1,1,91,0,0.1191983,"\int (c+d x)^4 \cosh (a+b x) \, dx","Int[(c + d*x)^4*Cosh[a + b*x],x]","\frac{12 d^2 (c+d x)^2 \sinh (a+b x)}{b^3}-\frac{24 d^3 (c+d x) \cosh (a+b x)}{b^4}-\frac{4 d (c+d x)^3 \cosh (a+b x)}{b^2}+\frac{24 d^4 \sinh (a+b x)}{b^5}+\frac{(c+d x)^4 \sinh (a+b x)}{b}","\frac{12 d^2 (c+d x)^2 \sinh (a+b x)}{b^3}-\frac{24 d^3 (c+d x) \cosh (a+b x)}{b^4}-\frac{4 d (c+d x)^3 \cosh (a+b x)}{b^2}+\frac{24 d^4 \sinh (a+b x)}{b^5}+\frac{(c+d x)^4 \sinh (a+b x)}{b}",1,"(-24*d^3*(c + d*x)*Cosh[a + b*x])/b^4 - (4*d*(c + d*x)^3*Cosh[a + b*x])/b^2 + (24*d^4*Sinh[a + b*x])/b^5 + (12*d^2*(c + d*x)^2*Sinh[a + b*x])/b^3 + ((c + d*x)^4*Sinh[a + b*x])/b","A",5,2,14,0.1429,1,"{3296, 2637}"
2,1,70,0,0.0789896,"\int (c+d x)^3 \cosh (a+b x) \, dx","Int[(c + d*x)^3*Cosh[a + b*x],x]","\frac{6 d^2 (c+d x) \sinh (a+b x)}{b^3}-\frac{3 d (c+d x)^2 \cosh (a+b x)}{b^2}-\frac{6 d^3 \cosh (a+b x)}{b^4}+\frac{(c+d x)^3 \sinh (a+b x)}{b}","\frac{6 d^2 (c+d x) \sinh (a+b x)}{b^3}-\frac{3 d (c+d x)^2 \cosh (a+b x)}{b^2}-\frac{6 d^3 \cosh (a+b x)}{b^4}+\frac{(c+d x)^3 \sinh (a+b x)}{b}",1,"(-6*d^3*Cosh[a + b*x])/b^4 - (3*d*(c + d*x)^2*Cosh[a + b*x])/b^2 + (6*d^2*(c + d*x)*Sinh[a + b*x])/b^3 + ((c + d*x)^3*Sinh[a + b*x])/b","A",4,2,14,0.1429,1,"{3296, 2638}"
3,1,49,0,0.0468619,"\int (c+d x)^2 \cosh (a+b x) \, dx","Int[(c + d*x)^2*Cosh[a + b*x],x]","-\frac{2 d (c+d x) \cosh (a+b x)}{b^2}+\frac{2 d^2 \sinh (a+b x)}{b^3}+\frac{(c+d x)^2 \sinh (a+b x)}{b}","-\frac{2 d (c+d x) \cosh (a+b x)}{b^2}+\frac{2 d^2 \sinh (a+b x)}{b^3}+\frac{(c+d x)^2 \sinh (a+b x)}{b}",1,"(-2*d*(c + d*x)*Cosh[a + b*x])/b^2 + (2*d^2*Sinh[a + b*x])/b^3 + ((c + d*x)^2*Sinh[a + b*x])/b","A",3,2,14,0.1429,1,"{3296, 2637}"
4,1,28,0,0.0195894,"\int (c+d x) \cosh (a+b x) \, dx","Int[(c + d*x)*Cosh[a + b*x],x]","\frac{(c+d x) \sinh (a+b x)}{b}-\frac{d \cosh (a+b x)}{b^2}","\frac{(c+d x) \sinh (a+b x)}{b}-\frac{d \cosh (a+b x)}{b^2}",1,"-((d*Cosh[a + b*x])/b^2) + ((c + d*x)*Sinh[a + b*x])/b","A",2,2,12,0.1667,1,"{3296, 2638}"
5,1,51,0,0.1009724,"\int \frac{\cosh (a+b x)}{c+d x} \, dx","Int[Cosh[a + b*x]/(c + d*x),x]","\frac{\cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{d}+\frac{\sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{d}","\frac{\cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{d}+\frac{\sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{d}",1,"(Cosh[a - (b*c)/d]*CoshIntegral[(b*c)/d + b*x])/d + (Sinh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/d","A",3,3,14,0.2143,1,"{3303, 3298, 3301}"
6,1,71,0,0.1185068,"\int \frac{\cosh (a+b x)}{(c+d x)^2} \, dx","Int[Cosh[a + b*x]/(c + d*x)^2,x]","\frac{b \sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{d^2}+\frac{b \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{d^2}-\frac{\cosh (a+b x)}{d (c+d x)}","\frac{b \sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{d^2}+\frac{b \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{d^2}-\frac{\cosh (a+b x)}{d (c+d x)}",1,"-(Cosh[a + b*x]/(d*(c + d*x))) + (b*CoshIntegral[(b*c)/d + b*x]*Sinh[a - (b*c)/d])/d^2 + (b*Cosh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/d^2","A",4,4,14,0.2857,1,"{3297, 3303, 3298, 3301}"
7,1,104,0,0.162841,"\int \frac{\cosh (a+b x)}{(c+d x)^3} \, dx","Int[Cosh[a + b*x]/(c + d*x)^3,x]","\frac{b^2 \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{2 d^3}+\frac{b^2 \sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{2 d^3}-\frac{b \sinh (a+b x)}{2 d^2 (c+d x)}-\frac{\cosh (a+b x)}{2 d (c+d x)^2}","\frac{b^2 \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{2 d^3}+\frac{b^2 \sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)}{2 d^3}-\frac{b \sinh (a+b x)}{2 d^2 (c+d x)}-\frac{\cosh (a+b x)}{2 d (c+d x)^2}",1,"-Cosh[a + b*x]/(2*d*(c + d*x)^2) + (b^2*Cosh[a - (b*c)/d]*CoshIntegral[(b*c)/d + b*x])/(2*d^3) - (b*Sinh[a + b*x])/(2*d^2*(c + d*x)) + (b^2*Sinh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/(2*d^3)","A",5,4,14,0.2857,1,"{3297, 3303, 3298, 3301}"
8,1,162,0,0.1014695,"\int (c+d x)^4 \cosh ^2(a+b x) \, dx","Int[(c + d*x)^4*Cosh[a + b*x]^2,x]","-\frac{3 d^3 (c+d x) \cosh ^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 \cosh ^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) \cosh ^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 \cosh ^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^3*(c + d*x)*Cosh[a + b*x]^2)/(2*b^4) - (d*(c + d*x)^3*Cosh[a + b*x]^2)/b^2 + (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)","A",6,4,16,0.2500,1,"{3311, 32, 2635, 8}"
9,1,134,0,0.0727015,"\int (c+d x)^3 \cosh ^2(a+b x) \, dx","Int[(c + d*x)^3*Cosh[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 \cosh ^2(a+b x)}{4 b^2}-\frac{3 d^3 \cosh ^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 \cosh ^2(a+b x)}{4 b^2}-\frac{3 d^3 \cosh ^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^3*Cosh[a + b*x]^2)/(8*b^4) - (3*d*(c + d*x)^2*Cosh[a + b*x]^2)/(4*b^2) + (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)","A",4,3,16,0.1875,1,"{3311, 32, 3310}"
10,1,95,0,0.0527716,"\int (c+d x)^2 \cosh ^2(a+b x) \, dx","Int[(c + d*x)^2*Cosh[a + b*x]^2,x]","-\frac{d (c+d x) \cosh ^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) \cosh ^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*(c + d*x)*Cosh[a + b*x]^2)/(2*b^2) + (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)","A",4,4,16,0.2500,1,"{3311, 32, 2635, 8}"
11,1,55,0,0.0249827,"\int (c+d x) \cosh ^2(a+b x) \, dx","Int[(c + d*x)*Cosh[a + b*x]^2,x]","-\frac{d \cosh ^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 \cosh ^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 - (d*Cosh[a + b*x]^2)/(4*b^2) + ((c + d*x)*Cosh[a + b*x]*Sinh[a + b*x])/(2*b)","A",2,1,14,0.07143,1,"{3310}"
12,1,78,0,0.1544539,"\int \frac{\cosh ^2(a+b x)}{c+d x} \, dx","Int[Cosh[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}"
13,1,81,0,0.1456473,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^2} \, dx","Int[Cosh[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{\cosh ^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{\cosh ^2(a+b x)}{d (c+d x)}",1,"-(Cosh[a + b*x]^2/(d*(c + d*x))) + (b*CoshIntegral[(2*b*c)/d + 2*b*x]*Sinh[2*a - (2*b*c)/d])/d^2 + (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}"
14,1,112,0,0.1870654,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^3} \, dx","Int[Cosh[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{\cosh ^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{\cosh ^2(a+b x)}{2 d (c+d x)^2}",1,"-Cosh[a + b*x]^2/(2*d*(c + d*x)^2) + (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)) + (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}"
15,1,162,0,0.1806053,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^4} \, dx","Int[Cosh[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 \cosh ^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{\cosh ^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 \cosh ^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{\cosh ^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)) - Cosh[a + b*x]^2/(3*d*(c + d*x)^3) - (2*b^2*Cosh[a + b*x]^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) + (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}"
16,1,225,0,0.2815447,"\int (c+d x)^4 \cosh ^3(a+b x) \, dx","Int[(c + d*x)^4*Cosh[a + b*x]^3,x]","\frac{80 d^2 (c+d x)^2 \sinh (a+b x)}{9 b^3}-\frac{8 d^3 (c+d x) \cosh ^3(a+b x)}{27 b^4}-\frac{160 d^3 (c+d x) \cosh (a+b x)}{9 b^4}+\frac{4 d^2 (c+d x)^2 \sinh (a+b x) \cosh ^2(a+b x)}{9 b^3}-\frac{4 d (c+d x)^3 \cosh ^3(a+b x)}{9 b^2}-\frac{8 d (c+d x)^3 \cosh (a+b x)}{3 b^2}+\frac{8 d^4 \sinh ^3(a+b x)}{81 b^5}+\frac{488 d^4 \sinh (a+b x)}{27 b^5}+\frac{2 (c+d x)^4 \sinh (a+b x)}{3 b}+\frac{(c+d x)^4 \sinh (a+b x) \cosh ^2(a+b x)}{3 b}","\frac{80 d^2 (c+d x)^2 \sinh (a+b x)}{9 b^3}-\frac{8 d^3 (c+d x) \cosh ^3(a+b x)}{27 b^4}-\frac{160 d^3 (c+d x) \cosh (a+b x)}{9 b^4}+\frac{4 d^2 (c+d x)^2 \sinh (a+b x) \cosh ^2(a+b x)}{9 b^3}-\frac{4 d (c+d x)^3 \cosh ^3(a+b x)}{9 b^2}-\frac{8 d (c+d x)^3 \cosh (a+b x)}{3 b^2}+\frac{8 d^4 \sinh ^3(a+b x)}{81 b^5}+\frac{488 d^4 \sinh (a+b x)}{27 b^5}+\frac{2 (c+d x)^4 \sinh (a+b x)}{3 b}+\frac{(c+d x)^4 \sinh (a+b x) \cosh ^2(a+b x)}{3 b}",1,"(-160*d^3*(c + d*x)*Cosh[a + b*x])/(9*b^4) - (8*d*(c + d*x)^3*Cosh[a + b*x])/(3*b^2) - (8*d^3*(c + d*x)*Cosh[a + b*x]^3)/(27*b^4) - (4*d*(c + d*x)^3*Cosh[a + b*x]^3)/(9*b^2) + (488*d^4*Sinh[a + b*x])/(27*b^5) + (80*d^2*(c + d*x)^2*Sinh[a + b*x])/(9*b^3) + (2*(c + d*x)^4*Sinh[a + b*x])/(3*b) + (4*d^2*(c + d*x)^2*Cosh[a + b*x]^2*Sinh[a + b*x])/(9*b^3) + ((c + d*x)^4*Cosh[a + b*x]^2*Sinh[a + b*x])/(3*b) + (8*d^4*Sinh[a + b*x]^3)/(81*b^5)","A",12,4,16,0.2500,1,"{3311, 3296, 2637, 2633}"
17,1,175,0,0.1756488,"\int (c+d x)^3 \cosh ^3(a+b x) \, dx","Int[(c + d*x)^3*Cosh[a + b*x]^3,x]","\frac{40 d^2 (c+d x) \sinh (a+b x)}{9 b^3}+\frac{2 d^2 (c+d x) \sinh (a+b x) \cosh ^2(a+b x)}{9 b^3}-\frac{d (c+d x)^2 \cosh ^3(a+b x)}{3 b^2}-\frac{2 d (c+d x)^2 \cosh (a+b x)}{b^2}-\frac{2 d^3 \cosh ^3(a+b x)}{27 b^4}-\frac{40 d^3 \cosh (a+b x)}{9 b^4}+\frac{2 (c+d x)^3 \sinh (a+b x)}{3 b}+\frac{(c+d x)^3 \sinh (a+b x) \cosh ^2(a+b x)}{3 b}","\frac{40 d^2 (c+d x) \sinh (a+b x)}{9 b^3}+\frac{2 d^2 (c+d x) \sinh (a+b x) \cosh ^2(a+b x)}{9 b^3}-\frac{d (c+d x)^2 \cosh ^3(a+b x)}{3 b^2}-\frac{2 d (c+d x)^2 \cosh (a+b x)}{b^2}-\frac{2 d^3 \cosh ^3(a+b x)}{27 b^4}-\frac{40 d^3 \cosh (a+b x)}{9 b^4}+\frac{2 (c+d x)^3 \sinh (a+b x)}{3 b}+\frac{(c+d x)^3 \sinh (a+b x) \cosh ^2(a+b x)}{3 b}",1,"(-40*d^3*Cosh[a + b*x])/(9*b^4) - (2*d*(c + d*x)^2*Cosh[a + b*x])/b^2 - (2*d^3*Cosh[a + b*x]^3)/(27*b^4) - (d*(c + d*x)^2*Cosh[a + b*x]^3)/(3*b^2) + (40*d^2*(c + d*x)*Sinh[a + b*x])/(9*b^3) + (2*(c + d*x)^3*Sinh[a + b*x])/(3*b) + (2*d^2*(c + d*x)*Cosh[a + b*x]^2*Sinh[a + b*x])/(9*b^3) + ((c + d*x)^3*Cosh[a + b*x]^2*Sinh[a + b*x])/(3*b)","A",8,4,16,0.2500,1,"{3311, 3296, 2638, 3310}"
18,1,123,0,0.1034241,"\int (c+d x)^2 \cosh ^3(a+b x) \, dx","Int[(c + d*x)^2*Cosh[a + b*x]^3,x]","-\frac{2 d (c+d x) \cosh ^3(a+b x)}{9 b^2}-\frac{4 d (c+d x) \cosh (a+b x)}{3 b^2}+\frac{2 d^2 \sinh ^3(a+b x)}{27 b^3}+\frac{14 d^2 \sinh (a+b x)}{9 b^3}+\frac{2 (c+d x)^2 \sinh (a+b x)}{3 b}+\frac{(c+d x)^2 \sinh (a+b x) \cosh ^2(a+b x)}{3 b}","-\frac{2 d (c+d x) \cosh ^3(a+b x)}{9 b^2}-\frac{4 d (c+d x) \cosh (a+b x)}{3 b^2}+\frac{2 d^2 \sinh ^3(a+b x)}{27 b^3}+\frac{14 d^2 \sinh (a+b x)}{9 b^3}+\frac{2 (c+d x)^2 \sinh (a+b x)}{3 b}+\frac{(c+d x)^2 \sinh (a+b x) \cosh ^2(a+b x)}{3 b}",1,"(-4*d*(c + d*x)*Cosh[a + b*x])/(3*b^2) - (2*d*(c + d*x)*Cosh[a + b*x]^3)/(9*b^2) + (14*d^2*Sinh[a + b*x])/(9*b^3) + (2*(c + d*x)^2*Sinh[a + b*x])/(3*b) + ((c + d*x)^2*Cosh[a + b*x]^2*Sinh[a + b*x])/(3*b) + (2*d^2*Sinh[a + b*x]^3)/(27*b^3)","A",6,4,16,0.2500,1,"{3311, 3296, 2637, 2633}"
19,1,75,0,0.0442555,"\int (c+d x) \cosh ^3(a+b x) \, dx","Int[(c + d*x)*Cosh[a + b*x]^3,x]","-\frac{d \cosh ^3(a+b x)}{9 b^2}-\frac{2 d \cosh (a+b x)}{3 b^2}+\frac{2 (c+d x) \sinh (a+b x)}{3 b}+\frac{(c+d x) \sinh (a+b x) \cosh ^2(a+b x)}{3 b}","-\frac{d \cosh ^3(a+b x)}{9 b^2}-\frac{2 d \cosh (a+b x)}{3 b^2}+\frac{2 (c+d x) \sinh (a+b x)}{3 b}+\frac{(c+d x) \sinh (a+b x) \cosh ^2(a+b x)}{3 b}",1,"(-2*d*Cosh[a + b*x])/(3*b^2) - (d*Cosh[a + b*x]^3)/(9*b^2) + (2*(c + d*x)*Sinh[a + b*x])/(3*b) + ((c + d*x)*Cosh[a + b*x]^2*Sinh[a + b*x])/(3*b)","A",3,3,14,0.2143,1,"{3310, 3296, 2638}"
20,1,121,0,0.23984,"\int \frac{\cosh ^3(a+b x)}{c+d x} \, dx","Int[Cosh[a + b*x]^3/(c + d*x),x]","\frac{3 \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{\cosh \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{Shi}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{\sinh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}","\frac{3 \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{\cosh \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{Shi}\left(\frac{b c}{d}+b x\right)}{4 d}+\frac{\sinh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b c}{d}+3 b x\right)}{4 d}",1,"(3*Cosh[a - (b*c)/d]*CoshIntegral[(b*c)/d + b*x])/(4*d) + (Cosh[3*a - (3*b*c)/d]*CoshIntegral[(3*b*c)/d + 3*b*x])/(4*d) + (3*Sinh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/(4*d) + (Sinh[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}"
21,1,145,0,0.2370698,"\int \frac{\cosh ^3(a+b x)}{(c+d x)^2} \, dx","Int[Cosh[a + b*x]^3/(c + d*x)^2,x]","\frac{3 b \sinh \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{Chi}\left(\frac{b c}{d}+b x\right)}{4 d^2}+\frac{3 b \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\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{Shi}\left(\frac{3 b c}{d}+3 b x\right)}{4 d^2}-\frac{\cosh ^3(a+b x)}{d (c+d x)}","\frac{3 b \sinh \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{Chi}\left(\frac{b c}{d}+b x\right)}{4 d^2}+\frac{3 b \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\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{Shi}\left(\frac{3 b c}{d}+3 b x\right)}{4 d^2}-\frac{\cosh ^3(a+b x)}{d (c+d x)}",1,"-(Cosh[a + b*x]^3/(d*(c + d*x))) + (3*b*CoshIntegral[(3*b*c)/d + 3*b*x]*Sinh[3*a - (3*b*c)/d])/(4*d^2) + (3*b*CoshIntegral[(b*c)/d + b*x]*Sinh[a - (b*c)/d])/(4*d^2) + (3*b*Cosh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/(4*d^2) + (3*b*Cosh[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}"
22,1,184,0,0.3400693,"\int \frac{\cosh ^3(a+b x)}{(c+d x)^3} \, dx","Int[Cosh[a + b*x]^3/(c + d*x)^3,x]","\frac{3 b^2 \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\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{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{Shi}\left(\frac{b c}{d}+b x\right)}{8 d^3}+\frac{9 b^2 \sinh \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 (a+b x) \cosh ^2(a+b x)}{2 d^2 (c+d x)}-\frac{\cosh ^3(a+b x)}{2 d (c+d x)^2}","\frac{3 b^2 \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\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{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{Shi}\left(\frac{b c}{d}+b x\right)}{8 d^3}+\frac{9 b^2 \sinh \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 (a+b x) \cosh ^2(a+b x)}{2 d^2 (c+d x)}-\frac{\cosh ^3(a+b x)}{2 d (c+d x)^2}",1,"-Cosh[a + b*x]^3/(2*d*(c + d*x)^2) + (3*b^2*Cosh[a - (b*c)/d]*CoshIntegral[(b*c)/d + b*x])/(8*d^3) + (9*b^2*Cosh[3*a - (3*b*c)/d]*CoshIntegral[(3*b*c)/d + 3*b*x])/(8*d^3) - (3*b*Cosh[a + b*x]^2*Sinh[a + b*x])/(2*d^2*(c + d*x)) + (3*b^2*Sinh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/(8*d^3) + (9*b^2*Sinh[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}"
