1,1,76,91,0.3130726,"\int (c+d x)^4 \cosh (a+b x) \, dx","Integrate[(c + d*x)^4*Cosh[a + b*x],x]","\frac{\sinh (a+b x) \left(b^4 (c+d x)^4+12 b^2 d^2 (c+d x)^2+24 d^4\right)-4 b d (c+d x) \cosh (a+b x) \left(b^2 (c+d x)^2+6 d^2\right)}{b^5}","\frac{24 d^4 \sinh (a+b x)}{b^5}-\frac{24 d^3 (c+d x) \cosh (a+b x)}{b^4}+\frac{12 d^2 (c+d x)^2 \sinh (a+b x)}{b^3}-\frac{4 d (c+d x)^3 \cosh (a+b x)}{b^2}+\frac{(c+d x)^4 \sinh (a+b x)}{b}",1,"(-4*b*d*(c + d*x)*(6*d^2 + b^2*(c + d*x)^2)*Cosh[a + b*x] + (24*d^4 + 12*b^2*d^2*(c + d*x)^2 + b^4*(c + d*x)^4)*Sinh[a + b*x])/b^5","A",1
2,1,61,70,0.2034562,"\int (c+d x)^3 \cosh (a+b x) \, dx","Integrate[(c + d*x)^3*Cosh[a + b*x],x]","\frac{b (c+d x) \sinh (a+b x) \left(b^2 (c+d x)^2+6 d^2\right)-3 d \cosh (a+b x) \left(b^2 (c+d x)^2+2 d^2\right)}{b^4}","-\frac{6 d^3 \cosh (a+b x)}{b^4}+\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{(c+d x)^3 \sinh (a+b x)}{b}",1,"(-3*d*(2*d^2 + b^2*(c + d*x)^2)*Cosh[a + b*x] + b*(c + d*x)*(6*d^2 + b^2*(c + d*x)^2)*Sinh[a + b*x])/b^4","A",1
3,1,44,49,0.1523696,"\int (c+d x)^2 \cosh (a+b x) \, dx","Integrate[(c + d*x)^2*Cosh[a + b*x],x]","\frac{\sinh (a+b x) \left(b^2 (c+d x)^2+2 d^2\right)-2 b d (c+d x) \cosh (a+b x)}{b^3}","\frac{2 d^2 \sinh (a+b x)}{b^3}-\frac{2 d (c+d x) \cosh (a+b x)}{b^2}+\frac{(c+d x)^2 \sinh (a+b x)}{b}",1,"(-2*b*d*(c + d*x)*Cosh[a + b*x] + (2*d^2 + b^2*(c + d*x)^2)*Sinh[a + b*x])/b^3","A",1
4,1,27,28,0.0568801,"\int (c+d x) \cosh (a+b x) \, dx","Integrate[(c + d*x)*Cosh[a + b*x],x]","\frac{b (c+d x) \sinh (a+b x)-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*(c + d*x)*Sinh[a + b*x])/b^2","A",1
5,1,49,51,0.0779519,"\int \frac{\cosh (a+b x)}{c+d x} \, dx","Integrate[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)+\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] + Sinh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x])/d","A",1
6,1,65,71,0.2472258,"\int \frac{\cosh (a+b x)}{(c+d x)^2} \, dx","Integrate[Cosh[a + b*x]/(c + d*x)^2,x]","\frac{b \sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(b \left(\frac{c}{d}+x\right)\right)+b \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(b \left(\frac{c}{d}+x\right)\right)-\frac{d \cosh (a+b x)}{c+d x}}{d^2}","\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,"(-((d*Cosh[a + b*x])/(c + d*x)) + b*CoshIntegral[b*(c/d + x)]*Sinh[a - (b*c)/d] + b*Cosh[a - (b*c)/d]*SinhIntegral[b*(c/d + x)])/d^2","A",1
7,1,88,104,0.5552022,"\int \frac{\cosh (a+b x)}{(c+d x)^3} \, dx","Integrate[Cosh[a + b*x]/(c + d*x)^3,x]","\frac{b^2 \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(b \left(\frac{c}{d}+x\right)\right)+b^2 \sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(b \left(\frac{c}{d}+x\right)\right)-\frac{d (b (c+d x) \sinh (a+b x)+d \cosh (a+b x))}{(c+d x)^2}}{2 d^3}","\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,"(b^2*Cosh[a - (b*c)/d]*CoshIntegral[b*(c/d + x)] - (d*(d*Cosh[a + b*x] + b*(c + d*x)*Sinh[a + b*x]))/(c + d*x)^2 + b^2*Sinh[a - (b*c)/d]*SinhIntegral[b*(c/d + x)])/(2*d^3)","A",1
8,1,132,162,0.656303,"\int (c+d x)^4 \cosh ^2(a+b x) \, dx","Integrate[(c + d*x)^4*Cosh[a + b*x]^2,x]","\frac{-20 b d (c+d x) \cosh (2 (a+b x)) \left(2 b^2 (c+d x)^2+3 d^2\right)+10 \sinh (2 (a+b x)) \left(2 b^4 (c+d x)^4+6 b^2 d^2 (c+d x)^2+3 d^4\right)+8 b^5 x \left(5 c^4+10 c^3 d x+10 c^2 d^2 x^2+5 c d^3 x^3+d^4 x^4\right)}{80 b^5}","\frac{3 d^4 \sinh (a+b x) \cosh (a+b x)}{4 b^5}-\frac{3 d^3 (c+d x) \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{(c+d x)^4 \sinh (a+b x) \cosh (a+b x)}{2 b}+\frac{3 d^4 x}{4 b^4}+\frac{d (c+d x)^3}{2 b^2}+\frac{(c+d x)^5}{10 d}",1,"(8*b^5*x*(5*c^4 + 10*c^3*d*x + 10*c^2*d^2*x^2 + 5*c*d^3*x^3 + d^4*x^4) - 20*b*d*(c + d*x)*(3*d^2 + 2*b^2*(c + d*x)^2)*Cosh[2*(a + b*x)] + 10*(3*d^4 + 6*b^2*d^2*(c + d*x)^2 + 2*b^4*(c + d*x)^4)*Sinh[2*(a + b*x)])/(80*b^5)","A",1
9,1,104,134,0.4316764,"\int (c+d x)^3 \cosh ^2(a+b x) \, dx","Integrate[(c + d*x)^3*Cosh[a + b*x]^2,x]","\frac{2 b (c+d x) \sinh (2 (a+b x)) \left(2 b^2 (c+d x)^2+3 d^2\right)-3 d \cosh (2 (a+b x)) \left(2 b^2 (c+d x)^2+d^2\right)+2 b^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)}{16 b^4}","-\frac{3 d^3 \cosh ^2(a+b x)}{8 b^4}+\frac{3 d^2 (c+d x) \sinh (a+b x) \cosh (a+b x)}{4 b^3}-\frac{3 d (c+d x)^2 \cosh ^2(a+b x)}{4 b^2}+\frac{(c+d x)^3 \sinh (a+b x) \cosh (a+b x)}{2 b}+\frac{3 c d^2 x}{4 b^2}+\frac{3 d^3 x^2}{8 b^2}+\frac{(c+d x)^4}{8 d}",1,"(2*b^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) - 3*d*(d^2 + 2*b^2*(c + d*x)^2)*Cosh[2*(a + b*x)] + 2*b*(c + d*x)*(3*d^2 + 2*b^2*(c + d*x)^2)*Sinh[2*(a + b*x)])/(16*b^4)","A",1
10,1,75,95,0.3015924,"\int (c+d x)^2 \cosh ^2(a+b x) \, dx","Integrate[(c + d*x)^2*Cosh[a + b*x]^2,x]","\frac{3 \sinh (2 (a+b x)) \left(2 b^2 (c+d x)^2+d^2\right)-6 b d (c+d x) \cosh (2 (a+b x))+4 b^3 x \left(3 c^2+3 c d x+d^2 x^2\right)}{24 b^3}","\frac{d^2 \sinh (a+b x) \cosh (a+b x)}{4 b^3}-\frac{d (c+d x) \cosh ^2(a+b x)}{2 b^2}+\frac{(c+d x)^2 \sinh (a+b x) \cosh (a+b x)}{2 b}+\frac{d^2 x}{4 b^2}+\frac{(c+d x)^3}{6 d}",1,"(4*b^3*x*(3*c^2 + 3*c*d*x + d^2*x^2) - 6*b*d*(c + d*x)*Cosh[2*(a + b*x)] + 3*(d^2 + 2*b^2*(c + d*x)^2)*Sinh[2*(a + b*x)])/(24*b^3)","A",1
11,1,51,55,0.160796,"\int (c+d x) \cosh ^2(a+b x) \, dx","Integrate[(c + d*x)*Cosh[a + b*x]^2,x]","\frac{2 b ((c+d x) \sinh (2 (a+b x))+2 a c+b x (2 c+d x))-d \cosh (2 (a+b x))}{8 b^2}","-\frac{d \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,"(-(d*Cosh[2*(a + b*x)]) + 2*b*(2*a*c + b*x*(2*c + d*x) + (c + d*x)*Sinh[2*(a + b*x)]))/(8*b^2)","A",1
12,1,64,78,0.1135896,"\int \frac{\cosh ^2(a+b x)}{c+d x} \, dx","Integrate[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 x)}{d}\right)+\sinh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b (c+d x)}{d}\right)+\log (c+d x)}{2 d}","\frac{\cosh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\sinh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b c}{d}+2 b x\right)}{2 d}+\frac{\log (c+d x)}{2 d}",1,"(Cosh[2*a - (2*b*c)/d]*CoshIntegral[(2*b*(c + d*x))/d] + Log[c + d*x] + Sinh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*(c + d*x))/d])/(2*d)","A",1
13,1,75,81,0.4130672,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^2} \, dx","Integrate[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 x)}{d}\right)+b \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b (c+d x)}{d}\right)-\frac{d \cosh ^2(a+b x)}{c+d x}}{d^2}","\frac{b \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}+\frac{b \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b c}{d}+2 b x\right)}{d^2}-\frac{\cosh ^2(a+b x)}{d (c+d x)}",1,"(-((d*Cosh[a + b*x]^2)/(c + d*x)) + b*CoshIntegral[(2*b*(c + d*x))/d]*Sinh[2*a - (2*b*c)/d] + b*Cosh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*(c + d*x))/d])/d^2","A",1
14,1,102,112,0.8765308,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^3} \, dx","Integrate[Cosh[a + b*x]^2/(c + d*x)^3,x]","\frac{2 b^2 \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b (c+d x)}{d}\right)+2 b^2 \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b (c+d x)}{d}\right)-\frac{d \left(b (c+d x) \sinh (2 (a+b x))+d \cosh ^2(a+b x)\right)}{(c+d x)^2}}{2 d^3}","\frac{b^2 \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}+\frac{b^2 \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b c}{d}+2 b x\right)}{d^3}-\frac{b \sinh (a+b x) \cosh (a+b x)}{d^2 (c+d x)}-\frac{\cosh ^2(a+b x)}{2 d (c+d x)^2}",1,"(2*b^2*Cosh[2*a - (2*b*c)/d]*CoshIntegral[(2*b*(c + d*x))/d] - (d*(d*Cosh[a + b*x]^2 + b*(c + d*x)*Sinh[2*(a + b*x)]))/(c + d*x)^2 + 2*b^2*Sinh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*(c + d*x))/d])/(2*d^3)","A",1
15,1,121,162,0.856264,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^4} \, dx","Integrate[Cosh[a + b*x]^2/(c + d*x)^4,x]","\frac{4 b^3 \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b (c+d x)}{d}\right)+4 b^3 \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b (c+d x)}{d}\right)-\frac{d \left(\cosh (2 (a+b x)) \left(2 b^2 (c+d x)^2+d^2\right)+d (b (c+d x) \sinh (2 (a+b x))+d)\right)}{(c+d x)^3}}{6 d^4}","\frac{2 b^3 \sinh \left(2 a-\frac{2 b c}{d}\right) \text{Chi}\left(\frac{2 b c}{d}+2 b x\right)}{3 d^4}+\frac{2 b^3 \cosh \left(2 a-\frac{2 b c}{d}\right) \text{Shi}\left(\frac{2 b c}{d}+2 b x\right)}{3 d^4}-\frac{2 b^2 \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,"(4*b^3*CoshIntegral[(2*b*(c + d*x))/d]*Sinh[2*a - (2*b*c)/d] - (d*((d^2 + 2*b^2*(c + d*x)^2)*Cosh[2*(a + b*x)] + d*(d + b*(c + d*x)*Sinh[2*(a + b*x)])))/(c + d*x)^3 + 4*b^3*Cosh[2*a - (2*b*c)/d]*SinhIntegral[(2*b*(c + d*x))/d])/(6*d^4)","A",1
16,1,385,225,0.9650116,"\int (c+d x)^4 \cosh ^3(a+b x) \, dx","Integrate[(c + d*x)^4*Cosh[a + b*x]^3,x]","\frac{243 b^4 c^4 \sinh (a+b x)+27 b^4 c^4 \sinh (3 (a+b x))+972 b^4 c^3 d x \sinh (a+b x)+108 b^4 c^3 d x \sinh (3 (a+b x))+1458 b^4 c^2 d^2 x^2 \sinh (a+b x)+162 b^4 c^2 d^2 x^2 \sinh (3 (a+b x))+972 b^4 c d^3 x^3 \sinh (a+b x)+108 b^4 c d^3 x^3 \sinh (3 (a+b x))+243 b^4 d^4 x^4 \sinh (a+b x)+27 b^4 d^4 x^4 \sinh (3 (a+b x))+2916 b^2 c^2 d^2 \sinh (a+b x)+36 b^2 c^2 d^2 \sinh (3 (a+b x))+5832 b^2 c d^3 x \sinh (a+b x)+72 b^2 c d^3 x \sinh (3 (a+b x))-972 b d (c+d x) \cosh (a+b x) \left(b^2 (c+d x)^2+6 d^2\right)-12 b d (c+d x) \cosh (3 (a+b x)) \left(3 b^2 (c+d x)^2+2 d^2\right)+2916 b^2 d^4 x^2 \sinh (a+b x)+36 b^2 d^4 x^2 \sinh (3 (a+b x))+5832 d^4 \sinh (a+b x)+8 d^4 \sinh (3 (a+b x))}{324 b^5}","\frac{8 d^4 \sinh ^3(a+b x)}{81 b^5}+\frac{488 d^4 \sinh (a+b x)}{27 b^5}-\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{80 d^2 (c+d x)^2 \sinh (a+b x)}{9 b^3}+\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{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,"(-972*b*d*(c + d*x)*(6*d^2 + b^2*(c + d*x)^2)*Cosh[a + b*x] - 12*b*d*(c + d*x)*(2*d^2 + 3*b^2*(c + d*x)^2)*Cosh[3*(a + b*x)] + 243*b^4*c^4*Sinh[a + b*x] + 2916*b^2*c^2*d^2*Sinh[a + b*x] + 5832*d^4*Sinh[a + b*x] + 972*b^4*c^3*d*x*Sinh[a + b*x] + 5832*b^2*c*d^3*x*Sinh[a + b*x] + 1458*b^4*c^2*d^2*x^2*Sinh[a + b*x] + 2916*b^2*d^4*x^2*Sinh[a + b*x] + 972*b^4*c*d^3*x^3*Sinh[a + b*x] + 243*b^4*d^4*x^4*Sinh[a + b*x] + 27*b^4*c^4*Sinh[3*(a + b*x)] + 36*b^2*c^2*d^2*Sinh[3*(a + b*x)] + 8*d^4*Sinh[3*(a + b*x)] + 108*b^4*c^3*d*x*Sinh[3*(a + b*x)] + 72*b^2*c*d^3*x*Sinh[3*(a + b*x)] + 162*b^4*c^2*d^2*x^2*Sinh[3*(a + b*x)] + 36*b^2*d^4*x^2*Sinh[3*(a + b*x)] + 108*b^4*c*d^3*x^3*Sinh[3*(a + b*x)] + 27*b^4*d^4*x^4*Sinh[3*(a + b*x)])/(324*b^5)","A",1
17,1,122,175,0.9622178,"\int (c+d x)^3 \cosh ^3(a+b x) \, dx","Integrate[(c + d*x)^3*Cosh[a + b*x]^3,x]","\frac{-486 d \cosh (a+b x) \left(b^2 (c+d x)^2+2 d^2\right)-2 d \cosh (3 (a+b x)) \left(9 b^2 (c+d x)^2+2 d^2\right)+12 b (c+d x) \sinh (a+b x) \left(\cosh (2 (a+b x)) \left(3 b^2 (c+d x)^2+2 d^2\right)+15 b^2 (c+d x)^2+82 d^2\right)}{216 b^4}","-\frac{2 d^3 \cosh ^3(a+b x)}{27 b^4}-\frac{40 d^3 \cosh (a+b x)}{9 b^4}+\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 (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,"(-486*d*(2*d^2 + b^2*(c + d*x)^2)*Cosh[a + b*x] - 2*d*(2*d^2 + 9*b^2*(c + d*x)^2)*Cosh[3*(a + b*x)] + 12*b*(c + d*x)*(82*d^2 + 15*b^2*(c + d*x)^2 + (2*d^2 + 3*b^2*(c + d*x)^2)*Cosh[2*(a + b*x)])*Sinh[a + b*x])/(216*b^4)","A",1
18,1,93,123,0.5545741,"\int (c+d x)^2 \cosh ^3(a+b x) \, dx","Integrate[(c + d*x)^2*Cosh[a + b*x]^3,x]","\frac{2 \sinh (a+b x) \left(\cosh (2 (a+b x)) \left(9 b^2 (c+d x)^2+2 d^2\right)+45 b^2 (c+d x)^2+82 d^2\right)-162 b d (c+d x) \cosh (a+b x)-6 b d (c+d x) \cosh (3 (a+b x))}{108 b^3}","\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 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 (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,"(-162*b*d*(c + d*x)*Cosh[a + b*x] - 6*b*d*(c + d*x)*Cosh[3*(a + b*x)] + 2*(82*d^2 + 45*b^2*(c + d*x)^2 + (2*d^2 + 9*b^2*(c + d*x)^2)*Cosh[2*(a + b*x)])*Sinh[a + b*x])/(108*b^3)","A",1
19,1,52,75,0.2410191,"\int (c+d x) \cosh ^3(a+b x) \, dx","Integrate[(c + d*x)*Cosh[a + b*x]^3,x]","-\frac{-3 b (c+d x) (9 \sinh (a+b x)+\sinh (3 (a+b x)))+27 d \cosh (a+b x)+d \cosh (3 (a+b x))}{36 b^2}","-\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,"-1/36*(27*d*Cosh[a + b*x] + d*Cosh[3*(a + b*x)] - 3*b*(c + d*x)*(9*Sinh[a + b*x] + Sinh[3*(a + b*x)]))/b^2","A",1
20,1,102,121,0.231501,"\int \frac{\cosh ^3(a+b x)}{c+d x} \, dx","Integrate[Cosh[a + b*x]^3/(c + d*x),x]","\frac{3 \cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(b \left(\frac{c}{d}+x\right)\right)+\cosh \left(3 a-\frac{3 b c}{d}\right) \text{Chi}\left(\frac{3 b (c+d x)}{d}\right)+3 \sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(b \left(\frac{c}{d}+x\right)\right)+\sinh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b (c+d x)}{d}\right)}{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 + x)] + Cosh[3*a - (3*b*c)/d]*CoshIntegral[(3*b*(c + d*x))/d] + 3*Sinh[a - (b*c)/d]*SinhIntegral[b*(c/d + x)] + Sinh[3*a - (3*b*c)/d]*SinhIntegral[(3*b*(c + d*x))/d])/(4*d)","A",1
21,1,196,145,0.5326369,"\int \frac{\cosh ^3(a+b x)}{(c+d x)^2} \, dx","Integrate[Cosh[a + b*x]^3/(c + d*x)^2,x]","-\frac{3 b \left(-2 \sinh \left(3 a-\frac{3 b c}{d}\right) \text{Chi}\left(\frac{3 b c}{d}+3 b x\right)-2 \sinh \left(a-\frac{b c}{d}\right) \text{Chi}\left(\frac{b c}{d}+b x\right)-2 \cosh \left(a-\frac{b c}{d}\right) \text{Shi}\left(\frac{b c}{d}+b x\right)-2 \cosh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b c}{d}+3 b x\right)\right)}{8 d^2}-\frac{3 \sinh (a) \sinh (b x)}{4 d (c+d x)}-\frac{\sinh (3 a) \sinh (3 b x)}{4 d (c+d x)}-\frac{3 \cosh (a) \cosh (b x)}{4 d (c+d x)}-\frac{\cosh (3 a) \cosh (3 b x)}{4 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,"(-3*Cosh[a]*Cosh[b*x])/(4*d*(c + d*x)) - (Cosh[3*a]*Cosh[3*b*x])/(4*d*(c + d*x)) - (3*Sinh[a]*Sinh[b*x])/(4*d*(c + d*x)) - (Sinh[3*a]*Sinh[3*b*x])/(4*d*(c + d*x)) - (3*b*(-2*CoshIntegral[(3*b*c)/d + 3*b*x]*Sinh[3*a - (3*b*c)/d] - 2*CoshIntegral[(b*c)/d + b*x]*Sinh[a - (b*c)/d] - 2*Cosh[a - (b*c)/d]*SinhIntegral[(b*c)/d + b*x] - 2*Cosh[3*a - (3*b*c)/d]*SinhIntegral[(3*b*c)/d + 3*b*x]))/(8*d^2)","A",1
