*x)/2] - (3*I)*d*e^3*Cosh[3*c + (3*d*x)/2] - (9*I)*d*e^2*f*x*Cosh[3*c + (3*d*x)/2] - (9*I)*d*e*f^2*x^2*Cosh[3*c + (3*d*x)/2] - (3*I)*d*f^3*x^3*Cosh[3*c + (3*d*x)/2] - (4*I)*d*e^3*Cosh[c + (5*d*x)/2] - (12*I)*d*e^2*f*x*Cosh[c + (5*d*x)/2] - (12*I)*d*e*f^2*x^2*Cosh[c + (5*d*x)/2] - (4*I)*d*f^3*x^3*Cosh[c + (5*d*x)/2] + (2*I)*d*e^3*Cosh[3*c + (5*d*x)/2] + (6*I)*d*e^2*f*x*Cosh[3*c + (5*d*x)/2] + (6*I)*d*e*f^2*x^2*Cosh[3*c + (5*d*x)/2] + (2*I)*d*f^3*x^3*Cosh[3*c + (5*d*x)/2] - d*e^3*Sinh[(d*x)/2] - 3*d*e^2*f*x*Sinh[(d*x)/2] - 3*d*e*f^2*x^2*Sinh[(d*x)/2] - d*f^3*x^3*Sinh[(d*x)/2] - d*e^3*Sinh[(3*d*x)/2] - 3*d*e^2*f*x*Sinh[(3*d*x)/2] - 3*d*e*f^2*x^2*Sinh[(3*d*x)/2] - d*f^3*x^3*Sinh[(3*d*x)/2] + (3*I)*e^2*f*Sinh[c - (d*x)/2] + (6*I)*e*f^2*x*Sinh[c - (d*x)/2] + (3*I)*f^3*x^2*Sinh[c - (d*x)/2] + (3*I)*e^2*f*Sinh[c + (d*x)/2] + (6*I)*e*f^2*x*Sinh[c + (d*x)/2] + (3*I)*f^3*x^2*Sinh[c + (d*x)/2] - 3*d*e^3*Sinh[2*c + (d*x)/2] - 9*d*e^2*f*x*Sinh[2*c + (d*x)/2] - 9*d*e*f^2*x^2*Sinh[2*c + (d*x)/2] - 3*d*f^3*x^3*Sinh[2*c + (d*x)/2] + (3*I)*e^2*f*Sinh[c + (3*d*x)/2] + (6*I)*e*f^2*x*Sinh[c + (3*d*x)/2] + (3*I)*f^3*x^2*Sinh[c + (3*d*x)/2] - d*e^3*Sinh[2*c + (3*d*x)/2] - 3*d*e^2*f*x*Sinh[2*c + (3*d*x)/2] - 3*d*e*f^2*x^2*Sinh[2*c + (3*d*x)/2] - d*f^3*x^3*Sinh[2*c + (3*d*x)/2] - (3*I)*e^2*f*Sinh[3*c + (3*d*x)/2] - (6*I)*e*f^2*x*Sinh[3*c + (3*d*x)/2] - (3*I)*f^3*x^2*Sinh[3*c + (3*d*x)/2] + 2*d*e^3*Sinh[2*c + (5*d*x)/2] + 6*d*e^2*f*x*Sinh[2*c + (5*d*x)/2] + 6*d*e*f^2*x^2*Sinh[2*c + (5*d*x)/2] + 2*d*f^3*x^3*Sinh[2*c + (5*d*x)/2]))/(8*a*d^2*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])) + ((3*I)*e*f^2*Csch[c]*Sech[c]*((d^2*x^2)/E^ArcTanh[Tanh[c]] - (I*(-(d*x*(-Pi + (2*I)*ArcTanh[Tanh[c]])) - Pi*Log[1 + E^(2*d*x)] - 2*(I*d*x + I*ArcTanh[Tanh[c]])*Log[1 - E^((2*I)*(I*d*x + I*ArcTanh[Tanh[c]]))] + Pi*Log[Cosh[d*x]] + (2*I)*ArcTanh[Tanh[c]]*Log[I*Sinh[d*x + ArcTanh[Tanh[c]]]] + I*PolyLog[2, E^((2*I)*(I*d*x + I*ArcTanh[Tanh[c]]))])*Tanh[c])/Sqrt[1 - Tanh[c]^2]))/(a*d^3*Sqrt[Sech[c]^2*(Cosh[c]^2 - Sinh[c]^2)])","B",0
218,1,1378,368,16.8470464,"\int \frac{(e+f x)^2 \text{csch}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{\text{csch}(c) \left(5 i d \cosh \left(c-\frac{d x}{2}\right) e^2-i d \cosh \left(c+\frac{d x}{2}\right) e^2+i d \cosh \left(c+\frac{3 d x}{2}\right) e^2-3 i d \cosh \left(3 c+\frac{3 d x}{2}\right) e^2-4 i d \cosh \left(c+\frac{5 d x}{2}\right) e^2+2 i d \cosh \left(3 c+\frac{5 d x}{2}\right) e^2-d \sinh \left(\frac{d x}{2}\right) e^2-d \sinh \left(\frac{3 d x}{2}\right) e^2-3 d \sinh \left(2 c+\frac{d x}{2}\right) e^2-d \sinh \left(2 c+\frac{3 d x}{2}\right) e^2+2 d \sinh \left(2 c+\frac{5 d x}{2}\right) e^2+2 f \cosh \left(\frac{d x}{2}\right) e+2 f \cosh \left(\frac{3 d x}{2}\right) e+10 i d f x \cosh \left(c-\frac{d x}{2}\right) e-2 i d f x \cosh \left(c+\frac{d x}{2}\right) e-2 f \cosh \left(2 c+\frac{d x}{2}\right) e+2 i d f x \cosh \left(c+\frac{3 d x}{2}\right) e-2 f \cosh \left(2 c+\frac{3 d x}{2}\right) e-6 i d f x \cosh \left(3 c+\frac{3 d x}{2}\right) e-8 i d f x \cosh \left(c+\frac{5 d x}{2}\right) e+4 i d f x \cosh \left(3 c+\frac{5 d x}{2}\right) e-2 d f x \sinh \left(\frac{d x}{2}\right) e-2 d f x \sinh \left(\frac{3 d x}{2}\right) e+2 i f \sinh \left(c-\frac{d x}{2}\right) e+2 i f \sinh \left(c+\frac{d x}{2}\right) e-6 d f x \sinh \left(2 c+\frac{d x}{2}\right) e+2 i f \sinh \left(c+\frac{3 d x}{2}\right) e-2 d f x \sinh \left(2 c+\frac{3 d x}{2}\right) e-2 i f \sinh \left(3 c+\frac{3 d x}{2}\right) e+4 d f x \sinh \left(2 c+\frac{5 d x}{2}\right) e+2 f^2 x \cosh \left(\frac{d x}{2}\right)+2 f^2 x \cosh \left(\frac{3 d x}{2}\right)+5 i d f^2 x^2 \cosh \left(c-\frac{d x}{2}\right)-i d f^2 x^2 \cosh \left(c+\frac{d x}{2}\right)-2 f^2 x \cosh \left(2 c+\frac{d x}{2}\right)+i d f^2 x^2 \cosh \left(c+\frac{3 d x}{2}\right)-2 f^2 x \cosh \left(2 c+\frac{3 d x}{2}\right)-3 i d f^2 x^2 \cosh \left(3 c+\frac{3 d x}{2}\right)-4 i d f^2 x^2 \cosh \left(c+\frac{5 d x}{2}\right)+2 i d f^2 x^2 \cosh \left(3 c+\frac{5 d x}{2}\right)-d f^2 x^2 \sinh \left(\frac{d x}{2}\right)-d f^2 x^2 \sinh \left(\frac{3 d x}{2}\right)+2 i f^2 x \sinh \left(c-\frac{d x}{2}\right)+2 i f^2 x \sinh \left(c+\frac{d x}{2}\right)-3 d f^2 x^2 \sinh \left(2 c+\frac{d x}{2}\right)+2 i f^2 x \sinh \left(c+\frac{3 d x}{2}\right)-d f^2 x^2 \sinh \left(2 c+\frac{3 d x}{2}\right)-2 i f^2 x \sinh \left(3 c+\frac{3 d x}{2}\right)+2 d f^2 x^2 \sinh \left(2 c+\frac{5 d x}{2}\right)\right) \text{csch}^2(c+d x)}{8 a d^2 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}+\frac{4 \left(1+i e^c\right) f^2 \text{Li}_2\left(i e^{-c-d x}\right)-2 d (e+f x) \left(d (e+f x)+2 \left(1+i e^c\right) f \log \left(1-i e^{-c-d x}\right)\right)}{a d^3 \left(-i+e^c\right)}+\frac{3 d^2 x^2 \log (\cosh (c+d x)-\sinh (c+d x)+1) f^2-3 d^2 x^2 \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^2+6 (d x \text{Li}_2(\cosh (c+d x)-\sinh (c+d x))+\text{Li}_3(\cosh (c+d x)-\sinh (c+d x))) f^2-6 (d x \text{Li}_2(\sinh (c+d x)-\cosh (c+d x))+\text{Li}_3(\sinh (c+d x)-\cosh (c+d x))) f^2+2 d (3 d e-2 i f) x \log (\cosh (c+d x)-\sinh (c+d x)+1) f-2 d (3 d e+2 i f) x \log (-\cosh (c+d x)+\sinh (c+d x)+1) f+2 (3 d e+2 i f) \text{Li}_2(\cosh (c+d x)-\sinh (c+d x)) f-2 (3 d e-2 i f) \text{Li}_2(\sinh (c+d x)-\cosh (c+d x)) f+2 i d^2 (e+f x)^2 (\coth (c)-1)+\left(3 d^2 e^2+4 i d f e-2 f^2\right) (d x-\log (-\cosh (c+d x)-\sinh (c+d x)+1))-\left(3 d^2 e^2-4 i d f e-2 f^2\right) (d x-\log (\cosh (c+d x)+\sinh (c+d x)+1))}{2 a d^3}","-\frac{4 i f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}-\frac{i f^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^3}-\frac{3 f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}+\frac{3 f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{f^2 \tanh ^{-1}(\cosh (c+d x))}{a d^3}+\frac{3 f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}-\frac{3 f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{4 i f (e+f x) \log \left(1+i e^{c+d x}\right)}{a d^2}-\frac{2 i f (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d^2}-\frac{f (e+f x) \text{csch}(c+d x)}{a d^2}+\frac{3 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{i (e+f x)^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}+\frac{i (e+f x)^2 \coth (c+d x)}{a d}-\frac{(e+f x)^2 \coth (c+d x) \text{csch}(c+d x)}{2 a d}+\frac{2 i (e+f x)^2}{a d}",1,"(-2*d*(e + f*x)*(d*(e + f*x) + 2*(1 + I*E^c)*f*Log[1 - I*E^(-c - d*x)]) + 4*(1 + I*E^c)*f^2*PolyLog[2, I*E^(-c - d*x)])/(a*d^3*(-I + E^c)) + ((2*I)*d^2*(e + f*x)^2*(-1 + Coth[c]) + (3*d^2*e^2 + (4*I)*d*e*f - 2*f^2)*(d*x - Log[1 - Cosh[c + d*x] - Sinh[c + d*x]]) + 2*d*(3*d*e - (2*I)*f)*f*x*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] + 3*d^2*f^2*x^2*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - 2*d*(3*d*e + (2*I)*f)*f*x*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] - 3*d^2*f^2*x^2*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] - (3*d^2*e^2 - (4*I)*d*e*f - 2*f^2)*(d*x - Log[1 + Cosh[c + d*x] + Sinh[c + d*x]]) + 2*(3*d*e + (2*I)*f)*f*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] - 2*(3*d*e - (2*I)*f)*f*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 6*f^2*(d*x*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]]) - 6*f^2*(d*x*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]]))/(2*a*d^3) + (Csch[c]*Csch[c + d*x]^2*(2*e*f*Cosh[(d*x)/2] + 2*f^2*x*Cosh[(d*x)/2] + 2*e*f*Cosh[(3*d*x)/2] + 2*f^2*x*Cosh[(3*d*x)/2] + (5*I)*d*e^2*Cosh[c - (d*x)/2] + (10*I)*d*e*f*x*Cosh[c - (d*x)/2] + (5*I)*d*f^2*x^2*Cosh[c - (d*x)/2] - I*d*e^2*Cosh[c + (d*x)/2] - (2*I)*d*e*f*x*Cosh[c + (d*x)/2] - I*d*f^2*x^2*Cosh[c + (d*x)/2] - 2*e*f*Cosh[2*c + (d*x)/2] - 2*f^2*x*Cosh[2*c + (d*x)/2] + I*d*e^2*Cosh[c + (3*d*x)/2] + (2*I)*d*e*f*x*Cosh[c + (3*d*x)/2] + I*d*f^2*x^2*Cosh[c + (3*d*x)/2] - 2*e*f*Cosh[2*c + (3*d*x)/2] - 2*f^2*x*Cosh[2*c + (3*d*x)/2] - (3*I)*d*e^2*Cosh[3*c + (3*d*x)/2] - (6*I)*d*e*f*x*Cosh[3*c + (3*d*x)/2] - (3*I)*d*f^2*x^2*Cosh[3*c + (3*d*x)/2] - (4*I)*d*e^2*Cosh[c + (5*d*x)/2] - (8*I)*d*e*f*x*Cosh[c + (5*d*x)/2] - (4*I)*d*f^2*x^2*Cosh[c + (5*d*x)/2] + (2*I)*d*e^2*Cosh[3*c + (5*d*x)/2] + (4*I)*d*e*f*x*Cosh[3*c + (5*d*x)/2] + (2*I)*d*f^2*x^2*Cosh[3*c + (5*d*x)/2] - d*e^2*Sinh[(d*x)/2] - 2*d*e*f*x*Sinh[(d*x)/2] - d*f^2*x^2*Sinh[(d*x)/2] - d*e^2*Sinh[(3*d*x)/2] - 2*d*e*f*x*Sinh[(3*d*x)/2] - d*f^2*x^2*Sinh[(3*d*x)/2] + (2*I)*e*f*Sinh[c - (d*x)/2] + (2*I)*f^2*x*Sinh[c - (d*x)/2] + (2*I)*e*f*Sinh[c + (d*x)/2] + (2*I)*f^2*x*Sinh[c + (d*x)/2] - 3*d*e^2*Sinh[2*c + (d*x)/2] - 6*d*e*f*x*Sinh[2*c + (d*x)/2] - 3*d*f^2*x^2*Sinh[2*c + (d*x)/2] + (2*I)*e*f*Sinh[c + (3*d*x)/2] + (2*I)*f^2*x*Sinh[c + (3*d*x)/2] - d*e^2*Sinh[2*c + (3*d*x)/2] - 2*d*e*f*x*Sinh[2*c + (3*d*x)/2] - d*f^2*x^2*Sinh[2*c + (3*d*x)/2] - (2*I)*e*f*Sinh[3*c + (3*d*x)/2] - (2*I)*f^2*x*Sinh[3*c + (3*d*x)/2] + 2*d*e^2*Sinh[2*c + (5*d*x)/2] + 4*d*e*f*x*Sinh[2*c + (5*d*x)/2] + 2*d*f^2*x^2*Sinh[2*c + (5*d*x)/2]))/(8*a*d^2*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2]))","B",1
219,1,541,214,2.7502262,"\int \frac{(e+f x) \text{csch}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{\left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(16 i d (e+f x) \sinh \left(\frac{1}{2} (c+d x)\right)+2 i \cosh \left(\frac{1}{2} (c+d x)\right) \left(\coth \left(\frac{1}{2} (c+d x)\right)+i\right) (2 d (e+f x)+i f)-d (e+f x) \left(\coth \left(\frac{1}{2} (c+d x)\right)+i\right) \text{csch}\left(\frac{1}{2} (c+d x)\right)-i d (e+f x) \left(\tanh \left(\frac{1}{2} (c+d x)\right)-i\right) \text{sech}\left(\frac{1}{2} (c+d x)\right)+2 \tanh \left(\frac{1}{2} (c+d x)\right) (f+2 i d (e+f x)) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)-12 d e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)-12 f \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)+(c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)-8 f (c+d x) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+8 f \log (\cosh (c+d x)) \left(\sinh \left(\frac{1}{2} (c+d x)\right)-i \cosh \left(\frac{1}{2} (c+d x)\right)\right)+8 f \log (\sinh (c+d x)) \left(\sinh \left(\frac{1}{2} (c+d x)\right)-i \cosh \left(\frac{1}{2} (c+d x)\right)\right)+12 c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+16 f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)\right)}{8 d^2 (a+i a \sinh (c+d x))}","\frac{3 f \text{Li}_2\left(-e^{c+d x}\right)}{2 a d^2}-\frac{3 f \text{Li}_2\left(e^{c+d x}\right)}{2 a d^2}-\frac{f \text{csch}(c+d x)}{2 a d^2}-\frac{i f \log (\sinh (c+d x))}{a d^2}-\frac{2 i f \log \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)\right)}{a d^2}+\frac{3 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{i (e+f x) \tanh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right)}{a d}+\frac{i (e+f x) \coth (c+d x)}{a d}-\frac{(e+f x) \coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"((Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*((2*I)*(I*f + 2*d*(e + f*x))*Cosh[(c + d*x)/2]*(I + Coth[(c + d*x)/2]) - d*(e + f*x)*(I + Coth[(c + d*x)/2])*Csch[(c + d*x)/2] - 8*f*(c + d*x)*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + 16*f*ArcTan[Tanh[(c + d*x)/2]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) - 12*d*e*Log[Tanh[(c + d*x)/2]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + 12*c*f*Log[Tanh[(c + d*x)/2]]*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) - 12*f*((c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]) + (16*I)*d*(e + f*x)*Sinh[(c + d*x)/2] + 8*f*Log[Cosh[c + d*x]]*((-I)*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2]) + 8*f*Log[Sinh[c + d*x]]*((-I)*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2]) + 2*(f + (2*I)*d*(e + f*x))*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*Tanh[(c + d*x)/2] - I*d*(e + f*x)*Sech[(c + d*x)/2]*(-I + Tanh[(c + d*x)/2])))/(8*d^2*(a + I*a*Sinh[c + d*x]))","B",1
220,1,90,87,0.4359842,"\int \frac{\text{csch}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Csch[c + d*x]^3/(a + I*a*Sinh[c + d*x]),x]","\frac{4 i \tanh (c+d x)+4 i \text{csch}(2 (c+d x))-3 \text{sech}(c+d x)+\text{csch}^2(c+d x) (-\text{sech}(c+d x))+3 \sqrt{\cosh ^2(c+d x)} \text{sech}(c+d x) \tanh ^{-1}\left(\sqrt{\cosh ^2(c+d x)}\right)}{2 a d}","\frac{2 i \coth (c+d x)}{a d}+\frac{3 \tanh ^{-1}(\cosh (c+d x))}{2 a d}-\frac{3 \coth (c+d x) \text{csch}(c+d x)}{2 a d}+\frac{\coth (c+d x) \text{csch}(c+d x)}{d (a+i a \sinh (c+d x))}",1,"((4*I)*Csch[2*(c + d*x)] - 3*Sech[c + d*x] + 3*ArcTanh[Sqrt[Cosh[c + d*x]^2]]*Sqrt[Cosh[c + d*x]^2]*Sech[c + d*x] - Csch[c + d*x]^2*Sech[c + d*x] + (4*I)*Tanh[c + d*x])/(2*a*d)","A",1
221,-1,0,34,180.0194759,"\int \frac{\text{csch}^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Csch[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{csch}^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
222,-1,0,34,180.041695,"\int \frac{\text{csch}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Csch[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{csch}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
223,1,607,453,2.2822964,"\int \frac{(e+f x)^3 \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{a \left(2 d^3 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-3 d^3 e^2 f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+3 d^3 e^2 f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-3 d^3 e f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+3 d^3 e f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-d^3 f^3 x^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+d^3 f^3 x^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-3 d^2 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+3 d^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+6 d e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-6 d e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+6 d f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-6 d f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-6 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{b d^4 \sqrt{a^2+b^2}}+\frac{x \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right)}{4 b}","-\frac{6 a f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^4 \sqrt{a^2+b^2}}+\frac{6 a f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^4 \sqrt{a^2+b^2}}+\frac{6 a f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{6 a f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{3 a f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2 \sqrt{a^2+b^2}}+\frac{3 a f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{a (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d \sqrt{a^2+b^2}}+\frac{a (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d \sqrt{a^2+b^2}}+\frac{(e+f x)^4}{4 b f}",1,"(x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3))/(4*b) + (a*(2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b*Sqrt[a^2 + b^2]*d^4)","A",1
224,1,366,337,1.6008757,"\int \frac{(e+f x)^2 \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{a \left(2 d^2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-2 d^2 e f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+2 d^2 e f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 d f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 d f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{b d^3 \sqrt{a^2+b^2}}+\frac{x \left(3 e^2+3 e f x+f^2 x^2\right)}{3 b}","\frac{2 a f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{2 a f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{2 a f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2 \sqrt{a^2+b^2}}+\frac{2 a f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{a (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d \sqrt{a^2+b^2}}+\frac{a (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d \sqrt{a^2+b^2}}+\frac{(e+f x)^3}{3 b f}",1,"(x*(3*e^2 + 3*e*f*x + f^2*x^2))/(3*b) + (a*(2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b*Sqrt[a^2 + b^2]*d^3)","A",1
225,1,163,220,0.6301199,"\int \frac{(e+f x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{x (2 e+f x)}{2 b}-\frac{a \left(d (e+f x) \left(\log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-\log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)\right)+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{b d^2 \sqrt{a^2+b^2}}","-\frac{a f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2 \sqrt{a^2+b^2}}+\frac{a f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{a (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d \sqrt{a^2+b^2}}+\frac{a (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d \sqrt{a^2+b^2}}+\frac{e x}{b}+\frac{f x^2}{2 b}",1,"(x*(2*e + f*x))/(2*b) - (a*(d*(e + f*x)*(Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])]) + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b*Sqrt[a^2 + b^2]*d^2)","A",1
226,1,64,54,0.1103513,"\int \frac{\sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Sinh[c + d*x]/(a + b*Sinh[c + d*x]),x]","\frac{-\frac{2 a \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{d \sqrt{-a^2-b^2}}+\frac{c}{d}+x}{b}","\frac{2 a \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b d \sqrt{a^2+b^2}}+\frac{x}{b}",1,"(c/d + x - (2*a*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d))/b","A",1
227,0,0,29,9.0937774,"\int \frac{\sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Sinh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Sinh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
228,1,979,551,2.9597142,"\int \frac{(e+f x)^3 \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{-a \sqrt{a^2+b^2} f^3 x^4 d^4-4 a \sqrt{a^2+b^2} e f^2 x^3 d^4-6 a \sqrt{a^2+b^2} e^2 f x^2 d^4-4 a \sqrt{a^2+b^2} e^3 x d^4-8 a^2 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3+4 b \sqrt{a^2+b^2} e^3 \cosh (c+d x) d^3+4 b \sqrt{a^2+b^2} f^3 x^3 \cosh (c+d x) d^3+12 b \sqrt{a^2+b^2} e f^2 x^2 \cosh (c+d x) d^3+12 b \sqrt{a^2+b^2} e^2 f x \cosh (c+d x) d^3+4 a^2 f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+12 a^2 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+12 a^2 e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-4 a^2 f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-12 a^2 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-12 a^2 e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+12 a^2 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2-12 a^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2-12 b \sqrt{a^2+b^2} f^3 x^2 \sinh (c+d x) d^2-12 b \sqrt{a^2+b^2} e^2 f \sinh (c+d x) d^2-24 b \sqrt{a^2+b^2} e f^2 x \sinh (c+d x) d^2+24 b \sqrt{a^2+b^2} e f^2 \cosh (c+d x) d+24 b \sqrt{a^2+b^2} f^3 x \cosh (c+d x) d-24 a^2 e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-24 a^2 f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+24 a^2 e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+24 a^2 f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+24 a^2 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-24 a^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-24 b \sqrt{a^2+b^2} f^3 \sinh (c+d x)}{4 b^2 \sqrt{a^2+b^2} d^4}","\frac{6 a^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^4 \sqrt{a^2+b^2}}-\frac{6 a^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^4 \sqrt{a^2+b^2}}-\frac{6 a^2 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^3 \sqrt{a^2+b^2}}+\frac{6 a^2 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^3 \sqrt{a^2+b^2}}+\frac{3 a^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2 \sqrt{a^2+b^2}}-\frac{3 a^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^2 \sqrt{a^2+b^2}}+\frac{a^2 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^2 d \sqrt{a^2+b^2}}-\frac{a^2 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^2 d \sqrt{a^2+b^2}}-\frac{a (e+f x)^4}{4 b^2 f}-\frac{6 f^3 \sinh (c+d x)}{b d^4}+\frac{6 f^2 (e+f x) \cosh (c+d x)}{b d^3}-\frac{3 f (e+f x)^2 \sinh (c+d x)}{b d^2}+\frac{(e+f x)^3 \cosh (c+d x)}{b d}",1,"(-4*a*Sqrt[a^2 + b^2]*d^4*e^3*x - 6*a*Sqrt[a^2 + b^2]*d^4*e^2*f*x^2 - 4*a*Sqrt[a^2 + b^2]*d^4*e*f^2*x^3 - a*Sqrt[a^2 + b^2]*d^4*f^3*x^4 - 8*a^2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 4*b*Sqrt[a^2 + b^2]*d^3*e^3*Cosh[c + d*x] + 24*b*Sqrt[a^2 + b^2]*d*e*f^2*Cosh[c + d*x] + 12*b*Sqrt[a^2 + b^2]*d^3*e^2*f*x*Cosh[c + d*x] + 24*b*Sqrt[a^2 + b^2]*d*f^3*x*Cosh[c + d*x] + 12*b*Sqrt[a^2 + b^2]*d^3*e*f^2*x^2*Cosh[c + d*x] + 4*b*Sqrt[a^2 + b^2]*d^3*f^3*x^3*Cosh[c + d*x] + 12*a^2*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 12*a^2*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 4*a^2*d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 12*a^2*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 12*a^2*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 4*a^2*d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 12*a^2*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 12*a^2*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 24*a^2*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 24*a^2*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 24*a^2*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 24*a^2*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 24*a^2*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 24*a^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 12*b*Sqrt[a^2 + b^2]*d^2*e^2*f*Sinh[c + d*x] - 24*b*Sqrt[a^2 + b^2]*f^3*Sinh[c + d*x] - 24*b*Sqrt[a^2 + b^2]*d^2*e*f^2*x*Sinh[c + d*x] - 12*b*Sqrt[a^2 + b^2]*d^2*f^3*x^2*Sinh[c + d*x])/(4*b^2*Sqrt[a^2 + b^2]*d^4)","A",1
229,1,453,407,2.9320672,"\int \frac{(e+f x)^2 \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\frac{3 a^2 \left(-2 d^2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)+2 d^2 e f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-2 d^2 e f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 d f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 d f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{d^3 \sqrt{a^2+b^2}}-a x \left(3 e^2+3 e f x+f^2 x^2\right)+\frac{3 b \cosh (d x) \left(\cosh (c) \left(d^2 (e+f x)^2+2 f^2\right)-2 d f \sinh (c) (e+f x)\right)}{d^3}+\frac{3 b \sinh (d x) \left(\sinh (c) \left(d^2 (e+f x)^2+2 f^2\right)-2 d f \cosh (c) (e+f x)\right)}{d^3}}{3 b^2}","-\frac{2 a^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^3 \sqrt{a^2+b^2}}+\frac{2 a^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^3 \sqrt{a^2+b^2}}+\frac{2 a^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2 \sqrt{a^2+b^2}}-\frac{2 a^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^2 \sqrt{a^2+b^2}}+\frac{a^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^2 d \sqrt{a^2+b^2}}-\frac{a^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^2 d \sqrt{a^2+b^2}}-\frac{a (e+f x)^3}{3 b^2 f}+\frac{2 f^2 \cosh (c+d x)}{b d^3}-\frac{2 f (e+f x) \sinh (c+d x)}{b d^2}+\frac{(e+f x)^2 \cosh (c+d x)}{b d}",1,"(-(a*x*(3*e^2 + 3*e*f*x + f^2*x^2)) + (3*a^2*(-2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) + (3*b*Cosh[d*x]*((2*f^2 + d^2*(e + f*x)^2)*Cosh[c] - 2*d*f*(e + f*x)*Sinh[c]))/d^3 + (3*b*(-2*d*f*(e + f*x)*Cosh[c] + (2*f^2 + d^2*(e + f*x)^2)*Sinh[c])*Sinh[d*x])/d^3)/(3*b^2)","A",1
230,1,299,264,2.1284567,"\int \frac{(e+f x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\frac{2 a^2 \left(-2 d e \tanh ^{-1}\left(\frac{a+b \sinh (c+d x)+b \cosh (c+d x)}{\sqrt{a^2+b^2}}\right)+f \text{Li}_2\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{a-\sqrt{a^2+b^2}}+1\right)-f (c+d x) \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{\sqrt{a^2+b^2}+a}+1\right)+2 c f \tanh ^{-1}\left(\frac{a+b \sinh (c+d x)+b \cosh (c+d x)}{\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2}}+a (c+d x) (c f-d (2 e+f x))+2 b d (e+f x) \cosh (c+d x)-2 b f \sinh (c+d x)}{2 b^2 d^2}","\frac{a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2 \sqrt{a^2+b^2}}-\frac{a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^2 \sqrt{a^2+b^2}}+\frac{a^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^2 d \sqrt{a^2+b^2}}-\frac{a^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^2 d \sqrt{a^2+b^2}}-\frac{a e x}{b^2}-\frac{a f x^2}{2 b^2}-\frac{f \sinh (c+d x)}{b d^2}+\frac{(e+f x) \cosh (c+d x)}{b d}",1,"(a*(c + d*x)*(c*f - d*(2*e + f*x)) + 2*b*d*(e + f*x)*Cosh[c + d*x] + (2*a^2*(-2*d*e*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + 2*c*f*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + f*(c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - f*(c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + f*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] - 2*b*f*Sinh[c + d*x])/(2*b^2*d^2)","A",1
231,1,74,71,0.2943691,"\int \frac{\sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Sinh[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","\frac{b \cosh (c+d x)-a \left(-\frac{2 a \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+c+d x\right)}{b^2 d}","-\frac{2 a^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b^2 d \sqrt{a^2+b^2}}-\frac{a x}{b^2}+\frac{\cosh (c+d x)}{b d}",1,"(-(a*(c + d*x - (2*a*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2])) + b*Cosh[c + d*x])/(b^2*d)","A",1
232,0,0,31,134.0467504,"\int \frac{\sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Sinh[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Sinh[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
233,1,1407,712,4.5394949,"\int \frac{(e+f x)^3 \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{4 a^2 \sqrt{a^2+b^2} f^3 x^4 d^4-2 b^2 \sqrt{a^2+b^2} f^3 x^4 d^4+16 a^2 \sqrt{a^2+b^2} e f^2 x^3 d^4-8 b^2 \sqrt{a^2+b^2} e f^2 x^3 d^4+24 a^2 \sqrt{a^2+b^2} e^2 f x^2 d^4-12 b^2 \sqrt{a^2+b^2} e^2 f x^2 d^4+16 a^2 \sqrt{a^2+b^2} e^3 x d^4-8 b^2 \sqrt{a^2+b^2} e^3 x d^4+32 a^3 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3-16 a b \sqrt{a^2+b^2} e^3 \cosh (c+d x) d^3-16 a b \sqrt{a^2+b^2} f^3 x^3 \cosh (c+d x) d^3-48 a b \sqrt{a^2+b^2} e f^2 x^2 \cosh (c+d x) d^3-48 a b \sqrt{a^2+b^2} e^2 f x \cosh (c+d x) d^3-16 a^3 f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-48 a^3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-48 a^3 e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+16 a^3 f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+48 a^3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+48 a^3 e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+4 b^2 \sqrt{a^2+b^2} e^3 \sinh (2 (c+d x)) d^3+4 b^2 \sqrt{a^2+b^2} f^3 x^3 \sinh (2 (c+d x)) d^3+12 b^2 \sqrt{a^2+b^2} e f^2 x^2 \sinh (2 (c+d x)) d^3+12 b^2 \sqrt{a^2+b^2} e^2 f x \sinh (2 (c+d x)) d^3-6 b^2 \sqrt{a^2+b^2} f^3 x^2 \cosh (2 (c+d x)) d^2-6 b^2 \sqrt{a^2+b^2} e^2 f \cosh (2 (c+d x)) d^2-12 b^2 \sqrt{a^2+b^2} e f^2 x \cosh (2 (c+d x)) d^2-48 a^3 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2+48 a^3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2+48 a b \sqrt{a^2+b^2} f^3 x^2 \sinh (c+d x) d^2+48 a b \sqrt{a^2+b^2} e^2 f \sinh (c+d x) d^2+96 a b \sqrt{a^2+b^2} e f^2 x \sinh (c+d x) d^2-96 a b \sqrt{a^2+b^2} e f^2 \cosh (c+d x) d-96 a b \sqrt{a^2+b^2} f^3 x \cosh (c+d x) d+96 a^3 e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+96 a^3 f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-96 a^3 e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-96 a^3 f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+6 b^2 \sqrt{a^2+b^2} e f^2 \sinh (2 (c+d x)) d+6 b^2 \sqrt{a^2+b^2} f^3 x \sinh (2 (c+d x)) d-3 b^2 \sqrt{a^2+b^2} f^3 \cosh (2 (c+d x))-96 a^3 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+96 a^3 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+96 a b \sqrt{a^2+b^2} f^3 \sinh (c+d x)}{16 b^3 \sqrt{a^2+b^2} d^4}","\frac{a^2 (e+f x)^4}{4 b^3 f}-\frac{6 a^3 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^4 \sqrt{a^2+b^2}}+\frac{6 a^3 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^4 \sqrt{a^2+b^2}}+\frac{6 a^3 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^3 \sqrt{a^2+b^2}}-\frac{6 a^3 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^3 \sqrt{a^2+b^2}}-\frac{3 a^3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2 \sqrt{a^2+b^2}}+\frac{3 a^3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2 \sqrt{a^2+b^2}}-\frac{a^3 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d \sqrt{a^2+b^2}}+\frac{a^3 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d \sqrt{a^2+b^2}}+\frac{6 a f^3 \sinh (c+d x)}{b^2 d^4}-\frac{6 a f^2 (e+f x) \cosh (c+d x)}{b^2 d^3}+\frac{3 a f (e+f x)^2 \sinh (c+d x)}{b^2 d^2}-\frac{a (e+f x)^3 \cosh (c+d x)}{b^2 d}-\frac{3 f^3 \sinh ^2(c+d x)}{8 b d^4}+\frac{3 f^2 (e+f x) \sinh (c+d x) \cosh (c+d x)}{4 b d^3}-\frac{3 f (e+f x)^2 \sinh ^2(c+d x)}{4 b d^2}+\frac{(e+f x)^3 \sinh (c+d x) \cosh (c+d x)}{2 b d}-\frac{3 e f^2 x}{4 b d^2}-\frac{3 f^3 x^2}{8 b d^2}-\frac{(e+f x)^4}{8 b f}",1,"(16*a^2*Sqrt[a^2 + b^2]*d^4*e^3*x - 8*b^2*Sqrt[a^2 + b^2]*d^4*e^3*x + 24*a^2*Sqrt[a^2 + b^2]*d^4*e^2*f*x^2 - 12*b^2*Sqrt[a^2 + b^2]*d^4*e^2*f*x^2 + 16*a^2*Sqrt[a^2 + b^2]*d^4*e*f^2*x^3 - 8*b^2*Sqrt[a^2 + b^2]*d^4*e*f^2*x^3 + 4*a^2*Sqrt[a^2 + b^2]*d^4*f^3*x^4 - 2*b^2*Sqrt[a^2 + b^2]*d^4*f^3*x^4 + 32*a^3*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 16*a*b*Sqrt[a^2 + b^2]*d^3*e^3*Cosh[c + d*x] - 96*a*b*Sqrt[a^2 + b^2]*d*e*f^2*Cosh[c + d*x] - 48*a*b*Sqrt[a^2 + b^2]*d^3*e^2*f*x*Cosh[c + d*x] - 96*a*b*Sqrt[a^2 + b^2]*d*f^3*x*Cosh[c + d*x] - 48*a*b*Sqrt[a^2 + b^2]*d^3*e*f^2*x^2*Cosh[c + d*x] - 16*a*b*Sqrt[a^2 + b^2]*d^3*f^3*x^3*Cosh[c + d*x] - 6*b^2*Sqrt[a^2 + b^2]*d^2*e^2*f*Cosh[2*(c + d*x)] - 3*b^2*Sqrt[a^2 + b^2]*f^3*Cosh[2*(c + d*x)] - 12*b^2*Sqrt[a^2 + b^2]*d^2*e*f^2*x*Cosh[2*(c + d*x)] - 6*b^2*Sqrt[a^2 + b^2]*d^2*f^3*x^2*Cosh[2*(c + d*x)] - 48*a^3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 48*a^3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 16*a^3*d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 48*a^3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 48*a^3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 16*a^3*d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 48*a^3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 48*a^3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 96*a^3*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 96*a^3*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 96*a^3*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 96*a^3*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 96*a^3*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 96*a^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 48*a*b*Sqrt[a^2 + b^2]*d^2*e^2*f*Sinh[c + d*x] + 96*a*b*Sqrt[a^2 + b^2]*f^3*Sinh[c + d*x] + 96*a*b*Sqrt[a^2 + b^2]*d^2*e*f^2*x*Sinh[c + d*x] + 48*a*b*Sqrt[a^2 + b^2]*d^2*f^3*x^2*Sinh[c + d*x] + 4*b^2*Sqrt[a^2 + b^2]*d^3*e^3*Sinh[2*(c + d*x)] + 6*b^2*Sqrt[a^2 + b^2]*d*e*f^2*Sinh[2*(c + d*x)] + 12*b^2*Sqrt[a^2 + b^2]*d^3*e^2*f*x*Sinh[2*(c + d*x)] + 6*b^2*Sqrt[a^2 + b^2]*d*f^3*x*Sinh[2*(c + d*x)] + 12*b^2*Sqrt[a^2 + b^2]*d^3*e*f^2*x^2*Sinh[2*(c + d*x)] + 4*b^2*Sqrt[a^2 + b^2]*d^3*f^3*x^3*Sinh[2*(c + d*x)])/(16*b^3*Sqrt[a^2 + b^2]*d^4)","A",1
234,1,740,522,4.2319537,"\int \frac{(e+f x)^2 \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{24 a^2 e^2 x+24 a^2 e f x^2+8 a^2 f^2 x^3+\frac{48 a^3 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)}{d^3 \sqrt{a^2+b^2}}-\frac{48 a^3 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^3 \sqrt{a^2+b^2}}-\frac{48 a^3 f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)}{d^2 \sqrt{a^2+b^2}}+\frac{48 a^3 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \sqrt{a^2+b^2}}+\frac{48 a^3 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)}{d \sqrt{a^2+b^2}}-\frac{48 a^3 e f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \sqrt{a^2+b^2}}+\frac{48 a^3 e f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \sqrt{a^2+b^2}}-\frac{24 a^3 f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \sqrt{a^2+b^2}}+\frac{24 a^3 f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \sqrt{a^2+b^2}}-\frac{48 a b f^2 \cosh (c+d x)}{d^3}+\frac{48 a b e f \sinh (c+d x)}{d^2}+\frac{48 a b f^2 x \sinh (c+d x)}{d^2}-\frac{24 a b e^2 \cosh (c+d x)}{d}-\frac{48 a b e f x \cosh (c+d x)}{d}-\frac{24 a b f^2 x^2 \cosh (c+d x)}{d}+\frac{3 b^2 f^2 \sinh (2 (c+d x))}{d^3}-\frac{6 b^2 e f \cosh (2 (c+d x))}{d^2}-\frac{6 b^2 f^2 x \cosh (2 (c+d x))}{d^2}+\frac{6 b^2 e^2 \sinh (2 (c+d x))}{d}+\frac{12 b^2 e f x \sinh (2 (c+d x))}{d}+\frac{6 b^2 f^2 x^2 \sinh (2 (c+d x))}{d}-12 b^2 e^2 x-12 b^2 e f x^2-4 b^2 f^2 x^3}{24 b^3}","\frac{a^2 (e+f x)^3}{3 b^3 f}+\frac{2 a^3 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^3 \sqrt{a^2+b^2}}-\frac{2 a^3 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^3 \sqrt{a^2+b^2}}-\frac{2 a^3 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2 \sqrt{a^2+b^2}}+\frac{2 a^3 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2 \sqrt{a^2+b^2}}-\frac{a^3 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d \sqrt{a^2+b^2}}+\frac{a^3 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d \sqrt{a^2+b^2}}-\frac{2 a f^2 \cosh (c+d x)}{b^2 d^3}+\frac{2 a f (e+f x) \sinh (c+d x)}{b^2 d^2}-\frac{a (e+f x)^2 \cosh (c+d x)}{b^2 d}+\frac{f^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^3}-\frac{f (e+f x) \sinh ^2(c+d x)}{2 b d^2}+\frac{(e+f x)^2 \sinh (c+d x) \cosh (c+d x)}{2 b d}-\frac{f^2 x}{4 b d^2}-\frac{(e+f x)^3}{6 b f}",1,"(24*a^2*e^2*x - 12*b^2*e^2*x + 24*a^2*e*f*x^2 - 12*b^2*e*f*x^2 + 8*a^2*f^2*x^3 - 4*b^2*f^2*x^3 + (48*a^3*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d) - (24*a*b*e^2*Cosh[c + d*x])/d - (48*a*b*f^2*Cosh[c + d*x])/d^3 - (48*a*b*e*f*x*Cosh[c + d*x])/d - (24*a*b*f^2*x^2*Cosh[c + d*x])/d - (6*b^2*e*f*Cosh[2*(c + d*x)])/d^2 - (6*b^2*f^2*x*Cosh[2*(c + d*x)])/d^2 - (48*a^3*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*d) - (24*a^3*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*d) + (48*a^3*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*d) + (24*a^3*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*d) - (48*a^3*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*d^2) + (48*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*d^2) + (48*a^3*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*d^3) - (48*a^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*d^3) + (48*a*b*e*f*Sinh[c + d*x])/d^2 + (48*a*b*f^2*x*Sinh[c + d*x])/d^2 + (6*b^2*e^2*Sinh[2*(c + d*x)])/d + (3*b^2*f^2*Sinh[2*(c + d*x)])/d^3 + (12*b^2*e*f*x*Sinh[2*(c + d*x)])/d + (6*b^2*f^2*x^2*Sinh[2*(c + d*x)])/d)/(24*b^3)","A",1
235,1,307,335,2.5587663,"\int \frac{(e+f x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{-2 \left(2 a^2-b^2\right) (c+d x) (c f-d (2 e+f x))+\frac{8 a^3 \left(2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2}}-8 a b d (e+f x) \cosh (c+d x)+8 a b f \sinh (c+d x)+2 b^2 d (e+f x) \sinh (2 (c+d x))-b^2 f \cosh (2 (c+d x))}{8 b^3 d^2}","\frac{a^2 e x}{b^3}+\frac{a^2 f x^2}{2 b^3}-\frac{a^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2 \sqrt{a^2+b^2}}+\frac{a^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2 \sqrt{a^2+b^2}}-\frac{a^3 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d \sqrt{a^2+b^2}}+\frac{a^3 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d \sqrt{a^2+b^2}}+\frac{a f \sinh (c+d x)}{b^2 d^2}-\frac{a (e+f x) \cosh (c+d x)}{b^2 d}-\frac{f \sinh ^2(c+d x)}{4 b d^2}+\frac{(e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b d}-\frac{e x}{2 b}-\frac{f x^2}{4 b}",1,"(-2*(2*a^2 - b^2)*(c + d*x)*(c*f - d*(2*e + f*x)) - 8*a*b*d*(e + f*x)*Cosh[c + d*x] - b^2*f*Cosh[2*(c + d*x)] + (8*a^3*(2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] + 8*a*b*f*Sinh[c + d*x] + 2*b^2*d*(e + f*x)*Sinh[2*(c + d*x)])/(8*b^3*d^2)","A",1
236,1,101,107,0.3055608,"\int \frac{\sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Sinh[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","\frac{-2 \left(b^2-2 a^2\right) (c+d x)-\frac{8 a^3 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-4 a b \cosh (c+d x)+b^2 \sinh (2 (c+d x))}{4 b^3 d}","\frac{x \left(2 a^2-b^2\right)}{2 b^3}+\frac{2 a^3 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b^3 d \sqrt{a^2+b^2}}-\frac{a \cosh (c+d x)}{b^2 d}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d}",1,"(-2*(-2*a^2 + b^2)*(c + d*x) - (8*a^3*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[c + d*x] + b^2*Sinh[2*(c + d*x)])/(4*b^3*d)","A",1
237,-1,0,31,180.0002073,"\int \frac{\sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Sinh[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
238,1,757,605,2.8960668,"\int \frac{(e+f x)^3 \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\frac{b \left(2 d^3 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-3 d^3 e^2 f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+3 d^3 e^2 f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-3 d^3 e f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+3 d^3 e f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-d^3 f^3 x^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+d^3 f^3 x^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-3 d^2 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+3 d^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+6 d e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-6 d e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+6 d f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-6 d f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-6 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2}}-2 d^3 (e+f x)^3 \tanh ^{-1}(\sinh (c+d x)+\cosh (c+d x))-3 f \left(d^2 (e+f x)^2 \text{Li}_2(-\cosh (c+d x)-\sinh (c+d x))-2 d f (e+f x) \text{Li}_3(-\cosh (c+d x)-\sinh (c+d x))+2 f^2 \text{Li}_4(-\cosh (c+d x)-\sinh (c+d x))\right)+3 f \left(d^2 (e+f x)^2 \text{Li}_2(\cosh (c+d x)+\sinh (c+d x))-2 d f (e+f x) \text{Li}_3(\cosh (c+d x)+\sinh (c+d x))+2 f^2 \text{Li}_4(\cosh (c+d x)+\sinh (c+d x))\right)}{a d^4}","-\frac{6 b f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^4 \sqrt{a^2+b^2}}+\frac{6 b f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^4 \sqrt{a^2+b^2}}+\frac{6 b f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{6 b f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{3 b f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}+\frac{3 b f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{b (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{b (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a d \sqrt{a^2+b^2}}-\frac{6 f^3 \text{Li}_4\left(-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{Li}_4\left(e^{c+d x}\right)}{a d^4}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}",1,"(-2*d^3*(e + f*x)^3*ArcTanh[Cosh[c + d*x] + Sinh[c + d*x]] + (b*(2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] - 3*f*(d^2*(e + f*x)^2*PolyLog[2, -Cosh[c + d*x] - Sinh[c + d*x]] - 2*d*f*(e + f*x)*PolyLog[3, -Cosh[c + d*x] - Sinh[c + d*x]] + 2*f^2*PolyLog[4, -Cosh[c + d*x] - Sinh[c + d*x]]) + 3*f*(d^2*(e + f*x)^2*PolyLog[2, Cosh[c + d*x] + Sinh[c + d*x]] - 2*d*f*(e + f*x)*PolyLog[3, Cosh[c + d*x] + Sinh[c + d*x]] + 2*f^2*PolyLog[4, Cosh[c + d*x] + Sinh[c + d*x]]))/(a*d^4)","A",0
239,1,454,433,1.9038052,"\int \frac{(e+f x)^2 \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\frac{b \left(2 d^2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-2 d^2 e f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+2 d^2 e f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 d f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 d f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2}}+d^2 (e+f x)^2 \log \left(1-e^{c+d x}\right)-d^2 (e+f x)^2 \log \left(e^{c+d x}+1\right)-2 d f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)+2 d f (e+f x) \text{Li}_2\left(e^{c+d x}\right)+2 f^2 \text{Li}_3\left(-e^{c+d x}\right)-2 f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}","\frac{2 b f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{2 b f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{2 b f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}+\frac{2 b f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{b (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{b (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{2 f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{2 f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{2 f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}",1,"(d^2*(e + f*x)^2*Log[1 - E^(c + d*x)] - d^2*(e + f*x)^2*Log[1 + E^(c + d*x)] - 2*d*f*(e + f*x)*PolyLog[2, -E^(c + d*x)] + 2*d*f*(e + f*x)*PolyLog[2, E^(c + d*x)] + 2*f^2*PolyLog[3, -E^(c + d*x)] - 2*f^2*PolyLog[3, E^(c + d*x)] + (b*(2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2])/(a*d^3)","A",1
240,1,306,261,1.8169729,"\int \frac{(e+f x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\frac{b \left(2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2}}+d e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+f \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)+(c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right)-c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a d^2}","-\frac{b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}+\frac{b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{b (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a d \sqrt{a^2+b^2}}+\frac{b (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a d \sqrt{a^2+b^2}}-\frac{f \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{f \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d}",1,"(d*e*Log[Tanh[(c + d*x)/2]] - c*f*Log[Tanh[(c + d*x)/2]] + f*((c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)]) + (b*(2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2])/(a*d^2)","A",1
241,1,69,64,0.0753514,"\int \frac{\text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Csch[c + d*x]/(a + b*Sinh[c + d*x]),x]","\frac{\log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)-\frac{2 b \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}}{a d}","\frac{2 b \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a d \sqrt{a^2+b^2}}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}",1,"((-2*b*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + Log[Tanh[(c + d*x)/2]])/(a*d)","A",1
242,0,0,29,5.7515629,"\int \frac{\text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Csch[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Csch[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
243,1,1353,745,17.5695149,"\int \frac{(e+f x)^3 \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(-2 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3+f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+3 e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2-3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2-6 e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-6 f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+6 e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+6 f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+6 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) b^2}{a^2 \sqrt{a^2+b^2} d^4}-\frac{-b d^3 x^3 \log (\cosh (c+d x)-\sinh (c+d x)+1) f^3+b d^3 x^3 \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^3-3 b \left(d^2 \text{Li}_2(\cosh (c+d x)-\sinh (c+d x)) x^2+2 (d x \text{Li}_3(\cosh (c+d x)-\sinh (c+d x))+\text{Li}_4(\cosh (c+d x)-\sinh (c+d x)))\right) f^3+3 b \left(d^2 \text{Li}_2(\sinh (c+d x)-\cosh (c+d x)) x^2+2 (d x \text{Li}_3(\sinh (c+d x)-\cosh (c+d x))+\text{Li}_4(\sinh (c+d x)-\cosh (c+d x)))\right) f^3-3 d^2 (b d e+a f) x^2 \log (\cosh (c+d x)-\sinh (c+d x)+1) f^2+3 d^2 (b d e-a f) x^2 \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^2+6 (a f-b d e) (d x \text{Li}_2(\cosh (c+d x)-\sinh (c+d x))+\text{Li}_3(\cosh (c+d x)-\sinh (c+d x))) f^2+6 (b d e+a f) (d x \text{Li}_2(\sinh (c+d x)-\cosh (c+d x))+\text{Li}_3(\sinh (c+d x)-\cosh (c+d x))) f^2-3 d^2 e (b d e+2 a f) x \log (\cosh (c+d x)-\sinh (c+d x)+1) f+3 d^2 e (b d e-2 a f) x \log (-\cosh (c+d x)+\sinh (c+d x)+1) f-3 d e (b d e-2 a f) \text{Li}_2(\cosh (c+d x)-\sinh (c+d x)) f+3 d e (b d e+2 a f) \text{Li}_2(\sinh (c+d x)-\cosh (c+d x)) f+a d^3 (e+f x)^3 (\coth (c)-1)-d^2 e^2 (b d e-3 a f) (d x-\log (-\cosh (c+d x)-\sinh (c+d x)+1))+d^2 e^2 (b d e+3 a f) (d x-\log (\cosh (c+d x)+\sinh (c+d x)+1))}{a^2 d^4}+\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(-\sinh \left(\frac{d x}{2}\right) e^3-3 f x \sinh \left(\frac{d x}{2}\right) e^2-3 f^2 x^2 \sinh \left(\frac{d x}{2}\right) e-f^3 x^3 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(\sinh \left(\frac{d x}{2}\right) e^3+3 f x \sinh \left(\frac{d x}{2}\right) e^2+3 f^2 x^2 \sinh \left(\frac{d x}{2}\right) e+f^3 x^3 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}","\frac{6 b^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^4 \sqrt{a^2+b^2}}-\frac{6 b^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^4 \sqrt{a^2+b^2}}-\frac{6 b^2 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^3 \sqrt{a^2+b^2}}+\frac{6 b^2 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^3 \sqrt{a^2+b^2}}+\frac{3 b^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2 \sqrt{a^2+b^2}}-\frac{3 b^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2 \sqrt{a^2+b^2}}+\frac{b^2 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d \sqrt{a^2+b^2}}-\frac{b^2 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d \sqrt{a^2+b^2}}+\frac{6 b f^3 \text{Li}_4\left(-e^{c+d x}\right)}{a^2 d^4}-\frac{6 b f^3 \text{Li}_4\left(e^{c+d x}\right)}{a^2 d^4}-\frac{6 b f^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right)}{a^2 d^3}+\frac{6 b f^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right)}{a^2 d^3}+\frac{3 b f (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right)}{a^2 d^2}-\frac{3 b f (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right)}{a^2 d^2}+\frac{2 b (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}-\frac{3 f^3 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a d^4}+\frac{3 f^2 (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^3}+\frac{3 f (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a d^2}-\frac{(e+f x)^3 \coth (c+d x)}{a d}-\frac{(e+f x)^3}{a d}",1,"(b^2*(-2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^2*Sqrt[a^2 + b^2]*d^4) - (a*d^3*(e + f*x)^3*(-1 + Coth[c]) - d^2*e^2*(b*d*e - 3*a*f)*(d*x - Log[1 - Cosh[c + d*x] - Sinh[c + d*x]]) - 3*d^2*e*f*(b*d*e + 2*a*f)*x*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - 3*d^2*f^2*(b*d*e + a*f)*x^2*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - b*d^3*f^3*x^3*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] + 3*d^2*e*f*(b*d*e - 2*a*f)*x*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] + 3*d^2*f^2*(b*d*e - a*f)*x^2*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] + b*d^3*f^3*x^3*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] + d^2*e^2*(b*d*e + 3*a*f)*(d*x - Log[1 + Cosh[c + d*x] + Sinh[c + d*x]]) - 3*d*e*f*(b*d*e - 2*a*f)*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 3*d*e*f*(b*d*e + 2*a*f)*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 6*f^2*(-(b*d*e) + a*f)*(d*x*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]]) + 6*f^2*(b*d*e + a*f)*(d*x*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]]) - 3*b*f^3*(d^2*x^2*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 2*(d*x*PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[4, Cosh[c + d*x] - Sinh[c + d*x]])) + 3*b*f^3*(d^2*x^2*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 2*(d*x*PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[4, -Cosh[c + d*x] + Sinh[c + d*x]])))/(a^2*d^4) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(-(e^3*Sinh[(d*x)/2]) - 3*e^2*f*x*Sinh[(d*x)/2] - 3*e*f^2*x^2*Sinh[(d*x)/2] - f^3*x^3*Sinh[(d*x)/2]))/(2*a*d) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2]))/(2*a*d)","A",1
244,1,795,535,15.6170477,"\int \frac{(e+f x)^2 \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(-2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^2+f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2+2 e f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2-f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2-2 e f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2+2 f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) b^2}{a^2 \sqrt{a^2+b^2} d^3}-\frac{b d^2 x^2 \log \left(1-e^{-c-d x}\right) f^2-b d^2 x^2 \log \left(1+e^{-c-d x}\right) f^2+2 b \left(d x \text{Li}_2\left(-e^{-c-d x}\right)+\text{Li}_3\left(-e^{-c-d x}\right)\right) f^2-2 b \left(d x \text{Li}_2\left(e^{-c-d x}\right)+\text{Li}_3\left(e^{-c-d x}\right)\right) f^2+2 d (b d e-a f) x \log \left(1-e^{-c-d x}\right) f-2 d (b d e+a f) x \log \left(1+e^{-c-d x}\right) f+2 (b d e+a f) \text{Li}_2\left(-e^{-c-d x}\right) f+2 (a f-b d e) \text{Li}_2\left(e^{-c-d x}\right) f+\frac{2 a d^2 (e+f x)^2}{-1+e^{2 c}}-d e (b d e-2 a f) \left(d x-\log \left(1-e^{c+d x}\right)\right)+d e (b d e+2 a f) \left(d x-\log \left(1+e^{c+d x}\right)\right)}{a^2 d^3}+\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(-\sinh \left(\frac{d x}{2}\right) e^2-2 f x \sinh \left(\frac{d x}{2}\right) e-f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(\sinh \left(\frac{d x}{2}\right) e^2+2 f x \sinh \left(\frac{d x}{2}\right) e+f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}","-\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^3 \sqrt{a^2+b^2}}+\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^3 \sqrt{a^2+b^2}}+\frac{2 b^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2 \sqrt{a^2+b^2}}-\frac{2 b^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2 \sqrt{a^2+b^2}}+\frac{b^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d \sqrt{a^2+b^2}}-\frac{b^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d \sqrt{a^2+b^2}}-\frac{2 b f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a^2 d^3}+\frac{2 b f^2 \text{Li}_3\left(e^{c+d x}\right)}{a^2 d^3}+\frac{2 b f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a^2 d^2}-\frac{2 b f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a^2 d^2}+\frac{2 b (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\frac{f^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^3}+\frac{2 f (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d^2}-\frac{(e+f x)^2 \coth (c+d x)}{a d}-\frac{(e+f x)^2}{a d}",1,"-(((2*a*d^2*(e + f*x)^2)/(-1 + E^(2*c)) + 2*d*f*(b*d*e - a*f)*x*Log[1 - E^(-c - d*x)] + b*d^2*f^2*x^2*Log[1 - E^(-c - d*x)] - 2*d*f*(b*d*e + a*f)*x*Log[1 + E^(-c - d*x)] - b*d^2*f^2*x^2*Log[1 + E^(-c - d*x)] - d*e*(b*d*e - 2*a*f)*(d*x - Log[1 - E^(c + d*x)]) + d*e*(b*d*e + 2*a*f)*(d*x - Log[1 + E^(c + d*x)]) + 2*f*(b*d*e + a*f)*PolyLog[2, -E^(-c - d*x)] + 2*f*(-(b*d*e) + a*f)*PolyLog[2, E^(-c - d*x)] + 2*b*f^2*(d*x*PolyLog[2, -E^(-c - d*x)] + PolyLog[3, -E^(-c - d*x)]) - 2*b*f^2*(d*x*PolyLog[2, E^(-c - d*x)] + PolyLog[3, E^(-c - d*x)]))/(a^2*d^3)) + (b^2*(-2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^2*Sqrt[a^2 + b^2]*d^3) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(-(e^2*Sinh[(d*x)/2]) - 2*e*f*x*Sinh[(d*x)/2] - f^2*x^2*Sinh[(d*x)/2]))/(2*a*d) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^2*Sinh[(d*x)/2] + 2*e*f*x*Sinh[(d*x)/2] + f^2*x^2*Sinh[(d*x)/2]))/(2*a*d)","A",1
245,1,405,306,5.2024542,"\int \frac{(e+f x) \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\frac{2 b^2 \left(-2 d e \tanh ^{-1}\left(\frac{a+b \sinh (c+d x)+b \cosh (c+d x)}{\sqrt{a^2+b^2}}\right)+f \text{Li}_2\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{a-\sqrt{a^2+b^2}}+1\right)-f (c+d x) \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{\sqrt{a^2+b^2}+a}+1\right)+2 c f \tanh ^{-1}\left(\frac{a+b \sinh (c+d x)+b \cosh (c+d x)}{\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2}}-a d (e+f x) \tanh \left(\frac{1}{2} (c+d x)\right)-a d (e+f x) \coth \left(\frac{1}{2} (c+d x)\right)+2 a f \log (\sinh (c+d x))-2 b d e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+2 b f \left(-\text{Li}_2\left(-e^{-c-d x}\right)+\text{Li}_2\left(e^{-c-d x}\right)-\left((c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right)\right)+2 b c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a^2 d^2}","\frac{b^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2 \sqrt{a^2+b^2}}-\frac{b^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2 \sqrt{a^2+b^2}}+\frac{b^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d \sqrt{a^2+b^2}}-\frac{b^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d \sqrt{a^2+b^2}}+\frac{b f \text{Li}_2\left(-e^{c+d x}\right)}{a^2 d^2}-\frac{b f \text{Li}_2\left(e^{c+d x}\right)}{a^2 d^2}+\frac{2 b (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\frac{f \log (\sinh (c+d x))}{a d^2}-\frac{(e+f x) \coth (c+d x)}{a d}",1,"(-(a*d*(e + f*x)*Coth[(c + d*x)/2]) + 2*a*f*Log[Sinh[c + d*x]] - 2*b*d*e*Log[Tanh[(c + d*x)/2]] + 2*b*c*f*Log[Tanh[(c + d*x)/2]] + 2*b*f*(-((c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)])) - PolyLog[2, -E^(-c - d*x)] + PolyLog[2, E^(-c - d*x)]) + (2*b^2*(-2*d*e*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + 2*c*f*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + f*(c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - f*(c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + f*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] - a*d*(e + f*x)*Tanh[(c + d*x)/2])/(2*a^2*d^2)","A",1
246,1,100,80,0.7385225,"\int \frac{\text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Csch[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","-\frac{2 b \left(\log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)-\frac{2 b \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}\right)+a \tanh \left(\frac{1}{2} (c+d x)\right)+a \coth \left(\frac{1}{2} (c+d x)\right)}{2 a^2 d}","-\frac{2 b^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a^2 d \sqrt{a^2+b^2}}+\frac{b \tanh ^{-1}(\cosh (c+d x))}{a^2 d}-\frac{\coth (c+d x)}{a d}",1,"-1/2*(a*Coth[(c + d*x)/2] + 2*b*((-2*b*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] + Log[Tanh[(c + d*x)/2]]) + a*Tanh[(c + d*x)/2])/(a^2*d)","A",1
247,0,0,31,114.2402857,"\int \frac{\text{csch}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Csch[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Csch[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
248,1,2800,1053,41.5347384,"\int \frac{(e+f x)^3 \text{csch}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Csch[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^3}{a^3 \sqrt{a^2+b^2} d}+\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^3}{a^3 \sqrt{a^2+b^2} d}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a^3 \sqrt{a^2+b^2} d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a^3 \sqrt{a^2+b^2} d^2}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a^3 \sqrt{a^2+b^2} d^3}-\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a^3 \sqrt{a^2+b^2} d^3}-\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a^3 \sqrt{a^2+b^2} d^4}+\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a^3 \sqrt{a^2+b^2} d^4}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right) b^2}{a^3 d}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right) b^2}{a^3 d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right) b^2}{a^3 d^2}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right) b^2}{a^3 d^3}-\frac{6 f^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right) b^2}{a^3 d^3}-\frac{6 f^3 \text{Li}_4\left(-e^{c+d x}\right) b^2}{a^3 d^4}+\frac{6 f^3 \text{Li}_4\left(e^{c+d x}\right) b^2}{a^3 d^4}+\frac{(e+f x)^3 b}{a^2 d}+\frac{(e+f x)^3 \coth (c+d x) b}{a^2 d}-\frac{3 f (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right) b}{a^2 d^2}-\frac{3 f^2 (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right) b}{a^2 d^3}+\frac{3 f^3 \text{Li}_3\left(e^{2 (c+d x)}\right) b}{2 a^2 d^4}+\frac{(e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{6 f^2 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{csch}(c+d x)}{2 a d^2}-\frac{(e+f x)^3 \coth (c+d x) \text{csch}(c+d x)}{2 a d}-\frac{3 f^3 \text{Li}_2\left(-e^{c+d x}\right)}{a d^4}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right)}{2 a d^2}+\frac{3 f^3 \text{Li}_2\left(e^{c+d x}\right)}{a d^4}-\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right)}{2 a d^2}-\frac{3 f^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}+\frac{3 f^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right)}{a d^3}+\frac{3 f^3 \text{Li}_4\left(-e^{c+d x}\right)}{a d^4}-\frac{3 f^3 \text{Li}_4\left(e^{c+d x}\right)}{a d^4}",1,"(12*a*b*d^3*e^2*E^(2*c)*f*x + 12*a*b*d^3*e*E^(2*c)*f^2*x^2 + 4*a*b*d^3*E^(2*c)*f^3*x^3 - 2*a^2*d^3*e^3*ArcTanh[E^(c + d*x)] + 4*b^2*d^3*e^3*ArcTanh[E^(c + d*x)] + 2*a^2*d^3*e^3*E^(2*c)*ArcTanh[E^(c + d*x)] - 4*b^2*d^3*e^3*E^(2*c)*ArcTanh[E^(c + d*x)] + 12*a^2*d*e*f^2*ArcTanh[E^(c + d*x)] - 12*a^2*d*e*E^(2*c)*f^2*ArcTanh[E^(c + d*x)] + 3*a^2*d^3*e^2*f*x*Log[1 - E^(c + d*x)] - 6*b^2*d^3*e^2*f*x*Log[1 - E^(c + d*x)] - 3*a^2*d^3*e^2*E^(2*c)*f*x*Log[1 - E^(c + d*x)] + 6*b^2*d^3*e^2*E^(2*c)*f*x*Log[1 - E^(c + d*x)] - 6*a^2*d*f^3*x*Log[1 - E^(c + d*x)] + 6*a^2*d*E^(2*c)*f^3*x*Log[1 - E^(c + d*x)] + 3*a^2*d^3*e*f^2*x^2*Log[1 - E^(c + d*x)] - 6*b^2*d^3*e*f^2*x^2*Log[1 - E^(c + d*x)] - 3*a^2*d^3*e*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] + 6*b^2*d^3*e*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] + a^2*d^3*f^3*x^3*Log[1 - E^(c + d*x)] - 2*b^2*d^3*f^3*x^3*Log[1 - E^(c + d*x)] - a^2*d^3*E^(2*c)*f^3*x^3*Log[1 - E^(c + d*x)] + 2*b^2*d^3*E^(2*c)*f^3*x^3*Log[1 - E^(c + d*x)] - 3*a^2*d^3*e^2*f*x*Log[1 + E^(c + d*x)] + 6*b^2*d^3*e^2*f*x*Log[1 + E^(c + d*x)] + 3*a^2*d^3*e^2*E^(2*c)*f*x*Log[1 + E^(c + d*x)] - 6*b^2*d^3*e^2*E^(2*c)*f*x*Log[1 + E^(c + d*x)] + 6*a^2*d*f^3*x*Log[1 + E^(c + d*x)] - 6*a^2*d*E^(2*c)*f^3*x*Log[1 + E^(c + d*x)] - 3*a^2*d^3*e*f^2*x^2*Log[1 + E^(c + d*x)] + 6*b^2*d^3*e*f^2*x^2*Log[1 + E^(c + d*x)] + 3*a^2*d^3*e*E^(2*c)*f^2*x^2*Log[1 + E^(c + d*x)] - 6*b^2*d^3*e*E^(2*c)*f^2*x^2*Log[1 + E^(c + d*x)] - a^2*d^3*f^3*x^3*Log[1 + E^(c + d*x)] + 2*b^2*d^3*f^3*x^3*Log[1 + E^(c + d*x)] + a^2*d^3*E^(2*c)*f^3*x^3*Log[1 + E^(c + d*x)] - 2*b^2*d^3*E^(2*c)*f^3*x^3*Log[1 + E^(c + d*x)] + 6*a*b*d^2*e^2*f*Log[1 - E^(2*(c + d*x))] - 6*a*b*d^2*e^2*E^(2*c)*f*Log[1 - E^(2*(c + d*x))] + 12*a*b*d^2*e*f^2*x*Log[1 - E^(2*(c + d*x))] - 12*a*b*d^2*e*E^(2*c)*f^2*x*Log[1 - E^(2*(c + d*x))] + 6*a*b*d^2*f^3*x^2*Log[1 - E^(2*(c + d*x))] - 6*a*b*d^2*E^(2*c)*f^3*x^2*Log[1 - E^(2*(c + d*x))] + 3*(-1 + E^(2*c))*f*(-2*b^2*d^2*(e + f*x)^2 + a^2*(-2*f^2 + d^2*(e + f*x)^2))*PolyLog[2, -E^(c + d*x)] - 3*(-1 + E^(2*c))*f*(-2*b^2*d^2*(e + f*x)^2 + a^2*(-2*f^2 + d^2*(e + f*x)^2))*PolyLog[2, E^(c + d*x)] + 6*a*b*d*e*f^2*PolyLog[2, E^(2*(c + d*x))] - 6*a*b*d*e*E^(2*c)*f^2*PolyLog[2, E^(2*(c + d*x))] + 6*a*b*d*f^3*x*PolyLog[2, E^(2*(c + d*x))] - 6*a*b*d*E^(2*c)*f^3*x*PolyLog[2, E^(2*(c + d*x))] + 6*a^2*d*e*f^2*PolyLog[3, -E^(c + d*x)] - 12*b^2*d*e*f^2*PolyLog[3, -E^(c + d*x)] - 6*a^2*d*e*E^(2*c)*f^2*PolyLog[3, -E^(c + d*x)] + 12*b^2*d*e*E^(2*c)*f^2*PolyLog[3, -E^(c + d*x)] + 6*a^2*d*f^3*x*PolyLog[3, -E^(c + d*x)] - 12*b^2*d*f^3*x*PolyLog[3, -E^(c + d*x)] - 6*a^2*d*E^(2*c)*f^3*x*PolyLog[3, -E^(c + d*x)] + 12*b^2*d*E^(2*c)*f^3*x*PolyLog[3, -E^(c + d*x)] - 6*a^2*d*e*f^2*PolyLog[3, E^(c + d*x)] + 12*b^2*d*e*f^2*PolyLog[3, E^(c + d*x)] + 6*a^2*d*e*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)] - 12*b^2*d*e*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)] - 6*a^2*d*f^3*x*PolyLog[3, E^(c + d*x)] + 12*b^2*d*f^3*x*PolyLog[3, E^(c + d*x)] + 6*a^2*d*E^(2*c)*f^3*x*PolyLog[3, E^(c + d*x)] - 12*b^2*d*E^(2*c)*f^3*x*PolyLog[3, E^(c + d*x)] - 3*a*b*f^3*PolyLog[3, E^(2*(c + d*x))] + 3*a*b*E^(2*c)*f^3*PolyLog[3, E^(2*(c + d*x))] - 6*a^2*f^3*PolyLog[4, -E^(c + d*x)] + 12*b^2*f^3*PolyLog[4, -E^(c + d*x)] + 6*a^2*E^(2*c)*f^3*PolyLog[4, -E^(c + d*x)] - 12*b^2*E^(2*c)*f^3*PolyLog[4, -E^(c + d*x)] + 6*a^2*f^3*PolyLog[4, E^(c + d*x)] - 12*b^2*f^3*PolyLog[4, E^(c + d*x)] - 6*a^2*E^(2*c)*f^3*PolyLog[4, E^(c + d*x)] + 12*b^2*E^(2*c)*f^3*PolyLog[4, E^(c + d*x)])/(2*a^3*d^4*(-1 + E^(2*c))) + (b^3*(2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^3*Sqrt[a^2 + b^2]*d^4) + (Csch[c]*Csch[c + d*x]^2*(2*b*d*e^3*Cosh[c] + 6*b*d*e^2*f*x*Cosh[c] + 6*b*d*e*f^2*x^2*Cosh[c] + 2*b*d*f^3*x^3*Cosh[c] + 3*a*e^2*f*Cosh[d*x] + 6*a*e*f^2*x*Cosh[d*x] + 3*a*f^3*x^2*Cosh[d*x] - 3*a*e^2*f*Cosh[2*c + d*x] - 6*a*e*f^2*x*Cosh[2*c + d*x] - 3*a*f^3*x^2*Cosh[2*c + d*x] - 2*b*d*e^3*Cosh[c + 2*d*x] - 6*b*d*e^2*f*x*Cosh[c + 2*d*x] - 6*b*d*e*f^2*x^2*Cosh[c + 2*d*x] - 2*b*d*f^3*x^3*Cosh[c + 2*d*x] + a*d*e^3*Sinh[d*x] + 3*a*d*e^2*f*x*Sinh[d*x] + 3*a*d*e*f^2*x^2*Sinh[d*x] + a*d*f^3*x^3*Sinh[d*x] - a*d*e^3*Sinh[2*c + d*x] - 3*a*d*e^2*f*x*Sinh[2*c + d*x] - 3*a*d*e*f^2*x^2*Sinh[2*c + d*x] - a*d*f^3*x^3*Sinh[2*c + d*x]))/(4*a^2*d^2)","B",0
249,1,1531,725,24.567645,"\int \frac{(e+f x)^2 \text{csch}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{\left(2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^2-f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2-2 e f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2+f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2+2 e f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2-2 f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) b^3}{a^3 \sqrt{a^2+b^2} d^3}+\frac{4 a b e^{2 c} f^2 x^2 d^2+8 a b e e^{2 c} f x d^2+2 a^2 e^2 e^{2 c} \tanh ^{-1}\left(e^{c+d x}\right) d^2-4 b^2 e^2 e^{2 c} \tanh ^{-1}\left(e^{c+d x}\right) d^2-2 a^2 e^2 \tanh ^{-1}\left(e^{c+d x}\right) d^2+4 b^2 e^2 \tanh ^{-1}\left(e^{c+d x}\right) d^2-a^2 e^{2 c} f^2 x^2 \log \left(1-e^{c+d x}\right) d^2+2 b^2 e^{2 c} f^2 x^2 \log \left(1-e^{c+d x}\right) d^2+a^2 f^2 x^2 \log \left(1-e^{c+d x}\right) d^2-2 b^2 f^2 x^2 \log \left(1-e^{c+d x}\right) d^2-2 a^2 e e^{2 c} f x \log \left(1-e^{c+d x}\right) d^2+4 b^2 e e^{2 c} f x \log \left(1-e^{c+d x}\right) d^2+2 a^2 e f x \log \left(1-e^{c+d x}\right) d^2-4 b^2 e f x \log \left(1-e^{c+d x}\right) d^2+a^2 e^{2 c} f^2 x^2 \log \left(1+e^{c+d x}\right) d^2-2 b^2 e^{2 c} f^2 x^2 \log \left(1+e^{c+d x}\right) d^2-a^2 f^2 x^2 \log \left(1+e^{c+d x}\right) d^2+2 b^2 f^2 x^2 \log \left(1+e^{c+d x}\right) d^2+2 a^2 e e^{2 c} f x \log \left(1+e^{c+d x}\right) d^2-4 b^2 e e^{2 c} f x \log \left(1+e^{c+d x}\right) d^2-2 a^2 e f x \log \left(1+e^{c+d x}\right) d^2+4 b^2 e f x \log \left(1+e^{c+d x}\right) d^2-4 a b e e^{2 c} f \log \left(1-e^{2 (c+d x)}\right) d+4 a b e f \log \left(1-e^{2 (c+d x)}\right) d-4 a b e^{2 c} f^2 x \log \left(1-e^{2 (c+d x)}\right) d+4 a b f^2 x \log \left(1-e^{2 (c+d x)}\right) d+2 \left(a^2-2 b^2\right) \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-e^{c+d x}\right) d-2 \left(a^2-2 b^2\right) \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(e^{c+d x}\right) d-4 a^2 e^{2 c} f^2 \tanh ^{-1}\left(e^{c+d x}\right)+4 a^2 f^2 \tanh ^{-1}\left(e^{c+d x}\right)-2 a b e^{2 c} f^2 \text{Li}_2\left(e^{2 (c+d x)}\right)+2 a b f^2 \text{Li}_2\left(e^{2 (c+d x)}\right)-2 a^2 e^{2 c} f^2 \text{Li}_3\left(-e^{c+d x}\right)+4 b^2 e^{2 c} f^2 \text{Li}_3\left(-e^{c+d x}\right)+2 a^2 f^2 \text{Li}_3\left(-e^{c+d x}\right)-4 b^2 f^2 \text{Li}_3\left(-e^{c+d x}\right)+2 a^2 e^{2 c} f^2 \text{Li}_3\left(e^{c+d x}\right)-4 b^2 e^{2 c} f^2 \text{Li}_3\left(e^{c+d x}\right)-2 a^2 f^2 \text{Li}_3\left(e^{c+d x}\right)+4 b^2 f^2 \text{Li}_3\left(e^{c+d x}\right)}{2 a^3 d^3 \left(-1+e^{2 c}\right)}+\frac{\text{csch}(c) \text{csch}^2(c+d x) \left(2 b d \cosh (c) e^2-2 b d \cosh (c+2 d x) e^2+a d \sinh (d x) e^2-a d \sinh (2 c+d x) e^2+4 b d f x \cosh (c) e+2 a f \cosh (d x) e-2 a f \cosh (2 c+d x) e-4 b d f x \cosh (c+2 d x) e+2 a d f x \sinh (d x) e-2 a d f x \sinh (2 c+d x) e+2 b d f^2 x^2 \cosh (c)+2 a f^2 x \cosh (d x)-2 a f^2 x \cosh (2 c+d x)-2 b d f^2 x^2 \cosh (c+2 d x)+a d f^2 x^2 \sinh (d x)-a d f^2 x^2 \sinh (2 c+d x)\right)}{4 a^2 d^2}","\frac{2 b^2 f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a^3 d^3}-\frac{2 b^2 f^2 \text{Li}_3\left(e^{c+d x}\right)}{a^3 d^3}-\frac{2 b^2 f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a^3 d^2}+\frac{2 b^2 f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a^3 d^2}-\frac{2 b^2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^3 d}-\frac{b f^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{a^2 d^3}-\frac{2 b f (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a^2 d^2}+\frac{b (e+f x)^2 \coth (c+d x)}{a^2 d}+\frac{b (e+f x)^2}{a^2 d}+\frac{2 b^3 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^3 \sqrt{a^2+b^2}}-\frac{2 b^3 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^3 \sqrt{a^2+b^2}}-\frac{2 b^3 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2 \sqrt{a^2+b^2}}+\frac{2 b^3 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2 \sqrt{a^2+b^2}}-\frac{b^3 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d \sqrt{a^2+b^2}}+\frac{b^3 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d \sqrt{a^2+b^2}}-\frac{f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}+\frac{f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{f^2 \tanh ^{-1}(\cosh (c+d x))}{a d^3}+\frac{f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}-\frac{f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{f (e+f x) \text{csch}(c+d x)}{a d^2}+\frac{(e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{(e+f x)^2 \coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"(8*a*b*d^2*e*E^(2*c)*f*x + 4*a*b*d^2*E^(2*c)*f^2*x^2 - 2*a^2*d^2*e^2*ArcTanh[E^(c + d*x)] + 4*b^2*d^2*e^2*ArcTanh[E^(c + d*x)] + 2*a^2*d^2*e^2*E^(2*c)*ArcTanh[E^(c + d*x)] - 4*b^2*d^2*e^2*E^(2*c)*ArcTanh[E^(c + d*x)] + 4*a^2*f^2*ArcTanh[E^(c + d*x)] - 4*a^2*E^(2*c)*f^2*ArcTanh[E^(c + d*x)] + 2*a^2*d^2*e*f*x*Log[1 - E^(c + d*x)] - 4*b^2*d^2*e*f*x*Log[1 - E^(c + d*x)] - 2*a^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(c + d*x)] + 4*b^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(c + d*x)] + a^2*d^2*f^2*x^2*Log[1 - E^(c + d*x)] - 2*b^2*d^2*f^2*x^2*Log[1 - E^(c + d*x)] - a^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] + 2*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] - 2*a^2*d^2*e*f*x*Log[1 + E^(c + d*x)] + 4*b^2*d^2*e*f*x*Log[1 + E^(c + d*x)] + 2*a^2*d^2*e*E^(2*c)*f*x*Log[1 + E^(c + d*x)] - 4*b^2*d^2*e*E^(2*c)*f*x*Log[1 + E^(c + d*x)] - a^2*d^2*f^2*x^2*Log[1 + E^(c + d*x)] + 2*b^2*d^2*f^2*x^2*Log[1 + E^(c + d*x)] + a^2*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(c + d*x)] - 2*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(c + d*x)] + 4*a*b*d*e*f*Log[1 - E^(2*(c + d*x))] - 4*a*b*d*e*E^(2*c)*f*Log[1 - E^(2*(c + d*x))] + 4*a*b*d*f^2*x*Log[1 - E^(2*(c + d*x))] - 4*a*b*d*E^(2*c)*f^2*x*Log[1 - E^(2*(c + d*x))] + 2*(a^2 - 2*b^2)*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -E^(c + d*x)] - 2*(a^2 - 2*b^2)*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, E^(c + d*x)] + 2*a*b*f^2*PolyLog[2, E^(2*(c + d*x))] - 2*a*b*E^(2*c)*f^2*PolyLog[2, E^(2*(c + d*x))] + 2*a^2*f^2*PolyLog[3, -E^(c + d*x)] - 4*b^2*f^2*PolyLog[3, -E^(c + d*x)] - 2*a^2*E^(2*c)*f^2*PolyLog[3, -E^(c + d*x)] + 4*b^2*E^(2*c)*f^2*PolyLog[3, -E^(c + d*x)] - 2*a^2*f^2*PolyLog[3, E^(c + d*x)] + 4*b^2*f^2*PolyLog[3, E^(c + d*x)] + 2*a^2*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)] - 4*b^2*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)])/(2*a^3*d^3*(-1 + E^(2*c))) + (b^3*(2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^3*Sqrt[a^2 + b^2]*d^3) + (Csch[c]*Csch[c + d*x]^2*(2*b*d*e^2*Cosh[c] + 4*b*d*e*f*x*Cosh[c] + 2*b*d*f^2*x^2*Cosh[c] + 2*a*e*f*Cosh[d*x] + 2*a*f^2*x*Cosh[d*x] - 2*a*e*f*Cosh[2*c + d*x] - 2*a*f^2*x*Cosh[2*c + d*x] - 2*b*d*e^2*Cosh[c + 2*d*x] - 4*b*d*e*f*x*Cosh[c + 2*d*x] - 2*b*d*f^2*x^2*Cosh[c + 2*d*x] + a*d*e^2*Sinh[d*x] + 2*a*d*e*f*x*Sinh[d*x] + a*d*f^2*x^2*Sinh[d*x] - a*d*e^2*Sinh[2*c + d*x] - 2*a*d*e*f*x*Sinh[2*c + d*x] - a*d*f^2*x^2*Sinh[2*c + d*x]))/(4*a^2*d^2)","B",1
250,1,736,420,7.9113207,"\int \frac{(e+f x) \text{csch}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{i b^2 f \left(i \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)\right)+i (c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right)}{a^3 d^2}-\frac{b^2 c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^3 d^2}+\frac{b^2 e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^3 d}+\frac{\text{csch}\left(\frac{1}{2} (c+d x)\right) \left(-a f \cosh \left(\frac{1}{2} (c+d x)\right)+2 b d e \cosh \left(\frac{1}{2} (c+d x)\right)-2 b c f \cosh \left(\frac{1}{2} (c+d x)\right)+2 b f (c+d x) \cosh \left(\frac{1}{2} (c+d x)\right)\right)}{4 a^2 d^2}+\frac{\text{sech}\left(\frac{1}{2} (c+d x)\right) \left(a f \sinh \left(\frac{1}{2} (c+d x)\right)+2 b d e \sinh \left(\frac{1}{2} (c+d x)\right)-2 b c f \sinh \left(\frac{1}{2} (c+d x)\right)+2 b f (c+d x) \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{4 a^2 d^2}-\frac{b f \log (\sinh (c+d x))}{a^2 d^2}+\frac{b^3 \left(2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)}{a^3 d^2 \sqrt{a^2+b^2}}+\frac{\text{csch}^2\left(\frac{1}{2} (c+d x)\right) (-f (c+d x)+c f-d e)}{8 a d^2}+\frac{\text{sech}^2\left(\frac{1}{2} (c+d x)\right) (-f (c+d x)+c f-d e)}{8 a d^2}+\frac{i f \left(i \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)\right)+i (c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right)}{2 a d^2}+\frac{c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a d^2}-\frac{e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a d}","-\frac{b^2 f \text{Li}_2\left(-e^{c+d x}\right)}{a^3 d^2}+\frac{b^2 f \text{Li}_2\left(e^{c+d x}\right)}{a^3 d^2}-\frac{2 b^2 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a^3 d}-\frac{b f \log (\sinh (c+d x))}{a^2 d^2}+\frac{b (e+f x) \coth (c+d x)}{a^2 d}-\frac{b^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2 \sqrt{a^2+b^2}}+\frac{b^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2 \sqrt{a^2+b^2}}-\frac{b^3 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d \sqrt{a^2+b^2}}+\frac{b^3 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d \sqrt{a^2+b^2}}+\frac{f \text{Li}_2\left(-e^{c+d x}\right)}{2 a d^2}-\frac{f \text{Li}_2\left(e^{c+d x}\right)}{2 a d^2}-\frac{f \text{csch}(c+d x)}{2 a d^2}+\frac{(e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{(e+f x) \coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"((2*b*d*e*Cosh[(c + d*x)/2] - a*f*Cosh[(c + d*x)/2] - 2*b*c*f*Cosh[(c + d*x)/2] + 2*b*f*(c + d*x)*Cosh[(c + d*x)/2])*Csch[(c + d*x)/2])/(4*a^2*d^2) + ((-(d*e) + c*f - f*(c + d*x))*Csch[(c + d*x)/2]^2)/(8*a*d^2) - (b*f*Log[Sinh[c + d*x]])/(a^2*d^2) - (e*Log[Tanh[(c + d*x)/2]])/(2*a*d) + (b^2*e*Log[Tanh[(c + d*x)/2]])/(a^3*d) + (c*f*Log[Tanh[(c + d*x)/2]])/(2*a*d^2) - (b^2*c*f*Log[Tanh[(c + d*x)/2]])/(a^3*d^2) + ((I/2)*f*(I*(c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + I*(PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)])))/(a*d^2) - (I*b^2*f*(I*(c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + I*(PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)])))/(a^3*d^2) + (b^3*(2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^3*Sqrt[a^2 + b^2]*d^2) + ((-(d*e) + c*f - f*(c + d*x))*Sech[(c + d*x)/2]^2)/(8*a*d^2) + (Sech[(c + d*x)/2]*(2*b*d*e*Sinh[(c + d*x)/2] + a*f*Sinh[(c + d*x)/2] - 2*b*c*f*Sinh[(c + d*x)/2] + 2*b*f*(c + d*x)*Sinh[(c + d*x)/2]))/(4*a^2*d^2)","C",1
251,1,145,113,1.8070135,"\int \frac{\text{csch}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Csch[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","-\frac{4 \left(a^2-2 b^2\right) \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+\frac{16 b^3 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}+a^2 \text{csch}^2\left(\frac{1}{2} (c+d x)\right)+a^2 \text{sech}^2\left(\frac{1}{2} (c+d x)\right)-4 a b \tanh \left(\frac{1}{2} (c+d x)\right)-4 a b \coth \left(\frac{1}{2} (c+d x)\right)}{8 a^3 d}","\frac{b \coth (c+d x)}{a^2 d}+\frac{\left(a^2-2 b^2\right) \tanh ^{-1}(\cosh (c+d x))}{2 a^3 d}+\frac{2 b^3 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a^3 d \sqrt{a^2+b^2}}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"-1/8*((16*b^3*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Coth[(c + d*x)/2] + a^2*Csch[(c + d*x)/2]^2 + 4*(a^2 - 2*b^2)*Log[Tanh[(c + d*x)/2]] + a^2*Sech[(c + d*x)/2]^2 - 4*a*b*Tanh[(c + d*x)/2])/(a^3*d)","A",1
252,-1,0,31,180.000413,"\int \frac{\text{csch}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Csch[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{csch}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
253,1,118,139,0.070162,"\int \frac{(e+f x)^3 \cosh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{i \left(-\frac{24 f \left(d^2 (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right)-2 d f (e+f x) \text{Li}_3\left(-i e^{c+d x}\right)+2 f^2 \text{Li}_4\left(-i e^{c+d x}\right)\right)}{d^4}-\frac{8 (e+f x)^3 \log \left(1+i e^{c+d x}\right)}{d}+\frac{(e+f x)^4}{f}\right)}{4 a}","-\frac{12 i f^3 \text{Li}_4\left(-i e^{c+d x}\right)}{a d^4}+\frac{12 i f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right)}{a d^3}-\frac{6 i f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^2}-\frac{2 i (e+f x)^3 \log \left(1+i e^{c+d x}\right)}{a d}+\frac{i (e+f x)^4}{4 a f}",1,"((I/4)*((e + f*x)^4/f - (8*(e + f*x)^3*Log[1 + I*E^(c + d*x)])/d - (24*f*(d^2*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)] - 2*d*f*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)] + 2*f^2*PolyLog[4, (-I)*E^(c + d*x)]))/d^4))/a","A",1
254,1,94,106,0.0483975,"\int \frac{(e+f x)^2 \cosh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{i \left(d^2 (e+f x)^2 \left(d (e+f x)-6 f \log \left(1+i e^{c+d x}\right)\right)-12 d f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)+12 f^3 \text{Li}_3\left(-i e^{c+d x}\right)\right)}{3 a d^3 f}","\frac{4 i f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^3}-\frac{4 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^2}-\frac{2 i (e+f x)^2 \log \left(1+i e^{c+d x}\right)}{a d}+\frac{i (e+f x)^3}{3 a f}",1,"((I/3)*(d^2*(e + f*x)^2*(d*(e + f*x) - 6*f*Log[1 + I*E^(c + d*x)]) - 12*d*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)] + 12*f^3*PolyLog[3, (-I)*E^(c + d*x)]))/(a*d^3*f)","A",1
255,1,66,73,0.0247025,"\int \frac{(e+f x) \cosh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{i \left(d (e+f x) \left(d (e+f x)-4 f \log \left(1+i e^{c+d x}\right)\right)-4 f^2 \text{Li}_2\left(-i e^{c+d x}\right)\right)}{2 a d^2 f}","-\frac{2 i f \text{Li}_2\left(-i e^{c+d x}\right)}{a d^2}-\frac{2 i (e+f x) \log \left(1+i e^{c+d x}\right)}{a d}+\frac{i (e+f x)^2}{2 a f}",1,"((I/2)*(d*(e + f*x)*(d*(e + f*x) - 4*f*Log[1 + I*E^(c + d*x)]) - 4*f^2*PolyLog[2, (-I)*E^(c + d*x)]))/(a*d^2*f)","A",1
256,1,23,23,0.0139276,"\int \frac{\cosh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Cosh[c + d*x]/(a + I*a*Sinh[c + d*x]),x]","-\frac{i \log (-\sinh (c+d x)+i)}{a d}","-\frac{i \log (-\sinh (c+d x)+i)}{a d}",1,"((-I)*Log[I - Sinh[c + d*x]])/(a*d)","A",1
257,0,0,32,27.6089244,"\int \frac{\cosh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Cosh[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\cosh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\cosh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"Integrate[Cosh[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",-1
258,0,0,32,32.3581998,"\int \frac{\cosh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Cosh[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\cosh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\cosh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"Integrate[Cosh[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",-1
259,1,106,108,0.7721449,"\int \frac{(e+f x)^3 \cosh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{12 i f \sinh (c+d x) \left(d^2 (e+f x)^2+2 f^2\right)-4 i d (e+f x) \cosh (c+d x) \left(d^2 (e+f x)^2+6 f^2\right)+d^4 x \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right)}{4 a d^4}","\frac{6 i f^3 \sinh (c+d x)}{a d^4}-\frac{6 i f^2 (e+f x) \cosh (c+d x)}{a d^3}+\frac{3 i f (e+f x)^2 \sinh (c+d x)}{a d^2}-\frac{i (e+f x)^3 \cosh (c+d x)}{a d}+\frac{(e+f x)^4}{4 a f}",1,"(d^4*x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3) - (4*I)*d*(e + f*x)*(6*f^2 + d^2*(e + f*x)^2)*Cosh[c + d*x] + (12*I)*f*(2*f^2 + d^2*(e + f*x)^2)*Sinh[c + d*x])/(4*a*d^4)","A",1
260,1,78,82,0.503343,"\int \frac{(e+f x)^2 \cosh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{-3 i \cosh (c+d x) \left(d^2 (e+f x)^2+2 f^2\right)+6 i d f (e+f x) \sinh (c+d x)+d^3 x \left(3 e^2+3 e f x+f^2 x^2\right)}{3 a d^3}","-\frac{2 i f^2 \cosh (c+d x)}{a d^3}+\frac{2 i f (e+f x) \sinh (c+d x)}{a d^2}-\frac{i (e+f x)^2 \cosh (c+d x)}{a d}+\frac{(e+f x)^3}{3 a f}",1,"(d^3*x*(3*e^2 + 3*e*f*x + f^2*x^2) - (3*I)*(2*f^2 + d^2*(e + f*x)^2)*Cosh[c + d*x] + (6*I)*d*f*(e + f*x)*Sinh[c + d*x])/(3*a*d^3)","A",1
261,1,57,56,0.6160992,"\int \frac{(e+f x) \cosh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","-\frac{(c+d x) (c f-2 d e-d f x)+2 i d (e+f x) \cosh (c+d x)-2 i f \sinh (c+d x)}{2 a d^2}","\frac{i f \sinh (c+d x)}{a d^2}-\frac{i (e+f x) \cosh (c+d x)}{a d}+\frac{e x}{a}+\frac{f x^2}{2 a}",1,"-1/2*((c + d*x)*(-2*d*e + c*f - d*f*x) + (2*I)*d*(e + f*x)*Cosh[c + d*x] - (2*I)*f*Sinh[c + d*x])/(a*d^2)","A",1
262,1,139,22,0.145086,"\int \frac{\cosh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Cosh[c + d*x]^2/(a + I*a*Sinh[c + d*x]),x]","\frac{\cosh ^3(c+d x) \left(-i \sqrt{1+i \sinh (c+d x)} \sinh (c+d x)+\sqrt{1+i \sinh (c+d x)}-2 \sqrt{1-i \sinh (c+d x)} \sin ^{-1}\left(\frac{\sqrt{1-i \sinh (c+d x)}}{\sqrt{2}}\right)\right)}{a d \sqrt{1+i \sinh (c+d x)} (\sinh (c+d x)-i) (\sinh (c+d x)+i)^2}","\frac{x}{a}-\frac{i \cosh (c+d x)}{a d}",1,"(Cosh[c + d*x]^3*(-2*ArcSin[Sqrt[1 - I*Sinh[c + d*x]]/Sqrt[2]]*Sqrt[1 - I*Sinh[c + d*x]] + Sqrt[1 + I*Sinh[c + d*x]] - I*Sqrt[1 + I*Sinh[c + d*x]]*Sinh[c + d*x]))/(a*d*Sqrt[1 + I*Sinh[c + d*x]]*(-I + Sinh[c + d*x])*(I + Sinh[c + d*x])^2)","B",1
263,1,62,76,0.3154889,"\int \frac{\cosh ^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Cosh[c + d*x]^2/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\frac{-i \sinh \left(c-\frac{d e}{f}\right) \text{Chi}\left(d \left(\frac{e}{f}+x\right)\right)-i \cosh \left(c-\frac{d e}{f}\right) \text{Shi}\left(d \left(\frac{e}{f}+x\right)\right)+\log (e+f x)}{a f}","-\frac{i \sinh \left(c-\frac{d e}{f}\right) \text{Chi}\left(\frac{d e}{f}+d x\right)}{a f}-\frac{i \cosh \left(c-\frac{d e}{f}\right) \text{Shi}\left(\frac{d e}{f}+d x\right)}{a f}+\frac{\log (e+f x)}{a f}",1,"(Log[e + f*x] - I*CoshIntegral[d*(e/f + x)]*Sinh[c - (d*e)/f] - I*Cosh[c - (d*e)/f]*SinhIntegral[d*(e/f + x)])/(a*f)","A",1
264,1,85,103,0.5088644,"\int \frac{\cosh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Cosh[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","-\frac{i \left(d (e+f x) \cosh \left(c-\frac{d e}{f}\right) \text{Chi}\left(d \left(\frac{e}{f}+x\right)\right)+d (e+f x) \sinh \left(c-\frac{d e}{f}\right) \text{Shi}\left(d \left(\frac{e}{f}+x\right)\right)-f (\sinh (c+d x)+i)\right)}{a f^2 (e+f x)}","-\frac{i d \cosh \left(c-\frac{d e}{f}\right) \text{Chi}\left(\frac{d e}{f}+d x\right)}{a f^2}-\frac{i d \sinh \left(c-\frac{d e}{f}\right) \text{Shi}\left(\frac{d e}{f}+d x\right)}{a f^2}+\frac{i \sinh (c+d x)}{a f (e+f x)}-\frac{1}{a f (e+f x)}",1,"((-I)*(d*(e + f*x)*Cosh[c - (d*e)/f]*CoshIntegral[d*(e/f + x)] - f*(I + Sinh[c + d*x]) + d*(e + f*x)*Sinh[c - (d*e)/f]*SinhIntegral[d*(e/f + x)]))/(a*f^2*(e + f*x))","A",1
265,1,134,231,1.2870069,"\int \frac{(e+f x)^3 \cosh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{-96 f \cosh (c+d x) \left(d^2 (e+f x)^2+2 f^2\right)-4 i d (e+f x) \cosh (2 (c+d x)) \left(2 d^2 (e+f x)^2+3 f^2\right)+4 \sinh (c+d x) \left(8 d (e+f x) \left(d^2 (e+f x)^2+6 f^2\right)+3 i f \cosh (c+d x) \left(2 d^2 (e+f x)^2+f^2\right)\right)}{32 a d^4}","-\frac{6 f^3 \cosh (c+d x)}{a d^4}+\frac{3 i f^3 \sinh (c+d x) \cosh (c+d x)}{8 a d^4}-\frac{3 i f^2 (e+f x) \sinh ^2(c+d x)}{4 a d^3}+\frac{6 f^2 (e+f x) \sinh (c+d x)}{a d^3}-\frac{3 f (e+f x)^2 \cosh (c+d x)}{a d^2}+\frac{3 i f (e+f x)^2 \sinh (c+d x) \cosh (c+d x)}{4 a d^2}-\frac{i (e+f x)^3 \sinh ^2(c+d x)}{2 a d}+\frac{(e+f x)^3 \sinh (c+d x)}{a d}-\frac{3 i f^3 x}{8 a d^3}-\frac{i (e+f x)^3}{4 a d}",1,"(-96*f*(2*f^2 + d^2*(e + f*x)^2)*Cosh[c + d*x] - (4*I)*d*(e + f*x)*(3*f^2 + 2*d^2*(e + f*x)^2)*Cosh[2*(c + d*x)] + 4*(8*d*(e + f*x)*(6*f^2 + d^2*(e + f*x)^2) + (3*I)*f*(f^2 + 2*d^2*(e + f*x)^2)*Cosh[c + d*x])*Sinh[c + d*x])/(32*a*d^4)","A",1
266,1,99,171,0.8695644,"\int \frac{(e+f x)^2 \cosh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{-2 i \cosh (2 (c+d x)) \left(2 d^2 (e+f x)^2+f^2\right)+8 \sinh (c+d x) \left(2 \left(d^2 (e+f x)^2+2 f^2\right)+i d f (e+f x) \cosh (c+d x)\right)-32 d f (e+f x) \cosh (c+d x)}{16 a d^3}","-\frac{i f^2 \sinh ^2(c+d x)}{4 a d^3}+\frac{2 f^2 \sinh (c+d x)}{a d^3}-\frac{2 f (e+f x) \cosh (c+d x)}{a d^2}+\frac{i f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 a d^2}-\frac{i (e+f x)^2 \sinh ^2(c+d x)}{2 a d}+\frac{(e+f x)^2 \sinh (c+d x)}{a d}-\frac{i e f x}{2 a d}-\frac{i f^2 x^2}{4 a d}",1,"(-32*d*f*(e + f*x)*Cosh[c + d*x] - (2*I)*(f^2 + 2*d^2*(e + f*x)^2)*Cosh[2*(c + d*x)] + 8*(2*(2*f^2 + d^2*(e + f*x)^2) + I*d*f*(e + f*x)*Cosh[c + d*x])*Sinh[c + d*x])/(16*a*d^3)","A",1
267,1,60,98,1.0912133,"\int \frac{(e+f x) \cosh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{d (e+f x) (4 \sinh (c+d x)-i \cosh (2 (c+d x)))+i f (\sinh (c+d x)+4 i) \cosh (c+d x)}{4 a d^2}","-\frac{f \cosh (c+d x)}{a d^2}+\frac{i f \sinh (c+d x) \cosh (c+d x)}{4 a d^2}-\frac{i (e+f x) \sinh ^2(c+d x)}{2 a d}+\frac{(e+f x) \sinh (c+d x)}{a d}-\frac{i f x}{4 a d}",1,"(I*f*Cosh[c + d*x]*(4*I + Sinh[c + d*x]) + d*(e + f*x)*((-I)*Cosh[2*(c + d*x)] + 4*Sinh[c + d*x]))/(4*a*d^2)","A",1
268,1,28,34,0.0455458,"\int \frac{\cosh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Cosh[c + d*x]^3/(a + I*a*Sinh[c + d*x]),x]","\frac{(2-i \sinh (c+d x)) \sinh (c+d x)}{2 a d}","\frac{\sinh (c+d x)}{a d}-\frac{i \sinh ^2(c+d x)}{2 a d}",1,"((2 - I*Sinh[c + d*x])*Sinh[c + d*x])/(2*a*d)","A",1
269,1,112,131,0.3951162,"\int \frac{\cosh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Cosh[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\frac{2 \cosh \left(c-\frac{d e}{f}\right) \text{Chi}\left(d \left(\frac{e}{f}+x\right)\right)-i \left(\sinh \left(2 c-\frac{2 d e}{f}\right) \text{Chi}\left(\frac{2 d (e+f x)}{f}\right)+2 i \sinh \left(c-\frac{d e}{f}\right) \text{Shi}\left(d \left(\frac{e}{f}+x\right)\right)+\cosh \left(2 c-\frac{2 d e}{f}\right) \text{Shi}\left(\frac{2 d (e+f x)}{f}\right)\right)}{2 a f}","-\frac{i \sinh \left(2 c-\frac{2 d e}{f}\right) \text{Chi}\left(\frac{2 d e}{f}+2 d x\right)}{2 a f}+\frac{\cosh \left(c-\frac{d e}{f}\right) \text{Chi}\left(\frac{d e}{f}+d x\right)}{a f}+\frac{\sinh \left(c-\frac{d e}{f}\right) \text{Shi}\left(\frac{d e}{f}+d x\right)}{a f}-\frac{i \cosh \left(2 c-\frac{2 d e}{f}\right) \text{Shi}\left(\frac{2 d e}{f}+2 d x\right)}{2 a f}",1,"(2*Cosh[c - (d*e)/f]*CoshIntegral[d*(e/f + x)] - I*(CoshIntegral[(2*d*(e + f*x))/f]*Sinh[2*c - (2*d*e)/f] + (2*I)*Sinh[c - (d*e)/f]*SinhIntegral[d*(e/f + x)] + Cosh[2*c - (2*d*e)/f]*SinhIntegral[(2*d*(e + f*x))/f]))/(2*a*f)","A",1
270,1,212,180,0.6270366,"\int \frac{\cosh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Cosh[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\frac{2 d (e+f x) \sinh \left(c-\frac{d e}{f}\right) \text{Chi}\left(d \left(\frac{e}{f}+x\right)\right)-2 i d (e+f x) \cosh \left(2 c-\frac{2 d e}{f}\right) \text{Chi}\left(\frac{2 d (e+f x)}{f}\right)-2 i d e \sinh \left(2 c-\frac{2 d e}{f}\right) \text{Shi}\left(\frac{2 d (e+f x)}{f}\right)-2 i d f x \sinh \left(2 c-\frac{2 d e}{f}\right) \text{Shi}\left(\frac{2 d (e+f x)}{f}\right)+2 d e \cosh \left(c-\frac{d e}{f}\right) \text{Shi}\left(d \left(\frac{e}{f}+x\right)\right)+2 d f x \cosh \left(c-\frac{d e}{f}\right) \text{Shi}\left(d \left(\frac{e}{f}+x\right)\right)+i f \sinh (2 (c+d x))-2 f \cosh (c+d x)}{2 a f^2 (e+f x)}","\frac{d \sinh \left(c-\frac{d e}{f}\right) \text{Chi}\left(\frac{d e}{f}+d x\right)}{a f^2}-\frac{i d \cosh \left(2 c-\frac{2 d e}{f}\right) \text{Chi}\left(\frac{2 d e}{f}+2 d x\right)}{a f^2}-\frac{i d \sinh \left(2 c-\frac{2 d e}{f}\right) \text{Shi}\left(\frac{2 d e}{f}+2 d x\right)}{a f^2}+\frac{d \cosh \left(c-\frac{d e}{f}\right) \text{Shi}\left(\frac{d e}{f}+d x\right)}{a f^2}+\frac{i \sinh (2 c+2 d x)}{2 a f (e+f x)}-\frac{\cosh (c+d x)}{a f (e+f x)}",1,"(-2*f*Cosh[c + d*x] - (2*I)*d*(e + f*x)*Cosh[2*c - (2*d*e)/f]*CoshIntegral[(2*d*(e + f*x))/f] + 2*d*(e + f*x)*CoshIntegral[d*(e/f + x)]*Sinh[c - (d*e)/f] + I*f*Sinh[2*(c + d*x)] + 2*d*e*Cosh[c - (d*e)/f]*SinhIntegral[d*(e/f + x)] + 2*d*f*x*Cosh[c - (d*e)/f]*SinhIntegral[d*(e/f + x)] - (2*I)*d*e*Sinh[2*c - (2*d*e)/f]*SinhIntegral[(2*d*(e + f*x))/f] - (2*I)*d*f*x*Sinh[2*c - (2*d*e)/f]*SinhIntegral[(2*d*(e + f*x))/f])/(2*a*f^2*(e + f*x))","A",1