23,1,172,0,0.1457868,"\int x^3 \cosh ^4(a+b x) \, dx","Int[x^3*Cosh[a + b*x]^4,x]","-\frac{3 x^2 \cosh ^4(a+b x)}{16 b^2}-\frac{9 x^2 \cosh ^2(a+b x)}{16 b^2}-\frac{3 \cosh ^4(a+b x)}{128 b^4}-\frac{45 \cosh ^2(a+b x)}{128 b^4}+\frac{3 x \sinh (a+b x) \cosh ^3(a+b x)}{32 b^3}+\frac{45 x \sinh (a+b x) \cosh (a+b x)}{64 b^3}+\frac{x^3 \sinh (a+b x) \cosh ^3(a+b x)}{4 b}+\frac{3 x^3 \sinh (a+b x) \cosh (a+b x)}{8 b}+\frac{45 x^2}{128 b^2}+\frac{3 x^4}{32}","-\frac{3 x^2 \cosh ^4(a+b x)}{16 b^2}-\frac{9 x^2 \cosh ^2(a+b x)}{16 b^2}-\frac{3 \cosh ^4(a+b x)}{128 b^4}-\frac{45 \cosh ^2(a+b x)}{128 b^4}+\frac{3 x \sinh (a+b x) \cosh ^3(a+b x)}{32 b^3}+\frac{45 x \sinh (a+b x) \cosh (a+b x)}{64 b^3}+\frac{x^3 \sinh (a+b x) \cosh ^3(a+b x)}{4 b}+\frac{3 x^3 \sinh (a+b x) \cosh (a+b x)}{8 b}+\frac{45 x^2}{128 b^2}+\frac{3 x^4}{32}",1,"(45*x^2)/(128*b^2) + (3*x^4)/32 - (45*Cosh[a + b*x]^2)/(128*b^4) - (9*x^2*Cosh[a + b*x]^2)/(16*b^2) - (3*Cosh[a + b*x]^4)/(128*b^4) - (3*x^2*Cosh[a + b*x]^4)/(16*b^2) + (45*x*Cosh[a + b*x]*Sinh[a + b*x])/(64*b^3) + (3*x^3*Cosh[a + b*x]*Sinh[a + b*x])/(8*b) + (3*x*Cosh[a + b*x]^3*Sinh[a + b*x])/(32*b^3) + (x^3*Cosh[a + b*x]^3*Sinh[a + b*x])/(4*b)","A",8,3,12,0.2500,1,"{3311, 30, 3310}"
24,1,134,0,0.1066922,"\int x^2 \cosh ^4(a+b x) \, dx","Int[x^2*Cosh[a + b*x]^4,x]","-\frac{x \cosh ^4(a+b x)}{8 b^2}-\frac{3 x \cosh ^2(a+b x)}{8 b^2}+\frac{\sinh (a+b x) \cosh ^3(a+b x)}{32 b^3}+\frac{15 \sinh (a+b x) \cosh (a+b x)}{64 b^3}+\frac{x^2 \sinh (a+b x) \cosh ^3(a+b x)}{4 b}+\frac{3 x^2 \sinh (a+b x) \cosh (a+b x)}{8 b}+\frac{15 x}{64 b^2}+\frac{x^3}{8}","-\frac{x \cosh ^4(a+b x)}{8 b^2}-\frac{3 x \cosh ^2(a+b x)}{8 b^2}+\frac{\sinh (a+b x) \cosh ^3(a+b x)}{32 b^3}+\frac{15 \sinh (a+b x) \cosh (a+b x)}{64 b^3}+\frac{x^2 \sinh (a+b x) \cosh ^3(a+b x)}{4 b}+\frac{3 x^2 \sinh (a+b x) \cosh (a+b x)}{8 b}+\frac{15 x}{64 b^2}+\frac{x^3}{8}",1,"(15*x)/(64*b^2) + x^3/8 - (3*x*Cosh[a + b*x]^2)/(8*b^2) - (x*Cosh[a + b*x]^4)/(8*b^2) + (15*Cosh[a + b*x]*Sinh[a + b*x])/(64*b^3) + (3*x^2*Cosh[a + b*x]*Sinh[a + b*x])/(8*b) + (Cosh[a + b*x]^3*Sinh[a + b*x])/(32*b^3) + (x^2*Cosh[a + b*x]^3*Sinh[a + b*x])/(4*b)","A",8,4,12,0.3333,1,"{3311, 30, 2635, 8}"
25,1,80,0,0.0436869,"\int x \cosh ^4(a+b x) \, dx","Int[x*Cosh[a + b*x]^4,x]","-\frac{\cosh ^4(a+b x)}{16 b^2}-\frac{3 \cosh ^2(a+b x)}{16 b^2}+\frac{x \sinh (a+b x) \cosh ^3(a+b x)}{4 b}+\frac{3 x \sinh (a+b x) \cosh (a+b x)}{8 b}+\frac{3 x^2}{16}","-\frac{\cosh ^4(a+b x)}{16 b^2}-\frac{3 \cosh ^2(a+b x)}{16 b^2}+\frac{x \sinh (a+b x) \cosh ^3(a+b x)}{4 b}+\frac{3 x \sinh (a+b x) \cosh (a+b x)}{8 b}+\frac{3 x^2}{16}",1,"(3*x^2)/16 - (3*Cosh[a + b*x]^2)/(16*b^2) - Cosh[a + b*x]^4/(16*b^2) + (3*x*Cosh[a + b*x]*Sinh[a + b*x])/(8*b) + (x*Cosh[a + b*x]^3*Sinh[a + b*x])/(4*b)","A",3,2,10,0.2000,1,"{3310, 30}"
26,1,179,0,0.1233866,"\int (c+d x)^3 \text{sech}(a+b x) \, dx","Int[(c + d*x)^3*Sech[a + b*x],x]","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}-\frac{6 i d^3 \text{PolyLog}\left(4,-i e^{a+b x}\right)}{b^4}+\frac{6 i d^3 \text{PolyLog}\left(4,i e^{a+b x}\right)}{b^4}+\frac{2 (c+d x)^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}","\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}-\frac{6 i d^3 \text{PolyLog}\left(4,-i e^{a+b x}\right)}{b^4}+\frac{6 i d^3 \text{PolyLog}\left(4,i e^{a+b x}\right)}{b^4}+\frac{2 (c+d x)^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(2*(c + d*x)^3*ArcTan[E^(a + b*x)])/b - ((3*I)*d*(c + d*x)^2*PolyLog[2, (-I)*E^(a + b*x)])/b^2 + ((3*I)*d*(c + d*x)^2*PolyLog[2, I*E^(a + b*x)])/b^2 + ((6*I)*d^2*(c + d*x)*PolyLog[3, (-I)*E^(a + b*x)])/b^3 - ((6*I)*d^2*(c + d*x)*PolyLog[3, I*E^(a + b*x)])/b^3 - ((6*I)*d^3*PolyLog[4, (-I)*E^(a + b*x)])/b^4 + ((6*I)*d^3*PolyLog[4, I*E^(a + b*x)])/b^4","A",9,5,14,0.3571,1,"{4180, 2531, 6609, 2282, 6589}"
27,1,119,0,0.0806661,"\int (c+d x)^2 \text{sech}(a+b x) \, dx","Int[(c + d*x)^2*Sech[a + b*x],x]","-\frac{2 i d (c+d x) \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{2 i d (c+d x) \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{2 i d^2 \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}+\frac{2 (c+d x)^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}","-\frac{2 i d (c+d x) \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{2 i d (c+d x) \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{2 i d^2 \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{2 i d^2 \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}+\frac{2 (c+d x)^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(2*(c + d*x)^2*ArcTan[E^(a + b*x)])/b - ((2*I)*d*(c + d*x)*PolyLog[2, (-I)*E^(a + b*x)])/b^2 + ((2*I)*d*(c + d*x)*PolyLog[2, I*E^(a + b*x)])/b^2 + ((2*I)*d^2*PolyLog[3, (-I)*E^(a + b*x)])/b^3 - ((2*I)*d^2*PolyLog[3, I*E^(a + b*x)])/b^3","A",7,4,14,0.2857,1,"{4180, 2531, 2282, 6589}"
28,1,61,0,0.037233,"\int (c+d x) \text{sech}(a+b x) \, dx","Int[(c + d*x)*Sech[a + b*x],x]","-\frac{i d \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{i d \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{2 (c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b}","-\frac{i d \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{i d \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{2 (c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(2*(c + d*x)*ArcTan[E^(a + b*x)])/b - (I*d*PolyLog[2, (-I)*E^(a + b*x)])/b^2 + (I*d*PolyLog[2, I*E^(a + b*x)])/b^2","A",5,3,12,0.2500,1,"{4180, 2279, 2391}"
29,0,0,0,0.0211822,"\int \frac{\text{sech}(a+b x)}{c+d x} \, dx","Int[Sech[a + b*x]/(c + d*x),x]","\int \frac{\text{sech}(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{sech}(a+b x)}{c+d x},x\right)",0,"Defer[Int][Sech[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
30,0,0,0,0.0204347,"\int \frac{\text{sech}(a+b x)}{(c+d x)^2} \, dx","Int[Sech[a + b*x]/(c + d*x)^2,x]","\int \frac{\text{sech}(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{sech}(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Sech[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
31,1,103,0,0.2059626,"\int (c+d x)^3 \text{sech}^2(a+b x) \, dx","Int[(c + d*x)^3*Sech[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(e^{2 (a+b x)}+1\right)}{b^2}+\frac{(c+d x)^3 \tanh (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(e^{2 (a+b x)}+1\right)}{b^2}+\frac{(c+d x)^3 \tanh (a+b x)}{b}+\frac{(c+d x)^3}{b}",1,"(c + d*x)^3/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) + ((c + d*x)^3*Tanh[a + b*x])/b","A",6,6,16,0.3750,1,"{4184, 3718, 2190, 2531, 2282, 6589}"
32,1,73,0,0.132696,"\int (c+d x)^2 \text{sech}^2(a+b x) \, dx","Int[(c + d*x)^2*Sech[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(e^{2 (a+b x)}+1\right)}{b^2}+\frac{(c+d x)^2 \tanh (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(e^{2 (a+b x)}+1\right)}{b^2}+\frac{(c+d x)^2 \tanh (a+b x)}{b}+\frac{(c+d x)^2}{b}",1,"(c + d*x)^2/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 + ((c + d*x)^2*Tanh[a + b*x])/b","A",5,5,16,0.3125,1,"{4184, 3718, 2190, 2279, 2391}"
33,1,29,0,0.0292901,"\int (c+d x) \text{sech}^2(a+b x) \, dx","Int[(c + d*x)*Sech[a + b*x]^2,x]","\frac{(c+d x) \tanh (a+b x)}{b}-\frac{d \log (\cosh (a+b x))}{b^2}","\frac{(c+d x) \tanh (a+b x)}{b}-\frac{d \log (\cosh (a+b x))}{b^2}",1,"-((d*Log[Cosh[a + b*x]])/b^2) + ((c + d*x)*Tanh[a + b*x])/b","A",2,2,14,0.1429,1,"{4184, 3475}"
34,0,0,0,0.0371998,"\int \frac{\text{sech}^2(a+b x)}{c+d x} \, dx","Int[Sech[a + b*x]^2/(c + d*x),x]","\int \frac{\text{sech}^2(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{sech}^2(a+b x)}{c+d x},x\right)",0,"Defer[Int][Sech[a + b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
35,0,0,0,0.0354581,"\int \frac{\text{sech}^2(a+b x)}{(c+d x)^2} \, dx","Int[Sech[a + b*x]^2/(c + d*x)^2,x]","\int \frac{\text{sech}^2(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{sech}^2(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Sech[a + b*x]^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
36,1,296,0,0.2167653,"\int (c+d x)^3 \text{sech}^3(a+b x) \, dx","Int[(c + d*x)^3*Sech[a + b*x]^3,x]","\frac{3 i d^2 (c+d x) \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{3 i d^2 (c+d x) \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b^2}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-i e^{a+b x}\right)}{b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,i e^{a+b x}\right)}{b^4}-\frac{6 d^2 (c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b^3}+\frac{3 d (c+d x)^2 \text{sech}(a+b x)}{2 b^2}+\frac{(c+d x)^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x)^3 \tanh (a+b x) \text{sech}(a+b x)}{2 b}","\frac{3 i d^2 (c+d x) \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{3 i d^2 (c+d x) \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b^2}+\frac{3 i d (c+d x)^2 \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b^2}+\frac{3 i d^3 \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^4}-\frac{3 i d^3 \text{PolyLog}\left(4,-i e^{a+b x}\right)}{b^4}+\frac{3 i d^3 \text{PolyLog}\left(4,i e^{a+b x}\right)}{b^4}-\frac{6 d^2 (c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b^3}+\frac{3 d (c+d x)^2 \text{sech}(a+b x)}{2 b^2}+\frac{(c+d x)^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x)^3 \tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"(-6*d^2*(c + d*x)*ArcTan[E^(a + b*x)])/b^3 + ((c + d*x)^3*ArcTan[E^(a + b*x)])/b + ((3*I)*d^3*PolyLog[2, (-I)*E^(a + b*x)])/b^4 - (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, (-I)*E^(a + b*x)])/b^2 - ((3*I)*d^3*PolyLog[2, I*E^(a + b*x)])/b^4 + (((3*I)/2)*d*(c + d*x)^2*PolyLog[2, I*E^(a + b*x)])/b^2 + ((3*I)*d^2*(c + d*x)*PolyLog[3, (-I)*E^(a + b*x)])/b^3 - ((3*I)*d^2*(c + d*x)*PolyLog[3, I*E^(a + b*x)])/b^3 - ((3*I)*d^3*PolyLog[4, (-I)*E^(a + b*x)])/b^4 + ((3*I)*d^3*PolyLog[4, I*E^(a + b*x)])/b^4 + (3*d*(c + d*x)^2*Sech[a + b*x])/(2*b^2) + ((c + d*x)^3*Sech[a + b*x]*Tanh[a + b*x])/(2*b)","A",15,8,16,0.5000,1,"{4186, 4180, 2279, 2391, 2531, 6609, 2282, 6589}"
37,1,175,0,0.1328254,"\int (c+d x)^2 \text{sech}^3(a+b x) \, dx","Int[(c + d*x)^2*Sech[a + b*x]^3,x]","-\frac{i d (c+d x) \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{i d (c+d x) \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{i d^2 \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{i d^2 \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}+\frac{d (c+d x) \text{sech}(a+b x)}{b^2}-\frac{d^2 \tan ^{-1}(\sinh (a+b x))}{b^3}+\frac{(c+d x)^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x)^2 \tanh (a+b x) \text{sech}(a+b x)}{2 b}","-\frac{i d (c+d x) \text{PolyLog}\left(2,-i e^{a+b x}\right)}{b^2}+\frac{i d (c+d x) \text{PolyLog}\left(2,i e^{a+b x}\right)}{b^2}+\frac{i d^2 \text{PolyLog}\left(3,-i e^{a+b x}\right)}{b^3}-\frac{i d^2 \text{PolyLog}\left(3,i e^{a+b x}\right)}{b^3}+\frac{d (c+d x) \text{sech}(a+b x)}{b^2}-\frac{d^2 \tan ^{-1}(\sinh (a+b x))}{b^3}+\frac{(c+d x)^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x)^2 \tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"((c + d*x)^2*ArcTan[E^(a + b*x)])/b - (d^2*ArcTan[Sinh[a + b*x]])/b^3 - (I*d*(c + d*x)*PolyLog[2, (-I)*E^(a + b*x)])/b^2 + (I*d*(c + d*x)*PolyLog[2, I*E^(a + b*x)])/b^2 + (I*d^2*PolyLog[3, (-I)*E^(a + b*x)])/b^3 - (I*d^2*PolyLog[3, I*E^(a + b*x)])/b^3 + (d*(c + d*x)*Sech[a + b*x])/b^2 + ((c + d*x)^2*Sech[a + b*x]*Tanh[a + b*x])/(2*b)","A",9,6,16,0.3750,1,"{4186, 3770, 4180, 2531, 2282, 6589}"
38,1,102,0,0.0628146,"\int (c+d x) \text{sech}^3(a+b x) \, dx","Int[(c + d*x)*Sech[a + b*x]^3,x]","-\frac{i d \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b^2}+\frac{i d \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b^2}+\frac{d \text{sech}(a+b x)}{2 b^2}+\frac{(c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x) \tanh (a+b x) \text{sech}(a+b x)}{2 b}","-\frac{i d \text{PolyLog}\left(2,-i e^{a+b x}\right)}{2 b^2}+\frac{i d \text{PolyLog}\left(2,i e^{a+b x}\right)}{2 b^2}+\frac{d \text{sech}(a+b x)}{2 b^2}+\frac{(c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b}+\frac{(c+d x) \tanh (a+b x) \text{sech}(a+b x)}{2 b}",1,"((c + d*x)*ArcTan[E^(a + b*x)])/b - ((I/2)*d*PolyLog[2, (-I)*E^(a + b*x)])/b^2 + ((I/2)*d*PolyLog[2, I*E^(a + b*x)])/b^2 + (d*Sech[a + b*x])/(2*b^2) + ((c + d*x)*Sech[a + b*x]*Tanh[a + b*x])/(2*b)","A",6,4,14,0.2857,1,"{4185, 4180, 2279, 2391}"
39,0,0,0,0.0366865,"\int \frac{\text{sech}^3(a+b x)}{c+d x} \, dx","Int[Sech[a + b*x]^3/(c + d*x),x]","\int \frac{\text{sech}^3(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{sech}^3(a+b x)}{c+d x},x\right)",0,"Defer[Int][Sech[a + b*x]^3/(c + d*x), x]","A",0,0,0,0,-1,"{}"
40,0,0,0,0.034078,"\int \frac{\text{sech}^3(a+b x)}{(c+d x)^2} \, dx","Int[Sech[a + b*x]^3/(c + d*x)^2,x]","\int \frac{\text{sech}^3(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{sech}^3(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][Sech[a + b*x]^3/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
41,1,171,0,0.3297705,"\int (c+d x)^{5/2} \cosh (a+b x) \, dx","Int[(c + d*x)^(5/2)*Cosh[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} \sinh (a+b x)}{4 b^3}-\frac{5 d (c+d x)^{3/2} \cosh (a+b x)}{2 b^2}+\frac{(c+d x)^{5/2} \sinh (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} \sinh (a+b x)}{4 b^3}-\frac{5 d (c+d x)^{3/2} \cosh (a+b x)}{2 b^2}+\frac{(c+d x)^{5/2} \sinh (a+b x)}{b}",1,"(-5*d*(c + d*x)^(3/2)*Cosh[a + b*x])/(2*b^2) + (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)) + (15*d^2*Sqrt[c + d*x]*Sinh[a + b*x])/(4*b^3) + ((c + d*x)^(5/2)*Sinh[a + b*x])/b","A",8,5,16,0.3125,1,"{3296, 3308, 2180, 2204, 2205}"