22,1,218,184,0.8861053,"\int \frac{\cosh ^3(a+b x)}{(c+d x)^3} \, dx","Integrate[Cosh[a + b*x]^3/(c + d*x)^3,x]","-\frac{-6 b^2 (c+d x)^2 \left(\cosh \left(a-\frac{b c}{d}\right) \text{Chi}\left(b \left(\frac{c}{d}+x\right)\right)+3 \cosh \left(3 a-\frac{3 b c}{d}\right) \text{Chi}\left(\frac{3 b (c+d x)}{d}\right)+\sinh \left(a-\frac{b c}{d}\right) \text{Shi}\left(b \left(\frac{c}{d}+x\right)\right)+3 \sinh \left(3 a-\frac{3 b c}{d}\right) \text{Shi}\left(\frac{3 b (c+d x)}{d}\right)\right)+6 d \cosh (b x) (b \sinh (a) (c+d x)+d \cosh (a))+2 d \cosh (3 b x) (3 b \sinh (3 a) (c+d x)+d \cosh (3 a))+6 d \sinh (b x) (b \cosh (a) (c+d x)+d \sinh (a))+2 d \sinh (3 b x) (3 b \cosh (3 a) (c+d x)+d \sinh (3 a))}{16 d^3 (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,"-1/16*(6*d*Cosh[b*x]*(d*Cosh[a] + b*(c + d*x)*Sinh[a]) + 2*d*Cosh[3*b*x]*(d*Cosh[3*a] + 3*b*(c + d*x)*Sinh[3*a]) + 6*d*(b*(c + d*x)*Cosh[a] + d*Sinh[a])*Sinh[b*x] + 2*d*(3*b*(c + d*x)*Cosh[3*a] + d*Sinh[3*a])*Sinh[3*b*x] - 6*b^2*(c + d*x)^2*(Cosh[a - (b*c)/d]*CoshIntegral[b*(c/d + x)] + 3*Cosh[3*a - (3*b*c)/d]*CoshIntegral[(3*b*(c + d*x))/d] + Sinh[a - (b*c)/d]*SinhIntegral[b*(c/d + x)] + 3*Sinh[3*a - (3*b*c)/d]*SinhIntegral[(3*b*(c + d*x))/d]))/(d^3*(c + d*x)^2)","A",1
23,1,100,172,0.414814,"\int x^3 \cosh ^4(a+b x) \, dx","Integrate[x^3*Cosh[a + b*x]^4,x]","\frac{-192 \left(2 b^2 x^2+1\right) \cosh (2 (a+b x))-3 \left(8 b^2 x^2+1\right) \cosh (4 (a+b x))+4 b x \left(32 \left(2 b^2 x^2+3\right) \sinh (2 (a+b x))+\left(8 b^2 x^2+3\right) \sinh (4 (a+b x))+24 b^3 x^3\right)}{1024 b^4}","-\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{3 x^2 \cosh ^4(a+b x)}{16 b^2}-\frac{9 x^2 \cosh ^2(a+b x)}{16 b^2}+\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,"(-192*(1 + 2*b^2*x^2)*Cosh[2*(a + b*x)] - 3*(1 + 8*b^2*x^2)*Cosh[4*(a + b*x)] + 4*b*x*(24*b^3*x^3 + 32*(3 + 2*b^2*x^2)*Sinh[2*(a + b*x)] + (3 + 8*b^2*x^2)*Sinh[4*(a + b*x)]))/(1024*b^4)","A",1
24,1,90,134,0.1625719,"\int x^2 \cosh ^4(a+b x) \, dx","Integrate[x^2*Cosh[a + b*x]^4,x]","\frac{64 b^2 x^2 \sinh (2 (a+b x))+8 b^2 x^2 \sinh (4 (a+b x))+32 \sinh (2 (a+b x))+\sinh (4 (a+b x))-64 b x \cosh (2 (a+b x))-4 b x \cosh (4 (a+b x))+32 b^3 x^3}{256 b^3}","\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 \cosh ^4(a+b x)}{8 b^2}-\frac{3 x \cosh ^2(a+b x)}{8 b^2}+\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,"(32*b^3*x^3 - 64*b*x*Cosh[2*(a + b*x)] - 4*b*x*Cosh[4*(a + b*x)] + 32*Sinh[2*(a + b*x)] + 64*b^2*x^2*Sinh[2*(a + b*x)] + Sinh[4*(a + b*x)] + 8*b^2*x^2*Sinh[4*(a + b*x)])/(256*b^3)","A",1
25,1,53,80,0.1824197,"\int x \cosh ^4(a+b x) \, dx","Integrate[x*Cosh[a + b*x]^4,x]","-\frac{-4 b x (8 \sinh (2 (a+b x))+\sinh (4 (a+b x))+6 b x)+16 \cosh (2 (a+b x))+\cosh (4 (a+b x))}{128 b^2}","-\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,"-1/128*(16*Cosh[2*(a + b*x)] + Cosh[4*(a + b*x)] - 4*b*x*(6*b*x + 8*Sinh[2*(a + b*x)] + Sinh[4*(a + b*x)]))/b^2","A",1
26,1,343,179,2.650495,"\int (c+d x)^3 \text{sech}(a+b x) \, dx","Integrate[(c + d*x)^3*Sech[a + b*x],x]","\frac{i \left(-2 i b^3 c^3 \tan ^{-1}\left(e^{a+b x}\right)+3 b^3 c^2 d x \log \left(1-i e^{a+b x}\right)-3 b^3 c^2 d x \log \left(1+i e^{a+b x}\right)+3 b^3 c d^2 x^2 \log \left(1-i e^{a+b x}\right)-3 b^3 c d^2 x^2 \log \left(1+i e^{a+b x}\right)+b^3 d^3 x^3 \log \left(1-i e^{a+b x}\right)-b^3 d^3 x^3 \log \left(1+i e^{a+b x}\right)-3 b^2 d (c+d x)^2 \text{Li}_2\left(-i e^{a+b x}\right)+3 b^2 d (c+d x)^2 \text{Li}_2\left(i e^{a+b x}\right)+6 b c d^2 \text{Li}_3\left(-i e^{a+b x}\right)-6 b c d^2 \text{Li}_3\left(i e^{a+b x}\right)+6 b d^3 x \text{Li}_3\left(-i e^{a+b x}\right)-6 b d^3 x \text{Li}_3\left(i e^{a+b x}\right)-6 d^3 \text{Li}_4\left(-i e^{a+b x}\right)+6 d^3 \text{Li}_4\left(i e^{a+b x}\right)\right)}{b^4}","-\frac{6 i d^3 \text{Li}_4\left(-i e^{a+b x}\right)}{b^4}+\frac{6 i d^3 \text{Li}_4\left(i e^{a+b x}\right)}{b^4}+\frac{6 i d^2 (c+d x) \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}-\frac{6 i d^2 (c+d x) \text{Li}_3\left(i e^{a+b x}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}+\frac{3 i d (c+d x)^2 \text{Li}_2\left(i e^{a+b x}\right)}{b^2}+\frac{2 (c+d x)^3 \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(I*((-2*I)*b^3*c^3*ArcTan[E^(a + b*x)] + 3*b^3*c^2*d*x*Log[1 - I*E^(a + b*x)] + 3*b^3*c*d^2*x^2*Log[1 - I*E^(a + b*x)] + b^3*d^3*x^3*Log[1 - I*E^(a + b*x)] - 3*b^3*c^2*d*x*Log[1 + I*E^(a + b*x)] - 3*b^3*c*d^2*x^2*Log[1 + I*E^(a + b*x)] - b^3*d^3*x^3*Log[1 + I*E^(a + b*x)] - 3*b^2*d*(c + d*x)^2*PolyLog[2, (-I)*E^(a + b*x)] + 3*b^2*d*(c + d*x)^2*PolyLog[2, I*E^(a + b*x)] + 6*b*c*d^2*PolyLog[3, (-I)*E^(a + b*x)] + 6*b*d^3*x*PolyLog[3, (-I)*E^(a + b*x)] - 6*b*c*d^2*PolyLog[3, I*E^(a + b*x)] - 6*b*d^3*x*PolyLog[3, I*E^(a + b*x)] - 6*d^3*PolyLog[4, (-I)*E^(a + b*x)] + 6*d^3*PolyLog[4, I*E^(a + b*x)]))/b^4","A",1
27,1,199,119,1.5180404,"\int (c+d x)^2 \text{sech}(a+b x) \, dx","Integrate[(c + d*x)^2*Sech[a + b*x],x]","\frac{i \left(-2 i b^2 c^2 \tan ^{-1}\left(e^{a+b x}\right)+2 b^2 c d x \log \left(1-i e^{a+b x}\right)-2 b^2 c d x \log \left(1+i e^{a+b x}\right)+b^2 d^2 x^2 \log \left(1-i e^{a+b x}\right)-b^2 d^2 x^2 \log \left(1+i e^{a+b x}\right)-2 b d (c+d x) \text{Li}_2\left(-i e^{a+b x}\right)+2 b d (c+d x) \text{Li}_2\left(i e^{a+b x}\right)+2 d^2 \text{Li}_3\left(-i e^{a+b x}\right)-2 d^2 \text{Li}_3\left(i e^{a+b x}\right)\right)}{b^3}","\frac{2 i d^2 \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}-\frac{2 i d^2 \text{Li}_3\left(i e^{a+b x}\right)}{b^3}-\frac{2 i d (c+d x) \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}+\frac{2 i d (c+d x) \text{Li}_2\left(i e^{a+b x}\right)}{b^2}+\frac{2 (c+d x)^2 \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(I*((-2*I)*b^2*c^2*ArcTan[E^(a + b*x)] + 2*b^2*c*d*x*Log[1 - I*E^(a + b*x)] + b^2*d^2*x^2*Log[1 - I*E^(a + b*x)] - 2*b^2*c*d*x*Log[1 + I*E^(a + b*x)] - b^2*d^2*x^2*Log[1 + I*E^(a + b*x)] - 2*b*d*(c + d*x)*PolyLog[2, (-I)*E^(a + b*x)] + 2*b*d*(c + d*x)*PolyLog[2, I*E^(a + b*x)] + 2*d^2*PolyLog[3, (-I)*E^(a + b*x)] - 2*d^2*PolyLog[3, I*E^(a + b*x)]))/b^3","A",1
28,1,127,61,0.1471546,"\int (c+d x) \text{sech}(a+b x) \, dx","Integrate[(c + d*x)*Sech[a + b*x],x]","\frac{b c \tan ^{-1}(\sinh (a+b x))+\frac{1}{2} d \left(-2 i \left(\text{Li}_2\left(-i e^{a+b x}\right)-\text{Li}_2\left(i e^{a+b x}\right)\right)-\left((-2 i a-2 i b x+\pi ) \left(\log \left(1-i e^{a+b x}\right)-\log \left(1+i e^{a+b x}\right)\right)\right)+(\pi -2 i a) \log \left(\cot \left(\frac{1}{4} (2 i a+2 i b x+\pi )\right)\right)\right)}{b^2}","-\frac{i d \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}+\frac{i d \text{Li}_2\left(i e^{a+b x}\right)}{b^2}+\frac{2 (c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b}",1,"(b*c*ArcTan[Sinh[a + b*x]] + (d*(-(((-2*I)*a + Pi - (2*I)*b*x)*(Log[1 - I*E^(a + b*x)] - Log[1 + I*E^(a + b*x)])) + ((-2*I)*a + Pi)*Log[Cot[((2*I)*a + Pi + (2*I)*b*x)/4]] - (2*I)*(PolyLog[2, (-I)*E^(a + b*x)] - PolyLog[2, I*E^(a + b*x)])))/2)/b^2","B",1
29,0,0,17,3.710589,"\int \frac{\text{sech}(a+b x)}{c+d x} \, dx","Integrate[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,"Integrate[Sech[a + b*x]/(c + d*x), x]","A",-1
30,0,0,17,7.2815483,"\int \frac{\text{sech}(a+b x)}{(c+d x)^2} \, dx","Integrate[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,"Integrate[Sech[a + b*x]/(c + d*x)^2, x]","A",-1
31,1,145,103,2.0744287,"\int (c+d x)^3 \text{sech}^2(a+b x) \, dx","Integrate[(c + d*x)^3*Sech[a + b*x]^2,x]","\frac{2 \text{sech}(a) \sinh (b x) (c+d x)^3 \text{sech}(a+b x)-\frac{e^{2 a} d \left(-\frac{3 \left(e^{-2 a}+1\right) d \left(2 b (c+d x) \text{Li}_2\left(-e^{-2 (a+b x)}\right)+d \text{Li}_3\left(-e^{-2 (a+b x)}\right)\right)}{b^3}+\frac{6 \left(e^{-2 a}+1\right) (c+d x)^2 \log \left(e^{-2 (a+b x)}+1\right)}{b}+\frac{4 e^{-2 a} (c+d x)^3}{d}\right)}{e^{2 a}+1}}{2 b}","\frac{3 d^3 \text{Li}_3\left(-e^{2 (a+b x)}\right)}{2 b^4}-\frac{3 d^2 (c+d x) \text{Li}_2\left(-e^{2 (a+b x)}\right)}{b^3}-\frac{3 d (c+d x)^2 \log \left(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,"(-((d*E^(2*a)*((4*(c + d*x)^3)/(d*E^(2*a)) + (6*(1 + E^(-2*a))*(c + d*x)^2*Log[1 + E^(-2*(a + b*x))])/b - (3*d*(1 + E^(-2*a))*(2*b*(c + d*x)*PolyLog[2, -E^(-2*(a + b*x))] + d*PolyLog[3, -E^(-2*(a + b*x))]))/b^3))/(1 + E^(2*a))) + 2*(c + d*x)^3*Sech[a]*Sech[a + b*x]*Sinh[b*x])/(2*b)","A",1
32,1,277,73,6.3026638,"\int (c+d x)^2 \text{sech}^2(a+b x) \, dx","Integrate[(c + d*x)^2*Sech[a + b*x]^2,x]","-\frac{2 c d \text{sech}(a) (\cosh (a) \log (\sinh (a) \sinh (b x)+\cosh (a) \cosh (b x))-b x \sinh (a))}{b^2 \left(\cosh ^2(a)-\sinh ^2(a)\right)}-\frac{d^2 \text{csch}(a) \text{sech}(a) \left(b^2 x^2 e^{-\tanh ^{-1}(\coth (a))}-\frac{i \coth (a) \left(i \text{Li}_2\left(e^{2 i \left(i b x+i \tanh ^{-1}(\coth (a))\right)}\right)-b x \left(-\pi +2 i \tanh ^{-1}(\coth (a))\right)-2 \left(i \tanh ^{-1}(\coth (a))+i b x\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}(\coth (a))+i b x\right)}\right)+2 i \tanh ^{-1}(\coth (a)) \log \left(i \sinh \left(\tanh ^{-1}(\coth (a))+b x\right)\right)-\pi  \log \left(e^{2 b x}+1\right)+\pi  \log (\cosh (b x))\right)}{\sqrt{1-\coth ^2(a)}}\right)}{b^3 \sqrt{\text{csch}^2(a) \left(\sinh ^2(a)-\cosh ^2(a)\right)}}+\frac{\text{sech}(a) \text{sech}(a+b x) \left(c^2 \sinh (b x)+2 c d x \sinh (b x)+d^2 x^2 \sinh (b x)\right)}{b}","-\frac{d^2 \text{Li}_2\left(-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,"(-2*c*d*Sech[a]*(Cosh[a]*Log[Cosh[a]*Cosh[b*x] + Sinh[a]*Sinh[b*x]] - b*x*Sinh[a]))/(b^2*(Cosh[a]^2 - Sinh[a]^2)) - (d^2*Csch[a]*((b^2*x^2)/E^ArcTanh[Coth[a]] - (I*Coth[a]*(-(b*x*(-Pi + (2*I)*ArcTanh[Coth[a]])) - Pi*Log[1 + E^(2*b*x)] - 2*(I*b*x + I*ArcTanh[Coth[a]])*Log[1 - E^((2*I)*(I*b*x + I*ArcTanh[Coth[a]]))] + Pi*Log[Cosh[b*x]] + (2*I)*ArcTanh[Coth[a]]*Log[I*Sinh[b*x + ArcTanh[Coth[a]]]] + I*PolyLog[2, E^((2*I)*(I*b*x + I*ArcTanh[Coth[a]]))]))/Sqrt[1 - Coth[a]^2])*Sech[a])/(b^3*Sqrt[Csch[a]^2*(-Cosh[a]^2 + Sinh[a]^2)]) + (Sech[a]*Sech[a + b*x]*(c^2*Sinh[b*x] + 2*c*d*x*Sinh[b*x] + d^2*x^2*Sinh[b*x]))/b","C",0
33,1,51,29,0.0921946,"\int (c+d x) \text{sech}^2(a+b x) \, dx","Integrate[(c + d*x)*Sech[a + b*x]^2,x]","-\frac{d \log (\cosh (a+b x))}{b^2}+\frac{c \tanh (a+b x)}{b}+\frac{d x \tanh (a)}{b}+\frac{d x \text{sech}(a) \sinh (b x) \text{sech}(a+b x)}{b}","\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) + (d*x*Sech[a]*Sech[a + b*x]*Sinh[b*x])/b + (d*x*Tanh[a])/b + (c*Tanh[a + b*x])/b","A",1
34,0,0,19,17.7831634,"\int \frac{\text{sech}^2(a+b x)}{c+d x} \, dx","Integrate[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,"Integrate[Sech[a + b*x]^2/(c + d*x), x]","A",-1
35,0,0,19,17.9602545,"\int \frac{\text{sech}^2(a+b x)}{(c+d x)^2} \, dx","Integrate[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,"Integrate[Sech[a + b*x]^2/(c + d*x)^2, x]","A",-1
36,1,455,296,29.522477,"\int (c+d x)^3 \text{sech}^3(a+b x) \, dx","Integrate[(c + d*x)^3*Sech[a + b*x]^3,x]","\frac{b^2 (c+d x)^2 \text{sech}(a+b x) (b (c+d x) \tanh (a+b x)+3 d)+i \left(-2 i b^3 c^3 \tan ^{-1}\left(e^{a+b x}\right)+3 b^3 c^2 d x \log \left(1-i e^{a+b x}\right)-3 b^3 c^2 d x \log \left(1+i e^{a+b x}\right)+3 b^3 c d^2 x^2 \log \left(1-i e^{a+b x}\right)-3 b^3 c d^2 x^2 \log \left(1+i e^{a+b x}\right)+b^3 d^3 x^3 \log \left(1-i e^{a+b x}\right)-b^3 d^3 x^3 \log \left(1+i e^{a+b x}\right)-3 d \text{Li}_2\left(-i e^{a+b x}\right) \left(b^2 (c+d x)^2-2 d^2\right)+3 d \text{Li}_2\left(i e^{a+b x}\right) \left(b^2 (c+d x)^2-2 d^2\right)+6 b c d^2 \text{Li}_3\left(-i e^{a+b x}\right)-6 b c d^2 \text{Li}_3\left(i e^{a+b x}\right)+12 i b c d^2 \tan ^{-1}\left(e^{a+b x}\right)+6 b d^3 x \text{Li}_3\left(-i e^{a+b x}\right)-6 b d^3 x \text{Li}_3\left(i e^{a+b x}\right)-6 d^3 \text{Li}_4\left(-i e^{a+b x}\right)+6 d^3 \text{Li}_4\left(i e^{a+b x}\right)-6 b d^3 x \log \left(1-i e^{a+b x}\right)+6 b d^3 x \log \left(1+i e^{a+b x}\right)\right)}{2 b^4}","\frac{3 i d^3 \text{Li}_2\left(-i e^{a+b x}\right)}{b^4}-\frac{3 i d^3 \text{Li}_2\left(i e^{a+b x}\right)}{b^4}-\frac{3 i d^3 \text{Li}_4\left(-i e^{a+b x}\right)}{b^4}+\frac{3 i d^3 \text{Li}_4\left(i e^{a+b x}\right)}{b^4}+\frac{3 i d^2 (c+d x) \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}-\frac{3 i d^2 (c+d x) \text{Li}_3\left(i e^{a+b x}\right)}{b^3}-\frac{6 d^2 (c+d x) \tan ^{-1}\left(e^{a+b x}\right)}{b^3}-\frac{3 i d (c+d x)^2 \text{Li}_2\left(-i e^{a+b x}\right)}{2 b^2}+\frac{3 i d (c+d x)^2 \text{Li}_2\left(i e^{a+b x}\right)}{2 b^2}+\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,"(I*((-2*I)*b^3*c^3*ArcTan[E^(a + b*x)] + (12*I)*b*c*d^2*ArcTan[E^(a + b*x)] + 3*b^3*c^2*d*x*Log[1 - I*E^(a + b*x)] - 6*b*d^3*x*Log[1 - I*E^(a + b*x)] + 3*b^3*c*d^2*x^2*Log[1 - I*E^(a + b*x)] + b^3*d^3*x^3*Log[1 - I*E^(a + b*x)] - 3*b^3*c^2*d*x*Log[1 + I*E^(a + b*x)] + 6*b*d^3*x*Log[1 + I*E^(a + b*x)] - 3*b^3*c*d^2*x^2*Log[1 + I*E^(a + b*x)] - b^3*d^3*x^3*Log[1 + I*E^(a + b*x)] - 3*d*(-2*d^2 + b^2*(c + d*x)^2)*PolyLog[2, (-I)*E^(a + b*x)] + 3*d*(-2*d^2 + b^2*(c + d*x)^2)*PolyLog[2, I*E^(a + b*x)] + 6*b*c*d^2*PolyLog[3, (-I)*E^(a + b*x)] + 6*b*d^3*x*PolyLog[3, (-I)*E^(a + b*x)] - 6*b*c*d^2*PolyLog[3, I*E^(a + b*x)] - 6*b*d^3*x*PolyLog[3, I*E^(a + b*x)] - 6*d^3*PolyLog[4, (-I)*E^(a + b*x)] + 6*d^3*PolyLog[4, I*E^(a + b*x)]) + b^2*(c + d*x)^2*Sech[a + b*x]*(3*d + b*(c + d*x)*Tanh[a + b*x]))/(2*b^4)","A",1
37,1,270,175,5.5189211,"\int (c+d x)^2 \text{sech}^3(a+b x) \, dx","Integrate[(c + d*x)^2*Sech[a + b*x]^3,x]","\frac{i \left(-2 i b^2 c^2 \tan ^{-1}\left(e^{a+b x}\right)+2 b^2 c d x \log \left(1-i e^{a+b x}\right)-2 b^2 c d x \log \left(1+i e^{a+b x}\right)+b^2 d^2 x^2 \log \left(1-i e^{a+b x}\right)-b^2 d^2 x^2 \log \left(1+i e^{a+b x}\right)-2 b d (c+d x) \text{Li}_2\left(-i e^{a+b x}\right)+2 b d (c+d x) \text{Li}_2\left(i e^{a+b x}\right)+2 d^2 \text{Li}_3\left(-i e^{a+b x}\right)-2 d^2 \text{Li}_3\left(i e^{a+b x}\right)+4 i d^2 \tan ^{-1}\left(e^{a+b x}\right)\right)+b^2 \text{sech}(a) \sinh (b x) (c+d x)^2 \text{sech}^2(a+b x)+b (c+d x) \text{sech}(a+b x) (b \tanh (a) (c+d x)+2 d)}{2 b^3}","\frac{i d^2 \text{Li}_3\left(-i e^{a+b x}\right)}{b^3}-\frac{i d^2 \text{Li}_3\left(i e^{a+b x}\right)}{b^3}-\frac{d^2 \tan ^{-1}(\sinh (a+b x))}{b^3}-\frac{i d (c+d x) \text{Li}_2\left(-i e^{a+b x}\right)}{b^2}+\frac{i d (c+d x) \text{Li}_2\left(i e^{a+b x}\right)}{b^2}+\frac{d (c+d x) \text{sech}(a+b x)}{b^2}+\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,"(I*((-2*I)*b^2*c^2*ArcTan[E^(a + b*x)] + (4*I)*d^2*ArcTan[E^(a + b*x)] + 2*b^2*c*d*x*Log[1 - I*E^(a + b*x)] + b^2*d^2*x^2*Log[1 - I*E^(a + b*x)] - 2*b^2*c*d*x*Log[1 + I*E^(a + b*x)] - b^2*d^2*x^2*Log[1 + I*E^(a + b*x)] - 2*b*d*(c + d*x)*PolyLog[2, (-I)*E^(a + b*x)] + 2*b*d*(c + d*x)*PolyLog[2, I*E^(a + b*x)] + 2*d^2*PolyLog[3, (-I)*E^(a + b*x)] - 2*d^2*PolyLog[3, I*E^(a + b*x)]) + b^2*(c + d*x)^2*Sech[a]*Sech[a + b*x]^2*Sinh[b*x] + b*(c + d*x)*Sech[a + b*x]*(2*d + b*(c + d*x)*Tanh[a]))/(2*b^3)","A",1
