1,1,91,0,0.1204526,"\int (c+d x)^4 \sinh (a+b x) \, dx","Int[(c + d*x)^4*Sinh[a + b*x],x]","-\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{24 d^4 \cosh (a+b x)}{b^5}+\frac{(c+d x)^4 \cosh (a+b x)}{b}","-\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{24 d^4 \cosh (a+b x)}{b^5}+\frac{(c+d x)^4 \cosh (a+b x)}{b}",1,"(24*d^4*Cosh[a + b*x])/b^5 + (12*d^2*(c + d*x)^2*Cosh[a + b*x])/b^3 + ((c + d*x)^4*Cosh[a + b*x])/b - (24*d^3*(c + d*x)*Sinh[a + b*x])/b^4 - (4*d*(c + d*x)^3*Sinh[a + b*x])/b^2","A",5,2,14,0.1429,1,"{3296, 2638}"
2,1,70,0,0.0790137,"\int (c+d x)^3 \sinh (a+b x) \, dx","Int[(c + d*x)^3*Sinh[a + b*x],x]","\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{6 d^3 \sinh (a+b x)}{b^4}+\frac{(c+d x)^3 \cosh (a+b x)}{b}","\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{6 d^3 \sinh (a+b x)}{b^4}+\frac{(c+d x)^3 \cosh (a+b x)}{b}",1,"(6*d^2*(c + d*x)*Cosh[a + b*x])/b^3 + ((c + d*x)^3*Cosh[a + b*x])/b - (6*d^3*Sinh[a + b*x])/b^4 - (3*d*(c + d*x)^2*Sinh[a + b*x])/b^2","A",4,2,14,0.1429,1,"{3296, 2637}"
3,1,49,0,0.0496901,"\int (c+d x)^2 \sinh (a+b x) \, dx","Int[(c + d*x)^2*Sinh[a + b*x],x]","-\frac{2 d (c+d x) \sinh (a+b x)}{b^2}+\frac{2 d^2 \cosh (a+b x)}{b^3}+\frac{(c+d x)^2 \cosh (a+b x)}{b}","-\frac{2 d (c+d x) \sinh (a+b x)}{b^2}+\frac{2 d^2 \cosh (a+b x)}{b^3}+\frac{(c+d x)^2 \cosh (a+b x)}{b}",1,"(2*d^2*Cosh[a + b*x])/b^3 + ((c + d*x)^2*Cosh[a + b*x])/b - (2*d*(c + d*x)*Sinh[a + b*x])/b^2","A",3,2,14,0.1429,1,"{3296, 2638}"
4,1,28,0,0.0199479,"\int (c+d x) \sinh (a+b x) \, dx","Int[(c + d*x)*Sinh[a + b*x],x]","\frac{(c+d x) \cosh (a+b x)}{b}-\frac{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,"((c + d*x)*Cosh[a + b*x])/b - (d*Sinh[a + b*x])/b^2","A",2,2,12,0.1667,1,"{3296, 2637}"
5,1,51,0,0.1092837,"\int \frac{\sinh (a+b x)}{c+d x} \, dx","Int[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)}{d}+\frac{\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])/d + (Cosh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/d","A",3,3,14,0.2143,1,"{3303, 3298, 3301}"
6,1,71,0,0.1268579,"\int \frac{\sinh (a+b x)}{(c+d x)^2} \, dx","Int[Sinh[a + b*x]/(c + d*x)^2,x]","\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)}","\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 + b*x])/d^2 - Sinh[a + b*x]/(d*(c + d*x)) + (b*Sinh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/d^2","A",4,4,14,0.2857,1,"{3297, 3303, 3298, 3301}"
7,1,104,0,0.1660217,"\int \frac{\sinh (a+b x)}{(c+d x)^3} \, dx","Int[Sinh[a + b*x]/(c + d*x)^3,x]","\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}","\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*Cosh[a + b*x])/(2*d^2*(c + d*x)) + (b^2*CoshIntegral[(b*c)/d + b*x]*Sinh[a - (b*c)/d])/(2*d^3) - Sinh[a + b*x]/(2*d*(c + d*x)^2) + (b^2*Cosh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/(2*d^3)","A",5,4,14,0.2857,1,"{3297, 3303, 3298, 3301}"
8,1,162,0,0.1048945,"\int (c+d x)^4 \sinh ^2(a+b x) \, dx","Int[(c + d*x)^4*Sinh[a + b*x]^2,x]","-\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{3 d^4 \sinh (a+b x) \cosh (a+b x)}{4 b^5}+\frac{(c+d x)^4 \sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{d (c+d x)^3}{2 b^2}-\frac{3 d^4 x}{4 b^4}-\frac{(c+d x)^5}{10 d}","-\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{3 d^4 \sinh (a+b x) \cosh (a+b x)}{4 b^5}+\frac{(c+d x)^4 \sinh (a+b x) \cosh (a+b x)}{2 b}-\frac{d (c+d x)^3}{2 b^2}-\frac{3 d^4 x}{4 b^4}-\frac{(c+d x)^5}{10 d}",1,"(-3*d^4*x)/(4*b^4) - (d*(c + d*x)^3)/(2*b^2) - (c + d*x)^5/(10*d) + (3*d^4*Cosh[a + b*x]*Sinh[a + b*x])/(4*b^5) + (3*d^2*(c + d*x)^2*Cosh[a + b*x]*Sinh[a + b*x])/(2*b^3) + ((c + d*x)^4*Cosh[a + b*x]*Sinh[a + b*x])/(2*b) - (3*d^3*(c + d*x)*Sinh[a + b*x]^2)/(2*b^4) - (d*(c + d*x)^3*Sinh[a + b*x]^2)/b^2","A",6,4,16,0.2500,1,"{3311, 32, 2635, 8}"
9,1,134,0,0.0742048,"\int (c+d x)^3 \sinh ^2(a+b x) \, dx","Int[(c + d*x)^3*Sinh[a + b*x]^2,x]","\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{3 d^3 \sinh ^2(a+b x)}{8 b^4}+\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}","\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{3 d^3 \sinh ^2(a+b x)}{8 b^4}+\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,"(-3*c*d^2*x)/(4*b^2) - (3*d^3*x^2)/(8*b^2) - (c + d*x)^4/(8*d) + (3*d^2*(c + d*x)*Cosh[a + b*x]*Sinh[a + b*x])/(4*b^3) + ((c + d*x)^3*Cosh[a + b*x]*Sinh[a + b*x])/(2*b) - (3*d^3*Sinh[a + b*x]^2)/(8*b^4) - (3*d*(c + d*x)^2*Sinh[a + b*x]^2)/(4*b^2)","A",4,3,16,0.1875,1,"{3311, 32, 3310}"
10,1,95,0,0.0543412,"\int (c+d x)^2 \sinh ^2(a+b x) \, dx","Int[(c + d*x)^2*Sinh[a + b*x]^2,x]","-\frac{d (c+d x) \sinh ^2(a+b x)}{2 b^2}+\frac{d^2 \sinh (a+b x) \cosh (a+b x)}{4 b^3}+\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}","-\frac{d (c+d x) \sinh ^2(a+b x)}{2 b^2}+\frac{d^2 \sinh (a+b x) \cosh (a+b x)}{4 b^3}+\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,"-(d^2*x)/(4*b^2) - (c + d*x)^3/(6*d) + (d^2*Cosh[a + b*x]*Sinh[a + b*x])/(4*b^3) + ((c + d*x)^2*Cosh[a + b*x]*Sinh[a + b*x])/(2*b) - (d*(c + d*x)*Sinh[a + b*x]^2)/(2*b^2)","A",4,4,16,0.2500,1,"{3311, 32, 2635, 8}"
11,1,55,0,0.0262664,"\int (c+d x) \sinh ^2(a+b x) \, dx","Int[(c + d*x)*Sinh[a + b*x]^2,x]","-\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}","-\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,"-(c*x)/2 - (d*x^2)/4 + ((c + d*x)*Cosh[a + b*x]*Sinh[a + b*x])/(2*b) - (d*Sinh[a + b*x]^2)/(4*b^2)","A",2,1,14,0.07143,1,"{3310}"
12,1,78,0,0.1654902,"\int \frac{\sinh ^2(a+b x)}{c+d x} \, dx","Int[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}+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}","\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 + 2*b*x])/(2*d) - Log[c + d*x]/(2*d) + (Sinh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*c)/d + 2*b*x])/(2*d)","A",5,4,16,0.2500,1,"{3312, 3303, 3298, 3301}"
13,1,81,0,0.154983,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^2} \, dx","Int[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}+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)}","\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 + 2*b*x]*Sinh[2*a - (2*b*c)/d])/d^2 - Sinh[a + b*x]^2/(d*(c + d*x)) + (b*Cosh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*c)/d + 2*b*x])/d^2","A",5,5,16,0.3125,1,"{3313, 12, 3303, 3298, 3301}"
14,1,112,0,0.1950812,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^3} \, dx","Int[Sinh[a + b*x]^2/(c + d*x)^3,x]","\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}","\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,"(b^2*Cosh[2*a - (2*b*c)/d]*CoshIntegral[(2*b*c)/d + 2*b*x])/d^3 - (b*Cosh[a + b*x]*Sinh[a + b*x])/(d^2*(c + d*x)) - Sinh[a + b*x]^2/(2*d*(c + d*x)^2) + (b^2*Sinh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*c)/d + 2*b*x])/d^3","A",7,6,16,0.3750,1,"{3314, 31, 3312, 3303, 3298, 3301}"
15,1,162,0,0.1872598,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^4} \, dx","Int[Sinh[a + b*x]^2/(c + d*x)^4,x]","\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)}","\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,"-b^2/(3*d^3*(c + d*x)) + (2*b^3*CoshIntegral[(2*b*c)/d + 2*b*x]*Sinh[2*a - (2*b*c)/d])/(3*d^4) - (b*Cosh[a + b*x]*Sinh[a + b*x])/(3*d^2*(c + d*x)^2) - Sinh[a + b*x]^2/(3*d*(c + d*x)^3) - (2*b^2*Sinh[a + b*x]^2)/(3*d^3*(c + d*x)) + (2*b^3*Cosh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*c)/d + 2*b*x])/(3*d^4)","A",7,7,16,0.4375,1,"{3314, 32, 3313, 12, 3303, 3298, 3301}"
16,1,225,0,0.3598906,"\int (c+d x)^4 \sinh ^3(a+b x) \, dx","Int[(c + d*x)^4*Sinh[a + b*x]^3,x]","-\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{8 d^4 \cosh ^3(a+b x)}{81 b^5}-\frac{488 d^4 \cosh (a+b x)}{27 b^5}-\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}","-\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{8 d^4 \cosh ^3(a+b x)}{81 b^5}-\frac{488 d^4 \cosh (a+b x)}{27 b^5}-\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,"(-488*d^4*Cosh[a + b*x])/(27*b^5) - (80*d^2*(c + d*x)^2*Cosh[a + b*x])/(9*b^3) - (2*(c + d*x)^4*Cosh[a + b*x])/(3*b) + (8*d^4*Cosh[a + b*x]^3)/(81*b^5) + (160*d^3*(c + d*x)*Sinh[a + b*x])/(9*b^4) + (8*d*(c + d*x)^3*Sinh[a + b*x])/(3*b^2) + (4*d^2*(c + d*x)^2*Cosh[a + b*x]*Sinh[a + b*x]^2)/(9*b^3) + ((c + d*x)^4*Cosh[a + b*x]*Sinh[a + b*x]^2)/(3*b) - (8*d^3*(c + d*x)*Sinh[a + b*x]^3)/(27*b^4) - (4*d*(c + d*x)^3*Sinh[a + b*x]^3)/(9*b^2)","A",12,4,16,0.2500,1,"{3311, 3296, 2638, 2633}"
17,1,175,0,0.2264846,"\int (c+d x)^3 \sinh ^3(a+b x) \, dx","Int[(c + d*x)^3*Sinh[a + b*x]^3,x]","-\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 d^3 \sinh ^3(a+b x)}{27 b^4}+\frac{40 d^3 \sinh (a+b x)}{9 b^4}-\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}","-\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 d^3 \sinh ^3(a+b x)}{27 b^4}+\frac{40 d^3 \sinh (a+b x)}{9 b^4}-\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,"(-40*d^2*(c + d*x)*Cosh[a + b*x])/(9*b^3) - (2*(c + d*x)^3*Cosh[a + b*x])/(3*b) + (40*d^3*Sinh[a + b*x])/(9*b^4) + (2*d*(c + d*x)^2*Sinh[a + b*x])/b^2 + (2*d^2*(c + d*x)*Cosh[a + b*x]*Sinh[a + b*x]^2)/(9*b^3) + ((c + d*x)^3*Cosh[a + b*x]*Sinh[a + b*x]^2)/(3*b) - (2*d^3*Sinh[a + b*x]^3)/(27*b^4) - (d*(c + d*x)^2*Sinh[a + b*x]^3)/(3*b^2)","A",8,4,16,0.2500,1,"{3311, 3296, 2637, 3310}"
18,1,123,0,0.131249,"\int (c+d x)^2 \sinh ^3(a+b x) \, dx","Int[(c + d*x)^2*Sinh[a + b*x]^3,x]","-\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 d^2 \cosh ^3(a+b x)}{27 b^3}-\frac{14 d^2 \cosh (a+b x)}{9 b^3}-\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}","-\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 d^2 \cosh ^3(a+b x)}{27 b^3}-\frac{14 d^2 \cosh (a+b x)}{9 b^3}-\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,"(-14*d^2*Cosh[a + b*x])/(9*b^3) - (2*(c + d*x)^2*Cosh[a + b*x])/(3*b) + (2*d^2*Cosh[a + b*x]^3)/(27*b^3) + (4*d*(c + d*x)*Sinh[a + b*x])/(3*b^2) + ((c + d*x)^2*Cosh[a + b*x]*Sinh[a + b*x]^2)/(3*b) - (2*d*(c + d*x)*Sinh[a + b*x]^3)/(9*b^2)","A",6,4,16,0.2500,1,"{3311, 3296, 2638, 2633}"
19,1,75,0,0.0576496,"\int (c+d x) \sinh ^3(a+b x) \, dx","Int[(c + d*x)*Sinh[a + b*x]^3,x]","-\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}","-\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,"(-2*(c + d*x)*Cosh[a + b*x])/(3*b) + (2*d*Sinh[a + b*x])/(3*b^2) + ((c + d*x)*Cosh[a + b*x]*Sinh[a + b*x]^2)/(3*b) - (d*Sinh[a + b*x]^3)/(9*b^2)","A",3,3,14,0.2143,1,"{3310, 3296, 2637}"
20,1,121,0,0.282192,"\int \frac{\sinh ^3(a+b x)}{c+d x} \, dx","Int[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}+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}","\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 + 3*b*x]*Sinh[3*a - (3*b*c)/d])/(4*d) - (3*CoshIntegral[(b*c)/d + b*x]*Sinh[a - (b*c)/d])/(4*d) - (3*Cosh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/(4*d) + (Cosh[3*a - (3*b*c)/d]*SinhIntegral[(3*b*c)/d + 3*b*x])/(4*d)","A",8,4,16,0.2500,1,"{3312, 3303, 3298, 3301}"
21,1,145,0,0.2622142,"\int \frac{\sinh ^3(a+b x)}{(c+d x)^2} \, dx","Int[Sinh[a + b*x]^3/(c + d*x)^2,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)}","-\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,"(-3*b*Cosh[a - (b*c)/d]*CoshIntegral[(b*c)/d + b*x])/(4*d^2) + (3*b*Cosh[3*a - (3*b*c)/d]*CoshIntegral[(3*b*c)/d + 3*b*x])/(4*d^2) - Sinh[a + b*x]^3/(d*(c + d*x)) - (3*b*Sinh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/(4*d^2) + (3*b*Sinh[3*a - (3*b*c)/d]*SinhIntegral[(3*b*c)/d + 3*b*x])/(4*d^2)","A",8,4,16,0.2500,1,"{3313, 3303, 3298, 3301}"
22,1,184,0,0.4248433,"\int \frac{\sinh ^3(a+b x)}{(c+d x)^3} \, dx","Int[Sinh[a + b*x]^3/(c + d*x)^3,x]","\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}","\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,"(9*b^2*CoshIntegral[(3*b*c)/d + 3*b*x]*Sinh[3*a - (3*b*c)/d])/(8*d^3) - (3*b^2*CoshIntegral[(b*c)/d + b*x]*Sinh[a - (b*c)/d])/(8*d^3) - (3*b*Cosh[a + b*x]*Sinh[a + b*x]^2)/(2*d^2*(c + d*x)) - Sinh[a + b*x]^3/(2*d*(c + d*x)^2) - (3*b^2*Cosh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/(8*d^3) + (9*b^2*Cosh[3*a - (3*b*c)/d]*SinhIntegral[(3*b*c)/d + 3*b*x])/(8*d^3)","A",12,5,16,0.3125,1,"{3314, 3303, 3298, 3301, 3312}"
23,1,149,0,0.1364566,"\int (c+d x)^3 \text{csch}(a+b x) \, dx","Int[(c + d*x)^3*Csch[a + b*x],x]","\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-e^{a+b x}\right)}{b^3}-\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,e^{a+b x}\right)}{b^3}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-e^{a+b x}\right)}{b^2}+\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,e^{a+b x}\right)}{b^2}-\frac{6 d^3 \text{PolyLog}\left(4,-e^{a+b x}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(4,e^{a+b x}\right)}{b^4}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}","\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-e^{a+b x}\right)}{b^3}-\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,e^{a+b x}\right)}{b^3}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-e^{a+b x}\right)}{b^2}+\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,e^{a+b x}\right)}{b^2}-\frac{6 d^3 \text{PolyLog}\left(4,-e^{a+b x}\right)}{b^4}+\frac{6 d^3 \text{PolyLog}\left(4,e^{a+b x}\right)}{b^4}-\frac{2 (c+d x)^3 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(-2*(c + d*x)^3*ArcTanh[E^(a + b*x)])/b - (3*d*(c + d*x)^2*PolyLog[2, -E^(a + b*x)])/b^2 + (3*d*(c + d*x)^2*PolyLog[2, E^(a + b*x)])/b^2 + (6*d^2*(c + d*x)*PolyLog[3, -E^(a + b*x)])/b^3 - (6*d^2*(c + d*x)*PolyLog[3, E^(a + b*x)])/b^3 - (6*d^3*PolyLog[4, -E^(a + b*x)])/b^4 + (6*d^3*PolyLog[4, E^(a + b*x)])/b^4","A",9,5,14,0.3571,1,"{4182, 2531, 6609, 2282, 6589}"
24,1,99,0,0.0903547,"\int (c+d x)^2 \text{csch}(a+b x) \, dx","Int[(c + d*x)^2*Csch[a + b*x],x]","-\frac{2 d (c+d x) \text{PolyLog}\left(2,-e^{a+b x}\right)}{b^2}+\frac{2 d (c+d x) \text{PolyLog}\left(2,e^{a+b x}\right)}{b^2}+\frac{2 d^2 \text{PolyLog}\left(3,-e^{a+b x}\right)}{b^3}-\frac{2 d^2 \text{PolyLog}\left(3,e^{a+b x}\right)}{b^3}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}","-\frac{2 d (c+d x) \text{PolyLog}\left(2,-e^{a+b x}\right)}{b^2}+\frac{2 d (c+d x) \text{PolyLog}\left(2,e^{a+b x}\right)}{b^2}+\frac{2 d^2 \text{PolyLog}\left(3,-e^{a+b x}\right)}{b^3}-\frac{2 d^2 \text{PolyLog}\left(3,e^{a+b x}\right)}{b^3}-\frac{2 (c+d x)^2 \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(-2*(c + d*x)^2*ArcTanh[E^(a + b*x)])/b - (2*d*(c + d*x)*PolyLog[2, -E^(a + b*x)])/b^2 + (2*d*(c + d*x)*PolyLog[2, E^(a + b*x)])/b^2 + (2*d^2*PolyLog[3, -E^(a + b*x)])/b^3 - (2*d^2*PolyLog[3, E^(a + b*x)])/b^3","A",7,4,14,0.2857,1,"{4182, 2531, 2282, 6589}"
25,1,50,0,0.04626,"\int (c+d x) \text{csch}(a+b x) \, dx","Int[(c + d*x)*Csch[a + b*x],x]","-\frac{d \text{PolyLog}\left(2,-e^{a+b x}\right)}{b^2}+\frac{d \text{PolyLog}\left(2,e^{a+b x}\right)}{b^2}-\frac{2 (c+d x) \tanh ^{-1}\left(e^{a+b x}\right)}{b}","-\frac{d \text{PolyLog}\left(2,-e^{a+b x}\right)}{b^2}+\frac{d \text{PolyLog}\left(2,e^{a+b x}\right)}{b^2}-\frac{2 (c+d x) \tanh ^{-1}\left(e^{a+b x}\right)}{b}",1,"(-2*(c + d*x)*ArcTanh[E^(a + b*x)])/b - (d*PolyLog[2, -E^(a + b*x)])/b^2 + (d*PolyLog[2, E^(a + b*x)])/b^2","A",5,3,12,0.2500,1,"{4182, 2279, 2391}"
26,0,0,0,0.0235079,"\int \frac{\text{csch}(a+b x)}{c+d x} \, dx","Int[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,"Defer[Int][Csch[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
27,0,0,0,0.0220008,"\int \frac{\text{csch}(a+b x)}{(c+d x)^2} \, dx","Int[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,"Defer[Int][Csch[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
28,1,103,0,0.2270859,"\int (c+d x)^3 \text{csch}^2(a+b x) \, dx","Int[(c + d*x)^3*Csch[a + b*x]^2,x]","\frac{3 d^2 (c+d x) \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{b^3}-\frac{3 d^3 \text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^4}+\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}","\frac{3 d^2 (c+d x) \text{PolyLog}\left(2,e^{2 (a+b x)}\right)}{b^3}-\frac{3 d^3 \text{PolyLog}\left(3,e^{2 (a+b x)}\right)}{2 b^4}+\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,"-((c + d*x)^3/b) - ((c + d*x)^3*Coth[a + b*x])/b + (3*d*(c + d*x)^2*Log[1 - E^(2*(a + b*x))])/b^2 + (3*d^2*(c + d*x)*PolyLog[2, E^(2*(a + b*x))])/b^3 - (3*d^3*PolyLog[3, E^(2*(a + b*x))])/(2*b^4)","A",6,6,16,0.3750,1,"{4184, 3716, 2190, 2531, 2282, 6589}"
29,1,74,0,0.1475428,"\int (c+d x)^2 \text{csch}^2(a+b x) \, dx","Int[(c + d*x)^2*Csch[a + b*x]^2,x]","\frac{d^2 \text{PolyLog}\left(2,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}","\frac{d^2 \text{PolyLog}\left(2,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,"-((c + d*x)^2/b) - ((c + d*x)^2*Coth[a + b*x])/b + (2*d*(c + d*x)*Log[1 - E^(2*(a + b*x))])/b^2 + (d^2*PolyLog[2, E^(2*(a + b*x))])/b^3","A",5,5,16,0.3125,1,"{4184, 3716, 2190, 2279, 2391}"
30,1,29,0,0.0303038,"\int (c+d x) \text{csch}^2(a+b x) \, dx","Int[(c + d*x)*Csch[a + b*x]^2,x]","\frac{d \log (\sinh (a+b x))}{b^2}-\frac{(c+d x) \coth (a+b x)}{b}","\frac{d \log (\sinh (a+b x))}{b^2}-\frac{(c+d x) \coth (a+b x)}{b}",1,"-(((c + d*x)*Coth[a + b*x])/b) + (d*Log[Sinh[a + b*x]])/b^2","A",2,2,14,0.1429,1,"{4184, 3475}"
31,0,0,0,0.0403233,"\int \frac{\text{csch}^2(a+b x)}{c+d x} \, dx","Int[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,"Defer[Int][Csch[a + b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
32,0,0,0,0.0378597,"\int \frac{\text{csch}^2(a+b x)}{(c+d x)^2} \, dx","Int[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,"Defer[Int][Csch[a + b*x]^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
33,1,256,0,0.2736159,"\int (c+d x)^3 \text{csch}^3(a+b x) \, dx","Int[(c + d*x)^3*Csch[a + b*x]^3,x]","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{a+b x}\right)}{b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{a+b x}\right)}{b^3}+\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-e^{a+b x}\right)}{2 b^2}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,e^{a+b x}\right)}{2 b^2}-\frac{3 d^3 \text{PolyLog}\left(2,-e^{a+b x}\right)}{b^4}+\frac{3 d^3 \text{PolyLog}\left(2,e^{a+b x}\right)}{b^4}+\frac{3 d^3 \text{PolyLog}\left(4,-e^{a+b x}\right)}{b^4}-\frac{3 d^3 \text{PolyLog}\left(4,e^{a+b x}\right)}{b^4}-\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{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}","-\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,-e^{a+b x}\right)}{b^3}+\frac{3 d^2 (c+d x) \text{PolyLog}\left(3,e^{a+b x}\right)}{b^3}+\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-e^{a+b x}\right)}{2 b^2}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,e^{a+b x}\right)}{2 b^2}-\frac{3 d^3 \text{PolyLog}\left(2,-e^{a+b x}\right)}{b^4}+\frac{3 d^3 \text{PolyLog}\left(2,e^{a+b x}\right)}{b^4}+\frac{3 d^3 \text{PolyLog}\left(4,-e^{a+b x}\right)}{b^4}-\frac{3 d^3 \text{PolyLog}\left(4,e^{a+b x}\right)}{b^4}-\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{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,"(-6*d^2*(c + d*x)*ArcTanh[E^(a + b*x)])/b^3 + ((c + d*x)^3*ArcTanh[E^(a + b*x)])/b - (3*d*(c + d*x)^2*Csch[a + b*x])/(2*b^2) - ((c + d*x)^3*Coth[a + b*x]*Csch[a + b*x])/(2*b) - (3*d^3*PolyLog[2, -E^(a + b*x)])/b^4 + (3*d*(c + d*x)^2*PolyLog[2, -E^(a + b*x)])/(2*b^2) + (3*d^3*PolyLog[2, E^(a + b*x)])/b^4 - (3*d*(c + d*x)^2*PolyLog[2, E^(a + b*x)])/(2*b^2) - (3*d^2*(c + d*x)*PolyLog[3, -E^(a + b*x)])/b^3 + (3*d^2*(c + d*x)*PolyLog[3, E^(a + b*x)])/b^3 + (3*d^3*PolyLog[4, -E^(a + b*x)])/b^4 - (3*d^3*PolyLog[4, E^(a + b*x)])/b^4","A",15,8,16,0.5000,1,"{4186, 4182, 2279, 2391, 2531, 6609, 2282, 6589}"
34,1,154,0,0.1656446,"\int (c+d x)^2 \text{csch}^3(a+b x) \, dx","Int[(c + d*x)^2*Csch[a + b*x]^3,x]","\frac{d (c+d x) \text{PolyLog}\left(2,-e^{a+b x}\right)}{b^2}-\frac{d (c+d x) \text{PolyLog}\left(2,e^{a+b x}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{a+b x}\right)}{b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{a+b x}\right)}{b^3}-\frac{d (c+d x) \text{csch}(a+b x)}{b^2}-\frac{d^2 \tanh ^{-1}(\cosh (a+b x))}{b^3}+\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}","\frac{d (c+d x) \text{PolyLog}\left(2,-e^{a+b x}\right)}{b^2}-\frac{d (c+d x) \text{PolyLog}\left(2,e^{a+b x}\right)}{b^2}-\frac{d^2 \text{PolyLog}\left(3,-e^{a+b x}\right)}{b^3}+\frac{d^2 \text{PolyLog}\left(3,e^{a+b x}\right)}{b^3}-\frac{d (c+d x) \text{csch}(a+b x)}{b^2}-\frac{d^2 \tanh ^{-1}(\cosh (a+b x))}{b^3}+\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,"((c + d*x)^2*ArcTanh[E^(a + b*x)])/b - (d^2*ArcTanh[Cosh[a + b*x]])/b^3 - (d*(c + d*x)*Csch[a + b*x])/b^2 - ((c + d*x)^2*Coth[a + b*x]*Csch[a + b*x])/(2*b) + (d*(c + d*x)*PolyLog[2, -E^(a + b*x)])/b^2 - (d*(c + d*x)*PolyLog[2, E^(a + b*x)])/b^2 - (d^2*PolyLog[3, -E^(a + b*x)])/b^3 + (d^2*PolyLog[3, E^(a + b*x)])/b^3","A",9,6,16,0.3750,1,"{4186, 3770, 4182, 2531, 2282, 6589}"
35,1,92,0,0.0813309,"\int (c+d x) \text{csch}^3(a+b x) \, dx","Int[(c + d*x)*Csch[a + b*x]^3,x]","\frac{d \text{PolyLog}\left(2,-e^{a+b x}\right)}{2 b^2}-\frac{d \text{PolyLog}\left(2,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}","\frac{d \text{PolyLog}\left(2,-e^{a+b x}\right)}{2 b^2}-\frac{d \text{PolyLog}\left(2,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,"((c + d*x)*ArcTanh[E^(a + b*x)])/b - (d*Csch[a + b*x])/(2*b^2) - ((c + d*x)*Coth[a + b*x]*Csch[a + b*x])/(2*b) + (d*PolyLog[2, -E^(a + b*x)])/(2*b^2) - (d*PolyLog[2, E^(a + b*x)])/(2*b^2)","A",6,4,14,0.2857,1,"{4185, 4182, 2279, 2391}"
36,0,0,0,0.0396201,"\int \frac{\text{csch}^3(a+b x)}{c+d x} \, dx","Int[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,"Defer[Int][Csch[a + b*x]^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
37,0,0,0,0.0372557,"\int \frac{\text{csch}^3(a+b x)}{(c+d x)^2} \, dx","Int[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,"Defer[Int][Csch[a + b*x]^3/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
38,1,171,0,0.3700483,"\int (c+d x)^{5/2} \sinh (a+b x) \, dx","Int[(c + d*x)^(5/2)*Sinh[a + b*x],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}","-\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,"(15*d^2*Sqrt[c + d*x]*Cosh[a + b*x])/(4*b^3) + ((c + d*x)^(5/2)*Cosh[a + b*x])/b - (15*d^(5/2)*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(16*b^(7/2)) - (15*d^(5/2)*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(16*b^(7/2)) - (5*d*(c + d*x)^(3/2)*Sinh[a + b*x])/(2*b^2)","A",8,5,16,0.3125,1,"{3296, 3307, 2180, 2204, 2205}"
39,1,146,0,0.2480105,"\int (c+d x)^{3/2} \sinh (a+b x) \, dx","Int[(c + d*x)^(3/2)*Sinh[a + b*x],x]","-\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}","-\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,"((c + d*x)^(3/2)*Cosh[a + b*x])/b - (3*d^(3/2)*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(8*b^(5/2)) + (3*d^(3/2)*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(8*b^(5/2)) - (3*d*Sqrt[c + d*x]*Sinh[a + b*x])/(2*b^2)","A",7,5,16,0.3125,1,"{3296, 3308, 2180, 2204, 2205}"
40,1,123,0,0.1874066,"\int \sqrt{c+d x} \sinh (a+b x) \, dx","Int[Sqrt[c + d*x]*Sinh[a + b*x],x]","-\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}","-\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,"(Sqrt[c + d*x]*Cosh[a + b*x])/b - (Sqrt[d]*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(4*b^(3/2)) - (Sqrt[d]*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(4*b^(3/2))","A",6,5,16,0.3125,1,"{3296, 3307, 2180, 2204, 2205}"
41,1,104,0,0.1346142,"\int \frac{\sinh (a+b x)}{\sqrt{c+d x}} \, dx","Int[Sinh[a + b*x]/Sqrt[c + d*x],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}}","\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)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(2*Sqrt[b]*Sqrt[d]) + (E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(2*Sqrt[b]*Sqrt[d])","A",5,4,16,0.2500,1,"{3308, 2180, 2204, 2205}"
42,1,118,0,0.2004033,"\int \frac{\sinh (a+b x)}{(c+d x)^{3/2}} \, dx","Int[Sinh[a + b*x]/(c + d*x)^(3/2),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}}","\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,"(Sqrt[b]*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/d^(3/2) + (Sqrt[b]*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/d^(3/2) - (2*Sinh[a + b*x])/(d*Sqrt[c + d*x])","A",6,5,16,0.3125,1,"{3297, 3307, 2180, 2204, 2205}"
43,1,149,0,0.2507527,"\int \frac{\sinh (a+b x)}{(c+d x)^{5/2}} \, dx","Int[Sinh[a + b*x]/(c + d*x)^(5/2),x]","-\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}}","-\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,"(-4*b*Cosh[a + b*x])/(3*d^2*Sqrt[c + d*x]) - (2*b^(3/2)*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(3*d^(5/2)) + (2*b^(3/2)*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(3*d^(5/2)) - (2*Sinh[a + b*x])/(3*d*(c + d*x)^(3/2))","A",7,5,16,0.3125,1,"{3297, 3308, 2180, 2204, 2205}"
44,1,174,0,0.3081542,"\int \frac{\sinh (a+b x)}{(c+d x)^{7/2}} \, dx","Int[Sinh[a + b*x]/(c + d*x)^(7/2),x]","\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}}","\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,"(-4*b*Cosh[a + b*x])/(15*d^2*(c + d*x)^(3/2)) + (4*b^(5/2)*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(15*d^(7/2)) + (4*b^(5/2)*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(15*d^(7/2)) - (2*Sinh[a + b*x])/(5*d*(c + d*x)^(5/2)) - (8*b^2*Sinh[a + b*x])/(15*d^3*Sqrt[c + d*x])","A",8,5,16,0.3125,1,"{3297, 3307, 2180, 2204, 2205}"
45,1,239,0,0.4486254,"\int (c+d x)^{5/2} \sinh ^2(a+b x) \, dx","Int[(c + d*x)^(5/2)*Sinh[a + b*x]^2,x]","\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}","\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,"(-5*d*(c + d*x)^(3/2))/(16*b^2) - (c + d*x)^(7/2)/(7*d) + (15*d^(5/2)*E^(-2*a + (2*b*c)/d)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(256*b^(7/2)) - (15*d^(5/2)*E^(2*a - (2*b*c)/d)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(256*b^(7/2)) + ((c + d*x)^(5/2)*Cosh[a + b*x]*Sinh[a + b*x])/(2*b) - (5*d*(c + d*x)^(3/2)*Sinh[a + b*x]^2)/(8*b^2) + (15*d^2*Sqrt[c + d*x]*Sinh[2*a + 2*b*x])/(64*b^3)","A",10,8,18,0.4444,1,"{3311, 32, 3312, 3296, 3308, 2180, 2204, 2205}"
46,1,211,0,0.3206988,"\int (c+d x)^{3/2} \sinh ^2(a+b x) \, dx","Int[(c + d*x)^(3/2)*Sinh[a + b*x]^2,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}","\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,"(-3*d*Sqrt[c + d*x])/(16*b^2) - (c + d*x)^(5/2)/(5*d) + (3*d^(3/2)*E^(-2*a + (2*b*c)/d)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(64*b^(5/2)) + (3*d^(3/2)*E^(2*a - (2*b*c)/d)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(64*b^(5/2)) + ((c + d*x)^(3/2)*Cosh[a + b*x]*Sinh[a + b*x])/(2*b) - (3*d*Sqrt[c + d*x]*Sinh[a + b*x]^2)/(8*b^2)","A",9,7,18,0.3889,1,"{3311, 32, 3312, 3307, 2180, 2204, 2205}"
47,1,166,0,0.2957109,"\int \sqrt{c+d x} \sinh ^2(a+b x) \, dx","Int[Sqrt[c + d*x]*Sinh[a + b*x]^2,x]","\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}","\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,"-(c + d*x)^(3/2)/(3*d) + (Sqrt[d]*E^(-2*a + (2*b*c)/d)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(16*b^(3/2)) - (Sqrt[d]*E^(2*a - (2*b*c)/d)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(16*b^(3/2)) + (Sqrt[c + d*x]*Sinh[2*a + 2*b*x])/(4*b)","A",8,6,18,0.3333,1,"{3312, 3296, 3308, 2180, 2204, 2205}"
48,1,139,0,0.2413076,"\int \frac{\sinh ^2(a+b x)}{\sqrt{c+d x}} \, dx","Int[Sinh[a + b*x]^2/Sqrt[c + d*x],x]","\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}","\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[Pi/2]*Erf[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(4*Sqrt[b]*Sqrt[d]) + (E^(2*a - (2*b*c)/d)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(4*Sqrt[b]*Sqrt[d])","A",7,5,18,0.2778,1,"{3312, 3307, 2180, 2204, 2205}"
49,1,142,0,0.2530185,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^{3/2}} \, dx","Int[Sinh[a + b*x]^2/(c + d*x)^(3/2),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}}","-\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,"-((Sqrt[b]*E^(-2*a + (2*b*c)/d)*Sqrt[Pi/2]*Erf[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/d^(3/2)) + (Sqrt[b]*E^(2*a - (2*b*c)/d)*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/d^(3/2) - (2*Sinh[a + b*x]^2)/(d*Sqrt[c + d*x])","A",7,6,18,0.3333,1,"{3313, 12, 3308, 2180, 2204, 2205}"
50,1,174,0,0.3212685,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^{5/2}} \, dx","Int[Sinh[a + b*x]^2/(c + d*x)^(5/2),x]","\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}}","\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*b^(3/2)*E^(-2*a + (2*b*c)/d)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(3*d^(5/2)) + (2*b^(3/2)*E^(2*a - (2*b*c)/d)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(3*d^(5/2)) - (8*b*Cosh[a + b*x]*Sinh[a + b*x])/(3*d^2*Sqrt[c + d*x]) - (2*Sinh[a + b*x]^2)/(3*d*(c + d*x)^(3/2))","A",9,7,18,0.3889,1,"{3314, 32, 3312, 3307, 2180, 2204, 2205}"
51,1,220,0,0.3215644,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^{7/2}} \, dx","Int[Sinh[a + b*x]^2/(c + d*x)^(7/2),x]","-\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}}","-\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,"(-16*b^2)/(15*d^3*Sqrt[c + d*x]) - (8*b^(5/2)*E^(-2*a + (2*b*c)/d)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(15*d^(7/2)) + (8*b^(5/2)*E^(2*a - (2*b*c)/d)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(15*d^(7/2)) - (8*b*Cosh[a + b*x]*Sinh[a + b*x])/(15*d^2*(c + d*x)^(3/2)) - (2*Sinh[a + b*x]^2)/(5*d*(c + d*x)^(5/2)) - (32*b^2*Sinh[a + b*x]^2)/(15*d^3*Sqrt[c + d*x])","A",9,8,18,0.4444,1,"{3314, 32, 3313, 12, 3308, 2180, 2204, 2205}"
52,1,251,0,0.3949816,"\int \frac{\sinh ^2(a+b x)}{(c+d x)^{9/2}} \, dx","Int[Sinh[a + b*x]^2/(c + d*x)^(9/2),x]","\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{32 b^2 \sinh ^2(a+b x)}{105 d^3 (c+d x)^{3/2}}-\frac{128 b^3 \sinh (a+b x) \cosh (a+b x)}{105 d^4 \sqrt{c+d x}}-\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}}","\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{32 b^2 \sinh ^2(a+b x)}{105 d^3 (c+d x)^{3/2}}-\frac{128 b^3 \sinh (a+b x) \cosh (a+b x)}{105 d^4 \sqrt{c+d x}}-\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,"(-16*b^2)/(105*d^3*(c + d*x)^(3/2)) + (32*b^(7/2)*E^(-2*a + (2*b*c)/d)*Sqrt[2*Pi]*Erf[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(105*d^(9/2)) + (32*b^(7/2)*E^(2*a - (2*b*c)/d)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(105*d^(9/2)) - (8*b*Cosh[a + b*x]*Sinh[a + b*x])/(35*d^2*(c + d*x)^(5/2)) - (128*b^3*Cosh[a + b*x]*Sinh[a + b*x])/(105*d^4*Sqrt[c + d*x]) - (2*Sinh[a + b*x]^2)/(7*d*(c + d*x)^(7/2)) - (32*b^2*Sinh[a + b*x]^2)/(105*d^3*(c + d*x)^(3/2))","A",11,7,18,0.3889,1,"{3314, 32, 3312, 3307, 2180, 2204, 2205}"
53,1,381,0,1.0660818,"\int (c+d x)^{5/2} \sinh ^3(a+b x) \, dx","Int[(c + d*x)^(5/2)*Sinh[a + b*x]^3,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}","\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,"(-45*d^2*Sqrt[c + d*x]*Cosh[a + b*x])/(16*b^3) - (2*(c + d*x)^(5/2)*Cosh[a + b*x])/(3*b) + (5*d^2*Sqrt[c + d*x]*Cosh[3*a + 3*b*x])/(144*b^3) + (45*d^(5/2)*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(64*b^(7/2)) - (5*d^(5/2)*E^(-3*a + (3*b*c)/d)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(576*b^(7/2)) + (45*d^(5/2)*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(64*b^(7/2)) - (5*d^(5/2)*E^(3*a - (3*b*c)/d)*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(576*b^(7/2)) + (5*d*(c + d*x)^(3/2)*Sinh[a + b*x])/(3*b^2) + ((c + d*x)^(5/2)*Cosh[a + b*x]*Sinh[a + b*x]^2)/(3*b) - (5*d*(c + d*x)^(3/2)*Sinh[a + b*x]^3)/(18*b^2)","A",23,7,18,0.3889,1,"{3311, 3296, 3307, 2180, 2204, 2205, 3312}"
54,1,325,0,0.7991318,"\int (c+d x)^{3/2} \sinh ^3(a+b x) \, dx","Int[(c + d*x)^(3/2)*Sinh[a + b*x]^3,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}","\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,"(-2*(c + d*x)^(3/2)*Cosh[a + b*x])/(3*b) + (9*d^(3/2)*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(32*b^(5/2)) - (d^(3/2)*E^(-3*a + (3*b*c)/d)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(96*b^(5/2)) - (9*d^(3/2)*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(32*b^(5/2)) + (d^(3/2)*E^(3*a - (3*b*c)/d)*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(96*b^(5/2)) + (d*Sqrt[c + d*x]*Sinh[a + b*x])/b^2 + ((c + d*x)^(3/2)*Cosh[a + b*x]*Sinh[a + b*x]^2)/(3*b) - (d*Sqrt[c + d*x]*Sinh[a + b*x]^3)/(6*b^2)","A",20,7,18,0.3889,1,"{3311, 3296, 3308, 2180, 2204, 2205, 3312}"
55,1,275,0,0.5219091,"\int \sqrt{c+d x} \sinh ^3(a+b x) \, dx","Int[Sqrt[c + d*x]*Sinh[a + b*x]^3,x]","\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}","\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,"(-3*Sqrt[c + d*x]*Cosh[a + b*x])/(4*b) + (Sqrt[c + d*x]*Cosh[3*a + 3*b*x])/(12*b) + (3*Sqrt[d]*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(16*b^(3/2)) - (Sqrt[d]*E^(-3*a + (3*b*c)/d)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(48*b^(3/2)) + (3*Sqrt[d]*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(16*b^(3/2)) - (Sqrt[d]*E^(3*a - (3*b*c)/d)*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(48*b^(3/2))","A",14,6,18,0.3333,1,"{3312, 3296, 3307, 2180, 2204, 2205}"
56,1,228,0,0.4011388,"\int \frac{\sinh ^3(a+b x)}{\sqrt{c+d x}} \, dx","Int[Sinh[a + b*x]^3/Sqrt[c + d*x],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}}","\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,"(3*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(8*Sqrt[b]*Sqrt[d]) - (E^(-3*a + (3*b*c)/d)*Sqrt[Pi/3]*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(8*Sqrt[b]*Sqrt[d]) - (3*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(8*Sqrt[b]*Sqrt[d]) + (E^(3*a - (3*b*c)/d)*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(8*Sqrt[b]*Sqrt[d])","A",12,5,18,0.2778,1,"{3312, 3308, 2180, 2204, 2205}"
57,1,246,0,0.4538344,"\int \frac{\sinh ^3(a+b x)}{(c+d x)^{3/2}} \, dx","Int[Sinh[a + b*x]^3/(c + d*x)^(3/2),x]","-\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}}","-\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*Sqrt[b]*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(4*d^(3/2)) + (Sqrt[b]*E^(-3*a + (3*b*c)/d)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(4*d^(3/2)) - (3*Sqrt[b]*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(4*d^(3/2)) + (Sqrt[b]*E^(3*a - (3*b*c)/d)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(4*d^(3/2)) - (2*Sinh[a + b*x]^3)/(d*Sqrt[c + d*x])","A",12,5,18,0.2778,1,"{3313, 3307, 2180, 2204, 2205}"
58,1,277,0,0.6726869,"\int \frac{\sinh ^3(a+b x)}{(c+d x)^{5/2}} \, dx","Int[Sinh[a + b*x]^3/(c + d*x)^(5/2),x]","\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}}","\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,"(b^(3/2)*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(2*d^(5/2)) - (b^(3/2)*E^(-3*a + (3*b*c)/d)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(2*d^(5/2)) - (b^(3/2)*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(2*d^(5/2)) + (b^(3/2)*E^(3*a - (3*b*c)/d)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(2*d^(5/2)) - (4*b*Cosh[a + b*x]*Sinh[a + b*x]^2)/(d^2*Sqrt[c + d*x]) - (2*Sinh[a + b*x]^3)/(3*d*(c + d*x)^(3/2))","A",18,6,18,0.3333,1,"{3314, 3308, 2180, 2204, 2205, 3312}"
59,1,331,0,0.7746468,"\int \frac{\sinh ^3(a+b x)}{(c+d x)^{7/2}} \, dx","Int[Sinh[a + b*x]^3/(c + d*x)^(7/2),x]","-\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}}","-\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,"-(b^(5/2)*E^(-a + (b*c)/d)*Sqrt[Pi]*Erf[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(5*d^(7/2)) + (3*b^(5/2)*E^(-3*a + (3*b*c)/d)*Sqrt[3*Pi]*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(5*d^(7/2)) - (b^(5/2)*E^(a - (b*c)/d)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(5*d^(7/2)) + (3*b^(5/2)*E^(3*a - (3*b*c)/d)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]])/(5*d^(7/2)) - (16*b^2*Sinh[a + b*x])/(5*d^3*Sqrt[c + d*x]) - (4*b*Cosh[a + b*x]*Sinh[a + b*x]^2)/(5*d^2*(c + d*x)^(3/2)) - (2*Sinh[a + b*x]^3)/(5*d*(c + d*x)^(5/2)) - (24*b^2*Sinh[a + b*x]^3)/(5*d^3*Sqrt[c + d*x])","A",19,7,18,0.3889,1,"{3314, 3297, 3307, 2180, 2204, 2205, 3313}"
60,1,111,0,0.1588844,"\int (d x)^{3/2} \sinh (f x) \, dx","Int[(d*x)^(3/2)*Sinh[f*x],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}","-\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*x)^(3/2)*Cosh[f*x])/f - (3*d^(3/2)*Sqrt[Pi]*Erf[(Sqrt[f]*Sqrt[d*x])/Sqrt[d]])/(8*f^(5/2)) + (3*d^(3/2)*Sqrt[Pi]*Erfi[(Sqrt[f]*Sqrt[d*x])/Sqrt[d]])/(8*f^(5/2)) - (3*d*Sqrt[d*x]*Sinh[f*x])/(2*f^2)","A",7,5,12,0.4167,1,"{3296, 3308, 2180, 2204, 2205}"
61,1,92,0,0.1101547,"\int \sqrt{d x} \sinh (f x) \, dx","Int[Sqrt[d*x]*Sinh[f*x],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}","-\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,"(Sqrt[d*x]*Cosh[f*x])/f - (Sqrt[d]*Sqrt[Pi]*Erf[(Sqrt[f]*Sqrt[d*x])/Sqrt[d]])/(4*f^(3/2)) - (Sqrt[d]*Sqrt[Pi]*Erfi[(Sqrt[f]*Sqrt[d*x])/Sqrt[d]])/(4*f^(3/2))","A",6,5,12,0.4167,1,"{3296, 3307, 2180, 2204, 2205}"
62,1,77,0,0.0761857,"\int \frac{\sinh (f x)}{\sqrt{d x}} \, dx","Int[Sinh[f*x]/Sqrt[d*x],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}}","\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[Pi]*Erf[(Sqrt[f]*Sqrt[d*x])/Sqrt[d]])/(2*Sqrt[d]*Sqrt[f]) + (Sqrt[Pi]*Erfi[(Sqrt[f]*Sqrt[d*x])/Sqrt[d]])/(2*Sqrt[d]*Sqrt[f])","A",5,4,12,0.3333,1,"{3308, 2180, 2204, 2205}"
63,1,87,0,0.1122842,"\int \frac{\sinh (f x)}{(d x)^{3/2}} \, dx","Int[Sinh[f*x]/(d*x)^(3/2),x]","\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}}","\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,"(Sqrt[f]*Sqrt[Pi]*Erf[(Sqrt[f]*Sqrt[d*x])/Sqrt[d]])/d^(3/2) + (Sqrt[f]*Sqrt[Pi]*Erfi[(Sqrt[f]*Sqrt[d*x])/Sqrt[d]])/d^(3/2) - (2*Sinh[f*x])/(d*Sqrt[d*x])","A",6,5,12,0.4167,1,"{3297, 3307, 2180, 2204, 2205}"
64,1,114,0,0.1490091,"\int \frac{\sinh (f x)}{(d x)^{5/2}} \, dx","Int[Sinh[f*x]/(d*x)^(5/2),x]","-\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}}","-\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,"(-4*f*Cosh[f*x])/(3*d^2*Sqrt[d*x]) - (2*f^(3/2)*Sqrt[Pi]*Erf[(Sqrt[f]*Sqrt[d*x])/Sqrt[d]])/(3*d^(5/2)) + (2*f^(3/2)*Sqrt[Pi]*Erfi[(Sqrt[f]*Sqrt[d*x])/Sqrt[d]])/(3*d^(5/2)) - (2*Sinh[f*x])/(3*d*(d*x)^(3/2))","A",7,5,12,0.4167,1,"{3297, 3308, 2180, 2204, 2205}"
65,0,0,0,0.0281708,"\int \sqrt{c+d x} \text{csch}(a+b x) \, dx","Int[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,"Defer[Int][Sqrt[c + d*x]*Csch[a + b*x], x]","A",0,0,0,0,-1,"{}"
66,0,0,0,0.0297394,"\int \frac{\text{csch}(a+b x)}{\sqrt{c+d x}} \, dx","Int[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,"Defer[Int][Csch[a + b*x]/Sqrt[c + d*x], x]","A",0,0,0,0,-1,"{}"
67,0,0,0,0.1071429,"\int \frac{\sinh ^{\frac{3}{2}}(x)}{x^3} \, dx","Int[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,"(-3*Cosh[x]*Sqrt[Sinh[x]])/(4*x) - Sinh[x]^(3/2)/(2*x^2) + (3*Defer[Int][1/(x*Sqrt[Sinh[x]]), x])/8 + (9*Defer[Int][Sinh[x]^(3/2)/x, x])/8","A",0,0,0,0,-1,"{}"
68,1,20,0,0.0583554,"\int \left(\frac{x}{\sinh ^{\frac{3}{2}}(x)}-x \sqrt{\sinh (x)}\right) \, dx","Int[x/Sinh[x]^(3/2) - x*Sqrt[Sinh[x]],x]","4 \sqrt{\sinh (x)}-\frac{2 x \cosh (x)}{\sqrt{\sinh (x)}}","4 \sqrt{\sinh (x)}-\frac{2 x \cosh (x)}{\sqrt{\sinh (x)}}",1,"(-2*x*Cosh[x])/Sqrt[Sinh[x]] + 4*Sqrt[Sinh[x]]","A",2,1,18,0.05556,1,"{3315}"
69,1,24,0,0.0602881,"\int \left(\frac{x}{\sinh ^{\frac{5}{2}}(x)}+\frac{x}{3 \sqrt{\sinh (x)}}\right) \, dx","Int[x/Sinh[x]^(5/2) + x/(3*Sqrt[Sinh[x]]),x]","-\frac{4}{3 \sqrt{\sinh (x)}}-\frac{2 x \cosh (x)}{3 \sinh ^{\frac{3}{2}}(x)}","-\frac{4}{3 \sqrt{\sinh (x)}}-\frac{2 x \cosh (x)}{3 \sinh ^{\frac{3}{2}}(x)}",1,"(-2*x*Cosh[x])/(3*Sinh[x]^(3/2)) - 4/(3*Sqrt[Sinh[x]])","A",2,1,20,0.05000,1,"{3315}"
70,1,47,0,0.0807323,"\int \left(\frac{x}{\sinh ^{\frac{7}{2}}(x)}+\frac{3}{5} x \sqrt{\sinh (x)}\right) \, dx","Int[x/Sinh[x]^(7/2) + (3*x*Sqrt[Sinh[x]])/5,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)}}","-\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,"(-2*x*Cosh[x])/(5*Sinh[x]^(5/2)) - 4/(15*Sinh[x]^(3/2)) + (6*x*Cosh[x])/(5*Sqrt[Sinh[x]]) - (12*Sqrt[Sinh[x]])/5","A",3,1,20,0.05000,1,"{3315}"
71,1,58,0,0.1184671,"\int \left(\frac{x^2}{\sinh ^{\frac{3}{2}}(x)}-x^2 \sqrt{\sinh (x)}\right) \, dx","Int[x^2/Sinh[x]^(3/2) - x^2*Sqrt[Sinh[x]],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)}}","-\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])/Sqrt[Sinh[x]] + 8*x*Sqrt[Sinh[x]] - ((16*I)*EllipticE[Pi/4 - (I/2)*x, 2]*Sqrt[Sinh[x]])/Sqrt[I*Sinh[x]]","A",4,3,22,0.1364,1,"{3316, 2640, 2639}"
72,0,0,0,0.0464853,"\int (c+d x)^m (b \sinh (e+f x))^n \, dx","Int[(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,"Defer[Int][(c + d*x)^m*(b*Sinh[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
73,1,237,0,0.3178318,"\int (c+d x)^m \sinh ^3(a+b x) \, dx","Int[(c + d*x)^m*Sinh[a + b*x]^3,x]","\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} \text{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} \text{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} \text{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} \text{Gamma}\left(m+1,\frac{3 b (c+d x)}{d}\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} \text{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} \text{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} \text{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} \text{Gamma}\left(m+1,\frac{3 b (c+d x)}{d}\right)}{8 b}",1,"(3^(-1 - m)*E^(3*a - (3*b*c)/d)*(c + d*x)^m*Gamma[1 + m, (-3*b*(c + d*x))/d])/(8*b*(-((b*(c + d*x))/d))^m) - (3*E^(a - (b*c)/d)*(c + d*x)^m*Gamma[1 + m, -((b*(c + d*x))/d)])/(8*b*(-((b*(c + d*x))/d))^m) - (3*E^(-a + (b*c)/d)*(c + d*x)^m*Gamma[1 + m, (b*(c + d*x))/d])/(8*b*((b*(c + d*x))/d)^m) + (3^(-1 - m)*E^(-3*a + (3*b*c)/d)*(c + d*x)^m*Gamma[1 + m, (3*b*(c + d*x))/d])/(8*b*((b*(c + d*x))/d)^m)","A",8,3,16,0.1875,1,"{3312, 3308, 2181}"
74,1,144,0,0.1973651,"\int (c+d x)^m \sinh ^2(a+b x) \, dx","Int[(c + d*x)^m*Sinh[a + b*x]^2,x]","\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} \text{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} \text{Gamma}\left(m+1,\frac{2 b (c+d x)}{d}\right)}{b}-\frac{(c+d x)^{m+1}}{2 d (m+1)}","\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} \text{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} \text{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)^(1 + m)/(2*d*(1 + m)) + (2^(-3 - m)*E^(2*a - (2*b*c)/d)*(c + d*x)^m*Gamma[1 + m, (-2*b*(c + d*x))/d])/(b*(-((b*(c + d*x))/d))^m) - (2^(-3 - m)*E^(-2*a + (2*b*c)/d)*(c + d*x)^m*Gamma[1 + m, (2*b*(c + d*x))/d])/(b*((b*(c + d*x))/d)^m)","A",5,3,16,0.1875,1,"{3312, 3307, 2181}"
75,1,110,0,0.0930162,"\int (c+d x)^m \sinh (a+b x) \, dx","Int[(c + d*x)^m*Sinh[a + b*x],x]","\frac{e^{a-\frac{b c}{d}} (c+d x)^m \left(-\frac{b (c+d x)}{d}\right)^{-m} \text{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} \text{Gamma}\left(m+1,\frac{b (c+d x)}{d}\right)}{2 b}","\frac{e^{a-\frac{b c}{d}} (c+d x)^m \left(-\frac{b (c+d x)}{d}\right)^{-m} \text{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} \text{Gamma}\left(m+1,\frac{b (c+d x)}{d}\right)}{2 b}",1,"(E^(a - (b*c)/d)*(c + d*x)^m*Gamma[1 + m, -((b*(c + d*x))/d)])/(2*b*(-((b*(c + d*x))/d))^m) + (E^(-a + (b*c)/d)*(c + d*x)^m*Gamma[1 + m, (b*(c + d*x))/d])/(2*b*((b*(c + d*x))/d)^m)","A",3,2,14,0.1429,1,"{3308, 2181}"
76,0,0,0,0.020653,"\int (c+d x)^m \text{csch}(a+b x) \, dx","Int[(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,"Defer[Int][(c + d*x)^m*Csch[a + b*x], x]","A",0,0,0,0,-1,"{}"
77,0,0,0,0.0369156,"\int (c+d x)^m \text{csch}^2(a+b x) \, dx","Int[(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,"Defer[Int][(c + d*x)^m*Csch[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
78,1,59,0,0.0777343,"\int x^{3+m} \sinh (a+b x) \, dx","Int[x^(3 + m)*Sinh[a + b*x],x]","\frac{e^{-a} x^m (b x)^{-m} \text{Gamma}(m+4,b x)}{2 b^4}-\frac{e^a x^m (-b x)^{-m} \text{Gamma}(m+4,-b x)}{2 b^4}","\frac{e^{-a} x^m (b x)^{-m} \text{Gamma}(m+4,b x)}{2 b^4}-\frac{e^a x^m (-b x)^{-m} \text{Gamma}(m+4,-b x)}{2 b^4}",1,"-(E^a*x^m*Gamma[4 + m, -(b*x)])/(2*b^4*(-(b*x))^m) + (x^m*Gamma[4 + m, b*x])/(2*b^4*E^a*(b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
79,1,59,0,0.0730884,"\int x^{2+m} \sinh (a+b x) \, dx","Int[x^(2 + m)*Sinh[a + b*x],x]","\frac{e^a x^m (-b x)^{-m} \text{Gamma}(m+3,-b x)}{2 b^3}+\frac{e^{-a} x^m (b x)^{-m} \text{Gamma}(m+3,b x)}{2 b^3}","\frac{e^a x^m (-b x)^{-m} \text{Gamma}(m+3,-b x)}{2 b^3}+\frac{e^{-a} x^m (b x)^{-m} \text{Gamma}(m+3,b x)}{2 b^3}",1,"(E^a*x^m*Gamma[3 + m, -(b*x)])/(2*b^3*(-(b*x))^m) + (x^m*Gamma[3 + m, b*x])/(2*b^3*E^a*(b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
80,1,59,0,0.0736857,"\int x^{1+m} \sinh (a+b x) \, dx","Int[x^(1 + m)*Sinh[a + b*x],x]","\frac{e^{-a} x^m (b x)^{-m} \text{Gamma}(m+2,b x)}{2 b^2}-\frac{e^a x^m (-b x)^{-m} \text{Gamma}(m+2,-b x)}{2 b^2}","\frac{e^{-a} x^m (b x)^{-m} \text{Gamma}(m+2,b x)}{2 b^2}-\frac{e^a x^m (-b x)^{-m} \text{Gamma}(m+2,-b x)}{2 b^2}",1,"-(E^a*x^m*Gamma[2 + m, -(b*x)])/(2*b^2*(-(b*x))^m) + (x^m*Gamma[2 + m, b*x])/(2*b^2*E^a*(b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
81,1,59,0,0.0701193,"\int x^m \sinh (a+b x) \, dx","Int[x^m*Sinh[a + b*x],x]","\frac{e^a x^m (-b x)^{-m} \text{Gamma}(m+1,-b x)}{2 b}+\frac{e^{-a} x^m (b x)^{-m} \text{Gamma}(m+1,b x)}{2 b}","\frac{e^a x^m (-b x)^{-m} \text{Gamma}(m+1,-b x)}{2 b}+\frac{e^{-a} x^m (b x)^{-m} \text{Gamma}(m+1,b x)}{2 b}",1,"(E^a*x^m*Gamma[1 + m, -(b*x)])/(2*b*(-(b*x))^m) + (x^m*Gamma[1 + m, b*x])/(2*b*E^a*(b*x)^m)","A",3,2,10,0.2000,1,"{3308, 2181}"
82,1,49,0,0.0694422,"\int x^{-1+m} \sinh (a+b x) \, dx","Int[x^(-1 + m)*Sinh[a + b*x],x]","\frac{1}{2} e^{-a} x^m (b x)^{-m} \text{Gamma}(m,b x)-\frac{1}{2} e^a x^m (-b x)^{-m} \text{Gamma}(m,-b x)","\frac{1}{2} e^{-a} x^m (b x)^{-m} \text{Gamma}(m,b x)-\frac{1}{2} e^a x^m (-b x)^{-m} \text{Gamma}(m,-b x)",1,"-(E^a*x^m*Gamma[m, -(b*x)])/(2*(-(b*x))^m) + (x^m*Gamma[m, b*x])/(2*E^a*(b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
83,1,55,0,0.069492,"\int x^{-2+m} \sinh (a+b x) \, dx","Int[x^(-2 + m)*Sinh[a + b*x],x]","\frac{1}{2} e^a b x^m (-b x)^{-m} \text{Gamma}(m-1,-b x)+\frac{1}{2} e^{-a} b x^m (b x)^{-m} \text{Gamma}(m-1,b x)","\frac{1}{2} e^a b x^m (-b x)^{-m} \text{Gamma}(m-1,-b x)+\frac{1}{2} e^{-a} b x^m (b x)^{-m} \text{Gamma}(m-1,b x)",1,"(b*E^a*x^m*Gamma[-1 + m, -(b*x)])/(2*(-(b*x))^m) + (b*x^m*Gamma[-1 + m, b*x])/(2*E^a*(b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
84,1,59,0,0.0708014,"\int x^{-3+m} \sinh (a+b x) \, dx","Int[x^(-3 + m)*Sinh[a + b*x],x]","\frac{1}{2} e^{-a} b^2 x^m (b x)^{-m} \text{Gamma}(m-2,b x)-\frac{1}{2} e^a b^2 x^m (-b x)^{-m} \text{Gamma}(m-2,-b x)","\frac{1}{2} e^{-a} b^2 x^m (b x)^{-m} \text{Gamma}(m-2,b x)-\frac{1}{2} e^a b^2 x^m (-b x)^{-m} \text{Gamma}(m-2,-b x)",1,"-(b^2*E^a*x^m*Gamma[-2 + m, -(b*x)])/(2*(-(b*x))^m) + (b^2*x^m*Gamma[-2 + m, b*x])/(2*E^a*(b*x)^m)","A",3,2,12,0.1667,1,"{3308, 2181}"
85,1,86,0,0.1585286,"\int x^{3+m} \sinh ^2(a+b x) \, dx","Int[x^(3 + m)*Sinh[a + b*x]^2,x]","-\frac{e^{2 a} 2^{-m-6} x^m (-b x)^{-m} \text{Gamma}(m+4,-2 b x)}{b^4}-\frac{e^{-2 a} 2^{-m-6} x^m (b x)^{-m} \text{Gamma}(m+4,2 b x)}{b^4}-\frac{x^{m+4}}{2 (m+4)}","-\frac{e^{2 a} 2^{-m-6} x^m (-b x)^{-m} \text{Gamma}(m+4,-2 b x)}{b^4}-\frac{e^{-2 a} 2^{-m-6} x^m (b x)^{-m} \text{Gamma}(m+4,2 b x)}{b^4}-\frac{x^{m+4}}{2 (m+4)}",1,"-x^(4 + m)/(2*(4 + m)) - (2^(-6 - m)*E^(2*a)*x^m*Gamma[4 + m, -2*b*x])/(b^4*(-(b*x))^m) - (2^(-6 - m)*x^m*Gamma[4 + m, 2*b*x])/(b^4*E^(2*a)*(b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
86,1,85,0,0.135763,"\int x^{2+m} \sinh ^2(a+b x) \, dx","Int[x^(2 + m)*Sinh[a + b*x]^2,x]","\frac{e^{2 a} 2^{-m-5} x^m (-b x)^{-m} \text{Gamma}(m+3,-2 b x)}{b^3}-\frac{e^{-2 a} 2^{-m-5} x^m (b x)^{-m} \text{Gamma}(m+3,2 b x)}{b^3}-\frac{x^{m+3}}{2 (m+3)}","\frac{e^{2 a} 2^{-m-5} x^m (-b x)^{-m} \text{Gamma}(m+3,-2 b x)}{b^3}-\frac{e^{-2 a} 2^{-m-5} x^m (b x)^{-m} \text{Gamma}(m+3,2 b x)}{b^3}-\frac{x^{m+3}}{2 (m+3)}",1,"-x^(3 + m)/(2*(3 + m)) + (2^(-5 - m)*E^(2*a)*x^m*Gamma[3 + m, -2*b*x])/(b^3*(-(b*x))^m) - (2^(-5 - m)*x^m*Gamma[3 + m, 2*b*x])/(b^3*E^(2*a)*(b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
87,1,86,0,0.1399438,"\int x^{1+m} \sinh ^2(a+b x) \, dx","Int[x^(1 + m)*Sinh[a + b*x]^2,x]","-\frac{e^{2 a} 2^{-m-4} x^m (-b x)^{-m} \text{Gamma}(m+2,-2 b x)}{b^2}-\frac{e^{-2 a} 2^{-m-4} x^m (b x)^{-m} \text{Gamma}(m+2,2 b x)}{b^2}-\frac{x^{m+2}}{2 (m+2)}","-\frac{e^{2 a} 2^{-m-4} x^m (-b x)^{-m} \text{Gamma}(m+2,-2 b x)}{b^2}-\frac{e^{-2 a} 2^{-m-4} x^m (b x)^{-m} \text{Gamma}(m+2,2 b x)}{b^2}-\frac{x^{m+2}}{2 (m+2)}",1,"-x^(2 + m)/(2*(2 + m)) - (2^(-4 - m)*E^(2*a)*x^m*Gamma[2 + m, -2*b*x])/(b^2*(-(b*x))^m) - (2^(-4 - m)*x^m*Gamma[2 + m, 2*b*x])/(b^2*E^(2*a)*(b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
88,1,85,0,0.1268697,"\int x^m \sinh ^2(a+b x) \, dx","Int[x^m*Sinh[a + b*x]^2,x]","\frac{e^{2 a} 2^{-m-3} x^m (-b x)^{-m} \text{Gamma}(m+1,-2 b x)}{b}-\frac{e^{-2 a} 2^{-m-3} x^m (b x)^{-m} \text{Gamma}(m+1,2 b x)}{b}-\frac{x^{m+1}}{2 (m+1)}","\frac{e^{2 a} 2^{-m-3} x^m (-b x)^{-m} \text{Gamma}(m+1,-2 b x)}{b}-\frac{e^{-2 a} 2^{-m-3} x^m (b x)^{-m} \text{Gamma}(m+1,2 b x)}{b}-\frac{x^{m+1}}{2 (m+1)}",1,"-x^(1 + m)/(2*(1 + m)) + (2^(-3 - m)*E^(2*a)*x^m*Gamma[1 + m, -2*b*x])/(b*(-(b*x))^m) - (2^(-3 - m)*x^m*Gamma[1 + m, 2*b*x])/(b*E^(2*a)*(b*x)^m)","A",5,3,12,0.2500,1,"{3312, 3307, 2181}"
89,1,72,0,0.1269155,"\int x^{-1+m} \sinh ^2(a+b x) \, dx","Int[x^(-1 + m)*Sinh[a + b*x]^2,x]","e^{2 a} \left(-2^{-m-2}\right) x^m (-b x)^{-m} \text{Gamma}(m,-2 b x)-e^{-2 a} 2^{-m-2} x^m (b x)^{-m} \text{Gamma}(m,2 b x)-\frac{x^m}{2 m}","e^{2 a} \left(-2^{-m-2}\right) x^m (-b x)^{-m} \text{Gamma}(m,-2 b x)-e^{-2 a} 2^{-m-2} x^m (b x)^{-m} \text{Gamma}(m,2 b x)-\frac{x^m}{2 m}",1,"-x^m/(2*m) - (2^(-2 - m)*E^(2*a)*x^m*Gamma[m, -2*b*x])/(-(b*x))^m - (2^(-2 - m)*x^m*Gamma[m, 2*b*x])/(E^(2*a)*(b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
90,1,83,0,0.1368256,"\int x^{-2+m} \sinh ^2(a+b x) \, dx","Int[x^(-2 + m)*Sinh[a + b*x]^2,x]","e^{2 a} b 2^{-m-1} x^m (-b x)^{-m} \text{Gamma}(m-1,-2 b x)-e^{-2 a} b 2^{-m-1} x^m (b x)^{-m} \text{Gamma}(m-1,2 b x)+\frac{x^{m-1}}{2 (1-m)}","e^{2 a} b 2^{-m-1} x^m (-b x)^{-m} \text{Gamma}(m-1,-2 b x)-e^{-2 a} b 2^{-m-1} x^m (b x)^{-m} \text{Gamma}(m-1,2 b x)+\frac{x^{m-1}}{2 (1-m)}",1,"x^(-1 + m)/(2*(1 - m)) + (2^(-1 - m)*b*E^(2*a)*x^m*Gamma[-1 + m, -2*b*x])/(-(b*x))^m - (2^(-1 - m)*b*x^m*Gamma[-1 + m, 2*b*x])/(E^(2*a)*(b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
91,1,84,0,0.1426524,"\int x^{-3+m} \sinh ^2(a+b x) \, dx","Int[x^(-3 + m)*Sinh[a + b*x]^2,x]","-e^{2 a} b^2 2^{-m} x^m (-b x)^{-m} \text{Gamma}(m-2,-2 b x)-e^{-2 a} b^2 2^{-m} x^m (b x)^{-m} \text{Gamma}(m-2,2 b x)+\frac{x^{m-2}}{2 (2-m)}","-e^{2 a} b^2 2^{-m} x^m (-b x)^{-m} \text{Gamma}(m-2,-2 b x)-e^{-2 a} b^2 2^{-m} x^m (b x)^{-m} \text{Gamma}(m-2,2 b x)+\frac{x^{m-2}}{2 (2-m)}",1,"x^(-2 + m)/(2*(2 - m)) - (b^2*E^(2*a)*x^m*Gamma[-2 + m, -2*b*x])/(2^m*(-(b*x))^m) - (b^2*x^m*Gamma[-2 + m, 2*b*x])/(2^m*E^(2*a)*(b*x)^m)","A",5,3,14,0.2143,1,"{3312, 3307, 2181}"
92,1,24,0,0.111688,"\int \left(\frac{x}{\text{csch}^{\frac{3}{2}}(x)}+\frac{1}{3} x \sqrt{\text{csch}(x)}\right) \, dx","Int[x/Csch[x]^(3/2) + (x*Sqrt[Csch[x]])/3,x]","\frac{2 x \cosh (x)}{3 \sqrt{\text{csch}(x)}}-\frac{4}{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,"-4/(9*Csch[x]^(3/2)) + (2*x*Cosh[x])/(3*Sqrt[Csch[x]])","A",4,2,20,0.1000,1,"{4187, 4189}"
93,1,24,0,0.117555,"\int \left(\frac{x}{\text{csch}^{\frac{5}{2}}(x)}+\frac{3 x}{5 \sqrt{\text{csch}(x)}}\right) \, dx","Int[x/Csch[x]^(5/2) + (3*x)/(5*Sqrt[Csch[x]]),x]","\frac{2 x \cosh (x)}{5 \text{csch}^{\frac{3}{2}}(x)}-\frac{4}{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,"-4/(25*Csch[x]^(5/2)) + (2*x*Cosh[x])/(5*Csch[x]^(3/2))","A",4,2,20,0.1000,1,"{4187, 4189}"
94,1,47,0,0.1296313,"\int \left(\frac{x}{\text{csch}^{\frac{7}{2}}(x)}-\frac{5}{21} x \sqrt{\text{csch}(x)}\right) \, dx","Int[x/Csch[x]^(7/2) - (5*x*Sqrt[Csch[x]])/21,x]","\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)}}","\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,"-4/(49*Csch[x]^(7/2)) + (2*x*Cosh[x])/(7*Csch[x]^(5/2)) + 20/(63*Csch[x]^(3/2)) - (10*x*Cosh[x])/(21*Sqrt[Csch[x]])","A",5,2,20,0.1000,1,"{4187, 4189}"
95,1,76,0,0.2070914,"\int \left(\frac{x^2}{\text{csch}^{\frac{3}{2}}(x)}+\frac{1}{3} x^2 \sqrt{\text{csch}(x)}\right) \, dx","Int[x^2/Csch[x]^(3/2) + (x^2*Sqrt[Csch[x]])/3,x]","\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)","\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,"(-8*x)/(9*Csch[x]^(3/2)) + (16*Cosh[x])/(27*Sqrt[Csch[x]]) + (2*x^2*Cosh[x])/(3*Sqrt[Csch[x]]) - ((16*I)/27)*Sqrt[Csch[x]]*EllipticF[Pi/4 - (I/2)*x, 2]*Sqrt[I*Sinh[x]]","A",7,5,24,0.2083,1,"{4188, 4189, 3769, 3771, 2641}"
96,1,98,0,0.1399521,"\int (c+d x)^3 (a+i a \sinh (e+f x)) \, dx","Int[(c + d*x)^3*(a + I*a*Sinh[e + f*x]),x]","\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}","\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*(c + d*x)^4)/(4*d) + ((6*I)*a*d^2*(c + d*x)*Cosh[e + f*x])/f^3 + (I*a*(c + d*x)^3*Cosh[e + f*x])/f - ((6*I)*a*d^3*Sinh[e + f*x])/f^4 - ((3*I)*a*d*(c + d*x)^2*Sinh[e + f*x])/f^2","A",6,3,21,0.1429,1,"{3317, 3296, 2637}"
97,1,74,0,0.0970964,"\int (c+d x)^2 (a+i a \sinh (e+f x)) \, dx","Int[(c + d*x)^2*(a + I*a*Sinh[e + f*x]),x]","-\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}","-\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*(c + d*x)^3)/(3*d) + ((2*I)*a*d^2*Cosh[e + f*x])/f^3 + (I*a*(c + d*x)^2*Cosh[e + f*x])/f - ((2*I)*a*d*(c + d*x)*Sinh[e + f*x])/f^2","A",5,3,21,0.1429,1,"{3317, 3296, 2638}"
98,1,50,0,0.0533599,"\int (c+d x) (a+i a \sinh (e+f x)) \, dx","Int[(c + d*x)*(a + I*a*Sinh[e + f*x]),x]","\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}","\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*(c + d*x)^2)/(2*d) + (I*a*(c + d*x)*Cosh[e + f*x])/f - (I*a*d*Sinh[e + f*x])/f^2","A",4,3,19,0.1579,1,"{3317, 3296, 2637}"
99,1,70,0,0.1614178,"\int \frac{a+i a \sinh (e+f x)}{c+d x} \, dx","Int[(a + I*a*Sinh[e + f*x])/(c + d*x),x]","\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}","\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])/d + (I*a*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d + (I*a*Cosh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d","A",5,4,21,0.1905,1,"{3317, 3303, 3298, 3301}"
100,1,95,0,0.1891068,"\int \frac{a+i a \sinh (e+f x)}{(c+d x)^2} \, dx","Int[(a + I*a*Sinh[e + f*x])/(c + d*x)^2,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)}","\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,"-(a/(d*(c + d*x))) + (I*a*f*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/d^2 - (I*a*Sinh[e + f*x])/(d*(c + d*x)) + (I*a*f*Sinh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d^2","A",6,5,21,0.2381,1,"{3317, 3297, 3303, 3298, 3301}"
101,1,131,0,0.2322278,"\int \frac{a+i a \sinh (e+f x)}{(c+d x)^3} \, dx","Int[(a + I*a*Sinh[e + f*x])/(c + d*x)^3,x]","\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}","\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,"-a/(2*d*(c + d*x)^2) - ((I/2)*a*f*Cosh[e + f*x])/(d^2*(c + d*x)) + ((I/2)*a*f^2*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d^3 - ((I/2)*a*Sinh[e + f*x])/(d*(c + d*x)^2) + ((I/2)*a*f^2*Cosh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d^3","A",7,5,21,0.2381,1,"{3317, 3297, 3303, 3298, 3301}"
102,1,245,0,0.2871256,"\int (c+d x)^3 (a+i a \sinh (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + I*a*Sinh[e + f*x])^2,x]","\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}","\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,"(3*a^2*c*d^2*x)/(4*f^2) + (3*a^2*d^3*x^2)/(8*f^2) + (3*a^2*(c + d*x)^4)/(8*d) + ((12*I)*a^2*d^2*(c + d*x)*Cosh[e + f*x])/f^3 + ((2*I)*a^2*(c + d*x)^3*Cosh[e + f*x])/f - ((12*I)*a^2*d^3*Sinh[e + f*x])/f^4 - ((6*I)*a^2*d*(c + d*x)^2*Sinh[e + f*x])/f^2 - (3*a^2*d^2*(c + d*x)*Cosh[e + f*x]*Sinh[e + f*x])/(4*f^3) - (a^2*(c + d*x)^3*Cosh[e + f*x]*Sinh[e + f*x])/(2*f) + (3*a^2*d^3*Sinh[e + f*x]^2)/(8*f^4) + (3*a^2*d*(c + d*x)^2*Sinh[e + f*x]^2)/(4*f^2)","A",10,6,23,0.2609,1,"{3317, 3296, 2637, 3311, 32, 3310}"
103,1,174,0,0.1971839,"\int (c+d x)^2 (a+i a \sinh (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + I*a*Sinh[e + f*x])^2,x]","\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}","\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*d^2*x)/(4*f^2) + (a^2*(c + d*x)^3)/(2*d) + ((4*I)*a^2*d^2*Cosh[e + f*x])/f^3 + ((2*I)*a^2*(c + d*x)^2*Cosh[e + f*x])/f - ((4*I)*a^2*d*(c + d*x)*Sinh[e + f*x])/f^2 - (a^2*d^2*Cosh[e + f*x]*Sinh[e + f*x])/(4*f^3) - (a^2*(c + d*x)^2*Cosh[e + f*x]*Sinh[e + f*x])/(2*f) + (a^2*d*(c + d*x)*Sinh[e + f*x]^2)/(2*f^2)","A",9,7,23,0.3043,1,"{3317, 3296, 2638, 3311, 32, 2635, 8}"
104,1,122,0,0.1050154,"\int (c+d x) (a+i a \sinh (e+f x))^2 \, dx","Int[(c + d*x)*(a + I*a*Sinh[e + f*x])^2,x]","\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","\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*c*x)/2 + (a^2*d*x^2)/4 + (a^2*(c + d*x)^2)/(2*d) + ((2*I)*a^2*(c + d*x)*Cosh[e + f*x])/f - ((2*I)*a^2*d*Sinh[e + f*x])/f^2 - (a^2*(c + d*x)*Cosh[e + f*x]*Sinh[e + f*x])/(2*f) + (a^2*d*Sinh[e + f*x]^2)/(4*f^2)","A",6,4,21,0.1905,1,"{3317, 3296, 2637, 3310}"
105,1,149,0,0.352419,"\int \frac{(a+i a \sinh (e+f x))^2}{c+d x} \, dx","Int[(a + I*a*Sinh[e + f*x])^2/(c + d*x),x]","\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}","\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,"-(a^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/(2*d) + (3*a^2*Log[c + d*x])/(2*d) + ((2*I)*a^2*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d + ((2*I)*a^2*Cosh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d - (a^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(2*d)","A",9,5,23,0.2174,1,"{3318, 3312, 3303, 3298, 3301}"
106,1,170,0,0.3399946,"\int \frac{(a+i a \sinh (e+f x))^2}{(c+d x)^2} \, dx","Int[(a + I*a*Sinh[e + f*x])^2/(c + d*x)^2,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)}","-\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,"(-4*a^2*Cosh[e/2 + (I/4)*Pi + (f*x)/2]^4)/(d*(c + d*x)) + ((2*I)*a^2*f*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/d^2 - (a^2*f*CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/d^2 + ((2*I)*a^2*f*Sinh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d^2 - (a^2*f*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/d^2","A",9,5,23,0.2174,1,"{3318, 3313, 3303, 3298, 3301}"
107,1,236,0,0.5300176,"\int \frac{(a+i a \sinh (e+f x))^2}{(c+d x)^3} \, dx","Int[(a + I*a*Sinh[e + f*x])^2/(c + d*x)^3,x]","\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}","\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,"(-2*a^2*Cosh[e/2 + (I/4)*Pi + (f*x)/2]^4)/(d*(c + d*x)^2) - (a^2*f^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/d^3 + (I*a^2*f^2*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d^3 - (4*a^2*f*Cosh[e/2 + (I/4)*Pi + (f*x)/2]^3*Sinh[e/2 + (I/4)*Pi + (f*x)/2])/(d^2*(c + d*x)) + (I*a^2*f^2*Cosh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d^3 - (a^2*f^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/d^3","A",15,6,23,0.2609,1,"{3318, 3314, 3312, 3303, 3298, 3301}"
108,1,132,0,0.3022917,"\int \frac{(c+d x)^3}{a+i a \sinh (e+f x)} \, dx","Int[(c + d*x)^3/(a + I*a*Sinh[e + f*x]),x]","-\frac{12 d^2 (c+d x) \text{PolyLog}\left(2,-i e^{e+f x}\right)}{a f^3}+\frac{12 d^3 \text{PolyLog}\left(3,-i e^{e+f x}\right)}{a f^4}-\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^2 (c+d x) \text{PolyLog}\left(2,-i e^{e+f x}\right)}{a f^3}+\frac{12 d^3 \text{PolyLog}\left(3,-i e^{e+f x}\right)}{a f^4}-\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}",1,"(c + d*x)^3/(a*f) - (6*d*(c + d*x)^2*Log[1 + I*E^(e + f*x)])/(a*f^2) - (12*d^2*(c + d*x)*PolyLog[2, (-I)*E^(e + f*x)])/(a*f^3) + (12*d^3*PolyLog[3, (-I)*E^(e + f*x)])/(a*f^4) + ((c + d*x)^3*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(a*f)","A",7,7,23,0.3043,1,"{3318, 4184, 3716, 2190, 2531, 2282, 6589}"
109,1,101,0,0.2187077,"\int \frac{(c+d x)^2}{a+i a \sinh (e+f x)} \, dx","Int[(c + d*x)^2/(a + I*a*Sinh[e + f*x]),x]","-\frac{4 d^2 \text{PolyLog}\left(2,-i e^{e+f x}\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{PolyLog}\left(2,-i e^{e+f x}\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}",1,"(c + d*x)^2/(a*f) - (4*d*(c + d*x)*Log[1 + I*E^(e + f*x)])/(a*f^2) - (4*d^2*PolyLog[2, (-I)*E^(e + f*x)])/(a*f^3) + ((c + d*x)^2*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(a*f)","A",6,6,23,0.2609,1,"{3318, 4184, 3716, 2190, 2279, 2391}"
110,1,63,0,0.0739995,"\int \frac{c+d x}{a+i a \sinh (e+f x)} \, dx","Int[(c + d*x)/(a + I*a*Sinh[e + f*x]),x]","\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}","\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,"(-2*d*Log[Cosh[e/2 + (I/4)*Pi + (f*x)/2]])/(a*f^2) + ((c + d*x)*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(a*f)","A",3,3,21,0.1429,1,"{3318, 4184, 3475}"
111,0,0,0,0.0641974,"\int \frac{1}{(c+d x) (a+i a \sinh (e+f x))} \, dx","Int[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,"Defer[Int][1/((c + d*x)*(a + I*a*Sinh[e + f*x])), x]","A",0,0,0,0,-1,"{}"
112,0,0,0,0.0597691,"\int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))} \, dx","Int[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,"Defer[Int][1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])), x]","A",0,0,0,0,-1,"{}"
113,1,305,0,0.397799,"\int \frac{(c+d x)^3}{(a+i a \sinh (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + I*a*Sinh[e + f*x])^2,x]","-\frac{4 d^2 (c+d x) \text{PolyLog}\left(2,-i e^{e+f x}\right)}{a^2 f^3}+\frac{4 d^3 \text{PolyLog}\left(3,-i e^{e+f x}\right)}{a^2 f^4}-\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 \log \left(\cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)\right)}{a^2 f^4}","-\frac{4 d^2 (c+d x) \text{PolyLog}\left(2,-i e^{e+f x}\right)}{a^2 f^3}+\frac{4 d^3 \text{PolyLog}\left(3,-i e^{e+f x}\right)}{a^2 f^4}-\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 \log \left(\cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)\right)}{a^2 f^4}",1,"(c + d*x)^3/(3*a^2*f) - (2*d*(c + d*x)^2*Log[1 + I*E^(e + f*x)])/(a^2*f^2) + (4*d^3*Log[Cosh[e/2 + (I/4)*Pi + (f*x)/2]])/(a^2*f^4) - (4*d^2*(c + d*x)*PolyLog[2, (-I)*E^(e + f*x)])/(a^2*f^3) + (4*d^3*PolyLog[3, (-I)*E^(e + f*x)])/(a^2*f^4) + (d*(c + d*x)^2*Sech[e/2 + (I/4)*Pi + (f*x)/2]^2)/(2*a^2*f^2) - (2*d^2*(c + d*x)*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(a^2*f^3) + ((c + d*x)^3*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(3*a^2*f) + ((c + d*x)^3*Sech[e/2 + (I/4)*Pi + (f*x)/2]^2*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(6*a^2*f)","A",10,9,23,0.3913,1,"{3318, 4186, 4184, 3475, 3716, 2190, 2531, 2282, 6589}"
114,1,241,0,0.2775982,"\int \frac{(c+d x)^2}{(a+i a \sinh (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + I*a*Sinh[e + f*x])^2,x]","-\frac{4 d^2 \text{PolyLog}\left(2,-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{2 d^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{3 a^2 f^3}","-\frac{4 d^2 \text{PolyLog}\left(2,-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{2 d^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right)}{3 a^2 f^3}",1,"(c + d*x)^2/(3*a^2*f) - (4*d*(c + d*x)*Log[1 + I*E^(e + f*x)])/(3*a^2*f^2) - (4*d^2*PolyLog[2, (-I)*E^(e + f*x)])/(3*a^2*f^3) + (d*(c + d*x)*Sech[e/2 + (I/4)*Pi + (f*x)/2]^2)/(3*a^2*f^2) - (2*d^2*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(3*a^2*f^3) + ((c + d*x)^2*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(3*a^2*f) + ((c + d*x)^2*Sech[e/2 + (I/4)*Pi + (f*x)/2]^2*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(6*a^2*f)","A",9,9,23,0.3913,1,"{3318, 4186, 3767, 8, 4184, 3716, 2190, 2279, 2391}"
115,1,158,0,0.1091389,"\int \frac{c+d x}{(a+i a \sinh (e+f x))^2} \, dx","Int[(c + d*x)/(a + I*a*Sinh[e + f*x])^2,x]","\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}","\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,"(-2*d*Log[Cosh[e/2 + (I/4)*Pi + (f*x)/2]])/(3*a^2*f^2) + (d*Sech[e/2 + (I/4)*Pi + (f*x)/2]^2)/(6*a^2*f^2) + ((c + d*x)*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(3*a^2*f) + ((c + d*x)*Sech[e/2 + (I/4)*Pi + (f*x)/2]^2*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(6*a^2*f)","A",4,4,21,0.1905,1,"{3318, 4185, 4184, 3475}"
116,0,0,0,0.0604981,"\int \frac{1}{(c+d x) (a+i a \sinh (e+f x))^2} \, dx","Int[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,"Defer[Int][1/((c + d*x)*(a + I*a*Sinh[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
117,0,0,0,0.0574974,"\int \frac{1}{(c+d x)^2 (a+i a \sinh (e+f x))^2} \, dx","Int[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,"Defer[Int][1/((c + d*x)^2*(a + I*a*Sinh[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
118,1,181,0,0.2123912,"\int x^4 \sqrt{a+i a \sinh (e+f x)} \, dx","Int[x^4*Sqrt[a + I*a*Sinh[e + f*x]],x]","-\frac{16 x^3 \sqrt{a+i a \sinh (e+f x)}}{f^2}+\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{384 x \sqrt{a+i a \sinh (e+f x)}}{f^4}+\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{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}","-\frac{16 x^3 \sqrt{a+i a \sinh (e+f x)}}{f^2}+\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{384 x \sqrt{a+i a \sinh (e+f x)}}{f^4}+\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{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,"(-384*x*Sqrt[a + I*a*Sinh[e + f*x]])/f^4 - (16*x^3*Sqrt[a + I*a*Sinh[e + f*x]])/f^2 + (768*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/f^5 + (96*x^2*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/f^3 + (2*x^4*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/f","A",6,3,21,0.1429,1,"{3319, 3296, 2638}"
119,1,136,0,0.1722166,"\int x^3 \sqrt{a+i a \sinh (e+f x)} \, dx","Int[x^3*Sqrt[a + I*a*Sinh[e + f*x]],x]","-\frac{12 x^2 \sqrt{a+i a \sinh (e+f x)}}{f^2}-\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{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}","-\frac{12 x^2 \sqrt{a+i a \sinh (e+f x)}}{f^2}-\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{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,"(-96*Sqrt[a + I*a*Sinh[e + f*x]])/f^4 - (12*x^2*Sqrt[a + I*a*Sinh[e + f*x]])/f^2 + (48*x*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/f^3 + (2*x^3*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/f","A",5,3,21,0.1429,1,"{3319, 3296, 2638}"
120,1,111,0,0.141345,"\int x^2 \sqrt{a+i a \sinh (e+f x)} \, dx","Int[x^2*Sqrt[a + I*a*Sinh[e + f*x]],x]","-\frac{8 x \sqrt{a+i a \sinh (e+f x)}}{f^2}+\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{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}","-\frac{8 x \sqrt{a+i a \sinh (e+f x)}}{f^2}+\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{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,"(-8*x*Sqrt[a + I*a*Sinh[e + f*x]])/f^2 + (16*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/f^3 + (2*x^2*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/f","A",4,3,21,0.1429,1,"{3319, 3296, 2638}"
121,1,66,0,0.0753615,"\int x \sqrt{a+i a \sinh (e+f x)} \, dx","Int[x*Sqrt[a + I*a*Sinh[e + f*x]],x]","\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}","\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,"(-4*Sqrt[a + I*a*Sinh[e + f*x]])/f^2 + (2*x*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/f","A",3,3,19,0.1579,1,"{3319, 3296, 2638}"
122,1,125,0,0.1455394,"\int \frac{\sqrt{a+i a \sinh (e+f x)}}{x} \, dx","Int[Sqrt[a + I*a*Sinh[e + f*x]]/x,x]","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)}","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,"I*CoshIntegral[(f*x)/2]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[(2*e - I*Pi)/4]*Sqrt[a + I*a*Sinh[e + f*x]] + I*Cosh[(2*e - I*Pi)/4]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]]*SinhIntegral[(f*x)/2]","A",4,4,21,0.1905,1,"{3319, 3303, 3298, 3301}"
123,1,149,0,0.1752017,"\int \frac{\sqrt{a+i a \sinh (e+f x)}}{x^2} \, dx","Int[Sqrt[a + I*a*Sinh[e + f*x]]/x^2,x]","\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}","\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]]/x) + (f*CoshIntegral[(f*x)/2]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[(2*e + I*Pi)/4]*Sqrt[a + I*a*Sinh[e + f*x]])/2 + (f*Cosh[(2*e + I*Pi)/4]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]]*SinhIntegral[(f*x)/2])/2","A",5,5,21,0.2381,1,"{3319, 3297, 3303, 3298, 3301}"
124,1,204,0,0.1981612,"\int \frac{\sqrt{a+i a \sinh (e+f x)}}{x^3} \, dx","Int[Sqrt[a + I*a*Sinh[e + f*x]]/x^3,x]","\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}","\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]]/(2*x^2) + (I/8)*f^2*CoshIntegral[(f*x)/2]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[(2*e - I*Pi)/4]*Sqrt[a + I*a*Sinh[e + f*x]] + (I/8)*f^2*Cosh[(2*e - I*Pi)/4]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]]*SinhIntegral[(f*x)/2] - (f*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(4*x)","A",6,5,21,0.2381,1,"{3319, 3297, 3303, 3298, 3301}"