42,1,146,0,0.2428387,"\int (c+d x)^{3/2} \cosh (a+b x) \, dx","Int[(c + d*x)^(3/2)*Cosh[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} \cosh (a+b x)}{2 b^2}+\frac{(c+d x)^{3/2} \sinh (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} \cosh (a+b x)}{2 b^2}+\frac{(c+d x)^{3/2} \sinh (a+b x)}{b}",1,"(-3*d*Sqrt[c + d*x]*Cosh[a + b*x])/(2*b^2) + (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)) + ((c + d*x)^(3/2)*Sinh[a + b*x])/b","A",7,5,16,0.3125,1,"{3296, 3307, 2180, 2204, 2205}"
43,1,123,0,0.1776662,"\int \sqrt{c+d x} \cosh (a+b x) \, dx","Int[Sqrt[c + d*x]*Cosh[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} \sinh (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} \sinh (a+b x)}{b}",1,"(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)) + (Sqrt[c + d*x]*Sinh[a + b*x])/b","A",6,5,16,0.3125,1,"{3296, 3308, 2180, 2204, 2205}"
44,1,104,0,0.1297744,"\int \frac{\cosh (a+b x)}{\sqrt{c+d x}} \, dx","Int[Cosh[a + b*x]/Sqrt[c + d*x],x]","\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}}+\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}}",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,"{3307, 2180, 2204, 2205}"
45,1,119,0,0.1826999,"\int \frac{\cosh (a+b x)}{(c+d x)^{3/2}} \, dx","Int[Cosh[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 \cosh (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 \cosh (a+b x)}{d \sqrt{c+d x}}",1,"(-2*Cosh[a + b*x])/(d*Sqrt[c + d*x]) - (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)","A",6,5,16,0.3125,1,"{3297, 3308, 2180, 2204, 2205}"
46,1,149,0,0.2481075,"\int \frac{\cosh (a+b x)}{(c+d x)^{5/2}} \, dx","Int[Cosh[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 \sinh (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \cosh (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 \sinh (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \cosh (a+b x)}{3 d (c+d x)^{3/2}}",1,"(-2*Cosh[a + b*x])/(3*d*(c + d*x)^(3/2)) + (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)) - (4*b*Sinh[a + b*x])/(3*d^2*Sqrt[c + d*x])","A",7,5,16,0.3125,1,"{3297, 3307, 2180, 2204, 2205}"
47,1,174,0,0.3120071,"\int \frac{\cosh (a+b x)}{(c+d x)^{7/2}} \, dx","Int[Cosh[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 \cosh (a+b x)}{15 d^3 \sqrt{c+d x}}-\frac{4 b \sinh (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \cosh (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 \cosh (a+b x)}{15 d^3 \sqrt{c+d x}}-\frac{4 b \sinh (a+b x)}{15 d^2 (c+d x)^{3/2}}-\frac{2 \cosh (a+b x)}{5 d (c+d x)^{5/2}}",1,"(-2*Cosh[a + b*x])/(5*d*(c + d*x)^(5/2)) - (8*b^2*Cosh[a + b*x])/(15*d^3*Sqrt[c + d*x]) - (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)) - (4*b*Sinh[a + b*x])/(15*d^2*(c + d*x)^(3/2))","A",8,5,16,0.3125,1,"{3297, 3308, 2180, 2204, 2205}"
48,1,239,0,0.3996979,"\int (c+d x)^{5/2} \cosh ^2(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cosh[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} \cosh ^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} \cosh ^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) - (5*d*(c + d*x)^(3/2)*Cosh[a + b*x]^2)/(8*b^2) + (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) + (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}"
49,1,211,0,0.3031361,"\int (c+d x)^{3/2} \cosh ^2(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cosh[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} \cosh ^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} \cosh ^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*Sqrt[c + d*x]*Cosh[a + b*x]^2)/(8*b^2) + (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)","A",9,7,18,0.3889,1,"{3311, 32, 3312, 3307, 2180, 2204, 2205}"
50,1,166,0,0.269155,"\int \sqrt{c+d x} \cosh ^2(a+b x) \, dx","Int[Sqrt[c + d*x]*Cosh[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}"
51,1,138,0,0.2140584,"\int \frac{\cosh ^2(a+b x)}{\sqrt{c+d x}} \, dx","Int[Cosh[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}"
52,1,142,0,0.230148,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^{3/2}} \, dx","Int[Cosh[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 \cosh ^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 \cosh ^2(a+b x)}{d \sqrt{c+d x}}",1,"(-2*Cosh[a + b*x]^2)/(d*Sqrt[c + d*x]) - (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)","A",7,6,18,0.3333,1,"{3313, 12, 3308, 2180, 2204, 2205}"
53,1,174,0,0.3088609,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^{5/2}} \, dx","Int[Cosh[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 \cosh ^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 \cosh ^2(a+b x)}{3 d (c+d x)^{3/2}}",1,"(-2*Cosh[a + b*x]^2)/(3*d*(c + d*x)^(3/2)) + (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])","A",9,7,18,0.3889,1,"{3314, 32, 3312, 3307, 2180, 2204, 2205}"
54,1,220,0,0.3114932,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^{7/2}} \, dx","Int[Cosh[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 \cosh ^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 \cosh ^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 \cosh ^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 \cosh ^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]) - (2*Cosh[a + b*x]^2)/(5*d*(c + d*x)^(5/2)) - (32*b^2*Cosh[a + b*x]^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))","A",9,8,18,0.4444,1,"{3314, 32, 3313, 12, 3308, 2180, 2204, 2205}"
55,1,251,0,0.37924,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^{9/2}} \, dx","Int[Cosh[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 \cosh ^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 \cosh ^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 \cosh ^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 \cosh ^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)) - (2*Cosh[a + b*x]^2)/(7*d*(c + d*x)^(7/2)) - (32*b^2*Cosh[a + b*x]^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])","A",11,7,18,0.3889,1,"{3314, 32, 3312, 3307, 2180, 2204, 2205}"
56,1,381,0,0.9063787,"\int (c+d x)^{5/2} \cosh ^3(a+b x) \, dx","Int[(c + d*x)^(5/2)*Cosh[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} \sinh (a+b x)}{16 b^3}+\frac{5 d^2 \sqrt{c+d x} \sinh (3 a+3 b x)}{144 b^3}-\frac{5 d (c+d x)^{3/2} \cosh ^3(a+b x)}{18 b^2}-\frac{5 d (c+d x)^{3/2} \cosh (a+b x)}{3 b^2}+\frac{2 (c+d x)^{5/2} \sinh (a+b x)}{3 b}+\frac{(c+d x)^{5/2} \sinh (a+b x) \cosh ^2(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} \sinh (a+b x)}{16 b^3}+\frac{5 d^2 \sqrt{c+d x} \sinh (3 a+3 b x)}{144 b^3}-\frac{5 d (c+d x)^{3/2} \cosh ^3(a+b x)}{18 b^2}-\frac{5 d (c+d x)^{3/2} \cosh (a+b x)}{3 b^2}+\frac{2 (c+d x)^{5/2} \sinh (a+b x)}{3 b}+\frac{(c+d x)^{5/2} \sinh (a+b x) \cosh ^2(a+b x)}{3 b}",1,"(-5*d*(c + d*x)^(3/2)*Cosh[a + b*x])/(3*b^2) - (5*d*(c + d*x)^(3/2)*Cosh[a + b*x]^3)/(18*b^2) + (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)) + (45*d^2*Sqrt[c + d*x]*Sinh[a + b*x])/(16*b^3) + (2*(c + d*x)^(5/2)*Sinh[a + b*x])/(3*b) + ((c + d*x)^(5/2)*Cosh[a + b*x]^2*Sinh[a + b*x])/(3*b) + (5*d^2*Sqrt[c + d*x]*Sinh[3*a + 3*b*x])/(144*b^3)","A",23,7,18,0.3889,1,"{3311, 3296, 3308, 2180, 2204, 2205, 3312}"
57,1,326,0,0.7123732,"\int (c+d x)^{3/2} \cosh ^3(a+b x) \, dx","Int[(c + d*x)^(3/2)*Cosh[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} \cosh ^3(a+b x)}{6 b^2}-\frac{d \sqrt{c+d x} \cosh (a+b x)}{b^2}+\frac{2 (c+d x)^{3/2} \sinh (a+b x)}{3 b}+\frac{(c+d x)^{3/2} \sinh (a+b x) \cosh ^2(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} \cosh ^3(a+b x)}{6 b^2}-\frac{d \sqrt{c+d x} \cosh (a+b x)}{b^2}+\frac{2 (c+d x)^{3/2} \sinh (a+b x)}{3 b}+\frac{(c+d x)^{3/2} \sinh (a+b x) \cosh ^2(a+b x)}{3 b}",1,"-((d*Sqrt[c + d*x]*Cosh[a + b*x])/b^2) - (d*Sqrt[c + d*x]*Cosh[a + b*x]^3)/(6*b^2) + (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)) + (2*(c + d*x)^(3/2)*Sinh[a + b*x])/(3*b) + ((c + d*x)^(3/2)*Cosh[a + b*x]^2*Sinh[a + b*x])/(3*b)","A",20,7,18,0.3889,1,"{3311, 3296, 3307, 2180, 2204, 2205, 3312}"
58,1,275,0,0.4835209,"\int \sqrt{c+d x} \cosh ^3(a+b x) \, dx","Int[Sqrt[c + d*x]*Cosh[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} \sinh (a+b x)}{4 b}+\frac{\sqrt{c+d x} \sinh (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} \sinh (a+b x)}{4 b}+\frac{\sqrt{c+d x} \sinh (3 a+3 b x)}{12 b}",1,"(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)) + (3*Sqrt[c + d*x]*Sinh[a + b*x])/(4*b) + (Sqrt[c + d*x]*Sinh[3*a + 3*b*x])/(12*b)","A",14,6,18,0.3333,1,"{3312, 3296, 3308, 2180, 2204, 2205}"
59,1,228,0,0.3737022,"\int \frac{\cosh ^3(a+b x)}{\sqrt{c+d x}} \, dx","Int[Cosh[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, 3307, 2180, 2204, 2205}"
60,1,246,0,0.4211955,"\int \frac{\cosh ^3(a+b x)}{(c+d x)^{3/2}} \, dx","Int[Cosh[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 \cosh ^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 \cosh ^3(a+b x)}{d \sqrt{c+d x}}",1,"(-2*Cosh[a + b*x]^3)/(d*Sqrt[c + d*x]) - (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))","A",12,5,18,0.2778,1,"{3313, 3308, 2180, 2204, 2205}"
61,1,277,0,0.6047162,"\int \frac{\cosh ^3(a+b x)}{(c+d x)^{5/2}} \, dx","Int[Cosh[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 (a+b x) \cosh ^2(a+b x)}{d^2 \sqrt{c+d x}}-\frac{2 \cosh ^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 (a+b x) \cosh ^2(a+b x)}{d^2 \sqrt{c+d x}}-\frac{2 \cosh ^3(a+b x)}{3 d (c+d x)^{3/2}}",1,"(-2*Cosh[a + b*x]^3)/(3*d*(c + d*x)^(3/2)) + (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]^2*Sinh[a + b*x])/(d^2*Sqrt[c + d*x])","A",18,6,18,0.3333,1,"{3314, 3307, 2180, 2204, 2205, 3312}"
62,1,331,0,0.6804564,"\int \frac{\cosh ^3(a+b x)}{(c+d x)^{7/2}} \, dx","Int[Cosh[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 \cosh ^3(a+b x)}{5 d^3 \sqrt{c+d x}}+\frac{16 b^2 \cosh (a+b x)}{5 d^3 \sqrt{c+d x}}-\frac{4 b \sinh (a+b x) \cosh ^2(a+b x)}{5 d^2 (c+d x)^{3/2}}-\frac{2 \cosh ^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 \cosh ^3(a+b x)}{5 d^3 \sqrt{c+d x}}+\frac{16 b^2 \cosh (a+b x)}{5 d^3 \sqrt{c+d x}}-\frac{4 b \sinh (a+b x) \cosh ^2(a+b x)}{5 d^2 (c+d x)^{3/2}}-\frac{2 \cosh ^3(a+b x)}{5 d (c+d x)^{5/2}}",1,"(16*b^2*Cosh[a + b*x])/(5*d^3*Sqrt[c + d*x]) - (2*Cosh[a + b*x]^3)/(5*d*(c + d*x)^(5/2)) - (24*b^2*Cosh[a + b*x]^3)/(5*d^3*Sqrt[c + d*x]) - (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)) - (4*b*Cosh[a + b*x]^2*Sinh[a + b*x])/(5*d^2*(c + d*x)^(3/2))","A",19,7,18,0.3889,1,"{3314, 3297, 3308, 2180, 2204, 2205, 3313}"
63,1,111,0,0.1554502,"\int (d x)^{3/2} \cosh (f x) \, dx","Int[(d*x)^(3/2)*Cosh[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} \cosh (f x)}{2 f^2}+\frac{(d x)^{3/2} \sinh (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} \cosh (f x)}{2 f^2}+\frac{(d x)^{3/2} \sinh (f x)}{f}",1,"(-3*d*Sqrt[d*x]*Cosh[f*x])/(2*f^2) + (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)) + ((d*x)^(3/2)*Sinh[f*x])/f","A",7,5,12,0.4167,1,"{3296, 3307, 2180, 2204, 2205}"
64,1,92,0,0.1064762,"\int \sqrt{d x} \cosh (f x) \, dx","Int[Sqrt[d*x]*Cosh[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} \sinh (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} \sinh (f x)}{f}",1,"(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)) + (Sqrt[d*x]*Sinh[f*x])/f","A",6,5,12,0.4167,1,"{3296, 3308, 2180, 2204, 2205}"
65,1,77,0,0.0774998,"\int \frac{\cosh (f x)}{\sqrt{d x}} \, dx","Int[Cosh[f*x]/Sqrt[d*x],x]","\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}}+\frac{\sqrt{\pi } \text{Erfi}\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,"{3307, 2180, 2204, 2205}"
66,1,88,0,0.1125316,"\int \frac{\cosh (f x)}{(d x)^{3/2}} \, dx","Int[Cosh[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 \cosh (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 \cosh (f x)}{d \sqrt{d x}}",1,"(-2*Cosh[f*x])/(d*Sqrt[d*x]) - (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)","A",6,5,12,0.4167,1,"{3297, 3308, 2180, 2204, 2205}"
67,1,114,0,0.1484599,"\int \frac{\cosh (f x)}{(d x)^{5/2}} \, dx","Int[Cosh[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 \sinh (f x)}{3 d^2 \sqrt{d x}}-\frac{2 \cosh (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 \sinh (f x)}{3 d^2 \sqrt{d x}}-\frac{2 \cosh (f x)}{3 d (d x)^{3/2}}",1,"(-2*Cosh[f*x])/(3*d*(d*x)^(3/2)) + (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)) - (4*f*Sinh[f*x])/(3*d^2*Sqrt[d*x])","A",7,5,12,0.4167,1,"{3297, 3307, 2180, 2204, 2205}"
68,0,0,0,0.0283211,"\int \sqrt{c+d x} \text{sech}(a+b x) \, dx","Int[Sqrt[c + d*x]*Sech[a + b*x],x]","\int \sqrt{c+d x} \text{sech}(a+b x) \, dx","\text{Int}\left(\sqrt{c+d x} \text{sech}(a+b x),x\right)",0,"Defer[Int][Sqrt[c + d*x]*Sech[a + b*x], x]","A",0,0,0,0,-1,"{}"
69,0,0,0,0.0295777,"\int \frac{\text{sech}(a+b x)}{\sqrt{c+d x}} \, dx","Int[Sech[a + b*x]/Sqrt[c + d*x],x]","\int \frac{\text{sech}(a+b x)}{\sqrt{c+d x}} \, dx","\text{Int}\left(\frac{\text{sech}(a+b x)}{\sqrt{c+d x}},x\right)",0,"Defer[Int][Sech[a + b*x]/Sqrt[c + d*x], x]","A",0,0,0,0,-1,"{}"
70,0,0,0,0.0853537,"\int \frac{\cosh ^{\frac{3}{2}}(x)}{x^3} \, dx","Int[Cosh[x]^(3/2)/x^3,x]","\int \frac{\cosh ^{\frac{3}{2}}(x)}{x^3} \, dx","\frac{9}{8} \text{Int}\left(\frac{\cosh ^{\frac{3}{2}}(x)}{x},x\right)-\frac{3}{8} \text{Int}\left(\frac{1}{x \sqrt{\cosh (x)}},x\right)-\frac{\cosh ^{\frac{3}{2}}(x)}{2 x^2}-\frac{3 \sinh (x) \sqrt{\cosh (x)}}{4 x}",0,"-Cosh[x]^(3/2)/(2*x^2) - (3*Sqrt[Cosh[x]]*Sinh[x])/(4*x) - (3*Defer[Int][1/(x*Sqrt[Cosh[x]]), x])/8 + (9*Defer[Int][Cosh[x]^(3/2)/x, x])/8","A",0,0,0,0,-1,"{}"
71,1,20,0,0.047739,"\int \left(\frac{x}{\cosh ^{\frac{3}{2}}(x)}+x \sqrt{\cosh (x)}\right) \, dx","Int[x/Cosh[x]^(3/2) + x*Sqrt[Cosh[x]],x]","\frac{2 x \sinh (x)}{\sqrt{\cosh (x)}}-4 \sqrt{\cosh (x)}","\frac{2 x \sinh (x)}{\sqrt{\cosh (x)}}-4 \sqrt{\cosh (x)}",1,"-4*Sqrt[Cosh[x]] + (2*x*Sinh[x])/Sqrt[Cosh[x]]","A",2,1,17,0.05882,1,"{3315}"
72,1,24,0,0.0499309,"\int \left(\frac{x}{\cosh ^{\frac{5}{2}}(x)}-\frac{x}{3 \sqrt{\cosh (x)}}\right) \, dx","Int[x/Cosh[x]^(5/2) - x/(3*Sqrt[Cosh[x]]),x]","\frac{4}{3 \sqrt{\cosh (x)}}+\frac{2 x \sinh (x)}{3 \cosh ^{\frac{3}{2}}(x)}","\frac{4}{3 \sqrt{\cosh (x)}}+\frac{2 x \sinh (x)}{3 \cosh ^{\frac{3}{2}}(x)}",1,"4/(3*Sqrt[Cosh[x]]) + (2*x*Sinh[x])/(3*Cosh[x]^(3/2))","A",2,1,20,0.05000,1,"{3315}"