38,1,178,102,3.0168738,"\int (c+d x) \text{sech}^3(a+b x) \, dx","Integrate[(c + d*x)*Sech[a + b*x]^3,x]","\frac{b c \tan ^{-1}(\sinh (a+b x))+b c \tanh (a+b x) \text{sech}(a+b x)+\frac{1}{2} d \left(-2 i \left(\text{Li}_2\left(-i e^{a+b x}\right)-\text{Li}_2\left(i e^{a+b x}\right)\right)-\left((-2 i a-2 i b x+\pi ) \left(\log \left(1-i e^{a+b x}\right)-\log \left(1+i e^{a+b x}\right)\right)\right)+(\pi -2 i a) \log \left(\cot \left(\frac{1}{4} (2 i a+2 i b x+\pi )\right)\right)\right)+b d x \text{sech}(a) \sinh (b x) \text{sech}^2(a+b x)+d (b x \tanh (a)+1) \text{sech}(a+b x)}{2 b^2}","-\frac{i d \text{Li}_2\left(-i e^{a+b x}\right)}{2 b^2}+\frac{i d \text{Li}_2\left(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,"(b*c*ArcTan[Sinh[a + b*x]] + (d*(-(((-2*I)*a + Pi - (2*I)*b*x)*(Log[1 - I*E^(a + b*x)] - Log[1 + I*E^(a + b*x)])) + ((-2*I)*a + Pi)*Log[Cot[((2*I)*a + Pi + (2*I)*b*x)/4]] - (2*I)*(PolyLog[2, (-I)*E^(a + b*x)] - PolyLog[2, I*E^(a + b*x)])))/2 + b*d*x*Sech[a]*Sech[a + b*x]^2*Sinh[b*x] + d*Sech[a + b*x]*(1 + b*x*Tanh[a]) + b*c*Sech[a + b*x]*Tanh[a + b*x])/(2*b^2)","A",1
39,-1,0,19,180.0077038,"\int \frac{\text{sech}^3(a+b x)}{c+d x} \, dx","Integrate[Sech[a + b*x]^3/(c + d*x),x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{sech}^3(a+b x)}{c+d x},x\right)",0,"$Aborted","F",-1
40,-1,0,19,180.016772,"\int \frac{\text{sech}^3(a+b x)}{(c+d x)^2} \, dx","Integrate[Sech[a + b*x]^3/(c + d*x)^2,x]","\text{\$Aborted}","\text{Int}\left(\frac{\text{sech}^3(a+b x)}{(c+d x)^2},x\right)",0,"$Aborted","F",-1
41,1,107,171,0.0513605,"\int (c+d x)^{5/2} \cosh (a+b x) \, dx","Integrate[(c + d*x)^(5/2)*Cosh[a + b*x],x]","-\frac{d^3 e^{-a-\frac{b c}{d}} \left(e^{2 a} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{7}{2},-\frac{b (c+d x)}{d}\right)+e^{\frac{2 b c}{d}} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{7}{2},\frac{b (c+d x)}{d}\right)\right)}{2 b^4 \sqrt{c+d x}}","\frac{15 \sqrt{\pi } d^{5/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}-\frac{15 \sqrt{\pi } d^{5/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \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,"-1/2*(d^3*E^(-a - (b*c)/d)*(E^(2*a)*Sqrt[-((b*(c + d*x))/d)]*Gamma[7/2, -((b*(c + d*x))/d)] + E^((2*b*c)/d)*Sqrt[(b*(c + d*x))/d]*Gamma[7/2, (b*(c + d*x))/d]))/(b^4*Sqrt[c + d*x])","A",1
42,1,107,146,0.1034869,"\int (c+d x)^{3/2} \cosh (a+b x) \, dx","Integrate[(c + d*x)^(3/2)*Cosh[a + b*x],x]","\frac{d \sqrt{c+d x} e^{-a-\frac{b c}{d}} \left(-\frac{e^{2 a} \Gamma \left(\frac{5}{2},-\frac{b (c+d x)}{d}\right)}{\sqrt{-\frac{b (c+d x)}{d}}}-\frac{e^{\frac{2 b c}{d}} \Gamma \left(\frac{5}{2},\frac{b (c+d x)}{d}\right)}{\sqrt{\frac{b (c+d x)}{d}}}\right)}{2 b^2}","\frac{3 \sqrt{\pi } d^{3/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}+\frac{3 \sqrt{\pi } d^{3/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 b^{5/2}}-\frac{3 d \sqrt{c+d x} \cosh (a+b x)}{2 b^2}+\frac{(c+d x)^{3/2} \sinh (a+b x)}{b}",1,"(d*E^(-a - (b*c)/d)*Sqrt[c + d*x]*(-((E^(2*a)*Gamma[5/2, -((b*(c + d*x))/d)])/Sqrt[-((b*(c + d*x))/d)]) - (E^((2*b*c)/d)*Gamma[5/2, (b*(c + d*x))/d])/Sqrt[(b*(c + d*x))/d]))/(2*b^2)","A",1
43,1,105,123,0.0906568,"\int \sqrt{c+d x} \cosh (a+b x) \, dx","Integrate[Sqrt[c + d*x]*Cosh[a + b*x],x]","\frac{\sqrt{c+d x} e^{-a-\frac{b c}{d}} \left(\frac{e^{2 a} \Gamma \left(\frac{3}{2},-\frac{b (c+d x)}{d}\right)}{\sqrt{-\frac{b (c+d x)}{d}}}-\frac{e^{\frac{2 b c}{d}} \Gamma \left(\frac{3}{2},\frac{b (c+d x)}{d}\right)}{\sqrt{\frac{b (c+d x)}{d}}}\right)}{2 b}","\frac{\sqrt{\pi } \sqrt{d} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 b^{3/2}}+\frac{\sqrt{c+d x} \sinh (a+b x)}{b}",1,"(E^(-a - (b*c)/d)*Sqrt[c + d*x]*((E^(2*a)*Gamma[3/2, -((b*(c + d*x))/d)])/Sqrt[-((b*(c + d*x))/d)] - (E^((2*b*c)/d)*Gamma[3/2, (b*(c + d*x))/d])/Sqrt[(b*(c + d*x))/d]))/(2*b)","A",1
44,1,105,104,0.0439149,"\int \frac{\cosh (a+b x)}{\sqrt{c+d x}} \, dx","Integrate[Cosh[a + b*x]/Sqrt[c + d*x],x]","\frac{e^{-a-\frac{b c}{d}} \left(e^{2 a} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)-e^{\frac{2 b c}{d}} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)\right)}{2 b \sqrt{c+d x}}","\frac{\sqrt{\pi } e^{\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)*(E^(2*a)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)] - E^((2*b*c)/d)*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (b*(c + d*x))/d]))/(2*b*Sqrt[c + d*x])","A",1
45,1,118,119,0.3647108,"\int \frac{\cosh (a+b x)}{(c+d x)^{3/2}} \, dx","Integrate[Cosh[a + b*x]/(c + d*x)^(3/2),x]","\frac{e^{-a} \left(e^{2 a-\frac{b c}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)-e^{-b x} \left(e^{2 (a+b x)}+1\right)+e^{\frac{b c}{d}} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},b \left(\frac{c}{d}+x\right)\right)\right)}{d \sqrt{c+d x}}","-\frac{\sqrt{\pi } \sqrt{b} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{\sqrt{\pi } \sqrt{b} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \cosh (a+b x)}{d \sqrt{c+d x}}",1,"(-((1 + E^(2*(a + b*x)))/E^(b*x)) + E^((b*c)/d)*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, b*(c/d + x)] + E^(2*a - (b*c)/d)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)])/(d*E^a*Sqrt[c + d*x])","A",1
46,1,150,149,0.7302556,"\int \frac{\cosh (a+b x)}{(c+d x)^{5/2}} \, dx","Integrate[Cosh[a + b*x]/(c + d*x)^(5/2),x]","\frac{e^{-a} \left(-2 d e^{2 a-\frac{b c}{d}} \left(-\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)-e^{-b x} \left(2 b \left(e^{2 (a+b x)}-1\right) (c+d x)+d \left(e^{2 (a+b x)}+1\right)+2 d e^{b \left(\frac{c}{d}+x\right)} \left(\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},b \left(\frac{c}{d}+x\right)\right)\right)\right)}{3 d^2 (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,"(-((d*(1 + E^(2*(a + b*x))) + 2*b*(-1 + E^(2*(a + b*x)))*(c + d*x) + 2*d*E^(b*(c/d + x))*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, b*(c/d + x)])/E^(b*x)) - 2*d*E^(2*a - (b*c)/d)*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, -((b*(c + d*x))/d)])/(3*d^2*E^a*(c + d*x)^(3/2))","A",1
47,1,191,174,0.4163902,"\int \frac{\cosh (a+b x)}{(c+d x)^{7/2}} \, dx","Integrate[Cosh[a + b*x]/(c + d*x)^(7/2),x]","\frac{e^{-a} \left(2 e^{2 a} \left(-2 b e^{-\frac{b c}{d}} (c+d x) \left(e^{b \left(\frac{c}{d}+x\right)} (2 b (c+d x)+d)+2 d \left(-\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)\right)-3 d^2 e^{b x}\right)+e^{-b x} \left(-8 b^2 (c+d x)^2+8 d^2 e^{b \left(\frac{c}{d}+x\right)} \left(\frac{b (c+d x)}{d}\right)^{5/2} \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)+4 b d (c+d x)-6 d^2\right)\right)}{30 d^3 (c+d x)^{5/2}}","-\frac{4 \sqrt{\pi } b^{5/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}+\frac{4 \sqrt{\pi } b^{5/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}-\frac{8 b^2 \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*E^(2*a)*(-3*d^2*E^(b*x) - (2*b*(c + d*x)*(E^(b*(c/d + x))*(d + 2*b*(c + d*x)) + 2*d*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, -((b*(c + d*x))/d)]))/E^((b*c)/d)) + (-6*d^2 + 4*b*d*(c + d*x) - 8*b^2*(c + d*x)^2 + 8*d^2*E^(b*(c/d + x))*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (b*(c + d*x))/d])/E^(b*x))/(30*d^3*E^a*(c + d*x)^(5/2))","A",1
48,1,189,239,1.2014379,"\int (c+d x)^{5/2} \cosh ^2(a+b x) \, dx","Integrate[(c + d*x)^(5/2)*Cosh[a + b*x]^2,x]","\frac{\sqrt{c+d x} \left(b (c+d x) \left(7 \sqrt{2} d^3 \Gamma \left(\frac{7}{2},\frac{2 b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)-\cosh \left(2 a-\frac{2 b c}{d}\right)\right)+64 b^3 (c+d x)^3 \sqrt{\frac{b (c+d x)}{d}}\right)-7 \sqrt{2} d^4 \sqrt{-\frac{b^2 (c+d x)^2}{d^2}} \Gamma \left(\frac{7}{2},-\frac{2 b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)+\cosh \left(2 a-\frac{2 b c}{d}\right)\right)\right)}{448 b^3 d^2 \left(\frac{b (c+d x)}{d}\right)^{3/2}}","\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{256 b^{7/2}}-\frac{15 \sqrt{\frac{\pi }{2}} d^{5/2} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{256 b^{7/2}}+\frac{15 d^2 \sqrt{c+d x} \sinh (2 a+2 b x)}{64 b^3}-\frac{5 d (c+d x)^{3/2} \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,"(Sqrt[c + d*x]*(-7*Sqrt[2]*d^4*Sqrt[-((b^2*(c + d*x)^2)/d^2)]*Gamma[7/2, (-2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]) + b*(c + d*x)*(64*b^3*(c + d*x)^3*Sqrt[(b*(c + d*x))/d] + 7*Sqrt[2]*d^3*Gamma[7/2, (2*b*(c + d*x))/d]*(-Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]))))/(448*b^3*d^2*((b*(c + d*x))/d)^(3/2))","A",0
49,1,163,211,0.6018414,"\int (c+d x)^{3/2} \cosh ^2(a+b x) \, dx","Integrate[(c + d*x)^(3/2)*Cosh[a + b*x]^2,x]","\frac{5 \sqrt{2} d^3 \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{5}{2},\frac{2 b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)-\cosh \left(2 a-\frac{2 b c}{d}\right)\right)+5 \sqrt{2} d^3 \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{5}{2},-\frac{2 b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)+\cosh \left(2 a-\frac{2 b c}{d}\right)\right)+32 b^3 (c+d x)^3}{160 b^3 d \sqrt{c+d x}}","\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{5/2}}+\frac{3 \sqrt{\frac{\pi }{2}} d^{3/2} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{5/2}}-\frac{3 d \sqrt{c+d x} \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,"(32*b^3*(c + d*x)^3 + 5*Sqrt[2]*d^3*Sqrt[(b*(c + d*x))/d]*Gamma[5/2, (2*b*(c + d*x))/d]*(-Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]) + 5*Sqrt[2]*d^3*Sqrt[-((b*(c + d*x))/d)]*Gamma[5/2, (-2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]))/(160*b^3*d*Sqrt[c + d*x])","A",1
50,1,129,166,0.4482464,"\int \sqrt{c+d x} \cosh ^2(a+b x) \, dx","Integrate[Sqrt[c + d*x]*Cosh[a + b*x]^2,x]","\frac{1}{48} \sqrt{c+d x} \left(\frac{3 \sqrt{2} e^{2 a-\frac{2 b c}{d}} \Gamma \left(\frac{3}{2},-\frac{2 b (c+d x)}{d}\right)}{b \sqrt{-\frac{b (c+d x)}{d}}}-\frac{3 \sqrt{2} e^{\frac{2 b c}{d}-2 a} \Gamma \left(\frac{3}{2},\frac{2 b (c+d x)}{d}\right)}{b \sqrt{\frac{b (c+d x)}{d}}}+\frac{16 (c+d x)}{d}\right)","\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sqrt{d} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{3/2}}+\frac{\sqrt{c+d x} \sinh (2 a+2 b x)}{4 b}+\frac{(c+d x)^{3/2}}{3 d}",1,"(Sqrt[c + d*x]*((16*(c + d*x))/d + (3*Sqrt[2]*E^(2*a - (2*b*c)/d)*Gamma[3/2, (-2*b*(c + d*x))/d])/(b*Sqrt[-((b*(c + d*x))/d)]) - (3*Sqrt[2]*E^(-2*a + (2*b*c)/d)*Gamma[3/2, (2*b*(c + d*x))/d])/(b*Sqrt[(b*(c + d*x))/d])))/48","A",1
51,1,141,138,0.1266372,"\int \frac{\cosh ^2(a+b x)}{\sqrt{c+d x}} \, dx","Integrate[Cosh[a + b*x]^2/Sqrt[c + d*x],x]","\frac{e^{2 a-\frac{2 b c}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{2 b (c+d x)}{d}\right)}{4 \sqrt{2} b \sqrt{c+d x}}-\frac{e^{\frac{2 b c}{d}-2 a} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},\frac{2 b (c+d x)}{d}\right)}{4 \sqrt{2} b \sqrt{c+d x}}+\frac{\sqrt{c+d x}}{d}","\frac{\sqrt{\frac{\pi }{2}} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 \sqrt{b} \sqrt{d}}+\frac{\sqrt{\frac{\pi }{2}} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{4 \sqrt{b} \sqrt{d}}+\frac{\sqrt{c+d x}}{d}",1,"Sqrt[c + d*x]/d + (E^(2*a - (2*b*c)/d)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-2*b*(c + d*x))/d])/(4*Sqrt[2]*b*Sqrt[c + d*x]) - (E^(-2*a + (2*b*c)/d)*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (2*b*(c + d*x))/d])/(4*Sqrt[2]*b*Sqrt[c + d*x])","A",1
52,1,570,142,2.9732254,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^{3/2}} \, dx","Integrate[Cosh[a + b*x]^2/(c + d*x)^(3/2),x]","\frac{e^{-\frac{2 b (c+d x)}{d}} \left(-\sqrt{2 \pi } \sqrt{b} \cosh (2 a) \sqrt{c+d x} e^{\frac{2 b (c+d x)}{d}} \sinh \left(\frac{2 b c}{d}\right) \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)-\sqrt{2 \pi } \sqrt{b} \cosh (2 a) \sqrt{c+d x} e^{\frac{2 b (c+d x)}{d}} \sinh \left(\frac{2 b c}{d}\right) \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)+\sqrt{d} \sinh (2 a) e^{\frac{4 b (c+d x)}{d}} \sinh \left(\frac{2 b c}{d}\right)-\sqrt{d} \cosh (2 a) e^{\frac{4 b (c+d x)}{d}} \cosh \left(\frac{2 b c}{d}\right)-\sqrt{d} \sinh (2 a) e^{\frac{4 b (c+d x)}{d}} \cosh \left(\frac{2 b c}{d}\right)+\sqrt{d} \cosh (2 a) e^{\frac{4 b (c+d x)}{d}} \sinh \left(\frac{2 b c}{d}\right)+\sqrt{2} \sqrt{d} e^{\frac{2 b (c+d x)}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{2 b (c+d x)}{d}\right) \left(\cosh \left(2 a-\frac{2 b c}{d}\right)+\sinh (2 a) \cosh \left(\frac{2 b c}{d}\right)\right)+\sqrt{2} \sqrt{d} e^{\frac{2 b (c+d x)}{d}} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},\frac{2 b (c+d x)}{d}\right) \left(\cosh (2 a) \cosh \left(\frac{2 b c}{d}\right)-\sinh (2 a) \left(\sinh \left(\frac{2 b c}{d}\right)+\cosh \left(\frac{2 b c}{d}\right)\right)\right)+\sqrt{d} \sinh (2 a) \sinh \left(\frac{2 b c}{d}\right)-\sqrt{d} \cosh (2 a) \cosh \left(\frac{2 b c}{d}\right)+\sqrt{d} \sinh (2 a) \cosh \left(\frac{2 b c}{d}\right)-\sqrt{d} \cosh (2 a) \sinh \left(\frac{2 b c}{d}\right)-2 \sqrt{d} e^{\frac{2 b (c+d x)}{d}}\right)}{2 d^{3/2} \sqrt{c+d x}}","-\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sqrt{b} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \cosh ^2(a+b x)}{d \sqrt{c+d x}}",1,"(-2*Sqrt[d]*E^((2*b*(c + d*x))/d) - Sqrt[d]*Cosh[2*a]*Cosh[(2*b*c)/d] - Sqrt[d]*E^((4*b*(c + d*x))/d)*Cosh[2*a]*Cosh[(2*b*c)/d] + Sqrt[d]*Cosh[(2*b*c)/d]*Sinh[2*a] - Sqrt[d]*E^((4*b*(c + d*x))/d)*Cosh[(2*b*c)/d]*Sinh[2*a] + Sqrt[2]*Sqrt[d]*E^((2*b*(c + d*x))/d)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] + Cosh[(2*b*c)/d]*Sinh[2*a]) - Sqrt[d]*Cosh[2*a]*Sinh[(2*b*c)/d] + Sqrt[d]*E^((4*b*(c + d*x))/d)*Cosh[2*a]*Sinh[(2*b*c)/d] - Sqrt[b]*E^((2*b*(c + d*x))/d)*Sqrt[2*Pi]*Sqrt[c + d*x]*Cosh[2*a]*Erf[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]*Sinh[(2*b*c)/d] - Sqrt[b]*E^((2*b*(c + d*x))/d)*Sqrt[2*Pi]*Sqrt[c + d*x]*Cosh[2*a]*Erfi[(Sqrt[2]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]*Sinh[(2*b*c)/d] + Sqrt[d]*Sinh[2*a]*Sinh[(2*b*c)/d] + Sqrt[d]*E^((4*b*(c + d*x))/d)*Sinh[2*a]*Sinh[(2*b*c)/d] + Sqrt[2]*Sqrt[d]*E^((2*b*(c + d*x))/d)*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (2*b*(c + d*x))/d]*(Cosh[2*a]*Cosh[(2*b*c)/d] - Sinh[2*a]*(Cosh[(2*b*c)/d] + Sinh[(2*b*c)/d])))/(2*d^(3/2)*E^((2*b*(c + d*x))/d)*Sqrt[c + d*x])","B",1