271,1,767,463,11.2174702,"\int \frac{(e+f x)^3 \text{sech}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sech[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{3 i \left(e^2 f \sinh \left(\frac{d x}{2}\right)+2 e f^2 x \sinh \left(\frac{d x}{2}\right)+f^3 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{a d^2 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}-\frac{\frac{12 i \left(e^c+i\right) f \left(d^2 (e+f x)^2 \text{Li}_2\left(-i e^{-c-d x}\right)+2 f \left(d (e+f x) \text{Li}_3\left(-i e^{-c-d x}\right)+f \text{Li}_4\left(-i e^{-c-d x}\right)\right)\right)}{d^4}+\frac{4 \left(1-i e^c\right) (e+f x)^3 \log \left(1+i e^{-c-d x}\right)}{d}+\frac{(e+f x)^4}{f}}{8 a \left(e^c+i\right)}-\frac{12 \left(1+i e^c\right) d^3 e f^3 x^2 \log \left(1-i e^{-c-d x}\right)+4 \left(1+i e^c\right) d^3 f^4 x^3 \log \left(1-i e^{-c-d x}\right)+12 \left(1+i e^c\right) f^2 \left(4 f^2-d^2 e^2\right) \text{Li}_2\left(i e^{-c-d x}\right)+12 \left(1+i e^c\right) d f^2 x \left(d^2 e^2-4 f^2\right) \log \left(1-i e^{-c-d x}\right)-4 \left(1+i e^c\right) d e f \left(d^2 e^2-12 f^2\right) \left(d x-\log \left(-e^{c+d x}+i\right)\right)-12 \left(1+i e^c\right) f^4 \left(d^2 x^2 \text{Li}_2\left(i e^{-c-d x}\right)+2 \left(d x \text{Li}_3\left(i e^{-c-d x}\right)+\text{Li}_4\left(i e^{-c-d x}\right)\right)\right)-24 \left(1+i e^c\right) d e f^3 \left(d x \text{Li}_2\left(i e^{-c-d x}\right)+\text{Li}_3\left(i e^{-c-d x}\right)\right)+\left(d^2 (e+f x)^2-12 f^2\right)^2}{8 a \left(e^c-i\right) d^4 f}+\frac{i (e+f x)^3}{2 a d \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^2}+\frac{x \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right)}{8 a \left(\cosh \left(\frac{c}{2}\right)-i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right)}","\frac{3 i f^3 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^4}-\frac{3 i f^3 \text{Li}_2\left(i e^{c+d x}\right)}{a d^4}+\frac{3 i f^3 \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 a d^4}-\frac{3 i f^3 \text{Li}_4\left(-i e^{c+d x}\right)}{a d^4}+\frac{3 i f^3 \text{Li}_4\left(i e^{c+d x}\right)}{a d^4}+\frac{3 i f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right)}{a d^3}-\frac{3 i f^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right)}{a d^3}+\frac{3 i f^2 (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{a d^3}-\frac{6 f^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{a d^3}-\frac{3 i f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right)}{2 a d^2}+\frac{3 i f (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right)}{2 a d^2}-\frac{3 i f (e+f x)^2 \tanh (c+d x)}{2 a d^2}+\frac{3 f (e+f x)^2 \text{sech}(c+d x)}{2 a d^2}+\frac{(e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{i (e+f x)^3 \text{sech}^2(c+d x)}{2 a d}+\frac{(e+f x)^3 \tanh (c+d x) \text{sech}(c+d x)}{2 a d}-\frac{3 i f (e+f x)^2}{2 a d^2}",1,"-1/8*((e + f*x)^4/f + (4*(1 - I*E^c)*(e + f*x)^3*Log[1 + I*E^(-c - d*x)])/d + ((12*I)*(I + E^c)*f*(d^2*(e + f*x)^2*PolyLog[2, (-I)*E^(-c - d*x)] + 2*f*(d*(e + f*x)*PolyLog[3, (-I)*E^(-c - d*x)] + f*PolyLog[4, (-I)*E^(-c - d*x)])))/d^4)/(a*(I + E^c)) - ((-12*f^2 + d^2*(e + f*x)^2)^2 + 12*d*(1 + I*E^c)*f^2*(d^2*e^2 - 4*f^2)*x*Log[1 - I*E^(-c - d*x)] + 12*d^3*e*(1 + I*E^c)*f^3*x^2*Log[1 - I*E^(-c - d*x)] + 4*d^3*(1 + I*E^c)*f^4*x^3*Log[1 - I*E^(-c - d*x)] - 4*d*e*(1 + I*E^c)*f*(d^2*e^2 - 12*f^2)*(d*x - Log[I - E^(c + d*x)]) + 12*(1 + I*E^c)*f^2*(-(d^2*e^2) + 4*f^2)*PolyLog[2, I*E^(-c - d*x)] - 24*d*e*(1 + I*E^c)*f^3*(d*x*PolyLog[2, I*E^(-c - d*x)] + PolyLog[3, I*E^(-c - d*x)]) - 12*(1 + I*E^c)*f^4*(d^2*x^2*PolyLog[2, I*E^(-c - d*x)] + 2*(d*x*PolyLog[3, I*E^(-c - d*x)] + PolyLog[4, I*E^(-c - d*x)])))/(8*a*d^4*(-I + E^c)*f) + (x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3))/(8*a*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) + ((I/2)*(e + f*x)^3)/(a*d*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^2) - ((3*I)*(e^2*f*Sinh[(d*x)/2] + 2*e*f^2*x*Sinh[(d*x)/2] + f^3*x^2*Sinh[(d*x)/2]))/(a*d^2*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2]))","A",0
272,1,501,268,11.7014286,"\int \frac{(e+f x)^2 \text{sech}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sech[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{\frac{\frac{6 i \left(e^c+i\right) f \left(d (e+f x) \text{Li}_2\left(-i e^{-c-d x}\right)+f \text{Li}_3\left(-i e^{-c-d x}\right)\right)}{d^3}+\frac{3 \left(1-i e^c\right) (e+f x)^2 \log \left(1+i e^{-c-d x}\right)}{d}+\frac{(e+f x)^3}{f}}{e^c+i}+\frac{-\frac{3 \left(1+i e^c\right) \left(d^2 e^2-4 f^2\right) \left(d x-\log \left(-e^{c+d x}+i\right)\right)}{d}-6 \left(1+i e^c\right) e f \text{Li}_2\left(i e^{-c-d x}\right)+6 \left(1+i e^c\right) d e f x \log \left(1-i e^{-c-d x}\right)-6 \left(1+i e^c\right) f^2 \left(x \text{Li}_2\left(i e^{-c-d x}\right)+\frac{\text{Li}_3\left(i e^{-c-d x}\right)}{d}\right)+3 \left(1+i e^c\right) d f^2 x^2 \log \left(1-i e^{-c-d x}\right)+3 x \left(d^2 e^2-4 f^2\right)+3 d^2 e f x^2+d^2 f^2 x^3}{\left(e^c-i\right) d^2}+\frac{12 i f \sinh \left(\frac{d x}{2}\right) (e+f x)}{d^2 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}-\frac{3 i (e+f x)^2}{d \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}-x \text{sech}(c) \left(3 e^2+3 e f x+f^2 x^2\right)}{6 a}","\frac{i f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^3}-\frac{i f^2 \text{Li}_3\left(i e^{c+d x}\right)}{a d^3}-\frac{f^2 \tan ^{-1}(\sinh (c+d x))}{a d^3}+\frac{i f^2 \log (\cosh (c+d x))}{a d^3}-\frac{i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^2}+\frac{i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{a d^2}-\frac{i f (e+f x) \tanh (c+d x)}{a d^2}+\frac{f (e+f x) \text{sech}(c+d x)}{a d^2}+\frac{(e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{i (e+f x)^2 \text{sech}^2(c+d x)}{2 a d}+\frac{(e+f x)^2 \tanh (c+d x) \text{sech}(c+d x)}{2 a d}",1,"-1/6*(((e + f*x)^3/f + (3*(1 - I*E^c)*(e + f*x)^2*Log[1 + I*E^(-c - d*x)])/d + ((6*I)*(I + E^c)*f*(d*(e + f*x)*PolyLog[2, (-I)*E^(-c - d*x)] + f*PolyLog[3, (-I)*E^(-c - d*x)]))/d^3)/(I + E^c) + (3*(d^2*e^2 - 4*f^2)*x + 3*d^2*e*f*x^2 + d^2*f^2*x^3 + 6*d*e*(1 + I*E^c)*f*x*Log[1 - I*E^(-c - d*x)] + 3*d*(1 + I*E^c)*f^2*x^2*Log[1 - I*E^(-c - d*x)] - (3*(1 + I*E^c)*(d^2*e^2 - 4*f^2)*(d*x - Log[I - E^(c + d*x)]))/d - 6*e*(1 + I*E^c)*f*PolyLog[2, I*E^(-c - d*x)] - 6*(1 + I*E^c)*f^2*(x*PolyLog[2, I*E^(-c - d*x)] + PolyLog[3, I*E^(-c - d*x)]/d))/(d^2*(-I + E^c)) - x*(3*e^2 + 3*e*f*x + f^2*x^2)*Sech[c] - ((3*I)*(e + f*x)^2)/(d*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2) + ((12*I)*f*(e + f*x)*Sinh[(d*x)/2])/(d^2*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])))/a","A",1
273,1,710,161,3.3258839,"\int \frac{(e+f x) \text{sech}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sech[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{(c+d x) (c f-d (2 e+f x)) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2+d e \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2 \left(-2 i \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+c+d x\right)+d e \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2 \left(2 i \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+c+d x\right)+\frac{f \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2 \left(-2 (-1)^{3/4} (c+d x)^2+\sqrt{2} \left(4 i \text{Li}_2\left(-i e^{-c-d x}\right)+2 (-2 i c-2 i d x+\pi ) \log \left(1+i e^{-c-d x}\right)+\pi  \left(-4 \log \left(e^{c+d x}+1\right)-2 \log \left(-\sin \left(\frac{1}{4} (\pi -2 i (c+d x))\right)\right)+4 \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)+3 c+3 d x\right)\right)\right)}{2 \sqrt{2}}+\frac{f \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2 \left(2 \sqrt[4]{-1} (c+d x)^2+\sqrt{2} \left(-4 i \text{Li}_2\left(i e^{-c-d x}\right)+2 (2 i c+2 i d x+\pi ) \log \left(1-i e^{-c-d x}\right)-\pi  \left(-4 \log \left(e^{c+d x}+1\right)+2 \log \left(\sin \left(\frac{1}{4} (\pi +2 i (c+d x))\right)\right)+4 \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)+c+d x\right)\right)\right)}{2 \sqrt{2}}-4 f \sinh \left(\frac{1}{2} (c+d x)\right) \left(\sinh \left(\frac{1}{2} (c+d x)\right)-i \cosh \left(\frac{1}{2} (c+d x)\right)\right)-c f \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2 \left(-2 i \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+c+d x\right)-c f \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2 \left(2 i \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)+c+d x\right)-2 i d (e+f x)}{4 d^2 (a+i a \sinh (c+d x))}","-\frac{i f \text{Li}_2\left(-i e^{c+d x}\right)}{2 a d^2}+\frac{i f \text{Li}_2\left(i e^{c+d x}\right)}{2 a d^2}-\frac{i f \tanh (c+d x)}{2 a d^2}+\frac{f \text{sech}(c+d x)}{2 a d^2}+\frac{(e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{i (e+f x) \text{sech}^2(c+d x)}{2 a d}+\frac{(e+f x) \tanh (c+d x) \text{sech}(c+d x)}{2 a d}",1,"-1/4*((-2*I)*d*(e + f*x) + (c + d*x)*(c*f - d*(2*e + f*x))*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2 + d*e*(c + d*x - (2*I)*Log[Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2]])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2 - c*f*(c + d*x - (2*I)*Log[Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2]])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2 + d*e*(c + d*x + (2*I)*Log[Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2 - c*f*(c + d*x + (2*I)*Log[Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2 + (f*(-2*(-1)^(3/4)*(c + d*x)^2 + Sqrt[2]*(2*((-2*I)*c + Pi - (2*I)*d*x)*Log[1 + I*E^(-c - d*x)] + Pi*(3*c + 3*d*x - 4*Log[1 + E^(c + d*x)] + 4*Log[Cosh[(c + d*x)/2]] - 2*Log[-Sin[(Pi - (2*I)*(c + d*x))/4]]) + (4*I)*PolyLog[2, (-I)*E^(-c - d*x)]))*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2)/(2*Sqrt[2]) + (f*(2*(-1)^(1/4)*(c + d*x)^2 + Sqrt[2]*(2*((2*I)*c + Pi + (2*I)*d*x)*Log[1 - I*E^(-c - d*x)] - Pi*(c + d*x - 4*Log[1 + E^(c + d*x)] + 4*Log[Cosh[(c + d*x)/2]] + 2*Log[Sin[(Pi + (2*I)*(c + d*x))/4]]) - (4*I)*PolyLog[2, I*E^(-c - d*x)]))*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2)/(2*Sqrt[2]) - 4*f*Sinh[(c + d*x)/2]*((-I)*Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2]))/(d^2*(a + I*a*Sinh[c + d*x]))","B",1
274,1,30,42,0.0456486,"\int \frac{\text{sech}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Sech[c + d*x]/(a + I*a*Sinh[c + d*x]),x]","\frac{\tan ^{-1}(\sinh (c+d x))+\frac{1}{\sinh (c+d x)-i}}{2 a d}","\frac{\tan ^{-1}(\sinh (c+d x))}{2 a d}+\frac{i}{2 d (a+i a \sinh (c+d x))}",1,"(ArcTan[Sinh[c + d*x]] + (-I + Sinh[c + d*x])^(-1))/(2*a*d)","A",1
275,0,0,32,66.3593742,"\int \frac{\text{sech}(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Sech[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{sech}(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{sech}(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"Integrate[Sech[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",-1
276,-1,0,32,180.0095879,"\int \frac{\text{sech}(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Sech[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{sech}(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
277,1,1049,450,12.4041483,"\int \frac{(e+f x)^3 \text{sech}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sech[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","-\frac{i f \left(\frac{(e+f x)^3}{f}+\frac{3 \left(1-i e^c\right) \log \left(1+i e^{-c-d x}\right) (e+f x)^2}{d}+\frac{6 i \left(i+e^c\right) f \left(d (e+f x) \text{Li}_2\left(-i e^{-c-d x}\right)+f \text{Li}_3\left(-i e^{-c-d x}\right)\right)}{d^3}\right)}{2 a d \left(i+e^c\right)}+\frac{i f \left(5 d^2 f^2 x^3+15 d^2 e f x^2+15 d \left(1+i e^c\right) f^2 \log \left(1-i e^{-c-d x}\right) x^2+3 \left(5 d^2 e^2-4 f^2\right) x+30 d e \left(1+i e^c\right) f \log \left(1-i e^{-c-d x}\right) x-\frac{3 \left(1+i e^c\right) \left(5 d^2 e^2-4 f^2\right) \left(d x-\log \left(i-e^{c+d x}\right)\right)}{d}-30 e \left(1+i e^c\right) f \text{Li}_2\left(i e^{-c-d x}\right)-30 \left(1+i e^c\right) f^2 \left(x \text{Li}_2\left(i e^{-c-d x}\right)+\frac{\text{Li}_3\left(i e^{-c-d x}\right)}{d}\right)\right)}{6 a d^3 \left(-i+e^c\right)}+\frac{\sinh \left(\frac{d x}{2}\right) e^3+3 f x \sinh \left(\frac{d x}{2}\right) e^2+3 f^2 x^2 \sinh \left(\frac{d x}{2}\right) e+f^3 x^3 \sinh \left(\frac{d x}{2}\right)}{2 a d \left(\cosh \left(\frac{c}{2}\right)-i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)-i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}+\frac{5 d^2 \sinh \left(\frac{d x}{2}\right) e^3+15 d^2 f x \sinh \left(\frac{d x}{2}\right) e^2-12 f^2 \sinh \left(\frac{d x}{2}\right) e+15 d^2 f^2 x^2 \sinh \left(\frac{d x}{2}\right) e+5 d^2 f^3 x^3 \sinh \left(\frac{d x}{2}\right)-12 f^3 x \sinh \left(\frac{d x}{2}\right)}{6 a d^3 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}+\frac{i d \cosh \left(\frac{c}{2}\right) e^3+d \sinh \left(\frac{c}{2}\right) e^3+3 f \cosh \left(\frac{c}{2}\right) e^2+3 i d f x \cosh \left(\frac{c}{2}\right) e^2+3 i f \sinh \left(\frac{c}{2}\right) e^2+3 d f x \sinh \left(\frac{c}{2}\right) e^2+3 i d f^2 x^2 \cosh \left(\frac{c}{2}\right) e+6 f^2 x \cosh \left(\frac{c}{2}\right) e+3 d f^2 x^2 \sinh \left(\frac{c}{2}\right) e+6 i f^2 x \sinh \left(\frac{c}{2}\right) e+i d f^3 x^3 \cosh \left(\frac{c}{2}\right)+3 f^3 x^2 \cosh \left(\frac{c}{2}\right)+d f^3 x^3 \sinh \left(\frac{c}{2}\right)+3 i f^3 x^2 \sinh \left(\frac{c}{2}\right)}{6 a d^2 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^2}+\frac{\sinh \left(\frac{d x}{2}\right) e^3+3 f x \sinh \left(\frac{d x}{2}\right) e^2+3 f^2 x^2 \sinh \left(\frac{d x}{2}\right) e+f^3 x^3 \sinh \left(\frac{d x}{2}\right)}{3 a d \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^3}","\frac{f^3 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^4}-\frac{f^3 \text{Li}_3\left(i e^{c+d x}\right)}{a d^4}+\frac{f^3 \text{Li}_3\left(-e^{2 (c+d x)}\right)}{a d^4}+\frac{i f^3 \tan ^{-1}(\sinh (c+d x))}{a d^4}+\frac{f^3 \log (\cosh (c+d x))}{a d^4}-\frac{f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}+\frac{f^2 (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{a d^3}-\frac{2 f^2 (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right)}{a d^3}-\frac{f^2 (e+f x) \tanh (c+d x)}{a d^3}-\frac{i f^2 (e+f x) \text{sech}(c+d x)}{a d^3}-\frac{2 f (e+f x)^2 \log \left(e^{2 (c+d x)}+1\right)}{a d^2}-\frac{i f (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{a d^2}+\frac{f (e+f x)^2 \text{sech}^2(c+d x)}{2 a d^2}-\frac{i f (e+f x)^2 \tanh (c+d x) \text{sech}(c+d x)}{2 a d^2}+\frac{2 (e+f x)^3 \tanh (c+d x)}{3 a d}+\frac{i (e+f x)^3 \text{sech}^3(c+d x)}{3 a d}+\frac{(e+f x)^3 \tanh (c+d x) \text{sech}^2(c+d x)}{3 a d}+\frac{2 (e+f x)^3}{3 a d}",1,"((-1/2*I)*f*((e + f*x)^3/f + (3*(1 - I*E^c)*(e + f*x)^2*Log[1 + I*E^(-c - d*x)])/d + ((6*I)*(I + E^c)*f*(d*(e + f*x)*PolyLog[2, (-I)*E^(-c - d*x)] + f*PolyLog[3, (-I)*E^(-c - d*x)]))/d^3))/(a*d*(I + E^c)) + ((I/6)*f*(3*(5*d^2*e^2 - 4*f^2)*x + 15*d^2*e*f*x^2 + 5*d^2*f^2*x^3 + 30*d*e*(1 + I*E^c)*f*x*Log[1 - I*E^(-c - d*x)] + 15*d*(1 + I*E^c)*f^2*x^2*Log[1 - I*E^(-c - d*x)] - (3*(1 + I*E^c)*(5*d^2*e^2 - 4*f^2)*(d*x - Log[I - E^(c + d*x)]))/d - 30*e*(1 + I*E^c)*f*PolyLog[2, I*E^(-c - d*x)] - 30*(1 + I*E^c)*f^2*(x*PolyLog[2, I*E^(-c - d*x)] + PolyLog[3, I*E^(-c - d*x)]/d)))/(a*d^3*(-I + E^c)) + (e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2])/(2*a*d*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] - I*Sinh[c/2 + (d*x)/2])) + (e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2])/(3*a*d*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^3) + (I*d*e^3*Cosh[c/2] + 3*e^2*f*Cosh[c/2] + (3*I)*d*e^2*f*x*Cosh[c/2] + 6*e*f^2*x*Cosh[c/2] + (3*I)*d*e*f^2*x^2*Cosh[c/2] + 3*f^3*x^2*Cosh[c/2] + I*d*f^3*x^3*Cosh[c/2] + d*e^3*Sinh[c/2] + (3*I)*e^2*f*Sinh[c/2] + 3*d*e^2*f*x*Sinh[c/2] + (6*I)*e*f^2*x*Sinh[c/2] + 3*d*e*f^2*x^2*Sinh[c/2] + (3*I)*f^3*x^2*Sinh[c/2] + d*f^3*x^3*Sinh[c/2])/(6*a*d^2*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^2) + (5*d^2*e^3*Sinh[(d*x)/2] - 12*e*f^2*Sinh[(d*x)/2] + 15*d^2*e^2*f*x*Sinh[(d*x)/2] - 12*f^3*x*Sinh[(d*x)/2] + 15*d^2*e*f^2*x^2*Sinh[(d*x)/2] + 5*d^2*f^3*x^3*Sinh[(d*x)/2])/(6*a*d^3*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2]))","B",0
278,1,564,325,8.1254799,"\int \frac{(e+f x)^2 \text{sech}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sech[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{\frac{d^2 e^2 \sinh (2 (c+d x))-2 i d^2 e^2 \cosh (c+d x)+4 i d^2 e^2 \cosh (c+2 d x)+2 d^2 e f x \sinh (2 (c+d x))-4 i d^2 e f x \cosh (c+d x)+8 i d^2 e f x \cosh (c+2 d x)+d^2 f^2 x^2 \sinh (2 (c+d x))-2 i d^2 f^2 x^2 \cosh (c+d x)+4 i d^2 f^2 x^2 \cosh (c+2 d x)+2 d e f \cosh (2 c+d x)-2 f^2 \sinh (2 (c+d x))+2 f^2 \sinh (2 c+d x)+2 d f^2 x \cosh (2 c+d x)+4 i f^2 \cosh (c+d x)-2 i f^2 \cosh (c+2 d x)-2 i f^2 \cosh (c)+8 d^2 e^2 \sinh (d x)+16 d^2 e f x \sinh (d x)+8 d^2 f^2 x^2 \sinh (d x)+2 d f \cosh (d x) (e+f x)-2 f^2 \sinh (d x)}{\left(\cosh \left(\frac{c}{2}\right)-i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^3}+\frac{10 i d (e+f x) \left(d (e+f x)+2 \left(1+i e^c\right) f \log \left(1-i e^{-c-d x}\right)\right)}{e^c-i}-\frac{6 i d (e+f x) \left(d (e+f x)+2 \left(1-i e^c\right) f \log \left(1+i e^{-c-d x}\right)\right)}{e^c+i}+12 f^2 \text{Li}_2\left(-i e^{-c-d x}\right)+20 f^2 \text{Li}_2\left(i e^{-c-d x}\right)}{12 a d^3}","-\frac{f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{3 a d^3}+\frac{f^2 \text{Li}_2\left(i e^{c+d x}\right)}{3 a d^3}-\frac{2 f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right)}{3 a d^3}-\frac{f^2 \tanh (c+d x)}{3 a d^3}-\frac{i f^2 \text{sech}(c+d x)}{3 a d^3}-\frac{4 f (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{3 a d^2}-\frac{2 i f (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{3 a d^2}+\frac{f (e+f x) \text{sech}^2(c+d x)}{3 a d^2}-\frac{i f (e+f x) \tanh (c+d x) \text{sech}(c+d x)}{3 a d^2}+\frac{2 (e+f x)^2 \tanh (c+d x)}{3 a d}+\frac{i (e+f x)^2 \text{sech}^3(c+d x)}{3 a d}+\frac{(e+f x)^2 \tanh (c+d x) \text{sech}^2(c+d x)}{3 a d}+\frac{2 (e+f x)^2}{3 a d}",1,"(((10*I)*d*(e + f*x)*(d*(e + f*x) + 2*(1 + I*E^c)*f*Log[1 - I*E^(-c - d*x)]))/(-I + E^c) - ((6*I)*d*(e + f*x)*(d*(e + f*x) + 2*(1 - I*E^c)*f*Log[1 + I*E^(-c - d*x)]))/(I + E^c) + 12*f^2*PolyLog[2, (-I)*E^(-c - d*x)] + 20*f^2*PolyLog[2, I*E^(-c - d*x)] + ((-2*I)*f^2*Cosh[c] + 2*d*f*(e + f*x)*Cosh[d*x] - (2*I)*d^2*e^2*Cosh[c + d*x] + (4*I)*f^2*Cosh[c + d*x] - (4*I)*d^2*e*f*x*Cosh[c + d*x] - (2*I)*d^2*f^2*x^2*Cosh[c + d*x] + 2*d*e*f*Cosh[2*c + d*x] + 2*d*f^2*x*Cosh[2*c + d*x] + (4*I)*d^2*e^2*Cosh[c + 2*d*x] - (2*I)*f^2*Cosh[c + 2*d*x] + (8*I)*d^2*e*f*x*Cosh[c + 2*d*x] + (4*I)*d^2*f^2*x^2*Cosh[c + 2*d*x] + 8*d^2*e^2*Sinh[d*x] - 2*f^2*Sinh[d*x] + 16*d^2*e*f*x*Sinh[d*x] + 8*d^2*f^2*x^2*Sinh[d*x] + d^2*e^2*Sinh[2*(c + d*x)] - 2*f^2*Sinh[2*(c + d*x)] + 2*d^2*e*f*x*Sinh[2*(c + d*x)] + d^2*f^2*x^2*Sinh[2*(c + d*x)] + 2*f^2*Sinh[2*c + d*x])/((Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^3))/(12*a*d^3)","A",1
279,1,194,158,1.1179674,"\int \frac{(e+f x) \text{sech}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sech[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{2 d (e+f x) (\cosh (2 (c+d x))-2 i \sinh (c+d x))+\cosh (c+d x) \left(-i \sinh (c+d x) \left(2 f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)-4 i f \log (\cosh (c+d x))-c f+d e\right)-2 f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+4 i f \log (\cosh (c+d x))+c f-d e-i f\right)}{6 a d^2 (\sinh (c+d x)-i) \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}","\frac{f \text{sech}^2(c+d x)}{6 a d^2}-\frac{i f \tan ^{-1}(\sinh (c+d x))}{6 a d^2}-\frac{2 f \log (\cosh (c+d x))}{3 a d^2}-\frac{i f \tanh (c+d x) \text{sech}(c+d x)}{6 a d^2}+\frac{2 (e+f x) \tanh (c+d x)}{3 a d}+\frac{i (e+f x) \text{sech}^3(c+d x)}{3 a d}+\frac{(e+f x) \tanh (c+d x) \text{sech}^2(c+d x)}{3 a d}",1,"(2*d*(e + f*x)*(Cosh[2*(c + d*x)] - (2*I)*Sinh[c + d*x]) + Cosh[c + d*x]*(-(d*e) - I*f + c*f - 2*f*ArcTan[Tanh[(c + d*x)/2]] + (4*I)*f*Log[Cosh[c + d*x]] - I*(d*e - c*f + 2*f*ArcTan[Tanh[(c + d*x)/2]] - (4*I)*f*Log[Cosh[c + d*x]])*Sinh[c + d*x]))/(6*a*d^2*(Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*(-I + Sinh[c + d*x]))","A",1
280,1,47,47,0.045545,"\int \frac{\text{sech}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Sech[c + d*x]^2/(a + I*a*Sinh[c + d*x]),x]","\frac{\text{sech}(c+d x) (\cosh (2 (c+d x))-2 i \sinh (c+d x))}{3 a d (\sinh (c+d x)-i)}","\frac{2 \tanh (c+d x)}{3 a d}+\frac{i \text{sech}(c+d x)}{3 d (a+i a \sinh (c+d x))}",1,"(Sech[c + d*x]*(Cosh[2*(c + d*x)] - (2*I)*Sinh[c + d*x]))/(3*a*d*(-I + Sinh[c + d*x]))","A",1
281,0,0,34,130.791822,"\int \frac{\text{sech}^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Sech[c + d*x]^2/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{sech}^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{sech}^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"Integrate[Sech[c + d*x]^2/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",-1
282,-1,0,34,180.0136403,"\int \frac{\text{sech}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Sech[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{sech}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
283,1,1804,667,13.4889542,"\int \frac{(e+f x)^3 \text{sech}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sech[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","-\frac{i \left(e^3+3 f x e^2+3 f^2 x^2 e+f^3 x^3\right)}{8 a d \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)-i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^2}+\frac{i \left(e^3+3 f x e^2+3 f^2 x^2 e+f^3 x^3\right)}{8 a d \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^4}-\frac{3 \left(f^3 x^4 d^4+4 e f^2 x^3 d^4+4 \left(1-i e^c\right) f^3 x^3 \log \left(1+i e^{-c-d x}\right) d^3+12 e \left(1-i e^c\right) f^2 x^2 \log \left(1+i e^{-c-d x}\right) d^3+2 f \left(3 d^2 e^2-4 f^2\right) x^2 d^2+4 e \left(d^2 e^2-4 f^2\right) x d^2+4 \left(1-i e^c\right) f \left(3 d^2 e^2-4 f^2\right) x \log \left(1+i e^{-c-d x}\right) d+4 i e \left(i+e^c\right) \left(d^2 e^2-4 f^2\right) \left(d x-\log \left(i+e^{c+d x}\right)\right) d+24 i e \left(i+e^c\right) f^2 \left(d x \text{Li}_2\left(-i e^{-c-d x}\right)+\text{Li}_3\left(-i e^{-c-d x}\right)\right) d+4 \left(1-i e^c\right) f \left(4 f^2-3 d^2 e^2\right) \text{Li}_2\left(-i e^{-c-d x}\right)+12 i \left(i+e^c\right) f^3 \left(d^2 \text{Li}_2\left(-i e^{-c-d x}\right) x^2+2 \left(d x \text{Li}_3\left(-i e^{-c-d x}\right)+\text{Li}_4\left(-i e^{-c-d x}\right)\right)\right)\right)}{32 a d^4 \left(i+e^c\right)}-\frac{36 d^3 \left(1+i e^c\right) x^3 \log \left(1-i e^{-c-d x}\right) f^4-108 \left(1+i e^c\right) \left(d^2 \text{Li}_2\left(i e^{-c-d x}\right) x^2+2 \left(d x \text{Li}_3\left(i e^{-c-d x}\right)+\text{Li}_4\left(i e^{-c-d x}\right)\right)\right) f^4+108 d^3 e \left(1+i e^c\right) x^2 \log \left(1-i e^{-c-d x}\right) f^3-216 d e \left(1+i e^c\right) \left(d x \text{Li}_2\left(i e^{-c-d x}\right)+\text{Li}_3\left(i e^{-c-d x}\right)\right) f^3+12 d \left(1+i e^c\right) \left(9 d^2 e^2-28 f^2\right) x \log \left(1-i e^{-c-d x}\right) f^2+12 \left(1+i e^c\right) \left(28 f^2-9 d^2 e^2\right) \text{Li}_2\left(i e^{-c-d x}\right) f^2-12 d e \left(1+i e^c\right) \left(3 d^2 e^2-28 f^2\right) \left(d x-\log \left(i-e^{c+d x}\right)\right) f+\left(28 f^2-3 d^2 (e+f x)^2\right)^2}{96 a d^4 \left(-i+e^c\right) f}+\frac{\frac{3 x \cosh (c) e^3}{4 a}+\frac{3 x \sinh (c) e^3}{4 a}}{\cosh (2 c)+\sinh (2 c)+1}+\frac{\frac{9 e^2 f \cosh (c) x^2}{8 a}+\frac{9 e^2 f \sinh (c) x^2}{8 a}}{\cosh (2 c)+\sinh (2 c)+1}+\frac{\frac{3 e f^2 \cosh (c) x^3}{4 a}+\frac{3 e f^2 \sinh (c) x^3}{4 a}}{\cosh (2 c)+\sinh (2 c)+1}+\frac{\frac{3 f^3 \cosh (c) x^4}{16 a}+\frac{3 f^3 \sinh (c) x^4}{16 a}}{\cosh (2 c)+\sinh (2 c)+1}+\frac{3 i \left(x^2 \sinh \left(\frac{d x}{2}\right) f^3+2 e x \sinh \left(\frac{d x}{2}\right) f^2+e^2 \sinh \left(\frac{d x}{2}\right) f\right)}{4 a d^2 \left(\cosh \left(\frac{c}{2}\right)-i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)-i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}-\frac{i \left(7 d^2 x^2 \sinh \left(\frac{d x}{2}\right) f^3-2 \sinh \left(\frac{d x}{2}\right) f^3+14 d^2 e x \sinh \left(\frac{d x}{2}\right) f^2+7 d^2 e^2 \sinh \left(\frac{d x}{2}\right) f\right)}{4 a d^4 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}+\frac{2 i d^2 \cosh \left(\frac{c}{2}\right) e^3-2 d^2 \sinh \left(\frac{c}{2}\right) e^3+d f \cosh \left(\frac{c}{2}\right) e^2+6 i d^2 f x \cosh \left(\frac{c}{2}\right) e^2-i d f \sinh \left(\frac{c}{2}\right) e^2-6 d^2 f x \sinh \left(\frac{c}{2}\right) e^2-2 i f^2 \cosh \left(\frac{c}{2}\right) e+6 i d^2 f^2 x^2 \cosh \left(\frac{c}{2}\right) e+2 d f^2 x \cosh \left(\frac{c}{2}\right) e+2 f^2 \sinh \left(\frac{c}{2}\right) e-6 d^2 f^2 x^2 \sinh \left(\frac{c}{2}\right) e-2 i d f^2 x \sinh \left(\frac{c}{2}\right) e+2 i d^2 f^3 x^3 \cosh \left(\frac{c}{2}\right)+d f^3 x^2 \cosh \left(\frac{c}{2}\right)-2 i f^3 x \cosh \left(\frac{c}{2}\right)-2 d^2 f^3 x^3 \sinh \left(\frac{c}{2}\right)-i d f^3 x^2 \sinh \left(\frac{c}{2}\right)+2 f^3 x \sinh \left(\frac{c}{2}\right)}{8 a d^3 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^2}-\frac{i \left(x^2 \sinh \left(\frac{d x}{2}\right) f^3+2 e x \sinh \left(\frac{d x}{2}\right) f^2+e^2 \sinh \left(\frac{d x}{2}\right) f\right)}{4 a d^2 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^3}","\frac{5 i f^3 \text{Li}_2\left(-i e^{c+d x}\right)}{2 a d^4}-\frac{5 i f^3 \text{Li}_2\left(i e^{c+d x}\right)}{2 a d^4}+\frac{i f^3 \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 a d^4}-\frac{9 i f^3 \text{Li}_4\left(-i e^{c+d x}\right)}{4 a d^4}+\frac{9 i f^3 \text{Li}_4\left(i e^{c+d x}\right)}{4 a d^4}+\frac{i f^3 \tanh (c+d x)}{4 a d^4}-\frac{f^3 \text{sech}(c+d x)}{4 a d^4}+\frac{9 i f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right)}{4 a d^3}-\frac{9 i f^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right)}{4 a d^3}+\frac{i f^2 (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{a d^3}-\frac{5 f^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{a d^3}-\frac{i f^2 (e+f x) \text{sech}^2(c+d x)}{4 a d^3}-\frac{f^2 (e+f x) \tanh (c+d x) \text{sech}(c+d x)}{4 a d^3}-\frac{9 i f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right)}{8 a d^2}+\frac{9 i f (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right)}{8 a d^2}-\frac{i f (e+f x)^2 \tanh (c+d x)}{2 a d^2}+\frac{f (e+f x)^2 \text{sech}^3(c+d x)}{4 a d^2}+\frac{9 f (e+f x)^2 \text{sech}(c+d x)}{8 a d^2}-\frac{i f (e+f x)^2 \tanh (c+d x) \text{sech}^2(c+d x)}{4 a d^2}+\frac{3 (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right)}{4 a d}+\frac{i (e+f x)^3 \text{sech}^4(c+d x)}{4 a d}+\frac{(e+f x)^3 \tanh (c+d x) \text{sech}^3(c+d x)}{4 a d}+\frac{3 (e+f x)^3 \tanh (c+d x) \text{sech}(c+d x)}{8 a d}-\frac{i f (e+f x)^2}{2 a d^2}",1,"(-3*(4*d^2*e*(d^2*e^2 - 4*f^2)*x + 2*d^2*f*(3*d^2*e^2 - 4*f^2)*x^2 + 4*d^4*e*f^2*x^3 + d^4*f^3*x^4 + 4*d*(1 - I*E^c)*f*(3*d^2*e^2 - 4*f^2)*x*Log[1 + I*E^(-c - d*x)] + 12*d^3*e*(1 - I*E^c)*f^2*x^2*Log[1 + I*E^(-c - d*x)] + 4*d^3*(1 - I*E^c)*f^3*x^3*Log[1 + I*E^(-c - d*x)] + (4*I)*d*e*(I + E^c)*(d^2*e^2 - 4*f^2)*(d*x - Log[I + E^(c + d*x)]) + 4*(1 - I*E^c)*f*(-3*d^2*e^2 + 4*f^2)*PolyLog[2, (-I)*E^(-c - d*x)] + (24*I)*d*e*(I + E^c)*f^2*(d*x*PolyLog[2, (-I)*E^(-c - d*x)] + PolyLog[3, (-I)*E^(-c - d*x)]) + (12*I)*(I + E^c)*f^3*(d^2*x^2*PolyLog[2, (-I)*E^(-c - d*x)] + 2*(d*x*PolyLog[3, (-I)*E^(-c - d*x)] + PolyLog[4, (-I)*E^(-c - d*x)]))))/(32*a*d^4*(I + E^c)) - ((28*f^2 - 3*d^2*(e + f*x)^2)^2 + 12*d*(1 + I*E^c)*f^2*(9*d^2*e^2 - 28*f^2)*x*Log[1 - I*E^(-c - d*x)] + 108*d^3*e*(1 + I*E^c)*f^3*x^2*Log[1 - I*E^(-c - d*x)] + 36*d^3*(1 + I*E^c)*f^4*x^3*Log[1 - I*E^(-c - d*x)] - 12*d*e*(1 + I*E^c)*f*(3*d^2*e^2 - 28*f^2)*(d*x - Log[I - E^(c + d*x)]) + 12*(1 + I*E^c)*f^2*(-9*d^2*e^2 + 28*f^2)*PolyLog[2, I*E^(-c - d*x)] - 216*d*e*(1 + I*E^c)*f^3*(d*x*PolyLog[2, I*E^(-c - d*x)] + PolyLog[3, I*E^(-c - d*x)]) - 108*(1 + I*E^c)*f^4*(d^2*x^2*PolyLog[2, I*E^(-c - d*x)] + 2*(d*x*PolyLog[3, I*E^(-c - d*x)] + PolyLog[4, I*E^(-c - d*x)])))/(96*a*d^4*(-I + E^c)*f) + ((3*e^3*x*Cosh[c])/(4*a) + (3*e^3*x*Sinh[c])/(4*a))/(1 + Cosh[2*c] + Sinh[2*c]) + ((9*e^2*f*x^2*Cosh[c])/(8*a) + (9*e^2*f*x^2*Sinh[c])/(8*a))/(1 + Cosh[2*c] + Sinh[2*c]) + ((3*e*f^2*x^3*Cosh[c])/(4*a) + (3*e*f^2*x^3*Sinh[c])/(4*a))/(1 + Cosh[2*c] + Sinh[2*c]) + ((3*f^3*x^4*Cosh[c])/(16*a) + (3*f^3*x^4*Sinh[c])/(16*a))/(1 + Cosh[2*c] + Sinh[2*c]) - ((I/8)*(e^3 + 3*e^2*f*x + 3*e*f^2*x^2 + f^3*x^3))/(a*d*(Cosh[c/2 + (d*x)/2] - I*Sinh[c/2 + (d*x)/2])^2) + (((3*I)/4)*(e^2*f*Sinh[(d*x)/2] + 2*e*f^2*x*Sinh[(d*x)/2] + f^3*x^2*Sinh[(d*x)/2]))/(a*d^2*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] - I*Sinh[c/2 + (d*x)/2])) + ((I/8)*(e^3 + 3*e^2*f*x + 3*e*f^2*x^2 + f^3*x^3))/(a*d*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^4) - ((I/4)*(e^2*f*Sinh[(d*x)/2] + 2*e*f^2*x*Sinh[(d*x)/2] + f^3*x^2*Sinh[(d*x)/2]))/(a*d^2*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^3) + ((2*I)*d^2*e^3*Cosh[c/2] + d*e^2*f*Cosh[c/2] - (2*I)*e*f^2*Cosh[c/2] + (6*I)*d^2*e^2*f*x*Cosh[c/2] + 2*d*e*f^2*x*Cosh[c/2] - (2*I)*f^3*x*Cosh[c/2] + (6*I)*d^2*e*f^2*x^2*Cosh[c/2] + d*f^3*x^2*Cosh[c/2] + (2*I)*d^2*f^3*x^3*Cosh[c/2] - 2*d^2*e^3*Sinh[c/2] - I*d*e^2*f*Sinh[c/2] + 2*e*f^2*Sinh[c/2] - 6*d^2*e^2*f*x*Sinh[c/2] - (2*I)*d*e*f^2*x*Sinh[c/2] + 2*f^3*x*Sinh[c/2] - 6*d^2*e*f^2*x^2*Sinh[c/2] - I*d*f^3*x^2*Sinh[c/2] - 2*d^2*f^3*x^3*Sinh[c/2])/(8*a*d^3*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^2) - ((I/4)*(7*d^2*e^2*f*Sinh[(d*x)/2] - 2*f^3*Sinh[(d*x)/2] + 14*d^2*e*f^2*x*Sinh[(d*x)/2] + 7*d^2*f^3*x^2*Sinh[(d*x)/2]))/(a*d^4*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2]))","B",0
284,1,1284,423,12.9553959,"\int \frac{(e+f x)^2 \text{sech}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sech[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","-\frac{i \left(e^2+2 f x e+f^2 x^2\right)}{8 a d \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)-i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^2}+\frac{i \left(e^2+2 f x e+f^2 x^2\right)}{8 a d \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^4}-\frac{3 d^2 f^2 x^3+9 d^2 e f x^2+9 d \left(1+i e^c\right) f^2 \log \left(1-i e^{-c-d x}\right) x^2+\left(9 d^2 e^2-28 f^2\right) x+18 d e \left(1+i e^c\right) f \log \left(1-i e^{-c-d x}\right) x-\frac{\left(1+i e^c\right) \left(9 d^2 e^2-28 f^2\right) \left(d x-\log \left(i-e^{c+d x}\right)\right)}{d}-18 e \left(1+i e^c\right) f \text{Li}_2\left(i e^{-c-d x}\right)-18 \left(1+i e^c\right) f^2 \left(x \text{Li}_2\left(i e^{-c-d x}\right)+\frac{\text{Li}_3\left(i e^{-c-d x}\right)}{d}\right)}{24 a d^2 \left(-i+e^c\right)}-\frac{d^2 f^2 x^3+3 d^2 e f x^2-3 i d f^2 \log (i \cosh (c+d x)-i \sinh (c+d x)+1) (\cosh (c)+\sinh (c)+i) x^2+3 d^2 e^2 x-4 f^2 x-6 i d e f \log (i \cosh (c+d x)-i \sinh (c+d x)+1) (\cosh (c)+\sinh (c)+i) x+\frac{i \left(3 d^2 e^2-4 f^2\right) (d x-\log (\cosh (c+d x)+\sinh (c+d x)+i)) (\cosh (c)+\sinh (c)+i)}{d}+6 i e f \text{Li}_2(-i (\cosh (c+d x)-\sinh (c+d x))) (\cosh (c)+\sinh (c)+i)+\frac{6 i f^2 (d x \text{Li}_2(-i (\cosh (c+d x)-\sinh (c+d x)))+\text{Li}_3(-i (\cosh (c+d x)-\sinh (c+d x)))) (\cosh (c)+\sinh (c)+i)}{d}}{8 a d^2 (\cosh (c)+\sinh (c)+i)}+\frac{\frac{3 x \cosh (c) e^2}{4 a}+\frac{3 x \sinh (c) e^2}{4 a}}{\cosh (2 c)+\sinh (2 c)+1}+\frac{\frac{3 e f \cosh (c) x^2}{4 a}+\frac{3 e f \sinh (c) x^2}{4 a}}{\cosh (2 c)+\sinh (2 c)+1}+\frac{\frac{f^2 \cosh (c) x^3}{4 a}+\frac{f^2 \sinh (c) x^3}{4 a}}{\cosh (2 c)+\sinh (2 c)+1}+\frac{i \left(x \sinh \left(\frac{d x}{2}\right) f^2+e \sinh \left(\frac{d x}{2}\right) f\right)}{2 a d^2 \left(\cosh \left(\frac{c}{2}\right)-i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)-i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}-\frac{7 i \left(x \sinh \left(\frac{d x}{2}\right) f^2+e \sinh \left(\frac{d x}{2}\right) f\right)}{6 a d^2 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)}+\frac{3 i e^2 \cosh \left(\frac{c}{2}\right) d^2+3 i f^2 x^2 \cosh \left(\frac{c}{2}\right) d^2+6 i e f x \cosh \left(\frac{c}{2}\right) d^2-3 e^2 \sinh \left(\frac{c}{2}\right) d^2-3 f^2 x^2 \sinh \left(\frac{c}{2}\right) d^2-6 e f x \sinh \left(\frac{c}{2}\right) d^2+e f \cosh \left(\frac{c}{2}\right) d+f^2 x \cosh \left(\frac{c}{2}\right) d-i e f \sinh \left(\frac{c}{2}\right) d-i f^2 x \sinh \left(\frac{c}{2}\right) d-i f^2 \cosh \left(\frac{c}{2}\right)+f^2 \sinh \left(\frac{c}{2}\right)}{12 a d^3 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^2}-\frac{i \left(x \sinh \left(\frac{d x}{2}\right) f^2+e \sinh \left(\frac{d x}{2}\right) f\right)}{6 a d^2 \left(\cosh \left(\frac{c}{2}\right)+i \sinh \left(\frac{c}{2}\right)\right) \left(\cosh \left(\frac{c}{2}+\frac{d x}{2}\right)+i \sinh \left(\frac{c}{2}+\frac{d x}{2}\right)\right)^3}","\frac{3 i f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{4 a d^3}-\frac{3 i f^2 \text{Li}_3\left(i e^{c+d x}\right)}{4 a d^3}-\frac{i f^2 \text{sech}^2(c+d x)}{12 a d^3}-\frac{5 f^2 \tan ^{-1}(\sinh (c+d x))}{6 a d^3}+\frac{i f^2 \log (\cosh (c+d x))}{3 a d^3}-\frac{f^2 \tanh (c+d x) \text{sech}(c+d x)}{12 a d^3}-\frac{3 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{4 a d^2}+\frac{3 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{4 a d^2}-\frac{i f (e+f x) \tanh (c+d x)}{3 a d^2}+\frac{f (e+f x) \text{sech}^3(c+d x)}{6 a d^2}+\frac{3 f (e+f x) \text{sech}(c+d x)}{4 a d^2}-\frac{i f (e+f x) \tanh (c+d x) \text{sech}^2(c+d x)}{6 a d^2}+\frac{3 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{4 a d}+\frac{i (e+f x)^2 \text{sech}^4(c+d x)}{4 a d}+\frac{(e+f x)^2 \tanh (c+d x) \text{sech}^3(c+d x)}{4 a d}+\frac{3 (e+f x)^2 \tanh (c+d x) \text{sech}(c+d x)}{8 a d}",1,"-1/24*((9*d^2*e^2 - 28*f^2)*x + 9*d^2*e*f*x^2 + 3*d^2*f^2*x^3 + 18*d*e*(1 + I*E^c)*f*x*Log[1 - I*E^(-c - d*x)] + 9*d*(1 + I*E^c)*f^2*x^2*Log[1 - I*E^(-c - d*x)] - ((1 + I*E^c)*(9*d^2*e^2 - 28*f^2)*(d*x - Log[I - E^(c + d*x)]))/d - 18*e*(1 + I*E^c)*f*PolyLog[2, I*E^(-c - d*x)] - 18*(1 + I*E^c)*f^2*(x*PolyLog[2, I*E^(-c - d*x)] + PolyLog[3, I*E^(-c - d*x)]/d))/(a*d^2*(-I + E^c)) - (3*d^2*e^2*x - 4*f^2*x + 3*d^2*e*f*x^2 + d^2*f^2*x^3 - (6*I)*d*e*f*x*Log[1 + I*Cosh[c + d*x] - I*Sinh[c + d*x]]*(I + Cosh[c] + Sinh[c]) - (3*I)*d*f^2*x^2*Log[1 + I*Cosh[c + d*x] - I*Sinh[c + d*x]]*(I + Cosh[c] + Sinh[c]) + (I*(3*d^2*e^2 - 4*f^2)*(d*x - Log[I + Cosh[c + d*x] + Sinh[c + d*x]])*(I + Cosh[c] + Sinh[c]))/d + (6*I)*e*f*PolyLog[2, (-I)*(Cosh[c + d*x] - Sinh[c + d*x])]*(I + Cosh[c] + Sinh[c]) + ((6*I)*f^2*(d*x*PolyLog[2, (-I)*(Cosh[c + d*x] - Sinh[c + d*x])] + PolyLog[3, (-I)*(Cosh[c + d*x] - Sinh[c + d*x])])*(I + Cosh[c] + Sinh[c]))/d)/(8*a*d^2*(I + Cosh[c] + Sinh[c])) + ((3*e^2*x*Cosh[c])/(4*a) + (3*e^2*x*Sinh[c])/(4*a))/(1 + Cosh[2*c] + Sinh[2*c]) + ((3*e*f*x^2*Cosh[c])/(4*a) + (3*e*f*x^2*Sinh[c])/(4*a))/(1 + Cosh[2*c] + Sinh[2*c]) + ((f^2*x^3*Cosh[c])/(4*a) + (f^2*x^3*Sinh[c])/(4*a))/(1 + Cosh[2*c] + Sinh[2*c]) - ((I/8)*(e^2 + 2*e*f*x + f^2*x^2))/(a*d*(Cosh[c/2 + (d*x)/2] - I*Sinh[c/2 + (d*x)/2])^2) + ((I/2)*(e*f*Sinh[(d*x)/2] + f^2*x*Sinh[(d*x)/2]))/(a*d^2*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] - I*Sinh[c/2 + (d*x)/2])) + ((I/8)*(e^2 + 2*e*f*x + f^2*x^2))/(a*d*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^4) - ((I/6)*(e*f*Sinh[(d*x)/2] + f^2*x*Sinh[(d*x)/2]))/(a*d^2*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^3) + ((3*I)*d^2*e^2*Cosh[c/2] + d*e*f*Cosh[c/2] - I*f^2*Cosh[c/2] + (6*I)*d^2*e*f*x*Cosh[c/2] + d*f^2*x*Cosh[c/2] + (3*I)*d^2*f^2*x^2*Cosh[c/2] - 3*d^2*e^2*Sinh[c/2] - I*d*e*f*Sinh[c/2] + f^2*Sinh[c/2] - 6*d^2*e*f*x*Sinh[c/2] - I*d*f^2*x*Sinh[c/2] - 3*d^2*f^2*x^2*Sinh[c/2])/(12*a*d^3*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2])^2) - (((7*I)/6)*(e*f*Sinh[(d*x)/2] + f^2*x*Sinh[(d*x)/2]))/(a*d^2*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c/2 + (d*x)/2] + I*Sinh[c/2 + (d*x)/2]))","B",0
285,1,1290,233,6.6634694,"\int \frac{(e+f x) \text{sech}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sech[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{3 (c+d x) (2 d e-2 c f+f (c+d x)) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}{16 d^2 (i \sinh (c+d x) a+a)}+\frac{3 i e \left(\frac{1}{2} i (c+d x)+\log \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}{8 d (i \sinh (c+d x) a+a)}-\frac{3 i c f \left(\frac{1}{2} i (c+d x)+\log \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}{8 d^2 (i \sinh (c+d x) a+a)}-\frac{3 i e \left(\log \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)-\frac{1}{2} i (c+d x)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}{8 d (i \sinh (c+d x) a+a)}+\frac{3 i c f \left(\log \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)-\frac{1}{2} i (c+d x)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}{8 d^2 (i \sinh (c+d x) a+a)}-\frac{3 f \left(\frac{1}{4} e^{-\frac{i \pi }{4}} (c+d x)^2+\frac{\frac{3}{4} \pi  (c+d x)-\pi  \log \left(1+e^{c+d x}\right)-2 \left(\frac{1}{2} i (c+d x)-\frac{\pi }{4}\right) \log \left(1-e^{2 i \left(\frac{1}{2} i (c+d x)-\frac{\pi }{4}\right)}\right)+\pi  \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)-\frac{1}{2} \pi  \log \left(-\sin \left(\frac{\pi }{4}-\frac{1}{2} i (c+d x)\right)\right)+i \text{Li}_2\left(e^{2 i \left(\frac{1}{2} i (c+d x)-\frac{\pi }{4}\right)}\right)}{\sqrt{2}}\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}{4 \sqrt{2} d^2 (i \sinh (c+d x) a+a)}-\frac{3 f \left(\frac{1}{4} e^{\frac{i \pi }{4}} (c+d x)^2-\frac{\frac{1}{4} \pi  (c+d x)-\pi  \log \left(1+e^{c+d x}\right)-2 \left(\frac{1}{2} i (c+d x)+\frac{\pi }{4}\right) \log \left(1-e^{2 i \left(\frac{1}{2} i (c+d x)+\frac{\pi }{4}\right)}\right)+\pi  \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)+\frac{1}{2} \pi  \log \left(\sin \left(\frac{1}{2} i (c+d x)+\frac{\pi }{4}\right)\right)+i \text{Li}_2\left(e^{2 i \left(\frac{1}{2} i (c+d x)+\frac{\pi }{4}\right)}\right)}{\sqrt{2}}\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}{4 \sqrt{2} d^2 (i \sinh (c+d x) a+a)}+\frac{i f \sinh \left(\frac{1}{2} (c+d x)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}{4 d^2 \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right) (i \sinh (c+d x) a+a)}-\frac{i (d e-c f+f (c+d x)) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}{8 d^2 \left(\cosh \left(\frac{1}{2} (c+d x)\right)-i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2 (i \sinh (c+d x) a+a)}-\frac{7 i f \sinh \left(\frac{1}{2} (c+d x)\right) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{12 d^2 (i \sinh (c+d x) a+a)}+\frac{i (6 d e-6 c f-i f+6 f (c+d x))}{24 d^2 (i \sinh (c+d x) a+a)}-\frac{i f \sinh \left(\frac{1}{2} (c+d x)\right)}{12 d^2 (i \sinh (c+d x) a+a) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)}+\frac{i (d e-c f+f (c+d x))}{8 d^2 (i \sinh (c+d x) a+a) \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)^2}","-\frac{3 i f \text{Li}_2\left(-i e^{c+d x}\right)}{8 a d^2}+\frac{3 i f \text{Li}_2\left(i e^{c+d x}\right)}{8 a d^2}+\frac{i f \tanh ^3(c+d x)}{12 a d^2}-\frac{i f \tanh (c+d x)}{4 a d^2}+\frac{f \text{sech}^3(c+d x)}{12 a d^2}+\frac{3 f \text{sech}(c+d x)}{8 a d^2}+\frac{3 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{4 a d}+\frac{i (e+f x) \text{sech}^4(c+d x)}{4 a d}+\frac{(e+f x) \tanh (c+d x) \text{sech}^3(c+d x)}{4 a d}+\frac{3 (e+f x) \tanh (c+d x) \text{sech}(c+d x)}{8 a d}",1,"((I/24)*(6*d*e - I*f - 6*c*f + 6*f*(c + d*x)))/(d^2*(a + I*a*Sinh[c + d*x])) + ((I/8)*(d*e - c*f + f*(c + d*x)))/(d^2*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2*(a + I*a*Sinh[c + d*x])) + (3*(c + d*x)*(2*d*e - 2*c*f + f*(c + d*x))*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2)/(16*d^2*(a + I*a*Sinh[c + d*x])) + (((3*I)/8)*e*((I/2)*(c + d*x) + Log[Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2]])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2)/(d*(a + I*a*Sinh[c + d*x])) - (((3*I)/8)*c*f*((I/2)*(c + d*x) + Log[Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2]])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2)/(d^2*(a + I*a*Sinh[c + d*x])) - (((3*I)/8)*e*((-1/2*I)*(c + d*x) + Log[Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2)/(d*(a + I*a*Sinh[c + d*x])) + (((3*I)/8)*c*f*((-1/2*I)*(c + d*x) + Log[Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2)/(d^2*(a + I*a*Sinh[c + d*x])) - (3*f*((c + d*x)^2/(4*E^((I/4)*Pi)) + ((3*Pi*(c + d*x))/4 - Pi*Log[1 + E^(c + d*x)] - 2*(-1/4*Pi + (I/2)*(c + d*x))*Log[1 - E^((2*I)*(-1/4*Pi + (I/2)*(c + d*x)))] + Pi*Log[Cosh[(c + d*x)/2]] - (Pi*Log[-Sin[Pi/4 - (I/2)*(c + d*x)]])/2 + I*PolyLog[2, E^((2*I)*(-1/4*Pi + (I/2)*(c + d*x)))])/Sqrt[2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2)/(4*Sqrt[2]*d^2*(a + I*a*Sinh[c + d*x])) - (3*f*((E^((I/4)*Pi)*(c + d*x)^2)/4 - ((Pi*(c + d*x))/4 - Pi*Log[1 + E^(c + d*x)] - 2*(Pi/4 + (I/2)*(c + d*x))*Log[1 - E^((2*I)*(Pi/4 + (I/2)*(c + d*x)))] + Pi*Log[Cosh[(c + d*x)/2]] + (Pi*Log[Sin[Pi/4 + (I/2)*(c + d*x)]])/2 + I*PolyLog[2, E^((2*I)*(Pi/4 + (I/2)*(c + d*x)))])/Sqrt[2])*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2)/(4*Sqrt[2]*d^2*(a + I*a*Sinh[c + d*x])) - ((I/8)*(d*e - c*f + f*(c + d*x))*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2)/(d^2*(Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2])^2*(a + I*a*Sinh[c + d*x])) - ((I/12)*f*Sinh[(c + d*x)/2])/(d^2*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*(a + I*a*Sinh[c + d*x])) - (((7*I)/12)*f*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])*Sinh[(c + d*x)/2])/(d^2*(a + I*a*Sinh[c + d*x])) + ((I/4)*f*(Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2])^2*Sinh[(c + d*x)/2])/(d^2*(Cosh[(c + d*x)/2] - I*Sinh[(c + d*x)/2])*(a + I*a*Sinh[c + d*x]))","B",1
286,1,101,91,0.1058125,"\int \frac{\text{sech}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Integrate[Sech[c + d*x]^3/(a + I*a*Sinh[c + d*x]),x]","\frac{\text{sech}^2(c+d x) \left(3 \sinh ^3(c+d x) \tan ^{-1}(\sinh (c+d x))+\sinh ^2(c+d x) \left(3-3 i \tan ^{-1}(\sinh (c+d x))\right)+3 \sinh (c+d x) \left(\tan ^{-1}(\sinh (c+d x))-i\right)-3 i \tan ^{-1}(\sinh (c+d x))+2\right)}{8 a d (\sinh (c+d x)-i)}","\frac{i a}{8 d (a+i a \sinh (c+d x))^2}-\frac{i}{8 d (a-i a \sinh (c+d x))}+\frac{i}{4 d (a+i a \sinh (c+d x))}+\frac{3 \tan ^{-1}(\sinh (c+d x))}{8 a d}",1,"(Sech[c + d*x]^2*(2 - (3*I)*ArcTan[Sinh[c + d*x]] + 3*(-I + ArcTan[Sinh[c + d*x]])*Sinh[c + d*x] + (3 - (3*I)*ArcTan[Sinh[c + d*x]])*Sinh[c + d*x]^2 + 3*ArcTan[Sinh[c + d*x]]*Sinh[c + d*x]^3))/(8*a*d*(-I + Sinh[c + d*x]))","A",1
287,0,0,34,118.2961583,"\int \frac{\text{sech}^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Integrate[Sech[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{sech}^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{sech}^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"Integrate[Sech[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",-1
288,-1,0,34,180.0278552,"\int \frac{\text{sech}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Integrate[Sech[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{sech}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
289,1,329,356,0.1379405,"\int \frac{(e+f x)^3 \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\frac{12 f \left(d^2 (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 d f (e+f x) \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 f^2 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)\right)}{d^4}+\frac{12 f \left(d^2 (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-2 d f (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+2 f^2 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{d^4}+\frac{4 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d}+\frac{4 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d}-\frac{(e+f x)^4}{f}}{4 b}","\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^4}+\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^4}-\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3}-\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{(e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d}+\frac{(e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d}-\frac{(e+f x)^4}{4 b f}",1,"(-((e + f*x)^4/f) + (4*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/d + (4*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/d + (12*f*(d^2*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*f^2*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])]))/d^4 + (12*f*(d^2*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*d*f*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/d^4)/(4*b)","A",1
290,1,244,264,0.1269856,"\int \frac{(e+f x)^2 \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\frac{6 f \left(d (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)\right)}{d^3}+\frac{6 f \left(d (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-f \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{d^3}+\frac{3 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d}+\frac{3 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d}-\frac{(e+f x)^3}{f}}{3 b}","-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{(e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d}+\frac{(e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d}-\frac{(e+f x)^3}{3 b f}",1,"(-((e + f*x)^3/f) + (3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/d + (3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/d + (6*f*(d*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])]))/d^3 + (6*f*(d*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - f*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/d^3)/(3*b)","A",1
291,1,157,170,0.0330003,"\int \frac{(e+f x) \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{-d (e+f x) \left(-2 f \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-2 f \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e+d f x\right)+2 f^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 f^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{2 b d^2 f}","\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{(e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d}+\frac{(e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d}-\frac{(e+f x)^2}{2 b f}",1,"(-(d*(e + f*x)*(d*e + d*f*x - 2*f*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*f*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])) + 2*f^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*f^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(2*b*d^2*f)","A",1
292,1,18,18,0.0071745,"\int \frac{\cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Cosh[c + d*x]/(a + b*Sinh[c + d*x]),x]","\frac{\log (a+b \sinh (c+d x))}{b d}","\frac{\log (a+b \sinh (c+d x))}{b d}",1,"Log[a + b*Sinh[c + d*x]]/(b*d)","A",1
293,0,0,29,13.1061789,"\int \frac{\cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Cosh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Cosh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
294,1,933,527,3.0928699,"\int \frac{(e+f x)^3 \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{a f^3 x^4 d^4+4 a e f^2 x^3 d^4+6 a e^2 f x^2 d^4+4 a e^3 x d^4+8 \sqrt{a^2+b^2} e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3-4 b e^3 \cosh (c+d x) d^3-4 b f^3 x^3 \cosh (c+d x) d^3-12 b e f^2 x^2 \cosh (c+d x) d^3-12 b e^2 f x \cosh (c+d x) d^3-4 \sqrt{a^2+b^2} f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-12 \sqrt{a^2+b^2} e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-12 \sqrt{a^2+b^2} e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+4 \sqrt{a^2+b^2} f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+12 \sqrt{a^2+b^2} e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+12 \sqrt{a^2+b^2} e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-12 \sqrt{a^2+b^2} f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2+12 \sqrt{a^2+b^2} f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2+12 b f^3 x^2 \sinh (c+d x) d^2+12 b e^2 f \sinh (c+d x) d^2+24 b e f^2 x \sinh (c+d x) d^2-24 b e f^2 \cosh (c+d x) d-24 b f^3 x \cosh (c+d x) d+24 \sqrt{a^2+b^2} e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+24 \sqrt{a^2+b^2} f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-24 \sqrt{a^2+b^2} e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-24 \sqrt{a^2+b^2} f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-24 \sqrt{a^2+b^2} f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+24 \sqrt{a^2+b^2} f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+24 b f^3 \sinh (c+d x)}{4 b^2 d^4}","\frac{6 f^3 \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^4}-\frac{6 f^3 \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^4}-\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^3}+\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^3}+\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^2}+\frac{\sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^2 d}-\frac{\sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^2 d}-\frac{a (e+f x)^4}{4 b^2 f}-\frac{6 f^3 \sinh (c+d x)}{b d^4}+\frac{6 f^2 (e+f x) \cosh (c+d x)}{b d^3}-\frac{3 f (e+f x)^2 \sinh (c+d x)}{b d^2}+\frac{(e+f x)^3 \cosh (c+d x)}{b d}",1,"-1/4*(4*a*d^4*e^3*x + 6*a*d^4*e^2*f*x^2 + 4*a*d^4*e*f^2*x^3 + a*d^4*f^3*x^4 + 8*Sqrt[a^2 + b^2]*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 4*b*d^3*e^3*Cosh[c + d*x] - 24*b*d*e*f^2*Cosh[c + d*x] - 12*b*d^3*e^2*f*x*Cosh[c + d*x] - 24*b*d*f^3*x*Cosh[c + d*x] - 12*b*d^3*e*f^2*x^2*Cosh[c + d*x] - 4*b*d^3*f^3*x^3*Cosh[c + d*x] - 12*Sqrt[a^2 + b^2]*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 12*Sqrt[a^2 + b^2]*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 4*Sqrt[a^2 + b^2]*d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 12*Sqrt[a^2 + b^2]*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 12*Sqrt[a^2 + b^2]*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 4*Sqrt[a^2 + b^2]*d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 12*Sqrt[a^2 + b^2]*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 12*Sqrt[a^2 + b^2]*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 24*Sqrt[a^2 + b^2]*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 24*Sqrt[a^2 + b^2]*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 24*Sqrt[a^2 + b^2]*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 24*Sqrt[a^2 + b^2]*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 24*Sqrt[a^2 + b^2]*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 24*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 12*b*d^2*e^2*f*Sinh[c + d*x] + 24*b*f^3*Sinh[c + d*x] + 24*b*d^2*e*f^2*x*Sinh[c + d*x] + 12*b*d^2*f^3*x^2*Sinh[c + d*x])/(b^2*d^4)","A",1
295,1,447,389,2.7667144,"\int \frac{(e+f x)^2 \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{3 \sqrt{a^2+b^2} \left(2 d^2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-2 d^2 e f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+2 d^2 e f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 d f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 d f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)+a d^3 x \left(3 e^2+3 e f x+f^2 x^2\right)-3 b \cosh (d x) \left(\cosh (c) \left(d^2 (e+f x)^2+2 f^2\right)-2 d f \sinh (c) (e+f x)\right)+3 b \sinh (d x) \left(2 d f \cosh (c) (e+f x)-\sinh (c) \left(d^2 (e+f x)^2+2 f^2\right)\right)}{3 b^2 d^3}","-\frac{2 f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^3}+\frac{2 f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^3}+\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^2}+\frac{\sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^2 d}-\frac{\sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^2 d}-\frac{a (e+f x)^3}{3 b^2 f}+\frac{2 f^2 \cosh (c+d x)}{b d^3}-\frac{2 f (e+f x) \sinh (c+d x)}{b d^2}+\frac{(e+f x)^2 \cosh (c+d x)}{b d}",1,"-1/3*(a*d^3*x*(3*e^2 + 3*e*f*x + f^2*x^2) + 3*Sqrt[a^2 + b^2]*(2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - 3*b*Cosh[d*x]*((2*f^2 + d^2*(e + f*x)^2)*Cosh[c] - 2*d*f*(e + f*x)*Sinh[c]) + 3*b*(2*d*f*(e + f*x)*Cosh[c] - (2*f^2 + d^2*(e + f*x)^2)*Sinh[c])*Sinh[d*x])/(b^2*d^3)","A",1
296,1,258,252,1.9074118,"\int \frac{(e+f x) \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 \sqrt{a^2+b^2} \left(-2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)+a (c+d x) (c f-d (2 e+f x))+2 b d (e+f x) \cosh (c+d x)-2 b f \sinh (c+d x)}{2 b^2 d^2}","\frac{f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^2}+\frac{\sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^2 d}-\frac{\sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^2 d}-\frac{a e x}{b^2}-\frac{a f x^2}{2 b^2}-\frac{f \sinh (c+d x)}{b d^2}+\frac{(e+f x) \cosh (c+d x)}{b d}",1,"(a*(c + d*x)*(c*f - d*(2*e + f*x)) + 2*b*d*(e + f*x)*Cosh[c + d*x] + 2*Sqrt[a^2 + b^2]*(-2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - 2*b*f*Sinh[c + d*x])/(2*b^2*d^2)","A",1
297,1,458,68,1.4178436,"\int \frac{\cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Cosh[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","\frac{\cosh (c+d x) \left(\sqrt{a+i b} \sqrt{-\frac{b (\sinh (c+d x)-i)}{a+i b}} \left(\sqrt{a-i b} \sqrt{1+i \sinh (c+d x)} \sqrt{-\frac{b (\sinh (c+d x)+i)}{a-i b}}-2 (-1)^{3/4} \sqrt{b} \sin ^{-1}\left(\frac{\sqrt[4]{-1} \sqrt{a-i b} \sqrt{-\frac{b (\sinh (c+d x)+i)}{a-i b}}}{\sqrt{2} \sqrt{b}}\right)\right)-2 \sqrt{a-i b} \sqrt{a+i b} \sqrt{1+i \sinh (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{-\frac{b (\sinh (c+d x)+i)}{a-i b}}}{\sqrt{-\frac{b (\sinh (c+d x)-i)}{a+i b}}}\right)+2 (a-i b) \sqrt{1+i \sinh (c+d x)} \tanh ^{-1}\left(\frac{\sqrt{a-i b} \sqrt{-\frac{b (\sinh (c+d x)+i)}{a-i b}}}{\sqrt{a+i b} \sqrt{-\frac{b (\sinh (c+d x)-i)}{a+i b}}}\right)\right)}{b d \sqrt{a-i b} \sqrt{a+i b} \sqrt{1+i \sinh (c+d x)} \sqrt{-\frac{b (\sinh (c+d x)-i)}{a+i b}} \sqrt{-\frac{b (\sinh (c+d x)+i)}{a-i b}}}","-\frac{2 \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b^2 d}-\frac{a x}{b^2}+\frac{\cosh (c+d x)}{b d}",1,"(Cosh[c + d*x]*(-2*Sqrt[a - I*b]*Sqrt[a + I*b]*ArcTanh[Sqrt[-((b*(I + Sinh[c + d*x]))/(a - I*b))]/Sqrt[-((b*(-I + Sinh[c + d*x]))/(a + I*b))]]*Sqrt[1 + I*Sinh[c + d*x]] + 2*(a - I*b)*ArcTanh[(Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[c + d*x]))/(a - I*b))])/(Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[c + d*x]))/(a + I*b))])]*Sqrt[1 + I*Sinh[c + d*x]] + Sqrt[a + I*b]*Sqrt[-((b*(-I + Sinh[c + d*x]))/(a + I*b))]*(-2*(-1)^(3/4)*Sqrt[b]*ArcSin[((-1)^(1/4)*Sqrt[a - I*b]*Sqrt[-((b*(I + Sinh[c + d*x]))/(a - I*b))])/(Sqrt[2]*Sqrt[b])] + Sqrt[a - I*b]*Sqrt[1 + I*Sinh[c + d*x]]*Sqrt[-((b*(I + Sinh[c + d*x]))/(a - I*b))])))/(Sqrt[a - I*b]*Sqrt[a + I*b]*b*d*Sqrt[1 + I*Sinh[c + d*x]]*Sqrt[-((b*(-I + Sinh[c + d*x]))/(a + I*b))]*Sqrt[-((b*(I + Sinh[c + d*x]))/(a - I*b))])","C",1
298,0,0,31,25.2657743,"\int \frac{\cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Cosh[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Cosh[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
299,1,10263,642,23.9226757,"\int \frac{(e+f x)^3 \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{6 f^3 \left(a^2+b^2\right) \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^4}+\frac{6 f^3 \left(a^2+b^2\right) \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^4}-\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^3}-\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^3}+\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{\left(a^2+b^2\right) (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d}+\frac{\left(a^2+b^2\right) (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d}-\frac{\left(a^2+b^2\right) (e+f x)^4}{4 b^3 f}+\frac{6 a f^3 \cosh (c+d x)}{b^2 d^4}-\frac{6 a f^2 (e+f x) \sinh (c+d x)}{b^2 d^3}+\frac{3 a f (e+f x)^2 \cosh (c+d x)}{b^2 d^2}-\frac{a (e+f x)^3 \sinh (c+d x)}{b^2 d}-\frac{3 f^3 \sinh (c+d x) \cosh (c+d x)}{8 b d^4}+\frac{3 f^2 (e+f x) \sinh ^2(c+d x)}{4 b d^3}-\frac{3 f (e+f x)^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^2}+\frac{(e+f x)^3 \sinh ^2(c+d x)}{2 b d}+\frac{3 f^3 x}{8 b d^3}+\frac{(e+f x)^3}{4 b d}",1,"Result too large to show","B",1
300,1,3021,477,16.3982096,"\int \frac{(e+f x)^2 \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{2 f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^3}-\frac{2 f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^3}+\frac{2 f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{2 f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{\left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d}+\frac{\left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d}-\frac{\left(a^2+b^2\right) (e+f x)^3}{3 b^3 f}-\frac{2 a f^2 \sinh (c+d x)}{b^2 d^3}+\frac{2 a f (e+f x) \cosh (c+d x)}{b^2 d^2}-\frac{a (e+f x)^2 \sinh (c+d x)}{b^2 d}+\frac{f^2 \sinh ^2(c+d x)}{4 b d^3}-\frac{f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b d^2}+\frac{(e+f x)^2 \sinh ^2(c+d x)}{2 b d}+\frac{e f x}{2 b d}+\frac{f^2 x^2}{4 b d}",1,"-1/3*((a^2 + b^2)*(6*e^2*E^(2*c)*x + 6*e*E^(2*c)*f*x^2 + 2*E^(2*c)*f^2*x^3 + (6*a*Sqrt[a^2 + b^2]*e^2*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/(Sqrt[-(a^2 + b^2)^2]*d) + (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) - (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (3*e^2*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d - (3*e^2*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (3*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (3*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (3*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (3*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3))/(b^3*(-1 + E^(2*c))) + Csch[c]*(Cosh[2*c + 2*d*x]/(96*b^3*d^3) - Sinh[2*c + 2*d*x]/(96*b^3*d^3))*(-24*a*b*d^2*e^2*Cosh[d*x] - 48*a*b*d*e*f*Cosh[d*x] - 48*a*b*f^2*Cosh[d*x] - 48*a*b*d^2*e*f*x*Cosh[d*x] - 48*a*b*d*f^2*x*Cosh[d*x] - 24*a*b*d^2*f^2*x^2*Cosh[d*x] + 24*a*b*d^2*e^2*Cosh[2*c + d*x] + 48*a*b*d*e*f*Cosh[2*c + d*x] + 48*a*b*f^2*Cosh[2*c + d*x] + 48*a*b*d^2*e*f*x*Cosh[2*c + d*x] + 48*a*b*d*f^2*x*Cosh[2*c + d*x] + 24*a*b*d^2*f^2*x^2*Cosh[2*c + d*x] + 48*a^2*d^3*e^2*x*Cosh[c + 2*d*x] + 48*b^2*d^3*e^2*x*Cosh[c + 2*d*x] + 48*a^2*d^3*e*f*x^2*Cosh[c + 2*d*x] + 48*b^2*d^3*e*f*x^2*Cosh[c + 2*d*x] + 16*a^2*d^3*f^2*x^3*Cosh[c + 2*d*x] + 16*b^2*d^3*f^2*x^3*Cosh[c + 2*d*x] + 48*a^2*d^3*e^2*x*Cosh[3*c + 2*d*x] + 48*b^2*d^3*e^2*x*Cosh[3*c + 2*d*x] + 48*a^2*d^3*e*f*x^2*Cosh[3*c + 2*d*x] + 48*b^2*d^3*e*f*x^2*Cosh[3*c + 2*d*x] + 16*a^2*d^3*f^2*x^3*Cosh[3*c + 2*d*x] + 16*b^2*d^3*f^2*x^3*Cosh[3*c + 2*d*x] + 24*a*b*d^2*e^2*Cosh[2*c + 3*d*x] - 48*a*b*d*e*f*Cosh[2*c + 3*d*x] + 48*a*b*f^2*Cosh[2*c + 3*d*x] + 48*a*b*d^2*e*f*x*Cosh[2*c + 3*d*x] - 48*a*b*d*f^2*x*Cosh[2*c + 3*d*x] + 24*a*b*d^2*f^2*x^2*Cosh[2*c + 3*d*x] - 24*a*b*d^2*e^2*Cosh[4*c + 3*d*x] + 48*a*b*d*e*f*Cosh[4*c + 3*d*x] - 48*a*b*f^2*Cosh[4*c + 3*d*x] - 48*a*b*d^2*e*f*x*Cosh[4*c + 3*d*x] + 48*a*b*d*f^2*x*Cosh[4*c + 3*d*x] - 24*a*b*d^2*f^2*x^2*Cosh[4*c + 3*d*x] - 6*b^2*d^2*e^2*Cosh[3*c + 4*d*x] + 6*b^2*d*e*f*Cosh[3*c + 4*d*x] - 3*b^2*f^2*Cosh[3*c + 4*d*x] - 12*b^2*d^2*e*f*x*Cosh[3*c + 4*d*x] + 6*b^2*d*f^2*x*Cosh[3*c + 4*d*x] - 6*b^2*d^2*f^2*x^2*Cosh[3*c + 4*d*x] + 6*b^2*d^2*e^2*Cosh[5*c + 4*d*x] - 6*b^2*d*e*f*Cosh[5*c + 4*d*x] + 3*b^2*f^2*Cosh[5*c + 4*d*x] + 12*b^2*d^2*e*f*x*Cosh[5*c + 4*d*x] - 6*b^2*d*f^2*x*Cosh[5*c + 4*d*x] + 6*b^2*d^2*f^2*x^2*Cosh[5*c + 4*d*x] + 12*b^2*d^2*e^2*Sinh[c] + 12*b^2*d*e*f*Sinh[c] + 6*b^2*f^2*Sinh[c] + 24*b^2*d^2*e*f*x*Sinh[c] + 12*b^2*d*f^2*x*Sinh[c] + 12*b^2*d^2*f^2*x^2*Sinh[c] - 24*a*b*d^2*e^2*Sinh[d*x] - 48*a*b*d*e*f*Sinh[d*x] - 48*a*b*f^2*Sinh[d*x] - 48*a*b*d^2*e*f*x*Sinh[d*x] - 48*a*b*d*f^2*x*Sinh[d*x] - 24*a*b*d^2*f^2*x^2*Sinh[d*x] + 24*a*b*d^2*e^2*Sinh[2*c + d*x] + 48*a*b*d*e*f*Sinh[2*c + d*x] + 48*a*b*f^2*Sinh[2*c + d*x] + 48*a*b*d^2*e*f*x*Sinh[2*c + d*x] + 48*a*b*d*f^2*x*Sinh[2*c + d*x] + 24*a*b*d^2*f^2*x^2*Sinh[2*c + d*x] + 48*a^2*d^3*e^2*x*Sinh[c + 2*d*x] + 48*b^2*d^3*e^2*x*Sinh[c + 2*d*x] + 48*a^2*d^3*e*f*x^2*Sinh[c + 2*d*x] + 48*b^2*d^3*e*f*x^2*Sinh[c + 2*d*x] + 16*a^2*d^3*f^2*x^3*Sinh[c + 2*d*x] + 16*b^2*d^3*f^2*x^3*Sinh[c + 2*d*x] + 48*a^2*d^3*e^2*x*Sinh[3*c + 2*d*x] + 48*b^2*d^3*e^2*x*Sinh[3*c + 2*d*x] + 48*a^2*d^3*e*f*x^2*Sinh[3*c + 2*d*x] + 48*b^2*d^3*e*f*x^2*Sinh[3*c + 2*d*x] + 16*a^2*d^3*f^2*x^3*Sinh[3*c + 2*d*x] + 16*b^2*d^3*f^2*x^3*Sinh[3*c + 2*d*x] + 24*a*b*d^2*e^2*Sinh[2*c + 3*d*x] - 48*a*b*d*e*f*Sinh[2*c + 3*d*x] + 48*a*b*f^2*Sinh[2*c + 3*d*x] + 48*a*b*d^2*e*f*x*Sinh[2*c + 3*d*x] - 48*a*b*d*f^2*x*Sinh[2*c + 3*d*x] + 24*a*b*d^2*f^2*x^2*Sinh[2*c + 3*d*x] - 24*a*b*d^2*e^2*Sinh[4*c + 3*d*x] + 48*a*b*d*e*f*Sinh[4*c + 3*d*x] - 48*a*b*f^2*Sinh[4*c + 3*d*x] - 48*a*b*d^2*e*f*x*Sinh[4*c + 3*d*x] + 48*a*b*d*f^2*x*Sinh[4*c + 3*d*x] - 24*a*b*d^2*f^2*x^2*Sinh[4*c + 3*d*x] - 6*b^2*d^2*e^2*Sinh[3*c + 4*d*x] + 6*b^2*d*e*f*Sinh[3*c + 4*d*x] - 3*b^2*f^2*Sinh[3*c + 4*d*x] - 12*b^2*d^2*e*f*x*Sinh[3*c + 4*d*x] + 6*b^2*d*f^2*x*Sinh[3*c + 4*d*x] - 6*b^2*d^2*f^2*x^2*Sinh[3*c + 4*d*x] + 6*b^2*d^2*e^2*Sinh[5*c + 4*d*x] - 6*b^2*d*e*f*Sinh[5*c + 4*d*x] + 3*b^2*f^2*Sinh[5*c + 4*d*x] + 12*b^2*d^2*e*f*x*Sinh[5*c + 4*d*x] - 6*b^2*d*f^2*x*Sinh[5*c + 4*d*x] + 6*b^2*d^2*f^2*x^2*Sinh[5*c + 4*d*x])","B",1
301,1,251,298,1.2778404,"\int \frac{(e+f x) \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{8 \left(a^2+b^2\right) \left(f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-\frac{1}{2} f (c+d x)^2\right)-8 a b d (e+f x) \sinh (c+d x)+8 a b f \cosh (c+d x)+2 b^2 d (e+f x) \cosh (2 (c+d x))-b^2 f \sinh (2 (c+d x))}{8 b^3 d^2}","\frac{f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{\left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d}+\frac{\left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d}-\frac{\left(a^2+b^2\right) (e+f x)^2}{2 b^3 f}+\frac{a f \cosh (c+d x)}{b^2 d^2}-\frac{a (e+f x) \sinh (c+d x)}{b^2 d}-\frac{f \sinh (c+d x) \cosh (c+d x)}{4 b d^2}+\frac{(e+f x) \sinh ^2(c+d x)}{2 b d}+\frac{f x}{4 b d}",1,"(8*a*b*f*Cosh[c + d*x] + 2*b^2*d*(e + f*x)*Cosh[2*(c + d*x)] + 8*(a^2 + b^2)*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - 8*a*b*d*(e + f*x)*Sinh[c + d*x] - b^2*f*Sinh[2*(c + d*x)])/(8*b^3*d^2)","A",1
302,1,53,59,0.0459718,"\int \frac{\cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Cosh[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","-\frac{-\left(a^2+b^2\right) \log (a+b \sinh (c+d x))+a b \sinh (c+d x)-\frac{1}{2} b^2 \sinh ^2(c+d x)}{b^3 d}","\frac{\left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{b^3 d}-\frac{a \sinh (c+d x)}{b^2 d}+\frac{\sinh ^2(c+d x)}{2 b d}",1,"-((-((a^2 + b^2)*Log[a + b*Sinh[c + d*x]]) + a*b*Sinh[c + d*x] - (b^2*Sinh[c + d*x]^2)/2)/(b^3*d))","A",1
303,0,0,31,77.1876347,"\int \frac{\cosh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Cosh[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\cosh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Cosh[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
304,1,3214,786,26.6102532,"\int \frac{(e+f x)^3 \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{6 i a f^3 \text{Li}_4\left(-i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{6 i a f^3 \text{Li}_4\left(i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{6 b f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^4 \left(a^2+b^2\right)}+\frac{6 b f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^4 \left(a^2+b^2\right)}-\frac{3 b f^3 \text{Li}_4\left(-e^{2 (c+d x)}\right)}{4 d^4 \left(a^2+b^2\right)}+\frac{6 i a f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 i a f^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 b f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 b f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)}+\frac{3 b f^2 (e+f x) \text{Li}_3\left(-e^{2 (c+d x)}\right)}{2 d^3 \left(a^2+b^2\right)}-\frac{3 i a f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 i a f (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 b f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 b f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)}-\frac{3 b f (e+f x)^2 \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)}+\frac{b (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)}+\frac{b (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)}-\frac{b (e+f x)^3 \log \left(e^{2 (c+d x)}+1\right)}{d \left(a^2+b^2\right)}+\frac{2 a (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)}",1,"-1/4*(-8*b*d^4*e^3*E^(2*c)*x - 12*b*d^4*e^2*E^(2*c)*f*x^2 - 8*b*d^4*e*E^(2*c)*f^2*x^3 - 2*b*d^4*E^(2*c)*f^3*x^4 - 8*a*d^3*e^3*ArcTan[E^(c + d*x)] - 8*a*d^3*e^3*E^(2*c)*ArcTan[E^(c + d*x)] - (12*I)*a*d^3*e^2*f*x*Log[1 - I*E^(c + d*x)] - (12*I)*a*d^3*e^2*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] - (12*I)*a*d^3*e*f^2*x^2*Log[1 - I*E^(c + d*x)] - (12*I)*a*d^3*e*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] - (4*I)*a*d^3*f^3*x^3*Log[1 - I*E^(c + d*x)] - (4*I)*a*d^3*E^(2*c)*f^3*x^3*Log[1 - I*E^(c + d*x)] + (12*I)*a*d^3*e^2*f*x*Log[1 + I*E^(c + d*x)] + (12*I)*a*d^3*e^2*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] + (12*I)*a*d^3*e*f^2*x^2*Log[1 + I*E^(c + d*x)] + (12*I)*a*d^3*e*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] + (4*I)*a*d^3*f^3*x^3*Log[1 + I*E^(c + d*x)] + (4*I)*a*d^3*E^(2*c)*f^3*x^3*Log[1 + I*E^(c + d*x)] + 4*b*d^3*e^3*Log[1 + E^(2*(c + d*x))] + 4*b*d^3*e^3*E^(2*c)*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e^2*f*x*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e^2*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 4*b*d^3*f^3*x^3*Log[1 + E^(2*(c + d*x))] + 4*b*d^3*E^(2*c)*f^3*x^3*Log[1 + E^(2*(c + d*x))] + (12*I)*a*d^2*(1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)] - (12*I)*a*d^2*(1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)] + 6*b*d^2*e^2*f*PolyLog[2, -E^(2*(c + d*x))] + 6*b*d^2*e^2*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 12*b*d^2*e*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 12*b*d^2*e*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 6*b*d^2*f^3*x^2*PolyLog[2, -E^(2*(c + d*x))] + 6*b*d^2*E^(2*c)*f^3*x^2*PolyLog[2, -E^(2*(c + d*x))] - (24*I)*a*d*e*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (24*I)*a*d*e*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (24*I)*a*d*f^3*x*PolyLog[3, (-I)*E^(c + d*x)] - (24*I)*a*d*E^(2*c)*f^3*x*PolyLog[3, (-I)*E^(c + d*x)] + (24*I)*a*d*e*f^2*PolyLog[3, I*E^(c + d*x)] + (24*I)*a*d*e*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] + (24*I)*a*d*f^3*x*PolyLog[3, I*E^(c + d*x)] + (24*I)*a*d*E^(2*c)*f^3*x*PolyLog[3, I*E^(c + d*x)] - 6*b*d*e*f^2*PolyLog[3, -E^(2*(c + d*x))] - 6*b*d*e*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))] - 6*b*d*f^3*x*PolyLog[3, -E^(2*(c + d*x))] - 6*b*d*E^(2*c)*f^3*x*PolyLog[3, -E^(2*(c + d*x))] + (24*I)*a*f^3*PolyLog[4, (-I)*E^(c + d*x)] + (24*I)*a*E^(2*c)*f^3*PolyLog[4, (-I)*E^(c + d*x)] - (24*I)*a*f^3*PolyLog[4, I*E^(c + d*x)] - (24*I)*a*E^(2*c)*f^3*PolyLog[4, I*E^(c + d*x)] + 3*b*f^3*PolyLog[4, -E^(2*(c + d*x))] + 3*b*E^(2*c)*f^3*PolyLog[4, -E^(2*(c + d*x))])/((a^2 + b^2)*d^4*(1 + E^(2*c))) - (b*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[a^2 + b^2]*e^3*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/(Sqrt[-(a^2 + b^2)^2]*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) - (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(2*(a^2 + b^2)*(-1 + E^(2*c))) + (b*x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3)*Csch[c/2]*Sech[c/2]*Sech[c])/(8*(a^2 + b^2))","B",1
305,1,1639,558,16.5517779,"\int \frac{(e+f x)^2 \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{-4 b f^2 x^3 d^3-12 b e f x^2 d^3+12 b e^2 e^{2 c} x d^3-12 b e^2 \left(1+e^{2 c}\right) x d^3+12 a e^2 \left(1+e^{2 c}\right) \tan ^{-1}\left(e^{c+d x}\right) d^2+6 b e^2 \left(1+e^{2 c}\right) \left(2 d x-\log \left(1+e^{2 (c+d x)}\right)\right) d^2+12 i a e \left(1+e^{2 c}\right) f \left(d x \left(\log \left(1-i e^{c+d x}\right)-\log \left(1+i e^{c+d x}\right)\right)-\text{Li}_2\left(-i e^{c+d x}\right)+\text{Li}_2\left(i e^{c+d x}\right)\right) d+6 b e \left(1+e^{2 c}\right) f \left(2 d x \left(d x-\log \left(1+e^{2 (c+d x)}\right)\right)-\text{Li}_2\left(-e^{2 (c+d x)}\right)\right) d+6 i a \left(1+e^{2 c}\right) f^2 \left(d^2 \log \left(1-i e^{c+d x}\right) x^2-d^2 \log \left(1+i e^{c+d x}\right) x^2-2 d \text{Li}_2\left(-i e^{c+d x}\right) x+2 d \text{Li}_2\left(i e^{c+d x}\right) x+2 \text{Li}_3\left(-i e^{c+d x}\right)-2 \text{Li}_3\left(i e^{c+d x}\right)\right)+b \left(1+e^{2 c}\right) f^2 \left(2 d^2 \left(2 d x-3 \log \left(1+e^{2 (c+d x)}\right)\right) x^2-6 d \text{Li}_2\left(-e^{2 (c+d x)}\right) x+3 \text{Li}_3\left(-e^{2 (c+d x)}\right)\right)}{6 \left(a^2+b^2\right) d^3 \left(1+e^{2 c}\right)}-\frac{b \left(2 e^{2 c} f^2 x^3+6 e e^{2 c} f x^2-\frac{3 e^{2 c} f^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}+\frac{3 f^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}-\frac{3 e^{2 c} f^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}+\frac{3 f^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}+6 e^2 e^{2 c} x-\frac{6 e e^{2 c} f \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}+\frac{6 e f \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}-\frac{6 e e^{2 c} f \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}+\frac{6 e f \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}+\frac{6 a \sqrt{-\left(a^2+b^2\right)^2} e^2 e^{2 c} \tan ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{-a^2-b^2}}\right)}{\left(a^2+b^2\right)^{3/2} d}+\frac{6 a \sqrt{a^2+b^2} e^2 \tan ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-\left(a^2+b^2\right)^2} d}+\frac{6 a \sqrt{-\left(a^2+b^2\right)^2} e^2 e^{2 c} \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)}{\left(-a^2-b^2\right)^{3/2} d}-\frac{6 a \sqrt{-\left(a^2+b^2\right)^2} e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)}{\left(-a^2-b^2\right)^{3/2} d}-\frac{3 e^2 e^{2 c} \log \left(2 e^{c+d x} a+b \left(-1+e^{2 (c+d x)}\right)\right)}{d}+\frac{3 e^2 \log \left(2 e^{c+d x} a+b \left(-1+e^{2 (c+d x)}\right)\right)}{d}-\frac{6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^2}-\frac{6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^2}+\frac{6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}-\frac{6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}+\frac{6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}-\frac{6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}\right)}{3 \left(a^2+b^2\right) \left(-1+e^{2 c}\right)}+\frac{b x \left(3 e^2+3 f x e+f^2 x^2\right) \text{csch}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}\right) \text{sech}(c)}{6 \left(a^2+b^2\right)}","\frac{2 i a f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 i a f^2 \text{Li}_3\left(i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 b f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 b f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)}+\frac{b f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right)}{2 d^3 \left(a^2+b^2\right)}-\frac{2 i a f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 i a f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)}-\frac{b f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right)}{d^2 \left(a^2+b^2\right)}+\frac{b (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)}+\frac{b (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)}-\frac{b (e+f x)^2 \log \left(e^{2 (c+d x)}+1\right)}{d \left(a^2+b^2\right)}+\frac{2 a (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)}",1,"(12*b*d^3*e^2*E^(2*c)*x - 12*b*d^3*e^2*(1 + E^(2*c))*x - 12*b*d^3*e*f*x^2 - 4*b*d^3*f^2*x^3 + 12*a*d^2*e^2*(1 + E^(2*c))*ArcTan[E^(c + d*x)] + 6*b*d^2*e^2*(1 + E^(2*c))*(2*d*x - Log[1 + E^(2*(c + d*x))]) + (12*I)*a*d*e*(1 + E^(2*c))*f*(d*x*(Log[1 - I*E^(c + d*x)] - Log[1 + I*E^(c + d*x)]) - PolyLog[2, (-I)*E^(c + d*x)] + PolyLog[2, I*E^(c + d*x)]) + 6*b*d*e*(1 + E^(2*c))*f*(2*d*x*(d*x - Log[1 + E^(2*(c + d*x))]) - PolyLog[2, -E^(2*(c + d*x))]) + (6*I)*a*(1 + E^(2*c))*f^2*(d^2*x^2*Log[1 - I*E^(c + d*x)] - d^2*x^2*Log[1 + I*E^(c + d*x)] - 2*d*x*PolyLog[2, (-I)*E^(c + d*x)] + 2*d*x*PolyLog[2, I*E^(c + d*x)] + 2*PolyLog[3, (-I)*E^(c + d*x)] - 2*PolyLog[3, I*E^(c + d*x)]) + b*(1 + E^(2*c))*f^2*(2*d^2*x^2*(2*d*x - 3*Log[1 + E^(2*(c + d*x))]) - 6*d*x*PolyLog[2, -E^(2*(c + d*x))] + 3*PolyLog[3, -E^(2*(c + d*x))]))/(6*(a^2 + b^2)*d^3*(1 + E^(2*c))) - (b*(6*e^2*E^(2*c)*x + 6*e*E^(2*c)*f*x^2 + 2*E^(2*c)*f^2*x^3 + (6*a*Sqrt[a^2 + b^2]*e^2*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/(Sqrt[-(a^2 + b^2)^2]*d) + (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) - (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (3*e^2*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d - (3*e^2*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (3*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (3*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (3*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (3*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3))/(3*(a^2 + b^2)*(-1 + E^(2*c))) + (b*x*(3*e^2 + 3*e*f*x + f^2*x^2)*Csch[c/2]*Sech[c/2]*Sech[c])/(6*(a^2 + b^2))","B",1
306,1,439,334,2.6083472,"\int \frac{(e+f x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{2 b f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+2 b c f \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+2 b c f \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 b d f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+2 b d f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 b d e \log (a+b \sinh (c+d x))-2 b c f \log (a+b \sinh (c+d x))+4 a d e \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))-2 i a f \text{Li}_2(-i (\cosh (c+d x)+\sinh (c+d x)))+2 i a f \text{Li}_2(i (\cosh (c+d x)+\sinh (c+d x)))+4 a d f x \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))-2 b c^2 f-2 b d e \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)+2 b c d e-b f \text{Li}_2(-\cosh (2 (c+d x))-\sinh (2 (c+d x)))-2 b c d f x-2 b d f x \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)+2 b d^2 e x}{2 d^2 \left(a^2+b^2\right)}","-\frac{i a f \text{Li}_2\left(-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{i a f \text{Li}_2\left(i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)}+\frac{b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)}-\frac{b f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)}+\frac{b (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)}+\frac{b (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)}-\frac{b (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{d \left(a^2+b^2\right)}+\frac{2 a (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)}",1,"(2*b*c*d*e - 2*b*c^2*f + 2*b*d^2*e*x - 2*b*c*d*f*x + 4*a*d*e*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] + 4*a*d*f*x*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] + 2*b*c*f*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*b*d*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*b*c*f*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*b*d*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*b*d*e*Log[a + b*Sinh[c + d*x]] - 2*b*c*f*Log[a + b*Sinh[c + d*x]] - 2*b*d*e*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] - 2*b*d*f*x*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] + 2*b*f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*b*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - (2*I)*a*f*PolyLog[2, (-I)*(Cosh[c + d*x] + Sinh[c + d*x])] + (2*I)*a*f*PolyLog[2, I*(Cosh[c + d*x] + Sinh[c + d*x])] - b*f*PolyLog[2, -Cosh[2*(c + d*x)] - Sinh[2*(c + d*x)]])/(2*(a^2 + b^2)*d^2)","A",0
307,1,114,69,0.0920336,"\int \frac{\text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Sech[c + d*x]/(a + b*Sinh[c + d*x]),x]","-\frac{b \left(\left(\sqrt{-b^2}-a\right) \log \left(\sqrt{-b^2}-b \sinh (c+d x)\right)-2 \sqrt{-b^2} \log (a+b \sinh (c+d x))+\left(a+\sqrt{-b^2}\right) \log \left(\sqrt{-b^2}+b \sinh (c+d x)\right)\right)}{2 \sqrt{-b^2} d \left(a^2+b^2\right)}","\frac{b \log (a+b \sinh (c+d x))}{d \left(a^2+b^2\right)}+\frac{a \tan ^{-1}(\sinh (c+d x))}{d \left(a^2+b^2\right)}-\frac{b \log (\cosh (c+d x))}{d \left(a^2+b^2\right)}",1,"-1/2*(b*((-a + Sqrt[-b^2])*Log[Sqrt[-b^2] - b*Sinh[c + d*x]] - 2*Sqrt[-b^2]*Log[a + b*Sinh[c + d*x]] + (a + Sqrt[-b^2])*Log[Sqrt[-b^2] + b*Sinh[c + d*x]]))/(Sqrt[-b^2]*(a^2 + b^2)*d)","A",1
308,0,0,29,17.7245661,"\int \frac{\text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Sech[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Sech[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
309,1,1143,780,13.4591141,"\int \frac{(e+f x)^3 \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(-2 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3+f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+3 e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2-3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2-6 e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-6 f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+6 e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+6 f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+6 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) b^2}{\left(a^2+b^2\right)^{3/2} d^4}-\frac{f \left(4 a f^2 x^3 d^3+12 a e f x^2 d^3-12 a e^2 e^{2 c} x d^3+12 a e^2 \left(1+e^{2 c}\right) x d^3+12 b e^2 \left(1+e^{2 c}\right) \tan ^{-1}\left(e^{c+d x}\right) d^2-6 a e^2 \left(1+e^{2 c}\right) \left(2 d x-\log \left(1+e^{2 (c+d x)}\right)\right) d^2+12 i b e \left(1+e^{2 c}\right) f \left(d x \left(\log \left(1-i e^{c+d x}\right)-\log \left(1+i e^{c+d x}\right)\right)-\text{Li}_2\left(-i e^{c+d x}\right)+\text{Li}_2\left(i e^{c+d x}\right)\right) d-6 a e \left(1+e^{2 c}\right) f \left(2 d x \left(d x-\log \left(1+e^{2 (c+d x)}\right)\right)-\text{Li}_2\left(-e^{2 (c+d x)}\right)\right) d+6 i b \left(1+e^{2 c}\right) f^2 \left(d^2 \log \left(1-i e^{c+d x}\right) x^2-d^2 \log \left(1+i e^{c+d x}\right) x^2-2 d \text{Li}_2\left(-i e^{c+d x}\right) x+2 d \text{Li}_2\left(i e^{c+d x}\right) x+2 \text{Li}_3\left(-i e^{c+d x}\right)-2 \text{Li}_3\left(i e^{c+d x}\right)\right)-a \left(1+e^{2 c}\right) f^2 \left(2 d^2 \left(2 d x-3 \log \left(1+e^{2 (c+d x)}\right)\right) x^2-6 d \text{Li}_2\left(-e^{2 (c+d x)}\right) x+3 \text{Li}_3\left(-e^{2 (c+d x)}\right)\right)\right)}{2 \left(a^2+b^2\right) d^4 \left(1+e^{2 c}\right)}+\frac{\text{sech}(c) \text{sech}(c+d x) \left(b \cosh (c) e^3+a \sinh (d x) e^3+3 b f x \cosh (c) e^2+3 a f x \sinh (d x) e^2+3 b f^2 x^2 \cosh (c) e+3 a f^2 x^2 \sinh (d x) e+b f^3 x^3 \cosh (c)+a f^3 x^3 \sinh (d x)\right)}{\left(a^2+b^2\right) d}","-\frac{6 i b f^3 \text{Li}_3\left(-i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{6 i b f^3 \text{Li}_3\left(i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{3 a f^3 \text{Li}_3\left(-e^{2 (c+d x)}\right)}{2 d^4 \left(a^2+b^2\right)}+\frac{6 b^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^4 \left(a^2+b^2\right)^{3/2}}-\frac{6 b^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^4 \left(a^2+b^2\right)^{3/2}}+\frac{6 i b f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 i b f^2 (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{3 a f^2 (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 b^2 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{6 b^2 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{3 b^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{3 b^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{3 a f (e+f x)^2 \log \left(e^{2 (c+d x)}+1\right)}{d^2 \left(a^2+b^2\right)}-\frac{6 b f (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{b^2 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)^{3/2}}-\frac{b^2 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)^{3/2}}+\frac{a (e+f x)^3 \tanh (c+d x)}{d \left(a^2+b^2\right)}+\frac{b (e+f x)^3 \text{sech}(c+d x)}{d \left(a^2+b^2\right)}+\frac{a (e+f x)^3}{d \left(a^2+b^2\right)}",1,"-1/2*(f*(-12*a*d^3*e^2*E^(2*c)*x + 12*a*d^3*e^2*(1 + E^(2*c))*x + 12*a*d^3*e*f*x^2 + 4*a*d^3*f^2*x^3 + 12*b*d^2*e^2*(1 + E^(2*c))*ArcTan[E^(c + d*x)] - 6*a*d^2*e^2*(1 + E^(2*c))*(2*d*x - Log[1 + E^(2*(c + d*x))]) + (12*I)*b*d*e*(1 + E^(2*c))*f*(d*x*(Log[1 - I*E^(c + d*x)] - Log[1 + I*E^(c + d*x)]) - PolyLog[2, (-I)*E^(c + d*x)] + PolyLog[2, I*E^(c + d*x)]) - 6*a*d*e*(1 + E^(2*c))*f*(2*d*x*(d*x - Log[1 + E^(2*(c + d*x))]) - PolyLog[2, -E^(2*(c + d*x))]) + (6*I)*b*(1 + E^(2*c))*f^2*(d^2*x^2*Log[1 - I*E^(c + d*x)] - d^2*x^2*Log[1 + I*E^(c + d*x)] - 2*d*x*PolyLog[2, (-I)*E^(c + d*x)] + 2*d*x*PolyLog[2, I*E^(c + d*x)] + 2*PolyLog[3, (-I)*E^(c + d*x)] - 2*PolyLog[3, I*E^(c + d*x)]) - a*(1 + E^(2*c))*f^2*(2*d^2*x^2*(2*d*x - 3*Log[1 + E^(2*(c + d*x))]) - 6*d*x*PolyLog[2, -E^(2*(c + d*x))] + 3*PolyLog[3, -E^(2*(c + d*x))])))/((a^2 + b^2)*d^4*(1 + E^(2*c))) + (b^2*(-2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/((a^2 + b^2)^(3/2)*d^4) + (Sech[c]*Sech[c + d*x]*(b*e^3*Cosh[c] + 3*b*e^2*f*x*Cosh[c] + 3*b*e*f^2*x^2*Cosh[c] + b*f^3*x^3*Cosh[c] + a*e^3*Sinh[d*x] + 3*a*e^2*f*x*Sinh[d*x] + 3*a*e*f^2*x^2*Sinh[d*x] + a*f^3*x^3*Sinh[d*x]))/((a^2 + b^2)*d)","A",1
310,1,905,548,8.1334574,"\int \frac{(e+f x)^2 \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(-2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^2+f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2+2 e f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2-f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2-2 e f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2+2 f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) b^2}{\left(a^2+b^2\right)^{3/2} d^3}-\frac{2 f^2 \left(-\frac{2 \tan ^{-1}\left(\frac{\sinh (c)+\cosh (c) \tanh \left(\frac{d x}{2}\right)}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right) \tanh ^{-1}(\coth (c))}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}-\frac{i \text{csch}(c) \left(i \left(d x+\tanh ^{-1}(\coth (c))\right) \left(\log \left(1-e^{-d x-\tanh ^{-1}(\coth (c))}\right)-\log \left(1+e^{-d x-\tanh ^{-1}(\coth (c))}\right)\right)+i \left(\text{Li}_2\left(-e^{-d x-\tanh ^{-1}(\coth (c))}\right)-\text{Li}_2\left(e^{-d x-\tanh ^{-1}(\coth (c))}\right)\right)\right)}{\sqrt{1-\coth ^2(c)}}\right) b}{\left(a^2+b^2\right) d^3}-\frac{4 e f \tan ^{-1}\left(\frac{\sinh (c)+\cosh (c) \tanh \left(\frac{d x}{2}\right)}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right) b}{\left(a^2+b^2\right) d^2 \sqrt{\cosh ^2(c)-\sinh ^2(c)}}+\frac{\text{sech}(c) \text{sech}(c+d x) \left(b \cosh (c) e^2+a \sinh (d x) e^2+2 b f x \cosh (c) e+2 a f x \sinh (d x) e+b f^2 x^2 \cosh (c)+a f^2 x^2 \sinh (d x)\right)}{\left(a^2+b^2\right) d}-\frac{a f^2 \text{csch}(c) \left(d^2 e^{-\tanh ^{-1}(\coth (c))} x^2-\frac{i \coth (c) \left(-d x \left(2 i \tanh ^{-1}(\coth (c))-\pi \right)-\pi  \log \left(1+e^{2 d x}\right)-2 \left(i d x+i \tanh ^{-1}(\coth (c))\right) \log \left(1-e^{2 i \left(i d x+i \tanh ^{-1}(\coth (c))\right)}\right)+\pi  \log (\cosh (d x))+2 i \tanh ^{-1}(\coth (c)) \log \left(i \sinh \left(d x+\tanh ^{-1}(\coth (c))\right)\right)+i \text{Li}_2\left(e^{2 i \left(i d x+i \tanh ^{-1}(\coth (c))\right)}\right)\right)}{\sqrt{1-\coth ^2(c)}}\right) \text{sech}(c)}{\left(a^2+b^2\right) d^3 \sqrt{\text{csch}^2(c) \left(\sinh ^2(c)-\cosh ^2(c)\right)}}-\frac{2 a e f \text{sech}(c) (\cosh (c) \log (\cosh (c) \cosh (d x)+\sinh (c) \sinh (d x))-d x \sinh (c))}{\left(a^2+b^2\right) d^2 \left(\cosh ^2(c)-\sinh ^2(c)\right)}","-\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{2 i b f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 i b f^2 \text{Li}_2\left(i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{a f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 b^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{2 b^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{2 a f (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{d^2 \left(a^2+b^2\right)}-\frac{4 b f (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{b^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)^{3/2}}-\frac{b^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)^{3/2}}+\frac{a (e+f x)^2 \tanh (c+d x)}{d \left(a^2+b^2\right)}+\frac{b (e+f x)^2 \text{sech}(c+d x)}{d \left(a^2+b^2\right)}+\frac{a (e+f x)^2}{d \left(a^2+b^2\right)}",1,"(b^2*(-2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/((a^2 + b^2)^(3/2)*d^3) - (2*a*e*f*Sech[c]*(Cosh[c]*Log[Cosh[c]*Cosh[d*x] + Sinh[c]*Sinh[d*x]] - d*x*Sinh[c]))/((a^2 + b^2)*d^2*(Cosh[c]^2 - Sinh[c]^2)) - (4*b*e*f*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]])/((a^2 + b^2)*d^2*Sqrt[Cosh[c]^2 - Sinh[c]^2]) - (a*f^2*Csch[c]*((d^2*x^2)/E^ArcTanh[Coth[c]] - (I*Coth[c]*(-(d*x*(-Pi + (2*I)*ArcTanh[Coth[c]])) - Pi*Log[1 + E^(2*d*x)] - 2*(I*d*x + I*ArcTanh[Coth[c]])*Log[1 - E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))] + Pi*Log[Cosh[d*x]] + (2*I)*ArcTanh[Coth[c]]*Log[I*Sinh[d*x + ArcTanh[Coth[c]]]] + I*PolyLog[2, E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))]))/Sqrt[1 - Coth[c]^2])*Sech[c])/((a^2 + b^2)*d^3*Sqrt[Csch[c]^2*(-Cosh[c]^2 + Sinh[c]^2)]) - (2*b*f^2*(((-I)*Csch[c]*(I*(d*x + ArcTanh[Coth[c]])*(Log[1 - E^(-(d*x) - ArcTanh[Coth[c]])] - Log[1 + E^(-(d*x) - ArcTanh[Coth[c]])]) + I*(PolyLog[2, -E^(-(d*x) - ArcTanh[Coth[c]])] - PolyLog[2, E^(-(d*x) - ArcTanh[Coth[c]])])))/Sqrt[1 - Coth[c]^2] - (2*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]]*ArcTanh[Coth[c]])/Sqrt[Cosh[c]^2 - Sinh[c]^2]))/((a^2 + b^2)*d^3) + (Sech[c]*Sech[c + d*x]*(b*e^2*Cosh[c] + 2*b*e*f*x*Cosh[c] + b*f^2*x^2*Cosh[c] + a*e^2*Sinh[d*x] + 2*a*e*f*x*Sinh[d*x] + a*f^2*x^2*Sinh[d*x]))/((a^2 + b^2)*d)","A",0