73,1,47,0,0.0657676,"\int \left(\frac{x}{\cosh ^{\frac{7}{2}}(x)}+\frac{3}{5} x \sqrt{\cosh (x)}\right) \, dx","Int[x/Cosh[x]^(7/2) + (3*x*Sqrt[Cosh[x]])/5,x]","\frac{4}{15 \cosh ^{\frac{3}{2}}(x)}-\frac{12 \sqrt{\cosh (x)}}{5}+\frac{2 x \sinh (x)}{5 \cosh ^{\frac{5}{2}}(x)}+\frac{6 x \sinh (x)}{5 \sqrt{\cosh (x)}}","\frac{4}{15 \cosh ^{\frac{3}{2}}(x)}-\frac{12 \sqrt{\cosh (x)}}{5}+\frac{2 x \sinh (x)}{5 \cosh ^{\frac{5}{2}}(x)}+\frac{6 x \sinh (x)}{5 \sqrt{\cosh (x)}}",1,"4/(15*Cosh[x]^(3/2)) - (12*Sqrt[Cosh[x]])/5 + (2*x*Sinh[x])/(5*Cosh[x]^(5/2)) + (6*x*Sinh[x])/(5*Sqrt[Cosh[x]])","A",3,1,20,0.05000,1,"{3315}"
74,1,36,0,0.0918835,"\int \left(\frac{x^2}{\cosh ^{\frac{3}{2}}(x)}+x^2 \sqrt{\cosh (x)}\right) \, dx","Int[x^2/Cosh[x]^(3/2) + x^2*Sqrt[Cosh[x]],x]","\frac{2 x^2 \sinh (x)}{\sqrt{\cosh (x)}}-8 x \sqrt{\cosh (x)}-16 i E\left(\left.\frac{i x}{2}\right|2\right)","\frac{2 x^2 \sinh (x)}{\sqrt{\cosh (x)}}-8 x \sqrt{\cosh (x)}-16 i E\left(\left.\frac{i x}{2}\right|2\right)",1,"-8*x*Sqrt[Cosh[x]] - (16*I)*EllipticE[(I/2)*x, 2] + (2*x^2*Sinh[x])/Sqrt[Cosh[x]]","A",3,2,21,0.09524,1,"{3316, 2639}"
75,0,0,0,0.0458665,"\int (c+d x)^m (b \cosh (e+f x))^n \, dx","Int[(c + d*x)^m*(b*Cosh[e + f*x])^n,x]","\int (c+d x)^m (b \cosh (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (b \cosh (e+f x))^n,x\right)",0,"Defer[Int][(c + d*x)^m*(b*Cosh[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
76,1,237,0,0.2837799,"\int (c+d x)^m \cosh ^3(a+b x) \, dx","Int[(c + d*x)^m*Cosh[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, 3307, 2181}"
77,1,144,0,0.1840353,"\int (c+d x)^m \cosh ^2(a+b x) \, dx","Int[(c + d*x)^m*Cosh[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}"
78,1,110,0,0.0913823,"\int (c+d x)^m \cosh (a+b x) \, dx","Int[(c + d*x)^m*Cosh[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,"{3307, 2181}"
79,0,0,0,0.0202649,"\int (c+d x)^m \text{sech}(a+b x) \, dx","Int[(c + d*x)^m*Sech[a + b*x],x]","\int (c+d x)^m \text{sech}(a+b x) \, dx","\text{Int}\left(\text{sech}(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Sech[a + b*x], x]","A",0,0,0,0,-1,"{}"
80,0,0,0,0.0358342,"\int (c+d x)^m \text{sech}^2(a+b x) \, dx","Int[(c + d*x)^m*Sech[a + b*x]^2,x]","\int (c+d x)^m \text{sech}^2(a+b x) \, dx","\text{Int}\left(\text{sech}^2(a+b x) (c+d x)^m,x\right)",0,"Defer[Int][(c + d*x)^m*Sech[a + b*x]^2, x]","A",0,0,0,0,-1,"{}"
81,1,59,0,0.0738787,"\int x^{3+m} \cosh (a+b x) \, dx","Int[x^(3 + m)*Cosh[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,"{3307, 2181}"
82,1,59,0,0.0721975,"\int x^{2+m} \cosh (a+b x) \, dx","Int[x^(2 + m)*Cosh[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,"{3307, 2181}"
83,1,59,0,0.0711949,"\int x^{1+m} \cosh (a+b x) \, dx","Int[x^(1 + m)*Cosh[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,"{3307, 2181}"
84,1,59,0,0.0687868,"\int x^m \cosh (a+b x) \, dx","Int[x^m*Cosh[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,"{3307, 2181}"
85,1,49,0,0.0690003,"\int x^{-1+m} \cosh (a+b x) \, dx","Int[x^(-1 + m)*Cosh[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,"{3307, 2181}"
86,1,55,0,0.0691807,"\int x^{-2+m} \cosh (a+b x) \, dx","Int[x^(-2 + m)*Cosh[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,"{3307, 2181}"
87,1,59,0,0.0704377,"\int x^{-3+m} \cosh (a+b x) \, dx","Int[x^(-3 + m)*Cosh[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,"{3307, 2181}"
88,1,86,0,0.1501471,"\int x^{3+m} \cosh ^2(a+b x) \, dx","Int[x^(3 + m)*Cosh[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}"
89,1,85,0,0.1334111,"\int x^{2+m} \cosh ^2(a+b x) \, dx","Int[x^(2 + m)*Cosh[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}"
90,1,86,0,0.133434,"\int x^{1+m} \cosh ^2(a+b x) \, dx","Int[x^(1 + m)*Cosh[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}"
91,1,85,0,0.1269344,"\int x^m \cosh ^2(a+b x) \, dx","Int[x^m*Cosh[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}"
92,1,72,0,0.1249533,"\int x^{-1+m} \cosh ^2(a+b x) \, dx","Int[x^(-1 + m)*Cosh[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}"
93,1,83,0,0.1295797,"\int x^{-2+m} \cosh ^2(a+b x) \, dx","Int[x^(-2 + m)*Cosh[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}"
94,1,84,0,0.1398588,"\int x^{-3+m} \cosh ^2(a+b x) \, dx","Int[x^(-3 + m)*Cosh[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}"
95,1,24,0,0.0906282,"\int \left(\frac{x}{\text{sech}^{\frac{3}{2}}(x)}-\frac{1}{3} x \sqrt{\text{sech}(x)}\right) \, dx","Int[x/Sech[x]^(3/2) - (x*Sqrt[Sech[x]])/3,x]","\frac{2 x \sinh (x)}{3 \sqrt{\text{sech}(x)}}-\frac{4}{9 \text{sech}^{\frac{3}{2}}(x)}","\frac{2 x \sinh (x)}{3 \sqrt{\text{sech}(x)}}-\frac{4}{9 \text{sech}^{\frac{3}{2}}(x)}",1,"-4/(9*Sech[x]^(3/2)) + (2*x*Sinh[x])/(3*Sqrt[Sech[x]])","A",4,2,20,0.1000,1,"{4187, 4189}"
96,1,24,0,0.0877239,"\int \left(\frac{x}{\text{sech}^{\frac{5}{2}}(x)}-\frac{3 x}{5 \sqrt{\text{sech}(x)}}\right) \, dx","Int[x/Sech[x]^(5/2) - (3*x)/(5*Sqrt[Sech[x]]),x]","\frac{2 x \sinh (x)}{5 \text{sech}^{\frac{3}{2}}(x)}-\frac{4}{25 \text{sech}^{\frac{5}{2}}(x)}","\frac{2 x \sinh (x)}{5 \text{sech}^{\frac{3}{2}}(x)}-\frac{4}{25 \text{sech}^{\frac{5}{2}}(x)}",1,"-4/(25*Sech[x]^(5/2)) + (2*x*Sinh[x])/(5*Sech[x]^(3/2))","A",4,2,20,0.1000,1,"{4187, 4189}"
97,1,47,0,0.104468,"\int \left(\frac{x}{\text{sech}^{\frac{7}{2}}(x)}-\frac{5}{21} x \sqrt{\text{sech}(x)}\right) \, dx","Int[x/Sech[x]^(7/2) - (5*x*Sqrt[Sech[x]])/21,x]","-\frac{20}{63 \text{sech}^{\frac{3}{2}}(x)}-\frac{4}{49 \text{sech}^{\frac{7}{2}}(x)}+\frac{2 x \sinh (x)}{7 \text{sech}^{\frac{5}{2}}(x)}+\frac{10 x \sinh (x)}{21 \sqrt{\text{sech}(x)}}","-\frac{20}{63 \text{sech}^{\frac{3}{2}}(x)}-\frac{4}{49 \text{sech}^{\frac{7}{2}}(x)}+\frac{2 x \sinh (x)}{7 \text{sech}^{\frac{5}{2}}(x)}+\frac{10 x \sinh (x)}{21 \sqrt{\text{sech}(x)}}",1,"-4/(49*Sech[x]^(7/2)) - 20/(63*Sech[x]^(3/2)) + (2*x*Sinh[x])/(7*Sech[x]^(5/2)) + (10*x*Sinh[x])/(21*Sqrt[Sech[x]])","A",5,2,20,0.1000,1,"{4187, 4189}"
98,1,66,0,0.1690321,"\int \left(\frac{x^2}{\text{sech}^{\frac{3}{2}}(x)}-\frac{1}{3} x^2 \sqrt{\text{sech}(x)}\right) \, dx","Int[x^2/Sech[x]^(3/2) - (x^2*Sqrt[Sech[x]])/3,x]","\frac{2 x^2 \sinh (x)}{3 \sqrt{\text{sech}(x)}}-\frac{8 x}{9 \text{sech}^{\frac{3}{2}}(x)}+\frac{16 \sinh (x)}{27 \sqrt{\text{sech}(x)}}-\frac{16}{27} i \sqrt{\cosh (x)} \sqrt{\text{sech}(x)} F\left(\left.\frac{i x}{2}\right|2\right)","\frac{2 x^2 \sinh (x)}{3 \sqrt{\text{sech}(x)}}-\frac{8 x}{9 \text{sech}^{\frac{3}{2}}(x)}+\frac{16 \sinh (x)}{27 \sqrt{\text{sech}(x)}}-\frac{16}{27} i \sqrt{\cosh (x)} \sqrt{\text{sech}(x)} F\left(\left.\frac{i x}{2}\right|2\right)",1,"(-8*x)/(9*Sech[x]^(3/2)) - ((16*I)/27)*Sqrt[Cosh[x]]*EllipticF[(I/2)*x, 2]*Sqrt[Sech[x]] + (16*Sinh[x])/(27*Sqrt[Sech[x]]) + (2*x^2*Sinh[x])/(3*Sqrt[Sech[x]])","A",7,5,24,0.2083,1,"{4188, 4189, 3769, 3771, 2641}"
99,1,89,0,0.1315402,"\int (c+d x)^3 (a+a \cosh (e+f x)) \, dx","Int[(c + d*x)^3*(a + a*Cosh[e + f*x]),x]","\frac{6 a d^2 (c+d x) \sinh (e+f x)}{f^3}-\frac{3 a d (c+d x)^2 \cosh (e+f x)}{f^2}+\frac{a (c+d x)^3 \sinh (e+f x)}{f}+\frac{a (c+d x)^4}{4 d}-\frac{6 a d^3 \cosh (e+f x)}{f^4}","\frac{6 a d^2 (c+d x) \sinh (e+f x)}{f^3}-\frac{3 a d (c+d x)^2 \cosh (e+f x)}{f^2}+\frac{a (c+d x)^3 \sinh (e+f x)}{f}+\frac{a (c+d x)^4}{4 d}-\frac{6 a d^3 \cosh (e+f x)}{f^4}",1,"(a*(c + d*x)^4)/(4*d) - (6*a*d^3*Cosh[e + f*x])/f^4 - (3*a*d*(c + d*x)^2*Cosh[e + f*x])/f^2 + (6*a*d^2*(c + d*x)*Sinh[e + f*x])/f^3 + (a*(c + d*x)^3*Sinh[e + f*x])/f","A",6,3,18,0.1667,1,"{3317, 3296, 2638}"
100,1,67,0,0.0906686,"\int (c+d x)^2 (a+a \cosh (e+f x)) \, dx","Int[(c + d*x)^2*(a + a*Cosh[e + f*x]),x]","-\frac{2 a d (c+d x) \cosh (e+f x)}{f^2}+\frac{a (c+d x)^2 \sinh (e+f x)}{f}+\frac{a (c+d x)^3}{3 d}+\frac{2 a d^2 \sinh (e+f x)}{f^3}","-\frac{2 a d (c+d x) \cosh (e+f x)}{f^2}+\frac{a (c+d x)^2 \sinh (e+f x)}{f}+\frac{a (c+d x)^3}{3 d}+\frac{2 a d^2 \sinh (e+f x)}{f^3}",1,"(a*(c + d*x)^3)/(3*d) - (2*a*d*(c + d*x)*Cosh[e + f*x])/f^2 + (2*a*d^2*Sinh[e + f*x])/f^3 + (a*(c + d*x)^2*Sinh[e + f*x])/f","A",5,3,18,0.1667,1,"{3317, 3296, 2637}"
101,1,45,0,0.044669,"\int (c+d x) (a+a \cosh (e+f x)) \, dx","Int[(c + d*x)*(a + a*Cosh[e + f*x]),x]","\frac{a (c+d x) \sinh (e+f x)}{f}+\frac{a (c+d x)^2}{2 d}-\frac{a d \cosh (e+f x)}{f^2}","\frac{a (c+d x) \sinh (e+f x)}{f}+\frac{a (c+d x)^2}{2 d}-\frac{a d \cosh (e+f x)}{f^2}",1,"(a*(c + d*x)^2)/(2*d) - (a*d*Cosh[e + f*x])/f^2 + (a*(c + d*x)*Sinh[e + f*x])/f","A",4,3,16,0.1875,1,"{3317, 3296, 2638}"
102,1,64,0,0.13797,"\int \frac{a+a \cosh (e+f x)}{c+d x} \, dx","Int[(a + a*Cosh[e + f*x])/(c + d*x),x]","\frac{a \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \left(e-\frac{c f}{d}\right)}{d}+\frac{a \sinh \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{a \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \left(e-\frac{c f}{d}\right)}{d}+\frac{a \sinh \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*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/d + (a*Log[c + d*x])/d + (a*Sinh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d","A",5,4,18,0.2222,1,"{3317, 3303, 3298, 3301}"
103,1,87,0,0.1720568,"\int \frac{a+a \cosh (e+f x)}{(c+d x)^2} \, dx","Int[(a + a*Cosh[e + f*x])/(c + d*x)^2,x]","\frac{a f \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{a f \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{a \cosh (e+f x)}{d (c+d x)}-\frac{a}{d (c+d x)}","\frac{a f \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{a f \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{a \cosh (e+f x)}{d (c+d x)}-\frac{a}{d (c+d x)}",1,"-(a/(d*(c + d*x))) - (a*Cosh[e + f*x])/(d*(c + d*x)) + (a*f*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d^2 + (a*f*Cosh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d^2","A",6,5,18,0.2778,1,"{3317, 3297, 3303, 3298, 3301}"
104,1,123,0,0.2157126,"\int \frac{a+a \cosh (e+f x)}{(c+d x)^3} \, dx","Int[(a + a*Cosh[e + f*x])/(c + d*x)^3,x]","\frac{a f^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \left(e-\frac{c f}{d}\right)}{2 d^3}+\frac{a f^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{2 d^3}-\frac{a f \sinh (e+f x)}{2 d^2 (c+d x)}-\frac{a \cosh (e+f x)}{2 d (c+d x)^2}-\frac{a}{2 d (c+d x)^2}","\frac{a f^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \left(e-\frac{c f}{d}\right)}{2 d^3}+\frac{a f^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{2 d^3}-\frac{a f \sinh (e+f x)}{2 d^2 (c+d x)}-\frac{a \cosh (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) - (a*Cosh[e + f*x])/(2*d*(c + d*x)^2) + (a*f^2*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/(2*d^3) - (a*f*Sinh[e + f*x])/(2*d^2*(c + d*x)) + (a*f^2*Sinh[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}"
105,1,237,0,0.2653978,"\int (c+d x)^3 (a+a \cosh (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + a*Cosh[e + f*x])^2,x]","\frac{12 a^2 d^2 (c+d x) \sinh (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 \cosh ^2(e+f x)}{4 f^2}-\frac{6 a^2 d (c+d x)^2 \cosh (e+f x)}{f^2}+\frac{2 a^2 (c+d x)^3 \sinh (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 \cosh ^2(e+f x)}{8 f^4}-\frac{12 a^2 d^3 \cosh (e+f x)}{f^4}+\frac{3 a^2 d^3 x^2}{8 f^2}","\frac{12 a^2 d^2 (c+d x) \sinh (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 \cosh ^2(e+f x)}{4 f^2}-\frac{6 a^2 d (c+d x)^2 \cosh (e+f x)}{f^2}+\frac{2 a^2 (c+d x)^3 \sinh (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 \cosh ^2(e+f x)}{8 f^4}-\frac{12 a^2 d^3 \cosh (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*a^2*d^3*Cosh[e + f*x])/f^4 - (6*a^2*d*(c + d*x)^2*Cosh[e + f*x])/f^2 - (3*a^2*d^3*Cosh[e + f*x]^2)/(8*f^4) - (3*a^2*d*(c + d*x)^2*Cosh[e + f*x]^2)/(4*f^2) + (12*a^2*d^2*(c + d*x)*Sinh[e + f*x])/f^3 + (2*a^2*(c + d*x)^3*Sinh[e + f*x])/f + (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)","A",10,6,20,0.3000,1,"{3317, 3296, 2638, 3311, 32, 3310}"
106,1,168,0,0.1876813,"\int (c+d x)^2 (a+a \cosh (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + a*Cosh[e + f*x])^2,x]","-\frac{a^2 d (c+d x) \cosh ^2(e+f x)}{2 f^2}-\frac{4 a^2 d (c+d x) \cosh (e+f x)}{f^2}+\frac{2 a^2 (c+d x)^2 \sinh (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 a^2 d^2 \sinh (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) \cosh ^2(e+f x)}{2 f^2}-\frac{4 a^2 d (c+d x) \cosh (e+f x)}{f^2}+\frac{2 a^2 (c+d x)^2 \sinh (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 a^2 d^2 \sinh (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*a^2*d*(c + d*x)*Cosh[e + f*x])/f^2 - (a^2*d*(c + d*x)*Cosh[e + f*x]^2)/(2*f^2) + (4*a^2*d^2*Sinh[e + f*x])/f^3 + (2*a^2*(c + d*x)^2*Sinh[e + f*x])/f + (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",9,7,20,0.3500,1,"{3317, 3296, 2637, 3311, 32, 2635, 8}"
107,1,118,0,0.099404,"\int (c+d x) (a+a \cosh (e+f x))^2 \, dx","Int[(c + d*x)*(a + a*Cosh[e + f*x])^2,x]","\frac{2 a^2 (c+d x) \sinh (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 \cosh ^2(e+f x)}{4 f^2}-\frac{2 a^2 d \cosh (e+f x)}{f^2}+\frac{1}{4} a^2 d x^2","\frac{2 a^2 (c+d x) \sinh (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 \cosh ^2(e+f x)}{4 f^2}-\frac{2 a^2 d \cosh (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*a^2*d*Cosh[e + f*x])/f^2 - (a^2*d*Cosh[e + f*x]^2)/(4*f^2) + (2*a^2*(c + d*x)*Sinh[e + f*x])/f + (a^2*(c + d*x)*Cosh[e + f*x]*Sinh[e + f*x])/(2*f)","A",6,4,18,0.2222,1,"{3317, 3296, 2638, 3310}"
108,1,145,0,0.3415067,"\int \frac{(a+a \cosh (e+f x))^2}{c+d x} \, dx","Int[(a + a*Cosh[e + f*x])^2/(c + d*x),x]","\frac{2 a^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \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{2 a^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{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{3 a^2 \log (c+d x)}{2 d}","\frac{2 a^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \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{2 a^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{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{3 a^2 \log (c+d x)}{2 d}",1,"(2*a^2*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/d + (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*a^2*Sinh[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",9,5,20,0.2500,1,"{3318, 3312, 3303, 3298, 3301}"