125,1,377,0,0.3514294,"\int x^3 (a+i a \sinh (e+f x))^{3/2} \, dx","Int[x^3*(a + I*a*Sinh[e + f*x])^(3/2),x]","-\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{1280 a \sqrt{a+i a \sinh (e+f x)}}{9 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{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{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{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}","-\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{1280 a \sqrt{a+i a \sinh (e+f x)}}{9 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{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{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{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,"(-1280*a*Sqrt[a + I*a*Sinh[e + f*x]])/(9*f^4) - (16*a*x^2*Sqrt[a + I*a*Sinh[e + f*x]])/f^2 - (64*a*Cosh[e/2 + (I/4)*Pi + (f*x)/2]^2*Sqrt[a + I*a*Sinh[e + f*x]])/(27*f^4) - (8*a*x^2*Cosh[e/2 + (I/4)*Pi + (f*x)/2]^2*Sqrt[a + I*a*Sinh[e + f*x]])/(3*f^2) + (32*a*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]])/(9*f^3) + (4*a*x^3*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]])/(3*f) + (640*a*x*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(9*f^3) + (8*a*x^3*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(3*f)","A",9,5,21,0.2381,1,"{3319, 3311, 3296, 2638, 3310}"
126,1,303,0,0.2509801,"\int x^2 (a+i a \sinh (e+f x))^{3/2} \, dx","Int[x^2*(a + I*a*Sinh[e + f*x])^(3/2),x]","-\frac{32 a x \sqrt{a+i a \sinh (e+f x)}}{3 f^2}+\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{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}","-\frac{32 a x \sqrt{a+i a \sinh (e+f x)}}{3 f^2}+\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{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,"(-32*a*x*Sqrt[a + I*a*Sinh[e + f*x]])/(3*f^2) - (16*a*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]^2*Sqrt[a + I*a*Sinh[e + f*x]])/(9*f^2) + (4*a*x^2*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]])/(3*f) + (224*a*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(9*f^3) + (8*a*x^2*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(3*f) + (32*a*Sinh[e/2 + (I/4)*Pi + (f*x)/2]^2*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(27*f^3)","A",7,5,21,0.2381,1,"{3319, 3311, 3296, 2638, 2633}"
127,1,185,0,0.1333723,"\int x (a+i a \sinh (e+f x))^{3/2} \, dx","Int[x*(a + I*a*Sinh[e + f*x])^(3/2),x]","-\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}","-\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,"(-16*a*Sqrt[a + I*a*Sinh[e + f*x]])/(3*f^2) - (8*a*Cosh[e/2 + (I/4)*Pi + (f*x)/2]^2*Sqrt[a + I*a*Sinh[e + f*x]])/(9*f^2) + (4*a*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]])/(3*f) + (8*a*x*Sqrt[a + I*a*Sinh[e + f*x]]*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(3*f)","A",4,4,19,0.2105,1,"{3319, 3310, 3296, 2638}"
128,1,261,0,0.2733794,"\int \frac{(a+i a \sinh (e+f x))^{3/2}}{x} \, dx","Int[(a + I*a*Sinh[e + f*x])^(3/2)/x,x]","\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)}","\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,"((3*I)/2)*a*CoshIntegral[(f*x)/2]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[(2*e - I*Pi)/4]*Sqrt[a + I*a*Sinh[e + f*x]] + (I/2)*a*CoshIntegral[(3*f*x)/2]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[(6*e + I*Pi)/4]*Sqrt[a + I*a*Sinh[e + f*x]] + ((3*I)/2)*a*Cosh[(2*e - I*Pi)/4]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]]*SinhIntegral[(f*x)/2] + (I/2)*a*Cosh[(6*e + I*Pi)/4]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]]*SinhIntegral[(3*f*x)/2]","A",9,5,21,0.2381,1,"{3319, 3312, 3303, 3298, 3301}"
129,1,302,0,0.2897032,"\int \frac{(a+i a \sinh (e+f x))^{3/2}}{x^2} \, dx","Int[(a + I*a*Sinh[e + f*x])^(3/2)/x^2,x]","-\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}","-\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,"(-2*a*Cosh[e/2 + (I/4)*Pi + (f*x)/2]^2*Sqrt[a + I*a*Sinh[e + f*x]])/x - (3*a*f*CoshIntegral[(3*f*x)/2]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[(6*e - I*Pi)/4]*Sqrt[a + I*a*Sinh[e + f*x]])/4 + (3*a*f*CoshIntegral[(f*x)/2]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sinh[(2*e + I*Pi)/4]*Sqrt[a + I*a*Sinh[e + f*x]])/4 + (3*a*f*Cosh[(2*e + I*Pi)/4]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]]*SinhIntegral[(f*x)/2])/4 - (3*a*f*Cosh[(6*e - I*Pi)/4]*Sech[e/2 + (I/4)*Pi + (f*x)/2]*Sqrt[a + I*a*Sinh[e + f*x]]*SinhIntegral[(3*f*x)/2])/4","A",9,5,21,0.2381,1,"{3319, 3313, 3303, 3298, 3301}"
130,1,638,0,0.639757,"\int x^3 (a+i a \sinh (c+d x))^{5/2} \, dx","Int[x^3*(a + I*a*Sinh[c + d*x])^(5/2),x]","-\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{265216 a^2 \sqrt{a+i a \sinh (c+d x)}}{1125 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{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{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{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{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{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}","-\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{265216 a^2 \sqrt{a+i a \sinh (c+d x)}}{1125 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{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{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{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{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{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,"(-265216*a^2*Sqrt[a + I*a*Sinh[c + d*x]])/(1125*d^4) - (128*a^2*x^2*Sqrt[a + I*a*Sinh[c + d*x]])/(5*d^2) - (17408*a^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^2*Sqrt[a + I*a*Sinh[c + d*x]])/(3375*d^4) - (64*a^2*x^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^2*Sqrt[a + I*a*Sinh[c + d*x]])/(15*d^2) - (384*a^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^4*Sqrt[a + I*a*Sinh[c + d*x]])/(625*d^4) - (48*a^2*x^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^4*Sqrt[a + I*a*Sinh[c + d*x]])/(25*d^2) + (8704*a^2*x*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]])/(1125*d^3) + (32*a^2*x^3*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]])/(15*d) + (192*a^2*x*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^3*Sinh[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]])/(125*d^3) + (8*a^2*x^3*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^3*Sinh[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]])/(5*d) + (132608*a^2*x*Sqrt[a + I*a*Sinh[c + d*x]]*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(1125*d^3) + (64*a^2*x^3*Sqrt[a + I*a*Sinh[c + d*x]]*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(15*d)","A",14,5,21,0.2381,1,"{3319, 3311, 3296, 2638, 3310}"
131,1,506,0,0.3897031,"\int x^2 (a+i a \sinh (c+d x))^{5/2} \, dx","Int[x^2*(a + I*a*Sinh[c + d*x])^(5/2),x]","-\frac{256 a^2 x \sqrt{a+i a \sinh (c+d x)}}{15 d^2}+\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{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}","-\frac{256 a^2 x \sqrt{a+i a \sinh (c+d x)}}{15 d^2}+\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{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,"(-256*a^2*x*Sqrt[a + I*a*Sinh[c + d*x]])/(15*d^2) - (128*a^2*x*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^2*Sqrt[a + I*a*Sinh[c + d*x]])/(45*d^2) - (32*a^2*x*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^4*Sqrt[a + I*a*Sinh[c + d*x]])/(25*d^2) + (32*a^2*x^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]])/(15*d) + (8*a^2*x^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^3*Sinh[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]])/(5*d) + (9536*a^2*Sqrt[a + I*a*Sinh[c + d*x]]*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(225*d^3) + (64*a^2*x^2*Sqrt[a + I*a*Sinh[c + d*x]]*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(15*d) + (2432*a^2*Sinh[c/2 + (I/4)*Pi + (d*x)/2]^2*Sqrt[a + I*a*Sinh[c + d*x]]*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(675*d^3) + (64*a^2*Sinh[c/2 + (I/4)*Pi + (d*x)/2]^4*Sqrt[a + I*a*Sinh[c + d*x]]*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(125*d^3)","A",10,5,21,0.2381,1,"{3319, 3311, 3296, 2638, 2633}"
132,1,312,0,0.2081569,"\int x (a+i a \sinh (c+d x))^{5/2} \, dx","Int[x*(a + I*a*Sinh[c + d*x])^(5/2),x]","-\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}","-\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,"(-128*a^2*Sqrt[a + I*a*Sinh[c + d*x]])/(15*d^2) - (64*a^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^2*Sqrt[a + I*a*Sinh[c + d*x]])/(45*d^2) - (16*a^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^4*Sqrt[a + I*a*Sinh[c + d*x]])/(25*d^2) + (32*a^2*x*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]])/(15*d) + (8*a^2*x*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^3*Sinh[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]])/(5*d) + (64*a^2*x*Sqrt[a + I*a*Sinh[c + d*x]]*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(15*d)","A",5,4,19,0.2105,1,"{3319, 3310, 3296, 2638}"
133,1,403,0,0.4177151,"\int \frac{(a+i a \sinh (c+d x))^{5/2}}{x} \, dx","Int[(a + I*a*Sinh[c + d*x])^(5/2)/x,x]","-\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)}","-\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,"(-I/4)*a^2*CoshIntegral[(5*d*x)/2]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[(5*c)/2 - (I/4)*Pi]*Sqrt[a + I*a*Sinh[c + d*x]] + ((5*I)/2)*a^2*CoshIntegral[(d*x)/2]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[(2*c - I*Pi)/4]*Sqrt[a + I*a*Sinh[c + d*x]] + ((5*I)/4)*a^2*CoshIntegral[(3*d*x)/2]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[(6*c + I*Pi)/4]*Sqrt[a + I*a*Sinh[c + d*x]] + ((5*I)/2)*a^2*Cosh[(2*c - I*Pi)/4]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]]*SinhIntegral[(d*x)/2] + ((5*I)/4)*a^2*Cosh[(6*c + I*Pi)/4]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]]*SinhIntegral[(3*d*x)/2] - (I/4)*a^2*Cosh[(5*c)/2 - (I/4)*Pi]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]]*SinhIntegral[(5*d*x)/2]","A",12,5,21,0.2381,1,"{3319, 3312, 3303, 3298, 3301}"
134,1,444,0,0.4366977,"\int \frac{(a+i a \sinh (c+d x))^{5/2}}{x^2} \, dx","Int[(a + I*a*Sinh[c + d*x])^(5/2)/x^2,x]","-\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}","-\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,"(-4*a^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^4*Sqrt[a + I*a*Sinh[c + d*x]])/x - (5*a^2*d*CoshIntegral[(5*d*x)/2]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[(5*c)/2 + (I/4)*Pi]*Sqrt[a + I*a*Sinh[c + d*x]])/8 - (15*a^2*d*CoshIntegral[(3*d*x)/2]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[(6*c - I*Pi)/4]*Sqrt[a + I*a*Sinh[c + d*x]])/8 + (5*a^2*d*CoshIntegral[(d*x)/2]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[(2*c + I*Pi)/4]*Sqrt[a + I*a*Sinh[c + d*x]])/4 + (5*a^2*d*Cosh[(2*c + I*Pi)/4]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]]*SinhIntegral[(d*x)/2])/4 - (15*a^2*d*Cosh[(6*c - I*Pi)/4]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]]*SinhIntegral[(3*d*x)/2])/8 - (5*a^2*d*Cosh[(5*c)/2 + (I/4)*Pi]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]]*SinhIntegral[(5*d*x)/2])/8","A",12,5,21,0.2381,1,"{3319, 3313, 3303, 3298, 3301}"
135,1,536,0,0.638273,"\int \frac{(a+i a \sinh (c+d x))^{5/2}}{x^3} \, dx","Int[(a + I*a*Sinh[c + d*x])^(5/2)/x^3,x]","-\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}","-\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*a^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^4*Sqrt[a + I*a*Sinh[c + d*x]])/x^2 - ((25*I)/32)*a^2*d^2*CoshIntegral[(5*d*x)/2]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[(5*c)/2 - (I/4)*Pi]*Sqrt[a + I*a*Sinh[c + d*x]] + ((5*I)/16)*a^2*d^2*CoshIntegral[(d*x)/2]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[(2*c - I*Pi)/4]*Sqrt[a + I*a*Sinh[c + d*x]] + ((45*I)/32)*a^2*d^2*CoshIntegral[(3*d*x)/2]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sinh[(6*c + I*Pi)/4]*Sqrt[a + I*a*Sinh[c + d*x]] - (5*a^2*d*Cosh[c/2 + (I/4)*Pi + (d*x)/2]^3*Sinh[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]])/x + ((5*I)/16)*a^2*d^2*Cosh[(2*c - I*Pi)/4]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]]*SinhIntegral[(d*x)/2] + ((45*I)/32)*a^2*d^2*Cosh[(6*c + I*Pi)/4]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]]*SinhIntegral[(3*d*x)/2] - ((25*I)/32)*a^2*d^2*Cosh[(5*c)/2 - (I/4)*Pi]*Sech[c/2 + (I/4)*Pi + (d*x)/2]*Sqrt[a + I*a*Sinh[c + d*x]]*SinhIntegral[(5*d*x)/2]","A",21,6,21,0.2857,1,"{3319, 3314, 3312, 3303, 3298, 3301}"
136,1,493,0,0.2607323,"\int \frac{x^3}{\sqrt{a+i a \sinh (e+f x)}} \, dx","Int[x^3/Sqrt[a + I*a*Sinh[e + f*x]],x]","\frac{12 i x^2 \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{12 i x^2 \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{48 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{48 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{96 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(4,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^4 \sqrt{a+i a \sinh (e+f x)}}-\frac{96 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(4,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^4 \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)}}","\frac{12 i x^2 \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{12 i x^2 \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{48 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{48 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{96 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(4,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^4 \sqrt{a+i a \sinh (e+f x)}}-\frac{96 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(4,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^4 \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,"((4*I)*x^3*ArcTanh[E^((2*e - I*Pi)/4 + (f*x)/2)]*Cosh[e/2 + (I/4)*Pi + (f*x)/2])/(f*Sqrt[a + I*a*Sinh[e + f*x]]) + ((12*I)*x^2*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - ((12*I)*x^2*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - ((48*I)*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[3, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^3*Sqrt[a + I*a*Sinh[e + f*x]]) + ((48*I)*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[3, E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^3*Sqrt[a + I*a*Sinh[e + f*x]]) + ((96*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[4, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^4*Sqrt[a + I*a*Sinh[e + f*x]]) - ((96*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[4, E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^4*Sqrt[a + I*a*Sinh[e + f*x]])","A",10,6,21,0.2857,1,"{3319, 4182, 2531, 6609, 2282, 6589}"
137,1,349,0,0.2019,"\int \frac{x^2}{\sqrt{a+i a \sinh (e+f x)}} \, dx","Int[x^2/Sqrt[a + I*a*Sinh[e + f*x]],x]","\frac{8 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{8 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{16 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{16 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^3 \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)}}","\frac{8 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{8 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{16 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{16 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^3 \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,"((4*I)*x^2*ArcTanh[E^((2*e - I*Pi)/4 + (f*x)/2)]*Cosh[e/2 + (I/4)*Pi + (f*x)/2])/(f*Sqrt[a + I*a*Sinh[e + f*x]]) + ((8*I)*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - ((8*I)*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - ((16*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[3, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^3*Sqrt[a + I*a*Sinh[e + f*x]]) + ((16*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[3, E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^3*Sqrt[a + I*a*Sinh[e + f*x]])","A",8,5,21,0.2381,1,"{3319, 4182, 2531, 2282, 6589}"
138,1,207,0,0.1047192,"\int \frac{x}{\sqrt{a+i a \sinh (e+f x)}} \, dx","Int[x/Sqrt[a + I*a*Sinh[e + f*x]],x]","\frac{4 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{4 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\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)}}","\frac{4 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{4 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\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,"((4*I)*x*ArcTanh[E^((2*e - I*Pi)/4 + (f*x)/2)]*Cosh[e/2 + (I/4)*Pi + (f*x)/2])/(f*Sqrt[a + I*a*Sinh[e + f*x]]) + ((4*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - ((4*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, E^((2*e - I*Pi)/4 + (f*x)/2)])/(f^2*Sqrt[a + I*a*Sinh[e + f*x]])","A",6,4,19,0.2105,1,"{3319, 4182, 2279, 2391}"
139,0,0,0,0.0776774,"\int \frac{1}{x \sqrt{a+i a \sinh (e+f x)}} \, dx","Int[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,"Defer[Int][1/(x*Sqrt[a + I*a*Sinh[e + f*x]]), x]","A",0,0,0,0,-1,"{}"
140,0,0,0,0.0757779,"\int \frac{1}{x^2 \sqrt{a+i a \sinh (e+f x)}} \, dx","Int[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,"Defer[Int][1/(x^2*Sqrt[a + I*a*Sinh[e + f*x]]), x]","A",0,0,0,0,-1,"{}"
141,1,807,0,0.4377238,"\int \frac{x^3}{(a+i a \sinh (e+f x))^{3/2}} \, dx","Int[x^3/(a + I*a*Sinh[e + f*x])^(3/2),x]","\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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(3,-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{PolyLog}\left(3,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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(4,-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{PolyLog}\left(4,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{\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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(3,-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{PolyLog}\left(3,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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(4,-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{PolyLog}\left(4,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,"(3*x^2)/(a*f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - ((24*I)*x*ArcTanh[E^((2*e - I*Pi)/4 + (f*x)/2)]*Cosh[e/2 + (I/4)*Pi + (f*x)/2])/(a*f^3*Sqrt[a + I*a*Sinh[e + f*x]]) + (I*x^3*ArcTanh[E^((2*e - I*Pi)/4 + (f*x)/2)]*Cosh[e/2 + (I/4)*Pi + (f*x)/2])/(a*f*Sqrt[a + I*a*Sinh[e + f*x]]) - ((24*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^4*Sqrt[a + I*a*Sinh[e + f*x]]) + ((3*I)*x^2*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^2*Sqrt[a + I*a*Sinh[e + f*x]]) + ((24*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^4*Sqrt[a + I*a*Sinh[e + f*x]]) - ((3*I)*x^2*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - ((12*I)*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[3, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^3*Sqrt[a + I*a*Sinh[e + f*x]]) + ((12*I)*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[3, E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^3*Sqrt[a + I*a*Sinh[e + f*x]]) + ((24*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[4, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^4*Sqrt[a + I*a*Sinh[e + f*x]]) - ((24*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[4, E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^4*Sqrt[a + I*a*Sinh[e + f*x]]) + (x^3*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(2*a*f*Sqrt[a + I*a*Sinh[e + f*x]])","A",16,9,21,0.4286,1,"{3319, 4186, 4182, 2279, 2391, 2531, 6609, 2282, 6589}"
142,1,506,0,0.3112285,"\int \frac{x^2}{(a+i a \sinh (e+f x))^{3/2}} \, dx","Int[x^2/(a + I*a*Sinh[e + f*x])^(3/2),x]","\frac{2 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{2 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{4 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{4 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{2 x}{a f^2 \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{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)}}","\frac{2 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{2 i x \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{4 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{4 i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f^3 \sqrt{a+i a \sinh (e+f x)}}+\frac{2 x}{a f^2 \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{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,"(2*x)/(a*f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - (4*ArcTan[Sinh[e/2 + (I/4)*Pi + (f*x)/2]]*Cosh[e/2 + (I/4)*Pi + (f*x)/2])/(a*f^3*Sqrt[a + I*a*Sinh[e + f*x]]) + (I*x^2*ArcTanh[E^((2*e - I*Pi)/4 + (f*x)/2)]*Cosh[e/2 + (I/4)*Pi + (f*x)/2])/(a*f*Sqrt[a + I*a*Sinh[e + f*x]]) + ((2*I)*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - ((2*I)*x*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - ((4*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[3, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^3*Sqrt[a + I*a*Sinh[e + f*x]]) + ((4*I)*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[3, E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^3*Sqrt[a + I*a*Sinh[e + f*x]]) + (x^2*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(2*a*f*Sqrt[a + I*a*Sinh[e + f*x]])","A",10,7,21,0.3333,1,"{3319, 4186, 3770, 4182, 2531, 2282, 6589}"
143,1,288,0,0.1693326,"\int \frac{x}{(a+i a \sinh (e+f x))^{3/2}} \, dx","Int[x/(a + I*a*Sinh[e + f*x])^(3/2),x]","\frac{i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\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)}}","\frac{i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\right)}{a f^2 \sqrt{a+i a \sinh (e+f x)}}-\frac{i \cosh \left(\frac{e}{2}+\frac{f x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{f x}{2}+\frac{1}{4} (2 e-i \pi )}\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,"1/(a*f^2*Sqrt[a + I*a*Sinh[e + f*x]]) + (I*x*ArcTanh[E^((2*e - I*Pi)/4 + (f*x)/2)]*Cosh[e/2 + (I/4)*Pi + (f*x)/2])/(a*f*Sqrt[a + I*a*Sinh[e + f*x]]) + (I*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, -E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^2*Sqrt[a + I*a*Sinh[e + f*x]]) - (I*Cosh[e/2 + (I/4)*Pi + (f*x)/2]*PolyLog[2, E^((2*e - I*Pi)/4 + (f*x)/2)])/(a*f^2*Sqrt[a + I*a*Sinh[e + f*x]]) + (x*Tanh[e/2 + (I/4)*Pi + (f*x)/2])/(2*a*f*Sqrt[a + I*a*Sinh[e + f*x]])","A",7,5,19,0.2632,1,"{3319, 4185, 4182, 2279, 2391}"
144,0,0,0,0.0876549,"\int \frac{1}{x (a+i a \sinh (e+f x))^{3/2}} \, dx","Int[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,"Defer[Int][1/(x*(a + I*a*Sinh[e + f*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
145,0,0,0,0.085883,"\int \frac{1}{x^2 (a+i a \sinh (e+f x))^{3/2}} \, dx","Int[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,"Defer[Int][1/(x^2*(a + I*a*Sinh[e + f*x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
146,1,1016,0,0.6765762,"\int \frac{x^3}{(a+i a \sinh (c+d x))^{5/2}} \, dx","Int[x^3/(a + I*a*Sinh[c + d*x])^(5/2),x]","\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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(3,-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{PolyLog}\left(3,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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(4,-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{PolyLog}\left(4,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}}","\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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(3,-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{PolyLog}\left(3,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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(4,-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{PolyLog}\left(4,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,"-(1/(a^2*d^4*Sqrt[a + I*a*Sinh[c + d*x]])) + (9*x^2)/(8*a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) - ((10*I)*x*ArcTanh[E^((2*c - I*Pi)/4 + (d*x)/2)]*Cosh[c/2 + (I/4)*Pi + (d*x)/2])/(a^2*d^3*Sqrt[a + I*a*Sinh[c + d*x]]) + (((3*I)/8)*x^3*ArcTanh[E^((2*c - I*Pi)/4 + (d*x)/2)]*Cosh[c/2 + (I/4)*Pi + (d*x)/2])/(a^2*d*Sqrt[a + I*a*Sinh[c + d*x]]) - ((10*I)*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[2, -E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^4*Sqrt[a + I*a*Sinh[c + d*x]]) + (((9*I)/8)*x^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[2, -E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) + ((10*I)*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[2, E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^4*Sqrt[a + I*a*Sinh[c + d*x]]) - (((9*I)/8)*x^2*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[2, E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) - (((9*I)/2)*x*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[3, -E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^3*Sqrt[a + I*a*Sinh[c + d*x]]) + (((9*I)/2)*x*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[3, E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^3*Sqrt[a + I*a*Sinh[c + d*x]]) + ((9*I)*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[4, -E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^4*Sqrt[a + I*a*Sinh[c + d*x]]) - ((9*I)*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[4, E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^4*Sqrt[a + I*a*Sinh[c + d*x]]) + (x^2*Sech[c/2 + (I/4)*Pi + (d*x)/2]^2)/(4*a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) - (x*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(2*a^2*d^3*Sqrt[a + I*a*Sinh[c + d*x]]) + (3*x^3*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(16*a^2*d*Sqrt[a + I*a*Sinh[c + d*x]]) + (x^3*Sech[c/2 + (I/4)*Pi + (d*x)/2]^2*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(8*a^2*d*Sqrt[a + I*a*Sinh[c + d*x]])","A",23,10,21,0.4762,1,"{3319, 4186, 4185, 4182, 2279, 2391, 2531, 6609, 2282, 6589}"
147,1,689,0,0.4600922,"\int \frac{x^2}{(a+i a \sinh (c+d x))^{5/2}} \, dx","Int[x^2/(a + I*a*Sinh[c + d*x])^(5/2),x]","\frac{3 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{4 a^2 d^2 \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) \text{PolyLog}\left(2,e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{4 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}-\frac{3 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{2 a^2 d^3 \sqrt{a+i a \sinh (c+d x)}}+\frac{3 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{2 a^2 d^3 \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{\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{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{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 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)}}","\frac{3 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{4 a^2 d^2 \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) \text{PolyLog}\left(2,e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{4 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}-\frac{3 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,-e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{2 a^2 d^3 \sqrt{a+i a \sinh (c+d x)}}+\frac{3 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(3,e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{2 a^2 d^3 \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{\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{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{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 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,"(3*x)/(4*a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) - (5*ArcTan[Sinh[c/2 + (I/4)*Pi + (d*x)/2]]*Cosh[c/2 + (I/4)*Pi + (d*x)/2])/(3*a^2*d^3*Sqrt[a + I*a*Sinh[c + d*x]]) + (((3*I)/8)*x^2*ArcTanh[E^((2*c - I*Pi)/4 + (d*x)/2)]*Cosh[c/2 + (I/4)*Pi + (d*x)/2])/(a^2*d*Sqrt[a + I*a*Sinh[c + d*x]]) + (((3*I)/4)*x*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[2, -E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) - (((3*I)/4)*x*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[2, E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) - (((3*I)/2)*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[3, -E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^3*Sqrt[a + I*a*Sinh[c + d*x]]) + (((3*I)/2)*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[3, E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^3*Sqrt[a + I*a*Sinh[c + d*x]]) + (x*Sech[c/2 + (I/4)*Pi + (d*x)/2]^2)/(6*a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) - Tanh[c/2 + (I/4)*Pi + (d*x)/2]/(6*a^2*d^3*Sqrt[a + I*a*Sinh[c + d*x]]) + (3*x^2*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(16*a^2*d*Sqrt[a + I*a*Sinh[c + d*x]]) + (x^2*Sech[c/2 + (I/4)*Pi + (d*x)/2]^2*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(8*a^2*d*Sqrt[a + I*a*Sinh[c + d*x]])","A",13,8,21,0.3810,1,"{3319, 4186, 3768, 3770, 4182, 2531, 2282, 6589}"
148,1,416,0,0.2429058,"\int \frac{x}{(a+i a \sinh (c+d x))^{5/2}} \, dx","Int[x/(a + I*a*Sinh[c + d*x])^(5/2),x]","\frac{3 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{8 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}-\frac{3 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\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)}}","\frac{3 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,-e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\right)}{8 a^2 d^2 \sqrt{a+i a \sinh (c+d x)}}-\frac{3 i \cosh \left(\frac{c}{2}+\frac{d x}{2}+\frac{i \pi }{4}\right) \text{PolyLog}\left(2,e^{\frac{d x}{2}+\frac{1}{4} (2 c-i \pi )}\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,"3/(8*a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) + (((3*I)/8)*x*ArcTanh[E^((2*c - I*Pi)/4 + (d*x)/2)]*Cosh[c/2 + (I/4)*Pi + (d*x)/2])/(a^2*d*Sqrt[a + I*a*Sinh[c + d*x]]) + (((3*I)/8)*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[2, -E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) - (((3*I)/8)*Cosh[c/2 + (I/4)*Pi + (d*x)/2]*PolyLog[2, E^((2*c - I*Pi)/4 + (d*x)/2)])/(a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) + Sech[c/2 + (I/4)*Pi + (d*x)/2]^2/(12*a^2*d^2*Sqrt[a + I*a*Sinh[c + d*x]]) + (3*x*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(16*a^2*d*Sqrt[a + I*a*Sinh[c + d*x]]) + (x*Sech[c/2 + (I/4)*Pi + (d*x)/2]^2*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(8*a^2*d*Sqrt[a + I*a*Sinh[c + d*x]])","A",8,5,19,0.2632,1,"{3319, 4185, 4182, 2279, 2391}"
149,0,0,0,0.0900751,"\int \frac{1}{x (a+i a \sinh (c+d x))^{5/2}} \, dx","Int[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,"Defer[Int][1/(x*(a + I*a*Sinh[c + d*x])^(5/2)), x]","A",0,0,0,0,-1,"{}"
150,0,0,0,0.0733574,"\int \frac{\sqrt[3]{a+i a \sinh (e+f x)}}{x} \, dx","Int[(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,"Defer[Int][(a + I*a*Sinh[e + f*x])^(1/3)/x, x]","A",0,0,0,0,-1,"{}"
151,0,0,0,0.0514336,"\int (c+d x)^m (a+i a \sinh (e+f x))^n \, dx","Int[(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,"Defer[Int][(c + d*x)^m*(a + I*a*Sinh[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
152,1,410,0,0.602034,"\int (c+d x)^m (a+i a \sinh (e+f x))^3 \, dx","Int[(c + d*x)^m*(a + I*a*Sinh[e + f*x])^3,x]","-\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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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)}","-\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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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,"(5*a^3*(c + d*x)^(1 + m))/(2*d*(1 + m)) - ((I/8)*3^(-1 - m)*a^3*E^(3*e - (3*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (-3*f*(c + d*x))/d])/(f*(-((f*(c + d*x))/d))^m) - (3*2^(-3 - m)*a^3*E^(2*e - (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (-2*f*(c + d*x))/d])/(f*(-((f*(c + d*x))/d))^m) + (((15*I)/8)*a^3*E^(e - (c*f)/d)*(c + d*x)^m*Gamma[1 + m, -((f*(c + d*x))/d)])/(f*(-((f*(c + d*x))/d))^m) + (((15*I)/8)*a^3*E^(-e + (c*f)/d)*(c + d*x)^m*Gamma[1 + m, (f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m) + (3*2^(-3 - m)*a^3*E^(-2*e + (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (2*f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m) - ((I/8)*3^(-1 - m)*a^3*E^(-3*e + (3*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (3*f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m)","A",12,5,23,0.2174,1,"{3318, 3312, 3307, 2181, 3308}"
153,1,268,0,0.3612444,"\int (c+d x)^m (a+i a \sinh (e+f x))^2 \, dx","Int[(c + d*x)^m*(a + I*a*Sinh[e + f*x])^2,x]","-\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} \text{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} \text{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} \text{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} \text{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)}","-\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} \text{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} \text{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} \text{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} \text{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,"(3*a^2*(c + d*x)^(1 + m))/(2*d*(1 + m)) - (2^(-3 - m)*a^2*E^(2*e - (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (-2*f*(c + d*x))/d])/(f*(-((f*(c + d*x))/d))^m) + (I*a^2*E^(e - (c*f)/d)*(c + d*x)^m*Gamma[1 + m, -((f*(c + d*x))/d)])/(f*(-((f*(c + d*x))/d))^m) + (I*a^2*E^(-e + (c*f)/d)*(c + d*x)^m*Gamma[1 + m, (f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m) + (2^(-3 - m)*a^2*E^(-2*e + (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (2*f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m)","A",9,5,23,0.2174,1,"{3318, 3312, 3307, 2181, 3308}"
154,1,135,0,0.1535408,"\int (c+d x)^m (a+i a \sinh (e+f x)) \, dx","Int[(c + d*x)^m*(a + I*a*Sinh[e + f*x]),x]","\frac{i a e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \text{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} \text{Gamma}\left(m+1,\frac{f (c+d x)}{d}\right)}{2 f}+\frac{a (c+d x)^{m+1}}{d (m+1)}","\frac{i a e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \text{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} \text{Gamma}\left(m+1,\frac{f (c+d x)}{d}\right)}{2 f}+\frac{a (c+d x)^{m+1}}{d (m+1)}",1,"(a*(c + d*x)^(1 + m))/(d*(1 + m)) + ((I/2)*a*E^(e - (c*f)/d)*(c + d*x)^m*Gamma[1 + m, -((f*(c + d*x))/d)])/(f*(-((f*(c + d*x))/d))^m) + ((I/2)*a*E^(-e + (c*f)/d)*(c + d*x)^m*Gamma[1 + m, (f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m)","A",5,3,21,0.1429,1,"{3317, 3308, 2181}"
155,0,0,0,0.0561594,"\int \frac{(c+d x)^m}{a+i a \sinh (e+f x)} \, dx","Int[(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,"Defer[Int][(c + d*x)^m/(a + I*a*Sinh[e + f*x]), x]","A",0,0,0,0,-1,"{}"
156,0,0,0,0.0572106,"\int \frac{(c+d x)^m}{(a+i a \sinh (e+f x))^2} \, dx","Int[(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,"Defer[Int][(c + d*x)^m/(a + I*a*Sinh[e + f*x])^2, x]","A",0,0,0,0,-1,"{}"
157,1,89,0,0.1427544,"\int (c+d x)^3 (a+b \sinh (e+f x)) \, dx","Int[(c + d*x)^3*(a + b*Sinh[e + f*x]),x]","\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}","\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*(c + d*x)^4)/(4*d) + (6*b*d^2*(c + d*x)*Cosh[e + f*x])/f^3 + (b*(c + d*x)^3*Cosh[e + f*x])/f - (6*b*d^3*Sinh[e + f*x])/f^4 - (3*b*d*(c + d*x)^2*Sinh[e + f*x])/f^2","A",6,3,18,0.1667,1,"{3317, 3296, 2637}"
158,1,67,0,0.0957637,"\int (c+d x)^2 (a+b \sinh (e+f x)) \, dx","Int[(c + d*x)^2*(a + b*Sinh[e + f*x]),x]","\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}","\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*(c + d*x)^3)/(3*d) + (2*b*d^2*Cosh[e + f*x])/f^3 + (b*(c + d*x)^2*Cosh[e + f*x])/f - (2*b*d*(c + d*x)*Sinh[e + f*x])/f^2","A",5,3,18,0.1667,1,"{3317, 3296, 2638}"
159,1,45,0,0.047893,"\int (c+d x) (a+b \sinh (e+f x)) \, dx","Int[(c + d*x)*(a + b*Sinh[e + f*x]),x]","\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}","\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*(c + d*x)^2)/(2*d) + (b*(c + d*x)*Cosh[e + f*x])/f - (b*d*Sinh[e + f*x])/f^2","A",4,3,16,0.1875,1,"{3317, 3296, 2637}"
160,1,64,0,0.124337,"\int \frac{a+b \sinh (e+f x)}{c+d x} \, dx","Int[(a + b*Sinh[e + f*x])/(c + d*x),x]","\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}","\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])/d + (b*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d + (b*Cosh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d","A",5,4,18,0.2222,1,"{3317, 3303, 3298, 3301}"
161,1,87,0,0.1692885,"\int \frac{a+b \sinh (e+f x)}{(c+d x)^2} \, dx","Int[(a + b*Sinh[e + f*x])/(c + d*x)^2,x]","-\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)}","-\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,"-(a/(d*(c + d*x))) + (b*f*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/d^2 - (b*Sinh[e + f*x])/(d*(c + d*x)) + (b*f*Sinh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d^2","A",6,5,18,0.2778,1,"{3317, 3297, 3303, 3298, 3301}"
162,1,123,0,0.2050684,"\int \frac{a+b \sinh (e+f x)}{(c+d x)^3} \, dx","Int[(a + b*Sinh[e + f*x])/(c + d*x)^3,x]","-\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}","-\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,"-a/(2*d*(c + d*x)^2) - (b*f*Cosh[e + f*x])/(2*d^2*(c + d*x)) + (b*f^2*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/(2*d^3) - (b*Sinh[e + f*x])/(2*d*(c + d*x)^2) + (b*f^2*Cosh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/(2*d^3)","A",7,5,18,0.2778,1,"{3317, 3297, 3303, 3298, 3301}"
163,1,250,0,0.2899634,"\int (c+d x)^3 (a+b \sinh (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + b*Sinh[e + f*x])^2,x]","\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}","\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,"(-3*b^2*c*d^2*x)/(4*f^2) - (3*b^2*d^3*x^2)/(8*f^2) + (a^2*(c + d*x)^4)/(4*d) - (b^2*(c + d*x)^4)/(8*d) + (12*a*b*d^2*(c + d*x)*Cosh[e + f*x])/f^3 + (2*a*b*(c + d*x)^3*Cosh[e + f*x])/f - (12*a*b*d^3*Sinh[e + f*x])/f^4 - (6*a*b*d*(c + d*x)^2*Sinh[e + f*x])/f^2 + (3*b^2*d^2*(c + d*x)*Cosh[e + f*x]*Sinh[e + f*x])/(4*f^3) + (b^2*(c + d*x)^3*Cosh[e + f*x]*Sinh[e + f*x])/(2*f) - (3*b^2*d^3*Sinh[e + f*x]^2)/(8*f^4) - (3*b^2*d*(c + d*x)^2*Sinh[e + f*x]^2)/(4*f^2)","A",10,6,20,0.3000,1,"{3317, 3296, 2637, 3311, 32, 3310}"
164,1,182,0,0.2020184,"\int (c+d x)^2 (a+b \sinh (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + b*Sinh[e + f*x])^2,x]","\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}","\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,"-(b^2*d^2*x)/(4*f^2) + (a^2*(c + d*x)^3)/(3*d) - (b^2*(c + d*x)^3)/(6*d) + (4*a*b*d^2*Cosh[e + f*x])/f^3 + (2*a*b*(c + d*x)^2*Cosh[e + f*x])/f - (4*a*b*d*(c + d*x)*Sinh[e + f*x])/f^2 + (b^2*d^2*Cosh[e + f*x]*Sinh[e + f*x])/(4*f^3) + (b^2*(c + d*x)^2*Cosh[e + f*x]*Sinh[e + f*x])/(2*f) - (b^2*d*(c + d*x)*Sinh[e + f*x]^2)/(2*f^2)","A",9,7,20,0.3500,1,"{3317, 3296, 2638, 3311, 32, 2635, 8}"
165,1,116,0,0.1055476,"\int (c+d x) (a+b \sinh (e+f x))^2 \, dx","Int[(c + d*x)*(a + b*Sinh[e + f*x])^2,x]","\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","\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,"-(b^2*c*x)/2 - (b^2*d*x^2)/4 + (a^2*(c + d*x)^2)/(2*d) + (2*a*b*(c + d*x)*Cosh[e + f*x])/f - (2*a*b*d*Sinh[e + f*x])/f^2 + (b^2*(c + d*x)*Cosh[e + f*x]*Sinh[e + f*x])/(2*f) - (b^2*d*Sinh[e + f*x]^2)/(4*f^2)","A",6,4,18,0.2222,1,"{3317, 3296, 2637, 3310}"
166,1,156,0,0.3251492,"\int \frac{(a+b \sinh (e+f x))^2}{c+d x} \, dx","Int[(a + b*Sinh[e + f*x])^2/(c + d*x),x]","\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}","\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*c*f)/d + 2*f*x])/(2*d) + (a^2*Log[c + d*x])/d - (b^2*Log[c + d*x])/(2*d) + (2*a*b*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d + (2*a*b*Cosh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d + (b^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/(2*d)","A",10,5,20,0.2500,1,"{3317, 3303, 3298, 3301, 3312}"
167,1,183,0,0.3500924,"\int \frac{(a+b \sinh (e+f x))^2}{(c+d x)^2} \, dx","Int[(a + b*Sinh[e + f*x])^2/(c + d*x)^2,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)}","-\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,"-(a^2/(d*(c + d*x))) + (2*a*b*f*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/d^2 + (b^2*f*CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/d^2 - (2*a*b*Sinh[e + f*x])/(d*(c + d*x)) - (b^2*Sinh[e + f*x]^2)/(d*(c + d*x)) + (2*a*b*f*Sinh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d^2 + (b^2*f*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/d^2","A",11,7,20,0.3500,1,"{3317, 3297, 3303, 3298, 3301, 3313, 12}"
168,1,242,0,0.4467643,"\int \frac{(a+b \sinh (e+f x))^2}{(c+d x)^3} \, dx","Int[(a + b*Sinh[e + f*x])^2/(c + d*x)^3,x]","-\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}","-\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,"-a^2/(2*d*(c + d*x)^2) - (a*b*f*Cosh[e + f*x])/(d^2*(c + d*x)) + (b^2*f^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/d^3 + (a*b*f^2*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d^3 - (a*b*Sinh[e + f*x])/(d*(c + d*x)^2) - (b^2*f*Cosh[e + f*x]*Sinh[e + f*x])/(d^2*(c + d*x)) - (b^2*Sinh[e + f*x]^2)/(2*d*(c + d*x)^2) + (a*b*f^2*Cosh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d^3 + (b^2*f^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*c*f)/d + 2*f*x])/d^3","A",14,8,20,0.4000,1,"{3317, 3297, 3303, 3298, 3301, 3314, 31, 3312}"
169,1,404,0,0.8258222,"\int \frac{(c+d x)^3}{a+b \sinh (e+f x)} \, dx","Int[(c + d*x)^3/(a + b*Sinh[e + f*x]),x]","-\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^3 \sqrt{a^2+b^2}}+\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^2 \sqrt{a^2+b^2}}+\frac{6 d^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^4 \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^2 (c+d x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^3 \sqrt{a^2+b^2}}+\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^2 \sqrt{a^2+b^2}}+\frac{6 d^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^4 \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}}",1,"((c + d*x)^3*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*f) - ((c + d*x)^3*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*f) + (3*d*(c + d*x)^2*PolyLog[2, -((b*E^(e + f*x))/(a - Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^2) - (3*d*(c + d*x)^2*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^2) - (6*d^2*(c + d*x)*PolyLog[3, -((b*E^(e + f*x))/(a - Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^3) + (6*d^2*(c + d*x)*PolyLog[3, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^3) + (6*d^3*PolyLog[4, -((b*E^(e + f*x))/(a - Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^4) - (6*d^3*PolyLog[4, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^4)","A",12,7,20,0.3500,1,"{3322, 2264, 2190, 2531, 6609, 2282, 6589}"
170,1,296,0,0.6689787,"\int \frac{(c+d x)^2}{a+b \sinh (e+f x)} \, dx","Int[(c + d*x)^2/(a + b*Sinh[e + f*x]),x]","\frac{2 d (c+d x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^2 \sqrt{a^2+b^2}}-\frac{2 d^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^3 \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 (c+d x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^2 \sqrt{a^2+b^2}}-\frac{2 d^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^3 \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}}",1,"((c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*f) - ((c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*f) + (2*d*(c + d*x)*PolyLog[2, -((b*E^(e + f*x))/(a - Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^2) - (2*d*(c + d*x)*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^2) - (2*d^2*PolyLog[3, -((b*E^(e + f*x))/(a - Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^3) + (2*d^2*PolyLog[3, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^3)","A",10,6,20,0.3000,1,"{3322, 2264, 2190, 2531, 2282, 6589}"
171,1,187,0,0.3689995,"\int \frac{c+d x}{a+b \sinh (e+f x)} \, dx","Int[(c + d*x)/(a + b*Sinh[e + f*x]),x]","\frac{d \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^2 \sqrt{a^2+b^2}}-\frac{d \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{a-\sqrt{a^2+b^2}}\right)}{f^2 \sqrt{a^2+b^2}}-\frac{d \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\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}}",1,"((c + d*x)*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*f) - ((c + d*x)*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])])/(Sqrt[a^2 + b^2]*f) + (d*PolyLog[2, -((b*E^(e + f*x))/(a - Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^2) - (d*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/(Sqrt[a^2 + b^2]*f^2)","A",8,5,18,0.2778,1,"{3322, 2264, 2190, 2279, 2391}"
172,0,0,0,0.0635657,"\int \frac{1}{(c+d x) (a+b \sinh (e+f x))} \, dx","Int[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,"Defer[Int][1/((c + d*x)*(a + b*Sinh[e + f*x])), x]","A",0,0,0,0,-1,"{}"
173,0,0,0,0.0595487,"\int \frac{1}{(c+d x)^2 (a+b \sinh (e+f x))} \, dx","Int[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,"Defer[Int][1/((c + d*x)^2*(a + b*Sinh[e + f*x])), x]","A",0,0,0,0,-1,"{}"
174,1,549,0,1.0366513,"\int \frac{(c+d x)^2}{(a+b \sinh (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + b*Sinh[e + f*x])^2,x]","\frac{2 a d (c+d x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^2 \left(a^2+b^2\right)^{3/2}}+\frac{2 d^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^3 \left(a^2+b^2\right)}-\frac{2 a d^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^3 \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 a d (c+d x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^2 \left(a^2+b^2\right)^{3/2}}+\frac{2 d^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^3 \left(a^2+b^2\right)}-\frac{2 a d^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^3 \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)}",1,"-((c + d*x)^2/((a^2 + b^2)*f)) + (2*d*(c + d*x)*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)*f^2) + (a*(c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*f) + (2*d*(c + d*x)*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)*f^2) - (a*(c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*f) + (2*d^2*PolyLog[2, -((b*E^(e + f*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*f^3) + (2*a*d*(c + d*x)*PolyLog[2, -((b*E^(e + f*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*f^2) + (2*d^2*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*f^3) - (2*a*d*(c + d*x)*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*f^2) - (2*a*d^2*PolyLog[3, -((b*E^(e + f*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*f^3) + (2*a*d^2*PolyLog[3, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*f^3) - (b*(c + d*x)^2*Cosh[e + f*x])/((a^2 + b^2)*f*(a + b*Sinh[e + f*x]))","A",18,10,20,0.5000,1,"{3324, 3322, 2264, 2190, 2531, 2282, 6589, 5561, 2279, 2391}"
175,1,254,0,0.4422472,"\int \frac{c+d x}{(a+b \sinh (e+f x))^2} \, dx","Int[(c + d*x)/(a + b*Sinh[e + f*x])^2,x]","\frac{a d \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^2 \left(a^2+b^2\right)^{3/2}}+\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{d \log (a+b \sinh (e+f x))}{f^2 \left(a^2+b^2\right)}","\frac{a d \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{e+f x}}{\sqrt{a^2+b^2}+a}\right)}{f^2 \left(a^2+b^2\right)^{3/2}}+\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{d \log (a+b \sinh (e+f x))}{f^2 \left(a^2+b^2\right)}",1,"(a*(c + d*x)*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*f) - (a*(c + d*x)*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*f) + (d*Log[a + b*Sinh[e + f*x]])/((a^2 + b^2)*f^2) + (a*d*PolyLog[2, -((b*E^(e + f*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*f^2) - (a*d*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*f^2) - (b*(c + d*x)*Cosh[e + f*x])/((a^2 + b^2)*f*(a + b*Sinh[e + f*x]))","A",11,8,18,0.4444,1,"{3324, 3322, 2264, 2190, 2279, 2391, 2668, 31}"
176,0,0,0,0.0615198,"\int \frac{1}{(c+d x) (a+b \sinh (e+f x))^2} \, dx","Int[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,"Defer[Int][1/((c + d*x)*(a + b*Sinh[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
177,0,0,0,0.0579459,"\int \frac{1}{(c+d x)^2 (a+b \sinh (e+f x))^2} \, dx","Int[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,"Defer[Int][1/((c + d*x)^2*(a + b*Sinh[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
178,1,544,0,2.0810608,"\int \frac{e+f x}{(a+b \sinh (c+d x))^3} \, dx","Int[(e + f*x)/(a + b*Sinh[c + d*x])^3,x]","\frac{3 a^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{2 d^2 \left(a^2+b^2\right)^{5/2}}-\frac{f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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}","\frac{3 a^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{2 d^2 \left(a^2+b^2\right)^{5/2}}-\frac{f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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,"(3*a^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(2*(a^2 + b^2)^(5/2)*d) - ((e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(2*(a^2 + b^2)^(3/2)*d) - (3*a^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(2*(a^2 + b^2)^(5/2)*d) + ((e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(2*(a^2 + b^2)^(3/2)*d) + (3*a*f*Log[a + b*Sinh[c + d*x]])/(2*(a^2 + b^2)^2*d^2) + (3*a^2*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(2*(a^2 + b^2)^(5/2)*d^2) - (f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(2*(a^2 + b^2)^(3/2)*d^2) - (3*a^2*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(2*(a^2 + b^2)^(5/2)*d^2) + (f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(2*(a^2 + b^2)^(3/2)*d^2) - (b*(e + f*x)*Cosh[c + d*x])/(2*(a^2 + b^2)*d*(a + b*Sinh[c + d*x])^2) - f/(2*(a^2 + b^2)*d^2*(a + b*Sinh[c + d*x])) - (3*a*b*(e + f*x)*Cosh[c + d*x])/(2*(a^2 + b^2)^2*d*(a + b*Sinh[c + d*x]))","A",35,11,18,0.6111,1,"{3325, 3324, 3322, 2264, 2190, 2279, 2391, 2668, 31, 6742, 32}"
179,0,0,0,0.0622738,"\int \frac{1}{(e+f x) (a+b \sinh (c+d x))^3} \, dx","Int[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,"Defer[Int][1/((e + f*x)*(a + b*Sinh[c + d*x])^3), x]","A",0,0,0,0,-1,"{}"
180,0,0,0,0.0611184,"\int \frac{1}{(e+f x)^2 (a+b \sinh (c+d x))^3} \, dx","Int[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,"Defer[Int][1/((e + f*x)^2*(a + b*Sinh[c + d*x])^3), x]","A",0,0,0,0,-1,"{}"
181,0,0,0,0.0546259,"\int (c+d x)^m (a+b \sinh (e+f x))^n \, dx","Int[(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,"Defer[Int][(c + d*x)^m*(a + b*Sinh[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
182,1,543,0,0.8073785,"\int (c+d x)^m (a+b \sinh (e+f x))^3 \, dx","Int[(c + d*x)^m*(a + b*Sinh[e + f*x])^3,x]","\frac{3 a^2 b e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \text{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} \text{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} \text{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} \text{Gamma}\left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}+\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} \text{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} \text{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} \text{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} \text{Gamma}\left(m+1,\frac{3 f (c+d x)}{d}\right)}{8 f}+\frac{a^3 (c+d x)^{m+1}}{d (m+1)}-\frac{3 a b^2 (c+d x)^{m+1}}{2 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} \text{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} \text{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} \text{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} \text{Gamma}\left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}+\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} \text{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} \text{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} \text{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} \text{Gamma}\left(m+1,\frac{3 f (c+d x)}{d}\right)}{8 f}+\frac{a^3 (c+d x)^{m+1}}{d (m+1)}-\frac{3 a b^2 (c+d x)^{m+1}}{2 d (m+1)}",1,"(a^3*(c + d*x)^(1 + m))/(d*(1 + m)) - (3*a*b^2*(c + d*x)^(1 + m))/(2*d*(1 + m)) + (3^(-1 - m)*b^3*E^(3*e - (3*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (-3*f*(c + d*x))/d])/(8*f*(-((f*(c + d*x))/d))^m) + (3*2^(-3 - m)*a*b^2*E^(2*e - (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (-2*f*(c + d*x))/d])/(f*(-((f*(c + d*x))/d))^m) + (3*a^2*b*E^(e - (c*f)/d)*(c + d*x)^m*Gamma[1 + m, -((f*(c + d*x))/d)])/(2*f*(-((f*(c + d*x))/d))^m) - (3*b^3*E^(e - (c*f)/d)*(c + d*x)^m*Gamma[1 + m, -((f*(c + d*x))/d)])/(8*f*(-((f*(c + d*x))/d))^m) + (3*a^2*b*E^(-e + (c*f)/d)*(c + d*x)^m*Gamma[1 + m, (f*(c + d*x))/d])/(2*f*((f*(c + d*x))/d)^m) - (3*b^3*E^(-e + (c*f)/d)*(c + d*x)^m*Gamma[1 + m, (f*(c + d*x))/d])/(8*f*((f*(c + d*x))/d)^m) - (3*2^(-3 - m)*a*b^2*E^(-2*e + (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (2*f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m) + (3^(-1 - m)*b^3*E^(-3*e + (3*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (3*f*(c + d*x))/d])/(8*f*((f*(c + d*x))/d)^m)","A",18,5,20,0.2500,1,"{3317, 3308, 2181, 3312, 3307}"
183,1,281,0,0.3749106,"\int (c+d x)^m (a+b \sinh (e+f x))^2 \, dx","Int[(c + d*x)^m*(a + b*Sinh[e + f*x])^2,x]","\frac{a b e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \text{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} \text{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} \text{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} \text{Gamma}\left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}+\frac{a^2 (c+d x)^{m+1}}{d (m+1)}-\frac{b^2 (c+d x)^{m+1}}{2 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} \text{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} \text{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} \text{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} \text{Gamma}\left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}+\frac{a^2 (c+d x)^{m+1}}{d (m+1)}-\frac{b^2 (c+d x)^{m+1}}{2 d (m+1)}",1,"(a^2*(c + d*x)^(1 + m))/(d*(1 + m)) - (b^2*(c + d*x)^(1 + m))/(2*d*(1 + m)) + (2^(-3 - m)*b^2*E^(2*e - (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (-2*f*(c + d*x))/d])/(f*(-((f*(c + d*x))/d))^m) + (a*b*E^(e - (c*f)/d)*(c + d*x)^m*Gamma[1 + m, -((f*(c + d*x))/d)])/(f*(-((f*(c + d*x))/d))^m) + (a*b*E^(-e + (c*f)/d)*(c + d*x)^m*Gamma[1 + m, (f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m) - (2^(-3 - m)*b^2*E^(-2*e + (2*c*f)/d)*(c + d*x)^m*Gamma[1 + m, (2*f*(c + d*x))/d])/(f*((f*(c + d*x))/d)^m)","A",10,5,20,0.2500,1,"{3317, 3308, 2181, 3312, 3307}"
184,1,131,0,0.1482233,"\int (c+d x)^m (a+b \sinh (e+f x)) \, dx","Int[(c + d*x)^m*(a + b*Sinh[e + f*x]),x]","\frac{b e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \text{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} \text{Gamma}\left(m+1,\frac{f (c+d x)}{d}\right)}{2 f}+\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} \text{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} \text{Gamma}\left(m+1,\frac{f (c+d x)}{d}\right)}{2 f}+\frac{a (c+d x)^{m+1}}{d (m+1)}",1,"(a*(c + d*x)^(1 + m))/(d*(1 + m)) + (b*E^(e - (c*f)/d)*(c + d*x)^m*Gamma[1 + m, -((f*(c + d*x))/d)])/(2*f*(-((f*(c + d*x))/d))^m) + (b*E^(-e + (c*f)/d)*(c + d*x)^m*Gamma[1 + m, (f*(c + d*x))/d])/(2*f*((f*(c + d*x))/d)^m)","A",5,3,18,0.1667,1,"{3317, 3308, 2181}"
185,0,0,0,0.0567216,"\int \frac{(c+d x)^m}{a+b \sinh (e+f x)} \, dx","Int[(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,"Defer[Int][(c + d*x)^m/(a + b*Sinh[e + f*x]), x]","A",0,0,0,0,-1,"{}"
186,0,0,0,0.055234,"\int \frac{(c+d x)^m}{(a+b \sinh (e+f x))^2} \, dx","Int[(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,"Defer[Int][(c + d*x)^m/(a + b*Sinh[e + f*x])^2, x]","A",0,0,0,0,-1,"{}"
187,1,163,0,0.356154,"\int \frac{(e+f x)^3 \sinh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sinh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{12 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}-\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}","-\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{12 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}-\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*(e + f*x)^3)/(a*d) - ((I/4)*(e + f*x)^4)/(a*f) - ((6*I)*f*(e + f*x)^2*Log[1 + I*E^(c + d*x)])/(a*d^2) - ((12*I)*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) + ((12*I)*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^4) + (I*(e + f*x)^3*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",9,9,29,0.3103,1,"{5557, 32, 3318, 4184, 3716, 2190, 2531, 2282, 6589}"
188,1,130,0,0.2720636,"\int \frac{(e+f x)^2 \sinh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sinh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{4 i f^2 \text{PolyLog}\left(2,-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}","-\frac{4 i f^2 \text{PolyLog}\left(2,-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*(e + f*x)^2)/(a*d) - ((I/3)*(e + f*x)^3)/(a*f) - ((4*I)*f*(e + f*x)*Log[1 + I*E^(c + d*x)])/(a*d^2) - ((4*I)*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) + (I*(e + f*x)^2*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",8,8,29,0.2759,1,"{5557, 32, 3318, 4184, 3716, 2190, 2279, 2391}"
189,1,90,0,0.1123815,"\int \frac{(e+f x) \sinh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Sinh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\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}","-\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,"((-I)*e*x)/a - ((I/2)*f*x^2)/a - ((2*I)*f*Log[Cosh[c/2 + (I/4)*Pi + (d*x)/2]])/(a*d^2) + (I*(e + f*x)*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",5,4,27,0.1481,1,"{5557, 3318, 4184, 3475}"
190,1,35,0,0.0438023,"\int \frac{\sinh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Sinh[c + d*x]/(a + I*a*Sinh[c + d*x]),x]","-\frac{\cosh (c+d x)}{d (a+i a \sinh (c+d x))}-\frac{i x}{a}","-\frac{\cosh (c+d x)}{d (a+i a \sinh (c+d x))}-\frac{i x}{a}",1,"((-I)*x)/a - Cosh[c + d*x]/(d*(a + I*a*Sinh[c + d*x]))","A",2,2,22,0.09091,1,"{2735, 2648}"
191,0,0,0,0.0504119,"\int \frac{\sinh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Sinh[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
192,0,0,0,0.0511999,"\int \frac{\sinh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Sinh[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
193,1,241,0,0.5261416,"\int \frac{(e+f x)^3 \sinh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sinh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{12 f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{12 f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}-\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{6 i f^3 \sinh (c+d x)}{a d^4}-\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}","\frac{12 f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{12 f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}-\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{6 i f^3 \sinh (c+d x)}{a d^4}-\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,"-((e + f*x)^3/(a*d)) + (e + f*x)^4/(4*a*f) - ((6*I)*f^2*(e + f*x)*Cosh[c + d*x])/(a*d^3) - (I*(e + f*x)^3*Cosh[c + d*x])/(a*d) + (6*f*(e + f*x)^2*Log[1 + I*E^(c + d*x)])/(a*d^2) + (12*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) - (12*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^4) + ((6*I)*f^3*Sinh[c + d*x])/(a*d^4) + ((3*I)*f*(e + f*x)^2*Sinh[c + d*x])/(a*d^2) - ((e + f*x)^3*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",14,11,31,0.3548,1,"{5557, 3296, 2637, 32, 3318, 4184, 3716, 2190, 2531, 2282, 6589}"
194,1,184,0,0.3907584,"\int \frac{(e+f x)^2 \sinh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sinh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{4 f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{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{2 i f^2 \cosh (c+d x)}{a d^3}-\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}","\frac{4 f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{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{2 i f^2 \cosh (c+d x)}{a d^3}-\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,"-((e + f*x)^2/(a*d)) + (e + f*x)^3/(3*a*f) - ((2*I)*f^2*Cosh[c + d*x])/(a*d^3) - (I*(e + f*x)^2*Cosh[c + d*x])/(a*d) + (4*f*(e + f*x)*Log[1 + I*E^(c + d*x)])/(a*d^2) + (4*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) + ((2*I)*f*(e + f*x)*Sinh[c + d*x])/(a*d^2) - ((e + f*x)^2*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",12,10,31,0.3226,1,"{5557, 3296, 2638, 32, 3318, 4184, 3716, 2190, 2279, 2391}"
195,1,119,0,0.1771174,"\int \frac{(e+f x) \sinh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Sinh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\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}","\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,"(e*x)/a + (f*x^2)/(2*a) - (I*(e + f*x)*Cosh[c + d*x])/(a*d) + (2*f*Log[Cosh[c/2 + (I/4)*Pi + (d*x)/2]])/(a*d^2) + (I*f*Sinh[c + d*x])/(a*d^2) - ((e + f*x)*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",8,6,29,0.2069,1,"{5557, 3296, 2637, 3318, 4184, 3475}"
196,1,52,0,0.08879,"\int \frac{\sinh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Sinh[c + d*x]^2/(a + I*a*Sinh[c + d*x]),x]","-\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}","-\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,"x/a - (I*Cosh[c + d*x])/(a*d) - (I*Cosh[c + d*x])/(a*d*(1 + I*Sinh[c + d*x]))","A",4,4,24,0.1667,1,"{2746, 12, 2735, 2648}"
197,0,0,0,0.0778347,"\int \frac{\sinh ^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[Sinh[c + d*x]^2/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\sinh ^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh ^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"Defer[Int][Sinh[c + d*x]^2/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
198,0,0,0,0.0751888,"\int \frac{\sinh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[Sinh[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\sinh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"Defer[Int][Sinh[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
199,1,393,0,0.7024153,"\int \frac{(e+f x)^3 \sinh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sinh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{12 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}+\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{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{(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}","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{12 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}+\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{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{(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,"(((3*I)/4)*e*f^2*x)/(a*d^2) + (((3*I)/8)*f^3*x^2)/(a*d^2) - (I*(e + f*x)^3)/(a*d) + (((3*I)/8)*(e + f*x)^4)/(a*f) + (6*f^2*(e + f*x)*Cosh[c + d*x])/(a*d^3) + ((e + f*x)^3*Cosh[c + d*x])/(a*d) + ((6*I)*f*(e + f*x)^2*Log[1 + I*E^(c + d*x)])/(a*d^2) + ((12*I)*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) - ((12*I)*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^4) - (6*f^3*Sinh[c + d*x])/(a*d^4) - (3*f*(e + f*x)^2*Sinh[c + d*x])/(a*d^2) - (((3*I)/4)*f^2*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(a*d^3) - ((I/2)*(e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x])/(a*d) + (((3*I)/8)*f^3*Sinh[c + d*x]^2)/(a*d^4) + (((3*I)/4)*f*(e + f*x)^2*Sinh[c + d*x]^2)/(a*d^2) - (I*(e + f*x)^3*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",19,13,31,0.4194,1,"{5557, 3311, 32, 3310, 3296, 2637, 3318, 4184, 3716, 2190, 2531, 2282, 6589}"
200,1,287,0,0.5468537,"\int \frac{(e+f x)^2 \sinh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sinh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{4 i f^2 \text{PolyLog}\left(2,-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 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{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{(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}","\frac{4 i f^2 \text{PolyLog}\left(2,-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 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{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{(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,"((I/4)*f^2*x)/(a*d^2) - (I*(e + f*x)^2)/(a*d) + ((I/2)*(e + f*x)^3)/(a*f) + (2*f^2*Cosh[c + d*x])/(a*d^3) + ((e + f*x)^2*Cosh[c + d*x])/(a*d) + ((4*I)*f*(e + f*x)*Log[1 + I*E^(c + d*x)])/(a*d^2) + ((4*I)*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) - (2*f*(e + f*x)*Sinh[c + d*x])/(a*d^2) - ((I/4)*f^2*Cosh[c + d*x]*Sinh[c + d*x])/(a*d^3) - ((I/2)*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(a*d) + ((I/2)*f*(e + f*x)*Sinh[c + d*x]^2)/(a*d^2) - (I*(e + f*x)^2*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",17,13,31,0.4194,1,"{5557, 3311, 32, 2635, 8, 3296, 2638, 3318, 4184, 3716, 2190, 2279, 2391}"
201,1,175,0,0.2627874,"\int \frac{(e+f x) \sinh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Sinh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\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}","\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,"(((3*I)/2)*e*x)/a + (((3*I)/4)*f*x^2)/a + ((e + f*x)*Cosh[c + d*x])/(a*d) + ((2*I)*f*Log[Cosh[c/2 + (I/4)*Pi + (d*x)/2]])/(a*d^2) - (f*Sinh[c + d*x])/(a*d^2) - ((I/2)*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(a*d) + ((I/4)*f*Sinh[c + d*x]^2)/(a*d^2) - (I*(e + f*x)*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",11,7,29,0.2414,1,"{5557, 3310, 3296, 2637, 3318, 4184, 3475}"
202,1,83,0,0.0795302,"\int \frac{\sinh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Sinh[c + d*x]^3/(a + I*a*Sinh[c + d*x]),x]","\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}","\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,"(((3*I)/2)*x)/a + (2*Cosh[c + d*x])/(a*d) - (((3*I)/2)*Cosh[c + d*x]*Sinh[c + d*x])/(a*d) - (Cosh[c + d*x]*Sinh[c + d*x]^2)/(d*(a + I*a*Sinh[c + d*x]))","A",2,2,24,0.08333,1,"{2767, 2734}"
203,0,0,0,0.0780933,"\int \frac{\sinh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[Sinh[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\sinh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"Defer[Int][Sinh[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
204,0,0,0,0.0786479,"\int \frac{\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[Sinh[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"Defer[Int][Sinh[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
205,1,313,0,0.4820133,"\int \frac{(e+f x)^3 \text{csch}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Csch[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{12 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}-\frac{6 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}+\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}","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{12 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}-\frac{6 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}+\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,"((-I)*(e + f*x)^3)/(a*d) - (2*(e + f*x)^3*ArcTanh[E^(c + d*x)])/(a*d) + ((6*I)*f*(e + f*x)^2*Log[1 + I*E^(c + d*x)])/(a*d^2) - (3*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(a*d^2) + ((12*I)*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) + (3*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(a*d^2) + (6*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a*d^3) - ((12*I)*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^4) - (6*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a*d^3) - (6*f^3*PolyLog[4, -E^(c + d*x)])/(a*d^4) + (6*f^3*PolyLog[4, E^(c + d*x)])/(a*d^4) - (I*(e + f*x)^3*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",17,10,29,0.3448,1,"{5575, 4182, 2531, 6609, 2282, 6589, 3318, 4184, 3716, 2190}"
206,1,224,0,0.3456846,"\int \frac{(e+f x)^2 \text{csch}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{2 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{4 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,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{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}","-\frac{2 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{4 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,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{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,"((-I)*(e + f*x)^2)/(a*d) - (2*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d) + ((4*I)*f*(e + f*x)*Log[1 + I*E^(c + d*x)])/(a*d^2) - (2*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^2) + ((4*I)*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) + (2*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^2) + (2*f^2*PolyLog[3, -E^(c + d*x)])/(a*d^3) - (2*f^2*PolyLog[3, E^(c + d*x)])/(a*d^3) - (I*(e + f*x)^2*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",14,11,29,0.3793,1,"{5575, 4182, 2531, 2282, 6589, 3318, 4184, 3716, 2190, 2279, 2391}"
207,1,126,0,0.147479,"\int \frac{(e+f x) \text{csch}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{f \text{PolyLog}\left(2,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}","-\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{f \text{PolyLog}\left(2,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,"(-2*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d) + ((2*I)*f*Log[Cosh[c/2 + (I/4)*Pi + (d*x)/2]])/(a*d^2) - (f*PolyLog[2, -E^(c + d*x)])/(a*d^2) + (f*PolyLog[2, E^(c + d*x)])/(a*d^2) - (I*(e + f*x)*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",9,7,27,0.2593,1,"{5575, 4182, 2279, 2391, 3318, 4184, 3475}"