311,1,284,295,2.8608605,"\int \frac{(e+f x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\frac{b^2 \left(-2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)}{\left(a^2+b^2\right)^{3/2}}+\frac{d (e+f x) \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a^2+b^2}-\frac{2 b f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^2+b^2}-\frac{a f \log (\cosh (c+d x))}{a^2+b^2}}{d^2}","\frac{b^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{b^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{b f \tan ^{-1}(\sinh (c+d x))}{d^2 \left(a^2+b^2\right)}-\frac{a f \log (\cosh (c+d x))}{d^2 \left(a^2+b^2\right)}+\frac{b^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)^{3/2}}-\frac{b^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)^{3/2}}+\frac{a (e+f x) \tanh (c+d x)}{d \left(a^2+b^2\right)}+\frac{b (e+f x) \text{sech}(c+d x)}{d \left(a^2+b^2\right)}",1,"((-2*b*f*ArcTan[Tanh[(c + d*x)/2]])/(a^2 + b^2) - (a*f*Log[Cosh[c + d*x]])/(a^2 + b^2) + (b^2*(-2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^2 + b^2)^(3/2) + (d*(e + f*x)*Sech[c + d*x]*(b + a*Sinh[c + d*x]))/(a^2 + b^2))/d^2","A",1
312,1,104,77,0.1595702,"\int \frac{\text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Sech[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","-\frac{a \sqrt{-a^2-b^2} \tanh (c+d x)+b \sqrt{-a^2-b^2} \text{sech}(c+d x)+2 b^2 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{d \left(-a^2-b^2\right)^{3/2}}","\frac{\text{sech}(c+d x) (a \sinh (c+d x)+b)}{d \left(a^2+b^2\right)}-\frac{2 b^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{3/2}}",1,"-((2*b^2*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] + b*Sqrt[-a^2 - b^2]*Sech[c + d*x] + a*Sqrt[-a^2 - b^2]*Tanh[c + d*x])/((-a^2 - b^2)^(3/2)*d))","A",1
313,0,0,31,66.0673695,"\int \frac{\text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Sech[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Sech[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
314,1,3368,928,28.3170146,"\int \frac{(e+f x)^2 \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^3}{\left(a^2+b^2\right)^2 d}+\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^3}{\left(a^2+b^2\right)^2 d}-\frac{(e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) b^3}{\left(a^2+b^2\right)^2 d}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{\left(a^2+b^2\right)^2 d^2}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{\left(a^2+b^2\right)^2 d^2}-\frac{f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) b^3}{\left(a^2+b^2\right)^2 d^2}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{\left(a^2+b^2\right)^2 d^3}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{\left(a^2+b^2\right)^2 d^3}+\frac{f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) b^3}{2 \left(a^2+b^2\right)^2 d^3}+\frac{2 a (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) b^2}{\left(a^2+b^2\right)^2 d}-\frac{2 i a f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) b^2}{\left(a^2+b^2\right)^2 d^2}+\frac{2 i a f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) b^2}{\left(a^2+b^2\right)^2 d^2}+\frac{2 i a f^2 \text{Li}_3\left(-i e^{c+d x}\right) b^2}{\left(a^2+b^2\right)^2 d^3}-\frac{2 i a f^2 \text{Li}_3\left(i e^{c+d x}\right) b^2}{\left(a^2+b^2\right)^2 d^3}+\frac{(e+f x)^2 \text{sech}^2(c+d x) b}{2 \left(a^2+b^2\right) d}+\frac{f^2 \log (\cosh (c+d x)) b}{\left(a^2+b^2\right) d^3}-\frac{f (e+f x) \tanh (c+d x) b}{\left(a^2+b^2\right) d^2}+\frac{a (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{\left(a^2+b^2\right) d}-\frac{a f^2 \tan ^{-1}(\sinh (c+d x))}{\left(a^2+b^2\right) d^3}-\frac{i a f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{\left(a^2+b^2\right) d^2}+\frac{i a f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{\left(a^2+b^2\right) d^2}+\frac{i a f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{\left(a^2+b^2\right) d^3}-\frac{i a f^2 \text{Li}_3\left(i e^{c+d x}\right)}{\left(a^2+b^2\right) d^3}+\frac{a f (e+f x) \text{sech}(c+d x)}{\left(a^2+b^2\right) d^2}+\frac{a (e+f x)^2 \text{sech}(c+d x) \tanh (c+d x)}{2 \left(a^2+b^2\right) d}",1,"-1/6*(-12*b^3*d^3*e^2*E^(2*c)*x + 12*a^2*b*d*E^(2*c)*f^2*x + 12*b^3*d*E^(2*c)*f^2*x - 12*b^3*d^3*e*E^(2*c)*f*x^2 - 4*b^3*d^3*E^(2*c)*f^2*x^3 - 6*a^3*d^2*e^2*ArcTan[E^(c + d*x)] - 18*a*b^2*d^2*e^2*ArcTan[E^(c + d*x)] - 6*a^3*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] - 18*a*b^2*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] + 12*a^3*f^2*ArcTan[E^(c + d*x)] + 12*a*b^2*f^2*ArcTan[E^(c + d*x)] + 12*a^3*E^(2*c)*f^2*ArcTan[E^(c + d*x)] + 12*a*b^2*E^(2*c)*f^2*ArcTan[E^(c + d*x)] - (6*I)*a^3*d^2*e*f*x*Log[1 - I*E^(c + d*x)] - (18*I)*a*b^2*d^2*e*f*x*Log[1 - I*E^(c + d*x)] - (6*I)*a^3*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] - (18*I)*a*b^2*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] - (3*I)*a^3*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] - (9*I)*a*b^2*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] - (3*I)*a^3*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] - (9*I)*a*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] + (6*I)*a^3*d^2*e*f*x*Log[1 + I*E^(c + d*x)] + (18*I)*a*b^2*d^2*e*f*x*Log[1 + I*E^(c + d*x)] + (6*I)*a^3*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] + (18*I)*a*b^2*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] + (3*I)*a^3*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] + (9*I)*a*b^2*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] + (3*I)*a^3*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] + (9*I)*a*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] + 6*b^3*d^2*e^2*Log[1 + E^(2*(c + d*x))] + 6*b^3*d^2*e^2*E^(2*c)*Log[1 + E^(2*(c + d*x))] - 6*a^2*b*f^2*Log[1 + E^(2*(c + d*x))] - 6*b^3*f^2*Log[1 + E^(2*(c + d*x))] - 6*a^2*b*E^(2*c)*f^2*Log[1 + E^(2*(c + d*x))] - 6*b^3*E^(2*c)*f^2*Log[1 + E^(2*(c + d*x))] + 12*b^3*d^2*e*f*x*Log[1 + E^(2*(c + d*x))] + 12*b^3*d^2*e*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 6*b^3*d^2*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 6*b^3*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] + (6*I)*a*(a^2 + 3*b^2)*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)] - (6*I)*a*(a^2 + 3*b^2)*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)] + 6*b^3*d*e*f*PolyLog[2, -E^(2*(c + d*x))] + 6*b^3*d*e*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 6*b^3*d*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 6*b^3*d*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] - (6*I)*a^3*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (18*I)*a*b^2*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (6*I)*a^3*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (18*I)*a*b^2*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (6*I)*a^3*f^2*PolyLog[3, I*E^(c + d*x)] + (18*I)*a*b^2*f^2*PolyLog[3, I*E^(c + d*x)] + (6*I)*a^3*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] + (18*I)*a*b^2*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - 3*b^3*f^2*PolyLog[3, -E^(2*(c + d*x))] - 3*b^3*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))])/((a^2 + b^2)^2*d^3*(1 + E^(2*c))) - (b^3*(6*e^2*E^(2*c)*x + 6*e*E^(2*c)*f*x^2 + 2*E^(2*c)*f^2*x^3 + (6*a*Sqrt[a^2 + b^2]*e^2*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/(Sqrt[-(a^2 + b^2)^2]*d) + (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) - (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (3*e^2*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d - (3*e^2*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (3*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (3*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (3*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (3*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3))/(3*(a^2 + b^2)^2*(-1 + E^(2*c))) + (Csch[c]*Sech[c]*Sech[c + d*x]^2*(-6*a^2*b*e*f - 6*b^3*e*f + 12*b^3*d^2*e^2*x - 6*a^2*b*f^2*x - 6*b^3*f^2*x + 12*b^3*d^2*e*f*x^2 + 4*b^3*d^2*f^2*x^3 + 6*a^2*b*e*f*Cosh[2*c] + 6*b^3*e*f*Cosh[2*c] + 6*a^2*b*f^2*x*Cosh[2*c] + 6*b^3*f^2*x*Cosh[2*c] + 6*a^2*b*e*f*Cosh[2*d*x] + 6*b^3*e*f*Cosh[2*d*x] + 6*a^2*b*f^2*x*Cosh[2*d*x] + 6*b^3*f^2*x*Cosh[2*d*x] - 3*a^3*d*e^2*Cosh[c - d*x] - 3*a*b^2*d*e^2*Cosh[c - d*x] - 6*a^3*d*e*f*x*Cosh[c - d*x] - 6*a*b^2*d*e*f*x*Cosh[c - d*x] - 3*a^3*d*f^2*x^2*Cosh[c - d*x] - 3*a*b^2*d*f^2*x^2*Cosh[c - d*x] + 3*a^3*d*e^2*Cosh[3*c + d*x] + 3*a*b^2*d*e^2*Cosh[3*c + d*x] + 6*a^3*d*e*f*x*Cosh[3*c + d*x] + 6*a*b^2*d*e*f*x*Cosh[3*c + d*x] + 3*a^3*d*f^2*x^2*Cosh[3*c + d*x] + 3*a*b^2*d*f^2*x^2*Cosh[3*c + d*x] - 6*a^2*b*e*f*Cosh[2*c + 2*d*x] - 6*b^3*e*f*Cosh[2*c + 2*d*x] + 12*b^3*d^2*e^2*x*Cosh[2*c + 2*d*x] - 6*a^2*b*f^2*x*Cosh[2*c + 2*d*x] - 6*b^3*f^2*x*Cosh[2*c + 2*d*x] + 12*b^3*d^2*e*f*x^2*Cosh[2*c + 2*d*x] + 4*b^3*d^2*f^2*x^3*Cosh[2*c + 2*d*x] + 6*a^2*b*d*e^2*Sinh[2*c] + 6*b^3*d*e^2*Sinh[2*c] + 12*a^2*b*d*e*f*x*Sinh[2*c] + 12*b^3*d*e*f*x*Sinh[2*c] + 6*a^2*b*d*f^2*x^2*Sinh[2*c] + 6*b^3*d*f^2*x^2*Sinh[2*c] + 6*a^3*e*f*Sinh[c - d*x] + 6*a*b^2*e*f*Sinh[c - d*x] + 6*a^3*f^2*x*Sinh[c - d*x] + 6*a*b^2*f^2*x*Sinh[c - d*x] + 6*a^3*e*f*Sinh[3*c + d*x] + 6*a*b^2*e*f*Sinh[3*c + d*x] + 6*a^3*f^2*x*Sinh[3*c + d*x] + 6*a*b^2*f^2*x*Sinh[3*c + d*x]))/(24*(a^2 + b^2)^2*d^2)","B",0
315,1,588,560,6.8736069,"\int \frac{(e+f x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{2 a^3 d e \tan ^{-1}\left(e^{c+d x}\right)+i a^3 f (c+d x) \log \left(1-i e^{c+d x}\right)-i a^3 f (c+d x) \log \left(1+i e^{c+d x}\right)-2 a^3 c f \tan ^{-1}\left(e^{c+d x}\right)+d \left(a^2+b^2\right) (e+f x) \text{sech}^2(c+d x) (a \sinh (c+d x)+b)-i a f \left(a^2+3 b^2\right) \text{Li}_2\left(-i e^{c+d x}\right)+i a f \left(a^2+3 b^2\right) \text{Li}_2\left(i e^{c+d x}\right)+f \left(a^2+b^2\right) \text{sech}(c+d x) (a-b \sinh (c+d x))+2 b^3 f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 b^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+2 b^3 f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+2 b^3 f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 b^3 d e \log (a+b \sinh (c+d x))-2 b^3 c f \log (a+b \sinh (c+d x))+6 a b^2 d e \tan ^{-1}\left(e^{c+d x}\right)+3 i a b^2 f (c+d x) \log \left(1-i e^{c+d x}\right)-3 i a b^2 f (c+d x) \log \left(1+i e^{c+d x}\right)-6 a b^2 c f \tan ^{-1}\left(e^{c+d x}\right)+2 b^3 d e (c+d x)-2 b^3 d e \log \left(e^{2 (c+d x)}+1\right)-b^3 f \text{Li}_2\left(-e^{2 (c+d x)}\right)-2 b^3 c f (c+d x)+2 b^3 c f \log \left(e^{2 (c+d x)}+1\right)-2 b^3 f (c+d x) \log \left(e^{2 (c+d x)}+1\right)}{2 d^2 \left(a^2+b^2\right)^2}","-\frac{i a b^2 f \text{Li}_2\left(-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{i a b^2 f \text{Li}_2\left(i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{i a f \text{Li}_2\left(-i e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)}+\frac{i a f \text{Li}_2\left(i e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{b f \tanh (c+d x)}{2 d^2 \left(a^2+b^2\right)}+\frac{a f \text{sech}(c+d x)}{2 d^2 \left(a^2+b^2\right)}+\frac{2 a b^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)^2}+\frac{a (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)}+\frac{b (e+f x) \text{sech}^2(c+d x)}{2 d \left(a^2+b^2\right)}+\frac{a (e+f x) \tanh (c+d x) \text{sech}(c+d x)}{2 d \left(a^2+b^2\right)}+\frac{b^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{b^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{b^3 f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)^2}+\frac{b^3 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)^2}+\frac{b^3 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)^2}-\frac{b^3 (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{d \left(a^2+b^2\right)^2}",1,"(2*b^3*d*e*(c + d*x) - 2*b^3*c*f*(c + d*x) + 2*a^3*d*e*ArcTan[E^(c + d*x)] + 6*a*b^2*d*e*ArcTan[E^(c + d*x)] - 2*a^3*c*f*ArcTan[E^(c + d*x)] - 6*a*b^2*c*f*ArcTan[E^(c + d*x)] + I*a^3*f*(c + d*x)*Log[1 - I*E^(c + d*x)] + (3*I)*a*b^2*f*(c + d*x)*Log[1 - I*E^(c + d*x)] - I*a^3*f*(c + d*x)*Log[1 + I*E^(c + d*x)] - (3*I)*a*b^2*f*(c + d*x)*Log[1 + I*E^(c + d*x)] + 2*b^3*f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*b^3*f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*b^3*d*e*Log[1 + E^(2*(c + d*x))] + 2*b^3*c*f*Log[1 + E^(2*(c + d*x))] - 2*b^3*f*(c + d*x)*Log[1 + E^(2*(c + d*x))] + 2*b^3*d*e*Log[a + b*Sinh[c + d*x]] - 2*b^3*c*f*Log[a + b*Sinh[c + d*x]] - I*a*(a^2 + 3*b^2)*f*PolyLog[2, (-I)*E^(c + d*x)] + I*a*(a^2 + 3*b^2)*f*PolyLog[2, I*E^(c + d*x)] + 2*b^3*f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*b^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - b^3*f*PolyLog[2, -E^(2*(c + d*x))] + (a^2 + b^2)*d*(e + f*x)*Sech[c + d*x]^2*(b + a*Sinh[c + d*x]) + (a^2 + b^2)*f*Sech[c + d*x]*(a - b*Sinh[c + d*x]))/(2*(a^2 + b^2)^2*d^2)","A",1
316,1,104,119,0.1793579,"\int \frac{\text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Sech[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","\frac{b \left(a^2+b^2\right) \text{sech}^2(c+d x)+2 a \left(a^2+3 b^2\right) \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+a \left(a^2+b^2\right) \tanh (c+d x) \text{sech}(c+d x)+2 b^3 (\log (a+b \sinh (c+d x))-\log (\cosh (c+d x)))}{2 d \left(a^2+b^2\right)^2}","\frac{a \left(a^2+3 b^2\right) \tan ^{-1}(\sinh (c+d x))}{2 d \left(a^2+b^2\right)^2}+\frac{\text{sech}^2(c+d x) (a \sinh (c+d x)+b)}{2 d \left(a^2+b^2\right)}+\frac{b^3 \log (a+b \sinh (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{b^3 \log (\cosh (c+d x))}{d \left(a^2+b^2\right)^2}",1,"(2*a*(a^2 + 3*b^2)*ArcTan[Tanh[(c + d*x)/2]] + 2*b^3*(-Log[Cosh[c + d*x]] + Log[a + b*Sinh[c + d*x]]) + b*(a^2 + b^2)*Sech[c + d*x]^2 + a*(a^2 + b^2)*Sech[c + d*x]*Tanh[c + d*x])/(2*(a^2 + b^2)^2*d)","A",1
317,0,0,31,130.1380803,"\int \frac{\text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Sech[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Sech[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
318,0,0,27,10.9793762,"\int \frac{x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(x^m*Cosh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\int \frac{x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","\text{Int}\left(\frac{x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)},x\right)",0,"Integrate[(x^m*Cosh[c + d*x]^3)/(a + b*Sinh[c + d*x]), x]","A",-1
319,0,0,27,8.0663035,"\int \frac{x^m \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(x^m*Cosh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\int \frac{x^m \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","\text{Int}\left(\frac{x^m \cosh ^2(c+d x)}{a+b \sinh (c+d x)},x\right)",0,"Integrate[(x^m*Cosh[c + d*x]^2)/(a + b*Sinh[c + d*x]), x]","A",-1
320,0,0,25,5.2510533,"\int \frac{x^m \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(x^m*Cosh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\int \frac{x^m \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","\text{Int}\left(\frac{x^m \cosh (c+d x)}{a+b \sinh (c+d x)},x\right)",0,"Integrate[(x^m*Cosh[c + d*x])/(a + b*Sinh[c + d*x]), x]","A",-1
321,1,78,74,0.4502094,"\int \frac{(e+f x) \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Integrate[((e + f*x)*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","\frac{\frac{2 f \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-\frac{d (e+f x)}{a+b \sinh (c+d x)}}{b d^2}","-\frac{2 f \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{e+f x}{b d (a+b \sinh (c+d x))}",1,"((2*f*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - (d*(e + f*x))/(a + b*Sinh[c + d*x]))/(b*d^2)","A",1
322,1,175,234,1.2952948,"\int \frac{(e+f x)^2 \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","\frac{2 f \left(d (e+f x) \left(\log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-\log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)\right)+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{(e+f x)^2}{b d (a+b \sinh (c+d x))}","\frac{2 f^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{2 f^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}+\frac{2 f (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{2 f (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{(e+f x)^2}{b d (a+b \sinh (c+d x))}",1,"(2*f*(d*(e + f*x)*(Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])]) + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b*Sqrt[a^2 + b^2]*d^3) - (e + f*x)^2/(b*d*(a + b*Sinh[c + d*x]))","A",1
323,1,368,348,2.2799,"\int \frac{(e+f x)^3 \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","\frac{3 f \left(-2 d^2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)+2 d^2 e f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-2 d^2 e f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 d f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 d f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{b d^4 \sqrt{a^2+b^2}}-\frac{(e+f x)^3}{b d (a+b \sinh (c+d x))}","-\frac{6 f^3 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^4 \sqrt{a^2+b^2}}+\frac{6 f^3 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^4 \sqrt{a^2+b^2}}+\frac{6 f^2 (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{6 f^2 (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}+\frac{3 f (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{3 f (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{(e+f x)^3}{b d (a+b \sinh (c+d x))}",1,"(3*f*(-2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b*Sqrt[a^2 + b^2]*d^4) - (e + f*x)^3/(b*d*(a + b*Sinh[c + d*x]))","A",1
324,1,78,74,0.3623853,"\int \frac{(e+f x) \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Integrate[((e + f*x)*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","\frac{\frac{2 f \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}-\frac{d (e+f x)}{a+b \sinh (c+d x)}}{b d^2}","-\frac{2 f \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{e+f x}{b d (a+b \sinh (c+d x))}",1,"((2*f*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - (d*(e + f*x))/(a + b*Sinh[c + d*x]))/(b*d^2)","A",1
325,1,175,234,0.5418474,"\int \frac{(e+f x)^2 \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","\frac{2 f \left(d (e+f x) \left(\log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-\log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)\right)+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{(e+f x)^2}{b d (a+b \sinh (c+d x))}","\frac{2 f^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{2 f^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}+\frac{2 f (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{2 f (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{(e+f x)^2}{b d (a+b \sinh (c+d x))}",1,"(2*f*(d*(e + f*x)*(Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])]) + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b*Sqrt[a^2 + b^2]*d^3) - (e + f*x)^2/(b*d*(a + b*Sinh[c + d*x]))","A",1
326,1,368,348,0.3391822,"\int \frac{(e+f x)^3 \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","\frac{3 f \left(-2 d^2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)+2 d^2 e f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-2 d^2 e f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 d f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 d f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{b d^4 \sqrt{a^2+b^2}}-\frac{(e+f x)^3}{b d (a+b \sinh (c+d x))}","-\frac{6 f^3 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^4 \sqrt{a^2+b^2}}+\frac{6 f^3 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^4 \sqrt{a^2+b^2}}+\frac{6 f^2 (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{6 f^2 (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3 \sqrt{a^2+b^2}}+\frac{3 f (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{3 f (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{(e+f x)^3}{b d (a+b \sinh (c+d x))}",1,"(3*f*(-2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b*Sqrt[a^2 + b^2]*d^4) - (e + f*x)^3/(b*d*(a + b*Sinh[c + d*x]))","A",1
327,1,112,112,1.0851788,"\int \frac{(e+f x) \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Integrate[((e + f*x)*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","-\frac{\frac{\frac{2 a f \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+\frac{d (e+f x)}{(a+b \sinh (c+d x))^2}}{b}+\frac{f \cosh (c+d x)}{\left(a^2+b^2\right) (a+b \sinh (c+d x))}}{2 d^2}","-\frac{a f \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b d^2 \left(a^2+b^2\right)^{3/2}}-\frac{f \cosh (c+d x)}{2 d^2 \left(a^2+b^2\right) (a+b \sinh (c+d x))}-\frac{e+f x}{2 b d (a+b \sinh (c+d x))^2}",1,"-1/2*((f*Cosh[c + d*x])/((a^2 + b^2)*(a + b*Sinh[c + d*x])) + ((2*a*f*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) + (d*(e + f*x))/(a + b*Sinh[c + d*x])^2)/b)/d^2","A",1
328,1,623,306,16.1587657,"\int \frac{(e+f x)^2 \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","\frac{\text{csch}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}\right) \left(a e f \cosh (c)+a f^2 x \cosh (c)+b e f \sinh (d x)+b f^2 x \sinh (d x)\right)}{2 b d^2 \left(a^2+b^2\right) (a+b \sinh (c+d x))}+\frac{2 e^c f \left(-\frac{a e^{-c} \left(e^{2 c}-1\right) e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}+\frac{a \left(e^{2 c}-1\right) f \left(\text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-\text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+d x \left(\log \left(\frac{b e^{2 c+d x}}{a e^c-\sqrt{e^{2 c} \left(a^2+b^2\right)}}+1\right)-\log \left(\frac{b e^{2 c+d x}}{\sqrt{e^{2 c} \left(a^2+b^2\right)}+a e^c}+1\right)\right)\right)}{2 d \sqrt{e^{2 c} \left(a^2+b^2\right)}}+\frac{a e^{-c} \left(e^{2 c}-1\right) f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)}{d \sqrt{a^2+b^2}}+\frac{1}{2} e^{-c} \left(e^{2 c}-1\right) f \left(\frac{2 a \tan ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{-a^2-b^2}}\right)}{d \sqrt{-a^2-b^2}}+\frac{\log \left(2 a e^{c+d x}+b \left(e^{2 (c+d x)}-1\right)\right)}{d}-2 x\right)-e^c f x+e^{-c} \left(e^{2 c}-1\right) f x\right)}{b \left(e^{2 c}-1\right) d^2 \left(a^2+b^2\right)}+\frac{f^2 x \coth (c)}{b d^2 \left(a^2+b^2\right)}-\frac{f^2 x \cosh (c) \text{csch}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}\right)}{2 b d^2 \left(a^2+b^2\right)}-\frac{(e+f x)^2}{2 b d (a+b \sinh (c+d x))^2}","\frac{a f^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}-\frac{a f^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\frac{f^2 \log (a+b \sinh (c+d x))}{b d^3 \left(a^2+b^2\right)}+\frac{a f (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d^2 \left(a^2+b^2\right)^{3/2}}-\frac{a f (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d^2 \left(a^2+b^2\right)^{3/2}}-\frac{f (e+f x) \cosh (c+d x)}{d^2 \left(a^2+b^2\right) (a+b \sinh (c+d x))}-\frac{(e+f x)^2}{2 b d (a+b \sinh (c+d x))^2}",1,"(f^2*x*Coth[c])/(b*(a^2 + b^2)*d^2) + (2*E^c*f*(-(E^c*f*x) + ((-1 + E^(2*c))*f*x)/E^c - (a*e*(-1 + E^(2*c))*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*E^c) + (a*(-1 + E^(2*c))*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d*E^c) + ((-1 + E^(2*c))*f*(-2*x + (2*a*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d) + Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))]/d))/(2*E^c) + (a*(-1 + E^(2*c))*f*(d*x*(Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])]) + PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(2*d*Sqrt[(a^2 + b^2)*E^(2*c)])))/(b*(a^2 + b^2)*d^2*(-1 + E^(2*c))) - (f^2*x*Cosh[c]*Csch[c/2]*Sech[c/2])/(2*b*(a^2 + b^2)*d^2) - (e + f*x)^2/(2*b*d*(a + b*Sinh[c + d*x])^2) + (Csch[c/2]*Sech[c/2]*(a*e*f*Cosh[c] + a*f^2*x*Cosh[c] + b*e*f*Sinh[d*x] + b*f^2*x*Sinh[d*x]))/(2*b*(a^2 + b^2)*d^2*(a + b*Sinh[c + d*x]))","B",1
329,1,5753,631,24.161423,"\int \frac{(e+f x)^3 \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","\text{Result too large to show}","\frac{3 f^3 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^4 \left(a^2+b^2\right)}+\frac{3 f^3 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^4 \left(a^2+b^2\right)}-\frac{3 a f^3 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^4 \left(a^2+b^2\right)^{3/2}}+\frac{3 a f^3 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^4 \left(a^2+b^2\right)^{3/2}}+\frac{3 a f^2 (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}-\frac{3 a f^2 (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\frac{3 f^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d^3 \left(a^2+b^2\right)}+\frac{3 f^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d^3 \left(a^2+b^2\right)}+\frac{3 a f (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{2 b d^2 \left(a^2+b^2\right)^{3/2}}-\frac{3 a f (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{2 b d^2 \left(a^2+b^2\right)^{3/2}}-\frac{3 f (e+f x)^2 \cosh (c+d x)}{2 d^2 \left(a^2+b^2\right) (a+b \sinh (c+d x))}-\frac{3 f (e+f x)^2}{2 b d^2 \left(a^2+b^2\right)}-\frac{(e+f x)^3}{2 b d (a+b \sinh (c+d x))^2}",1,"Result too large to show","B",0
330,1,112,112,1.2366966,"\int \frac{(e+f x) \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Integrate[((e + f*x)*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","-\frac{\frac{\frac{2 a f \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\left(-a^2-b^2\right)^{3/2}}+\frac{d (e+f x)}{(a+b \sinh (c+d x))^2}}{b}+\frac{f \cosh (c+d x)}{\left(a^2+b^2\right) (a+b \sinh (c+d x))}}{2 d^2}","-\frac{a f \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b d^2 \left(a^2+b^2\right)^{3/2}}-\frac{f \cosh (c+d x)}{2 d^2 \left(a^2+b^2\right) (a+b \sinh (c+d x))}-\frac{e+f x}{2 b d (a+b \sinh (c+d x))^2}",1,"-1/2*((f*Cosh[c + d*x])/((a^2 + b^2)*(a + b*Sinh[c + d*x])) + ((2*a*f*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(-a^2 - b^2)^(3/2) + (d*(e + f*x))/(a + b*Sinh[c + d*x])^2)/b)/d^2","A",1
331,1,623,306,7.1259229,"\int \frac{(e+f x)^2 \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","\frac{\text{csch}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}\right) \left(a e f \cosh (c)+a f^2 x \cosh (c)+b e f \sinh (d x)+b f^2 x \sinh (d x)\right)}{2 b d^2 \left(a^2+b^2\right) (a+b \sinh (c+d x))}+\frac{2 e^c f \left(-\frac{a e^{-c} \left(e^{2 c}-1\right) e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2}}+\frac{a \left(e^{2 c}-1\right) f \left(\text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-\text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+d x \left(\log \left(\frac{b e^{2 c+d x}}{a e^c-\sqrt{e^{2 c} \left(a^2+b^2\right)}}+1\right)-\log \left(\frac{b e^{2 c+d x}}{\sqrt{e^{2 c} \left(a^2+b^2\right)}+a e^c}+1\right)\right)\right)}{2 d \sqrt{e^{2 c} \left(a^2+b^2\right)}}+\frac{a e^{-c} \left(e^{2 c}-1\right) f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)}{d \sqrt{a^2+b^2}}+\frac{1}{2} e^{-c} \left(e^{2 c}-1\right) f \left(\frac{2 a \tan ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{-a^2-b^2}}\right)}{d \sqrt{-a^2-b^2}}+\frac{\log \left(2 a e^{c+d x}+b \left(e^{2 (c+d x)}-1\right)\right)}{d}-2 x\right)-e^c f x+e^{-c} \left(e^{2 c}-1\right) f x\right)}{b \left(e^{2 c}-1\right) d^2 \left(a^2+b^2\right)}+\frac{f^2 x \coth (c)}{b d^2 \left(a^2+b^2\right)}-\frac{f^2 x \cosh (c) \text{csch}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}\right)}{2 b d^2 \left(a^2+b^2\right)}-\frac{(e+f x)^2}{2 b d (a+b \sinh (c+d x))^2}","\frac{a f^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}-\frac{a f^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\frac{f^2 \log (a+b \sinh (c+d x))}{b d^3 \left(a^2+b^2\right)}+\frac{a f (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d^2 \left(a^2+b^2\right)^{3/2}}-\frac{a f (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d^2 \left(a^2+b^2\right)^{3/2}}-\frac{f (e+f x) \cosh (c+d x)}{d^2 \left(a^2+b^2\right) (a+b \sinh (c+d x))}-\frac{(e+f x)^2}{2 b d (a+b \sinh (c+d x))^2}",1,"(f^2*x*Coth[c])/(b*(a^2 + b^2)*d^2) + (2*E^c*f*(-(E^c*f*x) + ((-1 + E^(2*c))*f*x)/E^c - (a*e*(-1 + E^(2*c))*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*E^c) + (a*(-1 + E^(2*c))*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d*E^c) + ((-1 + E^(2*c))*f*(-2*x + (2*a*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d) + Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))]/d))/(2*E^c) + (a*(-1 + E^(2*c))*f*(d*x*(Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])]) + PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(2*d*Sqrt[(a^2 + b^2)*E^(2*c)])))/(b*(a^2 + b^2)*d^2*(-1 + E^(2*c))) - (f^2*x*Cosh[c]*Csch[c/2]*Sech[c/2])/(2*b*(a^2 + b^2)*d^2) - (e + f*x)^2/(2*b*d*(a + b*Sinh[c + d*x])^2) + (Csch[c/2]*Sech[c/2]*(a*e*f*Cosh[c] + a*f^2*x*Cosh[c] + b*e*f*Sinh[d*x] + b*f^2*x*Sinh[d*x]))/(2*b*(a^2 + b^2)*d^2*(a + b*Sinh[c + d*x]))","B",1
332,1,5753,631,7.4906497,"\int \frac{(e+f x)^3 \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","\text{Result too large to show}","\frac{3 f^3 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^4 \left(a^2+b^2\right)}+\frac{3 f^3 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^4 \left(a^2+b^2\right)}-\frac{3 a f^3 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^4 \left(a^2+b^2\right)^{3/2}}+\frac{3 a f^3 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^4 \left(a^2+b^2\right)^{3/2}}+\frac{3 a f^2 (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}-\frac{3 a f^2 (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\frac{3 f^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d^3 \left(a^2+b^2\right)}+\frac{3 f^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d^3 \left(a^2+b^2\right)}+\frac{3 a f (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{2 b d^2 \left(a^2+b^2\right)^{3/2}}-\frac{3 a f (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{2 b d^2 \left(a^2+b^2\right)^{3/2}}-\frac{3 f (e+f x)^2 \cosh (c+d x)}{2 d^2 \left(a^2+b^2\right) (a+b \sinh (c+d x))}-\frac{3 f (e+f x)^2}{2 b d^2 \left(a^2+b^2\right)}-\frac{(e+f x)^3}{2 b d (a+b \sinh (c+d x))^2}",1,"Result too large to show","B",0
333,1,2819,448,18.8783924,"\int \frac{(e+f x)^3 \cosh (c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{6 a f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^4}-\frac{6 a f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^4}+\frac{6 a f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^3}+\frac{6 a f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^3}-\frac{3 a f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{3 a f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{a (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^2 d}-\frac{a (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^2 d}+\frac{a (e+f x)^4}{4 b^2 f}-\frac{6 f^3 \cosh (c+d x)}{b d^4}+\frac{6 f^2 (e+f x) \sinh (c+d x)}{b d^3}-\frac{3 f (e+f x)^2 \cosh (c+d x)}{b d^2}+\frac{(e+f x)^3 \sinh (c+d x)}{b d}",1,"((a*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(b^2*(-1 + E^(2*c))) + Csch[c]*(Cosh[c + d*x]/(4*b^2*d^4) - Sinh[c + d*x]/(4*b^2*d^4))*(-4*a*d^4*e^3*x*Cosh[d*x] - 6*a*d^4*e^2*f*x^2*Cosh[d*x] - 4*a*d^4*e*f^2*x^3*Cosh[d*x] - a*d^4*f^3*x^4*Cosh[d*x] - 4*a*d^4*e^3*x*Cosh[2*c + d*x] - 6*a*d^4*e^2*f*x^2*Cosh[2*c + d*x] - 4*a*d^4*e*f^2*x^3*Cosh[2*c + d*x] - a*d^4*f^3*x^4*Cosh[2*c + d*x] - 2*b*d^3*e^3*Cosh[c + 2*d*x] + 6*b*d^2*e^2*f*Cosh[c + 2*d*x] - 12*b*d*e*f^2*Cosh[c + 2*d*x] + 12*b*f^3*Cosh[c + 2*d*x] - 6*b*d^3*e^2*f*x*Cosh[c + 2*d*x] + 12*b*d^2*e*f^2*x*Cosh[c + 2*d*x] - 12*b*d*f^3*x*Cosh[c + 2*d*x] - 6*b*d^3*e*f^2*x^2*Cosh[c + 2*d*x] + 6*b*d^2*f^3*x^2*Cosh[c + 2*d*x] - 2*b*d^3*f^3*x^3*Cosh[c + 2*d*x] + 2*b*d^3*e^3*Cosh[3*c + 2*d*x] - 6*b*d^2*e^2*f*Cosh[3*c + 2*d*x] + 12*b*d*e*f^2*Cosh[3*c + 2*d*x] - 12*b*f^3*Cosh[3*c + 2*d*x] + 6*b*d^3*e^2*f*x*Cosh[3*c + 2*d*x] - 12*b*d^2*e*f^2*x*Cosh[3*c + 2*d*x] + 12*b*d*f^3*x*Cosh[3*c + 2*d*x] + 6*b*d^3*e*f^2*x^2*Cosh[3*c + 2*d*x] - 6*b*d^2*f^3*x^2*Cosh[3*c + 2*d*x] + 2*b*d^3*f^3*x^3*Cosh[3*c + 2*d*x] - 4*b*d^3*e^3*Sinh[c] - 12*b*d^2*e^2*f*Sinh[c] - 24*b*d*e*f^2*Sinh[c] - 24*b*f^3*Sinh[c] - 12*b*d^3*e^2*f*x*Sinh[c] - 24*b*d^2*e*f^2*x*Sinh[c] - 24*b*d*f^3*x*Sinh[c] - 12*b*d^3*e*f^2*x^2*Sinh[c] - 12*b*d^2*f^3*x^2*Sinh[c] - 4*b*d^3*f^3*x^3*Sinh[c] - 4*a*d^4*e^3*x*Sinh[d*x] - 6*a*d^4*e^2*f*x^2*Sinh[d*x] - 4*a*d^4*e*f^2*x^3*Sinh[d*x] - a*d^4*f^3*x^4*Sinh[d*x] - 4*a*d^4*e^3*x*Sinh[2*c + d*x] - 6*a*d^4*e^2*f*x^2*Sinh[2*c + d*x] - 4*a*d^4*e*f^2*x^3*Sinh[2*c + d*x] - a*d^4*f^3*x^4*Sinh[2*c + d*x] - 2*b*d^3*e^3*Sinh[c + 2*d*x] + 6*b*d^2*e^2*f*Sinh[c + 2*d*x] - 12*b*d*e*f^2*Sinh[c + 2*d*x] + 12*b*f^3*Sinh[c + 2*d*x] - 6*b*d^3*e^2*f*x*Sinh[c + 2*d*x] + 12*b*d^2*e*f^2*x*Sinh[c + 2*d*x] - 12*b*d*f^3*x*Sinh[c + 2*d*x] - 6*b*d^3*e*f^2*x^2*Sinh[c + 2*d*x] + 6*b*d^2*f^3*x^2*Sinh[c + 2*d*x] - 2*b*d^3*f^3*x^3*Sinh[c + 2*d*x] + 2*b*d^3*e^3*Sinh[3*c + 2*d*x] - 6*b*d^2*e^2*f*Sinh[3*c + 2*d*x] + 12*b*d*e*f^2*Sinh[3*c + 2*d*x] - 12*b*f^3*Sinh[3*c + 2*d*x] + 6*b*d^3*e^2*f*x*Sinh[3*c + 2*d*x] - 12*b*d^2*e*f^2*x*Sinh[3*c + 2*d*x] + 12*b*d*f^3*x*Sinh[3*c + 2*d*x] + 6*b*d^3*e*f^2*x^2*Sinh[3*c + 2*d*x] - 6*b*d^2*f^3*x^2*Sinh[3*c + 2*d*x] + 2*b*d^3*f^3*x^3*Sinh[3*c + 2*d*x]))/2","B",1
334,1,1301,330,11.6455479,"\int \frac{(e+f x)^2 \cosh (c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{1}{2} \left(\frac{2 a \left(2 e^{2 c} f^2 x^3+6 e e^{2 c} f x^2-\frac{3 e^{2 c} f^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}+\frac{3 f^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}-\frac{3 e^{2 c} f^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}+\frac{3 f^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}+6 e^2 e^{2 c} x-\frac{6 e e^{2 c} f \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}+\frac{6 e f \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}-\frac{6 e e^{2 c} f \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}+\frac{6 e f \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}+\frac{6 a \sqrt{-\left(a^2+b^2\right)^2} e^2 e^{2 c} \tan ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{-a^2-b^2}}\right)}{\left(a^2+b^2\right)^{3/2} d}+\frac{6 a \sqrt{a^2+b^2} e^2 \tan ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-\left(a^2+b^2\right)^2} d}+\frac{6 a \sqrt{-\left(a^2+b^2\right)^2} e^2 e^{2 c} \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)}{\left(-a^2-b^2\right)^{3/2} d}-\frac{6 a \sqrt{-\left(a^2+b^2\right)^2} e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)}{\left(-a^2-b^2\right)^{3/2} d}-\frac{3 e^2 e^{2 c} \log \left(2 e^{c+d x} a+b \left(-1+e^{2 (c+d x)}\right)\right)}{d}+\frac{3 e^2 \log \left(2 e^{c+d x} a+b \left(-1+e^{2 (c+d x)}\right)\right)}{d}-\frac{6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^2}-\frac{6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^2}+\frac{6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}-\frac{6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}+\frac{6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}-\frac{6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}\right)}{3 b^2 \left(-1+e^{2 c}\right)}-\frac{a x \left(3 e^2+3 f x e+f^2 x^2\right) \cosh (c) \text{csch}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}\right)}{3 b^2}+\frac{2 \cosh (d x) \left(e^2 \sinh (c) d^2+f^2 x^2 \sinh (c) d^2+2 e f x \sinh (c) d^2-2 e f \cosh (c) d-2 f^2 x \cosh (c) d+2 f^2 \sinh (c)\right)}{b d^3}+\frac{2 \left(e^2 \cosh (c) d^2+f^2 x^2 \cosh (c) d^2+2 e f x \cosh (c) d^2-2 e f \sinh (c) d-2 f^2 x \sinh (c) d+2 f^2 \cosh (c)\right) \sinh (d x)}{b d^3}\right)","\frac{2 a f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^3}+\frac{2 a f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^3}-\frac{2 a f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{2 a f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{a (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^2 d}-\frac{a (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^2 d}+\frac{a (e+f x)^3}{3 b^2 f}+\frac{2 f^2 \sinh (c+d x)}{b d^3}-\frac{2 f (e+f x) \cosh (c+d x)}{b d^2}+\frac{(e+f x)^2 \sinh (c+d x)}{b d}",1,"((2*a*(6*e^2*E^(2*c)*x + 6*e*E^(2*c)*f*x^2 + 2*E^(2*c)*f^2*x^3 + (6*a*Sqrt[a^2 + b^2]*e^2*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/(Sqrt[-(a^2 + b^2)^2]*d) + (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) - (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (6*a*Sqrt[-(a^2 + b^2)^2]*e^2*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (3*e^2*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d - (3*e^2*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (3*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (3*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (3*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (3*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3))/(3*b^2*(-1 + E^(2*c))) - (a*x*(3*e^2 + 3*e*f*x + f^2*x^2)*Cosh[c]*Csch[c/2]*Sech[c/2])/(3*b^2) + (2*Cosh[d*x]*(-2*d*e*f*Cosh[c] - 2*d*f^2*x*Cosh[c] + d^2*e^2*Sinh[c] + 2*f^2*Sinh[c] + 2*d^2*e*f*x*Sinh[c] + d^2*f^2*x^2*Sinh[c]))/(b*d^3) + (2*(d^2*e^2*Cosh[c] + 2*f^2*Cosh[c] + 2*d^2*e*f*x*Cosh[c] + d^2*f^2*x^2*Cosh[c] - 2*d*e*f*Sinh[c] - 2*d*f^2*x*Sinh[c])*Sinh[d*x])/(b*d^3))/2","B",1
335,1,206,212,1.0720319,"\int \frac{(e+f x) \cosh (c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{-a \left(f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-\frac{1}{2} f (c+d x)^2\right)+b d (e+f x) \sinh (c+d x)-b f \cosh (c+d x)}{b^2 d^2}","-\frac{a f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{a f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{a (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^2 d}-\frac{a (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^2 d}+\frac{a (e+f x)^2}{2 b^2 f}-\frac{f \cosh (c+d x)}{b d^2}+\frac{(e+f x) \sinh (c+d x)}{b d}",1,"(-(b*f*Cosh[c + d*x]) - a*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + b*d*(e + f*x)*Sinh[c + d*x])/(b^2*d^2)","A",1
336,1,33,34,0.0371079,"\int \frac{\cosh (c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{\frac{a \log (a+b \sinh (c+d x))}{b^2}-\frac{\sinh (c+d x)}{b}}{d}","\frac{\sinh (c+d x)}{b d}-\frac{a \log (a+b \sinh (c+d x))}{b^2 d}",1,"-(((a*Log[a + b*Sinh[c + d*x]])/b^2 - Sinh[c + d*x]/b)/d)","A",1
337,0,0,35,73.2603875,"\int \frac{\cosh (c+d x) \sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]*Sinh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh (c+d x) \sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh (c+d x) \cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[(Cosh[c + d*x]*Sinh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
338,1,2963,696,14.1631633,"\int \frac{(e+f x)^3 \cosh ^2(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^2*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{a^2 (e+f x)^4}{4 b^3 f}-\frac{6 a f^3 \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^4}+\frac{6 a f^3 \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^4}+\frac{6 a f^2 \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^3}-\frac{6 a f^2 \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^3}-\frac{3 a f \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{3 a f \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2}-\frac{a \sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d}+\frac{a \sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d}+\frac{6 a f^3 \sinh (c+d x)}{b^2 d^4}-\frac{6 a f^2 (e+f x) \cosh (c+d x)}{b^2 d^3}+\frac{3 a f (e+f x)^2 \sinh (c+d x)}{b^2 d^2}-\frac{a (e+f x)^3 \cosh (c+d x)}{b^2 d}-\frac{3 f^3 \cosh ^2(c+d x)}{8 b d^4}+\frac{3 f^2 (e+f x) \sinh (c+d x) \cosh (c+d x)}{4 b d^3}-\frac{3 f (e+f x)^2 \cosh ^2(c+d x)}{4 b d^2}+\frac{(e+f x)^3 \sinh (c+d x) \cosh (c+d x)}{2 b d}+\frac{3 e f^2 x}{4 b d^2}+\frac{3 f^3 x^2}{8 b d^2}+\frac{(e+f x)^4}{8 b f}",1,"(e^3*(c/d + x - (2*a*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d)))/(4*b) + (3*e^2*f*(x^2 + ((2*I)*a*Pi*ArcTanh[(-b + a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d^2) + (2*a*(2*((-I)*c + ArcCos[((-I)*a)/b])*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ((-2*I)*c + Pi - (2*I)*d*x)*ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (ArcCos[((-I)*a)/b] + (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((I*a + b)*(a + I*(b + Sqrt[-a^2 - b^2]))*(-I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - (ArcCos[((-I)*a)/b] - (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((I*a + b)*(I*a - b + Sqrt[-a^2 - b^2])*(I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(a - I*b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] + (ArcCos[((-I)*a)/b] - (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (2*I)*ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[-(((-1)^(3/4)*Sqrt[-a^2 - b^2]*E^(-1/2*c - (d*x)/2))/(Sqrt[2]*Sqrt[(-I)*b]*Sqrt[a + b*Sinh[c + d*x]]))] + (ArcCos[((-I)*a)/b] + (2*I)*(ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]]))*Log[((-1)^(1/4)*Sqrt[-a^2 - b^2]*E^((c + d*x)/2))/(Sqrt[2]*Sqrt[(-I)*b]*Sqrt[a + b*Sinh[c + d*x]])] + I*(PolyLog[2, ((I*a + Sqrt[-a^2 - b^2])*(I*a + b - I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - PolyLog[2, ((a + I*Sqrt[-a^2 - b^2])*(-a + I*b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))])))/(Sqrt[-a^2 - b^2]*d^2)))/(8*b) + (e*f^2*(x^3 - (3*a*(d^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3)))/(4*b) + (f^3*(x^4 - (4*a*(d^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^2*x^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 3*d^2*x^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^4)))/(16*b) + (e*f^2*(2*(4*a^2 + b^2)*x^3 - (6*a*(4*a^2 + 3*b^2)*(d^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) - (24*a*b*Cosh[d*x]*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c]))/d^3 + (3*b^2*Cosh[2*d*x]*(-2*d*x*Cosh[2*c] + (1 + 2*d^2*x^2)*Sinh[2*c]))/d^3 - (24*a*b*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c])*Sinh[d*x])/d^3 + (3*b^2*((1 + 2*d^2*x^2)*Cosh[2*c] - 2*d*x*Sinh[2*c])*Sinh[2*d*x])/d^3))/(8*b^3) + (f^3*((4*a^2 + b^2)*x^4 - (4*a*(4*a^2 + 3*b^2)*(d^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^2*x^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 3*d^2*x^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^4) - (16*a*b*Cosh[d*x]*(d*x*(6 + d^2*x^2)*Cosh[c] - 3*(2 + d^2*x^2)*Sinh[c]))/d^4 + (b^2*Cosh[2*d*x]*(-3*(1 + 2*d^2*x^2)*Cosh[2*c] + 2*d*x*(3 + 2*d^2*x^2)*Sinh[2*c]))/d^4 - (16*a*b*(-3*(2 + d^2*x^2)*Cosh[c] + d*x*(6 + d^2*x^2)*Sinh[c])*Sinh[d*x])/d^4 + (b^2*(2*d*x*(3 + 2*d^2*x^2)*Cosh[2*c] - 3*(1 + 2*d^2*x^2)*Sinh[2*c])*Sinh[2*d*x])/d^4))/(16*b^3) + (e^3*((4*a^2 + b^2)*(c + d*x) - (2*a*(4*a^2 + 3*b^2)*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[c + d*x] + b^2*Sinh[2*(c + d*x)]))/(4*b^3*d) + (3*e^2*f*((4*a^2 + b^2)*(-c + d*x)*(c + d*x) - 8*a*b*d*x*Cosh[c + d*x] - b^2*Cosh[2*(c + d*x)] - (2*a*(4*a^2 + 3*b^2)*(2*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + (c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - (c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] + 8*a*b*Sinh[c + d*x] + 2*b^2*d*x*Sinh[2*(c + d*x)]))/(8*b^3*d^2)","C",0
339,1,2172,510,9.4230265,"\int \frac{(e+f x)^2 \cosh ^2(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{a^2 (e+f x)^3}{3 b^3 f}+\frac{2 a f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^3}-\frac{2 a f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^3}-\frac{2 a f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{2 a f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2}-\frac{a \sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d}+\frac{a \sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d}-\frac{2 a f^2 \cosh (c+d x)}{b^2 d^3}+\frac{2 a f (e+f x) \sinh (c+d x)}{b^2 d^2}-\frac{a (e+f x)^2 \cosh (c+d x)}{b^2 d}+\frac{f^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^3}-\frac{f (e+f x) \cosh ^2(c+d x)}{2 b d^2}+\frac{(e+f x)^2 \sinh (c+d x) \cosh (c+d x)}{2 b d}+\frac{f^2 x}{4 b d^2}+\frac{(e+f x)^3}{6 b f}",1,"(e^2*(c/d + x - (2*a*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d)))/(4*b) + (e*f*(x^2 + ((2*I)*a*Pi*ArcTanh[(-b + a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d^2) + (2*a*(2*((-I)*c + ArcCos[((-I)*a)/b])*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ((-2*I)*c + Pi - (2*I)*d*x)*ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (ArcCos[((-I)*a)/b] + (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((I*a + b)*(a + I*(b + Sqrt[-a^2 - b^2]))*(-I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - (ArcCos[((-I)*a)/b] - (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((I*a + b)*(I*a - b + Sqrt[-a^2 - b^2])*(I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(a - I*b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] + (ArcCos[((-I)*a)/b] - (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (2*I)*ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[-(((-1)^(3/4)*Sqrt[-a^2 - b^2]*E^(-1/2*c - (d*x)/2))/(Sqrt[2]*Sqrt[(-I)*b]*Sqrt[a + b*Sinh[c + d*x]]))] + (ArcCos[((-I)*a)/b] + (2*I)*(ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]]))*Log[((-1)^(1/4)*Sqrt[-a^2 - b^2]*E^((c + d*x)/2))/(Sqrt[2]*Sqrt[(-I)*b]*Sqrt[a + b*Sinh[c + d*x]])] + I*(PolyLog[2, ((I*a + Sqrt[-a^2 - b^2])*(I*a + b - I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - PolyLog[2, ((a + I*Sqrt[-a^2 - b^2])*(-a + I*b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))])))/(Sqrt[-a^2 - b^2]*d^2)))/(4*b) + (f^2*(x^3 - (3*a*(d^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3)))/(12*b) + (f^2*(2*(4*a^2 + b^2)*x^3 - (6*a*(4*a^2 + 3*b^2)*(d^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) - (24*a*b*Cosh[d*x]*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c]))/d^3 + (3*b^2*Cosh[2*d*x]*(-2*d*x*Cosh[2*c] + (1 + 2*d^2*x^2)*Sinh[2*c]))/d^3 - (24*a*b*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c])*Sinh[d*x])/d^3 + (3*b^2*((1 + 2*d^2*x^2)*Cosh[2*c] - 2*d*x*Sinh[2*c])*Sinh[2*d*x])/d^3))/(24*b^3) + (e^2*((4*a^2 + b^2)*(c + d*x) - (2*a*(4*a^2 + 3*b^2)*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[c + d*x] + b^2*Sinh[2*(c + d*x)]))/(4*b^3*d) + (e*f*((4*a^2 + b^2)*(-c + d*x)*(c + d*x) - 8*a*b*d*x*Cosh[c + d*x] - b^2*Cosh[2*(c + d*x)] - (2*a*(4*a^2 + 3*b^2)*(2*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + (c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - (c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] + 8*a*b*Sinh[c + d*x] + 2*b^2*d*x*Sinh[2*(c + d*x)]))/(4*b^3*d^2)","C",0
340,1,1551,327,3.4530753,"\int \frac{(e+f x) \cosh ^2(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{2 e \left(\frac{c}{d}+x-\frac{2 a \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2} d}\right) b^2+f \left(x^2+\frac{2 i a \pi  \tanh ^{-1}\left(\frac{a \tanh \left(\frac{1}{2} (c+d x)\right)-b}{\sqrt{a^2+b^2}}\right)}{\sqrt{a^2+b^2} d^2}+\frac{2 a \left(2 \left(\cos ^{-1}\left(-\frac{i a}{b}\right)-i c\right) \tanh ^{-1}\left(\frac{(a+i b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)+(-2 i c-2 i d x+\pi ) \tanh ^{-1}\left(\frac{(a-i b) \tan \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)-\left(\cos ^{-1}\left(-\frac{i a}{b}\right)+2 i \tanh ^{-1}\left(\frac{(a+i b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(\frac{(i a+b) \left(a+i \left(b+\sqrt{-a^2-b^2}\right)\right) \left(\cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)-i\right)}{b \left(i a+b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}\right)-\left(\cos ^{-1}\left(-\frac{i a}{b}\right)-2 i \tanh ^{-1}\left(\frac{(a+i b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(\frac{(i a+b) \left(i a-b+\sqrt{-a^2-b^2}\right) \left(\cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)+i\right)}{b \left(a-i b+\sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}\right)+\left(\cos ^{-1}\left(-\frac{i a}{b}\right)-2 i \tanh ^{-1}\left(\frac{(a+i b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)-2 i \tanh ^{-1}\left(\frac{(a-i b) \tan \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)\right) \log \left(-\frac{(-1)^{3/4} \sqrt{-a^2-b^2} e^{-\frac{c}{2}-\frac{d x}{2}}}{\sqrt{2} \sqrt{-i b} \sqrt{a+b \sinh (c+d x)}}\right)+\left(\cos ^{-1}\left(-\frac{i a}{b}\right)+2 i \left(\tanh ^{-1}\left(\frac{(a+i b) \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)+\tanh ^{-1}\left(\frac{(a-i b) \tan \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)}{\sqrt{-a^2-b^2}}\right)\right)\right) \log \left(\frac{\sqrt[4]{-1} \sqrt{-a^2-b^2} e^{\frac{1}{2} (c+d x)}}{\sqrt{2} \sqrt{-i b} \sqrt{a+b \sinh (c+d x)}}\right)+i \left(\text{Li}_2\left(\frac{\left(i a+\sqrt{-a^2-b^2}\right) \left(i a+b-i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}{b \left(i a+b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}\right)-\text{Li}_2\left(\frac{\left(a+i \sqrt{-a^2-b^2}\right) \left(-a+i b+\sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}{b \left(i a+b+i \sqrt{-a^2-b^2} \cot \left(\frac{1}{4} (2 i c+2 i d x+\pi )\right)\right)}\right)\right)\right)}{\sqrt{-a^2-b^2} d^2}\right) b^2+\frac{2 e \left(\sinh (2 (c+d x)) b^2-4 a \cosh (c+d x) b+\left(4 a^2+b^2\right) (c+d x)-\frac{2 a \left(4 a^2+3 b^2\right) \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{\sqrt{-a^2-b^2}}\right)}{d}+\frac{f \left(-\cosh (2 (c+d x)) b^2+2 d x \sinh (2 (c+d x)) b^2-8 a d x \cosh (c+d x) b+8 a \sinh (c+d x) b+\left(4 a^2+b^2\right) (d x-c) (c+d x)-\frac{2 a \left(4 a^2+3 b^2\right) \left(2 c \tanh ^{-1}\left(\frac{a+b \cosh (c+d x)+b \sinh (c+d x)}{\sqrt{a^2+b^2}}\right)+(c+d x) \log \left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a-\sqrt{a^2+b^2}}+1\right)-(c+d x) \log \left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}+1\right)+\text{Li}_2\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-a}\right)-\text{Li}_2\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}\right)\right)}{\sqrt{a^2+b^2}}\right)}{d^2}}{8 b^3}","\frac{a^2 e x}{b^3}+\frac{a^2 f x^2}{2 b^3}-\frac{a f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{a f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2}-\frac{a \sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d}+\frac{a \sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d}+\frac{a f \sinh (c+d x)}{b^2 d^2}-\frac{a (e+f x) \cosh (c+d x)}{b^2 d}-\frac{f \cosh ^2(c+d x)}{4 b d^2}+\frac{(e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b d}+\frac{e x}{2 b}+\frac{f x^2}{4 b}",1,"(2*b^2*e*(c/d + x - (2*a*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d)) + b^2*f*(x^2 + ((2*I)*a*Pi*ArcTanh[(-b + a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d^2) + (2*a*(2*((-I)*c + ArcCos[((-I)*a)/b])*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ((-2*I)*c + Pi - (2*I)*d*x)*ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (ArcCos[((-I)*a)/b] + (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((I*a + b)*(a + I*(b + Sqrt[-a^2 - b^2]))*(-I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - (ArcCos[((-I)*a)/b] - (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((I*a + b)*(I*a - b + Sqrt[-a^2 - b^2])*(I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(a - I*b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] + (ArcCos[((-I)*a)/b] - (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (2*I)*ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[-(((-1)^(3/4)*Sqrt[-a^2 - b^2]*E^(-1/2*c - (d*x)/2))/(Sqrt[2]*Sqrt[(-I)*b]*Sqrt[a + b*Sinh[c + d*x]]))] + (ArcCos[((-I)*a)/b] + (2*I)*(ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]]))*Log[((-1)^(1/4)*Sqrt[-a^2 - b^2]*E^((c + d*x)/2))/(Sqrt[2]*Sqrt[(-I)*b]*Sqrt[a + b*Sinh[c + d*x]])] + I*(PolyLog[2, ((I*a + Sqrt[-a^2 - b^2])*(I*a + b - I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - PolyLog[2, ((a + I*Sqrt[-a^2 - b^2])*(-a + I*b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))])))/(Sqrt[-a^2 - b^2]*d^2)) + (2*e*((4*a^2 + b^2)*(c + d*x) - (2*a*(4*a^2 + 3*b^2)*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[c + d*x] + b^2*Sinh[2*(c + d*x)]))/d + (f*((4*a^2 + b^2)*(-c + d*x)*(c + d*x) - 8*a*b*d*x*Cosh[c + d*x] - b^2*Cosh[2*(c + d*x)] - (2*a*(4*a^2 + 3*b^2)*(2*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + (c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - (c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] + 8*a*b*Sinh[c + d*x] + 2*b^2*d*x*Sinh[2*(c + d*x)]))/d^2)/(8*b^3)","C",0
341,1,109,95,0.3915105,"\int \frac{\cosh ^2(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]^2*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{8 a \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)+4 a^2 c+4 a^2 d x-4 a b \cosh (c+d x)+b^2 \sinh (2 (c+d x))+2 b^2 c+2 b^2 d x}{4 b^3 d}","\frac{2 a \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b^3 d}+\frac{x \left(2 a^2+b^2\right)}{2 b^3}-\frac{\cosh (c+d x) (2 a-b \sinh (c+d x))}{2 b^2 d}",1,"(4*a^2*c + 2*b^2*c + 4*a^2*d*x + 2*b^2*d*x + 8*a*Sqrt[-a^2 - b^2]*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] - 4*a*b*Cosh[c + d*x] + b^2*Sinh[2*(c + d*x)])/(4*b^3*d)","A",1
342,-1,0,37,180.0010162,"\int \frac{\cosh ^2(c+d x) \sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]^2*Sinh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh (c+d x) \cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
343,1,7375,864,48.5871573,"\int \frac{(e+f x)^3 \cosh ^3(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^3*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{a \left(a^2+b^2\right) (e+f x)^4}{4 b^4 f}-\frac{a \sinh ^2(c+d x) (e+f x)^3}{2 b^2 d}-\frac{a \left(a^2+b^2\right) \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{b^4 d}-\frac{a \left(a^2+b^2\right) \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{b^4 d}+\frac{\cosh ^2(c+d x) \sinh (c+d x) (e+f x)^3}{3 b d}+\frac{2 \sinh (c+d x) (e+f x)^3}{3 b d}+\frac{a^2 \sinh (c+d x) (e+f x)^3}{b^3 d}-\frac{a (e+f x)^3}{4 b^2 d}-\frac{f \cosh ^3(c+d x) (e+f x)^2}{3 b d^2}-\frac{2 f \cosh (c+d x) (e+f x)^2}{b d^2}-\frac{3 a^2 f \cosh (c+d x) (e+f x)^2}{b^3 d^2}-\frac{3 a \left(a^2+b^2\right) f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)^2}{b^4 d^2}-\frac{3 a \left(a^2+b^2\right) f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)^2}{b^4 d^2}+\frac{3 a f \cosh (c+d x) \sinh (c+d x) (e+f x)^2}{4 b^2 d^2}-\frac{3 a f^2 \sinh ^2(c+d x) (e+f x)}{4 b^2 d^3}+\frac{6 a \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)}{b^4 d^3}+\frac{6 a \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)}{b^4 d^3}+\frac{40 f^2 \sinh (c+d x) (e+f x)}{9 b d^3}+\frac{6 a^2 f^2 \sinh (c+d x) (e+f x)}{b^3 d^3}+\frac{2 f^2 \cosh ^2(c+d x) \sinh (c+d x) (e+f x)}{9 b d^3}-\frac{2 f^3 \cosh ^3(c+d x)}{27 b d^4}-\frac{3 a f^3 x}{8 b^2 d^3}-\frac{40 f^3 \cosh (c+d x)}{9 b d^4}-\frac{6 a^2 f^3 \cosh (c+d x)}{b^3 d^4}-\frac{6 a \left(a^2+b^2\right) f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^4}-\frac{6 a \left(a^2+b^2\right) f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^4}+\frac{3 a f^3 \cosh (c+d x) \sinh (c+d x)}{8 b^2 d^4}",1,"Result too large to show","B",0
344,1,3509,636,15.938238,"\int \frac{(e+f x)^2 \cosh ^3(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^3*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{2 a^2 f^2 \sinh (c+d x)}{b^3 d^3}-\frac{2 a^2 f (e+f x) \cosh (c+d x)}{b^3 d^2}+\frac{a^2 (e+f x)^2 \sinh (c+d x)}{b^3 d}+\frac{2 a f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^3}+\frac{2 a f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^3}-\frac{2 a f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{2 a f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{a \left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^4 d}-\frac{a \left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^4 d}+\frac{a \left(a^2+b^2\right) (e+f x)^3}{3 b^4 f}-\frac{a f^2 \sinh ^2(c+d x)}{4 b^2 d^3}+\frac{a f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^2 d^2}-\frac{a (e+f x)^2 \sinh ^2(c+d x)}{2 b^2 d}-\frac{a e f x}{2 b^2 d}-\frac{a f^2 x^2}{4 b^2 d}+\frac{2 f^2 \sinh ^3(c+d x)}{27 b d^3}+\frac{14 f^2 \sinh (c+d x)}{9 b d^3}-\frac{2 f (e+f x) \cosh ^3(c+d x)}{9 b d^2}-\frac{4 f (e+f x) \cosh (c+d x)}{3 b d^2}+\frac{2 (e+f x)^2 \sinh (c+d x)}{3 b d}+\frac{(e+f x)^2 \sinh (c+d x) \cosh ^2(c+d x)}{3 b d}",1,"(f^2*(2*a*x^3*(-1 + Coth[c]) - 2*a*x^3*Coth[c] - (6*a*b^2*(d^2*x^2*Log[1 + ((a - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*PolyLog[3, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b]))/(Sqrt[a^2 + b^2]*(-a + Sqrt[a^2 + b^2])*d^3) - (6*a*b^2*(d^2*x^2*Log[1 + ((a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 2*PolyLog[3, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b]))/(Sqrt[a^2 + b^2]*(a + Sqrt[a^2 + b^2])*d^3) + (6*a^2*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - 2*PolyLog[3, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])]))/(Sqrt[a^2 + b^2]*d^3) - (6*a^2*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) + (6*b*Cosh[d*x]*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c]))/d^3 + (6*b*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c])*Sinh[d*x])/d^3))/(12*b^2) - (e^2*((a*Log[a + b*Sinh[c + d*x]])/b^2 - Sinh[c + d*x]/b))/(2*d) + (e*f*(-(b*Cosh[c + d*x]) - a*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + b*d*x*Sinh[c + d*x]))/(b^2*d^2) + (e^2*(-3*a*(2*a^2 + b^2)*Log[a + b*Sinh[c + d*x]] + 3*b*(2*a^2 + b^2)*Sinh[c + d*x] - 3*a*b^2*Sinh[c + d*x]^2 + 2*b^3*Sinh[c + d*x]^3))/(6*b^4*d) + (e*f*(-18*b*(4*a^2 + b^2)*Cosh[c + d*x] - 18*a*b^2*d*x*Cosh[2*(c + d*x)] - 2*b^3*Cosh[3*(c + d*x)] - 36*a*(2*a^2 + b^2)*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + 18*b*(4*a^2 + b^2)*d*x*Sinh[c + d*x] + 9*a*b^2*Sinh[2*(c + d*x)] + 6*b^3*d*x*Sinh[3*(c + d*x)]))/(36*b^4*d^2) + (f^2*((2*a*(2*a^2 + b^2)*(-1 + Coth[c])*(2*x^3 + (6*a*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - 2*PolyLog[3, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])])*Sinh[c]*(Cosh[c] + Sinh[c]))/(Sqrt[a^2 + b^2]*d^3) - (3*b^2*(d^2*x^2*Log[1 + ((a - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*PolyLog[3, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(-a + Sqrt[a^2 + b^2])*d^3) - (3*b^2*(d^2*x^2*Log[1 + ((a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 2*PolyLog[3, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(a + Sqrt[a^2 + b^2])*d^3) - (3*a*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*d^3)))/(3*b^4) + Csch[c]*(Cosh[3*c + 3*d*x]/(108*b^4*d^3) - Sinh[3*c + 3*d*x]/(108*b^4*d^3))*(27*a*b^2*Cosh[d*x] + 54*a*b^2*d*x*Cosh[d*x] + 54*a*b^2*d^2*x^2*Cosh[d*x] - 27*a*b^2*Cosh[2*c + d*x] - 54*a*b^2*d*x*Cosh[2*c + d*x] - 54*a*b^2*d^2*x^2*Cosh[2*c + d*x] + 432*a^2*b*Cosh[c + 2*d*x] + 108*b^3*Cosh[c + 2*d*x] + 432*a^2*b*d*x*Cosh[c + 2*d*x] + 108*b^3*d*x*Cosh[c + 2*d*x] + 216*a^2*b*d^2*x^2*Cosh[c + 2*d*x] + 54*b^3*d^2*x^2*Cosh[c + 2*d*x] - 432*a^2*b*Cosh[3*c + 2*d*x] - 108*b^3*Cosh[3*c + 2*d*x] - 432*a^2*b*d*x*Cosh[3*c + 2*d*x] - 108*b^3*d*x*Cosh[3*c + 2*d*x] - 216*a^2*b*d^2*x^2*Cosh[3*c + 2*d*x] - 54*b^3*d^2*x^2*Cosh[3*c + 2*d*x] - 144*a^3*d^3*x^3*Cosh[2*c + 3*d*x] - 72*a*b^2*d^3*x^3*Cosh[2*c + 3*d*x] - 144*a^3*d^3*x^3*Cosh[4*c + 3*d*x] - 72*a*b^2*d^3*x^3*Cosh[4*c + 3*d*x] - 432*a^2*b*Cosh[3*c + 4*d*x] - 108*b^3*Cosh[3*c + 4*d*x] + 432*a^2*b*d*x*Cosh[3*c + 4*d*x] + 108*b^3*d*x*Cosh[3*c + 4*d*x] - 216*a^2*b*d^2*x^2*Cosh[3*c + 4*d*x] - 54*b^3*d^2*x^2*Cosh[3*c + 4*d*x] + 432*a^2*b*Cosh[5*c + 4*d*x] + 108*b^3*Cosh[5*c + 4*d*x] - 432*a^2*b*d*x*Cosh[5*c + 4*d*x] - 108*b^3*d*x*Cosh[5*c + 4*d*x] + 216*a^2*b*d^2*x^2*Cosh[5*c + 4*d*x] + 54*b^3*d^2*x^2*Cosh[5*c + 4*d*x] + 27*a*b^2*Cosh[4*c + 5*d*x] - 54*a*b^2*d*x*Cosh[4*c + 5*d*x] + 54*a*b^2*d^2*x^2*Cosh[4*c + 5*d*x] - 27*a*b^2*Cosh[6*c + 5*d*x] + 54*a*b^2*d*x*Cosh[6*c + 5*d*x] - 54*a*b^2*d^2*x^2*Cosh[6*c + 5*d*x] - 4*b^3*Cosh[5*c + 6*d*x] + 12*b^3*d*x*Cosh[5*c + 6*d*x] - 18*b^3*d^2*x^2*Cosh[5*c + 6*d*x] + 4*b^3*Cosh[7*c + 6*d*x] - 12*b^3*d*x*Cosh[7*c + 6*d*x] + 18*b^3*d^2*x^2*Cosh[7*c + 6*d*x] - 8*b^3*Sinh[c] - 24*b^3*d*x*Sinh[c] - 36*b^3*d^2*x^2*Sinh[c] + 27*a*b^2*Sinh[d*x] + 54*a*b^2*d*x*Sinh[d*x] + 54*a*b^2*d^2*x^2*Sinh[d*x] - 27*a*b^2*Sinh[2*c + d*x] - 54*a*b^2*d*x*Sinh[2*c + d*x] - 54*a*b^2*d^2*x^2*Sinh[2*c + d*x] + 432*a^2*b*Sinh[c + 2*d*x] + 108*b^3*Sinh[c + 2*d*x] + 432*a^2*b*d*x*Sinh[c + 2*d*x] + 108*b^3*d*x*Sinh[c + 2*d*x] + 216*a^2*b*d^2*x^2*Sinh[c + 2*d*x] + 54*b^3*d^2*x^2*Sinh[c + 2*d*x] - 432*a^2*b*Sinh[3*c + 2*d*x] - 108*b^3*Sinh[3*c + 2*d*x] - 432*a^2*b*d*x*Sinh[3*c + 2*d*x] - 108*b^3*d*x*Sinh[3*c + 2*d*x] - 216*a^2*b*d^2*x^2*Sinh[3*c + 2*d*x] - 54*b^3*d^2*x^2*Sinh[3*c + 2*d*x] - 144*a^3*d^3*x^3*Sinh[2*c + 3*d*x] - 72*a*b^2*d^3*x^3*Sinh[2*c + 3*d*x] - 144*a^3*d^3*x^3*Sinh[4*c + 3*d*x] - 72*a*b^2*d^3*x^3*Sinh[4*c + 3*d*x] - 432*a^2*b*Sinh[3*c + 4*d*x] - 108*b^3*Sinh[3*c + 4*d*x] + 432*a^2*b*d*x*Sinh[3*c + 4*d*x] + 108*b^3*d*x*Sinh[3*c + 4*d*x] - 216*a^2*b*d^2*x^2*Sinh[3*c + 4*d*x] - 54*b^3*d^2*x^2*Sinh[3*c + 4*d*x] + 432*a^2*b*Sinh[5*c + 4*d*x] + 108*b^3*Sinh[5*c + 4*d*x] - 432*a^2*b*d*x*Sinh[5*c + 4*d*x] - 108*b^3*d*x*Sinh[5*c + 4*d*x] + 216*a^2*b*d^2*x^2*Sinh[5*c + 4*d*x] + 54*b^3*d^2*x^2*Sinh[5*c + 4*d*x] + 27*a*b^2*Sinh[4*c + 5*d*x] - 54*a*b^2*d*x*Sinh[4*c + 5*d*x] + 54*a*b^2*d^2*x^2*Sinh[4*c + 5*d*x] - 27*a*b^2*Sinh[6*c + 5*d*x] + 54*a*b^2*d*x*Sinh[6*c + 5*d*x] - 54*a*b^2*d^2*x^2*Sinh[6*c + 5*d*x] - 4*b^3*Sinh[5*c + 6*d*x] + 12*b^3*d*x*Sinh[5*c + 6*d*x] - 18*b^3*d^2*x^2*Sinh[5*c + 6*d*x] + 4*b^3*Sinh[7*c + 6*d*x] - 12*b^3*d*x*Sinh[7*c + 6*d*x] + 18*b^3*d^2*x^2*Sinh[7*c + 6*d*x])))/8","B",0
345,1,551,400,2.7622404,"\int \frac{(e+f x) \cosh ^3(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^3*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{36 b^2 f \left(a \left(\text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+(c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+(c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-c \log (a+b \sinh (c+d x))-\frac{1}{2} (c+d x)^2\right)-b d x \sinh (c+d x)+b \cosh (c+d x)\right)+12 d e \left(-3 b \left(2 a^2+b^2\right) \sinh (c+d x)+3 a \left(2 a^2+b^2\right) \log (a+b \sinh (c+d x))+3 a b^2 \sinh ^2(c+d x)-2 b^3 \sinh ^3(c+d x)\right)+f \left(36 a \left(2 a^2+b^2\right) \left(\text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+(c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+(c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-c \log (a+b \sinh (c+d x))-\frac{1}{2} (c+d x)^2\right)-18 b d x \left(4 a^2+b^2\right) \sinh (c+d x)+18 b \left(4 a^2+b^2\right) \cosh (c+d x)-9 a b^2 \sinh (2 (c+d x))+18 a b^2 d x \cosh (2 (c+d x))-6 b^3 d x \sinh (3 (c+d x))+2 b^3 \cosh (3 (c+d x))\right)-36 b^2 d e (b \sinh (c+d x)-a \log (a+b \sinh (c+d x)))}{72 b^4 d^2}","-\frac{a^2 f \cosh (c+d x)}{b^3 d^2}+\frac{a^2 (e+f x) \sinh (c+d x)}{b^3 d}-\frac{a f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{a f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{a \left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^4 d}-\frac{a \left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^4 d}+\frac{a \left(a^2+b^2\right) (e+f x)^2}{2 b^4 f}+\frac{a f \sinh (c+d x) \cosh (c+d x)}{4 b^2 d^2}-\frac{a (e+f x) \sinh ^2(c+d x)}{2 b^2 d}-\frac{a f x}{4 b^2 d}-\frac{f \cosh ^3(c+d x)}{9 b d^2}-\frac{2 f \cosh (c+d x)}{3 b d^2}+\frac{2 (e+f x) \sinh (c+d x)}{3 b d}+\frac{(e+f x) \sinh (c+d x) \cosh ^2(c+d x)}{3 b d}",1,"-1/72*(-36*b^2*d*e*(-(a*Log[a + b*Sinh[c + d*x]]) + b*Sinh[c + d*x]) + 36*b^2*f*(b*Cosh[c + d*x] + a*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - b*d*x*Sinh[c + d*x]) + 12*d*e*(3*a*(2*a^2 + b^2)*Log[a + b*Sinh[c + d*x]] - 3*b*(2*a^2 + b^2)*Sinh[c + d*x] + 3*a*b^2*Sinh[c + d*x]^2 - 2*b^3*Sinh[c + d*x]^3) + f*(18*b*(4*a^2 + b^2)*Cosh[c + d*x] + 18*a*b^2*d*x*Cosh[2*(c + d*x)] + 2*b^3*Cosh[3*(c + d*x)] + 36*a*(2*a^2 + b^2)*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - 18*b*(4*a^2 + b^2)*d*x*Sinh[c + d*x] - 9*a*b^2*Sinh[2*(c + d*x)] - 6*b^3*d*x*Sinh[3*(c + d*x)]))/(b^4*d^2)","A",1
346,1,75,85,0.1632568,"\int \frac{\cosh ^3(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]^3*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 b \left(a^2+b^2\right) \sinh (c+d x)-6 a \left(a^2+b^2\right) \log (a+b \sinh (c+d x))-3 a b^2 \sinh ^2(c+d x)+2 b^3 \sinh ^3(c+d x)}{6 b^4 d}","-\frac{a \left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{b^4 d}+\frac{\left(a^2+b^2\right) \sinh (c+d x)}{b^3 d}-\frac{a \sinh ^2(c+d x)}{2 b^2 d}+\frac{\sinh ^3(c+d x)}{3 b d}",1,"(-6*a*(a^2 + b^2)*Log[a + b*Sinh[c + d*x]] + 6*b*(a^2 + b^2)*Sinh[c + d*x] - 3*a*b^2*Sinh[c + d*x]^2 + 2*b^3*Sinh[c + d*x]^3)/(6*b^4*d)","A",1
347,-1,0,37,180.000675,"\int \frac{\cosh ^3(c+d x) \sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]^3*Sinh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh (c+d x) \cosh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
348,1,3088,1021,23.8149861,"\int \frac{(e+f x)^3 \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{6 i \text{Li}_4\left(-i e^{c+d x}\right) f^3}{b d^4}+\frac{6 i a^2 \text{Li}_4\left(-i e^{c+d x}\right) f^3}{b \left(a^2+b^2\right) d^4}+\frac{6 i \text{Li}_4\left(i e^{c+d x}\right) f^3}{b d^4}-\frac{6 i a^2 \text{Li}_4\left(i e^{c+d x}\right) f^3}{b \left(a^2+b^2\right) d^4}-\frac{6 a \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f^3}{\left(a^2+b^2\right) d^4}-\frac{6 a \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f^3}{\left(a^2+b^2\right) d^4}+\frac{3 a \text{Li}_4\left(-e^{2 (c+d x)}\right) f^3}{4 \left(a^2+b^2\right) d^4}+\frac{6 i (e+f x) \text{Li}_3\left(-i e^{c+d x}\right) f^2}{b d^3}-\frac{6 i a^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right) f^2}{b \left(a^2+b^2\right) d^3}-\frac{6 i (e+f x) \text{Li}_3\left(i e^{c+d x}\right) f^2}{b d^3}+\frac{6 i a^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right) f^2}{b \left(a^2+b^2\right) d^3}+\frac{6 a (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f^2}{\left(a^2+b^2\right) d^3}+\frac{6 a (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f^2}{\left(a^2+b^2\right) d^3}-\frac{3 a (e+f x) \text{Li}_3\left(-e^{2 (c+d x)}\right) f^2}{2 \left(a^2+b^2\right) d^3}-\frac{3 i (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right) f}{b d^2}+\frac{3 i a^2 (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right) f}{b \left(a^2+b^2\right) d^2}+\frac{3 i (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right) f}{b d^2}-\frac{3 i a^2 (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right) f}{b \left(a^2+b^2\right) d^2}-\frac{3 a (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f}{\left(a^2+b^2\right) d^2}-\frac{3 a (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f}{\left(a^2+b^2\right) d^2}+\frac{3 a (e+f x)^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) f}{2 \left(a^2+b^2\right) d^2}+\frac{2 (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right)}{b d}-\frac{2 a^2 (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right)}{b \left(a^2+b^2\right) d}-\frac{a (e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right)}{\left(a^2+b^2\right) d}-\frac{a (e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right)}{\left(a^2+b^2\right) d}+\frac{a (e+f x)^3 \log \left(1+e^{2 (c+d x)}\right)}{\left(a^2+b^2\right) d}",1,"(-8*a*d^4*e^3*E^(2*c)*x - 12*a*d^4*e^2*E^(2*c)*f*x^2 - 8*a*d^4*e*E^(2*c)*f^2*x^3 - 2*a*d^4*E^(2*c)*f^3*x^4 + 8*b*d^3*e^3*ArcTan[E^(c + d*x)] + 8*b*d^3*e^3*E^(2*c)*ArcTan[E^(c + d*x)] + (12*I)*b*d^3*e^2*f*x*Log[1 - I*E^(c + d*x)] + (12*I)*b*d^3*e^2*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] + (12*I)*b*d^3*e*f^2*x^2*Log[1 - I*E^(c + d*x)] + (12*I)*b*d^3*e*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] + (4*I)*b*d^3*f^3*x^3*Log[1 - I*E^(c + d*x)] + (4*I)*b*d^3*E^(2*c)*f^3*x^3*Log[1 - I*E^(c + d*x)] - (12*I)*b*d^3*e^2*f*x*Log[1 + I*E^(c + d*x)] - (12*I)*b*d^3*e^2*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] - (12*I)*b*d^3*e*f^2*x^2*Log[1 + I*E^(c + d*x)] - (12*I)*b*d^3*e*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] - (4*I)*b*d^3*f^3*x^3*Log[1 + I*E^(c + d*x)] - (4*I)*b*d^3*E^(2*c)*f^3*x^3*Log[1 + I*E^(c + d*x)] + 4*a*d^3*e^3*Log[1 + E^(2*(c + d*x))] + 4*a*d^3*e^3*E^(2*c)*Log[1 + E^(2*(c + d*x))] + 12*a*d^3*e^2*f*x*Log[1 + E^(2*(c + d*x))] + 12*a*d^3*e^2*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 12*a*d^3*e*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 12*a*d^3*e*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 4*a*d^3*f^3*x^3*Log[1 + E^(2*(c + d*x))] + 4*a*d^3*E^(2*c)*f^3*x^3*Log[1 + E^(2*(c + d*x))] - (12*I)*b*d^2*(1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)] + (12*I)*b*d^2*(1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)] + 6*a*d^2*e^2*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a*d^2*e^2*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 12*a*d^2*e*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 12*a*d^2*e*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 6*a*d^2*f^3*x^2*PolyLog[2, -E^(2*(c + d*x))] + 6*a*d^2*E^(2*c)*f^3*x^2*PolyLog[2, -E^(2*(c + d*x))] + (24*I)*b*d*e*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (24*I)*b*d*e*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (24*I)*b*d*f^3*x*PolyLog[3, (-I)*E^(c + d*x)] + (24*I)*b*d*E^(2*c)*f^3*x*PolyLog[3, (-I)*E^(c + d*x)] - (24*I)*b*d*e*f^2*PolyLog[3, I*E^(c + d*x)] - (24*I)*b*d*e*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - (24*I)*b*d*f^3*x*PolyLog[3, I*E^(c + d*x)] - (24*I)*b*d*E^(2*c)*f^3*x*PolyLog[3, I*E^(c + d*x)] - 6*a*d*e*f^2*PolyLog[3, -E^(2*(c + d*x))] - 6*a*d*e*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))] - 6*a*d*f^3*x*PolyLog[3, -E^(2*(c + d*x))] - 6*a*d*E^(2*c)*f^3*x*PolyLog[3, -E^(2*(c + d*x))] - (24*I)*b*f^3*PolyLog[4, (-I)*E^(c + d*x)] - (24*I)*b*E^(2*c)*f^3*PolyLog[4, (-I)*E^(c + d*x)] + (24*I)*b*f^3*PolyLog[4, I*E^(c + d*x)] + (24*I)*b*E^(2*c)*f^3*PolyLog[4, I*E^(c + d*x)] + 3*a*f^3*PolyLog[4, -E^(2*(c + d*x))] + 3*a*E^(2*c)*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*(a^2 + b^2)*d^4*(1 + E^(2*c))) + (a*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(2*(a^2 + b^2)*(-1 + E^(2*c))) - (a*x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3)*Csch[c/2]*Sech[c/2]*Sech[c])/(8*(a^2 + b^2))","B",1
349,1,872,716,9.9267806,"\int \frac{(e+f x)^2 \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{-4 b e^2 \tan ^{-1}\left(e^{c+d x}\right) d^2-2 i b f^2 x^2 \log \left(1-i e^{c+d x}\right) d^2-4 i b e f x \log \left(1-i e^{c+d x}\right) d^2+2 i b f^2 x^2 \log \left(1+i e^{c+d x}\right) d^2+4 i b e f x \log \left(1+i e^{c+d x}\right) d^2-2 a e^2 \log \left(1+e^{2 (c+d x)}\right) d^2-2 a f^2 x^2 \log \left(1+e^{2 (c+d x)}\right) d^2-4 a e f x \log \left(1+e^{2 (c+d x)}\right) d^2+2 a e^2 \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2+2 a f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+4 a e f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+2 a f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+4 a e f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+4 i b f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) d-4 i b f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) d-2 a e f \text{Li}_2\left(-e^{2 (c+d x)}\right) d-2 a f^2 x \text{Li}_2\left(-e^{2 (c+d x)}\right) d+4 a e f \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+4 a f^2 x \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+4 a e f \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+4 a f^2 x \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-4 i b f^2 \text{Li}_3\left(-i e^{c+d x}\right)+4 i b f^2 \text{Li}_3\left(i e^{c+d x}\right)+a f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right)-4 a f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-4 a f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{2 \left(a^2+b^2\right) d^3}","-\frac{2 i a^2 f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}+\frac{2 i a^2 f^2 \text{Li}_3\left(i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}+\frac{2 a f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 a f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)}-\frac{a f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right)}{2 d^3 \left(a^2+b^2\right)}+\frac{2 i a^2 f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{2 i a^2 f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{2 a f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)}-\frac{2 a f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)}+\frac{a f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right)}{d^2 \left(a^2+b^2\right)}-\frac{a (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)}-\frac{a (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)}+\frac{a (e+f x)^2 \log \left(e^{2 (c+d x)}+1\right)}{d \left(a^2+b^2\right)}-\frac{2 a^2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{b d \left(a^2+b^2\right)}+\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{b d^3}-\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right)}{b d^3}-\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{b d^2}+\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{b d^2}+\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{b d}",1,"-1/2*(-4*b*d^2*e^2*ArcTan[E^(c + d*x)] - (4*I)*b*d^2*e*f*x*Log[1 - I*E^(c + d*x)] - (2*I)*b*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] + (4*I)*b*d^2*e*f*x*Log[1 + I*E^(c + d*x)] + (2*I)*b*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] - 2*a*d^2*e^2*Log[1 + E^(2*(c + d*x))] - 4*a*d^2*e*f*x*Log[1 + E^(2*(c + d*x))] - 2*a*d^2*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 2*a*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 4*a*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*a*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 4*a*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 2*a*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + (4*I)*b*d*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)] - (4*I)*b*d*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)] - 2*a*d*e*f*PolyLog[2, -E^(2*(c + d*x))] - 2*a*d*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 4*a*d*e*f*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 4*a*d*f^2*x*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 4*a*d*e*f*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 4*a*d*f^2*x*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - (4*I)*b*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (4*I)*b*f^2*PolyLog[3, I*E^(c + d*x)] + a*f^2*PolyLog[3, -E^(2*(c + d*x))] - 4*a*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 4*a*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/((a^2 + b^2)*d^3)","A",1
350,1,438,421,2.5528613,"\int \frac{(e+f x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{-2 a f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 a f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-2 a c f \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-2 a c f \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 a d f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-2 a d f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 a d e \log (a+b \sinh (c+d x))+2 a c f \log (a+b \sinh (c+d x))+2 a c^2 f+2 a d e \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)-2 a c d e+a f \text{Li}_2(-\cosh (2 (c+d x))-\sinh (2 (c+d x)))+2 a c d f x+2 a d f x \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)-2 a d^2 e x+4 b d e \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))-2 i b f \text{Li}_2(-i (\cosh (c+d x)+\sinh (c+d x)))+2 i b f \text{Li}_2(i (\cosh (c+d x)+\sinh (c+d x)))+4 b d f x \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))}{2 d^2 \left(a^2+b^2\right)}","\frac{i a^2 f \text{Li}_2\left(-i e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{i a^2 f \text{Li}_2\left(i e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{a f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)}-\frac{a f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)}+\frac{a f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{a (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)}-\frac{a (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)}+\frac{a (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{d \left(a^2+b^2\right)}-\frac{2 a^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b d \left(a^2+b^2\right)}-\frac{i f \text{Li}_2\left(-i e^{c+d x}\right)}{b d^2}+\frac{i f \text{Li}_2\left(i e^{c+d x}\right)}{b d^2}+\frac{2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b d}",1,"(-2*a*c*d*e + 2*a*c^2*f - 2*a*d^2*e*x + 2*a*c*d*f*x + 4*b*d*e*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] + 4*b*d*f*x*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] - 2*a*c*f*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*a*d*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*a*c*f*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*a*d*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*a*d*e*Log[a + b*Sinh[c + d*x]] + 2*a*c*f*Log[a + b*Sinh[c + d*x]] + 2*a*d*e*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] + 2*a*d*f*x*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] - 2*a*f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*a*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - (2*I)*b*f*PolyLog[2, (-I)*(Cosh[c + d*x] + Sinh[c + d*x])] + (2*I)*b*f*PolyLog[2, I*(Cosh[c + d*x] + Sinh[c + d*x])] + a*f*PolyLog[2, -Cosh[2*(c + d*x)] - Sinh[2*(c + d*x)]])/(2*(a^2 + b^2)*d^2)","A",0
351,1,51,69,0.0708199,"\int \frac{\tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Tanh[c + d*x]/(a + b*Sinh[c + d*x]),x]","\frac{a (\log (\cosh (c+d x))-\log (a+b \sinh (c+d x)))+2 b \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{d \left(a^2+b^2\right)}","-\frac{a \log (a+b \sinh (c+d x))}{d \left(a^2+b^2\right)}+\frac{b \tan ^{-1}(\sinh (c+d x))}{d \left(a^2+b^2\right)}+\frac{a \log (\cosh (c+d x))}{d \left(a^2+b^2\right)}",1,"(2*b*ArcTan[Tanh[(c + d*x)/2]] + a*(Log[Cosh[c + d*x]] - Log[a + b*Sinh[c + d*x]]))/((a^2 + b^2)*d)","A",1
352,0,0,29,16.4915508,"\int \frac{\tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Tanh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Tanh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
353,1,1143,917,12.9737036,"\int \frac{(e+f x)^3 \text{sech}(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sech[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{f \left(-4 b f^2 x^3 d^3-12 b e f x^2 d^3+12 b e^2 e^{2 c} x d^3-12 b e^2 \left(1+e^{2 c}\right) x d^3+12 a e^2 \left(1+e^{2 c}\right) \tan ^{-1}\left(e^{c+d x}\right) d^2+6 b e^2 \left(1+e^{2 c}\right) \left(2 d x-\log \left(1+e^{2 (c+d x)}\right)\right) d^2+12 i a e \left(1+e^{2 c}\right) f \left(d x \left(\log \left(1-i e^{c+d x}\right)-\log \left(1+i e^{c+d x}\right)\right)-\text{Li}_2\left(-i e^{c+d x}\right)+\text{Li}_2\left(i e^{c+d x}\right)\right) d+6 b e \left(1+e^{2 c}\right) f \left(2 d x \left(d x-\log \left(1+e^{2 (c+d x)}\right)\right)-\text{Li}_2\left(-e^{2 (c+d x)}\right)\right) d+6 i a \left(1+e^{2 c}\right) f^2 \left(d^2 \log \left(1-i e^{c+d x}\right) x^2-d^2 \log \left(1+i e^{c+d x}\right) x^2-2 d \text{Li}_2\left(-i e^{c+d x}\right) x+2 d \text{Li}_2\left(i e^{c+d x}\right) x+2 \text{Li}_3\left(-i e^{c+d x}\right)-2 \text{Li}_3\left(i e^{c+d x}\right)\right)+b \left(1+e^{2 c}\right) f^2 \left(2 d^2 \left(2 d x-3 \log \left(1+e^{2 (c+d x)}\right)\right) x^2-6 d \text{Li}_2\left(-e^{2 (c+d x)}\right) x+3 \text{Li}_3\left(-e^{2 (c+d x)}\right)\right)\right)}{2 \left(a^2+b^2\right) d^4 \left(1+e^{2 c}\right)}+\frac{a b \left(2 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3-f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-3 e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2+3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2+6 e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+6 f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-6 e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-6 f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-6 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{\left(a^2+b^2\right)^{3/2} d^4}+\frac{\text{sech}(c) \text{sech}(c+d x) \left(-a \cosh (c) e^3+b \sinh (d x) e^3-3 a f x \cosh (c) e^2+3 b f x \sinh (d x) e^2-3 a f^2 x^2 \cosh (c) e+3 b f^2 x^2 \sinh (d x) e-a f^3 x^3 \cosh (c)+b f^3 x^3 \sinh (d x)\right)}{\left(a^2+b^2\right) d}","\frac{6 i a \text{Li}_3\left(-i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}-\frac{6 i a \text{Li}_3\left(i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}+\frac{3 \text{Li}_3\left(-e^{2 (c+d x)}\right) f^3}{2 b d^4}-\frac{3 a^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) f^3}{2 b \left(a^2+b^2\right) d^4}-\frac{6 a b \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f^3}{\left(a^2+b^2\right)^{3/2} d^4}+\frac{6 a b \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f^3}{\left(a^2+b^2\right)^{3/2} d^4}-\frac{6 i a (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}+\frac{6 i a (e+f x) \text{Li}_2\left(i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}-\frac{3 (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) f^2}{b d^3}+\frac{3 a^2 (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) f^2}{b \left(a^2+b^2\right) d^3}+\frac{6 a b (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f^2}{\left(a^2+b^2\right)^{3/2} d^3}-\frac{6 a b (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f^2}{\left(a^2+b^2\right)^{3/2} d^3}+\frac{6 a (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) f}{\left(a^2+b^2\right) d^2}-\frac{3 (e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) f}{b d^2}+\frac{3 a^2 (e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) f}{b \left(a^2+b^2\right) d^2}-\frac{3 a b (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f}{\left(a^2+b^2\right)^{3/2} d^2}+\frac{3 a b (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f}{\left(a^2+b^2\right)^{3/2} d^2}+\frac{(e+f x)^3}{b d}-\frac{a^2 (e+f x)^3}{b \left(a^2+b^2\right) d}-\frac{a b (e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right)}{\left(a^2+b^2\right)^{3/2} d}+\frac{a b (e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right)}{\left(a^2+b^2\right)^{3/2} d}-\frac{a (e+f x)^3 \text{sech}(c+d x)}{\left(a^2+b^2\right) d}+\frac{(e+f x)^3 \tanh (c+d x)}{b d}-\frac{a^2 (e+f x)^3 \tanh (c+d x)}{b \left(a^2+b^2\right) d}",1,"(f*(12*b*d^3*e^2*E^(2*c)*x - 12*b*d^3*e^2*(1 + E^(2*c))*x - 12*b*d^3*e*f*x^2 - 4*b*d^3*f^2*x^3 + 12*a*d^2*e^2*(1 + E^(2*c))*ArcTan[E^(c + d*x)] + 6*b*d^2*e^2*(1 + E^(2*c))*(2*d*x - Log[1 + E^(2*(c + d*x))]) + (12*I)*a*d*e*(1 + E^(2*c))*f*(d*x*(Log[1 - I*E^(c + d*x)] - Log[1 + I*E^(c + d*x)]) - PolyLog[2, (-I)*E^(c + d*x)] + PolyLog[2, I*E^(c + d*x)]) + 6*b*d*e*(1 + E^(2*c))*f*(2*d*x*(d*x - Log[1 + E^(2*(c + d*x))]) - PolyLog[2, -E^(2*(c + d*x))]) + (6*I)*a*(1 + E^(2*c))*f^2*(d^2*x^2*Log[1 - I*E^(c + d*x)] - d^2*x^2*Log[1 + I*E^(c + d*x)] - 2*d*x*PolyLog[2, (-I)*E^(c + d*x)] + 2*d*x*PolyLog[2, I*E^(c + d*x)] + 2*PolyLog[3, (-I)*E^(c + d*x)] - 2*PolyLog[3, I*E^(c + d*x)]) + b*(1 + E^(2*c))*f^2*(2*d^2*x^2*(2*d*x - 3*Log[1 + E^(2*(c + d*x))]) - 6*d*x*PolyLog[2, -E^(2*(c + d*x))] + 3*PolyLog[3, -E^(2*(c + d*x))])))/(2*(a^2 + b^2)*d^4*(1 + E^(2*c))) + (a*b*(2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/((a^2 + b^2)^(3/2)*d^4) + (Sech[c]*Sech[c + d*x]*(-(a*e^3*Cosh[c]) - 3*a*e^2*f*x*Cosh[c] - 3*a*e*f^2*x^2*Cosh[c] - a*f^3*x^3*Cosh[c] + b*e^3*Sinh[d*x] + 3*b*e^2*f*x*Sinh[d*x] + 3*b*e*f^2*x^2*Sinh[d*x] + b*f^3*x^3*Sinh[d*x]))/((a^2 + b^2)*d)","A",1