109,1,157,0,0.332978,"\int \frac{(a+a \cosh (e+f x))^2}{(c+d x)^2} \, dx","Int[(a + a*Cosh[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 a^2 f \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{2 a^2 f \cosh \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}\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 a^2 f \text{Chi}\left(x f+\frac{c f}{d}\right) \sinh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{2 a^2 f \cosh \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}\right)}{d (c+d x)}",1,"(-4*a^2*Cosh[e/2 + (f*x)/2]^4)/(d*(c + d*x)) + (a^2*f*CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/d^2 + (2*a^2*f*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d^2 + (2*a^2*f*Cosh[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",9,5,20,0.2500,1,"{3318, 3313, 3303, 3298, 3301}"
110,1,207,0,0.5048321,"\int \frac{(a+a \cosh (e+f x))^2}{(c+d x)^3} \, dx","Int[(a + a*Cosh[e + f*x])^2/(c + d*x)^3,x]","\frac{a^2 f^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \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(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{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{4 a^2 f \sinh \left(\frac{e}{2}+\frac{f x}{2}\right) \cosh ^3\left(\frac{e}{2}+\frac{f x}{2}\right)}{d^2 (c+d x)}-\frac{2 a^2 \cosh ^4\left(\frac{e}{2}+\frac{f x}{2}\right)}{d (c+d x)^2}","\frac{a^2 f^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \cosh \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(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{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{4 a^2 f \sinh \left(\frac{e}{2}+\frac{f x}{2}\right) \cosh ^3\left(\frac{e}{2}+\frac{f x}{2}\right)}{d^2 (c+d x)}-\frac{2 a^2 \cosh ^4\left(\frac{e}{2}+\frac{f x}{2}\right)}{d (c+d x)^2}",1,"(-2*a^2*Cosh[e/2 + (f*x)/2]^4)/(d*(c + d*x)^2) + (a^2*f^2*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/d^3 + (a^2*f^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/d^3 - (4*a^2*f*Cosh[e/2 + (f*x)/2]^3*Sinh[e/2 + (f*x)/2])/(d^2*(c + d*x)) + (a^2*f^2*Sinh[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",15,6,20,0.3000,1,"{3318, 3314, 3312, 3303, 3298, 3301}"
111,1,117,0,0.272983,"\int \frac{(c+d x)^3}{a+a \cosh (e+f x)} \, dx","Int[(c + d*x)^3/(a + a*Cosh[e + f*x]),x]","-\frac{12 d^2 (c+d x) \text{PolyLog}\left(2,-e^{e+f x}\right)}{a f^3}+\frac{12 d^3 \text{PolyLog}\left(3,-e^{e+f x}\right)}{a f^4}-\frac{6 d (c+d x)^2 \log \left(e^{e+f x}+1\right)}{a f^2}+\frac{(c+d x)^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{(c+d x)^3}{a f}","-\frac{12 d^2 (c+d x) \text{PolyLog}\left(2,-e^{e+f x}\right)}{a f^3}+\frac{12 d^3 \text{PolyLog}\left(3,-e^{e+f x}\right)}{a f^4}-\frac{6 d (c+d x)^2 \log \left(e^{e+f x}+1\right)}{a f^2}+\frac{(c+d x)^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}\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 + E^(e + f*x)])/(a*f^2) - (12*d^2*(c + d*x)*PolyLog[2, -E^(e + f*x)])/(a*f^3) + (12*d^3*PolyLog[3, -E^(e + f*x)])/(a*f^4) + ((c + d*x)^3*Tanh[e/2 + (f*x)/2])/(a*f)","A",7,7,20,0.3500,1,"{3318, 4184, 3718, 2190, 2531, 2282, 6589}"
112,1,88,0,0.2013843,"\int \frac{(c+d x)^2}{a+a \cosh (e+f x)} \, dx","Int[(c + d*x)^2/(a + a*Cosh[e + f*x]),x]","-\frac{4 d^2 \text{PolyLog}\left(2,-e^{e+f x}\right)}{a f^3}-\frac{4 d (c+d x) \log \left(e^{e+f x}+1\right)}{a f^2}+\frac{(c+d x)^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{(c+d x)^2}{a f}","-\frac{4 d^2 \text{PolyLog}\left(2,-e^{e+f x}\right)}{a f^3}-\frac{4 d (c+d x) \log \left(e^{e+f x}+1\right)}{a f^2}+\frac{(c+d x)^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}+\frac{(c+d x)^2}{a f}",1,"(c + d*x)^2/(a*f) - (4*d*(c + d*x)*Log[1 + E^(e + f*x)])/(a*f^2) - (4*d^2*PolyLog[2, -E^(e + f*x)])/(a*f^3) + ((c + d*x)^2*Tanh[e/2 + (f*x)/2])/(a*f)","A",6,6,20,0.3000,1,"{3318, 4184, 3718, 2190, 2279, 2391}"
113,1,49,0,0.0681504,"\int \frac{c+d x}{a+a \cosh (e+f x)} \, dx","Int[(c + d*x)/(a + a*Cosh[e + f*x]),x]","\frac{(c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{2 d \log \left(\cosh \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a f^2}","\frac{(c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{a f}-\frac{2 d \log \left(\cosh \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a f^2}",1,"(-2*d*Log[Cosh[e/2 + (f*x)/2]])/(a*f^2) + ((c + d*x)*Tanh[e/2 + (f*x)/2])/(a*f)","A",3,3,18,0.1667,1,"{3318, 4184, 3475}"
114,0,0,0,0.0604593,"\int \frac{1}{(c+d x) (a+a \cosh (e+f x))} \, dx","Int[1/((c + d*x)*(a + a*Cosh[e + f*x])),x]","\int \frac{1}{(c+d x) (a+a \cosh (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a \cosh (e+f x)+a)},x\right)",0,"Defer[Int][1/((c + d*x)*(a + a*Cosh[e + f*x])), x]","A",0,0,0,0,-1,"{}"
115,0,0,0,0.0567993,"\int \frac{1}{(c+d x)^2 (a+a \cosh (e+f x))} \, dx","Int[1/((c + d*x)^2*(a + a*Cosh[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+a \cosh (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a \cosh (e+f x)+a)},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + a*Cosh[e + f*x])), x]","A",0,0,0,0,-1,"{}"
116,1,255,0,0.363557,"\int \frac{(c+d x)^3}{(a+a \cosh (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + a*Cosh[e + f*x])^2,x]","-\frac{4 d^2 (c+d x) \text{PolyLog}\left(2,-e^{e+f x}\right)}{a^2 f^3}+\frac{4 d^3 \text{PolyLog}\left(3,-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}\right)}{a^2 f^3}-\frac{2 d (c+d x)^2 \log \left(e^{e+f x}+1\right)}{a^2 f^2}+\frac{d (c+d x)^2 \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{2 a^2 f^2}+\frac{(c+d x)^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\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}\right)\right)}{a^2 f^4}","-\frac{4 d^2 (c+d x) \text{PolyLog}\left(2,-e^{e+f x}\right)}{a^2 f^3}+\frac{4 d^3 \text{PolyLog}\left(3,-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}\right)}{a^2 f^3}-\frac{2 d (c+d x)^2 \log \left(e^{e+f x}+1\right)}{a^2 f^2}+\frac{d (c+d x)^2 \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{2 a^2 f^2}+\frac{(c+d x)^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^3 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\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}\right)\right)}{a^2 f^4}",1,"(c + d*x)^3/(3*a^2*f) - (2*d*(c + d*x)^2*Log[1 + E^(e + f*x)])/(a^2*f^2) + (4*d^3*Log[Cosh[e/2 + (f*x)/2]])/(a^2*f^4) - (4*d^2*(c + d*x)*PolyLog[2, -E^(e + f*x)])/(a^2*f^3) + (4*d^3*PolyLog[3, -E^(e + f*x)])/(a^2*f^4) + (d*(c + d*x)^2*Sech[e/2 + (f*x)/2]^2)/(2*a^2*f^2) - (2*d^2*(c + d*x)*Tanh[e/2 + (f*x)/2])/(a^2*f^3) + ((c + d*x)^3*Tanh[e/2 + (f*x)/2])/(3*a^2*f) + ((c + d*x)^3*Sech[e/2 + (f*x)/2]^2*Tanh[e/2 + (f*x)/2])/(6*a^2*f)","A",10,9,20,0.4500,1,"{3318, 4186, 4184, 3475, 3718, 2190, 2531, 2282, 6589}"
117,1,200,0,0.2521436,"\int \frac{(c+d x)^2}{(a+a \cosh (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + a*Cosh[e + f*x])^2,x]","-\frac{4 d^2 \text{PolyLog}\left(2,-e^{e+f x}\right)}{3 a^2 f^3}-\frac{4 d (c+d x) \log \left(e^{e+f x}+1\right)}{3 a^2 f^2}+\frac{d (c+d x) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^2}+\frac{(c+d x)^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\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}\right)}{3 a^2 f^3}","-\frac{4 d^2 \text{PolyLog}\left(2,-e^{e+f x}\right)}{3 a^2 f^3}-\frac{4 d (c+d x) \log \left(e^{e+f x}+1\right)}{3 a^2 f^2}+\frac{d (c+d x) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^2}+\frac{(c+d x)^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x)^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\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}\right)}{3 a^2 f^3}",1,"(c + d*x)^2/(3*a^2*f) - (4*d*(c + d*x)*Log[1 + E^(e + f*x)])/(3*a^2*f^2) - (4*d^2*PolyLog[2, -E^(e + f*x)])/(3*a^2*f^3) + (d*(c + d*x)*Sech[e/2 + (f*x)/2]^2)/(3*a^2*f^2) - (2*d^2*Tanh[e/2 + (f*x)/2])/(3*a^2*f^3) + ((c + d*x)^2*Tanh[e/2 + (f*x)/2])/(3*a^2*f) + ((c + d*x)^2*Sech[e/2 + (f*x)/2]^2*Tanh[e/2 + (f*x)/2])/(6*a^2*f)","A",9,9,20,0.4500,1,"{3318, 4186, 3767, 8, 4184, 3718, 2190, 2279, 2391}"
118,1,123,0,0.0955596,"\int \frac{c+d x}{(a+a \cosh (e+f x))^2} \, dx","Int[(c + d*x)/(a + a*Cosh[e + f*x])^2,x]","\frac{(c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}\right) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}+\frac{d \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f^2}-\frac{2 d \log \left(\cosh \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 a^2 f^2}","\frac{(c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f}+\frac{(c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}\right) \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f}+\frac{d \text{sech}^2\left(\frac{e}{2}+\frac{f x}{2}\right)}{6 a^2 f^2}-\frac{2 d \log \left(\cosh \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{3 a^2 f^2}",1,"(-2*d*Log[Cosh[e/2 + (f*x)/2]])/(3*a^2*f^2) + (d*Sech[e/2 + (f*x)/2]^2)/(6*a^2*f^2) + ((c + d*x)*Tanh[e/2 + (f*x)/2])/(3*a^2*f) + ((c + d*x)*Sech[e/2 + (f*x)/2]^2*Tanh[e/2 + (f*x)/2])/(6*a^2*f)","A",4,4,18,0.2222,1,"{3318, 4185, 4184, 3475}"
119,0,0,0,0.0543908,"\int \frac{1}{(c+d x) (a+a \cosh (e+f x))^2} \, dx","Int[1/((c + d*x)*(a + a*Cosh[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+a \cosh (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a \cosh (e+f x)+a)^2},x\right)",0,"Defer[Int][1/((c + d*x)*(a + a*Cosh[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
120,0,0,0,0.0524199,"\int \frac{1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx","Int[1/((c + d*x)^2*(a + a*Cosh[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a \cosh (e+f x)+a)^2},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + a*Cosh[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
121,1,110,0,0.1477672,"\int x^3 \sqrt{a+a \cosh (c+d x)} \, dx","Int[x^3*Sqrt[a + a*Cosh[c + d*x]],x]","-\frac{12 x^2 \sqrt{a \cosh (c+d x)+a}}{d^2}-\frac{96 \sqrt{a \cosh (c+d x)+a}}{d^4}+\frac{48 x \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d^3}+\frac{2 x^3 \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d}","-\frac{12 x^2 \sqrt{a \cosh (c+d x)+a}}{d^2}-\frac{96 \sqrt{a \cosh (c+d x)+a}}{d^4}+\frac{48 x \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d^3}+\frac{2 x^3 \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d}",1,"(-96*Sqrt[a + a*Cosh[c + d*x]])/d^4 - (12*x^2*Sqrt[a + a*Cosh[c + d*x]])/d^2 + (48*x*Sqrt[a + a*Cosh[c + d*x]]*Tanh[c/2 + (d*x)/2])/d^3 + (2*x^3*Sqrt[a + a*Cosh[c + d*x]]*Tanh[c/2 + (d*x)/2])/d","A",5,3,18,0.1667,1,"{3319, 3296, 2638}"
122,1,88,0,0.1133279,"\int x^2 \sqrt{a+a \cosh (c+d x)} \, dx","Int[x^2*Sqrt[a + a*Cosh[c + d*x]],x]","-\frac{8 x \sqrt{a \cosh (c+d x)+a}}{d^2}+\frac{16 \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d^3}+\frac{2 x^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d}","-\frac{8 x \sqrt{a \cosh (c+d x)+a}}{d^2}+\frac{16 \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d^3}+\frac{2 x^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d}",1,"(-8*x*Sqrt[a + a*Cosh[c + d*x]])/d^2 + (16*Sqrt[a + a*Cosh[c + d*x]]*Tanh[c/2 + (d*x)/2])/d^3 + (2*x^2*Sqrt[a + a*Cosh[c + d*x]]*Tanh[c/2 + (d*x)/2])/d","A",4,3,18,0.1667,1,"{3319, 3296, 2637}"
123,1,53,0,0.0621659,"\int x \sqrt{a+a \cosh (c+d x)} \, dx","Int[x*Sqrt[a + a*Cosh[c + d*x]],x]","\frac{2 x \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d}-\frac{4 \sqrt{a \cosh (c+d x)+a}}{d^2}","\frac{2 x \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d}-\frac{4 \sqrt{a \cosh (c+d x)+a}}{d^2}",1,"(-4*Sqrt[a + a*Cosh[c + d*x]])/d^2 + (2*x*Sqrt[a + a*Cosh[c + d*x]]*Tanh[c/2 + (d*x)/2])/d","A",3,3,16,0.1875,1,"{3319, 3296, 2638}"
124,1,83,0,0.1317853,"\int \frac{\sqrt{a+a \cosh (c+d x)}}{x} \, dx","Int[Sqrt[a + a*Cosh[c + d*x]]/x,x]","\cosh \left(\frac{c}{2}\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}+\sinh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}","\cosh \left(\frac{c}{2}\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}+\sinh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}",1,"Cosh[c/2]*Sqrt[a + a*Cosh[c + d*x]]*CoshIntegral[(d*x)/2]*Sech[c/2 + (d*x)/2] + Sqrt[a + a*Cosh[c + d*x]]*Sech[c/2 + (d*x)/2]*Sinh[c/2]*SinhIntegral[(d*x)/2]","A",4,4,18,0.2222,1,"{3319, 3303, 3298, 3301}"
125,1,110,0,0.140128,"\int \frac{\sqrt{a+a \cosh (c+d x)}}{x^2} \, dx","Int[Sqrt[a + a*Cosh[c + d*x]]/x^2,x]","\frac{1}{2} d \sinh \left(\frac{c}{2}\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}+\frac{1}{2} d \cosh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}-\frac{\sqrt{a \cosh (c+d x)+a}}{x}","\frac{1}{2} d \sinh \left(\frac{c}{2}\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}+\frac{1}{2} d \cosh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}-\frac{\sqrt{a \cosh (c+d x)+a}}{x}",1,"-(Sqrt[a + a*Cosh[c + d*x]]/x) + (d*Sqrt[a + a*Cosh[c + d*x]]*CoshIntegral[(d*x)/2]*Sech[c/2 + (d*x)/2]*Sinh[c/2])/2 + (d*Cosh[c/2]*Sqrt[a + a*Cosh[c + d*x]]*Sech[c/2 + (d*x)/2]*SinhIntegral[(d*x)/2])/2","A",5,5,18,0.2778,1,"{3319, 3297, 3303, 3298, 3301}"
126,1,151,0,0.1695826,"\int \frac{\sqrt{a+a \cosh (c+d x)}}{x^3} \, dx","Int[Sqrt[a + a*Cosh[c + d*x]]/x^3,x]","\frac{1}{8} d^2 \cosh \left(\frac{c}{2}\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}+\frac{1}{8} d^2 \sinh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}-\frac{\sqrt{a \cosh (c+d x)+a}}{2 x^2}-\frac{d \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{4 x}","\frac{1}{8} d^2 \cosh \left(\frac{c}{2}\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}+\frac{1}{8} d^2 \sinh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}-\frac{\sqrt{a \cosh (c+d x)+a}}{2 x^2}-\frac{d \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{4 x}",1,"-Sqrt[a + a*Cosh[c + d*x]]/(2*x^2) + (d^2*Cosh[c/2]*Sqrt[a + a*Cosh[c + d*x]]*CoshIntegral[(d*x)/2]*Sech[c/2 + (d*x)/2])/8 + (d^2*Sqrt[a + a*Cosh[c + d*x]]*Sech[c/2 + (d*x)/2]*Sinh[c/2]*SinhIntegral[(d*x)/2])/8 - (d*Sqrt[a + a*Cosh[c + d*x]]*Tanh[c/2 + (d*x)/2])/(4*x)","A",6,5,18,0.2778,1,"{3319, 3297, 3303, 3298, 3301}"