208,1,41,0,0.0599134,"\int \frac{\text{csch}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Csch[c + d*x]/(a + I*a*Sinh[c + d*x]),x]","-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}+\frac{\cosh (c+d x)}{d (a+i a \sinh (c+d x))}","-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}+\frac{\cosh (c+d x)}{d (a+i a \sinh (c+d x))}",1,"-(ArcTanh[Cosh[c + d*x]]/(a*d)) + Cosh[c + d*x]/(d*(a + I*a*Sinh[c + d*x]))","A",3,3,22,0.1364,1,"{2747, 3770, 2648}"
209,0,0,0,0.0501509,"\int \frac{\text{csch}(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Csch[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
210,0,0,0,0.050252,"\int \frac{\text{csch}(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Csch[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
211,1,419,0,0.8052771,"\int \frac{(e+f x)^3 \text{csch}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Csch[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{12 f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{12 f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}-\frac{3 f^3 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}+\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}","\frac{12 f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{12 f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}-\frac{3 f^3 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}+\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*(e + f*x)^3)/(a*d) + ((2*I)*(e + f*x)^3*ArcTanh[E^(c + d*x)])/(a*d) - ((e + f*x)^3*Coth[c + d*x])/(a*d) + (6*f*(e + f*x)^2*Log[1 + I*E^(c + d*x)])/(a*d^2) + (3*f*(e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a*d^2) + ((3*I)*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(a*d^2) + (12*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) - ((3*I)*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(a*d^2) + (3*f^2*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a*d^3) - ((6*I)*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a*d^3) - (12*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^4) + ((6*I)*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a*d^3) - (3*f^3*PolyLog[3, E^(2*(c + d*x))])/(2*a*d^4) + ((6*I)*f^3*PolyLog[4, -E^(c + d*x)])/(a*d^4) - ((6*I)*f^3*PolyLog[4, E^(c + d*x)])/(a*d^4) - ((e + f*x)^3*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",24,10,31,0.3226,1,"{5575, 4184, 3716, 2190, 2531, 2282, 6589, 4182, 6609, 3318}"
212,1,296,0,0.583369,"\int \frac{(e+f x)^2 \text{csch}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{2 i f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{4 f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}+\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}","\frac{2 i f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{4 f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}+\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*(e + f*x)^2)/(a*d) + ((2*I)*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d) - ((e + f*x)^2*Coth[c + d*x])/(a*d) + (4*f*(e + f*x)*Log[1 + I*E^(c + d*x)])/(a*d^2) + (2*f*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a*d^2) + ((2*I)*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^2) + (4*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) - ((2*I)*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^2) + (f^2*PolyLog[2, E^(2*(c + d*x))])/(a*d^3) - ((2*I)*f^2*PolyLog[3, -E^(c + d*x)])/(a*d^3) + ((2*I)*f^2*PolyLog[3, E^(c + d*x)])/(a*d^3) - ((e + f*x)^2*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",20,11,31,0.3548,1,"{5575, 4184, 3716, 2190, 2279, 2391, 4182, 2531, 2282, 6589, 3318}"
213,1,163,0,0.2280426,"\int \frac{(e+f x) \text{csch}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{i f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,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}","\frac{i f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,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,"((2*I)*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d) - ((e + f*x)*Coth[c + d*x])/(a*d) + (2*f*Log[Cosh[c/2 + (I/4)*Pi + (d*x)/2]])/(a*d^2) + (f*Log[Sinh[c + d*x]])/(a*d^2) + (I*f*PolyLog[2, -E^(c + d*x)])/(a*d^2) - (I*f*PolyLog[2, E^(c + d*x)])/(a*d^2) - ((e + f*x)*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",12,7,29,0.2414,1,"{5575, 4184, 3475, 4182, 2279, 2391, 3318}"
214,1,57,0,0.0856202,"\int \frac{\text{csch}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Csch[c + d*x]^2/(a + I*a*Sinh[c + d*x]),x]","-\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))}","-\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,"(I*ArcTanh[Cosh[c + d*x]])/(a*d) - (2*Coth[c + d*x])/(a*d) + Coth[c + d*x]/(d*(a + I*a*Sinh[c + d*x]))","A",5,5,24,0.2083,1,"{2768, 2748, 3767, 8, 3770}"
215,0,0,0,0.075928,"\int \frac{\text{csch}^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Csch[c + d*x]^2/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
216,0,0,0,0.0744917,"\int \frac{\text{csch}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[Csch[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{csch}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"Defer[Int][Csch[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
217,1,546,0,1.2118264,"\int \frac{(e+f x)^3 \text{csch}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Csch[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","-\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}+\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}-\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{2 a d^2}-\frac{3 f^3 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^4}+\frac{3 f^3 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^4}+\frac{12 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}+\frac{3 i f^3 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^4}+\frac{9 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}-\frac{9 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}-\frac{6 f^2 (e+f x) \tanh ^{-1}\left(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{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}","-\frac{12 i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{9 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}+\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}-\frac{9 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{2 a d^2}-\frac{3 f^3 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^4}+\frac{3 f^3 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^4}+\frac{12 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}+\frac{3 i f^3 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^4}+\frac{9 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}-\frac{9 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}-\frac{6 f^2 (e+f x) \tanh ^{-1}\left(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{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,"((2*I)*(e + f*x)^3)/(a*d) - (6*f^2*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d^3) + (3*(e + f*x)^3*ArcTanh[E^(c + d*x)])/(a*d) + (I*(e + f*x)^3*Coth[c + d*x])/(a*d) - (3*f*(e + f*x)^2*Csch[c + d*x])/(2*a*d^2) - ((e + f*x)^3*Coth[c + d*x]*Csch[c + d*x])/(2*a*d) - ((6*I)*f*(e + f*x)^2*Log[1 + I*E^(c + d*x)])/(a*d^2) - ((3*I)*f*(e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a*d^2) - (3*f^3*PolyLog[2, -E^(c + d*x)])/(a*d^4) + (9*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(2*a*d^2) - ((12*I)*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) + (3*f^3*PolyLog[2, E^(c + d*x)])/(a*d^4) - (9*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(2*a*d^2) - ((3*I)*f^2*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a*d^3) - (9*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a*d^3) + ((12*I)*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^4) + (9*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a*d^3) + (((3*I)/2)*f^3*PolyLog[3, E^(2*(c + d*x))])/(a*d^4) + (9*f^3*PolyLog[4, -E^(c + d*x)])/(a*d^4) - (9*f^3*PolyLog[4, E^(c + d*x)])/(a*d^4) + (I*(e + f*x)^3*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",40,13,31,0.4194,1,"{5575, 4186, 4182, 2279, 2391, 2531, 6609, 2282, 6589, 4184, 3716, 2190, 3318}"
218,1,368,0,0.8559213,"\int \frac{(e+f x)^2 \text{csch}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{3 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{3 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{4 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{i f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{3 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{3 f^2 \text{PolyLog}\left(3,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{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{f^2 \tanh ^{-1}(\cosh (c+d x))}{a d^3}+\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}","\frac{3 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{3 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{4 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{i f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{3 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{3 f^2 \text{PolyLog}\left(3,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{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{f^2 \tanh ^{-1}(\cosh (c+d x))}{a d^3}+\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*I)*(e + f*x)^2)/(a*d) + (3*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d) - (f^2*ArcTanh[Cosh[c + d*x]])/(a*d^3) + (I*(e + f*x)^2*Coth[c + d*x])/(a*d) - (f*(e + f*x)*Csch[c + d*x])/(a*d^2) - ((e + f*x)^2*Coth[c + d*x]*Csch[c + d*x])/(2*a*d) - ((4*I)*f*(e + f*x)*Log[1 + I*E^(c + d*x)])/(a*d^2) - ((2*I)*f*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a*d^2) + (3*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^2) - ((4*I)*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) - (3*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^2) - (I*f^2*PolyLog[2, E^(2*(c + d*x))])/(a*d^3) - (3*f^2*PolyLog[3, -E^(c + d*x)])/(a*d^3) + (3*f^2*PolyLog[3, E^(c + d*x)])/(a*d^3) + (I*(e + f*x)^2*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",30,13,31,0.4194,1,"{5575, 4186, 3770, 4182, 2531, 2282, 6589, 4184, 3716, 2190, 2279, 2391, 3318}"
219,1,214,0,0.3674086,"\int \frac{(e+f x) \text{csch}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{3 f \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}-\frac{3 f \text{PolyLog}\left(2,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}","\frac{3 f \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}-\frac{3 f \text{PolyLog}\left(2,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,"(3*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d) + (I*(e + f*x)*Coth[c + d*x])/(a*d) - (f*Csch[c + d*x])/(2*a*d^2) - ((e + f*x)*Coth[c + d*x]*Csch[c + d*x])/(2*a*d) - ((2*I)*f*Log[Cosh[c/2 + (I/4)*Pi + (d*x)/2]])/(a*d^2) - (I*f*Log[Sinh[c + d*x]])/(a*d^2) + (3*f*PolyLog[2, -E^(c + d*x)])/(2*a*d^2) - (3*f*PolyLog[2, E^(c + d*x)])/(2*a*d^2) + (I*(e + f*x)*Tanh[c/2 + (I/4)*Pi + (d*x)/2])/(a*d)","A",19,8,29,0.2759,1,"{5575, 4185, 4182, 2279, 2391, 4184, 3475, 3318}"
220,1,87,0,0.1233597,"\int \frac{\text{csch}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Csch[c + d*x]^3/(a + I*a*Sinh[c + d*x]),x]","\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))}","\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,"(3*ArcTanh[Cosh[c + d*x]])/(2*a*d) + ((2*I)*Coth[c + d*x])/(a*d) - (3*Coth[c + d*x]*Csch[c + d*x])/(2*a*d) + (Coth[c + d*x]*Csch[c + d*x])/(d*(a + I*a*Sinh[c + d*x]))","A",6,6,24,0.2500,1,"{2768, 2748, 3768, 3770, 3767, 8}"
221,0,0,0,0.0749999,"\int \frac{\text{csch}^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[Csch[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{csch}^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))},x\right)",0,"Defer[Int][Csch[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
222,0,0,0,0.0739772,"\int \frac{\text{csch}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[Csch[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{csch}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"Defer[Int][Csch[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
223,1,453,0,0.7940954,"\int \frac{(e+f x)^3 \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 a f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{3 a f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{6 a f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \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}","\frac{6 a f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{3 a f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^2 \sqrt{a^2+b^2}}-\frac{6 a f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \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,"(e + f*x)^4/(4*b*f) - (a*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d) + (a*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d) - (3*a*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^2) + (3*a*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^2) + (6*a*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3) - (6*a*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3) - (6*a*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^4) + (6*a*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^4)","A",14,9,26,0.3462,1,"{5557, 32, 3322, 2264, 2190, 2531, 6609, 2282, 6589}"
224,1,337,0,0.7087012,"\int \frac{(e+f x)^2 \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 a f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^2 \sqrt{a^2+b^2}}+\frac{2 a f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \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}","-\frac{2 a f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^2 \sqrt{a^2+b^2}}+\frac{2 a f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \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,"(e + f*x)^3/(3*b*f) - (a*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d) + (a*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d) - (2*a*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^2) + (2*a*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^2) + (2*a*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3) - (2*a*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3)","A",12,8,26,0.3077,1,"{5557, 32, 3322, 2264, 2190, 2531, 2282, 6589}"
225,1,220,0,0.4126655,"\int \frac{(e+f x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{a f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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}","-\frac{a f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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,"(e*x)/b + (f*x^2)/(2*b) - (a*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d) + (a*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d) - (a*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^2) + (a*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^2)","A",10,6,24,0.2500,1,"{5557, 3322, 2264, 2190, 2279, 2391}"
226,1,54,0,0.0748817,"\int \frac{\sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Sinh[c + d*x]/(a + b*Sinh[c + d*x]),x]","\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}","\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,"x/b + (2*a*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b*Sqrt[a^2 + b^2]*d)","A",4,4,19,0.2105,1,"{2735, 2660, 618, 204}"
227,0,0,0,0.0490424,"\int \frac{\sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Sinh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
228,1,551,0,1.0273321,"\int \frac{(e+f x)^3 \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{6 a^2 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3 \sqrt{a^2+b^2}}+\frac{3 a^2 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2 \sqrt{a^2+b^2}}+\frac{6 a^2 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^4 \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^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{6 f^3 \sinh (c+d x)}{b d^4}+\frac{(e+f x)^3 \cosh (c+d x)}{b d}","-\frac{6 a^2 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3 \sqrt{a^2+b^2}}+\frac{3 a^2 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2 \sqrt{a^2+b^2}}+\frac{6 a^2 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^4 \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^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{6 f^3 \sinh (c+d x)}{b d^4}+\frac{(e+f x)^3 \cosh (c+d x)}{b d}",1,"-(a*(e + f*x)^4)/(4*b^2*f) + (6*f^2*(e + f*x)*Cosh[c + d*x])/(b*d^3) + ((e + f*x)^3*Cosh[c + d*x])/(b*d) + (a^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*Sqrt[a^2 + b^2]*d) - (a^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*Sqrt[a^2 + b^2]*d) + (3*a^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^2) - (3*a^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^2) - (6*a^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^3) + (6*a^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^3) + (6*a^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^4) - (6*a^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^4) - (6*f^3*Sinh[c + d*x])/(b*d^4) - (3*f*(e + f*x)^2*Sinh[c + d*x])/(b*d^2)","A",19,11,28,0.3929,1,"{5557, 3296, 2637, 32, 3322, 2264, 2190, 2531, 6609, 2282, 6589}"
229,1,407,0,0.853208,"\int \frac{(e+f x)^2 \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 a^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2 \sqrt{a^2+b^2}}-\frac{2 a^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3 \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 (e+f x) \sinh (c+d x)}{b d^2}+\frac{2 f^2 \cosh (c+d x)}{b d^3}+\frac{(e+f x)^2 \cosh (c+d x)}{b d}","\frac{2 a^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2 \sqrt{a^2+b^2}}-\frac{2 a^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3 \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 (e+f x) \sinh (c+d x)}{b d^2}+\frac{2 f^2 \cosh (c+d x)}{b d^3}+\frac{(e+f x)^2 \cosh (c+d x)}{b d}",1,"-(a*(e + f*x)^3)/(3*b^2*f) + (2*f^2*Cosh[c + d*x])/(b*d^3) + ((e + f*x)^2*Cosh[c + d*x])/(b*d) + (a^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*Sqrt[a^2 + b^2]*d) - (a^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*Sqrt[a^2 + b^2]*d) + (2*a^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^2) - (2*a^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^2) - (2*a^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^3) + (2*a^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^3) - (2*f*(e + f*x)*Sinh[c + d*x])/(b*d^2)","A",16,10,28,0.3571,1,"{5557, 3296, 2638, 32, 3322, 2264, 2190, 2531, 2282, 6589}"
230,1,264,0,0.4867144,"\int \frac{(e+f x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{a^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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}","\frac{a^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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*e*x)/b^2) - (a*f*x^2)/(2*b^2) + ((e + f*x)*Cosh[c + d*x])/(b*d) + (a^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*Sqrt[a^2 + b^2]*d) - (a^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*Sqrt[a^2 + b^2]*d) + (a^2*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^2) - (a^2*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*Sqrt[a^2 + b^2]*d^2) - (f*Sinh[c + d*x])/(b*d^2)","A",13,8,26,0.3077,1,"{5557, 3296, 2637, 3322, 2264, 2190, 2279, 2391}"
231,1,71,0,0.1277364,"\int \frac{\sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Sinh[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","-\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}","-\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*x)/b^2) - (2*a^2*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b^2*Sqrt[a^2 + b^2]*d) + Cosh[c + d*x]/(b*d)","A",6,6,21,0.2857,1,"{2746, 12, 2735, 2660, 618, 204}"
232,0,0,0,0.0755898,"\int \frac{\sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Sinh[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
233,1,712,0,1.2345634,"\int \frac{(e+f x)^3 \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{6 a^3 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3 \sqrt{a^2+b^2}}-\frac{3 a^3 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2 \sqrt{a^2+b^2}}-\frac{6 a^3 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^4 \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{a^2 (e+f x)^4}{4 b^3 f}-\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{6 a f^3 \sinh (c+d x)}{b^2 d^4}-\frac{a (e+f x)^3 \cosh (c+d x)}{b^2 d}+\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{3 f^3 \sinh ^2(c+d x)}{8 b d^4}+\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}","\frac{6 a^3 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3 \sqrt{a^2+b^2}}-\frac{3 a^3 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2 \sqrt{a^2+b^2}}-\frac{6 a^3 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^4 \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{a^2 (e+f x)^4}{4 b^3 f}-\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{6 a f^3 \sinh (c+d x)}{b^2 d^4}-\frac{a (e+f x)^3 \cosh (c+d x)}{b^2 d}+\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{3 f^3 \sinh ^2(c+d x)}{8 b d^4}+\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,"(-3*e*f^2*x)/(4*b*d^2) - (3*f^3*x^2)/(8*b*d^2) + (a^2*(e + f*x)^4)/(4*b^3*f) - (e + f*x)^4/(8*b*f) - (6*a*f^2*(e + f*x)*Cosh[c + d*x])/(b^2*d^3) - (a*(e + f*x)^3*Cosh[c + d*x])/(b^2*d) - (a^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*Sqrt[a^2 + b^2]*d) + (a^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*Sqrt[a^2 + b^2]*d) - (3*a^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^2) + (3*a^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^2) + (6*a^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^3) - (6*a^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^3) - (6*a^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^4) + (6*a^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^4) + (6*a*f^3*Sinh[c + d*x])/(b^2*d^4) + (3*a*f*(e + f*x)^2*Sinh[c + d*x])/(b^2*d^2) + (3*f^2*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(4*b*d^3) + ((e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d) - (3*f^3*Sinh[c + d*x]^2)/(8*b*d^4) - (3*f*(e + f*x)^2*Sinh[c + d*x]^2)/(4*b*d^2)","A",24,13,28,0.4643,1,"{5557, 3311, 32, 3310, 3296, 2637, 3322, 2264, 2190, 2531, 6609, 2282, 6589}"
234,1,522,0,1.0436337,"\int \frac{(e+f x)^2 \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{2 a^3 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2 \sqrt{a^2+b^2}}+\frac{2 a^3 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3 \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{a^2 (e+f x)^3}{3 b^3 f}+\frac{2 a f (e+f x) \sinh (c+d x)}{b^2 d^2}-\frac{2 a f^2 \cosh (c+d x)}{b^2 d^3}-\frac{a (e+f x)^2 \cosh (c+d x)}{b^2 d}-\frac{f (e+f x) \sinh ^2(c+d x)}{2 b d^2}+\frac{f^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^3}+\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}","-\frac{2 a^3 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2 \sqrt{a^2+b^2}}+\frac{2 a^3 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3 \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{a^2 (e+f x)^3}{3 b^3 f}+\frac{2 a f (e+f x) \sinh (c+d x)}{b^2 d^2}-\frac{2 a f^2 \cosh (c+d x)}{b^2 d^3}-\frac{a (e+f x)^2 \cosh (c+d x)}{b^2 d}-\frac{f (e+f x) \sinh ^2(c+d x)}{2 b d^2}+\frac{f^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^3}+\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,"-(f^2*x)/(4*b*d^2) + (a^2*(e + f*x)^3)/(3*b^3*f) - (e + f*x)^3/(6*b*f) - (2*a*f^2*Cosh[c + d*x])/(b^2*d^3) - (a*(e + f*x)^2*Cosh[c + d*x])/(b^2*d) - (a^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*Sqrt[a^2 + b^2]*d) + (a^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*Sqrt[a^2 + b^2]*d) - (2*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^2) + (2*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^2) + (2*a^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^3) - (2*a^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^3) + (2*a*f*(e + f*x)*Sinh[c + d*x])/(b^2*d^2) + (f^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b*d^3) + ((e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d) - (f*(e + f*x)*Sinh[c + d*x]^2)/(2*b*d^2)","A",21,13,28,0.4643,1,"{5557, 3311, 32, 2635, 8, 3296, 2638, 3322, 2264, 2190, 2531, 2282, 6589}"
235,1,335,0,0.5930894,"\int \frac{(e+f x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{a^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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^2 e x}{b^3}+\frac{a^2 f x^2}{2 b^3}+\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}","-\frac{a^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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^2 e x}{b^3}+\frac{a^2 f x^2}{2 b^3}+\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,"(a^2*e*x)/b^3 - (e*x)/(2*b) + (a^2*f*x^2)/(2*b^3) - (f*x^2)/(4*b) - (a*(e + f*x)*Cosh[c + d*x])/(b^2*d) - (a^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*Sqrt[a^2 + b^2]*d) + (a^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*Sqrt[a^2 + b^2]*d) - (a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^2) + (a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*Sqrt[a^2 + b^2]*d^2) + (a*f*Sinh[c + d*x])/(b^2*d^2) + ((e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d) - (f*Sinh[c + d*x]^2)/(4*b*d^2)","A",16,9,26,0.3462,1,"{5557, 3310, 3296, 2637, 3322, 2264, 2190, 2279, 2391}"
236,1,107,0,0.2207693,"\int \frac{\sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Sinh[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","\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{x \left(2 a^2-b^2\right)}{2 b^3}-\frac{a \cosh (c+d x)}{b^2 d}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d}","\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{x \left(2 a^2-b^2\right)}{2 b^3}-\frac{a \cosh (c+d x)}{b^2 d}+\frac{\sinh (c+d x) \cosh (c+d x)}{2 b d}",1,"((2*a^2 - b^2)*x)/(2*b^3) + (2*a^3*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b^3*Sqrt[a^2 + b^2]*d) - (a*Cosh[c + d*x])/(b^2*d) + (Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d)","A",6,6,21,0.2857,1,"{2793, 3023, 2735, 2660, 618, 204}"
237,0,0,0,0.0765824,"\int \frac{\sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[Sinh[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][Sinh[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
238,1,605,0,0.964937,"\int \frac{(e+f x)^3 \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{6 b f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^4 \sqrt{a^2+b^2}}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{6 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}-\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{2 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}","\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{6 b f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^4 \sqrt{a^2+b^2}}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{6 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}-\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{2 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}",1,"(-2*(e + f*x)^3*ArcTanh[E^(c + d*x)])/(a*d) - (b*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*Sqrt[a^2 + b^2]*d) + (b*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*Sqrt[a^2 + b^2]*d) - (3*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(a*d^2) + (3*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(a*d^2) - (3*b*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^2) + (3*b*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^2) + (6*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a*d^3) - (6*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a*d^3) + (6*b*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^3) - (6*b*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^3) - (6*f^3*PolyLog[4, -E^(c + d*x)])/(a*d^4) + (6*f^3*PolyLog[4, E^(c + d*x)])/(a*d^4) - (6*b*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^4) + (6*b*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^4)","A",22,9,26,0.3462,1,"{5575, 4182, 2531, 6609, 2282, 6589, 3322, 2264, 2190}"
239,1,433,0,0.8140571,"\int \frac{(e+f x)^2 \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 b f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \sqrt{a^2+b^2}}+\frac{2 b f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{2 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\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 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}","-\frac{2 b f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \sqrt{a^2+b^2}}+\frac{2 b f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^3 \sqrt{a^2+b^2}}-\frac{2 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\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 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}",1,"(-2*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d) - (b*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*Sqrt[a^2 + b^2]*d) + (b*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*Sqrt[a^2 + b^2]*d) - (2*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^2) + (2*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^2) - (2*b*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^2) + (2*b*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^2) + (2*f^2*PolyLog[3, -E^(c + d*x)])/(a*d^3) - (2*f^2*PolyLog[3, E^(c + d*x)])/(a*d^3) + (2*b*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^3) - (2*b*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^3)","A",18,8,26,0.3077,1,"{5575, 4182, 2531, 2282, 6589, 3322, 2264, 2190}"
240,1,261,0,0.4597858,"\int \frac{(e+f x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{b f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{f \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^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{2 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d}","-\frac{b f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \sqrt{a^2+b^2}}-\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{f \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^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{2 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d}",1,"(-2*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d) - (b*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*Sqrt[a^2 + b^2]*d) + (b*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*Sqrt[a^2 + b^2]*d) - (f*PolyLog[2, -E^(c + d*x)])/(a*d^2) + (f*PolyLog[2, E^(c + d*x)])/(a*d^2) - (b*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^2) + (b*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*Sqrt[a^2 + b^2]*d^2)","A",14,7,24,0.2917,1,"{5575, 4182, 2279, 2391, 3322, 2264, 2190}"
241,1,64,0,0.0878481,"\int \frac{\text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Csch[c + d*x]/(a + b*Sinh[c + d*x]),x]","\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}","\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,"-(ArcTanh[Cosh[c + d*x]]/(a*d)) + (2*b*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(a*Sqrt[a^2 + b^2]*d)","A",5,5,19,0.2632,1,"{2747, 3770, 2660, 618, 204}"
242,0,0,0,0.0487392,"\int \frac{\text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Csch[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
243,1,745,0,1.3107305,"\int \frac{(e+f x)^3 \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{6 b^2 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3 \sqrt{a^2+b^2}}+\frac{3 b^2 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2 \sqrt{a^2+b^2}}+\frac{6 b^2 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^4 \sqrt{a^2+b^2}}-\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^3}+\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^3}+\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^2}+\frac{6 b f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a^2 d^4}-\frac{6 b f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a^2 d^4}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{3 f^3 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^4}+\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{2 b (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\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}","-\frac{6 b^2 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3 \sqrt{a^2+b^2}}+\frac{3 b^2 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2 \sqrt{a^2+b^2}}+\frac{6 b^2 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^4 \sqrt{a^2+b^2}}-\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^3}+\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^3}+\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^2}+\frac{6 b f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a^2 d^4}-\frac{6 b f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a^2 d^4}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{3 f^3 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^4}+\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{2 b (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\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,"-((e + f*x)^3/(a*d)) + (2*b*(e + f*x)^3*ArcTanh[E^(c + d*x)])/(a^2*d) - ((e + f*x)^3*Coth[c + d*x])/(a*d) + (b^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*Sqrt[a^2 + b^2]*d) - (b^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*Sqrt[a^2 + b^2]*d) + (3*f*(e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a*d^2) + (3*b*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(a^2*d^2) - (3*b*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(a^2*d^2) + (3*b^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*Sqrt[a^2 + b^2]*d^2) - (3*b^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*Sqrt[a^2 + b^2]*d^2) + (3*f^2*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a*d^3) - (6*b*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a^2*d^3) + (6*b*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a^2*d^3) - (6*b^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*Sqrt[a^2 + b^2]*d^3) + (6*b^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*Sqrt[a^2 + b^2]*d^3) - (3*f^3*PolyLog[3, E^(2*(c + d*x))])/(2*a*d^4) + (6*b*f^3*PolyLog[4, -E^(c + d*x)])/(a^2*d^4) - (6*b*f^3*PolyLog[4, E^(c + d*x)])/(a^2*d^4) + (6*b^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*Sqrt[a^2 + b^2]*d^4) - (6*b^2*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",29,11,28,0.3929,1,"{5575, 4184, 3716, 2190, 2531, 2282, 6589, 4182, 6609, 3322, 2264}"
244,1,535,0,1.0796293,"\int \frac{(e+f x)^2 \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2 \sqrt{a^2+b^2}}-\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3 \sqrt{a^2+b^2}}+\frac{2 b f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{2 b f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^2}-\frac{2 b f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^3}+\frac{2 b f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^3}+\frac{f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}+\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 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\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}","\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2 \sqrt{a^2+b^2}}-\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3 \sqrt{a^2+b^2}}+\frac{2 b f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{2 b f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^2}-\frac{2 b f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^3}+\frac{2 b f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^3}+\frac{f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}+\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 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\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,"-((e + f*x)^2/(a*d)) + (2*b*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a^2*d) - ((e + f*x)^2*Coth[c + d*x])/(a*d) + (b^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*Sqrt[a^2 + b^2]*d) - (b^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*Sqrt[a^2 + b^2]*d) + (2*f*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a*d^2) + (2*b*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a^2*d^2) - (2*b*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a^2*d^2) + (2*b^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*Sqrt[a^2 + b^2]*d^2) - (2*b^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*Sqrt[a^2 + b^2]*d^2) + (f^2*PolyLog[2, E^(2*(c + d*x))])/(a*d^3) - (2*b*f^2*PolyLog[3, -E^(c + d*x)])/(a^2*d^3) + (2*b*f^2*PolyLog[3, E^(c + d*x)])/(a^2*d^3) - (2*b^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) + (2*b^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)","A",24,12,28,0.4286,1,"{5575, 4184, 3716, 2190, 2279, 2391, 4182, 2531, 2282, 6589, 3322, 2264}"
245,1,306,0,0.565233,"\int \frac{(e+f x) \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{b^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2 \sqrt{a^2+b^2}}+\frac{b f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{b f \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 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^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{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}","\frac{b^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2 \sqrt{a^2+b^2}}+\frac{b f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{b f \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 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^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{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,"(2*b*(e + f*x)*ArcTanh[E^(c + d*x)])/(a^2*d) - ((e + f*x)*Coth[c + d*x])/(a*d) + (b^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*Sqrt[a^2 + b^2]*d) - (b^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*Sqrt[a^2 + b^2]*d) + (f*Log[Sinh[c + d*x]])/(a*d^2) + (b*f*PolyLog[2, -E^(c + d*x)])/(a^2*d^2) - (b*f*PolyLog[2, E^(c + d*x)])/(a^2*d^2) + (b^2*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*Sqrt[a^2 + b^2]*d^2) - (b^2*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*Sqrt[a^2 + b^2]*d^2)","A",17,9,26,0.3462,1,"{5575, 4184, 3475, 4182, 2279, 2391, 3322, 2264, 2190}"
246,1,80,0,0.1470123,"\int \frac{\text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Csch[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","-\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}","-\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,"(b*ArcTanh[Cosh[c + d*x]])/(a^2*d) - (2*b^2*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(a^2*Sqrt[a^2 + b^2]*d) - Coth[c + d*x]/(a*d)","A",7,7,21,0.3333,1,"{2802, 12, 2747, 3770, 2660, 618, 204}"
247,0,0,0,0.0771399,"\int \frac{\text{csch}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Csch[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
248,1,1053,0,1.7516181,"\int \frac{(e+f x)^3 \text{csch}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Csch[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-e^{c+d x}\right) b^2}{a^3 d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right) b^2}{a^3 d^2}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right) b^2}{a^3 d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right) b^2}{a^3 d^3}-\frac{6 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right) b^2}{a^3 d^4}+\frac{6 f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,e^{2 (c+d x)}\right) b}{a^2 d^3}+\frac{3 f^3 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^4}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}+\frac{3 f^3 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^4}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{2 a d^2}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}+\frac{3 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}-\frac{3 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-e^{c+d x}\right) b^2}{a^3 d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right) b^2}{a^3 d^2}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right) b^2}{a^3 d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right) b^2}{a^3 d^3}-\frac{6 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right) b^2}{a^3 d^4}+\frac{6 f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,e^{2 (c+d x)}\right) b}{a^2 d^3}+\frac{3 f^3 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^4}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}+\frac{3 f^3 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^4}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{2 a d^2}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}+\frac{3 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}-\frac{3 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}",1,"(b*(e + f*x)^3)/(a^2*d) - (6*f^2*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d^3) + ((e + f*x)^3*ArcTanh[E^(c + d*x)])/(a*d) - (2*b^2*(e + f*x)^3*ArcTanh[E^(c + d*x)])/(a^3*d) + (b*(e + f*x)^3*Coth[c + d*x])/(a^2*d) - (3*f*(e + f*x)^2*Csch[c + d*x])/(2*a*d^2) - ((e + f*x)^3*Coth[c + d*x]*Csch[c + d*x])/(2*a*d) - (b^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*Sqrt[a^2 + b^2]*d) + (b^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*Sqrt[a^2 + b^2]*d) - (3*b*f*(e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a^2*d^2) - (3*f^3*PolyLog[2, -E^(c + d*x)])/(a*d^4) + (3*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(2*a*d^2) - (3*b^2*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(a^3*d^2) + (3*f^3*PolyLog[2, E^(c + d*x)])/(a*d^4) - (3*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(2*a*d^2) + (3*b^2*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(a^3*d^2) - (3*b^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^2) + (3*b^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^2) - (3*b*f^2*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a^2*d^3) - (3*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a*d^3) + (6*b^2*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a^3*d^3) + (3*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a*d^3) - (6*b^2*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a^3*d^3) + (6*b^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^3) - (6*b^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^3) + (3*b*f^3*PolyLog[3, E^(2*(c + d*x))])/(2*a^2*d^4) + (3*f^3*PolyLog[4, -E^(c + d*x)])/(a*d^4) - (6*b^2*f^3*PolyLog[4, -E^(c + d*x)])/(a^3*d^4) - (3*f^3*PolyLog[4, E^(c + d*x)])/(a*d^4) + (6*b^2*f^3*PolyLog[4, E^(c + d*x)])/(a^3*d^4) - (6*b^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^4) + (6*b^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^4)","A",45,14,28,0.5000,1,"{5575, 4186, 4182, 2279, 2391, 2531, 6609, 2282, 6589, 4184, 3716, 2190, 3322, 2264}"
249,1,725,0,1.3723358,"\int \frac{(e+f x)^2 \text{csch}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{2 b^3 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2 \sqrt{a^2+b^2}}-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^3 d^2}+\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a^3 d^2}+\frac{2 b^3 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^3 \sqrt{a^2+b^2}}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^3 d^3}-\frac{2 b^2 f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^3 d^3}-\frac{b f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^2 d^3}+\frac{f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\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{2 b^2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^3 d}-\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{f (e+f x) \text{csch}(c+d x)}{a d^2}-\frac{f^2 \tanh ^{-1}(\cosh (c+d x))}{a d^3}+\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}","-\frac{2 b^3 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2 \sqrt{a^2+b^2}}-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^3 d^2}+\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a^3 d^2}+\frac{2 b^3 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^3 \sqrt{a^2+b^2}}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^3 d^3}-\frac{2 b^2 f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^3 d^3}-\frac{b f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^2 d^3}+\frac{f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\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{2 b^2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^3 d}-\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{f (e+f x) \text{csch}(c+d x)}{a d^2}-\frac{f^2 \tanh ^{-1}(\cosh (c+d x))}{a d^3}+\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,"(b*(e + f*x)^2)/(a^2*d) + ((e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d) - (2*b^2*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a^3*d) - (f^2*ArcTanh[Cosh[c + d*x]])/(a*d^3) + (b*(e + f*x)^2*Coth[c + d*x])/(a^2*d) - (f*(e + f*x)*Csch[c + d*x])/(a*d^2) - ((e + f*x)^2*Coth[c + d*x]*Csch[c + d*x])/(2*a*d) - (b^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*Sqrt[a^2 + b^2]*d) + (b^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*Sqrt[a^2 + b^2]*d) - (2*b*f*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a^2*d^2) + (f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^2) - (2*b^2*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a^3*d^2) - (f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^2) + (2*b^2*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a^3*d^2) - (2*b^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^2) + (2*b^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^2) - (b*f^2*PolyLog[2, E^(2*(c + d*x))])/(a^2*d^3) - (f^2*PolyLog[3, -E^(c + d*x)])/(a*d^3) + (2*b^2*f^2*PolyLog[3, -E^(c + d*x)])/(a^3*d^3) + (f^2*PolyLog[3, E^(c + d*x)])/(a*d^3) - (2*b^2*f^2*PolyLog[3, E^(c + d*x)])/(a^3*d^3) + (2*b^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^3) - (2*b^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^3)","A",34,14,28,0.5000,1,"{5575, 4186, 3770, 4182, 2531, 2282, 6589, 4184, 3716, 2190, 2279, 2391, 3322, 2264}"
250,1,420,0,0.7255505,"\int \frac{(e+f x) \text{csch}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{b^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2 \sqrt{a^2+b^2}}-\frac{b^2 f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^3 d^2}+\frac{b^2 f \text{PolyLog}\left(2,e^{c+d x}\right)}{a^3 d^2}+\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}-\frac{f \text{PolyLog}\left(2,e^{c+d x}\right)}{2 a d^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{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{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}","-\frac{b^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2 \sqrt{a^2+b^2}}-\frac{b^2 f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^3 d^2}+\frac{b^2 f \text{PolyLog}\left(2,e^{c+d x}\right)}{a^3 d^2}+\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}-\frac{f \text{PolyLog}\left(2,e^{c+d x}\right)}{2 a d^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{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{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,"((e + f*x)*ArcTanh[E^(c + d*x)])/(a*d) - (2*b^2*(e + f*x)*ArcTanh[E^(c + d*x)])/(a^3*d) + (b*(e + f*x)*Coth[c + d*x])/(a^2*d) - (f*Csch[c + d*x])/(2*a*d^2) - ((e + f*x)*Coth[c + d*x]*Csch[c + d*x])/(2*a*d) - (b^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*Sqrt[a^2 + b^2]*d) + (b^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*Sqrt[a^2 + b^2]*d) - (b*f*Log[Sinh[c + d*x]])/(a^2*d^2) + (f*PolyLog[2, -E^(c + d*x)])/(2*a*d^2) - (b^2*f*PolyLog[2, -E^(c + d*x)])/(a^3*d^2) - (f*PolyLog[2, E^(c + d*x)])/(2*a*d^2) + (b^2*f*PolyLog[2, E^(c + d*x)])/(a^3*d^2) - (b^3*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^2) + (b^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*Sqrt[a^2 + b^2]*d^2)","A",24,10,26,0.3846,1,"{5575, 4185, 4182, 2279, 2391, 4184, 3475, 3322, 2264, 2190}"
251,1,113,0,0.4042594,"\int \frac{\text{csch}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Csch[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","\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{\left(a^2-2 b^2\right) \tanh ^{-1}(\cosh (c+d x))}{2 a^3 d}+\frac{b \coth (c+d x)}{a^2 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a 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{\left(a^2-2 b^2\right) \tanh ^{-1}(\cosh (c+d x))}{2 a^3 d}+\frac{b \coth (c+d x)}{a^2 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"((a^2 - 2*b^2)*ArcTanh[Cosh[c + d*x]])/(2*a^3*d) + (2*b^3*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(a^3*Sqrt[a^2 + b^2]*d) + (b*Coth[c + d*x])/(a^2*d) - (Coth[c + d*x]*Csch[c + d*x])/(2*a*d)","A",7,7,21,0.3333,1,"{2802, 3055, 3001, 3770, 2660, 618, 204}"
252,0,0,0,0.0793883,"\int \frac{\text{csch}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[Csch[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{csch}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][Csch[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
253,1,139,0,0.2127349,"\int \frac{(e+f x)^3 \cosh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}-\frac{6 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}-\frac{12 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{a d^4}-\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}","\frac{12 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}-\frac{6 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}-\frac{12 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{a d^4}-\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)/(a*f) - ((2*I)*(e + f*x)^3*Log[1 + I*E^(c + d*x)])/(a*d) - ((6*I)*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) + ((12*I)*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^3) - ((12*I)*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(a*d^4)","A",6,6,29,0.2069,1,"{5559, 2190, 2531, 6609, 2282, 6589}"
254,1,106,0,0.1840227,"\int \frac{(e+f x)^2 \cosh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{4 i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}+\frac{4 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}-\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}","-\frac{4 i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}+\frac{4 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}-\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)*(e + f*x)^3)/(a*f) - ((2*I)*(e + f*x)^2*Log[1 + I*E^(c + d*x)])/(a*d) - ((4*I)*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) + ((4*I)*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^3)","A",5,5,29,0.1724,1,"{5559, 2190, 2531, 2282, 6589}"
255,1,73,0,0.1111106,"\int \frac{(e+f x) \cosh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{2 i f \text{PolyLog}\left(2,-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}","-\frac{2 i f \text{PolyLog}\left(2,-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)*(e + f*x)^2)/(a*f) - ((2*I)*(e + f*x)*Log[1 + I*E^(c + d*x)])/(a*d) - ((2*I)*f*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2)","A",4,4,27,0.1481,1,"{5559, 2190, 2279, 2391}"
256,1,23,0,0.0273148,"\int \frac{\cosh (c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[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",2,2,22,0.09091,1,"{2667, 31}"
257,0,0,0,0.0491233,"\int \frac{\cosh (c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Cosh[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
258,0,0,0,0.0492806,"\int \frac{\cosh (c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Cosh[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
259,1,108,0,0.1636241,"\int \frac{(e+f x)^3 \cosh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","-\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{6 i f^3 \sinh (c+d x)}{a d^4}-\frac{i (e+f x)^3 \cosh (c+d x)}{a d}+\frac{(e+f x)^4}{4 a f}","-\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{6 i f^3 \sinh (c+d x)}{a d^4}-\frac{i (e+f x)^3 \cosh (c+d x)}{a d}+\frac{(e+f x)^4}{4 a f}",1,"(e + f*x)^4/(4*a*f) - ((6*I)*f^2*(e + f*x)*Cosh[c + d*x])/(a*d^3) - (I*(e + f*x)^3*Cosh[c + d*x])/(a*d) + ((6*I)*f^3*Sinh[c + d*x])/(a*d^4) + ((3*I)*f*(e + f*x)^2*Sinh[c + d*x])/(a*d^2)","A",6,4,31,0.1290,1,"{5563, 32, 3296, 2637}"
260,1,82,0,0.1264726,"\int \frac{(e+f x)^2 \cosh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\frac{2 i f (e+f x) \sinh (c+d x)}{a d^2}-\frac{2 i f^2 \cosh (c+d x)}{a d^3}-\frac{i (e+f x)^2 \cosh (c+d x)}{a d}+\frac{(e+f x)^3}{3 a f}","\frac{2 i f (e+f x) \sinh (c+d x)}{a d^2}-\frac{2 i f^2 \cosh (c+d x)}{a d^3}-\frac{i (e+f x)^2 \cosh (c+d x)}{a d}+\frac{(e+f x)^3}{3 a f}",1,"(e + f*x)^3/(3*a*f) - ((2*I)*f^2*Cosh[c + d*x])/(a*d^3) - (I*(e + f*x)^2*Cosh[c + d*x])/(a*d) + ((2*I)*f*(e + f*x)*Sinh[c + d*x])/(a*d^2)","A",5,4,31,0.1290,1,"{5563, 32, 3296, 2638}"
261,1,56,0,0.0715893,"\int \frac{(e+f x) \cosh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\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}","\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,"(e*x)/a + (f*x^2)/(2*a) - (I*(e + f*x)*Cosh[c + d*x])/(a*d) + (I*f*Sinh[c + d*x])/(a*d^2)","A",4,3,29,0.1034,1,"{5563, 3296, 2637}"
262,1,22,0,0.0431233,"\int \frac{\cosh ^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Cosh[c + d*x]^2/(a + I*a*Sinh[c + d*x]),x]","\frac{x}{a}-\frac{i \cosh (c+d x)}{a d}","\frac{x}{a}-\frac{i \cosh (c+d x)}{a d}",1,"x/a - (I*Cosh[c + d*x])/(a*d)","A",2,2,24,0.08333,1,"{2682, 8}"
263,1,76,0,0.204152,"\int \frac{\cosh ^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[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(\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}","-\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]/(a*f) - (I*CoshIntegral[(d*e)/f + d*x]*Sinh[c - (d*e)/f])/(a*f) - (I*Cosh[c - (d*e)/f]*SinhIntegral[(d*e)/f + d*x])/(a*f)","A",5,5,31,0.1613,1,"{5563, 31, 3303, 3298, 3301}"
264,1,103,0,0.2209794,"\int \frac{\cosh ^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[Cosh[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),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)}","-\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,"-(1/(a*f*(e + f*x))) - (I*d*Cosh[c - (d*e)/f]*CoshIntegral[(d*e)/f + d*x])/(a*f^2) + (I*Sinh[c + d*x])/(a*f*(e + f*x)) - (I*d*Sinh[c - (d*e)/f]*SinhIntegral[(d*e)/f + d*x])/(a*f^2)","A",6,6,31,0.1935,1,"{5563, 32, 3297, 3303, 3298, 3301}"
265,1,231,0,0.2607742,"\int \frac{(e+f x)^3 \cosh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","-\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{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{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}","-\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{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{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,"(((-3*I)/8)*f^3*x)/(a*d^3) - ((I/4)*(e + f*x)^3)/(a*d) - (6*f^3*Cosh[c + d*x])/(a*d^4) - (3*f*(e + f*x)^2*Cosh[c + d*x])/(a*d^2) + (6*f^2*(e + f*x)*Sinh[c + d*x])/(a*d^3) + ((e + f*x)^3*Sinh[c + d*x])/(a*d) + (((3*I)/8)*f^3*Cosh[c + d*x]*Sinh[c + d*x])/(a*d^4) + (((3*I)/4)*f*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(a*d^2) - (((3*I)/4)*f^2*(e + f*x)*Sinh[c + d*x]^2)/(a*d^3) - ((I/2)*(e + f*x)^3*Sinh[c + d*x]^2)/(a*d)","A",10,8,31,0.2581,1,"{5563, 3296, 2638, 5446, 3311, 32, 2635, 8}"
266,1,171,0,0.1861519,"\int \frac{(e+f x)^2 \cosh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","-\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 f^2 \sinh ^2(c+d x)}{4 a d^3}+\frac{2 f^2 \sinh (c+d x)}{a d^3}-\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}","-\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 f^2 \sinh ^2(c+d x)}{4 a d^3}+\frac{2 f^2 \sinh (c+d x)}{a d^3}-\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,"((-I/2)*e*f*x)/(a*d) - ((I/4)*f^2*x^2)/(a*d) - (2*f*(e + f*x)*Cosh[c + d*x])/(a*d^2) + (2*f^2*Sinh[c + d*x])/(a*d^3) + ((e + f*x)^2*Sinh[c + d*x])/(a*d) + ((I/2)*f*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(a*d^2) - ((I/4)*f^2*Sinh[c + d*x]^2)/(a*d^3) - ((I/2)*(e + f*x)^2*Sinh[c + d*x]^2)/(a*d)","A",7,5,31,0.1613,1,"{5563, 3296, 2637, 5446, 3310}"
267,1,98,0,0.0995435,"\int \frac{(e+f x) \cosh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","-\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}","-\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/4)*f*x)/(a*d) - (f*Cosh[c + d*x])/(a*d^2) + ((e + f*x)*Sinh[c + d*x])/(a*d) + ((I/4)*f*Cosh[c + d*x]*Sinh[c + d*x])/(a*d^2) - ((I/2)*(e + f*x)*Sinh[c + d*x]^2)/(a*d)","A",6,6,29,0.2069,1,"{5563, 3296, 2638, 5446, 2635, 8}"
268,1,34,0,0.047608,"\int \frac{\cosh ^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Cosh[c + d*x]^3/(a + I*a*Sinh[c + d*x]),x]","\frac{\sinh (c+d x)}{a d}-\frac{i \sinh ^2(c+d x)}{2 a d}","\frac{\sinh (c+d x)}{a d}-\frac{i \sinh ^2(c+d x)}{2 a d}",1,"Sinh[c + d*x]/(a*d) - ((I/2)*Sinh[c + d*x]^2)/(a*d)","A",2,1,24,0.04167,1,"{2667}"
269,1,131,0,0.3241255,"\int \frac{\cosh ^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[Cosh[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])),x]","-\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}","-\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,"(Cosh[c - (d*e)/f]*CoshIntegral[(d*e)/f + d*x])/(a*f) - ((I/2)*CoshIntegral[(2*d*e)/f + 2*d*x]*Sinh[2*c - (2*d*e)/f])/(a*f) + (Sinh[c - (d*e)/f]*SinhIntegral[(d*e)/f + d*x])/(a*f) - ((I/2)*Cosh[2*c - (2*d*e)/f]*SinhIntegral[(2*d*e)/f + 2*d*x])/(a*f)","A",9,6,31,0.1935,1,"{5563, 3303, 3298, 3301, 5448, 12}"
270,1,180,0,0.3918068,"\int \frac{\cosh ^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[Cosh[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),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)}","\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,"-(Cosh[c + d*x]/(a*f*(e + f*x))) - (I*d*Cosh[2*c - (2*d*e)/f]*CoshIntegral[(2*d*e)/f + 2*d*x])/(a*f^2) + (d*CoshIntegral[(d*e)/f + d*x]*Sinh[c - (d*e)/f])/(a*f^2) + ((I/2)*Sinh[2*c + 2*d*x])/(a*f*(e + f*x)) + (d*Cosh[c - (d*e)/f]*SinhIntegral[(d*e)/f + d*x])/(a*f^2) - (I*d*Sinh[2*c - (2*d*e)/f]*SinhIntegral[(2*d*e)/f + 2*d*x])/(a*f^2)","A",11,7,31,0.2258,1,"{5563, 3297, 3303, 3298, 3301, 5448, 12}"
271,1,463,0,0.4830548,"\int \frac{(e+f x)^3 \text{sech}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sech[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 a d^2}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 a d^2}+\frac{3 i f^3 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^4}-\frac{3 i f^3 \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^4}+\frac{3 i f^3 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a d^4}-\frac{3 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{a d^4}+\frac{3 i f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{a d^4}+\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 \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}","\frac{3 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}-\frac{3 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 a d^2}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 a d^2}+\frac{3 i f^3 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^4}-\frac{3 i f^3 \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^4}+\frac{3 i f^3 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a d^4}-\frac{3 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{a d^4}+\frac{3 i f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{a d^4}+\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 \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,"(((-3*I)/2)*f*(e + f*x)^2)/(a*d^2) - (6*f^2*(e + f*x)*ArcTan[E^(c + d*x)])/(a*d^3) + ((e + f*x)^3*ArcTan[E^(c + d*x)])/(a*d) + ((3*I)*f^2*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(a*d^3) + ((3*I)*f^3*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^4) - (((3*I)/2)*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) - ((3*I)*f^3*PolyLog[2, I*E^(c + d*x)])/(a*d^4) + (((3*I)/2)*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(a*d^2) + (((3*I)/2)*f^3*PolyLog[2, -E^(2*(c + d*x))])/(a*d^4) + ((3*I)*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^3) - ((3*I)*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(a*d^3) - ((3*I)*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(a*d^4) + ((3*I)*f^3*PolyLog[4, I*E^(c + d*x)])/(a*d^4) + (3*f*(e + f*x)^2*Sech[c + d*x])/(2*a*d^2) + ((I/2)*(e + f*x)^3*Sech[c + d*x]^2)/(a*d) - (((3*I)/2)*f*(e + f*x)^2*Tanh[c + d*x])/(a*d^2) + ((e + f*x)^3*Sech[c + d*x]*Tanh[c + d*x])/(2*a*d)","A",22,13,29,0.4483,1,"{5571, 4186, 4180, 2279, 2391, 2531, 6609, 2282, 6589, 5451, 4184, 3718, 2190}"
272,1,268,0,0.2639048,"\int \frac{(e+f x)^2 \text{sech}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sech[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}+\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^2}+\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}-\frac{i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^3}-\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{f^2 \tan ^{-1}(\sinh (c+d x))}{a d^3}+\frac{i f^2 \log (\cosh (c+d x))}{a d^3}+\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}","-\frac{i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}+\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^2}+\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}-\frac{i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^3}-\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{f^2 \tan ^{-1}(\sinh (c+d x))}{a d^3}+\frac{i f^2 \log (\cosh (c+d x))}{a d^3}+\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,"((e + f*x)^2*ArcTan[E^(c + d*x)])/(a*d) - (f^2*ArcTan[Sinh[c + d*x]])/(a*d^3) + (I*f^2*Log[Cosh[c + d*x]])/(a*d^3) - (I*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) + (I*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(a*d^2) + (I*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^3) - (I*f^2*PolyLog[3, I*E^(c + d*x)])/(a*d^3) + (f*(e + f*x)*Sech[c + d*x])/(a*d^2) + ((I/2)*(e + f*x)^2*Sech[c + d*x]^2)/(a*d) - (I*f*(e + f*x)*Tanh[c + d*x])/(a*d^2) + ((e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*a*d)","A",13,10,29,0.3448,1,"{5571, 4186, 3770, 4180, 2531, 2282, 6589, 5451, 4184, 3475}"
273,1,161,0,0.142473,"\int \frac{(e+f x) \text{sech}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Sech[c + d*x])/(a + I*a*Sinh[c + d*x]),x]","-\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 a d^2}+\frac{i f \text{PolyLog}\left(2,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}","-\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 a d^2}+\frac{i f \text{PolyLog}\left(2,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,"((e + f*x)*ArcTan[E^(c + d*x)])/(a*d) - ((I/2)*f*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) + ((I/2)*f*PolyLog[2, I*E^(c + d*x)])/(a*d^2) + (f*Sech[c + d*x])/(2*a*d^2) + ((I/2)*(e + f*x)*Sech[c + d*x]^2)/(a*d) - ((I/2)*f*Tanh[c + d*x])/(a*d^2) + ((e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*a*d)","A",10,8,27,0.2963,1,"{5571, 4185, 4180, 2279, 2391, 5451, 3767, 8}"
274,1,42,0,0.0566407,"\int \frac{\text{sech}(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Sech[c + d*x]/(a + I*a*Sinh[c + d*x]),x]","\frac{\tan ^{-1}(\sinh (c+d x))}{2 a d}+\frac{i}{2 d (a+i a \sinh (c+d x))}","\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]]/(2*a*d) + (I/2)/(d*(a + I*a*Sinh[c + d*x]))","A",4,3,22,0.1364,1,"{2667, 44, 206}"
275,0,0,0,0.0496738,"\int \frac{\text{sech}(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Sech[c + d*x]/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
276,0,0,0,0.0503592,"\int \frac{\text{sech}(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[Sech[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{sech}(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{sech}(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"Defer[Int][Sech[c + d*x]/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
277,1,450,0,0.5893661,"\int \frac{(e+f x)^3 \text{sech}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sech[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","-\frac{f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{f^2 (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^3}-\frac{2 f^2 (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{a d^3}+\frac{f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}-\frac{f^3 \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^4}+\frac{f^3 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{a d^4}-\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{i f^3 \tan ^{-1}(\sinh (c+d x))}{a d^4}+\frac{f^3 \log (\cosh (c+d x))}{a d^4}+\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}","-\frac{f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{f^2 (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^3}-\frac{2 f^2 (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{a d^3}+\frac{f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}-\frac{f^3 \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^4}+\frac{f^3 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{a d^4}-\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{i f^3 \tan ^{-1}(\sinh (c+d x))}{a d^4}+\frac{f^3 \log (\cosh (c+d x))}{a d^4}+\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,"(2*(e + f*x)^3)/(3*a*d) - (I*f*(e + f*x)^2*ArcTan[E^(c + d*x)])/(a*d^2) + (I*f^3*ArcTan[Sinh[c + d*x]])/(a*d^4) - (2*f*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(a*d^2) + (f^3*Log[Cosh[c + d*x]])/(a*d^4) - (f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) + (f^2*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(a*d^3) - (2*f^2*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(a*d^3) + (f^3*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^4) - (f^3*PolyLog[3, I*E^(c + d*x)])/(a*d^4) + (f^3*PolyLog[3, -E^(2*(c + d*x))])/(a*d^4) - (I*f^2*(e + f*x)*Sech[c + d*x])/(a*d^3) + (f*(e + f*x)^2*Sech[c + d*x]^2)/(2*a*d^2) + ((I/3)*(e + f*x)^3*Sech[c + d*x]^3)/(a*d) - (f^2*(e + f*x)*Tanh[c + d*x])/(a*d^3) + (2*(e + f*x)^3*Tanh[c + d*x])/(3*a*d) - ((I/2)*f*(e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(a*d^2) + ((e + f*x)^3*Sech[c + d*x]^2*Tanh[c + d*x])/(3*a*d)","A",20,12,31,0.3871,1,"{5571, 4186, 4184, 3475, 3718, 2190, 2531, 2282, 6589, 5451, 3770, 4180}"
278,1,325,0,0.3866007,"\int \frac{(e+f x)^2 \text{sech}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sech[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","-\frac{f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{3 a d^3}+\frac{f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{3 a d^3}-\frac{2 f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{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{f^2 \tanh (c+d x)}{3 a d^3}-\frac{i f^2 \text{sech}(c+d x)}{3 a d^3}+\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}","-\frac{f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{3 a d^3}+\frac{f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{3 a d^3}-\frac{2 f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{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{f^2 \tanh (c+d x)}{3 a d^3}-\frac{i f^2 \text{sech}(c+d x)}{3 a d^3}+\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,"(2*(e + f*x)^2)/(3*a*d) - (((2*I)/3)*f*(e + f*x)*ArcTan[E^(c + d*x)])/(a*d^2) - (4*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(3*a*d^2) - (f^2*PolyLog[2, (-I)*E^(c + d*x)])/(3*a*d^3) + (f^2*PolyLog[2, I*E^(c + d*x)])/(3*a*d^3) - (2*f^2*PolyLog[2, -E^(2*(c + d*x))])/(3*a*d^3) - ((I/3)*f^2*Sech[c + d*x])/(a*d^3) + (f*(e + f*x)*Sech[c + d*x]^2)/(3*a*d^2) + ((I/3)*(e + f*x)^2*Sech[c + d*x]^3)/(a*d) - (f^2*Tanh[c + d*x])/(3*a*d^3) + (2*(e + f*x)^2*Tanh[c + d*x])/(3*a*d) - ((I/3)*f*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(a*d^2) + ((e + f*x)^2*Sech[c + d*x]^2*Tanh[c + d*x])/(3*a*d)","A",16,12,31,0.3871,1,"{5571, 4186, 3767, 8, 4184, 3718, 2190, 2279, 2391, 5451, 4185, 4180}"
279,1,158,0,0.1575481,"\int \frac{(e+f x) \text{sech}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Sech[c + d*x]^2)/(a + I*a*Sinh[c + d*x]),x]","\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}","\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,"((-I/6)*f*ArcTan[Sinh[c + d*x]])/(a*d^2) - (2*f*Log[Cosh[c + d*x]])/(3*a*d^2) + (f*Sech[c + d*x]^2)/(6*a*d^2) + ((I/3)*(e + f*x)*Sech[c + d*x]^3)/(a*d) + (2*(e + f*x)*Tanh[c + d*x])/(3*a*d) - ((I/6)*f*Sech[c + d*x]*Tanh[c + d*x])/(a*d^2) + ((e + f*x)*Sech[c + d*x]^2*Tanh[c + d*x])/(3*a*d)","A",7,7,29,0.2414,1,"{5571, 4185, 4184, 3475, 5451, 3768, 3770}"
280,1,47,0,0.054996,"\int \frac{\text{sech}^2(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Sech[c + d*x]^2/(a + I*a*Sinh[c + d*x]),x]","\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))}","\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,"((I/3)*Sech[c + d*x])/(d*(a + I*a*Sinh[c + d*x])) + (2*Tanh[c + d*x])/(3*a*d)","A",3,3,24,0.1250,1,"{2672, 3767, 8}"