53,1,156,174,1.3831067,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^{5/2}} \, dx","Integrate[Cosh[a + b*x]^2/(c + d*x)^(5/2),x]","-\frac{2 e^{-2 \left(a+\frac{b c}{d}\right)} \left(\sqrt{2} e^{4 a} d \left(-\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{2 b (c+d x)}{d}\right)+e^{2 \left(a+\frac{b c}{d}\right)} \left(2 b (c+d x) \sinh (2 (a+b x))+d \cosh ^2(a+b x)\right)+\sqrt{2} d e^{\frac{4 b c}{d}} \left(\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{2 b (c+d x)}{d}\right)\right)}{3 d^2 (c+d x)^{3/2}}","\frac{2 \sqrt{2 \pi } b^{3/2} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{3 d^{5/2}}+\frac{2 \sqrt{2 \pi } b^{3/2} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{8 b \sinh (a+b x) \cosh (a+b x)}{3 d^2 \sqrt{c+d x}}-\frac{2 \cosh ^2(a+b x)}{3 d (c+d x)^{3/2}}",1,"(-2*(Sqrt[2]*d*E^(4*a)*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, (-2*b*(c + d*x))/d] + Sqrt[2]*d*E^((4*b*c)/d)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (2*b*(c + d*x))/d] + E^(2*(a + (b*c)/d))*(d*Cosh[a + b*x]^2 + 2*b*(c + d*x)*Sinh[2*(a + b*x)])))/(3*d^2*E^(2*(a + (b*c)/d))*(c + d*x)^(3/2))","A",1
54,1,825,220,3.1709629,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^{7/2}} \, dx","Integrate[Cosh[a + b*x]^2/(c + d*x)^(7/2),x]","\frac{e^{-\frac{2 b (c+d x)}{d}} \left(16 \sqrt{2} d^2 e^{\frac{2 b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{2 b (c+d x)}{d}\right) \left(\cosh \left(2 a-\frac{2 b c}{d}\right)+\sinh \left(2 a-\frac{2 b c}{d}\right)\right) \left(-\frac{b (c+d x)}{d}\right)^{5/2}-6 d^2 e^{\frac{2 b (c+d x)}{d}}-16 b^2 c^2 e^{\frac{4 b (c+d x)}{d}} \cosh \left(2 a-\frac{2 b c}{d}\right)-3 d^2 e^{\frac{4 b (c+d x)}{d}} \cosh \left(2 a-\frac{2 b c}{d}\right)-4 b c d e^{\frac{4 b (c+d x)}{d}} \cosh \left(2 a-\frac{2 b c}{d}\right)-16 b^2 c^2 \cosh \left(2 a-\frac{2 b c}{d}\right)-3 d^2 \cosh \left(2 a-\frac{2 b c}{d}\right)-16 b^2 d^2 e^{\frac{4 b (c+d x)}{d}} x^2 \cosh \left(2 a-\frac{2 b c}{d}\right)-16 b^2 d^2 x^2 \cosh \left(2 a-\frac{2 b c}{d}\right)+4 b c d \cosh \left(2 a-\frac{2 b c}{d}\right)-4 b d^2 e^{\frac{4 b (c+d x)}{d}} x \cosh \left(2 a-\frac{2 b c}{d}\right)-32 b^2 c d e^{\frac{4 b (c+d x)}{d}} x \cosh \left(2 a-\frac{2 b c}{d}\right)+4 b d^2 x \cosh \left(2 a-\frac{2 b c}{d}\right)-32 b^2 c d x \cosh \left(2 a-\frac{2 b c}{d}\right)+16 \sqrt{2} d^2 e^{\frac{2 b (c+d x)}{d}} \left(\frac{b (c+d x)}{d}\right)^{5/2} \Gamma \left(\frac{1}{2},\frac{2 b (c+d x)}{d}\right) \left(\cosh \left(2 a-\frac{2 b c}{d}\right)-\sinh \left(2 a-\frac{2 b c}{d}\right)\right)-16 b^2 c^2 e^{\frac{4 b (c+d x)}{d}} \sinh \left(2 a-\frac{2 b c}{d}\right)-3 d^2 e^{\frac{4 b (c+d x)}{d}} \sinh \left(2 a-\frac{2 b c}{d}\right)-4 b c d e^{\frac{4 b (c+d x)}{d}} \sinh \left(2 a-\frac{2 b c}{d}\right)+16 b^2 c^2 \sinh \left(2 a-\frac{2 b c}{d}\right)+3 d^2 \sinh \left(2 a-\frac{2 b c}{d}\right)-16 b^2 d^2 e^{\frac{4 b (c+d x)}{d}} x^2 \sinh \left(2 a-\frac{2 b c}{d}\right)+16 b^2 d^2 x^2 \sinh \left(2 a-\frac{2 b c}{d}\right)-4 b c d \sinh \left(2 a-\frac{2 b c}{d}\right)-4 b d^2 e^{\frac{4 b (c+d x)}{d}} x \sinh \left(2 a-\frac{2 b c}{d}\right)-32 b^2 c d e^{\frac{4 b (c+d x)}{d}} x \sinh \left(2 a-\frac{2 b c}{d}\right)-4 b d^2 x \sinh \left(2 a-\frac{2 b c}{d}\right)+32 b^2 c d x \sinh \left(2 a-\frac{2 b c}{d}\right)\right)}{30 d^3 (c+d x)^{5/2}}","-\frac{8 \sqrt{2 \pi } b^{5/2} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}+\frac{8 \sqrt{2 \pi } b^{5/2} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{15 d^{7/2}}-\frac{32 b^2 \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,"(-6*d^2*E^((2*b*(c + d*x))/d) - 16*b^2*c^2*Cosh[2*a - (2*b*c)/d] + 4*b*c*d*Cosh[2*a - (2*b*c)/d] - 3*d^2*Cosh[2*a - (2*b*c)/d] - 16*b^2*c^2*E^((4*b*(c + d*x))/d)*Cosh[2*a - (2*b*c)/d] - 4*b*c*d*E^((4*b*(c + d*x))/d)*Cosh[2*a - (2*b*c)/d] - 3*d^2*E^((4*b*(c + d*x))/d)*Cosh[2*a - (2*b*c)/d] - 32*b^2*c*d*x*Cosh[2*a - (2*b*c)/d] + 4*b*d^2*x*Cosh[2*a - (2*b*c)/d] - 32*b^2*c*d*E^((4*b*(c + d*x))/d)*x*Cosh[2*a - (2*b*c)/d] - 4*b*d^2*E^((4*b*(c + d*x))/d)*x*Cosh[2*a - (2*b*c)/d] - 16*b^2*d^2*x^2*Cosh[2*a - (2*b*c)/d] - 16*b^2*d^2*E^((4*b*(c + d*x))/d)*x^2*Cosh[2*a - (2*b*c)/d] + 16*Sqrt[2]*d^2*E^((2*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] - Sinh[2*a - (2*b*c)/d]) + 16*b^2*c^2*Sinh[2*a - (2*b*c)/d] - 4*b*c*d*Sinh[2*a - (2*b*c)/d] + 3*d^2*Sinh[2*a - (2*b*c)/d] - 16*b^2*c^2*E^((4*b*(c + d*x))/d)*Sinh[2*a - (2*b*c)/d] - 4*b*c*d*E^((4*b*(c + d*x))/d)*Sinh[2*a - (2*b*c)/d] - 3*d^2*E^((4*b*(c + d*x))/d)*Sinh[2*a - (2*b*c)/d] + 32*b^2*c*d*x*Sinh[2*a - (2*b*c)/d] - 4*b*d^2*x*Sinh[2*a - (2*b*c)/d] - 32*b^2*c*d*E^((4*b*(c + d*x))/d)*x*Sinh[2*a - (2*b*c)/d] - 4*b*d^2*E^((4*b*(c + d*x))/d)*x*Sinh[2*a - (2*b*c)/d] + 16*b^2*d^2*x^2*Sinh[2*a - (2*b*c)/d] - 16*b^2*d^2*E^((4*b*(c + d*x))/d)*x^2*Sinh[2*a - (2*b*c)/d] + 16*Sqrt[2]*d^2*E^((2*b*(c + d*x))/d)*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-2*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]))/(30*d^3*E^((2*b*(c + d*x))/d)*(c + d*x)^(5/2))","B",1
55,1,222,251,0.8535707,"\int \frac{\cosh ^2(a+b x)}{(c+d x)^{9/2}} \, dx","Integrate[Cosh[a + b*x]^2/(c + d*x)^(9/2),x]","\frac{2 \left(-32 b^3 (c+d x)^3 \sinh (2 (a+b x))+16 \sqrt{2} b^3 (c+d x)^3 e^{2 a-\frac{2 b c}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{2 b (c+d x)}{d}\right)-16 \sqrt{2} b^3 (c+d x)^3 e^{\frac{2 b c}{d}-2 a} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},\frac{2 b (c+d x)}{d}\right)-16 b^2 d (c+d x)^2 \cosh ^2(a+b x)-6 b d^2 (c+d x) \sinh (2 (a+b x))-15 d^3 \cosh ^2(a+b x)+8 b^2 d (c+d x)^2\right)}{105 d^4 (c+d x)^{7/2}}","\frac{32 \sqrt{2 \pi } b^{7/2} e^{\frac{2 b c}{d}-2 a} \text{erf}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{105 d^{9/2}}+\frac{32 \sqrt{2 \pi } b^{7/2} e^{2 a-\frac{2 b c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{105 d^{9/2}}-\frac{128 b^3 \sinh (a+b x) \cosh (a+b x)}{105 d^4 \sqrt{c+d x}}-\frac{32 b^2 \cosh ^2(a+b x)}{105 d^3 (c+d x)^{3/2}}-\frac{8 b \sinh (a+b x) \cosh (a+b x)}{35 d^2 (c+d x)^{5/2}}-\frac{2 \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,"(2*(8*b^2*d*(c + d*x)^2 - 15*d^3*Cosh[a + b*x]^2 - 16*b^2*d*(c + d*x)^2*Cosh[a + b*x]^2 + 16*Sqrt[2]*b^3*E^(2*a - (2*b*c)/d)*(c + d*x)^3*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-2*b*(c + d*x))/d] - 16*Sqrt[2]*b^3*E^(-2*a + (2*b*c)/d)*(c + d*x)^3*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (2*b*(c + d*x))/d] - 6*b*d^2*(c + d*x)*Sinh[2*(a + b*x)] - 32*b^3*(c + d*x)^3*Sinh[2*(a + b*x)]))/(105*d^4*(c + d*x)^(7/2))","A",1
56,1,243,381,3.9998202,"\int (c+d x)^{5/2} \cosh ^3(a+b x) \, dx","Integrate[(c + d*x)^(5/2)*Cosh[a + b*x]^3,x]","-\frac{d^3 \left(\sqrt{3} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{7}{2},-\frac{3 b (c+d x)}{d}\right) \left(\sinh \left(3 a-\frac{3 b c}{d}\right)+\cosh \left(3 a-\frac{3 b c}{d}\right)\right)+\left(\cosh \left(a-\frac{b c}{d}\right)-\sinh \left(a-\frac{b c}{d}\right)\right) \left(\sqrt{\frac{b (c+d x)}{d}} \left(\sqrt{3} \Gamma \left(\frac{7}{2},\frac{3 b (c+d x)}{d}\right) \left(\cosh \left(2 a-\frac{2 b c}{d}\right)-\sinh \left(2 a-\frac{2 b c}{d}\right)\right)+243 \Gamma \left(\frac{7}{2},\frac{b (c+d x)}{d}\right)\right)+243 \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{7}{2},-\frac{b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)+\cosh \left(2 a-\frac{2 b c}{d}\right)\right)\right)\right)}{648 b^4 \sqrt{c+d x}}","\frac{45 \sqrt{\pi } d^{5/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{7/2}}+\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{576 b^{7/2}}-\frac{45 \sqrt{\pi } d^{5/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{64 b^{7/2}}-\frac{5 \sqrt{\frac{\pi }{3}} d^{5/2} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{576 b^{7/2}}+\frac{45 d^2 \sqrt{c+d x} \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,"-1/648*(d^3*(Sqrt[3]*Sqrt[-((b*(c + d*x))/d)]*Gamma[7/2, (-3*b*(c + d*x))/d]*(Cosh[3*a - (3*b*c)/d] + Sinh[3*a - (3*b*c)/d]) + (Sqrt[(b*(c + d*x))/d]*(243*Gamma[7/2, (b*(c + d*x))/d] + Sqrt[3]*Gamma[7/2, (3*b*(c + d*x))/d]*(Cosh[2*a - (2*b*c)/d] - Sinh[2*a - (2*b*c)/d])) + 243*Sqrt[-((b*(c + d*x))/d)]*Gamma[7/2, -((b*(c + d*x))/d)]*(Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]))*(Cosh[a - (b*c)/d] - Sinh[a - (b*c)/d])))/(b^4*Sqrt[c + d*x])","A",1
57,1,243,326,2.0051152,"\int (c+d x)^{3/2} \cosh ^3(a+b x) \, dx","Integrate[(c + d*x)^(3/2)*Cosh[a + b*x]^3,x]","\frac{d^2 \left(\sqrt{3} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{5}{2},-\frac{3 b (c+d x)}{d}\right) \left(\sinh \left(3 a-\frac{3 b c}{d}\right)+\cosh \left(3 a-\frac{3 b c}{d}\right)\right)+\left(\cosh \left(a-\frac{b c}{d}\right)-\sinh \left(a-\frac{b c}{d}\right)\right) \left(81 \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{5}{2},-\frac{b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)+\cosh \left(2 a-\frac{2 b c}{d}\right)\right)+\sqrt{\frac{b (c+d x)}{d}} \left(\sqrt{3} \Gamma \left(\frac{5}{2},\frac{3 b (c+d x)}{d}\right) \left(\sinh \left(2 a-\frac{2 b c}{d}\right)-\cosh \left(2 a-\frac{2 b c}{d}\right)\right)-81 \Gamma \left(\frac{5}{2},\frac{b (c+d x)}{d}\right)\right)\right)\right)}{216 b^3 \sqrt{c+d x}}","\frac{9 \sqrt{\pi } d^{3/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{32 b^{5/2}}+\frac{\sqrt{\frac{\pi }{3}} d^{3/2} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{96 b^{5/2}}+\frac{9 \sqrt{\pi } d^{3/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{32 b^{5/2}}+\frac{\sqrt{\frac{\pi }{3}} d^{3/2} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{96 b^{5/2}}-\frac{d \sqrt{c+d x} \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^2*(Sqrt[3]*Sqrt[-((b*(c + d*x))/d)]*Gamma[5/2, (-3*b*(c + d*x))/d]*(Cosh[3*a - (3*b*c)/d] + Sinh[3*a - (3*b*c)/d]) + (81*Sqrt[-((b*(c + d*x))/d)]*Gamma[5/2, -((b*(c + d*x))/d)]*(Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d]) + Sqrt[(b*(c + d*x))/d]*(-81*Gamma[5/2, (b*(c + d*x))/d] + Sqrt[3]*Gamma[5/2, (3*b*(c + d*x))/d]*(-Cosh[2*a - (2*b*c)/d] + Sinh[2*a - (2*b*c)/d])))*(Cosh[a - (b*c)/d] - Sinh[a - (b*c)/d])))/(216*b^3*Sqrt[c + d*x])","A",1
58,1,210,275,0.2945343,"\int \sqrt{c+d x} \cosh ^3(a+b x) \, dx","Integrate[Sqrt[c + d*x]*Cosh[a + b*x]^3,x]","\frac{\sqrt{c+d x} e^{-3 \left(a+\frac{b c}{d}\right)} \left(\sqrt{3} e^{6 a} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{3}{2},-\frac{3 b (c+d x)}{d}\right)+27 e^{4 a+\frac{2 b c}{d}} \sqrt{\frac{b (c+d x)}{d}} \Gamma \left(\frac{3}{2},-\frac{b (c+d x)}{d}\right)-e^{\frac{4 b c}{d}} \sqrt{-\frac{b (c+d x)}{d}} \left(27 e^{2 a} \Gamma \left(\frac{3}{2},\frac{b (c+d x)}{d}\right)+\sqrt{3} e^{\frac{2 b c}{d}} \Gamma \left(\frac{3}{2},\frac{3 b (c+d x)}{d}\right)\right)\right)}{72 b \sqrt{-\frac{b^2 (c+d x)^2}{d^2}}}","\frac{3 \sqrt{\pi } \sqrt{d} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{3/2}}+\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{48 b^{3/2}}-\frac{3 \sqrt{\pi } \sqrt{d} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{16 b^{3/2}}-\frac{\sqrt{\frac{\pi }{3}} \sqrt{d} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{48 b^{3/2}}+\frac{3 \sqrt{c+d x} \sinh (a+b x)}{4 b}+\frac{\sqrt{c+d x} \sinh (3 a+3 b x)}{12 b}",1,"(Sqrt[c + d*x]*(Sqrt[3]*E^(6*a)*Sqrt[(b*(c + d*x))/d]*Gamma[3/2, (-3*b*(c + d*x))/d] + 27*E^(4*a + (2*b*c)/d)*Sqrt[(b*(c + d*x))/d]*Gamma[3/2, -((b*(c + d*x))/d)] - E^((4*b*c)/d)*Sqrt[-((b*(c + d*x))/d)]*(27*E^(2*a)*Gamma[3/2, (b*(c + d*x))/d] + Sqrt[3]*E^((2*b*c)/d)*Gamma[3/2, (3*b*(c + d*x))/d])))/(72*b*E^(3*(a + (b*c)/d))*Sqrt[-((b^2*(c + d*x)^2)/d^2)])","A",1
59,1,192,228,0.2035997,"\int \frac{\cosh ^3(a+b x)}{\sqrt{c+d x}} \, dx","Integrate[Cosh[a + b*x]^3/Sqrt[c + d*x],x]","\frac{e^{-3 \left(a+\frac{b c}{d}\right)} \left(\sqrt{3} e^{6 a} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{3 b (c+d x)}{d}\right)+9 e^{4 a+\frac{2 b c}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)-e^{\frac{4 b c}{d}} \sqrt{\frac{b (c+d x)}{d}} \left(9 e^{2 a} \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)+\sqrt{3} e^{\frac{2 b c}{d}} \Gamma \left(\frac{1}{2},\frac{3 b (c+d x)}{d}\right)\right)\right)}{24 b \sqrt{c+d x}}","\frac{3 \sqrt{\pi } e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 \sqrt{b} \sqrt{d}}+\frac{\sqrt{\frac{\pi }{3}} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 \sqrt{b} \sqrt{d}}+\frac{3 \sqrt{\pi } e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 \sqrt{b} \sqrt{d}}+\frac{\sqrt{\frac{\pi }{3}} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{8 \sqrt{b} \sqrt{d}}",1,"(Sqrt[3]*E^(6*a)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, (-3*b*(c + d*x))/d] + 9*E^(4*a + (2*b*c)/d)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)] - E^((4*b*c)/d)*Sqrt[(b*(c + d*x))/d]*(9*E^(2*a)*Gamma[1/2, (b*(c + d*x))/d] + Sqrt[3]*E^((2*b*c)/d)*Gamma[1/2, (3*b*(c + d*x))/d]))/(24*b*E^(3*(a + (b*c)/d))*Sqrt[c + d*x])","A",1