127,1,68,0,0.1168295,"\int x^3 \sqrt{a+a \cosh (x)} \, dx","Int[x^3*Sqrt[a + a*Cosh[x]],x]","-12 x^2 \sqrt{a \cosh (x)+a}+2 x^3 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-96 \sqrt{a \cosh (x)+a}+48 x \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}","-12 x^2 \sqrt{a \cosh (x)+a}+2 x^3 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-96 \sqrt{a \cosh (x)+a}+48 x \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}",1,"-96*Sqrt[a + a*Cosh[x]] - 12*x^2*Sqrt[a + a*Cosh[x]] + 48*x*Sqrt[a + a*Cosh[x]]*Tanh[x/2] + 2*x^3*Sqrt[a + a*Cosh[x]]*Tanh[x/2]","A",5,3,14,0.2143,1,"{3319, 3296, 2638}"
128,1,53,0,0.0973149,"\int x^2 \sqrt{a+a \cosh (x)} \, dx","Int[x^2*Sqrt[a + a*Cosh[x]],x]","2 x^2 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-8 x \sqrt{a \cosh (x)+a}+16 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}","2 x^2 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-8 x \sqrt{a \cosh (x)+a}+16 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}",1,"-8*x*Sqrt[a + a*Cosh[x]] + 16*Sqrt[a + a*Cosh[x]]*Tanh[x/2] + 2*x^2*Sqrt[a + a*Cosh[x]]*Tanh[x/2]","A",4,3,14,0.2143,1,"{3319, 3296, 2637}"
129,1,32,0,0.0508111,"\int x \sqrt{a+a \cosh (x)} \, dx","Int[x*Sqrt[a + a*Cosh[x]],x]","2 x \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-4 \sqrt{a \cosh (x)+a}","2 x \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-4 \sqrt{a \cosh (x)+a}",1,"-4*Sqrt[a + a*Cosh[x]] + 2*x*Sqrt[a + a*Cosh[x]]*Tanh[x/2]","A",3,3,12,0.2500,1,"{3319, 3296, 2638}"
130,1,23,0,0.0832048,"\int \frac{\sqrt{a+a \cosh (x)}}{x} \, dx","Int[Sqrt[a + a*Cosh[x]]/x,x]","\text{Chi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}","\text{Chi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}",1,"Sqrt[a + a*Cosh[x]]*CoshIntegral[x/2]*Sech[x/2]","A",2,2,14,0.1429,1,"{3319, 3301}"
131,1,42,0,0.0903072,"\int \frac{\sqrt{a+a \cosh (x)}}{x^2} \, dx","Int[Sqrt[a + a*Cosh[x]]/x^2,x]","\frac{1}{2} \text{Shi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{\sqrt{a \cosh (x)+a}}{x}","\frac{1}{2} \text{Shi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{\sqrt{a \cosh (x)+a}}{x}",1,"-(Sqrt[a + a*Cosh[x]]/x) + (Sqrt[a + a*Cosh[x]]*Sech[x/2]*SinhIntegral[x/2])/2","A",3,3,14,0.2143,1,"{3319, 3297, 3298}"
132,1,67,0,0.1061804,"\int \frac{\sqrt{a+a \cosh (x)}}{x^3} \, dx","Int[Sqrt[a + a*Cosh[x]]/x^3,x]","\frac{1}{8} \text{Chi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{\sqrt{a \cosh (x)+a}}{2 x^2}-\frac{\tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}}{4 x}","\frac{1}{8} \text{Chi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{\sqrt{a \cosh (x)+a}}{2 x^2}-\frac{\tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}}{4 x}",1,"-Sqrt[a + a*Cosh[x]]/(2*x^2) + (Sqrt[a + a*Cosh[x]]*CoshIntegral[x/2]*Sech[x/2])/8 - (Sqrt[a + a*Cosh[x]]*Tanh[x/2])/(4*x)","A",4,3,14,0.2143,1,"{3319, 3297, 3301}"
133,1,185,0,0.1947702,"\int x^3 (a+a \cosh (x))^{3/2} \, dx","Int[x^3*(a + a*Cosh[x])^(3/2),x]","-\frac{8}{3} a x^2 \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-16 a x^2 \sqrt{a \cosh (x)+a}+\frac{4}{3} a x^3 \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{8}{3} a x^3 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{64}{27} a \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{1280}{9} a \sqrt{a \cosh (x)+a}+\frac{32}{9} a x \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{640}{9} a x \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}","-\frac{8}{3} a x^2 \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-16 a x^2 \sqrt{a \cosh (x)+a}+\frac{4}{3} a x^3 \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{8}{3} a x^3 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{64}{27} a \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{1280}{9} a \sqrt{a \cosh (x)+a}+\frac{32}{9} a x \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{640}{9} a x \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}",1,"(-1280*a*Sqrt[a + a*Cosh[x]])/9 - 16*a*x^2*Sqrt[a + a*Cosh[x]] - (64*a*Cosh[x/2]^2*Sqrt[a + a*Cosh[x]])/27 - (8*a*x^2*Cosh[x/2]^2*Sqrt[a + a*Cosh[x]])/3 + (32*a*x*Cosh[x/2]*Sqrt[a + a*Cosh[x]]*Sinh[x/2])/9 + (4*a*x^3*Cosh[x/2]*Sqrt[a + a*Cosh[x]]*Sinh[x/2])/3 + (640*a*x*Sqrt[a + a*Cosh[x]]*Tanh[x/2])/9 + (8*a*x^3*Sqrt[a + a*Cosh[x]]*Tanh[x/2])/3","A",9,5,14,0.3571,1,"{3319, 3311, 3296, 2638, 3310}"
134,1,145,0,0.1491248,"\int x^2 (a+a \cosh (x))^{3/2} \, dx","Int[x^2*(a + a*Cosh[x])^(3/2),x]","\frac{4}{3} a x^2 \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{8}{3} a x^2 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{16}{9} a x \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{32}{3} a x \sqrt{a \cosh (x)+a}+\frac{224}{9} a \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{32}{27} a \sinh ^2\left(\frac{x}{2}\right) \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}","\frac{4}{3} a x^2 \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{8}{3} a x^2 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{16}{9} a x \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{32}{3} a x \sqrt{a \cosh (x)+a}+\frac{224}{9} a \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{32}{27} a \sinh ^2\left(\frac{x}{2}\right) \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}",1,"(-32*a*x*Sqrt[a + a*Cosh[x]])/3 - (16*a*x*Cosh[x/2]^2*Sqrt[a + a*Cosh[x]])/9 + (4*a*x^2*Cosh[x/2]*Sqrt[a + a*Cosh[x]]*Sinh[x/2])/3 + (224*a*Sqrt[a + a*Cosh[x]]*Tanh[x/2])/9 + (8*a*x^2*Sqrt[a + a*Cosh[x]]*Tanh[x/2])/3 + (32*a*Sqrt[a + a*Cosh[x]]*Sinh[x/2]^2*Tanh[x/2])/27","A",7,5,14,0.3571,1,"{3319, 3311, 3296, 2637, 2633}"
135,1,89,0,0.0749648,"\int x (a+a \cosh (x))^{3/2} \, dx","Int[x*(a + a*Cosh[x])^(3/2),x]","-\frac{8}{9} a \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{16}{3} a \sqrt{a \cosh (x)+a}+\frac{4}{3} a x \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{8}{3} a x \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}","-\frac{8}{9} a \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{16}{3} a \sqrt{a \cosh (x)+a}+\frac{4}{3} a x \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{8}{3} a x \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}",1,"(-16*a*Sqrt[a + a*Cosh[x]])/3 - (8*a*Cosh[x/2]^2*Sqrt[a + a*Cosh[x]])/9 + (4*a*x*Cosh[x/2]*Sqrt[a + a*Cosh[x]]*Sinh[x/2])/3 + (8*a*x*Sqrt[a + a*Cosh[x]]*Tanh[x/2])/3","A",4,4,12,0.3333,1,"{3319, 3310, 3296, 2638}"
136,1,55,0,0.128222,"\int \frac{(a+a \cosh (x))^{3/2}}{x} \, dx","Int[(a + a*Cosh[x])^(3/2)/x,x]","\frac{3}{2} a \text{Chi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{1}{2} a \text{Chi}\left(\frac{3 x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}","\frac{3}{2} a \text{Chi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{1}{2} a \text{Chi}\left(\frac{3 x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}",1,"(3*a*Sqrt[a + a*Cosh[x]]*CoshIntegral[x/2]*Sech[x/2])/2 + (a*Sqrt[a + a*Cosh[x]]*CoshIntegral[(3*x)/2]*Sech[x/2])/2","A",5,3,14,0.2143,1,"{3319, 3312, 3301}"
137,1,79,0,0.1307904,"\int \frac{(a+a \cosh (x))^{3/2}}{x^2} \, dx","Int[(a + a*Cosh[x])^(3/2)/x^2,x]","\frac{3}{4} a \text{Shi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{3}{4} a \text{Shi}\left(\frac{3 x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{2 a \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}}{x}","\frac{3}{4} a \text{Shi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{3}{4} a \text{Shi}\left(\frac{3 x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{2 a \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}}{x}",1,"(-2*a*Cosh[x/2]^2*Sqrt[a + a*Cosh[x]])/x + (3*a*Sqrt[a + a*Cosh[x]]*Sech[x/2]*SinhIntegral[x/2])/4 + (3*a*Sqrt[a + a*Cosh[x]]*Sech[x/2]*SinhIntegral[(3*x)/2])/4","A",5,3,14,0.2143,1,"{3319, 3313, 3298}"
138,1,109,0,0.1729927,"\int \frac{(a+a \cosh (x))^{3/2}}{x^3} \, dx","Int[(a + a*Cosh[x])^(3/2)/x^3,x]","\frac{3}{16} a \text{Chi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{9}{16} a \text{Chi}\left(\frac{3 x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{a \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}}{x^2}-\frac{3 a \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}}{2 x}","\frac{3}{16} a \text{Chi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}+\frac{9}{16} a \text{Chi}\left(\frac{3 x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-\frac{a \cosh ^2\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}}{x^2}-\frac{3 a \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}}{2 x}",1,"-((a*Cosh[x/2]^2*Sqrt[a + a*Cosh[x]])/x^2) + (3*a*Sqrt[a + a*Cosh[x]]*CoshIntegral[x/2]*Sech[x/2])/16 + (9*a*Sqrt[a + a*Cosh[x]]*CoshIntegral[(3*x)/2]*Sech[x/2])/16 - (3*a*Cosh[x/2]*Sqrt[a + a*Cosh[x]]*Sinh[x/2])/(2*x)","A",7,4,14,0.2857,1,"{3319, 3314, 3301, 3312}"
139,1,383,0,0.208099,"\int \frac{x^3}{\sqrt{a+a \cosh (c+d x)}} \, dx","Int[x^3/Sqrt[a + a*Cosh[c + d*x]],x]","-\frac{12 i x^2 \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{12 i x^2 \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{48 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(3,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}-\frac{48 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(3,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}-\frac{96 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(4,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^4 \sqrt{a \cosh (c+d x)+a}}+\frac{96 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(4,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^4 \sqrt{a \cosh (c+d x)+a}}+\frac{4 x^3 \tan ^{-1}\left(e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d \sqrt{a \cosh (c+d x)+a}}","-\frac{12 i x^2 \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{12 i x^2 \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{48 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(3,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}-\frac{48 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(3,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}-\frac{96 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(4,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^4 \sqrt{a \cosh (c+d x)+a}}+\frac{96 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(4,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^4 \sqrt{a \cosh (c+d x)+a}}+\frac{4 x^3 \tan ^{-1}\left(e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d \sqrt{a \cosh (c+d x)+a}}",1,"(4*x^3*ArcTan[E^(c/2 + (d*x)/2)]*Cosh[c/2 + (d*x)/2])/(d*Sqrt[a + a*Cosh[c + d*x]]) - ((12*I)*x^2*Cosh[c/2 + (d*x)/2]*PolyLog[2, (-I)*E^(c/2 + (d*x)/2)])/(d^2*Sqrt[a + a*Cosh[c + d*x]]) + ((12*I)*x^2*Cosh[c/2 + (d*x)/2]*PolyLog[2, I*E^(c/2 + (d*x)/2)])/(d^2*Sqrt[a + a*Cosh[c + d*x]]) + ((48*I)*x*Cosh[c/2 + (d*x)/2]*PolyLog[3, (-I)*E^(c/2 + (d*x)/2)])/(d^3*Sqrt[a + a*Cosh[c + d*x]]) - ((48*I)*x*Cosh[c/2 + (d*x)/2]*PolyLog[3, I*E^(c/2 + (d*x)/2)])/(d^3*Sqrt[a + a*Cosh[c + d*x]]) - ((96*I)*Cosh[c/2 + (d*x)/2]*PolyLog[4, (-I)*E^(c/2 + (d*x)/2)])/(d^4*Sqrt[a + a*Cosh[c + d*x]]) + ((96*I)*Cosh[c/2 + (d*x)/2]*PolyLog[4, I*E^(c/2 + (d*x)/2)])/(d^4*Sqrt[a + a*Cosh[c + d*x]])","A",10,6,18,0.3333,1,"{3319, 4180, 2531, 6609, 2282, 6589}"
140,1,269,0,0.1632329,"\int \frac{x^2}{\sqrt{a+a \cosh (c+d x)}} \, dx","Int[x^2/Sqrt[a + a*Cosh[c + d*x]],x]","-\frac{8 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{8 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{16 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(3,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}-\frac{16 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(3,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}+\frac{4 x^2 \tan ^{-1}\left(e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d \sqrt{a \cosh (c+d x)+a}}","-\frac{8 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{8 i x \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{16 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(3,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}-\frac{16 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(3,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}+\frac{4 x^2 \tan ^{-1}\left(e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d \sqrt{a \cosh (c+d x)+a}}",1,"(4*x^2*ArcTan[E^(c/2 + (d*x)/2)]*Cosh[c/2 + (d*x)/2])/(d*Sqrt[a + a*Cosh[c + d*x]]) - ((8*I)*x*Cosh[c/2 + (d*x)/2]*PolyLog[2, (-I)*E^(c/2 + (d*x)/2)])/(d^2*Sqrt[a + a*Cosh[c + d*x]]) + ((8*I)*x*Cosh[c/2 + (d*x)/2]*PolyLog[2, I*E^(c/2 + (d*x)/2)])/(d^2*Sqrt[a + a*Cosh[c + d*x]]) + ((16*I)*Cosh[c/2 + (d*x)/2]*PolyLog[3, (-I)*E^(c/2 + (d*x)/2)])/(d^3*Sqrt[a + a*Cosh[c + d*x]]) - ((16*I)*Cosh[c/2 + (d*x)/2]*PolyLog[3, I*E^(c/2 + (d*x)/2)])/(d^3*Sqrt[a + a*Cosh[c + d*x]])","A",8,5,18,0.2778,1,"{3319, 4180, 2531, 2282, 6589}"
141,1,157,0,0.0821126,"\int \frac{x}{\sqrt{a+a \cosh (c+d x)}} \, dx","Int[x/Sqrt[a + a*Cosh[c + d*x]],x]","-\frac{4 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{4 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{4 x \tan ^{-1}\left(e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d \sqrt{a \cosh (c+d x)+a}}","-\frac{4 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,-i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{4 i \cosh \left(\frac{c}{2}+\frac{d x}{2}\right) \text{PolyLog}\left(2,i e^{\frac{c}{2}+\frac{d x}{2}}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{4 x \tan ^{-1}\left(e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d \sqrt{a \cosh (c+d x)+a}}",1,"(4*x*ArcTan[E^(c/2 + (d*x)/2)]*Cosh[c/2 + (d*x)/2])/(d*Sqrt[a + a*Cosh[c + d*x]]) - ((4*I)*Cosh[c/2 + (d*x)/2]*PolyLog[2, (-I)*E^(c/2 + (d*x)/2)])/(d^2*Sqrt[a + a*Cosh[c + d*x]]) + ((4*I)*Cosh[c/2 + (d*x)/2]*PolyLog[2, I*E^(c/2 + (d*x)/2)])/(d^2*Sqrt[a + a*Cosh[c + d*x]])","A",6,4,16,0.2500,1,"{3319, 4180, 2279, 2391}"
142,0,0,0,0.0680483,"\int \frac{1}{x \sqrt{a+a \cosh (c+d x)}} \, dx","Int[1/(x*Sqrt[a + a*Cosh[c + d*x]]),x]","\int \frac{1}{x \sqrt{a+a \cosh (c+d x)}} \, dx","\text{Int}\left(\frac{1}{x \sqrt{a \cosh (c+d x)+a}},x\right)",0,"Defer[Int][1/(x*Sqrt[a + a*Cosh[c + d*x]]), x]","A",0,0,0,0,-1,"{}"