281,0,0,0,0.0780557,"\int \frac{\text{sech}^2(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Sech[c + d*x]^2/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
282,0,0,0,0.0767881,"\int \frac{\text{sech}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[Sech[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{sech}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{sech}^2(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"Defer[Int][Sech[c + d*x]^2/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
283,1,667,0,0.7111197,"\int \frac{(e+f x)^3 \text{sech}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sech[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{4 a d^3}-\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right)}{4 a d^3}-\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{8 a d^2}+\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{8 a d^2}+\frac{5 i f^3 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 a d^4}-\frac{5 i f^3 \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 a d^4}+\frac{i f^3 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a d^4}-\frac{9 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{4 a d^4}+\frac{9 i f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{4 a d^4}+\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{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{i f^3 \tanh (c+d x)}{4 a d^4}-\frac{f^3 \text{sech}(c+d x)}{4 a d^4}+\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}","\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{4 a d^3}-\frac{9 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right)}{4 a d^3}-\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{8 a d^2}+\frac{9 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{8 a d^2}+\frac{5 i f^3 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 a d^4}-\frac{5 i f^3 \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 a d^4}+\frac{i f^3 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a d^4}-\frac{9 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{4 a d^4}+\frac{9 i f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{4 a d^4}+\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{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{i f^3 \tanh (c+d x)}{4 a d^4}-\frac{f^3 \text{sech}(c+d x)}{4 a d^4}+\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,"((-I/2)*f*(e + f*x)^2)/(a*d^2) - (5*f^2*(e + f*x)*ArcTan[E^(c + d*x)])/(a*d^3) + (3*(e + f*x)^3*ArcTan[E^(c + d*x)])/(4*a*d) + (I*f^2*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(a*d^3) + (((5*I)/2)*f^3*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^4) - (((9*I)/8)*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) - (((5*I)/2)*f^3*PolyLog[2, I*E^(c + d*x)])/(a*d^4) + (((9*I)/8)*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(a*d^2) + ((I/2)*f^3*PolyLog[2, -E^(2*(c + d*x))])/(a*d^4) + (((9*I)/4)*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^3) - (((9*I)/4)*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(a*d^3) - (((9*I)/4)*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(a*d^4) + (((9*I)/4)*f^3*PolyLog[4, I*E^(c + d*x)])/(a*d^4) - (f^3*Sech[c + d*x])/(4*a*d^4) + (9*f*(e + f*x)^2*Sech[c + d*x])/(8*a*d^2) - ((I/4)*f^2*(e + f*x)*Sech[c + d*x]^2)/(a*d^3) + (f*(e + f*x)^2*Sech[c + d*x]^3)/(4*a*d^2) + ((I/4)*(e + f*x)^3*Sech[c + d*x]^4)/(a*d) + ((I/4)*f^3*Tanh[c + d*x])/(a*d^4) - ((I/2)*f*(e + f*x)^2*Tanh[c + d*x])/(a*d^2) - (f^2*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(4*a*d^3) + (3*(e + f*x)^3*Sech[c + d*x]*Tanh[c + d*x])/(8*a*d) - ((I/4)*f*(e + f*x)^2*Sech[c + d*x]^2*Tanh[c + d*x])/(a*d^2) + ((e + f*x)^3*Sech[c + d*x]^3*Tanh[c + d*x])/(4*a*d)","A",32,16,31,0.5161,1,"{5571, 4186, 4185, 4180, 2279, 2391, 2531, 6609, 2282, 6589, 5451, 3767, 8, 4184, 3718, 2190}"
284,1,423,0,0.3983296,"\int \frac{(e+f x)^2 \text{sech}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sech[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","-\frac{3 i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{4 a d^2}+\frac{3 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{4 a d^2}+\frac{3 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{4 a d^3}-\frac{3 i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{4 a d^3}-\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{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 (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}","-\frac{3 i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{4 a d^2}+\frac{3 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{4 a d^2}+\frac{3 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{4 a d^3}-\frac{3 i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{4 a d^3}-\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{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 (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,"(3*(e + f*x)^2*ArcTan[E^(c + d*x)])/(4*a*d) - (5*f^2*ArcTan[Sinh[c + d*x]])/(6*a*d^3) + ((I/3)*f^2*Log[Cosh[c + d*x]])/(a*d^3) - (((3*I)/4)*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) + (((3*I)/4)*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(a*d^2) + (((3*I)/4)*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^3) - (((3*I)/4)*f^2*PolyLog[3, I*E^(c + d*x)])/(a*d^3) + (3*f*(e + f*x)*Sech[c + d*x])/(4*a*d^2) - ((I/12)*f^2*Sech[c + d*x]^2)/(a*d^3) + (f*(e + f*x)*Sech[c + d*x]^3)/(6*a*d^2) + ((I/4)*(e + f*x)^2*Sech[c + d*x]^4)/(a*d) - ((I/3)*f*(e + f*x)*Tanh[c + d*x])/(a*d^2) - (f^2*Sech[c + d*x]*Tanh[c + d*x])/(12*a*d^3) + (3*(e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(8*a*d) - ((I/6)*f*(e + f*x)*Sech[c + d*x]^2*Tanh[c + d*x])/(a*d^2) + ((e + f*x)^2*Sech[c + d*x]^3*Tanh[c + d*x])/(4*a*d)","A",17,12,31,0.3871,1,"{5571, 4186, 3768, 3770, 4180, 2531, 2282, 6589, 5451, 4185, 4184, 3475}"
285,1,233,0,0.1898251,"\int \frac{(e+f x) \text{sech}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[((e + f*x)*Sech[c + d*x]^3)/(a + I*a*Sinh[c + d*x]),x]","-\frac{3 i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{8 a d^2}+\frac{3 i f \text{PolyLog}\left(2,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}","-\frac{3 i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{8 a d^2}+\frac{3 i f \text{PolyLog}\left(2,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,"(3*(e + f*x)*ArcTan[E^(c + d*x)])/(4*a*d) - (((3*I)/8)*f*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) + (((3*I)/8)*f*PolyLog[2, I*E^(c + d*x)])/(a*d^2) + (3*f*Sech[c + d*x])/(8*a*d^2) + (f*Sech[c + d*x]^3)/(12*a*d^2) + ((I/4)*(e + f*x)*Sech[c + d*x]^4)/(a*d) - ((I/4)*f*Tanh[c + d*x])/(a*d^2) + (3*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(8*a*d) + ((e + f*x)*Sech[c + d*x]^3*Tanh[c + d*x])/(4*a*d) + ((I/12)*f*Tanh[c + d*x]^3)/(a*d^2)","A",11,7,29,0.2414,1,"{5571, 4185, 4180, 2279, 2391, 5451, 3767}"
286,1,91,0,0.0811465,"\int \frac{\text{sech}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx","Int[Sech[c + d*x]^3/(a + I*a*Sinh[c + d*x]),x]","\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}","\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,"(3*ArcTan[Sinh[c + d*x]])/(8*a*d) - (I/8)/(d*(a - I*a*Sinh[c + d*x])) + ((I/8)*a)/(d*(a + I*a*Sinh[c + d*x])^2) + (I/4)/(d*(a + I*a*Sinh[c + d*x]))","A",4,3,24,0.1250,1,"{2667, 44, 206}"
287,0,0,0,0.0796316,"\int \frac{\text{sech}^3(c+d x)}{(e+f x) (a+i a \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Sech[c + d*x]^3/((e + f*x)*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
288,0,0,0,0.0811407,"\int \frac{\text{sech}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","Int[Sech[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])),x]","\int \frac{\text{sech}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\text{sech}^3(c+d x)}{(e+f x)^2 (a+i a \sinh (c+d x))},x\right)",0,"Defer[Int][Sech[c + d*x]^3/((e + f*x)^2*(a + I*a*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
289,1,356,0,0.4829975,"\int \frac{(e+f x)^3 \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^2}+\frac{6 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^4}+\frac{6 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4}+\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}","-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^2}+\frac{6 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^4}+\frac{6 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4}+\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/(4*b*f) + ((e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*d) + ((e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*d) + (3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*d^2) + (3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^2) - (6*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*d^3) - (6*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^3) + (6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*d^4) + (6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^4)","A",11,6,26,0.2308,1,"{5561, 2190, 2531, 6609, 2282, 6589}"
290,1,264,0,0.4113033,"\int \frac{(e+f x)^2 \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{2 f (e+f x) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{2 f (e+f x) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3}-\frac{2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3}+\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}","\frac{2 f (e+f x) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{2 f (e+f x) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^3}-\frac{2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3}+\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/(3*b*f) + ((e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*d) + ((e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*d) + (2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*d^2) + (2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^2) - (2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*d^3) - (2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^3)","A",9,5,26,0.1923,1,"{5561, 2190, 2531, 2282, 6589}"
291,1,170,0,0.2344744,"\int \frac{(e+f x) \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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}","\frac{f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b d^2}+\frac{f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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,"-(e + f*x)^2/(2*b*f) + ((e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*d) + ((e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*d) + (f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*d^2) + (f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*d^2)","A",7,4,24,0.1667,1,"{5561, 2190, 2279, 2391}"
292,1,18,0,0.0273205,"\int \frac{\cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[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",2,2,19,0.1053,1,"{2668, 31}"
293,0,0,0,0.0471313,"\int \frac{\cosh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Cosh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
294,1,527,0,0.9080793,"\int \frac{(e+f x)^3 \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3}+\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2}+\frac{6 f^3 \sqrt{a^2+b^2} \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^4}+\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^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{6 f^3 \sinh (c+d x)}{b d^4}+\frac{(e+f x)^3 \cosh (c+d x)}{b d}","-\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3}+\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2}+\frac{6 f^3 \sqrt{a^2+b^2} \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^4}+\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^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{6 f^3 \sinh (c+d x)}{b d^4}+\frac{(e+f x)^3 \cosh (c+d x)}{b d}",1,"-(a*(e + f*x)^4)/(4*b^2*f) + (6*f^2*(e + f*x)*Cosh[c + d*x])/(b*d^3) + ((e + f*x)^3*Cosh[c + d*x])/(b*d) + (Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*d) - (Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*d) + (3*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^2) - (3*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^2) - (6*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^3) + (6*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^3) + (6*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^4) - (6*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^4) - (6*f^3*Sinh[c + d*x])/(b*d^4) - (3*f*(e + f*x)^2*Sinh[c + d*x])/(b*d^2)","A",18,11,28,0.3929,1,"{5565, 32, 3296, 2637, 3322, 2264, 2190, 2531, 6609, 2282, 6589}"
295,1,389,0,0.785279,"\int \frac{(e+f x)^2 \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2}-\frac{2 f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3}+\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 (e+f x) \sinh (c+d x)}{b d^2}+\frac{2 f^2 \cosh (c+d x)}{b d^3}+\frac{(e+f x)^2 \cosh (c+d x)}{b d}","\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2}-\frac{2 f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3}+\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 (e+f x) \sinh (c+d x)}{b d^2}+\frac{2 f^2 \cosh (c+d x)}{b d^3}+\frac{(e+f x)^2 \cosh (c+d x)}{b d}",1,"-(a*(e + f*x)^3)/(3*b^2*f) + (2*f^2*Cosh[c + d*x])/(b*d^3) + ((e + f*x)^2*Cosh[c + d*x])/(b*d) + (Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*d) - (Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*d) + (2*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^2) - (2*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^2) - (2*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^3) + (2*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^3) - (2*f*(e + f*x)*Sinh[c + d*x])/(b*d^2)","A",15,10,28,0.3571,1,"{5565, 32, 3296, 2638, 3322, 2264, 2190, 2531, 2282, 6589}"
296,1,252,0,0.442924,"\int \frac{(e+f x) \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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}","\frac{f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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*e*x)/b^2) - (a*f*x^2)/(2*b^2) + ((e + f*x)*Cosh[c + d*x])/(b*d) + (Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*d) - (Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*d) + (Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^2) - (Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^2) - (f*Sinh[c + d*x])/(b*d^2)","A",12,8,26,0.3077,1,"{5565, 3296, 2637, 3322, 2264, 2190, 2279, 2391}"
297,1,68,0,0.1169623,"\int \frac{\cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Cosh[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","-\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}","-\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,"-((a*x)/b^2) - (2*Sqrt[a^2 + b^2]*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b^2*d) + Cosh[c + d*x]/(b*d)","A",5,5,21,0.2381,1,"{2695, 2735, 2660, 618, 204}"
298,0,0,0,0.0748446,"\int \frac{\cosh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Cosh[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
299,1,642,0,0.7849374,"\int \frac{(e+f x)^3 \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}+\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}+\frac{6 f^3 \left(a^2+b^2\right) \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^4}+\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^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{6 a f^3 \cosh (c+d x)}{b^2 d^4}-\frac{a (e+f x)^3 \sinh (c+d x)}{b^2 d}+\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{3 f^3 \sinh (c+d x) \cosh (c+d x)}{8 b d^4}+\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}","-\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}+\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}+\frac{6 f^3 \left(a^2+b^2\right) \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^4}+\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^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{6 a f^3 \cosh (c+d x)}{b^2 d^4}-\frac{a (e+f x)^3 \sinh (c+d x)}{b^2 d}+\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{3 f^3 \sinh (c+d x) \cosh (c+d x)}{8 b d^4}+\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,"(3*f^3*x)/(8*b*d^3) + (e + f*x)^3/(4*b*d) - ((a^2 + b^2)*(e + f*x)^4)/(4*b^3*f) + (6*a*f^3*Cosh[c + d*x])/(b^2*d^4) + (3*a*f*(e + f*x)^2*Cosh[c + d*x])/(b^2*d^2) + ((a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*d) + ((a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*d) + (3*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^2) + (3*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^2) - (6*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^3) - (6*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^3) + (6*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^4) + (6*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^4) - (6*a*f^2*(e + f*x)*Sinh[c + d*x])/(b^2*d^3) - (a*(e + f*x)^3*Sinh[c + d*x])/(b^2*d) - (3*f^3*Cosh[c + d*x]*Sinh[c + d*x])/(8*b*d^4) - (3*f*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b*d^2) + (3*f^2*(e + f*x)*Sinh[c + d*x]^2)/(4*b*d^3) + ((e + f*x)^3*Sinh[c + d*x]^2)/(2*b*d)","A",21,14,28,0.5000,1,"{5565, 3296, 2638, 5446, 3311, 32, 2635, 8, 5561, 2190, 2531, 6609, 2282, 6589}"
300,1,477,0,0.6424937,"\int \frac{(e+f x)^2 \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{2 f \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}-\frac{2 f^2 \left(a^2+b^2\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}+\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 (e+f x) \cosh (c+d x)}{b^2 d^2}-\frac{2 a f^2 \sinh (c+d x)}{b^2 d^3}-\frac{a (e+f x)^2 \sinh (c+d x)}{b^2 d}-\frac{f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b d^2}+\frac{f^2 \sinh ^2(c+d x)}{4 b d^3}+\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}","\frac{2 f \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}-\frac{2 f^2 \left(a^2+b^2\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}+\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 (e+f x) \cosh (c+d x)}{b^2 d^2}-\frac{2 a f^2 \sinh (c+d x)}{b^2 d^3}-\frac{a (e+f x)^2 \sinh (c+d x)}{b^2 d}-\frac{f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b d^2}+\frac{f^2 \sinh ^2(c+d x)}{4 b d^3}+\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,"(e*f*x)/(2*b*d) + (f^2*x^2)/(4*b*d) - ((a^2 + b^2)*(e + f*x)^3)/(3*b^3*f) + (2*a*f*(e + f*x)*Cosh[c + d*x])/(b^2*d^2) + ((a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*d) + ((a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*d) + (2*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^2) + (2*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^2) - (2*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^3) - (2*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^3) - (2*a*f^2*Sinh[c + d*x])/(b^2*d^3) - (a*(e + f*x)^2*Sinh[c + d*x])/(b^2*d) - (f*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d^2) + (f^2*Sinh[c + d*x]^2)/(4*b*d^3) + ((e + f*x)^2*Sinh[c + d*x]^2)/(2*b*d)","A",16,10,28,0.3571,1,"{5565, 3296, 2637, 5446, 3310, 5561, 2190, 2531, 2282, 6589}"
301,1,298,0,0.3577547,"\int \frac{(e+f x) \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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}","\frac{f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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,"(f*x)/(4*b*d) - ((a^2 + b^2)*(e + f*x)^2)/(2*b^3*f) + (a*f*Cosh[c + d*x])/(b^2*d^2) + ((a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*d) + ((a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*d) + ((a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^2) + ((a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^2) - (a*(e + f*x)*Sinh[c + d*x])/(b^2*d) - (f*Cosh[c + d*x]*Sinh[c + d*x])/(4*b*d^2) + ((e + f*x)*Sinh[c + d*x]^2)/(2*b*d)","A",13,10,26,0.3846,1,"{5565, 3296, 2638, 5446, 2635, 8, 5561, 2190, 2279, 2391}"
302,1,59,0,0.0692951,"\int \frac{\cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[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))}{b^3 d}-\frac{a \sinh (c+d x)}{b^2 d}+\frac{\sinh ^2(c+d x)}{2 b 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]])/(b^3*d) - (a*Sinh[c + d*x])/(b^2*d) + Sinh[c + d*x]^2/(2*b*d)","A",3,2,21,0.09524,1,"{2668, 697}"
303,0,0,0,0.0768147,"\int \frac{\cosh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Cosh[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
304,1,786,0,1.4570373,"\int \frac{(e+f x)^3 \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 i a f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 i a f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)}+\frac{3 b f^2 (e+f x) \text{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 i a f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{6 i a f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{6 i a f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{6 b f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^4 \left(a^2+b^2\right)}-\frac{3 b f^3 \text{PolyLog}\left(4,-e^{2 (c+d x)}\right)}{4 d^4 \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)}","\frac{6 i a f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 i a f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)}+\frac{3 b f^2 (e+f x) \text{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 i a f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{6 i a f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{6 i a f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{6 b f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^4 \left(a^2+b^2\right)}-\frac{3 b f^3 \text{PolyLog}\left(4,-e^{2 (c+d x)}\right)}{4 d^4 \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,"(2*a*(e + f*x)^3*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d) + (b*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) + (b*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) - (b*(e + f*x)^3*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)*d) - ((3*I)*a*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^2) + ((3*I)*a*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^2) + (3*b*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) + (3*b*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) - (3*b*f*(e + f*x)^2*PolyLog[2, -E^(2*(c + d*x))])/(2*(a^2 + b^2)*d^2) + ((6*I)*a*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^3) - ((6*I)*a*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)*d^3) - (6*b*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^3) - (6*b*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^3) + (3*b*f^2*(e + f*x)*PolyLog[3, -E^(2*(c + d*x))])/(2*(a^2 + b^2)*d^3) - ((6*I)*a*f^3*PolyLog[4, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^4) + ((6*I)*a*f^3*PolyLog[4, I*E^(c + d*x)])/((a^2 + b^2)*d^4) + (6*b*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^4) + (6*b*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^4) - (3*b*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*(a^2 + b^2)*d^4)","A",29,10,26,0.3846,1,"{5573, 5561, 2190, 2531, 6609, 2282, 6589, 6742, 4180, 3718}"
305,1,558,0,1.0344515,"\int \frac{(e+f x)^2 \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 i a f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 i a f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)}-\frac{b f (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 i a f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 i a f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 b f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)}+\frac{b f^2 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 d^3 \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)}","-\frac{2 i a f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 i a f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)}-\frac{b f (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 i a f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 i a f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 b f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)}+\frac{b f^2 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 d^3 \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,"(2*a*(e + f*x)^2*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d) + (b*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) + (b*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) - (b*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)*d) - ((2*I)*a*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^2) + ((2*I)*a*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^2) + (2*b*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) + (2*b*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) - (b*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/((a^2 + b^2)*d^2) + ((2*I)*a*f^2*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^3) - ((2*I)*a*f^2*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)*d^3) - (2*b*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^3) - (2*b*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^3) + (b*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*(a^2 + b^2)*d^3)","A",24,9,26,0.3462,1,"{5573, 5561, 2190, 2531, 2282, 6589, 6742, 4180, 3718}"
306,1,334,0,0.5962903,"\int \frac{(e+f x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{i a f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{i a f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{b f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)}-\frac{b f \text{PolyLog}\left(2,-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)}","-\frac{i a f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{i a f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{b f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)}-\frac{b f \text{PolyLog}\left(2,-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*a*(e + f*x)*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d) + (b*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) + (b*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) - (b*(e + f*x)*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)*d) - (I*a*f*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^2) + (I*a*f*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^2) + (b*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) + (b*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) - (b*f*PolyLog[2, -E^(2*(c + d*x))])/(2*(a^2 + b^2)*d^2)","A",19,8,24,0.3333,1,"{5573, 5561, 2190, 2279, 2391, 6742, 4180, 3718}"
307,1,69,0,0.0698349,"\int \frac{\text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Sech[c + d*x]/(a + b*Sinh[c + d*x]),x]","\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)}","\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,"(a*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d) - (b*Log[Cosh[c + d*x]])/((a^2 + b^2)*d) + (b*Log[a + b*Sinh[c + d*x]])/((a^2 + b^2)*d)","A",6,6,19,0.3158,1,"{2668, 706, 31, 635, 204, 260}"
308,0,0,0,0.0489457,"\int \frac{\text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Sech[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
309,1,780,0,1.6882174,"\int \frac{(e+f x)^3 \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{6 i b f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 i b f^2 (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{3 a f^2 (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 b^2 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{3 b^2 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{6 i b f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{6 i b f^3 \text{PolyLog}\left(3,i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{3 a f^3 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 d^4 \left(a^2+b^2\right)}+\frac{6 b^2 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^4 \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)}","\frac{6 i b f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 i b f^2 (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{3 a f^2 (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{d^3 \left(a^2+b^2\right)}-\frac{6 b^2 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{3 b^2 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{6 i b f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{6 i b f^3 \text{PolyLog}\left(3,i e^{c+d x}\right)}{d^4 \left(a^2+b^2\right)}+\frac{3 a f^3 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 d^4 \left(a^2+b^2\right)}+\frac{6 b^2 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^4 \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,"(a*(e + f*x)^3)/((a^2 + b^2)*d) - (6*b*f*(e + f*x)^2*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d^2) + (b^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (b^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (3*a*f*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)*d^2) + ((6*I)*b*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^3) - ((6*I)*b*f^2*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^3) + (3*b^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (3*b^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (3*a*f^2*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/((a^2 + b^2)*d^3) - ((6*I)*b*f^3*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^4) + ((6*I)*b*f^3*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)*d^4) - (6*b^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^3) + (6*b^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^3) + (3*a*f^3*PolyLog[3, -E^(2*(c + d*x))])/(2*(a^2 + b^2)*d^4) + (6*b^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^4) - (6*b^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^4) + (b*(e + f*x)^3*Sech[c + d*x])/((a^2 + b^2)*d) + (a*(e + f*x)^3*Tanh[c + d*x])/((a^2 + b^2)*d)","A",29,13,28,0.4643,1,"{5573, 3322, 2264, 2190, 2531, 6609, 2282, 6589, 6742, 4184, 3718, 5451, 4180}"
310,1,548,0,1.2954803,"\int \frac{(e+f x)^2 \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{2 i b f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 i b f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{a f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{d^3 \left(a^2+b^2\right)}-\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)}","\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{2 i b f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{2 i b f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{a f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{d^3 \left(a^2+b^2\right)}-\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,"(a*(e + f*x)^2)/((a^2 + b^2)*d) - (4*b*f*(e + f*x)*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d^2) + (b^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (b^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (2*a*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)*d^2) + ((2*I)*b*f^2*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^3) - ((2*I)*b*f^2*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^3) + (2*b^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (2*b^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (a*f^2*PolyLog[2, -E^(2*(c + d*x))])/((a^2 + b^2)*d^3) - (2*b^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^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^3) + (b*(e + f*x)^2*Sech[c + d*x])/((a^2 + b^2)*d) + (a*(e + f*x)^2*Tanh[c + d*x])/((a^2 + b^2)*d)","A",24,14,28,0.5000,1,"{5573, 3322, 2264, 2190, 2531, 2282, 6589, 6742, 4184, 3718, 2279, 2391, 5451, 4180}"
311,1,295,0,0.7170298,"\int \frac{(e+f x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{b^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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)}","\frac{b^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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,"-((b*f*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d^2)) + (b^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (b^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (a*f*Log[Cosh[c + d*x]])/((a^2 + b^2)*d^2) + (b^2*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (b^2*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) + (b*(e + f*x)*Sech[c + d*x])/((a^2 + b^2)*d) + (a*(e + f*x)*Tanh[c + d*x])/((a^2 + b^2)*d)","A",15,11,26,0.4231,1,"{5573, 3322, 2264, 2190, 2279, 2391, 6742, 4184, 3475, 5451, 3770}"
312,1,77,0,0.0996727,"\int \frac{\text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Sech[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","\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}}","\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*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/((a^2 + b^2)^(3/2)*d) + (Sech[c + d*x]*(b + a*Sinh[c + d*x]))/((a^2 + b^2)*d)","A",5,5,21,0.2381,1,"{2696, 12, 2660, 618, 204}"
313,0,0,0,0.0769621,"\int \frac{\text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Sech[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
314,1,928,0,1.7719157,"\int \frac{(e+f x)^2 \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) b^3}{\left(a^2+b^2\right)^2 d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) b^2}{\left(a^2+b^2\right)^2 d^2}+\frac{2 i a f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b^2}{\left(a^2+b^2\right)^2 d^3}-\frac{2 i a f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-i e^{c+d x}\right)}{\left(a^2+b^2\right) d^2}+\frac{i a f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{\left(a^2+b^2\right) d^2}+\frac{i a f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{\left(a^2+b^2\right) d^3}-\frac{i a f^2 \text{PolyLog}\left(3,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}","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) b^3}{\left(a^2+b^2\right)^2 d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) b^2}{\left(a^2+b^2\right)^2 d^2}+\frac{2 i a f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b^2}{\left(a^2+b^2\right)^2 d^3}-\frac{2 i a f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-i e^{c+d x}\right)}{\left(a^2+b^2\right) d^2}+\frac{i a f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{\left(a^2+b^2\right) d^2}+\frac{i a f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{\left(a^2+b^2\right) d^3}-\frac{i a f^2 \text{PolyLog}\left(3,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,"(2*a*b^2*(e + f*x)^2*ArcTan[E^(c + d*x)])/((a^2 + b^2)^2*d) + (a*(e + f*x)^2*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d) - (a*f^2*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d^3) + (b^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) + (b^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) - (b^3*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)^2*d) + (b*f^2*Log[Cosh[c + d*x]])/((a^2 + b^2)*d^3) - ((2*I)*a*b^2*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^2) - (I*a*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^2) + ((2*I)*a*b^2*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)^2*d^2) + (I*a*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^2) + (2*b^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) + (2*b^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) - (b^3*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/((a^2 + b^2)^2*d^2) + ((2*I)*a*b^2*f^2*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^3) + (I*a*f^2*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^3) - ((2*I)*a*b^2*f^2*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)^2*d^3) - (I*a*f^2*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)*d^3) - (2*b^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^3) - (2*b^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^3) + (b^3*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*(a^2 + b^2)^2*d^3) + (a*f*(e + f*x)*Sech[c + d*x])/((a^2 + b^2)*d^2) + (b*(e + f*x)^2*Sech[c + d*x]^2)/(2*(a^2 + b^2)*d) - (b*f*(e + f*x)*Tanh[c + d*x])/((a^2 + b^2)*d^2) + (a*(e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*(a^2 + b^2)*d)","A",39,14,28,0.5000,1,"{5573, 5561, 2190, 2531, 2282, 6589, 6742, 4180, 3718, 4186, 3770, 5451, 4184, 3475}"
315,1,560,0,0.9383465,"\int \frac{(e+f x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{b^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{b^3 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)^2}-\frac{i a b^2 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{i a b^2 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{i a f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)}+\frac{i a f \text{PolyLog}\left(2,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{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}+\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{b^3 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)^2}-\frac{i a b^2 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{i a b^2 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{i a f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)}+\frac{i a f \text{PolyLog}\left(2,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{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}+\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)}",1,"(2*a*b^2*(e + f*x)*ArcTan[E^(c + d*x)])/((a^2 + b^2)^2*d) + (a*(e + f*x)*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d) + (b^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) + (b^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) - (b^3*(e + f*x)*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)^2*d) - (I*a*b^2*f*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^2) - ((I/2)*a*f*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^2) + (I*a*b^2*f*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)^2*d^2) + ((I/2)*a*f*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^2) + (b^3*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) + (b^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) - (b^3*f*PolyLog[2, -E^(2*(c + d*x))])/(2*(a^2 + b^2)^2*d^2) + (a*f*Sech[c + d*x])/(2*(a^2 + b^2)*d^2) + (b*(e + f*x)*Sech[c + d*x]^2)/(2*(a^2 + b^2)*d) - (b*f*Tanh[c + d*x])/(2*(a^2 + b^2)*d^2) + (a*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*(a^2 + b^2)*d)","A",31,12,26,0.4615,1,"{5573, 5561, 2190, 2279, 2391, 6742, 4180, 3718, 4185, 5451, 3767, 8}"
316,1,119,0,0.1436038,"\int \frac{\text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Sech[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","\frac{b^3 \log (a+b \sinh (c+d x))}{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{b^3 \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^3 \log (a+b \sinh (c+d x))}{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{b^3 \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,"(a*(a^2 + 3*b^2)*ArcTan[Sinh[c + d*x]])/(2*(a^2 + b^2)^2*d) - (b^3*Log[Cosh[c + d*x]])/((a^2 + b^2)^2*d) + (b^3*Log[a + b*Sinh[c + d*x]])/((a^2 + b^2)^2*d) + (Sech[c + d*x]^2*(b + a*Sinh[c + d*x]))/(2*(a^2 + b^2)*d)","A",7,6,21,0.2857,1,"{2668, 741, 801, 635, 203, 260}"
317,0,0,0,0.0768256,"\int \frac{\text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Sech[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
318,0,0,0,0.0616135,"\int \frac{x^m \cosh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(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,"Defer[Int][(x^m*Cosh[c + d*x]^3)/(a + b*Sinh[c + d*x]), x]","A",0,0,0,0,-1,"{}"
319,0,0,0,0.0617755,"\int \frac{x^m \cosh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(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,"Defer[Int][(x^m*Cosh[c + d*x]^2)/(a + b*Sinh[c + d*x]), x]","A",0,0,0,0,-1,"{}"
320,0,0,0,0.0382973,"\int \frac{x^m \cosh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(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,"Defer[Int][(x^m*Cosh[c + d*x])/(a + b*Sinh[c + d*x]), x]","A",0,0,0,0,-1,"{}"
321,1,74,0,0.0729192,"\int \frac{(e+f x) \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Int[((e + f*x)*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","-\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))}","-\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*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b*Sqrt[a^2 + b^2]*d^2) - (e + f*x)/(b*d*(a + b*Sinh[c + d*x]))","A",4,4,24,0.1667,1,"{5464, 2660, 618, 204}"
322,1,234,0,0.440379,"\int \frac{(e+f x)^2 \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Int[((e + f*x)^2*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","\frac{2 f^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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))}","\frac{2 f^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d^2) - (2*f*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d^2) + (2*f^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3) - (2*f^2*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",9,6,26,0.2308,1,"{5464, 3322, 2264, 2190, 2279, 2391}"
323,1,348,0,0.7397123,"\int \frac{(e+f x)^3 \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Int[((e + f*x)^3*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{6 f^3 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \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))}","\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{6 f^3 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \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*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d^2) - (3*f*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d^2) + (6*f^2*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3) - (6*f^2*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3) - (6*f^3*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^4) + (6*f^3*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",11,7,26,0.2692,1,"{5464, 3322, 2264, 2190, 2531, 2282, 6589}"
324,1,74,0,0.0700089,"\int \frac{(e+f x) \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Int[((e + f*x)*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","-\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))}","-\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*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b*Sqrt[a^2 + b^2]*d^2) - (e + f*x)/(b*d*(a + b*Sinh[c + d*x]))","A",4,4,24,0.1667,1,"{5464, 2660, 618, 204}"
325,1,234,0,0.4399879,"\int \frac{(e+f x)^2 \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Int[((e + f*x)^2*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","\frac{2 f^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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))}","\frac{2 f^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d^2) - (2*f*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d^2) + (2*f^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3) - (2*f^2*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",9,6,26,0.2308,1,"{5464, 3322, 2264, 2190, 2279, 2391}"
326,1,348,0,0.7309103,"\int \frac{(e+f x)^3 \cosh (c+d x)}{(a+b \sinh (c+d x))^2} \, dx","Int[((e + f*x)^3*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^2,x]","\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{6 f^3 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \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))}","\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \sqrt{a^2+b^2}}-\frac{6 f^3 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \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*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d^2) - (3*f*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*Sqrt[a^2 + b^2]*d^2) + (6*f^2*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3) - (6*f^2*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^3) - (6*f^3*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*Sqrt[a^2 + b^2]*d^4) + (6*f^3*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",11,7,26,0.2692,1,"{5464, 3322, 2264, 2190, 2531, 2282, 6589}"
327,1,112,0,0.0983786,"\int \frac{(e+f x) \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Int[((e + f*x)*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","-\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}","-\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,"-((a*f*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b*(a^2 + b^2)^(3/2)*d^2)) - (e + f*x)/(2*b*d*(a + b*Sinh[c + d*x])^2) - (f*Cosh[c + d*x])/(2*(a^2 + b^2)*d^2*(a + b*Sinh[c + d*x]))","A",6,6,24,0.2500,1,"{5464, 2664, 12, 2660, 618, 204}"
328,1,306,0,0.5199484,"\int \frac{(e+f x)^2 \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Int[((e + f*x)^2*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","\frac{a f^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\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{f^2 \log (a+b \sinh (c+d x))}{b d^3 \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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\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{f^2 \log (a+b \sinh (c+d x))}{b d^3 \left(a^2+b^2\right)}-\frac{(e+f x)^2}{2 b d (a+b \sinh (c+d x))^2}",1,"(a*f*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)^(3/2)*d^2) - (a*f*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)^(3/2)*d^2) + (f^2*Log[a + b*Sinh[c + d*x]])/(b*(a^2 + b^2)*d^3) + (a*f^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) - (a*f^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) - (e + f*x)^2/(2*b*d*(a + b*Sinh[c + d*x])^2) - (f*(e + f*x)*Cosh[c + d*x])/((a^2 + b^2)*d^2*(a + b*Sinh[c + d*x]))","A",12,9,26,0.3462,1,"{5464, 3324, 3322, 2264, 2190, 2279, 2391, 2668, 31}"
329,1,631,0,1.0947873,"\int \frac{(e+f x)^3 \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Int[((e + f*x)^3*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","\frac{3 a f^2 (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\frac{3 f^3 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \left(a^2+b^2\right)}-\frac{3 a f^3 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \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}","\frac{3 a f^2 (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\frac{3 f^3 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \left(a^2+b^2\right)}-\frac{3 a f^3 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \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,"(-3*f*(e + f*x)^2)/(2*b*(a^2 + b^2)*d^2) + (3*f^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)*d^3) + (3*a*f*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(2*b*(a^2 + b^2)^(3/2)*d^2) + (3*f^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)*d^3) - (3*a*f*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(2*b*(a^2 + b^2)^(3/2)*d^2) + (3*f^3*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^4) + (3*a*f^2*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) + (3*f^3*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^4) - (3*a*f^2*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) - (3*a*f^3*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^4) + (3*a*f^3*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^4) - (e + f*x)^3/(2*b*d*(a + b*Sinh[c + d*x])^2) - (3*f*(e + f*x)^2*Cosh[c + d*x])/(2*(a^2 + b^2)*d^2*(a + b*Sinh[c + d*x]))","A",19,11,26,0.4231,1,"{5464, 3324, 3322, 2264, 2190, 2531, 2282, 6589, 5561, 2279, 2391}"
330,1,112,0,0.0951033,"\int \frac{(e+f x) \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Int[((e + f*x)*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","-\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}","-\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,"-((a*f*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b*(a^2 + b^2)^(3/2)*d^2)) - (e + f*x)/(2*b*d*(a + b*Sinh[c + d*x])^2) - (f*Cosh[c + d*x])/(2*(a^2 + b^2)*d^2*(a + b*Sinh[c + d*x]))","A",6,6,24,0.2500,1,"{5464, 2664, 12, 2660, 618, 204}"
331,1,306,0,0.5214156,"\int \frac{(e+f x)^2 \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Int[((e + f*x)^2*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","\frac{a f^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\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{f^2 \log (a+b \sinh (c+d x))}{b d^3 \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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\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{f^2 \log (a+b \sinh (c+d x))}{b d^3 \left(a^2+b^2\right)}-\frac{(e+f x)^2}{2 b d (a+b \sinh (c+d x))^2}",1,"(a*f*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)^(3/2)*d^2) - (a*f*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)^(3/2)*d^2) + (f^2*Log[a + b*Sinh[c + d*x]])/(b*(a^2 + b^2)*d^3) + (a*f^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) - (a*f^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) - (e + f*x)^2/(2*b*d*(a + b*Sinh[c + d*x])^2) - (f*(e + f*x)*Cosh[c + d*x])/((a^2 + b^2)*d^2*(a + b*Sinh[c + d*x]))","A",12,9,26,0.3462,1,"{5464, 3324, 3322, 2264, 2190, 2279, 2391, 2668, 31}"
332,1,631,0,1.0874597,"\int \frac{(e+f x)^3 \cosh (c+d x)}{(a+b \sinh (c+d x))^3} \, dx","Int[((e + f*x)^3*Cosh[c + d*x])/(a + b*Sinh[c + d*x])^3,x]","\frac{3 a f^2 (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\frac{3 f^3 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \left(a^2+b^2\right)}-\frac{3 a f^3 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \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}","\frac{3 a f^2 (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^3 \left(a^2+b^2\right)^{3/2}}+\frac{3 f^3 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \left(a^2+b^2\right)}-\frac{3 a f^3 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^4 \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,"(-3*f*(e + f*x)^2)/(2*b*(a^2 + b^2)*d^2) + (3*f^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)*d^3) + (3*a*f*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(2*b*(a^2 + b^2)^(3/2)*d^2) + (3*f^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)*d^3) - (3*a*f*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(2*b*(a^2 + b^2)^(3/2)*d^2) + (3*f^3*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^4) + (3*a*f^2*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) + (3*f^3*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^4) - (3*a*f^2*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) - (3*a*f^3*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^4) + (3*a*f^3*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^4) - (e + f*x)^3/(2*b*d*(a + b*Sinh[c + d*x])^2) - (3*f*(e + f*x)^2*Cosh[c + d*x])/(2*(a^2 + b^2)*d^2*(a + b*Sinh[c + d*x]))","A",19,11,26,0.4231,1,"{5464, 3324, 3322, 2264, 2190, 2531, 2282, 6589, 5561, 2279, 2391}"
333,1,448,0,0.6467033,"\int \frac{(e+f x)^3 \cosh (c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 a f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3}-\frac{3 a f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2}-\frac{6 a f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^4}-\frac{6 a f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^4}-\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^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{6 f^3 \cosh (c+d x)}{b d^4}+\frac{(e+f x)^3 \sinh (c+d x)}{b d}","\frac{6 a f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3}-\frac{3 a f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2}-\frac{6 a f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^4}-\frac{6 a f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^4}-\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^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{6 f^3 \cosh (c+d x)}{b d^4}+\frac{(e+f x)^3 \sinh (c+d x)}{b d}",1,"(a*(e + f*x)^4)/(4*b^2*f) - (6*f^3*Cosh[c + d*x])/(b*d^4) - (3*f*(e + f*x)^2*Cosh[c + d*x])/(b*d^2) - (a*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*d) - (a*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*d) - (3*a*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^2) - (3*a*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^2) + (6*a*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^3) + (6*a*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^3) - (6*a*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^4) - (6*a*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^4) + (6*f^2*(e + f*x)*Sinh[c + d*x])/(b*d^3) + ((e + f*x)^3*Sinh[c + d*x])/(b*d)","A",16,9,32,0.2812,1,"{5579, 3296, 2638, 5561, 2190, 2531, 6609, 2282, 6589}"
334,1,330,0,0.5495453,"\int \frac{(e+f x)^2 \cosh (c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 a f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2}+\frac{2 a f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^3}+\frac{2 a f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3}-\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 (e+f x) \cosh (c+d x)}{b d^2}+\frac{2 f^2 \sinh (c+d x)}{b d^3}+\frac{(e+f x)^2 \sinh (c+d x)}{b d}","-\frac{2 a f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2}+\frac{2 a f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^3}+\frac{2 a f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^3}-\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 (e+f x) \cosh (c+d x)}{b d^2}+\frac{2 f^2 \sinh (c+d x)}{b d^3}+\frac{(e+f x)^2 \sinh (c+d x)}{b d}",1,"(a*(e + f*x)^3)/(3*b^2*f) - (2*f*(e + f*x)*Cosh[c + d*x])/(b*d^2) - (a*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*d) - (a*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*d) - (2*a*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^2) - (2*a*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^2) + (2*a*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^3) + (2*a*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^3) + (2*f^2*Sinh[c + d*x])/(b*d^3) + ((e + f*x)^2*Sinh[c + d*x])/(b*d)","A",13,8,32,0.2500,1,"{5579, 3296, 2637, 5561, 2190, 2531, 2282, 6589}"
335,1,212,0,0.3121369,"\int \frac{(e+f x) \cosh (c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{a f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{a f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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}","-\frac{a f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^2 d^2}-\frac{a f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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,"(a*(e + f*x)^2)/(2*b^2*f) - (f*Cosh[c + d*x])/(b*d^2) - (a*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*d) - (a*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*d) - (a*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*d^2) - (a*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*d^2) + ((e + f*x)*Sinh[c + d*x])/(b*d)","A",10,7,30,0.2333,1,"{5579, 3296, 2638, 5561, 2190, 2279, 2391}"
336,1,34,0,0.0569536,"\int \frac{\cosh (c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\sinh (c+d x)}{b d}-\frac{a \log (a+b \sinh (c+d x))}{b^2 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*d)) + Sinh[c + d*x]/(b*d)","A",4,3,25,0.1200,1,"{2833, 12, 43}"
337,0,0,0,0.0571966,"\int \frac{\cosh (c+d x) \sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(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,"Defer[Int][(Cosh[c + d*x]*Sinh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
338,1,696,0,1.1295673,"\int \frac{(e+f x)^3 \cosh ^2(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^2*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 a f^2 \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}-\frac{3 a f \sqrt{a^2+b^2} (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}-\frac{6 a f^3 \sqrt{a^2+b^2} \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^4}-\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{a^2 (e+f x)^4}{4 b^3 f}-\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{6 a f^3 \sinh (c+d x)}{b^2 d^4}-\frac{a (e+f x)^3 \cosh (c+d x)}{b^2 d}+\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{3 f^3 \cosh ^2(c+d x)}{8 b d^4}+\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}","\frac{6 a f^2 \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}-\frac{3 a f \sqrt{a^2+b^2} (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}-\frac{6 a f^3 \sqrt{a^2+b^2} \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^4}-\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{a^2 (e+f x)^4}{4 b^3 f}-\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{6 a f^3 \sinh (c+d x)}{b^2 d^4}-\frac{a (e+f x)^3 \cosh (c+d x)}{b^2 d}+\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{3 f^3 \cosh ^2(c+d x)}{8 b d^4}+\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,"(3*e*f^2*x)/(4*b*d^2) + (3*f^3*x^2)/(8*b*d^2) + (a^2*(e + f*x)^4)/(4*b^3*f) + (e + f*x)^4/(8*b*f) - (6*a*f^2*(e + f*x)*Cosh[c + d*x])/(b^2*d^3) - (a*(e + f*x)^3*Cosh[c + d*x])/(b^2*d) - (3*f^3*Cosh[c + d*x]^2)/(8*b*d^4) - (3*f*(e + f*x)^2*Cosh[c + d*x]^2)/(4*b*d^2) - (a*Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*d) + (a*Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*d) - (3*a*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^2) + (3*a*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^2) + (6*a*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^3) - (6*a*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^3) - (6*a*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^4) + (6*a*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^4) + (6*a*f^3*Sinh[c + d*x])/(b^2*d^4) + (3*a*f*(e + f*x)^2*Sinh[c + d*x])/(b^2*d^2) + (3*f^2*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(4*b*d^3) + ((e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d)","A",23,14,34,0.4118,1,"{5579, 3311, 32, 3310, 5565, 3296, 2637, 3322, 2264, 2190, 2531, 6609, 2282, 6589}"
339,1,510,0,0.9622931,"\int \frac{(e+f x)^2 \cosh ^2(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 a f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}+\frac{2 a f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}-\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{a^2 (e+f x)^3}{3 b^3 f}+\frac{2 a f (e+f x) \sinh (c+d x)}{b^2 d^2}-\frac{2 a f^2 \cosh (c+d x)}{b^2 d^3}-\frac{a (e+f x)^2 \cosh (c+d x)}{b^2 d}-\frac{f (e+f x) \cosh ^2(c+d x)}{2 b d^2}+\frac{f^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^3}+\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}","-\frac{2 a f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}+\frac{2 a f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}-\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{a^2 (e+f x)^3}{3 b^3 f}+\frac{2 a f (e+f x) \sinh (c+d x)}{b^2 d^2}-\frac{2 a f^2 \cosh (c+d x)}{b^2 d^3}-\frac{a (e+f x)^2 \cosh (c+d x)}{b^2 d}-\frac{f (e+f x) \cosh ^2(c+d x)}{2 b d^2}+\frac{f^2 \sinh (c+d x) \cosh (c+d x)}{4 b d^3}+\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,"(f^2*x)/(4*b*d^2) + (a^2*(e + f*x)^3)/(3*b^3*f) + (e + f*x)^3/(6*b*f) - (2*a*f^2*Cosh[c + d*x])/(b^2*d^3) - (a*(e + f*x)^2*Cosh[c + d*x])/(b^2*d) - (f*(e + f*x)*Cosh[c + d*x]^2)/(2*b*d^2) - (a*Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*d) + (a*Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*d) - (2*a*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^2) + (2*a*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^2) + (2*a*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^3) - (2*a*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^3) + (2*a*f*(e + f*x)*Sinh[c + d*x])/(b^2*d^2) + (f^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b*d^3) + ((e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d)","A",20,14,34,0.4118,1,"{5579, 3311, 32, 2635, 8, 5565, 3296, 2638, 3322, 2264, 2190, 2531, 2282, 6589}"
340,1,327,0,0.5500042,"\int \frac{(e+f x) \cosh ^2(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{a f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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^2 e x}{b^3}+\frac{a^2 f x^2}{2 b^3}+\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}","-\frac{a f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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^2 e x}{b^3}+\frac{a^2 f x^2}{2 b^3}+\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,"(a^2*e*x)/b^3 + (e*x)/(2*b) + (a^2*f*x^2)/(2*b^3) + (f*x^2)/(4*b) - (a*(e + f*x)*Cosh[c + d*x])/(b^2*d) - (f*Cosh[c + d*x]^2)/(4*b*d^2) - (a*Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*d) + (a*Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*d) - (a*Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^2) + (a*Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^2) + (a*f*Sinh[c + d*x])/(b^2*d^2) + ((e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d)","A",15,10,32,0.3125,1,"{5579, 3310, 5565, 3296, 2637, 3322, 2264, 2190, 2279, 2391}"
341,1,95,0,0.180593,"\int \frac{\cosh ^2(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]^2*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\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}","\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,"((2*a^2 + b^2)*x)/(2*b^3) + (2*a*Sqrt[a^2 + b^2]*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b^3*d) - (Cosh[c + d*x]*(2*a - b*Sinh[c + d*x]))/(2*b^2*d)","A",5,5,27,0.1852,1,"{2865, 2735, 2660, 618, 204}"
342,0,0,0,0.0815182,"\int \frac{\cosh ^2(c+d x) \sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Cosh[c + d*x]^2*Sinh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh ^2(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 ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][(Cosh[c + d*x]^2*Sinh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
343,1,864,0,1.1173207,"\int \frac{(e+f x)^3 \cosh ^3(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^3*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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}","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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,"(-3*a*f^3*x)/(8*b^2*d^3) - (a*(e + f*x)^3)/(4*b^2*d) + (a*(a^2 + b^2)*(e + f*x)^4)/(4*b^4*f) - (6*a^2*f^3*Cosh[c + d*x])/(b^3*d^4) - (40*f^3*Cosh[c + d*x])/(9*b*d^4) - (3*a^2*f*(e + f*x)^2*Cosh[c + d*x])/(b^3*d^2) - (2*f*(e + f*x)^2*Cosh[c + d*x])/(b*d^2) - (2*f^3*Cosh[c + d*x]^3)/(27*b*d^4) - (f*(e + f*x)^2*Cosh[c + d*x]^3)/(3*b*d^2) - (a*(a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^4*d) - (a*(a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^4*d) - (3*a*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^2) - (3*a*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^2) + (6*a*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^3) + (6*a*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^3) - (6*a*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^4) - (6*a*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^4) + (6*a^2*f^2*(e + f*x)*Sinh[c + d*x])/(b^3*d^3) + (40*f^2*(e + f*x)*Sinh[c + d*x])/(9*b*d^3) + (a^2*(e + f*x)^3*Sinh[c + d*x])/(b^3*d) + (2*(e + f*x)^3*Sinh[c + d*x])/(3*b*d) + (3*a*f^3*Cosh[c + d*x]*Sinh[c + d*x])/(8*b^2*d^4) + (3*a*f*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^2*d^2) + (2*f^2*(e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x])/(9*b*d^3) + ((e + f*x)^3*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b*d) - (3*a*f^2*(e + f*x)*Sinh[c + d*x]^2)/(4*b^2*d^3) - (a*(e + f*x)^3*Sinh[c + d*x]^2)/(2*b^2*d)","A",30,16,34,0.4706,1,"{5579, 3311, 3296, 2638, 3310, 5565, 5446, 32, 2635, 8, 5561, 2190, 2531, 6609, 2282, 6589}"
344,1,636,0,0.8751948,"\int \frac{(e+f x)^2 \cosh ^3(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^3*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 a f \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}+\frac{2 a f^2 \left(a^2+b^2\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^3}-\frac{2 a^2 f (e+f x) \cosh (c+d x)}{b^3 d^2}+\frac{2 a^2 f^2 \sinh (c+d x)}{b^3 d^3}-\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^2 (e+f x)^2 \sinh (c+d x)}{b^3 d}+\frac{a \left(a^2+b^2\right) (e+f x)^3}{3 b^4 f}+\frac{a f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^2 d^2}-\frac{a f^2 \sinh ^2(c+d x)}{4 b^2 d^3}-\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 (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 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 (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}","-\frac{2 a f \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}+\frac{2 a f^2 \left(a^2+b^2\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^3}-\frac{2 a^2 f (e+f x) \cosh (c+d x)}{b^3 d^2}+\frac{2 a^2 f^2 \sinh (c+d x)}{b^3 d^3}-\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^2 (e+f x)^2 \sinh (c+d x)}{b^3 d}+\frac{a \left(a^2+b^2\right) (e+f x)^3}{3 b^4 f}+\frac{a f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^2 d^2}-\frac{a f^2 \sinh ^2(c+d x)}{4 b^2 d^3}-\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 (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 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 (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,"-(a*e*f*x)/(2*b^2*d) - (a*f^2*x^2)/(4*b^2*d) + (a*(a^2 + b^2)*(e + f*x)^3)/(3*b^4*f) - (2*a^2*f*(e + f*x)*Cosh[c + d*x])/(b^3*d^2) - (4*f*(e + f*x)*Cosh[c + d*x])/(3*b*d^2) - (2*f*(e + f*x)*Cosh[c + d*x]^3)/(9*b*d^2) - (a*(a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^4*d) - (a*(a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^4*d) - (2*a*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^2) - (2*a*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^2) + (2*a*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^3) + (2*a*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^3) + (2*a^2*f^2*Sinh[c + d*x])/(b^3*d^3) + (14*f^2*Sinh[c + d*x])/(9*b*d^3) + (a^2*(e + f*x)^2*Sinh[c + d*x])/(b^3*d) + (2*(e + f*x)^2*Sinh[c + d*x])/(3*b*d) + (a*f*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^2*d^2) + ((e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b*d) - (a*f^2*Sinh[c + d*x]^2)/(4*b^2*d^3) - (a*(e + f*x)^2*Sinh[c + d*x]^2)/(2*b^2*d) + (2*f^2*Sinh[c + d*x]^3)/(27*b*d^3)","A",23,13,34,0.3824,1,"{5579, 3311, 3296, 2637, 2633, 5565, 5446, 3310, 5561, 2190, 2531, 2282, 6589}"
345,1,400,0,0.4849245,"\int \frac{(e+f x) \cosh ^3(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^3*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{a f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}-\frac{a^2 f \cosh (c+d x)}{b^3 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^2 (e+f x) \sinh (c+d x)}{b^3 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}","-\frac{a f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}-\frac{a^2 f \cosh (c+d x)}{b^3 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^2 (e+f x) \sinh (c+d x)}{b^3 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,"-(a*f*x)/(4*b^2*d) + (a*(a^2 + b^2)*(e + f*x)^2)/(2*b^4*f) - (a^2*f*Cosh[c + d*x])/(b^3*d^2) - (2*f*Cosh[c + d*x])/(3*b*d^2) - (f*Cosh[c + d*x]^3)/(9*b*d^2) - (a*(a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^4*d) - (a*(a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^4*d) - (a*(a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^2) - (a*(a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^2) + (a^2*(e + f*x)*Sinh[c + d*x])/(b^3*d) + (2*(e + f*x)*Sinh[c + d*x])/(3*b*d) + (a*f*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^2*d^2) + ((e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b*d) - (a*(e + f*x)*Sinh[c + d*x]^2)/(2*b^2*d)","A",17,12,32,0.3750,1,"{5579, 3310, 3296, 2638, 5565, 5446, 2635, 8, 5561, 2190, 2279, 2391}"
346,1,85,0,0.1216603,"\int \frac{\cosh ^3(c+d x) \sinh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]^3*Sinh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{\left(a^2+b^2\right) \sinh (c+d x)}{b^3 d}-\frac{a \left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{b^4 d}-\frac{a \sinh ^2(c+d x)}{2 b^2 d}+\frac{\sinh ^3(c+d x)}{3 b d}","\frac{\left(a^2+b^2\right) \sinh (c+d x)}{b^3 d}-\frac{a \left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{b^4 d}-\frac{a \sinh ^2(c+d x)}{2 b^2 d}+\frac{\sinh ^3(c+d x)}{3 b d}",1,"-((a*(a^2 + b^2)*Log[a + b*Sinh[c + d*x]])/(b^4*d)) + ((a^2 + b^2)*Sinh[c + d*x])/(b^3*d) - (a*Sinh[c + d*x]^2)/(2*b^2*d) + Sinh[c + d*x]^3/(3*b*d)","A",4,3,27,0.1111,1,"{2837, 12, 772}"
347,0,0,0,0.0842915,"\int \frac{\cosh ^3(c+d x) \sinh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Cosh[c + d*x]^3*Sinh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh ^3(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 ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][(Cosh[c + d*x]^3*Sinh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