60,1,717,246,2.8860678,"\int \frac{\cosh ^3(a+b x)}{(c+d x)^{3/2}} \, dx","Integrate[Cosh[a + b*x]^3/(c + d*x)^(3/2),x]","\frac{e^{-\frac{3 b (c+d x)}{d}} \left(\sqrt{3 \pi } \sqrt{b} \sqrt{c+d x} e^{\frac{3 b (c+d x)}{d}} \sinh \left(3 a-\frac{3 b c}{d}\right) \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)+\sqrt{3 \pi } \sqrt{b} \sqrt{c+d x} e^{\frac{3 b (c+d x)}{d}} \sinh \left(3 a-\frac{3 b c}{d}\right) \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)-\sqrt{d} e^{\frac{6 b (c+d x)}{d}} \sinh \left(3 a-\frac{3 b c}{d}\right)+3 \sqrt{d} e^{\frac{2 b (c+d x)}{d}} \sinh \left(a-\frac{b c}{d}\right)-3 \sqrt{d} e^{\frac{4 b (c+d x)}{d}} \sinh \left(a-\frac{b c}{d}\right)-\sqrt{d} e^{\frac{6 b (c+d x)}{d}} \cosh \left(3 a-\frac{3 b c}{d}\right)-3 \sqrt{d} e^{\frac{2 b (c+d x)}{d}} \cosh \left(a-\frac{b c}{d}\right)-3 \sqrt{d} e^{\frac{4 b (c+d x)}{d}} \cosh \left(a-\frac{b c}{d}\right)+\sqrt{3} \sqrt{d} e^{\frac{3 b (c+d x)}{d}} \sqrt{-\frac{b (c+d x)}{d}} \cosh \left(3 a-\frac{3 b c}{d}\right) \Gamma \left(\frac{1}{2},-\frac{3 b (c+d x)}{d}\right)+\sqrt{3} \sqrt{d} e^{\frac{3 b (c+d x)}{d}} \sqrt{\frac{b (c+d x)}{d}} \cosh \left(3 a-\frac{3 b c}{d}\right) \Gamma \left(\frac{1}{2},\frac{3 b (c+d x)}{d}\right)+3 \sqrt{d} e^{\frac{3 b (c+d x)}{d}} \sqrt{\frac{b (c+d x)}{d}} \cosh \left(a-\frac{b c}{d}\right) \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)-3 \sqrt{d} e^{\frac{3 b (c+d x)}{d}} \sqrt{\frac{b (c+d x)}{d}} \sinh \left(a-\frac{b c}{d}\right) \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)+3 \sqrt{d} e^{\frac{3 b (c+d x)}{d}} \sqrt{-\frac{b (c+d x)}{d}} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right) \left(\sinh \left(a-\frac{b c}{d}\right)+\cosh \left(a-\frac{b c}{d}\right)\right)+\sqrt{d} \sinh \left(3 a-\frac{3 b c}{d}\right)-\sqrt{d} \cosh \left(3 a-\frac{3 b c}{d}\right)\right)}{4 d^{3/2} \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,"(-(Sqrt[d]*Cosh[3*a - (3*b*c)/d]) - Sqrt[d]*E^((6*b*(c + d*x))/d)*Cosh[3*a - (3*b*c)/d] - 3*Sqrt[d]*E^((2*b*(c + d*x))/d)*Cosh[a - (b*c)/d] - 3*Sqrt[d]*E^((4*b*(c + d*x))/d)*Cosh[a - (b*c)/d] + Sqrt[3]*Sqrt[d]*E^((3*b*(c + d*x))/d)*Sqrt[-((b*(c + d*x))/d)]*Cosh[3*a - (3*b*c)/d]*Gamma[1/2, (-3*b*(c + d*x))/d] + 3*Sqrt[d]*E^((3*b*(c + d*x))/d)*Sqrt[(b*(c + d*x))/d]*Cosh[a - (b*c)/d]*Gamma[1/2, (b*(c + d*x))/d] + Sqrt[3]*Sqrt[d]*E^((3*b*(c + d*x))/d)*Sqrt[(b*(c + d*x))/d]*Cosh[3*a - (3*b*c)/d]*Gamma[1/2, (3*b*(c + d*x))/d] + Sqrt[d]*Sinh[3*a - (3*b*c)/d] - Sqrt[d]*E^((6*b*(c + d*x))/d)*Sinh[3*a - (3*b*c)/d] + Sqrt[b]*E^((3*b*(c + d*x))/d)*Sqrt[3*Pi]*Sqrt[c + d*x]*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]*Sinh[3*a - (3*b*c)/d] + Sqrt[b]*E^((3*b*(c + d*x))/d)*Sqrt[3*Pi]*Sqrt[c + d*x]*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]]*Sinh[3*a - (3*b*c)/d] + 3*Sqrt[d]*E^((2*b*(c + d*x))/d)*Sinh[a - (b*c)/d] - 3*Sqrt[d]*E^((4*b*(c + d*x))/d)*Sinh[a - (b*c)/d] - 3*Sqrt[d]*E^((3*b*(c + d*x))/d)*Sqrt[(b*(c + d*x))/d]*Gamma[1/2, (b*(c + d*x))/d]*Sinh[a - (b*c)/d] + 3*Sqrt[d]*E^((3*b*(c + d*x))/d)*Sqrt[-((b*(c + d*x))/d)]*Gamma[1/2, -((b*(c + d*x))/d)]*(Cosh[a - (b*c)/d] + Sinh[a - (b*c)/d]))/(4*d^(3/2)*E^((3*b*(c + d*x))/d)*Sqrt[c + d*x])","B",1
61,1,253,277,2.9090494,"\int \frac{\cosh ^3(a+b x)}{(c+d x)^{5/2}} \, dx","Integrate[Cosh[a + b*x]^3/(c + d*x)^(5/2),x]","\frac{e^{-3 \left(a+\frac{b c}{d}\right)} \left(-3 \sqrt{3} e^{6 a} d \left(-\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{3 b (c+d x)}{d}\right)-3 d e^{4 a+\frac{2 b c}{d}} \left(-\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{b (c+d x)}{d}\right)-3 d e^{2 a+\frac{4 b c}{d}} \left(\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{b (c+d x)}{d}\right)-4 e^{3 \left(a+\frac{b c}{d}\right)} \cosh ^2(a+b x) (6 b (c+d x) \sinh (a+b x)+d \cosh (a+b x))-3 \sqrt{3} d e^{\frac{6 b c}{d}} \left(\frac{b (c+d x)}{d}\right)^{3/2} \Gamma \left(\frac{1}{2},\frac{3 b (c+d x)}{d}\right)\right)}{6 d^2 (c+d x)^{3/2}}","\frac{\sqrt{\pi } b^{3/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 d^{5/2}}+\frac{\sqrt{3 \pi } b^{3/2} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 d^{5/2}}+\frac{\sqrt{\pi } b^{3/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 d^{5/2}}+\frac{\sqrt{3 \pi } b^{3/2} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{2 d^{5/2}}-\frac{4 b \sinh (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,"(-3*Sqrt[3]*d*E^(6*a)*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, (-3*b*(c + d*x))/d] - 3*d*E^(4*a + (2*b*c)/d)*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, -((b*(c + d*x))/d)] - 3*d*E^(2*a + (4*b*c)/d)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d] - 3*Sqrt[3]*d*E^((6*b*c)/d)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (3*b*(c + d*x))/d] - 4*E^(3*(a + (b*c)/d))*Cosh[a + b*x]^2*(d*Cosh[a + b*x] + 6*b*(c + d*x)*Sinh[a + b*x]))/(6*d^2*E^(3*(a + (b*c)/d))*(c + d*x)^(3/2))","A",1
62,1,3211,331,6.3466282,"\int \frac{\cosh ^3(a+b x)}{(c+d x)^{7/2}} \, dx","Integrate[Cosh[a + b*x]^3/(c + d*x)^(7/2),x]","\text{Result too large to show}","-\frac{\sqrt{\pi } b^{5/2} e^{\frac{b c}{d}-a} \text{erf}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{3 \sqrt{3 \pi } b^{5/2} e^{\frac{3 b c}{d}-3 a} \text{erf}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{\sqrt{\pi } b^{5/2} e^{a-\frac{b c}{d}} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}+\frac{3 \sqrt{3 \pi } b^{5/2} e^{3 a-\frac{3 b c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{b} \sqrt{c+d x}}{\sqrt{d}}\right)}{5 d^{7/2}}-\frac{24 b^2 \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,"(3*(Sinh[a]*(-1/30*((-2*E^((b*(c + d*x))/d)*(3*d^2 + 2*b*d*(c + d*x) + 4*b^2*(c + d*x)^2) + 8*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, -((b*(c + d*x))/d)] + (-6*d^2 + 4*b*d*(c + d*x) - 8*b^2*(c + d*x)^2 + 8*b*d*E^((b*(c + d*x))/d)*(c + d*x)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d])/E^((b*(c + d*x))/d))*Sinh[(b*c)/d])/(d^3*(c + d*x)^(5/2)) + (2*Cosh[(b*c)/d]*(-1/2*(b*(c + d*x)*(2*E^((b*(c + d*x))/d)*(d + 2*b*(c + d*x)) + 4*d*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, -((b*(c + d*x))/d)] + (2*(d - 2*b*(c + d*x) + 2*d*E^((b*(c + d*x))/d)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d]))/E^((b*(c + d*x))/d))) - 3*d^2*Sinh[(b*(c + d*x))/d]))/(15*d^3*(c + d*x)^(5/2))) + Cosh[a]*((Cosh[(b*c)/d]*(-2*E^((b*(c + d*x))/d)*(3*d^2 + 2*b*d*(c + d*x) + 4*b^2*(c + d*x)^2) + 8*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, -((b*(c + d*x))/d)] + (-6*d^2 + 4*b*d*(c + d*x) - 8*b^2*(c + d*x)^2 + 8*b*d*E^((b*(c + d*x))/d)*(c + d*x)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d])/E^((b*(c + d*x))/d)))/(30*d^3*(c + d*x)^(5/2)) - (2*Sinh[(b*c)/d]*(-1/2*(b*(c + d*x)*(2*E^((b*(c + d*x))/d)*(d + 2*b*(c + d*x)) + 4*d*(-((b*(c + d*x))/d))^(3/2)*Gamma[1/2, -((b*(c + d*x))/d)] + (2*(d - 2*b*(c + d*x) + 2*d*E^((b*(c + d*x))/d)*((b*(c + d*x))/d)^(3/2)*Gamma[1/2, (b*(c + d*x))/d]))/E^((b*(c + d*x))/d))) - 3*d^2*Sinh[(b*(c + d*x))/d]))/(15*d^3*(c + d*x)^(5/2)))))/4 + (Sinh[3*a]*(-1/10*((1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d))*Sinh[(b*c)/d])/(d^3*(c + d*x)^(5/2)) - (2*Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2))) + Cosh[3*a]*((Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d)))/(10*d^3*(c + d*x)^(5/2)) + (2*(1 + 2*Cosh[(2*b*c)/d])*Sinh[(b*c)/d]*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2))))/4 + (-(Cosh[3*a]*(-1/10*((1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d))*Sinh[(b*c)/d])/(d^3*(c + d*x)^(5/2)) - (2*Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2)))) - Sinh[3*a]*((Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d)))/(10*d^3*(c + d*x)^(5/2)) + (2*(1 + 2*Cosh[(2*b*c)/d])*Sinh[(b*c)/d]*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2))))/8 + (Cosh[3*a]*(-1/10*((1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d))*Sinh[(b*c)/d])/(d^3*(c + d*x)^(5/2)) - (2*Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2))) + Sinh[3*a]*((Cosh[(b*c)/d]*(-1 + 2*Cosh[(2*b*c)/d])*(-2*E^((3*b*(c + d*x))/d)*(d^2 + 2*b*d*(c + d*x) + 12*b^2*(c + d*x)^2) + 24*Sqrt[3]*d^2*(-((b*(c + d*x))/d))^(5/2)*Gamma[1/2, (-3*b*(c + d*x))/d] + (-2*d^2 + 4*b*d*(c + d*x) - 24*b^2*(c + d*x)^2 + 24*Sqrt[3]*d^2*E^((3*b*(c + d*x))/d)*((b*(c + d*x))/d)^(5/2)*Gamma[1/2, (3*b*(c + d*x))/d])/E^((3*b*(c + d*x))/d)))/(10*d^3*(c + d*x)^(5/2)) + (2*(1 + 2*Cosh[(2*b*c)/d])*Sinh[(b*c)/d]*(-6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erf[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] - 6*b^(5/2)*Sqrt[3*Pi]*(c + d*x)^(5/2)*Erfi[(Sqrt[3]*Sqrt[b]*Sqrt[c + d*x])/Sqrt[d]] + Sqrt[d]*(2*b*d*(c + d*x)*Cosh[(3*b*(c + d*x))/d] + (d^2 + 12*b^2*(c + d*x)^2)*Sinh[(3*b*(c + d*x))/d])))/(5*d^(7/2)*(c + d*x)^(5/2))))/8","B",1
63,1,51,111,0.0141224,"\int (d x)^{3/2} \cosh (f x) \, dx","Integrate[(d*x)^(3/2)*Cosh[f*x],x]","\frac{d^2 \left(\sqrt{-f x} \Gamma \left(\frac{5}{2},-f x\right)-\sqrt{f x} \Gamma \left(\frac{5}{2},f x\right)\right)}{2 f^3 \sqrt{d x}}","\frac{3 \sqrt{\pi } d^{3/2} \text{erf}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{8 f^{5/2}}+\frac{3 \sqrt{\pi } d^{3/2} \text{erfi}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{8 f^{5/2}}-\frac{3 d \sqrt{d x} \cosh (f x)}{2 f^2}+\frac{(d x)^{3/2} \sinh (f x)}{f}",1,"(d^2*(Sqrt[-(f*x)]*Gamma[5/2, -(f*x)] - Sqrt[f*x]*Gamma[5/2, f*x]))/(2*f^3*Sqrt[d*x])","A",1
64,1,48,92,0.0126371,"\int \sqrt{d x} \cosh (f x) \, dx","Integrate[Sqrt[d*x]*Cosh[f*x],x]","-\frac{d \left(\sqrt{-f x} \Gamma \left(\frac{3}{2},-f x\right)+\sqrt{f x} \Gamma \left(\frac{3}{2},f x\right)\right)}{2 f^2 \sqrt{d x}}","\frac{\sqrt{\pi } \sqrt{d} \text{erf}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{4 f^{3/2}}-\frac{\sqrt{\pi } \sqrt{d} \text{erfi}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{4 f^{3/2}}+\frac{\sqrt{d x} \sinh (f x)}{f}",1,"-1/2*(d*(Sqrt[-(f*x)]*Gamma[3/2, -(f*x)] + Sqrt[f*x]*Gamma[3/2, f*x]))/(f^2*Sqrt[d*x])","A",1
65,1,48,77,0.0084569,"\int \frac{\cosh (f x)}{\sqrt{d x}} \, dx","Integrate[Cosh[f*x]/Sqrt[d*x],x]","\frac{\sqrt{-f x} \Gamma \left(\frac{1}{2},-f x\right)-\sqrt{f x} \Gamma \left(\frac{1}{2},f x\right)}{2 f \sqrt{d x}}","\frac{\sqrt{\pi } \text{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[-(f*x)]*Gamma[1/2, -(f*x)] - Sqrt[f*x]*Gamma[1/2, f*x])/(2*f*Sqrt[d*x])","A",1
66,1,67,88,0.0366012,"\int \frac{\cosh (f x)}{(d x)^{3/2}} \, dx","Integrate[Cosh[f*x]/(d*x)^(3/2),x]","\frac{x e^{-f x} \left(-e^{2 f x}+e^{f x} \sqrt{-f x} \Gamma \left(\frac{1}{2},-f x\right)+e^{f x} \sqrt{f x} \Gamma \left(\frac{1}{2},f x\right)-1\right)}{(d x)^{3/2}}","-\frac{\sqrt{\pi } \sqrt{f} \text{erf}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{\sqrt{\pi } \sqrt{f} \text{erfi}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \cosh (f x)}{d \sqrt{d x}}",1,"(x*(-1 - E^(2*f*x) + E^(f*x)*Sqrt[-(f*x)]*Gamma[1/2, -(f*x)] + E^(f*x)*Sqrt[f*x]*Gamma[1/2, f*x]))/(E^(f*x)*(d*x)^(3/2))","A",1
67,1,78,114,0.0993053,"\int \frac{\cosh (f x)}{(d x)^{5/2}} \, dx","Integrate[Cosh[f*x]/(d*x)^(5/2),x]","\frac{x \left(-2 e^{f x} (2 f x+1)-4 (-f x)^{3/2} \Gamma \left(\frac{1}{2},-f x\right)+e^{-f x} \left(4 f x-4 e^{f x} (f x)^{3/2} \Gamma \left(\frac{1}{2},f x\right)-2\right)\right)}{6 (d x)^{5/2}}","\frac{2 \sqrt{\pi } f^{3/2} \text{erf}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}+\frac{2 \sqrt{\pi } f^{3/2} \text{erfi}\left(\frac{\sqrt{f} \sqrt{d x}}{\sqrt{d}}\right)}{3 d^{5/2}}-\frac{4 f \sinh (f x)}{3 d^2 \sqrt{d x}}-\frac{2 \cosh (f x)}{3 d (d x)^{3/2}}",1,"(x*(-2*E^(f*x)*(1 + 2*f*x) - 4*(-(f*x))^(3/2)*Gamma[1/2, -(f*x)] + (-2 + 4*f*x - 4*E^(f*x)*(f*x)^(3/2)*Gamma[1/2, f*x])/E^(f*x)))/(6*(d*x)^(5/2))","A",1
68,0,0,19,11.3837459,"\int \sqrt{c+d x} \text{sech}(a+b x) \, dx","Integrate[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,"Integrate[Sqrt[c + d*x]*Sech[a + b*x], x]","A",-1
69,0,0,19,9.8883,"\int \frac{\text{sech}(a+b x)}{\sqrt{c+d x}} \, dx","Integrate[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,"Integrate[Sech[a + b*x]/Sqrt[c + d*x], x]","A",-1
70,0,0,63,4.0909827,"\int \frac{\cosh ^{\frac{3}{2}}(x)}{x^3} \, dx","Integrate[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,"Integrate[Cosh[x]^(3/2)/x^3, x]","A",-1
71,1,46,20,0.3878637,"\int \left(\frac{x}{\cosh ^{\frac{3}{2}}(x)}+x \sqrt{\cosh (x)}\right) \, dx","Integrate[x/Cosh[x]^(3/2) + x*Sqrt[Cosh[x]],x]","\frac{2 \sinh (x) \left(x-\frac{2 \sinh (x) \cosh (x) \sqrt{\tanh ^2\left(\frac{x}{2}\right)}}{(\cosh (x)-1)^{3/2} \sqrt{\cosh (x)+1}}\right)}{\sqrt{\cosh (x)}}","\frac{2 x \sinh (x)}{\sqrt{\cosh (x)}}-4 \sqrt{\cosh (x)}",1,"(2*Sinh[x]*(x - (2*Cosh[x]*Sinh[x]*Sqrt[Tanh[x/2]^2])/((-1 + Cosh[x])^(3/2)*Sqrt[1 + Cosh[x]])))/Sqrt[Cosh[x]]","B",0
72,1,16,24,0.0789103,"\int \left(\frac{x}{\cosh ^{\frac{5}{2}}(x)}-\frac{x}{3 \sqrt{\cosh (x)}}\right) \, dx","Integrate[x/Cosh[x]^(5/2) - x/(3*Sqrt[Cosh[x]]),x]","\frac{2 (x \tanh (x)+2)}{3 \sqrt{\cosh (x)}}","\frac{4}{3 \sqrt{\cosh (x)}}+\frac{2 x \sinh (x)}{3 \cosh ^{\frac{3}{2}}(x)}",1,"(2*(2 + x*Tanh[x]))/(3*Sqrt[Cosh[x]])","A",1
73,1,64,47,0.6382394,"\int \left(\frac{x}{\cosh ^{\frac{7}{2}}(x)}+\frac{3}{5} x \sqrt{\cosh (x)}\right) \, dx","Integrate[x/Cosh[x]^(7/2) + (3*x*Sqrt[Cosh[x]])/5,x]","\frac{1}{5} \sqrt{\cosh (x)} \left(6 x \tanh (x)+\left(2 x \tanh (x)+\frac{4}{3}\right) \text{sech}^2(x)-\frac{12 \sinh ^2(x)}{\sqrt{\cosh (x)-1} (\cosh (x)+1)^{3/2} \sqrt{\tanh ^2\left(\frac{x}{2}\right)}}\right)","\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,"(Sqrt[Cosh[x]]*((-12*Sinh[x]^2)/(Sqrt[-1 + Cosh[x]]*(1 + Cosh[x])^(3/2)*Sqrt[Tanh[x/2]^2]) + 6*x*Tanh[x] + Sech[x]^2*(4/3 + 2*x*Tanh[x])))/5","A",0
74,1,76,36,1.0265824,"\int \left(\frac{x^2}{\cosh ^{\frac{3}{2}}(x)}+x^2 \sqrt{\cosh (x)}\right) \, dx","Integrate[x^2/Cosh[x]^(3/2) + x^2*Sqrt[Cosh[x]],x]","\frac{4 \sqrt{\cosh (x)} (\sinh (x)+\cosh (x)) \left(8 \, _2F_1\left(-\frac{1}{4},\frac{1}{2};\frac{3}{4};-e^{2 x}\right) (\sinh (x)-\cosh (x)) \sqrt{\sinh (2 x)+\cosh (2 x)+1}+x^2 \sinh (x)-4 (x-2) \cosh (x)\right)}{e^{2 x}+1}","\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,"(4*Sqrt[Cosh[x]]*(Cosh[x] + Sinh[x])*(-4*(-2 + x)*Cosh[x] + x^2*Sinh[x] + 8*Hypergeometric2F1[-1/4, 1/2, 3/4, -E^(2*x)]*(-Cosh[x] + Sinh[x])*Sqrt[1 + Cosh[2*x] + Sinh[2*x]]))/(1 + E^(2*x))","C",1
75,0,0,21,3.1906699,"\int (c+d x)^m (b \cosh (e+f x))^n \, dx","Integrate[(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,"Integrate[(c + d*x)^m*(b*Cosh[e + f*x])^n, x]","A",-1
76,1,205,237,0.1960865,"\int (c+d x)^m \cosh ^3(a+b x) \, dx","Integrate[(c + d*x)^m*Cosh[a + b*x]^3,x]","\frac{3^{-m-1} e^{-3 \left(a+\frac{b c}{d}\right)} (c+d x)^m \left(-\frac{b^2 (c+d x)^2}{d^2}\right)^{-m} \left(e^{6 a} \left(b \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{3 b (c+d x)}{d}\right)+3^{m+2} e^{4 a+\frac{2 b c}{d}} \left(b \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{b (c+d x)}{d}\right)-e^{\frac{4 b c}{d}} \left(-\frac{b (c+d x)}{d}\right)^m \left(e^{2 a} 3^{m+2} \Gamma \left(m+1,\frac{b (c+d x)}{d}\right)+e^{\frac{2 b c}{d}} \Gamma \left(m+1,\frac{3 b (c+d x)}{d}\right)\right)\right)}{8 b}","\frac{3^{-m-1} e^{3 a-\frac{3 b c}{d}} (c+d x)^m \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{3 b (c+d x)}{d}\right)}{8 b}+\frac{3 e^{a-\frac{b c}{d}} (c+d x)^m \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{b (c+d x)}{d}\right)}{8 b}-\frac{3 e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{b (c+d x)}{d}\right)}{8 b}-\frac{3^{-m-1} e^{\frac{3 b c}{d}-3 a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{3 b (c+d x)}{d}\right)}{8 b}",1,"(3^(-1 - m)*(c + d*x)^m*(E^(6*a)*(b*(c/d + x))^m*Gamma[1 + m, (-3*b*(c + d*x))/d] + 3^(2 + m)*E^(4*a + (2*b*c)/d)*(b*(c/d + x))^m*Gamma[1 + m, -((b*(c + d*x))/d)] - E^((4*b*c)/d)*(-((b*(c + d*x))/d))^m*(3^(2 + m)*E^(2*a)*Gamma[1 + m, (b*(c + d*x))/d] + E^((2*b*c)/d)*Gamma[1 + m, (3*b*(c + d*x))/d])))/(8*b*E^(3*(a + (b*c)/d))*(-((b^2*(c + d*x)^2)/d^2))^m)","A",1