143,0,0,0,0.0664644,"\int \frac{1}{x^2 \sqrt{a+a \cosh (c+d x)}} \, dx","Int[1/(x^2*Sqrt[a + a*Cosh[c + d*x]]),x]","\int \frac{1}{x^2 \sqrt{a+a \cosh (c+d x)}} \, dx","\text{Int}\left(\frac{1}{x^2 \sqrt{a \cosh (c+d x)+a}},x\right)",0,"Defer[Int][1/(x^2*Sqrt[a + a*Cosh[c + d*x]]), x]","A",0,0,0,0,-1,"{}"
144,1,402,0,0.2573553,"\int \frac{x^3}{(a+a \cosh (x))^{3/2}} \, dx","Int[x^3/(a + a*Cosh[x])^(3/2),x]","-\frac{3 i x^2 \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{3 i x^2 \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{12 i x \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(3,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{12 i x \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(3,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{24 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{24 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{24 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(4,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{24 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(4,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{3 x^2}{a \sqrt{a \cosh (x)+a}}+\frac{x^3 \tan ^{-1}\left(e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{x^3 \tanh \left(\frac{x}{2}\right)}{2 a \sqrt{a \cosh (x)+a}}-\frac{24 x \tan ^{-1}\left(e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}","-\frac{3 i x^2 \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{3 i x^2 \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{12 i x \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(3,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{12 i x \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(3,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{24 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{24 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{24 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(4,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{24 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(4,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{3 x^2}{a \sqrt{a \cosh (x)+a}}+\frac{x^3 \tan ^{-1}\left(e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{x^3 \tanh \left(\frac{x}{2}\right)}{2 a \sqrt{a \cosh (x)+a}}-\frac{24 x \tan ^{-1}\left(e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}",1,"(3*x^2)/(a*Sqrt[a + a*Cosh[x]]) - (24*x*ArcTan[E^(x/2)]*Cosh[x/2])/(a*Sqrt[a + a*Cosh[x]]) + (x^3*ArcTan[E^(x/2)]*Cosh[x/2])/(a*Sqrt[a + a*Cosh[x]]) + ((24*I)*Cosh[x/2]*PolyLog[2, (-I)*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) - ((3*I)*x^2*Cosh[x/2]*PolyLog[2, (-I)*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) - ((24*I)*Cosh[x/2]*PolyLog[2, I*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) + ((3*I)*x^2*Cosh[x/2]*PolyLog[2, I*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) + ((12*I)*x*Cosh[x/2]*PolyLog[3, (-I)*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) - ((12*I)*x*Cosh[x/2]*PolyLog[3, I*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) - ((24*I)*Cosh[x/2]*PolyLog[4, (-I)*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) + ((24*I)*Cosh[x/2]*PolyLog[4, I*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) + (x^3*Tanh[x/2])/(2*a*Sqrt[a + a*Cosh[x]])","A",16,9,14,0.6429,1,"{3319, 4186, 4180, 2279, 2391, 2531, 6609, 2282, 6589}"
145,1,248,0,0.1912673,"\int \frac{x^2}{(a+a \cosh (x))^{3/2}} \, dx","Int[x^2/(a + a*Cosh[x])^(3/2),x]","-\frac{2 i x \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{2 i x \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{4 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(3,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{4 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(3,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{x^2 \tan ^{-1}\left(e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{x^2 \tanh \left(\frac{x}{2}\right)}{2 a \sqrt{a \cosh (x)+a}}+\frac{2 x}{a \sqrt{a \cosh (x)+a}}-\frac{4 \cosh \left(\frac{x}{2}\right) \tan ^{-1}\left(\sinh \left(\frac{x}{2}\right)\right)}{a \sqrt{a \cosh (x)+a}}","-\frac{2 i x \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{2 i x \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{4 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(3,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{4 i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(3,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{x^2 \tan ^{-1}\left(e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{x^2 \tanh \left(\frac{x}{2}\right)}{2 a \sqrt{a \cosh (x)+a}}+\frac{2 x}{a \sqrt{a \cosh (x)+a}}-\frac{4 \cosh \left(\frac{x}{2}\right) \tan ^{-1}\left(\sinh \left(\frac{x}{2}\right)\right)}{a \sqrt{a \cosh (x)+a}}",1,"(2*x)/(a*Sqrt[a + a*Cosh[x]]) + (x^2*ArcTan[E^(x/2)]*Cosh[x/2])/(a*Sqrt[a + a*Cosh[x]]) - (4*ArcTan[Sinh[x/2]]*Cosh[x/2])/(a*Sqrt[a + a*Cosh[x]]) - ((2*I)*x*Cosh[x/2]*PolyLog[2, (-I)*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) + ((2*I)*x*Cosh[x/2]*PolyLog[2, I*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) + ((4*I)*Cosh[x/2]*PolyLog[3, (-I)*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) - ((4*I)*Cosh[x/2]*PolyLog[3, I*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) + (x^2*Tanh[x/2])/(2*a*Sqrt[a + a*Cosh[x]])","A",10,7,14,0.5000,1,"{3319, 4186, 3770, 4180, 2531, 2282, 6589}"
146,1,140,0,0.1011973,"\int \frac{x}{(a+a \cosh (x))^{3/2}} \, dx","Int[x/(a + a*Cosh[x])^(3/2),x]","-\frac{i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{1}{a \sqrt{a \cosh (x)+a}}+\frac{x \tan ^{-1}\left(e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{x \tanh \left(\frac{x}{2}\right)}{2 a \sqrt{a \cosh (x)+a}}","-\frac{i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,-i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{i \cosh \left(\frac{x}{2}\right) \text{PolyLog}\left(2,i e^{x/2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{1}{a \sqrt{a \cosh (x)+a}}+\frac{x \tan ^{-1}\left(e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{x \tanh \left(\frac{x}{2}\right)}{2 a \sqrt{a \cosh (x)+a}}",1,"1/(a*Sqrt[a + a*Cosh[x]]) + (x*ArcTan[E^(x/2)]*Cosh[x/2])/(a*Sqrt[a + a*Cosh[x]]) - (I*Cosh[x/2]*PolyLog[2, (-I)*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) + (I*Cosh[x/2]*PolyLog[2, I*E^(x/2)])/(a*Sqrt[a + a*Cosh[x]]) + (x*Tanh[x/2])/(2*a*Sqrt[a + a*Cosh[x]])","A",7,5,12,0.4167,1,"{3319, 4185, 4180, 2279, 2391}"
147,0,0,0,0.0774498,"\int \frac{1}{x (a+a \cosh (x))^{3/2}} \, dx","Int[1/(x*(a + a*Cosh[x])^(3/2)),x]","\int \frac{1}{x (a+a \cosh (x))^{3/2}} \, dx","\text{Int}\left(\frac{1}{x (a \cosh (x)+a)^{3/2}},x\right)",0,"Defer[Int][1/(x*(a + a*Cosh[x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
148,0,0,0,0.0744424,"\int \frac{1}{x^2 (a+a \cosh (x))^{3/2}} \, dx","Int[1/(x^2*(a + a*Cosh[x])^(3/2)),x]","\int \frac{1}{x^2 (a+a \cosh (x))^{3/2}} \, dx","\text{Int}\left(\frac{1}{x^2 (a \cosh (x)+a)^{3/2}},x\right)",0,"Defer[Int][1/(x^2*(a + a*Cosh[x])^(3/2)), x]","A",0,0,0,0,-1,"{}"
149,0,0,0,0.0629971,"\int \frac{\sqrt[3]{a+a \cosh (c+d x)}}{x} \, dx","Int[(a + a*Cosh[c + d*x])^(1/3)/x,x]","\int \frac{\sqrt[3]{a+a \cosh (c+d x)}}{x} \, dx","\text{Int}\left(\frac{\sqrt[3]{a \cosh (c+d x)+a}}{x},x\right)",0,"Defer[Int][(a + a*Cosh[c + d*x])^(1/3)/x, x]","A",0,0,0,0,-1,"{}"
150,0,0,0,0.0452379,"\int (c+d x)^m (a+a \cosh (e+f x))^n \, dx","Int[(c + d*x)^m*(a + a*Cosh[e + f*x])^n,x]","\int (c+d x)^m (a+a \cosh (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (a \cosh (e+f x)+a)^n,x\right)",0,"Defer[Int][(c + d*x)^m*(a + a*Cosh[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
151,1,402,0,0.5528219,"\int (c+d x)^m (a+a \cosh (e+f x))^3 \, dx","Int[(c + d*x)^m*(a + a*Cosh[e + f*x])^3,x]","\frac{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 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 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{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{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 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 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{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)) + (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])/(8*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*a^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) - (15*a^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^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) - (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])/(8*f*((f*(c + d*x))/d)^m)","A",12,4,20,0.2000,1,"{3318, 3312, 3307, 2181}"
152,1,263,0,0.3415819,"\int (c+d x)^m (a+a \cosh (e+f x))^2 \, dx","Int[(c + d*x)^m*(a + a*Cosh[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{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{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{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{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) + (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) - (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",9,4,20,0.2000,1,"{3318, 3312, 3307, 2181}"
153,1,131,0,0.1471739,"\int (c+d x)^m (a+a \cosh (e+f x)) \, dx","Int[(c + d*x)^m*(a + a*Cosh[e + f*x]),x]","\frac{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{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{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{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)) + (a*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*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, 3307, 2181}"
154,0,0,0,0.0542267,"\int \frac{(c+d x)^m}{a+a \cosh (e+f x)} \, dx","Int[(c + d*x)^m/(a + a*Cosh[e + f*x]),x]","\int \frac{(c+d x)^m}{a+a \cosh (e+f x)} \, dx","\text{Int}\left(\frac{(c+d x)^m}{a \cosh (e+f x)+a},x\right)",0,"Defer[Int][(c + d*x)^m/(a + a*Cosh[e + f*x]), x]","A",0,0,0,0,-1,"{}"
155,0,0,0,0.0521821,"\int \frac{(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx","Int[(c + d*x)^m/(a + a*Cosh[e + f*x])^2,x]","\int \frac{(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx","\text{Int}\left(\frac{(c+d x)^m}{(a \cosh (e+f x)+a)^2},x\right)",0,"Defer[Int][(c + d*x)^m/(a + a*Cosh[e + f*x])^2, x]","A",0,0,0,0,-1,"{}"
156,1,89,0,0.1317935,"\int (c+d x)^3 (a+b \cosh (e+f x)) \, dx","Int[(c + d*x)^3*(a + b*Cosh[e + f*x]),x]","\frac{a (c+d x)^4}{4 d}+\frac{6 b d^2 (c+d x) \sinh (e+f x)}{f^3}-\frac{3 b d (c+d x)^2 \cosh (e+f x)}{f^2}+\frac{b (c+d x)^3 \sinh (e+f x)}{f}-\frac{6 b d^3 \cosh (e+f x)}{f^4}","\frac{a (c+d x)^4}{4 d}+\frac{6 b d^2 (c+d x) \sinh (e+f x)}{f^3}-\frac{3 b d (c+d x)^2 \cosh (e+f x)}{f^2}+\frac{b (c+d x)^3 \sinh (e+f x)}{f}-\frac{6 b d^3 \cosh (e+f x)}{f^4}",1,"(a*(c + d*x)^4)/(4*d) - (6*b*d^3*Cosh[e + f*x])/f^4 - (3*b*d*(c + d*x)^2*Cosh[e + f*x])/f^2 + (6*b*d^2*(c + d*x)*Sinh[e + f*x])/f^3 + (b*(c + d*x)^3*Sinh[e + f*x])/f","A",6,3,18,0.1667,1,"{3317, 3296, 2638}"
157,1,67,0,0.0901676,"\int (c+d x)^2 (a+b \cosh (e+f x)) \, dx","Int[(c + d*x)^2*(a + b*Cosh[e + f*x]),x]","\frac{a (c+d x)^3}{3 d}-\frac{2 b d (c+d x) \cosh (e+f x)}{f^2}+\frac{b (c+d x)^2 \sinh (e+f x)}{f}+\frac{2 b d^2 \sinh (e+f x)}{f^3}","\frac{a (c+d x)^3}{3 d}-\frac{2 b d (c+d x) \cosh (e+f x)}{f^2}+\frac{b (c+d x)^2 \sinh (e+f x)}{f}+\frac{2 b d^2 \sinh (e+f x)}{f^3}",1,"(a*(c + d*x)^3)/(3*d) - (2*b*d*(c + d*x)*Cosh[e + f*x])/f^2 + (2*b*d^2*Sinh[e + f*x])/f^3 + (b*(c + d*x)^2*Sinh[e + f*x])/f","A",5,3,18,0.1667,1,"{3317, 3296, 2637}"
158,1,45,0,0.0455859,"\int (c+d x) (a+b \cosh (e+f x)) \, dx","Int[(c + d*x)*(a + b*Cosh[e + f*x]),x]","\frac{a (c+d x)^2}{2 d}+\frac{b (c+d x) \sinh (e+f x)}{f}-\frac{b d \cosh (e+f x)}{f^2}","\frac{a (c+d x)^2}{2 d}+\frac{b (c+d x) \sinh (e+f x)}{f}-\frac{b d \cosh (e+f x)}{f^2}",1,"(a*(c + d*x)^2)/(2*d) - (b*d*Cosh[e + f*x])/f^2 + (b*(c + d*x)*Sinh[e + f*x])/f","A",4,3,16,0.1875,1,"{3317, 3296, 2638}"
159,1,64,0,0.1206646,"\int \frac{a+b \cosh (e+f x)}{c+d x} \, dx","Int[(a + b*Cosh[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) \cosh \left(e-\frac{c f}{d}\right)}{d}+\frac{b \sinh \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) \cosh \left(e-\frac{c f}{d}\right)}{d}+\frac{b \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d}",1,"(b*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/d + (a*Log[c + d*x])/d + (b*Sinh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d","A",5,4,18,0.2222,1,"{3317, 3303, 3298, 3301}"
160,1,87,0,0.1518819,"\int \frac{a+b \cosh (e+f x)}{(c+d x)^2} \, dx","Int[(a + b*Cosh[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) \sinh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{b f \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{b \cosh (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) \sinh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{b f \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{b \cosh (e+f x)}{d (c+d x)}",1,"-(a/(d*(c + d*x))) - (b*Cosh[e + f*x])/(d*(c + d*x)) + (b*f*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d^2 + (b*f*Cosh[e - (c*f)/d]*SinhIntegral[(c*f)/d + f*x])/d^2","A",6,5,18,0.2778,1,"{3317, 3297, 3303, 3298, 3301}"
161,1,123,0,0.1965389,"\int \frac{a+b \cosh (e+f x)}{(c+d x)^3} \, dx","Int[(a + b*Cosh[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) \cosh \left(e-\frac{c f}{d}\right)}{2 d^3}+\frac{b f^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{2 d^3}-\frac{b f \sinh (e+f x)}{2 d^2 (c+d x)}-\frac{b \cosh (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) \cosh \left(e-\frac{c f}{d}\right)}{2 d^3}+\frac{b f^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{2 d^3}-\frac{b f \sinh (e+f x)}{2 d^2 (c+d x)}-\frac{b \cosh (e+f x)}{2 d (c+d x)^2}",1,"-a/(2*d*(c + d*x)^2) - (b*Cosh[e + f*x])/(2*d*(c + d*x)^2) + (b*f^2*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/(2*d^3) - (b*f*Sinh[e + f*x])/(2*d^2*(c + d*x)) + (b*f^2*Sinh[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}"