348,1,1021,0,1.3295873,"\int \frac{(e+f x)^3 \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{6 i \text{PolyLog}\left(4,-i e^{c+d x}\right) f^3}{b d^4}+\frac{6 i a^2 \text{PolyLog}\left(4,-i e^{c+d x}\right) f^3}{b \left(a^2+b^2\right) d^4}+\frac{6 i \text{PolyLog}\left(4,i e^{c+d x}\right) f^3}{b d^4}-\frac{6 i a^2 \text{PolyLog}\left(4,i e^{c+d x}\right) f^3}{b \left(a^2+b^2\right) d^4}-\frac{6 a \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-e^{2 (c+d x)}\right) f^3}{4 \left(a^2+b^2\right) d^4}+\frac{6 i (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right) f^2}{b d^3}-\frac{6 i a^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right) f^2}{b \left(a^2+b^2\right) d^3}-\frac{6 i (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right) f^2}{b d^3}+\frac{6 i a^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right) f^2}{b \left(a^2+b^2\right) d^3}+\frac{6 a (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) f}{b d^2}+\frac{3 i a^2 (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right) f}{b \left(a^2+b^2\right) d^2}+\frac{3 i (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right) f}{b d^2}-\frac{3 i a^2 (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right) f}{b \left(a^2+b^2\right) d^2}-\frac{3 a (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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}","-\frac{6 i \text{PolyLog}\left(4,-i e^{c+d x}\right) f^3}{b d^4}+\frac{6 i a^2 \text{PolyLog}\left(4,-i e^{c+d x}\right) f^3}{b \left(a^2+b^2\right) d^4}+\frac{6 i \text{PolyLog}\left(4,i e^{c+d x}\right) f^3}{b d^4}-\frac{6 i a^2 \text{PolyLog}\left(4,i e^{c+d x}\right) f^3}{b \left(a^2+b^2\right) d^4}-\frac{6 a \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-e^{2 (c+d x)}\right) f^3}{4 \left(a^2+b^2\right) d^4}+\frac{6 i (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right) f^2}{b d^3}-\frac{6 i a^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right) f^2}{b \left(a^2+b^2\right) d^3}-\frac{6 i (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right) f^2}{b d^3}+\frac{6 i a^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right) f^2}{b \left(a^2+b^2\right) d^3}+\frac{6 a (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) f}{b d^2}+\frac{3 i a^2 (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right) f}{b \left(a^2+b^2\right) d^2}+\frac{3 i (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right) f}{b d^2}-\frac{3 i a^2 (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right) f}{b \left(a^2+b^2\right) d^2}-\frac{3 a (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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,"(2*(e + f*x)^3*ArcTan[E^(c + d*x)])/(b*d) - (2*a^2*(e + f*x)^3*ArcTan[E^(c + d*x)])/(b*(a^2 + b^2)*d) - (a*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) - (a*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) + (a*(e + f*x)^3*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)*d) - ((3*I)*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^2) + ((3*I)*a^2*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^2) + ((3*I)*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(b*d^2) - ((3*I)*a^2*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^2) - (3*a*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) - (3*a*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) + (3*a*f*(e + f*x)^2*PolyLog[2, -E^(2*(c + d*x))])/(2*(a^2 + b^2)*d^2) + ((6*I)*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(b*d^3) - ((6*I)*a^2*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^3) - ((6*I)*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(b*d^3) + ((6*I)*a^2*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^3) + (6*a*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^3) + (6*a*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^3) - (3*a*f^2*(e + f*x)*PolyLog[3, -E^(2*(c + d*x))])/(2*(a^2 + b^2)*d^3) - ((6*I)*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(b*d^4) + ((6*I)*a^2*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^4) + ((6*I)*f^3*PolyLog[4, I*E^(c + d*x)])/(b*d^4) - ((6*I)*a^2*f^3*PolyLog[4, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^4) - (6*a*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^4) - (6*a*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^4) + (3*a*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*(a^2 + b^2)*d^4)","A",39,11,26,0.4231,1,"{5567, 4180, 2531, 6609, 2282, 6589, 5573, 5561, 2190, 6742, 3718}"
349,1,716,0,1.0674645,"\int \frac{(e+f x)^2 \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{2 i a^2 f (e+f x) \text{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{2 a f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)}+\frac{a f (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{d^2 \left(a^2+b^2\right)}-\frac{2 i a^2 f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}+\frac{2 i a^2 f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}+\frac{2 a f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)}-\frac{a f^2 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 d^3 \left(a^2+b^2\right)}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{b d^3}-\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 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{b d}","\frac{2 i a^2 f (e+f x) \text{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{2 a f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)}+\frac{a f (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{d^2 \left(a^2+b^2\right)}-\frac{2 i a^2 f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}+\frac{2 i a^2 f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}+\frac{2 a f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)}-\frac{a f^2 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 d^3 \left(a^2+b^2\right)}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{b d^3}-\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 (e+f x)^2 \tan ^{-1}\left(e^{c+d x}\right)}{b d}",1,"(2*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b*d) - (2*a^2*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b*(a^2 + b^2)*d) - (a*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) - (a*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) + (a*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)*d) - ((2*I)*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^2) + ((2*I)*a^2*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^2) + ((2*I)*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b*d^2) - ((2*I)*a^2*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^2) - (2*a*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) - (2*a*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) + (a*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/((a^2 + b^2)*d^2) + ((2*I)*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b*d^3) - ((2*I)*a^2*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^3) - ((2*I)*f^2*PolyLog[3, I*E^(c + d*x)])/(b*d^3) + ((2*I)*a^2*f^2*PolyLog[3, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^3) + (2*a*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^3) + (2*a*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^3) - (a*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*(a^2 + b^2)*d^3)","A",32,10,26,0.3846,1,"{5567, 4180, 2531, 2282, 6589, 5573, 5561, 2190, 6742, 3718}"
350,1,421,0,0.5966357,"\int \frac{(e+f x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{i a^2 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{i a^2 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{a f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)}+\frac{a f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}+\frac{i f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}-\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{2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b d}","\frac{i a^2 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{i a^2 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{a f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)}+\frac{a f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}+\frac{i f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}-\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{2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b d}",1,"(2*(e + f*x)*ArcTan[E^(c + d*x)])/(b*d) - (2*a^2*(e + f*x)*ArcTan[E^(c + d*x)])/(b*(a^2 + b^2)*d) - (a*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) - (a*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)*d) + (a*(e + f*x)*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)*d) - (I*f*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^2) + (I*a^2*f*PolyLog[2, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^2) + (I*f*PolyLog[2, I*E^(c + d*x)])/(b*d^2) - (I*a^2*f*PolyLog[2, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^2) - (a*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) - (a*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)*d^2) + (a*f*PolyLog[2, -E^(2*(c + d*x))])/(2*(a^2 + b^2)*d^2)","A",25,9,24,0.3750,1,"{5567, 4180, 2279, 2391, 5573, 5561, 2190, 6742, 3718}"
351,1,69,0,0.0769974,"\int \frac{\tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Tanh[c + d*x]/(a + b*Sinh[c + d*x]),x]","-\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)}","-\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,"(b*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d) + (a*Log[Cosh[c + d*x]])/((a^2 + b^2)*d) - (a*Log[a + b*Sinh[c + d*x]])/((a^2 + b^2)*d)","A",6,5,19,0.2632,1,"{2721, 801, 635, 203, 260}"
352,0,0,0,0.0476321,"\int \frac{\tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Tanh[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
353,1,917,0,1.7120836,"\int \frac{(e+f x)^3 \text{sech}(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sech[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 i a \text{PolyLog}\left(3,-i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}-\frac{6 i a \text{PolyLog}\left(3,i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}+\frac{3 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right) f^3}{2 b d^4}-\frac{3 a^2 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right) f^3}{2 b \left(a^2+b^2\right) d^4}-\frac{6 a b \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}+\frac{6 i a (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}-\frac{3 (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right) f^2}{b d^3}+\frac{3 a^2 (e+f x) \text{PolyLog}\left(2,-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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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}","\frac{6 i a \text{PolyLog}\left(3,-i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}-\frac{6 i a \text{PolyLog}\left(3,i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}+\frac{3 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right) f^3}{2 b d^4}-\frac{3 a^2 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right) f^3}{2 b \left(a^2+b^2\right) d^4}-\frac{6 a b \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}+\frac{6 i a (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}-\frac{3 (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right) f^2}{b d^3}+\frac{3 a^2 (e+f x) \text{PolyLog}\left(2,-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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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,"(e + f*x)^3/(b*d) - (a^2*(e + f*x)^3)/(b*(a^2 + b^2)*d) + (6*a*f*(e + f*x)^2*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d^2) - (a*b*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) + (a*b*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (3*f*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b*d^2) + (3*a^2*f*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b*(a^2 + b^2)*d^2) - ((6*I)*a*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^3) + ((6*I)*a*f^2*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^3) - (3*a*b*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) + (3*a*b*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (3*f^2*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b*d^3) + (3*a^2*f^2*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b*(a^2 + b^2)*d^3) + ((6*I)*a*f^3*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^4) - ((6*I)*a*f^3*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)*d^4) + (6*a*b*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^3) - (6*a*b*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^3) + (3*f^3*PolyLog[3, -E^(2*(c + d*x))])/(2*b*d^4) - (3*a^2*f^3*PolyLog[3, -E^(2*(c + d*x))])/(2*b*(a^2 + b^2)*d^4) - (6*a*b*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^4) + (6*a*b*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^4) - (a*(e + f*x)^3*Sech[c + d*x])/((a^2 + b^2)*d) + ((e + f*x)^3*Tanh[c + d*x])/(b*d) - (a^2*(e + f*x)^3*Tanh[c + d*x])/(b*(a^2 + b^2)*d)","A",36,14,32,0.4375,1,"{5583, 4184, 3718, 2190, 2531, 2282, 6589, 5573, 3322, 2264, 6609, 6742, 5451, 4180}"
354,1,648,0,1.3214822,"\int \frac{(e+f x)^2 \text{sech}(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 a b f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}+\frac{a^2 f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b d^3 \left(a^2+b^2\right)}-\frac{2 i a f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 i a f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 a b f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}-\frac{f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b d^3}+\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{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}","-\frac{2 a b f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}+\frac{a^2 f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b d^3 \left(a^2+b^2\right)}-\frac{2 i a f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 i a f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 a b f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}-\frac{f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b d^3}+\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{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,"(e + f*x)^2/(b*d) - (a^2*(e + f*x)^2)/(b*(a^2 + b^2)*d) + (4*a*f*(e + f*x)*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d^2) - (a*b*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) + (a*b*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (2*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(b*d^2) + (2*a^2*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(b*(a^2 + b^2)*d^2) - ((2*I)*a*f^2*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^3) + ((2*I)*a*f^2*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^3) - (2*a*b*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) + (2*a*b*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (f^2*PolyLog[2, -E^(2*(c + d*x))])/(b*d^3) + (a^2*f^2*PolyLog[2, -E^(2*(c + d*x))])/(b*(a^2 + b^2)*d^3) + (2*a*b*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*b*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^3) - (a*(e + f*x)^2*Sech[c + d*x])/((a^2 + b^2)*d) + ((e + f*x)^2*Tanh[c + d*x])/(b*d) - (a^2*(e + f*x)^2*Tanh[c + d*x])/(b*(a^2 + b^2)*d)","A",30,15,32,0.4688,1,"{5583, 4184, 3718, 2190, 2279, 2391, 5573, 3322, 2264, 2531, 2282, 6589, 6742, 5451, 4180}"
355,1,335,0,0.6627956,"\int \frac{(e+f x) \text{sech}(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{a b f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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}","-\frac{a b f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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,"(a*f*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d^2) - (a*b*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) + (a*b*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (f*Log[Cosh[c + d*x]])/(b*d^2) + (a^2*f*Log[Cosh[c + d*x]])/(b*(a^2 + b^2)*d^2) - (a*b*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) + (a*b*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (a*(e + f*x)*Sech[c + d*x])/((a^2 + b^2)*d) + ((e + f*x)*Tanh[c + d*x])/(b*d) - (a^2*(e + f*x)*Tanh[c + d*x])/(b*(a^2 + b^2)*d)","A",18,12,30,0.4000,1,"{5583, 4184, 3475, 5573, 3322, 2264, 2190, 2279, 2391, 6742, 5451, 3770}"
356,1,78,0,0.1122289,"\int \frac{\text{sech}(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Sech[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\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)}","\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*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/((a^2 + b^2)^(3/2)*d) - (Sech[c + d*x]*(a - b*Sinh[c + d*x]))/((a^2 + b^2)*d)","A",5,5,25,0.2000,1,"{2866, 12, 2660, 618, 204}"
357,0,0,0,0.0586461,"\int \frac{\text{sech}(c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(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,"Defer[Int][(Sech[c + d*x]*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
358,1,1176,0,1.6957622,"\int \frac{(e+f x)^2 \text{sech}^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sech[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d^2}-\frac{i f (e+f x) \text{PolyLog}\left(2,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{PolyLog}\left(2,i e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d^2}-\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^3}-\frac{2 i b f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d^3}+\frac{i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^3}+\frac{2 i b f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a}{\left(a^2+b^2\right)^2 d^2}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}+\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}+\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3}-\frac{i f^2 \text{PolyLog}\left(3,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}","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d^2}-\frac{i f (e+f x) \text{PolyLog}\left(2,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{PolyLog}\left(2,i e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d^2}-\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^3}-\frac{2 i b f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{\left(a^2+b^2\right)^2 d^3}+\frac{i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^3}+\frac{2 i b f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a}{\left(a^2+b^2\right)^2 d^2}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}+\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}+\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3}-\frac{i f^2 \text{PolyLog}\left(3,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,"((e + f*x)^2*ArcTan[E^(c + d*x)])/(b*d) - (2*a^2*b*(e + f*x)^2*ArcTan[E^(c + d*x)])/((a^2 + b^2)^2*d) - (a^2*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b*(a^2 + b^2)*d) - (f^2*ArcTan[Sinh[c + d*x]])/(b*d^3) + (a^2*f^2*ArcTan[Sinh[c + d*x]])/(b*(a^2 + b^2)*d^3) - (a*b^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) - (a*b^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) + (a*b^2*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)^2*d) - (a*f^2*Log[Cosh[c + d*x]])/((a^2 + b^2)*d^3) - (I*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^2) + ((2*I)*a^2*b*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^2) + (I*a^2*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^2) + (I*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b*d^2) - ((2*I)*a^2*b*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)^2*d^2) - (I*a^2*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^2) - (2*a*b^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) - (2*a*b^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) + (a*b^2*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/((a^2 + b^2)^2*d^2) + (I*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b*d^3) - ((2*I)*a^2*b*f^2*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^3) - (I*a^2*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^3) - (I*f^2*PolyLog[3, I*E^(c + d*x)])/(b*d^3) + ((2*I)*a^2*b*f^2*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)^2*d^3) + (I*a^2*f^2*PolyLog[3, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^3) + (2*a*b^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^3) + (2*a*b^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^3) - (a*b^2*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*(a^2 + b^2)^2*d^3) + (f*(e + f*x)*Sech[c + d*x])/(b*d^2) - (a^2*f*(e + f*x)*Sech[c + d*x])/(b*(a^2 + b^2)*d^2) - (a*(e + f*x)^2*Sech[c + d*x]^2)/(2*(a^2 + b^2)*d) + (a*f*(e + f*x)*Tanh[c + d*x])/((a^2 + b^2)*d^2) + ((e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*b*d) - (a^2*(e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*b*(a^2 + b^2)*d)","A",49,15,34,0.4412,1,"{5583, 4186, 3770, 4180, 2531, 2282, 6589, 5573, 5561, 2190, 6742, 3718, 5451, 4184, 3475}"
359,1,711,0,0.9930333,"\int \frac{(e+f x) \text{sech}^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sech[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{i a^2 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 b d^2 \left(a^2+b^2\right)}+\frac{i a^2 b f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{i a^2 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 b d^2 \left(a^2+b^2\right)}-\frac{i a^2 b f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{a b^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{a b^2 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)^2}-\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 b d^2}+\frac{i f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 b d^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{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}","\frac{i a^2 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 b d^2 \left(a^2+b^2\right)}+\frac{i a^2 b f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{i a^2 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 b d^2 \left(a^2+b^2\right)}-\frac{i a^2 b f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{a b^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{a b^2 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)^2}-\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 b d^2}+\frac{i f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 b d^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{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,"((e + f*x)*ArcTan[E^(c + d*x)])/(b*d) - (2*a^2*b*(e + f*x)*ArcTan[E^(c + d*x)])/((a^2 + b^2)^2*d) - (a^2*(e + f*x)*ArcTan[E^(c + d*x)])/(b*(a^2 + b^2)*d) - (a*b^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) - (a*b^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) + (a*b^2*(e + f*x)*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)^2*d) - ((I/2)*f*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^2) + (I*a^2*b*f*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^2) + ((I/2)*a^2*f*PolyLog[2, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^2) + ((I/2)*f*PolyLog[2, I*E^(c + d*x)])/(b*d^2) - (I*a^2*b*f*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)^2*d^2) - ((I/2)*a^2*f*PolyLog[2, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^2) - (a*b^2*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) - (a*b^2*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) + (a*b^2*f*PolyLog[2, -E^(2*(c + d*x))])/(2*(a^2 + b^2)^2*d^2) + (f*Sech[c + d*x])/(2*b*d^2) - (a^2*f*Sech[c + d*x])/(2*b*(a^2 + b^2)*d^2) - (a*(e + f*x)*Sech[c + d*x]^2)/(2*(a^2 + b^2)*d) + (a*f*Tanh[c + d*x])/(2*(a^2 + b^2)*d^2) + ((e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*b*d) - (a^2*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*b*(a^2 + b^2)*d)","A",38,13,32,0.4062,1,"{5583, 4185, 4180, 2279, 2391, 5573, 5561, 2190, 6742, 3718, 5451, 3767, 8}"
360,1,122,0,0.1991318,"\int \frac{\text{sech}^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Sech[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\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)}","-\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,"-(b*(a^2 - b^2)*ArcTan[Sinh[c + d*x]])/(2*(a^2 + b^2)^2*d) + (a*b^2*Log[Cosh[c + d*x]])/((a^2 + b^2)^2*d) - (a*b^2*Log[a + b*Sinh[c + d*x]])/((a^2 + b^2)^2*d) - (Sech[c + d*x]^2*(a - b*Sinh[c + d*x]))/(2*(a^2 + b^2)*d)","A",8,7,27,0.2593,1,"{2837, 12, 823, 801, 635, 203, 260}"
361,0,0,0,0.0856575,"\int \frac{\text{sech}^2(c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(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,"Defer[Int][(Sech[c + d*x]^2*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
362,1,606,0,0.879494,"\int \frac{(e+f x)^3 \cosh (c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{6 a^2 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}+\frac{3 a^2 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}+\frac{6 a^2 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^4}+\frac{6 a^2 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^4}+\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{a^2 (e+f x)^4}{4 b^3 f}-\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{6 a f^3 \cosh (c+d x)}{b^2 d^4}-\frac{a (e+f x)^3 \sinh (c+d x)}{b^2 d}+\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{3 f^3 \sinh (c+d x) \cosh (c+d x)}{8 b d^4}+\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}","-\frac{6 a^2 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}+\frac{3 a^2 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}+\frac{6 a^2 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^4}+\frac{6 a^2 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^4}+\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{a^2 (e+f x)^4}{4 b^3 f}-\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{6 a f^3 \cosh (c+d x)}{b^2 d^4}-\frac{a (e+f x)^3 \sinh (c+d x)}{b^2 d}+\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{3 f^3 \sinh (c+d x) \cosh (c+d x)}{8 b d^4}+\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,"(3*f^3*x)/(8*b*d^3) + (e + f*x)^3/(4*b*d) - (a^2*(e + f*x)^4)/(4*b^3*f) + (6*a*f^3*Cosh[c + d*x])/(b^2*d^4) + (3*a*f*(e + f*x)^2*Cosh[c + d*x])/(b^2*d^2) + (a^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*d) + (a^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*d) + (3*a^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^2) + (3*a^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^2) - (6*a^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^3) - (6*a^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^3) + (6*a^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^4) + (6*a^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^4) - (6*a*f^2*(e + f*x)*Sinh[c + d*x])/(b^2*d^3) - (a*(e + f*x)^3*Sinh[c + d*x])/(b^2*d) - (3*f^3*Cosh[c + d*x]*Sinh[c + d*x])/(8*b*d^4) - (3*f*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b*d^2) + (3*f^2*(e + f*x)*Sinh[c + d*x]^2)/(4*b*d^3) + ((e + f*x)^3*Sinh[c + d*x]^2)/(2*b*d)","A",22,14,34,0.4118,1,"{5579, 5446, 3311, 32, 2635, 8, 3296, 2638, 5561, 2190, 2531, 6609, 2282, 6589}"
363,1,449,0,0.7167985,"\int \frac{(e+f x)^2 \cosh (c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 a^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}-\frac{2 a^2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^3}-\frac{2 a^2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}+\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{a^2 (e+f x)^3}{3 b^3 f}+\frac{2 a f (e+f x) \cosh (c+d x)}{b^2 d^2}-\frac{2 a f^2 \sinh (c+d x)}{b^2 d^3}-\frac{a (e+f x)^2 \sinh (c+d x)}{b^2 d}-\frac{f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b d^2}+\frac{f^2 \sinh ^2(c+d x)}{4 b d^3}+\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}","\frac{2 a^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^2}-\frac{2 a^2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^3}-\frac{2 a^2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^3 d^3}+\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{a^2 (e+f x)^3}{3 b^3 f}+\frac{2 a f (e+f x) \cosh (c+d x)}{b^2 d^2}-\frac{2 a f^2 \sinh (c+d x)}{b^2 d^3}-\frac{a (e+f x)^2 \sinh (c+d x)}{b^2 d}-\frac{f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b d^2}+\frac{f^2 \sinh ^2(c+d x)}{4 b d^3}+\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,"(e*f*x)/(2*b*d) + (f^2*x^2)/(4*b*d) - (a^2*(e + f*x)^3)/(3*b^3*f) + (2*a*f*(e + f*x)*Cosh[c + d*x])/(b^2*d^2) + (a^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*d) + (a^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*d) + (2*a^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^2) + (2*a^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^2) - (2*a^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^3) - (2*a^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^3) - (2*a*f^2*Sinh[c + d*x])/(b^2*d^3) - (a*(e + f*x)^2*Sinh[c + d*x])/(b^2*d) - (f*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(2*b*d^2) + (f^2*Sinh[c + d*x]^2)/(4*b*d^3) + ((e + f*x)^2*Sinh[c + d*x]^2)/(2*b*d)","A",17,10,34,0.2941,1,"{5579, 5446, 3310, 3296, 2637, 5561, 2190, 2531, 2282, 6589}"
364,1,278,0,0.418473,"\int \frac{(e+f x) \cosh (c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{a^2 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{a^2 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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^2 (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}","\frac{a^2 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^3 d^2}+\frac{a^2 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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^2 (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,"(f*x)/(4*b*d) - (a^2*(e + f*x)^2)/(2*b^3*f) + (a*f*Cosh[c + d*x])/(b^2*d^2) + (a^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^3*d) + (a^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^3*d) + (a^2*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^3*d^2) + (a^2*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^3*d^2) - (a*(e + f*x)*Sinh[c + d*x])/(b^2*d) - (f*Cosh[c + d*x]*Sinh[c + d*x])/(4*b*d^2) + ((e + f*x)*Sinh[c + d*x]^2)/(2*b*d)","A",14,10,32,0.3125,1,"{5579, 5446, 2635, 8, 3296, 2638, 5561, 2190, 2279, 2391}"
365,1,55,0,0.0808121,"\int \frac{\cosh (c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\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}","\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,"(a^2*Log[a + b*Sinh[c + d*x]])/(b^3*d) - (a*Sinh[c + d*x])/(b^2*d) + Sinh[c + d*x]^2/(2*b*d)","A",4,3,27,0.1111,1,"{2833, 12, 43}"
366,0,0,0,0.0869597,"\int \frac{\cosh (c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Cosh[c + d*x]*Sinh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh (c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Cosh[c + d*x]*Sinh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
367,1,897,0,1.4730054,"\int \frac{(e+f x)^3 \cosh ^2(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^2*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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,"(-3*a*e*f^2*x)/(4*b^2*d^2) - (3*a*f^3*x^2)/(8*b^2*d^2) - (a^3*(e + f*x)^4)/(4*b^4*f) - (a*(e + f*x)^4)/(8*b^2*f) + (6*a^2*f^2*(e + f*x)*Cosh[c + d*x])/(b^3*d^3) + (4*f^2*(e + f*x)*Cosh[c + d*x])/(3*b*d^3) + (a^2*(e + f*x)^3*Cosh[c + d*x])/(b^3*d) + (3*a*f^3*Cosh[c + d*x]^2)/(8*b^2*d^4) + (3*a*f*(e + f*x)^2*Cosh[c + d*x]^2)/(4*b^2*d^2) + (2*f^2*(e + f*x)*Cosh[c + d*x]^3)/(9*b*d^3) + ((e + f*x)^3*Cosh[c + d*x]^3)/(3*b*d) + (a^2*Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^4*d) - (a^2*Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^4*d) + (3*a^2*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^2) - (3*a^2*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^2) - (6*a^2*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^3) + (6*a^2*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^3) + (6*a^2*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^4) - (6*a^2*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^4) - (6*a^2*f^3*Sinh[c + d*x])/(b^3*d^4) - (14*f^3*Sinh[c + d*x])/(9*b*d^4) - (3*a^2*f*(e + f*x)^2*Sinh[c + d*x])/(b^3*d^2) - (2*f*(e + f*x)^2*Sinh[c + d*x])/(3*b*d^2) - (3*a*f^2*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^2*d^3) - (a*(e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^2*d) - (f*(e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b*d^2) - (2*f^3*Sinh[c + d*x]^3)/(27*b*d^4)","A",31,16,36,0.4444,1,"{5579, 5447, 3311, 3296, 2637, 2633, 32, 3310, 5565, 3322, 2264, 2190, 2531, 6609, 2282, 6589}"
368,1,649,0,1.2018568,"\int \frac{(e+f x)^2 \cosh ^2(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 a^2 f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}-\frac{2 a^2 f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^3}-\frac{2 a^2 f (e+f x) \sinh (c+d x)}{b^3 d^2}+\frac{2 a^2 f^2 \cosh (c+d x)}{b^3 d^3}+\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^2 (e+f x)^2 \cosh (c+d x)}{b^3 d}-\frac{a^3 (e+f x)^3}{3 b^4 f}+\frac{a f (e+f x) \cosh ^2(c+d x)}{2 b^2 d^2}-\frac{a f^2 \sinh (c+d x) \cosh (c+d x)}{4 b^2 d^3}-\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{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{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{(e+f x)^2 \cosh ^3(c+d x)}{3 b d}","\frac{2 a^2 f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}-\frac{2 a^2 f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^3}-\frac{2 a^2 f (e+f x) \sinh (c+d x)}{b^3 d^2}+\frac{2 a^2 f^2 \cosh (c+d x)}{b^3 d^3}+\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^2 (e+f x)^2 \cosh (c+d x)}{b^3 d}-\frac{a^3 (e+f x)^3}{3 b^4 f}+\frac{a f (e+f x) \cosh ^2(c+d x)}{2 b^2 d^2}-\frac{a f^2 \sinh (c+d x) \cosh (c+d x)}{4 b^2 d^3}-\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{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{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{(e+f x)^2 \cosh ^3(c+d x)}{3 b d}",1,"-(a*f^2*x)/(4*b^2*d^2) - (a^3*(e + f*x)^3)/(3*b^4*f) - (a*(e + f*x)^3)/(6*b^2*f) + (2*a^2*f^2*Cosh[c + d*x])/(b^3*d^3) + (4*f^2*Cosh[c + d*x])/(9*b*d^3) + (a^2*(e + f*x)^2*Cosh[c + d*x])/(b^3*d) + (a*f*(e + f*x)*Cosh[c + d*x]^2)/(2*b^2*d^2) + (2*f^2*Cosh[c + d*x]^3)/(27*b*d^3) + ((e + f*x)^2*Cosh[c + d*x]^3)/(3*b*d) + (a^2*Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^4*d) - (a^2*Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^4*d) + (2*a^2*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^2) - (2*a^2*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^2) - (2*a^2*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^3) + (2*a^2*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^3) - (2*a^2*f*(e + f*x)*Sinh[c + d*x])/(b^3*d^2) - (4*f*(e + f*x)*Sinh[c + d*x])/(9*b*d^2) - (a*f^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^2*d^3) - (a*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^2*d) - (2*f*(e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x])/(9*b*d^2)","A",25,16,36,0.4444,1,"{5579, 5447, 3310, 3296, 2638, 3311, 32, 2635, 8, 5565, 3322, 2264, 2190, 2531, 2282, 6589}"
369,1,403,0,0.6900128,"\int \frac{(e+f x) \cosh ^2(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{a^2 f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}-\frac{a^2 f \sinh (c+d x)}{b^3 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^2 (e+f x) \cosh (c+d x)}{b^3 d}-\frac{a^3 e x}{b^4}-\frac{a^3 f x^2}{2 b^4}+\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}","\frac{a^2 f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}-\frac{a^2 f \sinh (c+d x)}{b^3 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^2 (e+f x) \cosh (c+d x)}{b^3 d}-\frac{a^3 e x}{b^4}-\frac{a^3 f x^2}{2 b^4}+\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,"-((a^3*e*x)/b^4) - (a*e*x)/(2*b^2) - (a^3*f*x^2)/(2*b^4) - (a*f*x^2)/(4*b^2) + (a^2*(e + f*x)*Cosh[c + d*x])/(b^3*d) + (a*f*Cosh[c + d*x]^2)/(4*b^2*d^2) + ((e + f*x)*Cosh[c + d*x]^3)/(3*b*d) + (a^2*Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^4*d) - (a^2*Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^4*d) + (a^2*Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^2) - (a^2*Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^2) - (a^2*f*Sinh[c + d*x])/(b^3*d^2) - (f*Sinh[c + d*x])/(3*b*d^2) - (a*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^2*d) - (f*Sinh[c + d*x]^3)/(9*b*d^2)","A",19,12,34,0.3529,1,"{5579, 5447, 2633, 3310, 5565, 3296, 2637, 3322, 2264, 2190, 2279, 2391}"
370,1,141,0,0.4981987,"\int \frac{\cosh ^2(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]^2*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(3 a^2+b^2\right) \cosh (c+d x)}{3 b^3 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{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}","\frac{\left(3 a^2+b^2\right) \cosh (c+d x)}{3 b^3 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{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,"-(a*(2*a^2 + b^2)*x)/(2*b^4) - (2*a^2*Sqrt[a^2 + b^2]*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b^4*d) + ((3*a^2 + b^2)*Cosh[c + d*x])/(3*b^3*d) - (a*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^2*d) + (Cosh[c + d*x]*Sinh[c + d*x]^2)/(3*b*d)","A",8,8,29,0.2759,1,"{2889, 3050, 3049, 3023, 2735, 2660, 618, 204}"
371,0,0,0,0.1257685,"\int \frac{\cosh ^2(c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Cosh[c + d*x]^2*Sinh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh ^2(c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Cosh[c + d*x]^2*Sinh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
372,1,1123,0,1.5237113,"\int \frac{(e+f x)^3 \cosh ^3(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^3*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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,"(3*a^2*f^3*x)/(8*b^3*d^3) - (45*f^3*x)/(256*b*d^3) + (a^2*(e + f*x)^3)/(4*b^3*d) - (3*(e + f*x)^3)/(32*b*d) - (a^2*(a^2 + b^2)*(e + f*x)^4)/(4*b^5*f) + (6*a^3*f^3*Cosh[c + d*x])/(b^4*d^4) + (40*a*f^3*Cosh[c + d*x])/(9*b^2*d^4) + (3*a^3*f*(e + f*x)^2*Cosh[c + d*x])/(b^4*d^2) + (2*a*f*(e + f*x)^2*Cosh[c + d*x])/(b^2*d^2) + (9*f^2*(e + f*x)*Cosh[c + d*x]^2)/(32*b*d^3) + (2*a*f^3*Cosh[c + d*x]^3)/(27*b^2*d^4) + (a*f*(e + f*x)^2*Cosh[c + d*x]^3)/(3*b^2*d^2) + (3*f^2*(e + f*x)*Cosh[c + d*x]^4)/(32*b*d^3) + ((e + f*x)^3*Cosh[c + d*x]^4)/(4*b*d) + (a^2*(a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^5*d) + (a^2*(a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^5*d) + (3*a^2*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^2) + (3*a^2*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^2) - (6*a^2*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^3) - (6*a^2*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^3) + (6*a^2*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^4) + (6*a^2*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^4) - (6*a^3*f^2*(e + f*x)*Sinh[c + d*x])/(b^4*d^3) - (40*a*f^2*(e + f*x)*Sinh[c + d*x])/(9*b^2*d^3) - (a^3*(e + f*x)^3*Sinh[c + d*x])/(b^4*d) - (2*a*(e + f*x)^3*Sinh[c + d*x])/(3*b^2*d) - (3*a^2*f^3*Cosh[c + d*x]*Sinh[c + d*x])/(8*b^3*d^4) - (45*f^3*Cosh[c + d*x]*Sinh[c + d*x])/(256*b*d^4) - (3*a^2*f*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^3*d^2) - (9*f*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(32*b*d^2) - (2*a*f^2*(e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x])/(9*b^2*d^3) - (a*(e + f*x)^3*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b^2*d) - (3*f^3*Cosh[c + d*x]^3*Sinh[c + d*x])/(128*b*d^4) - (3*f*(e + f*x)^2*Cosh[c + d*x]^3*Sinh[c + d*x])/(16*b*d^2) + (3*a^2*f^2*(e + f*x)*Sinh[c + d*x]^2)/(4*b^3*d^3) + (a^2*(e + f*x)^3*Sinh[c + d*x]^2)/(2*b^3*d)","A",40,17,36,0.4722,1,"{5579, 5447, 3311, 32, 2635, 8, 3296, 2638, 3310, 5565, 5446, 5561, 2190, 2531, 6609, 2282, 6589}"
373,1,819,0,1.1710248,"\int \frac{(e+f x)^2 \cosh ^3(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^3*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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}","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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,"(a^2*e*f*x)/(2*b^3*d) - (3*e*f*x)/(16*b*d) + (a^2*f^2*x^2)/(4*b^3*d) - (3*f^2*x^2)/(32*b*d) - (a^2*(a^2 + b^2)*(e + f*x)^3)/(3*b^5*f) + (2*a^3*f*(e + f*x)*Cosh[c + d*x])/(b^4*d^2) + (4*a*f*(e + f*x)*Cosh[c + d*x])/(3*b^2*d^2) + (3*f^2*Cosh[c + d*x]^2)/(32*b*d^3) + (2*a*f*(e + f*x)*Cosh[c + d*x]^3)/(9*b^2*d^2) + (f^2*Cosh[c + d*x]^4)/(32*b*d^3) + ((e + f*x)^2*Cosh[c + d*x]^4)/(4*b*d) + (a^2*(a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^5*d) + (a^2*(a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^5*d) + (2*a^2*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^2) + (2*a^2*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^2) - (2*a^2*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^3) - (2*a^2*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^3) - (2*a^3*f^2*Sinh[c + d*x])/(b^4*d^3) - (14*a*f^2*Sinh[c + d*x])/(9*b^2*d^3) - (a^3*(e + f*x)^2*Sinh[c + d*x])/(b^4*d) - (2*a*(e + f*x)^2*Sinh[c + d*x])/(3*b^2*d) - (a^2*f*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^3*d^2) - (3*f*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(16*b*d^2) - (a*(e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b^2*d) - (f*(e + f*x)*Cosh[c + d*x]^3*Sinh[c + d*x])/(8*b*d^2) + (a^2*f^2*Sinh[c + d*x]^2)/(4*b^3*d^3) + (a^2*(e + f*x)^2*Sinh[c + d*x]^2)/(2*b^3*d) - (2*a*f^2*Sinh[c + d*x]^3)/(27*b^2*d^3)","A",28,14,36,0.3889,1,"{5579, 5447, 3310, 3311, 3296, 2637, 2633, 5565, 5446, 5561, 2190, 2531, 2282, 6589}"
374,1,499,0,0.6754011,"\int \frac{(e+f x) \cosh ^3(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^3*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{a^2 f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^5 d^2}+\frac{a^3 f \cosh (c+d x)}{b^4 d^2}-\frac{a^2 f \sinh (c+d x) \cosh (c+d x)}{4 b^3 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 (e+f x) \sinh ^2(c+d x)}{2 b^3 d}-\frac{a^3 (e+f x) \sinh (c+d x)}{b^4 d}+\frac{a^2 f x}{4 b^3 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}","\frac{a^2 f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^5 d^2}+\frac{a^3 f \cosh (c+d x)}{b^4 d^2}-\frac{a^2 f \sinh (c+d x) \cosh (c+d x)}{4 b^3 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 (e+f x) \sinh ^2(c+d x)}{2 b^3 d}-\frac{a^3 (e+f x) \sinh (c+d x)}{b^4 d}+\frac{a^2 f x}{4 b^3 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,"(a^2*f*x)/(4*b^3*d) - (3*f*x)/(32*b*d) - (a^2*(a^2 + b^2)*(e + f*x)^2)/(2*b^5*f) + (a^3*f*Cosh[c + d*x])/(b^4*d^2) + (2*a*f*Cosh[c + d*x])/(3*b^2*d^2) + (a*f*Cosh[c + d*x]^3)/(9*b^2*d^2) + ((e + f*x)*Cosh[c + d*x]^4)/(4*b*d) + (a^2*(a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^5*d) + (a^2*(a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^5*d) + (a^2*(a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^2) + (a^2*(a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^2) - (a^3*(e + f*x)*Sinh[c + d*x])/(b^4*d) - (2*a*(e + f*x)*Sinh[c + d*x])/(3*b^2*d) - (a^2*f*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^3*d^2) - (3*f*Cosh[c + d*x]*Sinh[c + d*x])/(32*b*d^2) - (a*(e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b^2*d) - (f*Cosh[c + d*x]^3*Sinh[c + d*x])/(16*b*d^2) + (a^2*(e + f*x)*Sinh[c + d*x]^2)/(2*b^3*d)","A",22,13,34,0.3824,1,"{5579, 5447, 2635, 8, 3310, 3296, 2638, 5565, 5446, 5561, 2190, 2279, 2391}"
375,1,113,0,0.1628312,"\int \frac{\cosh ^3(c+d x) \sinh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]^3*Sinh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{\left(a^2+b^2\right) \sinh ^2(c+d x)}{2 b^3 d}-\frac{a \left(a^2+b^2\right) \sinh (c+d x)}{b^4 d}+\frac{a^2 \left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{b^5 d}-\frac{a \sinh ^3(c+d x)}{3 b^2 d}+\frac{\sinh ^4(c+d x)}{4 b d}","\frac{\left(a^2+b^2\right) \sinh ^2(c+d x)}{2 b^3 d}-\frac{a \left(a^2+b^2\right) \sinh (c+d x)}{b^4 d}+\frac{a^2 \left(a^2+b^2\right) \log (a+b \sinh (c+d x))}{b^5 d}-\frac{a \sinh ^3(c+d x)}{3 b^2 d}+\frac{\sinh ^4(c+d x)}{4 b d}",1,"(a^2*(a^2 + b^2)*Log[a + b*Sinh[c + d*x]])/(b^5*d) - (a*(a^2 + b^2)*Sinh[c + d*x])/(b^4*d) + ((a^2 + b^2)*Sinh[c + d*x]^2)/(2*b^3*d) - (a*Sinh[c + d*x]^3)/(3*b^2*d) + Sinh[c + d*x]^4/(4*b*d)","A",4,3,29,0.1034,1,"{2837, 12, 894}"
376,0,0,0,0.13164,"\int \frac{\cosh ^3(c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Cosh[c + d*x]^3*Sinh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh ^3(c+d x) \sinh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Cosh[c + d*x]^3*Sinh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
377,1,1218,0,1.6943064,"\int \frac{(e+f x)^3 \sinh (c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sinh[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) (e+f x)^2}{b^2 d^2}+\frac{3 i a^3 f \text{PolyLog}\left(2,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{PolyLog}\left(2,i e^{c+d x}\right) (e+f x)^2}{b^2 d^2}+\frac{3 a^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) (e+f x)^2}{2 b d^2}-\frac{3 a^2 f \text{PolyLog}\left(2,-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{PolyLog}\left(3,-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{PolyLog}\left(3,-i e^{c+d x}\right) (e+f x)}{b^2 d^3}-\frac{6 i a^3 f^2 \text{PolyLog}\left(3,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{PolyLog}\left(3,i e^{c+d x}\right) (e+f x)}{b^2 d^3}-\frac{6 a^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-e^{2 (c+d x)}\right) (e+f x)}{2 b d^3}+\frac{3 a^2 f^2 \text{PolyLog}\left(3,-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{PolyLog}\left(4,-i e^{c+d x}\right)}{b^2 \left(a^2+b^2\right) d^4}+\frac{6 i a f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{b^2 d^4}+\frac{6 i a^3 f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{b^2 \left(a^2+b^2\right) d^4}-\frac{6 i a f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{b^2 d^4}+\frac{6 a^2 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-e^{2 (c+d x)}\right)}{4 b d^4}-\frac{3 a^2 f^3 \text{PolyLog}\left(4,-e^{2 (c+d x)}\right)}{4 b \left(a^2+b^2\right) d^4}","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) (e+f x)^2}{b^2 d^2}+\frac{3 i a^3 f \text{PolyLog}\left(2,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{PolyLog}\left(2,i e^{c+d x}\right) (e+f x)^2}{b^2 d^2}+\frac{3 a^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) (e+f x)^2}{2 b d^2}-\frac{3 a^2 f \text{PolyLog}\left(2,-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{PolyLog}\left(3,-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{PolyLog}\left(3,-i e^{c+d x}\right) (e+f x)}{b^2 d^3}-\frac{6 i a^3 f^2 \text{PolyLog}\left(3,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{PolyLog}\left(3,i e^{c+d x}\right) (e+f x)}{b^2 d^3}-\frac{6 a^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-e^{2 (c+d x)}\right) (e+f x)}{2 b d^3}+\frac{3 a^2 f^2 \text{PolyLog}\left(3,-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{PolyLog}\left(4,-i e^{c+d x}\right)}{b^2 \left(a^2+b^2\right) d^4}+\frac{6 i a f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{b^2 d^4}+\frac{6 i a^3 f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{b^2 \left(a^2+b^2\right) d^4}-\frac{6 i a f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{b^2 d^4}+\frac{6 a^2 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-e^{2 (c+d x)}\right)}{4 b d^4}-\frac{3 a^2 f^3 \text{PolyLog}\left(4,-e^{2 (c+d x)}\right)}{4 b \left(a^2+b^2\right) d^4}",1,"-(e + f*x)^4/(4*b*f) - (2*a*(e + f*x)^3*ArcTan[E^(c + d*x)])/(b^2*d) + (2*a^3*(e + f*x)^3*ArcTan[E^(c + d*x)])/(b^2*(a^2 + b^2)*d) + (a^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)*d) + (a^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)*d) + ((e + f*x)^3*Log[1 + E^(2*(c + d*x))])/(b*d) - (a^2*(e + f*x)^3*Log[1 + E^(2*(c + d*x))])/(b*(a^2 + b^2)*d) + ((3*I)*a*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*d^2) - ((3*I)*a^3*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) - ((3*I)*a*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(b^2*d^2) + ((3*I)*a^3*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) + (3*a^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^2) + (3*a^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^2) + (3*f*(e + f*x)^2*PolyLog[2, -E^(2*(c + d*x))])/(2*b*d^2) - (3*a^2*f*(e + f*x)^2*PolyLog[2, -E^(2*(c + d*x))])/(2*b*(a^2 + b^2)*d^2) - ((6*I)*a*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(b^2*d^3) + ((6*I)*a^3*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^3) + ((6*I)*a*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(b^2*d^3) - ((6*I)*a^3*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^3) - (6*a^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^3) - (6*a^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^3) - (3*f^2*(e + f*x)*PolyLog[3, -E^(2*(c + d*x))])/(2*b*d^3) + (3*a^2*f^2*(e + f*x)*PolyLog[3, -E^(2*(c + d*x))])/(2*b*(a^2 + b^2)*d^3) + ((6*I)*a*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(b^2*d^4) - ((6*I)*a^3*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^4) - ((6*I)*a*f^3*PolyLog[4, I*E^(c + d*x)])/(b^2*d^4) + ((6*I)*a^3*f^3*PolyLog[4, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^4) + (6*a^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^4) + (6*a^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^4) + (3*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*b*d^4) - (3*a^2*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*b*(a^2 + b^2)*d^4)","A",46,12,32,0.3750,1,"{5581, 3718, 2190, 2531, 6609, 2282, 6589, 5567, 4180, 5573, 5561, 6742}"
378,1,861,0,1.3664873,"\int \frac{(e+f x)^2 \sinh (c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sinh[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^2}{b \left(a^2+b^2\right) d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) a}{b^2 d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) a}{b^2 d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a}{b^2 d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b d^2}-\frac{f^2 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 b 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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^2}{b \left(a^2+b^2\right) d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) a}{b^2 d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) a}{b^2 d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a}{b^2 d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b d^2}-\frac{f^2 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 b d^3}",1,"-(e + f*x)^3/(3*b*f) - (2*a*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b^2*d) + (2*a^3*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b^2*(a^2 + b^2)*d) + (a^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)*d) + (a^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)*d) + ((e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b*d) - (a^2*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b*(a^2 + b^2)*d) + ((2*I)*a*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*d^2) - ((2*I)*a^3*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) - ((2*I)*a*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b^2*d^2) + ((2*I)*a^3*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) + (2*a^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^2) + (2*a^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^2) + (f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b*d^2) - (a^2*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b*(a^2 + b^2)*d^2) - ((2*I)*a*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b^2*d^3) + ((2*I)*a^3*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^3) + ((2*I)*a*f^2*PolyLog[3, I*E^(c + d*x)])/(b^2*d^3) - ((2*I)*a^3*f^2*PolyLog[3, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^3) - (2*a^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^3) - (2*a^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^3) - (f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*b*d^3) + (a^2*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*b*(a^2 + b^2)*d^3)","A",38,11,32,0.3438,1,"{5581, 3718, 2190, 2531, 2282, 6589, 5567, 4180, 5573, 5561, 6742}"
379,1,516,0,0.7758517,"\int \frac{(e+f x) \sinh (c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sinh[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{i a^3 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b^2 d^2 \left(a^2+b^2\right)}+\frac{i a^3 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b^2 d^2 \left(a^2+b^2\right)}+\frac{a^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{a^2 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 b d^2 \left(a^2+b^2\right)}+\frac{i a f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b^2 d^2}-\frac{i a f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b^2 d^2}+\frac{f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 b 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 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{2 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 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^2 d}+\frac{(e+f x) \log \left(e^{2 (c+d x)}+1\right)}{b d}-\frac{(e+f x)^2}{2 b f}","-\frac{i a^3 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b^2 d^2 \left(a^2+b^2\right)}+\frac{i a^3 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b^2 d^2 \left(a^2+b^2\right)}+\frac{a^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b d^2 \left(a^2+b^2\right)}-\frac{a^2 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 b d^2 \left(a^2+b^2\right)}+\frac{i a f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b^2 d^2}-\frac{i a f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b^2 d^2}+\frac{f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 b 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 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{2 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 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^2 d}+\frac{(e+f x) \log \left(e^{2 (c+d x)}+1\right)}{b d}-\frac{(e+f x)^2}{2 b f}",1,"-(e + f*x)^2/(2*b*f) - (2*a*(e + f*x)*ArcTan[E^(c + d*x)])/(b^2*d) + (2*a^3*(e + f*x)*ArcTan[E^(c + d*x)])/(b^2*(a^2 + b^2)*d) + (a^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)*d) + (a^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)*d) + ((e + f*x)*Log[1 + E^(2*(c + d*x))])/(b*d) - (a^2*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(b*(a^2 + b^2)*d) + (I*a*f*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*d^2) - (I*a^3*f*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) - (I*a*f*PolyLog[2, I*E^(c + d*x)])/(b^2*d^2) + (I*a^3*f*PolyLog[2, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) + (a^2*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^2) + (a^2*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)*d^2) + (f*PolyLog[2, -E^(2*(c + d*x))])/(2*b*d^2) - (a^2*f*PolyLog[2, -E^(2*(c + d*x))])/(2*b*(a^2 + b^2)*d^2)","A",30,10,30,0.3333,1,"{5581, 3718, 2190, 2279, 2391, 5567, 4180, 5573, 5561, 6742}"
380,1,74,0,0.1597608,"\int \frac{\sinh (c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Sinh[c + d*x]*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\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)}","\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,"-((a*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d)) + (b*Log[Cosh[c + d*x]])/((a^2 + b^2)*d) + (a^2*Log[a + b*Sinh[c + d*x]])/(b*(a^2 + b^2)*d)","A",7,6,25,0.2400,1,"{2837, 12, 1629, 635, 203, 260}"
381,0,0,0,0.0598635,"\int \frac{\sinh (c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Sinh[c + d*x]*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\sinh (c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\sinh (c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][(Sinh[c + d*x]*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
382,1,1118,0,1.9804391,"\int \frac{(e+f x)^3 \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{3 f^3 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^4}+\frac{6 i f^3 \text{PolyLog}\left(3,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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a}{b^2 d^3}-\frac{3 f^3 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^3}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^3}+\frac{6 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^4}-\frac{6 i f^3 \text{PolyLog}\left(3,i e^{c+d x}\right)}{b d^4}-\frac{(e+f x)^3 \text{sech}(c+d x)}{b 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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{3 f^3 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{b \left(a^2+b^2\right) d^4}+\frac{6 i f^3 \text{PolyLog}\left(3,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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a}{b^2 d^3}-\frac{3 f^3 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^3}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^3}+\frac{6 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^4}-\frac{6 i f^3 \text{PolyLog}\left(3,i e^{c+d x}\right)}{b d^4}-\frac{(e+f x)^3 \text{sech}(c+d x)}{b d}",1,"-((a*(e + f*x)^3)/(b^2*d)) + (a^3*(e + f*x)^3)/(b^2*(a^2 + b^2)*d) + (6*f*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b*d^2) - (6*a^2*f*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b*(a^2 + b^2)*d^2) + (a^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (a^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) + (3*a*f*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b^2*d^2) - (3*a^3*f*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b^2*(a^2 + b^2)*d^2) - ((6*I)*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^3) + ((6*I)*a^2*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^3) + ((6*I)*f^2*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b*d^3) - ((6*I)*a^2*f^2*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^3) + (3*a^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (3*a^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) + (3*a*f^2*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b^2*d^3) - (3*a^3*f^2*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b^2*(a^2 + b^2)*d^3) + ((6*I)*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(b*d^4) - ((6*I)*a^2*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^4) - ((6*I)*f^3*PolyLog[3, I*E^(c + d*x)])/(b*d^4) + ((6*I)*a^2*f^3*PolyLog[3, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^4) - (6*a^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^3) + (6*a^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^3) - (3*a*f^3*PolyLog[3, -E^(2*(c + d*x))])/(2*b^2*d^4) + (3*a^3*f^3*PolyLog[3, -E^(2*(c + d*x))])/(2*b^2*(a^2 + b^2)*d^4) + (6*a^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^4) - (6*a^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^4) - ((e + f*x)^3*Sech[c + d*x])/(b*d) + (a^2*(e + f*x)^3*Sech[c + d*x])/(b*(a^2 + b^2)*d) - (a*(e + f*x)^3*Tanh[c + d*x])/(b^2*d) + (a^3*(e + f*x)^3*Tanh[c + d*x])/(b^2*(a^2 + b^2)*d)","A",45,15,28,0.5357,1,"{5567, 5451, 4180, 2531, 2282, 6589, 5583, 4184, 3718, 2190, 5573, 3322, 2264, 6609, 6742}"
383,1,772,0,1.5328443,"\int \frac{(e+f x)^2 \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 a^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{a^3 f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b^2 d^3 \left(a^2+b^2\right)}+\frac{2 i a^2 f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}-\frac{2 i a^2 f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}-\frac{2 a^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{a f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b^2 d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^3}-\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{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^3 (e+f x)^2 \tanh (c+d x)}{b^2 d \left(a^2+b^2\right)}+\frac{a^2 (e+f x)^2 \text{sech}(c+d x)}{b d \left(a^2+b^2\right)}+\frac{a^3 (e+f x)^2}{b^2 d \left(a^2+b^2\right)}+\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{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}","\frac{2 a^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^{3/2}}-\frac{a^3 f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b^2 d^3 \left(a^2+b^2\right)}+\frac{2 i a^2 f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}-\frac{2 i a^2 f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^3 \left(a^2+b^2\right)}-\frac{2 a^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^3 \left(a^2+b^2\right)^{3/2}}+\frac{a f^2 \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b^2 d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^3}-\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{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^3 (e+f x)^2 \tanh (c+d x)}{b^2 d \left(a^2+b^2\right)}+\frac{a^2 (e+f x)^2 \text{sech}(c+d x)}{b d \left(a^2+b^2\right)}+\frac{a^3 (e+f x)^2}{b^2 d \left(a^2+b^2\right)}+\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{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*(e + f*x)^2)/(b^2*d)) + (a^3*(e + f*x)^2)/(b^2*(a^2 + b^2)*d) + (4*f*(e + f*x)*ArcTan[E^(c + d*x)])/(b*d^2) - (4*a^2*f*(e + f*x)*ArcTan[E^(c + d*x)])/(b*(a^2 + b^2)*d^2) + (a^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (a^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) + (2*a*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(b^2*d^2) - (2*a^3*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(b^2*(a^2 + b^2)*d^2) - ((2*I)*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^3) + ((2*I)*a^2*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)*d^3) + ((2*I)*f^2*PolyLog[2, I*E^(c + d*x)])/(b*d^3) - ((2*I)*a^2*f^2*PolyLog[2, I*E^(c + d*x)])/(b*(a^2 + b^2)*d^3) + (2*a^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (2*a^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) + (a*f^2*PolyLog[2, -E^(2*(c + d*x))])/(b^2*d^3) - (a^3*f^2*PolyLog[2, -E^(2*(c + d*x))])/(b^2*(a^2 + b^2)*d^3) - (2*a^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^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^3) - ((e + f*x)^2*Sech[c + d*x])/(b*d) + (a^2*(e + f*x)^2*Sech[c + d*x])/(b*(a^2 + b^2)*d) - (a*(e + f*x)^2*Tanh[c + d*x])/(b^2*d) + (a^3*(e + f*x)^2*Tanh[c + d*x])/(b^2*(a^2 + b^2)*d)","A",37,16,28,0.5714,1,"{5567, 5451, 4180, 2279, 2391, 5583, 4184, 3718, 2190, 5573, 3322, 2264, 2531, 2282, 6589, 6742}"
384,1,385,0,0.7580243,"\int \frac{(e+f x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{a^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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^3 f \log (\cosh (c+d x))}{b^2 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^3 (e+f x) \tanh (c+d x)}{b^2 d \left(a^2+b^2\right)}+\frac{a^2 (e+f x) \text{sech}(c+d x)}{b 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}","\frac{a^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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^3 f \log (\cosh (c+d x))}{b^2 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^3 (e+f x) \tanh (c+d x)}{b^2 d \left(a^2+b^2\right)}+\frac{a^2 (e+f x) \text{sech}(c+d x)}{b 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,"(f*ArcTan[Sinh[c + d*x]])/(b*d^2) - (a^2*f*ArcTan[Sinh[c + d*x]])/(b*(a^2 + b^2)*d^2) + (a^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) - (a^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^(3/2)*d) + (a*f*Log[Cosh[c + d*x]])/(b^2*d^2) - (a^3*f*Log[Cosh[c + d*x]])/(b^2*(a^2 + b^2)*d^2) + (a^2*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - (a^2*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^(3/2)*d^2) - ((e + f*x)*Sech[c + d*x])/(b*d) + (a^2*(e + f*x)*Sech[c + d*x])/(b*(a^2 + b^2)*d) - (a*(e + f*x)*Tanh[c + d*x])/(b^2*d) + (a^3*(e + f*x)*Tanh[c + d*x])/(b^2*(a^2 + b^2)*d)","A",21,13,26,0.5000,1,"{5567, 5451, 3770, 5583, 4184, 3475, 5573, 3322, 2264, 2190, 2279, 2391, 6742}"
385,1,90,0,0.1055445,"\int \frac{\tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Tanh[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","-\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)}","-\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,"(-2*a^2*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/((a^2 + b^2)^(3/2)*d) - (b*Sech[c + d*x])/((a^2 + b^2)*d) - (a*Tanh[c + d*x])/((a^2 + b^2)*d)","A",8,7,21,0.3333,1,"{2727, 3767, 8, 2606, 2660, 618, 204}"
386,0,0,0,0.0729658,"\int \frac{\tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[Tanh[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][Tanh[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
387,1,1256,0,1.9675383,"\int \frac{(e+f x)^2 \text{sech}(c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{i f (e+f x) \text{PolyLog}\left(2,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{PolyLog}\left(2,i e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d^3}-\frac{i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^2}{\left(a^2+b^2\right)^2 d^2}-\frac{2 b f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) a}{b^2 d^2}-\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) a}{b^2 d^2}-\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a}{b^2 d^3}+\frac{i f^2 \text{PolyLog}\left(3,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}","\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{i f (e+f x) \text{PolyLog}\left(2,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{PolyLog}\left(2,i e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^3}{\left(a^2+b^2\right)^2 d^3}-\frac{i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^2}{\left(a^2+b^2\right)^2 d^2}-\frac{2 b f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) a}{b^2 d^2}-\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) a}{b^2 d^2}-\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a}{b^2 d^3}+\frac{i f^2 \text{PolyLog}\left(3,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,"-((a*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b^2*d)) + (2*a^3*(e + f*x)^2*ArcTan[E^(c + d*x)])/((a^2 + b^2)^2*d) + (a^3*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b^2*(a^2 + b^2)*d) + (a*f^2*ArcTan[Sinh[c + d*x]])/(b^2*d^3) - (a^3*f^2*ArcTan[Sinh[c + d*x]])/(b^2*(a^2 + b^2)*d^3) + (a^2*b*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) + (a^2*b*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) - (a^2*b*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)^2*d) - (f^2*Log[Cosh[c + d*x]])/(b*d^3) + (a^2*f^2*Log[Cosh[c + d*x]])/(b*(a^2 + b^2)*d^3) + (I*a*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*d^2) - ((2*I)*a^3*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^2) - (I*a^3*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) - (I*a*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b^2*d^2) + ((2*I)*a^3*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)^2*d^2) + (I*a^3*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) + (2*a^2*b*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) + (2*a^2*b*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) - (a^2*b*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/((a^2 + b^2)^2*d^2) - (I*a*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b^2*d^3) + ((2*I)*a^3*f^2*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^3) + (I*a^3*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^3) + (I*a*f^2*PolyLog[3, I*E^(c + d*x)])/(b^2*d^3) - ((2*I)*a^3*f^2*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)^2*d^3) - (I*a^3*f^2*PolyLog[3, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^3) - (2*a^2*b*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^3) - (2*a^2*b*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^3) + (a^2*b*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*(a^2 + b^2)^2*d^3) - (a*f*(e + f*x)*Sech[c + d*x])/(b^2*d^2) + (a^3*f*(e + f*x)*Sech[c + d*x])/(b^2*(a^2 + b^2)*d^2) - ((e + f*x)^2*Sech[c + d*x]^2)/(2*b*d) + (a^2*(e + f*x)^2*Sech[c + d*x]^2)/(2*b*(a^2 + b^2)*d) + (f*(e + f*x)*Tanh[c + d*x])/(b*d^2) - (a^2*f*(e + f*x)*Tanh[c + d*x])/(b*(a^2 + b^2)*d^2) - (a*(e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*b^2*d) + (a^3*(e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*b^2*(a^2 + b^2)*d)","A",53,15,34,0.4412,1,"{5583, 5451, 4184, 3475, 4186, 3770, 4180, 2531, 2282, 6589, 5573, 5561, 2190, 6742, 3718}"