77,1,132,144,0.2157768,"\int (c+d x)^m \cosh ^2(a+b x) \, dx","Integrate[(c + d*x)^m*Cosh[a + b*x]^2,x]","\frac{1}{8} (c+d x)^m \left(\frac{2^{-m} e^{2 a-\frac{2 b c}{d}} \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 b (c+d x)}{d}\right)}{b}-\frac{2^{-m} e^{\frac{2 b c}{d}-2 a} \left(\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 b (c+d x)}{d}\right)}{b}+\frac{4 c+4 d x}{d m+d}\right)","\frac{2^{-m-3} e^{2 a-\frac{2 b c}{d}} (c+d x)^m \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 b (c+d x)}{d}\right)}{b}-\frac{2^{-m-3} e^{\frac{2 b c}{d}-2 a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 b (c+d x)}{d}\right)}{b}+\frac{(c+d x)^{m+1}}{2 d (m+1)}",1,"((c + d*x)^m*((4*c + 4*d*x)/(d + d*m) + (E^(2*a - (2*b*c)/d)*Gamma[1 + m, (-2*b*(c + d*x))/d])/(2^m*b*(-((b*(c + d*x))/d))^m) - (E^(-2*a + (2*b*c)/d)*Gamma[1 + m, (2*b*(c + d*x))/d])/(2^m*b*((b*(c + d*x))/d)^m)))/8","A",1
78,1,102,110,0.0577183,"\int (c+d x)^m \cosh (a+b x) \, dx","Integrate[(c + d*x)^m*Cosh[a + b*x],x]","\frac{e^{-a-\frac{b c}{d}} (c+d x)^m \left(e^{2 a} \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{b (c+d x)}{d}\right)-e^{\frac{2 b c}{d}} \left(b \left(\frac{c}{d}+x\right)\right)^{-m} \Gamma \left(m+1,\frac{b (c+d x)}{d}\right)\right)}{2 b}","\frac{e^{a-\frac{b c}{d}} (c+d x)^m \left(-\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{b (c+d x)}{d}\right)}{2 b}-\frac{e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{b (c+d x)}{d}\right)}{2 b}",1,"(E^(-a - (b*c)/d)*(c + d*x)^m*((E^(2*a)*Gamma[1 + m, -((b*(c + d*x))/d)])/(-((b*(c + d*x))/d))^m - (E^((2*b*c)/d)*Gamma[1 + m, (b*(c + d*x))/d])/(b*(c/d + x))^m))/(2*b)","A",1
79,0,0,17,5.9314254,"\int (c+d x)^m \text{sech}(a+b x) \, dx","Integrate[(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,"Integrate[(c + d*x)^m*Sech[a + b*x], x]","A",-1
80,0,0,19,3.4901534,"\int (c+d x)^m \text{sech}^2(a+b x) \, dx","Integrate[(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,"Integrate[(c + d*x)^m*Sech[a + b*x]^2, x]","A",-1
81,1,54,59,0.0388722,"\int x^{3+m} \cosh (a+b x) \, dx","Integrate[x^(3 + m)*Cosh[a + b*x],x]","-\frac{e^a x^m (-b x)^{-m} \Gamma (m+4,-b x)+e^{-a} x^m (b x)^{-m} \Gamma (m+4,b x)}{2 b^4}","-\frac{e^a x^m (-b x)^{-m} \Gamma (m+4,-b x)}{2 b^4}-\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+4,b x)}{2 b^4}",1,"-1/2*((E^a*x^m*Gamma[4 + m, -(b*x)])/(-(b*x))^m + (x^m*Gamma[4 + m, b*x])/(E^a*(b*x)^m))/b^4","A",1
82,1,54,59,0.020613,"\int x^{2+m} \cosh (a+b x) \, dx","Integrate[x^(2 + m)*Cosh[a + b*x],x]","\frac{e^{-a} x^m \left(e^{2 a} (-b x)^{-m} \Gamma (m+3,-b x)-(b x)^{-m} \Gamma (m+3,b x)\right)}{2 b^3}","\frac{e^a x^m (-b x)^{-m} \Gamma (m+3,-b x)}{2 b^3}-\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+3,b x)}{2 b^3}",1,"(x^m*((E^(2*a)*Gamma[3 + m, -(b*x)])/(-(b*x))^m - Gamma[3 + m, b*x]/(b*x)^m))/(2*b^3*E^a)","A",1
83,1,54,59,0.0331186,"\int x^{1+m} \cosh (a+b x) \, dx","Integrate[x^(1 + m)*Cosh[a + b*x],x]","-\frac{e^a x^m (-b x)^{-m} \Gamma (m+2,-b x)+e^{-a} x^m (b x)^{-m} \Gamma (m+2,b x)}{2 b^2}","-\frac{e^a x^m (-b x)^{-m} \Gamma (m+2,-b x)}{2 b^2}-\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+2,b x)}{2 b^2}",1,"-1/2*((E^a*x^m*Gamma[2 + m, -(b*x)])/(-(b*x))^m + (x^m*Gamma[2 + m, b*x])/(E^a*(b*x)^m))/b^2","A",1
84,1,54,59,0.0183773,"\int x^m \cosh (a+b x) \, dx","Integrate[x^m*Cosh[a + b*x],x]","\frac{e^{-a} x^m \left(e^{2 a} (-b x)^{-m} \Gamma (m+1,-b x)-(b x)^{-m} \Gamma (m+1,b x)\right)}{2 b}","\frac{e^a x^m (-b x)^{-m} \Gamma (m+1,-b x)}{2 b}-\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{2 b}",1,"(x^m*((E^(2*a)*Gamma[1 + m, -(b*x)])/(-(b*x))^m - Gamma[1 + m, b*x]/(b*x)^m))/(2*b*E^a)","A",1
85,1,49,49,0.0212532,"\int x^{-1+m} \cosh (a+b x) \, dx","Integrate[x^(-1 + m)*Cosh[a + b*x],x]","-\frac{1}{2} e^a x^m (-b x)^{-m} \Gamma (m,-b x)-\frac{1}{2} e^{-a} x^m (b x)^{-m} \Gamma (m,b x)","-\frac{1}{2} e^a x^m (-b x)^{-m} \Gamma (m,-b x)-\frac{1}{2} e^{-a} x^m (b x)^{-m} \Gamma (m,b x)",1,"-1/2*(E^a*x^m*Gamma[m, -(b*x)])/(-(b*x))^m - (x^m*Gamma[m, b*x])/(2*E^a*(b*x)^m)","A",1
86,1,52,55,0.0197232,"\int x^{-2+m} \cosh (a+b x) \, dx","Integrate[x^(-2 + m)*Cosh[a + b*x],x]","\frac{1}{2} e^{-a} b x^m \left(e^{2 a} (-b x)^{-m} \Gamma (m-1,-b x)-(b x)^{-m} \Gamma (m-1,b x)\right)","\frac{1}{2} e^a b x^m (-b x)^{-m} \Gamma (m-1,-b x)-\frac{1}{2} e^{-a} b x^m (b x)^{-m} \Gamma (m-1,b x)",1,"(b*x^m*((E^(2*a)*Gamma[-1 + m, -(b*x)])/(-(b*x))^m - Gamma[-1 + m, b*x]/(b*x)^m))/(2*E^a)","A",1
87,1,55,59,0.0220307,"\int x^{-3+m} \cosh (a+b x) \, dx","Integrate[x^(-3 + m)*Cosh[a + b*x],x]","\frac{1}{2} e^{-a} b^2 x^m \left(-e^{2 a} (-b x)^{-m} \Gamma (m-2,-b x)-(b x)^{-m} \Gamma (m-2,b x)\right)","-\frac{1}{2} e^a b^2 x^m (-b x)^{-m} \Gamma (m-2,-b x)-\frac{1}{2} e^{-a} b^2 x^m (b x)^{-m} \Gamma (m-2,b x)",1,"(b^2*x^m*(-((E^(2*a)*Gamma[-2 + m, -(b*x)])/(-(b*x))^m) - Gamma[-2 + m, b*x]/(b*x)^m))/(2*E^a)","A",1
88,1,79,86,0.1106767,"\int x^{3+m} \cosh ^2(a+b x) \, dx","Integrate[x^(3 + m)*Cosh[a + b*x]^2,x]","\frac{1}{64} x^m \left(-\frac{e^{2 a} 2^{-m} (-b x)^{-m} \Gamma (m+4,-2 b x)}{b^4}-\frac{e^{-2 a} 2^{-m} (b x)^{-m} \Gamma (m+4,2 b x)}{b^4}+\frac{32 x^4}{m+4}\right)","-\frac{e^{2 a} 2^{-m-6} x^m (-b x)^{-m} \Gamma (m+4,-2 b x)}{b^4}-\frac{e^{-2 a} 2^{-m-6} x^m (b x)^{-m} \Gamma (m+4,2 b x)}{b^4}+\frac{x^{m+4}}{2 (m+4)}",1,"(x^m*((32*x^4)/(4 + m) - (E^(2*a)*Gamma[4 + m, -2*b*x])/(2^m*b^4*(-(b*x))^m) - Gamma[4 + m, 2*b*x]/(2^m*b^4*E^(2*a)*(b*x)^m)))/64","A",1
89,1,78,85,0.1014749,"\int x^{2+m} \cosh ^2(a+b x) \, dx","Integrate[x^(2 + m)*Cosh[a + b*x]^2,x]","\frac{1}{32} x^m \left(\frac{e^{2 a} 2^{-m} (-b x)^{-m} \Gamma (m+3,-2 b x)}{b^3}-\frac{e^{-2 a} 2^{-m} (b x)^{-m} \Gamma (m+3,2 b x)}{b^3}+\frac{16 x^3}{m+3}\right)","\frac{e^{2 a} 2^{-m-5} x^m (-b x)^{-m} \Gamma (m+3,-2 b x)}{b^3}-\frac{e^{-2 a} 2^{-m-5} x^m (b x)^{-m} \Gamma (m+3,2 b x)}{b^3}+\frac{x^{m+3}}{2 (m+3)}",1,"(x^m*((16*x^3)/(3 + m) + (E^(2*a)*Gamma[3 + m, -2*b*x])/(2^m*b^3*(-(b*x))^m) - Gamma[3 + m, 2*b*x]/(2^m*b^3*E^(2*a)*(b*x)^m)))/32","A",1
90,1,79,86,0.1098364,"\int x^{1+m} \cosh ^2(a+b x) \, dx","Integrate[x^(1 + m)*Cosh[a + b*x]^2,x]","\frac{1}{16} x^m \left(-\frac{e^{2 a} 2^{-m} (-b x)^{-m} \Gamma (m+2,-2 b x)}{b^2}-\frac{e^{-2 a} 2^{-m} (b x)^{-m} \Gamma (m+2,2 b x)}{b^2}+\frac{8 x^2}{m+2}\right)","-\frac{e^{2 a} 2^{-m-4} x^m (-b x)^{-m} \Gamma (m+2,-2 b x)}{b^2}-\frac{e^{-2 a} 2^{-m-4} x^m (b x)^{-m} \Gamma (m+2,2 b x)}{b^2}+\frac{x^{m+2}}{2 (m+2)}",1,"(x^m*((8*x^2)/(2 + m) - (E^(2*a)*Gamma[2 + m, -2*b*x])/(2^m*b^2*(-(b*x))^m) - Gamma[2 + m, 2*b*x]/(2^m*b^2*E^(2*a)*(b*x)^m)))/16","A",1
91,1,76,85,0.0895673,"\int x^m \cosh ^2(a+b x) \, dx","Integrate[x^m*Cosh[a + b*x]^2,x]","\frac{1}{8} x^m \left(\frac{e^{2 a} 2^{-m} (-b x)^{-m} \Gamma (m+1,-2 b x)}{b}-\frac{e^{-2 a} 2^{-m} (b x)^{-m} \Gamma (m+1,2 b x)}{b}+\frac{4 x}{m+1}\right)","\frac{e^{2 a} 2^{-m-3} x^m (-b x)^{-m} \Gamma (m+1,-2 b x)}{b}-\frac{e^{-2 a} 2^{-m-3} x^m (b x)^{-m} \Gamma (m+1,2 b x)}{b}+\frac{x^{m+1}}{2 (m+1)}",1,"(x^m*((4*x)/(1 + m) + (E^(2*a)*Gamma[1 + m, -2*b*x])/(2^m*b*(-(b*x))^m) - Gamma[1 + m, 2*b*x]/(2^m*b*E^(2*a)*(b*x)^m)))/8","A",1
92,1,64,72,0.0598078,"\int x^{-1+m} \cosh ^2(a+b x) \, dx","Integrate[x^(-1 + m)*Cosh[a + b*x]^2,x]","\frac{1}{4} x^m \left(e^{2 a} \left(-2^{-m}\right) (-b x)^{-m} \Gamma (m,-2 b x)-e^{-2 a} 2^{-m} (b x)^{-m} \Gamma (m,2 b x)+\frac{2}{m}\right)","e^{2 a} \left(-2^{-m-2}\right) x^m (-b x)^{-m} \Gamma (m,-2 b x)-e^{-2 a} 2^{-m-2} x^m (b x)^{-m} \Gamma (m,2 b x)+\frac{x^m}{2 m}",1,"(x^m*(2/m - (E^(2*a)*Gamma[m, -2*b*x])/(2^m*(-(b*x))^m) - Gamma[m, 2*b*x]/(2^m*E^(2*a)*(b*x)^m)))/4","A",1
93,1,73,83,0.0997481,"\int x^{-2+m} \cosh ^2(a+b x) \, dx","Integrate[x^(-2 + m)*Cosh[a + b*x]^2,x]","\frac{1}{2} x^m \left(e^{2 a} b 2^{-m} (-b x)^{-m} \Gamma (m-1,-2 b x)-e^{-2 a} b 2^{-m} (b x)^{-m} \Gamma (m-1,2 b x)+\frac{1}{(m-1) x}\right)","e^{2 a} b 2^{-m-1} x^m (-b x)^{-m} \Gamma (m-1,-2 b x)-e^{-2 a} b 2^{-m-1} x^m (b x)^{-m} \Gamma (m-1,2 b x)-\frac{x^{m-1}}{2 (1-m)}",1,"(x^m*(1/((-1 + m)*x) + (b*E^(2*a)*Gamma[-1 + m, -2*b*x])/(2^m*(-(b*x))^m) - (b*Gamma[-1 + m, 2*b*x])/(2^m*E^(2*a)*(b*x)^m)))/2","A",1
94,1,84,84,0.1136349,"\int x^{-3+m} \cosh ^2(a+b x) \, dx","Integrate[x^(-3 + m)*Cosh[a + b*x]^2,x]","-e^{2 a} b^2 2^{-m} x^m (-b x)^{-m} \Gamma (m-2,-2 b x)-e^{-2 a} b^2 2^{-m} x^m (b x)^{-m} \Gamma (m-2,2 b x)-\frac{x^{m-2}}{2 (2-m)}","-e^{2 a} b^2 2^{-m} x^m (-b x)^{-m} \Gamma (m-2,-2 b x)-e^{-2 a} b^2 2^{-m} x^m (b x)^{-m} \Gamma (m-2,2 b x)-\frac{x^{m-2}}{2 (2-m)}",1,"-1/2*x^(-2 + m)/(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",1
95,1,17,24,0.0968647,"\int \left(\frac{x}{\text{sech}^{\frac{3}{2}}(x)}-\frac{1}{3} x \sqrt{\text{sech}(x)}\right) \, dx","Integrate[x/Sech[x]^(3/2) - (x*Sqrt[Sech[x]])/3,x]","\frac{2 (3 x \tanh (x)-2)}{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,"(2*(-2 + 3*x*Tanh[x]))/(9*Sech[x]^(3/2))","A",1
96,1,17,24,0.1508284,"\int \left(\frac{x}{\text{sech}^{\frac{5}{2}}(x)}-\frac{3 x}{5 \sqrt{\text{sech}(x)}}\right) \, dx","Integrate[x/Sech[x]^(5/2) - (3*x)/(5*Sqrt[Sech[x]]),x]","\frac{2 (5 x \tanh (x)-2)}{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,"(2*(-2 + 5*x*Tanh[x]))/(25*Sech[x]^(5/2))","A",1
97,1,45,47,0.1087951,"\int \left(\frac{x}{\text{sech}^{\frac{7}{2}}(x)}-\frac{5}{21} x \sqrt{\text{sech}(x)}\right) \, dx","Integrate[x/Sech[x]^(7/2) - (5*x*Sqrt[Sech[x]])/21,x]","\sqrt{\text{sech}(x)} \left(\frac{13}{42} x \sinh (2 x)+\frac{1}{28} x \sinh (4 x)-\frac{88}{441} \cosh (2 x)-\frac{1}{98} \cosh (4 x)-\frac{167}{882}\right)","-\frac{20}{63 \text{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,"Sqrt[Sech[x]]*(-167/882 - (88*Cosh[2*x])/441 - Cosh[4*x]/98 + (13*x*Sinh[2*x])/42 + (x*Sinh[4*x])/28)","A",1
98,1,55,66,0.1097888,"\int \left(\frac{x^2}{\text{sech}^{\frac{3}{2}}(x)}-\frac{1}{3} x^2 \sqrt{\text{sech}(x)}\right) \, dx","Integrate[x^2/Sech[x]^(3/2) - (x^2*Sqrt[Sech[x]])/3,x]","\frac{1}{27} \sqrt{\text{sech}(x)} \left(9 x^2 \sinh (2 x)-12 x+8 \sinh (2 x)-12 x \cosh (2 x)-16 i \sqrt{\cosh (x)} F\left(\left.\frac{i x}{2}\right|2\right)\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,"(Sqrt[Sech[x]]*(-12*x - 12*x*Cosh[2*x] - (16*I)*Sqrt[Cosh[x]]*EllipticF[(I/2)*x, 2] + 8*Sinh[2*x] + 9*x^2*Sinh[2*x]))/27","A",1
99,1,122,89,0.5635845,"\int (c+d x)^3 (a+a \cosh (e+f x)) \, dx","Integrate[(c + d*x)^3*(a + a*Cosh[e + f*x]),x]","a \left(-\frac{3 d \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \cosh (e+f x)}{f^4}+\frac{(c+d x) \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+6\right)\right) \sinh (e+f x)}{f^3}+\frac{1}{4} x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right)","\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*((x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3))/4 - (3*d*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Cosh[e + f*x])/f^4 + ((c + d*x)*(c^2*f^2 + 2*c*d*f^2*x + d^2*(6 + f^2*x^2))*Sinh[e + f*x])/f^3)","A",1
100,1,80,67,0.3311597,"\int (c+d x)^2 (a+a \cosh (e+f x)) \, dx","Integrate[(c + d*x)^2*(a + a*Cosh[e + f*x]),x]","a \left(\frac{\left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \sinh (e+f x)}{f^3}+c^2 x-\frac{2 d (c+d x) \cosh (e+f x)}{f^2}+c d x^2+\frac{d^2 x^3}{3}\right)","-\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^2*x + c*d*x^2 + (d^2*x^3)/3 - (2*d*(c + d*x)*Cosh[e + f*x])/f^2 + ((c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Sinh[e + f*x])/f^3)","A",1
101,1,52,45,0.220639,"\int (c+d x) (a+a \cosh (e+f x)) \, dx","Integrate[(c + d*x)*(a + a*Cosh[e + f*x]),x]","\frac{a (-2 (e+f x) (-2 c f+d e-d f x)+4 f (c+d x) \sinh (e+f x)-4 d \cosh (e+f x))}{4 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*(-2*(e + f*x)*(d*e - 2*c*f - d*f*x) - 4*d*Cosh[e + f*x] + 4*f*(c + d*x)*Sinh[e + f*x]))/(4*f^2)","A",1
102,1,54,64,0.1114136,"\int \frac{a+a \cosh (e+f x)}{c+d x} \, dx","Integrate[(a + a*Cosh[e + f*x])/(c + d*x),x]","\frac{a \left(\text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+\sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+\log (c+d x)\right)}{d}","\frac{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[f*(c/d + x)] + Log[c + d*x] + Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)]))/d","A",1
103,1,68,87,0.3169433,"\int \frac{a+a \cosh (e+f x)}{(c+d x)^2} \, dx","Integrate[(a + a*Cosh[e + f*x])/(c + d*x)^2,x]","\frac{a \left(f \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+f \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-\frac{d (\cosh (e+f x)+1)}{c+d x}\right)}{d^2}","\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*(1 + Cosh[e + f*x]))/(c + d*x)) + f*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] + f*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)]))/d^2","A",1
104,1,90,123,0.4584704,"\int \frac{a+a \cosh (e+f x)}{(c+d x)^3} \, dx","Integrate[(a + a*Cosh[e + f*x])/(c + d*x)^3,x]","\frac{a \left(f^2 \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+f^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-\frac{d (f (c+d x) \sinh (e+f x)+d \cosh (e+f x)+d)}{(c+d x)^2}\right)}{2 d^3}","\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*(f^2*Cosh[e - (c*f)/d]*CoshIntegral[f*(c/d + x)] - (d*(d + d*Cosh[e + f*x] + f*(c + d*x)*Sinh[e + f*x]))/(c + d*x)^2 + f^2*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)]))/(2*d^3)","A",1