354,1,906,648,8.1026757,"\int \frac{(e+f x)^2 \text{sech}(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{2 a \left(-\frac{2 \tan ^{-1}\left(\frac{\sinh (c)+\cosh (c) \tanh \left(\frac{d x}{2}\right)}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right) \tanh ^{-1}(\coth (c))}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}-\frac{i \text{csch}(c) \left(i \left(d x+\tanh ^{-1}(\coth (c))\right) \left(\log \left(1-e^{-d x-\tanh ^{-1}(\coth (c))}\right)-\log \left(1+e^{-d x-\tanh ^{-1}(\coth (c))}\right)\right)+i \left(\text{Li}_2\left(-e^{-d x-\tanh ^{-1}(\coth (c))}\right)-\text{Li}_2\left(e^{-d x-\tanh ^{-1}(\coth (c))}\right)\right)\right)}{\sqrt{1-\coth ^2(c)}}\right) f^2}{\left(a^2+b^2\right) d^3}-\frac{b \text{csch}(c) \left(d^2 e^{-\tanh ^{-1}(\coth (c))} x^2-\frac{i \coth (c) \left(-d x \left(2 i \tanh ^{-1}(\coth (c))-\pi \right)-\pi  \log \left(1+e^{2 d x}\right)-2 \left(i d x+i \tanh ^{-1}(\coth (c))\right) \log \left(1-e^{2 i \left(i d x+i \tanh ^{-1}(\coth (c))\right)}\right)+\pi  \log (\cosh (d x))+2 i \tanh ^{-1}(\coth (c)) \log \left(i \sinh \left(d x+\tanh ^{-1}(\coth (c))\right)\right)+i \text{Li}_2\left(e^{2 i \left(i d x+i \tanh ^{-1}(\coth (c))\right)}\right)\right)}{\sqrt{1-\coth ^2(c)}}\right) \text{sech}(c) f^2}{\left(a^2+b^2\right) d^3 \sqrt{\text{csch}^2(c) \left(\sinh ^2(c)-\cosh ^2(c)\right)}}+\frac{4 a e \tan ^{-1}\left(\frac{\sinh (c)+\cosh (c) \tanh \left(\frac{d x}{2}\right)}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right) f}{\left(a^2+b^2\right) d^2 \sqrt{\cosh ^2(c)-\sinh ^2(c)}}-\frac{2 b e \text{sech}(c) (\cosh (c) \log (\cosh (c) \cosh (d x)+\sinh (c) \sinh (d x))-d x \sinh (c)) f}{\left(a^2+b^2\right) d^2 \left(\cosh ^2(c)-\sinh ^2(c)\right)}+\frac{a b \left(2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^2-f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2-2 e f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2+f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2+2 e f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2-2 f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{\left(a^2+b^2\right)^{3/2} d^3}+\frac{\text{sech}(c) \text{sech}(c+d x) \left(-a \cosh (c) e^2+b \sinh (d x) e^2-2 a f x \cosh (c) e+2 b f x \sinh (d x) e-a f^2 x^2 \cosh (c)+b f^2 x^2 \sinh (d x)\right)}{\left(a^2+b^2\right) d}","\frac{a^2 f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right)}{b d^3 \left(a^2+b^2\right)}-\frac{2 i a f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 i a f^2 \text{Li}_2\left(i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 a b f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}-\frac{2 a b f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}-\frac{2 a b f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}+\frac{2 a b f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}+\frac{2 a^2 f (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{b d^2 \left(a^2+b^2\right)}+\frac{4 a f (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{a b (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)^{3/2}}+\frac{a b (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)^{3/2}}-\frac{a^2 (e+f x)^2 \tanh (c+d x)}{b d \left(a^2+b^2\right)}-\frac{a (e+f x)^2 \text{sech}(c+d x)}{d \left(a^2+b^2\right)}-\frac{a^2 (e+f x)^2}{b d \left(a^2+b^2\right)}-\frac{f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right)}{b d^3}-\frac{2 f (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{b d^2}+\frac{(e+f x)^2 \tanh (c+d x)}{b d}+\frac{(e+f x)^2}{b d}",1,"(a*b*(2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/((a^2 + b^2)^(3/2)*d^3) - (2*b*e*f*Sech[c]*(Cosh[c]*Log[Cosh[c]*Cosh[d*x] + Sinh[c]*Sinh[d*x]] - d*x*Sinh[c]))/((a^2 + b^2)*d^2*(Cosh[c]^2 - Sinh[c]^2)) + (4*a*e*f*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]])/((a^2 + b^2)*d^2*Sqrt[Cosh[c]^2 - Sinh[c]^2]) - (b*f^2*Csch[c]*((d^2*x^2)/E^ArcTanh[Coth[c]] - (I*Coth[c]*(-(d*x*(-Pi + (2*I)*ArcTanh[Coth[c]])) - Pi*Log[1 + E^(2*d*x)] - 2*(I*d*x + I*ArcTanh[Coth[c]])*Log[1 - E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))] + Pi*Log[Cosh[d*x]] + (2*I)*ArcTanh[Coth[c]]*Log[I*Sinh[d*x + ArcTanh[Coth[c]]]] + I*PolyLog[2, E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))]))/Sqrt[1 - Coth[c]^2])*Sech[c])/((a^2 + b^2)*d^3*Sqrt[Csch[c]^2*(-Cosh[c]^2 + Sinh[c]^2)]) + (2*a*f^2*(((-I)*Csch[c]*(I*(d*x + ArcTanh[Coth[c]])*(Log[1 - E^(-(d*x) - ArcTanh[Coth[c]])] - Log[1 + E^(-(d*x) - ArcTanh[Coth[c]])]) + I*(PolyLog[2, -E^(-(d*x) - ArcTanh[Coth[c]])] - PolyLog[2, E^(-(d*x) - ArcTanh[Coth[c]])])))/Sqrt[1 - Coth[c]^2] - (2*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]]*ArcTanh[Coth[c]])/Sqrt[Cosh[c]^2 - Sinh[c]^2]))/((a^2 + b^2)*d^3) + (Sech[c]*Sech[c + d*x]*(-(a*e^2*Cosh[c]) - 2*a*e*f*x*Cosh[c] - a*f^2*x^2*Cosh[c] + b*e^2*Sinh[d*x] + 2*b*e*f*x*Sinh[d*x] + b*f^2*x^2*Sinh[d*x]))/((a^2 + b^2)*d)","A",0
355,1,285,335,2.9047451,"\int \frac{(e+f x) \text{sech}(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\frac{a b \left(2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)}{\left(a^2+b^2\right)^{3/2}}+\frac{d (e+f x) \text{sech}(c+d x) (b \sinh (c+d x)-a)}{a^2+b^2}+\frac{2 a f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^2+b^2}-\frac{b f \log (\cosh (c+d x))}{a^2+b^2}}{d^2}","-\frac{a b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}+\frac{a b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}+\frac{a f \tan ^{-1}(\sinh (c+d x))}{d^2 \left(a^2+b^2\right)}+\frac{a^2 f \log (\cosh (c+d x))}{b d^2 \left(a^2+b^2\right)}-\frac{a b (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)^{3/2}}+\frac{a b (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)^{3/2}}-\frac{a^2 (e+f x) \tanh (c+d x)}{b d \left(a^2+b^2\right)}-\frac{a (e+f x) \text{sech}(c+d x)}{d \left(a^2+b^2\right)}-\frac{f \log (\cosh (c+d x))}{b d^2}+\frac{(e+f x) \tanh (c+d x)}{b d}",1,"((2*a*f*ArcTan[Tanh[(c + d*x)/2]])/(a^2 + b^2) - (b*f*Log[Cosh[c + d*x]])/(a^2 + b^2) + (a*b*(2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^2 + b^2)^(3/2) + (d*(e + f*x)*Sech[c + d*x]*(-a + b*Sinh[c + d*x]))/(a^2 + b^2))/d^2","A",1
356,1,104,78,0.1702883,"\int \frac{\text{sech}(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Sech[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{b \sqrt{-a^2-b^2} \tanh (c+d x)-a \sqrt{-a^2-b^2} \text{sech}(c+d x)-2 a b \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{d \left(-a^2-b^2\right)^{3/2}}","\frac{2 a b \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{3/2}}-\frac{\text{sech}(c+d x) (a-b \sinh (c+d x))}{d \left(a^2+b^2\right)}",1,"-((-2*a*b*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] - a*Sqrt[-a^2 - b^2]*Sech[c + d*x] + b*Sqrt[-a^2 - b^2]*Tanh[c + d*x])/((-a^2 - b^2)^(3/2)*d))","A",1
357,0,0,35,58.8573255,"\int \frac{\text{sech}(c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Sech[c + d*x]*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{sech}(c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\tanh (c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[(Sech[c + d*x]*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
358,1,3124,1176,27.0172728,"\int \frac{(e+f x)^2 \text{sech}^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sech[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{(e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d}-\frac{2 b (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d}+\frac{f^2 \tan ^{-1}(\sinh (c+d x)) a^2}{b \left(a^2+b^2\right) d^3}+\frac{i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^2}+\frac{2 i b f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d^2}-\frac{i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^2}-\frac{2 i b f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d^2}-\frac{i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^3}-\frac{2 i b f^2 \text{Li}_3\left(-i e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d^3}+\frac{i f^2 \text{Li}_3\left(i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^3}+\frac{2 i b f^2 \text{Li}_3\left(i e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d^3}-\frac{f (e+f x) \text{sech}(c+d x) a^2}{b \left(a^2+b^2\right) d^2}-\frac{(e+f x)^2 \text{sech}(c+d x) \tanh (c+d x) a^2}{2 b \left(a^2+b^2\right) d}-\frac{(e+f x)^2 \text{sech}^2(c+d x) a}{2 \left(a^2+b^2\right) d}-\frac{b^2 (e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a}{\left(a^2+b^2\right)^2 d}-\frac{b^2 (e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a}{\left(a^2+b^2\right)^2 d}+\frac{b^2 (e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) a}{\left(a^2+b^2\right)^2 d}-\frac{f^2 \log (\cosh (c+d x)) a}{\left(a^2+b^2\right) d^3}-\frac{2 b^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a}{\left(a^2+b^2\right)^2 d^2}-\frac{2 b^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a}{\left(a^2+b^2\right)^2 d^2}+\frac{b^2 f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) a}{\left(a^2+b^2\right)^2 d^2}+\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a}{\left(a^2+b^2\right)^2 d^3}+\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a}{\left(a^2+b^2\right)^2 d^3}-\frac{b^2 f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) a}{2 \left(a^2+b^2\right)^2 d^3}+\frac{f (e+f x) \tanh (c+d x) a}{\left(a^2+b^2\right) d^2}+\frac{(e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{b d}-\frac{f^2 \tan ^{-1}(\sinh (c+d x))}{b d^3}-\frac{i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{b d^2}+\frac{i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{b d^2}+\frac{i f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{b d^3}-\frac{i f^2 \text{Li}_3\left(i e^{c+d x}\right)}{b d^3}+\frac{f (e+f x) \text{sech}(c+d x)}{b d^2}+\frac{(e+f x)^2 \text{sech}(c+d x) \tanh (c+d x)}{2 b d}",1,"(-12*a*b^2*d^3*e^2*E^(2*c)*x + 12*a^3*d*E^(2*c)*f^2*x + 12*a*b^2*d*E^(2*c)*f^2*x - 12*a*b^2*d^3*e*E^(2*c)*f*x^2 - 4*a*b^2*d^3*E^(2*c)*f^2*x^3 - 6*a^2*b*d^2*e^2*ArcTan[E^(c + d*x)] + 6*b^3*d^2*e^2*ArcTan[E^(c + d*x)] - 6*a^2*b*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] + 6*b^3*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] - 12*a^2*b*f^2*ArcTan[E^(c + d*x)] - 12*b^3*f^2*ArcTan[E^(c + d*x)] - 12*a^2*b*E^(2*c)*f^2*ArcTan[E^(c + d*x)] - 12*b^3*E^(2*c)*f^2*ArcTan[E^(c + d*x)] - (6*I)*a^2*b*d^2*e*f*x*Log[1 - I*E^(c + d*x)] + (6*I)*b^3*d^2*e*f*x*Log[1 - I*E^(c + d*x)] - (6*I)*a^2*b*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] + (6*I)*b^3*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] - (3*I)*a^2*b*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] + (3*I)*b^3*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] - (3*I)*a^2*b*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] + (3*I)*b^3*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] + (6*I)*a^2*b*d^2*e*f*x*Log[1 + I*E^(c + d*x)] - (6*I)*b^3*d^2*e*f*x*Log[1 + I*E^(c + d*x)] + (6*I)*a^2*b*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] - (6*I)*b^3*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] + (3*I)*a^2*b*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] - (3*I)*b^3*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] + (3*I)*a^2*b*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] - (3*I)*b^3*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] + 6*a*b^2*d^2*e^2*Log[1 + E^(2*(c + d*x))] + 6*a*b^2*d^2*e^2*E^(2*c)*Log[1 + E^(2*(c + d*x))] - 6*a^3*f^2*Log[1 + E^(2*(c + d*x))] - 6*a*b^2*f^2*Log[1 + E^(2*(c + d*x))] - 6*a^3*E^(2*c)*f^2*Log[1 + E^(2*(c + d*x))] - 6*a*b^2*E^(2*c)*f^2*Log[1 + E^(2*(c + d*x))] + 12*a*b^2*d^2*e*f*x*Log[1 + E^(2*(c + d*x))] + 12*a*b^2*d^2*e*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 6*a*b^2*d^2*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 6*a*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] + (6*I)*b*(a^2 - b^2)*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)] + (6*I)*b*(-a^2 + b^2)*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)] + 6*a*b^2*d*e*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a*b^2*d*e*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a*b^2*d*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 6*a*b^2*d*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] - (6*I)*a^2*b*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (6*I)*b^3*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (6*I)*a^2*b*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (6*I)*b^3*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (6*I)*a^2*b*f^2*PolyLog[3, I*E^(c + d*x)] - (6*I)*b^3*f^2*PolyLog[3, I*E^(c + d*x)] + (6*I)*a^2*b*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - (6*I)*b^3*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - 3*a*b^2*f^2*PolyLog[3, -E^(2*(c + d*x))] - 3*a*b^2*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))])/(6*(a^2 + b^2)^2*d^3*(1 + E^(2*c))) + (a*b^2*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*(a^2 + b^2)^2*d^3*(-1 + E^(2*c))) + (Csch[c]*Sech[c]*Sech[c + d*x]^2*(6*a^3*e*f + 6*a*b^2*e*f - 12*a*b^2*d^2*e^2*x + 6*a^3*f^2*x + 6*a*b^2*f^2*x - 12*a*b^2*d^2*e*f*x^2 - 4*a*b^2*d^2*f^2*x^3 - 6*a^3*e*f*Cosh[2*c] - 6*a*b^2*e*f*Cosh[2*c] - 6*a^3*f^2*x*Cosh[2*c] - 6*a*b^2*f^2*x*Cosh[2*c] - 6*a^3*e*f*Cosh[2*d*x] - 6*a*b^2*e*f*Cosh[2*d*x] - 6*a^3*f^2*x*Cosh[2*d*x] - 6*a*b^2*f^2*x*Cosh[2*d*x] - 3*a^2*b*d*e^2*Cosh[c - d*x] - 3*b^3*d*e^2*Cosh[c - d*x] - 6*a^2*b*d*e*f*x*Cosh[c - d*x] - 6*b^3*d*e*f*x*Cosh[c - d*x] - 3*a^2*b*d*f^2*x^2*Cosh[c - d*x] - 3*b^3*d*f^2*x^2*Cosh[c - d*x] + 3*a^2*b*d*e^2*Cosh[3*c + d*x] + 3*b^3*d*e^2*Cosh[3*c + d*x] + 6*a^2*b*d*e*f*x*Cosh[3*c + d*x] + 6*b^3*d*e*f*x*Cosh[3*c + d*x] + 3*a^2*b*d*f^2*x^2*Cosh[3*c + d*x] + 3*b^3*d*f^2*x^2*Cosh[3*c + d*x] + 6*a^3*e*f*Cosh[2*c + 2*d*x] + 6*a*b^2*e*f*Cosh[2*c + 2*d*x] - 12*a*b^2*d^2*e^2*x*Cosh[2*c + 2*d*x] + 6*a^3*f^2*x*Cosh[2*c + 2*d*x] + 6*a*b^2*f^2*x*Cosh[2*c + 2*d*x] - 12*a*b^2*d^2*e*f*x^2*Cosh[2*c + 2*d*x] - 4*a*b^2*d^2*f^2*x^3*Cosh[2*c + 2*d*x] - 6*a^3*d*e^2*Sinh[2*c] - 6*a*b^2*d*e^2*Sinh[2*c] - 12*a^3*d*e*f*x*Sinh[2*c] - 12*a*b^2*d*e*f*x*Sinh[2*c] - 6*a^3*d*f^2*x^2*Sinh[2*c] - 6*a*b^2*d*f^2*x^2*Sinh[2*c] + 6*a^2*b*e*f*Sinh[c - d*x] + 6*b^3*e*f*Sinh[c - d*x] + 6*a^2*b*f^2*x*Sinh[c - d*x] + 6*b^3*f^2*x*Sinh[c - d*x] + 6*a^2*b*e*f*Sinh[3*c + d*x] + 6*b^3*e*f*Sinh[3*c + d*x] + 6*a^2*b*f^2*x*Sinh[3*c + d*x] + 6*b^3*f^2*x*Sinh[3*c + d*x]))/(24*(a^2 + b^2)^2*d^2)","B",0
359,1,587,711,7.9767896,"\int \frac{(e+f x) \text{sech}^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sech[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{b \left(i f \left(a^2-b^2\right) \text{Li}_2\left(-i e^{c+d x}\right)-i f \left(a^2-b^2\right) \text{Li}_2\left(i e^{c+d x}\right)-2 a^2 d e \tan ^{-1}\left(e^{c+d x}\right)-i a^2 f (c+d x) \log \left(1-i e^{c+d x}\right)+i a^2 f (c+d x) \log \left(1+i e^{c+d x}\right)+2 a^2 c f \tan ^{-1}\left(e^{c+d x}\right)-2 a b d e (c+d x)+2 a b d e \log \left(e^{2 (c+d x)}+1\right)+a b f \text{Li}_2\left(-e^{2 (c+d x)}\right)-a b f (c+d x)^2+2 a b c f (c+d x)-2 a b c f \log \left(e^{2 (c+d x)}+1\right)+2 a b f (c+d x) \log \left(e^{2 (c+d x)}+1\right)+2 b^2 d e \tan ^{-1}\left(e^{c+d x}\right)+i b^2 f (c+d x) \log \left(1-i e^{c+d x}\right)-i b^2 f (c+d x) \log \left(1+i e^{c+d x}\right)-2 b^2 c f \tan ^{-1}\left(e^{c+d x}\right)\right)-2 a b^2 \left(f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-\frac{1}{2} f (c+d x)^2\right)+d \left(a^2+b^2\right) (e+f x) \text{sech}^2(c+d x) (b \sinh (c+d x)-a)+f \left(a^2+b^2\right) \text{sech}(c+d x) (a \sinh (c+d x)+b)}{2 d^2 \left(a^2+b^2\right)^2}","\frac{i a^2 f \text{Li}_2\left(-i e^{c+d x}\right)}{2 b d^2 \left(a^2+b^2\right)}+\frac{i a^2 b f \text{Li}_2\left(-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{i a^2 f \text{Li}_2\left(i e^{c+d x}\right)}{2 b d^2 \left(a^2+b^2\right)}-\frac{i a^2 b f \text{Li}_2\left(i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{a b^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{a b^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{a b^2 f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)^2}+\frac{a f \tanh (c+d x)}{2 d^2 \left(a^2+b^2\right)}-\frac{a^2 f \text{sech}(c+d x)}{2 b d^2 \left(a^2+b^2\right)}-\frac{a b^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)^2}-\frac{a b^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)^2}+\frac{a b^2 (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{d \left(a^2+b^2\right)^2}-\frac{a^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b d \left(a^2+b^2\right)}-\frac{2 a^2 b (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)^2}-\frac{a (e+f x) \text{sech}^2(c+d x)}{2 d \left(a^2+b^2\right)}-\frac{a^2 (e+f x) \tanh (c+d x) \text{sech}(c+d x)}{2 b d \left(a^2+b^2\right)}-\frac{i f \text{Li}_2\left(-i e^{c+d x}\right)}{2 b d^2}+\frac{i f \text{Li}_2\left(i e^{c+d x}\right)}{2 b d^2}+\frac{f \text{sech}(c+d x)}{2 b d^2}+\frac{(e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b d}+\frac{(e+f x) \tanh (c+d x) \text{sech}(c+d x)}{2 b d}",1,"(-2*a*b^2*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + b*(-2*a*b*d*e*(c + d*x) + 2*a*b*c*f*(c + d*x) - a*b*f*(c + d*x)^2 - 2*a^2*d*e*ArcTan[E^(c + d*x)] + 2*b^2*d*e*ArcTan[E^(c + d*x)] + 2*a^2*c*f*ArcTan[E^(c + d*x)] - 2*b^2*c*f*ArcTan[E^(c + d*x)] - I*a^2*f*(c + d*x)*Log[1 - I*E^(c + d*x)] + I*b^2*f*(c + d*x)*Log[1 - I*E^(c + d*x)] + I*a^2*f*(c + d*x)*Log[1 + I*E^(c + d*x)] - I*b^2*f*(c + d*x)*Log[1 + I*E^(c + d*x)] + 2*a*b*d*e*Log[1 + E^(2*(c + d*x))] - 2*a*b*c*f*Log[1 + E^(2*(c + d*x))] + 2*a*b*f*(c + d*x)*Log[1 + E^(2*(c + d*x))] + I*(a^2 - b^2)*f*PolyLog[2, (-I)*E^(c + d*x)] - I*(a^2 - b^2)*f*PolyLog[2, I*E^(c + d*x)] + a*b*f*PolyLog[2, -E^(2*(c + d*x))]) + (a^2 + b^2)*f*Sech[c + d*x]*(b + a*Sinh[c + d*x]) + (a^2 + b^2)*d*(e + f*x)*Sech[c + d*x]^2*(-a + b*Sinh[c + d*x]))/(2*(a^2 + b^2)^2*d^2)","A",1
360,1,105,122,0.2046153,"\int \frac{\text{sech}^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Sech[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{-a \left(a^2+b^2\right) \text{sech}^2(c+d x)+b \left(a^2+b^2\right) \tanh (c+d x) \text{sech}(c+d x)+2 b \left(\left(b^2-a^2\right) \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+a b (\log (\cosh (c+d x))-\log (a+b \sinh (c+d x)))\right)}{2 d \left(a^2+b^2\right)^2}","-\frac{a b^2 \log (a+b \sinh (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{b \left(a^2-b^2\right) \tan ^{-1}(\sinh (c+d x))}{2 d \left(a^2+b^2\right)^2}+\frac{a b^2 \log (\cosh (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{\text{sech}^2(c+d x) (a-b \sinh (c+d x))}{2 d \left(a^2+b^2\right)}",1,"(2*b*((-a^2 + b^2)*ArcTan[Tanh[(c + d*x)/2]] + a*b*(Log[Cosh[c + d*x]] - Log[a + b*Sinh[c + d*x]])) - a*(a^2 + b^2)*Sech[c + d*x]^2 + b*(a^2 + b^2)*Sech[c + d*x]*Tanh[c + d*x])/(2*(a^2 + b^2)^2*d)","A",1
361,0,0,37,140.7851168,"\int \frac{\text{sech}^2(c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Sech[c + d*x]^2*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{sech}^2(c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\tanh (c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[(Sech[c + d*x]^2*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
362,1,2858,606,26.472628,"\int \frac{(e+f x)^3 \cosh (c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{a^2 (e+f x)^4}{4 b^3 f}+\frac{6 a^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^4}+\frac{6 a^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^4}-\frac{6 a^2 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^3}-\frac{6 a^2 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^3}+\frac{3 a^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{3 a^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{a^2 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d}+\frac{a^2 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d}+\frac{6 a f^3 \cosh (c+d x)}{b^2 d^4}-\frac{6 a f^2 (e+f x) \sinh (c+d x)}{b^2 d^3}+\frac{3 a f (e+f x)^2 \cosh (c+d x)}{b^2 d^2}-\frac{a (e+f x)^3 \sinh (c+d x)}{b^2 d}-\frac{3 f^3 \sinh (c+d x) \cosh (c+d x)}{8 b d^4}+\frac{3 f^2 (e+f x) \sinh ^2(c+d x)}{4 b d^3}-\frac{3 f (e+f x)^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^2}+\frac{(e+f x)^3 \sinh ^2(c+d x)}{2 b d}+\frac{3 f^3 x}{8 b d^3}+\frac{(e+f x)^3}{4 b d}",1,"-1/4*(e^3*Log[a + b*Sinh[c + d*x]])/(b*d) - (3*e^2*f*(-1/2*x^2/b + (x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*d) + (x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*d) + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])]/(b*d^2) + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]/(b*d^2)))/4 - (3*e*f^2*(-1/3*x^3/b + (x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*d) + (x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*d) + (2*x*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*d^2) + (2*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^2) - (2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])])/(b*d^3) - (2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^3)))/4 - (f^3*(-1/4*x^4/b + (x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*d) + (x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*d) + (3*x^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*d^2) + (3*x^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^2) - (6*x*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*d^3) - (6*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^3) + (6*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])])/(b*d^4) + (6*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^4)))/4 + (f^3*(((4*a^2 + b^2)*x^4*Cosh[c]*Csch[c/2]*Sech[c/2])/(8*b^3) - (4*a*Cosh[d*x]*(-6*Cosh[c] - 3*d^2*x^2*Cosh[c] + 6*d*x*Sinh[c] + d^3*x^3*Sinh[c]))/(b^2*d^4) + (Cosh[2*d*x]*(6*d*x*Cosh[2*c] + 4*d^3*x^3*Cosh[2*c] - 3*Sinh[2*c] - 6*d^2*x^2*Sinh[2*c]))/(4*b*d^4) - ((4*a^2 + b^2)*(-1 + Coth[c])*(x^4 + (4*a*(d^3*x^3*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + 3*d^2*x^2*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - 6*d*x*PolyLog[3, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] + 6*PolyLog[4, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])])*Sinh[c]*(Cosh[c] + Sinh[c]))/(Sqrt[a^2 + b^2]*d^4) - (2*b^2*(d^3*x^3*Log[1 + ((a - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 3*d^2*x^2*PolyLog[2, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 6*d*x*PolyLog[3, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 6*PolyLog[4, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(-a + Sqrt[a^2 + b^2])*d^4) - (2*b^2*(d^3*x^3*Log[1 + ((a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 3*d^2*x^2*PolyLog[2, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 6*d*x*PolyLog[3, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 6*PolyLog[4, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(a + Sqrt[a^2 + b^2])*d^4) - (2*a*(d^3*x^3*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 3*d^2*x^2*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] - 6*d*x*PolyLog[3, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] + 6*PolyLog[4, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*d^4)))/(4*b^3) - (4*a*(6*d*x*Cosh[c] + d^3*x^3*Cosh[c] - 6*Sinh[c] - 3*d^2*x^2*Sinh[c])*Sinh[d*x])/(b^2*d^4) + ((-3*Cosh[2*c] - 6*d^2*x^2*Cosh[2*c] + 6*d*x*Sinh[2*c] + 4*d^3*x^3*Sinh[2*c])*Sinh[2*d*x])/(4*b*d^4)))/4 + (e*f^2*(2*(4*a^2 + b^2)*x^3*Coth[c] - (24*a*b*Cosh[d*x]*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c]))/d^3 + (3*b^2*Cosh[2*d*x]*((1 + 2*d^2*x^2)*Cosh[2*c] - 2*d*x*Sinh[2*c]))/d^3 - (4*a^2 + b^2)*(-1 + Coth[c])*(2*x^3 + (6*a*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - 2*PolyLog[3, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])])*Sinh[c]*(Cosh[c] + Sinh[c]))/(Sqrt[a^2 + b^2]*d^3) - (3*b^2*(d^2*x^2*Log[1 + ((a - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*PolyLog[3, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(-a + Sqrt[a^2 + b^2])*d^3) - (3*b^2*(d^2*x^2*Log[1 + ((a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 2*PolyLog[3, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(a + Sqrt[a^2 + b^2])*d^3) - (3*a*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*d^3)) - (24*a*b*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c])*Sinh[d*x])/d^3 + (3*b^2*(-2*d*x*Cosh[2*c] + (1 + 2*d^2*x^2)*Sinh[2*c])*Sinh[2*d*x])/d^3))/(8*b^3) + (e^3*((4*a^2 + b^2)*Log[a + b*Sinh[c + d*x]] - 4*a*b*Sinh[c + d*x] + 2*b^2*Sinh[c + d*x]^2))/(4*b^3*d) + (3*e^2*f*(8*a*b*Cosh[c + d*x] + 2*b^2*d*x*Cosh[2*(c + d*x)] + 2*(4*a^2 + b^2)*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - 8*a*b*d*x*Sinh[c + d*x] - b^2*Sinh[2*(c + d*x)]))/(8*b^3*d^2)","B",0
363,1,1496,449,11.1829552,"\int \frac{(e+f x)^2 \cosh (c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{\log (a+b \sinh (c+d x)) e^2}{4 b d}+\frac{\left(2 b^2 \sinh ^2(c+d x)-4 a b \sinh (c+d x)+\left(4 a^2+b^2\right) \log (a+b \sinh (c+d x))\right) e^2}{4 b^3 d}-\frac{1}{2} f \left(-\frac{x^2}{2 b}+\frac{\log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) x}{b d}+\frac{\log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) x}{b d}+\frac{\text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)}{b d^2}+\frac{\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^2}\right) e+\frac{f \left(2 d x \cosh (2 (c+d x)) b^2-\sinh (2 (c+d x)) b^2+8 a \cosh (c+d x) b-8 a d x \sinh (c+d x) b+2 \left(4 a^2+b^2\right) \left(-\frac{1}{2} (c+d x)^2+\log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (c+d x)+\log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (c+d x)-c \log (a+b \sinh (c+d x))+\text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)\right) e}{4 b^3 d^2}-\frac{1}{4} f^2 \left(-\frac{x^3}{3 b}+\frac{\log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) x^2}{b d}+\frac{\log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) x^2}{b d}+\frac{2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) x}{b d^2}+\frac{2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) x}{b d^2}-\frac{2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)}{b d^3}-\frac{2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^3}\right)+\frac{f^2 \left(2 \left(4 a^2+b^2\right) \coth (c) x^3-\frac{24 a b \cosh (d x) \left(\left(d^2 x^2+2\right) \sinh (c)-2 d x \cosh (c)\right)}{d^3}+\frac{3 b^2 \cosh (2 d x) \left(\left(2 d^2 x^2+1\right) \cosh (2 c)-2 d x \sinh (2 c)\right)}{d^3}-\left(4 a^2+b^2\right) (\coth (c)-1) \left(2 x^3+\frac{6 a \left(d^2 \log \left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a-\sqrt{a^2+b^2}}+1\right) x^2+2 d \text{Li}_2\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-a}\right) x-2 \text{Li}_3\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-a}\right)\right) \sinh (c) (\cosh (c)+\sinh (c))}{\sqrt{a^2+b^2} d^3}-\frac{3 b^2 \left(d^2 \log \left(\frac{\left(a-\sqrt{a^2+b^2}\right) (\cosh (c+d x)-\sinh (c+d x))}{b}+1\right) x^2-2 d \text{Li}_2\left(\frac{\left(\sqrt{a^2+b^2}-a\right) (\cosh (c+d x)-\sinh (c+d x))}{b}\right) x-2 \text{Li}_3\left(\frac{\left(\sqrt{a^2+b^2}-a\right) (\cosh (c+d x)-\sinh (c+d x))}{b}\right)\right) (\cosh (2 c)+\sinh (2 c)-1)}{\sqrt{a^2+b^2} \left(\sqrt{a^2+b^2}-a\right) d^3}-\frac{3 b^2 \left(d^2 \log \left(\frac{\left(a+\sqrt{a^2+b^2}\right) (\cosh (c+d x)-\sinh (c+d x))}{b}+1\right) x^2-2 d \text{Li}_2\left(\frac{\left(a+\sqrt{a^2+b^2}\right) (\sinh (c+d x)-\cosh (c+d x))}{b}\right) x-2 \text{Li}_3\left(\frac{\left(a+\sqrt{a^2+b^2}\right) (\sinh (c+d x)-\cosh (c+d x))}{b}\right)\right) (\cosh (2 c)+\sinh (2 c)-1)}{\sqrt{a^2+b^2} \left(a+\sqrt{a^2+b^2}\right) d^3}-\frac{3 a \left(d^2 \log \left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}+1\right) x^2+2 d \text{Li}_2\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}\right) x-2 \text{Li}_3\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}\right)\right) (\cosh (2 c)+\sinh (2 c)-1)}{\sqrt{a^2+b^2} d^3}\right)-\frac{24 a b \left(\left(d^2 x^2+2\right) \cosh (c)-2 d x \sinh (c)\right) \sinh (d x)}{d^3}+\frac{3 b^2 \left(\left(2 d^2 x^2+1\right) \sinh (2 c)-2 d x \cosh (2 c)\right) \sinh (2 d x)}{d^3}\right)}{24 b^3}","-\frac{a^2 (e+f x)^3}{3 b^3 f}-\frac{2 a^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^3}-\frac{2 a^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^3}+\frac{2 a^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{2 a^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{a^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d}+\frac{a^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d}-\frac{2 a f^2 \sinh (c+d x)}{b^2 d^3}+\frac{2 a f (e+f x) \cosh (c+d x)}{b^2 d^2}-\frac{a (e+f x)^2 \sinh (c+d x)}{b^2 d}+\frac{f^2 \sinh ^2(c+d x)}{4 b d^3}-\frac{f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b d^2}+\frac{(e+f x)^2 \sinh ^2(c+d x)}{2 b d}+\frac{e f x}{2 b d}+\frac{f^2 x^2}{4 b d}",1,"-1/4*(e^2*Log[a + b*Sinh[c + d*x]])/(b*d) - (e*f*(-1/2*x^2/b + (x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*d) + (x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*d) + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])]/(b*d^2) + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]/(b*d^2)))/2 - (f^2*(-1/3*x^3/b + (x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*d) + (x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*d) + (2*x*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*d^2) + (2*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^2) - (2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])])/(b*d^3) - (2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^3)))/4 + (f^2*(2*(4*a^2 + b^2)*x^3*Coth[c] - (24*a*b*Cosh[d*x]*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c]))/d^3 + (3*b^2*Cosh[2*d*x]*((1 + 2*d^2*x^2)*Cosh[2*c] - 2*d*x*Sinh[2*c]))/d^3 - (4*a^2 + b^2)*(-1 + Coth[c])*(2*x^3 + (6*a*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - 2*PolyLog[3, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])])*Sinh[c]*(Cosh[c] + Sinh[c]))/(Sqrt[a^2 + b^2]*d^3) - (3*b^2*(d^2*x^2*Log[1 + ((a - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*PolyLog[3, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(-a + Sqrt[a^2 + b^2])*d^3) - (3*b^2*(d^2*x^2*Log[1 + ((a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 2*PolyLog[3, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(a + Sqrt[a^2 + b^2])*d^3) - (3*a*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*d^3)) - (24*a*b*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c])*Sinh[d*x])/d^3 + (3*b^2*(-2*d*x*Cosh[2*c] + (1 + 2*d^2*x^2)*Sinh[2*c])*Sinh[2*d*x])/d^3))/(24*b^3) + (e^2*((4*a^2 + b^2)*Log[a + b*Sinh[c + d*x]] - 4*a*b*Sinh[c + d*x] + 2*b^2*Sinh[c + d*x]^2))/(4*b^3*d) + (e*f*(8*a*b*Cosh[c + d*x] + 2*b^2*d*x*Cosh[2*(c + d*x)] + 2*(4*a^2 + b^2)*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - 8*a*b*d*x*Sinh[c + d*x] - b^2*Sinh[2*(c + d*x)]))/(4*b^3*d^2)","B",0
364,1,423,278,0.9691539,"\int \frac{(e+f x) \cosh (c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 d e \left(\left(4 a^2+b^2\right) \log (a+b \sinh (c+d x))-4 a b \sinh (c+d x)+2 b^2 \sinh ^2(c+d x)\right)+b^2 f \left(-2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+d x \left(-2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d x\right)\right)+f \left(2 \left(4 a^2+b^2\right) \left(\text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+(c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+(c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-c \log (a+b \sinh (c+d x))-\frac{1}{2} (c+d x)^2\right)-8 a b d x \sinh (c+d x)+8 a b \cosh (c+d x)-b^2 \sinh (2 (c+d x))+2 b^2 d x \cosh (2 (c+d x))\right)-2 b^2 d e \log (a+b \sinh (c+d x))}{8 b^3 d^2}","-\frac{a^2 (e+f x)^2}{2 b^3 f}+\frac{a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{a^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^3 d}+\frac{a^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^3 d}+\frac{a f \cosh (c+d x)}{b^2 d^2}-\frac{a (e+f x) \sinh (c+d x)}{b^2 d}-\frac{f \sinh (c+d x) \cosh (c+d x)}{4 b d^2}+\frac{(e+f x) \sinh ^2(c+d x)}{2 b d}+\frac{f x}{4 b d}",1,"(-2*b^2*d*e*Log[a + b*Sinh[c + d*x]] + b^2*f*(d*x*(d*x - 2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])]) - 2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + 2*d*e*((4*a^2 + b^2)*Log[a + b*Sinh[c + d*x]] - 4*a*b*Sinh[c + d*x] + 2*b^2*Sinh[c + d*x]^2) + f*(8*a*b*Cosh[c + d*x] + 2*b^2*d*x*Cosh[2*(c + d*x)] + 2*(4*a^2 + b^2)*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - 8*a*b*d*x*Sinh[c + d*x] - b^2*Sinh[2*(c + d*x)]))/(8*b^3*d^2)","A",1
365,1,49,55,0.073801,"\int \frac{\cosh (c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 a^2 \log (a+b \sinh (c+d x))-2 a b \sinh (c+d x)+b^2 \sinh ^2(c+d x)}{2 b^3 d}","\frac{a^2 \log (a+b \sinh (c+d x))}{b^3 d}-\frac{a \sinh (c+d x)}{b^2 d}+\frac{\sinh ^2(c+d x)}{2 b d}",1,"(2*a^2*Log[a + b*Sinh[c + d*x]] - 2*a*b*Sinh[c + d*x] + b^2*Sinh[c + d*x]^2)/(2*b^3*d)","A",1
366,-1,0,37,180.0012199,"\int \frac{\cosh (c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]*Sinh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^2(c+d x) \cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
367,1,1667,897,7.3706926,"\int \frac{(e+f x)^3 \cosh ^2(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^2*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{108 a^3 f^3 x^4 d^4+54 a b^2 f^3 x^4 d^4+432 a^3 e f^2 x^3 d^4+216 a b^2 e f^2 x^3 d^4+648 a^3 e^2 f x^2 d^4+324 a b^2 e^2 f x^2 d^4+432 a^3 e^3 x d^4+216 a b^2 e^3 x d^4+864 a^2 \sqrt{a^2+b^2} e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3-108 b^3 e^3 \cosh (c+d x) d^3-432 a^2 b e^3 \cosh (c+d x) d^3-108 b^3 f^3 x^3 \cosh (c+d x) d^3-432 a^2 b f^3 x^3 \cosh (c+d x) d^3-324 b^3 e f^2 x^2 \cosh (c+d x) d^3-1296 a^2 b e f^2 x^2 \cosh (c+d x) d^3-324 b^3 e^2 f x \cosh (c+d x) d^3-1296 a^2 b e^2 f x \cosh (c+d x) d^3-36 b^3 e^3 \cosh (3 (c+d x)) d^3-36 b^3 f^3 x^3 \cosh (3 (c+d x)) d^3-108 b^3 e f^2 x^2 \cosh (3 (c+d x)) d^3-108 b^3 e^2 f x \cosh (3 (c+d x)) d^3-432 a^2 \sqrt{a^2+b^2} f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-1296 a^2 \sqrt{a^2+b^2} e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-1296 a^2 \sqrt{a^2+b^2} e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+432 a^2 \sqrt{a^2+b^2} f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+1296 a^2 \sqrt{a^2+b^2} e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+1296 a^2 \sqrt{a^2+b^2} e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+108 a b^2 e^3 \sinh (2 (c+d x)) d^3+108 a b^2 f^3 x^3 \sinh (2 (c+d x)) d^3+324 a b^2 e f^2 x^2 \sinh (2 (c+d x)) d^3+324 a b^2 e^2 f x \sinh (2 (c+d x)) d^3-162 a b^2 f^3 x^2 \cosh (2 (c+d x)) d^2-162 a b^2 e^2 f \cosh (2 (c+d x)) d^2-324 a b^2 e f^2 x \cosh (2 (c+d x)) d^2-1296 a^2 \sqrt{a^2+b^2} f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2+1296 a^2 \sqrt{a^2+b^2} f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2+324 b^3 f^3 x^2 \sinh (c+d x) d^2+1296 a^2 b f^3 x^2 \sinh (c+d x) d^2+324 b^3 e^2 f \sinh (c+d x) d^2+1296 a^2 b e^2 f \sinh (c+d x) d^2+648 b^3 e f^2 x \sinh (c+d x) d^2+2592 a^2 b e f^2 x \sinh (c+d x) d^2+36 b^3 f^3 x^2 \sinh (3 (c+d x)) d^2+36 b^3 e^2 f \sinh (3 (c+d x)) d^2+72 b^3 e f^2 x \sinh (3 (c+d x)) d^2-648 b^3 e f^2 \cosh (c+d x) d-2592 a^2 b e f^2 \cosh (c+d x) d-648 b^3 f^3 x \cosh (c+d x) d-2592 a^2 b f^3 x \cosh (c+d x) d-24 b^3 e f^2 \cosh (3 (c+d x)) d-24 b^3 f^3 x \cosh (3 (c+d x)) d+2592 a^2 \sqrt{a^2+b^2} e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+2592 a^2 \sqrt{a^2+b^2} f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-2592 a^2 \sqrt{a^2+b^2} e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-2592 a^2 \sqrt{a^2+b^2} f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+162 a b^2 e f^2 \sinh (2 (c+d x)) d+162 a b^2 f^3 x \sinh (2 (c+d x)) d-81 a b^2 f^3 \cosh (2 (c+d x))-2592 a^2 \sqrt{a^2+b^2} f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2592 a^2 \sqrt{a^2+b^2} f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+648 b^3 f^3 \sinh (c+d x)+2592 a^2 b f^3 \sinh (c+d x)+8 b^3 f^3 \sinh (3 (c+d x))}{432 b^4 d^4}","-\frac{a (e+f x)^4}{8 b^2 f}-\frac{a^3 (e+f x)^4}{4 b^4 f}+\frac{\cosh ^3(c+d x) (e+f x)^3}{3 b d}+\frac{a^2 \cosh (c+d x) (e+f x)^3}{b^3 d}+\frac{a^2 \sqrt{a^2+b^2} \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{b^4 d}-\frac{a^2 \sqrt{a^2+b^2} \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{b^4 d}-\frac{a \cosh (c+d x) \sinh (c+d x) (e+f x)^3}{2 b^2 d}+\frac{3 a f \cosh ^2(c+d x) (e+f x)^2}{4 b^2 d^2}+\frac{3 a^2 \sqrt{a^2+b^2} f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)^2}{b^4 d^2}-\frac{3 a^2 \sqrt{a^2+b^2} f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)^2}{b^4 d^2}-\frac{f \cosh ^2(c+d x) \sinh (c+d x) (e+f x)^2}{3 b d^2}-\frac{2 f \sinh (c+d x) (e+f x)^2}{3 b d^2}-\frac{3 a^2 f \sinh (c+d x) (e+f x)^2}{b^3 d^2}+\frac{2 f^2 \cosh ^3(c+d x) (e+f x)}{9 b d^3}+\frac{4 f^2 \cosh (c+d x) (e+f x)}{3 b d^3}+\frac{6 a^2 f^2 \cosh (c+d x) (e+f x)}{b^3 d^3}-\frac{6 a^2 \sqrt{a^2+b^2} f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)}{b^4 d^3}+\frac{6 a^2 \sqrt{a^2+b^2} f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)}{b^4 d^3}-\frac{3 a f^2 \cosh (c+d x) \sinh (c+d x) (e+f x)}{4 b^2 d^3}-\frac{2 f^3 \sinh ^3(c+d x)}{27 b d^4}-\frac{3 a f^3 x^2}{8 b^2 d^2}+\frac{3 a f^3 \cosh ^2(c+d x)}{8 b^2 d^4}-\frac{3 a e f^2 x}{4 b^2 d^2}+\frac{6 a^2 \sqrt{a^2+b^2} f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^4}-\frac{6 a^2 \sqrt{a^2+b^2} f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^4}-\frac{14 f^3 \sinh (c+d x)}{9 b d^4}-\frac{6 a^2 f^3 \sinh (c+d x)}{b^3 d^4}",1,"-1/432*(432*a^3*d^4*e^3*x + 216*a*b^2*d^4*e^3*x + 648*a^3*d^4*e^2*f*x^2 + 324*a*b^2*d^4*e^2*f*x^2 + 432*a^3*d^4*e*f^2*x^3 + 216*a*b^2*d^4*e*f^2*x^3 + 108*a^3*d^4*f^3*x^4 + 54*a*b^2*d^4*f^3*x^4 + 864*a^2*Sqrt[a^2 + b^2]*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 432*a^2*b*d^3*e^3*Cosh[c + d*x] - 108*b^3*d^3*e^3*Cosh[c + d*x] - 2592*a^2*b*d*e*f^2*Cosh[c + d*x] - 648*b^3*d*e*f^2*Cosh[c + d*x] - 1296*a^2*b*d^3*e^2*f*x*Cosh[c + d*x] - 324*b^3*d^3*e^2*f*x*Cosh[c + d*x] - 2592*a^2*b*d*f^3*x*Cosh[c + d*x] - 648*b^3*d*f^3*x*Cosh[c + d*x] - 1296*a^2*b*d^3*e*f^2*x^2*Cosh[c + d*x] - 324*b^3*d^3*e*f^2*x^2*Cosh[c + d*x] - 432*a^2*b*d^3*f^3*x^3*Cosh[c + d*x] - 108*b^3*d^3*f^3*x^3*Cosh[c + d*x] - 162*a*b^2*d^2*e^2*f*Cosh[2*(c + d*x)] - 81*a*b^2*f^3*Cosh[2*(c + d*x)] - 324*a*b^2*d^2*e*f^2*x*Cosh[2*(c + d*x)] - 162*a*b^2*d^2*f^3*x^2*Cosh[2*(c + d*x)] - 36*b^3*d^3*e^3*Cosh[3*(c + d*x)] - 24*b^3*d*e*f^2*Cosh[3*(c + d*x)] - 108*b^3*d^3*e^2*f*x*Cosh[3*(c + d*x)] - 24*b^3*d*f^3*x*Cosh[3*(c + d*x)] - 108*b^3*d^3*e*f^2*x^2*Cosh[3*(c + d*x)] - 36*b^3*d^3*f^3*x^3*Cosh[3*(c + d*x)] - 1296*a^2*Sqrt[a^2 + b^2]*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 1296*a^2*Sqrt[a^2 + b^2]*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 432*a^2*Sqrt[a^2 + b^2]*d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 1296*a^2*Sqrt[a^2 + b^2]*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 1296*a^2*Sqrt[a^2 + b^2]*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 432*a^2*Sqrt[a^2 + b^2]*d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 1296*a^2*Sqrt[a^2 + b^2]*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 1296*a^2*Sqrt[a^2 + b^2]*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2592*a^2*Sqrt[a^2 + b^2]*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2592*a^2*Sqrt[a^2 + b^2]*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2592*a^2*Sqrt[a^2 + b^2]*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2592*a^2*Sqrt[a^2 + b^2]*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2592*a^2*Sqrt[a^2 + b^2]*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2592*a^2*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 1296*a^2*b*d^2*e^2*f*Sinh[c + d*x] + 324*b^3*d^2*e^2*f*Sinh[c + d*x] + 2592*a^2*b*f^3*Sinh[c + d*x] + 648*b^3*f^3*Sinh[c + d*x] + 2592*a^2*b*d^2*e*f^2*x*Sinh[c + d*x] + 648*b^3*d^2*e*f^2*x*Sinh[c + d*x] + 1296*a^2*b*d^2*f^3*x^2*Sinh[c + d*x] + 324*b^3*d^2*f^3*x^2*Sinh[c + d*x] + 108*a*b^2*d^3*e^3*Sinh[2*(c + d*x)] + 162*a*b^2*d*e*f^2*Sinh[2*(c + d*x)] + 324*a*b^2*d^3*e^2*f*x*Sinh[2*(c + d*x)] + 162*a*b^2*d*f^3*x*Sinh[2*(c + d*x)] + 324*a*b^2*d^3*e*f^2*x^2*Sinh[2*(c + d*x)] + 108*a*b^2*d^3*f^3*x^3*Sinh[2*(c + d*x)] + 36*b^3*d^2*e^2*f*Sinh[3*(c + d*x)] + 8*b^3*f^3*Sinh[3*(c + d*x)] + 72*b^3*d^2*e*f^2*x*Sinh[3*(c + d*x)] + 36*b^3*d^2*f^3*x^2*Sinh[3*(c + d*x)])/(b^4*d^4)","A",1
368,1,966,649,4.5606584,"\int \frac{(e+f x)^2 \cosh ^2(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{-54 d^2 e^2 \cosh (c+d x) b^3-108 f^2 \cosh (c+d x) b^3-54 d^2 f^2 x^2 \cosh (c+d x) b^3-108 d^2 e f x \cosh (c+d x) b^3-18 d^2 e^2 \cosh (3 (c+d x)) b^3-4 f^2 \cosh (3 (c+d x)) b^3-18 d^2 f^2 x^2 \cosh (3 (c+d x)) b^3-36 d^2 e f x \cosh (3 (c+d x)) b^3+108 d e f \sinh (c+d x) b^3+108 d f^2 x \sinh (c+d x) b^3+12 d e f \sinh (3 (c+d x)) b^3+12 d f^2 x \sinh (3 (c+d x)) b^3+36 a d^3 f^2 x^3 b^2+108 a d^3 e f x^2 b^2+108 a d^3 e^2 x b^2-54 a d e f \cosh (2 (c+d x)) b^2-54 a d f^2 x \cosh (2 (c+d x)) b^2+54 a d^2 e^2 \sinh (2 (c+d x)) b^2+27 a f^2 \sinh (2 (c+d x)) b^2+54 a d^2 f^2 x^2 \sinh (2 (c+d x)) b^2+108 a d^2 e f x \sinh (2 (c+d x)) b^2-216 a^2 d^2 e^2 \cosh (c+d x) b-432 a^2 f^2 \cosh (c+d x) b-216 a^2 d^2 f^2 x^2 \cosh (c+d x) b-432 a^2 d^2 e f x \cosh (c+d x) b+432 a^2 d e f \sinh (c+d x) b+432 a^2 d f^2 x \sinh (c+d x) b+72 a^3 d^3 f^2 x^3+216 a^3 d^3 e f x^2+216 a^3 d^3 e^2 x+432 a^2 \sqrt{a^2+b^2} d^2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-216 a^2 \sqrt{a^2+b^2} d^2 f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right)-432 a^2 \sqrt{a^2+b^2} d^2 e f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right)+216 a^2 \sqrt{a^2+b^2} d^2 f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right)+432 a^2 \sqrt{a^2+b^2} d^2 e f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right)-432 a^2 \sqrt{a^2+b^2} d f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+432 a^2 \sqrt{a^2+b^2} d f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+432 a^2 \sqrt{a^2+b^2} f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-432 a^2 \sqrt{a^2+b^2} f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{216 b^4 d^3}","-\frac{a^3 (e+f x)^3}{3 b^4 f}+\frac{2 a^2 f^2 \cosh (c+d x)}{b^3 d^3}-\frac{2 a^2 f (e+f x) \sinh (c+d x)}{b^3 d^2}+\frac{a^2 (e+f x)^2 \cosh (c+d x)}{b^3 d}-\frac{2 a^2 f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^3}+\frac{2 a^2 f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^3}+\frac{2 a^2 f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{2 a^2 f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^2}+\frac{a^2 \sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^4 d}-\frac{a^2 \sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^4 d}-\frac{a f^2 \sinh (c+d x) \cosh (c+d x)}{4 b^2 d^3}+\frac{a f (e+f x) \cosh ^2(c+d x)}{2 b^2 d^2}-\frac{a (e+f x)^2 \sinh (c+d x) \cosh (c+d x)}{2 b^2 d}-\frac{a f^2 x}{4 b^2 d^2}-\frac{a (e+f x)^3}{6 b^2 f}+\frac{2 f^2 \cosh ^3(c+d x)}{27 b d^3}+\frac{4 f^2 \cosh (c+d x)}{9 b d^3}-\frac{4 f (e+f x) \sinh (c+d x)}{9 b d^2}-\frac{2 f (e+f x) \sinh (c+d x) \cosh ^2(c+d x)}{9 b d^2}+\frac{(e+f x)^2 \cosh ^3(c+d x)}{3 b d}",1,"-1/216*(216*a^3*d^3*e^2*x + 108*a*b^2*d^3*e^2*x + 216*a^3*d^3*e*f*x^2 + 108*a*b^2*d^3*e*f*x^2 + 72*a^3*d^3*f^2*x^3 + 36*a*b^2*d^3*f^2*x^3 + 432*a^2*Sqrt[a^2 + b^2]*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 216*a^2*b*d^2*e^2*Cosh[c + d*x] - 54*b^3*d^2*e^2*Cosh[c + d*x] - 432*a^2*b*f^2*Cosh[c + d*x] - 108*b^3*f^2*Cosh[c + d*x] - 432*a^2*b*d^2*e*f*x*Cosh[c + d*x] - 108*b^3*d^2*e*f*x*Cosh[c + d*x] - 216*a^2*b*d^2*f^2*x^2*Cosh[c + d*x] - 54*b^3*d^2*f^2*x^2*Cosh[c + d*x] - 54*a*b^2*d*e*f*Cosh[2*(c + d*x)] - 54*a*b^2*d*f^2*x*Cosh[2*(c + d*x)] - 18*b^3*d^2*e^2*Cosh[3*(c + d*x)] - 4*b^3*f^2*Cosh[3*(c + d*x)] - 36*b^3*d^2*e*f*x*Cosh[3*(c + d*x)] - 18*b^3*d^2*f^2*x^2*Cosh[3*(c + d*x)] - 432*a^2*Sqrt[a^2 + b^2]*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 216*a^2*Sqrt[a^2 + b^2]*d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 432*a^2*Sqrt[a^2 + b^2]*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 216*a^2*Sqrt[a^2 + b^2]*d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 432*a^2*Sqrt[a^2 + b^2]*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 432*a^2*Sqrt[a^2 + b^2]*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 432*a^2*Sqrt[a^2 + b^2]*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 432*a^2*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 432*a^2*b*d*e*f*Sinh[c + d*x] + 108*b^3*d*e*f*Sinh[c + d*x] + 432*a^2*b*d*f^2*x*Sinh[c + d*x] + 108*b^3*d*f^2*x*Sinh[c + d*x] + 54*a*b^2*d^2*e^2*Sinh[2*(c + d*x)] + 27*a*b^2*f^2*Sinh[2*(c + d*x)] + 108*a*b^2*d^2*e*f*x*Sinh[2*(c + d*x)] + 54*a*b^2*d^2*f^2*x^2*Sinh[2*(c + d*x)] + 12*b^3*d*e*f*Sinh[3*(c + d*x)] + 12*b^3*d*f^2*x*Sinh[3*(c + d*x)])/(b^4*d^3)","A",1
369,1,676,403,2.7786267,"\int \frac{(e+f x) \cosh ^2(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{-36 a^3 c^2 f+72 a^3 c d e+72 a^3 d^2 e x+36 a^3 d^2 f x^2+144 a^2 d e \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{a+b \sinh (c+d x)+b \cosh (c+d x)}{\sqrt{a^2+b^2}}\right)-72 a^2 f \sqrt{a^2+b^2} \text{Li}_2\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-a}\right)+72 a^2 f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}\right)-72 a^2 c f \sqrt{a^2+b^2} \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{a-\sqrt{a^2+b^2}}+1\right)-72 a^2 d f x \sqrt{a^2+b^2} \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{a-\sqrt{a^2+b^2}}+1\right)+72 a^2 c f \sqrt{a^2+b^2} \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{\sqrt{a^2+b^2}+a}+1\right)+72 a^2 d f x \sqrt{a^2+b^2} \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{\sqrt{a^2+b^2}+a}+1\right)-144 a^2 c f \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{a+b \sinh (c+d x)+b \cosh (c+d x)}{\sqrt{a^2+b^2}}\right)-72 a^2 b d e \cosh (c+d x)+72 a^2 b f \sinh (c+d x)-72 a^2 b d f x \cosh (c+d x)-18 a b^2 c^2 f+18 a b^2 d e \sinh (2 (c+d x))+36 a b^2 c d e+18 a b^2 d f x \sinh (2 (c+d x))-9 a b^2 f \cosh (2 (c+d x))+36 a b^2 d^2 e x+18 a b^2 d^2 f x^2-18 b^3 d e \cosh (c+d x)-6 b^3 d e \cosh (3 (c+d x))+18 b^3 f \sinh (c+d x)+2 b^3 f \sinh (3 (c+d x))-18 b^3 d f x \cosh (c+d x)-6 b^3 d f x \cosh (3 (c+d x))}{72 b^4 d^2}","-\frac{a^3 e x}{b^4}-\frac{a^3 f x^2}{2 b^4}-\frac{a^2 f \sinh (c+d x)}{b^3 d^2}+\frac{a^2 (e+f x) \cosh (c+d x)}{b^3 d}+\frac{a^2 f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{a^2 f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^2}+\frac{a^2 \sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^4 d}-\frac{a^2 \sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^4 d}+\frac{a f \cosh ^2(c+d x)}{4 b^2 d^2}-\frac{a (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^2 d}-\frac{a e x}{2 b^2}-\frac{a f x^2}{4 b^2}-\frac{f \sinh ^3(c+d x)}{9 b d^2}-\frac{f \sinh (c+d x)}{3 b d^2}+\frac{(e+f x) \cosh ^3(c+d x)}{3 b d}",1,"-1/72*(72*a^3*c*d*e + 36*a*b^2*c*d*e - 36*a^3*c^2*f - 18*a*b^2*c^2*f + 72*a^3*d^2*e*x + 36*a*b^2*d^2*e*x + 36*a^3*d^2*f*x^2 + 18*a*b^2*d^2*f*x^2 + 144*a^2*Sqrt[a^2 + b^2]*d*e*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] - 144*a^2*Sqrt[a^2 + b^2]*c*f*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] - 72*a^2*b*d*e*Cosh[c + d*x] - 18*b^3*d*e*Cosh[c + d*x] - 72*a^2*b*d*f*x*Cosh[c + d*x] - 18*b^3*d*f*x*Cosh[c + d*x] - 9*a*b^2*f*Cosh[2*(c + d*x)] - 6*b^3*d*e*Cosh[3*(c + d*x)] - 6*b^3*d*f*x*Cosh[3*(c + d*x)] - 72*a^2*Sqrt[a^2 + b^2]*c*f*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 72*a^2*Sqrt[a^2 + b^2]*d*f*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + 72*a^2*Sqrt[a^2 + b^2]*c*f*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 72*a^2*Sqrt[a^2 + b^2]*d*f*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] - 72*a^2*Sqrt[a^2 + b^2]*f*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] + 72*a^2*Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] + 72*a^2*b*f*Sinh[c + d*x] + 18*b^3*f*Sinh[c + d*x] + 18*a*b^2*d*e*Sinh[2*(c + d*x)] + 18*a*b^2*d*f*x*Sinh[2*(c + d*x)] + 2*b^3*f*Sinh[3*(c + d*x)])/(b^4*d^2)","A",1
370,1,123,141,0.3512332,"\int \frac{\cosh ^2(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]^2*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{3 b \left(4 a^2+b^2\right) \cosh (c+d x)-3 a \left(2 \left(2 a^2+b^2\right) (c+d x)+8 a \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)+b^2 \sinh (2 (c+d x))\right)+b^3 \cosh (3 (c+d x))}{12 b^4 d}","-\frac{2 a^2 \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b^4 d}-\frac{a x \left(2 a^2+b^2\right)}{2 b^4}+\frac{\left(3 a^2+b^2\right) \cosh (c+d x)}{3 b^3 d}-\frac{a \sinh (c+d x) \cosh (c+d x)}{2 b^2 d}+\frac{\sinh ^2(c+d x) \cosh (c+d x)}{3 b d}",1,"(3*b*(4*a^2 + b^2)*Cosh[c + d*x] + b^3*Cosh[3*(c + d*x)] - 3*a*(2*(2*a^2 + b^2)*(c + d*x) + 8*a*Sqrt[-a^2 - b^2]*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] + b^2*Sinh[2*(c + d*x)]))/(12*b^4*d)","A",1
371,-1,0,39,180.0013109,"\int \frac{\cosh ^2(c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]^2*Sinh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^2(c+d x) \cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
372,1,8706,1123,40.40904,"\int \frac{(e+f x)^3 \cosh ^3(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^3*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{a^2 \left(a^2+b^2\right) (e+f x)^4}{4 b^5 f}+\frac{\cosh ^4(c+d x) (e+f x)^3}{4 b d}+\frac{a^2 \sinh ^2(c+d x) (e+f x)^3}{2 b^3 d}+\frac{a^2 \left(a^2+b^2\right) \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{b^5 d}+\frac{a^2 \left(a^2+b^2\right) \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{b^5 d}-\frac{a \cosh ^2(c+d x) \sinh (c+d x) (e+f x)^3}{3 b^2 d}-\frac{2 a \sinh (c+d x) (e+f x)^3}{3 b^2 d}-\frac{a^3 \sinh (c+d x) (e+f x)^3}{b^4 d}-\frac{3 (e+f x)^3}{32 b d}+\frac{a^2 (e+f x)^3}{4 b^3 d}+\frac{a f \cosh ^3(c+d x) (e+f x)^2}{3 b^2 d^2}+\frac{2 a f \cosh (c+d x) (e+f x)^2}{b^2 d^2}+\frac{3 a^3 f \cosh (c+d x) (e+f x)^2}{b^4 d^2}+\frac{3 a^2 \left(a^2+b^2\right) f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)^2}{b^5 d^2}+\frac{3 a^2 \left(a^2+b^2\right) f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)^2}{b^5 d^2}-\frac{3 f \cosh ^3(c+d x) \sinh (c+d x) (e+f x)^2}{16 b d^2}-\frac{9 f \cosh (c+d x) \sinh (c+d x) (e+f x)^2}{32 b d^2}-\frac{3 a^2 f \cosh (c+d x) \sinh (c+d x) (e+f x)^2}{4 b^3 d^2}+\frac{3 f^2 \cosh ^4(c+d x) (e+f x)}{32 b d^3}+\frac{9 f^2 \cosh ^2(c+d x) (e+f x)}{32 b d^3}+\frac{3 a^2 f^2 \sinh ^2(c+d x) (e+f x)}{4 b^3 d^3}-\frac{6 a^2 \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)}{b^5 d^3}-\frac{6 a^2 \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)}{b^5 d^3}-\frac{40 a f^2 \sinh (c+d x) (e+f x)}{9 b^2 d^3}-\frac{6 a^3 f^2 \sinh (c+d x) (e+f x)}{b^4 d^3}-\frac{2 a f^2 \cosh ^2(c+d x) \sinh (c+d x) (e+f x)}{9 b^2 d^3}+\frac{2 a f^3 \cosh ^3(c+d x)}{27 b^2 d^4}-\frac{45 f^3 x}{256 b d^3}+\frac{3 a^2 f^3 x}{8 b^3 d^3}+\frac{40 a f^3 \cosh (c+d x)}{9 b^2 d^4}+\frac{6 a^3 f^3 \cosh (c+d x)}{b^4 d^4}+\frac{6 a^2 \left(a^2+b^2\right) f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^5 d^4}+\frac{6 a^2 \left(a^2+b^2\right) f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^5 d^4}-\frac{3 f^3 \cosh ^3(c+d x) \sinh (c+d x)}{128 b d^4}-\frac{45 f^3 \cosh (c+d x) \sinh (c+d x)}{256 b d^4}-\frac{3 a^2 f^3 \cosh (c+d x) \sinh (c+d x)}{8 b^3 d^4}",1,"Result too large to show","B",0
373,1,5198,819,18.2534764,"\int \frac{(e+f x)^2 \cosh ^3(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^3*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{f^2 \cosh ^4(c+d x)}{32 b d^3}+\frac{(e+f x)^2 \cosh ^4(c+d x)}{4 b d}+\frac{2 a f (e+f x) \cosh ^3(c+d x)}{9 b^2 d^2}-\frac{f (e+f x) \sinh (c+d x) \cosh ^3(c+d x)}{8 b d^2}+\frac{3 f^2 \cosh ^2(c+d x)}{32 b d^3}-\frac{a (e+f x)^2 \sinh (c+d x) \cosh ^2(c+d x)}{3 b^2 d}+\frac{4 a f (e+f x) \cosh (c+d x)}{3 b^2 d^2}+\frac{2 a^3 f (e+f x) \cosh (c+d x)}{b^4 d^2}-\frac{3 f (e+f x) \sinh (c+d x) \cosh (c+d x)}{16 b d^2}-\frac{a^2 f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^3 d^2}-\frac{a^2 \left(a^2+b^2\right) (e+f x)^3}{3 b^5 f}-\frac{2 a f^2 \sinh ^3(c+d x)}{27 b^2 d^3}-\frac{3 f^2 x^2}{32 b d}+\frac{a^2 f^2 x^2}{4 b^3 d}+\frac{a^2 f^2 \sinh ^2(c+d x)}{4 b^3 d^3}+\frac{a^2 (e+f x)^2 \sinh ^2(c+d x)}{2 b^3 d}-\frac{3 e f x}{16 b d}+\frac{a^2 e f x}{2 b^3 d}+\frac{a^2 \left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right)}{b^5 d}+\frac{a^2 \left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right)}{b^5 d}+\frac{2 a^2 \left(a^2+b^2\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^5 d^2}+\frac{2 a^2 \left(a^2+b^2\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^5 d^2}-\frac{2 a^2 \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^5 d^3}-\frac{2 a^2 \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^5 d^3}-\frac{14 a f^2 \sinh (c+d x)}{9 b^2 d^3}-\frac{2 a^3 f^2 \sinh (c+d x)}{b^4 d^3}-\frac{2 a (e+f x)^2 \sinh (c+d x)}{3 b^2 d}-\frac{a^3 (e+f x)^2 \sinh (c+d x)}{b^4 d}",1,"Result too large to show","B",0
374,1,853,499,2.9501219,"\int \frac{(e+f x) \cosh ^3(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^3*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{-144 d e \log (a+b \sinh (c+d x)) b^4+72 f \left(d x \left(d x-2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right)-2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right)\right)-2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) b^4+72 d e \left(2 b^2 \sinh ^2(c+d x)-4 a b \sinh (c+d x)+\left(4 a^2+b^2\right) \log (a+b \sinh (c+d x))\right) b^2+36 f \left(2 d x \cosh (2 (c+d x)) b^2-\sinh (2 (c+d x)) b^2+8 a \cosh (c+d x) b-8 a d x \sinh (c+d x) b+2 \left(4 a^2+b^2\right) \left(-\frac{1}{2} (c+d x)^2+\log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (c+d x)+\log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (c+d x)-c \log (a+b \sinh (c+d x))+\text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)\right) b^2+24 d e \left(12 b^4 \sinh ^4(c+d x)-16 a b^3 \sinh ^3(c+d x)+6 b^2 \left(4 a^2+3 b^2\right) \sinh ^2(c+d x)-12 a b \left(4 a^2+3 b^2\right) \sinh (c+d x)+3 \left(16 a^4+12 b^2 a^2+b^4\right) \log (a+b \sinh (c+d x))\right)+f \left(36 d x \cosh (4 (c+d x)) b^4-9 \sinh (4 (c+d x)) b^4+32 a \cosh (3 (c+d x)) b^3-96 a d x \sinh (3 (c+d x)) b^3+72 \left(4 a^2+b^2\right) d x \cosh (2 (c+d x)) b^2-36 \left(4 a^2+b^2\right) \sinh (2 (c+d x)) b^2+576 a \left(2 a^2+b^2\right) \cosh (c+d x) b-576 a \left(2 a^2+b^2\right) d x \sinh (c+d x) b+72 \left(16 a^4+12 b^2 a^2+b^4\right) \left(-\frac{1}{2} (c+d x)^2+\log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (c+d x)+\log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (c+d x)-c \log (a+b \sinh (c+d x))+\text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)\right)}{1152 b^5 d^2}","\frac{a^3 f \cosh (c+d x)}{b^4 d^2}-\frac{a^3 (e+f x) \sinh (c+d x)}{b^4 d}-\frac{a^2 f \sinh (c+d x) \cosh (c+d x)}{4 b^3 d^2}+\frac{a^2 (e+f x) \sinh ^2(c+d x)}{2 b^3 d}+\frac{a^2 f x}{4 b^3 d}+\frac{a^2 f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^5 d^2}+\frac{a^2 f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^5 d^2}+\frac{a^2 \left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^5 d}+\frac{a^2 \left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^5 d}-\frac{a^2 \left(a^2+b^2\right) (e+f x)^2}{2 b^5 f}+\frac{a f \cosh ^3(c+d x)}{9 b^2 d^2}+\frac{2 a f \cosh (c+d x)}{3 b^2 d^2}-\frac{2 a (e+f x) \sinh (c+d x)}{3 b^2 d}-\frac{a (e+f x) \sinh (c+d x) \cosh ^2(c+d x)}{3 b^2 d}-\frac{f \sinh (c+d x) \cosh ^3(c+d x)}{16 b d^2}-\frac{3 f \sinh (c+d x) \cosh (c+d x)}{32 b d^2}+\frac{(e+f x) \cosh ^4(c+d x)}{4 b d}-\frac{3 f x}{32 b d}",1,"(-144*b^4*d*e*Log[a + b*Sinh[c + d*x]] + 72*b^4*f*(d*x*(d*x - 2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])]) - 2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + 72*b^2*d*e*((4*a^2 + b^2)*Log[a + b*Sinh[c + d*x]] - 4*a*b*Sinh[c + d*x] + 2*b^2*Sinh[c + d*x]^2) + 24*d*e*(3*(16*a^4 + 12*a^2*b^2 + b^4)*Log[a + b*Sinh[c + d*x]] - 12*a*b*(4*a^2 + 3*b^2)*Sinh[c + d*x] + 6*b^2*(4*a^2 + 3*b^2)*Sinh[c + d*x]^2 - 16*a*b^3*Sinh[c + d*x]^3 + 12*b^4*Sinh[c + d*x]^4) + 36*b^2*f*(8*a*b*Cosh[c + d*x] + 2*b^2*d*x*Cosh[2*(c + d*x)] + 2*(4*a^2 + b^2)*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - 8*a*b*d*x*Sinh[c + d*x] - b^2*Sinh[2*(c + d*x)]) + f*(576*a*b*(2*a^2 + b^2)*Cosh[c + d*x] + 72*b^2*(4*a^2 + b^2)*d*x*Cosh[2*(c + d*x)] + 32*a*b^3*Cosh[3*(c + d*x)] + 36*b^4*d*x*Cosh[4*(c + d*x)] + 72*(16*a^4 + 12*a^2*b^2 + b^4)*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - 576*a*b*(2*a^2 + b^2)*d*x*Sinh[c + d*x] - 36*b^2*(4*a^2 + b^2)*Sinh[2*(c + d*x)] - 96*a*b^3*d*x*Sinh[3*(c + d*x)] - 9*b^4*Sinh[4*(c + d*x)]))/(1152*b^5*d^2)","A",1
375,1,98,113,0.2310791,"\int \frac{\cosh ^3(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]^3*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{6 b^2 \left(a^2+b^2\right) \sinh ^2(c+d x)-12 a b \left(a^2+b^2\right) \sinh (c+d x)+12 a^2 \left(a^2+b^2\right) \log (a+b \sinh (c+d x))-4 a b^3 \sinh ^3(c+d x)+3 b^4 \sinh ^4(c+d x)}{12 b^5 d}","\frac{a^2 \left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{b^5 d}-\frac{a \left(a^2+b^2\right) \sinh (c+d x)}{b^4 d}+\frac{\left(a^2+b^2\right) \sinh ^2(c+d x)}{2 b^3 d}-\frac{a \sinh ^3(c+d x)}{3 b^2 d}+\frac{\sinh ^4(c+d x)}{4 b d}",1,"(12*a^2*(a^2 + b^2)*Log[a + b*Sinh[c + d*x]] - 12*a*b*(a^2 + b^2)*Sinh[c + d*x] + 6*b^2*(a^2 + b^2)*Sinh[c + d*x]^2 - 4*a*b^3*Sinh[c + d*x]^3 + 3*b^4*Sinh[c + d*x]^4)/(12*b^5*d)","A",1
376,-1,0,39,180.0025575,"\int \frac{\cosh ^3(c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]^3*Sinh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^2(c+d x) \cosh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
377,1,3261,1218,22.7341541,"\int \frac{(e+f x)^3 \sinh (c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sinh[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{(e+f x)^4}{4 b f}+\frac{2 a^3 \tan ^{-1}\left(e^{c+d x}\right) (e+f x)^3}{b^2 \left(a^2+b^2\right) d}-\frac{2 a \tan ^{-1}\left(e^{c+d x}\right) (e+f x)^3}{b^2 d}+\frac{a^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{b \left(a^2+b^2\right) d}+\frac{a^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{b \left(a^2+b^2\right) d}+\frac{\log \left(1+e^{2 (c+d x)}\right) (e+f x)^3}{b d}-\frac{a^2 \log \left(1+e^{2 (c+d x)}\right) (e+f x)^3}{b \left(a^2+b^2\right) d}-\frac{3 i a^3 f \text{Li}_2\left(-i e^{c+d x}\right) (e+f x)^2}{b^2 \left(a^2+b^2\right) d^2}+\frac{3 i a f \text{Li}_2\left(-i e^{c+d x}\right) (e+f x)^2}{b^2 d^2}+\frac{3 i a^3 f \text{Li}_2\left(i e^{c+d x}\right) (e+f x)^2}{b^2 \left(a^2+b^2\right) d^2}-\frac{3 i a f \text{Li}_2\left(i e^{c+d x}\right) (e+f x)^2}{b^2 d^2}+\frac{3 a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)^2}{b \left(a^2+b^2\right) d^2}+\frac{3 a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)^2}{b \left(a^2+b^2\right) d^2}+\frac{3 f \text{Li}_2\left(-e^{2 (c+d x)}\right) (e+f x)^2}{2 b d^2}-\frac{3 a^2 f \text{Li}_2\left(-e^{2 (c+d x)}\right) (e+f x)^2}{2 b \left(a^2+b^2\right) d^2}+\frac{6 i a^3 f^2 \text{Li}_3\left(-i e^{c+d x}\right) (e+f x)}{b^2 \left(a^2+b^2\right) d^3}-\frac{6 i a f^2 \text{Li}_3\left(-i e^{c+d x}\right) (e+f x)}{b^2 d^3}-\frac{6 i a^3 f^2 \text{Li}_3\left(i e^{c+d x}\right) (e+f x)}{b^2 \left(a^2+b^2\right) d^3}+\frac{6 i a f^2 \text{Li}_3\left(i e^{c+d x}\right) (e+f x)}{b^2 d^3}-\frac{6 a^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)}{b \left(a^2+b^2\right) d^3}-\frac{6 a^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)}{b \left(a^2+b^2\right) d^3}-\frac{3 f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) (e+f x)}{2 b d^3}+\frac{3 a^2 f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) (e+f x)}{2 b \left(a^2+b^2\right) d^3}-\frac{6 i a^3 f^3 \text{Li}_4\left(-i e^{c+d x}\right)}{b^2 \left(a^2+b^2\right) d^4}+\frac{6 i a f^3 \text{Li}_4\left(-i e^{c+d x}\right)}{b^2 d^4}+\frac{6 i a^3 f^3 \text{Li}_4\left(i e^{c+d x}\right)}{b^2 \left(a^2+b^2\right) d^4}-\frac{6 i a f^3 \text{Li}_4\left(i e^{c+d x}\right)}{b^2 d^4}+\frac{6 a^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b \left(a^2+b^2\right) d^4}+\frac{6 a^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b \left(a^2+b^2\right) d^4}+\frac{3 f^3 \text{Li}_4\left(-e^{2 (c+d x)}\right)}{4 b d^4}-\frac{3 a^2 f^3 \text{Li}_4\left(-e^{2 (c+d x)}\right)}{4 b \left(a^2+b^2\right) d^4}",1,"(-8*b*d^4*e^3*E^(2*c)*x - 12*b*d^4*e^2*E^(2*c)*f*x^2 - 8*b*d^4*e*E^(2*c)*f^2*x^3 - 2*b*d^4*E^(2*c)*f^3*x^4 - 8*a*d^3*e^3*ArcTan[E^(c + d*x)] - 8*a*d^3*e^3*E^(2*c)*ArcTan[E^(c + d*x)] - (12*I)*a*d^3*e^2*f*x*Log[1 - I*E^(c + d*x)] - (12*I)*a*d^3*e^2*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] - (12*I)*a*d^3*e*f^2*x^2*Log[1 - I*E^(c + d*x)] - (12*I)*a*d^3*e*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] - (4*I)*a*d^3*f^3*x^3*Log[1 - I*E^(c + d*x)] - (4*I)*a*d^3*E^(2*c)*f^3*x^3*Log[1 - I*E^(c + d*x)] + (12*I)*a*d^3*e^2*f*x*Log[1 + I*E^(c + d*x)] + (12*I)*a*d^3*e^2*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] + (12*I)*a*d^3*e*f^2*x^2*Log[1 + I*E^(c + d*x)] + (12*I)*a*d^3*e*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] + (4*I)*a*d^3*f^3*x^3*Log[1 + I*E^(c + d*x)] + (4*I)*a*d^3*E^(2*c)*f^3*x^3*Log[1 + I*E^(c + d*x)] + 4*b*d^3*e^3*Log[1 + E^(2*(c + d*x))] + 4*b*d^3*e^3*E^(2*c)*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e^2*f*x*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e^2*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 4*b*d^3*f^3*x^3*Log[1 + E^(2*(c + d*x))] + 4*b*d^3*E^(2*c)*f^3*x^3*Log[1 + E^(2*(c + d*x))] + (12*I)*a*d^2*(1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)] - (12*I)*a*d^2*(1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)] + 6*b*d^2*e^2*f*PolyLog[2, -E^(2*(c + d*x))] + 6*b*d^2*e^2*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 12*b*d^2*e*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 12*b*d^2*e*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 6*b*d^2*f^3*x^2*PolyLog[2, -E^(2*(c + d*x))] + 6*b*d^2*E^(2*c)*f^3*x^2*PolyLog[2, -E^(2*(c + d*x))] - (24*I)*a*d*e*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (24*I)*a*d*e*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (24*I)*a*d*f^3*x*PolyLog[3, (-I)*E^(c + d*x)] - (24*I)*a*d*E^(2*c)*f^3*x*PolyLog[3, (-I)*E^(c + d*x)] + (24*I)*a*d*e*f^2*PolyLog[3, I*E^(c + d*x)] + (24*I)*a*d*e*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] + (24*I)*a*d*f^3*x*PolyLog[3, I*E^(c + d*x)] + (24*I)*a*d*E^(2*c)*f^3*x*PolyLog[3, I*E^(c + d*x)] - 6*b*d*e*f^2*PolyLog[3, -E^(2*(c + d*x))] - 6*b*d*e*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))] - 6*b*d*f^3*x*PolyLog[3, -E^(2*(c + d*x))] - 6*b*d*E^(2*c)*f^3*x*PolyLog[3, -E^(2*(c + d*x))] + (24*I)*a*f^3*PolyLog[4, (-I)*E^(c + d*x)] + (24*I)*a*E^(2*c)*f^3*PolyLog[4, (-I)*E^(c + d*x)] - (24*I)*a*f^3*PolyLog[4, I*E^(c + d*x)] - (24*I)*a*E^(2*c)*f^3*PolyLog[4, I*E^(c + d*x)] + 3*b*f^3*PolyLog[4, -E^(2*(c + d*x))] + 3*b*E^(2*c)*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*(a^2 + b^2)*d^4*(1 + E^(2*c))) - (a^2*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(2*b*(a^2 + b^2)*(-1 + E^(2*c))) + ((4*a^2*e^3*x - 4*b^2*e^3*x + 6*a^2*e^2*f*x^2 - 6*b^2*e^2*f*x^2 + 4*a^2*e*f^2*x^3 - 4*b^2*e*f^2*x^3 + a^2*f^3*x^4 - b^2*f^3*x^4 + 4*a^2*e^3*x*Cosh[2*c] + 4*b^2*e^3*x*Cosh[2*c] + 6*a^2*e^2*f*x^2*Cosh[2*c] + 6*b^2*e^2*f*x^2*Cosh[2*c] + 4*a^2*e*f^2*x^3*Cosh[2*c] + 4*b^2*e*f^2*x^3*Cosh[2*c] + a^2*f^3*x^4*Cosh[2*c] + b^2*f^3*x^4*Cosh[2*c])*Csch[c]*Sech[c])/(8*b*(a^2 + b^2))","B",0
378,1,997,861,10.6581743,"\int \frac{(e+f x)^2 \sinh (c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sinh[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{-2 a^2 f^2 x^3 d^3-2 b^2 f^2 x^3 d^3-6 a^2 e f x^2 d^3-6 b^2 e f x^2 d^3-6 a^2 e^2 x d^3-6 b^2 e^2 x d^3-12 a b e^2 \tan ^{-1}\left(e^{c+d x}\right) d^2-6 i a b f^2 x^2 \log \left(1-i e^{c+d x}\right) d^2-12 i a b e f x \log \left(1-i e^{c+d x}\right) d^2+6 i a b f^2 x^2 \log \left(1+i e^{c+d x}\right) d^2+12 i a b e f x \log \left(1+i e^{c+d x}\right) d^2+6 b^2 e^2 \log \left(1+e^{2 (c+d x)}\right) d^2+6 b^2 f^2 x^2 \log \left(1+e^{2 (c+d x)}\right) d^2+12 b^2 e f x \log \left(1+e^{2 (c+d x)}\right) d^2+6 a^2 e^2 \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2+6 a^2 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+12 a^2 e f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 a^2 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+12 a^2 e f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+12 i a b f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) d-12 i a b f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) d+6 b^2 e f \text{Li}_2\left(-e^{2 (c+d x)}\right) d+6 b^2 f^2 x \text{Li}_2\left(-e^{2 (c+d x)}\right) d+12 a^2 e f \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+12 a^2 f^2 x \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+12 a^2 e f \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+12 a^2 f^2 x \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-12 i a b f^2 \text{Li}_3\left(-i e^{c+d x}\right)+12 i a b f^2 \text{Li}_3\left(i e^{c+d x}\right)-3 b^2 f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right)-12 a^2 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-12 a^2 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{6 b \left(a^2+b^2\right) d^3}","\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d}-\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^2}{b \left(a^2+b^2\right) d}+\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^2}{b \left(a^2+b^2\right) d}-\frac{(e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) a^2}{b \left(a^2+b^2\right) d}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^2}{b \left(a^2+b^2\right) d^2}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^2}{b \left(a^2+b^2\right) d^2}-\frac{f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) a^2}{b \left(a^2+b^2\right) d^2}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^2}{b \left(a^2+b^2\right) d^3}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^2}{b \left(a^2+b^2\right) d^3}+\frac{f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) a^2}{2 b \left(a^2+b^2\right) d^3}-\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a}{b^2 d}+\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a}{b^2 d^2}-\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a}{b^2 d^2}-\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a}{b^2 d^3}+\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right) a}{b^2 d^3}-\frac{(e+f x)^3}{3 b f}+\frac{(e+f x)^2 \log \left(1+e^{2 (c+d x)}\right)}{b d}+\frac{f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right)}{b d^2}-\frac{f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right)}{2 b d^3}",1,"(-6*a^2*d^3*e^2*x - 6*b^2*d^3*e^2*x - 6*a^2*d^3*e*f*x^2 - 6*b^2*d^3*e*f*x^2 - 2*a^2*d^3*f^2*x^3 - 2*b^2*d^3*f^2*x^3 - 12*a*b*d^2*e^2*ArcTan[E^(c + d*x)] - (12*I)*a*b*d^2*e*f*x*Log[1 - I*E^(c + d*x)] - (6*I)*a*b*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] + (12*I)*a*b*d^2*e*f*x*Log[1 + I*E^(c + d*x)] + (6*I)*a*b*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] + 6*b^2*d^2*e^2*Log[1 + E^(2*(c + d*x))] + 12*b^2*d^2*e*f*x*Log[1 + E^(2*(c + d*x))] + 6*b^2*d^2*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 6*a^2*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 12*a^2*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*a^2*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 12*a^2*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*a^2*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + (12*I)*a*b*d*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)] - (12*I)*a*b*d*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)] + 6*b^2*d*e*f*PolyLog[2, -E^(2*(c + d*x))] + 6*b^2*d*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 12*a^2*d*e*f*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 12*a^2*d*f^2*x*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 12*a^2*d*e*f*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 12*a^2*d*f^2*x*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - (12*I)*a*b*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (12*I)*a*b*f^2*PolyLog[3, I*E^(c + d*x)] - 3*b^2*f^2*PolyLog[3, -E^(2*(c + d*x))] - 12*a^2*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 12*a^2*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/(6*b*(a^2 + b^2)*d^3)","A",1
379,1,438,516,2.7958317,"\int \frac{(e+f x) \sinh (c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sinh[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\frac{a^2 \left(f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-\frac{1}{2} f (c+d x)^2\right)}{b}-2 a d e \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))+i a f \text{Li}_2(-i (\cosh (c+d x)+\sinh (c+d x)))-i a f \text{Li}_2(i (\cosh (c+d x)+\sinh (c+d x)))+2 a c f \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))-2 a f (c+d x) \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))-b d e (c+d x)+b d e \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)+\frac{1}{2} b f \text{Li}_2(-\cosh (2 (c+d x))-\sinh (2 (c+d x)))-\frac{1}{2} b f (c+d x)^2+b c f (c+d x)-b c f \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)+b f (c+d x) \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)}{d^2 \left(a^2+b^2\right)}","\frac{a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2 \left(a^2+b^2\right)}+\frac{a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{a^2 f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 b d^2 \left(a^2+b^2\right)}+\frac{a^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d \left(a^2+b^2\right)}+\frac{a^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d \left(a^2+b^2\right)}-\frac{a^2 (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{b d \left(a^2+b^2\right)}-\frac{i a^3 f \text{Li}_2\left(-i e^{c+d x}\right)}{b^2 d^2 \left(a^2+b^2\right)}+\frac{i a^3 f \text{Li}_2\left(i e^{c+d x}\right)}{b^2 d^2 \left(a^2+b^2\right)}+\frac{2 a^3 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^2 d \left(a^2+b^2\right)}+\frac{i a f \text{Li}_2\left(-i e^{c+d x}\right)}{b^2 d^2}-\frac{i a f \text{Li}_2\left(i e^{c+d x}\right)}{b^2 d^2}-\frac{2 a (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^2 d}+\frac{f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 b d^2}+\frac{(e+f x) \log \left(e^{2 (c+d x)}+1\right)}{b d}-\frac{(e+f x)^2}{2 b f}",1,"(-(b*d*e*(c + d*x)) + b*c*f*(c + d*x) - (b*f*(c + d*x)^2)/2 - 2*a*d*e*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] + 2*a*c*f*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] - 2*a*f*(c + d*x)*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] + b*d*e*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] - b*c*f*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] + b*f*(c + d*x)*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] + (a^2*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/b + I*a*f*PolyLog[2, (-I)*(Cosh[c + d*x] + Sinh[c + d*x])] - I*a*f*PolyLog[2, I*(Cosh[c + d*x] + Sinh[c + d*x])] + (b*f*PolyLog[2, -Cosh[2*(c + d*x)] - Sinh[2*(c + d*x)]])/2)/((a^2 + b^2)*d^2)","A",0
380,1,78,74,0.0823391,"\int \frac{\sinh (c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Sinh[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{2 a^2 \log (a+b \sinh (c+d x))+b (b+i a) \log (-\sinh (c+d x)+i)+b (b-i a) \log (\sinh (c+d x)+i)}{2 b d \left(a^2+b^2\right)}","\frac{a^2 \log (a+b \sinh (c+d x))}{b d \left(a^2+b^2\right)}-\frac{a \tan ^{-1}(\sinh (c+d x))}{d \left(a^2+b^2\right)}+\frac{b \log (\cosh (c+d x))}{d \left(a^2+b^2\right)}",1,"(b*(I*a + b)*Log[I - Sinh[c + d*x]] + b*((-I)*a + b)*Log[I + Sinh[c + d*x]] + 2*a^2*Log[a + b*Sinh[c + d*x]])/(2*b*(a^2 + b^2)*d)","C",1
381,-1,0,35,180.0008096,"\int \frac{\sinh (c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Sinh[c + d*x]*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh (c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
382,1,1118,1118,13.3054909,"\int \frac{(e+f x)^3 \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(-2 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3+f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+3 e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2-3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2-6 e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-6 f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+6 e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+6 f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+6 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) a^2}{\left(a^2+b^2\right)^{3/2} d^4}+\frac{f \left(-4 a e^{2 c} f^2 x^3 d^3-12 a e e^{2 c} f x^2 d^3-12 a e^2 e^{2 c} x d^3+12 b e^2 \left(1+e^{2 c}\right) \tan ^{-1}\left(e^{c+d x}\right) d^2+6 a e^2 \left(1+e^{2 c}\right) \log \left(1+e^{2 (c+d x)}\right) d^2+12 i b e \left(1+e^{2 c}\right) f \left(d x \left(\log \left(1-i e^{c+d x}\right)-\log \left(1+i e^{c+d x}\right)\right)-\text{Li}_2\left(-i e^{c+d x}\right)+\text{Li}_2\left(i e^{c+d x}\right)\right) d+6 a e \left(1+e^{2 c}\right) f \left(2 d x \log \left(1+e^{2 (c+d x)}\right)+\text{Li}_2\left(-e^{2 (c+d x)}\right)\right) d+6 i b \left(1+e^{2 c}\right) f^2 \left(d^2 \log \left(1-i e^{c+d x}\right) x^2-d^2 \log \left(1+i e^{c+d x}\right) x^2-2 d \text{Li}_2\left(-i e^{c+d x}\right) x+2 d \text{Li}_2\left(i e^{c+d x}\right) x+2 \text{Li}_3\left(-i e^{c+d x}\right)-2 \text{Li}_3\left(i e^{c+d x}\right)\right)+3 a \left(1+e^{2 c}\right) f^2 \left(2 d^2 \log \left(1+e^{2 (c+d x)}\right) x^2+2 d \text{Li}_2\left(-e^{2 (c+d x)}\right) x-\text{Li}_3\left(-e^{2 (c+d x)}\right)\right)\right)}{2 \left(a^2+b^2\right) d^4 \left(1+e^{2 c}\right)}+\frac{\text{sech}(c) \text{sech}(c+d x) \left(-b \cosh (c) e^3-a \sinh (d x) e^3-3 b f x \cosh (c) e^2-3 a f x \sinh (d x) e^2-3 b f^2 x^2 \cosh (c) e-3 a f^2 x^2 \sinh (d x) e-b f^3 x^3 \cosh (c)-a f^3 x^3 \sinh (d x)\right)}{\left(a^2+b^2\right) d}","\frac{(e+f x)^3 a^3}{b^2 \left(a^2+b^2\right) d}-\frac{3 f (e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}-\frac{3 f^2 (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{3 f^3 \text{Li}_3\left(-e^{2 (c+d x)}\right) a^3}{2 b^2 \left(a^2+b^2\right) d^4}+\frac{(e+f x)^3 \tanh (c+d x) a^3}{b^2 \left(a^2+b^2\right) d}-\frac{6 f (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^2}+\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^2}{\left(a^2+b^2\right)^{3/2} d}-\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^2}{\left(a^2+b^2\right)^{3/2} d}+\frac{6 i f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^3}-\frac{6 i f^2 (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^3}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^2}{\left(a^2+b^2\right)^{3/2} d^2}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^2}{\left(a^2+b^2\right)^{3/2} d^2}-\frac{6 i f^3 \text{Li}_3\left(-i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^4}+\frac{6 i f^3 \text{Li}_3\left(i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^4}-\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^2}{\left(a^2+b^2\right)^{3/2} d^3}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^2}{\left(a^2+b^2\right)^{3/2} d^3}+\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^2}{\left(a^2+b^2\right)^{3/2} d^4}-\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^2}{\left(a^2+b^2\right)^{3/2} d^4}+\frac{(e+f x)^3 \text{sech}(c+d x) a^2}{b \left(a^2+b^2\right) d}-\frac{(e+f x)^3 a}{b^2 d}+\frac{3 f (e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) a}{b^2 d^2}+\frac{3 f^2 (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) a}{b^2 d^3}-\frac{3 f^3 \text{Li}_3\left(-e^{2 (c+d x)}\right) a}{2 b^2 d^4}-\frac{(e+f x)^3 \tanh (c+d x) a}{b^2 d}+\frac{6 f (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{b d^2}-\frac{6 i f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{b d^3}+\frac{6 i f^2 (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{b d^3}+\frac{6 i f^3 \text{Li}_3\left(-i e^{c+d x}\right)}{b d^4}-\frac{6 i f^3 \text{Li}_3\left(i e^{c+d x}\right)}{b d^4}-\frac{(e+f x)^3 \text{sech}(c+d x)}{b d}",1,"(f*(-12*a*d^3*e^2*E^(2*c)*x - 12*a*d^3*e*E^(2*c)*f*x^2 - 4*a*d^3*E^(2*c)*f^2*x^3 + 12*b*d^2*e^2*(1 + E^(2*c))*ArcTan[E^(c + d*x)] + 6*a*d^2*e^2*(1 + E^(2*c))*Log[1 + E^(2*(c + d*x))] + (12*I)*b*d*e*(1 + E^(2*c))*f*(d*x*(Log[1 - I*E^(c + d*x)] - Log[1 + I*E^(c + d*x)]) - PolyLog[2, (-I)*E^(c + d*x)] + PolyLog[2, I*E^(c + d*x)]) + 6*a*d*e*(1 + E^(2*c))*f*(2*d*x*Log[1 + E^(2*(c + d*x))] + PolyLog[2, -E^(2*(c + d*x))]) + (6*I)*b*(1 + E^(2*c))*f^2*(d^2*x^2*Log[1 - I*E^(c + d*x)] - d^2*x^2*Log[1 + I*E^(c + d*x)] - 2*d*x*PolyLog[2, (-I)*E^(c + d*x)] + 2*d*x*PolyLog[2, I*E^(c + d*x)] + 2*PolyLog[3, (-I)*E^(c + d*x)] - 2*PolyLog[3, I*E^(c + d*x)]) + 3*a*(1 + E^(2*c))*f^2*(2*d^2*x^2*Log[1 + E^(2*(c + d*x))] + 2*d*x*PolyLog[2, -E^(2*(c + d*x))] - PolyLog[3, -E^(2*(c + d*x))])))/(2*(a^2 + b^2)*d^4*(1 + E^(2*c))) + (a^2*(-2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/((a^2 + b^2)^(3/2)*d^4) + (Sech[c]*Sech[c + d*x]*(-(b*e^3*Cosh[c]) - 3*b*e^2*f*x*Cosh[c] - 3*b*e*f^2*x^2*Cosh[c] - b*f^3*x^3*Cosh[c] - a*e^3*Sinh[d*x] - 3*a*e^2*f*x*Sinh[d*x] - 3*a*e*f^2*x^2*Sinh[d*x] - a*f^3*x^3*Sinh[d*x]))/((a^2 + b^2)*d)","A",1
383,1,908,772,8.386201,"\int \frac{(e+f x)^2 \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(-2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^2+f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2+2 e f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2-f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2-2 e f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2+2 f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) a^2}{\left(a^2+b^2\right)^{3/2} d^3}+\frac{f^2 \text{csch}(c) \left(d^2 e^{-\tanh ^{-1}(\coth (c))} x^2-\frac{i \coth (c) \left(-d x \left(2 i \tanh ^{-1}(\coth (c))-\pi \right)-\pi  \log \left(1+e^{2 d x}\right)-2 \left(i d x+i \tanh ^{-1}(\coth (c))\right) \log \left(1-e^{2 i \left(i d x+i \tanh ^{-1}(\coth (c))\right)}\right)+\pi  \log (\cosh (d x))+2 i \tanh ^{-1}(\coth (c)) \log \left(i \sinh \left(d x+\tanh ^{-1}(\coth (c))\right)\right)+i \text{Li}_2\left(e^{2 i \left(i d x+i \tanh ^{-1}(\coth (c))\right)}\right)\right)}{\sqrt{1-\coth ^2(c)}}\right) \text{sech}(c) a}{\left(a^2+b^2\right) d^3 \sqrt{\text{csch}^2(c) \left(\sinh ^2(c)-\cosh ^2(c)\right)}}+\frac{2 e f \text{sech}(c) (\cosh (c) \log (\cosh (c) \cosh (d x)+\sinh (c) \sinh (d x))-d x \sinh (c)) a}{\left(a^2+b^2\right) d^2 \left(\cosh ^2(c)-\sinh ^2(c)\right)}+\frac{2 b f^2 \left(-\frac{2 \tan ^{-1}\left(\frac{\sinh (c)+\cosh (c) \tanh \left(\frac{d x}{2}\right)}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right) \tanh ^{-1}(\coth (c))}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}-\frac{i \text{csch}(c) \left(i \left(d x+\tanh ^{-1}(\coth (c))\right) \left(\log \left(1-e^{-d x-\tanh ^{-1}(\coth (c))}\right)-\log \left(1+e^{-d x-\tanh ^{-1}(\coth (c))}\right)\right)+i \left(\text{Li}_2\left(-e^{-d x-\tanh ^{-1}(\coth (c))}\right)-\text{Li}_2\left(e^{-d x-\tanh ^{-1}(\coth (c))}\right)\right)\right)}{\sqrt{1-\coth ^2(c)}}\right)}{\left(a^2+b^2\right) d^3}+\frac{\text{sech}(c) \text{sech}(c+d x) \left(-b \cosh (c) e^2-a \sinh (d x) e^2-2 b f x \cosh (c) e-2 a f x \sinh (d x) e-b f^2 x^2 \cosh (c)-a f^2 x^2 \sinh (d x)\right)}{\left(a^2+b^2\right) d}+\frac{4 b e f \tan ^{-1}\left(\frac{\sinh (c)+\cosh (c) \tanh \left(\frac{d x}{2}\right)}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right)}{\left(a^2+b^2\right) d^2 \sqrt{\cosh ^2(c)-\sinh ^2(c)}}","\frac{2 i a^2 f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}-\frac{2 i a^2 f^2 \text{Li}_2\left(i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}-\frac{2 a^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{2 a^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{2 a^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{2 a^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{4 a^2 f (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}+\frac{a^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)^{3/2}}-\frac{a^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)^{3/2}}+\frac{a^2 (e+f x)^2 \text{sech}(c+d x)}{b d \left(a^2+b^2\right)}-\frac{a^3 f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right)}{b^2 d^3 \left(a^2+b^2\right)}-\frac{2 a^3 f (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{b^2 d^2 \left(a^2+b^2\right)}+\frac{a^3 (e+f x)^2 \tanh (c+d x)}{b^2 d \left(a^2+b^2\right)}+\frac{a^3 (e+f x)^2}{b^2 d \left(a^2+b^2\right)}+\frac{a f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right)}{b^2 d^3}+\frac{2 a f (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{b^2 d^2}-\frac{a (e+f x)^2 \tanh (c+d x)}{b^2 d}-\frac{a (e+f x)^2}{b^2 d}-\frac{2 i f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{b d^3}+\frac{2 i f^2 \text{Li}_2\left(i e^{c+d x}\right)}{b d^3}+\frac{4 f (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b d^2}-\frac{(e+f x)^2 \text{sech}(c+d x)}{b d}",1,"(a^2*(-2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/((a^2 + b^2)^(3/2)*d^3) + (2*a*e*f*Sech[c]*(Cosh[c]*Log[Cosh[c]*Cosh[d*x] + Sinh[c]*Sinh[d*x]] - d*x*Sinh[c]))/((a^2 + b^2)*d^2*(Cosh[c]^2 - Sinh[c]^2)) + (4*b*e*f*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]])/((a^2 + b^2)*d^2*Sqrt[Cosh[c]^2 - Sinh[c]^2]) + (a*f^2*Csch[c]*((d^2*x^2)/E^ArcTanh[Coth[c]] - (I*Coth[c]*(-(d*x*(-Pi + (2*I)*ArcTanh[Coth[c]])) - Pi*Log[1 + E^(2*d*x)] - 2*(I*d*x + I*ArcTanh[Coth[c]])*Log[1 - E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))] + Pi*Log[Cosh[d*x]] + (2*I)*ArcTanh[Coth[c]]*Log[I*Sinh[d*x + ArcTanh[Coth[c]]]] + I*PolyLog[2, E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))]))/Sqrt[1 - Coth[c]^2])*Sech[c])/((a^2 + b^2)*d^3*Sqrt[Csch[c]^2*(-Cosh[c]^2 + Sinh[c]^2)]) + (2*b*f^2*(((-I)*Csch[c]*(I*(d*x + ArcTanh[Coth[c]])*(Log[1 - E^(-(d*x) - ArcTanh[Coth[c]])] - Log[1 + E^(-(d*x) - ArcTanh[Coth[c]])]) + I*(PolyLog[2, -E^(-(d*x) - ArcTanh[Coth[c]])] - PolyLog[2, E^(-(d*x) - ArcTanh[Coth[c]])])))/Sqrt[1 - Coth[c]^2] - (2*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]]*ArcTanh[Coth[c]])/Sqrt[Cosh[c]^2 - Sinh[c]^2]))/((a^2 + b^2)*d^3) + (Sech[c]*Sech[c + d*x]*(-(b*e^2*Cosh[c]) - 2*b*e*f*x*Cosh[c] - b*f^2*x^2*Cosh[c] - a*e^2*Sinh[d*x] - 2*a*e*f*x*Sinh[d*x] - a*f^2*x^2*Sinh[d*x]))/((a^2 + b^2)*d)","A",0
384,1,284,385,2.9128462,"\int \frac{(e+f x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\frac{a^2 \left(-2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)}{\left(a^2+b^2\right)^{3/2}}-\frac{d (e+f x) \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a^2+b^2}+\frac{2 b f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^2+b^2}+\frac{a f \log (\cosh (c+d x))}{a^2+b^2}}{d^2}","\frac{a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{a^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{a^2 f \tan ^{-1}(\sinh (c+d x))}{b d^2 \left(a^2+b^2\right)}+\frac{a^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)^{3/2}}-\frac{a^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)^{3/2}}+\frac{a^2 (e+f x) \text{sech}(c+d x)}{b d \left(a^2+b^2\right)}-\frac{a^3 f \log (\cosh (c+d x))}{b^2 d^2 \left(a^2+b^2\right)}+\frac{a^3 (e+f x) \tanh (c+d x)}{b^2 d \left(a^2+b^2\right)}+\frac{a f \log (\cosh (c+d x))}{b^2 d^2}-\frac{a (e+f x) \tanh (c+d x)}{b^2 d}+\frac{f \tan ^{-1}(\sinh (c+d x))}{b d^2}-\frac{(e+f x) \text{sech}(c+d x)}{b d}",1,"((2*b*f*ArcTan[Tanh[(c + d*x)/2]])/(a^2 + b^2) + (a*f*Log[Cosh[c + d*x]])/(a^2 + b^2) + (a^2*(-2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^2 + b^2)^(3/2) - (d*(e + f*x)*Sech[c + d*x]*(b + a*Sinh[c + d*x]))/(a^2 + b^2))/d^2","A",1
385,1,106,90,0.1821657,"\int \frac{\tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Tanh[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","-\frac{a \left(2 a \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)-\sqrt{-a^2-b^2} \tanh (c+d x)\right)-b \sqrt{-a^2-b^2} \text{sech}(c+d x)}{d \left(-a^2-b^2\right)^{3/2}}","-\frac{2 a^2 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{d \left(a^2+b^2\right)^{3/2}}-\frac{a \tanh (c+d x)}{d \left(a^2+b^2\right)}-\frac{b \text{sech}(c+d x)}{d \left(a^2+b^2\right)}",1,"-((-(b*Sqrt[-a^2 - b^2]*Sech[c + d*x]) + a*(2*a*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] - Sqrt[-a^2 - b^2]*Tanh[c + d*x]))/((-a^2 - b^2)^(3/2)*d))","A",1
386,-1,0,31,180.0010453,"\int \frac{\tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Tanh[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