388,1,760,0,1.148083,"\int \frac{(e+f x) \text{sech}(c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sech[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{i a^3 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 b^2 d^2 \left(a^2+b^2\right)}-\frac{i a^3 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{i a^3 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 b^2 d^2 \left(a^2+b^2\right)}+\frac{i a^3 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{a^2 b f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{a^2 b f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)^2}+\frac{i a f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 b^2 d^2}-\frac{i a f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 b^2 d^2}-\frac{a^2 f \tanh (c+d x)}{2 b d^2 \left(a^2+b^2\right)}+\frac{a^3 f \text{sech}(c+d x)}{2 b^2 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^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^2 (e+f x) \text{sech}^2(c+d x)}{2 b d \left(a^2+b^2\right)}+\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{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}","-\frac{i a^3 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 b^2 d^2 \left(a^2+b^2\right)}-\frac{i a^3 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{i a^3 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 b^2 d^2 \left(a^2+b^2\right)}+\frac{i a^3 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{a^2 b f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{a^2 b f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 d^2 \left(a^2+b^2\right)^2}+\frac{i a f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 b^2 d^2}-\frac{i a f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 b^2 d^2}-\frac{a^2 f \tanh (c+d x)}{2 b d^2 \left(a^2+b^2\right)}+\frac{a^3 f \text{sech}(c+d x)}{2 b^2 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^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^2 (e+f x) \text{sech}^2(c+d x)}{2 b d \left(a^2+b^2\right)}+\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{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,"-((a*(e + f*x)*ArcTan[E^(c + d*x)])/(b^2*d)) + (2*a^3*(e + f*x)*ArcTan[E^(c + d*x)])/((a^2 + b^2)^2*d) + (a^3*(e + f*x)*ArcTan[E^(c + d*x)])/(b^2*(a^2 + b^2)*d) + (a^2*b*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) + (a^2*b*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) - (a^2*b*(e + f*x)*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)^2*d) + ((I/2)*a*f*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*d^2) - (I*a^3*f*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^2) - ((I/2)*a^3*f*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) - ((I/2)*a*f*PolyLog[2, I*E^(c + d*x)])/(b^2*d^2) + (I*a^3*f*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)^2*d^2) + ((I/2)*a^3*f*PolyLog[2, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) + (a^2*b*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) + (a^2*b*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) - (a^2*b*f*PolyLog[2, -E^(2*(c + d*x))])/(2*(a^2 + b^2)^2*d^2) - (a*f*Sech[c + d*x])/(2*b^2*d^2) + (a^3*f*Sech[c + d*x])/(2*b^2*(a^2 + b^2)*d^2) - ((e + f*x)*Sech[c + d*x]^2)/(2*b*d) + (a^2*(e + f*x)*Sech[c + d*x]^2)/(2*b*(a^2 + b^2)*d) + (f*Tanh[c + d*x])/(2*b*d^2) - (a^2*f*Tanh[c + d*x])/(2*b*(a^2 + b^2)*d^2) - (a*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*b^2*d) + (a^3*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*b^2*(a^2 + b^2)*d)","A",42,13,32,0.4062,1,"{5583, 5451, 3767, 8, 4185, 4180, 2279, 2391, 5573, 5561, 2190, 6742, 3718}"
389,1,121,0,0.2291123,"\int \frac{\text{sech}(c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Sech[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\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)}","\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,"(a*(a^2 - b^2)*ArcTan[Sinh[c + d*x]])/(2*(a^2 + b^2)^2*d) - (a^2*b*Log[Cosh[c + d*x]])/((a^2 + b^2)^2*d) + (a^2*b*Log[a + b*Sinh[c + d*x]])/((a^2 + b^2)^2*d) - (Sech[c + d*x]^2*(b + a*Sinh[c + d*x]))/(2*(a^2 + b^2)*d)","A",8,7,27,0.2593,1,"{2837, 12, 1647, 801, 635, 203, 260}"
390,0,0,0,0.0818747,"\int \frac{\text{sech}(c+d x) \tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Sech[c + d*x]*Tanh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{sech}(c+d x) \tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Sech[c + d*x]*Tanh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
391,1,792,0,1.1967302,"\int \frac{(e+f x)^3 \cosh (c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{6 a^3 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^3}-\frac{3 a^3 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}-\frac{6 a^3 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^4}-\frac{6 a^3 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 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{6 a^2 f^3 \cosh (c+d x)}{b^3 d^4}-\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{a^2 (e+f x)^3 \sinh (c+d x)}{b^3 d}+\frac{a^3 (e+f x)^4}{4 b^4 f}-\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{3 a f^3 \sinh (c+d x) \cosh (c+d x)}{8 b^2 d^4}-\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^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{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{(e+f x)^3 \sinh ^3(c+d x)}{3 b d}","\frac{6 a^3 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^3}-\frac{3 a^3 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}-\frac{6 a^3 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^4}-\frac{6 a^3 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 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{6 a^2 f^3 \cosh (c+d x)}{b^3 d^4}-\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{a^2 (e+f x)^3 \sinh (c+d x)}{b^3 d}+\frac{a^3 (e+f x)^4}{4 b^4 f}-\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{3 a f^3 \sinh (c+d x) \cosh (c+d x)}{8 b^2 d^4}-\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^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{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{(e+f x)^3 \sinh ^3(c+d x)}{3 b d}",1,"(-3*a*f^3*x)/(8*b^2*d^3) - (a*(e + f*x)^3)/(4*b^2*d) + (a^3*(e + f*x)^4)/(4*b^4*f) - (6*a^2*f^3*Cosh[c + d*x])/(b^3*d^4) + (14*f^3*Cosh[c + d*x])/(9*b*d^4) - (3*a^2*f*(e + f*x)^2*Cosh[c + d*x])/(b^3*d^2) + (2*f*(e + f*x)^2*Cosh[c + d*x])/(3*b*d^2) - (2*f^3*Cosh[c + d*x]^3)/(27*b*d^4) - (a^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^4*d) - (a^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^4*d) - (3*a^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^2) - (3*a^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^2) + (6*a^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^3) + (6*a^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^3) - (6*a^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^4) - (6*a^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^4) + (6*a^2*f^2*(e + f*x)*Sinh[c + d*x])/(b^3*d^3) - (4*f^2*(e + f*x)*Sinh[c + d*x])/(3*b*d^3) + (a^2*(e + f*x)^3*Sinh[c + d*x])/(b^3*d) + (3*a*f^3*Cosh[c + d*x]*Sinh[c + d*x])/(8*b^2*d^4) + (3*a*f*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^2*d^2) - (3*a*f^2*(e + f*x)*Sinh[c + d*x]^2)/(4*b^2*d^3) - (a*(e + f*x)^3*Sinh[c + d*x]^2)/(2*b^2*d) - (f*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x]^2)/(3*b*d^2) + (2*f^2*(e + f*x)*Sinh[c + d*x]^3)/(9*b*d^3) + ((e + f*x)^3*Sinh[c + d*x]^3)/(3*b*d)","A",30,15,34,0.4412,1,"{5579, 5446, 3311, 3296, 2638, 2633, 32, 2635, 8, 5561, 2190, 2531, 6609, 2282, 6589}"
392,1,578,0,0.928188,"\int \frac{(e+f x)^2 \cosh (c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{2 a^3 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}+\frac{2 a^3 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^3}+\frac{2 a^3 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^3}-\frac{2 a^2 f (e+f x) \cosh (c+d x)}{b^3 d^2}+\frac{2 a^2 f^2 \sinh (c+d x)}{b^3 d^3}-\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^2 (e+f x)^2 \sinh (c+d x)}{b^3 d}+\frac{a^3 (e+f x)^3}{3 b^4 f}+\frac{a f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^2 d^2}-\frac{a f^2 \sinh ^2(c+d x)}{4 b^2 d^3}-\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{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{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{(e+f x)^2 \sinh ^3(c+d x)}{3 b d}","-\frac{2 a^3 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}+\frac{2 a^3 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^3}+\frac{2 a^3 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^3}-\frac{2 a^2 f (e+f x) \cosh (c+d x)}{b^3 d^2}+\frac{2 a^2 f^2 \sinh (c+d x)}{b^3 d^3}-\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^2 (e+f x)^2 \sinh (c+d x)}{b^3 d}+\frac{a^3 (e+f x)^3}{3 b^4 f}+\frac{a f (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^2 d^2}-\frac{a f^2 \sinh ^2(c+d x)}{4 b^2 d^3}-\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{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{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{(e+f x)^2 \sinh ^3(c+d x)}{3 b d}",1,"-(a*e*f*x)/(2*b^2*d) - (a*f^2*x^2)/(4*b^2*d) + (a^3*(e + f*x)^3)/(3*b^4*f) - (2*a^2*f*(e + f*x)*Cosh[c + d*x])/(b^3*d^2) + (4*f*(e + f*x)*Cosh[c + d*x])/(9*b*d^2) - (a^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^4*d) - (a^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^4*d) - (2*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^2) - (2*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^2) + (2*a^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^3) + (2*a^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^3) + (2*a^2*f^2*Sinh[c + d*x])/(b^3*d^3) - (4*f^2*Sinh[c + d*x])/(9*b*d^3) + (a^2*(e + f*x)^2*Sinh[c + d*x])/(b^3*d) + (a*f*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^2*d^2) - (a*f^2*Sinh[c + d*x]^2)/(4*b^2*d^3) - (a*(e + f*x)^2*Sinh[c + d*x]^2)/(2*b^2*d) - (2*f*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x]^2)/(9*b*d^2) + (2*f^2*Sinh[c + d*x]^3)/(27*b*d^3) + ((e + f*x)^2*Sinh[c + d*x]^3)/(3*b*d)","A",22,10,34,0.2941,1,"{5579, 5446, 3310, 3296, 2637, 5561, 2190, 2531, 2282, 6589}"
393,1,348,0,0.5256098,"\int \frac{(e+f x) \cosh (c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{a^3 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{a^3 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}-\frac{a^2 f \cosh (c+d x)}{b^3 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^2 (e+f x) \sinh (c+d x)}{b^3 d}+\frac{a^3 (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{f \cosh (c+d x)}{3 b d^2}+\frac{(e+f x) \sinh ^3(c+d x)}{3 b d}","-\frac{a^3 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{b^4 d^2}-\frac{a^3 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^4 d^2}-\frac{a^2 f \cosh (c+d x)}{b^3 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^2 (e+f x) \sinh (c+d x)}{b^3 d}+\frac{a^3 (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{f \cosh (c+d x)}{3 b d^2}+\frac{(e+f x) \sinh ^3(c+d x)}{3 b d}",1,"-(a*f*x)/(4*b^2*d) + (a^3*(e + f*x)^2)/(2*b^4*f) - (a^2*f*Cosh[c + d*x])/(b^3*d^2) + (f*Cosh[c + d*x])/(3*b*d^2) - (f*Cosh[c + d*x]^3)/(9*b*d^2) - (a^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^4*d) - (a^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^4*d) - (a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^4*d^2) - (a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^4*d^2) + (a^2*(e + f*x)*Sinh[c + d*x])/(b^3*d) + (a*f*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^2*d^2) - (a*(e + f*x)*Sinh[c + d*x]^2)/(2*b^2*d) + ((e + f*x)*Sinh[c + d*x]^3)/(3*b*d)","A",18,11,32,0.3438,1,"{5579, 5446, 2633, 2635, 8, 3296, 2638, 5561, 2190, 2279, 2391}"
394,1,76,0,0.0966879,"\int \frac{\cosh (c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{a^2 \sinh (c+d x)}{b^3 d}-\frac{a^3 \log (a+b \sinh (c+d x))}{b^4 d}-\frac{a \sinh ^2(c+d x)}{2 b^2 d}+\frac{\sinh ^3(c+d x)}{3 b d}","\frac{a^2 \sinh (c+d x)}{b^3 d}-\frac{a^3 \log (a+b \sinh (c+d x))}{b^4 d}-\frac{a \sinh ^2(c+d x)}{2 b^2 d}+\frac{\sinh ^3(c+d x)}{3 b d}",1,"-((a^3*Log[a + b*Sinh[c + d*x]])/(b^4*d)) + (a^2*Sinh[c + d*x])/(b^3*d) - (a*Sinh[c + d*x]^2)/(2*b^2*d) + Sinh[c + d*x]^3/(3*b*d)","A",4,3,27,0.1111,1,"{2833, 12, 43}"
395,0,0,0,0.0829812,"\int \frac{\cosh (c+d x) \sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Cosh[c + d*x]*Sinh[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh (c+d x) \sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Cosh[c + d*x]*Sinh[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
396,1,1038,0,1.826679,"\int \frac{(e+f x)^3 \cosh ^2(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^2*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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,"(3*a^2*e*f^2*x)/(4*b^3*d^2) + (3*a^2*f^3*x^2)/(8*b^3*d^2) + (a^4*(e + f*x)^4)/(4*b^5*f) + (a^2*(e + f*x)^4)/(8*b^3*f) - (e + f*x)^4/(32*b*f) - (6*a^3*f^2*(e + f*x)*Cosh[c + d*x])/(b^4*d^3) - (4*a*f^2*(e + f*x)*Cosh[c + d*x])/(3*b^2*d^3) - (a^3*(e + f*x)^3*Cosh[c + d*x])/(b^4*d) - (3*a^2*f^3*Cosh[c + d*x]^2)/(8*b^3*d^4) - (3*a^2*f*(e + f*x)^2*Cosh[c + d*x]^2)/(4*b^3*d^2) - (2*a*f^2*(e + f*x)*Cosh[c + d*x]^3)/(9*b^2*d^3) - (a*(e + f*x)^3*Cosh[c + d*x]^3)/(3*b^2*d) - (3*f^3*Cosh[4*c + 4*d*x])/(1024*b*d^4) - (3*f*(e + f*x)^2*Cosh[4*c + 4*d*x])/(128*b*d^2) - (a^3*Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^5*d) + (a^3*Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^5*d) - (3*a^3*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^2) + (3*a^3*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^2) + (6*a^3*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^3) - (6*a^3*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^3) - (6*a^3*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^4) + (6*a^3*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^4) + (6*a^3*f^3*Sinh[c + d*x])/(b^4*d^4) + (14*a*f^3*Sinh[c + d*x])/(9*b^2*d^4) + (3*a^3*f*(e + f*x)^2*Sinh[c + d*x])/(b^4*d^2) + (2*a*f*(e + f*x)^2*Sinh[c + d*x])/(3*b^2*d^2) + (3*a^2*f^2*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^3*d^3) + (a^2*(e + f*x)^3*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^3*d) + (a*f*(e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b^2*d^2) + (2*a*f^3*Sinh[c + d*x]^3)/(27*b^2*d^4) + (3*f^2*(e + f*x)*Sinh[4*c + 4*d*x])/(256*b*d^3) + ((e + f*x)^3*Sinh[4*c + 4*d*x])/(32*b*d)","A",38,18,36,0.5000,1,"{5579, 5448, 3296, 2638, 5447, 3311, 2637, 2633, 32, 3310, 5565, 3322, 2264, 2190, 2531, 6609, 2282, 6589}"
397,1,755,0,1.513979,"\int \frac{(e+f x)^2 \cosh ^2(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{2 a^3 f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^5 d^2}+\frac{2 a^3 f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^5 d^3}+\frac{2 a^3 f (e+f x) \sinh (c+d x)}{b^4 d^2}-\frac{a^2 f (e+f x) \cosh ^2(c+d x)}{2 b^3 d^2}-\frac{2 a^3 f^2 \cosh (c+d x)}{b^4 d^3}+\frac{a^2 f^2 \sinh (c+d x) \cosh (c+d x)}{4 b^3 d^3}-\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{a^3 (e+f x)^2 \cosh (c+d x)}{b^4 d}+\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^4 (e+f x)^3}{3 b^5 f}+\frac{a^2 (e+f x)^3}{6 b^3 f}+\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{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{a (e+f x)^2 \cosh ^3(c+d x)}{3 b^2 d}-\frac{f (e+f x) \cosh (4 c+4 d x)}{64 b d^2}+\frac{f^2 \sinh (4 c+4 d x)}{256 b d^3}+\frac{(e+f x)^2 \sinh (4 c+4 d x)}{32 b d}-\frac{(e+f x)^3}{24 b f}","-\frac{2 a^3 f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^5 d^2}+\frac{2 a^3 f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^5 d^3}+\frac{2 a^3 f (e+f x) \sinh (c+d x)}{b^4 d^2}-\frac{a^2 f (e+f x) \cosh ^2(c+d x)}{2 b^3 d^2}-\frac{2 a^3 f^2 \cosh (c+d x)}{b^4 d^3}+\frac{a^2 f^2 \sinh (c+d x) \cosh (c+d x)}{4 b^3 d^3}-\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{a^3 (e+f x)^2 \cosh (c+d x)}{b^4 d}+\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^4 (e+f x)^3}{3 b^5 f}+\frac{a^2 (e+f x)^3}{6 b^3 f}+\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{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{a (e+f x)^2 \cosh ^3(c+d x)}{3 b^2 d}-\frac{f (e+f x) \cosh (4 c+4 d x)}{64 b d^2}+\frac{f^2 \sinh (4 c+4 d x)}{256 b d^3}+\frac{(e+f x)^2 \sinh (4 c+4 d x)}{32 b d}-\frac{(e+f x)^3}{24 b f}",1,"(a^2*f^2*x)/(4*b^3*d^2) + (a^4*(e + f*x)^3)/(3*b^5*f) + (a^2*(e + f*x)^3)/(6*b^3*f) - (e + f*x)^3/(24*b*f) - (2*a^3*f^2*Cosh[c + d*x])/(b^4*d^3) - (4*a*f^2*Cosh[c + d*x])/(9*b^2*d^3) - (a^3*(e + f*x)^2*Cosh[c + d*x])/(b^4*d) - (a^2*f*(e + f*x)*Cosh[c + d*x]^2)/(2*b^3*d^2) - (2*a*f^2*Cosh[c + d*x]^3)/(27*b^2*d^3) - (a*(e + f*x)^2*Cosh[c + d*x]^3)/(3*b^2*d) - (f*(e + f*x)*Cosh[4*c + 4*d*x])/(64*b*d^2) - (a^3*Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^5*d) + (a^3*Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^5*d) - (2*a^3*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^2) + (2*a^3*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^2) + (2*a^3*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^3) - (2*a^3*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^3) + (2*a^3*f*(e + f*x)*Sinh[c + d*x])/(b^4*d^2) + (4*a*f*(e + f*x)*Sinh[c + d*x])/(9*b^2*d^2) + (a^2*f^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^3*d^3) + (a^2*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^3*d) + (2*a*f*(e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x])/(9*b^2*d^2) + (f^2*Sinh[4*c + 4*d*x])/(256*b*d^3) + ((e + f*x)^2*Sinh[4*c + 4*d*x])/(32*b*d)","A",31,18,36,0.5000,1,"{5579, 5448, 3296, 2637, 5447, 3310, 2638, 3311, 32, 2635, 8, 5565, 3322, 2264, 2190, 2531, 2282, 6589}"
398,1,474,0,0.8645199,"\int \frac{(e+f x) \cosh ^2(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{a^3 f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^5 d^2}+\frac{a^3 f \sinh (c+d x)}{b^4 d^2}-\frac{a^2 f \cosh ^2(c+d x)}{4 b^3 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^3 (e+f x) \cosh (c+d x)}{b^4 d}+\frac{a^2 (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^3 d}+\frac{a^4 e x}{b^5}+\frac{a^2 e x}{2 b^3}+\frac{a^4 f x^2}{2 b^5}+\frac{a^2 f x^2}{4 b^3}+\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}","-\frac{a^3 f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^5 d^2}+\frac{a^3 f \sinh (c+d x)}{b^4 d^2}-\frac{a^2 f \cosh ^2(c+d x)}{4 b^3 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^3 (e+f x) \cosh (c+d x)}{b^4 d}+\frac{a^2 (e+f x) \sinh (c+d x) \cosh (c+d x)}{2 b^3 d}+\frac{a^4 e x}{b^5}+\frac{a^2 e x}{2 b^3}+\frac{a^4 f x^2}{2 b^5}+\frac{a^2 f x^2}{4 b^3}+\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,"(a^4*e*x)/b^5 + (a^2*e*x)/(2*b^3) + (a^4*f*x^2)/(2*b^5) + (a^2*f*x^2)/(4*b^3) - (e + f*x)^2/(16*b*f) - (a^3*(e + f*x)*Cosh[c + d*x])/(b^4*d) - (a^2*f*Cosh[c + d*x]^2)/(4*b^3*d^2) - (a*(e + f*x)*Cosh[c + d*x]^3)/(3*b^2*d) - (f*Cosh[4*c + 4*d*x])/(128*b*d^2) - (a^3*Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^5*d) + (a^3*Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^5*d) - (a^3*Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^5*d^2) + (a^3*Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^5*d^2) + (a^3*f*Sinh[c + d*x])/(b^4*d^2) + (a*f*Sinh[c + d*x])/(3*b^2*d^2) + (a^2*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^3*d) + (a*f*Sinh[c + d*x]^3)/(9*b^2*d^2) + ((e + f*x)*Sinh[4*c + 4*d*x])/(32*b*d)","A",24,14,34,0.4118,1,"{5579, 5448, 3296, 2638, 5447, 2633, 3310, 5565, 2637, 3322, 2264, 2190, 2279, 2391}"
399,1,184,0,0.79298,"\int \frac{\cosh ^2(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]^2*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{a \left(3 a^2+b^2\right) \cosh (c+d x)}{3 b^4 d}+\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{\left(4 a^2+b^2\right) \sinh (c+d x) \cosh (c+d x)}{8 b^3 d}+\frac{x \left(4 a^2 b^2+8 a^4-b^4\right)}{8 b^5}-\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}","-\frac{a \left(3 a^2+b^2\right) \cosh (c+d x)}{3 b^4 d}+\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{\left(4 a^2+b^2\right) \sinh (c+d x) \cosh (c+d x)}{8 b^3 d}+\frac{x \left(4 a^2 b^2+8 a^4-b^4\right)}{8 b^5}-\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,"((8*a^4 + 4*a^2*b^2 - b^4)*x)/(8*b^5) + (2*a^3*Sqrt[a^2 + b^2]*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b^5*d) - (a*(3*a^2 + b^2)*Cosh[c + d*x])/(3*b^4*d) + ((4*a^2 + b^2)*Cosh[c + d*x]*Sinh[c + d*x])/(8*b^3*d) - (a*Cosh[c + d*x]*Sinh[c + d*x]^2)/(3*b^2*d) + (Cosh[c + d*x]*Sinh[c + d*x]^3)/(4*b*d)","A",9,8,29,0.2759,1,"{2889, 3050, 3049, 3023, 2735, 2660, 618, 204}"
400,0,0,0,0.1270506,"\int \frac{\cosh ^2(c+d x) \sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Cosh[c + d*x]^2*Sinh[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh ^2(c+d x) \sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Cosh[c + d*x]^2*Sinh[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
401,1,1443,0,2.1869453,"\int \frac{(e+f x)^3 \cosh ^3(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^3*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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,"(-3*a^3*f^3*x)/(8*b^4*d^3) + (45*a*f^3*x)/(256*b^2*d^3) - (a^3*(e + f*x)^3)/(4*b^4*d) + (3*a*(e + f*x)^3)/(32*b^2*d) + (a^3*(a^2 + b^2)*(e + f*x)^4)/(4*b^6*f) - (6*a^4*f^3*Cosh[c + d*x])/(b^5*d^4) - (40*a^2*f^3*Cosh[c + d*x])/(9*b^3*d^4) + (3*f^3*Cosh[c + d*x])/(4*b*d^4) - (3*a^4*f*(e + f*x)^2*Cosh[c + d*x])/(b^5*d^2) - (2*a^2*f*(e + f*x)^2*Cosh[c + d*x])/(b^3*d^2) + (3*f*(e + f*x)^2*Cosh[c + d*x])/(8*b*d^2) - (9*a*f^2*(e + f*x)*Cosh[c + d*x]^2)/(32*b^2*d^3) - (2*a^2*f^3*Cosh[c + d*x]^3)/(27*b^3*d^4) - (a^2*f*(e + f*x)^2*Cosh[c + d*x]^3)/(3*b^3*d^2) - (3*a*f^2*(e + f*x)*Cosh[c + d*x]^4)/(32*b^2*d^3) - (a*(e + f*x)^3*Cosh[c + d*x]^4)/(4*b^2*d) - (f^3*Cosh[3*c + 3*d*x])/(216*b*d^4) - (f*(e + f*x)^2*Cosh[3*c + 3*d*x])/(48*b*d^2) - (3*f^3*Cosh[5*c + 5*d*x])/(5000*b*d^4) - (3*f*(e + f*x)^2*Cosh[5*c + 5*d*x])/(400*b*d^2) - (a^3*(a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^6*d) - (a^3*(a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^6*d) - (3*a^3*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^6*d^2) - (3*a^3*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^6*d^2) + (6*a^3*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^6*d^3) + (6*a^3*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^6*d^3) - (6*a^3*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^6*d^4) - (6*a^3*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^6*d^4) + (6*a^4*f^2*(e + f*x)*Sinh[c + d*x])/(b^5*d^3) + (40*a^2*f^2*(e + f*x)*Sinh[c + d*x])/(9*b^3*d^3) - (3*f^2*(e + f*x)*Sinh[c + d*x])/(4*b*d^3) + (a^4*(e + f*x)^3*Sinh[c + d*x])/(b^5*d) + (2*a^2*(e + f*x)^3*Sinh[c + d*x])/(3*b^3*d) - ((e + f*x)^3*Sinh[c + d*x])/(8*b*d) + (3*a^3*f^3*Cosh[c + d*x]*Sinh[c + d*x])/(8*b^4*d^4) + (45*a*f^3*Cosh[c + d*x]*Sinh[c + d*x])/(256*b^2*d^4) + (3*a^3*f*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^4*d^2) + (9*a*f*(e + f*x)^2*Cosh[c + d*x]*Sinh[c + d*x])/(32*b^2*d^2) + (2*a^2*f^2*(e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x])/(9*b^3*d^3) + (a^2*(e + f*x)^3*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b^3*d) + (3*a*f^3*Cosh[c + d*x]^3*Sinh[c + d*x])/(128*b^2*d^4) + (3*a*f*(e + f*x)^2*Cosh[c + d*x]^3*Sinh[c + d*x])/(16*b^2*d^2) - (3*a^3*f^2*(e + f*x)*Sinh[c + d*x]^2)/(4*b^4*d^3) - (a^3*(e + f*x)^3*Sinh[c + d*x]^2)/(2*b^4*d) + (f^2*(e + f*x)*Sinh[3*c + 3*d*x])/(72*b*d^3) + ((e + f*x)^3*Sinh[3*c + 3*d*x])/(48*b*d) + (3*f^2*(e + f*x)*Sinh[5*c + 5*d*x])/(1000*b*d^3) + ((e + f*x)^3*Sinh[5*c + 5*d*x])/(80*b*d)","A",55,18,36,0.5000,1,"{5579, 5448, 3296, 2638, 5447, 3311, 32, 2635, 8, 3310, 5565, 5446, 5561, 2190, 2531, 6609, 2282, 6589}"
402,1,1049,0,1.6234654,"\int \frac{(e+f x)^2 \cosh ^3(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^3*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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,"-(a^3*e*f*x)/(2*b^4*d) + (3*a*e*f*x)/(16*b^2*d) - (a^3*f^2*x^2)/(4*b^4*d) + (3*a*f^2*x^2)/(32*b^2*d) + (a^3*(a^2 + b^2)*(e + f*x)^3)/(3*b^6*f) - (2*a^4*f*(e + f*x)*Cosh[c + d*x])/(b^5*d^2) - (4*a^2*f*(e + f*x)*Cosh[c + d*x])/(3*b^3*d^2) + (f*(e + f*x)*Cosh[c + d*x])/(4*b*d^2) - (3*a*f^2*Cosh[c + d*x]^2)/(32*b^2*d^3) - (2*a^2*f*(e + f*x)*Cosh[c + d*x]^3)/(9*b^3*d^2) - (a*f^2*Cosh[c + d*x]^4)/(32*b^2*d^3) - (a*(e + f*x)^2*Cosh[c + d*x]^4)/(4*b^2*d) - (f*(e + f*x)*Cosh[3*c + 3*d*x])/(72*b*d^2) - (f*(e + f*x)*Cosh[5*c + 5*d*x])/(200*b*d^2) - (a^3*(a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^6*d) - (a^3*(a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^6*d) - (2*a^3*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^6*d^2) - (2*a^3*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^6*d^2) + (2*a^3*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^6*d^3) + (2*a^3*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^6*d^3) + (2*a^4*f^2*Sinh[c + d*x])/(b^5*d^3) + (14*a^2*f^2*Sinh[c + d*x])/(9*b^3*d^3) - (f^2*Sinh[c + d*x])/(4*b*d^3) + (a^4*(e + f*x)^2*Sinh[c + d*x])/(b^5*d) + (2*a^2*(e + f*x)^2*Sinh[c + d*x])/(3*b^3*d) - ((e + f*x)^2*Sinh[c + d*x])/(8*b*d) + (a^3*f*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(2*b^4*d^2) + (3*a*f*(e + f*x)*Cosh[c + d*x]*Sinh[c + d*x])/(16*b^2*d^2) + (a^2*(e + f*x)^2*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b^3*d) + (a*f*(e + f*x)*Cosh[c + d*x]^3*Sinh[c + d*x])/(8*b^2*d^2) - (a^3*f^2*Sinh[c + d*x]^2)/(4*b^4*d^3) - (a^3*(e + f*x)^2*Sinh[c + d*x]^2)/(2*b^4*d) + (2*a^2*f^2*Sinh[c + d*x]^3)/(27*b^3*d^3) + (f^2*Sinh[3*c + 3*d*x])/(216*b*d^3) + ((e + f*x)^2*Sinh[3*c + 3*d*x])/(48*b*d) + (f^2*Sinh[5*c + 5*d*x])/(1000*b*d^3) + ((e + f*x)^2*Sinh[5*c + 5*d*x])/(80*b*d)","A",40,15,36,0.4167,1,"{5579, 5448, 3296, 2637, 5447, 3310, 3311, 2633, 5565, 5446, 5561, 2190, 2531, 2282, 6589}"
403,1,641,0,0.9442584,"\int \frac{(e+f x) \cosh ^3(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^3*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{a^3 f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^6 d^2}-\frac{a^2 f \cosh ^3(c+d x)}{9 b^3 d^2}-\frac{a^4 f \cosh (c+d x)}{b^5 d^2}-\frac{2 a^2 f \cosh (c+d x)}{3 b^3 d^2}+\frac{a^3 f \sinh (c+d x) \cosh (c+d x)}{4 b^4 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 (e+f x) \sinh ^2(c+d x)}{2 b^4 d}+\frac{a^4 (e+f x) \sinh (c+d x)}{b^5 d}+\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 x}{4 b^4 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}","-\frac{a^3 f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^6 d^2}-\frac{a^2 f \cosh ^3(c+d x)}{9 b^3 d^2}-\frac{a^4 f \cosh (c+d x)}{b^5 d^2}-\frac{2 a^2 f \cosh (c+d x)}{3 b^3 d^2}+\frac{a^3 f \sinh (c+d x) \cosh (c+d x)}{4 b^4 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 (e+f x) \sinh ^2(c+d x)}{2 b^4 d}+\frac{a^4 (e+f x) \sinh (c+d x)}{b^5 d}+\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 x}{4 b^4 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,"-(a^3*f*x)/(4*b^4*d) + (3*a*f*x)/(32*b^2*d) + (a^3*(a^2 + b^2)*(e + f*x)^2)/(2*b^6*f) - (a^4*f*Cosh[c + d*x])/(b^5*d^2) - (2*a^2*f*Cosh[c + d*x])/(3*b^3*d^2) + (f*Cosh[c + d*x])/(8*b*d^2) - (a^2*f*Cosh[c + d*x]^3)/(9*b^3*d^2) - (a*(e + f*x)*Cosh[c + d*x]^4)/(4*b^2*d) - (f*Cosh[3*c + 3*d*x])/(144*b*d^2) - (f*Cosh[5*c + 5*d*x])/(400*b*d^2) - (a^3*(a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^6*d) - (a^3*(a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^6*d) - (a^3*(a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^6*d^2) - (a^3*(a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^6*d^2) + (a^4*(e + f*x)*Sinh[c + d*x])/(b^5*d) + (2*a^2*(e + f*x)*Sinh[c + d*x])/(3*b^3*d) - ((e + f*x)*Sinh[c + d*x])/(8*b*d) + (a^3*f*Cosh[c + d*x]*Sinh[c + d*x])/(4*b^4*d^2) + (3*a*f*Cosh[c + d*x]*Sinh[c + d*x])/(32*b^2*d^2) + (a^2*(e + f*x)*Cosh[c + d*x]^2*Sinh[c + d*x])/(3*b^3*d) + (a*f*Cosh[c + d*x]^3*Sinh[c + d*x])/(16*b^2*d^2) - (a^3*(e + f*x)*Sinh[c + d*x]^2)/(2*b^4*d) + ((e + f*x)*Sinh[3*c + 3*d*x])/(48*b*d) + ((e + f*x)*Sinh[5*c + 5*d*x])/(80*b*d)","A",31,14,34,0.4118,1,"{5579, 5448, 3296, 2638, 5447, 2635, 8, 3310, 5565, 5446, 5561, 2190, 2279, 2391}"
404,1,141,0,0.2234345,"\int \frac{\cosh ^3(c+d x) \sinh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]^3*Sinh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{\left(a^2+b^2\right) \sinh ^3(c+d x)}{3 b^3 d}-\frac{a \left(a^2+b^2\right) \sinh ^2(c+d x)}{2 b^4 d}+\frac{a^2 \left(a^2+b^2\right) \sinh (c+d x)}{b^5 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}","\frac{\left(a^2+b^2\right) \sinh ^3(c+d x)}{3 b^3 d}-\frac{a \left(a^2+b^2\right) \sinh ^2(c+d x)}{2 b^4 d}+\frac{a^2 \left(a^2+b^2\right) \sinh (c+d x)}{b^5 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,"-((a^3*(a^2 + b^2)*Log[a + b*Sinh[c + d*x]])/(b^6*d)) + (a^2*(a^2 + b^2)*Sinh[c + d*x])/(b^5*d) - (a*(a^2 + b^2)*Sinh[c + d*x]^2)/(2*b^4*d) + ((a^2 + b^2)*Sinh[c + d*x]^3)/(3*b^3*d) - (a*Sinh[c + d*x]^4)/(4*b^2*d) + Sinh[c + d*x]^5/(5*b*d)","A",4,3,29,0.1034,1,"{2837, 12, 894}"
405,0,0,0,0.1266845,"\int \frac{\cosh ^3(c+d x) \sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Cosh[c + d*x]^3*Sinh[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh ^3(c+d x) \sinh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Cosh[c + d*x]^3*Sinh[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
406,1,1519,0,2.1535174,"\int \frac{(e+f x)^3 \sinh ^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sinh[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(3,-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{PolyLog}\left(3,i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-e^{2 (c+d x)}\right) a^3}{2 b^2 \left(a^2+b^2\right) d^3}-\frac{6 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right) a^2}{b^3 d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a}{2 b^2 d^2}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-e^{2 (c+d x)}\right) a}{2 b^2 d^3}-\frac{3 f^3 \text{PolyLog}\left(4,-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{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right)}{b d^3}+\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{b d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,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}","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(3,-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{PolyLog}\left(3,i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-e^{2 (c+d x)}\right) a^3}{2 b^2 \left(a^2+b^2\right) d^3}-\frac{6 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right) a^2}{b^3 d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a}{2 b^2 d^2}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-e^{2 (c+d x)}\right) a}{2 b^2 d^3}-\frac{3 f^3 \text{PolyLog}\left(4,-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{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right)}{b d^3}+\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{b d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,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,"(a*(e + f*x)^4)/(4*b^2*f) + (2*a^2*(e + f*x)^3*ArcTan[E^(c + d*x)])/(b^3*d) - (2*(e + f*x)^3*ArcTan[E^(c + d*x)])/(b*d) - (2*a^4*(e + f*x)^3*ArcTan[E^(c + d*x)])/(b^3*(a^2 + b^2)*d) - (6*f^3*Cosh[c + d*x])/(b*d^4) - (3*f*(e + f*x)^2*Cosh[c + d*x])/(b*d^2) - (a^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*(a^2 + b^2)*d) - (a^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*(a^2 + b^2)*d) - (a*(e + f*x)^3*Log[1 + E^(2*(c + d*x))])/(b^2*d) + (a^3*(e + f*x)^3*Log[1 + E^(2*(c + d*x))])/(b^2*(a^2 + b^2)*d) - ((3*I)*a^2*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(b^3*d^2) + ((3*I)*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^2) + ((3*I)*a^4*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^2) + ((3*I)*a^2*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(b^3*d^2) - ((3*I)*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(b*d^2) - ((3*I)*a^4*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^2) - (3*a^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^2) - (3*a^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^2) - (3*a*f*(e + f*x)^2*PolyLog[2, -E^(2*(c + d*x))])/(2*b^2*d^2) + (3*a^3*f*(e + f*x)^2*PolyLog[2, -E^(2*(c + d*x))])/(2*b^2*(a^2 + b^2)*d^2) + ((6*I)*a^2*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(b^3*d^3) - ((6*I)*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(b*d^3) - ((6*I)*a^4*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^3) - ((6*I)*a^2*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(b^3*d^3) + ((6*I)*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(b*d^3) + ((6*I)*a^4*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^3) + (6*a^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^3) + (6*a^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^3) + (3*a*f^2*(e + f*x)*PolyLog[3, -E^(2*(c + d*x))])/(2*b^2*d^3) - (3*a^3*f^2*(e + f*x)*PolyLog[3, -E^(2*(c + d*x))])/(2*b^2*(a^2 + b^2)*d^3) - ((6*I)*a^2*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(b^3*d^4) + ((6*I)*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(b*d^4) + ((6*I)*a^4*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^4) + ((6*I)*a^2*f^3*PolyLog[4, I*E^(c + d*x)])/(b^3*d^4) - ((6*I)*f^3*PolyLog[4, I*E^(c + d*x)])/(b*d^4) - ((6*I)*a^4*f^3*PolyLog[4, I*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^4) - (6*a^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^4) - (6*a^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^4) - (3*a*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*b^2*d^4) + (3*a^3*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*b^2*(a^2 + b^2)*d^4) + (6*f^2*(e + f*x)*Sinh[c + d*x])/(b*d^3) + ((e + f*x)^3*Sinh[c + d*x])/(b*d)","A",61,15,34,0.4412,1,"{5581, 5449, 3296, 2638, 4180, 2531, 6609, 2282, 6589, 3718, 2190, 5567, 5573, 5561, 6742}"
407,1,1067,0,1.690943,"\int \frac{(e+f x)^2 \sinh ^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sinh[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a}{b^2 d^2}+\frac{f^2 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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}","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^3}{b^2 \left(a^2+b^2\right) d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a}{b^2 d^2}+\frac{f^2 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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,"(a*(e + f*x)^3)/(3*b^2*f) + (2*a^2*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b^3*d) - (2*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b*d) - (2*a^4*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b^3*(a^2 + b^2)*d) - (2*f*(e + f*x)*Cosh[c + d*x])/(b*d^2) - (a^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*(a^2 + b^2)*d) - (a^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*(a^2 + b^2)*d) - (a*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b^2*d) + (a^3*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b^2*(a^2 + b^2)*d) - ((2*I)*a^2*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b^3*d^2) + ((2*I)*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^2) + ((2*I)*a^4*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^2) + ((2*I)*a^2*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b^3*d^2) - ((2*I)*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b*d^2) - ((2*I)*a^4*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^2) - (2*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^2) - (2*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^2) - (a*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b^2*d^2) + (a^3*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b^2*(a^2 + b^2)*d^2) + ((2*I)*a^2*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b^3*d^3) - ((2*I)*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b*d^3) - ((2*I)*a^4*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^3) - ((2*I)*a^2*f^2*PolyLog[3, I*E^(c + d*x)])/(b^3*d^3) + ((2*I)*f^2*PolyLog[3, I*E^(c + d*x)])/(b*d^3) + ((2*I)*a^4*f^2*PolyLog[3, I*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^3) + (2*a^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^3) + (2*a^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^3) + (a*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*b^2*d^3) - (a^3*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*b^2*(a^2 + b^2)*d^3) + (2*f^2*Sinh[c + d*x])/(b*d^3) + ((e + f*x)^2*Sinh[c + d*x])/(b*d)","A",50,14,34,0.4118,1,"{5581, 5449, 3296, 2637, 4180, 2531, 2282, 6589, 3718, 2190, 5567, 5573, 5561, 6742}"
408,1,631,0,0.9570455,"\int \frac{(e+f x) \sinh ^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sinh[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{i a^4 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b^3 d^2 \left(a^2+b^2\right)}-\frac{i a^4 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b^3 d^2 \left(a^2+b^2\right)}-\frac{a^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2 \left(a^2+b^2\right)}+\frac{a^3 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 b^2 d^2 \left(a^2+b^2\right)}-\frac{i a^2 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b^3 d^2}+\frac{i a^2 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b^3 d^2}-\frac{a f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 b^2 d^2}+\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}-\frac{i f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b 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^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{2 a^4 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^3 d \left(a^2+b^2\right)}+\frac{2 a^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^3 d}-\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{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}","\frac{i a^4 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b^3 d^2 \left(a^2+b^2\right)}-\frac{i a^4 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b^3 d^2 \left(a^2+b^2\right)}-\frac{a^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{b^2 d^2 \left(a^2+b^2\right)}+\frac{a^3 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 b^2 d^2 \left(a^2+b^2\right)}-\frac{i a^2 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b^3 d^2}+\frac{i a^2 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b^3 d^2}-\frac{a f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 b^2 d^2}+\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}-\frac{i f \text{PolyLog}\left(2,i e^{c+d x}\right)}{b 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^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{2 a^4 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^3 d \left(a^2+b^2\right)}+\frac{2 a^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{b^3 d}-\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{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,"(a*(e + f*x)^2)/(2*b^2*f) + (2*a^2*(e + f*x)*ArcTan[E^(c + d*x)])/(b^3*d) - (2*(e + f*x)*ArcTan[E^(c + d*x)])/(b*d) - (2*a^4*(e + f*x)*ArcTan[E^(c + d*x)])/(b^3*(a^2 + b^2)*d) - (f*Cosh[c + d*x])/(b*d^2) - (a^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b^2*(a^2 + b^2)*d) - (a^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b^2*(a^2 + b^2)*d) - (a*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(b^2*d) + (a^3*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(b^2*(a^2 + b^2)*d) - (I*a^2*f*PolyLog[2, (-I)*E^(c + d*x)])/(b^3*d^2) + (I*f*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^2) + (I*a^4*f*PolyLog[2, (-I)*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^2) + (I*a^2*f*PolyLog[2, I*E^(c + d*x)])/(b^3*d^2) - (I*f*PolyLog[2, I*E^(c + d*x)])/(b*d^2) - (I*a^4*f*PolyLog[2, I*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^2) - (a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^2) - (a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b^2*(a^2 + b^2)*d^2) - (a*f*PolyLog[2, -E^(2*(c + d*x))])/(2*b^2*d^2) + (a^3*f*PolyLog[2, -E^(2*(c + d*x))])/(2*b^2*(a^2 + b^2)*d^2) + ((e + f*x)*Sinh[c + d*x])/(b*d)","A",39,13,32,0.4062,1,"{5581, 5449, 3296, 2638, 4180, 2279, 2391, 3718, 2190, 5567, 5573, 5561, 6742}"
409,1,89,0,0.1958581,"\int \frac{\sinh ^2(c+d x) \tanh (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Sinh[c + d*x]^2*Tanh[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{a^3 \log (a+b \sinh (c+d x))}{b^2 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{\sinh (c+d x)}{b d}","-\frac{a^3 \log (a+b \sinh (c+d x))}{b^2 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{\sinh (c+d x)}{b d}",1,"-((b*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d)) - (a*Log[Cosh[c + d*x]])/((a^2 + b^2)*d) - (a^3*Log[a + b*Sinh[c + d*x]])/(b^2*(a^2 + b^2)*d) + Sinh[c + d*x]/(b*d)","A",7,6,27,0.2222,1,"{2837, 12, 1629, 635, 203, 260}"
410,0,0,0,0.0891297,"\int \frac{\sinh ^2(c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Sinh[c + d*x]^2*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\sinh ^2(c+d x) \tanh (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Sinh[c + d*x]^2*Tanh[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
411,1,1294,0,2.4546418,"\int \frac{(e+f x)^3 \sinh (c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Sinh[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}-\frac{3 f^3 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{PolyLog}\left(3,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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^2}{b^3 d^3}+\frac{3 f^3 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) a}{b^2 d^3}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) a}{b^2 d^3}-\frac{6 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right) a}{b^2 d^4}+\frac{6 i f^3 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b d^3}-\frac{3 f^3 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 b d^4}-\frac{(e+f x)^3 \tanh (c+d x)}{b 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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}-\frac{3 f^3 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{PolyLog}\left(3,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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^2}{b^3 d^3}+\frac{3 f^3 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) a}{b^2 d^3}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) a}{b^2 d^3}-\frac{6 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right) a}{b^2 d^4}+\frac{6 i f^3 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b d^3}-\frac{3 f^3 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 b d^4}-\frac{(e+f x)^3 \tanh (c+d x)}{b d}",1,"(a^2*(e + f*x)^3)/(b^3*d) - (e + f*x)^3/(b*d) - (a^4*(e + f*x)^3)/(b^3*(a^2 + b^2)*d) + (e + f*x)^4/(4*b*f) - (6*a*f*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b^2*d^2) + (6*a^3*f*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) - (a^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)^(3/2)*d) + (a^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)^(3/2)*d) - (3*a^2*f*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b^3*d^2) + (3*f*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b*d^2) + (3*a^4*f*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(b^3*(a^2 + b^2)*d^2) + ((6*I)*a*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*d^3) - ((6*I)*a^3*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^3) - ((6*I)*a*f^2*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b^2*d^3) + ((6*I)*a^3*f^2*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^3) - (3*a^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^2) + (3*a^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^2) - (3*a^2*f^2*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b^3*d^3) + (3*f^2*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b*d^3) + (3*a^4*f^2*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(b^3*(a^2 + b^2)*d^3) - ((6*I)*a*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(b^2*d^4) + ((6*I)*a^3*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^4) + ((6*I)*a*f^3*PolyLog[3, I*E^(c + d*x)])/(b^2*d^4) - ((6*I)*a^3*f^3*PolyLog[3, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^4) + (6*a^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) - (6*a^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) + (3*a^2*f^3*PolyLog[3, -E^(2*(c + d*x))])/(2*b^3*d^4) - (3*f^3*PolyLog[3, -E^(2*(c + d*x))])/(2*b*d^4) - (3*a^4*f^3*PolyLog[3, -E^(2*(c + d*x))])/(2*b^3*(a^2 + b^2)*d^4) - (6*a^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^4) + (6*a^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^4) + (a*(e + f*x)^3*Sech[c + d*x])/(b^2*d) - (a^3*(e + f*x)^3*Sech[c + d*x])/(b^2*(a^2 + b^2)*d) + (a^2*(e + f*x)^3*Tanh[c + d*x])/(b^3*d) - ((e + f*x)^3*Tanh[c + d*x])/(b*d) - (a^4*(e + f*x)^3*Tanh[c + d*x])/(b^3*(a^2 + b^2)*d)","A",53,18,34,0.5294,1,"{5581, 3720, 3718, 2190, 2531, 2282, 6589, 32, 5567, 5451, 4180, 5583, 4184, 5573, 3322, 2264, 6609, 6742}"
412,1,904,0,1.8213721,"\int \frac{(e+f x)^2 \sinh (c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Sinh[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) a}{b^2 d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,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{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b d^3}-\frac{(e+f x)^2 \tanh (c+d x)}{b d}","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^3}{b^2 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) a}{b^2 d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,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{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{b d^3}-\frac{(e+f x)^2 \tanh (c+d x)}{b d}",1,"(a^2*(e + f*x)^2)/(b^3*d) - (e + f*x)^2/(b*d) - (a^4*(e + f*x)^2)/(b^3*(a^2 + b^2)*d) + (e + f*x)^3/(3*b*f) - (4*a*f*(e + f*x)*ArcTan[E^(c + d*x)])/(b^2*d^2) + (4*a^3*f*(e + f*x)*ArcTan[E^(c + d*x)])/(b^2*(a^2 + b^2)*d^2) - (a^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)^(3/2)*d) + (a^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)^(3/2)*d) - (2*a^2*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(b^3*d^2) + (2*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(b*d^2) + (2*a^4*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(b^3*(a^2 + b^2)*d^2) + ((2*I)*a*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*d^3) - ((2*I)*a^3*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^3) - ((2*I)*a*f^2*PolyLog[2, I*E^(c + d*x)])/(b^2*d^3) + ((2*I)*a^3*f^2*PolyLog[2, I*E^(c + d*x)])/(b^2*(a^2 + b^2)*d^3) - (2*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^2) + (2*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^2) - (a^2*f^2*PolyLog[2, -E^(2*(c + d*x))])/(b^3*d^3) + (f^2*PolyLog[2, -E^(2*(c + d*x))])/(b*d^3) + (a^4*f^2*PolyLog[2, -E^(2*(c + d*x))])/(b^3*(a^2 + b^2)*d^3) + (2*a^3*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*a^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^3) + (a*(e + f*x)^2*Sech[c + d*x])/(b^2*d) - (a^3*(e + f*x)^2*Sech[c + d*x])/(b^2*(a^2 + b^2)*d) + (a^2*(e + f*x)^2*Tanh[c + d*x])/(b^3*d) - ((e + f*x)^2*Tanh[c + d*x])/(b*d) - (a^4*(e + f*x)^2*Tanh[c + d*x])/(b^3*(a^2 + b^2)*d)","A",44,19,34,0.5588,1,"{5581, 3720, 3718, 2190, 2279, 2391, 32, 5567, 5451, 4180, 5583, 4184, 5573, 3322, 2264, 2531, 2282, 6589, 6742}"
413,1,454,0,0.8917631,"\int \frac{(e+f x) \sinh (c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Sinh[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{a^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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^4 f \log (\cosh (c+d x))}{b^3 d^2 \left(a^2+b^2\right)}-\frac{a^2 f \log (\cosh (c+d x))}{b^3 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 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^4 (e+f x) \tanh (c+d x)}{b^3 d \left(a^2+b^2\right)}+\frac{a^2 (e+f x) \tanh (c+d x)}{b^3 d}-\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}","-\frac{a^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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^4 f \log (\cosh (c+d x))}{b^3 d^2 \left(a^2+b^2\right)}-\frac{a^2 f \log (\cosh (c+d x))}{b^3 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 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^4 (e+f x) \tanh (c+d x)}{b^3 d \left(a^2+b^2\right)}+\frac{a^2 (e+f x) \tanh (c+d x)}{b^3 d}-\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,"(e*x)/b + (f*x^2)/(2*b) - (a*f*ArcTan[Sinh[c + d*x]])/(b^2*d^2) + (a^3*f*ArcTan[Sinh[c + d*x]])/(b^2*(a^2 + b^2)*d^2) - (a^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)^(3/2)*d) + (a^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(b*(a^2 + b^2)^(3/2)*d) - (a^2*f*Log[Cosh[c + d*x]])/(b^3*d^2) + (f*Log[Cosh[c + d*x]])/(b*d^2) + (a^4*f*Log[Cosh[c + d*x]])/(b^3*(a^2 + b^2)*d^2) - (a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^2) + (a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(b*(a^2 + b^2)^(3/2)*d^2) + (a*(e + f*x)*Sech[c + d*x])/(b^2*d) - (a^3*(e + f*x)*Sech[c + d*x])/(b^2*(a^2 + b^2)*d) + (a^2*(e + f*x)*Tanh[c + d*x])/(b^3*d) - ((e + f*x)*Tanh[c + d*x])/(b*d) - (a^4*(e + f*x)*Tanh[c + d*x])/(b^3*(a^2 + b^2)*d)","A",25,15,32,0.4688,1,"{5581, 3720, 3475, 5567, 5451, 3770, 5583, 4184, 5573, 3322, 2264, 2190, 2279, 2391, 6742}"
414,1,121,0,0.20893,"\int \frac{\sinh (c+d x) \tanh ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Sinh[c + d*x]*Tanh[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\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}}-\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}}-\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}",1,"(a^2*x)/(b*(a^2 + b^2)) + (b*x)/(a^2 + b^2) + (2*a^3*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(b*(a^2 + b^2)^(3/2)*d) + (a*Sech[c + d*x])/((a^2 + b^2)*d) - (b*Tanh[c + d*x])/((a^2 + b^2)*d)","A",9,8,27,0.2963,1,"{2902, 2606, 8, 3473, 2735, 2660, 618, 204}"
415,0,0,0,0.0811154,"\int \frac{\sinh (c+d x) \tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Sinh[c + d*x]*Tanh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\sinh (c+d x) \tanh ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Sinh[c + d*x]*Tanh[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
416,1,1479,0,2.4532354,"\int \frac{(e+f x)^2 \tanh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Tanh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(2,i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^2}-\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^3}+\frac{i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}+\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}+\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3}-\frac{i f^2 \text{PolyLog}\left(3,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}","-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(2,i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^2}-\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^3}+\frac{i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right) a^4}{b^3 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) a^3}{\left(a^2+b^2\right)^2 d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) a^2}{b^3 d^2}+\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) a^2}{b^3 d^3}-\frac{i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-i e^{c+d x}\right)}{b d^2}+\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{b d^2}+\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{b d^3}-\frac{i f^2 \text{PolyLog}\left(3,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,"(a^2*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b^3*d) + ((e + f*x)^2*ArcTan[E^(c + d*x)])/(b*d) - (2*a^4*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b*(a^2 + b^2)^2*d) - (a^4*(e + f*x)^2*ArcTan[E^(c + d*x)])/(b^3*(a^2 + b^2)*d) - (a^2*f^2*ArcTan[Sinh[c + d*x]])/(b^3*d^3) + (f^2*ArcTan[Sinh[c + d*x]])/(b*d^3) + (a^4*f^2*ArcTan[Sinh[c + d*x]])/(b^3*(a^2 + b^2)*d^3) - (a^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) - (a^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) + (a^3*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)^2*d) + (a*f^2*Log[Cosh[c + d*x]])/(b^2*d^3) - (a^3*f^2*Log[Cosh[c + d*x]])/(b^2*(a^2 + b^2)*d^3) - (I*a^2*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b^3*d^2) - (I*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^2) + ((2*I)*a^4*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)^2*d^2) + (I*a^4*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^2) + (I*a^2*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b^3*d^2) + (I*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b*d^2) - ((2*I)*a^4*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b*(a^2 + b^2)^2*d^2) - (I*a^4*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^2) - (2*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) - (2*a^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) + (a^3*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/((a^2 + b^2)^2*d^2) + (I*a^2*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b^3*d^3) + (I*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b*d^3) - ((2*I)*a^4*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)^2*d^3) - (I*a^4*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^3) - (I*a^2*f^2*PolyLog[3, I*E^(c + d*x)])/(b^3*d^3) - (I*f^2*PolyLog[3, I*E^(c + d*x)])/(b*d^3) + ((2*I)*a^4*f^2*PolyLog[3, I*E^(c + d*x)])/(b*(a^2 + b^2)^2*d^3) + (I*a^4*f^2*PolyLog[3, I*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^3) + (2*a^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^3) + (2*a^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^3) - (a^3*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*(a^2 + b^2)^2*d^3) + (a^2*f*(e + f*x)*Sech[c + d*x])/(b^3*d^2) - (f*(e + f*x)*Sech[c + d*x])/(b*d^2) - (a^4*f*(e + f*x)*Sech[c + d*x])/(b^3*(a^2 + b^2)*d^2) + (a*(e + f*x)^2*Sech[c + d*x]^2)/(2*b^2*d) - (a^3*(e + f*x)^2*Sech[c + d*x]^2)/(2*b^2*(a^2 + b^2)*d) - (a*f*(e + f*x)*Tanh[c + d*x])/(b^2*d^2) + (a^3*f*(e + f*x)*Tanh[c + d*x])/(b^2*(a^2 + b^2)*d^2) + (a^2*(e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*b^3*d) - ((e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*b*d) - (a^4*(e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*b^3*(a^2 + b^2)*d)","A",71,17,28,0.6071,1,"{5567, 5455, 4180, 2531, 2282, 6589, 4186, 3770, 5583, 5451, 4184, 3475, 5573, 5561, 2190, 6742, 3718}"
417,1,894,0,1.4152439,"\int \frac{(e+f x) \tanh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Tanh[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-i e^{c+d x}\right) a^4}{2 b^3 \left(a^2+b^2\right) d^2}+\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^2}-\frac{i f \text{PolyLog}\left(2,i e^{c+d x}\right) a^4}{2 b^3 \left(a^2+b^2\right) d^2}-\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^2}{2 b^3 d^2}+\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-i e^{c+d x}\right)}{2 b d^2}+\frac{i f \text{PolyLog}\left(2,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}","-\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{PolyLog}\left(2,-i e^{c+d x}\right) a^4}{2 b^3 \left(a^2+b^2\right) d^2}+\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right) a^4}{b \left(a^2+b^2\right)^2 d^2}-\frac{i f \text{PolyLog}\left(2,i e^{c+d x}\right) a^4}{2 b^3 \left(a^2+b^2\right) d^2}-\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) a^2}{2 b^3 d^2}+\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-i e^{c+d x}\right)}{2 b d^2}+\frac{i f \text{PolyLog}\left(2,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,"(a^2*(e + f*x)*ArcTan[E^(c + d*x)])/(b^3*d) + ((e + f*x)*ArcTan[E^(c + d*x)])/(b*d) - (2*a^4*(e + f*x)*ArcTan[E^(c + d*x)])/(b*(a^2 + b^2)^2*d) - (a^4*(e + f*x)*ArcTan[E^(c + d*x)])/(b^3*(a^2 + b^2)*d) - (a^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) - (a^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/((a^2 + b^2)^2*d) + (a^3*(e + f*x)*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)^2*d) - ((I/2)*a^2*f*PolyLog[2, (-I)*E^(c + d*x)])/(b^3*d^2) - ((I/2)*f*PolyLog[2, (-I)*E^(c + d*x)])/(b*d^2) + (I*a^4*f*PolyLog[2, (-I)*E^(c + d*x)])/(b*(a^2 + b^2)^2*d^2) + ((I/2)*a^4*f*PolyLog[2, (-I)*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^2) + ((I/2)*a^2*f*PolyLog[2, I*E^(c + d*x)])/(b^3*d^2) + ((I/2)*f*PolyLog[2, I*E^(c + d*x)])/(b*d^2) - (I*a^4*f*PolyLog[2, I*E^(c + d*x)])/(b*(a^2 + b^2)^2*d^2) - ((I/2)*a^4*f*PolyLog[2, I*E^(c + d*x)])/(b^3*(a^2 + b^2)*d^2) - (a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) - (a^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/((a^2 + b^2)^2*d^2) + (a^3*f*PolyLog[2, -E^(2*(c + d*x))])/(2*(a^2 + b^2)^2*d^2) + (a^2*f*Sech[c + d*x])/(2*b^3*d^2) - (f*Sech[c + d*x])/(2*b*d^2) - (a^4*f*Sech[c + d*x])/(2*b^3*(a^2 + b^2)*d^2) + (a*(e + f*x)*Sech[c + d*x]^2)/(2*b^2*d) - (a^3*(e + f*x)*Sech[c + d*x]^2)/(2*b^2*(a^2 + b^2)*d) - (a*f*Tanh[c + d*x])/(2*b^2*d^2) + (a^3*f*Tanh[c + d*x])/(2*b^2*(a^2 + b^2)*d^2) + (a^2*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*b^3*d) - ((e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*b*d) - (a^4*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*b^3*(a^2 + b^2)*d)","A",55,15,26,0.5769,1,"{5567, 5455, 4180, 2279, 2391, 4185, 5583, 5451, 3767, 8, 5573, 5561, 2190, 6742, 3718}"
418,1,120,0,0.2011827,"\int \frac{\tanh ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Tanh[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","-\frac{a^3 \log (a+b \sinh (c+d x))}{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{a^3 \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{a^3 \log (a+b \sinh (c+d x))}{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{a^3 \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,"(b*(3*a^2 + b^2)*ArcTan[Sinh[c + d*x]])/(2*(a^2 + b^2)^2*d) + (a^3*Log[Cosh[c + d*x]])/((a^2 + b^2)^2*d) - (a^3*Log[a + b*Sinh[c + d*x]])/((a^2 + b^2)^2*d) + (Sech[c + d*x]^2*(a - b*Sinh[c + d*x]))/(2*(a^2 + b^2)*d)","A",7,6,21,0.2857,1,"{2721, 1647, 801, 635, 203, 260}"
419,0,0,0,0.0757226,"\int \frac{\tanh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[Tanh[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\tanh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\tanh ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][Tanh[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
420,1,451,0,0.7699985,"\int \frac{(e+f x)^3 \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2}-\frac{6 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^4}-\frac{6 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^4}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^2}+\frac{3 f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a d^4}-\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{(e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a d}","\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2}-\frac{6 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^4}-\frac{6 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^4}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^2}+\frac{3 f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a d^4}-\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{(e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a d}",1,"-(((e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*d)) - ((e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*d) + ((e + f*x)^3*Log[1 - E^(2*(c + d*x))])/(a*d) - (3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*d^2) - (3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*d^2) + (3*f*(e + f*x)^2*PolyLog[2, E^(2*(c + d*x))])/(2*a*d^2) + (6*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*d^3) + (6*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*d^3) - (3*f^2*(e + f*x)*PolyLog[3, E^(2*(c + d*x))])/(2*a*d^3) - (6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*d^4) - (6*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*d^4) + (3*f^3*PolyLog[4, E^(2*(c + d*x))])/(4*a*d^4)","A",18,8,26,0.3077,1,"{5569, 3716, 2190, 2531, 6609, 2282, 6589, 5561}"
421,1,325,0,0.6538681,"\int \frac{(e+f x)^2 \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 f (e+f x) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{2 f (e+f x) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^3}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^3}-\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{(e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a d}","-\frac{2 f (e+f x) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{2 f (e+f x) \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^3}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^3}-\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{(e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a d}",1,"-(((e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*d)) - ((e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*d) + ((e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a*d) - (2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*d^2) - (2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*d^2) + (f*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a*d^2) + (2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*d^3) + (2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*d^3) - (f^2*PolyLog[3, E^(2*(c + d*x))])/(2*a*d^3)","A",15,7,26,0.2692,1,"{5569, 3716, 2190, 2531, 2282, 6589, 5561}"
422,1,205,0,0.3800619,"\int \frac{(e+f x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2}+\frac{f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 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{(e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d}","-\frac{f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a d^2}-\frac{f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2}+\frac{f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 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{(e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a d}",1,"-(((e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*d)) - ((e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*d) + ((e + f*x)*Log[1 - E^(2*(c + d*x))])/(a*d) - (f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*d^2) - (f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*d^2) + (f*PolyLog[2, E^(2*(c + d*x))])/(2*a*d^2)","A",12,6,24,0.2500,1,"{5569, 3716, 2190, 2279, 2391, 5561}"
423,1,34,0,0.0473075,"\int \frac{\coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Coth[c + d*x]/(a + b*Sinh[c + d*x]),x]","\frac{\log (\sinh (c+d x))}{a d}-\frac{\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]]/(a*d) - Log[a + b*Sinh[c + d*x]]/(a*d)","A",4,4,19,0.2105,1,"{2721, 36, 29, 31}"
424,0,0,0,0.049565,"\int \frac{\coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Coth[c + d*x]/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
425,1,638,0,1.2752051,"\int \frac{(e+f x)^3 \cosh (c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^3}-\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^2}-\frac{6 f^3 \sqrt{a^2+b^2} \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^4}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{6 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}-\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{2 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{(e+f x)^4}{4 b f}","\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^3}-\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^2}-\frac{6 f^3 \sqrt{a^2+b^2} \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^4}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{6 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}-\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{2 (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{(e+f x)^4}{4 b f}",1,"(e + f*x)^4/(4*b*f) - (2*(e + f*x)^3*ArcTanh[E^(c + d*x)])/(a*d) - (Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*b*d) + (Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*b*d) - (3*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(a*d^2) + (3*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(a*d^2) - (3*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b*d^2) + (3*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b*d^2) + (6*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a*d^3) - (6*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a*d^3) + (6*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b*d^3) - (6*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b*d^3) - (6*f^3*PolyLog[4, -E^(c + d*x)])/(a*d^4) + (6*f^3*PolyLog[4, E^(c + d*x)])/(a*d^4) - (6*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b*d^4) + (6*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b*d^4)","A",33,14,32,0.4375,1,"{5585, 5450, 3296, 2637, 4182, 2531, 6609, 2282, 6589, 5565, 32, 3322, 2264, 2190}"
426,1,462,0,1.0402215,"\int \frac{(e+f x)^2 \cosh (c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^2}+\frac{2 f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^3}-\frac{2 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\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 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{(e+f x)^3}{3 b f}","-\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^2}+\frac{2 f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^3}-\frac{2 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\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 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{(e+f x)^3}{3 b f}",1,"(e + f*x)^3/(3*b*f) - (2*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d) - (Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*b*d) + (Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*b*d) - (2*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^2) + (2*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^2) - (2*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b*d^2) + (2*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b*d^2) + (2*f^2*PolyLog[3, -E^(c + d*x)])/(a*d^3) - (2*f^2*PolyLog[3, E^(c + d*x)])/(a*d^3) + (2*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b*d^3) - (2*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b*d^3)","A",27,13,32,0.4062,1,"{5585, 5450, 3296, 2638, 4182, 2531, 2282, 6589, 5565, 32, 3322, 2264, 2190}"
427,1,286,0,0.579288,"\int \frac{(e+f x) \cosh (c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^2}-\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{f \text{PolyLog}\left(2,e^{c+d x}\right)}{a 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{2 (e+f x) \tanh ^{-1}\left(e^{c+d x}\right)}{a d}+\frac{e x}{b}+\frac{f x^2}{2 b}","-\frac{f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b d^2}-\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{f \text{PolyLog}\left(2,e^{c+d x}\right)}{a 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{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,"(e*x)/b + (f*x^2)/(2*b) - (2*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d) - (Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*b*d) + (Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*b*d) - (f*PolyLog[2, -E^(c + d*x)])/(a*d^2) + (f*PolyLog[2, E^(c + d*x)])/(a*d^2) - (Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b*d^2) + (Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b*d^2)","A",21,11,30,0.3667,1,"{5585, 5450, 3296, 2637, 4182, 2279, 2391, 5565, 3322, 2264, 2190}"
428,1,71,0,0.2129422,"\int \frac{\cosh (c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\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}","\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,"x/b - ArcTanh[Cosh[c + d*x]]/(a*d) + (2*Sqrt[a^2 + b^2]*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(a*b*d)","A",6,6,25,0.2400,1,"{2889, 3058, 2660, 618, 204, 3770}"
429,0,0,0,0.059309,"\int \frac{\cosh (c+d x) \coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(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,"Defer[Int][(Cosh[c + d*x]*Coth[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
430,1,656,0,1.229671,"\int \frac{(e+f x)^3 \cosh ^2(c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]^2*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^3}-\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^2}-\frac{6 f^3 \left(a^2+b^2\right) \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^4}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^2}+\frac{3 f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a d^4}-\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{(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^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{6 f^3 \cosh (c+d x)}{b d^4}+\frac{(e+f x)^3 \sinh (c+d x)}{b d}","\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^3}-\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^2}-\frac{6 f^3 \left(a^2+b^2\right) \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^4}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^2}+\frac{3 f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a d^4}-\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{(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^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{6 f^3 \cosh (c+d x)}{b d^4}+\frac{(e+f x)^3 \sinh (c+d x)}{b d}",1,"-(e + f*x)^4/(4*a*f) + ((a^2 + b^2)*(e + f*x)^4)/(4*a*b^2*f) - (6*f^3*Cosh[c + d*x])/(b*d^4) - (3*f*(e + f*x)^2*Cosh[c + d*x])/(b*d^2) - ((a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*b^2*d) - ((a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*b^2*d) + ((e + f*x)^3*Log[1 - E^(2*(c + d*x))])/(a*d) - (3*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b^2*d^2) - (3*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b^2*d^2) + (3*f*(e + f*x)^2*PolyLog[2, E^(2*(c + d*x))])/(2*a*d^2) + (6*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b^2*d^3) + (6*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b^2*d^3) - (3*f^2*(e + f*x)*PolyLog[3, E^(2*(c + d*x))])/(2*a*d^3) - (6*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b^2*d^4) - (6*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b^2*d^4) + (3*f^3*PolyLog[4, E^(2*(c + d*x))])/(4*a*d^4) + (6*f^2*(e + f*x)*Sinh[c + d*x])/(b*d^3) + ((e + f*x)^3*Sinh[c + d*x])/(b*d)","A",34,17,34,0.5000,1,"{5585, 5450, 5446, 3311, 32, 2635, 8, 3716, 2190, 2531, 6609, 2282, 6589, 5565, 3296, 2638, 5561}"