105,1,217,237,1.4934362,"\int (c+d x)^3 (a+a \cosh (e+f x))^2 \, dx","Integrate[(c + d*x)^3*(a + a*Cosh[e + f*x])^2,x]","\frac{a^2 \left(-96 d \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \cosh (e+f x)-3 d \left(2 c^2 f^2+4 c d f^2 x+d^2 \left(2 f^2 x^2+1\right)\right) \cosh (2 (e+f x))+2 f \left(16 (c+d x) \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+6\right)\right) \sinh (e+f x)+(c+d x) \left(2 c^2 f^2+4 c d f^2 x+d^2 \left(2 f^2 x^2+3\right)\right) \sinh (2 (e+f x))+3 f^3 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right)\right)}{16 f^4}","\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,"(a^2*(-96*d*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Cosh[e + f*x] - 3*d*(2*c^2*f^2 + 4*c*d*f^2*x + d^2*(1 + 2*f^2*x^2))*Cosh[2*(e + f*x)] + 2*f*(3*f^3*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) + 16*(c + d*x)*(c^2*f^2 + 2*c*d*f^2*x + d^2*(6 + f^2*x^2))*Sinh[e + f*x] + (c + d*x)*(2*c^2*f^2 + 4*c*d*f^2*x + d^2*(3 + 2*f^2*x^2))*Sinh[2*(e + f*x)])))/(16*f^4)","A",1
106,1,192,168,0.5358337,"\int (c+d x)^2 (a+a \cosh (e+f x))^2 \, dx","Integrate[(c + d*x)^2*(a + a*Cosh[e + f*x])^2,x]","\frac{a^2 \left(16 c^2 f^2 \sinh (e+f x)+2 c^2 f^2 \sinh (2 (e+f x))+12 c^2 f^3 x+32 c d f^2 x \sinh (e+f x)+4 c d f^2 x \sinh (2 (e+f x))-32 d f (c+d x) \cosh (e+f x)-2 d f (c+d x) \cosh (2 (e+f x))+12 c d f^3 x^2+16 d^2 f^2 x^2 \sinh (e+f x)+2 d^2 f^2 x^2 \sinh (2 (e+f x))+32 d^2 \sinh (e+f x)+d^2 \sinh (2 (e+f x))+4 d^2 f^3 x^3\right)}{8 f^3}","-\frac{a^2 d (c+d x) \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*(12*c^2*f^3*x + 12*c*d*f^3*x^2 + 4*d^2*f^3*x^3 - 32*d*f*(c + d*x)*Cosh[e + f*x] - 2*d*f*(c + d*x)*Cosh[2*(e + f*x)] + 32*d^2*Sinh[e + f*x] + 16*c^2*f^2*Sinh[e + f*x] + 32*c*d*f^2*x*Sinh[e + f*x] + 16*d^2*f^2*x^2*Sinh[e + f*x] + d^2*Sinh[2*(e + f*x)] + 2*c^2*f^2*Sinh[2*(e + f*x)] + 4*c*d*f^2*x*Sinh[2*(e + f*x)] + 2*d^2*f^2*x^2*Sinh[2*(e + f*x)]))/(8*f^3)","A",1
107,1,81,118,0.5417371,"\int (c+d x) (a+a \cosh (e+f x))^2 \, dx","Integrate[(c + d*x)*(a + a*Cosh[e + f*x])^2,x]","\frac{a^2 (-6 (e+f x) (d (e-f x)-2 c f)+16 f (c+d x) \sinh (e+f x)+2 f (c+d x) \sinh (2 (e+f x))-16 d \cosh (e+f x)-d \cosh (2 (e+f x)))}{8 f^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*(-6*(e + f*x)*(-2*c*f + d*(e - f*x)) - 16*d*Cosh[e + f*x] - d*Cosh[2*(e + f*x)] + 16*f*(c + d*x)*Sinh[e + f*x] + 2*f*(c + d*x)*Sinh[2*(e + f*x)]))/(8*f^2)","A",1
108,1,113,145,0.2100757,"\int \frac{(a+a \cosh (e+f x))^2}{c+d x} \, dx","Integrate[(a + a*Cosh[e + f*x])^2/(c + d*x),x]","\frac{a^2 \left(4 \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+\text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)+4 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+\sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+3 \log (c+d x)\right)}{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,"(a^2*(4*Cosh[e - (c*f)/d]*CoshIntegral[f*(c/d + x)] + Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*f*(c + d*x))/d] + 3*Log[c + d*x] + 4*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d]))/(2*d)","A",1
109,1,207,157,0.7432915,"\int \frac{(a+a \cosh (e+f x))^2}{(c+d x)^2} \, dx","Integrate[(a + a*Cosh[e + f*x])^2/(c + d*x)^2,x]","\frac{a^2 \left(2 f (c+d x) \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)+4 f (c+d x) \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+4 d f x \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+2 d f x \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+4 c f \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+2 c f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-4 d \cosh (e+f x)-d \cosh (2 (e+f x))-3 d\right)}{2 d^2 (c+d x)}","\frac{a^2 f \text{Chi}\left(2 x f+\frac{2 c f}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)}{d^2}+\frac{2 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,"(a^2*(-3*d - 4*d*Cosh[e + f*x] - d*Cosh[2*(e + f*x)] + 2*f*(c + d*x)*CoshIntegral[(2*f*(c + d*x))/d]*Sinh[2*e - (2*c*f)/d] + 4*f*(c + d*x)*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] + 4*c*f*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 4*d*f*x*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 2*c*f*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] + 2*d*f*x*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d]))/(2*d^2*(c + d*x))","A",1
110,1,353,207,1.2167852,"\int \frac{(a+a \cosh (e+f x))^2}{(c+d x)^3} \, dx","Integrate[(a + a*Cosh[e + f*x])^2/(c + d*x)^3,x]","\frac{a^2 \left(4 c^2 f^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+4 c^2 f^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+4 f^2 (c+d x)^2 \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+4 f^2 (c+d x)^2 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)+4 d^2 f^2 x^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+4 d^2 f^2 x^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+8 c d f^2 x \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+8 c d f^2 x \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-4 c d f \sinh (e+f x)-2 c d f \sinh (2 (e+f x))-4 d^2 f x \sinh (e+f x)-2 d^2 f x \sinh (2 (e+f x))-4 d^2 \cosh (e+f x)-d^2 \cosh (2 (e+f x))-3 d^2\right)}{4 d^3 (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,"(a^2*(-3*d^2 - 4*d^2*Cosh[e + f*x] - d^2*Cosh[2*(e + f*x)] + 4*f^2*(c + d*x)^2*Cosh[e - (c*f)/d]*CoshIntegral[f*(c/d + x)] + 4*f^2*(c + d*x)^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*f*(c + d*x))/d] - 4*c*d*f*Sinh[e + f*x] - 4*d^2*f*x*Sinh[e + f*x] - 2*c*d*f*Sinh[2*(e + f*x)] - 2*d^2*f*x*Sinh[2*(e + f*x)] + 4*c^2*f^2*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 8*c*d*f^2*x*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 4*d^2*f^2*x^2*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 4*c^2*f^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] + 8*c*d*f^2*x*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] + 4*d^2*f^2*x^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d]))/(4*d^3*(c + d*x)^2)","A",1
111,1,154,117,2.2991451,"\int \frac{(c+d x)^3}{a+a \cosh (e+f x)} \, dx","Integrate[(c + d*x)^3/(a + a*Cosh[e + f*x]),x]","\frac{2 \cosh \left(\frac{1}{2} (e+f x)\right) \left(2 \cosh \left(\frac{1}{2} (e+f x)\right) \left(6 d^2 \left(f (c+d x) \text{Li}_2\left(-e^{-e-f x}\right)+d \text{Li}_3\left(-e^{-e-f x}\right)\right)-\frac{f^3 (c+d x)^3}{e^e+1}-3 d f^2 (c+d x)^2 \log \left(e^{-e-f x}+1\right)\right)+f^3 \text{sech}\left(\frac{e}{2}\right) (c+d x)^3 \sinh \left(\frac{f x}{2}\right)\right)}{a f^4 (\cosh (e+f x)+1)}","-\frac{12 d^2 (c+d x) \text{Li}_2\left(-e^{e+f x}\right)}{a f^3}-\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^3 \text{Li}_3\left(-e^{e+f x}\right)}{a f^4}",1,"(2*Cosh[(e + f*x)/2]*(2*Cosh[(e + f*x)/2]*(-((f^3*(c + d*x)^3)/(1 + E^e)) - 3*d*f^2*(c + d*x)^2*Log[1 + E^(-e - f*x)] + 6*d^2*(f*(c + d*x)*PolyLog[2, -E^(-e - f*x)] + d*PolyLog[3, -E^(-e - f*x)])) + f^3*(c + d*x)^3*Sech[e/2]*Sinh[(f*x)/2]))/(a*f^4*(1 + Cosh[e + f*x]))","A",1
112,1,472,88,6.3785047,"\int \frac{(c+d x)^2}{a+a \cosh (e+f x)} \, dx","Integrate[(c + d*x)^2/(a + a*Cosh[e + f*x]),x]","\frac{2 \text{sech}\left(\frac{e}{2}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c^2 \sinh \left(\frac{f x}{2}\right)+2 c d x \sinh \left(\frac{f x}{2}\right)+d^2 x^2 \sinh \left(\frac{f x}{2}\right)\right)}{f (a \cosh (e+f x)+a)}-\frac{8 c d \text{sech}\left(\frac{e}{2}\right) \cosh ^2\left(\frac{e}{2}+\frac{f x}{2}\right) \left(\cosh \left(\frac{e}{2}\right) \log \left(\sinh \left(\frac{e}{2}\right) \sinh \left(\frac{f x}{2}\right)+\cosh \left(\frac{e}{2}\right) \cosh \left(\frac{f x}{2}\right)\right)-\frac{1}{2} f x \sinh \left(\frac{e}{2}\right)\right)}{f^2 \left(\cosh ^2\left(\frac{e}{2}\right)-\sinh ^2\left(\frac{e}{2}\right)\right) (a \cosh (e+f x)+a)}-\frac{8 d^2 \text{csch}\left(\frac{e}{2}\right) \text{sech}\left(\frac{e}{2}\right) \cosh ^2\left(\frac{e}{2}+\frac{f x}{2}\right) \left(\frac{1}{4} f^2 x^2 e^{-\tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)}-\frac{i \coth \left(\frac{e}{2}\right) \left(i \text{Li}_2\left(e^{2 i \left(\frac{i f x}{2}+i \tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)\right)}\right)-\frac{1}{2} f x \left(-\pi +2 i \tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)\right)-2 \left(i \tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)+\frac{i f x}{2}\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)+\frac{i f x}{2}\right)}\right)+2 i \tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right) \log \left(i \sinh \left(\tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)+\frac{f x}{2}\right)\right)-\pi  \log \left(e^{f x}+1\right)+\pi  \log \left(\cosh \left(\frac{f x}{2}\right)\right)\right)}{\sqrt{1-\coth ^2\left(\frac{e}{2}\right)}}\right)}{f^3 \sqrt{\text{csch}^2\left(\frac{e}{2}\right) \left(\sinh ^2\left(\frac{e}{2}\right)-\cosh ^2\left(\frac{e}{2}\right)\right)} (a \cosh (e+f x)+a)}","-\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{Li}_2\left(-e^{e+f x}\right)}{a f^3}",1,"(-8*c*d*Cosh[e/2 + (f*x)/2]^2*Sech[e/2]*(Cosh[e/2]*Log[Cosh[e/2]*Cosh[(f*x)/2] + Sinh[e/2]*Sinh[(f*x)/2]] - (f*x*Sinh[e/2])/2))/(f^2*(a + a*Cosh[e + f*x])*(Cosh[e/2]^2 - Sinh[e/2]^2)) - (8*d^2*Cosh[e/2 + (f*x)/2]^2*Csch[e/2]*((f^2*x^2)/(4*E^ArcTanh[Coth[e/2]]) - (I*Coth[e/2]*(-1/2*(f*x*(-Pi + (2*I)*ArcTanh[Coth[e/2]])) - Pi*Log[1 + E^(f*x)] - 2*((I/2)*f*x + I*ArcTanh[Coth[e/2]])*Log[1 - E^((2*I)*((I/2)*f*x + I*ArcTanh[Coth[e/2]]))] + Pi*Log[Cosh[(f*x)/2]] + (2*I)*ArcTanh[Coth[e/2]]*Log[I*Sinh[(f*x)/2 + ArcTanh[Coth[e/2]]]] + I*PolyLog[2, E^((2*I)*((I/2)*f*x + I*ArcTanh[Coth[e/2]]))]))/Sqrt[1 - Coth[e/2]^2])*Sech[e/2])/(f^3*(a + a*Cosh[e + f*x])*Sqrt[Csch[e/2]^2*(-Cosh[e/2]^2 + Sinh[e/2]^2)]) + (2*Cosh[e/2 + (f*x)/2]*Sech[e/2]*(c^2*Sinh[(f*x)/2] + 2*c*d*x*Sinh[(f*x)/2] + d^2*x^2*Sinh[(f*x)/2]))/(f*(a + a*Cosh[e + f*x]))","C",0
113,1,70,49,0.2746196,"\int \frac{c+d x}{a+a \cosh (e+f x)} \, dx","Integrate[(c + d*x)/(a + a*Cosh[e + f*x]),x]","\frac{2 \cosh \left(\frac{1}{2} (e+f x)\right) \left(f (c+d x) \sinh \left(\frac{1}{2} (e+f x)\right)-2 d \cosh \left(\frac{1}{2} (e+f x)\right) \log \left(\cosh \left(\frac{1}{2} (e+f x)\right)\right)\right)}{a f^2 (\cosh (e+f x)+1)}","\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*Cosh[(e + f*x)/2]*(-2*d*Cosh[(e + f*x)/2]*Log[Cosh[(e + f*x)/2]] + f*(c + d*x)*Sinh[(e + f*x)/2]))/(a*f^2*(1 + Cosh[e + f*x]))","A",1
114,0,0,23,9.2464499,"\int \frac{1}{(c+d x) (a+a \cosh (e+f x))} \, dx","Integrate[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,"Integrate[1/((c + d*x)*(a + a*Cosh[e + f*x])), x]","A",-1
115,0,0,23,9.6083569,"\int \frac{1}{(c+d x)^2 (a+a \cosh (e+f x))} \, dx","Integrate[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,"Integrate[1/((c + d*x)^2*(a + a*Cosh[e + f*x])), x]","A",-1
116,1,462,255,3.4863974,"\int \frac{(c+d x)^3}{(a+a \cosh (e+f x))^2} \, dx","Integrate[(c + d*x)^3/(a + a*Cosh[e + f*x])^2,x]","\frac{\cosh \left(\frac{1}{2} (e+f x)\right) \left(\text{sech}\left(\frac{e}{2}\right) (c+d x) \left(c^2 f^2 \sinh \left(e+\frac{3 f x}{2}\right)+3 c^2 f^2 \sinh \left(\frac{f x}{2}\right)+2 c d f^2 x \sinh \left(e+\frac{3 f x}{2}\right)+3 d f (c+d x) \cosh \left(e+\frac{f x}{2}\right)+6 c d f^2 x \sinh \left(\frac{f x}{2}\right)+3 d f (c+d x) \cosh \left(\frac{f x}{2}\right)+d^2 f^2 x^2 \sinh \left(e+\frac{3 f x}{2}\right)+6 d^2 \sinh \left(e+\frac{f x}{2}\right)-6 d^2 \sinh \left(e+\frac{3 f x}{2}\right)+3 d^2 f^2 x^2 \sinh \left(\frac{f x}{2}\right)-12 d^2 \sinh \left(\frac{f x}{2}\right)\right)-\frac{8 d \cosh ^3\left(\frac{1}{2} (e+f x)\right) \left(-\frac{3 \left(c^2 f^2-2 d^2\right) (\sinh (e)+\cosh (e)+1) (f x-\log (\sinh (e+f x)+\cosh (e+f x)+1))}{f}+3 c^2 f^2 x-6 c d (\sinh (e)+\cosh (e)+1) \text{Li}_2(\sinh (e+f x)-\cosh (e+f x))+6 c d f x (\sinh (e)+\cosh (e)+1) \log (-\sinh (e+f x)+\cosh (e+f x)+1)+3 c d f^2 x^2-\frac{6 d^2 (\sinh (e)+\cosh (e)+1) (f x \text{Li}_2(\sinh (e+f x)-\cosh (e+f x))+\text{Li}_3(\sinh (e+f x)-\cosh (e+f x)))}{f}+3 d^2 f x^2 (\sinh (e)+\cosh (e)+1) \log (-\sinh (e+f x)+\cosh (e+f x)+1)+d^2 f^2 x^3-6 d^2 x\right)}{\sinh (e)+\cosh (e)+1}\right)}{3 a^2 f^3 (\cosh (e+f x)+1)^2}","-\frac{4 d^2 (c+d x) \text{Li}_2\left(-e^{e+f x}\right)}{a^2 f^3}-\frac{2 d^2 (c+d x) \tanh \left(\frac{e}{2}+\frac{f x}{2}\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 \text{Li}_3\left(-e^{e+f x}\right)}{a^2 f^4}+\frac{4 d^3 \log \left(\cosh \left(\frac{e}{2}+\frac{f x}{2}\right)\right)}{a^2 f^4}",1,"(Cosh[(e + f*x)/2]*((-8*d*Cosh[(e + f*x)/2]^3*(-6*d^2*x + 3*c^2*f^2*x + 3*c*d*f^2*x^2 + d^2*f^2*x^3 + 6*c*d*f*x*Log[1 + Cosh[e + f*x] - Sinh[e + f*x]]*(1 + Cosh[e] + Sinh[e]) + 3*d^2*f*x^2*Log[1 + Cosh[e + f*x] - Sinh[e + f*x]]*(1 + Cosh[e] + Sinh[e]) - (3*(-2*d^2 + c^2*f^2)*(f*x - Log[1 + Cosh[e + f*x] + Sinh[e + f*x]])*(1 + Cosh[e] + Sinh[e]))/f - 6*c*d*PolyLog[2, -Cosh[e + f*x] + Sinh[e + f*x]]*(1 + Cosh[e] + Sinh[e]) - (6*d^2*(f*x*PolyLog[2, -Cosh[e + f*x] + Sinh[e + f*x]] + PolyLog[3, -Cosh[e + f*x] + Sinh[e + f*x]])*(1 + Cosh[e] + Sinh[e]))/f))/(1 + Cosh[e] + Sinh[e]) + (c + d*x)*Sech[e/2]*(3*d*f*(c + d*x)*Cosh[(f*x)/2] + 3*d*f*(c + d*x)*Cosh[e + (f*x)/2] - 12*d^2*Sinh[(f*x)/2] + 3*c^2*f^2*Sinh[(f*x)/2] + 6*c*d*f^2*x*Sinh[(f*x)/2] + 3*d^2*f^2*x^2*Sinh[(f*x)/2] + 6*d^2*Sinh[e + (f*x)/2] - 6*d^2*Sinh[e + (3*f*x)/2] + c^2*f^2*Sinh[e + (3*f*x)/2] + 2*c*d*f^2*x*Sinh[e + (3*f*x)/2] + d^2*f^2*x^2*Sinh[e + (3*f*x)/2])))/(3*a^2*f^3*(1 + Cosh[e + f*x])^2)","A",1