387,1,3124,1256,27.86676,"\int \frac{(e+f x)^2 \text{sech}(c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{(e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d}+\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d}-\frac{f^2 \tan ^{-1}(\sinh (c+d x)) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}-\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d^3}-\frac{i f^2 \text{Li}_3\left(i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d^3}+\frac{f (e+f x) \text{sech}(c+d x) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{(e+f x)^2 \text{sech}(c+d x) \tanh (c+d x) a^3}{2 b^2 \left(a^2+b^2\right) d}+\frac{(e+f x)^2 \text{sech}^2(c+d x) a^2}{2 b \left(a^2+b^2\right) d}+\frac{b (e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^2}{\left(a^2+b^2\right)^2 d}+\frac{b (e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^2}{\left(a^2+b^2\right)^2 d}-\frac{b (e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) a^2}{\left(a^2+b^2\right)^2 d}+\frac{f^2 \log (\cosh (c+d x)) a^2}{b \left(a^2+b^2\right) d^3}+\frac{2 b f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^2}{\left(a^2+b^2\right)^2 d^2}+\frac{2 b f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^2}{\left(a^2+b^2\right)^2 d^2}-\frac{b f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) a^2}{\left(a^2+b^2\right)^2 d^2}-\frac{2 b f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^2}{\left(a^2+b^2\right)^2 d^3}-\frac{2 b f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^2}{\left(a^2+b^2\right)^2 d^3}+\frac{b f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) a^2}{2 \left(a^2+b^2\right)^2 d^3}-\frac{f (e+f x) \tanh (c+d x) a^2}{b \left(a^2+b^2\right) d^2}-\frac{(e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a}{b^2 d}+\frac{f^2 \tan ^{-1}(\sinh (c+d x)) a}{b^2 d^3}+\frac{i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a}{b^2 d^2}-\frac{i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a}{b^2 d^2}-\frac{i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a}{b^2 d^3}+\frac{i f^2 \text{Li}_3\left(i e^{c+d x}\right) a}{b^2 d^3}-\frac{f (e+f x) \text{sech}(c+d x) a}{b^2 d^2}-\frac{(e+f x)^2 \text{sech}(c+d x) \tanh (c+d x) a}{2 b^2 d}-\frac{(e+f x)^2 \text{sech}^2(c+d x)}{2 b d}-\frac{f^2 \log (\cosh (c+d x))}{b d^3}+\frac{f (e+f x) \tanh (c+d x)}{b d^2}",1,"-1/6*(-12*a^2*b*d^3*e^2*E^(2*c)*x - 12*a^2*b*d*E^(2*c)*f^2*x - 12*b^3*d*E^(2*c)*f^2*x - 12*a^2*b*d^3*e*E^(2*c)*f*x^2 - 4*a^2*b*d^3*E^(2*c)*f^2*x^3 - 6*a^3*d^2*e^2*ArcTan[E^(c + d*x)] + 6*a*b^2*d^2*e^2*ArcTan[E^(c + d*x)] - 6*a^3*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] + 6*a*b^2*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] - 12*a^3*f^2*ArcTan[E^(c + d*x)] - 12*a*b^2*f^2*ArcTan[E^(c + d*x)] - 12*a^3*E^(2*c)*f^2*ArcTan[E^(c + d*x)] - 12*a*b^2*E^(2*c)*f^2*ArcTan[E^(c + d*x)] - (6*I)*a^3*d^2*e*f*x*Log[1 - I*E^(c + d*x)] + (6*I)*a*b^2*d^2*e*f*x*Log[1 - I*E^(c + d*x)] - (6*I)*a^3*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] + (6*I)*a*b^2*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] - (3*I)*a^3*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] + (3*I)*a*b^2*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] - (3*I)*a^3*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] + (3*I)*a*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] + (6*I)*a^3*d^2*e*f*x*Log[1 + I*E^(c + d*x)] - (6*I)*a*b^2*d^2*e*f*x*Log[1 + I*E^(c + d*x)] + (6*I)*a^3*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] - (6*I)*a*b^2*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] + (3*I)*a^3*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] - (3*I)*a*b^2*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] + (3*I)*a^3*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] - (3*I)*a*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] + 6*a^2*b*d^2*e^2*Log[1 + E^(2*(c + d*x))] + 6*a^2*b*d^2*e^2*E^(2*c)*Log[1 + E^(2*(c + d*x))] + 6*a^2*b*f^2*Log[1 + E^(2*(c + d*x))] + 6*b^3*f^2*Log[1 + E^(2*(c + d*x))] + 6*a^2*b*E^(2*c)*f^2*Log[1 + E^(2*(c + d*x))] + 6*b^3*E^(2*c)*f^2*Log[1 + E^(2*(c + d*x))] + 12*a^2*b*d^2*e*f*x*Log[1 + E^(2*(c + d*x))] + 12*a^2*b*d^2*e*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 6*a^2*b*d^2*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 6*a^2*b*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] + (6*I)*a*(a^2 - b^2)*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)] - (6*I)*a*(a^2 - b^2)*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)] + 6*a^2*b*d*e*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a^2*b*d*e*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a^2*b*d*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 6*a^2*b*d*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] - (6*I)*a^3*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (6*I)*a*b^2*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (6*I)*a^3*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (6*I)*a*b^2*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (6*I)*a^3*f^2*PolyLog[3, I*E^(c + d*x)] - (6*I)*a*b^2*f^2*PolyLog[3, I*E^(c + d*x)] + (6*I)*a^3*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - (6*I)*a*b^2*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - 3*a^2*b*f^2*PolyLog[3, -E^(2*(c + d*x))] - 3*a^2*b*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))])/((a^2 + b^2)^2*d^3*(1 + E^(2*c))) - (a^2*b*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*(a^2 + b^2)^2*d^3*(-1 + E^(2*c))) + (Csch[c]*Sech[c]*Sech[c + d*x]^2*(6*a^2*b*e*f + 6*b^3*e*f + 12*a^2*b*d^2*e^2*x + 6*a^2*b*f^2*x + 6*b^3*f^2*x + 12*a^2*b*d^2*e*f*x^2 + 4*a^2*b*d^2*f^2*x^3 - 6*a^2*b*e*f*Cosh[2*c] - 6*b^3*e*f*Cosh[2*c] - 6*a^2*b*f^2*x*Cosh[2*c] - 6*b^3*f^2*x*Cosh[2*c] - 6*a^2*b*e*f*Cosh[2*d*x] - 6*b^3*e*f*Cosh[2*d*x] - 6*a^2*b*f^2*x*Cosh[2*d*x] - 6*b^3*f^2*x*Cosh[2*d*x] + 3*a^3*d*e^2*Cosh[c - d*x] + 3*a*b^2*d*e^2*Cosh[c - d*x] + 6*a^3*d*e*f*x*Cosh[c - d*x] + 6*a*b^2*d*e*f*x*Cosh[c - d*x] + 3*a^3*d*f^2*x^2*Cosh[c - d*x] + 3*a*b^2*d*f^2*x^2*Cosh[c - d*x] - 3*a^3*d*e^2*Cosh[3*c + d*x] - 3*a*b^2*d*e^2*Cosh[3*c + d*x] - 6*a^3*d*e*f*x*Cosh[3*c + d*x] - 6*a*b^2*d*e*f*x*Cosh[3*c + d*x] - 3*a^3*d*f^2*x^2*Cosh[3*c + d*x] - 3*a*b^2*d*f^2*x^2*Cosh[3*c + d*x] + 6*a^2*b*e*f*Cosh[2*c + 2*d*x] + 6*b^3*e*f*Cosh[2*c + 2*d*x] + 12*a^2*b*d^2*e^2*x*Cosh[2*c + 2*d*x] + 6*a^2*b*f^2*x*Cosh[2*c + 2*d*x] + 6*b^3*f^2*x*Cosh[2*c + 2*d*x] + 12*a^2*b*d^2*e*f*x^2*Cosh[2*c + 2*d*x] + 4*a^2*b*d^2*f^2*x^3*Cosh[2*c + 2*d*x] - 6*a^2*b*d*e^2*Sinh[2*c] - 6*b^3*d*e^2*Sinh[2*c] - 12*a^2*b*d*e*f*x*Sinh[2*c] - 12*b^3*d*e*f*x*Sinh[2*c] - 6*a^2*b*d*f^2*x^2*Sinh[2*c] - 6*b^3*d*f^2*x^2*Sinh[2*c] - 6*a^3*e*f*Sinh[c - d*x] - 6*a*b^2*e*f*Sinh[c - d*x] - 6*a^3*f^2*x*Sinh[c - d*x] - 6*a*b^2*f^2*x*Sinh[c - d*x] - 6*a^3*e*f*Sinh[3*c + d*x] - 6*a*b^2*e*f*Sinh[3*c + d*x] - 6*a^3*f^2*x*Sinh[3*c + d*x] - 6*a*b^2*f^2*x*Sinh[3*c + d*x]))/(24*(a^2 + b^2)^2*d^2)","B",0
388,1,588,760,8.0625342,"\int \frac{(e+f x) \text{sech}(c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sech[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{a \left(-i f \left(a^2-b^2\right) \text{Li}_2\left(-i e^{c+d x}\right)+i f \left(a^2-b^2\right) \text{Li}_2\left(i e^{c+d x}\right)+2 a^2 d e \tan ^{-1}\left(e^{c+d x}\right)+i a^2 f (c+d x) \log \left(1-i e^{c+d x}\right)-i a^2 f (c+d x) \log \left(1+i e^{c+d x}\right)-2 a^2 c f \tan ^{-1}\left(e^{c+d x}\right)+2 a b d e (c+d x)-2 a b d e \log \left(e^{2 (c+d x)}+1\right)-a b f \text{Li}_2\left(-e^{2 (c+d x)}\right)+a b f (c+d x)^2-2 a b c f (c+d x)+2 a b c f \log \left(e^{2 (c+d x)}+1\right)-2 a b f (c+d x) \log \left(e^{2 (c+d x)}+1\right)-2 b^2 d e \tan ^{-1}\left(e^{c+d x}\right)-i b^2 f (c+d x) \log \left(1-i e^{c+d x}\right)+i b^2 f (c+d x) \log \left(1+i e^{c+d x}\right)+2 b^2 c f \tan ^{-1}\left(e^{c+d x}\right)\right)+2 a^2 b \left(f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-\frac{1}{2} f (c+d x)^2\right)-d \left(a^2+b^2\right) (e+f x) \text{sech}^2(c+d x) (a \sinh (c+d x)+b)+f \left(a^2+b^2\right) \text{sech}(c+d x) (b \sinh (c+d x)-a)}{2 d^2 \left(a^2+b^2\right)^2}","\frac{a^2 b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{a^2 b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{a^2 b f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)^2}-\frac{a^2 f \tanh (c+d x)}{2 b d^2 \left(a^2+b^2\right)}+\frac{a^2 b (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{d \left(a^2+b^2\right)^2}+\frac{a^2 b (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{d \left(a^2+b^2\right)^2}-\frac{a^2 b (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{d \left(a^2+b^2\right)^2}+\frac{a^2 (e+f x) \text{sech}^2(c+d x)}{2 b d \left(a^2+b^2\right)}-\frac{i a^3 f \text{Li}_2\left(-i e^{c+d x}\right)}{2 b^2 d^2 \left(a^2+b^2\right)}-\frac{i a^3 f \text{Li}_2\left(-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{i a^3 f \text{Li}_2\left(i e^{c+d x}\right)}{2 b^2 d^2 \left(a^2+b^2\right)}+\frac{i a^3 f \text{Li}_2\left(i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{a^3 f \text{sech}(c+d x)}{2 b^2 d^2 \left(a^2+b^2\right)}+\frac{a^3 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^2 d \left(a^2+b^2\right)}+\frac{2 a^3 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)^2}+\frac{a^3 (e+f x) \tanh (c+d x) \text{sech}(c+d x)}{2 b^2 d \left(a^2+b^2\right)}+\frac{i a f \text{Li}_2\left(-i e^{c+d x}\right)}{2 b^2 d^2}-\frac{i a f \text{Li}_2\left(i e^{c+d x}\right)}{2 b^2 d^2}-\frac{a f \text{sech}(c+d x)}{2 b^2 d^2}-\frac{a (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^2 d}-\frac{a (e+f x) \tanh (c+d x) \text{sech}(c+d x)}{2 b^2 d}+\frac{f \tanh (c+d x)}{2 b d^2}-\frac{(e+f x) \text{sech}^2(c+d x)}{2 b d}",1,"(2*a^2*b*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + a*(2*a*b*d*e*(c + d*x) - 2*a*b*c*f*(c + d*x) + a*b*f*(c + d*x)^2 + 2*a^2*d*e*ArcTan[E^(c + d*x)] - 2*b^2*d*e*ArcTan[E^(c + d*x)] - 2*a^2*c*f*ArcTan[E^(c + d*x)] + 2*b^2*c*f*ArcTan[E^(c + d*x)] + I*a^2*f*(c + d*x)*Log[1 - I*E^(c + d*x)] - I*b^2*f*(c + d*x)*Log[1 - I*E^(c + d*x)] - I*a^2*f*(c + d*x)*Log[1 + I*E^(c + d*x)] + I*b^2*f*(c + d*x)*Log[1 + I*E^(c + d*x)] - 2*a*b*d*e*Log[1 + E^(2*(c + d*x))] + 2*a*b*c*f*Log[1 + E^(2*(c + d*x))] - 2*a*b*f*(c + d*x)*Log[1 + E^(2*(c + d*x))] - I*(a^2 - b^2)*f*PolyLog[2, (-I)*E^(c + d*x)] + I*(a^2 - b^2)*f*PolyLog[2, I*E^(c + d*x)] - a*b*f*PolyLog[2, -E^(2*(c + d*x))]) - (a^2 + b^2)*d*(e + f*x)*Sech[c + d*x]^2*(b + a*Sinh[c + d*x]) + (a^2 + b^2)*f*Sech[c + d*x]*(-a + b*Sinh[c + d*x]))/(2*(a^2 + b^2)^2*d^2)","A",1
389,1,130,121,0.3251185,"\int \frac{\text{sech}(c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Sech[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{b \left(a^2+b^2\right) \text{sech}^2(c+d x)+a \left(a^2+b^2\right) \tanh (c+d x) \text{sech}(c+d x)+a \left(\left(a^2+b^2\right) \tan ^{-1}(\sinh (c+d x))+a ((b+i a) \log (-\sinh (c+d x)+i)+(b-i a) \log (\sinh (c+d x)+i)-2 b \log (a+b \sinh (c+d x)))\right)}{2 d \left(a^2+b^2\right)^2}","\frac{a^2 b \log (a+b \sinh (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{a \left(a^2-b^2\right) \tan ^{-1}(\sinh (c+d x))}{2 d \left(a^2+b^2\right)^2}-\frac{a^2 b \log (\cosh (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{\text{sech}^2(c+d x) (a \sinh (c+d x)+b)}{2 d \left(a^2+b^2\right)}",1,"-1/2*(a*((a^2 + b^2)*ArcTan[Sinh[c + d*x]] + a*((I*a + b)*Log[I - Sinh[c + d*x]] + ((-I)*a + b)*Log[I + Sinh[c + d*x]] - 2*b*Log[a + b*Sinh[c + d*x]])) + b*(a^2 + b^2)*Sech[c + d*x]^2 + a*(a^2 + b^2)*Sech[c + d*x]*Tanh[c + d*x])/((a^2 + b^2)^2*d)","C",1
390,-1,0,37,180.0024352,"\int \frac{\text{sech}(c+d x) \tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Sech[c + d*x]*Tanh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\tanh ^2(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
391,1,7375,792,25.8705382,"\int \frac{(e+f x)^3 \cosh (c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{a^3 (e+f x)^4}{4 b^4 f}-\frac{6 a^2 f^3 \cosh (c+d x)}{b^3 d^4}+\frac{6 a^2 f^2 (e+f x) \sinh (c+d x)}{b^3 d^3}-\frac{3 a^2 f (e+f x)^2 \cosh (c+d x)}{b^3 d^2}+\frac{a^2 (e+f x)^3 \sinh (c+d x)}{b^3 d}-\frac{6 a^3 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^4}-\frac{6 a^3 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^4}+\frac{6 a^3 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^3}+\frac{6 a^3 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^3}-\frac{3 a^3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{3 a^3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{a^3 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^4 d}-\frac{a^3 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^4 d}+\frac{3 a f^3 \sinh (c+d x) \cosh (c+d x)}{8 b^2 d^4}-\frac{3 a f^2 (e+f x) \sinh ^2(c+d x)}{4 b^2 d^3}+\frac{3 a f (e+f x)^2 \sinh (c+d x) \cosh (c+d x)}{4 b^2 d^2}-\frac{a (e+f x)^3 \sinh ^2(c+d x)}{2 b^2 d}-\frac{3 a f^3 x}{8 b^2 d^3}-\frac{a (e+f x)^3}{4 b^2 d}-\frac{2 f^3 \cosh ^3(c+d x)}{27 b d^4}+\frac{14 f^3 \cosh (c+d x)}{9 b d^4}+\frac{2 f^2 (e+f x) \sinh ^3(c+d x)}{9 b d^3}-\frac{4 f^2 (e+f x) \sinh (c+d x)}{3 b d^3}+\frac{2 f (e+f x)^2 \cosh (c+d x)}{3 b d^2}-\frac{f (e+f x)^2 \sinh ^2(c+d x) \cosh (c+d x)}{3 b d^2}+\frac{(e+f x)^3 \sinh ^3(c+d x)}{3 b d}",1,"Result too large to show","B",0
392,1,3510,578,13.684035,"\int \frac{(e+f x)^2 \cosh (c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{a^3 (e+f x)^3}{3 b^4 f}+\frac{2 a^2 f^2 \sinh (c+d x)}{b^3 d^3}-\frac{2 a^2 f (e+f x) \cosh (c+d x)}{b^3 d^2}+\frac{a^2 (e+f x)^2 \sinh (c+d x)}{b^3 d}+\frac{2 a^3 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^3}+\frac{2 a^3 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^3}-\frac{2 a^3 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{2 a^3 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{a^3 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^4 d}-\frac{a^3 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^4 d}-\frac{a f^2 \sinh ^2(c+d x)}{4 b^2 d^3}+\frac{a f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^2 d^2}-\frac{a (e+f x)^2 \sinh ^2(c+d x)}{2 b^2 d}-\frac{a e f x}{2 b^2 d}-\frac{a f^2 x^2}{4 b^2 d}+\frac{2 f^2 \sinh ^3(c+d x)}{27 b d^3}-\frac{4 f^2 \sinh (c+d x)}{9 b d^3}+\frac{4 f (e+f x) \cosh (c+d x)}{9 b d^2}-\frac{2 f (e+f x) \sinh ^2(c+d x) \cosh (c+d x)}{9 b d^2}+\frac{(e+f x)^2 \sinh ^3(c+d x)}{3 b d}",1,"-1/12*(f^2*(2*a*x^3*(-1 + Coth[c]) - 2*a*x^3*Coth[c] - (6*a*b^2*(d^2*x^2*Log[1 + ((a - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*PolyLog[3, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b]))/(Sqrt[a^2 + b^2]*(-a + Sqrt[a^2 + b^2])*d^3) - (6*a*b^2*(d^2*x^2*Log[1 + ((a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 2*PolyLog[3, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b]))/(Sqrt[a^2 + b^2]*(a + Sqrt[a^2 + b^2])*d^3) + (6*a^2*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - 2*PolyLog[3, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])]))/(Sqrt[a^2 + b^2]*d^3) - (6*a^2*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) + (6*b*Cosh[d*x]*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c]))/d^3 + (6*b*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c])*Sinh[d*x])/d^3))/b^2 + (e^2*((a*Log[a + b*Sinh[c + d*x]])/b^2 - Sinh[c + d*x]/b))/(2*d) - (e*f*(-(b*Cosh[c + d*x]) - a*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + b*d*x*Sinh[c + d*x]))/(b^2*d^2) + (e^2*(-3*a*(2*a^2 + b^2)*Log[a + b*Sinh[c + d*x]] + 3*b*(2*a^2 + b^2)*Sinh[c + d*x] - 3*a*b^2*Sinh[c + d*x]^2 + 2*b^3*Sinh[c + d*x]^3))/(6*b^4*d) + (e*f*(-18*b*(4*a^2 + b^2)*Cosh[c + d*x] - 18*a*b^2*d*x*Cosh[2*(c + d*x)] - 2*b^3*Cosh[3*(c + d*x)] - 36*a*(2*a^2 + b^2)*(-1/2*(c + d*x)^2 + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + (c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - c*Log[a + b*Sinh[c + d*x]] + PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + 18*b*(4*a^2 + b^2)*d*x*Sinh[c + d*x] + 9*a*b^2*Sinh[2*(c + d*x)] + 6*b^3*d*x*Sinh[3*(c + d*x)]))/(36*b^4*d^2) + (f^2*((2*a*(2*a^2 + b^2)*(-1 + Coth[c])*(2*x^3 + (6*a*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - 2*PolyLog[3, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])])*Sinh[c]*(Cosh[c] + Sinh[c]))/(Sqrt[a^2 + b^2]*d^3) - (3*b^2*(d^2*x^2*Log[1 + ((a - Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*PolyLog[3, ((-a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(-a + Sqrt[a^2 + b^2])*d^3) - (3*b^2*(d^2*x^2*Log[1 + ((a + Sqrt[a^2 + b^2])*(Cosh[c + d*x] - Sinh[c + d*x]))/b] - 2*d*x*PolyLog[2, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b] - 2*PolyLog[3, ((a + Sqrt[a^2 + b^2])*(-Cosh[c + d*x] + Sinh[c + d*x]))/b])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*(a + Sqrt[a^2 + b^2])*d^3) - (3*a*(d^2*x^2*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))])*(-1 + Cosh[2*c] + Sinh[2*c]))/(Sqrt[a^2 + b^2]*d^3)))/(3*b^4) + Csch[c]*(Cosh[3*c + 3*d*x]/(108*b^4*d^3) - Sinh[3*c + 3*d*x]/(108*b^4*d^3))*(27*a*b^2*Cosh[d*x] + 54*a*b^2*d*x*Cosh[d*x] + 54*a*b^2*d^2*x^2*Cosh[d*x] - 27*a*b^2*Cosh[2*c + d*x] - 54*a*b^2*d*x*Cosh[2*c + d*x] - 54*a*b^2*d^2*x^2*Cosh[2*c + d*x] + 432*a^2*b*Cosh[c + 2*d*x] + 108*b^3*Cosh[c + 2*d*x] + 432*a^2*b*d*x*Cosh[c + 2*d*x] + 108*b^3*d*x*Cosh[c + 2*d*x] + 216*a^2*b*d^2*x^2*Cosh[c + 2*d*x] + 54*b^3*d^2*x^2*Cosh[c + 2*d*x] - 432*a^2*b*Cosh[3*c + 2*d*x] - 108*b^3*Cosh[3*c + 2*d*x] - 432*a^2*b*d*x*Cosh[3*c + 2*d*x] - 108*b^3*d*x*Cosh[3*c + 2*d*x] - 216*a^2*b*d^2*x^2*Cosh[3*c + 2*d*x] - 54*b^3*d^2*x^2*Cosh[3*c + 2*d*x] - 144*a^3*d^3*x^3*Cosh[2*c + 3*d*x] - 72*a*b^2*d^3*x^3*Cosh[2*c + 3*d*x] - 144*a^3*d^3*x^3*Cosh[4*c + 3*d*x] - 72*a*b^2*d^3*x^3*Cosh[4*c + 3*d*x] - 432*a^2*b*Cosh[3*c + 4*d*x] - 108*b^3*Cosh[3*c + 4*d*x] + 432*a^2*b*d*x*Cosh[3*c + 4*d*x] + 108*b^3*d*x*Cosh[3*c + 4*d*x] - 216*a^2*b*d^2*x^2*Cosh[3*c + 4*d*x] - 54*b^3*d^2*x^2*Cosh[3*c + 4*d*x] + 432*a^2*b*Cosh[5*c + 4*d*x] + 108*b^3*Cosh[5*c + 4*d*x] - 432*a^2*b*d*x*Cosh[5*c + 4*d*x] - 108*b^3*d*x*Cosh[5*c + 4*d*x] + 216*a^2*b*d^2*x^2*Cosh[5*c + 4*d*x] + 54*b^3*d^2*x^2*Cosh[5*c + 4*d*x] + 27*a*b^2*Cosh[4*c + 5*d*x] - 54*a*b^2*d*x*Cosh[4*c + 5*d*x] + 54*a*b^2*d^2*x^2*Cosh[4*c + 5*d*x] - 27*a*b^2*Cosh[6*c + 5*d*x] + 54*a*b^2*d*x*Cosh[6*c + 5*d*x] - 54*a*b^2*d^2*x^2*Cosh[6*c + 5*d*x] - 4*b^3*Cosh[5*c + 6*d*x] + 12*b^3*d*x*Cosh[5*c + 6*d*x] - 18*b^3*d^2*x^2*Cosh[5*c + 6*d*x] + 4*b^3*Cosh[7*c + 6*d*x] - 12*b^3*d*x*Cosh[7*c + 6*d*x] + 18*b^3*d^2*x^2*Cosh[7*c + 6*d*x] - 8*b^3*Sinh[c] - 24*b^3*d*x*Sinh[c] - 36*b^3*d^2*x^2*Sinh[c] + 27*a*b^2*Sinh[d*x] + 54*a*b^2*d*x*Sinh[d*x] + 54*a*b^2*d^2*x^2*Sinh[d*x] - 27*a*b^2*Sinh[2*c + d*x] - 54*a*b^2*d*x*Sinh[2*c + d*x] - 54*a*b^2*d^2*x^2*Sinh[2*c + d*x] + 432*a^2*b*Sinh[c + 2*d*x] + 108*b^3*Sinh[c + 2*d*x] + 432*a^2*b*d*x*Sinh[c + 2*d*x] + 108*b^3*d*x*Sinh[c + 2*d*x] + 216*a^2*b*d^2*x^2*Sinh[c + 2*d*x] + 54*b^3*d^2*x^2*Sinh[c + 2*d*x] - 432*a^2*b*Sinh[3*c + 2*d*x] - 108*b^3*Sinh[3*c + 2*d*x] - 432*a^2*b*d*x*Sinh[3*c + 2*d*x] - 108*b^3*d*x*Sinh[3*c + 2*d*x] - 216*a^2*b*d^2*x^2*Sinh[3*c + 2*d*x] - 54*b^3*d^2*x^2*Sinh[3*c + 2*d*x] - 144*a^3*d^3*x^3*Sinh[2*c + 3*d*x] - 72*a*b^2*d^3*x^3*Sinh[2*c + 3*d*x] - 144*a^3*d^3*x^3*Sinh[4*c + 3*d*x] - 72*a*b^2*d^3*x^3*Sinh[4*c + 3*d*x] - 432*a^2*b*Sinh[3*c + 4*d*x] - 108*b^3*Sinh[3*c + 4*d*x] + 432*a^2*b*d*x*Sinh[3*c + 4*d*x] + 108*b^3*d*x*Sinh[3*c + 4*d*x] - 216*a^2*b*d^2*x^2*Sinh[3*c + 4*d*x] - 54*b^3*d^2*x^2*Sinh[3*c + 4*d*x] + 432*a^2*b*Sinh[5*c + 4*d*x] + 108*b^3*Sinh[5*c + 4*d*x] - 432*a^2*b*d*x*Sinh[5*c + 4*d*x] - 108*b^3*d*x*Sinh[5*c + 4*d*x] + 216*a^2*b*d^2*x^2*Sinh[5*c + 4*d*x] + 54*b^3*d^2*x^2*Sinh[5*c + 4*d*x] + 27*a*b^2*Sinh[4*c + 5*d*x] - 54*a*b^2*d*x*Sinh[4*c + 5*d*x] + 54*a*b^2*d^2*x^2*Sinh[4*c + 5*d*x] - 27*a*b^2*Sinh[6*c + 5*d*x] + 54*a*b^2*d*x*Sinh[6*c + 5*d*x] - 54*a*b^2*d^2*x^2*Sinh[6*c + 5*d*x] - 4*b^3*Sinh[5*c + 6*d*x] + 12*b^3*d*x*Sinh[5*c + 6*d*x] - 18*b^3*d^2*x^2*Sinh[5*c + 6*d*x] + 4*b^3*Sinh[7*c + 6*d*x] - 12*b^3*d*x*Sinh[7*c + 6*d*x] + 18*b^3*d^2*x^2*Sinh[7*c + 6*d*x])))/8","B",0
393,1,447,348,1.499646,"\int \frac{(e+f x) \cosh (c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{72 a^3 d e \log (a+b \sinh (c+d x))-72 a^3 c f \log (a+b \sinh (c+d x))-36 a^3 c^2 f-72 a^3 c d f x-36 a^3 d^2 f x^2-72 a^2 b d e \sinh (c+d x)-72 a^2 b d f x \sinh (c+d x)+72 a^2 b f \cosh (c+d x)+72 a^3 f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+72 a^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+72 a^3 c f \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+72 a^3 d f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+72 a^3 c f \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+72 a^3 d f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+36 a b^2 d e \sinh ^2(c+d x)-9 a b^2 f \sinh (2 (c+d x))+18 a b^2 d f x \cosh (2 (c+d x))-24 b^3 d e \sinh ^3(c+d x)+18 b^3 d f x \sinh (c+d x)-6 b^3 d f x \sinh (3 (c+d x))-18 b^3 f \cosh (c+d x)+2 b^3 f \cosh (3 (c+d x))}{72 b^4 d^2}","\frac{a^3 (e+f x)^2}{2 b^4 f}-\frac{a^2 f \cosh (c+d x)}{b^3 d^2}+\frac{a^2 (e+f x) \sinh (c+d x)}{b^3 d}-\frac{a^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{a^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{a^3 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^4 d}-\frac{a^3 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^4 d}+\frac{a f \sinh (c+d x) \cosh (c+d x)}{4 b^2 d^2}-\frac{a (e+f x) \sinh ^2(c+d x)}{2 b^2 d}-\frac{a f x}{4 b^2 d}-\frac{f \cosh ^3(c+d x)}{9 b d^2}+\frac{f \cosh (c+d x)}{3 b d^2}+\frac{(e+f x) \sinh ^3(c+d x)}{3 b d}",1,"-1/72*(-36*a^3*c^2*f - 72*a^3*c*d*f*x - 36*a^3*d^2*f*x^2 + 72*a^2*b*f*Cosh[c + d*x] - 18*b^3*f*Cosh[c + d*x] + 18*a*b^2*d*f*x*Cosh[2*(c + d*x)] + 2*b^3*f*Cosh[3*(c + d*x)] + 72*a^3*c*f*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 72*a^3*d*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 72*a^3*c*f*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 72*a^3*d*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 72*a^3*d*e*Log[a + b*Sinh[c + d*x]] - 72*a^3*c*f*Log[a + b*Sinh[c + d*x]] + 72*a^3*f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 72*a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 72*a^2*b*d*e*Sinh[c + d*x] - 72*a^2*b*d*f*x*Sinh[c + d*x] + 18*b^3*d*f*x*Sinh[c + d*x] + 36*a*b^2*d*e*Sinh[c + d*x]^2 - 24*b^3*d*e*Sinh[c + d*x]^3 - 9*a*b^2*f*Sinh[2*(c + d*x)] - 6*b^3*d*f*x*Sinh[3*(c + d*x)])/(b^4*d^2)","A",1
394,1,66,76,0.1245554,"\int \frac{\cosh (c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{-6 a^3 \log (a+b \sinh (c+d x))+6 a^2 b \sinh (c+d x)-3 a b^2 \sinh ^2(c+d x)+2 b^3 \sinh ^3(c+d x)}{6 b^4 d}","-\frac{a^3 \log (a+b \sinh (c+d x))}{b^4 d}+\frac{a^2 \sinh (c+d x)}{b^3 d}-\frac{a \sinh ^2(c+d x)}{2 b^2 d}+\frac{\sinh ^3(c+d x)}{3 b d}",1,"(-6*a^3*Log[a + b*Sinh[c + d*x]] + 6*a^2*b*Sinh[c + d*x] - 3*a*b^2*Sinh[c + d*x]^2 + 2*b^3*Sinh[c + d*x]^3)/(6*b^4*d)","A",1
395,-1,0,37,180.0015723,"\int \frac{\cosh (c+d x) \sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]*Sinh[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^3(c+d x) \cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
396,1,7058,1038,26.9441517,"\int \frac{(e+f x)^3 \cosh ^2(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^2*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{(e+f x)^4}{32 b f}+\frac{a^2 (e+f x)^4}{8 b^3 f}+\frac{a^4 (e+f x)^4}{4 b^5 f}-\frac{a \cosh ^3(c+d x) (e+f x)^3}{3 b^2 d}-\frac{a^3 \cosh (c+d x) (e+f x)^3}{b^4 d}-\frac{a^3 \sqrt{a^2+b^2} \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{b^5 d}+\frac{a^3 \sqrt{a^2+b^2} \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{b^5 d}+\frac{a^2 \cosh (c+d x) \sinh (c+d x) (e+f x)^3}{2 b^3 d}+\frac{\sinh (4 c+4 d x) (e+f x)^3}{32 b d}-\frac{3 a^2 f \cosh ^2(c+d x) (e+f x)^2}{4 b^3 d^2}-\frac{3 f \cosh (4 c+4 d x) (e+f x)^2}{128 b d^2}-\frac{3 a^3 \sqrt{a^2+b^2} f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)^2}{b^5 d^2}+\frac{3 a^3 \sqrt{a^2+b^2} f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)^2}{b^5 d^2}+\frac{a f \cosh ^2(c+d x) \sinh (c+d x) (e+f x)^2}{3 b^2 d^2}+\frac{2 a f \sinh (c+d x) (e+f x)^2}{3 b^2 d^2}+\frac{3 a^3 f \sinh (c+d x) (e+f x)^2}{b^4 d^2}-\frac{2 a f^2 \cosh ^3(c+d x) (e+f x)}{9 b^2 d^3}-\frac{4 a f^2 \cosh (c+d x) (e+f x)}{3 b^2 d^3}-\frac{6 a^3 f^2 \cosh (c+d x) (e+f x)}{b^4 d^3}+\frac{6 a^3 \sqrt{a^2+b^2} f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)}{b^5 d^3}-\frac{6 a^3 \sqrt{a^2+b^2} f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)}{b^5 d^3}+\frac{3 a^2 f^2 \cosh (c+d x) \sinh (c+d x) (e+f x)}{4 b^3 d^3}+\frac{3 f^2 \sinh (4 c+4 d x) (e+f x)}{256 b d^3}+\frac{2 a f^3 \sinh ^3(c+d x)}{27 b^2 d^4}+\frac{3 a^2 f^3 x^2}{8 b^3 d^2}-\frac{3 a^2 f^3 \cosh ^2(c+d x)}{8 b^3 d^4}+\frac{3 a^2 e f^2 x}{4 b^3 d^2}-\frac{3 f^3 \cosh (4 c+4 d x)}{1024 b d^4}-\frac{6 a^3 \sqrt{a^2+b^2} f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^5 d^4}+\frac{6 a^3 \sqrt{a^2+b^2} f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^5 d^4}+\frac{14 a f^3 \sinh (c+d x)}{9 b^2 d^4}+\frac{6 a^3 f^3 \sinh (c+d x)}{b^4 d^4}",1,"Result too large to show","C",0
397,1,4653,755,16.2521681,"\int \frac{(e+f x)^2 \cosh ^2(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{a^4 (e+f x)^3}{3 b^5 f}-\frac{2 a^3 f^2 \cosh (c+d x)}{b^4 d^3}+\frac{2 a^3 f (e+f x) \sinh (c+d x)}{b^4 d^2}-\frac{a^3 (e+f x)^2 \cosh (c+d x)}{b^4 d}+\frac{a^2 f^2 \sinh (c+d x) \cosh (c+d x)}{4 b^3 d^3}-\frac{a^2 f (e+f x) \cosh ^2(c+d x)}{2 b^3 d^2}+\frac{a^2 (e+f x)^2 \sinh (c+d x) \cosh (c+d x)}{2 b^3 d}+\frac{a^2 f^2 x}{4 b^3 d^2}+\frac{a^2 (e+f x)^3}{6 b^3 f}+\frac{2 a^3 f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^5 d^3}-\frac{2 a^3 f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^5 d^3}-\frac{2 a^3 f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^5 d^2}+\frac{2 a^3 f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^5 d^2}-\frac{a^3 \sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^5 d}+\frac{a^3 \sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^5 d}-\frac{2 a f^2 \cosh ^3(c+d x)}{27 b^2 d^3}-\frac{4 a f^2 \cosh (c+d x)}{9 b^2 d^3}+\frac{4 a f (e+f x) \sinh (c+d x)}{9 b^2 d^2}+\frac{2 a f (e+f x) \sinh (c+d x) \cosh ^2(c+d x)}{9 b^2 d^2}-\frac{a (e+f x)^2 \cosh ^3(c+d x)}{3 b^2 d}+\frac{f^2 \sinh (4 c+4 d x)}{256 b d^3}-\frac{f (e+f x) \cosh (4 c+4 d x)}{64 b d^2}+\frac{(e+f x)^2 \sinh (4 c+4 d x)}{32 b d}-\frac{(e+f x)^3}{24 b f}",1,"-1/8*(e^2*(c/d + x - (2*a*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d)))/b - (e*f*(x^2 + ((2*I)*a*Pi*ArcTanh[(-b + a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d^2) + (2*a*(2*((-I)*c + ArcCos[((-I)*a)/b])*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ((-2*I)*c + Pi - (2*I)*d*x)*ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (ArcCos[((-I)*a)/b] + (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((I*a + b)*(a + I*(b + Sqrt[-a^2 - b^2]))*(-I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - (ArcCos[((-I)*a)/b] - (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((I*a + b)*(I*a - b + Sqrt[-a^2 - b^2])*(I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(a - I*b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] + (ArcCos[((-I)*a)/b] - (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (2*I)*ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[-(((-1)^(3/4)*Sqrt[-a^2 - b^2]*E^(-1/2*c - (d*x)/2))/(Sqrt[2]*Sqrt[(-I)*b]*Sqrt[a + b*Sinh[c + d*x]]))] + (ArcCos[((-I)*a)/b] + (2*I)*(ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]]))*Log[((-1)^(1/4)*Sqrt[-a^2 - b^2]*E^((c + d*x)/2))/(Sqrt[2]*Sqrt[(-I)*b]*Sqrt[a + b*Sinh[c + d*x]])] + I*(PolyLog[2, ((I*a + Sqrt[-a^2 - b^2])*(I*a + b - I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - PolyLog[2, ((a + I*Sqrt[-a^2 - b^2])*(-a + I*b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))])))/(Sqrt[-a^2 - b^2]*d^2)))/(8*b) - (f^2*(x^3 - (3*a*(d^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3)))/(24*b) - (f^2*(2*(4*a^2 + b^2)*x^3 - (6*a*(4*a^2 + 3*b^2)*(d^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*x*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(Sqrt[a^2 + b^2]*d^3) - (24*a*b*Cosh[d*x]*((2 + d^2*x^2)*Cosh[c] - 2*d*x*Sinh[c]))/d^3 + (3*b^2*Cosh[2*d*x]*(-2*d*x*Cosh[2*c] + (1 + 2*d^2*x^2)*Sinh[2*c]))/d^3 - (24*a*b*(-2*d*x*Cosh[c] + (2 + d^2*x^2)*Sinh[c])*Sinh[d*x])/d^3 + (3*b^2*((1 + 2*d^2*x^2)*Cosh[2*c] - 2*d*x*Sinh[2*c])*Sinh[2*d*x])/d^3))/(96*b^3) - (e^2*((4*a^2 + b^2)*(c + d*x) - (2*a*(4*a^2 + 3*b^2)*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[c + d*x] + b^2*Sinh[2*(c + d*x)]))/(16*b^3*d) - (e*f*((4*a^2 + b^2)*(-c + d*x)*(c + d*x) - 8*a*b*d*x*Cosh[c + d*x] - b^2*Cosh[2*(c + d*x)] - (2*a*(4*a^2 + 3*b^2)*(2*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + (c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - (c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] + 8*a*b*Sinh[c + d*x] + 2*b^2*d*x*Sinh[2*(c + d*x)]))/(16*b^3*d^2) + (e^2*(6*(16*a^4 + 12*a^2*b^2 + b^4)*(c + d*x) - (12*a*(16*a^4 + 20*a^2*b^2 + 5*b^4)*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 48*a*b*(2*a^2 + b^2)*Cosh[c + d*x] - 8*a*b^3*Cosh[3*(c + d*x)] + 6*b^2*(4*a^2 + b^2)*Sinh[2*(c + d*x)] + 3*b^4*Sinh[4*(c + d*x)]))/(96*b^5*d) + (e*f*(-576*a^4*Sqrt[a^2 + b^2]*c^2 - 432*a^2*b^2*Sqrt[a^2 + b^2]*c^2 - 36*b^4*Sqrt[a^2 + b^2]*c^2 + 576*a^4*Sqrt[a^2 + b^2]*d^2*x^2 + 432*a^2*b^2*Sqrt[a^2 + b^2]*d^2*x^2 + 36*b^4*Sqrt[a^2 + b^2]*d^2*x^2 - 2304*a^5*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] - 2880*a^3*b^2*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] - 720*a*b^4*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] - 1152*a^3*b*Sqrt[a^2 + b^2]*d*x*Cosh[c + d*x] - 576*a*b^3*Sqrt[a^2 + b^2]*d*x*Cosh[c + d*x] - 144*a^2*b^2*Sqrt[a^2 + b^2]*Cosh[2*(c + d*x)] - 36*b^4*Sqrt[a^2 + b^2]*Cosh[2*(c + d*x)] - 96*a*b^3*Sqrt[a^2 + b^2]*d*x*Cosh[3*(c + d*x)] - 9*b^4*Sqrt[a^2 + b^2]*Cosh[4*(c + d*x)] - 1152*a^5*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 1440*a^3*b^2*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 360*a*b^4*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 1152*a^5*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 1440*a^3*b^2*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 360*a*b^4*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + 1152*a^5*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 1440*a^3*b^2*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 360*a*b^4*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 1152*a^5*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 1440*a^3*b^2*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 360*a*b^4*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] - 72*a*(16*a^4 + 20*a^2*b^2 + 5*b^4)*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] + 72*a*(16*a^4 + 20*a^2*b^2 + 5*b^4)*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] + 1152*a^3*b*Sqrt[a^2 + b^2]*Sinh[c + d*x] + 576*a*b^3*Sqrt[a^2 + b^2]*Sinh[c + d*x] + 288*a^2*b^2*Sqrt[a^2 + b^2]*d*x*Sinh[2*(c + d*x)] + 72*b^4*Sqrt[a^2 + b^2]*d*x*Sinh[2*(c + d*x)] + 32*a*b^3*Sqrt[a^2 + b^2]*Sinh[3*(c + d*x)] + 36*b^4*Sqrt[a^2 + b^2]*d*x*Sinh[4*(c + d*x)]))/(576*b^5*Sqrt[a^2 + b^2]*d^2) + (f^2*((16*a^4*x^3)/(3*b^5) + (4*a^2*x^3)/b^3 + x^3/(3*b) - (32*a^3*Cosh[c + d*x])/(b^4*d^3) - (16*a*Cosh[c + d*x])/(b^2*d^3) - (16*a^3*x^2*Cosh[c + d*x])/(b^4*d) - (8*a*x^2*Cosh[c + d*x])/(b^2*d) - (4*a^2*x*Cosh[2*(c + d*x)])/(b^3*d^2) - (x*Cosh[2*(c + d*x)])/(b*d^2) - (8*a*Cosh[3*(c + d*x)])/(27*b^2*d^3) - (4*a*x^2*Cosh[3*(c + d*x)])/(3*b^2*d) - (x*Cosh[4*(c + d*x)])/(4*b*d^2) - (16*a^5*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^5*Sqrt[a^2 + b^2]*d) - (20*a^3*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*Sqrt[a^2 + b^2]*d) - (5*a*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d) + (16*a^5*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^5*Sqrt[a^2 + b^2]*d) + (20*a^3*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*Sqrt[a^2 + b^2]*d) + (5*a*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d) - (2*(16*a^5 + 20*a^3*b^2 + 5*a*b^4)*x*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])])/(b^5*Sqrt[a^2 + b^2]*d^2) + (2*(16*a^5 + 20*a^3*b^2 + 5*a*b^4)*x*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*Sqrt[a^2 + b^2]*d^2) + (32*a^5*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])])/(b^5*Sqrt[a^2 + b^2]*d^3) + (40*a^3*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])])/(b^3*Sqrt[a^2 + b^2]*d^3) + (10*a*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d^3) - (32*a^5*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*Sqrt[a^2 + b^2]*d^3) - (40*a^3*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^3) - (10*a*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3) + (32*a^3*x*Sinh[c + d*x])/(b^4*d^2) + (16*a*x*Sinh[c + d*x])/(b^2*d^2) + (2*a^2*Sinh[2*(c + d*x)])/(b^3*d^3) + Sinh[2*(c + d*x)]/(2*b*d^3) + (4*a^2*x^2*Sinh[2*(c + d*x)])/(b^3*d) + (x^2*Sinh[2*(c + d*x)])/(b*d) + (8*a*x*Sinh[3*(c + d*x)])/(9*b^2*d^2) + Sinh[4*(c + d*x)]/(16*b*d^3) + (x^2*Sinh[4*(c + d*x)])/(2*b*d)))/16","C",0
398,1,2917,474,10.3531433,"\int \frac{(e+f x) \cosh ^2(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{a^4 e x}{b^5}+\frac{a^4 f x^2}{2 b^5}+\frac{a^3 f \sinh (c+d x)}{b^4 d^2}-\frac{a^3 (e+f x) \cosh (c+d x)}{b^4 d}-\frac{a^2 f \cosh ^2(c+d x)}{4 b^3 d^2}+\frac{a^2 (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^3 d}+\frac{a^2 e x}{2 b^3}+\frac{a^2 f x^2}{4 b^3}-\frac{a^3 f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^5 d^2}+\frac{a^3 f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^5 d^2}-\frac{a^3 \sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^5 d}+\frac{a^3 \sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^5 d}+\frac{a f \sinh ^3(c+d x)}{9 b^2 d^2}+\frac{a f \sinh (c+d x)}{3 b^2 d^2}-\frac{a (e+f x) \cosh ^3(c+d x)}{3 b^2 d}-\frac{f \cosh (4 c+4 d x)}{128 b d^2}+\frac{(e+f x) \sinh (4 c+4 d x)}{32 b d}-\frac{(e+f x)^2}{16 b f}",1,"-1/8*(e*(c/d + x - (2*a*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(Sqrt[-a^2 - b^2]*d)))/b - (f*(x^2 + ((2*I)*a*Pi*ArcTanh[(-b + a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(Sqrt[a^2 + b^2]*d^2) + (2*a*(2*((-I)*c + ArcCos[((-I)*a)/b])*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ((-2*I)*c + Pi - (2*I)*d*x)*ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (ArcCos[((-I)*a)/b] + (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((I*a + b)*(a + I*(b + Sqrt[-a^2 - b^2]))*(-I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - (ArcCos[((-I)*a)/b] - (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[((I*a + b)*(I*a - b + Sqrt[-a^2 - b^2])*(I + Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(a - I*b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] + (ArcCos[((-I)*a)/b] - (2*I)*ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] - (2*I)*ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]])*Log[-(((-1)^(3/4)*Sqrt[-a^2 - b^2]*E^(-1/2*c - (d*x)/2))/(Sqrt[2]*Sqrt[(-I)*b]*Sqrt[a + b*Sinh[c + d*x]]))] + (ArcCos[((-I)*a)/b] + (2*I)*(ArcTanh[((a + I*b)*Cot[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]] + ArcTanh[((a - I*b)*Tan[((2*I)*c + Pi + (2*I)*d*x)/4])/Sqrt[-a^2 - b^2]]))*Log[((-1)^(1/4)*Sqrt[-a^2 - b^2]*E^((c + d*x)/2))/(Sqrt[2]*Sqrt[(-I)*b]*Sqrt[a + b*Sinh[c + d*x]])] + I*(PolyLog[2, ((I*a + Sqrt[-a^2 - b^2])*(I*a + b - I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))] - PolyLog[2, ((a + I*Sqrt[-a^2 - b^2])*(-a + I*b + Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))/(b*(I*a + b + I*Sqrt[-a^2 - b^2]*Cot[((2*I)*c + Pi + (2*I)*d*x)/4]))])))/(Sqrt[-a^2 - b^2]*d^2)))/(16*b) - (e*((4*a^2 + b^2)*(c + d*x) - (2*a*(4*a^2 + 3*b^2)*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 4*a*b*Cosh[c + d*x] + b^2*Sinh[2*(c + d*x)]))/(16*b^3*d) - (f*((4*a^2 + b^2)*(-c + d*x)*(c + d*x) - 8*a*b*d*x*Cosh[c + d*x] - b^2*Cosh[2*(c + d*x)] - (2*a*(4*a^2 + 3*b^2)*(2*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + (c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - (c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/Sqrt[a^2 + b^2] + 8*a*b*Sinh[c + d*x] + 2*b^2*d*x*Sinh[2*(c + d*x)]))/(32*b^3*d^2) + (e*(6*(16*a^4 + 12*a^2*b^2 + b^4)*(c + d*x) - (12*a*(16*a^4 + 20*a^2*b^2 + 5*b^4)*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/Sqrt[-a^2 - b^2] - 48*a*b*(2*a^2 + b^2)*Cosh[c + d*x] - 8*a*b^3*Cosh[3*(c + d*x)] + 6*b^2*(4*a^2 + b^2)*Sinh[2*(c + d*x)] + 3*b^4*Sinh[4*(c + d*x)]))/(96*b^5*d) + (f*(-576*a^4*Sqrt[a^2 + b^2]*c^2 - 432*a^2*b^2*Sqrt[a^2 + b^2]*c^2 - 36*b^4*Sqrt[a^2 + b^2]*c^2 + 576*a^4*Sqrt[a^2 + b^2]*d^2*x^2 + 432*a^2*b^2*Sqrt[a^2 + b^2]*d^2*x^2 + 36*b^4*Sqrt[a^2 + b^2]*d^2*x^2 - 2304*a^5*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] - 2880*a^3*b^2*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] - 720*a*b^4*c*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] - 1152*a^3*b*Sqrt[a^2 + b^2]*d*x*Cosh[c + d*x] - 576*a*b^3*Sqrt[a^2 + b^2]*d*x*Cosh[c + d*x] - 144*a^2*b^2*Sqrt[a^2 + b^2]*Cosh[2*(c + d*x)] - 36*b^4*Sqrt[a^2 + b^2]*Cosh[2*(c + d*x)] - 96*a*b^3*Sqrt[a^2 + b^2]*d*x*Cosh[3*(c + d*x)] - 9*b^4*Sqrt[a^2 + b^2]*Cosh[4*(c + d*x)] - 1152*a^5*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 1440*a^3*b^2*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 360*a*b^4*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 1152*a^5*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 1440*a^3*b^2*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - 360*a*b^4*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + 1152*a^5*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 1440*a^3*b^2*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 360*a*b^4*c*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 1152*a^5*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 1440*a^3*b^2*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + 360*a*b^4*d*x*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] - 72*a*(16*a^4 + 20*a^2*b^2 + 5*b^4)*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] + 72*a*(16*a^4 + 20*a^2*b^2 + 5*b^4)*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))] + 1152*a^3*b*Sqrt[a^2 + b^2]*Sinh[c + d*x] + 576*a*b^3*Sqrt[a^2 + b^2]*Sinh[c + d*x] + 288*a^2*b^2*Sqrt[a^2 + b^2]*d*x*Sinh[2*(c + d*x)] + 72*b^4*Sqrt[a^2 + b^2]*d*x*Sinh[2*(c + d*x)] + 32*a*b^3*Sqrt[a^2 + b^2]*Sinh[3*(c + d*x)] + 36*b^4*Sqrt[a^2 + b^2]*d*x*Sinh[4*(c + d*x)]))/(1152*b^5*Sqrt[a^2 + b^2]*d^2)","C",0
399,1,153,184,1.8104352,"\int \frac{\cosh ^2(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]^2*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{-24 a b \left(4 a^2+b^2\right) \cosh (c+d x)+3 \left(8 a^2 b^2 \sinh (2 (c+d x))+4 \left(8 a^4+4 a^2 b^2-b^4\right) (c+d x)+64 a^3 \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)+b^4 \sinh (4 (c+d x))\right)-8 a b^3 \cosh (3 (c+d x))}{96 b^5 d}","-\frac{a \left(3 a^2+b^2\right) \cosh (c+d x)}{3 b^4 d}+\frac{\left(4 a^2+b^2\right) \sinh (c+d x) \cosh (c+d x)}{8 b^3 d}+\frac{x \left(8 a^4+4 a^2 b^2-b^4\right)}{8 b^5}+\frac{2 a^3 \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b^5 d}-\frac{a \sinh ^2(c+d x) \cosh (c+d x)}{3 b^2 d}+\frac{\sinh ^3(c+d x) \cosh (c+d x)}{4 b d}",1,"(-24*a*b*(4*a^2 + b^2)*Cosh[c + d*x] - 8*a*b^3*Cosh[3*(c + d*x)] + 3*(4*(8*a^4 + 4*a^2*b^2 - b^4)*(c + d*x) + 64*a^3*Sqrt[-a^2 - b^2]*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] + 8*a^2*b^2*Sinh[2*(c + d*x)] + b^4*Sinh[4*(c + d*x)]))/(96*b^5*d)","A",1
400,-1,0,39,180.0014142,"\int \frac{\cosh ^2(c+d x) \sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]^2*Sinh[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^3(c+d x) \cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
401,1,5157,1443,18.2037761,"\int \frac{(e+f x)^3 \cosh ^3(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^3*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{6 f^3 \cosh (c+d x) a^4}{b^5 d^4}-\frac{3 f (e+f x)^2 \cosh (c+d x) a^4}{b^5 d^2}+\frac{(e+f x)^3 \sinh (c+d x) a^4}{b^5 d}+\frac{6 f^2 (e+f x) \sinh (c+d x) a^4}{b^5 d^3}+\frac{\left(a^2+b^2\right) (e+f x)^4 a^3}{4 b^6 f}-\frac{(e+f x)^3 a^3}{4 b^4 d}-\frac{(e+f x)^3 \sinh ^2(c+d x) a^3}{2 b^4 d}-\frac{3 f^2 (e+f x) \sinh ^2(c+d x) a^3}{4 b^4 d^3}-\frac{3 f^3 x a^3}{8 b^4 d^3}-\frac{\left(a^2+b^2\right) (e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^3}{b^6 d}-\frac{\left(a^2+b^2\right) (e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^3}{b^6 d}-\frac{3 \left(a^2+b^2\right) f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b^6 d^2}-\frac{3 \left(a^2+b^2\right) f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b^6 d^2}+\frac{6 \left(a^2+b^2\right) f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b^6 d^3}+\frac{6 \left(a^2+b^2\right) f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b^6 d^3}-\frac{6 \left(a^2+b^2\right) f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b^6 d^4}-\frac{6 \left(a^2+b^2\right) f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b^6 d^4}+\frac{3 f^3 \cosh (c+d x) \sinh (c+d x) a^3}{8 b^4 d^4}+\frac{3 f (e+f x)^2 \cosh (c+d x) \sinh (c+d x) a^3}{4 b^4 d^2}-\frac{2 f^3 \cosh ^3(c+d x) a^2}{27 b^3 d^4}-\frac{f (e+f x)^2 \cosh ^3(c+d x) a^2}{3 b^3 d^2}-\frac{40 f^3 \cosh (c+d x) a^2}{9 b^3 d^4}-\frac{2 f (e+f x)^2 \cosh (c+d x) a^2}{b^3 d^2}+\frac{2 (e+f x)^3 \sinh (c+d x) a^2}{3 b^3 d}+\frac{(e+f x)^3 \cosh ^2(c+d x) \sinh (c+d x) a^2}{3 b^3 d}+\frac{2 f^2 (e+f x) \cosh ^2(c+d x) \sinh (c+d x) a^2}{9 b^3 d^3}+\frac{40 f^2 (e+f x) \sinh (c+d x) a^2}{9 b^3 d^3}-\frac{(e+f x)^3 \cosh ^4(c+d x) a}{4 b^2 d}-\frac{3 f^2 (e+f x) \cosh ^4(c+d x) a}{32 b^2 d^3}+\frac{3 (e+f x)^3 a}{32 b^2 d}-\frac{9 f^2 (e+f x) \cosh ^2(c+d x) a}{32 b^2 d^3}+\frac{45 f^3 x a}{256 b^2 d^3}+\frac{3 f^3 \cosh ^3(c+d x) \sinh (c+d x) a}{128 b^2 d^4}+\frac{3 f (e+f x)^2 \cosh ^3(c+d x) \sinh (c+d x) a}{16 b^2 d^2}+\frac{45 f^3 \cosh (c+d x) \sinh (c+d x) a}{256 b^2 d^4}+\frac{9 f (e+f x)^2 \cosh (c+d x) \sinh (c+d x) a}{32 b^2 d^2}+\frac{3 f^3 \cosh (c+d x)}{4 b d^4}+\frac{3 f (e+f x)^2 \cosh (c+d x)}{8 b d^2}-\frac{f^3 \cosh (3 c+3 d x)}{216 b d^4}-\frac{f (e+f x)^2 \cosh (3 c+3 d x)}{48 b d^2}-\frac{3 f^3 \cosh (5 c+5 d x)}{5000 b d^4}-\frac{3 f (e+f x)^2 \cosh (5 c+5 d x)}{400 b d^2}-\frac{(e+f x)^3 \sinh (c+d x)}{8 b d}-\frac{3 f^2 (e+f x) \sinh (c+d x)}{4 b d^3}+\frac{(e+f x)^3 \sinh (3 c+3 d x)}{48 b d}+\frac{f^2 (e+f x) \sinh (3 c+3 d x)}{72 b d^3}+\frac{(e+f x)^3 \sinh (5 c+5 d x)}{80 b d}+\frac{3 f^2 (e+f x) \sinh (5 c+5 d x)}{1000 b d^3}",1,"Result too large to show","B",0
402,1,1545,1049,9.9458089,"\int \frac{(e+f x)^2 \cosh ^3(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^3*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{1}{8} \left(-\frac{8 \left(a^2+b^2\right) f^2 x^3 \coth (c) a^3}{3 b^6}-\frac{8 \left(a^2+b^2\right) e f x^2 \coth (c) a^3}{b^6}-\frac{8 \left(a^2+b^2\right) e^2 x \coth (c) a^3}{b^6}+\frac{8 \left(a^2+b^2\right) \left(2 e^{2 c} f^2 x^3 d^3+6 e e^{2 c} f x^2 d^3+6 e^2 e^{2 c} x d^3-3 e^2 e^{2 c} \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2+3 e^2 \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right) a^3}{3 b^6 d^3 \left(-1+e^{2 c}\right)}+\frac{\left(2 a^2+b^2\right) \left(f^2+2 d (e+f x) f+2 d^2 (e+f x)^2\right) (\sinh (2 (c+d x))-\cosh (2 (c+d x))) a}{4 b^4 d^3}-\frac{\left(2 a^2+b^2\right) \left(f^2-2 d (e+f x) f+2 d^2 (e+f x)^2\right) (\cosh (2 (c+d x))+\sinh (2 (c+d x))) a}{4 b^4 d^3}+\frac{\left(f^2+4 d (e+f x) f+8 d^2 (e+f x)^2\right) (\sinh (4 (c+d x))-\cosh (4 (c+d x))) a}{64 b^2 d^3}-\frac{\left(f^2-4 d (e+f x) f+8 d^2 (e+f x)^2\right) (\cosh (4 (c+d x))+\sinh (4 (c+d x))) a}{64 b^2 d^3}+\frac{\left(-8 a^4-6 b^2 a^2+b^4\right) \left(2 f^2+2 d (e+f x) f+d^2 (e+f x)^2\right) (\cosh (c+d x)-\sinh (c+d x))}{2 b^5 d^3}+\frac{\left(8 a^4+6 b^2 a^2-b^4\right) \left(2 f^2-2 d (e+f x) f+d^2 (e+f x)^2\right) (\cosh (c+d x)+\sinh (c+d x))}{2 b^5 d^3}+\frac{\left(4 a^2+b^2\right) \left(2 f^2+6 d (e+f x) f+9 d^2 (e+f x)^2\right) (\sinh (3 (c+d x))-\cosh (3 (c+d x)))}{108 b^3 d^3}+\frac{\left(4 a^2+b^2\right) \left(2 f^2-6 d (e+f x) f+9 d^2 (e+f x)^2\right) (\cosh (3 (c+d x))+\sinh (3 (c+d x)))}{108 b^3 d^3}+\frac{\left(2 f^2+10 d (e+f x) f+25 d^2 (e+f x)^2\right) (\sinh (5 (c+d x))-\cosh (5 (c+d x)))}{500 b d^3}+\frac{\left(2 f^2-10 d (e+f x) f+25 d^2 (e+f x)^2\right) (\cosh (5 (c+d x))+\sinh (5 (c+d x)))}{500 b d^3}\right)","-\frac{2 f (e+f x) \cosh (c+d x) a^4}{b^5 d^2}+\frac{2 f^2 \sinh (c+d x) a^4}{b^5 d^3}+\frac{(e+f x)^2 \sinh (c+d x) a^4}{b^5 d}+\frac{\left(a^2+b^2\right) (e+f x)^3 a^3}{3 b^6 f}-\frac{f^2 x^2 a^3}{4 b^4 d}-\frac{f^2 \sinh ^2(c+d x) a^3}{4 b^4 d^3}-\frac{(e+f x)^2 \sinh ^2(c+d x) a^3}{2 b^4 d}-\frac{e f x a^3}{2 b^4 d}-\frac{\left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^3}{b^6 d}-\frac{\left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^3}{b^6 d}-\frac{2 \left(a^2+b^2\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b^6 d^2}-\frac{2 \left(a^2+b^2\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b^6 d^2}+\frac{2 \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b^6 d^3}+\frac{2 \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b^6 d^3}+\frac{f (e+f x) \cosh (c+d x) \sinh (c+d x) a^3}{2 b^4 d^2}-\frac{2 f (e+f x) \cosh ^3(c+d x) a^2}{9 b^3 d^2}+\frac{2 f^2 \sinh ^3(c+d x) a^2}{27 b^3 d^3}-\frac{4 f (e+f x) \cosh (c+d x) a^2}{3 b^3 d^2}+\frac{14 f^2 \sinh (c+d x) a^2}{9 b^3 d^3}+\frac{2 (e+f x)^2 \sinh (c+d x) a^2}{3 b^3 d}+\frac{(e+f x)^2 \cosh ^2(c+d x) \sinh (c+d x) a^2}{3 b^3 d}-\frac{f^2 \cosh ^4(c+d x) a}{32 b^2 d^3}-\frac{(e+f x)^2 \cosh ^4(c+d x) a}{4 b^2 d}+\frac{3 f^2 x^2 a}{32 b^2 d}-\frac{3 f^2 \cosh ^2(c+d x) a}{32 b^2 d^3}+\frac{3 e f x a}{16 b^2 d}+\frac{f (e+f x) \cosh ^3(c+d x) \sinh (c+d x) a}{8 b^2 d^2}+\frac{3 f (e+f x) \cosh (c+d x) \sinh (c+d x) a}{16 b^2 d^2}+\frac{f (e+f x) \cosh (c+d x)}{4 b d^2}-\frac{f (e+f x) \cosh (3 c+3 d x)}{72 b d^2}-\frac{f (e+f x) \cosh (5 c+5 d x)}{200 b d^2}-\frac{f^2 \sinh (c+d x)}{4 b d^3}-\frac{(e+f x)^2 \sinh (c+d x)}{8 b d}+\frac{f^2 \sinh (3 c+3 d x)}{216 b d^3}+\frac{(e+f x)^2 \sinh (3 c+3 d x)}{48 b d}+\frac{f^2 \sinh (5 c+5 d x)}{1000 b d^3}+\frac{(e+f x)^2 \sinh (5 c+5 d x)}{80 b d}",1,"((-8*a^3*(a^2 + b^2)*e^2*x*Coth[c])/b^6 - (8*a^3*(a^2 + b^2)*e*f*x^2*Coth[c])/b^6 - (8*a^3*(a^2 + b^2)*f^2*x^3*Coth[c])/(3*b^6) + (8*a^3*(a^2 + b^2)*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*b^6*d^3*(-1 + E^(2*c))) + ((-8*a^4 - 6*a^2*b^2 + b^4)*(2*f^2 + 2*d*f*(e + f*x) + d^2*(e + f*x)^2)*(Cosh[c + d*x] - Sinh[c + d*x]))/(2*b^5*d^3) + ((8*a^4 + 6*a^2*b^2 - b^4)*(2*f^2 - 2*d*f*(e + f*x) + d^2*(e + f*x)^2)*(Cosh[c + d*x] + Sinh[c + d*x]))/(2*b^5*d^3) + (a*(2*a^2 + b^2)*(f^2 + 2*d*f*(e + f*x) + 2*d^2*(e + f*x)^2)*(-Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]))/(4*b^4*d^3) - (a*(2*a^2 + b^2)*(f^2 - 2*d*f*(e + f*x) + 2*d^2*(e + f*x)^2)*(Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]))/(4*b^4*d^3) + ((4*a^2 + b^2)*(2*f^2 + 6*d*f*(e + f*x) + 9*d^2*(e + f*x)^2)*(-Cosh[3*(c + d*x)] + Sinh[3*(c + d*x)]))/(108*b^3*d^3) + ((4*a^2 + b^2)*(2*f^2 - 6*d*f*(e + f*x) + 9*d^2*(e + f*x)^2)*(Cosh[3*(c + d*x)] + Sinh[3*(c + d*x)]))/(108*b^3*d^3) + (a*(f^2 + 4*d*f*(e + f*x) + 8*d^2*(e + f*x)^2)*(-Cosh[4*(c + d*x)] + Sinh[4*(c + d*x)]))/(64*b^2*d^3) - (a*(f^2 - 4*d*f*(e + f*x) + 8*d^2*(e + f*x)^2)*(Cosh[4*(c + d*x)] + Sinh[4*(c + d*x)]))/(64*b^2*d^3) + ((2*f^2 + 10*d*f*(e + f*x) + 25*d^2*(e + f*x)^2)*(-Cosh[5*(c + d*x)] + Sinh[5*(c + d*x)]))/(500*b*d^3) + ((2*f^2 - 10*d*f*(e + f*x) + 25*d^2*(e + f*x)^2)*(Cosh[5*(c + d*x)] + Sinh[5*(c + d*x)]))/(500*b*d^3))/8","A",1
403,1,958,641,4.1130984,"\int \frac{(e+f x) \cosh ^3(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^3*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{-14400 d^2 f x^2 a^5-14400 c^2 f a^5-28800 c d f x a^5+28800 c f \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^5+28800 d f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^5+28800 c f \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^5+28800 d f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^5+28800 d e \log (a+b \sinh (c+d x)) a^5-28800 c f \log (a+b \sinh (c+d x)) a^5+28800 b f \cosh (c+d x) a^4-28800 b d e \sinh (c+d x) a^4-28800 b d f x \sinh (c+d x) a^4-14400 b^2 d^2 f x^2 a^3-14400 b^2 c^2 f a^3-28800 b^2 c d f x a^3+7200 b^2 d e \cosh (2 (c+d x)) a^3+7200 b^2 d f x \cosh (2 (c+d x)) a^3+28800 b^2 c f \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^3+28800 b^2 d f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^3+28800 b^2 c f \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^3+28800 b^2 d f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^3+28800 b^2 d e \log (a+b \sinh (c+d x)) a^3-28800 b^2 c f \log (a+b \sinh (c+d x)) a^3+28800 \left(a^2+b^2\right) f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) a^3+28800 \left(a^2+b^2\right) f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3-3600 b^2 f \sinh (2 (c+d x)) a^3+21600 b^3 f \cosh (c+d x) a^2+800 b^3 f \cosh (3 (c+d x)) a^2-21600 b^3 d e \sinh (c+d x) a^2-21600 b^3 d f x \sinh (c+d x) a^2-2400 b^3 d e \sinh (3 (c+d x)) a^2-2400 b^3 d f x \sinh (3 (c+d x)) a^2+3600 b^4 d e \cosh (2 (c+d x)) a+3600 b^4 d f x \cosh (2 (c+d x)) a+900 b^4 d e \cosh (4 (c+d x)) a+900 b^4 d f x \cosh (4 (c+d x)) a-1800 b^4 f \sinh (2 (c+d x)) a-225 b^4 f \sinh (4 (c+d x)) a-3600 b^5 f \cosh (c+d x)+200 b^5 f \cosh (3 (c+d x))+72 b^5 f \cosh (5 (c+d x))+3600 b^5 d e \sinh (c+d x)+3600 b^5 d f x \sinh (c+d x)-600 b^5 d e \sinh (3 (c+d x))-600 b^5 d f x \sinh (3 (c+d x))-360 b^5 d e \sinh (5 (c+d x))-360 b^5 d f x \sinh (5 (c+d x))}{28800 b^6 d^2}","-\frac{a^4 f \cosh (c+d x)}{b^5 d^2}+\frac{a^4 (e+f x) \sinh (c+d x)}{b^5 d}+\frac{a^3 f \sinh (c+d x) \cosh (c+d x)}{4 b^4 d^2}-\frac{a^3 (e+f x) \sinh ^2(c+d x)}{2 b^4 d}-\frac{a^3 f x}{4 b^4 d}-\frac{a^2 f \cosh ^3(c+d x)}{9 b^3 d^2}-\frac{2 a^2 f \cosh (c+d x)}{3 b^3 d^2}+\frac{2 a^2 (e+f x) \sinh (c+d x)}{3 b^3 d}+\frac{a^2 (e+f x) \sinh (c+d x) \cosh ^2(c+d x)}{3 b^3 d}-\frac{a^3 f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^6 d^2}-\frac{a^3 f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^6 d^2}-\frac{a^3 \left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^6 d}-\frac{a^3 \left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^6 d}+\frac{a^3 \left(a^2+b^2\right) (e+f x)^2}{2 b^6 f}+\frac{a f \sinh (c+d x) \cosh ^3(c+d x)}{16 b^2 d^2}+\frac{3 a f \sinh (c+d x) \cosh (c+d x)}{32 b^2 d^2}-\frac{a (e+f x) \cosh ^4(c+d x)}{4 b^2 d}+\frac{3 a f x}{32 b^2 d}+\frac{f \cosh (c+d x)}{8 b d^2}-\frac{f \cosh (3 c+3 d x)}{144 b d^2}-\frac{f \cosh (5 c+5 d x)}{400 b d^2}-\frac{(e+f x) \sinh (c+d x)}{8 b d}+\frac{(e+f x) \sinh (3 c+3 d x)}{48 b d}+\frac{(e+f x) \sinh (5 c+5 d x)}{80 b d}",1,"-1/28800*(-14400*a^5*c^2*f - 14400*a^3*b^2*c^2*f - 28800*a^5*c*d*f*x - 28800*a^3*b^2*c*d*f*x - 14400*a^5*d^2*f*x^2 - 14400*a^3*b^2*d^2*f*x^2 + 28800*a^4*b*f*Cosh[c + d*x] + 21600*a^2*b^3*f*Cosh[c + d*x] - 3600*b^5*f*Cosh[c + d*x] + 7200*a^3*b^2*d*e*Cosh[2*(c + d*x)] + 3600*a*b^4*d*e*Cosh[2*(c + d*x)] + 7200*a^3*b^2*d*f*x*Cosh[2*(c + d*x)] + 3600*a*b^4*d*f*x*Cosh[2*(c + d*x)] + 800*a^2*b^3*f*Cosh[3*(c + d*x)] + 200*b^5*f*Cosh[3*(c + d*x)] + 900*a*b^4*d*e*Cosh[4*(c + d*x)] + 900*a*b^4*d*f*x*Cosh[4*(c + d*x)] + 72*b^5*f*Cosh[5*(c + d*x)] + 28800*a^5*c*f*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 28800*a^3*b^2*c*f*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 28800*a^5*d*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 28800*a^3*b^2*d*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 28800*a^5*c*f*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 28800*a^3*b^2*c*f*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 28800*a^5*d*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 28800*a^3*b^2*d*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 28800*a^5*d*e*Log[a + b*Sinh[c + d*x]] + 28800*a^3*b^2*d*e*Log[a + b*Sinh[c + d*x]] - 28800*a^5*c*f*Log[a + b*Sinh[c + d*x]] - 28800*a^3*b^2*c*f*Log[a + b*Sinh[c + d*x]] + 28800*a^3*(a^2 + b^2)*f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 28800*a^3*(a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 28800*a^4*b*d*e*Sinh[c + d*x] - 21600*a^2*b^3*d*e*Sinh[c + d*x] + 3600*b^5*d*e*Sinh[c + d*x] - 28800*a^4*b*d*f*x*Sinh[c + d*x] - 21600*a^2*b^3*d*f*x*Sinh[c + d*x] + 3600*b^5*d*f*x*Sinh[c + d*x] - 3600*a^3*b^2*f*Sinh[2*(c + d*x)] - 1800*a*b^4*f*Sinh[2*(c + d*x)] - 2400*a^2*b^3*d*e*Sinh[3*(c + d*x)] - 600*b^5*d*e*Sinh[3*(c + d*x)] - 2400*a^2*b^3*d*f*x*Sinh[3*(c + d*x)] - 600*b^5*d*f*x*Sinh[3*(c + d*x)] - 225*a*b^4*f*Sinh[4*(c + d*x)] - 360*b^5*d*e*Sinh[5*(c + d*x)] - 360*b^5*d*f*x*Sinh[5*(c + d*x)])/(b^6*d^2)","A",1
404,1,123,141,0.3631584,"\int \frac{\cosh ^3(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]^3*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{-\frac{60 a^2 \left(a^2+b^2\right) \sinh (c+d x)}{b^5}+\frac{30 a \left(a^2+b^2\right) \sinh ^2(c+d x)}{b^4}-\frac{20 \left(a^2+b^2\right) \sinh ^3(c+d x)}{b^3}+\frac{60 a^3 \left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{b^6}+\frac{15 a \sinh ^4(c+d x)}{b^2}-\frac{12 \sinh ^5(c+d x)}{b}}{60 d}","\frac{a^2 \left(a^2+b^2\right) \sinh (c+d x)}{b^5 d}-\frac{a \left(a^2+b^2\right) \sinh ^2(c+d x)}{2 b^4 d}+\frac{\left(a^2+b^2\right) \sinh ^3(c+d x)}{3 b^3 d}-\frac{a^3 \left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{b^6 d}-\frac{a \sinh ^4(c+d x)}{4 b^2 d}+\frac{\sinh ^5(c+d x)}{5 b d}",1,"-1/60*((60*a^3*(a^2 + b^2)*Log[a + b*Sinh[c + d*x]])/b^6 - (60*a^2*(a^2 + b^2)*Sinh[c + d*x])/b^5 + (30*a*(a^2 + b^2)*Sinh[c + d*x]^2)/b^4 - (20*(a^2 + b^2)*Sinh[c + d*x]^3)/b^3 + (15*a*Sinh[c + d*x]^4)/b^2 - (12*Sinh[c + d*x]^5)/b)/d","A",1
405,-1,0,39,180.0016249,"\int \frac{\cosh ^3(c+d x) \sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]^3*Sinh[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^3(c+d x) \cosh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
406,1,2861,1519,23.3703303,"\int \frac{(e+f x)^3 \sinh ^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sinh[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{2 (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d}+\frac{3 i f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^2}-\frac{3 i f (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^2}-\frac{6 i f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{6 i f^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{6 i f^3 \text{Li}_4\left(-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{Li}_4\left(i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^4}-\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^3}{b^2 \left(a^2+b^2\right) d}-\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^3}{b^2 \left(a^2+b^2\right) d}+\frac{(e+f x)^3 \log \left(1+e^{2 (c+d x)}\right) a^3}{b^2 \left(a^2+b^2\right) d}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) a^3}{2 b^2 \left(a^2+b^2\right) d^2}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{3 f^2 (e+f x) \text{Li}_3\left(-e^{2 (c+d x)}\right) a^3}{2 b^2 \left(a^2+b^2\right) d^3}-\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b^2 \left(a^2+b^2\right) d^4}-\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b^2 \left(a^2+b^2\right) d^4}+\frac{3 f^3 \text{Li}_4\left(-e^{2 (c+d x)}\right) a^3}{4 b^2 \left(a^2+b^2\right) d^4}+\frac{2 (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right) a^2}{b^3 d}-\frac{3 i f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{3 i f (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{6 i f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{6 i f^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{6 i f^3 \text{Li}_4\left(-i e^{c+d x}\right) a^2}{b^3 d^4}+\frac{6 i f^3 \text{Li}_4\left(i e^{c+d x}\right) a^2}{b^3 d^4}+\frac{(e+f x)^4 a}{4 b^2 f}-\frac{(e+f x)^3 \log \left(1+e^{2 (c+d x)}\right) a}{b^2 d}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) a}{2 b^2 d^2}+\frac{3 f^2 (e+f x) \text{Li}_3\left(-e^{2 (c+d x)}\right) a}{2 b^2 d^3}-\frac{3 f^3 \text{Li}_4\left(-e^{2 (c+d x)}\right) a}{4 b^2 d^4}-\frac{2 (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right)}{b d}-\frac{6 f^3 \cosh (c+d x)}{b d^4}-\frac{3 f (e+f x)^2 \cosh (c+d x)}{b d^2}+\frac{3 i f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right)}{b d^2}-\frac{3 i f (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right)}{b d^2}-\frac{6 i f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right)}{b d^3}+\frac{6 i f^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right)}{b d^3}+\frac{6 i f^3 \text{Li}_4\left(-i e^{c+d x}\right)}{b d^4}-\frac{6 i f^3 \text{Li}_4\left(i e^{c+d x}\right)}{b d^4}+\frac{(e+f x)^3 \sinh (c+d x)}{b d}+\frac{6 f^2 (e+f x) \sinh (c+d x)}{b d^3}",1,"-1/4*(8*b*d^3*e^3*(1 + E^(2*c))*ArcTan[E^(c + d*x)] - 4*a*d^3*e^3*E^(2*c)*(2*d*x - Log[1 + E^(2*(c + d*x))]) + 4*a*d^3*e^3*Log[1 + E^(2*(c + d*x))] + (12*I)*b*d^2*e^2*(1 + E^(2*c))*f*(d*x*(Log[1 - I*E^(c + d*x)] - Log[1 + I*E^(c + d*x)]) - PolyLog[2, (-I)*E^(c + d*x)] + PolyLog[2, I*E^(c + d*x)]) - 6*a*d^2*e^2*E^(2*c)*f*(2*d*x*(d*x - Log[1 + E^(2*(c + d*x))]) - PolyLog[2, -E^(2*(c + d*x))]) + 6*a*d^2*e^2*f*(2*d*x*Log[1 + E^(2*(c + d*x))] + PolyLog[2, -E^(2*(c + d*x))]) + (12*I)*b*d*e*(1 + E^(2*c))*f^2*(d^2*x^2*Log[1 - I*E^(c + d*x)] - d^2*x^2*Log[1 + I*E^(c + d*x)] - 2*d*x*PolyLog[2, (-I)*E^(c + d*x)] + 2*d*x*PolyLog[2, I*E^(c + d*x)] + 2*PolyLog[3, (-I)*E^(c + d*x)] - 2*PolyLog[3, I*E^(c + d*x)]) + 6*a*d*e*f^2*(2*d^2*x^2*Log[1 + E^(2*(c + d*x))] + 2*d*x*PolyLog[2, -E^(2*(c + d*x))] - PolyLog[3, -E^(2*(c + d*x))]) - 2*a*d*e*E^(2*c)*f^2*(2*d^2*x^2*(2*d*x - 3*Log[1 + E^(2*(c + d*x))]) - 6*d*x*PolyLog[2, -E^(2*(c + d*x))] + 3*PolyLog[3, -E^(2*(c + d*x))]) + (4*I)*b*(1 + E^(2*c))*f^3*(d^3*x^3*Log[1 - I*E^(c + d*x)] - d^3*x^3*Log[1 + I*E^(c + d*x)] - 3*d^2*x^2*PolyLog[2, (-I)*E^(c + d*x)] + 3*d^2*x^2*PolyLog[2, I*E^(c + d*x)] + 6*d*x*PolyLog[3, (-I)*E^(c + d*x)] - 6*d*x*PolyLog[3, I*E^(c + d*x)] - 6*PolyLog[4, (-I)*E^(c + d*x)] + 6*PolyLog[4, I*E^(c + d*x)]) - a*E^(2*c)*f^3*(2*d^4*x^4 - 4*d^3*x^3*Log[1 + E^(2*(c + d*x))] - 6*d^2*x^2*PolyLog[2, -E^(2*(c + d*x))] + 6*d*x*PolyLog[3, -E^(2*(c + d*x))] - 3*PolyLog[4, -E^(2*(c + d*x))]) + a*f^3*(4*d^3*x^3*Log[1 + E^(2*(c + d*x))] + 6*d^2*x^2*PolyLog[2, -E^(2*(c + d*x))] - 6*d*x*PolyLog[3, -E^(2*(c + d*x))] + 3*PolyLog[4, -E^(2*(c + d*x))]))/((a^2 + b^2)*d^4*(1 + E^(2*c))) + (a^3*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(2*b^2*(a^2 + b^2)*(-1 + E^(2*c))) - (a*e^3*x*(a^2 - b^2 + (a^2 + b^2)*Cosh[2*c])*Csch[c]*Sech[c])/(2*b^2*(a^2 + b^2)) - (3*a*e^2*f*x^2*(a^2 - b^2 + (a^2 + b^2)*Cosh[2*c])*Csch[c]*Sech[c])/(4*b^2*(a^2 + b^2)) - (a*e*f^2*x^3*(a^2 - b^2 + (a^2 + b^2)*Cosh[2*c])*Csch[c]*Sech[c])/(2*b^2*(a^2 + b^2)) - (a*f^3*x^4*(a^2 - b^2 + (a^2 + b^2)*Cosh[2*c])*Csch[c]*Sech[c])/(8*b^2*(a^2 + b^2)) + ((6*f^3 + 6*d*f^2*(e + f*x) + 3*d^2*f*(e + f*x)^2 + d^3*(e + f*x)^3)*(-Cosh[c + d*x] + Sinh[c + d*x]))/(2*b*d^4) + ((-6*f^3 + 6*d*f^2*(e + f*x) - 3*d^2*f*(e + f*x)^2 + d^3*(e + f*x)^3)*(Cosh[c + d*x] + Sinh[c + d*x]))/(2*b*d^4)","A",1
407,1,1948,1067,11.6524963,"\int \frac{(e+f x)^2 \sinh ^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sinh[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{e^{-c} \left(2 d^3 e^c f^2 x^3 a^3+6 d^3 e e^c f x^2 a^3+6 d^3 e^2 e^c x a^3-6 d^2 e^2 e^c \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) a^3-6 d^2 e^c f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) a^3-12 d^2 e e^c f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) a^3-6 d^2 e^c f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) a^3-12 d^2 e e^c f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) a^3-12 d e e^c f \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) a^3-12 d e^c f^2 x \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) a^3-12 d e e^c f \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) a^3-12 d e^c f^2 x \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) a^3+12 e^c f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) a^3+12 e^c f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) a^3+3 b d^2 e^2 e^{2 c} \cosh (d x) a^2-3 b d^2 e^2 \cosh (d x) a^2+6 b e^{2 c} f^2 \cosh (d x) a^2-6 b f^2 \cosh (d x) a^2+3 b d^2 e^{2 c} f^2 x^2 \cosh (d x) a^2-3 b d^2 f^2 x^2 \cosh (d x) a^2-6 b d e e^{2 c} f \cosh (d x) a^2-6 b d e f \cosh (d x) a^2-6 b d e^{2 c} f^2 x \cosh (d x) a^2-6 b d f^2 x \cosh (d x) a^2+6 b d^2 e e^{2 c} f x \cosh (d x) a^2-6 b d^2 e f x \cosh (d x) a^2+3 b d^2 e^2 e^{2 c} \sinh (d x) a^2+3 b d^2 e^2 \sinh (d x) a^2+6 b e^{2 c} f^2 \sinh (d x) a^2+6 b f^2 \sinh (d x) a^2+3 b d^2 e^{2 c} f^2 x^2 \sinh (d x) a^2+3 b d^2 f^2 x^2 \sinh (d x) a^2-6 b d e e^{2 c} f \sinh (d x) a^2+6 b d e f \sinh (d x) a^2-6 b d e^{2 c} f^2 x \sinh (d x) a^2+6 b d f^2 x \sinh (d x) a^2+6 b d^2 e e^{2 c} f x \sinh (d x) a^2+6 b d^2 e f x \sinh (d x) a^2+2 b^2 d^3 e^c f^2 x^3 a+6 b^2 d^3 e e^c f x^2 a+6 b^2 d^3 e^2 e^c x a-6 b^2 d^2 e^2 e^c \log \left(1+e^{2 (c+d x)}\right) a-6 b^2 d^2 e^c f^2 x^2 \log \left(1+e^{2 (c+d x)}\right) a-12 b^2 d^2 e e^c f x \log \left(1+e^{2 (c+d x)}\right) a-6 b^2 d e e^c f \text{Li}_2\left(-e^{2 (c+d x)}\right) a-6 b^2 d e^c f^2 x \text{Li}_2\left(-e^{2 (c+d x)}\right) a+3 b^2 e^c f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) a-12 b^3 d^2 e^2 e^c \tan ^{-1}\left(e^{c+d x}\right)+3 b^3 d^2 e^2 e^{2 c} \cosh (d x)-3 b^3 d^2 e^2 \cosh (d x)+6 b^3 e^{2 c} f^2 \cosh (d x)-6 b^3 f^2 \cosh (d x)+3 b^3 d^2 e^{2 c} f^2 x^2 \cosh (d x)-3 b^3 d^2 f^2 x^2 \cosh (d x)-6 b^3 d e e^{2 c} f \cosh (d x)-6 b^3 d e f \cosh (d x)-6 b^3 d e^{2 c} f^2 x \cosh (d x)-6 b^3 d f^2 x \cosh (d x)+6 b^3 d^2 e e^{2 c} f x \cosh (d x)-6 b^3 d^2 e f x \cosh (d x)-6 i b^3 d^2 e^c f^2 x^2 \log \left(1-i e^{c+d x}\right)-12 i b^3 d^2 e e^c f x \log \left(1-i e^{c+d x}\right)+6 i b^3 d^2 e^c f^2 x^2 \log \left(1+i e^{c+d x}\right)+12 i b^3 d^2 e e^c f x \log \left(1+i e^{c+d x}\right)+12 i b^3 d e^c f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)-12 i b^3 d e^c f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)-12 i b^3 e^c f^2 \text{Li}_3\left(-i e^{c+d x}\right)+12 i b^3 e^c f^2 \text{Li}_3\left(i e^{c+d x}\right)+3 b^3 d^2 e^2 e^{2 c} \sinh (d x)+3 b^3 d^2 e^2 \sinh (d x)+6 b^3 e^{2 c} f^2 \sinh (d x)+6 b^3 f^2 \sinh (d x)+3 b^3 d^2 e^{2 c} f^2 x^2 \sinh (d x)+3 b^3 d^2 f^2 x^2 \sinh (d x)-6 b^3 d e e^{2 c} f \sinh (d x)+6 b^3 d e f \sinh (d x)-6 b^3 d e^{2 c} f^2 x \sinh (d x)+6 b^3 d f^2 x \sinh (d x)+6 b^3 d^2 e e^{2 c} f x \sinh (d x)+6 b^3 d^2 e f x \sinh (d x)\right)}{6 b^2 \left(a^2+b^2\right) d^3}","-\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d}+\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^2}-\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^2}-\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^3}{b^2 \left(a^2+b^2\right) d}-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^3}{b^2 \left(a^2+b^2\right) d}+\frac{(e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) a^3}{b^2 \left(a^2+b^2\right) d}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) a^3}{2 b^2 \left(a^2+b^2\right) d^3}+\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^2}{b^3 d}-\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right) a^2}{b^3 d^3}+\frac{(e+f x)^3 a}{3 b^2 f}-\frac{(e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) a}{b^2 d}-\frac{f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) a}{b^2 d^2}+\frac{f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) a}{2 b^2 d^3}-\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{b d}-\frac{2 f (e+f x) \cosh (c+d x)}{b d^2}+\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{b d^2}-\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{b d^2}-\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{b d^3}+\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right)}{b d^3}+\frac{2 f^2 \sinh (c+d x)}{b d^3}+\frac{(e+f x)^2 \sinh (c+d x)}{b d}",1,"(6*a^3*d^3*e^2*E^c*x + 6*a*b^2*d^3*e^2*E^c*x + 6*a^3*d^3*e*E^c*f*x^2 + 6*a*b^2*d^3*e*E^c*f*x^2 + 2*a^3*d^3*E^c*f^2*x^3 + 2*a*b^2*d^3*E^c*f^2*x^3 - 12*b^3*d^2*e^2*E^c*ArcTan[E^(c + d*x)] - 3*a^2*b*d^2*e^2*Cosh[d*x] - 3*b^3*d^2*e^2*Cosh[d*x] + 3*a^2*b*d^2*e^2*E^(2*c)*Cosh[d*x] + 3*b^3*d^2*e^2*E^(2*c)*Cosh[d*x] - 6*a^2*b*d*e*f*Cosh[d*x] - 6*b^3*d*e*f*Cosh[d*x] - 6*a^2*b*d*e*E^(2*c)*f*Cosh[d*x] - 6*b^3*d*e*E^(2*c)*f*Cosh[d*x] - 6*a^2*b*f^2*Cosh[d*x] - 6*b^3*f^2*Cosh[d*x] + 6*a^2*b*E^(2*c)*f^2*Cosh[d*x] + 6*b^3*E^(2*c)*f^2*Cosh[d*x] - 6*a^2*b*d^2*e*f*x*Cosh[d*x] - 6*b^3*d^2*e*f*x*Cosh[d*x] + 6*a^2*b*d^2*e*E^(2*c)*f*x*Cosh[d*x] + 6*b^3*d^2*e*E^(2*c)*f*x*Cosh[d*x] - 6*a^2*b*d*f^2*x*Cosh[d*x] - 6*b^3*d*f^2*x*Cosh[d*x] - 6*a^2*b*d*E^(2*c)*f^2*x*Cosh[d*x] - 6*b^3*d*E^(2*c)*f^2*x*Cosh[d*x] - 3*a^2*b*d^2*f^2*x^2*Cosh[d*x] - 3*b^3*d^2*f^2*x^2*Cosh[d*x] + 3*a^2*b*d^2*E^(2*c)*f^2*x^2*Cosh[d*x] + 3*b^3*d^2*E^(2*c)*f^2*x^2*Cosh[d*x] - (12*I)*b^3*d^2*e*E^c*f*x*Log[1 - I*E^(c + d*x)] - (6*I)*b^3*d^2*E^c*f^2*x^2*Log[1 - I*E^(c + d*x)] + (12*I)*b^3*d^2*e*E^c*f*x*Log[1 + I*E^(c + d*x)] + (6*I)*b^3*d^2*E^c*f^2*x^2*Log[1 + I*E^(c + d*x)] - 6*a*b^2*d^2*e^2*E^c*Log[1 + E^(2*(c + d*x))] - 12*a*b^2*d^2*e*E^c*f*x*Log[1 + E^(2*(c + d*x))] - 6*a*b^2*d^2*E^c*f^2*x^2*Log[1 + E^(2*(c + d*x))] - 6*a^3*d^2*e^2*E^c*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 12*a^3*d^2*e*E^c*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*a^3*d^2*E^c*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 12*a^3*d^2*e*E^c*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*a^3*d^2*E^c*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + (12*I)*b^3*d*E^c*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)] - (12*I)*b^3*d*E^c*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)] - 6*a*b^2*d*e*E^c*f*PolyLog[2, -E^(2*(c + d*x))] - 6*a*b^2*d*E^c*f^2*x*PolyLog[2, -E^(2*(c + d*x))] - 12*a^3*d*e*E^c*f*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 12*a^3*d*E^c*f^2*x*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 12*a^3*d*e*E^c*f*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 12*a^3*d*E^c*f^2*x*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - (12*I)*b^3*E^c*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (12*I)*b^3*E^c*f^2*PolyLog[3, I*E^(c + d*x)] + 3*a*b^2*E^c*f^2*PolyLog[3, -E^(2*(c + d*x))] + 12*a^3*E^c*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 12*a^3*E^c*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 3*a^2*b*d^2*e^2*Sinh[d*x] + 3*b^3*d^2*e^2*Sinh[d*x] + 3*a^2*b*d^2*e^2*E^(2*c)*Sinh[d*x] + 3*b^3*d^2*e^2*E^(2*c)*Sinh[d*x] + 6*a^2*b*d*e*f*Sinh[d*x] + 6*b^3*d*e*f*Sinh[d*x] - 6*a^2*b*d*e*E^(2*c)*f*Sinh[d*x] - 6*b^3*d*e*E^(2*c)*f*Sinh[d*x] + 6*a^2*b*f^2*Sinh[d*x] + 6*b^3*f^2*Sinh[d*x] + 6*a^2*b*E^(2*c)*f^2*Sinh[d*x] + 6*b^3*E^(2*c)*f^2*Sinh[d*x] + 6*a^2*b*d^2*e*f*x*Sinh[d*x] + 6*b^3*d^2*e*f*x*Sinh[d*x] + 6*a^2*b*d^2*e*E^(2*c)*f*x*Sinh[d*x] + 6*b^3*d^2*e*E^(2*c)*f*x*Sinh[d*x] + 6*a^2*b*d*f^2*x*Sinh[d*x] + 6*b^3*d*f^2*x*Sinh[d*x] - 6*a^2*b*d*E^(2*c)*f^2*x*Sinh[d*x] - 6*b^3*d*E^(2*c)*f^2*x*Sinh[d*x] + 3*a^2*b*d^2*f^2*x^2*Sinh[d*x] + 3*b^3*d^2*f^2*x^2*Sinh[d*x] + 3*a^2*b*d^2*E^(2*c)*f^2*x^2*Sinh[d*x] + 3*b^3*d^2*E^(2*c)*f^2*x^2*Sinh[d*x])/(6*b^2*(a^2 + b^2)*d^3*E^c)","A",1
408,1,429,631,4.3045157,"\int \frac{(e+f x) \sinh ^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sinh[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{\frac{a c^2 f+2 a d e \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)-2 a c d e+a f \text{Li}_2(-\cosh (2 (c+d x))-\sinh (2 (c+d x)))+2 a d f x \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)-2 a d^2 e x-a d^2 f x^2+4 b d e \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))-2 i b f \text{Li}_2(-i (\cosh (c+d x)+\sinh (c+d x)))+2 i b f \text{Li}_2(i (\cosh (c+d x)+\sinh (c+d x)))+4 b d f x \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))}{2 \left(a^2+b^2\right)}+\frac{a^3 \left(f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-\frac{1}{2} f (c+d x)^2\right)}{b^2 \left(a^2+b^2\right)}-\frac{d (e+f x) \sinh (c+d x)}{b}+\frac{f \cosh (c+d x)}{b}}{d^2}","-\frac{i a^2 f \text{Li}_2\left(-i e^{c+d x}\right)}{b^3 d^2}+\frac{i a^2 f \text{Li}_2\left(i e^{c+d x}\right)}{b^3 d^2}+\frac{2 a^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^3 d}+\frac{i a^4 f \text{Li}_2\left(-i e^{c+d x}\right)}{b^3 d^2 \left(a^2+b^2\right)}-\frac{i a^4 f \text{Li}_2\left(i e^{c+d x}\right)}{b^3 d^2 \left(a^2+b^2\right)}-\frac{2 a^4 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^3 d \left(a^2+b^2\right)}-\frac{a^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2 \left(a^2+b^2\right)}-\frac{a^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b^2 d^2 \left(a^2+b^2\right)}+\frac{a^3 f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 b^2 d^2 \left(a^2+b^2\right)}-\frac{a^3 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b^2 d \left(a^2+b^2\right)}-\frac{a^3 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b^2 d \left(a^2+b^2\right)}+\frac{a^3 (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{b^2 d \left(a^2+b^2\right)}-\frac{a f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 b^2 d^2}-\frac{a (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{b^2 d}+\frac{a (e+f x)^2}{2 b^2 f}+\frac{i f \text{Li}_2\left(-i e^{c+d x}\right)}{b d^2}-\frac{i f \text{Li}_2\left(i e^{c+d x}\right)}{b d^2}-\frac{f \cosh (c+d x)}{b d^2}-\frac{2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b d}+\frac{(e+f x) \sinh (c+d x)}{b d}",1,"-(((f*Cosh[c + d*x])/b + (a^3*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b^2*(a^2 + b^2)) + (-2*a*c*d*e + a*c^2*f - 2*a*d^2*e*x - a*d^2*f*x^2 + 4*b*d*e*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] + 4*b*d*f*x*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] + 2*a*d*e*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] + 2*a*d*f*x*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] - (2*I)*b*f*PolyLog[2, (-I)*(Cosh[c + d*x] + Sinh[c + d*x])] + (2*I)*b*f*PolyLog[2, I*(Cosh[c + d*x] + Sinh[c + d*x])] + a*f*PolyLog[2, -Cosh[2*(c + d*x)] - Sinh[2*(c + d*x)]])/(2*(a^2 + b^2)) - (d*(e + f*x)*Sinh[c + d*x])/b)/d^2)","A",0
409,1,91,89,0.1718577,"\int \frac{\sinh ^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Sinh[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{\frac{2 a^3 \log (a+b \sinh (c+d x))}{b^2 \left(a^2+b^2\right)}+\frac{\log (-\sinh (c+d x)+i)}{a+i b}+\frac{\log (\sinh (c+d x)+i)}{a-i b}-\frac{2 \sinh (c+d x)}{b}}{2 d}","-\frac{b \tan ^{-1}(\sinh (c+d x))}{d \left(a^2+b^2\right)}-\frac{a \log (\cosh (c+d x))}{d \left(a^2+b^2\right)}-\frac{a^3 \log (a+b \sinh (c+d x))}{b^2 d \left(a^2+b^2\right)}+\frac{\sinh (c+d x)}{b d}",1,"-1/2*(Log[I - Sinh[c + d*x]]/(a + I*b) + Log[I + Sinh[c + d*x]]/(a - I*b) + (2*a^3*Log[a + b*Sinh[c + d*x]])/(b^2*(a^2 + b^2)) - (2*Sinh[c + d*x])/b)/d","C",1
410,-1,0,37,180.0023215,"\int \frac{\sinh ^2(c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Sinh[c + d*x]^2*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh ^2(c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
411,1,1111,1294,11.8164398,"\int \frac{(e+f x)^3 \sinh (c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Sinh[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(2 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3-f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-3 e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2+3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2+6 e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+6 f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-6 e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-6 f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-6 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^4}+\frac{x \left(4 e^3+6 f x e^2+4 f^2 x^2 e+f^3 x^3\right)}{4 b}-\frac{f \left(-4 b f^2 x^3 d^3-12 b e f x^2 d^3+12 b e^2 e^{2 c} x d^3-12 b e^2 \left(1+e^{2 c}\right) x d^3+12 a e^2 \left(1+e^{2 c}\right) \tan ^{-1}\left(e^{c+d x}\right) d^2+6 b e^2 \left(1+e^{2 c}\right) \left(2 d x-\log \left(1+e^{2 (c+d x)}\right)\right) d^2+12 i a e \left(1+e^{2 c}\right) f \left(d x \left(\log \left(1-i e^{c+d x}\right)-\log \left(1+i e^{c+d x}\right)\right)-\text{Li}_2\left(-i e^{c+d x}\right)+\text{Li}_2\left(i e^{c+d x}\right)\right) d+6 b e \left(1+e^{2 c}\right) f \left(2 d x \left(d x-\log \left(1+e^{2 (c+d x)}\right)\right)-\text{Li}_2\left(-e^{2 (c+d x)}\right)\right) d+6 i a \left(1+e^{2 c}\right) f^2 \left(d^2 \log \left(1-i e^{c+d x}\right) x^2-d^2 \log \left(1+i e^{c+d x}\right) x^2-2 d \text{Li}_2\left(-i e^{c+d x}\right) x+2 d \text{Li}_2\left(i e^{c+d x}\right) x+2 \text{Li}_3\left(-i e^{c+d x}\right)-2 \text{Li}_3\left(i e^{c+d x}\right)\right)+b \left(1+e^{2 c}\right) f^2 \left(2 d^2 \left(2 d x-3 \log \left(1+e^{2 (c+d x)}\right)\right) x^2-6 d \text{Li}_2\left(-e^{2 (c+d x)}\right) x+3 \text{Li}_3\left(-e^{2 (c+d x)}\right)\right)\right)}{2 \left(a^2+b^2\right) d^4 \left(1+e^{2 c}\right)}+\frac{(e+f x)^3 \text{sech}(c+d x) (a-b \text{sech}(c) \sinh (d x))}{\left(a^2+b^2\right) d}","-\frac{(e+f x)^3 a^4}{b^3 \left(a^2+b^2\right) d}+\frac{3 f (e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) a^4}{b^3 \left(a^2+b^2\right) d^2}+\frac{3 f^2 (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}-\frac{3 f^3 \text{Li}_3\left(-e^{2 (c+d x)}\right) a^4}{2 b^3 \left(a^2+b^2\right) d^4}-\frac{(e+f x)^3 \tanh (c+d x) a^4}{b^3 \left(a^2+b^2\right) d}+\frac{6 f (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}-\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^3}{b \left(a^2+b^2\right)^{3/2} d}+\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^3}{b \left(a^2+b^2\right)^{3/2} d}-\frac{6 i f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{6 i f^2 (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^2}+\frac{6 i f^3 \text{Li}_3\left(-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{Li}_3\left(i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^4}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^3}-\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^3}-\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^4}+\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^4}-\frac{(e+f x)^3 \text{sech}(c+d x) a^3}{b^2 \left(a^2+b^2\right) d}+\frac{(e+f x)^3 a^2}{b^3 d}-\frac{3 f (e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) a^2}{b^3 d^2}-\frac{3 f^2 (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) a^2}{b^3 d^3}+\frac{3 f^3 \text{Li}_3\left(-e^{2 (c+d x)}\right) a^2}{2 b^3 d^4}+\frac{(e+f x)^3 \tanh (c+d x) a^2}{b^3 d}-\frac{6 f (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a}{b^2 d^2}+\frac{6 i f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a}{b^2 d^3}-\frac{6 i f^2 (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a}{b^2 d^3}-\frac{6 i f^3 \text{Li}_3\left(-i e^{c+d x}\right) a}{b^2 d^4}+\frac{6 i f^3 \text{Li}_3\left(i e^{c+d x}\right) a}{b^2 d^4}+\frac{(e+f x)^3 \text{sech}(c+d x) a}{b^2 d}+\frac{(e+f x)^4}{4 b f}-\frac{(e+f x)^3}{b d}+\frac{3 f (e+f x)^2 \log \left(1+e^{2 (c+d x)}\right)}{b d^2}+\frac{3 f^2 (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right)}{b d^3}-\frac{3 f^3 \text{Li}_3\left(-e^{2 (c+d x)}\right)}{2 b d^4}-\frac{(e+f x)^3 \tanh (c+d x)}{b d}",1,"(x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3))/(4*b) - (f*(12*b*d^3*e^2*E^(2*c)*x - 12*b*d^3*e^2*(1 + E^(2*c))*x - 12*b*d^3*e*f*x^2 - 4*b*d^3*f^2*x^3 + 12*a*d^2*e^2*(1 + E^(2*c))*ArcTan[E^(c + d*x)] + 6*b*d^2*e^2*(1 + E^(2*c))*(2*d*x - Log[1 + E^(2*(c + d*x))]) + (12*I)*a*d*e*(1 + E^(2*c))*f*(d*x*(Log[1 - I*E^(c + d*x)] - Log[1 + I*E^(c + d*x)]) - PolyLog[2, (-I)*E^(c + d*x)] + PolyLog[2, I*E^(c + d*x)]) + 6*b*d*e*(1 + E^(2*c))*f*(2*d*x*(d*x - Log[1 + E^(2*(c + d*x))]) - PolyLog[2, -E^(2*(c + d*x))]) + (6*I)*a*(1 + E^(2*c))*f^2*(d^2*x^2*Log[1 - I*E^(c + d*x)] - d^2*x^2*Log[1 + I*E^(c + d*x)] - 2*d*x*PolyLog[2, (-I)*E^(c + d*x)] + 2*d*x*PolyLog[2, I*E^(c + d*x)] + 2*PolyLog[3, (-I)*E^(c + d*x)] - 2*PolyLog[3, I*E^(c + d*x)]) + b*(1 + E^(2*c))*f^2*(2*d^2*x^2*(2*d*x - 3*Log[1 + E^(2*(c + d*x))]) - 6*d*x*PolyLog[2, -E^(2*(c + d*x))] + 3*PolyLog[3, -E^(2*(c + d*x))])))/(2*(a^2 + b^2)*d^4*(1 + E^(2*c))) + (a^3*(2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b*(a^2 + b^2)^(3/2)*d^4) + ((e + f*x)^3*Sech[c + d*x]*(a - b*Sech[c]*Sinh[d*x]))/((a^2 + b^2)*d)","A",1
412,1,935,904,8.4019625,"\int \frac{(e+f x)^2 \sinh (c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Sinh[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^2-f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2-2 e f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2+f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2+2 e f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2-2 f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^3}-\frac{2 f^2 \left(-\frac{2 \tan ^{-1}\left(\frac{\sinh (c)+\cosh (c) \tanh \left(\frac{d x}{2}\right)}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right) \tanh ^{-1}(\coth (c))}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}-\frac{i \text{csch}(c) \left(i \left(d x+\tanh ^{-1}(\coth (c))\right) \left(\log \left(1-e^{-d x-\tanh ^{-1}(\coth (c))}\right)-\log \left(1+e^{-d x-\tanh ^{-1}(\coth (c))}\right)\right)+i \left(\text{Li}_2\left(-e^{-d x-\tanh ^{-1}(\coth (c))}\right)-\text{Li}_2\left(e^{-d x-\tanh ^{-1}(\coth (c))}\right)\right)\right)}{\sqrt{1-\coth ^2(c)}}\right) a}{\left(a^2+b^2\right) d^3}-\frac{4 e f \tan ^{-1}\left(\frac{\sinh (c)+\cosh (c) \tanh \left(\frac{d x}{2}\right)}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right) a}{\left(a^2+b^2\right) d^2 \sqrt{\cosh ^2(c)-\sinh ^2(c)}}+\frac{x \left(3 e^2+3 f x e+f^2 x^2\right)}{3 b}+\frac{\text{sech}(c) \text{sech}(c+d x) \left(a \cosh (c) e^2-b \sinh (d x) e^2+2 a f x \cosh (c) e-2 b f x \sinh (d x) e+a f^2 x^2 \cosh (c)-b f^2 x^2 \sinh (d x)\right)}{\left(a^2+b^2\right) d}+\frac{b f^2 \text{csch}(c) \left(d^2 e^{-\tanh ^{-1}(\coth (c))} x^2-\frac{i \coth (c) \left(-d x \left(2 i \tanh ^{-1}(\coth (c))-\pi \right)-\pi  \log \left(1+e^{2 d x}\right)-2 \left(i d x+i \tanh ^{-1}(\coth (c))\right) \log \left(1-e^{2 i \left(i d x+i \tanh ^{-1}(\coth (c))\right)}\right)+\pi  \log (\cosh (d x))+2 i \tanh ^{-1}(\coth (c)) \log \left(i \sinh \left(d x+\tanh ^{-1}(\coth (c))\right)\right)+i \text{Li}_2\left(e^{2 i \left(i d x+i \tanh ^{-1}(\coth (c))\right)}\right)\right)}{\sqrt{1-\coth ^2(c)}}\right) \text{sech}(c)}{\left(a^2+b^2\right) d^3 \sqrt{\text{csch}^2(c) \left(\sinh ^2(c)-\cosh ^2(c)\right)}}+\frac{2 b e f \text{sech}(c) (\cosh (c) \log (\cosh (c) \cosh (d x)+\sinh (c) \sinh (d x))-d x \sinh (c))}{\left(a^2+b^2\right) d^2 \left(\cosh ^2(c)-\sinh ^2(c)\right)}","-\frac{(e+f x)^2 a^4}{b^3 \left(a^2+b^2\right) d}+\frac{2 f (e+f x) \log \left(1+e^{2 (c+d x)}\right) a^4}{b^3 \left(a^2+b^2\right) d^2}+\frac{f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}-\frac{(e+f x)^2 \tanh (c+d x) a^4}{b^3 \left(a^2+b^2\right) d}+\frac{4 f (e+f x) \tan ^{-1}\left(e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^3}{b \left(a^2+b^2\right)^{3/2} d}+\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^3}{b \left(a^2+b^2\right)^{3/2} d}-\frac{2 i f^2 \text{Li}_2\left(-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{Li}_2\left(i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^2}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^2}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^3}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{b \left(a^2+b^2\right)^{3/2} d^3}-\frac{(e+f x)^2 \text{sech}(c+d x) a^3}{b^2 \left(a^2+b^2\right) d}+\frac{(e+f x)^2 a^2}{b^3 d}-\frac{2 f (e+f x) \log \left(1+e^{2 (c+d x)}\right) a^2}{b^3 d^2}-\frac{f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) a^2}{b^3 d^3}+\frac{(e+f x)^2 \tanh (c+d x) a^2}{b^3 d}-\frac{4 f (e+f x) \tan ^{-1}\left(e^{c+d x}\right) a}{b^2 d^2}+\frac{2 i f^2 \text{Li}_2\left(-i e^{c+d x}\right) a}{b^2 d^3}-\frac{2 i f^2 \text{Li}_2\left(i e^{c+d x}\right) a}{b^2 d^3}+\frac{(e+f x)^2 \text{sech}(c+d x) a}{b^2 d}+\frac{(e+f x)^3}{3 b f}-\frac{(e+f x)^2}{b d}+\frac{2 f (e+f x) \log \left(1+e^{2 (c+d x)}\right)}{b d^2}+\frac{f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right)}{b d^3}-\frac{(e+f x)^2 \tanh (c+d x)}{b d}",1,"(x*(3*e^2 + 3*e*f*x + f^2*x^2))/(3*b) + (a^3*(2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b*(a^2 + b^2)^(3/2)*d^3) + (2*b*e*f*Sech[c]*(Cosh[c]*Log[Cosh[c]*Cosh[d*x] + Sinh[c]*Sinh[d*x]] - d*x*Sinh[c]))/((a^2 + b^2)*d^2*(Cosh[c]^2 - Sinh[c]^2)) - (4*a*e*f*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]])/((a^2 + b^2)*d^2*Sqrt[Cosh[c]^2 - Sinh[c]^2]) + (b*f^2*Csch[c]*((d^2*x^2)/E^ArcTanh[Coth[c]] - (I*Coth[c]*(-(d*x*(-Pi + (2*I)*ArcTanh[Coth[c]])) - Pi*Log[1 + E^(2*d*x)] - 2*(I*d*x + I*ArcTanh[Coth[c]])*Log[1 - E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))] + Pi*Log[Cosh[d*x]] + (2*I)*ArcTanh[Coth[c]]*Log[I*Sinh[d*x + ArcTanh[Coth[c]]]] + I*PolyLog[2, E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))]))/Sqrt[1 - Coth[c]^2])*Sech[c])/((a^2 + b^2)*d^3*Sqrt[Csch[c]^2*(-Cosh[c]^2 + Sinh[c]^2)]) - (2*a*f^2*(((-I)*Csch[c]*(I*(d*x + ArcTanh[Coth[c]])*(Log[1 - E^(-(d*x) - ArcTanh[Coth[c]])] - Log[1 + E^(-(d*x) - ArcTanh[Coth[c]])]) + I*(PolyLog[2, -E^(-(d*x) - ArcTanh[Coth[c]])] - PolyLog[2, E^(-(d*x) - ArcTanh[Coth[c]])])))/Sqrt[1 - Coth[c]^2] - (2*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]]*ArcTanh[Coth[c]])/Sqrt[Cosh[c]^2 - Sinh[c]^2]))/((a^2 + b^2)*d^3) + (Sech[c]*Sech[c + d*x]*(a*e^2*Cosh[c] + 2*a*e*f*x*Cosh[c] + a*f^2*x^2*Cosh[c] - b*e^2*Sinh[d*x] - 2*b*e*f*x*Sinh[d*x] - b*f^2*x^2*Sinh[d*x]))/((a^2 + b^2)*d)","A",0
413,1,317,454,3.9043335,"\int \frac{(e+f x) \sinh (c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Sinh[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\frac{2 d (e+f x) \text{sech}(c+d x) (a-b \sinh (c+d x))}{a^2+b^2}-\frac{4 a f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^2+b^2}+\frac{2 b f \log (\cosh (c+d x))}{a^2+b^2}+\frac{2 a^3 \left(2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)}{b \left(a^2+b^2\right)^{3/2}}-\frac{(c+d x) (c f-d (2 e+f x))}{b}}{2 d^2}","-\frac{a^2 f \log (\cosh (c+d x))}{b^3 d^2}+\frac{a^2 (e+f x) \tanh (c+d x)}{b^3 d}+\frac{a^4 f \log (\cosh (c+d x))}{b^3 d^2 \left(a^2+b^2\right)}-\frac{a^4 (e+f x) \tanh (c+d x)}{b^3 d \left(a^2+b^2\right)}-\frac{a^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2 \left(a^2+b^2\right)^{3/2}}+\frac{a^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{b d^2 \left(a^2+b^2\right)^{3/2}}+\frac{a^3 f \tan ^{-1}(\sinh (c+d x))}{b^2 d^2 \left(a^2+b^2\right)}-\frac{a^3 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{b d \left(a^2+b^2\right)^{3/2}}+\frac{a^3 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{b d \left(a^2+b^2\right)^{3/2}}-\frac{a^3 (e+f x) \text{sech}(c+d x)}{b^2 d \left(a^2+b^2\right)}-\frac{a f \tan ^{-1}(\sinh (c+d x))}{b^2 d^2}+\frac{a (e+f x) \text{sech}(c+d x)}{b^2 d}+\frac{f \log (\cosh (c+d x))}{b d^2}-\frac{(e+f x) \tanh (c+d x)}{b d}+\frac{e x}{b}+\frac{f x^2}{2 b}",1,"(-(((c + d*x)*(c*f - d*(2*e + f*x)))/b) - (4*a*f*ArcTan[Tanh[(c + d*x)/2]])/(a^2 + b^2) + (2*b*f*Log[Cosh[c + d*x]])/(a^2 + b^2) + (2*a^3*(2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(b*(a^2 + b^2)^(3/2)) + (2*d*(e + f*x)*Sech[c + d*x]*(a - b*Sinh[c + d*x]))/(a^2 + b^2))/(2*d^2)","A",1
414,1,96,121,0.4647569,"\int \frac{\sinh (c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Sinh[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\frac{\text{sech}(c+d x) (a-b \sinh (c+d x))}{a^2+b^2}+\frac{2 a^3 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{b \left(-a^2-b^2\right)^{3/2}}+\frac{c+d x}{b}}{d}","-\frac{b \tanh (c+d x)}{d \left(a^2+b^2\right)}+\frac{a \text{sech}(c+d x)}{d \left(a^2+b^2\right)}+\frac{a^2 x}{b \left(a^2+b^2\right)}+\frac{b x}{a^2+b^2}+\frac{2 a^3 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{b d \left(a^2+b^2\right)^{3/2}}",1,"((c + d*x)/b + (2*a^3*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(b*(-a^2 - b^2)^(3/2)) + (Sech[c + d*x]*(a - b*Sinh[c + d*x]))/(a^2 + b^2))/d","A",1
415,-1,0,37,180.0017696,"\int \frac{\sinh (c+d x) \tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Sinh[c + d*x]*Tanh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\sinh (c+d x) \tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