431,1,486,0,1.0253071,"\int \frac{(e+f x)^2 \cosh ^2(c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]^2*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 f \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^2}+\frac{2 f^2 \left(a^2+b^2\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^3}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^3}-\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{(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 (e+f x) \cosh (c+d x)}{b d^2}+\frac{2 f^2 \sinh (c+d x)}{b d^3}+\frac{(e+f x)^2 \sinh (c+d x)}{b d}","-\frac{2 f \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^2}+\frac{2 f^2 \left(a^2+b^2\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^3}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^3}-\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{(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 (e+f x) \cosh (c+d x)}{b d^2}+\frac{2 f^2 \sinh (c+d x)}{b d^3}+\frac{(e+f x)^2 \sinh (c+d x)}{b d}",1,"-(e + f*x)^3/(3*a*f) + ((a^2 + b^2)*(e + f*x)^3)/(3*a*b^2*f) - (2*f*(e + f*x)*Cosh[c + d*x])/(b*d^2) - ((a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*b^2*d) - ((a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*b^2*d) + ((e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a*d) - (2*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b^2*d^2) - (2*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b^2*d^2) + (f*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a*d^2) + (2*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b^2*d^3) + (2*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b^2*d^3) - (f^2*PolyLog[3, E^(2*(c + d*x))])/(2*a*d^3) + (2*f^2*Sinh[c + d*x])/(b*d^3) + ((e + f*x)^2*Sinh[c + d*x])/(b*d)","A",26,13,34,0.3824,1,"{5585, 5450, 5446, 3310, 3716, 2190, 2531, 2282, 6589, 5565, 3296, 2637, 5561}"
432,1,322,0,0.5919846,"\int \frac{(e+f x) \cosh ^2(c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]^2*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^2}+\frac{f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a 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{(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}","-\frac{f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a b^2 d^2}+\frac{f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a 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{(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,"-(e + f*x)^2/(2*a*f) + ((a^2 + b^2)*(e + f*x)^2)/(2*a*b^2*f) - (f*Cosh[c + d*x])/(b*d^2) - ((a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*b^2*d) - ((a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*b^2*d) + ((e + f*x)*Log[1 - E^(2*(c + d*x))])/(a*d) - ((a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*b^2*d^2) - ((a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*b^2*d^2) + (f*PolyLog[2, E^(2*(c + d*x))])/(2*a*d^2) + ((e + f*x)*Sinh[c + d*x])/(b*d)","A",22,13,32,0.4062,1,"{5585, 5450, 5446, 2635, 8, 3716, 2190, 2279, 2391, 5565, 3296, 2638, 5561}"
433,1,57,0,0.1280751,"\int \frac{\cosh ^2(c+d x) \coth (c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Cosh[c + d*x]^2*Coth[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\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}","-\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*d) - ((a^2 + b^2)*Log[a + b*Sinh[c + d*x]])/(a*b^2*d) + Sinh[c + d*x]/(b*d)","A",4,3,27,0.1111,1,"{2837, 12, 894}"
434,0,0,0,0.0834457,"\int \frac{\cosh ^2(c+d x) \coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Cosh[c + d*x]^2*Coth[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh ^2(c+d x) \coth (c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Cosh[c + d*x]^2*Coth[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
435,1,1049,0,1.3408305,"\int \frac{(e+f x)^3 \text{csch}(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Csch[c + d*x]*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{6 i b \text{PolyLog}\left(4,-i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}-\frac{6 i b \text{PolyLog}\left(4,i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}-\frac{6 b^2 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-e^{2 (c+d x)}\right) f^3}{4 a \left(a^2+b^2\right) d^4}-\frac{3 \text{PolyLog}\left(4,-e^{2 c+2 d x}\right) f^3}{4 a d^4}+\frac{3 \text{PolyLog}\left(4,e^{2 c+2 d x}\right) f^3}{4 a d^4}-\frac{6 i b (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}+\frac{6 i b (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}+\frac{6 b^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-e^{2 (c+d x)}\right) f^2}{2 a \left(a^2+b^2\right) d^3}+\frac{3 (e+f x) \text{PolyLog}\left(3,-e^{2 c+2 d x}\right) f^2}{2 a d^3}-\frac{3 (e+f x) \text{PolyLog}\left(3,e^{2 c+2 d x}\right) f^2}{2 a d^3}+\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right) f}{\left(a^2+b^2\right) d^2}-\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right) f}{\left(a^2+b^2\right) d^2}-\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) f}{2 a \left(a^2+b^2\right) d^2}-\frac{3 (e+f x)^2 \text{PolyLog}\left(2,-e^{2 c+2 d x}\right) f}{2 a d^2}+\frac{3 (e+f x)^2 \text{PolyLog}\left(2,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}","\frac{6 i b \text{PolyLog}\left(4,-i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}-\frac{6 i b \text{PolyLog}\left(4,i e^{c+d x}\right) f^3}{\left(a^2+b^2\right) d^4}-\frac{6 b^2 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-e^{2 (c+d x)}\right) f^3}{4 a \left(a^2+b^2\right) d^4}-\frac{3 \text{PolyLog}\left(4,-e^{2 c+2 d x}\right) f^3}{4 a d^4}+\frac{3 \text{PolyLog}\left(4,e^{2 c+2 d x}\right) f^3}{4 a d^4}-\frac{6 i b (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}+\frac{6 i b (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right) f^2}{\left(a^2+b^2\right) d^3}+\frac{6 b^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-e^{2 (c+d x)}\right) f^2}{2 a \left(a^2+b^2\right) d^3}+\frac{3 (e+f x) \text{PolyLog}\left(3,-e^{2 c+2 d x}\right) f^2}{2 a d^3}-\frac{3 (e+f x) \text{PolyLog}\left(3,e^{2 c+2 d x}\right) f^2}{2 a d^3}+\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right) f}{\left(a^2+b^2\right) d^2}-\frac{3 i b (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right) f}{\left(a^2+b^2\right) d^2}-\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) f}{2 a \left(a^2+b^2\right) d^2}-\frac{3 (e+f x)^2 \text{PolyLog}\left(2,-e^{2 c+2 d x}\right) f}{2 a d^2}+\frac{3 (e+f x)^2 \text{PolyLog}\left(2,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*b*(e + f*x)^3*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d) - (2*(e + f*x)^3*ArcTanh[E^(2*c + 2*d*x)])/(a*d) - (b^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)*d) - (b^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)*d) + (b^2*(e + f*x)^3*Log[1 + E^(2*(c + d*x))])/(a*(a^2 + b^2)*d) + ((3*I)*b*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^2) - ((3*I)*b*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^2) - (3*b^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^2) - (3*b^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^2) + (3*b^2*f*(e + f*x)^2*PolyLog[2, -E^(2*(c + d*x))])/(2*a*(a^2 + b^2)*d^2) - (3*f*(e + f*x)^2*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a*d^2) + (3*f*(e + f*x)^2*PolyLog[2, E^(2*c + 2*d*x)])/(2*a*d^2) - ((6*I)*b*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^3) + ((6*I)*b*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)*d^3) + (6*b^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^3) + (6*b^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^3) - (3*b^2*f^2*(e + f*x)*PolyLog[3, -E^(2*(c + d*x))])/(2*a*(a^2 + b^2)*d^3) + (3*f^2*(e + f*x)*PolyLog[3, -E^(2*c + 2*d*x)])/(2*a*d^3) - (3*f^2*(e + f*x)*PolyLog[3, E^(2*c + 2*d*x)])/(2*a*d^3) + ((6*I)*b*f^3*PolyLog[4, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^4) - ((6*I)*b*f^3*PolyLog[4, I*E^(c + d*x)])/((a^2 + b^2)*d^4) - (6*b^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^4) - (6*b^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^4) + (3*b^2*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*a*(a^2 + b^2)*d^4) - (3*f^3*PolyLog[4, -E^(2*c + 2*d*x)])/(4*a*d^4) + (3*f^3*PolyLog[4, E^(2*c + 2*d*x)])/(4*a*d^4)","A",40,13,32,0.4062,1,"{5589, 5461, 4182, 2531, 6609, 2282, 6589, 5573, 5561, 2190, 6742, 4180, 3718}"
436,1,734,0,1.0972755,"\int \frac{(e+f x)^2 \text{csch}(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x]*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{b^2 f (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{2 i b f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{2 i b f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^3 \left(a^2+b^2\right)}-\frac{b^2 f^2 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 a d^3 \left(a^2+b^2\right)}-\frac{2 i b f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 i b f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{f (e+f x) \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{a d^2}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{a d^2}+\frac{f^2 \text{PolyLog}\left(3,-e^{2 c+2 d x}\right)}{2 a d^3}-\frac{f^2 \text{PolyLog}\left(3,e^{2 c+2 d x}\right)}{2 a d^3}-\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{2 (e+f x)^2 \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}","-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{b^2 f (e+f x) \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{2 i b f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{2 i b f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^3 \left(a^2+b^2\right)}-\frac{b^2 f^2 \text{PolyLog}\left(3,-e^{2 (c+d x)}\right)}{2 a d^3 \left(a^2+b^2\right)}-\frac{2 i b f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}+\frac{2 i b f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{d^3 \left(a^2+b^2\right)}-\frac{f (e+f x) \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{a d^2}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{a d^2}+\frac{f^2 \text{PolyLog}\left(3,-e^{2 c+2 d x}\right)}{2 a d^3}-\frac{f^2 \text{PolyLog}\left(3,e^{2 c+2 d x}\right)}{2 a d^3}-\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{2 (e+f x)^2 \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}",1,"(-2*b*(e + f*x)^2*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d) - (2*(e + f*x)^2*ArcTanh[E^(2*c + 2*d*x)])/(a*d) - (b^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)*d) - (b^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)*d) + (b^2*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(a*(a^2 + b^2)*d) + ((2*I)*b*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^2) - ((2*I)*b*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^2) - (2*b^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^2) - (2*b^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^2) + (b^2*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(a*(a^2 + b^2)*d^2) - (f*(e + f*x)*PolyLog[2, -E^(2*c + 2*d*x)])/(a*d^2) + (f*(e + f*x)*PolyLog[2, E^(2*c + 2*d*x)])/(a*d^2) - ((2*I)*b*f^2*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^3) + ((2*I)*b*f^2*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)*d^3) + (2*b^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^3) + (2*b^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^3) - (b^2*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*a*(a^2 + b^2)*d^3) + (f^2*PolyLog[3, -E^(2*c + 2*d*x)])/(2*a*d^3) - (f^2*PolyLog[3, E^(2*c + 2*d*x)])/(2*a*d^3)","A",33,12,32,0.3750,1,"{5589, 5461, 4182, 2531, 2282, 6589, 5573, 5561, 2190, 6742, 4180, 3718}"
437,1,439,0,0.6366833,"\int \frac{(e+f x) \text{csch}(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{b^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{b^2 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a d^2 \left(a^2+b^2\right)}+\frac{i b f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{i b f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{f \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a d^2}+\frac{f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a 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 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{2 (e+f x) \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}","-\frac{b^2 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{b^2 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a d^2 \left(a^2+b^2\right)}+\frac{i b f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{i b f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)}-\frac{f \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a d^2}+\frac{f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a 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 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{2 (e+f x) \tanh ^{-1}\left(e^{2 c+2 d x}\right)}{a d}",1,"(-2*b*(e + f*x)*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d) - (2*(e + f*x)*ArcTanh[E^(2*c + 2*d*x)])/(a*d) - (b^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)*d) - (b^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)*d) + (b^2*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(a*(a^2 + b^2)*d) + (I*b*f*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^2) - (I*b*f*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^2) - (b^2*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^2) - (b^2*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)*d^2) + (b^2*f*PolyLog[2, -E^(2*(c + d*x))])/(2*a*(a^2 + b^2)*d^2) - (f*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a*d^2) + (f*PolyLog[2, E^(2*c + 2*d*x)])/(2*a*d^2)","A",26,11,30,0.3667,1,"{5589, 5461, 4182, 2279, 2391, 5573, 5561, 2190, 6742, 4180, 3718}"
438,1,90,0,0.1696375,"\int \frac{\text{csch}(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Csch[c + d*x]*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\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}","-\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,"-((b*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d)) - (a*Log[Cosh[c + d*x]])/((a^2 + b^2)*d) + Log[Sinh[c + d*x]]/(a*d) - (b^2*Log[a + b*Sinh[c + d*x]])/(a*(a^2 + b^2)*d)","A",7,6,25,0.2400,1,"{2837, 12, 894, 635, 203, 260}"
439,0,0,0,0.0632793,"\int \frac{\text{csch}(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(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,"Defer[Int][(Csch[c + d*x]*Sech[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
440,1,1164,0,2.1988745,"\int \frac{(e+f x)^3 \text{csch}(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Csch[c + d*x]*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}+\frac{6 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 (c+d x)}\right) b}{\left(a^2+b^2\right) d^3}-\frac{3 f^3 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{6 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^4}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\frac{6 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}+\frac{(e+f x)^3 \text{sech}(c+d x)}{a 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{(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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}+\frac{6 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 (c+d x)}\right) b}{\left(a^2+b^2\right) d^3}-\frac{3 f^3 \text{PolyLog}\left(3,-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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^3}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{6 i f^3 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^4}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\frac{6 f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a d^4}+\frac{6 f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a d^4}+\frac{(e+f x)^3 \text{sech}(c+d x)}{a d}",1,"-((b*(e + f*x)^3)/((a^2 + b^2)*d)) - (6*f*(e + f*x)^2*ArcTan[E^(c + d*x)])/(a*d^2) + (6*b^2*f*(e + f*x)^2*ArcTan[E^(c + d*x)])/(a*(a^2 + b^2)*d^2) - (2*(e + f*x)^3*ArcTanh[E^(c + d*x)])/(a*d) - (b^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)^(3/2)*d) + (b^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)^(3/2)*d) + (3*b*f*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)*d^2) - (3*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(a*d^2) + ((6*I)*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) - ((6*I)*b^2*f^2*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)*d^3) - ((6*I)*f^2*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(a*d^3) + ((6*I)*b^2*f^2*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(a*(a^2 + b^2)*d^3) + (3*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(a*d^2) - (3*b^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^2) + (3*b^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^2) + (3*b*f^2*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/((a^2 + b^2)*d^3) + (6*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a*d^3) - ((6*I)*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^4) + ((6*I)*b^2*f^3*PolyLog[3, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)*d^4) + ((6*I)*f^3*PolyLog[3, I*E^(c + d*x)])/(a*d^4) - ((6*I)*b^2*f^3*PolyLog[3, I*E^(c + d*x)])/(a*(a^2 + b^2)*d^4) - (6*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a*d^3) + (6*b^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^3) - (6*b^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^3) - (3*b*f^3*PolyLog[3, -E^(2*(c + d*x))])/(2*(a^2 + b^2)*d^4) - (6*f^3*PolyLog[4, -E^(c + d*x)])/(a*d^4) + (6*f^3*PolyLog[4, E^(c + d*x)])/(a*d^4) - (6*b^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^4) + (6*b^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^4) + ((e + f*x)^3*Sech[c + d*x])/(a*d) - (b^2*(e + f*x)^3*Sech[c + d*x])/(a*(a^2 + b^2)*d) - (b*(e + f*x)^3*Tanh[c + d*x])/((a^2 + b^2)*d)","A",53,22,34,0.6471,1,"{5589, 2622, 321, 207, 5462, 6741, 12, 6742, 6273, 4182, 2531, 6609, 2282, 6589, 4180, 5573, 3322, 2264, 2190, 4184, 3718, 5451}"
441,1,795,0,1.6140947,"\int \frac{(e+f x)^2 \text{csch}(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x]*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,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{PolyLog}\left(2,-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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{2 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^3}+\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}+\frac{(e+f x)^2 \text{sech}(c+d x)}{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 \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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,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{PolyLog}\left(2,-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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{2 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^3}+\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{2 f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}+\frac{(e+f x)^2 \text{sech}(c+d x)}{a d}",1,"-((b*(e + f*x)^2)/((a^2 + b^2)*d)) - (4*f*(e + f*x)*ArcTan[E^(c + d*x)])/(a*d^2) + (4*b^2*f*(e + f*x)*ArcTan[E^(c + d*x)])/(a*(a^2 + b^2)*d^2) - (2*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d) - (b^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)^(3/2)*d) + (b^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)^(3/2)*d) + (2*b*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/((a^2 + b^2)*d^2) - (2*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^2) + ((2*I)*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) - ((2*I)*b^2*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)*d^3) - ((2*I)*f^2*PolyLog[2, I*E^(c + d*x)])/(a*d^3) + ((2*I)*b^2*f^2*PolyLog[2, I*E^(c + d*x)])/(a*(a^2 + b^2)*d^3) + (2*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^2) - (2*b^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^2) + (2*b^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^2) + (b*f^2*PolyLog[2, -E^(2*(c + d*x))])/((a^2 + b^2)*d^3) + (2*f^2*PolyLog[3, -E^(c + d*x)])/(a*d^3) - (2*f^2*PolyLog[3, E^(c + d*x)])/(a*d^3) + (2*b^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^3) - (2*b^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^3) + ((e + f*x)^2*Sech[c + d*x])/(a*d) - (b^2*(e + f*x)^2*Sech[c + d*x])/(a*(a^2 + b^2)*d) - (b*(e + f*x)^2*Tanh[c + d*x])/((a^2 + b^2)*d)","A",44,23,34,0.6765,1,"{5589, 2622, 321, 207, 5462, 6741, 12, 6742, 6273, 4182, 2531, 2282, 6589, 4180, 2279, 2391, 5573, 3322, 2264, 2190, 4184, 3718, 5451}"
442,1,442,0,0.8057063,"\int \frac{(e+f x) \text{csch}(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{b^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \left(a^2+b^2\right)^{3/2}}-\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{f \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\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^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{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{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}","-\frac{b^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \left(a^2+b^2\right)^{3/2}}-\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{f \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\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^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{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{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,"-((f*ArcTan[Sinh[c + d*x]])/(a*d^2)) + (b^2*f*ArcTan[Sinh[c + d*x]])/(a*(a^2 + b^2)*d^2) - (2*f*x*ArcTanh[E^(c + d*x)])/(a*d) + (f*x*ArcTanh[Cosh[c + d*x]])/(a*d) - ((e + f*x)*ArcTanh[Cosh[c + d*x]])/(a*d) - (b^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)^(3/2)*d) + (b^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)^(3/2)*d) + (b*f*Log[Cosh[c + d*x]])/((a^2 + b^2)*d^2) - (f*PolyLog[2, -E^(c + d*x)])/(a*d^2) + (f*PolyLog[2, E^(c + d*x)])/(a*d^2) - (b^3*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^2) + (b^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^(3/2)*d^2) + ((e + f*x)*Sech[c + d*x])/(a*d) - (b^2*(e + f*x)*Sech[c + d*x])/(a*(a^2 + b^2)*d) - (b*(e + f*x)*Tanh[c + d*x])/((a^2 + b^2)*d)","A",26,19,32,0.5938,1,"{5589, 2622, 321, 207, 5462, 6271, 12, 4182, 2279, 2391, 3770, 5573, 3322, 2264, 2190, 6742, 4184, 3475, 5451}"
443,1,113,0,0.2599429,"\int \frac{\text{csch}(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Csch[c + d*x]*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\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{b \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a d \left(a^2+b^2\right)}+\frac{\text{sech}(c+d x)}{a d}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a 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 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{\text{sech}(c+d x)}{a d}-\frac{\tanh ^{-1}(\cosh (c+d x))}{a d}",1,"-(ArcTanh[Cosh[c + d*x]]/(a*d)) + (2*b^3*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(a*(a^2 + b^2)^(3/2)*d) + Sech[c + d*x]/(a*d) - (b*Sech[c + d*x]*(b + a*Sinh[c + d*x]))/(a*(a^2 + b^2)*d)","A",10,9,27,0.3333,1,"{2898, 2622, 321, 207, 2696, 12, 2660, 618, 204}"
444,0,0,0,0.0893257,"\int \frac{\text{csch}(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Csch[c + d*x]*Sech[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}(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}(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][(Csch[c + d*x]*Sech[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
445,1,1185,0,2.2249001,"\int \frac{(e+f x)^2 \text{csch}(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x]*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) b^4}{a \left(a^2+b^2\right)^2 d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) b^3}{\left(a^2+b^2\right)^2 d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b^3}{\left(a^2+b^2\right)^2 d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-i e^{c+d x}\right) b}{\left(a^2+b^2\right) d^2}-\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) b}{\left(a^2+b^2\right) d^2}-\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b}{\left(a^2+b^2\right) d^3}+\frac{i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{a d^2}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{a d^2}+\frac{f^2 \text{PolyLog}\left(3,-e^{2 c+2 d x}\right)}{2 a d^3}-\frac{f^2 \text{PolyLog}\left(3,e^{2 c+2 d x}\right)}{2 a d^3}-\frac{f (e+f x) \tanh (c+d x)}{a d^2}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) b^4}{a \left(a^2+b^2\right)^2 d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) b^3}{\left(a^2+b^2\right)^2 d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b^3}{\left(a^2+b^2\right)^2 d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-i e^{c+d x}\right) b}{\left(a^2+b^2\right) d^2}-\frac{i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) b}{\left(a^2+b^2\right) d^2}-\frac{i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b}{\left(a^2+b^2\right) d^3}+\frac{i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{a d^2}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{a d^2}+\frac{f^2 \text{PolyLog}\left(3,-e^{2 c+2 d x}\right)}{2 a d^3}-\frac{f^2 \text{PolyLog}\left(3,e^{2 c+2 d x}\right)}{2 a d^3}-\frac{f (e+f x) \tanh (c+d x)}{a d^2}",1,"(e*f*x)/(a*d) + (f^2*x^2)/(2*a*d) - (2*b^3*(e + f*x)^2*ArcTan[E^(c + d*x)])/((a^2 + b^2)^2*d) - (b*(e + f*x)^2*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d) + (b*f^2*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d^3) - (2*(e + f*x)^2*ArcTanh[E^(2*c + 2*d*x)])/(a*d) - (b^4*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)^2*d) - (b^4*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)^2*d) + (b^4*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(a*(a^2 + b^2)^2*d) + (f^2*Log[Cosh[c + d*x]])/(a*d^3) - (b^2*f^2*Log[Cosh[c + d*x]])/(a*(a^2 + b^2)*d^3) + ((2*I)*b^3*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^2) + (I*b*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^2) - ((2*I)*b^3*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)^2*d^2) - (I*b*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^2) - (2*b^4*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^2*d^2) - (2*b^4*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^2*d^2) + (b^4*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(a*(a^2 + b^2)^2*d^2) - (f*(e + f*x)*PolyLog[2, -E^(2*c + 2*d*x)])/(a*d^2) + (f*(e + f*x)*PolyLog[2, E^(2*c + 2*d*x)])/(a*d^2) - ((2*I)*b^3*f^2*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^3) - (I*b*f^2*PolyLog[3, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^3) + ((2*I)*b^3*f^2*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)^2*d^3) + (I*b*f^2*PolyLog[3, I*E^(c + d*x)])/((a^2 + b^2)*d^3) + (2*b^4*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^2*d^3) + (2*b^4*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^2*d^3) - (b^4*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*a*(a^2 + b^2)^2*d^3) + (f^2*PolyLog[3, -E^(2*c + 2*d*x)])/(2*a*d^3) - (f^2*PolyLog[3, E^(2*c + 2*d*x)])/(2*a*d^3) - (b*f*(e + f*x)*Sech[c + d*x])/((a^2 + b^2)*d^2) - (b^2*(e + f*x)^2*Sech[c + d*x]^2)/(2*a*(a^2 + b^2)*d) - (f*(e + f*x)*Tanh[c + d*x])/(a*d^2) + (b^2*f*(e + f*x)*Tanh[c + d*x])/(a*(a^2 + b^2)*d^2) - (b*(e + f*x)^2*Sech[c + d*x]*Tanh[c + d*x])/(2*(a^2 + b^2)*d) - ((e + f*x)^2*Tanh[c + d*x]^2)/(2*a*d)","A",57,23,34,0.6765,1,"{5589, 2620, 14, 5462, 6741, 12, 6742, 2551, 4182, 2531, 2282, 6589, 3720, 3475, 5573, 5561, 2190, 4180, 3718, 4186, 3770, 5451, 4184}"
446,1,746,0,1.0590923,"\int \frac{(e+f x) \text{csch}(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{b^4 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \left(a^2+b^2\right)^2}+\frac{b^4 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a d^2 \left(a^2+b^2\right)^2}+\frac{i b^3 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{i b^3 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{i b f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{i b f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{f \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a d^2}+\frac{f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a d^2}+\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^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{2 b^3 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)^2}-\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{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}","-\frac{b^4 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a d^2 \left(a^2+b^2\right)^2}+\frac{b^4 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a d^2 \left(a^2+b^2\right)^2}+\frac{i b^3 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}-\frac{i b^3 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{d^2 \left(a^2+b^2\right)^2}+\frac{i b f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{i b f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 d^2 \left(a^2+b^2\right)}-\frac{f \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a d^2}+\frac{f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a d^2}+\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^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{2 b^3 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{d \left(a^2+b^2\right)^2}-\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{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,"(f*x)/(2*a*d) - (2*b^3*(e + f*x)*ArcTan[E^(c + d*x)])/((a^2 + b^2)^2*d) - (b*(e + f*x)*ArcTan[E^(c + d*x)])/((a^2 + b^2)*d) - (2*f*x*ArcTanh[E^(2*c + 2*d*x)])/(a*d) - (b^4*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)^2*d) - (b^4*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a*(a^2 + b^2)^2*d) + (b^4*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(a*(a^2 + b^2)^2*d) - (f*x*Log[Tanh[c + d*x]])/(a*d) + ((e + f*x)*Log[Tanh[c + d*x]])/(a*d) + (I*b^3*f*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)^2*d^2) + ((I/2)*b*f*PolyLog[2, (-I)*E^(c + d*x)])/((a^2 + b^2)*d^2) - (I*b^3*f*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)^2*d^2) - ((I/2)*b*f*PolyLog[2, I*E^(c + d*x)])/((a^2 + b^2)*d^2) - (b^4*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^2*d^2) - (b^4*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a*(a^2 + b^2)^2*d^2) + (b^4*f*PolyLog[2, -E^(2*(c + d*x))])/(2*a*(a^2 + b^2)^2*d^2) - (f*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a*d^2) + (f*PolyLog[2, E^(2*c + 2*d*x)])/(2*a*d^2) - (b*f*Sech[c + d*x])/(2*(a^2 + b^2)*d^2) - (b^2*(e + f*x)*Sech[c + d*x]^2)/(2*a*(a^2 + b^2)*d) - (f*Tanh[c + d*x])/(2*a*d^2) + (b^2*f*Tanh[c + d*x])/(2*a*(a^2 + b^2)*d^2) - (b*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*(a^2 + b^2)*d) - ((e + f*x)*Tanh[c + d*x]^2)/(2*a*d)","A",43,20,32,0.6250,1,"{5589, 2620, 14, 5462, 2548, 12, 4182, 2279, 2391, 3473, 8, 5573, 5561, 2190, 6742, 4180, 3718, 4185, 5451, 3767}"
447,1,160,0,0.2705466,"\int \frac{\text{csch}(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Csch[c + d*x]*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\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{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{\log (\sinh (c+d x))}{a d}","-\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{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{\log (\sinh (c+d x))}{a d}",1,"-((b^3*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)^2*d)) - (b*ArcTan[Sinh[c + d*x]])/(2*(a^2 + b^2)*d) - (a*(a^2 + 2*b^2)*Log[Cosh[c + d*x]])/((a^2 + b^2)^2*d) + Log[Sinh[c + d*x]]/(a*d) - (b^4*Log[a + b*Sinh[c + d*x]])/(a*(a^2 + b^2)^2*d) + (Sech[c + d*x]^2*(a - b*Sinh[c + d*x]))/(2*(a^2 + b^2)*d)","A",9,7,27,0.2593,1,"{2837, 12, 894, 639, 203, 635, 260}"
448,0,0,0,0.0894066,"\int \frac{\text{csch}(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(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,"Defer[Int][(Csch[c + d*x]*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
449,1,601,0,1.0029692,"\int \frac{(e+f x)^3 \coth (c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Coth[c + d*x]*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3}+\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}+\frac{6 b f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^4}+\frac{6 b f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^4}+\frac{3 b f^2 (e+f x) \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a^2 d^2}-\frac{3 b f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a^2 d^4}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}+\frac{6 f^3 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^4}-\frac{6 f^3 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^4}+\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{b (e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a^2 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 b f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3}+\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}+\frac{6 b f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^4}+\frac{6 b f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^4}+\frac{3 b f^2 (e+f x) \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a^2 d^2}-\frac{3 b f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a^2 d^4}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}+\frac{6 f^3 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^4}-\frac{6 f^3 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^4}+\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{b (e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a^2 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}",1,"(-6*f*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d^2) - ((e + f*x)^3*Csch[c + d*x])/(a*d) + (b*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*d) + (b*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*d) - (b*(e + f*x)^3*Log[1 - E^(2*(c + d*x))])/(a^2*d) - (6*f^2*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^3) + (6*f^2*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^3) + (3*b*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^2) + (3*b*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^2) - (3*b*f*(e + f*x)^2*PolyLog[2, E^(2*(c + d*x))])/(2*a^2*d^2) + (6*f^3*PolyLog[3, -E^(c + d*x)])/(a*d^4) - (6*f^3*PolyLog[3, E^(c + d*x)])/(a*d^4) - (6*b*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^3) - (6*b*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^3) + (3*b*f^2*(e + f*x)*PolyLog[3, E^(2*(c + d*x))])/(2*a^2*d^3) + (6*b*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^4) + (6*b*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^4) - (3*b*f^3*PolyLog[4, E^(2*(c + d*x))])/(4*a^2*d^4)","A",27,11,32,0.3438,1,"{5587, 5452, 4182, 2531, 2282, 6589, 5569, 3716, 2190, 6609, 5561}"
450,1,419,0,0.8178586,"\int \frac{(e+f x)^2 \coth (c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Coth[c + d*x]*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{2 b f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}-\frac{2 b f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^3}-\frac{2 b f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3}-\frac{b f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^2 d^2}+\frac{b f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{2 f^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}+\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 (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a^2 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 b f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}-\frac{2 b f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^3}-\frac{2 b f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3}-\frac{b f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^2 d^2}+\frac{b f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{2 f^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}+\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 (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a^2 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}",1,"(-4*f*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d^2) - ((e + f*x)^2*Csch[c + d*x])/(a*d) + (b*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*d) + (b*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*d) - (b*(e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a^2*d) - (2*f^2*PolyLog[2, -E^(c + d*x)])/(a*d^3) + (2*f^2*PolyLog[2, E^(c + d*x)])/(a*d^3) + (2*b*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^2) + (2*b*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^2) - (b*f*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a^2*d^2) - (2*b*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^3) - (2*b*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^3) + (b*f^2*PolyLog[3, E^(2*(c + d*x))])/(2*a^2*d^3)","A",22,12,32,0.3750,1,"{5587, 5452, 4182, 2279, 2391, 5569, 3716, 2190, 2531, 2282, 6589, 5561}"
451,1,243,0,0.4641303,"\int \frac{(e+f x) \coth (c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Coth[c + d*x]*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{b f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{b f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}-\frac{b f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 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 (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}","\frac{b f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^2 d^2}+\frac{b f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}-\frac{b f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 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 (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,"-((f*ArcTanh[Cosh[c + d*x]])/(a*d^2)) - ((e + f*x)*Csch[c + d*x])/(a*d) + (b*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*d) + (b*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*d) - (b*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a^2*d) + (b*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^2) + (b*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^2) - (b*f*PolyLog[2, E^(2*(c + d*x))])/(2*a^2*d^2)","A",15,9,30,0.3000,1,"{5587, 5452, 3770, 5569, 3716, 2190, 2279, 2391, 5561}"
452,1,50,0,0.0749684,"\int \frac{\coth (c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(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",4,3,25,0.1200,1,"{2833, 12, 44}"
453,0,0,0,0.0663352,"\int \frac{\coth (c+d x) \text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Coth[c + d*x]*Csch[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\coth (c+d x) \text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Coth[c + d*x]*Csch[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
454,1,721,0,1.6362796,"\int \frac{(e+f x)^3 \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3}+\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}+\frac{6 f^3 \sqrt{a^2+b^2} \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^4}-\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^3}+\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^3}+\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^2}+\frac{6 b f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a^2 d^4}-\frac{6 b f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a^2 d^4}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{3 f^3 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^4}+\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{2 b (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\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}","-\frac{6 f^2 \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3}+\frac{3 f \sqrt{a^2+b^2} (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}+\frac{6 f^3 \sqrt{a^2+b^2} \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^4}-\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^3}+\frac{6 b f^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^3}+\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^2}+\frac{6 b f^3 \text{PolyLog}\left(4,-e^{c+d x}\right)}{a^2 d^4}-\frac{6 b f^3 \text{PolyLog}\left(4,e^{c+d x}\right)}{a^2 d^4}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}-\frac{3 f^3 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^4}+\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{2 b (e+f x)^3 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\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,"-((e + f*x)^3/(a*d)) + (2*b*(e + f*x)^3*ArcTanh[E^(c + d*x)])/(a^2*d) - ((e + f*x)^3*Coth[c + d*x])/(a*d) + (Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*d) - (Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*d) + (3*f*(e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a*d^2) + (3*b*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(a^2*d^2) - (3*b*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(a^2*d^2) + (3*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^2) - (3*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^2) + (3*f^2*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a*d^3) - (6*b*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a^2*d^3) + (6*b*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a^2*d^3) - (6*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^3) + (6*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^3) - (3*f^3*PolyLog[3, E^(2*(c + d*x))])/(2*a*d^4) + (6*b*f^3*PolyLog[4, -E^(c + d*x)])/(a^2*d^4) - (6*b*f^3*PolyLog[4, E^(c + d*x)])/(a^2*d^4) + (6*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^4) - (6*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^4)","A",41,17,28,0.6071,1,"{5569, 3720, 3716, 2190, 2531, 2282, 6589, 32, 5585, 5450, 3296, 2637, 4182, 6609, 5565, 3322, 2264}"
455,1,517,0,1.2959252,"\int \frac{(e+f x)^2 \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}-\frac{2 f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3}+\frac{2 b f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{2 b f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^2}-\frac{2 b f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^3}+\frac{2 b f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^3}+\frac{f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}+\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 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\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}","\frac{2 f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}-\frac{2 f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^3}+\frac{2 b f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{2 b f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^2}-\frac{2 b f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^3}+\frac{2 b f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^3}+\frac{f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^3}+\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 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^2 d}+\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,"-((e + f*x)^2/(a*d)) + (2*b*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a^2*d) - ((e + f*x)^2*Coth[c + d*x])/(a*d) + (Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*d) - (Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*d) + (2*f*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a*d^2) + (2*b*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a^2*d^2) - (2*b*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a^2*d^2) + (2*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^2) - (2*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^2) + (f^2*PolyLog[2, E^(2*(c + d*x))])/(a*d^3) - (2*b*f^2*PolyLog[3, -E^(c + d*x)])/(a^2*d^3) + (2*b*f^2*PolyLog[3, E^(c + d*x)])/(a^2*d^3) - (2*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^3) + (2*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^3)","A",34,18,28,0.6429,1,"{5569, 3720, 3716, 2190, 2279, 2391, 32, 5585, 5450, 3296, 2638, 4182, 2531, 2282, 6589, 5565, 3322, 2264}"
456,1,294,0,0.688467,"\int \frac{(e+f x) \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}+\frac{b f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{b f \text{PolyLog}\left(2,e^{c+d x}\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{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}","\frac{f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2}+\frac{b f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{b f \text{PolyLog}\left(2,e^{c+d x}\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{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,"(2*b*(e + f*x)*ArcTanh[E^(c + d*x)])/(a^2*d) - ((e + f*x)*Coth[c + d*x])/(a*d) + (Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*d) - (Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*d) + (f*Log[Sinh[c + d*x]])/(a*d^2) + (b*f*PolyLog[2, -E^(c + d*x)])/(a^2*d^2) - (b*f*PolyLog[2, E^(c + d*x)])/(a^2*d^2) + (Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*d^2) - (Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*d^2)","A",25,14,26,0.5385,1,"{5569, 3720, 3475, 5585, 5450, 3296, 2637, 4182, 2279, 2391, 5565, 3322, 2264, 2190}"
457,1,77,0,0.2662817,"\int \frac{\coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Coth[c + d*x]^2/(a + b*Sinh[c + d*x]),x]","-\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}","-\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,"(b*ArcTanh[Cosh[c + d*x]])/(a^2*d) - (2*Sqrt[a^2 + b^2]*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(a^2*d) - Coth[c + d*x]/(a*d)","A",7,7,21,0.3333,1,"{2723, 3056, 3001, 3770, 2660, 618, 204}"
458,0,0,0,0.0734448,"\int \frac{\coth ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[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,"Defer[Int][Coth[c + d*x]^2/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
459,1,718,0,1.6447522,"\int \frac{(e+f x)^3 \cosh (c+d x) \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Cosh[c + d*x]*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{6 f^2 \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^3}+\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^2}+\frac{6 f^3 \left(a^2+b^2\right) \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^4}+\frac{3 b f^2 (e+f x) \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a^2 d^2}-\frac{3 b f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a^2 d^4}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}+\frac{6 f^3 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^4}-\frac{6 f^3 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^4}+\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{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 (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 \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^3}+\frac{3 f \left(a^2+b^2\right) (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^2}+\frac{6 f^3 \left(a^2+b^2\right) \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^4}+\frac{3 b f^2 (e+f x) \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{3 b f (e+f x)^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a^2 d^2}-\frac{3 b f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a^2 d^4}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}+\frac{6 f^3 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^4}-\frac{6 f^3 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^4}+\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{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 (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,"(b*(e + f*x)^4)/(4*a^2*f) - ((a^2 + b^2)*(e + f*x)^4)/(4*a^2*b*f) - (6*f*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d^2) - ((e + f*x)^3*Csch[c + d*x])/(a*d) + ((a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*b*d) + ((a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*b*d) - (b*(e + f*x)^3*Log[1 - E^(2*(c + d*x))])/(a^2*d) - (6*f^2*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^3) + (6*f^2*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^3) + (3*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*b*d^2) + (3*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*b*d^2) - (3*b*f*(e + f*x)^2*PolyLog[2, E^(2*(c + d*x))])/(2*a^2*d^2) + (6*f^3*PolyLog[3, -E^(c + d*x)])/(a*d^4) - (6*f^3*PolyLog[3, E^(c + d*x)])/(a*d^4) - (6*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*b*d^3) - (6*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*b*d^3) + (3*b*f^2*(e + f*x)*PolyLog[3, E^(2*(c + d*x))])/(2*a^2*d^3) + (6*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*b*d^4) + (6*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*b*d^4) - (3*b*f^3*PolyLog[4, E^(2*(c + d*x))])/(4*a^2*d^4)","A",48,19,34,0.5588,1,"{5585, 5450, 3296, 2638, 5452, 4182, 2531, 2282, 6589, 5446, 3311, 32, 2635, 8, 3716, 2190, 6609, 5565, 5561}"
460,1,518,0,1.2867341,"\int \frac{(e+f x)^2 \cosh (c+d x) \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Cosh[c + d*x]*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{2 f \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^2}-\frac{2 f^2 \left(a^2+b^2\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^3}-\frac{b f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^2 d^2}+\frac{b f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{2 f^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}+\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 (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{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 \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^2}-\frac{2 f^2 \left(a^2+b^2\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^3}-\frac{b f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^2 d^2}+\frac{b f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^2 d^3}-\frac{2 f^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{2 f^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}+\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 (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{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,"(b*(e + f*x)^3)/(3*a^2*f) - ((a^2 + b^2)*(e + f*x)^3)/(3*a^2*b*f) - (4*f*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d^2) - ((e + f*x)^2*Csch[c + d*x])/(a*d) + ((a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*b*d) + ((a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*b*d) - (b*(e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a^2*d) - (2*f^2*PolyLog[2, -E^(c + d*x)])/(a*d^3) + (2*f^2*PolyLog[2, E^(c + d*x)])/(a*d^3) + (2*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*b*d^2) + (2*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*b*d^2) - (b*f*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a^2*d^2) - (2*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*b*d^3) - (2*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*b*d^3) + (b*f^2*PolyLog[3, E^(2*(c + d*x))])/(2*a^2*d^3)","A",37,17,34,0.5000,1,"{5585, 5450, 3296, 2637, 5452, 4182, 2279, 2391, 5446, 3310, 3716, 2190, 2531, 2282, 6589, 5565, 5561}"
461,1,324,0,0.7426318,"\int \frac{(e+f x) \cosh (c+d x) \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Cosh[c + d*x]*Coth[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^2}-\frac{b f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a^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^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 (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}","\frac{f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 b d^2}-\frac{b f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a^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^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 (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,"(b*(e + f*x)^2)/(2*a^2*f) - ((a^2 + b^2)*(e + f*x)^2)/(2*a^2*b*f) - (f*ArcTanh[Cosh[c + d*x]])/(a*d^2) - ((e + f*x)*Csch[c + d*x])/(a*d) + ((a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*b*d) + ((a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*b*d) - (b*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a^2*d) + ((a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*b*d^2) + ((a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*b*d^2) - (b*f*PolyLog[2, E^(2*(c + d*x))])/(2*a^2*d^2)","A",28,15,32,0.4688,1,"{5585, 5450, 3296, 2638, 5452, 3770, 5446, 2635, 8, 3716, 2190, 2279, 2391, 5565, 5561}"
462,1,59,0,0.1225734,"\int \frac{\cosh (c+d x) \coth ^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(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^2 b d}-\frac{b \log (\sinh (c+d x))}{a^2 d}-\frac{\text{csch}(c+d x)}{a 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,"-(Csch[c + d*x]/(a*d)) - (b*Log[Sinh[c + d*x]])/(a^2*d) + ((a^2 + b^2)*Log[a + b*Sinh[c + d*x]])/(a^2*b*d)","A",4,3,27,0.1111,1,"{2837, 12, 894}"
463,0,0,0,0.0854025,"\int \frac{\cosh (c+d x) \coth ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Cosh[c + d*x]*Coth[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\cosh (c+d x) \coth ^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Cosh[c + d*x]*Coth[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
464,1,1428,0,2.2837454,"\int \frac{(e+f x)^3 \text{csch}^2(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Csch[c + d*x]^2*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-e^{2 (c+d x)}\right) b^3}{2 a^2 \left(a^2+b^2\right) d^3}+\frac{6 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(3,-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{PolyLog}\left(3,i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}-\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b}{2 a^2 d^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 c+2 d x}\right) b}{2 a^2 d^2}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-e^{2 c+2 d x}\right) b}{2 a^2 d^3}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 c+2 d x}\right) b}{2 a^2 d^3}+\frac{3 f^3 \text{PolyLog}\left(4,-e^{2 c+2 d x}\right) b}{4 a^2 d^4}-\frac{3 f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^2}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}+\frac{6 f^3 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^4}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^3}-\frac{6 f^3 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{a d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{a d^4}","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-e^{2 (c+d x)}\right) b^3}{2 a^2 \left(a^2+b^2\right) d^3}+\frac{6 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(3,-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{PolyLog}\left(3,i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}-\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b}{2 a^2 d^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 c+2 d x}\right) b}{2 a^2 d^2}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-e^{2 c+2 d x}\right) b}{2 a^2 d^3}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 c+2 d x}\right) b}{2 a^2 d^3}+\frac{3 f^3 \text{PolyLog}\left(4,-e^{2 c+2 d x}\right) b}{4 a^2 d^4}-\frac{3 f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^2}+\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}+\frac{6 f^3 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^4}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^3}-\frac{6 f^3 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right)}{a d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,i e^{c+d x}\right)}{a d^4}",1,"(-2*(e + f*x)^3*ArcTan[E^(c + d*x)])/(a*d) + (2*b^2*(e + f*x)^3*ArcTan[E^(c + d*x)])/(a*(a^2 + b^2)*d) - (6*f*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d^2) + (2*b*(e + f*x)^3*ArcTanh[E^(2*c + 2*d*x)])/(a^2*d) - ((e + f*x)^3*Csch[c + d*x])/(a*d) + (b^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)*d) + (b^3*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)*d) - (b^3*(e + f*x)^3*Log[1 + E^(2*(c + d*x))])/(a^2*(a^2 + b^2)*d) - (6*f^2*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^3) + ((3*I)*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) - ((3*I)*b^2*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)*d^2) - ((3*I)*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(a*d^2) + ((3*I)*b^2*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(a*(a^2 + b^2)*d^2) + (6*f^2*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^3) + (3*b^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^2) + (3*b^3*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^2) - (3*b^3*f*(e + f*x)^2*PolyLog[2, -E^(2*(c + d*x))])/(2*a^2*(a^2 + b^2)*d^2) + (3*b*f*(e + f*x)^2*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a^2*d^2) - (3*b*f*(e + f*x)^2*PolyLog[2, E^(2*c + 2*d*x)])/(2*a^2*d^2) + (6*f^3*PolyLog[3, -E^(c + d*x)])/(a*d^4) - ((6*I)*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^3) + ((6*I)*b^2*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)*d^3) + ((6*I)*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(a*d^3) - ((6*I)*b^2*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(a*(a^2 + b^2)*d^3) - (6*f^3*PolyLog[3, E^(c + d*x)])/(a*d^4) - (6*b^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^3) - (6*b^3*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^3) + (3*b^3*f^2*(e + f*x)*PolyLog[3, -E^(2*(c + d*x))])/(2*a^2*(a^2 + b^2)*d^3) - (3*b*f^2*(e + f*x)*PolyLog[3, -E^(2*c + 2*d*x)])/(2*a^2*d^3) + (3*b*f^2*(e + f*x)*PolyLog[3, E^(2*c + 2*d*x)])/(2*a^2*d^3) + ((6*I)*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(a*d^4) - ((6*I)*b^2*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)*d^4) - ((6*I)*f^3*PolyLog[4, I*E^(c + d*x)])/(a*d^4) + ((6*I)*b^2*f^3*PolyLog[4, I*E^(c + d*x)])/(a*(a^2 + b^2)*d^4) + (6*b^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^4) + (6*b^3*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^4) - (3*b^3*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*a^2*(a^2 + b^2)*d^4) + (3*b*f^3*PolyLog[4, -E^(2*c + 2*d*x)])/(4*a^2*d^4) - (3*b*f^3*PolyLog[4, E^(2*c + 2*d*x)])/(4*a^2*d^4)","A",64,20,34,0.5882,1,"{5589, 2621, 321, 207, 5462, 6741, 12, 6742, 5205, 4180, 2531, 6609, 2282, 6589, 4182, 5461, 5573, 5561, 2190, 3718}"
465,1,982,0,1.6675563,"\int \frac{(e+f x)^2 \text{csch}^2(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x]^2*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^2}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b}{a^2 d^2}-\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 c+2 d x}\right) b}{a^2 d^2}-\frac{f^2 \text{PolyLog}\left(3,-e^{2 c+2 d x}\right) b}{2 a^2 d^3}+\frac{f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^2}+\frac{2 f^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^3}","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^2}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b^2}{a \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b}{a^2 d^2}-\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 c+2 d x}\right) b}{a^2 d^2}-\frac{f^2 \text{PolyLog}\left(3,-e^{2 c+2 d x}\right) b}{2 a^2 d^3}+\frac{f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^3}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^2}+\frac{2 f^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right)}{a d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,i e^{c+d x}\right)}{a d^3}",1,"(-2*(e + f*x)^2*ArcTan[E^(c + d*x)])/(a*d) + (2*b^2*(e + f*x)^2*ArcTan[E^(c + d*x)])/(a*(a^2 + b^2)*d) - (4*f*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d^2) + (2*b*(e + f*x)^2*ArcTanh[E^(2*c + 2*d*x)])/(a^2*d) - ((e + f*x)^2*Csch[c + d*x])/(a*d) + (b^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)*d) + (b^3*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)*d) - (b^3*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(a^2*(a^2 + b^2)*d) - (2*f^2*PolyLog[2, -E^(c + d*x)])/(a*d^3) + ((2*I)*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) - ((2*I)*b^2*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)*d^2) - ((2*I)*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(a*d^2) + ((2*I)*b^2*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(a*(a^2 + b^2)*d^2) + (2*f^2*PolyLog[2, E^(c + d*x)])/(a*d^3) + (2*b^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^2) + (2*b^3*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^2) - (b^3*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(a^2*(a^2 + b^2)*d^2) + (b*f*(e + f*x)*PolyLog[2, -E^(2*c + 2*d*x)])/(a^2*d^2) - (b*f*(e + f*x)*PolyLog[2, E^(2*c + 2*d*x)])/(a^2*d^2) - ((2*I)*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(a*d^3) + ((2*I)*b^2*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)*d^3) + ((2*I)*f^2*PolyLog[3, I*E^(c + d*x)])/(a*d^3) - ((2*I)*b^2*f^2*PolyLog[3, I*E^(c + d*x)])/(a*(a^2 + b^2)*d^3) - (2*b^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^3) - (2*b^3*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^3) + (b^3*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*a^2*(a^2 + b^2)*d^3) - (b*f^2*PolyLog[3, -E^(2*c + 2*d*x)])/(2*a^2*d^3) + (b*f^2*PolyLog[3, E^(2*c + 2*d*x)])/(2*a^2*d^3)","A",53,21,34,0.6176,1,"{5589, 2621, 321, 207, 5462, 6741, 12, 6742, 5205, 4180, 2531, 2282, 6589, 4182, 2279, 2391, 5461, 5573, 5561, 2190, 3718}"
466,1,591,0,0.900204,"\int \frac{(e+f x) \text{csch}^2(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]^2*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{b^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2 \left(a^2+b^2\right)}-\frac{b^3 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a^2 d^2 \left(a^2+b^2\right)}-\frac{i b^2 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{i b^2 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{b f \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a^2 d^2}-\frac{b f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a^2 d^2}+\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^2}+\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{2 b^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{a d \left(a^2+b^2\right)}+\frac{2 b (e+f x) \tanh ^{-1}\left(e^{2 c+2 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}-\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}","\frac{b^3 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2 \left(a^2+b^2\right)}-\frac{b^3 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a^2 d^2 \left(a^2+b^2\right)}-\frac{i b^2 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{i b^2 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^2 \left(a^2+b^2\right)}+\frac{b f \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a^2 d^2}-\frac{b f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a^2 d^2}+\frac{i f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^2}-\frac{i f \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^2}+\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{2 b^2 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{a d \left(a^2+b^2\right)}+\frac{2 b (e+f x) \tanh ^{-1}\left(e^{2 c+2 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}-\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,"(-2*f*x*ArcTan[E^(c + d*x)])/(a*d) + (2*b^2*(e + f*x)*ArcTan[E^(c + d*x)])/(a*(a^2 + b^2)*d) + (f*x*ArcTan[Sinh[c + d*x]])/(a*d) - ((e + f*x)*ArcTan[Sinh[c + d*x]])/(a*d) + (2*b*(e + f*x)*ArcTanh[E^(2*c + 2*d*x)])/(a^2*d) - (f*ArcTanh[Cosh[c + d*x]])/(a*d^2) - ((e + f*x)*Csch[c + d*x])/(a*d) + (b^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)*d) + (b^3*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)*d) - (b^3*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(a^2*(a^2 + b^2)*d) + (I*f*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) - (I*b^2*f*PolyLog[2, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)*d^2) - (I*f*PolyLog[2, I*E^(c + d*x)])/(a*d^2) + (I*b^2*f*PolyLog[2, I*E^(c + d*x)])/(a*(a^2 + b^2)*d^2) + (b^3*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^2) + (b^3*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)*d^2) - (b^3*f*PolyLog[2, -E^(2*(c + d*x))])/(2*a^2*(a^2 + b^2)*d^2) + (b*f*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a^2*d^2) - (b*f*PolyLog[2, E^(2*c + 2*d*x)])/(2*a^2*d^2)","A",37,18,32,0.5625,1,"{5589, 2621, 321, 207, 5462, 5203, 12, 4180, 2279, 2391, 3770, 5461, 4182, 5573, 5561, 2190, 6742, 3718}"
467,1,104,0,0.1696447,"\int \frac{\text{csch}^2(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Csch[c + d*x]^2*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","\frac{b^3 \log (a+b \sinh (c+d x))}{a^2 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)}-\frac{b \log (\sinh (c+d x))}{a^2 d}-\frac{\text{csch}(c+d x)}{a d}","\frac{b^3 \log (a+b \sinh (c+d x))}{a^2 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)}-\frac{b \log (\sinh (c+d x))}{a^2 d}-\frac{\text{csch}(c+d x)}{a d}",1,"-((a*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d)) - Csch[c + d*x]/(a*d) + (b*Log[Cosh[c + d*x]])/((a^2 + b^2)*d) - (b*Log[Sinh[c + d*x]])/(a^2*d) + (b^3*Log[a + b*Sinh[c + d*x]])/(a^2*(a^2 + b^2)*d)","A",7,6,27,0.2222,1,"{2837, 12, 894, 635, 203, 260}"
468,0,0,0,0.0924191,"\int \frac{\text{csch}^2(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(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,"Defer[Int][(Csch[c + d*x]^2*Sech[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
469,1,914,0,2.037388,"\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","Int[((e + f*x)^2*Csch[c + d*x]^2*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,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{PolyLog}\left(2,-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{PolyLog}\left(2,-e^{c+d x}\right) b}{a^2 d^2}-\frac{2 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right) b}{a^2 d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,i e^{c+d x}\right) b}{a^2 d^3}-\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right) b}{a^2 d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right) b}{a^2 d^3}+\frac{2 f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,e^{4 (c+d x)}\right)}{2 a d^3}","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,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{PolyLog}\left(2,-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{PolyLog}\left(2,-e^{c+d x}\right) b}{a^2 d^2}-\frac{2 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right) b}{a^2 d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,i e^{c+d x}\right) b}{a^2 d^3}-\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right) b}{a^2 d^2}-\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right) b}{a^2 d^3}+\frac{2 f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,e^{4 (c+d x)}\right)}{2 a d^3}",1,"(-2*(e + f*x)^2)/(a*d) + (b^2*(e + f*x)^2)/(a*(a^2 + b^2)*d) + (4*b*f*(e + f*x)*ArcTan[E^(c + d*x)])/(a^2*d^2) - (4*b^3*f*(e + f*x)*ArcTan[E^(c + d*x)])/(a^2*(a^2 + b^2)*d^2) + (2*b*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a^2*d) - (2*(e + f*x)^2*Coth[2*c + 2*d*x])/(a*d) + (b^4*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)^(3/2)*d) - (b^4*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)^(3/2)*d) - (2*b^2*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(a*(a^2 + b^2)*d^2) + (2*f*(e + f*x)*Log[1 - E^(4*(c + d*x))])/(a*d^2) + (2*b*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a^2*d^2) - ((2*I)*b*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*d^3) + ((2*I)*b^3*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^3) + ((2*I)*b*f^2*PolyLog[2, I*E^(c + d*x)])/(a^2*d^3) - ((2*I)*b^3*f^2*PolyLog[2, I*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^3) - (2*b*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a^2*d^2) + (2*b^4*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)^(3/2)*d^2) - (2*b^4*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)^(3/2)*d^2) - (b^2*f^2*PolyLog[2, -E^(2*(c + d*x))])/(a*(a^2 + b^2)*d^3) + (f^2*PolyLog[2, E^(4*(c + d*x))])/(2*a*d^3) - (2*b*f^2*PolyLog[3, -E^(c + d*x)])/(a^2*d^3) + (2*b*f^2*PolyLog[3, E^(c + d*x)])/(a^2*d^3) - (2*b^4*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)^(3/2)*d^3) + (2*b^4*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)^(3/2)*d^3) - (b*(e + f*x)^2*Sech[c + d*x])/(a^2*d) + (b^3*(e + f*x)^2*Sech[c + d*x])/(a^2*(a^2 + b^2)*d) + (b^2*(e + f*x)^2*Tanh[c + d*x])/(a*(a^2 + b^2)*d)","A",51,25,36,0.6944,1,"{5589, 5461, 4184, 3716, 2190, 2279, 2391, 2622, 321, 207, 5462, 6741, 12, 6742, 6273, 4182, 2531, 2282, 6589, 4180, 5573, 3322, 2264, 3718, 5451}"
470,1,499,0,0.9775823,"\int \frac{(e+f x) \text{csch}^2(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]^2*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{b^4 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2 \left(a^2+b^2\right)^{3/2}}+\frac{b f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{b f \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^2}-\frac{b^3 f \tan ^{-1}(\sinh (c+d x))}{a^2 d^2 \left(a^2+b^2\right)}-\frac{b^2 f \log (\cosh (c+d x))}{a 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^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^2 (e+f x) \tanh (c+d x)}{a d \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 \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}","\frac{b^4 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^2 d^2 \left(a^2+b^2\right)^{3/2}}+\frac{b f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^2}-\frac{b f \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^2}-\frac{b^3 f \tan ^{-1}(\sinh (c+d x))}{a^2 d^2 \left(a^2+b^2\right)}-\frac{b^2 f \log (\cosh (c+d x))}{a 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^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^2 (e+f x) \tanh (c+d x)}{a d \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 \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,"(b*f*ArcTan[Sinh[c + d*x]])/(a^2*d^2) - (b^3*f*ArcTan[Sinh[c + d*x]])/(a^2*(a^2 + b^2)*d^2) + (2*b*f*x*ArcTanh[E^(c + d*x)])/(a^2*d) - (b*f*x*ArcTanh[Cosh[c + d*x]])/(a^2*d) + (b*(e + f*x)*ArcTanh[Cosh[c + d*x]])/(a^2*d) - (2*(e + f*x)*Coth[2*c + 2*d*x])/(a*d) + (b^4*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)^(3/2)*d) - (b^4*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)^(3/2)*d) - (b^2*f*Log[Cosh[c + d*x]])/(a*(a^2 + b^2)*d^2) + (f*Log[Sinh[2*c + 2*d*x]])/(a*d^2) + (b*f*PolyLog[2, -E^(c + d*x)])/(a^2*d^2) - (b*f*PolyLog[2, E^(c + d*x)])/(a^2*d^2) + (b^4*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)^(3/2)*d^2) - (b^4*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)^(3/2)*d^2) - (b*(e + f*x)*Sech[c + d*x])/(a^2*d) + (b^3*(e + f*x)*Sech[c + d*x])/(a^2*(a^2 + b^2)*d) + (b^2*(e + f*x)*Tanh[c + d*x])/(a*(a^2 + b^2)*d)","A",30,20,34,0.5882,1,"{5589, 5461, 4184, 3475, 2622, 321, 207, 5462, 6271, 12, 4182, 2279, 2391, 3770, 5573, 3322, 2264, 2190, 6742, 5451}"