162,1,250,0,0.284548,"\int (c+d x)^3 (a+b \cosh (e+f x))^2 \, dx","Int[(c + d*x)^3*(a + b*Cosh[e + f*x])^2,x]","\frac{a^2 (c+d x)^4}{4 d}+\frac{12 a b d^2 (c+d x) \sinh (e+f x)}{f^3}-\frac{6 a b d (c+d x)^2 \cosh (e+f x)}{f^2}+\frac{2 a b (c+d x)^3 \sinh (e+f x)}{f}-\frac{12 a b d^3 \cosh (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 \cosh ^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 \cosh ^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) \sinh (e+f x)}{f^3}-\frac{6 a b d (c+d x)^2 \cosh (e+f x)}{f^2}+\frac{2 a b (c+d x)^3 \sinh (e+f x)}{f}-\frac{12 a b d^3 \cosh (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 \cosh ^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 \cosh ^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^3*Cosh[e + f*x])/f^4 - (6*a*b*d*(c + d*x)^2*Cosh[e + f*x])/f^2 - (3*b^2*d^3*Cosh[e + f*x]^2)/(8*f^4) - (3*b^2*d*(c + d*x)^2*Cosh[e + f*x]^2)/(4*f^2) + (12*a*b*d^2*(c + d*x)*Sinh[e + f*x])/f^3 + (2*a*b*(c + d*x)^3*Sinh[e + f*x])/f + (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)","A",10,6,20,0.3000,1,"{3317, 3296, 2638, 3311, 32, 3310}"
163,1,182,0,0.1942222,"\int (c+d x)^2 (a+b \cosh (e+f x))^2 \, dx","Int[(c + d*x)^2*(a + b*Cosh[e + f*x])^2,x]","\frac{a^2 (c+d x)^3}{3 d}-\frac{4 a b d (c+d x) \cosh (e+f x)}{f^2}+\frac{2 a b (c+d x)^2 \sinh (e+f x)}{f}+\frac{4 a b d^2 \sinh (e+f x)}{f^3}-\frac{b^2 d (c+d x) \cosh ^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) \cosh (e+f x)}{f^2}+\frac{2 a b (c+d x)^2 \sinh (e+f x)}{f}+\frac{4 a b d^2 \sinh (e+f x)}{f^3}-\frac{b^2 d (c+d x) \cosh ^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*(c + d*x)*Cosh[e + f*x])/f^2 - (b^2*d*(c + d*x)*Cosh[e + f*x]^2)/(2*f^2) + (4*a*b*d^2*Sinh[e + f*x])/f^3 + (2*a*b*(c + d*x)^2*Sinh[e + f*x])/f + (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)","A",9,7,20,0.3500,1,"{3317, 3296, 2637, 3311, 32, 2635, 8}"
164,1,116,0,0.1010398,"\int (c+d x) (a+b \cosh (e+f x))^2 \, dx","Int[(c + d*x)*(a + b*Cosh[e + f*x])^2,x]","\frac{a^2 (c+d x)^2}{2 d}+\frac{2 a b (c+d x) \sinh (e+f x)}{f}-\frac{2 a b d \cosh (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 \cosh ^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) \sinh (e+f x)}{f}-\frac{2 a b d \cosh (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 \cosh ^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*d*Cosh[e + f*x])/f^2 - (b^2*d*Cosh[e + f*x]^2)/(4*f^2) + (2*a*b*(c + d*x)*Sinh[e + f*x])/f + (b^2*(c + d*x)*Cosh[e + f*x]*Sinh[e + f*x])/(2*f)","A",6,4,18,0.2222,1,"{3317, 3296, 2638, 3310}"
165,1,156,0,0.3101771,"\int \frac{(a+b \cosh (e+f x))^2}{c+d x} \, dx","Int[(a + b*Cosh[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) \cosh \left(e-\frac{c f}{d}\right)}{d}+\frac{2 a b \sinh \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) \cosh \left(e-\frac{c f}{d}\right)}{d}+\frac{2 a b \sinh \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,"(2*a*b*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/d + (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*Sinh[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}"
166,1,183,0,0.3449794,"\int \frac{(a+b \cosh (e+f x))^2}{(c+d x)^2} \, dx","Int[(a + b*Cosh[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) \sinh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{2 a b f \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{2 a b \cosh (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 \cosh ^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) \sinh \left(e-\frac{c f}{d}\right)}{d^2}+\frac{2 a b f \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^2}-\frac{2 a b \cosh (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 \cosh ^2(e+f x)}{d (c+d x)}",1,"-(a^2/(d*(c + d*x))) - (2*a*b*Cosh[e + f*x])/(d*(c + d*x)) - (b^2*Cosh[e + f*x]^2)/(d*(c + d*x)) + (b^2*f*CoshIntegral[(2*c*f)/d + 2*f*x]*Sinh[2*e - (2*c*f)/d])/d^2 + (2*a*b*f*CoshIntegral[(c*f)/d + f*x]*Sinh[e - (c*f)/d])/d^2 + (2*a*b*f*Cosh[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}"
167,1,242,0,0.4284401,"\int \frac{(a+b \cosh (e+f x))^2}{(c+d x)^3} \, dx","Int[(a + b*Cosh[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) \cosh \left(e-\frac{c f}{d}\right)}{d^3}+\frac{a b f^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^3}-\frac{a b f \sinh (e+f x)}{d^2 (c+d x)}-\frac{a b \cosh (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 \cosh ^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) \cosh \left(e-\frac{c f}{d}\right)}{d^3}+\frac{a b f^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(x f+\frac{c f}{d}\right)}{d^3}-\frac{a b f \sinh (e+f x)}{d^2 (c+d x)}-\frac{a b \cosh (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 \cosh ^2(e+f x)}{2 d (c+d x)^2}",1,"-a^2/(2*d*(c + d*x)^2) - (a*b*Cosh[e + f*x])/(d*(c + d*x)^2) - (b^2*Cosh[e + f*x]^2)/(2*d*(c + d*x)^2) + (a*b*f^2*Cosh[e - (c*f)/d]*CoshIntegral[(c*f)/d + f*x])/d^3 + (b^2*f^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*c*f)/d + 2*f*x])/d^3 - (a*b*f*Sinh[e + f*x])/(d^2*(c + d*x)) - (b^2*f*Cosh[e + f*x]*Sinh[e + f*x])/(d^2*(c + d*x)) + (a*b*f^2*Sinh[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}"
168,1,436,0,0.820881,"\int \frac{(c+d x)^3}{a+b \cosh (e+f x)} \, dx","Int[(c + d*x)^3/(a + b*Cosh[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,"{3320, 2264, 2190, 2531, 6609, 2282, 6589}"
169,1,320,0,0.6699732,"\int \frac{(c+d x)^2}{a+b \cosh (e+f x)} \, dx","Int[(c + d*x)^2/(a + b*Cosh[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,"{3320, 2264, 2190, 2531, 2282, 6589}"
170,1,203,0,0.3760675,"\int \frac{c+d x}{a+b \cosh (e+f x)} \, dx","Int[(c + d*x)/(a + b*Cosh[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,"{3320, 2264, 2190, 2279, 2391}"
171,0,0,0,0.0613819,"\int \frac{1}{(c+d x) (a+b \cosh (e+f x))} \, dx","Int[1/((c + d*x)*(a + b*Cosh[e + f*x])),x]","\int \frac{1}{(c+d x) (a+b \cosh (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \cosh (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)*(a + b*Cosh[e + f*x])), x]","A",0,0,0,0,-1,"{}"
172,0,0,0,0.0590852,"\int \frac{1}{(c+d x)^2 (a+b \cosh (e+f x))} \, dx","Int[1/((c + d*x)^2*(a + b*Cosh[e + f*x])),x]","\int \frac{1}{(c+d x)^2 (a+b \cosh (e+f x))} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \cosh (e+f x))},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + b*Cosh[e + f*x])), x]","A",0,0,0,0,-1,"{}"
173,1,823,0,1.3534546,"\int \frac{(c+d x)^3}{(a+b \cosh (e+f x))^2} \, dx","Int[(c + d*x)^3/(a + b*Cosh[e + f*x])^2,x]","-\frac{6 \text{PolyLog}\left(3,-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right) f^4}-\frac{6 \text{PolyLog}\left(3,-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right) f^4}+\frac{6 a \text{PolyLog}\left(4,-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right)^{3/2} f^4}-\frac{6 a \text{PolyLog}\left(4,-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right)^{3/2} f^4}+\frac{6 (c+d x) \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right) f^3}+\frac{6 (c+d x) \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right) f^3}-\frac{6 a (c+d x) \text{PolyLog}\left(3,-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right)^{3/2} f^3}+\frac{6 a (c+d x) \text{PolyLog}\left(3,-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right)^{3/2} f^3}+\frac{3 (c+d x)^2 \log \left(\frac{e^{e+f x} b}{a-\sqrt{a^2-b^2}}+1\right) d}{\left(a^2-b^2\right) f^2}+\frac{3 (c+d x)^2 \log \left(\frac{e^{e+f x} b}{a+\sqrt{a^2-b^2}}+1\right) d}{\left(a^2-b^2\right) f^2}+\frac{3 a (c+d x)^2 \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right)^{3/2} f^2}-\frac{3 a (c+d x)^2 \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right)^{3/2} f^2}-\frac{(c+d x)^3}{\left(a^2-b^2\right) f}+\frac{a (c+d x)^3 \log \left(\frac{e^{e+f x} b}{a-\sqrt{a^2-b^2}}+1\right)}{\left(a^2-b^2\right)^{3/2} f}-\frac{a (c+d x)^3 \log \left(\frac{e^{e+f x} b}{a+\sqrt{a^2-b^2}}+1\right)}{\left(a^2-b^2\right)^{3/2} f}-\frac{b (c+d x)^3 \sinh (e+f x)}{\left(a^2-b^2\right) f (a+b \cosh (e+f x))}","-\frac{6 \text{PolyLog}\left(3,-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right) f^4}-\frac{6 \text{PolyLog}\left(3,-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right) f^4}+\frac{6 a \text{PolyLog}\left(4,-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right)^{3/2} f^4}-\frac{6 a \text{PolyLog}\left(4,-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right) d^3}{\left(a^2-b^2\right)^{3/2} f^4}+\frac{6 (c+d x) \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right) f^3}+\frac{6 (c+d x) \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right) f^3}-\frac{6 a (c+d x) \text{PolyLog}\left(3,-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right)^{3/2} f^3}+\frac{6 a (c+d x) \text{PolyLog}\left(3,-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right) d^2}{\left(a^2-b^2\right)^{3/2} f^3}+\frac{3 (c+d x)^2 \log \left(\frac{e^{e+f x} b}{a-\sqrt{a^2-b^2}}+1\right) d}{\left(a^2-b^2\right) f^2}+\frac{3 (c+d x)^2 \log \left(\frac{e^{e+f x} b}{a+\sqrt{a^2-b^2}}+1\right) d}{\left(a^2-b^2\right) f^2}+\frac{3 a (c+d x)^2 \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right)^{3/2} f^2}-\frac{3 a (c+d x)^2 \text{PolyLog}\left(2,-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right) d}{\left(a^2-b^2\right)^{3/2} f^2}-\frac{(c+d x)^3}{\left(a^2-b^2\right) f}+\frac{a (c+d x)^3 \log \left(\frac{e^{e+f x} b}{a-\sqrt{a^2-b^2}}+1\right)}{\left(a^2-b^2\right)^{3/2} f}-\frac{a (c+d x)^3 \log \left(\frac{e^{e+f x} b}{a+\sqrt{a^2-b^2}}+1\right)}{\left(a^2-b^2\right)^{3/2} f}-\frac{b (c+d x)^3 \sinh (e+f x)}{\left(a^2-b^2\right) f (a+b \cosh (e+f x))}",1,"-((c + d*x)^3/((a^2 - b^2)*f)) + (3*d*(c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^2) + (a*(c + d*x)^3*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f) + (3*d*(c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*f^2) - (a*(c + d*x)^3*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*f) + (6*d^2*(c + d*x)*PolyLog[2, -((b*E^(e + f*x))/(a - Sqrt[a^2 - b^2]))])/((a^2 - b^2)*f^3) + (3*a*d*(c + d*x)^2*PolyLog[2, -((b*E^(e + f*x))/(a - Sqrt[a^2 - b^2]))])/((a^2 - b^2)^(3/2)*f^2) + (6*d^2*(c + d*x)*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 - b^2]))])/((a^2 - b^2)*f^3) - (3*a*d*(c + d*x)^2*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 - b^2]))])/((a^2 - b^2)^(3/2)*f^2) - (6*d^3*PolyLog[3, -((b*E^(e + f*x))/(a - Sqrt[a^2 - b^2]))])/((a^2 - b^2)*f^4) - (6*a*d^2*(c + d*x)*PolyLog[3, -((b*E^(e + f*x))/(a - Sqrt[a^2 - b^2]))])/((a^2 - b^2)^(3/2)*f^3) - (6*d^3*PolyLog[3, -((b*E^(e + f*x))/(a + Sqrt[a^2 - b^2]))])/((a^2 - b^2)*f^4) + (6*a*d^2*(c + d*x)*PolyLog[3, -((b*E^(e + f*x))/(a + Sqrt[a^2 - b^2]))])/((a^2 - b^2)^(3/2)*f^3) + (6*a*d^3*PolyLog[4, -((b*E^(e + f*x))/(a - Sqrt[a^2 - b^2]))])/((a^2 - b^2)^(3/2)*f^4) - (6*a*d^3*PolyLog[4, -((b*E^(e + f*x))/(a + Sqrt[a^2 - b^2]))])/((a^2 - b^2)^(3/2)*f^4) - (b*(c + d*x)^3*Sinh[e + f*x])/((a^2 - b^2)*f*(a + b*Cosh[e + f*x]))","A",22,9,20,0.4500,1,"{3324, 3320, 2264, 2190, 2531, 6609, 2282, 6589, 5562}"
174,1,593,0,1.0250535,"\int \frac{(c+d x)^2}{(a+b \cosh (e+f x))^2} \, dx","Int[(c + d*x)^2/(a + b*Cosh[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 \sinh (e+f x)}{f \left(a^2-b^2\right) (a+b \cosh (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 \sinh (e+f x)}{f \left(a^2-b^2\right) (a+b \cosh (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*Sinh[e + f*x])/((a^2 - b^2)*f*(a + b*Cosh[e + f*x]))","A",18,10,20,0.5000,1,"{3324, 3320, 2264, 2190, 2531, 2282, 6589, 5562, 2279, 2391}"
175,1,274,0,0.4568866,"\int \frac{c+d x}{(a+b \cosh (e+f x))^2} \, dx","Int[(c + d*x)/(a + b*Cosh[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) \sinh (e+f x)}{f \left(a^2-b^2\right) (a+b \cosh (e+f x))}+\frac{d \log (a+b \cosh (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) \sinh (e+f x)}{f \left(a^2-b^2\right) (a+b \cosh (e+f x))}+\frac{d \log (a+b \cosh (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*Cosh[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)*Sinh[e + f*x])/((a^2 - b^2)*f*(a + b*Cosh[e + f*x]))","A",11,8,18,0.4444,1,"{3324, 3320, 2264, 2190, 2279, 2391, 2668, 31}"
176,0,0,0,0.0556963,"\int \frac{1}{(c+d x) (a+b \cosh (e+f x))^2} \, dx","Int[1/((c + d*x)*(a + b*Cosh[e + f*x])^2),x]","\int \frac{1}{(c+d x) (a+b \cosh (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x) (a+b \cosh (e+f x))^2},x\right)",0,"Defer[Int][1/((c + d*x)*(a + b*Cosh[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
177,0,0,0,0.0543985,"\int \frac{1}{(c+d x)^2 (a+b \cosh (e+f x))^2} \, dx","Int[1/((c + d*x)^2*(a + b*Cosh[e + f*x])^2),x]","\int \frac{1}{(c+d x)^2 (a+b \cosh (e+f x))^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 (a+b \cosh (e+f x))^2},x\right)",0,"Defer[Int][1/((c + d*x)^2*(a + b*Cosh[e + f*x])^2), x]","A",0,0,0,0,-1,"{}"
178,0,0,0,0.0503341,"\int (c+d x)^m (a+b \cosh (e+f x))^n \, dx","Int[(c + d*x)^m*(a + b*Cosh[e + f*x])^n,x]","\int (c+d x)^m (a+b \cosh (e+f x))^n \, dx","\text{Int}\left((c+d x)^m (a+b \cosh (e+f x))^n,x\right)",0,"Defer[Int][(c + d*x)^m*(a + b*Cosh[e + f*x])^n, x]","A",0,0,0,0,-1,"{}"
179,1,543,0,0.7434322,"\int (c+d x)^m (a+b \cosh (e+f x))^3 \, dx","Int[(c + d*x)^m*(a + b*Cosh[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",18,4,20,0.2000,1,"{3317, 3307, 2181, 3312}"
180,1,282,0,0.362635,"\int (c+d x)^m (a+b \cosh (e+f x))^2 \, dx","Int[(c + d*x)^m*(a + b*Cosh[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",10,4,20,0.2000,1,"{3317, 3307, 2181, 3312}"
181,1,131,0,0.1454416,"\int (c+d x)^m (a+b \cosh (e+f x)) \, dx","Int[(c + d*x)^m*(a + b*Cosh[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, 3307, 2181}"
182,0,0,0,0.0563509,"\int \frac{(c+d x)^m}{a+b \cosh (e+f x)} \, dx","Int[(c + d*x)^m/(a + b*Cosh[e + f*x]),x]","\int \frac{(c+d x)^m}{a+b \cosh (e+f x)} \, dx","\text{Int}\left(\frac{(c+d x)^m}{a+b \cosh (e+f x)},x\right)",0,"Defer[Int][(c + d*x)^m/(a + b*Cosh[e + f*x]), x]","A",0,0,0,0,-1,"{}"
183,0,0,0,0.0550124,"\int \frac{(c+d x)^m}{(a+b \cosh (e+f x))^2} \, dx","Int[(c + d*x)^m/(a + b*Cosh[e + f*x])^2,x]","\int \frac{(c+d x)^m}{(a+b \cosh (e+f x))^2} \, dx","\text{Int}\left(\frac{(c+d x)^m}{(a+b \cosh (e+f x))^2},x\right)",0,"Defer[Int][(c + d*x)^m/(a + b*Cosh[e + f*x])^2, x]","A",0,0,0,0,-1,"{}"