416,1,3102,1479,26.9191767,"\int \frac{(e+f x)^2 \tanh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Tanh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{(e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d}-\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d}+\frac{f^2 \tan ^{-1}(\sinh (c+d x)) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^2}+\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^2}-\frac{i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^2}-\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^2}-\frac{i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^3}+\frac{i f^2 \text{Li}_3\left(i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^3}-\frac{f (e+f x) \text{sech}(c+d x) a^4}{b^3 \left(a^2+b^2\right) d^2}-\frac{(e+f x)^2 \text{sech}(c+d x) \tanh (c+d x) a^4}{2 b^3 \left(a^2+b^2\right) d}-\frac{(e+f x)^2 \text{sech}^2(c+d x) a^3}{2 b^2 \left(a^2+b^2\right) d}-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^3}{\left(a^2+b^2\right)^2 d}-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^3}{\left(a^2+b^2\right)^2 d}+\frac{(e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) a^3}{\left(a^2+b^2\right)^2 d}-\frac{f^2 \log (\cosh (c+d x)) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{\left(a^2+b^2\right)^2 d^2}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{\left(a^2+b^2\right)^2 d^3}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{\left(a^2+b^2\right)^2 d^3}-\frac{f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) a^3}{2 \left(a^2+b^2\right)^2 d^3}+\frac{f (e+f x) \tanh (c+d x) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{(e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) a^2}{b^3 d}-\frac{f^2 \tan ^{-1}(\sinh (c+d x)) a^2}{b^3 d^3}-\frac{i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{i f^2 \text{Li}_3\left(-i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{i f^2 \text{Li}_3\left(i e^{c+d x}\right) a^2}{b^3 d^3}+\frac{f (e+f x) \text{sech}(c+d x) a^2}{b^3 d^2}+\frac{(e+f x)^2 \text{sech}(c+d x) \tanh (c+d x) a^2}{2 b^3 d}+\frac{(e+f x)^2 \text{sech}^2(c+d x) a}{2 b^2 d}+\frac{f^2 \log (\cosh (c+d x)) a}{b^2 d^3}-\frac{f (e+f x) \tanh (c+d x) a}{b^2 d^2}+\frac{(e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{b d}+\frac{f^2 \tan ^{-1}(\sinh (c+d x))}{b d^3}-\frac{i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{b d^2}+\frac{i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{b d^2}+\frac{i f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{b d^3}-\frac{i f^2 \text{Li}_3\left(i e^{c+d x}\right)}{b d^3}-\frac{f (e+f x) \text{sech}(c+d x)}{b d^2}-\frac{(e+f x)^2 \text{sech}(c+d x) \tanh (c+d x)}{2 b d}",1,"(-12*a^3*d^3*e^2*E^(2*c)*x - 12*a^3*d*E^(2*c)*f^2*x - 12*a*b^2*d*E^(2*c)*f^2*x - 12*a^3*d^3*e*E^(2*c)*f*x^2 - 4*a^3*d^3*E^(2*c)*f^2*x^3 + 18*a^2*b*d^2*e^2*ArcTan[E^(c + d*x)] + 6*b^3*d^2*e^2*ArcTan[E^(c + d*x)] + 18*a^2*b*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] + 6*b^3*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] + 12*a^2*b*f^2*ArcTan[E^(c + d*x)] + 12*b^3*f^2*ArcTan[E^(c + d*x)] + 12*a^2*b*E^(2*c)*f^2*ArcTan[E^(c + d*x)] + 12*b^3*E^(2*c)*f^2*ArcTan[E^(c + d*x)] + (18*I)*a^2*b*d^2*e*f*x*Log[1 - I*E^(c + d*x)] + (6*I)*b^3*d^2*e*f*x*Log[1 - I*E^(c + d*x)] + (18*I)*a^2*b*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] + (6*I)*b^3*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] + (9*I)*a^2*b*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] + (3*I)*b^3*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] + (9*I)*a^2*b*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] + (3*I)*b^3*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] - (18*I)*a^2*b*d^2*e*f*x*Log[1 + I*E^(c + d*x)] - (6*I)*b^3*d^2*e*f*x*Log[1 + I*E^(c + d*x)] - (18*I)*a^2*b*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] - (6*I)*b^3*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] - (9*I)*a^2*b*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] - (3*I)*b^3*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] - (9*I)*a^2*b*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] - (3*I)*b^3*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] + 6*a^3*d^2*e^2*Log[1 + E^(2*(c + d*x))] + 6*a^3*d^2*e^2*E^(2*c)*Log[1 + E^(2*(c + d*x))] + 6*a^3*f^2*Log[1 + E^(2*(c + d*x))] + 6*a*b^2*f^2*Log[1 + E^(2*(c + d*x))] + 6*a^3*E^(2*c)*f^2*Log[1 + E^(2*(c + d*x))] + 6*a*b^2*E^(2*c)*f^2*Log[1 + E^(2*(c + d*x))] + 12*a^3*d^2*e*f*x*Log[1 + E^(2*(c + d*x))] + 12*a^3*d^2*e*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 6*a^3*d^2*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 6*a^3*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] - (6*I)*b*(3*a^2 + b^2)*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)] + (6*I)*b*(3*a^2 + b^2)*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)] + 6*a^3*d*e*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a^3*d*e*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a^3*d*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 6*a^3*d*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + (18*I)*a^2*b*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (6*I)*b^3*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (18*I)*a^2*b*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (6*I)*b^3*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (18*I)*a^2*b*f^2*PolyLog[3, I*E^(c + d*x)] - (6*I)*b^3*f^2*PolyLog[3, I*E^(c + d*x)] - (18*I)*a^2*b*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - (6*I)*b^3*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - 3*a^3*f^2*PolyLog[3, -E^(2*(c + d*x))] - 3*a^3*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))])/(6*(a^2 + b^2)^2*d^3*(1 + E^(2*c))) + (a^3*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*(a^2 + b^2)^2*d^3*(-1 + E^(2*c))) + (Csch[c]*Sech[c]*Sech[c + d*x]^2*(-6*a^3*e*f - 6*a*b^2*e*f - 12*a^3*d^2*e^2*x - 6*a^3*f^2*x - 6*a*b^2*f^2*x - 12*a^3*d^2*e*f*x^2 - 4*a^3*d^2*f^2*x^3 + 6*a^3*e*f*Cosh[2*c] + 6*a*b^2*e*f*Cosh[2*c] + 6*a^3*f^2*x*Cosh[2*c] + 6*a*b^2*f^2*x*Cosh[2*c] + 6*a^3*e*f*Cosh[2*d*x] + 6*a*b^2*e*f*Cosh[2*d*x] + 6*a^3*f^2*x*Cosh[2*d*x] + 6*a*b^2*f^2*x*Cosh[2*d*x] + 3*a^2*b*d*e^2*Cosh[c - d*x] + 3*b^3*d*e^2*Cosh[c - d*x] + 6*a^2*b*d*e*f*x*Cosh[c - d*x] + 6*b^3*d*e*f*x*Cosh[c - d*x] + 3*a^2*b*d*f^2*x^2*Cosh[c - d*x] + 3*b^3*d*f^2*x^2*Cosh[c - d*x] - 3*a^2*b*d*e^2*Cosh[3*c + d*x] - 3*b^3*d*e^2*Cosh[3*c + d*x] - 6*a^2*b*d*e*f*x*Cosh[3*c + d*x] - 6*b^3*d*e*f*x*Cosh[3*c + d*x] - 3*a^2*b*d*f^2*x^2*Cosh[3*c + d*x] - 3*b^3*d*f^2*x^2*Cosh[3*c + d*x] - 6*a^3*e*f*Cosh[2*c + 2*d*x] - 6*a*b^2*e*f*Cosh[2*c + 2*d*x] - 12*a^3*d^2*e^2*x*Cosh[2*c + 2*d*x] - 6*a^3*f^2*x*Cosh[2*c + 2*d*x] - 6*a*b^2*f^2*x*Cosh[2*c + 2*d*x] - 12*a^3*d^2*e*f*x^2*Cosh[2*c + 2*d*x] - 4*a^3*d^2*f^2*x^3*Cosh[2*c + 2*d*x] + 6*a^3*d*e^2*Sinh[2*c] + 6*a*b^2*d*e^2*Sinh[2*c] + 12*a^3*d*e*f*x*Sinh[2*c] + 12*a*b^2*d*e*f*x*Sinh[2*c] + 6*a^3*d*f^2*x^2*Sinh[2*c] + 6*a*b^2*d*f^2*x^2*Sinh[2*c] - 6*a^2*b*e*f*Sinh[c - d*x] - 6*b^3*e*f*Sinh[c - d*x] - 6*a^2*b*f^2*x*Sinh[c - d*x] - 6*b^3*f^2*x*Sinh[c - d*x] - 6*a^2*b*e*f*Sinh[3*c + d*x] - 6*b^3*e*f*Sinh[3*c + d*x] - 6*a^2*b*f^2*x*Sinh[3*c + d*x] - 6*b^3*f^2*x*Sinh[3*c + d*x]))/(24*(a^2 + b^2)^2*d^2)","B",0
417,1,588,894,7.2966927,"\int \frac{(e+f x) \tanh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Tanh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{-2 a^3 d e \log (a+b \sinh (c+d x))+2 a^3 c f \log (a+b \sinh (c+d x))-2 a^3 d e (c+d x)+2 a^3 d e \log \left(e^{2 (c+d x)}+1\right)+a^3 f \text{Li}_2\left(-e^{2 (c+d x)}\right)+2 a^3 c f (c+d x)-2 a^3 c f \log \left(e^{2 (c+d x)}+1\right)+2 a^3 f (c+d x) \log \left(e^{2 (c+d x)}+1\right)+d \left(a^2+b^2\right) (e+f x) \text{sech}^2(c+d x) (a-b \sinh (c+d x))-i b f \left(3 a^2+b^2\right) \text{Li}_2\left(-i e^{c+d x}\right)+i b f \left(3 a^2+b^2\right) \text{Li}_2\left(i e^{c+d x}\right)-f \left(a^2+b^2\right) \text{sech}(c+d x) (a \sinh (c+d x)+b)+6 a^2 b d e \tan ^{-1}\left(e^{c+d x}\right)+3 i a^2 b f (c+d x) \log \left(1-i e^{c+d x}\right)-3 i a^2 b f (c+d x) \log \left(1+i e^{c+d x}\right)-6 a^2 b c f \tan ^{-1}\left(e^{c+d x}\right)-2 a^3 f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 a^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-2 a^3 f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-2 a^3 f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 b^3 d e \tan ^{-1}\left(e^{c+d x}\right)+i b^3 f (c+d x) \log \left(1-i e^{c+d x}\right)-i b^3 f (c+d x) \log \left(1+i e^{c+d x}\right)-2 b^3 c f \tan ^{-1}\left(e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)^2}","-\frac{(e+f x) \tan ^{-1}\left(e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d}-\frac{2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d}+\frac{i f \text{Li}_2\left(-i e^{c+d x}\right) a^4}{2 b^3 \left(a^2+b^2\right) d^2}+\frac{i f \text{Li}_2\left(-i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^2}-\frac{i f \text{Li}_2\left(i e^{c+d x}\right) a^4}{2 b^3 \left(a^2+b^2\right) d^2}-\frac{i f \text{Li}_2\left(i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^2}-\frac{f \text{sech}(c+d x) a^4}{2 b^3 \left(a^2+b^2\right) d^2}-\frac{(e+f x) \text{sech}(c+d x) \tanh (c+d x) a^4}{2 b^3 \left(a^2+b^2\right) d}-\frac{(e+f x) \text{sech}^2(c+d x) a^3}{2 b^2 \left(a^2+b^2\right) d}-\frac{(e+f x) \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) a^3}{\left(a^2+b^2\right)^2 d}-\frac{(e+f x) \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) a^3}{\left(a^2+b^2\right)^2 d}+\frac{(e+f x) \log \left(1+e^{2 (c+d x)}\right) a^3}{\left(a^2+b^2\right)^2 d}-\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) a^3}{\left(a^2+b^2\right)^2 d^2}-\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{f \text{Li}_2\left(-e^{2 (c+d x)}\right) a^3}{2 \left(a^2+b^2\right)^2 d^2}+\frac{f \tanh (c+d x) a^3}{2 b^2 \left(a^2+b^2\right) d^2}+\frac{(e+f x) \tan ^{-1}\left(e^{c+d x}\right) a^2}{b^3 d}-\frac{i f \text{Li}_2\left(-i e^{c+d x}\right) a^2}{2 b^3 d^2}+\frac{i f \text{Li}_2\left(i e^{c+d x}\right) a^2}{2 b^3 d^2}+\frac{f \text{sech}(c+d x) a^2}{2 b^3 d^2}+\frac{(e+f x) \text{sech}(c+d x) \tanh (c+d x) a^2}{2 b^3 d}+\frac{(e+f x) \text{sech}^2(c+d x) a}{2 b^2 d}-\frac{f \tanh (c+d x) a}{2 b^2 d^2}+\frac{(e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b d}-\frac{i f \text{Li}_2\left(-i e^{c+d x}\right)}{2 b d^2}+\frac{i f \text{Li}_2\left(i e^{c+d x}\right)}{2 b d^2}-\frac{f \text{sech}(c+d x)}{2 b d^2}-\frac{(e+f x) \text{sech}(c+d x) \tanh (c+d x)}{2 b d}",1,"(-2*a^3*d*e*(c + d*x) + 2*a^3*c*f*(c + d*x) + 6*a^2*b*d*e*ArcTan[E^(c + d*x)] + 2*b^3*d*e*ArcTan[E^(c + d*x)] - 6*a^2*b*c*f*ArcTan[E^(c + d*x)] - 2*b^3*c*f*ArcTan[E^(c + d*x)] + (3*I)*a^2*b*f*(c + d*x)*Log[1 - I*E^(c + d*x)] + I*b^3*f*(c + d*x)*Log[1 - I*E^(c + d*x)] - (3*I)*a^2*b*f*(c + d*x)*Log[1 + I*E^(c + d*x)] - I*b^3*f*(c + d*x)*Log[1 + I*E^(c + d*x)] - 2*a^3*f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*a^3*f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*a^3*d*e*Log[1 + E^(2*(c + d*x))] - 2*a^3*c*f*Log[1 + E^(2*(c + d*x))] + 2*a^3*f*(c + d*x)*Log[1 + E^(2*(c + d*x))] - 2*a^3*d*e*Log[a + b*Sinh[c + d*x]] + 2*a^3*c*f*Log[a + b*Sinh[c + d*x]] - I*b*(3*a^2 + b^2)*f*PolyLog[2, (-I)*E^(c + d*x)] + I*b*(3*a^2 + b^2)*f*PolyLog[2, I*E^(c + d*x)] - 2*a^3*f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + a^3*f*PolyLog[2, -E^(2*(c + d*x))] - (a^2 + b^2)*f*Sech[c + d*x]*(b + a*Sinh[c + d*x]) + (a^2 + b^2)*d*(e + f*x)*Sech[c + d*x]^2*(a - b*Sinh[c + d*x]))/(2*(a^2 + b^2)^2*d^2)","A",1
418,1,152,120,0.3870735,"\int \frac{\tanh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Tanh[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","-\frac{2 a^3 \log (a+b \sinh (c+d x))-a \left(a^2+b^2\right) \text{sech}^2(c+d x)+b \left(a^2+b^2\right) \tan ^{-1}(\sinh (c+d x))+b \left(a^2+b^2\right) \tanh (c+d x) \text{sech}(c+d x)-\left(a^3-i \left(2 a^2 b+b^3\right)\right) \log (-\sinh (c+d x)+i)-\left(a^3+i \left(2 a^2 b+b^3\right)\right) \log (\sinh (c+d x)+i)}{2 d \left(a^2+b^2\right)^2}","\frac{b \left(3 a^2+b^2\right) \tan ^{-1}(\sinh (c+d x))}{2 d \left(a^2+b^2\right)^2}+\frac{\text{sech}^2(c+d x) (a-b \sinh (c+d x))}{2 d \left(a^2+b^2\right)}-\frac{a^3 \log (a+b \sinh (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{a^3 \log (\cosh (c+d x))}{d \left(a^2+b^2\right)^2}",1,"-1/2*(b*(a^2 + b^2)*ArcTan[Sinh[c + d*x]] - (a^3 - I*(2*a^2*b + b^3))*Log[I - Sinh[c + d*x]] - (a^3 + I*(2*a^2*b + b^3))*Log[I + Sinh[c + d*x]] + 2*a^3*Log[a + b*Sinh[c + d*x]] - a*(a^2 + b^2)*Sech[c + d*x]^2 + b*(a^2 + b^2)*Sech[c + d*x]*Tanh[c + d*x])/((a^2 + b^2)^2*d)","C",1
419,-1,0,31,180.0007004,"\int \frac{\tanh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Tanh[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\tanh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
420,1,1924,451,17.0521373,"\int \frac{(e+f x)^3 \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{e^{2 c} f^3 x^4+4 e e^{2 c} f^2 x^3-\frac{2 e^{2 c} f^3 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^3}{d}+\frac{2 f^3 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^3}{d}-\frac{2 e^{2 c} f^3 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^3}{d}+\frac{2 f^3 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^3}{d}+6 e^2 e^{2 c} f x^2-\frac{6 e e^{2 c} f^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}+\frac{6 e f^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}-\frac{6 e e^{2 c} f^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}+\frac{6 e f^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x^2}{d}+4 e^3 e^{2 c} x-\frac{6 e^2 e^{2 c} f \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}+\frac{6 e^2 f \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}-\frac{6 e^2 e^{2 c} f \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}+\frac{6 e^2 f \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) x}{d}+\frac{12 e^{2 c} f^3 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) x}{d^3}-\frac{12 f^3 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) x}{d^3}+\frac{12 e^{2 c} f^3 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) x}{d^3}-\frac{12 f^3 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) x}{d^3}+\frac{4 a \sqrt{-\left(a^2+b^2\right)^2} e^3 e^{2 c} \tan ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{-a^2-b^2}}\right)}{\left(a^2+b^2\right)^{3/2} d}+\frac{4 a \sqrt{-\left(a^2+b^2\right)^2} e^3 e^{2 c} \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)}{\left(-a^2-b^2\right)^{3/2} d}+\frac{2 e^3 \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right)}{d}-\frac{2 e^3 e^{2 c} \log \left(2 e^{c+d x} a+b \left(-1+e^{2 (c+d x)}\right)\right)}{d}-\frac{6 \left(-1+e^{2 c}\right) f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^2}-\frac{6 \left(-1+e^{2 c}\right) f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^2}+\frac{12 e e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}-\frac{12 e f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}+\frac{12 e e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}-\frac{12 e f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3}-\frac{12 e^{2 c} f^3 \text{Li}_4\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^4}+\frac{12 f^3 \text{Li}_4\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^4}-\frac{12 e^{2 c} f^3 \text{Li}_4\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^4}+\frac{12 f^3 \text{Li}_4\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^4}}{2 a \left(-1+e^{2 c}\right)}-\frac{e^{2 c} \left(\frac{e^{-2 c} (e+f x)^4}{f}-\frac{2 \left(1-e^{-2 c}\right) \log \left(1-e^{-c-d x}\right) (e+f x)^3}{d}-\frac{2 \left(1-e^{-2 c}\right) \log \left(1+e^{-c-d x}\right) (e+f x)^3}{d}+\frac{6 e^{-2 c} \left(-1+e^{2 c}\right) f \left(d^2 \text{Li}_2\left(-e^{-c-d x}\right) (e+f x)^2+2 f \left(d (e+f x) \text{Li}_3\left(-e^{-c-d x}\right)+f \text{Li}_4\left(-e^{-c-d x}\right)\right)\right)}{d^4}+\frac{6 e^{-2 c} \left(-1+e^{2 c}\right) f \left(d^2 \text{Li}_2\left(e^{-c-d x}\right) (e+f x)^2+2 f \left(d (e+f x) \text{Li}_3\left(e^{-c-d x}\right)+f \text{Li}_4\left(e^{-c-d x}\right)\right)\right)}{d^4}\right)}{2 a \left(-1+e^{2 c}\right)}","-\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^4}-\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^4}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{(e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a d}-\frac{(e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a d}+\frac{3 f^3 \text{Li}_4\left(e^{2 (c+d x)}\right)}{4 a d^4}-\frac{3 f^2 (e+f x) \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a d^3}+\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a d^2}+\frac{(e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a d}",1,"-1/2*(E^(2*c)*((e + f*x)^4/(E^(2*c)*f) - (2*(1 - E^(-2*c))*(e + f*x)^3*Log[1 - E^(-c - d*x)])/d - (2*(1 - E^(-2*c))*(e + f*x)^3*Log[1 + E^(-c - d*x)])/d + (6*(-1 + E^(2*c))*f*(d^2*(e + f*x)^2*PolyLog[2, -E^(-c - d*x)] + 2*f*(d*(e + f*x)*PolyLog[3, -E^(-c - d*x)] + f*PolyLog[4, -E^(-c - d*x)])))/(d^4*E^(2*c)) + (6*(-1 + E^(2*c))*f*(d^2*(e + f*x)^2*PolyLog[2, E^(-c - d*x)] + 2*f*(d*(e + f*x)*PolyLog[3, E^(-c - d*x)] + f*PolyLog[4, E^(-c - d*x)])))/(d^4*E^(2*c))))/(a*(-1 + E^(2*c))) + (4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4)/(2*a*(-1 + E^(2*c)))","B",1
421,1,1013,325,5.7465688,"\int \frac{(e+f x)^2 \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{-\frac{2 (e+f x)^3}{\left(-1+e^{2 c}\right) f}+\frac{3 \log \left(1-e^{-c-d x}\right) (e+f x)^2}{d}+\frac{3 \log \left(1+e^{-c-d x}\right) (e+f x)^2}{d}-\frac{6 f \left(d (e+f x) \text{Li}_2\left(-e^{-c-d x}\right)+f \text{Li}_3\left(-e^{-c-d x}\right)\right)}{d^3}-\frac{6 f \left(d (e+f x) \text{Li}_2\left(e^{-c-d x}\right)+f \text{Li}_3\left(e^{-c-d x}\right)\right)}{d^3}+\frac{2 e^{2 c} f^2 x^3 d^3+6 e e^{2 c} f x^2 d^3+6 e^2 e^{2 c} x d^3-3 e^2 e^{2 c} \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2+3 e^2 \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)}{d^3 \left(-1+e^{2 c}\right)}}{3 a}","\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^3}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^3}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{(e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a d}-\frac{(e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a d}-\frac{f^2 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a d^3}+\frac{f (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^2}+\frac{(e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a d}",1,"((-2*(e + f*x)^3)/((-1 + E^(2*c))*f) + (3*(e + f*x)^2*Log[1 - E^(-c - d*x)])/d + (3*(e + f*x)^2*Log[1 + E^(-c - d*x)])/d - (6*f*(d*(e + f*x)*PolyLog[2, -E^(-c - d*x)] + f*PolyLog[3, -E^(-c - d*x)]))/d^3 - (6*f*(d*(e + f*x)*PolyLog[2, E^(-c - d*x)] + f*PolyLog[3, E^(-c - d*x)]))/d^3 + (6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/(d^3*(-1 + E^(2*c))))/(3*a)","B",1
422,1,236,205,0.8806929,"\int \frac{(e+f x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-d e \log (\sinh (c+d x))+\frac{1}{2} f \text{Li}_2\left(e^{-2 (c+d x)}\right)-f (c+d x)^2-f (c+d x) \log \left(1-e^{-2 (c+d x)}\right)+c f \log (\sinh (c+d x))}{a d^2}","-\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{(e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a d}-\frac{(e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a d}+\frac{f \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a d^2}+\frac{(e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d}",1,"-((-(f*(c + d*x)^2) - f*(c + d*x)*Log[1 - E^(-2*(c + d*x))] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d*e*Log[Sinh[c + d*x]] + c*f*Log[Sinh[c + d*x]] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + (f*PolyLog[2, E^(-2*(c + d*x))])/2 + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*d^2))","A",1
423,1,28,34,0.0198466,"\int \frac{\coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Coth[c + d*x]/(a + b*Sinh[c + d*x]),x]","\frac{\log (\sinh (c+d x))-\log (a+b \sinh (c+d x))}{a d}","\frac{\log (\sinh (c+d x))}{a d}-\frac{\log (a+b \sinh (c+d x))}{a d}",1,"(Log[Sinh[c + d*x]] - Log[a + b*Sinh[c + d*x]])/(a*d)","A",1
424,0,0,29,28.6269423,"\int \frac{\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Coth[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Coth[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
425,1,802,638,2.2295012,"\int \frac{(e+f x)^3 \cosh (c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{a x \left(4 e^3+6 f x e^2+4 f^2 x^2 e+f^3 x^3\right) d^4+4 \sqrt{a^2+b^2} \left(2 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3-f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-3 e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2+3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2+6 e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+6 f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-6 e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-6 f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-6 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)-4 b \left(2 d^3 \tanh ^{-1}(\cosh (c+d x)+\sinh (c+d x)) (e+f x)^3+3 f \left(2 \text{Li}_4(-\cosh (c+d x)-\sinh (c+d x)) f^2-2 d (e+f x) \text{Li}_3(-\cosh (c+d x)-\sinh (c+d x)) f+d^2 (e+f x)^2 \text{Li}_2(-\cosh (c+d x)-\sinh (c+d x))\right)-3 f \left(2 \text{Li}_4(\cosh (c+d x)+\sinh (c+d x)) f^2-2 d (e+f x) \text{Li}_3(\cosh (c+d x)+\sinh (c+d x)) f+d^2 (e+f x)^2 \text{Li}_2(\cosh (c+d x)+\sinh (c+d x))\right)\right)}{4 a b d^4}","-\frac{6 f^3 \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b d^4}+\frac{6 f^3 \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b d^4}+\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b d^3}-\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b d^3}-\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b d^2}+\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b d^2}-\frac{\sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a b d}+\frac{\sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a b d}-\frac{6 f^3 \text{Li}_4\left(-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{Li}_4\left(e^{c+d x}\right)}{a d^4}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{(e+f x)^4}{4 b f}",1,"(a*d^4*x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3) + 4*Sqrt[a^2 + b^2]*(2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - 4*b*(2*d^3*(e + f*x)^3*ArcTanh[Cosh[c + d*x] + Sinh[c + d*x]] + 3*f*(d^2*(e + f*x)^2*PolyLog[2, -Cosh[c + d*x] - Sinh[c + d*x]] - 2*d*f*(e + f*x)*PolyLog[3, -Cosh[c + d*x] - Sinh[c + d*x]] + 2*f^2*PolyLog[4, -Cosh[c + d*x] - Sinh[c + d*x]]) - 3*f*(d^2*(e + f*x)^2*PolyLog[2, Cosh[c + d*x] + Sinh[c + d*x]] - 2*d*f*(e + f*x)*PolyLog[3, Cosh[c + d*x] + Sinh[c + d*x]] + 2*f^2*PolyLog[4, Cosh[c + d*x] + Sinh[c + d*x]])))/(4*a*b*d^4)","A",0
426,1,489,462,1.7124949,"\int \frac{(e+f x)^2 \cosh (c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\sqrt{a^2+b^2} \left(2 d^2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-2 d^2 e f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+2 d^2 e f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 d f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 d f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{a b d^3}+\frac{-\frac{2 f \left(d (e+f x) \text{Li}_2\left(-e^{c+d x}\right)-f \text{Li}_3\left(-e^{c+d x}\right)\right)}{d^2}+\frac{2 f \left(d (e+f x) \text{Li}_2\left(e^{c+d x}\right)-f \text{Li}_3\left(e^{c+d x}\right)\right)}{d^2}+(e+f x)^2 \log \left(1-e^{c+d x}\right)-(e+f x)^2 \log \left(e^{c+d x}+1\right)}{a d}+\frac{x \left(3 e^2+3 e f x+f^2 x^2\right)}{3 b}","\frac{2 f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b d^3}-\frac{2 f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b d^3}-\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b d^2}+\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b d^2}-\frac{\sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a b d}+\frac{\sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a b d}+\frac{2 f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{2 f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{2 f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{(e+f x)^3}{3 b f}",1,"(x*(3*e^2 + 3*e*f*x + f^2*x^2))/(3*b) + ((e + f*x)^2*Log[1 - E^(c + d*x)] - (e + f*x)^2*Log[1 + E^(c + d*x)] - (2*f*(d*(e + f*x)*PolyLog[2, -E^(c + d*x)] - f*PolyLog[3, -E^(c + d*x)]))/d^2 + (2*f*(d*(e + f*x)*PolyLog[2, E^(c + d*x)] - f*PolyLog[3, E^(c + d*x)]))/d^2)/(a*d) + (Sqrt[a^2 + b^2]*(2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a*b*d^3)","A",1
427,1,339,286,1.7843807,"\int \frac{(e+f x) \cosh (c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{2 \sqrt{a^2+b^2} \left(2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)-a (c+d x) (c f-d (2 e+f x))+2 b d e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+2 b f \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)+(c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right)-2 b c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a b d^2}","-\frac{f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b d^2}+\frac{f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b d^2}-\frac{\sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a b d}+\frac{\sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a b d}-\frac{f \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{f \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{e x}{b}+\frac{f x^2}{2 b}",1,"(-(a*(c + d*x)*(c*f - d*(2*e + f*x))) + 2*b*d*e*Log[Tanh[(c + d*x)/2]] - 2*b*c*f*Log[Tanh[(c + d*x)/2]] + 2*b*f*((c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)]) + 2*Sqrt[a^2 + b^2]*(2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(2*a*b*d^2)","A",1
428,1,80,71,0.1362434,"\int \frac{\cosh (c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{2 \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)+a (c+d x)+b \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a b d}","\frac{2 \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a b d}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}+\frac{x}{b}",1,"(a*(c + d*x) + 2*Sqrt[-a^2 - b^2]*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] + b*Log[Tanh[(c + d*x)/2]])/(a*b*d)","A",1
429,0,0,35,57.1431672,"\int \frac{\cosh (c+d x) \coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]*Coth[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh (c+d x) \coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\cosh (c+d x) \coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[(Cosh[c + d*x]*Coth[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
430,1,3099,656,16.3783956,"\int \frac{(e+f x)^3 \cosh ^2(c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]^2*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{6 f^3 \left(a^2+b^2\right) \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b^2 d^4}-\frac{6 f^3 \left(a^2+b^2\right) \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b^2 d^4}+\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b^2 d^3}+\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b^2 d^3}-\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b^2 d^2}-\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b^2 d^2}-\frac{\left(a^2+b^2\right) (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a b^2 d}-\frac{\left(a^2+b^2\right) (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a b^2 d}+\frac{\left(a^2+b^2\right) (e+f x)^4}{4 a b^2 f}+\frac{3 f^3 \text{Li}_4\left(e^{2 (c+d x)}\right)}{4 a d^4}-\frac{3 f^2 (e+f x) \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a d^3}+\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a d^2}+\frac{(e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a d}-\frac{(e+f x)^4}{4 a f}-\frac{6 f^3 \cosh (c+d x)}{b d^4}+\frac{6 f^2 (e+f x) \sinh (c+d x)}{b d^3}-\frac{3 f (e+f x)^2 \cosh (c+d x)}{b d^2}+\frac{(e+f x)^3 \sinh (c+d x)}{b d}",1,"-1/2*(E^(2*c)*((e + f*x)^4/(E^(2*c)*f) - (2*(1 - E^(-2*c))*(e + f*x)^3*Log[1 - E^(-c - d*x)])/d - (2*(1 - E^(-2*c))*(e + f*x)^3*Log[1 + E^(-c - d*x)])/d + (6*(-1 + E^(2*c))*f*(d^2*(e + f*x)^2*PolyLog[2, -E^(-c - d*x)] + 2*f*(d*(e + f*x)*PolyLog[3, -E^(-c - d*x)] + f*PolyLog[4, -E^(-c - d*x)])))/(d^4*E^(2*c)) + (6*(-1 + E^(2*c))*f*(d^2*(e + f*x)^2*PolyLog[2, E^(-c - d*x)] + 2*f*(d*(e + f*x)*PolyLog[3, E^(-c - d*x)] + f*PolyLog[4, E^(-c - d*x)])))/(d^4*E^(2*c))))/(a*(-1 + E^(2*c))) + ((a^2 + b^2)*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(2*a*b^2*(-1 + E^(2*c))) + Csch[c]*(Cosh[c + d*x]/(8*b^2*d^4) - Sinh[c + d*x]/(8*b^2*d^4))*(-4*a*d^4*e^3*x*Cosh[d*x] - 6*a*d^4*e^2*f*x^2*Cosh[d*x] - 4*a*d^4*e*f^2*x^3*Cosh[d*x] - a*d^4*f^3*x^4*Cosh[d*x] - 4*a*d^4*e^3*x*Cosh[2*c + d*x] - 6*a*d^4*e^2*f*x^2*Cosh[2*c + d*x] - 4*a*d^4*e*f^2*x^3*Cosh[2*c + d*x] - a*d^4*f^3*x^4*Cosh[2*c + d*x] - 2*b*d^3*e^3*Cosh[c + 2*d*x] + 6*b*d^2*e^2*f*Cosh[c + 2*d*x] - 12*b*d*e*f^2*Cosh[c + 2*d*x] + 12*b*f^3*Cosh[c + 2*d*x] - 6*b*d^3*e^2*f*x*Cosh[c + 2*d*x] + 12*b*d^2*e*f^2*x*Cosh[c + 2*d*x] - 12*b*d*f^3*x*Cosh[c + 2*d*x] - 6*b*d^3*e*f^2*x^2*Cosh[c + 2*d*x] + 6*b*d^2*f^3*x^2*Cosh[c + 2*d*x] - 2*b*d^3*f^3*x^3*Cosh[c + 2*d*x] + 2*b*d^3*e^3*Cosh[3*c + 2*d*x] - 6*b*d^2*e^2*f*Cosh[3*c + 2*d*x] + 12*b*d*e*f^2*Cosh[3*c + 2*d*x] - 12*b*f^3*Cosh[3*c + 2*d*x] + 6*b*d^3*e^2*f*x*Cosh[3*c + 2*d*x] - 12*b*d^2*e*f^2*x*Cosh[3*c + 2*d*x] + 12*b*d*f^3*x*Cosh[3*c + 2*d*x] + 6*b*d^3*e*f^2*x^2*Cosh[3*c + 2*d*x] - 6*b*d^2*f^3*x^2*Cosh[3*c + 2*d*x] + 2*b*d^3*f^3*x^3*Cosh[3*c + 2*d*x] - 4*b*d^3*e^3*Sinh[c] - 12*b*d^2*e^2*f*Sinh[c] - 24*b*d*e*f^2*Sinh[c] - 24*b*f^3*Sinh[c] - 12*b*d^3*e^2*f*x*Sinh[c] - 24*b*d^2*e*f^2*x*Sinh[c] - 24*b*d*f^3*x*Sinh[c] - 12*b*d^3*e*f^2*x^2*Sinh[c] - 12*b*d^2*f^3*x^2*Sinh[c] - 4*b*d^3*f^3*x^3*Sinh[c] - 4*a*d^4*e^3*x*Sinh[d*x] - 6*a*d^4*e^2*f*x^2*Sinh[d*x] - 4*a*d^4*e*f^2*x^3*Sinh[d*x] - a*d^4*f^3*x^4*Sinh[d*x] - 4*a*d^4*e^3*x*Sinh[2*c + d*x] - 6*a*d^4*e^2*f*x^2*Sinh[2*c + d*x] - 4*a*d^4*e*f^2*x^3*Sinh[2*c + d*x] - a*d^4*f^3*x^4*Sinh[2*c + d*x] - 2*b*d^3*e^3*Sinh[c + 2*d*x] + 6*b*d^2*e^2*f*Sinh[c + 2*d*x] - 12*b*d*e*f^2*Sinh[c + 2*d*x] + 12*b*f^3*Sinh[c + 2*d*x] - 6*b*d^3*e^2*f*x*Sinh[c + 2*d*x] + 12*b*d^2*e*f^2*x*Sinh[c + 2*d*x] - 12*b*d*f^3*x*Sinh[c + 2*d*x] - 6*b*d^3*e*f^2*x^2*Sinh[c + 2*d*x] + 6*b*d^2*f^3*x^2*Sinh[c + 2*d*x] - 2*b*d^3*f^3*x^3*Sinh[c + 2*d*x] + 2*b*d^3*e^3*Sinh[3*c + 2*d*x] - 6*b*d^2*e^2*f*Sinh[3*c + 2*d*x] + 12*b*d*e*f^2*Sinh[3*c + 2*d*x] - 12*b*f^3*Sinh[3*c + 2*d*x] + 6*b*d^3*e^2*f*x*Sinh[3*c + 2*d*x] - 12*b*d^2*e*f^2*x*Sinh[3*c + 2*d*x] + 12*b*d*f^3*x*Sinh[3*c + 2*d*x] + 6*b*d^3*e*f^2*x^2*Sinh[3*c + 2*d*x] - 6*b*d^2*f^3*x^2*Sinh[3*c + 2*d*x] + 2*b*d^3*f^3*x^3*Sinh[3*c + 2*d*x])","B",0
431,1,1196,486,7.2237304,"\int \frac{(e+f x)^2 \cosh ^2(c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]^2*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{1}{3} \left(-\frac{a x \left(3 e^2+3 f x e+f^2 x^2\right) \coth (c)}{b^2}-\frac{e^{2 c} \left(\frac{2 e^{-2 c} (e+f x)^3}{f}-\frac{3 \left(1-e^{-2 c}\right) \log \left(1-e^{-c-d x}\right) (e+f x)^2}{d}-\frac{3 \left(1-e^{-2 c}\right) \log \left(1+e^{-c-d x}\right) (e+f x)^2}{d}+\frac{6 e^{-2 c} \left(-1+e^{2 c}\right) f \left(d (e+f x) \text{Li}_2\left(-e^{-c-d x}\right)+f \text{Li}_3\left(-e^{-c-d x}\right)\right)}{d^3}+\frac{6 e^{-2 c} \left(-1+e^{2 c}\right) f \left(d (e+f x) \text{Li}_2\left(e^{-c-d x}\right)+f \text{Li}_3\left(e^{-c-d x}\right)\right)}{d^3}\right)}{a \left(-1+e^{2 c}\right)}+\frac{\left(a^2+b^2\right) \left(2 e^{2 c} f^2 x^3 d^3+6 e e^{2 c} f x^2 d^3+6 e^2 e^{2 c} x d^3-3 e^2 e^{2 c} \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2+3 e^2 \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right)}{a b^2 d^3 \left(-1+e^{2 c}\right)}+\frac{3 \cosh (d x) \left(\left(2 f^2+d^2 (e+f x)^2\right) \sinh (c)-2 d f (e+f x) \cosh (c)\right)}{b d^3}+\frac{3 \left(\left(2 f^2+d^2 (e+f x)^2\right) \cosh (c)-2 d f (e+f x) \sinh (c)\right) \sinh (d x)}{b d^3}\right)","\frac{2 f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b^2 d^3}+\frac{2 f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b^2 d^3}-\frac{2 f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b^2 d^2}-\frac{2 f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b^2 d^2}-\frac{\left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a b^2 d}-\frac{\left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a b^2 d}+\frac{\left(a^2+b^2\right) (e+f x)^3}{3 a b^2 f}-\frac{f^2 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a d^3}+\frac{f (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^2}+\frac{(e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a d}-\frac{(e+f x)^3}{3 a f}+\frac{2 f^2 \sinh (c+d x)}{b d^3}-\frac{2 f (e+f x) \cosh (c+d x)}{b d^2}+\frac{(e+f x)^2 \sinh (c+d x)}{b d}",1,"(-((a*x*(3*e^2 + 3*e*f*x + f^2*x^2)*Coth[c])/b^2) - (E^(2*c)*((2*(e + f*x)^3)/(E^(2*c)*f) - (3*(1 - E^(-2*c))*(e + f*x)^2*Log[1 - E^(-c - d*x)])/d - (3*(1 - E^(-2*c))*(e + f*x)^2*Log[1 + E^(-c - d*x)])/d + (6*(-1 + E^(2*c))*f*(d*(e + f*x)*PolyLog[2, -E^(-c - d*x)] + f*PolyLog[3, -E^(-c - d*x)]))/(d^3*E^(2*c)) + (6*(-1 + E^(2*c))*f*(d*(e + f*x)*PolyLog[2, E^(-c - d*x)] + f*PolyLog[3, E^(-c - d*x)]))/(d^3*E^(2*c))))/(a*(-1 + E^(2*c))) + ((a^2 + b^2)*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(a*b^2*d^3*(-1 + E^(2*c))) + (3*Cosh[d*x]*(-2*d*f*(e + f*x)*Cosh[c] + (2*f^2 + d^2*(e + f*x)^2)*Sinh[c]))/(b*d^3) + (3*((2*f^2 + d^2*(e + f*x)^2)*Cosh[c] - 2*d*f*(e + f*x)*Sinh[c])*Sinh[d*x])/(b*d^3))/3","B",1
432,1,296,322,1.633865,"\int \frac{(e+f x) \cosh ^2(c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]^2*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\left(a^2+b^2\right) \left(-f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-d e \log (a+b \sinh (c+d x))+c f \log (a+b \sinh (c+d x))+\frac{1}{2} f (c+d x)^2\right)+a b d (e+f x) \sinh (c+d x)-a b f \cosh (c+d x)+b^2 d e \log (\sinh (c+d x))+\frac{1}{2} b^2 f \left((c+d x) \left(2 \log \left(1-e^{-2 (c+d x)}\right)+c+d x\right)-\text{Li}_2\left(e^{-2 (c+d x)}\right)\right)-b^2 c f \log (\sinh (c+d x))}{a b^2 d^2}","-\frac{f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a b^2 d^2}-\frac{f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a b^2 d^2}-\frac{\left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a b^2 d}-\frac{\left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a b^2 d}+\frac{\left(a^2+b^2\right) (e+f x)^2}{2 a b^2 f}+\frac{f \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a d^2}+\frac{(e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d}-\frac{(e+f x)^2}{2 a f}-\frac{f \cosh (c+d x)}{b d^2}+\frac{(e+f x) \sinh (c+d x)}{b d}",1,"(-(a*b*f*Cosh[c + d*x]) + b^2*d*e*Log[Sinh[c + d*x]] - b^2*c*f*Log[Sinh[c + d*x]] + (b^2*f*((c + d*x)*(c + d*x + 2*Log[1 - E^(-2*(c + d*x))]) - PolyLog[2, E^(-2*(c + d*x))]))/2 + (a^2 + b^2)*((f*(c + d*x)^2)/2 - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d*e*Log[a + b*Sinh[c + d*x]] + c*f*Log[a + b*Sinh[c + d*x]] - f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + a*b*d*(e + f*x)*Sinh[c + d*x])/(a*b^2*d^2)","A",1
433,1,48,57,0.0757673,"\int \frac{\cosh ^2(c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]^2*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{-\left(\frac{a}{b^2}+\frac{1}{a}\right) \log (a+b \sinh (c+d x))+\frac{\log (\sinh (c+d x))}{a}+\frac{\sinh (c+d x)}{b}}{d}","-\frac{\left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{a b^2 d}+\frac{\log (\sinh (c+d x))}{a d}+\frac{\sinh (c+d x)}{b d}",1,"(Log[Sinh[c + d*x]]/a - (a^(-1) + a/b^2)*Log[a + b*Sinh[c + d*x]] + Sinh[c + d*x]/b)/d","A",1
434,-1,0,37,180.0003183,"\int \frac{\cosh ^2(c+d x) \coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]^2*Coth[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\cosh ^2(c+d x) \coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
435,1,3872,1049,34.4750692,"\int \frac{(e+f x)^3 \text{csch}(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Csch[c + d*x]*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{6 i b \text{Li}_4\left(-i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}-\frac{6 i b \text{Li}_4\left(i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}-\frac{6 b^2 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f^3}{a \left(a^2+b^2\right) d^4}-\frac{6 b^2 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f^3}{a \left(a^2+b^2\right) d^4}+\frac{3 b^2 \text{Li}_4\left(-e^{2 (c+d x)}\right) f^3}{4 a \left(a^2+b^2\right) d^4}-\frac{3 \text{Li}_4\left(-e^{2 c+2 d x}\right) f^3}{4 a d^4}+\frac{3 \text{Li}_4\left(e^{2 c+2 d x}\right) f^3}{4 a d^4}-\frac{6 i b (e+f x) \text{Li}_3\left(-i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}+\frac{6 i b (e+f x) \text{Li}_3\left(i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}+\frac{6 b^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f^2}{a \left(a^2+b^2\right) d^3}+\frac{6 b^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f^2}{a \left(a^2+b^2\right) d^3}-\frac{3 b^2 (e+f x) \text{Li}_3\left(-e^{2 (c+d x)}\right) f^2}{2 a \left(a^2+b^2\right) d^3}+\frac{3 (e+f x) \text{Li}_3\left(-e^{2 c+2 d x}\right) f^2}{2 a d^3}-\frac{3 (e+f x) \text{Li}_3\left(e^{2 c+2 d x}\right) f^2}{2 a d^3}+\frac{3 i b (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right) f}{\left(a^2+b^2\right) d^2}-\frac{3 i b (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right) f}{\left(a^2+b^2\right) d^2}-\frac{3 b^2 (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f}{a \left(a^2+b^2\right) d^2}-\frac{3 b^2 (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f}{a \left(a^2+b^2\right) d^2}+\frac{3 b^2 (e+f x)^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) f}{2 a \left(a^2+b^2\right) d^2}-\frac{3 (e+f x)^2 \text{Li}_2\left(-e^{2 c+2 d x}\right) f}{2 a d^2}+\frac{3 (e+f x)^2 \text{Li}_2\left(e^{2 c+2 d x}\right) f}{2 a d^2}-\frac{2 b (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right)}{\left(a^2+b^2\right) d}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}-\frac{b^2 (e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right)}{a \left(a^2+b^2\right) d}-\frac{b^2 (e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right)}{a \left(a^2+b^2\right) d}+\frac{b^2 (e+f x)^3 \log \left(1+e^{2 (c+d x)}\right)}{a \left(a^2+b^2\right) d}",1,"2*((a*E^c*((e + f*x)^4/(4*E^c*f) + ((1 + E^(-c))*(e + f*x)^3*Log[1 + E^(-c - d*x)])/d - (3*(1 + E^c)*f*(d^2*(e + f*x)^2*PolyLog[2, -E^(-c - d*x)] + 2*f*(d*(e + f*x)*PolyLog[3, -E^(-c - d*x)] + f*PolyLog[4, -E^(-c - d*x)])))/(d^4*E^c)))/(2*(a^2 + b^2)*(1 + E^c)) + ((I/2)*a*E^c*((e + f*x)^4/(4*E^c*f) + ((I + E^(-c))*(e + f*x)^3*Log[1 - I*E^(-c - d*x)])/d - (3*(1 + I*E^c)*f*(d^2*(e + f*x)^2*PolyLog[2, I*E^(-c - d*x)] + 2*f*(d*(e + f*x)*PolyLog[3, I*E^(-c - d*x)] + f*PolyLog[4, I*E^(-c - d*x)])))/(d^4*E^c)))/((a^2 + b^2)*(-I + E^c)) - (b^2*E^(2*c)*((e + f*x)^4/(E^(2*c)*f) - (2*(1 - E^(-2*c))*(e + f*x)^3*Log[1 - E^(-c - d*x)])/d - (2*(1 - E^(-2*c))*(e + f*x)^3*Log[1 + E^(-c - d*x)])/d + (6*(-1 + E^(2*c))*f*(d^2*(e + f*x)^2*PolyLog[2, -E^(-c - d*x)] + 2*f*(d*(e + f*x)*PolyLog[3, -E^(-c - d*x)] + f*PolyLog[4, -E^(-c - d*x)])))/(d^4*E^(2*c)) + (6*(-1 + E^(2*c))*f*(d^2*(e + f*x)^2*PolyLog[2, E^(-c - d*x)] + 2*f*(d*(e + f*x)*PolyLog[3, E^(-c - d*x)] + f*PolyLog[4, E^(-c - d*x)])))/(d^4*E^(2*c))))/(4*a*(a^2 + b^2)*(-1 + E^(2*c))) - ((I/2)*b*((-2*I)*d^3*e^3*ArcTan[E^(c + d*x)] + 3*d^3*e^2*f*x*Log[1 - I*E^(c + d*x)] + 3*d^3*e*f^2*x^2*Log[1 - I*E^(c + d*x)] + d^3*f^3*x^3*Log[1 - I*E^(c + d*x)] - 3*d^3*e^2*f*x*Log[1 + I*E^(c + d*x)] - 3*d^3*e*f^2*x^2*Log[1 + I*E^(c + d*x)] - d^3*f^3*x^3*Log[1 + I*E^(c + d*x)] - 3*d^2*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)] + 3*d^2*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)] + 6*d*e*f^2*PolyLog[3, (-I)*E^(c + d*x)] + 6*d*f^3*x*PolyLog[3, (-I)*E^(c + d*x)] - 6*d*e*f^2*PolyLog[3, I*E^(c + d*x)] - 6*d*f^3*x*PolyLog[3, I*E^(c + d*x)] - 6*f^3*PolyLog[4, (-I)*E^(c + d*x)] + 6*f^3*PolyLog[4, I*E^(c + d*x)]))/((a^2 + b^2)*d^4) - (a*(-((e + f*x)^3*Log[1 - E^(c + d*x)]) + (e + f*x)^3*Log[1 - I*E^(c + d*x)] + (3*f*(d^2*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)] - 2*d*f*(e + f*x)*PolyLog[3, I*E^(c + d*x)] + 2*f^2*PolyLog[4, I*E^(c + d*x)]))/d^3 - (3*f*(d^2*(e + f*x)^2*PolyLog[2, E^(c + d*x)] - 2*d*f*(e + f*x)*PolyLog[3, E^(c + d*x)] + 2*f^2*PolyLog[4, E^(c + d*x)]))/d^3))/(2*(a^2 + b^2)*d) + (b^2*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(4*a*(a^2 + b^2)*(-1 + E^(2*c))) - (b^2*x*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3)*Csch[c/2]*Sech[c/2]*Sech[c])/(32*a*(a^2 + b^2)) + (3*a*e^2*f*x^2*Csch[c/2]*Sech[c/2])/(16*(a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) + (3*b^2*e^2*f*x^2*Csch[c/2]*Sech[c/2])/(16*a*(a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) + (a*e*f^2*x^3*Csch[c/2]*Sech[c/2])/(8*(a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) + (b^2*e*f^2*x^3*Csch[c/2]*Sech[c/2])/(8*a*(a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) + (a*f^3*x^4*Csch[c/2]*Sech[c/2])/(32*(a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) + (b^2*f^3*x^4*Csch[c/2]*Sech[c/2])/(32*a*(a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) - (3*a*e^2*f*x^2*Cosh[c]*Csch[c/2]*Sech[c/2])/(16*(a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) - (a*e*f^2*x^3*Cosh[c]*Csch[c/2]*Sech[c/2])/(8*(a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) - (a*f^3*x^4*Cosh[c]*Csch[c/2]*Sech[c/2])/(32*(a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) - (((3*I)/16)*a*e^2*f*x^2*Csch[c/2]*Sech[c/2]*Sinh[c])/((a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) - ((I/8)*a*e*f^2*x^3*Csch[c/2]*Sech[c/2]*Sinh[c])/((a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) - ((I/32)*a*f^3*x^4*Csch[c/2]*Sech[c/2]*Sinh[c])/((a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])) - (e^3*x*Csch[c/2]*Sech[c/2]*(-a^2 - b^2 + a^2*Cosh[c] + I*a^2*Sinh[c]))/(8*a*(a^2 + b^2)*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])))","B",0
436,1,3002,734,28.7071959,"\int \frac{(e+f x)^2 \text{csch}(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^3 \left(a^2+b^2\right)}+\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^3 \left(a^2+b^2\right)}-\frac{b^2 f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right)}{2 a d^3 \left(a^2+b^2\right)}-\frac{2 i b f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 i b f^2 \text{Li}_3\left(i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 b^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2 \left(a^2+b^2\right)}-\frac{2 b^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{b^2 f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{2 i b f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{2 i b f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{b^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a d \left(a^2+b^2\right)}-\frac{b^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a d \left(a^2+b^2\right)}+\frac{b^2 (e+f x)^2 \log \left(e^{2 (c+d x)}+1\right)}{a d \left(a^2+b^2\right)}-\frac{2 b (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)}+\frac{f^2 \text{Li}_3\left(-e^{2 c+2 d x}\right)}{2 a d^3}-\frac{f^2 \text{Li}_3\left(e^{2 c+2 d x}\right)}{2 a d^3}-\frac{f (e+f x) \text{Li}_2\left(-e^{2 c+2 d x}\right)}{a d^2}+\frac{f (e+f x) \text{Li}_2\left(e^{2 c+2 d x}\right)}{a d^2}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}",1,"2*(-1/6*(b^2*x*(3*e^2 + 3*e*f*x + f^2*x^2)*Csch[2*c])/(a*(a^2 + b^2)) + (a*E^c*((e + f*x)^3/(3*E^c*f) + ((1 + E^(-c))*(e + f*x)^2*Log[1 + E^(-c - d*x)])/d - (2*(1 + E^c)*f*(d*(e + f*x)*PolyLog[2, -E^(-c - d*x)] + f*PolyLog[3, -E^(-c - d*x)]))/(d^3*E^c)))/(2*(a^2 + b^2)*(1 + E^c)) + (d^2*(d*x*((-3*I)*b*e*f*x + a*((-3*I)*e^2*E^c + 3*e*f*x + f^2*x^2)) + 3*(1 + I*E^c)*f*x*(2*a*e - (2*I)*b*e + a*f*x)*Log[1 - I*E^(-c - d*x)] + 3*a*e^2*(1 + I*E^c)*Log[I - E^(c + d*x)]) - (6*I)*d*(-I + E^c)*f*((-I)*b*e + a*(e + f*x))*PolyLog[2, I*E^(-c - d*x)] - (6*I)*a*(-I + E^c)*f^2*PolyLog[3, I*E^(-c - d*x)])/(6*(a - I*b)*((-I)*a + b)*d^3*(-I + E^c)) - (b^2*E^(2*c)*((2*(e + f*x)^3)/(E^(2*c)*f) - (3*(1 - E^(-2*c))*(e + f*x)^2*Log[1 - E^(-c - d*x)])/d - (3*(1 - E^(-2*c))*(e + f*x)^2*Log[1 + E^(-c - d*x)])/d + (6*(-1 + E^(2*c))*f*(d*(e + f*x)*PolyLog[2, -E^(-c - d*x)] + f*PolyLog[3, -E^(-c - d*x)]))/(d^3*E^(2*c)) + (6*(-1 + E^(2*c))*f*(d*(e + f*x)*PolyLog[2, E^(-c - d*x)] + f*PolyLog[3, E^(-c - d*x)]))/(d^3*E^(2*c))))/(6*a*(a^2 + b^2)*(-1 + E^(2*c))) - ((I/2)*b*((-2*I)*d^2*e^2*ArcTan[E^(c + d*x)] + d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] - d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] - 2*d*f^2*x*PolyLog[2, (-I)*E^(c + d*x)] + 2*d*f^2*x*PolyLog[2, I*E^(c + d*x)] + 2*f^2*PolyLog[3, (-I)*E^(c + d*x)] - 2*f^2*PolyLog[3, I*E^(c + d*x)]))/((a^2 + b^2)*d^3) - ((-I)*b*d^3*e*E^(2*c)*f*x^2 + 2*a*d^2*e^2*ArcTan[1 - (1 + I)*E^(c + d*x)] + (2*I)*a*d^2*e^2*E^(2*c)*ArcTan[1 - (1 + I)*E^(c + d*x)] + (2*I)*a*d^2*e*f*x*Log[1 - E^(c + d*x)] - 2*a*d^2*e*E^(2*c)*f*x*Log[1 - E^(c + d*x)] + I*a*d^2*f^2*x^2*Log[1 - E^(c + d*x)] - a*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] - (2*I)*a*d^2*e*f*x*Log[1 - I*E^(c + d*x)] + 2*b*d^2*e*f*x*Log[1 - I*E^(c + d*x)] + 2*a*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] + (2*I)*b*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] - I*a*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] + a*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] + 2*d*(-I + E^(2*c))*f*(I*b*e + a*(e + f*x))*PolyLog[2, I*E^(c + d*x)] - 2*a*d*(-I + E^(2*c))*f*(e + f*x)*PolyLog[2, E^(c + d*x)] + (2*I)*a*f^2*PolyLog[3, I*E^(c + d*x)] - 2*a*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - (2*I)*a*f^2*PolyLog[3, E^(c + d*x)] + 2*a*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)])/(2*(a^2 + b^2)*d^3*(-I + E^(2*c))) + (b^2*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(6*a*(a^2 + b^2)*d^3*(-1 + E^(2*c))) + (b^2*e*f*x^2)/(2*a*(a^2 + b^2)*(Cosh[c] + Sinh[c])^2) + (b^2*f^2*x^3)/(6*a*(a^2 + b^2)*(Cosh[c] + Sinh[c])^2) + (b^2*f^2*x^3*Coth[2*c])/(6*a*(a^2 + b^2)*(Cosh[c] + Sinh[c])^2) + (b^2*e*f*x^2*Cosh[2*c]*Csch[c]*Sech[c])/(4*a*(a^2 + b^2)*(Cosh[c] + Sinh[c])^2) + (e^2*x*Csch[c]^2*(-(a^2*Coth[c]) + Csch[c]*(a^2 + b^2 - I*a^2*Sinh[c])))/(a*(a^2 + b^2)*(Csch[c/2] - I*Sech[c/2])*(Csch[c/2] + I*Sech[c/2])) - ((1/4 - I/4)*a*e*f*x^2*Cosh[c])/((a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(-I - I*Cosh[c] + Sinh[c] + Sinh[2*c])) + (b*e*f*x^2*Cosh[c])/(4*(a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(-I - I*Cosh[c] + Sinh[c] + Sinh[2*c])) - ((1/12 - I/12)*a*f^2*x^3*Cosh[c])/((a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(-I - I*Cosh[c] + Sinh[c] + Sinh[2*c])) - (b*e*f*x^2*Cosh[3*c])/(4*(a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(-I - I*Cosh[c] + Sinh[c] + Sinh[2*c])) - ((1/4 - I/4)*a*e*f*x^2*Sinh[c])/((a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(-I - I*Cosh[c] + Sinh[c] + Sinh[2*c])) + (b*e*f*x^2*Sinh[c])/(4*(a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(-I - I*Cosh[c] + Sinh[c] + Sinh[2*c])) - ((1/12 - I/12)*a*f^2*x^3*Sinh[c])/((a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(-I - I*Cosh[c] + Sinh[c] + Sinh[2*c])) + ((1/4 - I/4)*a*e*f*x^2*Cosh[3*c])/((a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(Cosh[c] + I*(-I + Sinh[c] + Sinh[2*c]))) + ((1/12 - I/12)*a*f^2*x^3*Cosh[3*c])/((a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(Cosh[c] + I*(-I + Sinh[c] + Sinh[2*c]))) - (b*e*f*x^2*Sinh[3*c])/(4*(a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(-I - I*Cosh[c] + Sinh[c] + Sinh[2*c])) + ((1/4 - I/4)*a*e*f*x^2*Sinh[3*c])/((a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(Cosh[c] + I*(-I + Sinh[c] + Sinh[2*c]))) + ((1/12 - I/12)*a*f^2*x^3*Sinh[3*c])/((a^2 + b^2)*(Cosh[c] + Sinh[c])^2*(Cosh[c] + I*(-I + Sinh[c] + Sinh[2*c]))))","B",0
437,1,1541,439,2.7280556,"\int \frac{(e+f x) \text{csch}(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","2 \left(-\frac{\left(-\frac{1}{2} f (c+d x)^2+f \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (c+d x)+f \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (c+d x)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) b^2}{2 a \left(a^2+b^2\right) d^2}+\frac{i e \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right) b}{a (a-i b) d}-\frac{i c f \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right) b}{a (a-i b) d^2}-\frac{i e \left(-i (c+d x)+2 \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right)+\log (\cosh (c+d x)+i \sinh (c+d x)-1)\right) b}{4 a (a-i b) d}+\frac{i c f \left(-i (c+d x)+2 \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right)+\log (\cosh (c+d x)+i \sinh (c+d x)-1)\right) b}{4 a (a-i b) d^2}-\frac{i f \left(\frac{1}{4} i \left((1-i) (c+d x)^2+3 \pi  (c+d x)+2 (\pi -2 i (c+d x)) \log \left(1+i e^{-c-d x}\right)-4 \pi  \log \left(1+e^{c+d x}\right)-2 \pi  \log \left(-\cos \left(\frac{1}{4} (2 i (c+d x)+\pi )\right)\right)+4 \pi  \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)+4 i \text{Li}_2\left(-i e^{-c-d x}\right)\right)-\frac{1}{2} i (c+d x)^2\right) b}{2 a (a-i b) d^2}+\frac{f \left(\frac{1}{4} (c+d x)^2+\frac{1}{4} \left((-1+i) (c+d x)^2-3 \pi  (c+d x)-2 (\pi -2 i (c+d x)) \log \left(1+i e^{-c-d x}\right)+4 \pi  \log \left(1+e^{c+d x}\right)+2 \pi  \log \left(-\cos \left(\frac{1}{4} (2 i (c+d x)+\pi )\right)\right)-4 \pi  \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)-4 i \text{Li}_2\left(-i e^{-c-d x}\right)\right)-\frac{1}{2} i \left(-\frac{1}{2} (c+d x)^2+2 \log \left(1-e^{c+d x}\right) (c+d x)+2 \text{Li}_2\left(e^{c+d x}\right)\right)\right) b}{2 a (a-i b) d^2}-\frac{i \left(a^2-b^2\right) f (c+d x)^2}{8 a \left(a^2+b^2\right) d^2}-\frac{i \left(a^2-b^2\right) (d e-c f) (c+d x)}{4 a \left(a^2+b^2\right) d^2}-\frac{e \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{(a-i b) d}+\frac{c f \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{(a-i b) d^2}+\frac{e \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a d}-\frac{c f \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a d^2}-\frac{e \left(\log \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)-\frac{1}{2} i (c+d x)\right)}{2 (a+i b) d}+\frac{c f \left(\log \left(\cosh \left(\frac{1}{2} (c+d x)\right)+i \sinh \left(\frac{1}{2} (c+d x)\right)\right)-\frac{1}{2} i (c+d x)\right)}{2 (a+i b) d^2}+\frac{i f \left(-\frac{1}{8} i (c+d x)^2-\frac{1}{2} i \log \left(1+e^{-c-d x}\right) (c+d x)+\frac{1}{2} i \text{Li}_2\left(-e^{-c-d x}\right)\right)}{a d^2}+\frac{i f \left(\frac{1}{4} (c+d x)^2+\frac{1}{4} \left((-1+i) (c+d x)^2-3 \pi  (c+d x)-2 (\pi -2 i (c+d x)) \log \left(1+i e^{-c-d x}\right)+4 \pi  \log \left(1+e^{c+d x}\right)+2 \pi  \log \left(-\cos \left(\frac{1}{4} (2 i (c+d x)+\pi )\right)\right)-4 \pi  \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)-4 i \text{Li}_2\left(-i e^{-c-d x}\right)\right)-\frac{1}{2} i \left(-\frac{1}{2} (c+d x)^2+2 \log \left(1-e^{c+d x}\right) (c+d x)+2 \text{Li}_2\left(e^{c+d x}\right)\right)\right)}{2 (a-i b) d^2}+\frac{i f \left(\frac{1}{4} e^{\frac{i \pi }{4}} (c+d x)^2-\frac{\frac{1}{4} \pi  (c+d x)-\pi  \log \left(1+e^{c+d x}\right)-2 \left(\frac{1}{2} i (c+d x)+\frac{\pi }{4}\right) \log \left(1-e^{2 i \left(\frac{1}{2} i (c+d x)+\frac{\pi }{4}\right)}\right)+\pi  \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)+\frac{1}{2} \pi  \log \left(\sin \left(\frac{1}{2} i (c+d x)+\frac{\pi }{4}\right)\right)+i \text{Li}_2\left(e^{2 i \left(\frac{1}{2} i (c+d x)+\frac{\pi }{4}\right)}\right)}{\sqrt{2}}\right)}{\sqrt{2} (a+i b) d^2}\right)","-\frac{b^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2 \left(a^2+b^2\right)}-\frac{b^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{b^2 f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 a d^2 \left(a^2+b^2\right)}+\frac{i b f \text{Li}_2\left(-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{i b f \text{Li}_2\left(i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{b^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a d \left(a^2+b^2\right)}-\frac{b^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a d \left(a^2+b^2\right)}+\frac{b^2 (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{a d \left(a^2+b^2\right)}-\frac{2 b (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)}-\frac{f \text{Li}_2\left(-e^{2 c+2 d x}\right)}{2 a d^2}+\frac{f \text{Li}_2\left(e^{2 c+2 d x}\right)}{2 a d^2}-\frac{2 (e+f x) \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}",1,"2*(((-1/4*I)*(a^2 - b^2)*(d*e - c*f)*(c + d*x))/(a*(a^2 + b^2)*d^2) - ((I/8)*(a^2 - b^2)*f*(c + d*x)^2)/(a*(a^2 + b^2)*d^2) - (e*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/((a - I*b)*d) + (I*b*e*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(a*(a - I*b)*d) + (c*f*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/((a - I*b)*d^2) - (I*b*c*f*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(a*(a - I*b)*d^2) + (e*Log[Cosh[(c + d*x)/2]])/(2*a*d) - (c*f*Log[Cosh[(c + d*x)/2]])/(2*a*d^2) - (e*((-1/2*I)*(c + d*x) + Log[Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]]))/(2*(a + I*b)*d) + (c*f*((-1/2*I)*(c + d*x) + Log[Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]]))/(2*(a + I*b)*d^2) - ((I/4)*b*e*((-I)*(c + d*x) + 2*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]] + Log[-1 + Cosh[c + d*x] + I*Sinh[c + d*x]]))/(a*(a - I*b)*d) + ((I/4)*b*c*f*((-I)*(c + d*x) + 2*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]] + Log[-1 + Cosh[c + d*x] + I*Sinh[c + d*x]]))/(a*(a - I*b)*d^2) + (I*f*((-1/8*I)*(c + d*x)^2 - (I/2)*(c + d*x)*Log[1 + E^(-c - d*x)] + (I/2)*PolyLog[2, -E^(-c - d*x)]))/(a*d^2) - ((I/2)*b*f*((-1/2*I)*(c + d*x)^2 + (I/4)*(3*Pi*(c + d*x) + (1 - I)*(c + d*x)^2 + 2*(Pi - (2*I)*(c + d*x))*Log[1 + I*E^(-c - d*x)] - 4*Pi*Log[1 + E^(c + d*x)] - 2*Pi*Log[-Cos[(Pi + (2*I)*(c + d*x))/4]] + 4*Pi*Log[Cosh[(c + d*x)/2]] + (4*I)*PolyLog[2, (-I)*E^(-c - d*x)])))/(a*(a - I*b)*d^2) + ((I/2)*f*((c + d*x)^2/4 + (-3*Pi*(c + d*x) - (1 - I)*(c + d*x)^2 - 2*(Pi - (2*I)*(c + d*x))*Log[1 + I*E^(-c - d*x)] + 4*Pi*Log[1 + E^(c + d*x)] + 2*Pi*Log[-Cos[(Pi + (2*I)*(c + d*x))/4]] - 4*Pi*Log[Cosh[(c + d*x)/2]] - (4*I)*PolyLog[2, (-I)*E^(-c - d*x)])/4 - (I/2)*(-1/2*(c + d*x)^2 + 2*(c + d*x)*Log[1 - E^(c + d*x)] + 2*PolyLog[2, E^(c + d*x)])))/((a - I*b)*d^2) + (b*f*((c + d*x)^2/4 + (-3*Pi*(c + d*x) - (1 - I)*(c + d*x)^2 - 2*(Pi - (2*I)*(c + d*x))*Log[1 + I*E^(-c - d*x)] + 4*Pi*Log[1 + E^(c + d*x)] + 2*Pi*Log[-Cos[(Pi + (2*I)*(c + d*x))/4]] - 4*Pi*Log[Cosh[(c + d*x)/2]] - (4*I)*PolyLog[2, (-I)*E^(-c - d*x)])/4 - (I/2)*(-1/2*(c + d*x)^2 + 2*(c + d*x)*Log[1 - E^(c + d*x)] + 2*PolyLog[2, E^(c + d*x)])))/(2*a*(a - I*b)*d^2) - (b^2*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(2*a*(a^2 + b^2)*d^2) + (I*f*((E^((I/4)*Pi)*(c + d*x)^2)/4 - ((Pi*(c + d*x))/4 - Pi*Log[1 + E^(c + d*x)] - 2*(Pi/4 + (I/2)*(c + d*x))*Log[1 - E^((2*I)*(Pi/4 + (I/2)*(c + d*x)))] + Pi*Log[Cosh[(c + d*x)/2]] + (Pi*Log[Sin[Pi/4 + (I/2)*(c + d*x)]])/2 + I*PolyLog[2, E^((2*I)*(Pi/4 + (I/2)*(c + d*x)))])/Sqrt[2]))/(Sqrt[2]*(a + I*b)*d^2))","B",1
438,1,92,90,0.1493895,"\int \frac{\text{csch}(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Csch[c + d*x]*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{\frac{2 b^2 \log (a+b \sinh (c+d x))}{a \left(a^2+b^2\right)}+\frac{\log (-\sinh (c+d x)+i)}{a+i b}+\frac{\log (\sinh (c+d x)+i)}{a-i b}-\frac{2 \log (\sinh (c+d x))}{a}}{2 d}","-\frac{b^2 \log (a+b \sinh (c+d x))}{a d \left(a^2+b^2\right)}-\frac{b \tan ^{-1}(\sinh (c+d x))}{d \left(a^2+b^2\right)}-\frac{a \log (\cosh (c+d x))}{d \left(a^2+b^2\right)}+\frac{\log (\sinh (c+d x))}{a d}",1,"-1/2*(Log[I - Sinh[c + d*x]]/(a + I*b) - (2*Log[Sinh[c + d*x]])/a + Log[I + Sinh[c + d*x]]/(a - I*b) + (2*b^2*Log[a + b*Sinh[c + d*x]])/(a*(a^2 + b^2)))/d","C",1
439,0,0,35,28.4035774,"\int \frac{\text{csch}(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Csch[c + d*x]*Sech[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[(Csch[c + d*x]*Sech[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
440,1,1467,1164,17.2639393,"\int \frac{(e+f x)^3 \text{csch}(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Csch[c + d*x]*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","4 \left(\frac{\text{csch}(c+d x) \left(2 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3-f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-3 e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2+3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2+6 e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+6 f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-6 e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-6 f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d-6 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) (a+b \sinh (c+d x)) b^3}{4 a \left(a^2+b^2\right)^{3/2} d^4 (b+a \text{csch}(c+d x))}-\frac{f \text{csch}(c+d x) \left(-4 b f^2 x^3 d^3-12 b e f x^2 d^3+12 b e^2 e^{2 c} x d^3-12 b e^2 \left(1+e^{2 c}\right) x d^3+12 a e^2 \left(1+e^{2 c}\right) \tan ^{-1}\left(e^{c+d x}\right) d^2+6 b e^2 \left(1+e^{2 c}\right) \left(2 d x-\log \left(1+e^{2 (c+d x)}\right)\right) d^2+12 i a e \left(1+e^{2 c}\right) f \left(d x \left(\log \left(1-i e^{c+d x}\right)-\log \left(1+i e^{c+d x}\right)\right)-\text{Li}_2\left(-i e^{c+d x}\right)+\text{Li}_2\left(i e^{c+d x}\right)\right) d+6 b e \left(1+e^{2 c}\right) f \left(2 d x \left(d x-\log \left(1+e^{2 (c+d x)}\right)\right)-\text{Li}_2\left(-e^{2 (c+d x)}\right)\right) d+6 i a \left(1+e^{2 c}\right) f^2 \left(d^2 \log \left(1-i e^{c+d x}\right) x^2-d^2 \log \left(1+i e^{c+d x}\right) x^2-2 d \text{Li}_2\left(-i e^{c+d x}\right) x+2 d \text{Li}_2\left(i e^{c+d x}\right) x+2 \text{Li}_3\left(-i e^{c+d x}\right)-2 \text{Li}_3\left(i e^{c+d x}\right)\right)+b \left(1+e^{2 c}\right) f^2 \left(2 d^2 \left(2 d x-3 \log \left(1+e^{2 (c+d x)}\right)\right) x^2-6 d \text{Li}_2\left(-e^{2 (c+d x)}\right) x+3 \text{Li}_3\left(-e^{2 (c+d x)}\right)\right)\right) (a+b \sinh (c+d x))}{8 \left(a^2+b^2\right) d^4 \left(1+e^{2 c}\right) (b+a \text{csch}(c+d x))}+\frac{\text{csch}(c+d x) \left(-2 \tanh ^{-1}(\cosh (c+d x)+\sinh (c+d x)) (e+f x)^3-\frac{3 f \left(2 \text{Li}_4(-\cosh (c+d x)-\sinh (c+d x)) f^2-2 d (e+f x) \text{Li}_3(-\cosh (c+d x)-\sinh (c+d x)) f+d^2 (e+f x)^2 \text{Li}_2(-\cosh (c+d x)-\sinh (c+d x))\right)}{d^3}+\frac{3 f \left(2 \text{Li}_4(\cosh (c+d x)+\sinh (c+d x)) f^2-2 d (e+f x) \text{Li}_3(\cosh (c+d x)+\sinh (c+d x)) f+d^2 (e+f x)^2 \text{Li}_2(\cosh (c+d x)+\sinh (c+d x))\right)}{d^3}\right) (a+b \sinh (c+d x))}{4 a d (b+a \text{csch}(c+d x))}+\frac{\text{csch}(c+d x) \text{sech}(c) \text{sech}(c+d x) \left(a \cosh (c) e^3-b \sinh (d x) e^3+3 a f x \cosh (c) e^2-3 b f x \sinh (d x) e^2+3 a f^2 x^2 \cosh (c) e-3 b f^2 x^2 \sinh (d x) e+a f^3 x^3 \cosh (c)-b f^3 x^3 \sinh (d x)\right) (a+b \sinh (c+d x))}{4 \left(a^2+b^2\right) d (b+a \text{csch}(c+d x))}\right)","-\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^3}{a \left(a^2+b^2\right)^{3/2} d}+\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^3}{a \left(a^2+b^2\right)^{3/2} d}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a \left(a^2+b^2\right)^{3/2} d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a \left(a^2+b^2\right)^{3/2} d^2}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a \left(a^2+b^2\right)^{3/2} d^3}-\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a \left(a^2+b^2\right)^{3/2} d^3}-\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a \left(a^2+b^2\right)^{3/2} d^4}+\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a \left(a^2+b^2\right)^{3/2} d^4}+\frac{6 f (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^2}-\frac{6 i f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}+\frac{6 i f^2 (e+f x) \text{Li}_2\left(i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}+\frac{6 i f^3 \text{Li}_3\left(-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{Li}_3\left(i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^4}-\frac{(e+f x)^3 \text{sech}(c+d x) b^2}{a \left(a^2+b^2\right) d}-\frac{(e+f x)^3 b}{\left(a^2+b^2\right) d}+\frac{3 f (e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) b}{\left(a^2+b^2\right) d^2}+\frac{3 f^2 (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) b}{\left(a^2+b^2\right) d^3}-\frac{3 f^3 \text{Li}_3\left(-e^{2 (c+d x)}\right) b}{2 \left(a^2+b^2\right) d^4}-\frac{(e+f x)^3 \tanh (c+d x) b}{\left(a^2+b^2\right) d}-\frac{6 f (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{a d^2}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{6 i f^2 (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}-\frac{6 i f^2 (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{a d^3}+\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right)}{a d^2}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}-\frac{6 i f^3 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^4}+\frac{6 i f^3 \text{Li}_3\left(i e^{c+d x}\right)}{a d^4}-\frac{6 f^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{6 f^3 \text{Li}_4\left(-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{Li}_4\left(e^{c+d x}\right)}{a d^4}+\frac{(e+f x)^3 \text{sech}(c+d x)}{a d}",1,"4*(-1/8*(f*Csch[c + d*x]*(12*b*d^3*e^2*E^(2*c)*x - 12*b*d^3*e^2*(1 + E^(2*c))*x - 12*b*d^3*e*f*x^2 - 4*b*d^3*f^2*x^3 + 12*a*d^2*e^2*(1 + E^(2*c))*ArcTan[E^(c + d*x)] + 6*b*d^2*e^2*(1 + E^(2*c))*(2*d*x - Log[1 + E^(2*(c + d*x))]) + (12*I)*a*d*e*(1 + E^(2*c))*f*(d*x*(Log[1 - I*E^(c + d*x)] - Log[1 + I*E^(c + d*x)]) - PolyLog[2, (-I)*E^(c + d*x)] + PolyLog[2, I*E^(c + d*x)]) + 6*b*d*e*(1 + E^(2*c))*f*(2*d*x*(d*x - Log[1 + E^(2*(c + d*x))]) - PolyLog[2, -E^(2*(c + d*x))]) + (6*I)*a*(1 + E^(2*c))*f^2*(d^2*x^2*Log[1 - I*E^(c + d*x)] - d^2*x^2*Log[1 + I*E^(c + d*x)] - 2*d*x*PolyLog[2, (-I)*E^(c + d*x)] + 2*d*x*PolyLog[2, I*E^(c + d*x)] + 2*PolyLog[3, (-I)*E^(c + d*x)] - 2*PolyLog[3, I*E^(c + d*x)]) + b*(1 + E^(2*c))*f^2*(2*d^2*x^2*(2*d*x - 3*Log[1 + E^(2*(c + d*x))]) - 6*d*x*PolyLog[2, -E^(2*(c + d*x))] + 3*PolyLog[3, -E^(2*(c + d*x))]))*(a + b*Sinh[c + d*x]))/((a^2 + b^2)*d^4*(1 + E^(2*c))*(b + a*Csch[c + d*x])) + (b^3*Csch[c + d*x]*(2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])*(a + b*Sinh[c + d*x]))/(4*a*(a^2 + b^2)^(3/2)*d^4*(b + a*Csch[c + d*x])) + (Csch[c + d*x]*(-2*(e + f*x)^3*ArcTanh[Cosh[c + d*x] + Sinh[c + d*x]] - (3*f*(d^2*(e + f*x)^2*PolyLog[2, -Cosh[c + d*x] - Sinh[c + d*x]] - 2*d*f*(e + f*x)*PolyLog[3, -Cosh[c + d*x] - Sinh[c + d*x]] + 2*f^2*PolyLog[4, -Cosh[c + d*x] - Sinh[c + d*x]]))/d^3 + (3*f*(d^2*(e + f*x)^2*PolyLog[2, Cosh[c + d*x] + Sinh[c + d*x]] - 2*d*f*(e + f*x)*PolyLog[3, Cosh[c + d*x] + Sinh[c + d*x]] + 2*f^2*PolyLog[4, Cosh[c + d*x] + Sinh[c + d*x]]))/d^3)*(a + b*Sinh[c + d*x]))/(4*a*d*(b + a*Csch[c + d*x])) + (Csch[c + d*x]*Sech[c]*Sech[c + d*x]*(a*e^3*Cosh[c] + 3*a*e^2*f*x*Cosh[c] + 3*a*e*f^2*x^2*Cosh[c] + a*f^3*x^3*Cosh[c] - b*e^3*Sinh[d*x] - 3*b*e^2*f*x*Sinh[d*x] - 3*b*e*f^2*x^2*Sinh[d*x] - b*f^3*x^3*Sinh[d*x])*(a + b*Sinh[c + d*x]))/(4*(a^2 + b^2)*d*(b + a*Csch[c + d*x])))","A",0
441,1,1244,795,11.8135042,"\int \frac{(e+f x)^2 \text{csch}(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","4 \left(\frac{\text{csch}(c+d x) \left(2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^2-f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2-2 e f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2+f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2+2 e f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2-2 f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) (a+b \sinh (c+d x)) b^3}{4 a \left(a^2+b^2\right)^{3/2} d^3 (b+a \text{csch}(c+d x))}+\frac{f^2 \text{csch}(c) \text{csch}(c+d x) \left(d^2 e^{-\tanh ^{-1}(\coth (c))} x^2-\frac{i \coth (c) \left(-d x \left(2 i \tanh ^{-1}(\coth (c))-\pi \right)-\pi  \log \left(1+e^{2 d x}\right)-2 \left(i d x+i \tanh ^{-1}(\coth (c))\right) \log \left(1-e^{2 i \left(i d x+i \tanh ^{-1}(\coth (c))\right)}\right)+\pi  \log (\cosh (d x))+2 i \tanh ^{-1}(\coth (c)) \log \left(i \sinh \left(d x+\tanh ^{-1}(\coth (c))\right)\right)+i \text{Li}_2\left(e^{2 i \left(i d x+i \tanh ^{-1}(\coth (c))\right)}\right)\right)}{\sqrt{1-\coth ^2(c)}}\right) \text{sech}(c) (a+b \sinh (c+d x)) b}{4 \left(a^2+b^2\right) d^3 (b+a \text{csch}(c+d x)) \sqrt{\text{csch}^2(c) \left(\sinh ^2(c)-\cosh ^2(c)\right)}}+\frac{e f \text{csch}(c+d x) \text{sech}(c) (\cosh (c) \log (\cosh (c) \cosh (d x)+\sinh (c) \sinh (d x))-d x \sinh (c)) (a+b \sinh (c+d x)) b}{2 \left(a^2+b^2\right) d^2 (b+a \text{csch}(c+d x)) \left(\cosh ^2(c)-\sinh ^2(c)\right)}+\frac{\text{csch}(c+d x) \left(\log \left(1-e^{c+d x}\right) (e+f x)^2-\log \left(1+e^{c+d x}\right) (e+f x)^2-\frac{2 f \left(d (e+f x) \text{Li}_2\left(-e^{c+d x}\right)-f \text{Li}_3\left(-e^{c+d x}\right)\right)}{d^2}+\frac{2 f \left(d (e+f x) \text{Li}_2\left(e^{c+d x}\right)-f \text{Li}_3\left(e^{c+d x}\right)\right)}{d^2}\right) (a+b \sinh (c+d x))}{4 a d (b+a \text{csch}(c+d x))}-\frac{a f^2 \text{csch}(c+d x) \left(-\frac{2 \tan ^{-1}\left(\frac{\sinh (c)+\cosh (c) \tanh \left(\frac{d x}{2}\right)}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right) \tanh ^{-1}(\coth (c))}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}-\frac{i \text{csch}(c) \left(i \left(d x+\tanh ^{-1}(\coth (c))\right) \left(\log \left(1-e^{-d x-\tanh ^{-1}(\coth (c))}\right)-\log \left(1+e^{-d x-\tanh ^{-1}(\coth (c))}\right)\right)+i \left(\text{Li}_2\left(-e^{-d x-\tanh ^{-1}(\coth (c))}\right)-\text{Li}_2\left(e^{-d x-\tanh ^{-1}(\coth (c))}\right)\right)\right)}{\sqrt{1-\coth ^2(c)}}\right) (a+b \sinh (c+d x))}{2 \left(a^2+b^2\right) d^3 (b+a \text{csch}(c+d x))}+\frac{\text{csch}(c+d x) \text{sech}(c) \text{sech}(c+d x) \left(a \cosh (c) e^2-b \sinh (d x) e^2+2 a f x \cosh (c) e-2 b f x \sinh (d x) e+a f^2 x^2 \cosh (c)-b f^2 x^2 \sinh (d x)\right) (a+b \sinh (c+d x))}{4 \left(a^2+b^2\right) d (b+a \text{csch}(c+d x))}-\frac{a e f \tan ^{-1}\left(\frac{\sinh (c)+\cosh (c) \tanh \left(\frac{d x}{2}\right)}{\sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right) \text{csch}(c+d x) (a+b \sinh (c+d x))}{\left(a^2+b^2\right) d^2 (b+a \text{csch}(c+d x)) \sqrt{\cosh ^2(c)-\sinh ^2(c)}}\right)","-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^3}{a \left(a^2+b^2\right)^{3/2} d}+\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^3}{a \left(a^2+b^2\right)^{3/2} d}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a \left(a^2+b^2\right)^{3/2} d^2}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a \left(a^2+b^2\right)^{3/2} d^2}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a \left(a^2+b^2\right)^{3/2} d^3}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a \left(a^2+b^2\right)^{3/2} d^3}+\frac{4 f (e+f x) \tan ^{-1}\left(e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^2}-\frac{2 i f^2 \text{Li}_2\left(-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{Li}_2\left(i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}-\frac{(e+f x)^2 \text{sech}(c+d x) b^2}{a \left(a^2+b^2\right) d}-\frac{(e+f x)^2 b}{\left(a^2+b^2\right) d}+\frac{2 f (e+f x) \log \left(1+e^{2 (c+d x)}\right) b}{\left(a^2+b^2\right) d^2}+\frac{f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) b}{\left(a^2+b^2\right) d^3}-\frac{(e+f x)^2 \tanh (c+d x) b}{\left(a^2+b^2\right) d}-\frac{4 f (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{a d^2}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{2 f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{2 i f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}-\frac{2 i f^2 \text{Li}_2\left(i e^{c+d x}\right)}{a d^3}+\frac{2 f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^2}+\frac{2 f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}+\frac{(e+f x)^2 \text{sech}(c+d x)}{a d}",1,"4*((Csch[c + d*x]*((e + f*x)^2*Log[1 - E^(c + d*x)] - (e + f*x)^2*Log[1 + E^(c + d*x)] - (2*f*(d*(e + f*x)*PolyLog[2, -E^(c + d*x)] - f*PolyLog[3, -E^(c + d*x)]))/d^2 + (2*f*(d*(e + f*x)*PolyLog[2, E^(c + d*x)] - f*PolyLog[3, E^(c + d*x)]))/d^2)*(a + b*Sinh[c + d*x]))/(4*a*d*(b + a*Csch[c + d*x])) + (b^3*Csch[c + d*x]*(2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])*(a + b*Sinh[c + d*x]))/(4*a*(a^2 + b^2)^(3/2)*d^3*(b + a*Csch[c + d*x])) + (b*e*f*Csch[c + d*x]*Sech[c]*(Cosh[c]*Log[Cosh[c]*Cosh[d*x] + Sinh[c]*Sinh[d*x]] - d*x*Sinh[c])*(a + b*Sinh[c + d*x]))/(2*(a^2 + b^2)*d^2*(b + a*Csch[c + d*x])*(Cosh[c]^2 - Sinh[c]^2)) - (a*e*f*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]]*Csch[c + d*x]*(a + b*Sinh[c + d*x]))/((a^2 + b^2)*d^2*(b + a*Csch[c + d*x])*Sqrt[Cosh[c]^2 - Sinh[c]^2]) + (b*f^2*Csch[c]*Csch[c + d*x]*((d^2*x^2)/E^ArcTanh[Coth[c]] - (I*Coth[c]*(-(d*x*(-Pi + (2*I)*ArcTanh[Coth[c]])) - Pi*Log[1 + E^(2*d*x)] - 2*(I*d*x + I*ArcTanh[Coth[c]])*Log[1 - E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))] + Pi*Log[Cosh[d*x]] + (2*I)*ArcTanh[Coth[c]]*Log[I*Sinh[d*x + ArcTanh[Coth[c]]]] + I*PolyLog[2, E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))]))/Sqrt[1 - Coth[c]^2])*Sech[c]*(a + b*Sinh[c + d*x]))/(4*(a^2 + b^2)*d^3*(b + a*Csch[c + d*x])*Sqrt[Csch[c]^2*(-Cosh[c]^2 + Sinh[c]^2)]) - (a*f^2*Csch[c + d*x]*(((-I)*Csch[c]*(I*(d*x + ArcTanh[Coth[c]])*(Log[1 - E^(-(d*x) - ArcTanh[Coth[c]])] - Log[1 + E^(-(d*x) - ArcTanh[Coth[c]])]) + I*(PolyLog[2, -E^(-(d*x) - ArcTanh[Coth[c]])] - PolyLog[2, E^(-(d*x) - ArcTanh[Coth[c]])])))/Sqrt[1 - Coth[c]^2] - (2*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]]*ArcTanh[Coth[c]])/Sqrt[Cosh[c]^2 - Sinh[c]^2])*(a + b*Sinh[c + d*x]))/(2*(a^2 + b^2)*d^3*(b + a*Csch[c + d*x])) + (Csch[c + d*x]*Sech[c]*Sech[c + d*x]*(a*e^2*Cosh[c] + 2*a*e*f*x*Cosh[c] + a*f^2*x^2*Cosh[c] - b*e^2*Sinh[d*x] - 2*b*e*f*x*Sinh[d*x] - b*f^2*x^2*Sinh[d*x])*(a + b*Sinh[c + d*x]))/(4*(a^2 + b^2)*d*(b + a*Csch[c + d*x])))","A",0
442,1,459,442,6.4983414,"\int \frac{(e+f x) \text{csch}(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\text{csch}(c+d x) (a+b \sinh (c+d x)) \left(\frac{d (e+f x) \text{sech}(c+d x) (a-b \sinh (c+d x))}{a^2+b^2}-\frac{2 a f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^2+b^2}+\frac{b f \log (\cosh (c+d x))}{a^2+b^2}+\frac{b^3 \left(2 d e \tanh ^{-1}\left(\frac{a+b \sinh (c+d x)+b \cosh (c+d x)}{\sqrt{a^2+b^2}}\right)-f \text{Li}_2\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}\right)-f (c+d x) \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b (\sinh (c+d x)+\cosh (c+d x))}{\sqrt{a^2+b^2}+a}+1\right)-2 c f \tanh ^{-1}\left(\frac{a+b \sinh (c+d x)+b \cosh (c+d x)}{\sqrt{a^2+b^2}}\right)\right)}{a \left(a^2+b^2\right)^{3/2}}+\frac{d e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a}+\frac{f \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)+(c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right)}{a}-\frac{c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a}\right)}{d^2 (a \text{csch}(c+d x)+b)}","\frac{b^2 f \tan ^{-1}(\sinh (c+d x))}{a d^2 \left(a^2+b^2\right)}+\frac{b f \log (\cosh (c+d x))}{d^2 \left(a^2+b^2\right)}-\frac{b (e+f x) \tanh (c+d x)}{d \left(a^2+b^2\right)}-\frac{b^2 (e+f x) \text{sech}(c+d x)}{a d \left(a^2+b^2\right)}-\frac{b^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2 \left(a^2+b^2\right)^{3/2}}+\frac{b^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^2 \left(a^2+b^2\right)^{3/2}}-\frac{b^3 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a d \left(a^2+b^2\right)^{3/2}}+\frac{b^3 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a d \left(a^2+b^2\right)^{3/2}}-\frac{f \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{f \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{f \tan ^{-1}(\sinh (c+d x))}{a d^2}+\frac{(e+f x) \text{sech}(c+d x)}{a d}-\frac{(e+f x) \tanh ^{-1}(\cosh (c+d x))}{a d}-\frac{2 f x \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{f x \tanh ^{-1}(\cosh (c+d x))}{a d}",1,"(Csch[c + d*x]*(a + b*Sinh[c + d*x])*((-2*a*f*ArcTan[Tanh[(c + d*x)/2]])/(a^2 + b^2) + (b*f*Log[Cosh[c + d*x]])/(a^2 + b^2) + (d*e*Log[Tanh[(c + d*x)/2]])/a - (c*f*Log[Tanh[(c + d*x)/2]])/a + (f*((c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)]))/a + (b^3*(2*d*e*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] - 2*c*f*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] - f*(c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] - f*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/(a*(a^2 + b^2)^(3/2)) + (d*(e + f*x)*Sech[c + d*x]*(a - b*Sinh[c + d*x]))/(a^2 + b^2)))/(d^2*(b + a*Csch[c + d*x]))","A",1
443,1,171,113,0.2237024,"\int \frac{\text{csch}(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Csch[c + d*x]*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{-a b \sqrt{-a^2-b^2} \tanh (c+d x)+a^2 \sqrt{-a^2-b^2} \text{sech}(c+d x)+b^2 \sqrt{-a^2-b^2} \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+a^2 \sqrt{-a^2-b^2} \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)-2 b^3 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{a d \left(-a^2-b^2\right)^{3/2}}","-\frac{b \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a d \left(a^2+b^2\right)}+\frac{2 b^3 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a d \left(a^2+b^2\right)^{3/2}}+\frac{\text{sech}(c+d x)}{a d}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}",1,"-((-2*b^3*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] + a^2*Sqrt[-a^2 - b^2]*Log[Tanh[(c + d*x)/2]] + b^2*Sqrt[-a^2 - b^2]*Log[Tanh[(c + d*x)/2]] + a^2*Sqrt[-a^2 - b^2]*Sech[c + d*x] - a*b*Sqrt[-a^2 - b^2]*Tanh[c + d*x])/(a*(-a^2 - b^2)^(3/2)*d))","A",1
444,-1,0,37,180.0002519,"\int \frac{\text{csch}(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Csch[c + d*x]*Sech[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{csch}(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
445,1,3806,1185,32.5788655,"\int \frac{(e+f x)^2 \text{csch}(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^4}{a \left(a^2+b^2\right)^2 d}-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^4}{a \left(a^2+b^2\right)^2 d}+\frac{(e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) b^4}{a \left(a^2+b^2\right)^2 d}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^4}{a \left(a^2+b^2\right)^2 d^2}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^4}{a \left(a^2+b^2\right)^2 d^2}+\frac{f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) b^4}{a \left(a^2+b^2\right)^2 d^2}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^4}{a \left(a^2+b^2\right)^2 d^3}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^4}{a \left(a^2+b^2\right)^2 d^3}-\frac{f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) b^4}{2 a \left(a^2+b^2\right)^2 d^3}-\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) b^3}{\left(a^2+b^2\right)^2 d}+\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) b^3}{\left(a^2+b^2\right)^2 d^2}-\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) b^3}{\left(a^2+b^2\right)^2 d^2}-\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right) b^3}{\left(a^2+b^2\right)^2 d^3}+\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right) b^3}{\left(a^2+b^2\right)^2 d^3}-\frac{(e+f x)^2 \text{sech}^2(c+d x) b^2}{2 a \left(a^2+b^2\right) d}-\frac{f^2 \log (\cosh (c+d x)) b^2}{a \left(a^2+b^2\right) d^3}+\frac{f (e+f x) \tanh (c+d x) b^2}{a \left(a^2+b^2\right) d^2}-\frac{(e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) b}{\left(a^2+b^2\right) d}+\frac{f^2 \tan ^{-1}(\sinh (c+d x)) b}{\left(a^2+b^2\right) d^3}+\frac{i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) b}{\left(a^2+b^2\right) d^2}-\frac{i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) b}{\left(a^2+b^2\right) d^2}-\frac{i f^2 \text{Li}_3\left(-i e^{c+d x}\right) b}{\left(a^2+b^2\right) d^3}+\frac{i f^2 \text{Li}_3\left(i e^{c+d x}\right) b}{\left(a^2+b^2\right) d^3}-\frac{f (e+f x) \text{sech}(c+d x) b}{\left(a^2+b^2\right) d^2}-\frac{(e+f x)^2 \text{sech}(c+d x) \tanh (c+d x) b}{2 \left(a^2+b^2\right) d}+\frac{f^2 x^2}{2 a d}-\frac{(e+f x)^2 \tanh ^2(c+d x)}{2 a d}+\frac{e f x}{a d}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}+\frac{f^2 \log (\cosh (c+d x))}{a d^3}-\frac{f (e+f x) \text{Li}_2\left(-e^{2 c+2 d x}\right)}{a d^2}+\frac{f (e+f x) \text{Li}_2\left(e^{2 c+2 d x}\right)}{a d^2}+\frac{f^2 \text{Li}_3\left(-e^{2 c+2 d x}\right)}{2 a d^3}-\frac{f^2 \text{Li}_3\left(e^{2 c+2 d x}\right)}{2 a d^3}-\frac{f (e+f x) \tanh (c+d x)}{a d^2}",1,"-1/3*(E^(2*c)*((2*(e + f*x)^3)/(E^(2*c)*f) - (3*(1 - E^(-2*c))*(e + f*x)^2*Log[1 - E^(-c - d*x)])/d - (3*(1 - E^(-2*c))*(e + f*x)^2*Log[1 + E^(-c - d*x)])/d + (6*(-1 + E^(2*c))*f*(d*(e + f*x)*PolyLog[2, -E^(-c - d*x)] + f*PolyLog[3, -E^(-c - d*x)]))/(d^3*E^(2*c)) + (6*(-1 + E^(2*c))*f*(d*(e + f*x)*PolyLog[2, E^(-c - d*x)] + f*PolyLog[3, E^(-c - d*x)]))/(d^3*E^(2*c))))/(a*(-1 + E^(2*c))) - (-12*a^3*d^3*e^2*E^(2*c)*x - 24*a*b^2*d^3*e^2*E^(2*c)*x + 12*a^3*d*E^(2*c)*f^2*x + 12*a*b^2*d*E^(2*c)*f^2*x - 12*a^3*d^3*e*E^(2*c)*f*x^2 - 24*a*b^2*d^3*e*E^(2*c)*f*x^2 - 4*a^3*d^3*E^(2*c)*f^2*x^3 - 8*a*b^2*d^3*E^(2*c)*f^2*x^3 + 6*a^2*b*d^2*e^2*ArcTan[E^(c + d*x)] + 18*b^3*d^2*e^2*ArcTan[E^(c + d*x)] + 6*a^2*b*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] + 18*b^3*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] - 12*a^2*b*f^2*ArcTan[E^(c + d*x)] - 12*b^3*f^2*ArcTan[E^(c + d*x)] - 12*a^2*b*E^(2*c)*f^2*ArcTan[E^(c + d*x)] - 12*b^3*E^(2*c)*f^2*ArcTan[E^(c + d*x)] + (6*I)*a^2*b*d^2*e*f*x*Log[1 - I*E^(c + d*x)] + (18*I)*b^3*d^2*e*f*x*Log[1 - I*E^(c + d*x)] + (6*I)*a^2*b*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] + (18*I)*b^3*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] + (3*I)*a^2*b*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] + (9*I)*b^3*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] + (3*I)*a^2*b*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] + (9*I)*b^3*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] - (6*I)*a^2*b*d^2*e*f*x*Log[1 + I*E^(c + d*x)] - (18*I)*b^3*d^2*e*f*x*Log[1 + I*E^(c + d*x)] - (6*I)*a^2*b*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] - (18*I)*b^3*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] - (3*I)*a^2*b*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] - (9*I)*b^3*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] - (3*I)*a^2*b*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] - (9*I)*b^3*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] + 6*a^3*d^2*e^2*Log[1 + E^(2*(c + d*x))] + 12*a*b^2*d^2*e^2*Log[1 + E^(2*(c + d*x))] + 6*a^3*d^2*e^2*E^(2*c)*Log[1 + E^(2*(c + d*x))] + 12*a*b^2*d^2*e^2*E^(2*c)*Log[1 + E^(2*(c + d*x))] - 6*a^3*f^2*Log[1 + E^(2*(c + d*x))] - 6*a*b^2*f^2*Log[1 + E^(2*(c + d*x))] - 6*a^3*E^(2*c)*f^2*Log[1 + E^(2*(c + d*x))] - 6*a*b^2*E^(2*c)*f^2*Log[1 + E^(2*(c + d*x))] + 12*a^3*d^2*e*f*x*Log[1 + E^(2*(c + d*x))] + 24*a*b^2*d^2*e*f*x*Log[1 + E^(2*(c + d*x))] + 12*a^3*d^2*e*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 24*a*b^2*d^2*e*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 6*a^3*d^2*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 12*a*b^2*d^2*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 6*a^3*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 12*a*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] - (6*I)*b*(a^2 + 3*b^2)*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)] + (6*I)*b*(a^2 + 3*b^2)*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)] + 6*a^3*d*e*f*PolyLog[2, -E^(2*(c + d*x))] + 12*a*b^2*d*e*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a^3*d*e*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 12*a*b^2*d*e*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a^3*d*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 12*a*b^2*d*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 6*a^3*d*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 12*a*b^2*d*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + (6*I)*a^2*b*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (18*I)*b^3*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (6*I)*a^2*b*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (18*I)*b^3*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (6*I)*a^2*b*f^2*PolyLog[3, I*E^(c + d*x)] - (18*I)*b^3*f^2*PolyLog[3, I*E^(c + d*x)] - (6*I)*a^2*b*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - (18*I)*b^3*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - 3*a^3*f^2*PolyLog[3, -E^(2*(c + d*x))] - 6*a*b^2*f^2*PolyLog[3, -E^(2*(c + d*x))] - 3*a^3*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))] - 6*a*b^2*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))])/(6*(a^2 + b^2)^2*d^3*(1 + E^(2*c))) + (b^4*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*a*(a^2 + b^2)^2*d^3*(-1 + E^(2*c))) + (Csch[c]*Sech[c]*Sech[c + d*x]^2*(-6*a^3*e*f - 6*a*b^2*e*f + 12*a^3*d^2*e^2*x + 24*a*b^2*d^2*e^2*x - 6*a^3*f^2*x - 6*a*b^2*f^2*x + 12*a^3*d^2*e*f*x^2 + 24*a*b^2*d^2*e*f*x^2 + 4*a^3*d^2*f^2*x^3 + 8*a*b^2*d^2*f^2*x^3 + 6*a^3*e*f*Cosh[2*c] + 6*a*b^2*e*f*Cosh[2*c] + 6*a^3*f^2*x*Cosh[2*c] + 6*a*b^2*f^2*x*Cosh[2*c] + 6*a^3*e*f*Cosh[2*d*x] + 6*a*b^2*e*f*Cosh[2*d*x] + 6*a^3*f^2*x*Cosh[2*d*x] + 6*a*b^2*f^2*x*Cosh[2*d*x] + 3*a^2*b*d*e^2*Cosh[c - d*x] + 3*b^3*d*e^2*Cosh[c - d*x] + 6*a^2*b*d*e*f*x*Cosh[c - d*x] + 6*b^3*d*e*f*x*Cosh[c - d*x] + 3*a^2*b*d*f^2*x^2*Cosh[c - d*x] + 3*b^3*d*f^2*x^2*Cosh[c - d*x] - 3*a^2*b*d*e^2*Cosh[3*c + d*x] - 3*b^3*d*e^2*Cosh[3*c + d*x] - 6*a^2*b*d*e*f*x*Cosh[3*c + d*x] - 6*b^3*d*e*f*x*Cosh[3*c + d*x] - 3*a^2*b*d*f^2*x^2*Cosh[3*c + d*x] - 3*b^3*d*f^2*x^2*Cosh[3*c + d*x] - 6*a^3*e*f*Cosh[2*c + 2*d*x] - 6*a*b^2*e*f*Cosh[2*c + 2*d*x] + 12*a^3*d^2*e^2*x*Cosh[2*c + 2*d*x] + 24*a*b^2*d^2*e^2*x*Cosh[2*c + 2*d*x] - 6*a^3*f^2*x*Cosh[2*c + 2*d*x] - 6*a*b^2*f^2*x*Cosh[2*c + 2*d*x] + 12*a^3*d^2*e*f*x^2*Cosh[2*c + 2*d*x] + 24*a*b^2*d^2*e*f*x^2*Cosh[2*c + 2*d*x] + 4*a^3*d^2*f^2*x^3*Cosh[2*c + 2*d*x] + 8*a*b^2*d^2*f^2*x^3*Cosh[2*c + 2*d*x] + 6*a^3*d*e^2*Sinh[2*c] + 6*a*b^2*d*e^2*Sinh[2*c] + 12*a^3*d*e*f*x*Sinh[2*c] + 12*a*b^2*d*e*f*x*Sinh[2*c] + 6*a^3*d*f^2*x^2*Sinh[2*c] + 6*a*b^2*d*f^2*x^2*Sinh[2*c] - 6*a^2*b*e*f*Sinh[c - d*x] - 6*b^3*e*f*Sinh[c - d*x] - 6*a^2*b*f^2*x*Sinh[c - d*x] - 6*b^3*f^2*x*Sinh[c - d*x] - 6*a^2*b*e*f*Sinh[3*c + d*x] - 6*b^3*e*f*Sinh[3*c + d*x] - 6*a^2*b*f^2*x*Sinh[3*c + d*x] - 6*b^3*f^2*x*Sinh[3*c + d*x]))/(24*(a^2 + b^2)^2*d^2)","B",1
446,1,886,746,10.7077294,"\int \frac{(e+f x) \text{csch}(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{\left(-\frac{1}{2} f (c+d x)^2+f \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (c+d x)+f \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (c+d x)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) b^4}{a \left(a^2+b^2\right)^2 d^2}+\frac{e \log (\sinh (c+d x))}{a d}-\frac{c f \log (\sinh (c+d x))}{a d^2}-\frac{i f \left(i (c+d x) \log \left(1-e^{-2 (c+d x)}\right)-\frac{1}{2} i \left(\text{Li}_2\left(e^{-2 (c+d x)}\right)-(c+d x)^2\right)\right)}{a d^2}-\frac{-f (c+d x)^2 a^3-2 d e (c+d x) a^3+2 c f (c+d x) a^3+2 d e \log \left(1+e^{2 (c+d x)}\right) a^3-2 c f \log \left(1+e^{2 (c+d x)}\right) a^3+2 f (c+d x) \log \left(1+e^{2 (c+d x)}\right) a^3+f \text{Li}_2\left(-e^{2 (c+d x)}\right) a^3+2 b d e \tan ^{-1}\left(e^{c+d x}\right) a^2-2 b c f \tan ^{-1}\left(e^{c+d x}\right) a^2+i b f (c+d x) \log \left(1-i e^{c+d x}\right) a^2-i b f (c+d x) \log \left(1+i e^{c+d x}\right) a^2-2 b^2 f (c+d x)^2 a-4 b^2 d e (c+d x) a+4 b^2 c f (c+d x) a+4 b^2 d e \log \left(1+e^{2 (c+d x)}\right) a-4 b^2 c f \log \left(1+e^{2 (c+d x)}\right) a+4 b^2 f (c+d x) \log \left(1+e^{2 (c+d x)}\right) a+2 b^2 f \text{Li}_2\left(-e^{2 (c+d x)}\right) a+6 b^3 d e \tan ^{-1}\left(e^{c+d x}\right)-6 b^3 c f \tan ^{-1}\left(e^{c+d x}\right)+3 i b^3 f (c+d x) \log \left(1-i e^{c+d x}\right)-3 i b^3 f (c+d x) \log \left(1+i e^{c+d x}\right)-i b \left(a^2+3 b^2\right) f \text{Li}_2\left(-i e^{c+d x}\right)+i b \left(a^2+3 b^2\right) f \text{Li}_2\left(i e^{c+d x}\right)}{2 \left(a^2+b^2\right)^2 d^2}+\frac{\text{sech}(c+d x) (-b f-a \sinh (c+d x) f)}{2 \left(a^2+b^2\right) d^2}+\frac{\text{sech}^2(c+d x) (a d e-b d \sinh (c+d x) e-a c f+a f (c+d x)+b c f \sinh (c+d x)-b f (c+d x) \sinh (c+d x))}{2 \left(a^2+b^2\right) d^2}","\frac{i b f \text{Li}_2\left(-i e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{i b f \text{Li}_2\left(i e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)}+\frac{b^2 f \tanh (c+d x)}{2 a d^2 \left(a^2+b^2\right)}-\frac{b f \text{sech}(c+d x)}{2 d^2 \left(a^2+b^2\right)}-\frac{b (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)}-\frac{b^2 (e+f x) \text{sech}^2(c+d x)}{2 a d \left(a^2+b^2\right)}-\frac{b (e+f x) \tanh (c+d x) \text{sech}(c+d x)}{2 d \left(a^2+b^2\right)}-\frac{b^4 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2 \left(a^2+b^2\right)^2}-\frac{b^4 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a d^2 \left(a^2+b^2\right)^2}+\frac{b^4 f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 a d^2 \left(a^2+b^2\right)^2}-\frac{b^4 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a d \left(a^2+b^2\right)^2}-\frac{b^4 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a d \left(a^2+b^2\right)^2}+\frac{b^4 (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{a d \left(a^2+b^2\right)^2}+\frac{i b^3 f \text{Li}_2\left(-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{i b^3 f \text{Li}_2\left(i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{2 b^3 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)^2}-\frac{f \text{Li}_2\left(-e^{2 c+2 d x}\right)}{2 a d^2}+\frac{f \text{Li}_2\left(e^{2 c+2 d x}\right)}{2 a d^2}-\frac{f \tanh (c+d x)}{2 a d^2}-\frac{(e+f x) \tanh ^2(c+d x)}{2 a d}+\frac{(e+f x) \log (\tanh (c+d x))}{a d}-\frac{2 f x \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}-\frac{f x \log (\tanh (c+d x))}{a d}+\frac{f x}{2 a d}",1,"(e*Log[Sinh[c + d*x]])/(a*d) - (c*f*Log[Sinh[c + d*x]])/(a*d^2) - (I*f*(I*(c + d*x)*Log[1 - E^(-2*(c + d*x))] - (I/2)*(-(c + d*x)^2 + PolyLog[2, E^(-2*(c + d*x))])))/(a*d^2) - (b^4*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a*(a^2 + b^2)^2*d^2) - (-2*a^3*d*e*(c + d*x) - 4*a*b^2*d*e*(c + d*x) + 2*a^3*c*f*(c + d*x) + 4*a*b^2*c*f*(c + d*x) - a^3*f*(c + d*x)^2 - 2*a*b^2*f*(c + d*x)^2 + 2*a^2*b*d*e*ArcTan[E^(c + d*x)] + 6*b^3*d*e*ArcTan[E^(c + d*x)] - 2*a^2*b*c*f*ArcTan[E^(c + d*x)] - 6*b^3*c*f*ArcTan[E^(c + d*x)] + I*a^2*b*f*(c + d*x)*Log[1 - I*E^(c + d*x)] + (3*I)*b^3*f*(c + d*x)*Log[1 - I*E^(c + d*x)] - I*a^2*b*f*(c + d*x)*Log[1 + I*E^(c + d*x)] - (3*I)*b^3*f*(c + d*x)*Log[1 + I*E^(c + d*x)] + 2*a^3*d*e*Log[1 + E^(2*(c + d*x))] + 4*a*b^2*d*e*Log[1 + E^(2*(c + d*x))] - 2*a^3*c*f*Log[1 + E^(2*(c + d*x))] - 4*a*b^2*c*f*Log[1 + E^(2*(c + d*x))] + 2*a^3*f*(c + d*x)*Log[1 + E^(2*(c + d*x))] + 4*a*b^2*f*(c + d*x)*Log[1 + E^(2*(c + d*x))] - I*b*(a^2 + 3*b^2)*f*PolyLog[2, (-I)*E^(c + d*x)] + I*b*(a^2 + 3*b^2)*f*PolyLog[2, I*E^(c + d*x)] + a^3*f*PolyLog[2, -E^(2*(c + d*x))] + 2*a*b^2*f*PolyLog[2, -E^(2*(c + d*x))])/(2*(a^2 + b^2)^2*d^2) + (Sech[c + d*x]*(-(b*f) - a*f*Sinh[c + d*x]))/(2*(a^2 + b^2)*d^2) + (Sech[c + d*x]^2*(a*d*e - a*c*f + a*f*(c + d*x) - b*d*e*Sinh[c + d*x] + b*c*f*Sinh[c + d*x] - b*f*(c + d*x)*Sinh[c + d*x]))/(2*(a^2 + b^2)*d^2)","A",1