471,1,144,0,0.3107518,"\int \frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Csch[c + d*x]^2*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\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^2 \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a^2 d \left(a^2+b^2\right)}-\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}","-\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^2 \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a^2 d \left(a^2+b^2\right)}-\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,"(b*ArcTanh[Cosh[c + d*x]])/(a^2*d) - (2*b^4*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(a^2*(a^2 + b^2)^(3/2)*d) - Coth[c + d*x]/(a*d) - (b*Sech[c + d*x])/(a^2*d) + (b^2*Sech[c + d*x]*(b + a*Sinh[c + d*x]))/(a^2*(a^2 + b^2)*d) - Tanh[c + d*x]/(a*d)","A",13,11,29,0.3793,1,"{2898, 2622, 321, 207, 2620, 14, 2696, 12, 2660, 618, 204}"
472,0,0,0,0.1290607,"\int \frac{\text{csch}^2(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(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,"Defer[Int][(Csch[c + d*x]^2*Sech[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
473,1,978,0,1.4109984,"\int \frac{(e+f x) \text{csch}^2(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]^2*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) b^4}{a \left(a^2+b^2\right)^2 d^2}+\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-i e^{c+d x}\right) b^2}{2 a \left(a^2+b^2\right) d^2}+\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b}{2 a^2 d^2}-\frac{f \text{PolyLog}\left(2,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{PolyLog}\left(2,-i e^{c+d x}\right)}{2 a d^2}-\frac{3 i f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 a d^2}-\frac{f \text{sech}(c+d x)}{2 a d^2}","\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) b^4}{a \left(a^2+b^2\right)^2 d^2}+\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-i e^{c+d x}\right) b^2}{2 a \left(a^2+b^2\right) d^2}+\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b}{2 a^2 d^2}-\frac{f \text{PolyLog}\left(2,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{PolyLog}\left(2,-i e^{c+d x}\right)}{2 a d^2}-\frac{3 i f \text{PolyLog}\left(2,i e^{c+d x}\right)}{2 a d^2}-\frac{f \text{sech}(c+d x)}{2 a d^2}",1,"-(b*f*x)/(2*a^2*d) - (3*f*x*ArcTan[E^(c + d*x)])/(a*d) + (2*b^4*(e + f*x)*ArcTan[E^(c + d*x)])/(a*(a^2 + b^2)^2*d) + (b^2*(e + f*x)*ArcTan[E^(c + d*x)])/(a*(a^2 + b^2)*d) + (3*f*x*ArcTan[Sinh[c + d*x]])/(2*a*d) - (3*(e + f*x)*ArcTan[Sinh[c + d*x]])/(2*a*d) + (2*b*f*x*ArcTanh[E^(2*c + 2*d*x)])/(a^2*d) - (f*ArcTanh[Cosh[c + d*x]])/(a*d^2) - (3*(e + f*x)*Csch[c + d*x])/(2*a*d) + (b^5*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)^2*d) + (b^5*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^2*(a^2 + b^2)^2*d) - (b^5*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(a^2*(a^2 + b^2)^2*d) + (b*f*x*Log[Tanh[c + d*x]])/(a^2*d) - (b*(e + f*x)*Log[Tanh[c + d*x]])/(a^2*d) + (((3*I)/2)*f*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^2) - (I*b^4*f*PolyLog[2, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)^2*d^2) - ((I/2)*b^2*f*PolyLog[2, (-I)*E^(c + d*x)])/(a*(a^2 + b^2)*d^2) - (((3*I)/2)*f*PolyLog[2, I*E^(c + d*x)])/(a*d^2) + (I*b^4*f*PolyLog[2, I*E^(c + d*x)])/(a*(a^2 + b^2)^2*d^2) + ((I/2)*b^2*f*PolyLog[2, I*E^(c + d*x)])/(a*(a^2 + b^2)*d^2) + (b^5*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)^2*d^2) + (b^5*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^2*(a^2 + b^2)^2*d^2) - (b^5*f*PolyLog[2, -E^(2*(c + d*x))])/(2*a^2*(a^2 + b^2)^2*d^2) + (b*f*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a^2*d^2) - (b*f*PolyLog[2, E^(2*c + 2*d*x)])/(2*a^2*d^2) - (f*Sech[c + d*x])/(2*a*d^2) + (b^2*f*Sech[c + d*x])/(2*a*(a^2 + b^2)*d^2) + (b^3*(e + f*x)*Sech[c + d*x]^2)/(2*a^2*(a^2 + b^2)*d) + ((e + f*x)*Csch[c + d*x]*Sech[c + d*x]^2)/(2*a*d) + (b*f*Tanh[c + d*x])/(2*a^2*d^2) - (b^3*f*Tanh[c + d*x])/(2*a^2*(a^2 + b^2)*d^2) + (b^2*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*a*(a^2 + b^2)*d) + (b*(e + f*x)*Tanh[c + d*x]^2)/(2*a^2*d)","A",57,27,34,0.7941,1,"{5589, 2621, 288, 321, 207, 5462, 5203, 12, 4180, 2279, 2391, 3770, 2622, 2620, 14, 2548, 4182, 3473, 8, 5573, 5561, 2190, 6742, 3718, 4185, 5451, 3767}"
474,1,180,0,0.2591578,"\int \frac{\text{csch}^2(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Csch[c + d*x]^2*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{b^5 \log (a+b \sinh (c+d x))}{a^2 d \left(a^2+b^2\right)^2}-\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 \log (\sinh (c+d x))}{a^2 d}-\frac{\text{csch}(c+d x)}{a d}","\frac{b^5 \log (a+b \sinh (c+d x))}{a^2 d \left(a^2+b^2\right)^2}-\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 \log (\sinh (c+d x))}{a^2 d}-\frac{\text{csch}(c+d x)}{a d}",1,"-(a*ArcTan[Sinh[c + d*x]])/(2*(a^2 + b^2)*d) - (a*(a^2 + 2*b^2)*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)^2*d) - Csch[c + d*x]/(a*d) + (b*(a^2 + 2*b^2)*Log[Cosh[c + d*x]])/((a^2 + b^2)^2*d) - (b*Log[Sinh[c + d*x]])/(a^2*d) + (b^5*Log[a + b*Sinh[c + d*x]])/(a^2*(a^2 + b^2)^2*d) - (Sech[c + d*x]^2*(b + a*Sinh[c + d*x]))/(2*(a^2 + b^2)*d)","A",9,7,29,0.2414,1,"{2837, 12, 894, 639, 203, 635, 260}"
475,0,0,0,0.1352287,"\int \frac{\text{csch}^2(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Csch[c + d*x]^2*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}^2(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}^2(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][(Csch[c + d*x]^2*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
476,1,752,0,1.3530449,"\int \frac{(e+f x)^3 \coth (c+d x) \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Coth[c + d*x]*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\frac{6 b^2 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^3}-\frac{3 b^2 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^3 d^3}-\frac{3 b^2 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{3 b^2 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a^3 d^2}-\frac{6 b^2 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^4}-\frac{6 b^2 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^4}+\frac{3 b^2 f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a^3 d^4}+\frac{6 b f^2 (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^3}-\frac{6 b f^2 (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^3}-\frac{6 b f^3 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^4}+\frac{6 b f^3 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^4}+\frac{3 f^3 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^4}-\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{b^2 (e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}+\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{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}","\frac{6 b^2 f^2 (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^3}-\frac{3 b^2 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^3 d^3}-\frac{3 b^2 f (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{3 b^2 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a^3 d^2}-\frac{6 b^2 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^4}-\frac{6 b^2 f^3 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^4}+\frac{3 b^2 f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a^3 d^4}+\frac{6 b f^2 (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^3}-\frac{6 b f^2 (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^3}-\frac{6 b f^3 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^4}+\frac{6 b f^3 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^4}+\frac{3 f^3 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^4}-\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{b^2 (e+f x)^3 \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}+\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{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,"(-3*f*(e + f*x)^2)/(2*a*d^2) + (6*b*f*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a^2*d^2) - (3*f*(e + f*x)^2*Coth[c + d*x])/(2*a*d^2) + (b*(e + f*x)^3*Csch[c + d*x])/(a^2*d) - ((e + f*x)^3*Csch[c + d*x]^2)/(2*a*d) - (b^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*d) - (b^2*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*d) + (3*f^2*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a*d^3) + (b^2*(e + f*x)^3*Log[1 - E^(2*(c + d*x))])/(a^3*d) + (6*b*f^2*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a^2*d^3) - (6*b*f^2*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a^2*d^3) - (3*b^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^2) - (3*b^2*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^2) + (3*f^3*PolyLog[2, E^(2*(c + d*x))])/(2*a*d^4) + (3*b^2*f*(e + f*x)^2*PolyLog[2, E^(2*(c + d*x))])/(2*a^3*d^2) - (6*b*f^3*PolyLog[3, -E^(c + d*x)])/(a^2*d^4) + (6*b*f^3*PolyLog[3, E^(c + d*x)])/(a^2*d^4) + (6*b^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^3) + (6*b^2*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^3) - (3*b^2*f^2*(e + f*x)*PolyLog[3, E^(2*(c + d*x))])/(2*a^3*d^3) - (6*b^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^4) - (6*b^2*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^4) + (3*b^2*f^3*PolyLog[4, E^(2*(c + d*x))])/(4*a^3*d^4)","A",34,14,34,0.4118,1,"{5587, 5452, 4184, 3716, 2190, 2279, 2391, 4182, 2531, 2282, 6589, 5569, 6609, 5561}"
477,1,502,0,1.0040159,"\int \frac{(e+f x)^2 \coth (c+d x) \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Coth[c + d*x]*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{b^2 f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^3 d^2}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^3}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^3}-\frac{b^2 f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^3 d^3}+\frac{2 b f^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^3}-\frac{2 b f^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^3}-\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{b^2 (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}+\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{f (e+f x) \coth (c+d x)}{a d^2}+\frac{f^2 \log (\sinh (c+d x))}{a d^3}-\frac{(e+f x)^2 \text{csch}^2(c+d x)}{2 a d}","-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{b^2 f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^3 d^2}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^3}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^3}-\frac{b^2 f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^3 d^3}+\frac{2 b f^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^3}-\frac{2 b f^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^3}-\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{b^2 (e+f x)^2 \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}+\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{f (e+f x) \coth (c+d x)}{a d^2}+\frac{f^2 \log (\sinh (c+d x))}{a d^3}-\frac{(e+f x)^2 \text{csch}^2(c+d x)}{2 a d}",1,"(4*b*f*(e + f*x)*ArcTanh[E^(c + d*x)])/(a^2*d^2) - (f*(e + f*x)*Coth[c + d*x])/(a*d^2) + (b*(e + f*x)^2*Csch[c + d*x])/(a^2*d) - ((e + f*x)^2*Csch[c + d*x]^2)/(2*a*d) - (b^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*d) - (b^2*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*d) + (b^2*(e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a^3*d) + (f^2*Log[Sinh[c + d*x]])/(a*d^3) + (2*b*f^2*PolyLog[2, -E^(c + d*x)])/(a^2*d^3) - (2*b*f^2*PolyLog[2, E^(c + d*x)])/(a^2*d^3) - (2*b^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^2) - (2*b^2*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^2) + (b^2*f*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a^3*d^2) + (2*b^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^3) + (2*b^2*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^3) - (b^2*f^2*PolyLog[3, E^(2*(c + d*x))])/(2*a^3*d^3)","A",26,14,34,0.4118,1,"{5587, 5452, 4184, 3475, 4182, 2279, 2391, 5569, 3716, 2190, 2531, 2282, 6589, 5561}"
478,1,298,0,0.5704514,"\int \frac{(e+f x) \coth (c+d x) \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Coth[c + d*x]*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{b^2 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b^2 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{b^2 f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 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{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{f \coth (c+d x)}{2 a d^2}-\frac{(e+f x) \text{csch}^2(c+d x)}{2 a d}","-\frac{b^2 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{a^3 d^2}-\frac{b^2 f \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{b^2 f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 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{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{f \coth (c+d x)}{2 a d^2}-\frac{(e+f x) \text{csch}^2(c+d x)}{2 a d}",1,"(b*f*ArcTanh[Cosh[c + d*x]])/(a^2*d^2) - (f*Coth[c + d*x])/(2*a*d^2) + (b*(e + f*x)*Csch[c + d*x])/(a^2*d) - ((e + f*x)*Csch[c + d*x]^2)/(2*a*d) - (b^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*d) - (b^2*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*d) + (b^2*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a^3*d) - (b^2*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^2) - (b^2*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^2) + (b^2*f*PolyLog[2, E^(2*(c + d*x))])/(2*a^3*d^2)","A",19,11,32,0.3438,1,"{5587, 5452, 3767, 8, 3770, 5569, 3716, 2190, 2279, 2391, 5561}"
479,1,72,0,0.110946,"\int \frac{\coth (c+d x) \text{csch}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Coth[c + d*x]*Csch[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\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}","\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,"(b*Csch[c + d*x])/(a^2*d) - Csch[c + d*x]^2/(2*a*d) + (b^2*Log[Sinh[c + d*x]])/(a^3*d) - (b^2*Log[a + b*Sinh[c + d*x]])/(a^3*d)","A",4,3,27,0.1111,1,"{2833, 12, 44}"
480,0,0,0,0.0920873,"\int \frac{\coth (c+d x) \text{csch}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Coth[c + d*x]*Csch[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\coth (c+d x) \text{csch}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Coth[c + d*x]*Csch[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
481,1,1038,0,2.2407689,"\int \frac{(e+f x)^3 \coth ^2(c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Coth[c + d*x]^2*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{3 \text{PolyLog}\left(2,-e^{c+d x}\right) f^3}{a d^4}+\frac{3 \text{PolyLog}\left(2,e^{c+d x}\right) f^3}{a d^4}+\frac{3 b \text{PolyLog}\left(3,e^{2 (c+d x)}\right) f^3}{2 a^2 d^4}-\frac{6 b^2 \text{PolyLog}\left(4,-e^{c+d x}\right) f^3}{a^3 d^4}-\frac{3 \text{PolyLog}\left(4,-e^{c+d x}\right) f^3}{a d^4}+\frac{6 b^2 \text{PolyLog}\left(4,e^{c+d x}\right) f^3}{a^3 d^4}+\frac{3 \text{PolyLog}\left(4,e^{c+d x}\right) f^3}{a d^4}-\frac{6 b \sqrt{a^2+b^2} \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,e^{2 (c+d x)}\right) f^2}{a^2 d^3}+\frac{6 b^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right) f^2}{a^3 d^3}+\frac{3 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right) f^2}{a d^3}-\frac{6 b^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right) f^2}{a^3 d^3}-\frac{3 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right) f^2}{a d^3}+\frac{6 b \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-e^{c+d x}\right) f}{a^3 d^2}-\frac{3 (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right) f}{2 a d^2}+\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right) f}{a^3 d^2}+\frac{3 (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right) f}{2 a d^2}-\frac{3 b \sqrt{a^2+b^2} (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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}","-\frac{3 \text{PolyLog}\left(2,-e^{c+d x}\right) f^3}{a d^4}+\frac{3 \text{PolyLog}\left(2,e^{c+d x}\right) f^3}{a d^4}+\frac{3 b \text{PolyLog}\left(3,e^{2 (c+d x)}\right) f^3}{2 a^2 d^4}-\frac{6 b^2 \text{PolyLog}\left(4,-e^{c+d x}\right) f^3}{a^3 d^4}-\frac{3 \text{PolyLog}\left(4,-e^{c+d x}\right) f^3}{a d^4}+\frac{6 b^2 \text{PolyLog}\left(4,e^{c+d x}\right) f^3}{a^3 d^4}+\frac{3 \text{PolyLog}\left(4,e^{c+d x}\right) f^3}{a d^4}-\frac{6 b \sqrt{a^2+b^2} \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(2,e^{2 (c+d x)}\right) f^2}{a^2 d^3}+\frac{6 b^2 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right) f^2}{a^3 d^3}+\frac{3 (e+f x) \text{PolyLog}\left(3,-e^{c+d x}\right) f^2}{a d^3}-\frac{6 b^2 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right) f^2}{a^3 d^3}-\frac{3 (e+f x) \text{PolyLog}\left(3,e^{c+d x}\right) f^2}{a d^3}+\frac{6 b \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-e^{c+d x}\right) f}{a^3 d^2}-\frac{3 (e+f x)^2 \text{PolyLog}\left(2,-e^{c+d x}\right) f}{2 a d^2}+\frac{3 b^2 (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right) f}{a^3 d^2}+\frac{3 (e+f x)^2 \text{PolyLog}\left(2,e^{c+d x}\right) f}{2 a d^2}-\frac{3 b \sqrt{a^2+b^2} (e+f x)^2 \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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,"(b*(e + f*x)^3)/(a^2*d) - (6*f^2*(e + f*x)*ArcTanh[E^(c + d*x)])/(a*d^3) - ((e + f*x)^3*ArcTanh[E^(c + d*x)])/(a*d) - (2*b^2*(e + f*x)^3*ArcTanh[E^(c + d*x)])/(a^3*d) + (b*(e + f*x)^3*Coth[c + d*x])/(a^2*d) - (3*f*(e + f*x)^2*Csch[c + d*x])/(2*a*d^2) - ((e + f*x)^3*Coth[c + d*x]*Csch[c + d*x])/(2*a*d) - (b*Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*d) + (b*Sqrt[a^2 + b^2]*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*d) - (3*b*f*(e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a^2*d^2) - (3*f^3*PolyLog[2, -E^(c + d*x)])/(a*d^4) - (3*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(2*a*d^2) - (3*b^2*f*(e + f*x)^2*PolyLog[2, -E^(c + d*x)])/(a^3*d^2) + (3*f^3*PolyLog[2, E^(c + d*x)])/(a*d^4) + (3*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(2*a*d^2) + (3*b^2*f*(e + f*x)^2*PolyLog[2, E^(c + d*x)])/(a^3*d^2) - (3*b*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^2) + (3*b*Sqrt[a^2 + b^2]*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^2) - (3*b*f^2*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a^2*d^3) + (3*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a*d^3) + (6*b^2*f^2*(e + f*x)*PolyLog[3, -E^(c + d*x)])/(a^3*d^3) - (3*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a*d^3) - (6*b^2*f^2*(e + f*x)*PolyLog[3, E^(c + d*x)])/(a^3*d^3) + (6*b*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^3) - (6*b*Sqrt[a^2 + b^2]*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^3) + (3*b*f^3*PolyLog[3, E^(2*(c + d*x))])/(2*a^2*d^4) - (3*f^3*PolyLog[4, -E^(c + d*x)])/(a*d^4) - (6*b^2*f^3*PolyLog[4, -E^(c + d*x)])/(a^3*d^4) + (3*f^3*PolyLog[4, E^(c + d*x)])/(a*d^4) + (6*b^2*f^3*PolyLog[4, E^(c + d*x)])/(a^3*d^4) - (6*b*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^4) + (6*b*Sqrt[a^2 + b^2]*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^4)","A",67,22,34,0.6471,1,"{5587, 5457, 4182, 2531, 6609, 2282, 6589, 4186, 2279, 2391, 5569, 3720, 3716, 2190, 32, 5585, 5450, 3296, 2637, 5565, 3322, 2264}"
482,1,714,0,1.7279959,"\int \frac{(e+f x)^2 \coth ^2(c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Coth[c + d*x]^2*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^3 d^2}+\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a^3 d^2}-\frac{2 b f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^3 d^3}-\frac{2 b^2 f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^3 d^3}+\frac{2 b f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^3}-\frac{b f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^2 d^3}-\frac{f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\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{2 b^2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^3 d}-\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{f (e+f x) \text{csch}(c+d x)}{a d^2}-\frac{f^2 \tanh ^{-1}(\cosh (c+d x))}{a d^3}-\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}","-\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^3 d^2}+\frac{2 b^2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a^3 d^2}-\frac{2 b f \sqrt{a^2+b^2} (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{2 b^2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^3 d^3}-\frac{2 b^2 f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^3 d^3}+\frac{2 b f^2 \sqrt{a^2+b^2} \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^3}-\frac{b f^2 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^2 d^3}-\frac{f (e+f x) \text{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}+\frac{f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}-\frac{f^2 \text{PolyLog}\left(3,e^{c+d x}\right)}{a d^3}-\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{2 b^2 (e+f x)^2 \tanh ^{-1}\left(e^{c+d x}\right)}{a^3 d}-\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{f (e+f x) \text{csch}(c+d x)}{a d^2}-\frac{f^2 \tanh ^{-1}(\cosh (c+d x))}{a d^3}-\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,"(b*(e + f*x)^2)/(a^2*d) - ((e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d) - (2*b^2*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a^3*d) - (f^2*ArcTanh[Cosh[c + d*x]])/(a*d^3) + (b*(e + f*x)^2*Coth[c + d*x])/(a^2*d) - (f*(e + f*x)*Csch[c + d*x])/(a*d^2) - ((e + f*x)^2*Coth[c + d*x]*Csch[c + d*x])/(2*a*d) - (b*Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*d) + (b*Sqrt[a^2 + b^2]*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*d) - (2*b*f*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a^2*d^2) - (f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^2) - (2*b^2*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a^3*d^2) + (f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^2) + (2*b^2*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a^3*d^2) - (2*b*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^2) + (2*b*Sqrt[a^2 + b^2]*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^2) - (b*f^2*PolyLog[2, E^(2*(c + d*x))])/(a^2*d^3) + (f^2*PolyLog[3, -E^(c + d*x)])/(a*d^3) + (2*b^2*f^2*PolyLog[3, -E^(c + d*x)])/(a^3*d^3) - (f^2*PolyLog[3, E^(c + d*x)])/(a*d^3) - (2*b^2*f^2*PolyLog[3, E^(c + d*x)])/(a^3*d^3) + (2*b*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^3) - (2*b*Sqrt[a^2 + b^2]*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^3)","A",52,22,34,0.6471,1,"{5587, 5457, 4182, 2531, 2282, 6589, 4186, 3770, 5569, 3720, 3716, 2190, 2279, 2391, 32, 5585, 5450, 3296, 2638, 5565, 3322, 2264}"
483,1,413,0,0.9287635,"\int \frac{(e+f x) \coth ^2(c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Coth[c + d*x]^2*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{b^2 f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^3 d^2}+\frac{b^2 f \text{PolyLog}\left(2,e^{c+d x}\right)}{a^3 d^2}-\frac{b f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}-\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}+\frac{f \text{PolyLog}\left(2,e^{c+d x}\right)}{2 a 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{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{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}","-\frac{b^2 f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^3 d^2}+\frac{b^2 f \text{PolyLog}\left(2,e^{c+d x}\right)}{a^3 d^2}-\frac{b f \sqrt{a^2+b^2} \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}-\frac{f \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}+\frac{f \text{PolyLog}\left(2,e^{c+d x}\right)}{2 a 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{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{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,"-(((e + f*x)*ArcTanh[E^(c + d*x)])/(a*d)) - (2*b^2*(e + f*x)*ArcTanh[E^(c + d*x)])/(a^3*d) + (b*(e + f*x)*Coth[c + d*x])/(a^2*d) - (f*Csch[c + d*x])/(2*a*d^2) - ((e + f*x)*Coth[c + d*x]*Csch[c + d*x])/(2*a*d) - (b*Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*d) + (b*Sqrt[a^2 + b^2]*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*d) - (b*f*Log[Sinh[c + d*x]])/(a^2*d^2) - (f*PolyLog[2, -E^(c + d*x)])/(2*a*d^2) - (b^2*f*PolyLog[2, -E^(c + d*x)])/(a^3*d^2) + (f*PolyLog[2, E^(c + d*x)])/(2*a*d^2) + (b^2*f*PolyLog[2, E^(c + d*x)])/(a^3*d^2) - (b*Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^2) + (b*Sqrt[a^2 + b^2]*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^2)","A",38,17,32,0.5312,1,"{5587, 5457, 4182, 2279, 2391, 4185, 5569, 3720, 3475, 5585, 5450, 3296, 2637, 5565, 3322, 2264, 2190}"
484,1,111,0,0.5694312,"\int \frac{\coth ^2(c+d x) \text{csch}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Coth[c + d*x]^2*Csch[c + d*x])/(a + b*Sinh[c + d*x]),x]","\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{b \coth (c+d x)}{a^2 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a 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{b \coth (c+d x)}{a^2 d}-\frac{\coth (c+d x) \text{csch}(c+d x)}{2 a d}",1,"-((a^2 + 2*b^2)*ArcTanh[Cosh[c + d*x]])/(2*a^3*d) + (2*b*Sqrt[a^2 + b^2]*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(a^3*d) + (b*Coth[c + d*x])/(a^2*d) - (Coth[c + d*x]*Csch[c + d*x])/(2*a*d)","A",8,8,27,0.2963,1,"{2889, 3056, 3055, 3001, 3770, 2660, 618, 204}"
485,0,0,0,0.0877947,"\int \frac{\coth ^2(c+d x) \text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Coth[c + d*x]^2*Csch[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\coth ^2(c+d x) \text{csch}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\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,"Defer[Int][(Coth[c + d*x]^2*Csch[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
486,1,972,0,2.2027674,"\int \frac{(e+f x)^3 \coth ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Coth[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,e^{2 (c+d x)}\right) (e+f x)^2}{2 a^3 d^2}+\frac{3 f \text{PolyLog}\left(2,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{PolyLog}\left(2,-e^{c+d x}\right) (e+f x)}{a^2 d^3}-\frac{6 b f^2 \text{PolyLog}\left(2,e^{c+d x}\right) (e+f x)}{a^2 d^3}+\frac{6 \left(a^2+b^2\right) f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,e^{2 (c+d x)}\right) (e+f x)}{2 a^3 d^3}-\frac{3 f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right) (e+f x)}{2 a d^3}+\frac{3 f^3 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^4}-\frac{6 b f^3 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^4}+\frac{6 b f^3 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^4}-\frac{6 \left(a^2+b^2\right) f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^4}+\frac{3 b^2 f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a^3 d^4}+\frac{3 f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a d^4}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,e^{2 (c+d x)}\right) (e+f x)^2}{2 a^3 d^2}+\frac{3 f \text{PolyLog}\left(2,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{PolyLog}\left(2,-e^{c+d x}\right) (e+f x)}{a^2 d^3}-\frac{6 b f^2 \text{PolyLog}\left(2,e^{c+d x}\right) (e+f x)}{a^2 d^3}+\frac{6 \left(a^2+b^2\right) f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,e^{2 (c+d x)}\right) (e+f x)}{2 a^3 d^3}-\frac{3 f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right) (e+f x)}{2 a d^3}+\frac{3 f^3 \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^4}-\frac{6 b f^3 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a^2 d^4}+\frac{6 b f^3 \text{PolyLog}\left(3,e^{c+d x}\right)}{a^2 d^4}-\frac{6 \left(a^2+b^2\right) f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{a^3 d^4}+\frac{3 b^2 f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a^3 d^4}+\frac{3 f^3 \text{PolyLog}\left(4,e^{2 (c+d x)}\right)}{4 a d^4}",1,"(-3*f*(e + f*x)^2)/(2*a*d^2) + (e + f*x)^3/(2*a*d) - (e + f*x)^4/(4*a*f) - (b^2*(e + f*x)^4)/(4*a^3*f) + ((a^2 + b^2)*(e + f*x)^4)/(4*a^3*f) + (6*b*f*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a^2*d^2) - (3*f*(e + f*x)^2*Coth[c + d*x])/(2*a*d^2) - ((e + f*x)^3*Coth[c + d*x]^2)/(2*a*d) + (b*(e + f*x)^3*Csch[c + d*x])/(a^2*d) - ((a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*d) - ((a^2 + b^2)*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*d) + (3*f^2*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a*d^3) + ((e + f*x)^3*Log[1 - E^(2*(c + d*x))])/(a*d) + (b^2*(e + f*x)^3*Log[1 - E^(2*(c + d*x))])/(a^3*d) + (6*b*f^2*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a^2*d^3) - (6*b*f^2*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a^2*d^3) - (3*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^2) - (3*(a^2 + b^2)*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^2) + (3*f^3*PolyLog[2, E^(2*(c + d*x))])/(2*a*d^4) + (3*f*(e + f*x)^2*PolyLog[2, E^(2*(c + d*x))])/(2*a*d^2) + (3*b^2*f*(e + f*x)^2*PolyLog[2, E^(2*(c + d*x))])/(2*a^3*d^2) - (6*b*f^3*PolyLog[3, -E^(c + d*x)])/(a^2*d^4) + (6*b*f^3*PolyLog[3, E^(c + d*x)])/(a^2*d^4) + (6*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^3) + (6*(a^2 + b^2)*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^3) - (3*f^2*(e + f*x)*PolyLog[3, E^(2*(c + d*x))])/(2*a*d^3) - (3*b^2*f^2*(e + f*x)*PolyLog[3, E^(2*(c + d*x))])/(2*a^3*d^3) - (6*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^4) - (6*(a^2 + b^2)*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^4) + (3*f^3*PolyLog[4, E^(2*(c + d*x))])/(4*a*d^4) + (3*b^2*f^3*PolyLog[4, E^(2*(c + d*x))])/(4*a^3*d^4)","A",62,23,28,0.8214,1,"{5569, 3720, 3716, 2190, 2279, 2391, 32, 2531, 6609, 2282, 6589, 5585, 5450, 3296, 2638, 5452, 4182, 5446, 3311, 2635, 8, 5565, 5561}"
487,1,689,0,1.7084992,"\int \frac{(e+f x)^2 \coth ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Coth[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{2 f \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{b^2 f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^3 d^2}+\frac{2 f^2 \left(a^2+b^2\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^3}-\frac{b^2 f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^3 d^3}+\frac{2 b f^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^3}-\frac{2 b f^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^3}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^3}-\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{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{\left(a^2+b^2\right) (e+f x)^3}{3 a^3 f}+\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{f (e+f x) \coth (c+d x)}{a d^2}+\frac{f^2 \log (\sinh (c+d x))}{a d^3}+\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}","-\frac{2 f \left(a^2+b^2\right) (e+f x) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{b^2 f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a^3 d^2}+\frac{2 f^2 \left(a^2+b^2\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^3}-\frac{b^2 f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a^3 d^3}+\frac{2 b f^2 \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^2 d^3}-\frac{2 b f^2 \text{PolyLog}\left(2,e^{c+d x}\right)}{a^2 d^3}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,e^{2 (c+d x)}\right)}{2 a d^3}-\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{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{\left(a^2+b^2\right) (e+f x)^3}{3 a^3 f}+\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{f (e+f x) \coth (c+d x)}{a d^2}+\frac{f^2 \log (\sinh (c+d x))}{a d^3}+\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,"(e*f*x)/(a*d) + (f^2*x^2)/(2*a*d) - (e + f*x)^3/(3*a*f) - (b^2*(e + f*x)^3)/(3*a^3*f) + ((a^2 + b^2)*(e + f*x)^3)/(3*a^3*f) + (4*b*f*(e + f*x)*ArcTanh[E^(c + d*x)])/(a^2*d^2) - (f*(e + f*x)*Coth[c + d*x])/(a*d^2) - ((e + f*x)^2*Coth[c + d*x]^2)/(2*a*d) + (b*(e + f*x)^2*Csch[c + d*x])/(a^2*d) - ((a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*d) - ((a^2 + b^2)*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*d) + ((e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a*d) + (b^2*(e + f*x)^2*Log[1 - E^(2*(c + d*x))])/(a^3*d) + (f^2*Log[Sinh[c + d*x]])/(a*d^3) + (2*b*f^2*PolyLog[2, -E^(c + d*x)])/(a^2*d^3) - (2*b*f^2*PolyLog[2, E^(c + d*x)])/(a^2*d^3) - (2*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^2) - (2*(a^2 + b^2)*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^2) + (f*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a*d^2) + (b^2*f*(e + f*x)*PolyLog[2, E^(2*(c + d*x))])/(a^3*d^2) + (2*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^3) + (2*(a^2 + b^2)*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^3) - (f^2*PolyLog[3, E^(2*(c + d*x))])/(2*a*d^3) - (b^2*f^2*PolyLog[3, E^(2*(c + d*x))])/(2*a^3*d^3)","A",47,20,28,0.7143,1,"{5569, 3720, 3475, 3716, 2190, 2531, 2282, 6589, 5585, 5450, 3296, 2637, 5452, 4182, 2279, 2391, 5446, 3310, 5565, 5561}"
488,1,435,0,0.9761582,"\int \frac{(e+f x) \coth ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Coth[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","\frac{b^2 f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a^3 d^2}-\frac{f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^2}+\frac{b^2 (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}-\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{b^2 (e+f x)^2}{2 a^3 f}+\frac{\left(a^2+b^2\right) (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 \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}","\frac{b^2 f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a^3 d^2}-\frac{f \left(a^2+b^2\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2}+\frac{f \text{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^2}+\frac{b^2 (e+f x) \log \left(1-e^{2 (c+d x)}\right)}{a^3 d}-\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{b^2 (e+f x)^2}{2 a^3 f}+\frac{\left(a^2+b^2\right) (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 \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,"(f*x)/(2*a*d) - (e + f*x)^2/(2*a*f) - (b^2*(e + f*x)^2)/(2*a^3*f) + ((a^2 + b^2)*(e + f*x)^2)/(2*a^3*f) + (b*f*ArcTanh[Cosh[c + d*x]])/(a^2*d^2) - (f*Coth[c + d*x])/(2*a*d^2) - ((e + f*x)*Coth[c + d*x]^2)/(2*a*d) + (b*(e + f*x)*Csch[c + d*x])/(a^2*d) - ((a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*d) - ((a^2 + b^2)*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*d) + ((e + f*x)*Log[1 - E^(2*(c + d*x))])/(a*d) + (b^2*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a^3*d) - ((a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*d^2) - ((a^2 + b^2)*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*d^2) + (f*PolyLog[2, E^(2*(c + d*x))])/(2*a*d^2) + (b^2*f*PolyLog[2, E^(2*(c + d*x))])/(2*a^3*d^2)","A",36,18,26,0.6923,1,"{5569, 3720, 3473, 8, 3716, 2190, 2279, 2391, 5585, 5450, 3296, 2638, 5452, 3770, 5446, 2635, 5565, 5561}"
489,1,80,0,0.1051653,"\int \frac{\coth ^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[Coth[c + d*x]^3/(a + b*Sinh[c + d*x]),x]","\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{b \text{csch}(c+d x)}{a^2 d}-\frac{\text{csch}^2(c+d x)}{2 a 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{b \text{csch}(c+d x)}{a^2 d}-\frac{\text{csch}^2(c+d x)}{2 a d}",1,"(b*Csch[c + d*x])/(a^2*d) - Csch[c + d*x]^2/(2*a*d) + ((a^2 + b^2)*Log[Sinh[c + d*x]])/(a^3*d) - ((a^2 + b^2)*Log[a + b*Sinh[c + d*x]])/(a^3*d)","A",3,2,21,0.09524,1,"{2721, 894}"
490,0,0,0,0.0761779,"\int \frac{\coth ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[Coth[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\coth ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","\text{Int}\left(\frac{\coth ^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][Coth[c + d*x]^3/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
491,1,1795,0,3.2720866,"\int \frac{(e+f x)^3 \text{csch}^3(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^3*Csch[c + d*x]^3*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-e^{2 (c+d x)}\right) b^4}{2 a^3 \left(a^2+b^2\right) d^3}-\frac{6 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(3,-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{PolyLog}\left(3,i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}+\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b^2}{2 a^3 d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 c+2 d x}\right) b^2}{2 a^3 d^2}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-e^{2 c+2 d x}\right) b^2}{2 a^3 d^3}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 c+2 d x}\right) b^2}{2 a^3 d^3}-\frac{3 f^3 \text{PolyLog}\left(4,-e^{2 c+2 d x}\right) b^2}{4 a^3 d^4}+\frac{3 f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-e^{c+d x}\right) b}{a^2 d^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right) b}{a^2 d^2}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right) b}{a^2 d^2}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right) b}{a^2 d^3}-\frac{6 f^3 \text{PolyLog}\left(3,-e^{c+d x}\right) b}{a^2 d^4}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right) b}{a^2 d^3}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right) b}{a^2 d^3}+\frac{6 f^3 \text{PolyLog}\left(3,e^{c+d x}\right) b}{a^2 d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right) b}{a^2 d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^4}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a d^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a d^2}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-e^{2 c+2 d x}\right)}{2 a d^3}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 c+2 d x}\right)}{2 a d^3}+\frac{3 f^3 \text{PolyLog}\left(4,-e^{2 c+2 d x}\right)}{4 a d^4}-\frac{3 f^3 \text{PolyLog}\left(4,e^{2 c+2 d x}\right)}{4 a d^4}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-e^{2 (c+d x)}\right) b^4}{2 a^3 \left(a^2+b^2\right) d^3}-\frac{6 f^3 \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\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{PolyLog}\left(4,-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{PolyLog}\left(2,-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{PolyLog}\left(2,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{PolyLog}\left(3,-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{PolyLog}\left(3,i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}+\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b^2}{2 a^3 d^2}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 c+2 d x}\right) b^2}{2 a^3 d^2}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-e^{2 c+2 d x}\right) b^2}{2 a^3 d^3}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 c+2 d x}\right) b^2}{2 a^3 d^3}-\frac{3 f^3 \text{PolyLog}\left(4,-e^{2 c+2 d x}\right) b^2}{4 a^3 d^4}+\frac{3 f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,-e^{c+d x}\right) b}{a^2 d^3}-\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,-i e^{c+d x}\right) b}{a^2 d^2}+\frac{3 i f (e+f x)^2 \text{PolyLog}\left(2,i e^{c+d x}\right) b}{a^2 d^2}-\frac{6 f^2 (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right) b}{a^2 d^3}-\frac{6 f^3 \text{PolyLog}\left(3,-e^{c+d x}\right) b}{a^2 d^4}+\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,-i e^{c+d x}\right) b}{a^2 d^3}-\frac{6 i f^2 (e+f x) \text{PolyLog}\left(3,i e^{c+d x}\right) b}{a^2 d^3}+\frac{6 f^3 \text{PolyLog}\left(3,e^{c+d x}\right) b}{a^2 d^4}-\frac{6 i f^3 \text{PolyLog}\left(4,-i e^{c+d x}\right) b}{a^2 d^4}+\frac{6 i f^3 \text{PolyLog}\left(4,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{PolyLog}\left(2,e^{2 (c+d x)}\right)}{2 a d^4}+\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a d^2}-\frac{3 f (e+f x)^2 \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a d^2}-\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,-e^{2 c+2 d x}\right)}{2 a d^3}+\frac{3 f^2 (e+f x) \text{PolyLog}\left(3,e^{2 c+2 d x}\right)}{2 a d^3}+\frac{3 f^3 \text{PolyLog}\left(4,-e^{2 c+2 d x}\right)}{4 a d^4}-\frac{3 f^3 \text{PolyLog}\left(4,e^{2 c+2 d x}\right)}{4 a d^4}",1,"(-3*f*(e + f*x)^2)/(2*a*d^2) + (e + f*x)^3/(2*a*d) + (2*b*(e + f*x)^3*ArcTan[E^(c + d*x)])/(a^2*d) - (2*b^3*(e + f*x)^3*ArcTan[E^(c + d*x)])/(a^2*(a^2 + b^2)*d) + (6*b*f*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a^2*d^2) + (2*(e + f*x)^3*ArcTanh[E^(2*c + 2*d*x)])/(a*d) - (2*b^2*(e + f*x)^3*ArcTanh[E^(2*c + 2*d*x)])/(a^3*d) - (3*f*(e + f*x)^2*Coth[c + d*x])/(2*a*d^2) - ((e + f*x)^3*Coth[c + d*x]^2)/(2*a*d) + (b*(e + f*x)^3*Csch[c + d*x])/(a^2*d) - (b^4*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)*d) - (b^4*(e + f*x)^3*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)*d) + (3*f^2*(e + f*x)*Log[1 - E^(2*(c + d*x))])/(a*d^3) + (b^4*(e + f*x)^3*Log[1 + E^(2*(c + d*x))])/(a^3*(a^2 + b^2)*d) + (6*b*f^2*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a^2*d^3) - ((3*I)*b*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*d^2) + ((3*I)*b^3*f*(e + f*x)^2*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^2) + ((3*I)*b*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(a^2*d^2) - ((3*I)*b^3*f*(e + f*x)^2*PolyLog[2, I*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^2) - (6*b*f^2*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a^2*d^3) - (3*b^4*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^2) - (3*b^4*f*(e + f*x)^2*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^2) + (3*b^4*f*(e + f*x)^2*PolyLog[2, -E^(2*(c + d*x))])/(2*a^3*(a^2 + b^2)*d^2) + (3*f^3*PolyLog[2, E^(2*(c + d*x))])/(2*a*d^4) + (3*f*(e + f*x)^2*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a*d^2) - (3*b^2*f*(e + f*x)^2*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a^3*d^2) - (3*f*(e + f*x)^2*PolyLog[2, E^(2*c + 2*d*x)])/(2*a*d^2) + (3*b^2*f*(e + f*x)^2*PolyLog[2, E^(2*c + 2*d*x)])/(2*a^3*d^2) - (6*b*f^3*PolyLog[3, -E^(c + d*x)])/(a^2*d^4) + ((6*I)*b*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(a^2*d^3) - ((6*I)*b^3*f^2*(e + f*x)*PolyLog[3, (-I)*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^3) - ((6*I)*b*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(a^2*d^3) + ((6*I)*b^3*f^2*(e + f*x)*PolyLog[3, I*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^3) + (6*b*f^3*PolyLog[3, E^(c + d*x)])/(a^2*d^4) + (6*b^4*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^3) + (6*b^4*f^2*(e + f*x)*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^3) - (3*b^4*f^2*(e + f*x)*PolyLog[3, -E^(2*(c + d*x))])/(2*a^3*(a^2 + b^2)*d^3) - (3*f^2*(e + f*x)*PolyLog[3, -E^(2*c + 2*d*x)])/(2*a*d^3) + (3*b^2*f^2*(e + f*x)*PolyLog[3, -E^(2*c + 2*d*x)])/(2*a^3*d^3) + (3*f^2*(e + f*x)*PolyLog[3, E^(2*c + 2*d*x)])/(2*a*d^3) - (3*b^2*f^2*(e + f*x)*PolyLog[3, E^(2*c + 2*d*x)])/(2*a^3*d^3) - ((6*I)*b*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(a^2*d^4) + ((6*I)*b^3*f^3*PolyLog[4, (-I)*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^4) + ((6*I)*b*f^3*PolyLog[4, I*E^(c + d*x)])/(a^2*d^4) - ((6*I)*b^3*f^3*PolyLog[4, I*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^4) - (6*b^4*f^3*PolyLog[4, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^4) - (6*b^4*f^3*PolyLog[4, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^4) + (3*b^4*f^3*PolyLog[4, -E^(2*(c + d*x))])/(4*a^3*(a^2 + b^2)*d^4) + (3*f^3*PolyLog[4, -E^(2*c + 2*d*x)])/(4*a*d^4) - (3*b^2*f^3*PolyLog[4, -E^(2*c + 2*d*x)])/(4*a^3*d^4) - (3*f^3*PolyLog[4, E^(2*c + 2*d*x)])/(4*a*d^4) + (3*b^2*f^3*PolyLog[4, E^(2*c + 2*d*x)])/(4*a^3*d^4)","A",87,28,34,0.8235,1,"{5589, 2620, 14, 5462, 6741, 12, 6742, 3720, 3716, 2190, 2279, 2391, 32, 2551, 4182, 2531, 6609, 2282, 6589, 2621, 321, 207, 5205, 4180, 5461, 5573, 5561, 3718}"
492,1,1219,0,2.2224308,"\int \frac{(e+f x)^2 \text{csch}^3(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)^2*Csch[c + d*x]^3*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) b^4}{a^3 \left(a^2+b^2\right) d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b^2}{a^3 d^2}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 c+2 d x}\right) b^2}{a^3 d^2}+\frac{f^2 \text{PolyLog}\left(3,-e^{2 c+2 d x}\right) b^2}{2 a^3 d^3}-\frac{f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{c+d x}\right) b}{a^2 d^3}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right) b}{a^2 d^2}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) b}{a^2 d^2}-\frac{2 f^2 \text{PolyLog}\left(2,e^{c+d x}\right) b}{a^2 d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b}{a^2 d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{a d^2}-\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,-e^{2 c+2 d x}\right)}{2 a d^3}+\frac{f^2 \text{PolyLog}\left(3,e^{2 c+2 d x}\right)}{2 a d^3}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-e^{2 (c+d x)}\right) b^4}{a^3 \left(a^2+b^2\right) d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-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{PolyLog}\left(2,-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{PolyLog}\left(2,i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^2}-\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b^3}{a^2 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b^2}{a^3 d^2}+\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 c+2 d x}\right) b^2}{a^3 d^2}+\frac{f^2 \text{PolyLog}\left(3,-e^{2 c+2 d x}\right) b^2}{2 a^3 d^3}-\frac{f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{c+d x}\right) b}{a^2 d^3}-\frac{2 i f (e+f x) \text{PolyLog}\left(2,-i e^{c+d x}\right) b}{a^2 d^2}+\frac{2 i f (e+f x) \text{PolyLog}\left(2,i e^{c+d x}\right) b}{a^2 d^2}-\frac{2 f^2 \text{PolyLog}\left(2,e^{c+d x}\right) b}{a^2 d^3}+\frac{2 i f^2 \text{PolyLog}\left(3,-i e^{c+d x}\right) b}{a^2 d^3}-\frac{2 i f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{a d^2}-\frac{f (e+f x) \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{a d^2}-\frac{f^2 \text{PolyLog}\left(3,-e^{2 c+2 d x}\right)}{2 a d^3}+\frac{f^2 \text{PolyLog}\left(3,e^{2 c+2 d x}\right)}{2 a d^3}",1,"(e*f*x)/(a*d) + (f^2*x^2)/(2*a*d) + (2*b*(e + f*x)^2*ArcTan[E^(c + d*x)])/(a^2*d) - (2*b^3*(e + f*x)^2*ArcTan[E^(c + d*x)])/(a^2*(a^2 + b^2)*d) + (4*b*f*(e + f*x)*ArcTanh[E^(c + d*x)])/(a^2*d^2) + (2*(e + f*x)^2*ArcTanh[E^(2*c + 2*d*x)])/(a*d) - (2*b^2*(e + f*x)^2*ArcTanh[E^(2*c + 2*d*x)])/(a^3*d) - (f*(e + f*x)*Coth[c + d*x])/(a*d^2) - ((e + f*x)^2*Coth[c + d*x]^2)/(2*a*d) + (b*(e + f*x)^2*Csch[c + d*x])/(a^2*d) - (b^4*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)*d) - (b^4*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)*d) + (b^4*(e + f*x)^2*Log[1 + E^(2*(c + d*x))])/(a^3*(a^2 + b^2)*d) + (f^2*Log[Sinh[c + d*x]])/(a*d^3) + (2*b*f^2*PolyLog[2, -E^(c + d*x)])/(a^2*d^3) - ((2*I)*b*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*d^2) + ((2*I)*b^3*f*(e + f*x)*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^2) + ((2*I)*b*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(a^2*d^2) - ((2*I)*b^3*f*(e + f*x)*PolyLog[2, I*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^2) - (2*b*f^2*PolyLog[2, E^(c + d*x)])/(a^2*d^3) - (2*b^4*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^2) - (2*b^4*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^2) + (b^4*f*(e + f*x)*PolyLog[2, -E^(2*(c + d*x))])/(a^3*(a^2 + b^2)*d^2) + (f*(e + f*x)*PolyLog[2, -E^(2*c + 2*d*x)])/(a*d^2) - (b^2*f*(e + f*x)*PolyLog[2, -E^(2*c + 2*d*x)])/(a^3*d^2) - (f*(e + f*x)*PolyLog[2, E^(2*c + 2*d*x)])/(a*d^2) + (b^2*f*(e + f*x)*PolyLog[2, E^(2*c + 2*d*x)])/(a^3*d^2) + ((2*I)*b*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(a^2*d^3) - ((2*I)*b^3*f^2*PolyLog[3, (-I)*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^3) - ((2*I)*b*f^2*PolyLog[3, I*E^(c + d*x)])/(a^2*d^3) + ((2*I)*b^3*f^2*PolyLog[3, I*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^3) + (2*b^4*f^2*PolyLog[3, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^3) + (2*b^4*f^2*PolyLog[3, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^3) - (b^4*f^2*PolyLog[3, -E^(2*(c + d*x))])/(2*a^3*(a^2 + b^2)*d^3) - (f^2*PolyLog[3, -E^(2*c + 2*d*x)])/(2*a*d^3) + (b^2*f^2*PolyLog[3, -E^(2*c + 2*d*x)])/(2*a^3*d^3) + (f^2*PolyLog[3, E^(2*c + 2*d*x)])/(2*a*d^3) - (b^2*f^2*PolyLog[3, E^(2*c + 2*d*x)])/(2*a^3*d^3)","A",71,26,34,0.7647,1,"{5589, 2620, 14, 5462, 6741, 12, 6742, 3720, 3475, 2551, 4182, 2531, 2282, 6589, 2621, 321, 207, 5205, 4180, 2279, 2391, 5461, 5573, 5561, 2190, 3718}"
493,1,762,0,1.1378503,"\int \frac{(e+f x) \text{csch}^3(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]^3*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{b^4 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2 \left(a^2+b^2\right)}+\frac{b^4 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a^3 d^2 \left(a^2+b^2\right)}+\frac{i b^3 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a^2 d^2 \left(a^2+b^2\right)}-\frac{i b^3 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{a^2 d^2 \left(a^2+b^2\right)}-\frac{b^2 f \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a^3 d^2}+\frac{b^2 f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a^3 d^2}-\frac{i b f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a^2 d^2}+\frac{i b f \text{PolyLog}\left(2,i e^{c+d x}\right)}{a^2 d^2}+\frac{f \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a d^2}-\frac{f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a d^2}-\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{2 b^3 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{a^2 d \left(a^2+b^2\right)}-\frac{2 b^2 (e+f x) \tanh ^{-1}\left(e^{2 c+2 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 (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{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}","-\frac{b^4 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2 \left(a^2+b^2\right)}+\frac{b^4 f \text{PolyLog}\left(2,-e^{2 (c+d x)}\right)}{2 a^3 d^2 \left(a^2+b^2\right)}+\frac{i b^3 f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a^2 d^2 \left(a^2+b^2\right)}-\frac{i b^3 f \text{PolyLog}\left(2,i e^{c+d x}\right)}{a^2 d^2 \left(a^2+b^2\right)}-\frac{b^2 f \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a^3 d^2}+\frac{b^2 f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a^3 d^2}-\frac{i b f \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a^2 d^2}+\frac{i b f \text{PolyLog}\left(2,i e^{c+d x}\right)}{a^2 d^2}+\frac{f \text{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{2 a d^2}-\frac{f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{2 a d^2}-\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{2 b^3 (e+f x) \tan ^{-1}\left(e^{c+d x}\right)}{a^2 d \left(a^2+b^2\right)}-\frac{2 b^2 (e+f x) \tanh ^{-1}\left(e^{2 c+2 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 (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{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,"(f*x)/(2*a*d) + (2*b*f*x*ArcTan[E^(c + d*x)])/(a^2*d) - (2*b^3*(e + f*x)*ArcTan[E^(c + d*x)])/(a^2*(a^2 + b^2)*d) - (b*f*x*ArcTan[Sinh[c + d*x]])/(a^2*d) + (b*(e + f*x)*ArcTan[Sinh[c + d*x]])/(a^2*d) + (2*f*x*ArcTanh[E^(2*c + 2*d*x)])/(a*d) - (2*b^2*(e + f*x)*ArcTanh[E^(2*c + 2*d*x)])/(a^3*d) + (b*f*ArcTanh[Cosh[c + d*x]])/(a^2*d^2) - (f*Coth[c + d*x])/(2*a*d^2) - ((e + f*x)*Coth[c + d*x]^2)/(2*a*d) + (b*(e + f*x)*Csch[c + d*x])/(a^2*d) - (b^4*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)*d) - (b^4*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)*d) + (b^4*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(a^3*(a^2 + b^2)*d) + (f*x*Log[Tanh[c + d*x]])/(a*d) - ((e + f*x)*Log[Tanh[c + d*x]])/(a*d) - (I*b*f*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*d^2) + (I*b^3*f*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^2) + (I*b*f*PolyLog[2, I*E^(c + d*x)])/(a^2*d^2) - (I*b^3*f*PolyLog[2, I*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^2) - (b^4*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^2) - (b^4*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)*d^2) + (b^4*f*PolyLog[2, -E^(2*(c + d*x))])/(2*a^3*(a^2 + b^2)*d^2) + (f*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a*d^2) - (b^2*f*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a^3*d^2) - (f*PolyLog[2, E^(2*c + 2*d*x)])/(2*a*d^2) + (b^2*f*PolyLog[2, E^(2*c + 2*d*x)])/(2*a^3*d^2)","A",49,23,32,0.7188,1,"{5589, 2620, 14, 5462, 3473, 8, 2548, 12, 4182, 2279, 2391, 2621, 321, 207, 5203, 4180, 3770, 5461, 5573, 5561, 2190, 6742, 3718}"
494,1,130,0,0.2354706,"\int \frac{\text{csch}^3(c+d x) \text{sech}(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Csch[c + d*x]^3*Sech[c + d*x])/(a + b*Sinh[c + d*x]),x]","-\frac{b^4 \log (a+b \sinh (c+d x))}{a^3 d \left(a^2+b^2\right)}-\frac{\left(a^2-b^2\right) \log (\sinh (c+d x))}{a^3 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{\text{csch}^2(c+d x)}{2 a d}","-\frac{b^4 \log (a+b \sinh (c+d x))}{a^3 d \left(a^2+b^2\right)}-\frac{\left(a^2-b^2\right) \log (\sinh (c+d x))}{a^3 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{\text{csch}^2(c+d x)}{2 a d}",1,"(b*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)*d) + (b*Csch[c + d*x])/(a^2*d) - Csch[c + d*x]^2/(2*a*d) + (a*Log[Cosh[c + d*x]])/((a^2 + b^2)*d) - ((a^2 - b^2)*Log[Sinh[c + d*x]])/(a^3*d) - (b^4*Log[a + b*Sinh[c + d*x]])/(a^3*(a^2 + b^2)*d)","A",7,6,27,0.2222,1,"{2837, 12, 894, 635, 203, 260}"
495,0,0,0,0.09124,"\int \frac{\text{csch}^3(c+d x) \text{sech}(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(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,"Defer[Int][(Csch[c + d*x]^3*Sech[c + d*x])/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
496,1,1245,0,3.4373317,"\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","Int[((e + f*x)^2*Csch[c + d*x]^3*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-i e^{c+d x}\right) b^4}{a^3 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,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{PolyLog}\left(2,-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{PolyLog}\left(2,-e^{c+d x}\right) b^2}{a^3 d^2}+\frac{2 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right) b^2}{a^3 d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,i e^{c+d x}\right) b^2}{a^3 d^3}+\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right) b^2}{a^3 d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right) b^2}{a^3 d^3}-\frac{2 f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{2 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{3 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{3 f^2 \text{PolyLog}\left(3,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}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(3,-\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{PolyLog}\left(3,-\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{PolyLog}\left(2,-i e^{c+d x}\right) b^4}{a^3 \left(a^2+b^2\right) d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,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{PolyLog}\left(2,-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{PolyLog}\left(2,-e^{c+d x}\right) b^2}{a^3 d^2}+\frac{2 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right) b^2}{a^3 d^3}-\frac{2 i f^2 \text{PolyLog}\left(2,i e^{c+d x}\right) b^2}{a^3 d^3}+\frac{2 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right) b^2}{a^3 d^2}+\frac{2 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right) b^2}{a^3 d^3}-\frac{2 f^2 \text{PolyLog}\left(3,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{PolyLog}\left(2,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{PolyLog}\left(2,-e^{c+d x}\right)}{a d^2}-\frac{2 i f^2 \text{PolyLog}\left(2,-i e^{c+d x}\right)}{a d^3}+\frac{2 i f^2 \text{PolyLog}\left(2,i e^{c+d x}\right)}{a d^3}-\frac{3 f (e+f x) \text{PolyLog}\left(2,e^{c+d x}\right)}{a d^2}-\frac{3 f^2 \text{PolyLog}\left(3,-e^{c+d x}\right)}{a d^3}+\frac{3 f^2 \text{PolyLog}\left(3,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,"(2*b*(e + f*x)^2)/(a^2*d) - (b^3*(e + f*x)^2)/(a^2*(a^2 + b^2)*d) + (4*f^2*x*ArcTan[E^(c + d*x)])/(a*d^2) - (4*b^2*f*(e + f*x)*ArcTan[E^(c + d*x)])/(a^3*d^2) + (4*b^4*f*(e + f*x)*ArcTan[E^(c + d*x)])/(a^3*(a^2 + b^2)*d^2) + (2*e*f*ArcTan[Sinh[c + d*x]])/(a*d^2) + (3*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a*d) - (2*b^2*(e + f*x)^2*ArcTanh[E^(c + d*x)])/(a^3*d) - (f^2*ArcTanh[Cosh[c + d*x]])/(a*d^3) + (2*b*(e + f*x)^2*Coth[2*c + 2*d*x])/(a^2*d) - (e*f*Csch[c + d*x])/(a*d^2) - (f^2*x*Csch[c + d*x])/(a*d^2) - (b^5*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)^(3/2)*d) + (b^5*(e + f*x)^2*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)^(3/2)*d) + (2*b^3*f*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(a^2*(a^2 + b^2)*d^2) - (2*b*f*(e + f*x)*Log[1 - E^(4*(c + d*x))])/(a^2*d^2) + (3*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a*d^2) - (2*b^2*f*(e + f*x)*PolyLog[2, -E^(c + d*x)])/(a^3*d^2) - ((2*I)*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a*d^3) + ((2*I)*b^2*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a^3*d^3) - ((2*I)*b^4*f^2*PolyLog[2, (-I)*E^(c + d*x)])/(a^3*(a^2 + b^2)*d^3) + ((2*I)*f^2*PolyLog[2, I*E^(c + d*x)])/(a*d^3) - ((2*I)*b^2*f^2*PolyLog[2, I*E^(c + d*x)])/(a^3*d^3) + ((2*I)*b^4*f^2*PolyLog[2, I*E^(c + d*x)])/(a^3*(a^2 + b^2)*d^3) - (3*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a*d^2) + (2*b^2*f*(e + f*x)*PolyLog[2, E^(c + d*x)])/(a^3*d^2) - (2*b^5*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)^(3/2)*d^2) + (2*b^5*f*(e + f*x)*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)^(3/2)*d^2) + (b^3*f^2*PolyLog[2, -E^(2*(c + d*x))])/(a^2*(a^2 + b^2)*d^3) - (b*f^2*PolyLog[2, E^(4*(c + d*x))])/(2*a^2*d^3) - (3*f^2*PolyLog[3, -E^(c + d*x)])/(a*d^3) + (2*b^2*f^2*PolyLog[3, -E^(c + d*x)])/(a^3*d^3) + (3*f^2*PolyLog[3, E^(c + d*x)])/(a*d^3) - (2*b^2*f^2*PolyLog[3, E^(c + d*x)])/(a^3*d^3) + (2*b^5*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^5*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) - (3*(e + f*x)^2*Sech[c + d*x])/(2*a*d) + (b^2*(e + f*x)^2*Sech[c + d*x])/(a^3*d) - (b^4*(e + f*x)^2*Sech[c + d*x])/(a^3*(a^2 + b^2)*d) - ((e + f*x)^2*Csch[c + d*x]^2*Sech[c + d*x])/(2*a*d) - (b^3*(e + f*x)^2*Tanh[c + d*x])/(a^2*(a^2 + b^2)*d)","A",88,33,36,0.9167,1,"{5589, 2622, 288, 321, 207, 5462, 6688, 12, 6742, 6273, 4182, 2531, 2282, 6589, 4133, 453, 203, 4180, 2279, 2391, 2621, 5203, 3770, 5461, 4184, 3716, 2190, 6741, 5573, 3322, 2264, 3718, 5451}"
497,1,699,0,1.3563508,"\int \frac{(e+f x) \text{csch}^3(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]^3*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","-\frac{b^5 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2 \left(a^2+b^2\right)^{3/2}}-\frac{b^2 f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^3 d^2}+\frac{b^2 f \text{PolyLog}\left(2,e^{c+d x}\right)}{a^3 d^2}+\frac{3 f \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}-\frac{3 f \text{PolyLog}\left(2,e^{c+d x}\right)}{2 a d^2}+\frac{b^4 f \tan ^{-1}(\sinh (c+d x))}{a^3 d^2 \left(a^2+b^2\right)}-\frac{b^2 f \tan ^{-1}(\sinh (c+d x))}{a^3 d^2}+\frac{b^3 f \log (\cosh (c+d x))}{a^2 d^2 \left(a^2+b^2\right)}-\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^3 (e+f x) \tanh (c+d x)}{a^2 d \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{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 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{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}","-\frac{b^5 f \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\right)}{a^3 d^2 \left(a^2+b^2\right)^{3/2}}-\frac{b^2 f \text{PolyLog}\left(2,-e^{c+d x}\right)}{a^3 d^2}+\frac{b^2 f \text{PolyLog}\left(2,e^{c+d x}\right)}{a^3 d^2}+\frac{3 f \text{PolyLog}\left(2,-e^{c+d x}\right)}{2 a d^2}-\frac{3 f \text{PolyLog}\left(2,e^{c+d x}\right)}{2 a d^2}+\frac{b^4 f \tan ^{-1}(\sinh (c+d x))}{a^3 d^2 \left(a^2+b^2\right)}-\frac{b^2 f \tan ^{-1}(\sinh (c+d x))}{a^3 d^2}+\frac{b^3 f \log (\cosh (c+d x))}{a^2 d^2 \left(a^2+b^2\right)}-\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^3 (e+f x) \tanh (c+d x)}{a^2 d \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{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 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{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,"(f*ArcTan[Sinh[c + d*x]])/(a*d^2) - (b^2*f*ArcTan[Sinh[c + d*x]])/(a^3*d^2) + (b^4*f*ArcTan[Sinh[c + d*x]])/(a^3*(a^2 + b^2)*d^2) + (3*f*x*ArcTanh[E^(c + d*x)])/(a*d) - (2*b^2*f*x*ArcTanh[E^(c + d*x)])/(a^3*d) - (3*f*x*ArcTanh[Cosh[c + d*x]])/(2*a*d) + (b^2*f*x*ArcTanh[Cosh[c + d*x]])/(a^3*d) + (3*(e + f*x)*ArcTanh[Cosh[c + d*x]])/(2*a*d) - (b^2*(e + f*x)*ArcTanh[Cosh[c + d*x]])/(a^3*d) + (2*b*(e + f*x)*Coth[2*c + 2*d*x])/(a^2*d) - (f*Csch[c + d*x])/(2*a*d^2) - (b^5*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)^(3/2)*d) + (b^5*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)^(3/2)*d) + (b^3*f*Log[Cosh[c + d*x]])/(a^2*(a^2 + b^2)*d^2) - (b*f*Log[Sinh[2*c + 2*d*x]])/(a^2*d^2) + (3*f*PolyLog[2, -E^(c + d*x)])/(2*a*d^2) - (b^2*f*PolyLog[2, -E^(c + d*x)])/(a^3*d^2) - (3*f*PolyLog[2, E^(c + d*x)])/(2*a*d^2) + (b^2*f*PolyLog[2, E^(c + d*x)])/(a^3*d^2) - (b^5*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)^(3/2)*d^2) + (b^5*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)^(3/2)*d^2) - (3*(e + f*x)*Sech[c + d*x])/(2*a*d) + (b^2*(e + f*x)*Sech[c + d*x])/(a^3*d) - (b^4*(e + f*x)*Sech[c + d*x])/(a^3*(a^2 + b^2)*d) - ((e + f*x)*Csch[c + d*x]^2*Sech[c + d*x])/(2*a*d) - (b^3*(e + f*x)*Tanh[c + d*x])/(a^2*(a^2 + b^2)*d)","A",44,22,34,0.6471,1,"{5589, 2622, 288, 321, 207, 5462, 6271, 12, 4182, 2279, 2391, 3770, 2621, 5461, 4184, 3475, 5573, 3322, 2264, 2190, 6742, 5451}"
498,1,206,0,0.4200267,"\int \frac{\text{csch}^3(c+d x) \text{sech}^2(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Csch[c + d*x]^3*Sech[c + d*x]^2)/(a + b*Sinh[c + d*x]),x]","\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^2 \text{sech}(c+d x)}{a^3 d}-\frac{b^2 \tanh ^{-1}(\cosh (c+d x))}{a^3 d}-\frac{b^3 \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a^3 d \left(a^2+b^2\right)}+\frac{b \tanh (c+d x)}{a^2 d}+\frac{b \coth (c+d x)}{a^2 d}-\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}","\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^2 \text{sech}(c+d x)}{a^3 d}-\frac{b^2 \tanh ^{-1}(\cosh (c+d x))}{a^3 d}-\frac{b^3 \text{sech}(c+d x) (a \sinh (c+d x)+b)}{a^3 d \left(a^2+b^2\right)}+\frac{b \tanh (c+d x)}{a^2 d}+\frac{b \coth (c+d x)}{a^2 d}-\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,"(3*ArcTanh[Cosh[c + d*x]])/(2*a*d) - (b^2*ArcTanh[Cosh[c + d*x]])/(a^3*d) + (2*b^5*ArcTanh[(b - a*Tanh[(c + d*x)/2])/Sqrt[a^2 + b^2]])/(a^3*(a^2 + b^2)^(3/2)*d) + (b*Coth[c + d*x])/(a^2*d) - (3*Sech[c + d*x])/(2*a*d) + (b^2*Sech[c + d*x])/(a^3*d) - (Csch[c + d*x]^2*Sech[c + d*x])/(2*a*d) - (b^3*Sech[c + d*x]*(b + a*Sinh[c + d*x]))/(a^3*(a^2 + b^2)*d) + (b*Tanh[c + d*x])/(a^2*d)","A",17,12,29,0.4138,1,"{2898, 2622, 321, 207, 2620, 14, 288, 2696, 12, 2660, 618, 204}"
499,0,0,0,0.1341324,"\int \frac{\text{csch}^3(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Csch[c + d*x]^3*Sech[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}^3(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}^3(c+d x) \text{sech}^2(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][(Csch[c + d*x]^3*Sech[c + d*x]^2)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"
500,1,1122,0,1.8069837,"\int \frac{(e+f x) \text{csch}^3(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[((e + f*x)*Csch[c + d*x]^3*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) b^5}{a^2 \left(a^2+b^2\right)^2 d^2}-\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-i e^{c+d x}\right) b^3}{2 a^2 \left(a^2+b^2\right) d^2}-\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b^2}{2 a^3 d^2}+\frac{f \text{PolyLog}\left(2,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{PolyLog}\left(2,-i e^{c+d x}\right) b}{2 a^2 d^2}+\frac{3 i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{a d^2}-\frac{f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{a d^2}","-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-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{PolyLog}\left(2,-i e^{c+d x}\right) b^5}{a^2 \left(a^2+b^2\right)^2 d^2}-\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-i e^{c+d x}\right) b^3}{2 a^2 \left(a^2+b^2\right) d^2}-\frac{i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-e^{2 c+2 d x}\right) b^2}{2 a^3 d^2}+\frac{f \text{PolyLog}\left(2,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{PolyLog}\left(2,-i e^{c+d x}\right) b}{2 a^2 d^2}+\frac{3 i f \text{PolyLog}\left(2,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{PolyLog}\left(2,-e^{2 c+2 d x}\right)}{a d^2}-\frac{f \text{PolyLog}\left(2,e^{2 c+2 d x}\right)}{a d^2}",1,"(b^2*f*x)/(2*a^3*d) + (3*b*f*x*ArcTan[E^(c + d*x)])/(a^2*d) - (2*b^5*(e + f*x)*ArcTan[E^(c + d*x)])/(a^2*(a^2 + b^2)^2*d) - (b^3*(e + f*x)*ArcTan[E^(c + d*x)])/(a^2*(a^2 + b^2)*d) - (3*b*f*x*ArcTan[Sinh[c + d*x]])/(2*a^2*d) + (3*b*(e + f*x)*ArcTan[Sinh[c + d*x]])/(2*a^2*d) - (2*b^2*f*x*ArcTanh[E^(2*c + 2*d*x)])/(a^3*d) + (4*(e + f*x)*ArcTanh[E^(2*c + 2*d*x)])/(a*d) + (b*f*ArcTanh[Cosh[c + d*x]])/(a^2*d^2) + (3*b*(e + f*x)*Csch[c + d*x])/(2*a^2*d) - (f*Csch[2*c + 2*d*x])/(a*d^2) - (2*(e + f*x)*Coth[2*c + 2*d*x]*Csch[2*c + 2*d*x])/(a*d) - (b^6*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)^2*d) - (b^6*(e + f*x)*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(a^3*(a^2 + b^2)^2*d) + (b^6*(e + f*x)*Log[1 + E^(2*(c + d*x))])/(a^3*(a^2 + b^2)^2*d) - (b^2*f*x*Log[Tanh[c + d*x]])/(a^3*d) + (b^2*(e + f*x)*Log[Tanh[c + d*x]])/(a^3*d) - (((3*I)/2)*b*f*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*d^2) + (I*b^5*f*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*(a^2 + b^2)^2*d^2) + ((I/2)*b^3*f*PolyLog[2, (-I)*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^2) + (((3*I)/2)*b*f*PolyLog[2, I*E^(c + d*x)])/(a^2*d^2) - (I*b^5*f*PolyLog[2, I*E^(c + d*x)])/(a^2*(a^2 + b^2)^2*d^2) - ((I/2)*b^3*f*PolyLog[2, I*E^(c + d*x)])/(a^2*(a^2 + b^2)*d^2) - (b^6*f*PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)^2*d^2) - (b^6*f*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(a^3*(a^2 + b^2)^2*d^2) + (b^6*f*PolyLog[2, -E^(2*(c + d*x))])/(2*a^3*(a^2 + b^2)^2*d^2) + (f*PolyLog[2, -E^(2*c + 2*d*x)])/(a*d^2) - (b^2*f*PolyLog[2, -E^(2*c + 2*d*x)])/(2*a^3*d^2) - (f*PolyLog[2, E^(2*c + 2*d*x)])/(a*d^2) + (b^2*f*PolyLog[2, E^(2*c + 2*d*x)])/(2*a^3*d^2) + (b*f*Sech[c + d*x])/(2*a^2*d^2) - (b^3*f*Sech[c + d*x])/(2*a^2*(a^2 + b^2)*d^2) - (b^4*(e + f*x)*Sech[c + d*x]^2)/(2*a^3*(a^2 + b^2)*d) - (b*(e + f*x)*Csch[c + d*x]*Sech[c + d*x]^2)/(2*a^2*d) - (b^2*f*Tanh[c + d*x])/(2*a^3*d^2) + (b^4*f*Tanh[c + d*x])/(2*a^3*(a^2 + b^2)*d^2) - (b^3*(e + f*x)*Sech[c + d*x]*Tanh[c + d*x])/(2*a^2*(a^2 + b^2)*d) - (b^2*(e + f*x)*Tanh[c + d*x]^2)/(2*a^3*d)","A",65,28,34,0.8235,1,"{5589, 5461, 4185, 4182, 2279, 2391, 2621, 288, 321, 207, 5462, 5203, 12, 4180, 3770, 2622, 2620, 14, 2548, 3473, 8, 5573, 5561, 2190, 6742, 3718, 5451, 3767}"
501,1,211,0,0.3667147,"\int \frac{\text{csch}^3(c+d x) \text{sech}^3(c+d x)}{a+b \sinh (c+d x)} \, dx","Int[(Csch[c + d*x]^3*Sech[c + d*x]^3)/(a + b*Sinh[c + d*x]),x]","-\frac{b^6 \log (a+b \sinh (c+d x))}{a^3 d \left(a^2+b^2\right)^2}-\frac{\left(2 a^2-b^2\right) \log (\sinh (c+d x))}{a^3 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{\text{csch}^2(c+d x)}{2 a d}","-\frac{b^6 \log (a+b \sinh (c+d x))}{a^3 d \left(a^2+b^2\right)^2}-\frac{\left(2 a^2-b^2\right) \log (\sinh (c+d x))}{a^3 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{\text{csch}^2(c+d x)}{2 a d}",1,"(b*ArcTan[Sinh[c + d*x]])/(2*(a^2 + b^2)*d) + (b*(a^2 + 2*b^2)*ArcTan[Sinh[c + d*x]])/((a^2 + b^2)^2*d) + (b*Csch[c + d*x])/(a^2*d) - Csch[c + d*x]^2/(2*a*d) + (a*(2*a^2 + 3*b^2)*Log[Cosh[c + d*x]])/((a^2 + b^2)^2*d) - ((2*a^2 - b^2)*Log[Sinh[c + d*x]])/(a^3*d) - (b^6*Log[a + b*Sinh[c + d*x]])/(a^3*(a^2 + b^2)^2*d) - (Sech[c + d*x]^2*(a - b*Sinh[c + d*x]))/(2*(a^2 + b^2)*d)","A",9,7,29,0.2414,1,"{2837, 12, 894, 639, 203, 635, 260}"
502,0,0,0,0.1336289,"\int \frac{\text{csch}^3(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))} \, dx","Int[(Csch[c + d*x]^3*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])),x]","\int \frac{\text{csch}^3(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}^3(c+d x) \text{sech}^3(c+d x)}{(e+f x) (a+b \sinh (c+d x))},x\right)",0,"Defer[Int][(Csch[c + d*x]^3*Sech[c + d*x]^3)/((e + f*x)*(a + b*Sinh[c + d*x])), x]","A",0,0,0,0,-1,"{}"