447,1,196,160,0.7668146,"\int \frac{\text{csch}(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Csch[c + d*x]*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{a \left(a^3+2 a b^2+\left(-b^2\right)^{3/2}\right) \log \left(\sqrt{-b^2}-b \sinh (c+d x)\right)+a \left(a^3+2 a b^2-\left(-b^2\right)^{3/2}\right) \log \left(\sqrt{-b^2}+b \sinh (c+d x)\right)-a^2 \left(a^2+b^2\right) \text{sech}^2(c+d x)-2 \left(a^2+b^2\right)^2 \log (\sinh (c+d x))+a b \left(a^2+b^2\right) \tan ^{-1}(\sinh (c+d x))+a b \left(a^2+b^2\right) \tanh (c+d x) \text{sech}(c+d x)+2 b^4 \log (a+b \sinh (c+d x))}{2 a d \left(a^2+b^2\right)^2}","-\frac{b \tan ^{-1}(\sinh (c+d x))}{2 d \left(a^2+b^2\right)}-\frac{a \left(a^2+2 b^2\right) \log (\cosh (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{\text{sech}^2(c+d x) (a-b \sinh (c+d x))}{2 d \left(a^2+b^2\right)}-\frac{b^4 \log (a+b \sinh (c+d x))}{a d \left(a^2+b^2\right)^2}-\frac{b^3 \tan ^{-1}(\sinh (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{\log (\sinh (c+d x))}{a d}",1,"-1/2*(a*b*(a^2 + b^2)*ArcTan[Sinh[c + d*x]] - 2*(a^2 + b^2)^2*Log[Sinh[c + d*x]] + a*(a^3 + 2*a*b^2 + (-b^2)^(3/2))*Log[Sqrt[-b^2] - b*Sinh[c + d*x]] + 2*b^4*Log[a + b*Sinh[c + d*x]] + a*(a^3 + 2*a*b^2 - (-b^2)^(3/2))*Log[Sqrt[-b^2] + b*Sinh[c + d*x]] - a^2*(a^2 + b^2)*Sech[c + d*x]^2 + a*b*(a^2 + b^2)*Sech[c + d*x]*Tanh[c + d*x])/(a*(a^2 + b^2)^2*d)","A",1
448,0,0,37,173.5515213,"\int \frac{\text{csch}(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Csch[c + d*x]*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[(Csch[c + d*x]*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
449,1,2469,601,25.9554392,"\int \frac{(e+f x)^3 \coth (c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Coth[c + d*x]*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{6 b f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^4}+\frac{6 b f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^4}-\frac{6 b f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^3}-\frac{6 b f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^3}+\frac{3 b f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{3 b f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{b (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d}+\frac{b (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d}-\frac{3 b f^3 \text{Li}_4\left(e^{2 (c+d x)}\right)}{4 a^2 d^4}+\frac{3 b f^2 (e+f x) \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{3 b f (e+f x)^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a^2 d^2}-\frac{b (e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a^2 d}+\frac{6 f^3 \text{Li}_3\left(-e^{c+d x}\right)}{a d^4}-\frac{6 f^3 \text{Li}_3\left(e^{c+d x}\right)}{a d^4}-\frac{6 f^2 (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^3}-\frac{6 f (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d^2}-\frac{(e+f x)^3 \text{csch}(c+d x)}{a d}",1,"-(((e + f*x)^3*Csch[c])/(a*d)) - (b*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(2*a^2*(-1 + E^(2*c))) + ((b*(e + f*x)^4*(-1 + Coth[c]))/(2*f) + (2*e^2*(b*d*e - 3*a*f)*(d*x - Log[1 - Cosh[c + d*x] - Sinh[c + d*x]]))/d^2 - (6*e*f*(b*d*e + 2*a*f)*x*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]])/d^2 - (6*f^2*(b*d*e + a*f)*x^2*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]])/d^2 - (2*b*f^3*x^3*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]])/d - (6*e*f*(b*d*e - 2*a*f)*x*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]])/d^2 + (6*f^2*(-(b*d*e) + a*f)*x^2*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]])/d^2 - (2*b*f^3*x^3*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]])/d + (2*e^2*(b*d*e + 3*a*f)*(d*x - Log[1 + Cosh[c + d*x] + Sinh[c + d*x]]))/d^2 + (6*e*f*(b*d*e - 2*a*f)*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]])/d^3 + (6*e*f*(b*d*e + 2*a*f)*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]])/d^3 + (12*f^2*(b*d*e - a*f)*(d*x*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]]))/d^4 + (12*f^2*(b*d*e + a*f)*(d*x*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]]))/d^4 + (6*b*f^3*(d^2*x^2*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 2*(d*x*PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[4, Cosh[c + d*x] - Sinh[c + d*x]])))/d^4 + (6*b*f^3*(d^2*x^2*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 2*(d*x*PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[4, -Cosh[c + d*x] + Sinh[c + d*x]])))/d^4)/(2*a^2) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2]))/(2*a*d) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2]))/(2*a*d)","B",0
450,1,1383,419,17.0915925,"\int \frac{(e+f x)^2 \coth (c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Coth[c + d*x]*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{\text{csch}(c) (e+f x)^2}{a d}-\frac{b \left(2 e^{2 c} f^2 x^3 d^3+6 e e^{2 c} f x^2 d^3+6 e^2 e^{2 c} x d^3-3 e^2 e^{2 c} \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2+3 e^2 \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right)}{3 a^2 d^3 \left(-1+e^{2 c}\right)}+\frac{-3 b d^2 x^2 \log (\cosh (c+d x)-\sinh (c+d x)+1) f^3-3 b d^2 x^2 \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^3+6 b (d x \text{Li}_2(\cosh (c+d x)-\sinh (c+d x))+\text{Li}_3(\cosh (c+d x)-\sinh (c+d x))) f^3+6 b (d x \text{Li}_2(\sinh (c+d x)-\cosh (c+d x))+\text{Li}_3(\sinh (c+d x)-\cosh (c+d x))) f^3-6 d (b d e+a f) x \log (\cosh (c+d x)-\sinh (c+d x)+1) f^2-6 d (b d e-a f) x \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^2+6 (b d e-a f) \text{Li}_2(\cosh (c+d x)-\sinh (c+d x)) f^2+6 (b d e+a f) \text{Li}_2(\sinh (c+d x)-\cosh (c+d x)) f^2+3 d e (b d e-2 a f) (d x-\log (-\cosh (c+d x)-\sinh (c+d x)+1)) f+3 d e (b d e+2 a f) (d x-\log (\cosh (c+d x)+\sinh (c+d x)+1)) f+b d^3 (e+f x)^3 (\coth (c)-1)}{3 a^2 d^3 f}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(\sinh \left(\frac{d x}{2}\right) e^2+2 f x \sinh \left(\frac{d x}{2}\right) e+f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}+\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(\sinh \left(\frac{d x}{2}\right) e^2+2 f x \sinh \left(\frac{d x}{2}\right) e+f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}","-\frac{2 b f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^3}-\frac{2 b f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^3}+\frac{2 b f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{2 b f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{b (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d}+\frac{b (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d}+\frac{b f^2 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{b f (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a^2 d^2}-\frac{b (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a^2 d}-\frac{2 f^2 \text{Li}_2\left(-e^{c+d x}\right)}{a d^3}+\frac{2 f^2 \text{Li}_2\left(e^{c+d x}\right)}{a d^3}-\frac{4 f (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d^2}-\frac{(e+f x)^2 \text{csch}(c+d x)}{a d}",1,"-(((e + f*x)^2*Csch[c])/(a*d)) - (b*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*a^2*d^3*(-1 + E^(2*c))) + (b*d^3*(e + f*x)^3*(-1 + Coth[c]) + 3*d*e*f*(b*d*e - 2*a*f)*(d*x - Log[1 - Cosh[c + d*x] - Sinh[c + d*x]]) - 6*d*f^2*(b*d*e + a*f)*x*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - 3*b*d^2*f^3*x^2*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - 6*d*f^2*(b*d*e - a*f)*x*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] - 3*b*d^2*f^3*x^2*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] + 3*d*e*f*(b*d*e + 2*a*f)*(d*x - Log[1 + Cosh[c + d*x] + Sinh[c + d*x]]) + 6*f^2*(b*d*e - a*f)*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 6*f^2*(b*d*e + a*f)*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 6*b*f^3*(d*x*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]]) + 6*b*f^3*(d*x*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]]))/(3*a^2*d^3*f) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^2*Sinh[(d*x)/2] + 2*e*f*x*Sinh[(d*x)/2] + f^2*x^2*Sinh[(d*x)/2]))/(2*a*d) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(e^2*Sinh[(d*x)/2] + 2*e*f*x*Sinh[(d*x)/2] + f^2*x^2*Sinh[(d*x)/2]))/(2*a*d)","B",1
451,1,416,243,1.798646,"\int \frac{(e+f x) \coth (c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Coth[c + d*x]*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{2 b f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+2 b c f \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+2 b c f \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 b d f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+2 b d f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 b d e \log (a+b \sinh (c+d x))-2 b c f \log (a+b \sinh (c+d x))+a d e \tanh \left(\frac{1}{2} (c+d x)\right)-a d e \coth \left(\frac{1}{2} (c+d x)\right)+a d f x \tanh \left(\frac{1}{2} (c+d x)\right)-a d f x \coth \left(\frac{1}{2} (c+d x)\right)+2 a f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)-2 b c^2 f-2 b d e \log (\sinh (c+d x))+b f \text{Li}_2\left(e^{-2 (c+d x)}\right)-4 b c d f x-2 b c f \log \left(1-e^{-2 (c+d x)}\right)-2 b d f x \log \left(1-e^{-2 (c+d x)}\right)+2 b c f \log (\sinh (c+d x))-2 b d^2 f x^2}{2 a^2 d^2}","\frac{b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{b f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{b (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d}+\frac{b (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d}-\frac{b f \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a^2 d^2}-\frac{b (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a^2 d}-\frac{f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac{(e+f x) \text{csch}(c+d x)}{a d}",1,"(-2*b*c^2*f - 4*b*c*d*f*x - 2*b*d^2*f*x^2 - a*d*e*Coth[(c + d*x)/2] - a*d*f*x*Coth[(c + d*x)/2] - 2*b*c*f*Log[1 - E^(-2*(c + d*x))] - 2*b*d*f*x*Log[1 - E^(-2*(c + d*x))] + 2*b*c*f*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*b*d*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*b*c*f*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*b*d*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*b*d*e*Log[Sinh[c + d*x]] + 2*b*c*f*Log[Sinh[c + d*x]] + 2*b*d*e*Log[a + b*Sinh[c + d*x]] - 2*b*c*f*Log[a + b*Sinh[c + d*x]] + 2*a*f*Log[Tanh[(c + d*x)/2]] + b*f*PolyLog[2, E^(-2*(c + d*x))] + 2*b*f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*b*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + a*d*e*Tanh[(c + d*x)/2] + a*d*f*x*Tanh[(c + d*x)/2])/(2*a^2*d^2)","A",1
452,1,50,50,0.035578,"\int \frac{\coth (c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Coth[c + d*x]*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{b \log (\sinh (c+d x))}{a^2 d}+\frac{b \log (a+b \sinh (c+d x))}{a^2 d}-\frac{\text{csch}(c+d x)}{a d}","-\frac{b \log (\sinh (c+d x))}{a^2 d}+\frac{b \log (a+b \sinh (c+d x))}{a^2 d}-\frac{\text{csch}(c+d x)}{a d}",1,"-(Csch[c + d*x]/(a*d)) - (b*Log[Sinh[c + d*x]])/(a^2*d) + (b*Log[a + b*Sinh[c + d*x]])/(a^2*d)","A",1
453,-1,0,35,180.0003065,"\int \frac{\coth (c+d x) \text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Coth[c + d*x]*Csch[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\coth (c+d x) \text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
454,1,1350,721,8.4785057,"\int \frac{(e+f x)^3 \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\sqrt{a^2+b^2} \left(-2 e^3 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^3+f^3 x^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3+3 e^2 f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^3-f^3 x^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 e f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3-3 e^2 f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^3+3 f (e+f x)^2 \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d^2-3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d^2-6 e f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d-6 f^3 x \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+6 e f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+6 f^3 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+6 f^3 \text{Li}_4\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{a^2 d^4}-\frac{-b d^3 x^3 \log (\cosh (c+d x)-\sinh (c+d x)+1) f^3+b d^3 x^3 \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^3-3 b \left(d^2 \text{Li}_2(\cosh (c+d x)-\sinh (c+d x)) x^2+2 (d x \text{Li}_3(\cosh (c+d x)-\sinh (c+d x))+\text{Li}_4(\cosh (c+d x)-\sinh (c+d x)))\right) f^3+3 b \left(d^2 \text{Li}_2(\sinh (c+d x)-\cosh (c+d x)) x^2+2 (d x \text{Li}_3(\sinh (c+d x)-\cosh (c+d x))+\text{Li}_4(\sinh (c+d x)-\cosh (c+d x)))\right) f^3-3 d^2 (b d e+a f) x^2 \log (\cosh (c+d x)-\sinh (c+d x)+1) f^2+3 d^2 (b d e-a f) x^2 \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^2+6 (a f-b d e) (d x \text{Li}_2(\cosh (c+d x)-\sinh (c+d x))+\text{Li}_3(\cosh (c+d x)-\sinh (c+d x))) f^2+6 (b d e+a f) (d x \text{Li}_2(\sinh (c+d x)-\cosh (c+d x))+\text{Li}_3(\sinh (c+d x)-\cosh (c+d x))) f^2-3 d^2 e (b d e+2 a f) x \log (\cosh (c+d x)-\sinh (c+d x)+1) f+3 d^2 e (b d e-2 a f) x \log (-\cosh (c+d x)+\sinh (c+d x)+1) f-3 d e (b d e-2 a f) \text{Li}_2(\cosh (c+d x)-\sinh (c+d x)) f+3 d e (b d e+2 a f) \text{Li}_2(\sinh (c+d x)-\cosh (c+d x)) f+a d^3 (e+f x)^3 (\coth (c)-1)-d^2 e^2 (b d e-3 a f) (d x-\log (-\cosh (c+d x)-\sinh (c+d x)+1))+d^2 e^2 (b d e+3 a f) (d x-\log (\cosh (c+d x)+\sinh (c+d x)+1))}{a^2 d^4}+\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(-\sinh \left(\frac{d x}{2}\right) e^3-3 f x \sinh \left(\frac{d x}{2}\right) e^2-3 f^2 x^2 \sinh \left(\frac{d x}{2}\right) e-f^3 x^3 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(\sinh \left(\frac{d x}{2}\right) e^3+3 f x \sinh \left(\frac{d x}{2}\right) e^2+3 f^2 x^2 \sinh \left(\frac{d x}{2}\right) e+f^3 x^3 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}","\frac{6 f^3 \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^4}-\frac{6 f^3 \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^4}-\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^3}+\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^3}+\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2}-\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{\sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d}-\frac{\sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d}+\frac{6 b f^3 \text{Li}_4\left(-e^{c+d x}\right)}{a^2 d^4}-\frac{6 b f^3 \text{Li}_4\left(e^{c+d x}\right)}{a^2 d^4}-\frac{6 b f^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right)}{a^2 d^3}+\frac{6 b f^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right)}{a^2 d^3}+\frac{3 b f (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right)}{a^2 d^2}-\frac{3 b f (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right)}{a^2 d^2}+\frac{2 b (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}-\frac{3 f^3 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a d^4}+\frac{3 f^2 (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^3}+\frac{3 f (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a d^2}-\frac{(e+f x)^3 \coth (c+d x)}{a d}-\frac{(e+f x)^3}{a d}",1,"(Sqrt[a^2 + b^2]*(-2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^2*d^4) - (a*d^3*(e + f*x)^3*(-1 + Coth[c]) - d^2*e^2*(b*d*e - 3*a*f)*(d*x - Log[1 - Cosh[c + d*x] - Sinh[c + d*x]]) - 3*d^2*e*f*(b*d*e + 2*a*f)*x*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - 3*d^2*f^2*(b*d*e + a*f)*x^2*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - b*d^3*f^3*x^3*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] + 3*d^2*e*f*(b*d*e - 2*a*f)*x*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] + 3*d^2*f^2*(b*d*e - a*f)*x^2*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] + b*d^3*f^3*x^3*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] + d^2*e^2*(b*d*e + 3*a*f)*(d*x - Log[1 + Cosh[c + d*x] + Sinh[c + d*x]]) - 3*d*e*f*(b*d*e - 2*a*f)*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 3*d*e*f*(b*d*e + 2*a*f)*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 6*f^2*(-(b*d*e) + a*f)*(d*x*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]]) + 6*f^2*(b*d*e + a*f)*(d*x*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]]) - 3*b*f^3*(d^2*x^2*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 2*(d*x*PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[4, Cosh[c + d*x] - Sinh[c + d*x]])) + 3*b*f^3*(d^2*x^2*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 2*(d*x*PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[4, -Cosh[c + d*x] + Sinh[c + d*x]])))/(a^2*d^4) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(-(e^3*Sinh[(d*x)/2]) - 3*e^2*f*x*Sinh[(d*x)/2] - 3*e*f^2*x^2*Sinh[(d*x)/2] - f^3*x^3*Sinh[(d*x)/2]))/(2*a*d) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2]))/(2*a*d)","A",1
455,1,792,517,7.8799766,"\int \frac{(e+f x)^2 \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\sqrt{a^2+b^2} \left(-2 d^2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)+2 d^2 e f x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-2 d^2 e f x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-d^2 f^2 x^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 d f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 d f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{a^2 d^3}-\frac{2 f \text{Li}_2\left(-e^{-c-d x}\right) (a f+b d e)+2 f \text{Li}_2\left(e^{-c-d x}\right) (a f-b d e)+2 d f x \log \left(1-e^{-c-d x}\right) (b d e-a f)-2 d f x \log \left(e^{-c-d x}+1\right) (a f+b d e)-d e \left(d x-\log \left(1-e^{c+d x}\right)\right) (b d e-2 a f)+d e \left(d x-\log \left(e^{c+d x}+1\right)\right) (2 a f+b d e)+\frac{2 a d^2 (e+f x)^2}{e^{2 c}-1}+b d^2 f^2 x^2 \log \left(1-e^{-c-d x}\right)-b d^2 f^2 x^2 \log \left(e^{-c-d x}+1\right)+2 b f^2 \left(d x \text{Li}_2\left(-e^{-c-d x}\right)+\text{Li}_3\left(-e^{-c-d x}\right)\right)-2 b f^2 \left(d x \text{Li}_2\left(e^{-c-d x}\right)+\text{Li}_3\left(e^{-c-d x}\right)\right)}{a^2 d^3}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(e^2 \sinh \left(\frac{d x}{2}\right)+2 e f x \sinh \left(\frac{d x}{2}\right)+f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}+\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(e^2 \left(-\sinh \left(\frac{d x}{2}\right)\right)-2 e f x \sinh \left(\frac{d x}{2}\right)-f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}","-\frac{2 f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^3}+\frac{2 f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^3}+\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2}-\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{\sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d}-\frac{\sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d}-\frac{2 b f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a^2 d^3}+\frac{2 b f^2 \text{Li}_3\left(e^{c+d x}\right)}{a^2 d^3}+\frac{2 b f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a^2 d^2}-\frac{2 b f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a^2 d^2}+\frac{2 b (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\frac{f^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^3}+\frac{2 f (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d^2}-\frac{(e+f x)^2 \coth (c+d x)}{a d}-\frac{(e+f x)^2}{a d}",1,"-(((2*a*d^2*(e + f*x)^2)/(-1 + E^(2*c)) + 2*d*f*(b*d*e - a*f)*x*Log[1 - E^(-c - d*x)] + b*d^2*f^2*x^2*Log[1 - E^(-c - d*x)] - 2*d*f*(b*d*e + a*f)*x*Log[1 + E^(-c - d*x)] - b*d^2*f^2*x^2*Log[1 + E^(-c - d*x)] - d*e*(b*d*e - 2*a*f)*(d*x - Log[1 - E^(c + d*x)]) + d*e*(b*d*e + 2*a*f)*(d*x - Log[1 + E^(c + d*x)]) + 2*f*(b*d*e + a*f)*PolyLog[2, -E^(-c - d*x)] + 2*f*(-(b*d*e) + a*f)*PolyLog[2, E^(-c - d*x)] + 2*b*f^2*(d*x*PolyLog[2, -E^(-c - d*x)] + PolyLog[3, -E^(-c - d*x)]) - 2*b*f^2*(d*x*PolyLog[2, E^(-c - d*x)] + PolyLog[3, E^(-c - d*x)]))/(a^2*d^3)) + (Sqrt[a^2 + b^2]*(-2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^2*d^3) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(-(e^2*Sinh[(d*x)/2]) - 2*e*f*x*Sinh[(d*x)/2] - f^2*x^2*Sinh[(d*x)/2]))/(2*a*d) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^2*Sinh[(d*x)/2] + 2*e*f*x*Sinh[(d*x)/2] + f^2*x^2*Sinh[(d*x)/2]))/(2*a*d)","A",1
456,1,364,294,3.5951206,"\int \frac{(e+f x) \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 \sqrt{a^2+b^2} \left(-2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)-a d (e+f x) \tanh \left(\frac{1}{2} (c+d x)\right)-a d (e+f x) \coth \left(\frac{1}{2} (c+d x)\right)+2 a f \log (\sinh (c+d x))-2 b d e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+2 b f \left(-\text{Li}_2\left(-e^{-c-d x}\right)+\text{Li}_2\left(e^{-c-d x}\right)-\left((c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right)\right)+2 b c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a^2 d^2}","\frac{f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2}-\frac{f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{\sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d}-\frac{\sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d}+\frac{b f \text{Li}_2\left(-e^{c+d x}\right)}{a^2 d^2}-\frac{b f \text{Li}_2\left(e^{c+d x}\right)}{a^2 d^2}+\frac{2 b (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\frac{f \log (\sinh (c+d x))}{a d^2}-\frac{(e+f x) \coth (c+d x)}{a d}",1,"(-(a*d*(e + f*x)*Coth[(c + d*x)/2]) + 2*a*f*Log[Sinh[c + d*x]] - 2*b*d*e*Log[Tanh[(c + d*x)/2]] + 2*b*c*f*Log[Tanh[(c + d*x)/2]] + 2*b*f*(-((c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)])) - PolyLog[2, -E^(-c - d*x)] + PolyLog[2, E^(-c - d*x)]) + 2*Sqrt[a^2 + b^2]*(-2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) - a*d*(e + f*x)*Tanh[(c + d*x)/2])/(2*a^2*d^2)","A",1
457,1,98,77,0.4112068,"\int \frac{\coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Coth[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","-\frac{4 \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)+a \tanh \left(\frac{1}{2} (c+d x)\right)+a \coth \left(\frac{1}{2} (c+d x)\right)+2 b \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a^2 d}","-\frac{2 \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a^2 d}+\frac{b \tanh ^{-1}(\cosh (c+d x))}{a^2 d}-\frac{\coth (c+d x)}{a d}",1,"-1/2*(4*Sqrt[-a^2 - b^2]*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] + a*Coth[(c + d*x)/2] + 2*b*Log[Tanh[(c + d*x)/2]] + a*Tanh[(c + d*x)/2])/(a^2*d)","A",1
458,0,0,31,179.7670646,"\int \frac{\coth ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Coth[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\coth ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\coth ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[Coth[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
459,1,2567,718,16.8154442,"\int \frac{(e+f x)^3 \cosh (c+d x) \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Cosh[c + d*x]*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{6 f^3 \left(a^2+b^2\right) \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 b d^4}+\frac{6 f^3 \left(a^2+b^2\right) \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 b d^4}-\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 b d^3}-\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 b d^3}+\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 b d^2}+\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 b d^2}+\frac{\left(a^2+b^2\right) (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 b d}+\frac{\left(a^2+b^2\right) (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 b d}-\frac{\left(a^2+b^2\right) (e+f x)^4}{4 a^2 b f}-\frac{3 b f^3 \text{Li}_4\left(e^{2 (c+d x)}\right)}{4 a^2 d^4}+\frac{3 b f^2 (e+f x) \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{3 b f (e+f x)^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a^2 d^2}-\frac{b (e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a^2 d}+\frac{b (e+f x)^4}{4 a^2 f}+\frac{6 f^3 \text{Li}_3\left(-e^{c+d x}\right)}{a d^4}-\frac{6 f^3 \text{Li}_3\left(e^{c+d x}\right)}{a d^4}-\frac{6 f^2 (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^3}-\frac{6 f (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d^2}-\frac{(e+f x)^3 \text{csch}(c+d x)}{a d}",1,"-1/2*((a^2 + b^2)*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(a^2*b*(-1 + E^(2*c))) + ((b*(e + f*x)^4*(-1 + Coth[c]))/(2*f) + (2*e^2*(b*d*e - 3*a*f)*(d*x - Log[1 - Cosh[c + d*x] - Sinh[c + d*x]]))/d^2 - (6*e*f*(b*d*e + 2*a*f)*x*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]])/d^2 - (6*f^2*(b*d*e + a*f)*x^2*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]])/d^2 - (2*b*f^3*x^3*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]])/d - (6*e*f*(b*d*e - 2*a*f)*x*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]])/d^2 + (6*f^2*(-(b*d*e) + a*f)*x^2*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]])/d^2 - (2*b*f^3*x^3*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]])/d + (2*e^2*(b*d*e + 3*a*f)*(d*x - Log[1 + Cosh[c + d*x] + Sinh[c + d*x]]))/d^2 + (6*e*f*(b*d*e - 2*a*f)*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]])/d^3 + (6*e*f*(b*d*e + 2*a*f)*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]])/d^3 + (12*f^2*(b*d*e - a*f)*(d*x*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]]))/d^4 + (12*f^2*(b*d*e + a*f)*(d*x*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]]))/d^4 + (6*b*f^3*(d^2*x^2*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 2*(d*x*PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[4, Cosh[c + d*x] - Sinh[c + d*x]])))/d^4 + (6*b*f^3*(d^2*x^2*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 2*(d*x*PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[4, -Cosh[c + d*x] + Sinh[c + d*x]])))/d^4)/(2*a^2) + ((-4*b*e^3 - 12*b*e^2*f*x - 12*b*e*f^2*x^2 - 4*b*f^3*x^3 + 4*a*d*e^3*x*Cosh[c] + 6*a*d*e^2*f*x^2*Cosh[c] + 4*a*d*e*f^2*x^3*Cosh[c] + a*d*f^3*x^4*Cosh[c])*Csch[c/2]*Sech[c/2])/(8*a*b*d) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2]))/(2*a*d) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2]))/(2*a*d)","B",0
460,1,1454,518,11.3741722,"\int \frac{(e+f x)^2 \cosh (c+d x) \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Cosh[c + d*x]*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{\left(a^2+b^2\right) \left(2 e^{2 c} f^2 x^3 d^3+6 e e^{2 c} f x^2 d^3+6 e^2 e^{2 c} x d^3-3 e^2 e^{2 c} \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2+3 e^2 \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right)}{3 a^2 b d^3 \left(-1+e^{2 c}\right)}+\frac{-3 b d^2 x^2 \log (\cosh (c+d x)-\sinh (c+d x)+1) f^3-3 b d^2 x^2 \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^3+6 b (d x \text{Li}_2(\cosh (c+d x)-\sinh (c+d x))+\text{Li}_3(\cosh (c+d x)-\sinh (c+d x))) f^3+6 b (d x \text{Li}_2(\sinh (c+d x)-\cosh (c+d x))+\text{Li}_3(\sinh (c+d x)-\cosh (c+d x))) f^3-6 d (b d e+a f) x \log (\cosh (c+d x)-\sinh (c+d x)+1) f^2-6 d (b d e-a f) x \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^2+6 (b d e-a f) \text{Li}_2(\cosh (c+d x)-\sinh (c+d x)) f^2+6 (b d e+a f) \text{Li}_2(\sinh (c+d x)-\cosh (c+d x)) f^2+3 d e (b d e-2 a f) (d x-\log (-\cosh (c+d x)-\sinh (c+d x)+1)) f+3 d e (b d e+2 a f) (d x-\log (\cosh (c+d x)+\sinh (c+d x)+1)) f+b d^3 (e+f x)^3 (\coth (c)-1)}{3 a^2 d^3 f}+\frac{\left(a d f^2 \cosh (c) x^3-3 b f^2 x^2+3 a d e f \cosh (c) x^2-6 b e f x+3 a d e^2 \cosh (c) x-3 b e^2\right) \text{csch}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}\right)}{6 a b d}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(\sinh \left(\frac{d x}{2}\right) e^2+2 f x \sinh \left(\frac{d x}{2}\right) e+f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}+\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(\sinh \left(\frac{d x}{2}\right) e^2+2 f x \sinh \left(\frac{d x}{2}\right) e+f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}","-\frac{2 f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 b d^3}-\frac{2 f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 b d^3}+\frac{2 f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 b d^2}+\frac{2 f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 b d^2}+\frac{\left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 b d}+\frac{\left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 b d}-\frac{\left(a^2+b^2\right) (e+f x)^3}{3 a^2 b f}+\frac{b f^2 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{b f (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a^2 d^2}-\frac{b (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a^2 d}+\frac{b (e+f x)^3}{3 a^2 f}-\frac{2 f^2 \text{Li}_2\left(-e^{c+d x}\right)}{a d^3}+\frac{2 f^2 \text{Li}_2\left(e^{c+d x}\right)}{a d^3}-\frac{4 f (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d^2}-\frac{(e+f x)^2 \text{csch}(c+d x)}{a d}",1,"-1/3*((a^2 + b^2)*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(a^2*b*d^3*(-1 + E^(2*c))) + (b*d^3*(e + f*x)^3*(-1 + Coth[c]) + 3*d*e*f*(b*d*e - 2*a*f)*(d*x - Log[1 - Cosh[c + d*x] - Sinh[c + d*x]]) - 6*d*f^2*(b*d*e + a*f)*x*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - 3*b*d^2*f^3*x^2*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - 6*d*f^2*(b*d*e - a*f)*x*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] - 3*b*d^2*f^3*x^2*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] + 3*d*e*f*(b*d*e + 2*a*f)*(d*x - Log[1 + Cosh[c + d*x] + Sinh[c + d*x]]) + 6*f^2*(b*d*e - a*f)*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 6*f^2*(b*d*e + a*f)*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 6*b*f^3*(d*x*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]]) + 6*b*f^3*(d*x*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]]))/(3*a^2*d^3*f) + ((-3*b*e^2 - 6*b*e*f*x - 3*b*f^2*x^2 + 3*a*d*e^2*x*Cosh[c] + 3*a*d*e*f*x^2*Cosh[c] + a*d*f^2*x^3*Cosh[c])*Csch[c/2]*Sech[c/2])/(6*a*b*d) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^2*Sinh[(d*x)/2] + 2*e*f*x*Sinh[(d*x)/2] + f^2*x^2*Sinh[(d*x)/2]))/(2*a*d) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(e^2*Sinh[(d*x)/2] + 2*e*f*x*Sinh[(d*x)/2] + f^2*x^2*Sinh[(d*x)/2]))/(2*a*d)","B",1
461,1,313,324,2.3827555,"\int \frac{(e+f x) \cosh (c+d x) \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Cosh[c + d*x]*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\frac{2 \left(a^2+b^2\right) \left(f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-\frac{1}{2} f (c+d x)^2\right)}{b}+a d (e+f x) \tanh \left(\frac{1}{2} (c+d x)\right)-a d (e+f x) \coth \left(\frac{1}{2} (c+d x)\right)+2 a f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)-2 b d e \log (\sinh (c+d x))+b f \left(\text{Li}_2\left(e^{-2 (c+d x)}\right)-(c+d x) \left(2 \log \left(1-e^{-2 (c+d x)}\right)+c+d x\right)\right)+2 b c f \log (\sinh (c+d x))}{2 a^2 d^2}","\frac{f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 b d^2}+\frac{f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 b d^2}+\frac{\left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 b d}+\frac{\left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 b d}-\frac{\left(a^2+b^2\right) (e+f x)^2}{2 a^2 b f}-\frac{b f \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a^2 d^2}-\frac{b (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a^2 d}+\frac{b (e+f x)^2}{2 a^2 f}-\frac{f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac{(e+f x) \text{csch}(c+d x)}{a d}",1,"(-(a*d*(e + f*x)*Coth[(c + d*x)/2]) - 2*b*d*e*Log[Sinh[c + d*x]] + 2*b*c*f*Log[Sinh[c + d*x]] + 2*a*f*Log[Tanh[(c + d*x)/2]] + b*f*(-((c + d*x)*(c + d*x + 2*Log[1 - E^(-2*(c + d*x))])) + PolyLog[2, E^(-2*(c + d*x))]) + (2*(a^2 + b^2)*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/b + a*d*(e + f*x)*Tanh[(c + d*x)/2])/(2*a^2*d^2)","A",1
462,1,52,59,0.0784611,"\int \frac{\cosh (c+d x) \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Cosh[c + d*x]*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(a^2+b^2\right) \log (a+b \sinh (c+d x))-a b \text{csch}(c+d x)+b^2 (-\log (\sinh (c+d x)))}{a^2 b d}","\frac{\left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{a^2 b d}-\frac{b \log (\sinh (c+d x))}{a^2 d}-\frac{\text{csch}(c+d x)}{a d}",1,"(-(a*b*Csch[c + d*x]) - b^2*Log[Sinh[c + d*x]] + (a^2 + b^2)*Log[a + b*Sinh[c + d*x]])/(a^2*b*d)","A",1
463,-1,0,37,180.0018656,"\int \frac{\cosh (c+d x) \coth ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Cosh[c + d*x]*Coth[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\cosh (c+d x) \coth ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
464,1,4010,1428,17.1919187,"\int \frac{(e+f x)^3 \text{csch}^2(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Csch[c + d*x]^2*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right) d}+\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right) d}-\frac{(e+f x)^3 \log \left(1+e^{2 (c+d x)}\right) b^3}{a^2 \left(a^2+b^2\right) d}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) b^3}{2 a^2 \left(a^2+b^2\right) d^2}-\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}-\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}+\frac{3 f^2 (e+f x) \text{Li}_3\left(-e^{2 (c+d x)}\right) b^3}{2 a^2 \left(a^2+b^2\right) d^3}+\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right) d^4}+\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right) d^4}-\frac{3 f^3 \text{Li}_4\left(-e^{2 (c+d x)}\right) b^3}{4 a^2 \left(a^2+b^2\right) d^4}+\frac{2 (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d}-\frac{3 i f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^2}+\frac{3 i f (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^2}+\frac{6 i f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}-\frac{6 i f^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}-\frac{6 i f^3 \text{Li}_4\left(-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^4}+\frac{6 i f^3 \text{Li}_4\left(i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^4}+\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{2 c+2 d x}\right) b}{a^2 d}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{2 c+2 d x}\right) b}{2 a^2 d^2}-\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{2 c+2 d x}\right) b}{2 a^2 d^2}-\frac{3 f^2 (e+f x) \text{Li}_3\left(-e^{2 c+2 d x}\right) b}{2 a^2 d^3}+\frac{3 f^2 (e+f x) \text{Li}_3\left(e^{2 c+2 d x}\right) b}{2 a^2 d^3}+\frac{3 f^3 \text{Li}_4\left(-e^{2 c+2 d x}\right) b}{4 a^2 d^4}-\frac{3 f^3 \text{Li}_4\left(e^{2 c+2 d x}\right) b}{4 a^2 d^4}-\frac{2 (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{6 f (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d^2}-\frac{(e+f x)^3 \text{csch}(c+d x)}{a d}-\frac{6 f^2 (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right)}{a d^2}+\frac{6 f^2 (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^3}+\frac{6 f^3 \text{Li}_3\left(-e^{c+d x}\right)}{a d^4}-\frac{6 i f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right)}{a d^3}+\frac{6 i f^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right)}{a d^3}-\frac{6 f^3 \text{Li}_3\left(e^{c+d x}\right)}{a d^4}+\frac{6 i f^3 \text{Li}_4\left(-i e^{c+d x}\right)}{a d^4}-\frac{6 i f^3 \text{Li}_4\left(i e^{c+d x}\right)}{a d^4}",1,"(-8*b*d^4*e^3*E^(2*c)*x - 12*b*d^4*e^2*E^(2*c)*f*x^2 - 8*b*d^4*e*E^(2*c)*f^2*x^3 - 2*b*d^4*E^(2*c)*f^3*x^4 - 8*a*d^3*e^3*ArcTan[E^(c + d*x)] - 8*a*d^3*e^3*E^(2*c)*ArcTan[E^(c + d*x)] - (12*I)*a*d^3*e^2*f*x*Log[1 - I*E^(c + d*x)] - (12*I)*a*d^3*e^2*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] - (12*I)*a*d^3*e*f^2*x^2*Log[1 - I*E^(c + d*x)] - (12*I)*a*d^3*e*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] - (4*I)*a*d^3*f^3*x^3*Log[1 - I*E^(c + d*x)] - (4*I)*a*d^3*E^(2*c)*f^3*x^3*Log[1 - I*E^(c + d*x)] + (12*I)*a*d^3*e^2*f*x*Log[1 + I*E^(c + d*x)] + (12*I)*a*d^3*e^2*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] + (12*I)*a*d^3*e*f^2*x^2*Log[1 + I*E^(c + d*x)] + (12*I)*a*d^3*e*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] + (4*I)*a*d^3*f^3*x^3*Log[1 + I*E^(c + d*x)] + (4*I)*a*d^3*E^(2*c)*f^3*x^3*Log[1 + I*E^(c + d*x)] + 4*b*d^3*e^3*Log[1 + E^(2*(c + d*x))] + 4*b*d^3*e^3*E^(2*c)*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e^2*f*x*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e^2*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 12*b*d^3*e*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 4*b*d^3*f^3*x^3*Log[1 + E^(2*(c + d*x))] + 4*b*d^3*E^(2*c)*f^3*x^3*Log[1 + E^(2*(c + d*x))] + (12*I)*a*d^2*(1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)] - (12*I)*a*d^2*(1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)] + 6*b*d^2*e^2*f*PolyLog[2, -E^(2*(c + d*x))] + 6*b*d^2*e^2*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 12*b*d^2*e*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 12*b*d^2*e*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 6*b*d^2*f^3*x^2*PolyLog[2, -E^(2*(c + d*x))] + 6*b*d^2*E^(2*c)*f^3*x^2*PolyLog[2, -E^(2*(c + d*x))] - (24*I)*a*d*e*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (24*I)*a*d*e*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (24*I)*a*d*f^3*x*PolyLog[3, (-I)*E^(c + d*x)] - (24*I)*a*d*E^(2*c)*f^3*x*PolyLog[3, (-I)*E^(c + d*x)] + (24*I)*a*d*e*f^2*PolyLog[3, I*E^(c + d*x)] + (24*I)*a*d*e*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] + (24*I)*a*d*f^3*x*PolyLog[3, I*E^(c + d*x)] + (24*I)*a*d*E^(2*c)*f^3*x*PolyLog[3, I*E^(c + d*x)] - 6*b*d*e*f^2*PolyLog[3, -E^(2*(c + d*x))] - 6*b*d*e*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))] - 6*b*d*f^3*x*PolyLog[3, -E^(2*(c + d*x))] - 6*b*d*E^(2*c)*f^3*x*PolyLog[3, -E^(2*(c + d*x))] + (24*I)*a*f^3*PolyLog[4, (-I)*E^(c + d*x)] + (24*I)*a*E^(2*c)*f^3*PolyLog[4, (-I)*E^(c + d*x)] - (24*I)*a*f^3*PolyLog[4, I*E^(c + d*x)] - (24*I)*a*E^(2*c)*f^3*PolyLog[4, I*E^(c + d*x)] + 3*b*f^3*PolyLog[4, -E^(2*(c + d*x))] + 3*b*E^(2*c)*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*(a^2 + b^2)*d^4*(1 + E^(2*c))) - (b^3*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(2*a^2*(a^2 + b^2)*(-1 + E^(2*c))) + ((b*(e + f*x)^4*(-1 + Coth[c]))/(2*f) + (2*e^2*(b*d*e - 3*a*f)*(d*x - Log[1 - Cosh[c + d*x] - Sinh[c + d*x]]))/d^2 - (6*e*f*(b*d*e + 2*a*f)*x*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]])/d^2 - (6*f^2*(b*d*e + a*f)*x^2*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]])/d^2 - (2*b*f^3*x^3*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]])/d - (6*e*f*(b*d*e - 2*a*f)*x*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]])/d^2 + (6*f^2*(-(b*d*e) + a*f)*x^2*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]])/d^2 - (2*b*f^3*x^3*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]])/d + (2*e^2*(b*d*e + 3*a*f)*(d*x - Log[1 + Cosh[c + d*x] + Sinh[c + d*x]]))/d^2 + (6*e*f*(b*d*e - 2*a*f)*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]])/d^3 + (6*e*f*(b*d*e + 2*a*f)*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]])/d^3 + (12*f^2*(b*d*e - a*f)*(d*x*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]]))/d^4 + (12*f^2*(b*d*e + a*f)*(d*x*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]]))/d^4 + (6*b*f^3*(d^2*x^2*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 2*(d*x*PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[4, Cosh[c + d*x] - Sinh[c + d*x]])))/d^4 + (6*b*f^3*(d^2*x^2*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 2*(d*x*PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[4, -Cosh[c + d*x] + Sinh[c + d*x]])))/d^4)/(2*a^2) + ((-4*a*b*d*e^3*x - 6*a*b*d*e^2*f*x^2 - 4*a*b*d*e*f^2*x^3 - a*b*d*f^3*x^4 - 4*a^2*e^3*Cosh[c] - 4*b^2*e^3*Cosh[c] - 12*a^2*e^2*f*x*Cosh[c] - 12*b^2*e^2*f*x*Cosh[c] - 12*a^2*e*f^2*x^2*Cosh[c] - 12*b^2*e*f^2*x^2*Cosh[c] - 4*a^2*f^3*x^3*Cosh[c] - 4*b^2*f^3*x^3*Cosh[c])*Csch[c/2]*Sech[c/2]*Sech[c])/(8*a*(a^2 + b^2)*d) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2]))/(2*a*d) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(e^3*Sinh[(d*x)/2] + 3*e^2*f*x*Sinh[(d*x)/2] + 3*e*f^2*x^2*Sinh[(d*x)/2] + f^3*x^3*Sinh[(d*x)/2]))/(2*a*d)","B",0
465,1,1971,982,11.7656426,"\int \frac{(e+f x)^2 \text{csch}^2(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]^2*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{\left(2 e^{2 c} f^2 x^3 d^3+6 e e^{2 c} f x^2 d^3+6 e^2 e^{2 c} x d^3-3 e^2 e^{2 c} \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2+3 e^2 \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right) b^3}{3 a^2 \left(a^2+b^2\right) d^3 \left(-1+e^{2 c}\right)}-\frac{-4 b f^2 x^3 d^3-12 b e f x^2 d^3+12 b e^2 e^{2 c} x d^3-12 b e^2 \left(1+e^{2 c}\right) x d^3+12 a e^2 \left(1+e^{2 c}\right) \tan ^{-1}\left(e^{c+d x}\right) d^2+6 b e^2 \left(1+e^{2 c}\right) \left(2 d x-\log \left(1+e^{2 (c+d x)}\right)\right) d^2+12 i a e \left(1+e^{2 c}\right) f \left(d x \left(\log \left(1-i e^{c+d x}\right)-\log \left(1+i e^{c+d x}\right)\right)-\text{Li}_2\left(-i e^{c+d x}\right)+\text{Li}_2\left(i e^{c+d x}\right)\right) d+6 b e \left(1+e^{2 c}\right) f \left(2 d x \left(d x-\log \left(1+e^{2 (c+d x)}\right)\right)-\text{Li}_2\left(-e^{2 (c+d x)}\right)\right) d+6 i a \left(1+e^{2 c}\right) f^2 \left(d^2 \log \left(1-i e^{c+d x}\right) x^2-d^2 \log \left(1+i e^{c+d x}\right) x^2-2 d \text{Li}_2\left(-i e^{c+d x}\right) x+2 d \text{Li}_2\left(i e^{c+d x}\right) x+2 \text{Li}_3\left(-i e^{c+d x}\right)-2 \text{Li}_3\left(i e^{c+d x}\right)\right)+b \left(1+e^{2 c}\right) f^2 \left(2 d^2 \left(2 d x-3 \log \left(1+e^{2 (c+d x)}\right)\right) x^2-6 d \text{Li}_2\left(-e^{2 (c+d x)}\right) x+3 \text{Li}_3\left(-e^{2 (c+d x)}\right)\right)}{6 \left(a^2+b^2\right) d^3 \left(1+e^{2 c}\right)}+\frac{-3 b d^2 x^2 \log (\cosh (c+d x)-\sinh (c+d x)+1) f^3-3 b d^2 x^2 \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^3+6 b (d x \text{Li}_2(\cosh (c+d x)-\sinh (c+d x))+\text{Li}_3(\cosh (c+d x)-\sinh (c+d x))) f^3+6 b (d x \text{Li}_2(\sinh (c+d x)-\cosh (c+d x))+\text{Li}_3(\sinh (c+d x)-\cosh (c+d x))) f^3-6 d (b d e+a f) x \log (\cosh (c+d x)-\sinh (c+d x)+1) f^2-6 d (b d e-a f) x \log (-\cosh (c+d x)+\sinh (c+d x)+1) f^2+6 (b d e-a f) \text{Li}_2(\cosh (c+d x)-\sinh (c+d x)) f^2+6 (b d e+a f) \text{Li}_2(\sinh (c+d x)-\cosh (c+d x)) f^2+3 d e (b d e-2 a f) (d x-\log (-\cosh (c+d x)-\sinh (c+d x)+1)) f+3 d e (b d e+2 a f) (d x-\log (\cosh (c+d x)+\sinh (c+d x)+1)) f+b d^3 (e+f x)^3 (\coth (c)-1)}{3 a^2 d^3 f}+\frac{\left(-a b d f^2 x^3-3 a b d e f x^2-3 a^2 f^2 \cosh (c) x^2-3 b^2 f^2 \cosh (c) x^2-3 a b d e^2 x-6 a^2 e f \cosh (c) x-6 b^2 e f \cosh (c) x-3 a^2 e^2 \cosh (c)-3 b^2 e^2 \cosh (c)\right) \text{csch}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}\right) \text{sech}(c)}{6 a \left(a^2+b^2\right) d}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(\sinh \left(\frac{d x}{2}\right) e^2+2 f x \sinh \left(\frac{d x}{2}\right) e+f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}+\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(\sinh \left(\frac{d x}{2}\right) e^2+2 f x \sinh \left(\frac{d x}{2}\right) e+f^2 x^2 \sinh \left(\frac{d x}{2}\right)\right)}{2 a d}","\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right) d}+\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^3}{a^2 \left(a^2+b^2\right) d}-\frac{(e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) b^3}{a^2 \left(a^2+b^2\right) d}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}+\frac{f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) b^3}{2 a^2 \left(a^2+b^2\right) d^3}+\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d}-\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^2}+\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^2}+\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}+\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{2 c+2 d x}\right) b}{a^2 d}+\frac{f (e+f x) \text{Li}_2\left(-e^{2 c+2 d x}\right) b}{a^2 d^2}-\frac{f (e+f x) \text{Li}_2\left(e^{2 c+2 d x}\right) b}{a^2 d^2}-\frac{f^2 \text{Li}_3\left(-e^{2 c+2 d x}\right) b}{2 a^2 d^3}+\frac{f^2 \text{Li}_3\left(e^{2 c+2 d x}\right) b}{2 a^2 d^3}-\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{4 f (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d^2}-\frac{(e+f x)^2 \text{csch}(c+d x)}{a d}-\frac{2 f^2 \text{Li}_2\left(-e^{c+d x}\right)}{a d^3}+\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right)}{a d^2}-\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right)}{a d^2}+\frac{2 f^2 \text{Li}_2\left(e^{c+d x}\right)}{a d^3}-\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right)}{a d^3}+\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right)}{a d^3}",1,"-1/6*(12*b*d^3*e^2*E^(2*c)*x - 12*b*d^3*e^2*(1 + E^(2*c))*x - 12*b*d^3*e*f*x^2 - 4*b*d^3*f^2*x^3 + 12*a*d^2*e^2*(1 + E^(2*c))*ArcTan[E^(c + d*x)] + 6*b*d^2*e^2*(1 + E^(2*c))*(2*d*x - Log[1 + E^(2*(c + d*x))]) + (12*I)*a*d*e*(1 + E^(2*c))*f*(d*x*(Log[1 - I*E^(c + d*x)] - Log[1 + I*E^(c + d*x)]) - PolyLog[2, (-I)*E^(c + d*x)] + PolyLog[2, I*E^(c + d*x)]) + 6*b*d*e*(1 + E^(2*c))*f*(2*d*x*(d*x - Log[1 + E^(2*(c + d*x))]) - PolyLog[2, -E^(2*(c + d*x))]) + (6*I)*a*(1 + E^(2*c))*f^2*(d^2*x^2*Log[1 - I*E^(c + d*x)] - d^2*x^2*Log[1 + I*E^(c + d*x)] - 2*d*x*PolyLog[2, (-I)*E^(c + d*x)] + 2*d*x*PolyLog[2, I*E^(c + d*x)] + 2*PolyLog[3, (-I)*E^(c + d*x)] - 2*PolyLog[3, I*E^(c + d*x)]) + b*(1 + E^(2*c))*f^2*(2*d^2*x^2*(2*d*x - 3*Log[1 + E^(2*(c + d*x))]) - 6*d*x*PolyLog[2, -E^(2*(c + d*x))] + 3*PolyLog[3, -E^(2*(c + d*x))]))/((a^2 + b^2)*d^3*(1 + E^(2*c))) - (b^3*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*a^2*(a^2 + b^2)*d^3*(-1 + E^(2*c))) + (b*d^3*(e + f*x)^3*(-1 + Coth[c]) + 3*d*e*f*(b*d*e - 2*a*f)*(d*x - Log[1 - Cosh[c + d*x] - Sinh[c + d*x]]) - 6*d*f^2*(b*d*e + a*f)*x*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - 3*b*d^2*f^3*x^2*Log[1 + Cosh[c + d*x] - Sinh[c + d*x]] - 6*d*f^2*(b*d*e - a*f)*x*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] - 3*b*d^2*f^3*x^2*Log[1 - Cosh[c + d*x] + Sinh[c + d*x]] + 3*d*e*f*(b*d*e + 2*a*f)*(d*x - Log[1 + Cosh[c + d*x] + Sinh[c + d*x]]) + 6*f^2*(b*d*e - a*f)*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + 6*f^2*(b*d*e + a*f)*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + 6*b*f^3*(d*x*PolyLog[2, Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] - Sinh[c + d*x]]) + 6*b*f^3*(d*x*PolyLog[2, -Cosh[c + d*x] + Sinh[c + d*x]] + PolyLog[3, -Cosh[c + d*x] + Sinh[c + d*x]]))/(3*a^2*d^3*f) + ((-3*a*b*d*e^2*x - 3*a*b*d*e*f*x^2 - a*b*d*f^2*x^3 - 3*a^2*e^2*Cosh[c] - 3*b^2*e^2*Cosh[c] - 6*a^2*e*f*x*Cosh[c] - 6*b^2*e*f*x*Cosh[c] - 3*a^2*f^2*x^2*Cosh[c] - 3*b^2*f^2*x^2*Cosh[c])*Csch[c/2]*Sech[c/2]*Sech[c])/(6*a*(a^2 + b^2)*d) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(e^2*Sinh[(d*x)/2] + 2*e*f*x*Sinh[(d*x)/2] + f^2*x^2*Sinh[(d*x)/2]))/(2*a*d) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(e^2*Sinh[(d*x)/2] + 2*e*f*x*Sinh[(d*x)/2] + f^2*x^2*Sinh[(d*x)/2]))/(2*a*d)","B",1
466,1,535,591,6.4309704,"\int \frac{(e+f x) \text{csch}^2(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]^2*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\frac{-4 a d e \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))+2 i a f \text{Li}_2(-i (\cosh (c+d x)+\sinh (c+d x)))-2 i a f \text{Li}_2(i (\cosh (c+d x)+\sinh (c+d x)))-4 a d f x \tan ^{-1}(\sinh (c+d x)+\cosh (c+d x))+b c^2 f+2 b d e \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)-2 b c d e+b f \text{Li}_2(-\cosh (2 (c+d x))-\sinh (2 (c+d x)))+2 b d f x \log (\sinh (2 (c+d x))+\cosh (2 (c+d x))+1)-2 b d^2 e x-b d^2 f x^2}{a^2+b^2}+\frac{2 b^3 \left(f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-\frac{1}{2} f (c+d x)^2\right)}{a^2 \left(a^2+b^2\right)}-\frac{2 b d e \log (\sinh (c+d x))}{a^2}+\frac{b f \left(\text{Li}_2\left(e^{-2 (c+d x)}\right)-(c+d x) \left(2 \log \left(1-e^{-2 (c+d x)}\right)+c+d x\right)\right)}{a^2}+\frac{2 b c f \log (\sinh (c+d x))}{a^2}+\frac{d (e+f x) \tanh \left(\frac{1}{2} (c+d x)\right)}{a}-\frac{d (e+f x) \coth \left(\frac{1}{2} (c+d x)\right)}{a}+\frac{2 f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a}}{2 d^2}","-\frac{i b^2 f \text{Li}_2\left(-i e^{c+d x}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{i b^2 f \text{Li}_2\left(i e^{c+d x}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{2 b^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{a d \left(a^2+b^2\right)}+\frac{b^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2 \left(a^2+b^2\right)}+\frac{b^3 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2 \left(a^2+b^2\right)}-\frac{b^3 f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 a^2 d^2 \left(a^2+b^2\right)}+\frac{b^3 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d \left(a^2+b^2\right)}+\frac{b^3 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d \left(a^2+b^2\right)}-\frac{b^3 (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{a^2 d \left(a^2+b^2\right)}+\frac{b f \text{Li}_2\left(-e^{2 c+2 d x}\right)}{2 a^2 d^2}-\frac{b f \text{Li}_2\left(e^{2 c+2 d x}\right)}{2 a^2 d^2}+\frac{2 b (e+f x) \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a^2 d}+\frac{i f \text{Li}_2\left(-i e^{c+d x}\right)}{a d^2}-\frac{i f \text{Li}_2\left(i e^{c+d x}\right)}{a d^2}-\frac{f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac{(e+f x) \text{csch}(c+d x)}{a d}-\frac{(e+f x) \tan ^{-1}(\sinh (c+d x))}{a d}-\frac{2 f x \tan ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{f x \tan ^{-1}(\sinh (c+d x))}{a d}",1,"(-((d*(e + f*x)*Coth[(c + d*x)/2])/a) - (2*b*d*e*Log[Sinh[c + d*x]])/a^2 + (2*b*c*f*Log[Sinh[c + d*x]])/a^2 + (2*f*Log[Tanh[(c + d*x)/2]])/a + (b*f*(-((c + d*x)*(c + d*x + 2*Log[1 - E^(-2*(c + d*x))])) + PolyLog[2, E^(-2*(c + d*x))]))/a^2 + (2*b^3*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^2*(a^2 + b^2)) + (-2*b*c*d*e + b*c^2*f - 2*b*d^2*e*x - b*d^2*f*x^2 - 4*a*d*e*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] - 4*a*d*f*x*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] + 2*b*d*e*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] + 2*b*d*f*x*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] + (2*I)*a*f*PolyLog[2, (-I)*(Cosh[c + d*x] + Sinh[c + d*x])] - (2*I)*a*f*PolyLog[2, I*(Cosh[c + d*x] + Sinh[c + d*x])] + b*f*PolyLog[2, -Cosh[2*(c + d*x)] - Sinh[2*(c + d*x)]])/(a^2 + b^2) + (d*(e + f*x)*Tanh[(c + d*x)/2])/a)/(2*d^2)","A",0
467,1,160,104,0.6014034,"\int \frac{\text{csch}^2(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Csch[c + d*x]^2*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{b^3 \left(\frac{\log (\sinh (c+d x))}{a^2 b^2}-\frac{\log (a+b \sinh (c+d x))}{a^2 \left(a^2+b^2\right)}-\frac{\left(\frac{a}{\sqrt{-b^2}}+1\right) \log \left(\sqrt{-b^2}+b \sinh (c+d x)\right)}{2 b^2 \left(a^2+b^2\right)}-\frac{\left(a \sqrt{-b^2}+b^2\right) \log \left(\sqrt{-b^2}-b \sinh (c+d x)\right)}{2 b^4 \left(a^2+b^2\right)}+\frac{\text{csch}(c+d x)}{a b^3}\right)}{d}","-\frac{a \tan ^{-1}(\sinh (c+d x))}{d \left(a^2+b^2\right)}+\frac{b \log (\cosh (c+d x))}{d \left(a^2+b^2\right)}+\frac{b^3 \log (a+b \sinh (c+d x))}{a^2 d \left(a^2+b^2\right)}-\frac{b \log (\sinh (c+d x))}{a^2 d}-\frac{\text{csch}(c+d x)}{a d}",1,"-((b^3*(Csch[c + d*x]/(a*b^3) + Log[Sinh[c + d*x]]/(a^2*b^2) - ((b^2 + a*Sqrt[-b^2])*Log[Sqrt[-b^2] - b*Sinh[c + d*x]])/(2*b^4*(a^2 + b^2)) - Log[a + b*Sinh[c + d*x]]/(a^2*(a^2 + b^2)) - ((1 + a/Sqrt[-b^2])*Log[Sqrt[-b^2] + b*Sinh[c + d*x]])/(2*b^2*(a^2 + b^2))))/d)","A",1
468,0,0,37,76.1478148,"\int \frac{\text{csch}^2(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Csch[c + d*x]^2*Sech[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}^2(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}^2(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[(Csch[c + d*x]^2*Sech[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
469,1,2677,914,28.0704964,"\int \frac{(e+f x)^2 \text{csch}^2(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]^2*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^4}{a^2 \left(a^2+b^2\right)^{3/2} d}-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^4}{a^2 \left(a^2+b^2\right)^{3/2} d}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^4}{a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^4}{a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^4}{a^2 \left(a^2+b^2\right)^{3/2} d^3}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^4}{a^2 \left(a^2+b^2\right)^{3/2} d^3}-\frac{4 f (e+f x) \tan ^{-1}\left(e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}+\frac{2 i f^2 \text{Li}_2\left(-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{Li}_2\left(i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}+\frac{(e+f x)^2 \text{sech}(c+d x) b^3}{a^2 \left(a^2+b^2\right) d}+\frac{(e+f x)^2 b^2}{a \left(a^2+b^2\right) d}-\frac{2 f (e+f x) \log \left(1+e^{2 (c+d x)}\right) b^2}{a \left(a^2+b^2\right) d^2}-\frac{f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) b^2}{a \left(a^2+b^2\right) d^3}+\frac{(e+f x)^2 \tanh (c+d x) b^2}{a \left(a^2+b^2\right) d}+\frac{4 f (e+f x) \tan ^{-1}\left(e^{c+d x}\right) b}{a^2 d^2}+\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right) b}{a^2 d}+\frac{2 f (e+f x) \text{Li}_2\left(-e^{c+d x}\right) b}{a^2 d^2}-\frac{2 i f^2 \text{Li}_2\left(-i e^{c+d x}\right) b}{a^2 d^3}+\frac{2 i f^2 \text{Li}_2\left(i e^{c+d x}\right) b}{a^2 d^3}-\frac{2 f (e+f x) \text{Li}_2\left(e^{c+d x}\right) b}{a^2 d^2}-\frac{2 f^2 \text{Li}_3\left(-e^{c+d x}\right) b}{a^2 d^3}+\frac{2 f^2 \text{Li}_3\left(e^{c+d x}\right) b}{a^2 d^3}-\frac{(e+f x)^2 \text{sech}(c+d x) b}{a^2 d}-\frac{2 (e+f x)^2}{a d}-\frac{2 (e+f x)^2 \coth (2 c+2 d x)}{a d}+\frac{2 f (e+f x) \log \left(1-e^{4 (c+d x)}\right)}{a d^2}+\frac{f^2 \text{Li}_2\left(e^{4 (c+d x)}\right)}{2 a d^3}",1,"4*(((I/2)*a*(-(d*(e + f*x)*(d*(e + f*x) + (1 + I*E^(2*c))*f*Log[1 - E^(-c - d*x)] + (1 + I*E^(2*c))*f*Log[1 + I*E^(-c - d*x)])) + (1 + I*E^(2*c))*f^2*PolyLog[2, (-I)*E^(-c - d*x)] + (1 + I*E^(2*c))*f^2*PolyLog[2, E^(-c - d*x)]))/((a^2 + b^2)*d^3*(-I + E^(2*c))) - (b*(4*a*b*d^2*e*E^(2*c)*f*x + 2*a*b*d^2*E^(2*c)*f^2*x^2 + 2*a^2*d^2*e^2*ArcTanh[E^(c + d*x)] + 2*b^2*d^2*e^2*ArcTanh[E^(c + d*x)] - 2*a^2*d^2*e^2*E^(2*c)*ArcTanh[E^(c + d*x)] - 2*b^2*d^2*e^2*E^(2*c)*ArcTanh[E^(c + d*x)] - 2*a^2*d^2*e*f*x*Log[1 - E^(c + d*x)] - 2*b^2*d^2*e*f*x*Log[1 - E^(c + d*x)] + 2*a^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(c + d*x)] + 2*b^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(c + d*x)] - a^2*d^2*f^2*x^2*Log[1 - E^(c + d*x)] - b^2*d^2*f^2*x^2*Log[1 - E^(c + d*x)] + a^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] + b^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] + 2*a^2*d^2*e*f*x*Log[1 + E^(c + d*x)] + 2*b^2*d^2*e*f*x*Log[1 + E^(c + d*x)] - 2*a^2*d^2*e*E^(2*c)*f*x*Log[1 + E^(c + d*x)] - 2*b^2*d^2*e*E^(2*c)*f*x*Log[1 + E^(c + d*x)] + a^2*d^2*f^2*x^2*Log[1 + E^(c + d*x)] + b^2*d^2*f^2*x^2*Log[1 + E^(c + d*x)] - a^2*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(c + d*x)] - b^2*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(c + d*x)] + 2*a*b*d*e*f*Log[1 - E^(2*(c + d*x))] - 2*a*b*d*e*E^(2*c)*f*Log[1 - E^(2*(c + d*x))] + 2*a*b*d*f^2*x*Log[1 - E^(2*(c + d*x))] - 2*a*b*d*E^(2*c)*f^2*x*Log[1 - E^(2*(c + d*x))] - 2*(a^2 + b^2)*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -E^(c + d*x)] + 2*(a^2 + b^2)*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, E^(c + d*x)] + a*b*f^2*PolyLog[2, E^(2*(c + d*x))] - a*b*E^(2*c)*f^2*PolyLog[2, E^(2*(c + d*x))] - 2*a^2*f^2*PolyLog[3, -E^(c + d*x)] - 2*b^2*f^2*PolyLog[3, -E^(c + d*x)] + 2*a^2*E^(2*c)*f^2*PolyLog[3, -E^(c + d*x)] + 2*b^2*E^(2*c)*f^2*PolyLog[3, -E^(c + d*x)] + 2*a^2*f^2*PolyLog[3, E^(c + d*x)] + 2*b^2*f^2*PolyLog[3, E^(c + d*x)] - 2*a^2*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)] - 2*b^2*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)]))/(4*a^2*(a^2 + b^2)*d^3*(-1 + E^(2*c))) + (b^4*(-2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(4*a^2*(a^2 + b^2)^(3/2)*d^3) + (a*e*f*Sech[c/2]*(Cosh[c/2]*Log[Cosh[c/2]*Cosh[(d*x)/2] + Sinh[c/2]*Sinh[(d*x)/2]] - (d*x*Sinh[c/2])/2))/(2*(a^2 + b^2)*d^2*(Cosh[c/2]^2 - Sinh[c/2]^2)) + (a*f^2*Csch[c/2]*((d^2*x^2)/(4*E^ArcTanh[Coth[c/2]]) - (I*Coth[c/2]*(-1/2*(d*x*(-Pi + (2*I)*ArcTanh[Coth[c/2]])) - Pi*Log[1 + E^(d*x)] - 2*((I/2)*d*x + I*ArcTanh[Coth[c/2]])*Log[1 - E^((2*I)*((I/2)*d*x + I*ArcTanh[Coth[c/2]]))] + Pi*Log[Cosh[(d*x)/2]] + (2*I)*ArcTanh[Coth[c/2]]*Log[I*Sinh[(d*x)/2 + ArcTanh[Coth[c/2]]]] + I*PolyLog[2, E^((2*I)*((I/2)*d*x + I*ArcTanh[Coth[c/2]]))]))/Sqrt[1 - Coth[c/2]^2])*Sech[c/2])/(2*(a^2 + b^2)*d^3*Sqrt[Csch[c/2]^2*(-Cosh[c/2]^2 + Sinh[c/2]^2)]) - (e*f*x*Csch[c/2]*Sech[c/2]*(a^2*Cosh[c] - b^2*Cosh[c] + a^2*Cosh[2*c] - I*a^2*Sinh[c] - I*b^2*Sinh[c]))/(8*a*(a^2 + b^2)*d*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c] + I*Sinh[c])) - (f^2*x^2*Csch[c/2]*Sech[c/2]*(a^2*Cosh[c] - b^2*Cosh[c] + a^2*Cosh[2*c] - I*a^2*Sinh[c] - I*b^2*Sinh[c]))/(16*a*(a^2 + b^2)*d*(Cosh[c/2] - I*Sinh[c/2])*(Cosh[c/2] + I*Sinh[c/2])*(Cosh[c] + I*Sinh[c])) + (b*e*f*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]])/((a^2 + b^2)*d^2*Sqrt[Cosh[c]^2 - Sinh[c]^2]) - ((I/2)*a*f*(Cosh[c] + Sinh[c])*(((e + f*x)^2*(Cosh[c] - Sinh[c]))/(2*f) + ((e + f*x)*Log[1 - I*Cosh[c + d*x] + I*Sinh[c + d*x]]*(I + Cosh[c] - Sinh[c]))/d - (I*f*PolyLog[2, I*(Cosh[c + d*x] - Sinh[c + d*x])]*(Cosh[c] - Sinh[c])*(-I + Cosh[c] + Sinh[c]))/d^2))/((a^2 + b^2)*d*(-I + Cosh[c] + Sinh[c])) + (b*f^2*(((-I)*Csch[c]*(I*(d*x + ArcTanh[Coth[c]])*(Log[1 - E^(-(d*x) - ArcTanh[Coth[c]])] - Log[1 + E^(-(d*x) - ArcTanh[Coth[c]])]) + I*(PolyLog[2, -E^(-(d*x) - ArcTanh[Coth[c]])] - PolyLog[2, E^(-(d*x) - ArcTanh[Coth[c]])])))/Sqrt[1 - Coth[c]^2] - (2*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]]*ArcTanh[Coth[c]])/Sqrt[Cosh[c]^2 - Sinh[c]^2]))/(2*(a^2 + b^2)*d^3) + (Csch[2*c]*Csch[2*c + 2*d*x]*(a*b*e^2*Cosh[c - d*x] + 2*a*b*e*f*x*Cosh[c - d*x] + a*b*f^2*x^2*Cosh[c - d*x] - a*b*e^2*Cosh[3*c + d*x] - 2*a*b*e*f*x*Cosh[3*c + d*x] - a*b*f^2*x^2*Cosh[3*c + d*x] - b^2*e^2*Sinh[2*c] - 2*b^2*e*f*x*Sinh[2*c] - b^2*f^2*x^2*Sinh[2*c] + 2*a^2*e^2*Sinh[2*d*x] + b^2*e^2*Sinh[2*d*x] + 4*a^2*e*f*x*Sinh[2*d*x] + 2*b^2*e*f*x*Sinh[2*d*x] + 2*a^2*f^2*x^2*Sinh[2*d*x] + b^2*f^2*x^2*Sinh[2*d*x]))/(4*a*(a^2 + b^2)*d))","B",0
470,1,1862,499,8.9923644,"\int \frac{(e+f x) \text{csch}^2(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]^2*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","4 \left(\frac{\left(-2 d e \tanh ^{-1}\left(\frac{a+b \cosh (c+d x)+b \sinh (c+d x)}{\sqrt{a^2+b^2}}\right)+2 c f \tanh ^{-1}\left(\frac{a+b \cosh (c+d x)+b \sinh (c+d x)}{\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a-\sqrt{a^2+b^2}}+1\right)-f (c+d x) \log \left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}+1\right)+f \text{Li}_2\left(\frac{b (\cosh (c+d x)+\sinh (c+d x))}{\sqrt{a^2+b^2}-a}\right)-f \text{Li}_2\left(-\frac{b (\cosh (c+d x)+\sinh (c+d x))}{a+\sqrt{a^2+b^2}}\right)\right) b^4}{4 a^2 \left(a^2+b^2\right)^{3/2} d^2}-\frac{e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) b^3}{4 a^2 \left(a^2+b^2\right) d}+\frac{c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) b^3}{4 a^2 \left(a^2+b^2\right) d^2}+\frac{i f \left(i (c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(1+e^{-c-d x}\right)\right)+i \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)\right)\right) b^3}{4 a^2 \left(a^2+b^2\right) d^2}-\frac{f \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right) b^2}{2 a \left(a^2+b^2\right) d^2}+\frac{f \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right) b^2}{4 a \left(a^2+b^2\right) d^2}+\frac{f \left(-i (c+d x)+2 \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right)+\log (\cosh (c+d x)+i \sinh (c+d x)-1)\right) b^2}{8 a \left(a^2+b^2\right) d^2}-\frac{i f (c+d x)^2 b}{16 \left(a^2+b^2\right) d^2}-\frac{c f \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right) b}{2 \left(a^2+b^2\right) d^2}-\frac{c f \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right) b}{4 \left(a^2+b^2\right) d^2}+\frac{c f \left(-i (c+d x)+2 \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right)+\log (\cosh (c+d x)+i \sinh (c+d x)-1)\right) b}{8 \left(a^2+b^2\right) d^2}+\frac{i f \left(-i (c+d x)+2 \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right)+\log (\cosh (c+d x)+i \sinh (c+d x)-1)\right) b}{8 \left(a^2+b^2\right) d^2}-\frac{e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) b}{4 \left(a^2+b^2\right) d}+\frac{i f \left(-\frac{1}{8} i (c+d x)^2-\frac{1}{2} i \log \left(1+e^{-c-d x}\right) (c+d x)+\frac{1}{2} i \text{Li}_2\left(-e^{-c-d x}\right)\right) b}{2 \left(a^2+b^2\right) d^2}-\frac{f \left(\frac{1}{4} i \left((1-i) (c+d x)^2+3 \pi  (c+d x)+2 (\pi -2 i (c+d x)) \log \left(1+i e^{-c-d x}\right)-4 \pi  \log \left(1+e^{c+d x}\right)-2 \pi  \log \left(-\cos \left(\frac{1}{4} (2 i (c+d x)+\pi )\right)\right)+4 \pi  \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)+4 i \text{Li}_2\left(-i e^{-c-d x}\right)\right)-\frac{1}{2} i (c+d x)^2\right) b}{4 \left(a^2+b^2\right) d^2}-\frac{i f \left(\frac{1}{4} (c+d x)^2+\frac{1}{4} \left((-1+i) (c+d x)^2-3 \pi  (c+d x)-2 (\pi -2 i (c+d x)) \log \left(1+i e^{-c-d x}\right)+4 \pi  \log \left(1+e^{c+d x}\right)+2 \pi  \log \left(-\cos \left(\frac{1}{4} (2 i (c+d x)+\pi )\right)\right)-4 \pi  \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)-4 i \text{Li}_2\left(-i e^{-c-d x}\right)\right)-\frac{1}{2} i \left(-\frac{1}{2} (c+d x)^2+2 \log \left(1-e^{c+d x}\right) (c+d x)+2 \text{Li}_2\left(e^{c+d x}\right)\right)\right) b}{4 \left(a^2+b^2\right) d^2}-\frac{f (c+d x)}{8 (a+i b) d^2}+\frac{i \left((2-i) d f a^3+3 i b d f a^2+b c d f a^2-i b^2 d f a+i b^2 c d f a+i b^3 d f\right) (c+d x)}{8 a (a+i b) \left(a^2+b^2\right) d^3}+\frac{i f \tan ^{-1}\left(\frac{a \cosh \left(\frac{1}{2} (c+d x)\right)-b \cosh \left(\frac{1}{2} (c+d x)\right)+a \sinh \left(\frac{1}{2} (c+d x)\right)+b \sinh \left(\frac{1}{2} (c+d x)\right)}{a \cosh \left(\frac{1}{2} (c+d x)\right)+b \cosh \left(\frac{1}{2} (c+d x)\right)-a \sinh \left(\frac{1}{2} (c+d x)\right)+b \sinh \left(\frac{1}{2} (c+d x)\right)}\right)}{4 (a+i b) d^2}-\frac{a f \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 \left(a^2+b^2\right) d^2}+\frac{\left(-d e \cosh \left(\frac{1}{2} (c+d x)\right)+c f \cosh \left(\frac{1}{2} (c+d x)\right)-f (c+d x) \cosh \left(\frac{1}{2} (c+d x)\right)\right) \text{csch}\left(\frac{1}{2} (c+d x)\right)}{8 a d^2}+\frac{a f \log \left(\cosh \left(\frac{1}{2} (c+d x)\right)\right)}{4 \left(a^2+b^2\right) d^2}+\frac{f \log (\cosh (c+d x))}{8 (a+i b) d^2}+\frac{a f \left(-i (c+d x)+2 \tanh ^{-1}\left(1-2 i \tanh \left(\frac{1}{2} (c+d x)\right)\right)+\log (\cosh (c+d x)+i \sinh (c+d x)-1)\right)}{4 \left(a^2+b^2\right) d^2}+\frac{\text{sech}\left(\frac{1}{2} (c+d x)\right) \left(-d e \sinh \left(\frac{1}{2} (c+d x)\right)+c f \sinh \left(\frac{1}{2} (c+d x)\right)-f (c+d x) \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{8 a d^2}+\frac{\text{sech}(c+d x) (-b d e-a d \sinh (c+d x) e+b c f-b f (c+d x)+a c f \sinh (c+d x)-a f (c+d x) \sinh (c+d x))}{4 \left(a^2+b^2\right) d^2}\right)","-\frac{b^2 f \log (\cosh (c+d x))}{a d^2 \left(a^2+b^2\right)}+\frac{b^2 (e+f x) \tanh (c+d x)}{a d \left(a^2+b^2\right)}+\frac{b^4 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2 \left(a^2+b^2\right)^{3/2}}-\frac{b^4 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^2 d^2 \left(a^2+b^2\right)^{3/2}}+\frac{b^4 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^2 d \left(a^2+b^2\right)^{3/2}}-\frac{b^4 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^2 d \left(a^2+b^2\right)^{3/2}}-\frac{b^3 f \tan ^{-1}(\sinh (c+d x))}{a^2 d^2 \left(a^2+b^2\right)}+\frac{b^3 (e+f x) \text{sech}(c+d x)}{a^2 d \left(a^2+b^2\right)}+\frac{b f \text{Li}_2\left(-e^{c+d x}\right)}{a^2 d^2}-\frac{b f \text{Li}_2\left(e^{c+d x}\right)}{a^2 d^2}+\frac{b f \tan ^{-1}(\sinh (c+d x))}{a^2 d^2}-\frac{b (e+f x) \text{sech}(c+d x)}{a^2 d}+\frac{b (e+f x) \tanh ^{-1}(\cosh (c+d x))}{a^2 d}+\frac{2 b f x \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}-\frac{b f x \tanh ^{-1}(\cosh (c+d x))}{a^2 d}+\frac{f \log (\sinh (2 c+2 d x))}{a d^2}-\frac{2 (e+f x) \coth (2 c+2 d x)}{a d}",1,"4*(-1/8*(f*(c + d*x))/((a + I*b)*d^2) + ((I/8)*((2 - I)*a^3*d*f + (3*I)*a^2*b*d*f - I*a*b^2*d*f + I*b^3*d*f + a^2*b*c*d*f + I*a*b^2*c*d*f)*(c + d*x))/(a*(a + I*b)*(a^2 + b^2)*d^3) - ((I/16)*b*f*(c + d*x)^2)/((a^2 + b^2)*d^2) + ((I/4)*f*ArcTan[(a*Cosh[(c + d*x)/2] - b*Cosh[(c + d*x)/2] + a*Sinh[(c + d*x)/2] + b*Sinh[(c + d*x)/2])/(a*Cosh[(c + d*x)/2] + b*Cosh[(c + d*x)/2] - a*Sinh[(c + d*x)/2] + b*Sinh[(c + d*x)/2])])/((a + I*b)*d^2) - (a*f*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(2*(a^2 + b^2)*d^2) - (b^2*f*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(2*a*(a^2 + b^2)*d^2) - (b*c*f*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(2*(a^2 + b^2)*d^2) + ((-(d*e*Cosh[(c + d*x)/2]) + c*f*Cosh[(c + d*x)/2] - f*(c + d*x)*Cosh[(c + d*x)/2])*Csch[(c + d*x)/2])/(8*a*d^2) + (a*f*Log[Cosh[(c + d*x)/2]])/(4*(a^2 + b^2)*d^2) + (b^2*f*Log[Cosh[(c + d*x)/2]])/(4*a*(a^2 + b^2)*d^2) - (b*c*f*Log[Cosh[(c + d*x)/2]])/(4*(a^2 + b^2)*d^2) + (f*Log[Cosh[c + d*x]])/(8*(a + I*b)*d^2) + (a*f*((-I)*(c + d*x) + 2*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]] + Log[-1 + Cosh[c + d*x] + I*Sinh[c + d*x]]))/(4*(a^2 + b^2)*d^2) + ((I/8)*b*f*((-I)*(c + d*x) + 2*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]] + Log[-1 + Cosh[c + d*x] + I*Sinh[c + d*x]]))/((a^2 + b^2)*d^2) + (b^2*f*((-I)*(c + d*x) + 2*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]] + Log[-1 + Cosh[c + d*x] + I*Sinh[c + d*x]]))/(8*a*(a^2 + b^2)*d^2) + (b*c*f*((-I)*(c + d*x) + 2*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]] + Log[-1 + Cosh[c + d*x] + I*Sinh[c + d*x]]))/(8*(a^2 + b^2)*d^2) - (b*e*Log[Tanh[(c + d*x)/2]])/(4*(a^2 + b^2)*d) - (b^3*e*Log[Tanh[(c + d*x)/2]])/(4*a^2*(a^2 + b^2)*d) + (b^3*c*f*Log[Tanh[(c + d*x)/2]])/(4*a^2*(a^2 + b^2)*d^2) + ((I/2)*b*f*((-1/8*I)*(c + d*x)^2 - (I/2)*(c + d*x)*Log[1 + E^(-c - d*x)] + (I/2)*PolyLog[2, -E^(-c - d*x)]))/((a^2 + b^2)*d^2) - (b*f*((-1/2*I)*(c + d*x)^2 + (I/4)*(3*Pi*(c + d*x) + (1 - I)*(c + d*x)^2 + 2*(Pi - (2*I)*(c + d*x))*Log[1 + I*E^(-c - d*x)] - 4*Pi*Log[1 + E^(c + d*x)] - 2*Pi*Log[-Cos[(Pi + (2*I)*(c + d*x))/4]] + 4*Pi*Log[Cosh[(c + d*x)/2]] + (4*I)*PolyLog[2, (-I)*E^(-c - d*x)])))/(4*(a^2 + b^2)*d^2) + ((I/4)*b^3*f*(I*(c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + I*(PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)])))/(a^2*(a^2 + b^2)*d^2) - ((I/4)*b*f*((c + d*x)^2/4 + (-3*Pi*(c + d*x) - (1 - I)*(c + d*x)^2 - 2*(Pi - (2*I)*(c + d*x))*Log[1 + I*E^(-c - d*x)] + 4*Pi*Log[1 + E^(c + d*x)] + 2*Pi*Log[-Cos[(Pi + (2*I)*(c + d*x))/4]] - 4*Pi*Log[Cosh[(c + d*x)/2]] - (4*I)*PolyLog[2, (-I)*E^(-c - d*x)])/4 - (I/2)*(-1/2*(c + d*x)^2 + 2*(c + d*x)*Log[1 - E^(c + d*x)] + 2*PolyLog[2, E^(c + d*x)])))/((a^2 + b^2)*d^2) + (b^4*(-2*d*e*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + 2*c*f*ArcTanh[(a + b*Cosh[c + d*x] + b*Sinh[c + d*x])/Sqrt[a^2 + b^2]] + f*(c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a - Sqrt[a^2 + b^2])] - f*(c + d*x)*Log[1 + (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2])] + f*PolyLog[2, (b*(Cosh[c + d*x] + Sinh[c + d*x]))/(-a + Sqrt[a^2 + b^2])] - f*PolyLog[2, -((b*(Cosh[c + d*x] + Sinh[c + d*x]))/(a + Sqrt[a^2 + b^2]))]))/(4*a^2*(a^2 + b^2)^(3/2)*d^2) + (Sech[(c + d*x)/2]*(-(d*e*Sinh[(c + d*x)/2]) + c*f*Sinh[(c + d*x)/2] - f*(c + d*x)*Sinh[(c + d*x)/2]))/(8*a*d^2) + (Sech[c + d*x]*(-(b*d*e) + b*c*f - b*f*(c + d*x) - a*d*e*Sinh[c + d*x] + a*c*f*Sinh[c + d*x] - a*f*(c + d*x)*Sinh[c + d*x]))/(4*(a^2 + b^2)*d^2))","C",0
471,1,135,144,2.5690895,"\int \frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Csch[c + d*x]^2*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{\frac{2 \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a^2+b^2}+\frac{4 b^4 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{a^2 \left(-a^2-b^2\right)^{3/2}}+\frac{2 b \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^2}+\frac{\tanh \left(\frac{1}{2} (c+d x)\right)}{a}+\frac{\coth \left(\frac{1}{2} (c+d x)\right)}{a}}{2 d}","\frac{b^2 \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a^2 d \left(a^2+b^2\right)}-\frac{2 b^4 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a^2 d \left(a^2+b^2\right)^{3/2}}-\frac{b \text{sech}(c+d x)}{a^2 d}+\frac{b \tanh ^{-1}(\cosh (c+d x))}{a^2 d}-\frac{\tanh (c+d x)}{a d}-\frac{\coth (c+d x)}{a d}",1,"-1/2*((4*b^4*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(a^2*(-a^2 - b^2)^(3/2)) + Coth[(c + d*x)/2]/a + (2*b*Log[Tanh[(c + d*x)/2]])/a^2 + (2*Sech[c + d*x]*(b + a*Sinh[c + d*x]))/(a^2 + b^2) + Tanh[(c + d*x)/2]/a)/d","A",1
472,0,0,39,153.9665282,"\int \frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Csch[c + d*x]^2*Sech[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[(Csch[c + d*x]^2*Sech[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
473,1,1337,978,10.924012,"\int \frac{(e+f x) \text{csch}^2(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]^2*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","8 \left(\frac{\text{csch}(c+d x) \left(-\frac{1}{2} f (c+d x)^2+f \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (c+d x)+f \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (c+d x)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) (a+b \sinh (c+d x)) b^5}{8 a^2 \left(a^2+b^2\right)^2 d^2 (b+a \text{csch}(c+d x))}-\frac{e \text{csch}(c+d x) \log (\sinh (c+d x)) (a+b \sinh (c+d x)) b}{8 a^2 d (b+a \text{csch}(c+d x))}+\frac{c f \text{csch}(c+d x) \log (\sinh (c+d x)) (a+b \sinh (c+d x)) b}{8 a^2 d^2 (b+a \text{csch}(c+d x))}+\frac{i f \text{csch}(c+d x) \left(i (c+d x) \log \left(1-e^{-2 (c+d x)}\right)-\frac{1}{2} i \left(\text{Li}_2\left(e^{-2 (c+d x)}\right)-(c+d x)^2\right)\right) (a+b \sinh (c+d x)) b}{8 a^2 d^2 (b+a \text{csch}(c+d x))}+\frac{f \text{csch}(c+d x) \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) (a+b \sinh (c+d x))}{8 a d^2 (b+a \text{csch}(c+d x))}+\frac{\text{csch}(c+d x) \left(-6 d e \tan ^{-1}\left(e^{c+d x}\right) a^3+6 c f \tan ^{-1}\left(e^{c+d x}\right) a^3-3 i f (c+d x) \log \left(1-i e^{c+d x}\right) a^3+3 i f (c+d x) \log \left(1+i e^{c+d x}\right) a^3-b f (c+d x)^2 a^2-2 b d e (c+d x) a^2+2 b c f (c+d x) a^2+2 b d e \log \left(1+e^{2 (c+d x)}\right) a^2-2 b c f \log \left(1+e^{2 (c+d x)}\right) a^2+2 b f (c+d x) \log \left(1+e^{2 (c+d x)}\right) a^2+b f \text{Li}_2\left(-e^{2 (c+d x)}\right) a^2-10 b^2 d e \tan ^{-1}\left(e^{c+d x}\right) a+10 b^2 c f \tan ^{-1}\left(e^{c+d x}\right) a-5 i b^2 f (c+d x) \log \left(1-i e^{c+d x}\right) a+5 i b^2 f (c+d x) \log \left(1+i e^{c+d x}\right) a+i \left(3 a^2+5 b^2\right) f \text{Li}_2\left(-i e^{c+d x}\right) a-i \left(3 a^2+5 b^2\right) f \text{Li}_2\left(i e^{c+d x}\right) a-2 b^3 f (c+d x)^2-4 b^3 d e (c+d x)+4 b^3 c f (c+d x)+4 b^3 d e \log \left(1+e^{2 (c+d x)}\right)-4 b^3 c f \log \left(1+e^{2 (c+d x)}\right)+4 b^3 f (c+d x) \log \left(1+e^{2 (c+d x)}\right)+2 b^3 f \text{Li}_2\left(-e^{2 (c+d x)}\right)\right) (a+b \sinh (c+d x))}{16 \left(a^2+b^2\right)^2 d^2 (b+a \text{csch}(c+d x))}+\frac{\text{csch}(c+d x) \text{sech}\left(\frac{1}{2} (c+d x)\right) \left(d e \sinh \left(\frac{1}{2} (c+d x)\right)-c f \sinh \left(\frac{1}{2} (c+d x)\right)+f (c+d x) \sinh \left(\frac{1}{2} (c+d x)\right)\right) (a+b \sinh (c+d x))}{16 a d^2 (b+a \text{csch}(c+d x))}+\frac{\left(-d e \cosh \left(\frac{1}{2} (c+d x)\right)+c f \cosh \left(\frac{1}{2} (c+d x)\right)-f (c+d x) \cosh \left(\frac{1}{2} (c+d x)\right)\right) \text{csch}\left(\frac{1}{2} (c+d x)\right) \text{csch}(c+d x) (a+b \sinh (c+d x))}{16 a d^2 (b+a \text{csch}(c+d x))}+\frac{\text{csch}(c+d x) \text{sech}(c+d x) (a+b \sinh (c+d x)) (b f \sinh (c+d x)-a f)}{16 \left(a^2+b^2\right) d^2 (b+a \text{csch}(c+d x))}+\frac{\text{csch}(c+d x) \text{sech}^2(c+d x) (a+b \sinh (c+d x)) (-b d e-a d \sinh (c+d x) e+b c f-b f (c+d x)+a c f \sinh (c+d x)-a f (c+d x) \sinh (c+d x))}{16 \left(a^2+b^2\right) d^2 (b+a \text{csch}(c+d x))}\right)","\frac{(e+f x) \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^5}{a^2 \left(a^2+b^2\right)^2 d}+\frac{(e+f x) \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^5}{a^2 \left(a^2+b^2\right)^2 d}-\frac{(e+f x) \log \left(1+e^{2 (c+d x)}\right) b^5}{a^2 \left(a^2+b^2\right)^2 d}+\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^5}{a^2 \left(a^2+b^2\right)^2 d^2}+\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^5}{a^2 \left(a^2+b^2\right)^2 d^2}-\frac{f \text{Li}_2\left(-e^{2 (c+d x)}\right) b^5}{2 a^2 \left(a^2+b^2\right)^2 d^2}+\frac{2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right) b^4}{a \left(a^2+b^2\right)^2 d}-\frac{i f \text{Li}_2\left(-i e^{c+d x}\right) b^4}{a \left(a^2+b^2\right)^2 d^2}+\frac{i f \text{Li}_2\left(i e^{c+d x}\right) b^4}{a \left(a^2+b^2\right)^2 d^2}+\frac{(e+f x) \text{sech}^2(c+d x) b^3}{2 a^2 \left(a^2+b^2\right) d}-\frac{f \tanh (c+d x) b^3}{2 a^2 \left(a^2+b^2\right) d^2}+\frac{(e+f x) \tan ^{-1}\left(e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d}-\frac{i f \text{Li}_2\left(-i e^{c+d x}\right) b^2}{2 a \left(a^2+b^2\right) d^2}+\frac{i f \text{Li}_2\left(i e^{c+d x}\right) b^2}{2 a \left(a^2+b^2\right) d^2}+\frac{f \text{sech}(c+d x) b^2}{2 a \left(a^2+b^2\right) d^2}+\frac{(e+f x) \text{sech}(c+d x) \tanh (c+d x) b^2}{2 a \left(a^2+b^2\right) d}+\frac{(e+f x) \tanh ^2(c+d x) b}{2 a^2 d}-\frac{f x b}{2 a^2 d}+\frac{2 f x \tanh ^{-1}\left(e^{2 c+2 d x}\right) b}{a^2 d}+\frac{f x \log (\tanh (c+d x)) b}{a^2 d}-\frac{(e+f x) \log (\tanh (c+d x)) b}{a^2 d}+\frac{f \text{Li}_2\left(-e^{2 c+2 d x}\right) b}{2 a^2 d^2}-\frac{f \text{Li}_2\left(e^{2 c+2 d x}\right) b}{2 a^2 d^2}+\frac{f \tanh (c+d x) b}{2 a^2 d^2}+\frac{(e+f x) \text{csch}(c+d x) \text{sech}^2(c+d x)}{2 a d}-\frac{3 f x \tan ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{3 f x \tan ^{-1}(\sinh (c+d x))}{2 a d}-\frac{3 (e+f x) \tan ^{-1}(\sinh (c+d x))}{2 a d}-\frac{f \tanh ^{-1}(\cosh (c+d x))}{a d^2}-\frac{3 (e+f x) \text{csch}(c+d x)}{2 a d}+\frac{3 i f \text{Li}_2\left(-i e^{c+d x}\right)}{2 a d^2}-\frac{3 i f \text{Li}_2\left(i e^{c+d x}\right)}{2 a d^2}-\frac{f \text{sech}(c+d x)}{2 a d^2}",1,"8*(((-(d*e*Cosh[(c + d*x)/2]) + c*f*Cosh[(c + d*x)/2] - f*(c + d*x)*Cosh[(c + d*x)/2])*Csch[(c + d*x)/2]*Csch[c + d*x]*(a + b*Sinh[c + d*x]))/(16*a*d^2*(b + a*Csch[c + d*x])) - (b*e*Csch[c + d*x]*Log[Sinh[c + d*x]]*(a + b*Sinh[c + d*x]))/(8*a^2*d*(b + a*Csch[c + d*x])) + (b*c*f*Csch[c + d*x]*Log[Sinh[c + d*x]]*(a + b*Sinh[c + d*x]))/(8*a^2*d^2*(b + a*Csch[c + d*x])) + (f*Csch[c + d*x]*Log[Tanh[(c + d*x)/2]]*(a + b*Sinh[c + d*x]))/(8*a*d^2*(b + a*Csch[c + d*x])) + ((I/8)*b*f*Csch[c + d*x]*(I*(c + d*x)*Log[1 - E^(-2*(c + d*x))] - (I/2)*(-(c + d*x)^2 + PolyLog[2, E^(-2*(c + d*x))]))*(a + b*Sinh[c + d*x]))/(a^2*d^2*(b + a*Csch[c + d*x])) + (b^5*Csch[c + d*x]*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])*(a + b*Sinh[c + d*x]))/(8*a^2*(a^2 + b^2)^2*d^2*(b + a*Csch[c + d*x])) + (Csch[c + d*x]*(-2*a^2*b*d*e*(c + d*x) - 4*b^3*d*e*(c + d*x) + 2*a^2*b*c*f*(c + d*x) + 4*b^3*c*f*(c + d*x) - a^2*b*f*(c + d*x)^2 - 2*b^3*f*(c + d*x)^2 - 6*a^3*d*e*ArcTan[E^(c + d*x)] - 10*a*b^2*d*e*ArcTan[E^(c + d*x)] + 6*a^3*c*f*ArcTan[E^(c + d*x)] + 10*a*b^2*c*f*ArcTan[E^(c + d*x)] - (3*I)*a^3*f*(c + d*x)*Log[1 - I*E^(c + d*x)] - (5*I)*a*b^2*f*(c + d*x)*Log[1 - I*E^(c + d*x)] + (3*I)*a^3*f*(c + d*x)*Log[1 + I*E^(c + d*x)] + (5*I)*a*b^2*f*(c + d*x)*Log[1 + I*E^(c + d*x)] + 2*a^2*b*d*e*Log[1 + E^(2*(c + d*x))] + 4*b^3*d*e*Log[1 + E^(2*(c + d*x))] - 2*a^2*b*c*f*Log[1 + E^(2*(c + d*x))] - 4*b^3*c*f*Log[1 + E^(2*(c + d*x))] + 2*a^2*b*f*(c + d*x)*Log[1 + E^(2*(c + d*x))] + 4*b^3*f*(c + d*x)*Log[1 + E^(2*(c + d*x))] + I*a*(3*a^2 + 5*b^2)*f*PolyLog[2, (-I)*E^(c + d*x)] - I*a*(3*a^2 + 5*b^2)*f*PolyLog[2, I*E^(c + d*x)] + a^2*b*f*PolyLog[2, -E^(2*(c + d*x))] + 2*b^3*f*PolyLog[2, -E^(2*(c + d*x))])*(a + b*Sinh[c + d*x]))/(16*(a^2 + b^2)^2*d^2*(b + a*Csch[c + d*x])) + (Csch[c + d*x]*Sech[(c + d*x)/2]*(d*e*Sinh[(c + d*x)/2] - c*f*Sinh[(c + d*x)/2] + f*(c + d*x)*Sinh[(c + d*x)/2])*(a + b*Sinh[c + d*x]))/(16*a*d^2*(b + a*Csch[c + d*x])) + (Csch[c + d*x]*Sech[c + d*x]*(a + b*Sinh[c + d*x])*(-(a*f) + b*f*Sinh[c + d*x]))/(16*(a^2 + b^2)*d^2*(b + a*Csch[c + d*x])) + (Csch[c + d*x]*Sech[c + d*x]^2*(a + b*Sinh[c + d*x])*(-(b*d*e) + b*c*f - b*f*(c + d*x) - a*d*e*Sinh[c + d*x] + a*c*f*Sinh[c + d*x] - a*f*(c + d*x)*Sinh[c + d*x]))/(16*(a^2 + b^2)*d^2*(b + a*Csch[c + d*x])))","A",1
474,1,227,180,0.9436953,"\int \frac{\text{csch}^2(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Csch[c + d*x]^2*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{\text{csch}(c+d x) (a+b \sinh (c+d x)) \left(\frac{b \text{sech}^2(c+d x)}{a^2+b^2}-\frac{(b+i a) \left(a^2+2 b^2\right) \log (-\sinh (c+d x)+i)}{\left(a^2+b^2\right)^2}+\frac{(-b+i a) \left(a^2+2 b^2\right) \log (\sinh (c+d x)+i)}{\left(a^2+b^2\right)^2}+\frac{a \tan ^{-1}(\sinh (c+d x))}{a^2+b^2}+\frac{a \tanh (c+d x) \text{sech}(c+d x)}{a^2+b^2}-\frac{2 b^5 \log (a+b \sinh (c+d x))}{a^2 \left(a^2+b^2\right)^2}+\frac{2 b \log (\sinh (c+d x))}{a^2}+\frac{2 \text{csch}(c+d x)}{a}\right)}{2 d (a \text{csch}(c+d x)+b)}","-\frac{a \left(a^2+2 b^2\right) \tan ^{-1}(\sinh (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{a \tan ^{-1}(\sinh (c+d x))}{2 d \left(a^2+b^2\right)}+\frac{b \left(a^2+2 b^2\right) \log (\cosh (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{\text{sech}^2(c+d x) (a \sinh (c+d x)+b)}{2 d \left(a^2+b^2\right)}+\frac{b^5 \log (a+b \sinh (c+d x))}{a^2 d \left(a^2+b^2\right)^2}-\frac{b \log (\sinh (c+d x))}{a^2 d}-\frac{\text{csch}(c+d x)}{a d}",1,"-1/2*(Csch[c + d*x]*(a + b*Sinh[c + d*x])*((a*ArcTan[Sinh[c + d*x]])/(a^2 + b^2) + (2*Csch[c + d*x])/a - ((I*a + b)*(a^2 + 2*b^2)*Log[I - Sinh[c + d*x]])/(a^2 + b^2)^2 + (2*b*Log[Sinh[c + d*x]])/a^2 + ((I*a - b)*(a^2 + 2*b^2)*Log[I + Sinh[c + d*x]])/(a^2 + b^2)^2 - (2*b^5*Log[a + b*Sinh[c + d*x]])/(a^2*(a^2 + b^2)^2) + (b*Sech[c + d*x]^2)/(a^2 + b^2) + (a*Sech[c + d*x]*Tanh[c + d*x])/(a^2 + b^2)))/(d*(b + a*Csch[c + d*x]))","C",1
475,-1,0,39,180.0016945,"\int \frac{\text{csch}^2(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Csch[c + d*x]^2*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{csch}^2(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
476,1,3043,752,69.3198271,"\int \frac{(e+f x)^3 \coth (c+d x) \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Coth[c + d*x]*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","\frac{3 b^2 f^3 \text{Li}_4\left(e^{2 (c+d x)}\right)}{4 a^3 d^4}-\frac{3 b^2 f^2 (e+f x) \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a^3 d^3}+\frac{3 b^2 f (e+f x)^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a^3 d^2}+\frac{b^2 (e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}-\frac{6 b f^3 \text{Li}_3\left(-e^{c+d x}\right)}{a^2 d^4}+\frac{6 b f^3 \text{Li}_3\left(e^{c+d x}\right)}{a^2 d^4}+\frac{6 b f^2 (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a^2 d^3}-\frac{6 b f^2 (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a^2 d^3}+\frac{6 b f (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d^2}+\frac{b (e+f x)^3 \text{csch}(c+d x)}{a^2 d}-\frac{6 b^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^4}-\frac{6 b^2 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^4}+\frac{6 b^2 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^3}+\frac{6 b^2 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^3}-\frac{3 b^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{3 b^2 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b^2 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d}-\frac{b^2 (e+f x)^3 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d}+\frac{3 f^3 \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a d^4}+\frac{3 f^2 (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d^3}-\frac{3 f (e+f x)^2 \coth (c+d x)}{2 a d^2}-\frac{(e+f x)^3 \text{csch}^2(c+d x)}{2 a d}-\frac{3 f (e+f x)^2}{2 a d^2}",1,"(b*(e + f*x)^3*Csch[c])/(a^2*d) - ((e + f*x)^3*Csch[(c + d*x)/2]^2)/(8*a*d) - (8*b^2*d^4*e^3*E^(2*c)*x + 24*a^2*d^2*e*E^(2*c)*f^2*x + 12*b^2*d^4*e^2*E^(2*c)*f*x^2 + 12*a^2*d^2*E^(2*c)*f^3*x^2 + 8*b^2*d^4*e*E^(2*c)*f^2*x^3 + 2*b^2*d^4*E^(2*c)*f^3*x^4 + 24*a*b*d^2*e^2*f*ArcTanh[E^(c + d*x)] - 24*a*b*d^2*e^2*E^(2*c)*f*ArcTanh[E^(c + d*x)] - 24*a*b*d^2*e*f^2*x*Log[1 - E^(c + d*x)] + 24*a*b*d^2*e*E^(2*c)*f^2*x*Log[1 - E^(c + d*x)] - 12*a*b*d^2*f^3*x^2*Log[1 - E^(c + d*x)] + 12*a*b*d^2*E^(2*c)*f^3*x^2*Log[1 - E^(c + d*x)] + 24*a*b*d^2*e*f^2*x*Log[1 + E^(c + d*x)] - 24*a*b*d^2*e*E^(2*c)*f^2*x*Log[1 + E^(c + d*x)] + 12*a*b*d^2*f^3*x^2*Log[1 + E^(c + d*x)] - 12*a*b*d^2*E^(2*c)*f^3*x^2*Log[1 + E^(c + d*x)] + 4*b^2*d^3*e^3*Log[1 - E^(2*(c + d*x))] - 4*b^2*d^3*e^3*E^(2*c)*Log[1 - E^(2*(c + d*x))] + 12*a^2*d*e*f^2*Log[1 - E^(2*(c + d*x))] - 12*a^2*d*e*E^(2*c)*f^2*Log[1 - E^(2*(c + d*x))] + 12*b^2*d^3*e^2*f*x*Log[1 - E^(2*(c + d*x))] - 12*b^2*d^3*e^2*E^(2*c)*f*x*Log[1 - E^(2*(c + d*x))] + 12*a^2*d*f^3*x*Log[1 - E^(2*(c + d*x))] - 12*a^2*d*E^(2*c)*f^3*x*Log[1 - E^(2*(c + d*x))] + 12*b^2*d^3*e*f^2*x^2*Log[1 - E^(2*(c + d*x))] - 12*b^2*d^3*e*E^(2*c)*f^2*x^2*Log[1 - E^(2*(c + d*x))] + 4*b^2*d^3*f^3*x^3*Log[1 - E^(2*(c + d*x))] - 4*b^2*d^3*E^(2*c)*f^3*x^3*Log[1 - E^(2*(c + d*x))] - 24*a*b*d*(-1 + E^(2*c))*f^2*(e + f*x)*PolyLog[2, -E^(c + d*x)] + 24*a*b*d*(-1 + E^(2*c))*f^2*(e + f*x)*PolyLog[2, E^(c + d*x)] + 6*b^2*d^2*e^2*f*PolyLog[2, E^(2*(c + d*x))] - 6*b^2*d^2*e^2*E^(2*c)*f*PolyLog[2, E^(2*(c + d*x))] + 6*a^2*f^3*PolyLog[2, E^(2*(c + d*x))] - 6*a^2*E^(2*c)*f^3*PolyLog[2, E^(2*(c + d*x))] + 12*b^2*d^2*e*f^2*x*PolyLog[2, E^(2*(c + d*x))] - 12*b^2*d^2*e*E^(2*c)*f^2*x*PolyLog[2, E^(2*(c + d*x))] + 6*b^2*d^2*f^3*x^2*PolyLog[2, E^(2*(c + d*x))] - 6*b^2*d^2*E^(2*c)*f^3*x^2*PolyLog[2, E^(2*(c + d*x))] - 24*a*b*f^3*PolyLog[3, -E^(c + d*x)] + 24*a*b*E^(2*c)*f^3*PolyLog[3, -E^(c + d*x)] + 24*a*b*f^3*PolyLog[3, E^(c + d*x)] - 24*a*b*E^(2*c)*f^3*PolyLog[3, E^(c + d*x)] - 6*b^2*d*e*f^2*PolyLog[3, E^(2*(c + d*x))] + 6*b^2*d*e*E^(2*c)*f^2*PolyLog[3, E^(2*(c + d*x))] - 6*b^2*d*f^3*x*PolyLog[3, E^(2*(c + d*x))] + 6*b^2*d*E^(2*c)*f^3*x*PolyLog[3, E^(2*(c + d*x))] + 3*b^2*f^3*PolyLog[4, E^(2*(c + d*x))] - 3*b^2*E^(2*c)*f^3*PolyLog[4, E^(2*(c + d*x))])/(4*a^3*d^4*(-1 + E^(2*c))) + (b^2*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(2*a^3*(-1 + E^(2*c))) + ((e + f*x)^3*Sech[(c + d*x)/2]^2)/(8*a*d) + ((e + f*x)^2*(3*a*f - 2*b*d*(e + f*x))*Csch[c/2]*Csch[(c + d*x)/2]*Sinh[(d*x)/2])/(4*a^2*d^2) - ((e + f*x)^2*(3*a*f + 2*b*d*(e + f*x))*Sech[c/2]*Sech[(c + d*x)/2]*Sinh[(d*x)/2])/(4*a^2*d^2)","B",0
477,1,1550,502,28.0876044,"\int \frac{(e+f x)^2 \coth (c+d x) \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Coth[c + d*x]*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(2 e^{2 c} f^2 x^3 d^3+6 e e^{2 c} f x^2 d^3+6 e^2 e^{2 c} x d^3-3 e^2 e^{2 c} \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2+3 e^2 \log \left(-2 e^{c+d x} a-b e^{2 (c+d x)}+b\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-3 e^{2 c} f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+3 f^2 x^2 \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 e e^{2 c} f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2+6 e f x \log \left(\frac{e^{2 c+d x} b}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}+1\right) d^2-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d-6 \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right) d+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{a e^c-\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)+6 e^{2 c} f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)-6 f^2 \text{Li}_3\left(-\frac{b e^{2 c+d x}}{e^c a+\sqrt{\left(a^2+b^2\right) e^{2 c}}}\right)\right) b^2}{3 a^3 d^3 \left(-1+e^{2 c}\right)}+\frac{(e+f x)^2 \text{csch}(c) b}{a^2 d}+\frac{\left(-e^2-2 f x e-f^2 x^2\right) \text{csch}^2\left(\frac{c}{2}+\frac{d x}{2}\right)}{8 a d}+\frac{\left(e^2+2 f x e+f^2 x^2\right) \text{sech}^2\left(\frac{c}{2}+\frac{d x}{2}\right)}{8 a d}-\frac{4 b^2 f^2 x^3 d^3+12 b^2 e f x^2 d^3+6 b^2 e^2 \left(-1+e^{2 c}\right) \left(2 d x-\log \left(1-e^{2 (c+d x)}\right)\right) d^2+12 e^{2 c} \left(b^2 d^2 e^2+a^2 f^2\right) x d-12 \left(-1+e^{2 c}\right) \left(b^2 d^2 e^2+a^2 f^2\right) x d-24 a b e \left(-1+e^{2 c}\right) f \tanh ^{-1}\left(e^{c+d x}\right) d+6 b^2 e \left(-1+e^{2 c}\right) f \left(2 d x \left(d x-\log \left(1-e^{2 (c+d x)}\right)\right)-\text{Li}_2\left(e^{2 (c+d x)}\right)\right) d+6 a^2 \left(-1+e^{2 c}\right) f^2 \left(2 d x-\log \left(1-e^{2 (c+d x)}\right)\right)+12 a b \left(-1+e^{2 c}\right) f^2 \left(d x \left(\log \left(1-e^{c+d x}\right)-\log \left(1+e^{c+d x}\right)\right)-\text{Li}_2\left(-e^{c+d x}\right)+\text{Li}_2\left(e^{c+d x}\right)\right)+b^2 \left(-1+e^{2 c}\right) f^2 \left(2 d^2 \left(2 d x-3 \log \left(1-e^{2 (c+d x)}\right)\right) x^2-6 d \text{Li}_2\left(e^{2 (c+d x)}\right) x+3 \text{Li}_3\left(e^{2 (c+d x)}\right)\right)}{6 a^3 d^3 \left(-1+e^{2 c}\right)}+\frac{\text{sech}\left(\frac{c}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(-b d \sinh \left(\frac{d x}{2}\right) e^2-a f \sinh \left(\frac{d x}{2}\right) e-2 b d f x \sinh \left(\frac{d x}{2}\right) e-b d f^2 x^2 \sinh \left(\frac{d x}{2}\right)-a f^2 x \sinh \left(\frac{d x}{2}\right)\right)}{2 a^2 d^2}+\frac{\text{csch}\left(\frac{c}{2}\right) \text{csch}\left(\frac{c}{2}+\frac{d x}{2}\right) \left(-b d \sinh \left(\frac{d x}{2}\right) e^2+a f \sinh \left(\frac{d x}{2}\right) e-2 b d f x \sinh \left(\frac{d x}{2}\right) e-b d f^2 x^2 \sinh \left(\frac{d x}{2}\right)+a f^2 x \sinh \left(\frac{d x}{2}\right)\right)}{2 a^2 d^2}","-\frac{b^2 f^2 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a^3 d^3}+\frac{b^2 f (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a^3 d^2}+\frac{b^2 (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}+\frac{2 b f^2 \text{Li}_2\left(-e^{c+d x}\right)}{a^2 d^3}-\frac{2 b f^2 \text{Li}_2\left(e^{c+d x}\right)}{a^2 d^3}+\frac{4 b f (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d^2}+\frac{b (e+f x)^2 \text{csch}(c+d x)}{a^2 d}+\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^3}+\frac{2 b^2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^3}-\frac{2 b^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{2 b^2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d}-\frac{b^2 (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d}+\frac{f^2 \log (\sinh (c+d x))}{a d^3}-\frac{f (e+f x) \coth (c+d x)}{a d^2}-\frac{(e+f x)^2 \text{csch}^2(c+d x)}{2 a d}",1,"(b*(e + f*x)^2*Csch[c])/(a^2*d) + ((-e^2 - 2*e*f*x - f^2*x^2)*Csch[c/2 + (d*x)/2]^2)/(8*a*d) - (12*d*E^(2*c)*(b^2*d^2*e^2 + a^2*f^2)*x - 12*d*(-1 + E^(2*c))*(b^2*d^2*e^2 + a^2*f^2)*x + 12*b^2*d^3*e*f*x^2 + 4*b^2*d^3*f^2*x^3 - 24*a*b*d*e*(-1 + E^(2*c))*f*ArcTanh[E^(c + d*x)] + 6*b^2*d^2*e^2*(-1 + E^(2*c))*(2*d*x - Log[1 - E^(2*(c + d*x))]) + 6*a^2*(-1 + E^(2*c))*f^2*(2*d*x - Log[1 - E^(2*(c + d*x))]) + 12*a*b*(-1 + E^(2*c))*f^2*(d*x*(Log[1 - E^(c + d*x)] - Log[1 + E^(c + d*x)]) - PolyLog[2, -E^(c + d*x)] + PolyLog[2, E^(c + d*x)]) + 6*b^2*d*e*(-1 + E^(2*c))*f*(2*d*x*(d*x - Log[1 - E^(2*(c + d*x))]) - PolyLog[2, E^(2*(c + d*x))]) + b^2*(-1 + E^(2*c))*f^2*(2*d^2*x^2*(2*d*x - 3*Log[1 - E^(2*(c + d*x))]) - 6*d*x*PolyLog[2, E^(2*(c + d*x))] + 3*PolyLog[3, E^(2*(c + d*x))]))/(6*a^3*d^3*(-1 + E^(2*c))) + (b^2*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*a^3*d^3*(-1 + E^(2*c))) + ((e^2 + 2*e*f*x + f^2*x^2)*Sech[c/2 + (d*x)/2]^2)/(8*a*d) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(-(b*d*e^2*Sinh[(d*x)/2]) - a*e*f*Sinh[(d*x)/2] - 2*b*d*e*f*x*Sinh[(d*x)/2] - a*f^2*x*Sinh[(d*x)/2] - b*d*f^2*x^2*Sinh[(d*x)/2]))/(2*a^2*d^2) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(-(b*d*e^2*Sinh[(d*x)/2]) + a*e*f*Sinh[(d*x)/2] - 2*b*d*e*f*x*Sinh[(d*x)/2] + a*f^2*x*Sinh[(d*x)/2] - b*d*f^2*x^2*Sinh[(d*x)/2]))/(2*a^2*d^2)","B",0
478,1,376,298,7.0359204,"\int \frac{(e+f x) \coth (c+d x) \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Coth[c + d*x]*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{-8 b^2 \left(f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-\frac{1}{2} f (c+d x)^2\right)-a^2 d (e+f x) \text{csch}^2\left(\frac{1}{2} (c+d x)\right)+a^2 d (e+f x) \text{sech}^2\left(\frac{1}{2} (c+d x)\right)-2 a \tanh \left(\frac{1}{2} (c+d x)\right) (a f+2 b d (e+f x))+2 a \coth \left(\frac{1}{2} (c+d x)\right) (2 b d (e+f x)-a f)-8 a b f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+8 b^2 d e \log (\sinh (c+d x))+4 b^2 f \left((c+d x) \left(2 \log \left(1-e^{-2 (c+d x)}\right)+c+d x\right)-\text{Li}_2\left(e^{-2 (c+d x)}\right)\right)-8 b^2 c f \log (\sinh (c+d x))}{8 a^3 d^2}","\frac{b^2 f \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a^3 d^2}+\frac{b^2 (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}+\frac{b f \tanh ^{-1}(\cosh (c+d x))}{a^2 d^2}+\frac{b (e+f x) \text{csch}(c+d x)}{a^2 d}-\frac{b^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b^2 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b^2 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d}-\frac{b^2 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d}-\frac{f \coth (c+d x)}{2 a d^2}-\frac{(e+f x) \text{csch}^2(c+d x)}{2 a d}",1,"(2*a*(-(a*f) + 2*b*d*(e + f*x))*Coth[(c + d*x)/2] - a^2*d*(e + f*x)*Csch[(c + d*x)/2]^2 + 8*b^2*d*e*Log[Sinh[c + d*x]] - 8*b^2*c*f*Log[Sinh[c + d*x]] - 8*a*b*f*Log[Tanh[(c + d*x)/2]] + 4*b^2*f*((c + d*x)*(c + d*x + 2*Log[1 - E^(-2*(c + d*x))]) - PolyLog[2, E^(-2*(c + d*x))]) - 8*b^2*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + a^2*d*(e + f*x)*Sech[(c + d*x)/2]^2 - 2*a*(a*f + 2*b*d*(e + f*x))*Tanh[(c + d*x)/2])/(8*a^3*d^2)","A",1
479,1,60,72,0.0968098,"\int \frac{\coth (c+d x) \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Coth[c + d*x]*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{-a^2 \text{csch}^2(c+d x)+2 b^2 (\log (\sinh (c+d x))-\log (a+b \sinh (c+d x)))+2 a b \text{csch}(c+d x)}{2 a^3 d}","\frac{b^2 \log (\sinh (c+d x))}{a^3 d}-\frac{b^2 \log (a+b \sinh (c+d x))}{a^3 d}+\frac{b \text{csch}(c+d x)}{a^2 d}-\frac{\text{csch}^2(c+d x)}{2 a d}",1,"(2*a*b*Csch[c + d*x] - a^2*Csch[c + d*x]^2 + 2*b^2*(Log[Sinh[c + d*x]] - Log[a + b*Sinh[c + d*x]]))/(2*a^3*d)","A",1
480,-1,0,37,180.0003311,"\int \frac{\coth (c+d x) \text{csch}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Coth[c + d*x]*Csch[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\coth (c+d x) \text{csch}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
481,1,2383,1038,42.7504511,"\int \frac{(e+f x)^3 \coth ^2(c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Coth[c + d*x]^2*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{3 \text{Li}_2\left(-e^{c+d x}\right) f^3}{a d^4}+\frac{3 \text{Li}_2\left(e^{c+d x}\right) f^3}{a d^4}+\frac{3 b \text{Li}_3\left(e^{2 (c+d x)}\right) f^3}{2 a^2 d^4}-\frac{6 b^2 \text{Li}_4\left(-e^{c+d x}\right) f^3}{a^3 d^4}-\frac{3 \text{Li}_4\left(-e^{c+d x}\right) f^3}{a d^4}+\frac{6 b^2 \text{Li}_4\left(e^{c+d x}\right) f^3}{a^3 d^4}+\frac{3 \text{Li}_4\left(e^{c+d x}\right) f^3}{a d^4}-\frac{6 b \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f^3}{a^3 d^4}+\frac{6 b \sqrt{a^2+b^2} \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f^3}{a^3 d^4}-\frac{6 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right) f^2}{a d^3}-\frac{3 b (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right) f^2}{a^2 d^3}+\frac{6 b^2 (e+f x) \text{Li}_3\left(-e^{c+d x}\right) f^2}{a^3 d^3}+\frac{3 (e+f x) \text{Li}_3\left(-e^{c+d x}\right) f^2}{a d^3}-\frac{6 b^2 (e+f x) \text{Li}_3\left(e^{c+d x}\right) f^2}{a^3 d^3}-\frac{3 (e+f x) \text{Li}_3\left(e^{c+d x}\right) f^2}{a d^3}+\frac{6 b \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f^2}{a^3 d^3}-\frac{6 b \sqrt{a^2+b^2} (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f^2}{a^3 d^3}-\frac{3 (e+f x)^2 \text{csch}(c+d x) f}{2 a d^2}-\frac{3 b (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right) f}{a^2 d^2}-\frac{3 b^2 (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right) f}{a^3 d^2}-\frac{3 (e+f x)^2 \text{Li}_2\left(-e^{c+d x}\right) f}{2 a d^2}+\frac{3 b^2 (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right) f}{a^3 d^2}+\frac{3 (e+f x)^2 \text{Li}_2\left(e^{c+d x}\right) f}{2 a d^2}-\frac{3 b \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) f}{a^3 d^2}+\frac{3 b \sqrt{a^2+b^2} (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) f}{a^3 d^2}+\frac{b (e+f x)^3}{a^2 d}-\frac{2 b^2 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a^3 d}-\frac{(e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{b (e+f x)^3 \coth (c+d x)}{a^2 d}-\frac{(e+f x)^3 \coth (c+d x) \text{csch}(c+d x)}{2 a d}-\frac{b \sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d}+\frac{b \sqrt{a^2+b^2} (e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right)}{a^3 d}",1,"(e^3*Log[Tanh[(c + d*x)/2]])/(2*a*d) + (b^2*e^3*Log[Tanh[(c + d*x)/2]])/(a^3*d) + (3*e*f^2*Log[Tanh[(c + d*x)/2]])/(a*d^3) + (3*e^2*f*(-(c*Log[Tanh[(c + d*x)/2]]) - I*((I*c + I*d*x)*(Log[1 - E^(I*(I*c + I*d*x))] - Log[1 + E^(I*(I*c + I*d*x))]) + I*(PolyLog[2, -E^(I*(I*c + I*d*x))] - PolyLog[2, E^(I*(I*c + I*d*x))]))))/(2*a*d^2) + (3*b^2*e^2*f*(-(c*Log[Tanh[(c + d*x)/2]]) - I*((I*c + I*d*x)*(Log[1 - E^(I*(I*c + I*d*x))] - Log[1 + E^(I*(I*c + I*d*x))]) + I*(PolyLog[2, -E^(I*(I*c + I*d*x))] - PolyLog[2, E^(I*(I*c + I*d*x))]))))/(a^3*d^2) + (3*f^3*(-(c*Log[Tanh[(c + d*x)/2]]) - I*((I*c + I*d*x)*(Log[1 - E^(I*(I*c + I*d*x))] - Log[1 + E^(I*(I*c + I*d*x))]) + I*(PolyLog[2, -E^(I*(I*c + I*d*x))] - PolyLog[2, E^(I*(I*c + I*d*x))]))))/(a*d^4) + (b*E^c*f^3*Csch[c]*((2*d^3*x^3)/E^(2*c) - 3*d^2*(1 - E^(-2*c))*x^2*Log[1 - E^(-c - d*x)] - 3*d^2*(1 - E^(-2*c))*x^2*Log[1 + E^(-c - d*x)] + 6*(1 - E^(-2*c))*(d*x*PolyLog[2, -E^(-c - d*x)] + PolyLog[3, -E^(-c - d*x)]) + 6*(1 - E^(-2*c))*(d*x*PolyLog[2, E^(-c - d*x)] + PolyLog[3, E^(-c - d*x)])))/(2*a^2*d^4) - (3*e*f^2*(d^2*x^2*ArcTanh[Cosh[c + d*x] + Sinh[c + d*x]] + d*x*PolyLog[2, -Cosh[c + d*x] - Sinh[c + d*x]] - d*x*PolyLog[2, Cosh[c + d*x] + Sinh[c + d*x]] - PolyLog[3, -Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] + Sinh[c + d*x]]))/(a*d^3) - (6*b^2*e*f^2*(d^2*x^2*ArcTanh[Cosh[c + d*x] + Sinh[c + d*x]] + d*x*PolyLog[2, -Cosh[c + d*x] - Sinh[c + d*x]] - d*x*PolyLog[2, Cosh[c + d*x] + Sinh[c + d*x]] - PolyLog[3, -Cosh[c + d*x] - Sinh[c + d*x]] + PolyLog[3, Cosh[c + d*x] + Sinh[c + d*x]]))/(a^3*d^3) + (b*Sqrt[a^2 + b^2]*(2*d^3*e^3*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 3*d^3*e^2*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + 3*d^3*e*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^3*f^3*x^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 3*d^2*f*(e + f*x)^2*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 3*d^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 6*d*e*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*d*f^3*x*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 6*d*e*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*d*f^3*x*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] - 6*f^3*PolyLog[4, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^3*d^4) + (f^3*(-2*d^3*x^3*ArcTanh[Cosh[c + d*x] + Sinh[c + d*x]] - 3*d^2*x^2*PolyLog[2, -Cosh[c + d*x] - Sinh[c + d*x]] + 3*d^2*x^2*PolyLog[2, Cosh[c + d*x] + Sinh[c + d*x]] + 6*d*x*PolyLog[3, -Cosh[c + d*x] - Sinh[c + d*x]] - 6*d*x*PolyLog[3, Cosh[c + d*x] + Sinh[c + d*x]] - 6*PolyLog[4, -Cosh[c + d*x] - Sinh[c + d*x]] + 6*PolyLog[4, Cosh[c + d*x] + Sinh[c + d*x]]))/(2*a*d^4) + (b^2*f^3*(-2*d^3*x^3*ArcTanh[Cosh[c + d*x] + Sinh[c + d*x]] - 3*d^2*x^2*PolyLog[2, -Cosh[c + d*x] - Sinh[c + d*x]] + 3*d^2*x^2*PolyLog[2, Cosh[c + d*x] + Sinh[c + d*x]] + 6*d*x*PolyLog[3, -Cosh[c + d*x] - Sinh[c + d*x]] - 6*d*x*PolyLog[3, Cosh[c + d*x] + Sinh[c + d*x]] - 6*PolyLog[4, -Cosh[c + d*x] - Sinh[c + d*x]] + 6*PolyLog[4, Cosh[c + d*x] + Sinh[c + d*x]]))/(a^3*d^4) + (3*b*e^2*f*Csch[c]*(-(d*x*Cosh[c]) + Log[Cosh[d*x]*Sinh[c] + Cosh[c]*Sinh[d*x]]*Sinh[c]))/(a^2*d^2*(-Cosh[c]^2 + Sinh[c]^2)) + (Csch[c]*Csch[c + d*x]^2*(2*b*d*e^3*Cosh[c] + 6*b*d*e^2*f*x*Cosh[c] + 6*b*d*e*f^2*x^2*Cosh[c] + 2*b*d*f^3*x^3*Cosh[c] + 3*a*e^2*f*Cosh[d*x] + 6*a*e*f^2*x*Cosh[d*x] + 3*a*f^3*x^2*Cosh[d*x] - 3*a*e^2*f*Cosh[2*c + d*x] - 6*a*e*f^2*x*Cosh[2*c + d*x] - 3*a*f^3*x^2*Cosh[2*c + d*x] - 2*b*d*e^3*Cosh[c + 2*d*x] - 6*b*d*e^2*f*x*Cosh[c + 2*d*x] - 6*b*d*e*f^2*x^2*Cosh[c + 2*d*x] - 2*b*d*f^3*x^3*Cosh[c + 2*d*x] + a*d*e^3*Sinh[d*x] + 3*a*d*e^2*f*x*Sinh[d*x] + 3*a*d*e*f^2*x^2*Sinh[d*x] + a*d*f^3*x^3*Sinh[d*x] - a*d*e^3*Sinh[2*c + d*x] - 3*a*d*e^2*f*x*Sinh[2*c + d*x] - 3*a*d*e*f^2*x^2*Sinh[2*c + d*x] - a*d*f^3*x^3*Sinh[2*c + d*x]))/(4*a^2*d^2) + (3*b*e*f^2*Csch[c]*Sech[c]*((d^2*x^2)/E^ArcTanh[Tanh[c]] - (I*(-(d*x*(-Pi + (2*I)*ArcTanh[Tanh[c]])) - Pi*Log[1 + E^(2*d*x)] - 2*(I*d*x + I*ArcTanh[Tanh[c]])*Log[1 - E^((2*I)*(I*d*x + I*ArcTanh[Tanh[c]]))] + Pi*Log[Cosh[d*x]] + (2*I)*ArcTanh[Tanh[c]]*Log[I*Sinh[d*x + ArcTanh[Tanh[c]]]] + I*PolyLog[2, E^((2*I)*(I*d*x + I*ArcTanh[Tanh[c]]))])*Tanh[c])/Sqrt[1 - Tanh[c]^2]))/(a^2*d^3*Sqrt[Sech[c]^2*(Cosh[c]^2 - Sinh[c]^2)])","C",0
482,1,1529,714,24.5755888,"\int \frac{(e+f x)^2 \coth ^2(c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Coth[c + d*x]^2*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\text{csch}(c) \left(2 b d \cosh (c) e^2-2 b d \cosh (c+2 d x) e^2+a d \sinh (d x) e^2-a d \sinh (2 c+d x) e^2+4 b d f x \cosh (c) e+2 a f \cosh (d x) e-2 a f \cosh (2 c+d x) e-4 b d f x \cosh (c+2 d x) e+2 a d f x \sinh (d x) e-2 a d f x \sinh (2 c+d x) e+2 b d f^2 x^2 \cosh (c)+2 a f^2 x \cosh (d x)-2 a f^2 x \cosh (2 c+d x)-2 b d f^2 x^2 \cosh (c+2 d x)+a d f^2 x^2 \sinh (d x)-a d f^2 x^2 \sinh (2 c+d x)\right) \text{csch}^2(c+d x)}{4 a^2 d^2}+\frac{4 a b e^{2 c} f^2 x^2 d^2+8 a b e e^{2 c} f x d^2-2 a^2 e^2 e^{2 c} \tanh ^{-1}\left(e^{c+d x}\right) d^2-4 b^2 e^2 e^{2 c} \tanh ^{-1}\left(e^{c+d x}\right) d^2+2 a^2 e^2 \tanh ^{-1}\left(e^{c+d x}\right) d^2+4 b^2 e^2 \tanh ^{-1}\left(e^{c+d x}\right) d^2+a^2 e^{2 c} f^2 x^2 \log \left(1-e^{c+d x}\right) d^2+2 b^2 e^{2 c} f^2 x^2 \log \left(1-e^{c+d x}\right) d^2-a^2 f^2 x^2 \log \left(1-e^{c+d x}\right) d^2-2 b^2 f^2 x^2 \log \left(1-e^{c+d x}\right) d^2+2 a^2 e e^{2 c} f x \log \left(1-e^{c+d x}\right) d^2+4 b^2 e e^{2 c} f x \log \left(1-e^{c+d x}\right) d^2-2 a^2 e f x \log \left(1-e^{c+d x}\right) d^2-4 b^2 e f x \log \left(1-e^{c+d x}\right) d^2-a^2 e^{2 c} f^2 x^2 \log \left(1+e^{c+d x}\right) d^2-2 b^2 e^{2 c} f^2 x^2 \log \left(1+e^{c+d x}\right) d^2+a^2 f^2 x^2 \log \left(1+e^{c+d x}\right) d^2+2 b^2 f^2 x^2 \log \left(1+e^{c+d x}\right) d^2-2 a^2 e e^{2 c} f x \log \left(1+e^{c+d x}\right) d^2-4 b^2 e e^{2 c} f x \log \left(1+e^{c+d x}\right) d^2+2 a^2 e f x \log \left(1+e^{c+d x}\right) d^2+4 b^2 e f x \log \left(1+e^{c+d x}\right) d^2-4 a b e e^{2 c} f \log \left(1-e^{2 (c+d x)}\right) d+4 a b e f \log \left(1-e^{2 (c+d x)}\right) d-4 a b e^{2 c} f^2 x \log \left(1-e^{2 (c+d x)}\right) d+4 a b f^2 x \log \left(1-e^{2 (c+d x)}\right) d-2 \left(a^2+2 b^2\right) \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(-e^{c+d x}\right) d+2 \left(a^2+2 b^2\right) \left(-1+e^{2 c}\right) f (e+f x) \text{Li}_2\left(e^{c+d x}\right) d-4 a^2 e^{2 c} f^2 \tanh ^{-1}\left(e^{c+d x}\right)+4 a^2 f^2 \tanh ^{-1}\left(e^{c+d x}\right)-2 a b e^{2 c} f^2 \text{Li}_2\left(e^{2 (c+d x)}\right)+2 a b f^2 \text{Li}_2\left(e^{2 (c+d x)}\right)+2 a^2 e^{2 c} f^2 \text{Li}_3\left(-e^{c+d x}\right)+4 b^2 e^{2 c} f^2 \text{Li}_3\left(-e^{c+d x}\right)-2 a^2 f^2 \text{Li}_3\left(-e^{c+d x}\right)-4 b^2 f^2 \text{Li}_3\left(-e^{c+d x}\right)-2 a^2 e^{2 c} f^2 \text{Li}_3\left(e^{c+d x}\right)-4 b^2 e^{2 c} f^2 \text{Li}_3\left(e^{c+d x}\right)+2 a^2 f^2 \text{Li}_3\left(e^{c+d x}\right)+4 b^2 f^2 \text{Li}_3\left(e^{c+d x}\right)}{2 a^3 d^3 \left(-1+e^{2 c}\right)}+\frac{b \sqrt{a^2+b^2} \left(2 e^2 \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right) d^2-f^2 x^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2-2 e f x \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) d^2+f^2 x^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2+2 e f x \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) d^2-2 f (e+f x) \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right) d+2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) d+2 f^2 \text{Li}_3\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right)}{a^3 d^3}","\frac{2 b^2 f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a^3 d^3}-\frac{2 b^2 f^2 \text{Li}_3\left(e^{c+d x}\right)}{a^3 d^3}-\frac{2 b^2 f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a^3 d^2}+\frac{2 b^2 f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a^3 d^2}-\frac{2 b^2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^3 d}-\frac{b f^2 \text{Li}_2\left(e^{2 (c+d x)}\right)}{a^2 d^3}-\frac{2 b f (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a^2 d^2}+\frac{b (e+f x)^2 \coth (c+d x)}{a^2 d}+\frac{b (e+f x)^2}{a^2 d}+\frac{2 b f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^3}-\frac{2 b f^2 \sqrt{a^2+b^2} \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^3}-\frac{2 b f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2}+\frac{2 b f \sqrt{a^2+b^2} (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b \sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d}+\frac{b \sqrt{a^2+b^2} (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d}+\frac{f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}-\frac{f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{f^2 \tanh ^{-1}(\cosh (c+d x))}{a d^3}-\frac{f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}+\frac{f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{f (e+f x) \text{csch}(c+d x)}{a d^2}-\frac{(e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{(e+f x)^2 \coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"(8*a*b*d^2*e*E^(2*c)*f*x + 4*a*b*d^2*E^(2*c)*f^2*x^2 + 2*a^2*d^2*e^2*ArcTanh[E^(c + d*x)] + 4*b^2*d^2*e^2*ArcTanh[E^(c + d*x)] - 2*a^2*d^2*e^2*E^(2*c)*ArcTanh[E^(c + d*x)] - 4*b^2*d^2*e^2*E^(2*c)*ArcTanh[E^(c + d*x)] + 4*a^2*f^2*ArcTanh[E^(c + d*x)] - 4*a^2*E^(2*c)*f^2*ArcTanh[E^(c + d*x)] - 2*a^2*d^2*e*f*x*Log[1 - E^(c + d*x)] - 4*b^2*d^2*e*f*x*Log[1 - E^(c + d*x)] + 2*a^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(c + d*x)] + 4*b^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(c + d*x)] - a^2*d^2*f^2*x^2*Log[1 - E^(c + d*x)] - 2*b^2*d^2*f^2*x^2*Log[1 - E^(c + d*x)] + a^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] + 2*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] + 2*a^2*d^2*e*f*x*Log[1 + E^(c + d*x)] + 4*b^2*d^2*e*f*x*Log[1 + E^(c + d*x)] - 2*a^2*d^2*e*E^(2*c)*f*x*Log[1 + E^(c + d*x)] - 4*b^2*d^2*e*E^(2*c)*f*x*Log[1 + E^(c + d*x)] + a^2*d^2*f^2*x^2*Log[1 + E^(c + d*x)] + 2*b^2*d^2*f^2*x^2*Log[1 + E^(c + d*x)] - a^2*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(c + d*x)] - 2*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(c + d*x)] + 4*a*b*d*e*f*Log[1 - E^(2*(c + d*x))] - 4*a*b*d*e*E^(2*c)*f*Log[1 - E^(2*(c + d*x))] + 4*a*b*d*f^2*x*Log[1 - E^(2*(c + d*x))] - 4*a*b*d*E^(2*c)*f^2*x*Log[1 - E^(2*(c + d*x))] - 2*(a^2 + 2*b^2)*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -E^(c + d*x)] + 2*(a^2 + 2*b^2)*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, E^(c + d*x)] + 2*a*b*f^2*PolyLog[2, E^(2*(c + d*x))] - 2*a*b*E^(2*c)*f^2*PolyLog[2, E^(2*(c + d*x))] - 2*a^2*f^2*PolyLog[3, -E^(c + d*x)] - 4*b^2*f^2*PolyLog[3, -E^(c + d*x)] + 2*a^2*E^(2*c)*f^2*PolyLog[3, -E^(c + d*x)] + 4*b^2*E^(2*c)*f^2*PolyLog[3, -E^(c + d*x)] + 2*a^2*f^2*PolyLog[3, E^(c + d*x)] + 4*b^2*f^2*PolyLog[3, E^(c + d*x)] - 2*a^2*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)] - 4*b^2*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)])/(2*a^3*d^3*(-1 + E^(2*c))) + (b*Sqrt[a^2 + b^2]*(2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^3*d^3) + (Csch[c]*Csch[c + d*x]^2*(2*b*d*e^2*Cosh[c] + 4*b*d*e*f*x*Cosh[c] + 2*b*d*f^2*x^2*Cosh[c] + 2*a*e*f*Cosh[d*x] + 2*a*f^2*x*Cosh[d*x] - 2*a*e*f*Cosh[2*c + d*x] - 2*a*f^2*x*Cosh[2*c + d*x] - 2*b*d*e^2*Cosh[c + 2*d*x] - 4*b*d*e*f*x*Cosh[c + 2*d*x] - 2*b*d*f^2*x^2*Cosh[c + 2*d*x] + a*d*e^2*Sinh[d*x] + 2*a*d*e*f*x*Sinh[d*x] + a*d*f^2*x^2*Sinh[d*x] - a*d*e^2*Sinh[2*c + d*x] - 2*a*d*e*f*x*Sinh[2*c + d*x] - a*d*f^2*x^2*Sinh[2*c + d*x]))/(4*a^2*d^2)","B",1
483,1,734,413,8.0876832,"\int \frac{(e+f x) \coth ^2(c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Coth[c + d*x]^2*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{i b^2 f \left(i \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)\right)+i (c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right)}{a^3 d^2}-\frac{b^2 c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^3 d^2}+\frac{b^2 e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^3 d}+\frac{\text{csch}\left(\frac{1}{2} (c+d x)\right) \left(-a f \cosh \left(\frac{1}{2} (c+d x)\right)+2 b d e \cosh \left(\frac{1}{2} (c+d x)\right)-2 b c f \cosh \left(\frac{1}{2} (c+d x)\right)+2 b f (c+d x) \cosh \left(\frac{1}{2} (c+d x)\right)\right)}{4 a^2 d^2}+\frac{\text{sech}\left(\frac{1}{2} (c+d x)\right) \left(a f \sinh \left(\frac{1}{2} (c+d x)\right)+2 b d e \sinh \left(\frac{1}{2} (c+d x)\right)-2 b c f \sinh \left(\frac{1}{2} (c+d x)\right)+2 b f (c+d x) \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{4 a^2 d^2}-\frac{b f \log (\sinh (c+d x))}{a^2 d^2}+\frac{b \sqrt{a^2+b^2} \left(2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)-2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)\right)}{a^3 d^2}+\frac{\text{csch}^2\left(\frac{1}{2} (c+d x)\right) (-f (c+d x)+c f-d e)}{8 a d^2}+\frac{\text{sech}^2\left(\frac{1}{2} (c+d x)\right) (-f (c+d x)+c f-d e)}{8 a d^2}-\frac{i f \left(i \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)\right)+i (c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(e^{-c-d x}+1\right)\right)\right)}{2 a d^2}-\frac{c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a d^2}+\frac{e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a d}","-\frac{b^2 f \text{Li}_2\left(-e^{c+d x}\right)}{a^3 d^2}+\frac{b^2 f \text{Li}_2\left(e^{c+d x}\right)}{a^3 d^2}-\frac{2 b^2 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a^3 d}-\frac{b f \log (\sinh (c+d x))}{a^2 d^2}+\frac{b (e+f x) \coth (c+d x)}{a^2 d}-\frac{b f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2}+\frac{b f \sqrt{a^2+b^2} \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b \sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d}+\frac{b \sqrt{a^2+b^2} (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d}-\frac{f \text{Li}_2\left(-e^{c+d x}\right)}{2 a d^2}+\frac{f \text{Li}_2\left(e^{c+d x}\right)}{2 a d^2}-\frac{f \text{csch}(c+d x)}{2 a d^2}-\frac{(e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{(e+f x) \coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"((2*b*d*e*Cosh[(c + d*x)/2] - a*f*Cosh[(c + d*x)/2] - 2*b*c*f*Cosh[(c + d*x)/2] + 2*b*f*(c + d*x)*Cosh[(c + d*x)/2])*Csch[(c + d*x)/2])/(4*a^2*d^2) + ((-(d*e) + c*f - f*(c + d*x))*Csch[(c + d*x)/2]^2)/(8*a*d^2) - (b*f*Log[Sinh[c + d*x]])/(a^2*d^2) + (e*Log[Tanh[(c + d*x)/2]])/(2*a*d) + (b^2*e*Log[Tanh[(c + d*x)/2]])/(a^3*d) - (c*f*Log[Tanh[(c + d*x)/2]])/(2*a*d^2) - (b^2*c*f*Log[Tanh[(c + d*x)/2]])/(a^3*d^2) - ((I/2)*f*(I*(c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + I*(PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)])))/(a*d^2) - (I*b^2*f*(I*(c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + I*(PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)])))/(a^3*d^2) + (b*Sqrt[a^2 + b^2]*(2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^3*d^2) + ((-(d*e) + c*f - f*(c + d*x))*Sech[(c + d*x)/2]^2)/(8*a*d^2) + (Sech[(c + d*x)/2]*(2*b*d*e*Sinh[(c + d*x)/2] + a*f*Sinh[(c + d*x)/2] - 2*b*c*f*Sinh[(c + d*x)/2] + 2*b*f*(c + d*x)*Sinh[(c + d*x)/2]))/(4*a^2*d^2)","C",1
484,1,145,111,1.2188281,"\int \frac{\coth ^2(c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Coth[c + d*x]^2*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{4 \left(a^2+2 b^2\right) \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+16 b \sqrt{-a^2-b^2} \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)-a^2 \text{csch}^2\left(\frac{1}{2} (c+d x)\right)-a^2 \text{sech}^2\left(\frac{1}{2} (c+d x)\right)+4 a b \tanh \left(\frac{1}{2} (c+d x)\right)+4 a b \coth \left(\frac{1}{2} (c+d x)\right)}{8 a^3 d}","\frac{b \coth (c+d x)}{a^2 d}+\frac{2 b \sqrt{a^2+b^2} \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a^3 d}-\frac{\left(a^2+2 b^2\right) \tanh ^{-1}(\cosh (c+d x))}{2 a^3 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"(16*b*Sqrt[-a^2 - b^2]*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]] + 4*a*b*Coth[(c + d*x)/2] - a^2*Csch[(c + d*x)/2]^2 + 4*(a^2 + 2*b^2)*Log[Tanh[(c + d*x)/2]] - a^2*Sech[(c + d*x)/2]^2 + 4*a*b*Tanh[(c + d*x)/2])/(8*a^3*d)","A",1
485,-1,0,37,180.001825,"\int \frac{\coth ^2(c+d x) \text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Coth[c + d*x]^2*Csch[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\coth ^2(c+d x) \text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
486,1,3657,972,75.7552362,"\int \frac{(e+f x)^3 \coth ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Coth[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{b^2 (e+f x)^4}{4 a^3 f}+\frac{\left(a^2+b^2\right) (e+f x)^4}{4 a^3 f}-\frac{(e+f x)^4}{4 a f}-\frac{\coth ^2(c+d x) (e+f x)^3}{2 a d}+\frac{b \text{csch}(c+d x) (e+f x)^3}{a^2 d}-\frac{\left(a^2+b^2\right) \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{a^3 d}-\frac{\left(a^2+b^2\right) \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (e+f x)^3}{a^3 d}+\frac{b^2 \log \left(1-e^{2 (c+d x)}\right) (e+f x)^3}{a^3 d}+\frac{\log \left(1-e^{2 (c+d x)}\right) (e+f x)^3}{a d}+\frac{(e+f x)^3}{2 a d}-\frac{3 f (e+f x)^2}{2 a d^2}+\frac{6 b f \tanh ^{-1}\left(e^{c+d x}\right) (e+f x)^2}{a^2 d^2}-\frac{3 f \coth (c+d x) (e+f x)^2}{2 a d^2}-\frac{3 \left(a^2+b^2\right) f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)^2}{a^3 d^2}-\frac{3 \left(a^2+b^2\right) f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)^2}{a^3 d^2}+\frac{3 b^2 f \text{Li}_2\left(e^{2 (c+d x)}\right) (e+f x)^2}{2 a^3 d^2}+\frac{3 f \text{Li}_2\left(e^{2 (c+d x)}\right) (e+f x)^2}{2 a d^2}+\frac{3 f^2 \log \left(1-e^{2 (c+d x)}\right) (e+f x)}{a d^3}+\frac{6 b f^2 \text{Li}_2\left(-e^{c+d x}\right) (e+f x)}{a^2 d^3}-\frac{6 b f^2 \text{Li}_2\left(e^{c+d x}\right) (e+f x)}{a^2 d^3}+\frac{6 \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) (e+f x)}{a^3 d^3}+\frac{6 \left(a^2+b^2\right) f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) (e+f x)}{a^3 d^3}-\frac{3 b^2 f^2 \text{Li}_3\left(e^{2 (c+d x)}\right) (e+f x)}{2 a^3 d^3}-\frac{3 f^2 \text{Li}_3\left(e^{2 (c+d x)}\right) (e+f x)}{2 a d^3}+\frac{3 f^3 \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a d^4}-\frac{6 b f^3 \text{Li}_3\left(-e^{c+d x}\right)}{a^2 d^4}+\frac{6 b f^3 \text{Li}_3\left(e^{c+d x}\right)}{a^2 d^4}-\frac{6 \left(a^2+b^2\right) f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^4}-\frac{6 \left(a^2+b^2\right) f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^4}+\frac{3 b^2 f^3 \text{Li}_4\left(e^{2 (c+d x)}\right)}{4 a^3 d^4}+\frac{3 f^3 \text{Li}_4\left(e^{2 (c+d x)}\right)}{4 a d^4}",1,"(b*(e + f*x)^3*Csch[c])/(a^2*d) - ((e + f*x)^3*Csch[(c + d*x)/2]^2)/(8*a*d) - (8*a^2*d^4*e^3*E^(2*c)*x + 8*b^2*d^4*e^3*E^(2*c)*x + 24*a^2*d^2*e*E^(2*c)*f^2*x + 12*a^2*d^4*e^2*E^(2*c)*f*x^2 + 12*b^2*d^4*e^2*E^(2*c)*f*x^2 + 12*a^2*d^2*E^(2*c)*f^3*x^2 + 8*a^2*d^4*e*E^(2*c)*f^2*x^3 + 8*b^2*d^4*e*E^(2*c)*f^2*x^3 + 2*a^2*d^4*E^(2*c)*f^3*x^4 + 2*b^2*d^4*E^(2*c)*f^3*x^4 + 24*a*b*d^2*e^2*f*ArcTanh[E^(c + d*x)] - 24*a*b*d^2*e^2*E^(2*c)*f*ArcTanh[E^(c + d*x)] - 24*a*b*d^2*e*f^2*x*Log[1 - E^(c + d*x)] + 24*a*b*d^2*e*E^(2*c)*f^2*x*Log[1 - E^(c + d*x)] - 12*a*b*d^2*f^3*x^2*Log[1 - E^(c + d*x)] + 12*a*b*d^2*E^(2*c)*f^3*x^2*Log[1 - E^(c + d*x)] + 24*a*b*d^2*e*f^2*x*Log[1 + E^(c + d*x)] - 24*a*b*d^2*e*E^(2*c)*f^2*x*Log[1 + E^(c + d*x)] + 12*a*b*d^2*f^3*x^2*Log[1 + E^(c + d*x)] - 12*a*b*d^2*E^(2*c)*f^3*x^2*Log[1 + E^(c + d*x)] + 4*a^2*d^3*e^3*Log[1 - E^(2*(c + d*x))] + 4*b^2*d^3*e^3*Log[1 - E^(2*(c + d*x))] - 4*a^2*d^3*e^3*E^(2*c)*Log[1 - E^(2*(c + d*x))] - 4*b^2*d^3*e^3*E^(2*c)*Log[1 - E^(2*(c + d*x))] + 12*a^2*d*e*f^2*Log[1 - E^(2*(c + d*x))] - 12*a^2*d*e*E^(2*c)*f^2*Log[1 - E^(2*(c + d*x))] + 12*a^2*d^3*e^2*f*x*Log[1 - E^(2*(c + d*x))] + 12*b^2*d^3*e^2*f*x*Log[1 - E^(2*(c + d*x))] - 12*a^2*d^3*e^2*E^(2*c)*f*x*Log[1 - E^(2*(c + d*x))] - 12*b^2*d^3*e^2*E^(2*c)*f*x*Log[1 - E^(2*(c + d*x))] + 12*a^2*d*f^3*x*Log[1 - E^(2*(c + d*x))] - 12*a^2*d*E^(2*c)*f^3*x*Log[1 - E^(2*(c + d*x))] + 12*a^2*d^3*e*f^2*x^2*Log[1 - E^(2*(c + d*x))] + 12*b^2*d^3*e*f^2*x^2*Log[1 - E^(2*(c + d*x))] - 12*a^2*d^3*e*E^(2*c)*f^2*x^2*Log[1 - E^(2*(c + d*x))] - 12*b^2*d^3*e*E^(2*c)*f^2*x^2*Log[1 - E^(2*(c + d*x))] + 4*a^2*d^3*f^3*x^3*Log[1 - E^(2*(c + d*x))] + 4*b^2*d^3*f^3*x^3*Log[1 - E^(2*(c + d*x))] - 4*a^2*d^3*E^(2*c)*f^3*x^3*Log[1 - E^(2*(c + d*x))] - 4*b^2*d^3*E^(2*c)*f^3*x^3*Log[1 - E^(2*(c + d*x))] - 24*a*b*d*(-1 + E^(2*c))*f^2*(e + f*x)*PolyLog[2, -E^(c + d*x)] + 24*a*b*d*(-1 + E^(2*c))*f^2*(e + f*x)*PolyLog[2, E^(c + d*x)] + 6*a^2*d^2*e^2*f*PolyLog[2, E^(2*(c + d*x))] + 6*b^2*d^2*e^2*f*PolyLog[2, E^(2*(c + d*x))] - 6*a^2*d^2*e^2*E^(2*c)*f*PolyLog[2, E^(2*(c + d*x))] - 6*b^2*d^2*e^2*E^(2*c)*f*PolyLog[2, E^(2*(c + d*x))] + 6*a^2*f^3*PolyLog[2, E^(2*(c + d*x))] - 6*a^2*E^(2*c)*f^3*PolyLog[2, E^(2*(c + d*x))] + 12*a^2*d^2*e*f^2*x*PolyLog[2, E^(2*(c + d*x))] + 12*b^2*d^2*e*f^2*x*PolyLog[2, E^(2*(c + d*x))] - 12*a^2*d^2*e*E^(2*c)*f^2*x*PolyLog[2, E^(2*(c + d*x))] - 12*b^2*d^2*e*E^(2*c)*f^2*x*PolyLog[2, E^(2*(c + d*x))] + 6*a^2*d^2*f^3*x^2*PolyLog[2, E^(2*(c + d*x))] + 6*b^2*d^2*f^3*x^2*PolyLog[2, E^(2*(c + d*x))] - 6*a^2*d^2*E^(2*c)*f^3*x^2*PolyLog[2, E^(2*(c + d*x))] - 6*b^2*d^2*E^(2*c)*f^3*x^2*PolyLog[2, E^(2*(c + d*x))] - 24*a*b*f^3*PolyLog[3, -E^(c + d*x)] + 24*a*b*E^(2*c)*f^3*PolyLog[3, -E^(c + d*x)] + 24*a*b*f^3*PolyLog[3, E^(c + d*x)] - 24*a*b*E^(2*c)*f^3*PolyLog[3, E^(c + d*x)] - 6*a^2*d*e*f^2*PolyLog[3, E^(2*(c + d*x))] - 6*b^2*d*e*f^2*PolyLog[3, E^(2*(c + d*x))] + 6*a^2*d*e*E^(2*c)*f^2*PolyLog[3, E^(2*(c + d*x))] + 6*b^2*d*e*E^(2*c)*f^2*PolyLog[3, E^(2*(c + d*x))] - 6*a^2*d*f^3*x*PolyLog[3, E^(2*(c + d*x))] - 6*b^2*d*f^3*x*PolyLog[3, E^(2*(c + d*x))] + 6*a^2*d*E^(2*c)*f^3*x*PolyLog[3, E^(2*(c + d*x))] + 6*b^2*d*E^(2*c)*f^3*x*PolyLog[3, E^(2*(c + d*x))] + 3*a^2*f^3*PolyLog[4, E^(2*(c + d*x))] + 3*b^2*f^3*PolyLog[4, E^(2*(c + d*x))] - 3*a^2*E^(2*c)*f^3*PolyLog[4, E^(2*(c + d*x))] - 3*b^2*E^(2*c)*f^3*PolyLog[4, E^(2*(c + d*x))])/(4*a^3*d^4*(-1 + E^(2*c))) + ((a^2 + b^2)*(4*e^3*E^(2*c)*x + 6*e^2*E^(2*c)*f*x^2 + 4*e*E^(2*c)*f^2*x^3 + E^(2*c)*f^3*x^4 + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTan[(a + b*E^(c + d*x))/Sqrt[-a^2 - b^2]])/((a^2 + b^2)^(3/2)*d) + (4*a*Sqrt[-(a^2 + b^2)^2]*e^3*E^(2*c)*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]])/((-a^2 - b^2)^(3/2)*d) + (2*e^3*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))])/d - (2*e^3*E^(2*c)*Log[2*a*E^(c + d*x) + b*(-1 + E^(2*(c + d*x)))])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e^2*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e^2*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (6*e*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*e*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d + (2*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (2*E^(2*c)*f^3*x^3*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])])/d - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (6*(-1 + E^(2*c))*f*(e + f*x)^2*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^2 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*e*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*e*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 - (12*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*E^(2*c)*f^3*x*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^3 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 + (12*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4 - (12*E^(2*c)*f^3*PolyLog[4, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))])/d^4))/(2*a^3*(-1 + E^(2*c))) + ((e + f*x)^3*Sech[(c + d*x)/2]^2)/(8*a*d) + ((e + f*x)^2*(3*a*f - 2*b*d*(e + f*x))*Csch[c/2]*Csch[(c + d*x)/2]*Sinh[(d*x)/2])/(4*a^2*d^2) - ((e + f*x)^2*(3*a*f + 2*b*d*(e + f*x))*Sech[c/2]*Sech[(c + d*x)/2]*Sinh[(d*x)/2])/(4*a^2*d^2)","B",0
487,1,2137,689,38.9555771,"\int \frac{(e+f x)^2 \coth ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Coth[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{b^2 f^2 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a^3 d^3}+\frac{b^2 f (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a^3 d^2}+\frac{b^2 (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}-\frac{b^2 (e+f x)^3}{3 a^3 f}+\frac{2 b f^2 \text{Li}_2\left(-e^{c+d x}\right)}{a^2 d^3}-\frac{2 b f^2 \text{Li}_2\left(e^{c+d x}\right)}{a^2 d^3}+\frac{4 b f (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d^2}+\frac{b (e+f x)^2 \text{csch}(c+d x)}{a^2 d}+\frac{2 f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^3}+\frac{2 f^2 \left(a^2+b^2\right) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^3}-\frac{2 f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{2 f \left(a^2+b^2\right) (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{\left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d}-\frac{\left(a^2+b^2\right) (e+f x)^2 \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d}+\frac{\left(a^2+b^2\right) (e+f x)^3}{3 a^3 f}-\frac{f^2 \text{Li}_3\left(e^{2 (c+d x)}\right)}{2 a d^3}+\frac{f^2 \log (\sinh (c+d x))}{a d^3}+\frac{f (e+f x) \text{Li}_2\left(e^{2 (c+d x)}\right)}{a d^2}-\frac{f (e+f x) \coth (c+d x)}{a d^2}+\frac{(e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a d}-\frac{(e+f x)^2 \coth ^2(c+d x)}{2 a d}+\frac{e f x}{a d}+\frac{f^2 x^2}{2 a d}-\frac{(e+f x)^3}{3 a f}",1,"(b*(e + f*x)^2*Csch[c])/(a^2*d) + ((-e^2 - 2*e*f*x - f^2*x^2)*Csch[c/2 + (d*x)/2]^2)/(8*a*d) - (12*a^2*d^3*e^2*E^(2*c)*x + 12*b^2*d^3*e^2*E^(2*c)*x + 12*a^2*d*E^(2*c)*f^2*x + 12*a^2*d^3*e*E^(2*c)*f*x^2 + 12*b^2*d^3*e*E^(2*c)*f*x^2 + 4*a^2*d^3*E^(2*c)*f^2*x^3 + 4*b^2*d^3*E^(2*c)*f^2*x^3 + 24*a*b*d*e*f*ArcTanh[E^(c + d*x)] - 24*a*b*d*e*E^(2*c)*f*ArcTanh[E^(c + d*x)] - 12*a*b*d*f^2*x*Log[1 - E^(c + d*x)] + 12*a*b*d*E^(2*c)*f^2*x*Log[1 - E^(c + d*x)] + 12*a*b*d*f^2*x*Log[1 + E^(c + d*x)] - 12*a*b*d*E^(2*c)*f^2*x*Log[1 + E^(c + d*x)] + 6*a^2*d^2*e^2*Log[1 - E^(2*(c + d*x))] + 6*b^2*d^2*e^2*Log[1 - E^(2*(c + d*x))] - 6*a^2*d^2*e^2*E^(2*c)*Log[1 - E^(2*(c + d*x))] - 6*b^2*d^2*e^2*E^(2*c)*Log[1 - E^(2*(c + d*x))] + 6*a^2*f^2*Log[1 - E^(2*(c + d*x))] - 6*a^2*E^(2*c)*f^2*Log[1 - E^(2*(c + d*x))] + 12*a^2*d^2*e*f*x*Log[1 - E^(2*(c + d*x))] + 12*b^2*d^2*e*f*x*Log[1 - E^(2*(c + d*x))] - 12*a^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(2*(c + d*x))] - 12*b^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(2*(c + d*x))] + 6*a^2*d^2*f^2*x^2*Log[1 - E^(2*(c + d*x))] + 6*b^2*d^2*f^2*x^2*Log[1 - E^(2*(c + d*x))] - 6*a^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(2*(c + d*x))] - 6*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(2*(c + d*x))] - 12*a*b*(-1 + E^(2*c))*f^2*PolyLog[2, -E^(c + d*x)] + 12*a*b*(-1 + E^(2*c))*f^2*PolyLog[2, E^(c + d*x)] + 6*a^2*d*e*f*PolyLog[2, E^(2*(c + d*x))] + 6*b^2*d*e*f*PolyLog[2, E^(2*(c + d*x))] - 6*a^2*d*e*E^(2*c)*f*PolyLog[2, E^(2*(c + d*x))] - 6*b^2*d*e*E^(2*c)*f*PolyLog[2, E^(2*(c + d*x))] + 6*a^2*d*f^2*x*PolyLog[2, E^(2*(c + d*x))] + 6*b^2*d*f^2*x*PolyLog[2, E^(2*(c + d*x))] - 6*a^2*d*E^(2*c)*f^2*x*PolyLog[2, E^(2*(c + d*x))] - 6*b^2*d*E^(2*c)*f^2*x*PolyLog[2, E^(2*(c + d*x))] - 3*a^2*f^2*PolyLog[3, E^(2*(c + d*x))] - 3*b^2*f^2*PolyLog[3, E^(2*(c + d*x))] + 3*a^2*E^(2*c)*f^2*PolyLog[3, E^(2*(c + d*x))] + 3*b^2*E^(2*c)*f^2*PolyLog[3, E^(2*(c + d*x))])/(6*a^3*d^3*(-1 + E^(2*c))) + ((a^2 + b^2)*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*a^3*d^3*(-1 + E^(2*c))) + ((e^2 + 2*e*f*x + f^2*x^2)*Sech[c/2 + (d*x)/2]^2)/(8*a*d) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(-(b*d*e^2*Sinh[(d*x)/2]) - a*e*f*Sinh[(d*x)/2] - 2*b*d*e*f*x*Sinh[(d*x)/2] - a*f^2*x*Sinh[(d*x)/2] - b*d*f^2*x^2*Sinh[(d*x)/2]))/(2*a^2*d^2) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(-(b*d*e^2*Sinh[(d*x)/2]) + a*e*f*Sinh[(d*x)/2] - 2*b*d*e*f*x*Sinh[(d*x)/2] + a*f^2*x*Sinh[(d*x)/2] - b*d*f^2*x^2*Sinh[(d*x)/2]))/(2*a^2*d^2)","B",1
488,1,455,435,4.2617455,"\int \frac{(e+f x) \coth ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Coth[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{-8 \left(a^2+b^2\right) \left(f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))-\frac{1}{2} f (c+d x)^2\right)+a^2 (-d) (e+f x) \text{csch}^2\left(\frac{1}{2} (c+d x)\right)+a^2 d (e+f x) \text{sech}^2\left(\frac{1}{2} (c+d x)\right)+8 a^2 d e \log (\sinh (c+d x))+4 a^2 f \left((c+d x) \left(2 \log \left(1-e^{-2 (c+d x)}\right)+c+d x\right)-\text{Li}_2\left(e^{-2 (c+d x)}\right)\right)-8 a^2 c f \log (\sinh (c+d x))-2 a \tanh \left(\frac{1}{2} (c+d x)\right) (a f+2 b d (e+f x))+2 a \coth \left(\frac{1}{2} (c+d x)\right) (2 b d (e+f x)-a f)-8 a b f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)+8 b^2 d e \log (\sinh (c+d x))+4 b^2 f \left((c+d x) \left(2 \log \left(1-e^{-2 (c+d x)}\right)+c+d x\right)-\text{Li}_2\left(e^{-2 (c+d x)}\right)\right)-8 b^2 c f \log (\sinh (c+d x))}{8 a^3 d^2}","\frac{b^2 f \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a^3 d^2}+\frac{b^2 (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}-\frac{b^2 (e+f x)^2}{2 a^3 f}+\frac{b f \tanh ^{-1}(\cosh (c+d x))}{a^2 d^2}+\frac{b (e+f x) \text{csch}(c+d x)}{a^2 d}-\frac{f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{f \left(a^2+b^2\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{\left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d}-\frac{\left(a^2+b^2\right) (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d}+\frac{\left(a^2+b^2\right) (e+f x)^2}{2 a^3 f}+\frac{f \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a d^2}-\frac{f \coth (c+d x)}{2 a d^2}+\frac{(e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d}-\frac{(e+f x) \coth ^2(c+d x)}{2 a d}+\frac{f x}{2 a d}-\frac{(e+f x)^2}{2 a f}",1,"(2*a*(-(a*f) + 2*b*d*(e + f*x))*Coth[(c + d*x)/2] - a^2*d*(e + f*x)*Csch[(c + d*x)/2]^2 + 8*a^2*d*e*Log[Sinh[c + d*x]] + 8*b^2*d*e*Log[Sinh[c + d*x]] - 8*a^2*c*f*Log[Sinh[c + d*x]] - 8*b^2*c*f*Log[Sinh[c + d*x]] - 8*a*b*f*Log[Tanh[(c + d*x)/2]] + 4*a^2*f*((c + d*x)*(c + d*x + 2*Log[1 - E^(-2*(c + d*x))]) - PolyLog[2, E^(-2*(c + d*x))]) + 4*b^2*f*((c + d*x)*(c + d*x + 2*Log[1 - E^(-2*(c + d*x))]) - PolyLog[2, E^(-2*(c + d*x))]) - 8*(a^2 + b^2)*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]) + a^2*d*(e + f*x)*Sech[(c + d*x)/2]^2 - 2*a*(a*f + 2*b*d*(e + f*x))*Tanh[(c + d*x)/2])/(8*a^3*d^2)","A",1
489,1,64,80,0.1110056,"\int \frac{\coth ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[Coth[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","\frac{2 \left(a^2+b^2\right) (\log (\sinh (c+d x))-\log (a+b \sinh (c+d x)))-a^2 \text{csch}^2(c+d x)+2 a b \text{csch}(c+d x)}{2 a^3 d}","\frac{b \text{csch}(c+d x)}{a^2 d}+\frac{\left(a^2+b^2\right) \log (\sinh (c+d x))}{a^3 d}-\frac{\left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{a^3 d}-\frac{\text{csch}^2(c+d x)}{2 a d}",1,"(2*a*b*Csch[c + d*x] - a^2*Csch[c + d*x]^2 + 2*(a^2 + b^2)*(Log[Sinh[c + d*x]] - Log[a + b*Sinh[c + d*x]]))/(2*a^3*d)","A",1
490,-1,0,31,180.0007288,"\int \frac{\coth ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[Coth[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\coth ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
491,1,5823,1795,90.0027122,"\int \frac{(e+f x)^3 \text{csch}^3(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^3*Csch[c + d*x]^3*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^4}{a^3 \left(a^2+b^2\right) d}-\frac{(e+f x)^3 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^4}{a^3 \left(a^2+b^2\right) d}+\frac{(e+f x)^3 \log \left(1+e^{2 (c+d x)}\right) b^4}{a^3 \left(a^2+b^2\right) d}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^4}{a^3 \left(a^2+b^2\right) d^2}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^4}{a^3 \left(a^2+b^2\right) d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) b^4}{2 a^3 \left(a^2+b^2\right) d^2}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^4}{a^3 \left(a^2+b^2\right) d^3}+\frac{6 f^2 (e+f x) \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^4}{a^3 \left(a^2+b^2\right) d^3}-\frac{3 f^2 (e+f x) \text{Li}_3\left(-e^{2 (c+d x)}\right) b^4}{2 a^3 \left(a^2+b^2\right) d^3}-\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^4}{a^3 \left(a^2+b^2\right) d^4}-\frac{6 f^3 \text{Li}_4\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^4}{a^3 \left(a^2+b^2\right) d^4}+\frac{3 f^3 \text{Li}_4\left(-e^{2 (c+d x)}\right) b^4}{4 a^3 \left(a^2+b^2\right) d^4}-\frac{2 (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d}+\frac{3 i f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{3 i f (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{6 i f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}+\frac{6 i f^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}+\frac{6 i f^3 \text{Li}_4\left(-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{Li}_4\left(i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^4}-\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{2 c+2 d x}\right) b^2}{a^3 d}-\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{2 c+2 d x}\right) b^2}{2 a^3 d^2}+\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{2 c+2 d x}\right) b^2}{2 a^3 d^2}+\frac{3 f^2 (e+f x) \text{Li}_3\left(-e^{2 c+2 d x}\right) b^2}{2 a^3 d^3}-\frac{3 f^2 (e+f x) \text{Li}_3\left(e^{2 c+2 d x}\right) b^2}{2 a^3 d^3}-\frac{3 f^3 \text{Li}_4\left(-e^{2 c+2 d x}\right) b^2}{4 a^3 d^4}+\frac{3 f^3 \text{Li}_4\left(e^{2 c+2 d x}\right) b^2}{4 a^3 d^4}+\frac{2 (e+f x)^3 \tan ^{-1}\left(e^{c+d x}\right) b}{a^2 d}+\frac{6 f (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right) b}{a^2 d^2}+\frac{(e+f x)^3 \text{csch}(c+d x) b}{a^2 d}+\frac{6 f^2 (e+f x) \text{Li}_2\left(-e^{c+d x}\right) b}{a^2 d^3}-\frac{3 i f (e+f x)^2 \text{Li}_2\left(-i e^{c+d x}\right) b}{a^2 d^2}+\frac{3 i f (e+f x)^2 \text{Li}_2\left(i e^{c+d x}\right) b}{a^2 d^2}-\frac{6 f^2 (e+f x) \text{Li}_2\left(e^{c+d x}\right) b}{a^2 d^3}-\frac{6 f^3 \text{Li}_3\left(-e^{c+d x}\right) b}{a^2 d^4}+\frac{6 i f^2 (e+f x) \text{Li}_3\left(-i e^{c+d x}\right) b}{a^2 d^3}-\frac{6 i f^2 (e+f x) \text{Li}_3\left(i e^{c+d x}\right) b}{a^2 d^3}+\frac{6 f^3 \text{Li}_3\left(e^{c+d x}\right) b}{a^2 d^4}-\frac{6 i f^3 \text{Li}_4\left(-i e^{c+d x}\right) b}{a^2 d^4}+\frac{6 i f^3 \text{Li}_4\left(i e^{c+d x}\right) b}{a^2 d^4}+\frac{(e+f x)^3}{2 a d}-\frac{3 f (e+f x)^2}{2 a d^2}-\frac{(e+f x)^3 \coth ^2(c+d x)}{2 a d}+\frac{2 (e+f x)^3 \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}-\frac{3 f (e+f x)^2 \coth (c+d x)}{2 a d^2}+\frac{3 f^2 (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d^3}+\frac{3 f^3 \text{Li}_2\left(e^{2 (c+d x)}\right)}{2 a d^4}+\frac{3 f (e+f x)^2 \text{Li}_2\left(-e^{2 c+2 d x}\right)}{2 a d^2}-\frac{3 f (e+f x)^2 \text{Li}_2\left(e^{2 c+2 d x}\right)}{2 a d^2}-\frac{3 f^2 (e+f x) \text{Li}_3\left(-e^{2 c+2 d x}\right)}{2 a d^3}+\frac{3 f^2 (e+f x) \text{Li}_3\left(e^{2 c+2 d x}\right)}{2 a d^3}+\frac{3 f^3 \text{Li}_4\left(-e^{2 c+2 d x}\right)}{4 a d^4}-\frac{3 f^3 \text{Li}_4\left(e^{2 c+2 d x}\right)}{4 a d^4}",1,"Result too large to show","B",0
492,1,3044,1219,39.3443967,"\int \frac{(e+f x)^2 \text{csch}^3(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]^3*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^4}{a^3 \left(a^2+b^2\right) d}-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^4}{a^3 \left(a^2+b^2\right) d}+\frac{(e+f x)^2 \log \left(1+e^{2 (c+d x)}\right) b^4}{a^3 \left(a^2+b^2\right) d}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^4}{a^3 \left(a^2+b^2\right) d^2}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^4}{a^3 \left(a^2+b^2\right) d^2}+\frac{f (e+f x) \text{Li}_2\left(-e^{2 (c+d x)}\right) b^4}{a^3 \left(a^2+b^2\right) d^2}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^4}{a^3 \left(a^2+b^2\right) d^3}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^4}{a^3 \left(a^2+b^2\right) d^3}-\frac{f^2 \text{Li}_3\left(-e^{2 (c+d x)}\right) b^4}{2 a^3 \left(a^2+b^2\right) d^3}-\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d}+\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{2 c+2 d x}\right) b^2}{a^3 d}-\frac{f (e+f x) \text{Li}_2\left(-e^{2 c+2 d x}\right) b^2}{a^3 d^2}+\frac{f (e+f x) \text{Li}_2\left(e^{2 c+2 d x}\right) b^2}{a^3 d^2}+\frac{f^2 \text{Li}_3\left(-e^{2 c+2 d x}\right) b^2}{2 a^3 d^3}-\frac{f^2 \text{Li}_3\left(e^{2 c+2 d x}\right) b^2}{2 a^3 d^3}+\frac{2 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right) b}{a^2 d}+\frac{4 f (e+f x) \tanh ^{-1}\left(e^{c+d x}\right) b}{a^2 d^2}+\frac{(e+f x)^2 \text{csch}(c+d x) b}{a^2 d}+\frac{2 f^2 \text{Li}_2\left(-e^{c+d x}\right) b}{a^2 d^3}-\frac{2 i f (e+f x) \text{Li}_2\left(-i e^{c+d x}\right) b}{a^2 d^2}+\frac{2 i f (e+f x) \text{Li}_2\left(i e^{c+d x}\right) b}{a^2 d^2}-\frac{2 f^2 \text{Li}_2\left(e^{c+d x}\right) b}{a^2 d^3}+\frac{2 i f^2 \text{Li}_3\left(-i e^{c+d x}\right) b}{a^2 d^3}-\frac{2 i f^2 \text{Li}_3\left(i e^{c+d x}\right) b}{a^2 d^3}+\frac{f^2 x^2}{2 a d}-\frac{(e+f x)^2 \coth ^2(c+d x)}{2 a d}+\frac{e f x}{a d}+\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}-\frac{f (e+f x) \coth (c+d x)}{a d^2}+\frac{f^2 \log (\sinh (c+d x))}{a d^3}+\frac{f (e+f x) \text{Li}_2\left(-e^{2 c+2 d x}\right)}{a d^2}-\frac{f (e+f x) \text{Li}_2\left(e^{2 c+2 d x}\right)}{a d^2}-\frac{f^2 \text{Li}_3\left(-e^{2 c+2 d x}\right)}{2 a d^3}+\frac{f^2 \text{Li}_3\left(e^{2 c+2 d x}\right)}{2 a d^3}",1,"((-e^2 - 2*e*f*x - f^2*x^2)*Csch[c/2 + (d*x)/2]^2)/(8*a*d) + (-12*a*d^3*e^2*E^(2*c)*x - 12*a*d^3*e*E^(2*c)*f*x^2 - 4*a*d^3*E^(2*c)*f^2*x^3 + 12*b*d^2*e^2*ArcTan[E^(c + d*x)] + 12*b*d^2*e^2*E^(2*c)*ArcTan[E^(c + d*x)] + (12*I)*b*d^2*e*f*x*Log[1 - I*E^(c + d*x)] + (12*I)*b*d^2*e*E^(2*c)*f*x*Log[1 - I*E^(c + d*x)] + (6*I)*b*d^2*f^2*x^2*Log[1 - I*E^(c + d*x)] + (6*I)*b*d^2*E^(2*c)*f^2*x^2*Log[1 - I*E^(c + d*x)] - (12*I)*b*d^2*e*f*x*Log[1 + I*E^(c + d*x)] - (12*I)*b*d^2*e*E^(2*c)*f*x*Log[1 + I*E^(c + d*x)] - (6*I)*b*d^2*f^2*x^2*Log[1 + I*E^(c + d*x)] - (6*I)*b*d^2*E^(2*c)*f^2*x^2*Log[1 + I*E^(c + d*x)] + 6*a*d^2*e^2*Log[1 + E^(2*(c + d*x))] + 6*a*d^2*e^2*E^(2*c)*Log[1 + E^(2*(c + d*x))] + 12*a*d^2*e*f*x*Log[1 + E^(2*(c + d*x))] + 12*a*d^2*e*E^(2*c)*f*x*Log[1 + E^(2*(c + d*x))] + 6*a*d^2*f^2*x^2*Log[1 + E^(2*(c + d*x))] + 6*a*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(2*(c + d*x))] - (12*I)*b*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)] + (12*I)*b*d*(1 + E^(2*c))*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)] + 6*a*d*e*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a*d*e*E^(2*c)*f*PolyLog[2, -E^(2*(c + d*x))] + 6*a*d*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + 6*a*d*E^(2*c)*f^2*x*PolyLog[2, -E^(2*(c + d*x))] + (12*I)*b*f^2*PolyLog[3, (-I)*E^(c + d*x)] + (12*I)*b*E^(2*c)*f^2*PolyLog[3, (-I)*E^(c + d*x)] - (12*I)*b*f^2*PolyLog[3, I*E^(c + d*x)] - (12*I)*b*E^(2*c)*f^2*PolyLog[3, I*E^(c + d*x)] - 3*a*f^2*PolyLog[3, -E^(2*(c + d*x))] - 3*a*E^(2*c)*f^2*PolyLog[3, -E^(2*(c + d*x))])/(6*(a^2 + b^2)*d^3*(1 + E^(2*c))) - (-12*a^2*d^3*e^2*E^(2*c)*x + 12*b^2*d^3*e^2*E^(2*c)*x + 12*a^2*d*E^(2*c)*f^2*x - 12*a^2*d^3*e*E^(2*c)*f*x^2 + 12*b^2*d^3*e*E^(2*c)*f*x^2 - 4*a^2*d^3*E^(2*c)*f^2*x^3 + 4*b^2*d^3*E^(2*c)*f^2*x^3 + 24*a*b*d*e*f*ArcTanh[E^(c + d*x)] - 24*a*b*d*e*E^(2*c)*f*ArcTanh[E^(c + d*x)] - 12*a*b*d*f^2*x*Log[1 - E^(c + d*x)] + 12*a*b*d*E^(2*c)*f^2*x*Log[1 - E^(c + d*x)] + 12*a*b*d*f^2*x*Log[1 + E^(c + d*x)] - 12*a*b*d*E^(2*c)*f^2*x*Log[1 + E^(c + d*x)] - 6*a^2*d^2*e^2*Log[1 - E^(2*(c + d*x))] + 6*b^2*d^2*e^2*Log[1 - E^(2*(c + d*x))] + 6*a^2*d^2*e^2*E^(2*c)*Log[1 - E^(2*(c + d*x))] - 6*b^2*d^2*e^2*E^(2*c)*Log[1 - E^(2*(c + d*x))] + 6*a^2*f^2*Log[1 - E^(2*(c + d*x))] - 6*a^2*E^(2*c)*f^2*Log[1 - E^(2*(c + d*x))] - 12*a^2*d^2*e*f*x*Log[1 - E^(2*(c + d*x))] + 12*b^2*d^2*e*f*x*Log[1 - E^(2*(c + d*x))] + 12*a^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(2*(c + d*x))] - 12*b^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(2*(c + d*x))] - 6*a^2*d^2*f^2*x^2*Log[1 - E^(2*(c + d*x))] + 6*b^2*d^2*f^2*x^2*Log[1 - E^(2*(c + d*x))] + 6*a^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(2*(c + d*x))] - 6*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(2*(c + d*x))] - 12*a*b*(-1 + E^(2*c))*f^2*PolyLog[2, -E^(c + d*x)] + 12*a*b*(-1 + E^(2*c))*f^2*PolyLog[2, E^(c + d*x)] - 6*a^2*d*e*f*PolyLog[2, E^(2*(c + d*x))] + 6*b^2*d*e*f*PolyLog[2, E^(2*(c + d*x))] + 6*a^2*d*e*E^(2*c)*f*PolyLog[2, E^(2*(c + d*x))] - 6*b^2*d*e*E^(2*c)*f*PolyLog[2, E^(2*(c + d*x))] - 6*a^2*d*f^2*x*PolyLog[2, E^(2*(c + d*x))] + 6*b^2*d*f^2*x*PolyLog[2, E^(2*(c + d*x))] + 6*a^2*d*E^(2*c)*f^2*x*PolyLog[2, E^(2*(c + d*x))] - 6*b^2*d*E^(2*c)*f^2*x*PolyLog[2, E^(2*(c + d*x))] + 3*a^2*f^2*PolyLog[3, E^(2*(c + d*x))] - 3*b^2*f^2*PolyLog[3, E^(2*(c + d*x))] - 3*a^2*E^(2*c)*f^2*PolyLog[3, E^(2*(c + d*x))] + 3*b^2*E^(2*c)*f^2*PolyLog[3, E^(2*(c + d*x))])/(6*a^3*d^3*(-1 + E^(2*c))) + (b^4*(6*d^3*e^2*E^(2*c)*x + 6*d^3*e*E^(2*c)*f*x^2 + 2*d^3*E^(2*c)*f^2*x^3 + 3*d^2*e^2*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] - 3*d^2*e^2*E^(2*c)*Log[b - 2*a*E^(c + d*x) - b*E^(2*(c + d*x))] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)])] + 6*d^2*e*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d^2*e*E^(2*c)*f*x*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] + 3*d^2*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 3*d^2*E^(2*c)*f^2*x^2*Log[1 + (b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)])] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c - Sqrt[(a^2 + b^2)*E^(2*c)]))] - 6*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))] + 6*E^(2*c)*f^2*PolyLog[3, -((b*E^(2*c + d*x))/(a*E^c + Sqrt[(a^2 + b^2)*E^(2*c)]))]))/(3*a^3*(a^2 + b^2)*d^3*(-1 + E^(2*c))) + ((-3*a^3*d*e^2*x - 3*a^3*d*e*f*x^2 - a^3*d*f^2*x^3 + 3*a^2*b*e^2*Cosh[c] + 3*b^3*e^2*Cosh[c] + 6*a^2*b*e*f*x*Cosh[c] + 6*b^3*e*f*x*Cosh[c] + 3*a^2*b*f^2*x^2*Cosh[c] + 3*b^3*f^2*x^2*Cosh[c])*Csch[c/2]*Sech[c/2]*Sech[c])/(6*a^2*(a^2 + b^2)*d) + ((e^2 + 2*e*f*x + f^2*x^2)*Sech[c/2 + (d*x)/2]^2)/(8*a*d) + (Sech[c/2]*Sech[c/2 + (d*x)/2]*(-(b*d*e^2*Sinh[(d*x)/2]) - a*e*f*Sinh[(d*x)/2] - 2*b*d*e*f*x*Sinh[(d*x)/2] - a*f^2*x*Sinh[(d*x)/2] - b*d*f^2*x^2*Sinh[(d*x)/2]))/(2*a^2*d^2) + (Csch[c/2]*Csch[c/2 + (d*x)/2]*(-(b*d*e^2*Sinh[(d*x)/2]) + a*e*f*Sinh[(d*x)/2] - 2*b*d*e*f*x*Sinh[(d*x)/2] + a*f^2*x*Sinh[(d*x)/2] - b*d*f^2*x^2*Sinh[(d*x)/2]))/(2*a^2*d^2)","B",0
493,1,913,762,7.7347749,"\int \frac{(e+f x) \text{csch}^3(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]^3*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{\left(-\frac{1}{2} f (c+d x)^2+f \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) (c+d x)+f \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) (c+d x)+d e \log (a+b \sinh (c+d x))-c f \log (a+b \sinh (c+d x))+f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) b^4}{a^3 \left(a^2+b^2\right) d^2}+\frac{e \log (\sinh (c+d x)) b^2}{a^3 d}-\frac{c f \log (\sinh (c+d x)) b^2}{a^3 d^2}-\frac{i f \left(i (c+d x) \log \left(1-e^{-2 (c+d x)}\right)-\frac{1}{2} i \left(\text{Li}_2\left(e^{-2 (c+d x)}\right)-(c+d x)^2\right)\right) b^2}{a^3 d^2}-\frac{f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) b}{a^2 d^2}+\frac{(-d e+c f-f (c+d x)) \text{csch}^2\left(\frac{1}{2} (c+d x)\right)}{8 a d^2}+\frac{(d e-c f+f (c+d x)) \text{sech}^2\left(\frac{1}{2} (c+d x)\right)}{8 a d^2}+\frac{\left(2 b d e \cosh \left(\frac{1}{2} (c+d x)\right)-a f \cosh \left(\frac{1}{2} (c+d x)\right)-2 b c f \cosh \left(\frac{1}{2} (c+d x)\right)+2 b f (c+d x) \cosh \left(\frac{1}{2} (c+d x)\right)\right) \text{csch}\left(\frac{1}{2} (c+d x)\right)}{4 a^2 d^2}-\frac{e \log (\sinh (c+d x))}{a d}+\frac{c f \log (\sinh (c+d x))}{a d^2}+\frac{i f \left(i (c+d x) \log \left(1-e^{-2 (c+d x)}\right)-\frac{1}{2} i \left(\text{Li}_2\left(e^{-2 (c+d x)}\right)-(c+d x)^2\right)\right)}{a d^2}+\frac{-\frac{1}{2} a f (c+d x)^2-a d e (c+d x)+a c f (c+d x)+2 b f \tan ^{-1}(\cosh (c+d x)+\sinh (c+d x)) (c+d x)+a f \log (\cosh (2 (c+d x))+\sinh (2 (c+d x))+1) (c+d x)+2 b d e \tan ^{-1}(\cosh (c+d x)+\sinh (c+d x))-2 b c f \tan ^{-1}(\cosh (c+d x)+\sinh (c+d x))+a d e \log (\cosh (2 (c+d x))+\sinh (2 (c+d x))+1)-a c f \log (\cosh (2 (c+d x))+\sinh (2 (c+d x))+1)-i b f \text{Li}_2(-i (\cosh (c+d x)+\sinh (c+d x)))+i b f \text{Li}_2(i (\cosh (c+d x)+\sinh (c+d x)))+\frac{1}{2} a f \text{Li}_2(-\cosh (2 (c+d x))-\sinh (2 (c+d x)))}{\left(a^2+b^2\right) d^2}+\frac{\text{sech}\left(\frac{1}{2} (c+d x)\right) \left(-2 b d e \sinh \left(\frac{1}{2} (c+d x)\right)-a f \sinh \left(\frac{1}{2} (c+d x)\right)+2 b c f \sinh \left(\frac{1}{2} (c+d x)\right)-2 b f (c+d x) \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{4 a^2 d^2}","-\frac{b^2 f \text{Li}_2\left(-e^{2 c+2 d x}\right)}{2 a^3 d^2}+\frac{b^2 f \text{Li}_2\left(e^{2 c+2 d x}\right)}{2 a^3 d^2}-\frac{2 b^2 (e+f x) \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a^3 d}+\frac{i b^3 f \text{Li}_2\left(-i e^{c+d x}\right)}{a^2 d^2 \left(a^2+b^2\right)}-\frac{i b^3 f \text{Li}_2\left(i e^{c+d x}\right)}{a^2 d^2 \left(a^2+b^2\right)}-\frac{2 b^3 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{a^2 d \left(a^2+b^2\right)}-\frac{i b f \text{Li}_2\left(-i e^{c+d x}\right)}{a^2 d^2}+\frac{i b f \text{Li}_2\left(i e^{c+d x}\right)}{a^2 d^2}+\frac{b f \tanh ^{-1}(\cosh (c+d x))}{a^2 d^2}+\frac{b (e+f x) \text{csch}(c+d x)}{a^2 d}+\frac{b (e+f x) \tan ^{-1}(\sinh (c+d x))}{a^2 d}+\frac{2 b f x \tan ^{-1}\left(e^{c+d x}\right)}{a^2 d}-\frac{b f x \tan ^{-1}(\sinh (c+d x))}{a^2 d}-\frac{b^4 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2 \left(a^2+b^2\right)}-\frac{b^4 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2 \left(a^2+b^2\right)}+\frac{b^4 f \text{Li}_2\left(-e^{2 (c+d x)}\right)}{2 a^3 d^2 \left(a^2+b^2\right)}-\frac{b^4 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d \left(a^2+b^2\right)}-\frac{b^4 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d \left(a^2+b^2\right)}+\frac{b^4 (e+f x) \log \left(e^{2 (c+d x)}+1\right)}{a^3 d \left(a^2+b^2\right)}+\frac{f \text{Li}_2\left(-e^{2 c+2 d x}\right)}{2 a d^2}-\frac{f \text{Li}_2\left(e^{2 c+2 d x}\right)}{2 a d^2}-\frac{f \coth (c+d x)}{2 a d^2}-\frac{(e+f x) \coth ^2(c+d x)}{2 a d}-\frac{(e+f x) \log (\tanh (c+d x))}{a d}+\frac{2 f x \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}+\frac{f x \log (\tanh (c+d x))}{a d}+\frac{f x}{2 a d}",1,"((2*b*d*e*Cosh[(c + d*x)/2] - a*f*Cosh[(c + d*x)/2] - 2*b*c*f*Cosh[(c + d*x)/2] + 2*b*f*(c + d*x)*Cosh[(c + d*x)/2])*Csch[(c + d*x)/2])/(4*a^2*d^2) + ((-(d*e) + c*f - f*(c + d*x))*Csch[(c + d*x)/2]^2)/(8*a*d^2) - (e*Log[Sinh[c + d*x]])/(a*d) + (b^2*e*Log[Sinh[c + d*x]])/(a^3*d) + (c*f*Log[Sinh[c + d*x]])/(a*d^2) - (b^2*c*f*Log[Sinh[c + d*x]])/(a^3*d^2) - (b*f*Log[Tanh[(c + d*x)/2]])/(a^2*d^2) + (I*f*(I*(c + d*x)*Log[1 - E^(-2*(c + d*x))] - (I/2)*(-(c + d*x)^2 + PolyLog[2, E^(-2*(c + d*x))])))/(a*d^2) - (I*b^2*f*(I*(c + d*x)*Log[1 - E^(-2*(c + d*x))] - (I/2)*(-(c + d*x)^2 + PolyLog[2, E^(-2*(c + d*x))])))/(a^3*d^2) - (b^4*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^3*(a^2 + b^2)*d^2) + (-(a*d*e*(c + d*x)) + a*c*f*(c + d*x) - (a*f*(c + d*x)^2)/2 + 2*b*d*e*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] - 2*b*c*f*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] + 2*b*f*(c + d*x)*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] + a*d*e*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] - a*c*f*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] + a*f*(c + d*x)*Log[1 + Cosh[2*(c + d*x)] + Sinh[2*(c + d*x)]] - I*b*f*PolyLog[2, (-I)*(Cosh[c + d*x] + Sinh[c + d*x])] + I*b*f*PolyLog[2, I*(Cosh[c + d*x] + Sinh[c + d*x])] + (a*f*PolyLog[2, -Cosh[2*(c + d*x)] - Sinh[2*(c + d*x)]])/2)/((a^2 + b^2)*d^2) + ((d*e - c*f + f*(c + d*x))*Sech[(c + d*x)/2]^2)/(8*a*d^2) + (Sech[(c + d*x)/2]*(-2*b*d*e*Sinh[(c + d*x)/2] - a*f*Sinh[(c + d*x)/2] + 2*b*c*f*Sinh[(c + d*x)/2] - 2*b*f*(c + d*x)*Sinh[(c + d*x)/2]))/(4*a^2*d^2)","A",0
494,1,164,130,0.364375,"\int \frac{\text{csch}^3(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Csch[c + d*x]^3*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{-\frac{2 (a-b) (a+b) \log (\sinh (c+d x))}{a^3}+\frac{\left(a-\sqrt{-b^2}\right) \log \left(\sqrt{-b^2}-b \sinh (c+d x)\right)}{a^2+b^2}+\frac{\left(a+\sqrt{-b^2}\right) \log \left(\sqrt{-b^2}+b \sinh (c+d x)\right)}{a^2+b^2}+\frac{2 b \text{csch}(c+d x)}{a^2}-\frac{2 b^4 \log (a+b \sinh (c+d x))}{a^3 \left(a^2+b^2\right)}-\frac{\text{csch}^2(c+d x)}{a}}{2 d}","\frac{b \tan ^{-1}(\sinh (c+d x))}{d \left(a^2+b^2\right)}+\frac{a \log (\cosh (c+d x))}{d \left(a^2+b^2\right)}+\frac{b \text{csch}(c+d x)}{a^2 d}-\frac{\left(a^2-b^2\right) \log (\sinh (c+d x))}{a^3 d}-\frac{b^4 \log (a+b \sinh (c+d x))}{a^3 d \left(a^2+b^2\right)}-\frac{\text{csch}^2(c+d x)}{2 a d}",1,"((2*b*Csch[c + d*x])/a^2 - Csch[c + d*x]^2/a - (2*(a - b)*(a + b)*Log[Sinh[c + d*x]])/a^3 + ((a - Sqrt[-b^2])*Log[Sqrt[-b^2] - b*Sinh[c + d*x]])/(a^2 + b^2) - (2*b^4*Log[a + b*Sinh[c + d*x]])/(a^3*(a^2 + b^2)) + ((a + Sqrt[-b^2])*Log[Sqrt[-b^2] + b*Sinh[c + d*x]])/(a^2 + b^2))/(2*d)","A",1
495,0,0,37,158.1034846,"\int \frac{\text{csch}^3(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Csch[c + d*x]^3*Sech[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}^3(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}^3(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Integrate[(Csch[c + d*x]^3*Sech[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",-1
496,1,2574,1245,27.0603147,"\int \frac{(e+f x)^2 \text{csch}^3(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)^2*Csch[c + d*x]^3*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^5}{a^3 \left(a^2+b^2\right)^{3/2} d}+\frac{(e+f x)^2 \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^5}{a^3 \left(a^2+b^2\right)^{3/2} d}-\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^5}{a^3 \left(a^2+b^2\right)^{3/2} d^2}+\frac{2 f (e+f x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^5}{a^3 \left(a^2+b^2\right)^{3/2} d^2}+\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^5}{a^3 \left(a^2+b^2\right)^{3/2} d^3}-\frac{2 f^2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^5}{a^3 \left(a^2+b^2\right)^{3/2} d^3}+\frac{4 f (e+f x) \tan ^{-1}\left(e^{c+d x}\right) b^4}{a^3 \left(a^2+b^2\right) d^2}-\frac{2 i f^2 \text{Li}_2\left(-i e^{c+d x}\right) b^4}{a^3 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{Li}_2\left(i e^{c+d x}\right) b^4}{a^3 \left(a^2+b^2\right) d^3}-\frac{(e+f x)^2 \text{sech}(c+d x) b^4}{a^3 \left(a^2+b^2\right) d}-\frac{(e+f x)^2 b^3}{a^2 \left(a^2+b^2\right) d}+\frac{2 f (e+f x) \log \left(1+e^{2 (c+d x)}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}+\frac{f^2 \text{Li}_2\left(-e^{2 (c+d x)}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}-\frac{(e+f x)^2 \tanh (c+d x) b^3}{a^2 \left(a^2+b^2\right) d}-\frac{4 f (e+f x) \tan ^{-1}\left(e^{c+d x}\right) b^2}{a^3 d^2}-\frac{2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right) b^2}{a^3 d}-\frac{2 f (e+f x) \text{Li}_2\left(-e^{c+d x}\right) b^2}{a^3 d^2}+\frac{2 i f^2 \text{Li}_2\left(-i e^{c+d x}\right) b^2}{a^3 d^3}-\frac{2 i f^2 \text{Li}_2\left(i e^{c+d x}\right) b^2}{a^3 d^3}+\frac{2 f (e+f x) \text{Li}_2\left(e^{c+d x}\right) b^2}{a^3 d^2}+\frac{2 f^2 \text{Li}_3\left(-e^{c+d x}\right) b^2}{a^3 d^3}-\frac{2 f^2 \text{Li}_3\left(e^{c+d x}\right) b^2}{a^3 d^3}+\frac{(e+f x)^2 \text{sech}(c+d x) b^2}{a^3 d}+\frac{2 (e+f x)^2 b}{a^2 d}+\frac{2 (e+f x)^2 \coth (2 c+2 d x) b}{a^2 d}-\frac{2 f (e+f x) \log \left(1-e^{4 (c+d x)}\right) b}{a^2 d^2}-\frac{f^2 \text{Li}_2\left(e^{4 (c+d x)}\right) b}{2 a^2 d^3}+\frac{4 f^2 x \tan ^{-1}\left(e^{c+d x}\right)}{a d^2}+\frac{2 e f \tan ^{-1}(\sinh (c+d x))}{a d^2}+\frac{3 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{f^2 \tanh ^{-1}(\cosh (c+d x))}{a d^3}-\frac{e f \text{csch}(c+d x)}{a d^2}-\frac{f^2 x \text{csch}(c+d x)}{a d^2}+\frac{3 f (e+f x) \text{Li}_2\left(-e^{c+d x}\right)}{a d^2}-\frac{2 i f^2 \text{Li}_2\left(-i e^{c+d x}\right)}{a d^3}+\frac{2 i f^2 \text{Li}_2\left(i e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x) \text{Li}_2\left(e^{c+d x}\right)}{a d^2}-\frac{3 f^2 \text{Li}_3\left(-e^{c+d x}\right)}{a d^3}+\frac{3 f^2 \text{Li}_3\left(e^{c+d x}\right)}{a d^3}-\frac{3 (e+f x)^2 \text{sech}(c+d x)}{2 a d}-\frac{(e+f x)^2 \text{csch}^2(c+d x) \text{sech}(c+d x)}{2 a d}",1,"(8*a*b*d^2*e*E^(2*c)*f*x + 4*a*b*d^2*E^(2*c)*f^2*x^2 - 6*a^2*d^2*e^2*ArcTanh[E^(c + d*x)] + 4*b^2*d^2*e^2*ArcTanh[E^(c + d*x)] + 6*a^2*d^2*e^2*E^(2*c)*ArcTanh[E^(c + d*x)] - 4*b^2*d^2*e^2*E^(2*c)*ArcTanh[E^(c + d*x)] + 4*a^2*f^2*ArcTanh[E^(c + d*x)] - 4*a^2*E^(2*c)*f^2*ArcTanh[E^(c + d*x)] + 6*a^2*d^2*e*f*x*Log[1 - E^(c + d*x)] - 4*b^2*d^2*e*f*x*Log[1 - E^(c + d*x)] - 6*a^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(c + d*x)] + 4*b^2*d^2*e*E^(2*c)*f*x*Log[1 - E^(c + d*x)] + 3*a^2*d^2*f^2*x^2*Log[1 - E^(c + d*x)] - 2*b^2*d^2*f^2*x^2*Log[1 - E^(c + d*x)] - 3*a^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] + 2*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 - E^(c + d*x)] - 6*a^2*d^2*e*f*x*Log[1 + E^(c + d*x)] + 4*b^2*d^2*e*f*x*Log[1 + E^(c + d*x)] + 6*a^2*d^2*e*E^(2*c)*f*x*Log[1 + E^(c + d*x)] - 4*b^2*d^2*e*E^(2*c)*f*x*Log[1 + E^(c + d*x)] - 3*a^2*d^2*f^2*x^2*Log[1 + E^(c + d*x)] + 2*b^2*d^2*f^2*x^2*Log[1 + E^(c + d*x)] + 3*a^2*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(c + d*x)] - 2*b^2*d^2*E^(2*c)*f^2*x^2*Log[1 + E^(c + d*x)] + 4*a*b*d*e*f*Log[1 - E^(2*(c + d*x))] - 4*a*b*d*e*E^(2*c)*f*Log[1 - E^(2*(c + d*x))] + 4*a*b*d*f^2*x*Log[1 - E^(2*(c + d*x))] - 4*a*b*d*E^(2*c)*f^2*x*Log[1 - E^(2*(c + d*x))] + 2*(3*a^2 - 2*b^2)*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, -E^(c + d*x)] - 2*(3*a^2 - 2*b^2)*d*(-1 + E^(2*c))*f*(e + f*x)*PolyLog[2, E^(c + d*x)] + 2*a*b*f^2*PolyLog[2, E^(2*(c + d*x))] - 2*a*b*E^(2*c)*f^2*PolyLog[2, E^(2*(c + d*x))] + 6*a^2*f^2*PolyLog[3, -E^(c + d*x)] - 4*b^2*f^2*PolyLog[3, -E^(c + d*x)] - 6*a^2*E^(2*c)*f^2*PolyLog[3, -E^(c + d*x)] + 4*b^2*E^(2*c)*f^2*PolyLog[3, -E^(c + d*x)] - 6*a^2*f^2*PolyLog[3, E^(c + d*x)] + 4*b^2*f^2*PolyLog[3, E^(c + d*x)] + 6*a^2*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)] - 4*b^2*E^(2*c)*f^2*PolyLog[3, E^(c + d*x)])/(2*a^3*d^3*(-1 + E^(2*c))) + (b^5*(2*d^2*e^2*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + 2*d^2*e*f*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d^2*f^2*x^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - 2*d*f*(e + f*x)*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + 2*d*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))] + 2*f^2*PolyLog[3, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - 2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^3*(a^2 + b^2)^(3/2)*d^3) - (2*b*e*f*Sech[c]*(Cosh[c]*Log[Cosh[c]*Cosh[d*x] + Sinh[c]*Sinh[d*x]] - d*x*Sinh[c]))/((a^2 + b^2)*d^2*(Cosh[c]^2 - Sinh[c]^2)) + (4*a*e*f*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]])/((a^2 + b^2)*d^2*Sqrt[Cosh[c]^2 - Sinh[c]^2]) - (b*f^2*Csch[c]*((d^2*x^2)/E^ArcTanh[Coth[c]] - (I*Coth[c]*(-(d*x*(-Pi + (2*I)*ArcTanh[Coth[c]])) - Pi*Log[1 + E^(2*d*x)] - 2*(I*d*x + I*ArcTanh[Coth[c]])*Log[1 - E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))] + Pi*Log[Cosh[d*x]] + (2*I)*ArcTanh[Coth[c]]*Log[I*Sinh[d*x + ArcTanh[Coth[c]]]] + I*PolyLog[2, E^((2*I)*(I*d*x + I*ArcTanh[Coth[c]]))]))/Sqrt[1 - Coth[c]^2])*Sech[c])/((a^2 + b^2)*d^3*Sqrt[Csch[c]^2*(-Cosh[c]^2 + Sinh[c]^2)]) + (2*a*f^2*(((-I)*Csch[c]*(I*(d*x + ArcTanh[Coth[c]])*(Log[1 - E^(-(d*x) - ArcTanh[Coth[c]])] - Log[1 + E^(-(d*x) - ArcTanh[Coth[c]])]) + I*(PolyLog[2, -E^(-(d*x) - ArcTanh[Coth[c]])] - PolyLog[2, E^(-(d*x) - ArcTanh[Coth[c]])])))/Sqrt[1 - Coth[c]^2] - (2*ArcTan[(Sinh[c] + Cosh[c]*Tanh[(d*x)/2])/Sqrt[Cosh[c]^2 - Sinh[c]^2]]*ArcTanh[Coth[c]])/Sqrt[Cosh[c]^2 - Sinh[c]^2]))/((a^2 + b^2)*d^3) + (Csch[c]*Csch[c + d*x]^2*Sech[c]*Sech[c + d*x]*(2*a^3*e*f*Cosh[2*d*x] + 2*a*b^2*e*f*Cosh[2*d*x] + 2*a^3*f^2*x*Cosh[2*d*x] + 2*a*b^2*f^2*x*Cosh[2*d*x] + 4*a^2*b*d*e^2*Cosh[c - d*x] + 8*a^2*b*d*e*f*x*Cosh[c - d*x] + 4*a^2*b*d*f^2*x^2*Cosh[c - d*x] + 2*b^3*d*e^2*Cosh[c + d*x] + 4*b^3*d*e*f*x*Cosh[c + d*x] + 2*b^3*d*f^2*x^2*Cosh[c + d*x] + 2*b^3*d*e^2*Cosh[3*c + d*x] + 4*b^3*d*e*f*x*Cosh[3*c + d*x] + 2*b^3*d*f^2*x^2*Cosh[3*c + d*x] - 2*a^3*e*f*Cosh[4*c + 2*d*x] - 2*a*b^2*e*f*Cosh[4*c + 2*d*x] - 2*a^3*f^2*x*Cosh[4*c + 2*d*x] - 2*a*b^2*f^2*x*Cosh[4*c + 2*d*x] - 4*a^2*b*d*e^2*Cosh[c + 3*d*x] - 2*b^3*d*e^2*Cosh[c + 3*d*x] - 8*a^2*b*d*e*f*x*Cosh[c + 3*d*x] - 4*b^3*d*e*f*x*Cosh[c + 3*d*x] - 4*a^2*b*d*f^2*x^2*Cosh[c + 3*d*x] - 2*b^3*d*f^2*x^2*Cosh[c + 3*d*x] - 2*b^3*d*e^2*Cosh[3*c + 3*d*x] - 4*b^3*d*e*f*x*Cosh[3*c + 3*d*x] - 2*b^3*d*f^2*x^2*Cosh[3*c + 3*d*x] + 2*a^3*d*e^2*Sinh[2*c] - 2*a*b^2*d*e^2*Sinh[2*c] + 4*a^3*d*e*f*x*Sinh[2*c] - 4*a*b^2*d*e*f*x*Sinh[2*c] + 2*a^3*d*f^2*x^2*Sinh[2*c] - 2*a*b^2*d*f^2*x^2*Sinh[2*c] + 3*a^3*d*e^2*Sinh[2*d*x] + a*b^2*d*e^2*Sinh[2*d*x] + 6*a^3*d*e*f*x*Sinh[2*d*x] + 2*a*b^2*d*e*f*x*Sinh[2*d*x] + 3*a^3*d*f^2*x^2*Sinh[2*d*x] + a*b^2*d*f^2*x^2*Sinh[2*d*x] - 3*a^3*d*e^2*Sinh[4*c + 2*d*x] - a*b^2*d*e^2*Sinh[4*c + 2*d*x] - 6*a^3*d*e*f*x*Sinh[4*c + 2*d*x] - 2*a*b^2*d*e*f*x*Sinh[4*c + 2*d*x] - 3*a^3*d*f^2*x^2*Sinh[4*c + 2*d*x] - a*b^2*d*f^2*x^2*Sinh[4*c + 2*d*x]))/(16*a^2*(a^2 + b^2)*d^2)","B",0
497,1,863,699,8.4033757,"\int \frac{(e+f x) \text{csch}^3(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]^3*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(2 d e \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-2 c f \tanh ^{-1}\left(\frac{a+b e^{c+d x}}{\sqrt{a^2+b^2}}\right)-f (c+d x) \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right)+f (c+d x) \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right)-f \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)+f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)\right) b^5}{a^3 \left(a^2+b^2\right)^{3/2} d^2}+\frac{e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) b^2}{a^3 d}-\frac{c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right) b^2}{a^3 d^2}-\frac{i f \left(i (c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(1+e^{-c-d x}\right)\right)+i \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)\right)\right) b^2}{a^3 d^2}-\frac{f \log (\cosh (c+d x)) b}{\left(a^2+b^2\right) d^2}-\frac{f \log (\sinh (c+d x)) b}{a^2 d^2}+\frac{(-d e+c f-f (c+d x)) \text{csch}^2\left(\frac{1}{2} (c+d x)\right)}{8 a d^2}+\frac{(-d e+c f-f (c+d x)) \text{sech}^2\left(\frac{1}{2} (c+d x)\right)}{8 a d^2}+\frac{2 a f \tan ^{-1}\left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{d \left(d a^2+b^2 d\right)}+\frac{\left(2 b d e \cosh \left(\frac{1}{2} (c+d x)\right)-a f \cosh \left(\frac{1}{2} (c+d x)\right)-2 b c f \cosh \left(\frac{1}{2} (c+d x)\right)+2 b f (c+d x) \cosh \left(\frac{1}{2} (c+d x)\right)\right) \text{csch}\left(\frac{1}{2} (c+d x)\right)}{4 a^2 d^2}-\frac{3 e \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a d}+\frac{3 c f \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{2 a d^2}+\frac{3 i f \left(i (c+d x) \left(\log \left(1-e^{-c-d x}\right)-\log \left(1+e^{-c-d x}\right)\right)+i \left(\text{Li}_2\left(-e^{-c-d x}\right)-\text{Li}_2\left(e^{-c-d x}\right)\right)\right)}{2 a d^2}+\frac{\text{sech}\left(\frac{1}{2} (c+d x)\right) \left(2 b d e \sinh \left(\frac{1}{2} (c+d x)\right)+a f \sinh \left(\frac{1}{2} (c+d x)\right)-2 b c f \sinh \left(\frac{1}{2} (c+d x)\right)+2 b f (c+d x) \sinh \left(\frac{1}{2} (c+d x)\right)\right)}{4 a^2 d^2}+\frac{\text{sech}(c+d x) (-a d e+b d \sinh (c+d x) e+a c f-a f (c+d x)-b c f \sinh (c+d x)+b f (c+d x) \sinh (c+d x))}{\left(a^2+b^2\right) d^2}","-\frac{b^2 f \text{Li}_2\left(-e^{c+d x}\right)}{a^3 d^2}+\frac{b^2 f \text{Li}_2\left(e^{c+d x}\right)}{a^3 d^2}-\frac{b^2 f \tan ^{-1}(\sinh (c+d x))}{a^3 d^2}+\frac{b^2 (e+f x) \text{sech}(c+d x)}{a^3 d}-\frac{b^2 (e+f x) \tanh ^{-1}(\cosh (c+d x))}{a^3 d}-\frac{2 b^2 f x \tanh ^{-1}\left(e^{c+d x}\right)}{a^3 d}+\frac{b^2 f x \tanh ^{-1}(\cosh (c+d x))}{a^3 d}+\frac{b^3 f \log (\cosh (c+d x))}{a^2 d^2 \left(a^2+b^2\right)}-\frac{b^3 (e+f x) \tanh (c+d x)}{a^2 d \left(a^2+b^2\right)}-\frac{b f \log (\sinh (2 c+2 d x))}{a^2 d^2}+\frac{2 b (e+f x) \coth (2 c+2 d x)}{a^2 d}-\frac{b^5 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2 \left(a^2+b^2\right)^{3/2}}+\frac{b^5 f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^2 \left(a^2+b^2\right)^{3/2}}-\frac{b^5 (e+f x) \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{a^3 d \left(a^2+b^2\right)^{3/2}}+\frac{b^5 (e+f x) \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{a^3 d \left(a^2+b^2\right)^{3/2}}+\frac{b^4 f \tan ^{-1}(\sinh (c+d x))}{a^3 d^2 \left(a^2+b^2\right)}-\frac{b^4 (e+f x) \text{sech}(c+d x)}{a^3 d \left(a^2+b^2\right)}+\frac{3 f \text{Li}_2\left(-e^{c+d x}\right)}{2 a d^2}-\frac{3 f \text{Li}_2\left(e^{c+d x}\right)}{2 a d^2}-\frac{f \text{csch}(c+d x)}{2 a d^2}+\frac{f \tan ^{-1}(\sinh (c+d x))}{a d^2}-\frac{3 (e+f x) \text{sech}(c+d x)}{2 a d}+\frac{3 (e+f x) \tanh ^{-1}(\cosh (c+d x))}{2 a d}-\frac{(e+f x) \text{csch}^2(c+d x) \text{sech}(c+d x)}{2 a d}+\frac{3 f x \tanh ^{-1}\left(e^{c+d x}\right)}{a d}-\frac{3 f x \tanh ^{-1}(\cosh (c+d x))}{2 a d}",1,"(2*a*f*ArcTan[Tanh[(c + d*x)/2]])/(d*(a^2*d + b^2*d)) + ((2*b*d*e*Cosh[(c + d*x)/2] - a*f*Cosh[(c + d*x)/2] - 2*b*c*f*Cosh[(c + d*x)/2] + 2*b*f*(c + d*x)*Cosh[(c + d*x)/2])*Csch[(c + d*x)/2])/(4*a^2*d^2) + ((-(d*e) + c*f - f*(c + d*x))*Csch[(c + d*x)/2]^2)/(8*a*d^2) - (b*f*Log[Cosh[c + d*x]])/((a^2 + b^2)*d^2) - (b*f*Log[Sinh[c + d*x]])/(a^2*d^2) - (3*e*Log[Tanh[(c + d*x)/2]])/(2*a*d) + (b^2*e*Log[Tanh[(c + d*x)/2]])/(a^3*d) + (3*c*f*Log[Tanh[(c + d*x)/2]])/(2*a*d^2) - (b^2*c*f*Log[Tanh[(c + d*x)/2]])/(a^3*d^2) + (((3*I)/2)*f*(I*(c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + I*(PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)])))/(a*d^2) - (I*b^2*f*(I*(c + d*x)*(Log[1 - E^(-c - d*x)] - Log[1 + E^(-c - d*x)]) + I*(PolyLog[2, -E^(-c - d*x)] - PolyLog[2, E^(-c - d*x)])))/(a^3*d^2) + (b^5*(2*d*e*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - 2*c*f*ArcTanh[(a + b*E^(c + d*x))/Sqrt[a^2 + b^2]] - f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] - f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(a^3*(a^2 + b^2)^(3/2)*d^2) + ((-(d*e) + c*f - f*(c + d*x))*Sech[(c + d*x)/2]^2)/(8*a*d^2) + (Sech[(c + d*x)/2]*(2*b*d*e*Sinh[(c + d*x)/2] + a*f*Sinh[(c + d*x)/2] - 2*b*c*f*Sinh[(c + d*x)/2] + 2*b*f*(c + d*x)*Sinh[(c + d*x)/2]))/(4*a^2*d^2) + (Sech[c + d*x]*(-(a*d*e) + a*c*f - a*f*(c + d*x) + b*d*e*Sinh[c + d*x] - b*c*f*Sinh[c + d*x] + b*f*(c + d*x)*Sinh[c + d*x]))/((a^2 + b^2)*d^2)","C",0
498,1,185,206,2.4304835,"\int \frac{\text{csch}^3(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Csch[c + d*x]^3*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\frac{8 \text{sech}(c+d x) (b \sinh (c+d x)-a)}{a^2+b^2}+\frac{4 b \tanh \left(\frac{1}{2} (c+d x)\right)}{a^2}+\frac{4 b \coth \left(\frac{1}{2} (c+d x)\right)}{a^2}-\frac{4 \left(3 a^2-2 b^2\right) \log \left(\tanh \left(\frac{1}{2} (c+d x)\right)\right)}{a^3}+\frac{16 b^5 \tan ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{-a^2-b^2}}\right)}{a^3 \left(-a^2-b^2\right)^{3/2}}-\frac{\text{csch}^2\left(\frac{1}{2} (c+d x)\right)}{a}-\frac{\text{sech}^2\left(\frac{1}{2} (c+d x)\right)}{a}}{8 d}","\frac{b^2 \text{sech}(c+d x)}{a^3 d}-\frac{b^2 \tanh ^{-1}(\cosh (c+d x))}{a^3 d}+\frac{b \tanh (c+d x)}{a^2 d}+\frac{b \coth (c+d x)}{a^2 d}+\frac{2 b^5 \tanh ^{-1}\left(\frac{b-a \tanh \left(\frac{1}{2} (c+d x)\right)}{\sqrt{a^2+b^2}}\right)}{a^3 d \left(a^2+b^2\right)^{3/2}}-\frac{b^3 \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a^3 d \left(a^2+b^2\right)}-\frac{3 \text{sech}(c+d x)}{2 a d}+\frac{3 \tanh ^{-1}(\cosh (c+d x))}{2 a d}-\frac{\text{csch}^2(c+d x) \text{sech}(c+d x)}{2 a d}",1,"((16*b^5*ArcTan[(b - a*Tanh[(c + d*x)/2])/Sqrt[-a^2 - b^2]])/(a^3*(-a^2 - b^2)^(3/2)) + (4*b*Coth[(c + d*x)/2])/a^2 - Csch[(c + d*x)/2]^2/a - (4*(3*a^2 - 2*b^2)*Log[Tanh[(c + d*x)/2]])/a^3 - Sech[(c + d*x)/2]^2/a + (8*Sech[c + d*x]*(-a + b*Sinh[c + d*x]))/(a^2 + b^2) + (4*b*Tanh[(c + d*x)/2])/a^2)/(8*d)","A",1
499,-1,0,39,180.0017386,"\int \frac{\text{csch}^3(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Csch[c + d*x]^3*Sech[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{csch}^3(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1
500,1,2870,1122,10.1041803,"\int \frac{(e+f x) \text{csch}^3(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[((e + f*x)*Csch[c + d*x]^3*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\text{Result too large to show}","-\frac{(e+f x) \log \left(\frac{e^{c+d x} b}{a-\sqrt{a^2+b^2}}+1\right) b^6}{a^3 \left(a^2+b^2\right)^2 d}-\frac{(e+f x) \log \left(\frac{e^{c+d x} b}{a+\sqrt{a^2+b^2}}+1\right) b^6}{a^3 \left(a^2+b^2\right)^2 d}+\frac{(e+f x) \log \left(1+e^{2 (c+d x)}\right) b^6}{a^3 \left(a^2+b^2\right)^2 d}-\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right) b^6}{a^3 \left(a^2+b^2\right)^2 d^2}-\frac{f \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right) b^6}{a^3 \left(a^2+b^2\right)^2 d^2}+\frac{f \text{Li}_2\left(-e^{2 (c+d x)}\right) b^6}{2 a^3 \left(a^2+b^2\right)^2 d^2}-\frac{2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right) b^5}{a^2 \left(a^2+b^2\right)^2 d}+\frac{i f \text{Li}_2\left(-i e^{c+d x}\right) b^5}{a^2 \left(a^2+b^2\right)^2 d^2}-\frac{i f \text{Li}_2\left(i e^{c+d x}\right) b^5}{a^2 \left(a^2+b^2\right)^2 d^2}-\frac{(e+f x) \text{sech}^2(c+d x) b^4}{2 a^3 \left(a^2+b^2\right) d}+\frac{f \tanh (c+d x) b^4}{2 a^3 \left(a^2+b^2\right) d^2}-\frac{(e+f x) \tan ^{-1}\left(e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d}+\frac{i f \text{Li}_2\left(-i e^{c+d x}\right) b^3}{2 a^2 \left(a^2+b^2\right) d^2}-\frac{i f \text{Li}_2\left(i e^{c+d x}\right) b^3}{2 a^2 \left(a^2+b^2\right) d^2}-\frac{f \text{sech}(c+d x) b^3}{2 a^2 \left(a^2+b^2\right) d^2}-\frac{(e+f x) \text{sech}(c+d x) \tanh (c+d x) b^3}{2 a^2 \left(a^2+b^2\right) d}-\frac{(e+f x) \tanh ^2(c+d x) b^2}{2 a^3 d}+\frac{f x b^2}{2 a^3 d}-\frac{2 f x \tanh ^{-1}\left(e^{2 c+2 d x}\right) b^2}{a^3 d}-\frac{f x \log (\tanh (c+d x)) b^2}{a^3 d}+\frac{(e+f x) \log (\tanh (c+d x)) b^2}{a^3 d}-\frac{f \text{Li}_2\left(-e^{2 c+2 d x}\right) b^2}{2 a^3 d^2}+\frac{f \text{Li}_2\left(e^{2 c+2 d x}\right) b^2}{2 a^3 d^2}-\frac{f \tanh (c+d x) b^2}{2 a^3 d^2}-\frac{(e+f x) \text{csch}(c+d x) \text{sech}^2(c+d x) b}{2 a^2 d}+\frac{3 f x \tan ^{-1}\left(e^{c+d x}\right) b}{a^2 d}-\frac{3 f x \tan ^{-1}(\sinh (c+d x)) b}{2 a^2 d}+\frac{3 (e+f x) \tan ^{-1}(\sinh (c+d x)) b}{2 a^2 d}+\frac{f \tanh ^{-1}(\cosh (c+d x)) b}{a^2 d^2}+\frac{3 (e+f x) \text{csch}(c+d x) b}{2 a^2 d}-\frac{3 i f \text{Li}_2\left(-i e^{c+d x}\right) b}{2 a^2 d^2}+\frac{3 i f \text{Li}_2\left(i e^{c+d x}\right) b}{2 a^2 d^2}+\frac{f \text{sech}(c+d x) b}{2 a^2 d^2}+\frac{4 (e+f x) \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}-\frac{f \text{csch}(2 c+2 d x)}{a d^2}-\frac{2 (e+f x) \coth (2 c+2 d x) \text{csch}(2 c+2 d x)}{a d}+\frac{f \text{Li}_2\left(-e^{2 c+2 d x}\right)}{a d^2}-\frac{f \text{Li}_2\left(e^{2 c+2 d x}\right)}{a d^2}",1,"8*(((I/16)*(2*a^6 + 3*a^4*b^2 + b^6)*(d*e - c*f)*(c + d*x))/(a^3*(a^2 + b^2)^2*d^2) + ((I/32)*(2*a^6 + 3*a^4*b^2 + b^6)*f*(c + d*x)^2)/(a^3*(a^2 + b^2)^2*d^2) + (a^3*e*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(2*(a^2 + b^2)^2*d) + (3*a*b^2*e*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(4*(a^2 + b^2)^2*d) - (b^6*e*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(4*a^3*(a^2 + b^2)^2*d) - (a^3*c*f*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(2*(a^2 + b^2)^2*d^2) - (3*a*b^2*c*f*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(4*(a^2 + b^2)^2*d^2) + (b^6*c*f*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]])/(4*a^3*(a^2 + b^2)^2*d^2) - (e*Log[Cosh[(c + d*x)/2]])/(4*a*d) + (b^2*e*Log[Cosh[(c + d*x)/2]])/(8*a^3*d) + (c*f*Log[Cosh[(c + d*x)/2]])/(4*a*d^2) - (b^2*c*f*Log[Cosh[(c + d*x)/2]])/(8*a^3*d^2) + (a^3*e*((-1/2*I)*(c + d*x) + Log[Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]]))/(4*(a^2 + b^2)^2*d) + (3*a*b^2*e*((-1/2*I)*(c + d*x) + Log[Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]]))/(8*(a^2 + b^2)^2*d) - (a^3*c*f*((-1/2*I)*(c + d*x) + Log[Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]]))/(4*(a^2 + b^2)^2*d^2) - (3*a*b^2*c*f*((-1/2*I)*(c + d*x) + Log[Cosh[(c + d*x)/2] + I*Sinh[(c + d*x)/2]]))/(8*(a^2 + b^2)^2*d^2) + (b^6*e*((-I)*(c + d*x) + 2*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]] + Log[-1 + Cosh[c + d*x] + I*Sinh[c + d*x]]))/(16*a^3*(a^2 + b^2)^2*d) - (b^6*c*f*((-I)*(c + d*x) + 2*ArcTanh[1 - (2*I)*Tanh[(c + d*x)/2]] + Log[-1 + Cosh[c + d*x] + I*Sinh[c + d*x]]))/(16*a^3*(a^2 + b^2)^2*d^2) - (b*f*Log[Tanh[(c + d*x)/2]])/(8*a^2*d^2) - ((I/2)*f*((-1/8*I)*(c + d*x)^2 - (I/2)*(c + d*x)*Log[1 + E^(-c - d*x)] + (I/2)*PolyLog[2, -E^(-c - d*x)]))/(a*d^2) + ((I/4)*b^2*f*((-1/8*I)*(c + d*x)^2 - (I/2)*(c + d*x)*Log[1 + E^(-c - d*x)] + (I/2)*PolyLog[2, -E^(-c - d*x)]))/(a^3*d^2) + (b^6*f*((-1/2*I)*(c + d*x)^2 + (I/4)*(3*Pi*(c + d*x) + (1 - I)*(c + d*x)^2 + 2*(Pi - (2*I)*(c + d*x))*Log[1 + I*E^(-c - d*x)] - 4*Pi*Log[1 + E^(c + d*x)] - 2*Pi*Log[-Cos[(Pi + (2*I)*(c + d*x))/4]] + 4*Pi*Log[Cosh[(c + d*x)/2]] + (4*I)*PolyLog[2, (-I)*E^(-c - d*x)])))/(8*a^3*(a^2 + b^2)^2*d^2) - ((I/4)*a^3*f*((c + d*x)^2/4 + (-3*Pi*(c + d*x) - (1 - I)*(c + d*x)^2 - 2*(Pi - (2*I)*(c + d*x))*Log[1 + I*E^(-c - d*x)] + 4*Pi*Log[1 + E^(c + d*x)] + 2*Pi*Log[-Cos[(Pi + (2*I)*(c + d*x))/4]] - 4*Pi*Log[Cosh[(c + d*x)/2]] - (4*I)*PolyLog[2, (-I)*E^(-c - d*x)])/4 - (I/2)*(-1/2*(c + d*x)^2 + 2*(c + d*x)*Log[1 - E^(c + d*x)] + 2*PolyLog[2, E^(c + d*x)])))/((a^2 + b^2)^2*d^2) - (((3*I)/8)*a*b^2*f*((c + d*x)^2/4 + (-3*Pi*(c + d*x) - (1 - I)*(c + d*x)^2 - 2*(Pi - (2*I)*(c + d*x))*Log[1 + I*E^(-c - d*x)] + 4*Pi*Log[1 + E^(c + d*x)] + 2*Pi*Log[-Cos[(Pi + (2*I)*(c + d*x))/4]] - 4*Pi*Log[Cosh[(c + d*x)/2]] - (4*I)*PolyLog[2, (-I)*E^(-c - d*x)])/4 - (I/2)*(-1/2*(c + d*x)^2 + 2*(c + d*x)*Log[1 - E^(c + d*x)] + 2*PolyLog[2, E^(c + d*x)])))/((a^2 + b^2)^2*d^2) + ((I/8)*b^6*f*((c + d*x)^2/4 + (-3*Pi*(c + d*x) - (1 - I)*(c + d*x)^2 - 2*(Pi - (2*I)*(c + d*x))*Log[1 + I*E^(-c - d*x)] + 4*Pi*Log[1 + E^(c + d*x)] + 2*Pi*Log[-Cos[(Pi + (2*I)*(c + d*x))/4]] - 4*Pi*Log[Cosh[(c + d*x)/2]] - (4*I)*PolyLog[2, (-I)*E^(-c - d*x)])/4 - (I/2)*(-1/2*(c + d*x)^2 + 2*(c + d*x)*Log[1 - E^(c + d*x)] + 2*PolyLog[2, E^(c + d*x)])))/(a^3*(a^2 + b^2)^2*d^2) - (b^6*(-1/2*(f*(c + d*x)^2) + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] + f*(c + d*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + d*e*Log[a + b*Sinh[c + d*x]] - c*f*Log[a + b*Sinh[c + d*x]] + f*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] + f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]))/(8*a^3*(a^2 + b^2)^2*d^2) - ((I/2)*a^3*f*((E^((I/4)*Pi)*(c + d*x)^2)/4 - ((Pi*(c + d*x))/4 - Pi*Log[1 + E^(c + d*x)] - 2*(Pi/4 + (I/2)*(c + d*x))*Log[1 - E^((2*I)*(Pi/4 + (I/2)*(c + d*x)))] + Pi*Log[Cosh[(c + d*x)/2]] + (Pi*Log[Sin[Pi/4 + (I/2)*(c + d*x)]])/2 + I*PolyLog[2, E^((2*I)*(Pi/4 + (I/2)*(c + d*x)))])/Sqrt[2]))/(Sqrt[2]*(a^2 + b^2)^2*d^2) - (((3*I)/4)*a*b^2*f*((E^((I/4)*Pi)*(c + d*x)^2)/4 - ((Pi*(c + d*x))/4 - Pi*Log[1 + E^(c + d*x)] - 2*(Pi/4 + (I/2)*(c + d*x))*Log[1 - E^((2*I)*(Pi/4 + (I/2)*(c + d*x)))] + Pi*Log[Cosh[(c + d*x)/2]] + (Pi*Log[Sin[Pi/4 + (I/2)*(c + d*x)]])/2 + I*PolyLog[2, E^((2*I)*(Pi/4 + (I/2)*(c + d*x)))])/Sqrt[2]))/(Sqrt[2]*(a^2 + b^2)^2*d^2) + (b*(3*a^2 + 5*b^2)*(2*(d*e - c*f + f*(c + d*x))*ArcTan[Cosh[c + d*x] + Sinh[c + d*x]] - I*f*PolyLog[2, (-I)*(Cosh[c + d*x] + Sinh[c + d*x])] + I*f*PolyLog[2, I*(Cosh[c + d*x] + Sinh[c + d*x])]))/(16*(a^2 + b^2)^2*d^2) + (Csch[c + d*x]^2*Sech[c + d*x]^2*(-4*a*b^2*d*e + 4*a*b^2*c*f - 4*a*b^2*f*(c + d*x) - 2*a^2*b*f*Cosh[c + d*x] - 8*a^3*d*e*Cosh[2*(c + d*x)] - 4*a*b^2*d*e*Cosh[2*(c + d*x)] + 8*a^3*c*f*Cosh[2*(c + d*x)] + 4*a*b^2*c*f*Cosh[2*(c + d*x)] - 8*a^3*f*(c + d*x)*Cosh[2*(c + d*x)] - 4*a*b^2*f*(c + d*x)*Cosh[2*(c + d*x)] + 2*a^2*b*f*Cosh[3*(c + d*x)] - 2*a^2*b*d*e*Sinh[c + d*x] + 4*b^3*d*e*Sinh[c + d*x] + 2*a^2*b*c*f*Sinh[c + d*x] - 4*b^3*c*f*Sinh[c + d*x] - 2*a^2*b*f*(c + d*x)*Sinh[c + d*x] + 4*b^3*f*(c + d*x)*Sinh[c + d*x] - 4*a^3*f*Sinh[2*(c + d*x)] - 2*a*b^2*f*Sinh[2*(c + d*x)] + 6*a^2*b*d*e*Sinh[3*(c + d*x)] + 4*b^3*d*e*Sinh[3*(c + d*x)] - 6*a^2*b*c*f*Sinh[3*(c + d*x)] - 4*b^3*c*f*Sinh[3*(c + d*x)] + 6*a^2*b*f*(c + d*x)*Sinh[3*(c + d*x)] + 4*b^3*f*(c + d*x)*Sinh[3*(c + d*x)] - a*b^2*f*Sinh[4*(c + d*x)]))/(128*a^2*(a^2 + b^2)*d^2))","B",0
501,1,237,211,0.7855087,"\int \frac{\text{csch}^3(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Integrate[(Csch[c + d*x]^3*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{-\frac{a \text{sech}^2(c+d x)}{a^2+b^2}+\frac{(a-i b) \left(2 a^2+i a b+2 b^2\right) \log (-\sinh (c+d x)+i)}{\left(a^2+b^2\right)^2}+\frac{(a+i b) \left(2 a^2-i a b+2 b^2\right) \log (\sinh (c+d x)+i)}{\left(a^2+b^2\right)^2}+\frac{b \tan ^{-1}(\sinh (c+d x))}{a^2+b^2}+\frac{b \tanh (c+d x) \text{sech}(c+d x)}{a^2+b^2}+\frac{2 b \text{csch}(c+d x)}{a^2}-\frac{2 \left(2 a^2-b^2\right) \log (\sinh (c+d x))}{a^3}-\frac{2 b^6 \log (a+b \sinh (c+d x))}{a^3 \left(a^2+b^2\right)^2}-\frac{\text{csch}^2(c+d x)}{a}}{2 d}","\frac{b \left(a^2+2 b^2\right) \tan ^{-1}(\sinh (c+d x))}{d \left(a^2+b^2\right)^2}+\frac{b \tan ^{-1}(\sinh (c+d x))}{2 d \left(a^2+b^2\right)}+\frac{a \left(2 a^2+3 b^2\right) \log (\cosh (c+d x))}{d \left(a^2+b^2\right)^2}-\frac{\text{sech}^2(c+d x) (a-b \sinh (c+d x))}{2 d \left(a^2+b^2\right)}+\frac{b \text{csch}(c+d x)}{a^2 d}-\frac{\left(2 a^2-b^2\right) \log (\sinh (c+d x))}{a^3 d}-\frac{b^6 \log (a+b \sinh (c+d x))}{a^3 d \left(a^2+b^2\right)^2}-\frac{\text{csch}^2(c+d x)}{2 a d}",1,"((b*ArcTan[Sinh[c + d*x]])/(a^2 + b^2) + (2*b*Csch[c + d*x])/a^2 - Csch[c + d*x]^2/a + ((a - I*b)*(2*a^2 + I*a*b + 2*b^2)*Log[I - Sinh[c + d*x]])/(a^2 + b^2)^2 - (2*(2*a^2 - b^2)*Log[Sinh[c + d*x]])/a^3 + ((a + I*b)*(2*a^2 - I*a*b + 2*b^2)*Log[I + Sinh[c + d*x]])/(a^2 + b^2)^2 - (2*b^6*Log[a + b*Sinh[c + d*x]])/(a^3*(a^2 + b^2)^2) - (a*Sech[c + d*x]^2)/(a^2 + b^2) + (b*Sech[c + d*x]*Tanh[c + d*x])/(a^2 + b^2))/(2*d)","C",1
502,-1,0,39,180.0025489,"\int \frac{\text{csch}^3(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Integrate[(Csch[c + d*x]^3*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{csch}^3(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"$Aborted","F",-1