117,1,637,200,6.4783498,"\int \frac{(c+d x)^2}{(a+a \cosh (e+f x))^2} \, dx","Integrate[(c + d*x)^2/(a + a*Cosh[e + f*x])^2,x]","\frac{\text{sech}\left(\frac{e}{2}\right) \cosh \left(\frac{e}{2}+\frac{f x}{2}\right) \left(c^2 f^2 \sinh \left(e+\frac{3 f x}{2}\right)+3 c^2 f^2 \sinh \left(\frac{f x}{2}\right)+2 c d f^2 x \sinh \left(e+\frac{3 f x}{2}\right)+2 c d f \cosh \left(e+\frac{f x}{2}\right)+6 c d f^2 x \sinh \left(\frac{f x}{2}\right)+2 c d f \cosh \left(\frac{f x}{2}\right)+d^2 f^2 x^2 \sinh \left(e+\frac{3 f x}{2}\right)+2 d^2 \sinh \left(e+\frac{f x}{2}\right)-2 d^2 \sinh \left(e+\frac{3 f x}{2}\right)+2 d^2 f x \cosh \left(e+\frac{f x}{2}\right)+3 d^2 f^2 x^2 \sinh \left(\frac{f x}{2}\right)-4 d^2 \sinh \left(\frac{f x}{2}\right)+2 d^2 f x \cosh \left(\frac{f x}{2}\right)\right)}{3 f^3 (a \cosh (e+f x)+a)^2}-\frac{16 c d \text{sech}\left(\frac{e}{2}\right) \cosh ^4\left(\frac{e}{2}+\frac{f x}{2}\right) \left(\cosh \left(\frac{e}{2}\right) \log \left(\sinh \left(\frac{e}{2}\right) \sinh \left(\frac{f x}{2}\right)+\cosh \left(\frac{e}{2}\right) \cosh \left(\frac{f x}{2}\right)\right)-\frac{1}{2} f x \sinh \left(\frac{e}{2}\right)\right)}{3 f^2 \left(\cosh ^2\left(\frac{e}{2}\right)-\sinh ^2\left(\frac{e}{2}\right)\right) (a \cosh (e+f x)+a)^2}-\frac{16 d^2 \text{csch}\left(\frac{e}{2}\right) \text{sech}\left(\frac{e}{2}\right) \cosh ^4\left(\frac{e}{2}+\frac{f x}{2}\right) \left(\frac{1}{4} f^2 x^2 e^{-\tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)}-\frac{i \coth \left(\frac{e}{2}\right) \left(i \text{Li}_2\left(e^{2 i \left(\frac{i f x}{2}+i \tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)\right)}\right)-\frac{1}{2} f x \left(-\pi +2 i \tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)\right)-2 \left(i \tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)+\frac{i f x}{2}\right) \log \left(1-e^{2 i \left(i \tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)+\frac{i f x}{2}\right)}\right)+2 i \tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right) \log \left(i \sinh \left(\tanh ^{-1}\left(\coth \left(\frac{e}{2}\right)\right)+\frac{f x}{2}\right)\right)-\pi  \log \left(e^{f x}+1\right)+\pi  \log \left(\cosh \left(\frac{f x}{2}\right)\right)\right)}{\sqrt{1-\coth ^2\left(\frac{e}{2}\right)}}\right)}{3 f^3 \sqrt{\text{csch}^2\left(\frac{e}{2}\right) \left(\sinh ^2\left(\frac{e}{2}\right)-\cosh ^2\left(\frac{e}{2}\right)\right)} (a \cosh (e+f x)+a)^2}","-\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{4 d^2 \text{Li}_2\left(-e^{e+f x}\right)}{3 a^2 f^3}-\frac{2 d^2 \tanh \left(\frac{e}{2}+\frac{f x}{2}\right)}{3 a^2 f^3}",1,"(-16*c*d*Cosh[e/2 + (f*x)/2]^4*Sech[e/2]*(Cosh[e/2]*Log[Cosh[e/2]*Cosh[(f*x)/2] + Sinh[e/2]*Sinh[(f*x)/2]] - (f*x*Sinh[e/2])/2))/(3*f^2*(a + a*Cosh[e + f*x])^2*(Cosh[e/2]^2 - Sinh[e/2]^2)) - (16*d^2*Cosh[e/2 + (f*x)/2]^4*Csch[e/2]*((f^2*x^2)/(4*E^ArcTanh[Coth[e/2]]) - (I*Coth[e/2]*(-1/2*(f*x*(-Pi + (2*I)*ArcTanh[Coth[e/2]])) - Pi*Log[1 + E^(f*x)] - 2*((I/2)*f*x + I*ArcTanh[Coth[e/2]])*Log[1 - E^((2*I)*((I/2)*f*x + I*ArcTanh[Coth[e/2]]))] + Pi*Log[Cosh[(f*x)/2]] + (2*I)*ArcTanh[Coth[e/2]]*Log[I*Sinh[(f*x)/2 + ArcTanh[Coth[e/2]]]] + I*PolyLog[2, E^((2*I)*((I/2)*f*x + I*ArcTanh[Coth[e/2]]))]))/Sqrt[1 - Coth[e/2]^2])*Sech[e/2])/(3*f^3*(a + a*Cosh[e + f*x])^2*Sqrt[Csch[e/2]^2*(-Cosh[e/2]^2 + Sinh[e/2]^2)]) + (Cosh[e/2 + (f*x)/2]*Sech[e/2]*(2*c*d*f*Cosh[(f*x)/2] + 2*d^2*f*x*Cosh[(f*x)/2] + 2*c*d*f*Cosh[e + (f*x)/2] + 2*d^2*f*x*Cosh[e + (f*x)/2] - 4*d^2*Sinh[(f*x)/2] + 3*c^2*f^2*Sinh[(f*x)/2] + 6*c*d*f^2*x*Sinh[(f*x)/2] + 3*d^2*f^2*x^2*Sinh[(f*x)/2] + 2*d^2*Sinh[e + (f*x)/2] - 2*d^2*Sinh[e + (3*f*x)/2] + c^2*f^2*Sinh[e + (3*f*x)/2] + 2*c*d*f^2*x*Sinh[e + (3*f*x)/2] + d^2*f^2*x^2*Sinh[e + (3*f*x)/2]))/(3*f^3*(a + a*Cosh[e + f*x])^2)","C",0
118,1,114,123,0.4568467,"\int \frac{c+d x}{(a+a \cosh (e+f x))^2} \, dx","Integrate[(c + d*x)/(a + a*Cosh[e + f*x])^2,x]","\frac{\cosh \left(\frac{1}{2} (e+f x)\right) \left(f (c+d x) \left(3 \sinh \left(\frac{1}{2} (e+f x)\right)+\sinh \left(\frac{3}{2} (e+f x)\right)\right)-2 d \cosh \left(\frac{3}{2} (e+f x)\right) \log \left(\cosh \left(\frac{1}{2} (e+f x)\right)\right)+\cosh \left(\frac{1}{2} (e+f x)\right) \left(2 d-6 d \log \left(\cosh \left(\frac{1}{2} (e+f x)\right)\right)\right)\right)}{3 a^2 f^2 (\cosh (e+f x)+1)^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,"(Cosh[(e + f*x)/2]*(-2*d*Cosh[(3*(e + f*x))/2]*Log[Cosh[(e + f*x)/2]] + Cosh[(e + f*x)/2]*(2*d - 6*d*Log[Cosh[(e + f*x)/2]]) + f*(c + d*x)*(3*Sinh[(e + f*x)/2] + Sinh[(3*(e + f*x))/2])))/(3*a^2*f^2*(1 + Cosh[e + f*x])^2)","A",1
119,0,0,23,30.7644587,"\int \frac{1}{(c+d x) (a+a \cosh (e+f x))^2} \, dx","Integrate[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,"Integrate[1/((c + d*x)*(a + a*Cosh[e + f*x])^2), x]","A",-1
120,0,0,23,32.2774581,"\int \frac{1}{(c+d x)^2 (a+a \cosh (e+f x))^2} \, dx","Integrate[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,"Integrate[1/((c + d*x)^2*(a + a*Cosh[e + f*x])^2), x]","A",-1
121,1,53,110,0.2274452,"\int x^3 \sqrt{a+a \cosh (c+d x)} \, dx","Integrate[x^3*Sqrt[a + a*Cosh[c + d*x]],x]","\frac{2 \left(d x \left(d^2 x^2+24\right) \tanh \left(\frac{1}{2} (c+d x)\right)-6 \left(d^2 x^2+8\right)\right) \sqrt{a (\cosh (c+d x)+1)}}{d^4}","-\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{12 x^2 \sqrt{a \cosh (c+d x)+a}}{d^2}+\frac{2 x^3 \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d}",1,"(2*Sqrt[a*(1 + Cosh[c + d*x])]*(-6*(8 + d^2*x^2) + d*x*(24 + d^2*x^2)*Tanh[(c + d*x)/2]))/d^4","A",1
122,1,44,88,0.1593269,"\int x^2 \sqrt{a+a \cosh (c+d x)} \, dx","Integrate[x^2*Sqrt[a + a*Cosh[c + d*x]],x]","\frac{2 \left(\left(d^2 x^2+8\right) \tanh \left(\frac{1}{2} (c+d x)\right)-4 d x\right) \sqrt{a (\cosh (c+d x)+1)}}{d^3}","\frac{16 \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d^3}-\frac{8 x \sqrt{a \cosh (c+d x)+a}}{d^2}+\frac{2 x^2 \tanh \left(\frac{c}{2}+\frac{d x}{2}\right) \sqrt{a \cosh (c+d x)+a}}{d}",1,"(2*Sqrt[a*(1 + Cosh[c + d*x])]*(-4*d*x + (8 + d^2*x^2)*Tanh[(c + d*x)/2]))/d^3","A",1
123,1,34,53,0.1293554,"\int x \sqrt{a+a \cosh (c+d x)} \, dx","Integrate[x*Sqrt[a + a*Cosh[c + d*x]],x]","\frac{2 \left(d x \tanh \left(\frac{1}{2} (c+d x)\right)-2\right) \sqrt{a (\cosh (c+d x)+1)}}{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,"(2*Sqrt[a*(1 + Cosh[c + d*x])]*(-2 + d*x*Tanh[(c + d*x)/2]))/d^2","A",1
124,1,54,83,0.0749416,"\int \frac{\sqrt{a+a \cosh (c+d x)}}{x} \, dx","Integrate[Sqrt[a + a*Cosh[c + d*x]]/x,x]","\text{sech}\left(\frac{1}{2} (c+d x)\right) \sqrt{a (\cosh (c+d x)+1)} \left(\cosh \left(\frac{c}{2}\right) \text{Chi}\left(\frac{d x}{2}\right)+\sinh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right)\right)","\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,"Sqrt[a*(1 + Cosh[c + d*x])]*Sech[(c + d*x)/2]*(Cosh[c/2]*CoshIntegral[(d*x)/2] + Sinh[c/2]*SinhIntegral[(d*x)/2])","A",1
125,1,75,110,0.1407996,"\int \frac{\sqrt{a+a \cosh (c+d x)}}{x^2} \, dx","Integrate[Sqrt[a + a*Cosh[c + d*x]]/x^2,x]","\frac{\sqrt{a (\cosh (c+d x)+1)} \left(d x \sinh \left(\frac{c}{2}\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{1}{2} (c+d x)\right)+d x \cosh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{1}{2} (c+d x)\right)-2\right)}{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}",1,"(Sqrt[a*(1 + Cosh[c + d*x])]*(-2 + d*x*CoshIntegral[(d*x)/2]*Sech[(c + d*x)/2]*Sinh[c/2] + d*x*Cosh[c/2]*Sech[(c + d*x)/2]*SinhIntegral[(d*x)/2]))/(2*x)","A",1
126,1,97,151,0.2132457,"\int \frac{\sqrt{a+a \cosh (c+d x)}}{x^3} \, dx","Integrate[Sqrt[a + a*Cosh[c + d*x]]/x^3,x]","\frac{\sqrt{a (\cosh (c+d x)+1)} \left(d^2 x^2 \cosh \left(\frac{c}{2}\right) \text{Chi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{1}{2} (c+d x)\right)+d^2 x^2 \sinh \left(\frac{c}{2}\right) \text{Shi}\left(\frac{d x}{2}\right) \text{sech}\left(\frac{1}{2} (c+d x)\right)-2 d x \tanh \left(\frac{1}{2} (c+d x)\right)-4\right)}{8 x^2}","\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*(1 + Cosh[c + d*x])]*(-4 + d^2*x^2*Cosh[c/2]*CoshIntegral[(d*x)/2]*Sech[(c + d*x)/2] + d^2*x^2*Sech[(c + d*x)/2]*Sinh[c/2]*SinhIntegral[(d*x)/2] - 2*d*x*Tanh[(c + d*x)/2]))/(8*x^2)","A",1
127,1,33,68,0.0558221,"\int x^3 \sqrt{a+a \cosh (x)} \, dx","Integrate[x^3*Sqrt[a + a*Cosh[x]],x]","2 \left(x \left(x^2+24\right) \tanh \left(\frac{x}{2}\right)-6 \left(x^2+8\right)\right) \sqrt{a (\cosh (x)+1)}","2 x^3 \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-12 x^2 \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,"2*Sqrt[a*(1 + Cosh[x])]*(-6*(8 + x^2) + x*(24 + x^2)*Tanh[x/2])","A",1
128,1,31,53,0.0436437,"\int x^2 \sqrt{a+a \cosh (x)} \, dx","Integrate[x^2*Sqrt[a + a*Cosh[x]],x]","8 \left(\frac{1}{4} \left(x^2+8\right) \tanh \left(\frac{x}{2}\right)-x\right) \sqrt{a (\cosh (x)+1)}","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*Sqrt[a*(1 + Cosh[x])]*(-x + ((8 + x^2)*Tanh[x/2])/4)","A",1
129,1,22,32,0.0217755,"\int x \sqrt{a+a \cosh (x)} \, dx","Integrate[x*Sqrt[a + a*Cosh[x]],x]","2 \left(x \tanh \left(\frac{x}{2}\right)-2\right) \sqrt{a (\cosh (x)+1)}","2 x \tanh \left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}-4 \sqrt{a \cosh (x)+a}",1,"2*Sqrt[a*(1 + Cosh[x])]*(-2 + x*Tanh[x/2])","A",1
130,1,23,23,0.0079206,"\int \frac{\sqrt{a+a \cosh (x)}}{x} \, dx","Integrate[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)+1)}","\text{Chi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a \cosh (x)+a}",1,"Sqrt[a*(1 + Cosh[x])]*CoshIntegral[x/2]*Sech[x/2]","A",1
131,1,33,42,0.053925,"\int \frac{\sqrt{a+a \cosh (x)}}{x^2} \, dx","Integrate[Sqrt[a + a*Cosh[x]]/x^2,x]","\frac{\sqrt{a (\cosh (x)+1)} \left(x \text{Shi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right)-2\right)}{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}",1,"(Sqrt[a*(1 + Cosh[x])]*(-2 + x*Sech[x/2]*SinhIntegral[x/2]))/(2*x)","A",1
132,1,44,67,0.0733385,"\int \frac{\sqrt{a+a \cosh (x)}}{x^3} \, dx","Integrate[Sqrt[a + a*Cosh[x]]/x^3,x]","\frac{\sqrt{a (\cosh (x)+1)} \left(x^2 \text{Chi}\left(\frac{x}{2}\right) \text{sech}\left(\frac{x}{2}\right)-2 x \tanh \left(\frac{x}{2}\right)-4\right)}{8 x^2}","\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*(1 + Cosh[x])]*(-4 + x^2*CoshIntegral[x/2]*Sech[x/2] - 2*x*Tanh[x/2]))/(8*x^2)","A",1
133,1,70,185,0.2889395,"\int x^3 (a+a \cosh (x))^{3/2} \, dx","Integrate[x^3*(a + a*Cosh[x])^(3/2),x]","\frac{2}{27} a \sqrt{a (\cosh (x)+1)} \left(-2 \left(117 x^2+968\right)+3 x \left(15 x^2+328\right) \tanh \left(\frac{x}{2}\right)+\cosh (x) \left(3 x \left(3 x^2+8\right) \tanh \left(\frac{x}{2}\right)-2 \left(9 x^2+8\right)\right)\right)","\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{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{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,"(2*a*Sqrt[a*(1 + Cosh[x])]*(-2*(968 + 117*x^2) + 3*x*(328 + 15*x^2)*Tanh[x/2] + Cosh[x]*(-2*(8 + 9*x^2) + 3*x*(8 + 3*x^2)*Tanh[x/2])))/27","A",1
134,1,54,145,0.2187442,"\int x^2 (a+a \cosh (x))^{3/2} \, dx","Integrate[x^2*(a + a*Cosh[x])^(3/2),x]","\frac{2}{27} a \sqrt{a (\cosh (x)+1)} \left(\left(45 x^2+328\right) \tanh \left(\frac{x}{2}\right)+\cosh (x) \left(\left(9 x^2+8\right) \tanh \left(\frac{x}{2}\right)-12 x\right)-156 x\right)","\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,"(2*a*Sqrt[a*(1 + Cosh[x])]*(-156*x + (328 + 45*x^2)*Tanh[x/2] + Cosh[x]*(-12*x + (8 + 9*x^2)*Tanh[x/2])))/27","A",1
135,1,56,89,0.0852462,"\int x (a+a \cosh (x))^{3/2} \, dx","Integrate[x*(a + a*Cosh[x])^(3/2),x]","\frac{1}{9} a \text{sech}\left(\frac{x}{2}\right) \sqrt{a (\cosh (x)+1)} \left(3 x \left(9 \sinh \left(\frac{x}{2}\right)+\sinh \left(\frac{3 x}{2}\right)\right)-54 \cosh \left(\frac{x}{2}\right)-2 \cosh \left(\frac{3 x}{2}\right)\right)","-\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,"(a*Sqrt[a*(1 + Cosh[x])]*Sech[x/2]*(-54*Cosh[x/2] - 2*Cosh[(3*x)/2] + 3*x*(9*Sinh[x/2] + Sinh[(3*x)/2])))/9","A",1
136,1,36,55,0.0205049,"\int \frac{(a+a \cosh (x))^{3/2}}{x} \, dx","Integrate[(a + a*Cosh[x])^(3/2)/x,x]","\frac{1}{2} a \left(3 \text{Chi}\left(\frac{x}{2}\right)+\text{Chi}\left(\frac{3 x}{2}\right)\right) \text{sech}\left(\frac{x}{2}\right) \sqrt{a (\cosh (x)+1)}","\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,"(a*Sqrt[a*(1 + Cosh[x])]*(3*CoshIntegral[x/2] + CoshIntegral[(3*x)/2])*Sech[x/2])/2","A",1
137,1,53,79,0.0863242,"\int \frac{(a+a \cosh (x))^{3/2}}{x^2} \, dx","Integrate[(a + a*Cosh[x])^(3/2)/x^2,x]","-\frac{a \text{sech}\left(\frac{x}{2}\right) \sqrt{a (\cosh (x)+1)} \left(-3 x \text{Shi}\left(\frac{x}{2}\right)-3 x \text{Shi}\left(\frac{3 x}{2}\right)+8 \cosh ^3\left(\frac{x}{2}\right)\right)}{4 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,"-1/4*(a*Sqrt[a*(1 + Cosh[x])]*Sech[x/2]*(8*Cosh[x/2]^3 - 3*x*SinhIntegral[x/2] - 3*x*SinhIntegral[(3*x)/2]))/x","A",1
138,1,69,109,0.0649492,"\int \frac{(a+a \cosh (x))^{3/2}}{x^3} \, dx","Integrate[(a + a*Cosh[x])^(3/2)/x^3,x]","\frac{(a (\cosh (x)+1))^{3/2} \left(3 x^2 \text{Chi}\left(\frac{x}{2}\right) \text{sech}^3\left(\frac{x}{2}\right)+9 x^2 \text{Chi}\left(\frac{3 x}{2}\right) \text{sech}^3\left(\frac{x}{2}\right)-8 \left(3 x \tanh \left(\frac{x}{2}\right)+2\right)\right)}{32 x^2}","\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*(1 + Cosh[x]))^(3/2)*(3*x^2*CoshIntegral[x/2]*Sech[x/2]^3 + 9*x^2*CoshIntegral[(3*x)/2]*Sech[x/2]^3 - 8*(2 + 3*x*Tanh[x/2])))/(32*x^2)","A",1
139,1,213,383,1.7830273,"\int \frac{x^3}{\sqrt{a+a \cosh (c+d x)}} \, dx","Integrate[x^3/Sqrt[a + a*Cosh[c + d*x]],x]","\frac{2 i \cosh \left(\frac{1}{2} (c+d x)\right) \left(d^3 x^3 \log \left(1-i e^{\frac{1}{2} (c+d x)}\right)-d^3 x^3 \log \left(1+i e^{\frac{1}{2} (c+d x)}\right)-6 d^2 x^2 \text{Li}_2\left(-i e^{\frac{1}{2} (c+d x)}\right)+6 d^2 x^2 \text{Li}_2\left(i e^{\frac{1}{2} (c+d x)}\right)+24 d x \text{Li}_3\left(-i e^{\frac{1}{2} (c+d x)}\right)-24 d x \text{Li}_3\left(i e^{\frac{1}{2} (c+d x)}\right)-48 \text{Li}_4\left(-i e^{\frac{1}{2} (c+d x)}\right)+48 \text{Li}_4\left(i e^{\frac{1}{2} (c+d x)}\right)\right)}{d^4 \sqrt{a (\cosh (c+d x)+1)}}","-\frac{96 i \text{Li}_4\left(-i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^4 \sqrt{a \cosh (c+d x)+a}}+\frac{96 i \text{Li}_4\left(i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^4 \sqrt{a \cosh (c+d x)+a}}+\frac{48 i x \text{Li}_3\left(-i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}-\frac{48 i x \text{Li}_3\left(i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}-\frac{12 i x^2 \text{Li}_2\left(-i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{12 i x^2 \text{Li}_2\left(i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \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,"((2*I)*Cosh[(c + d*x)/2]*(d^3*x^3*Log[1 - I*E^((c + d*x)/2)] - d^3*x^3*Log[1 + I*E^((c + d*x)/2)] - 6*d^2*x^2*PolyLog[2, (-I)*E^((c + d*x)/2)] + 6*d^2*x^2*PolyLog[2, I*E^((c + d*x)/2)] + 24*d*x*PolyLog[3, (-I)*E^((c + d*x)/2)] - 24*d*x*PolyLog[3, I*E^((c + d*x)/2)] - 48*PolyLog[4, (-I)*E^((c + d*x)/2)] + 48*PolyLog[4, I*E^((c + d*x)/2)]))/(d^4*Sqrt[a*(1 + Cosh[c + d*x])])","A",1
140,1,163,269,1.7510532,"\int \frac{x^2}{\sqrt{a+a \cosh (c+d x)}} \, dx","Integrate[x^2/Sqrt[a + a*Cosh[c + d*x]],x]","\frac{2 i \cosh \left(\frac{1}{2} (c+d x)\right) \left(d^2 x^2 \log \left(1-i e^{\frac{1}{2} (c+d x)}\right)-d^2 x^2 \log \left(1+i e^{\frac{1}{2} (c+d x)}\right)-4 d x \text{Li}_2\left(-i e^{\frac{1}{2} (c+d x)}\right)+4 d x \text{Li}_2\left(i e^{\frac{1}{2} (c+d x)}\right)+8 \text{Li}_3\left(-i e^{\frac{1}{2} (c+d x)}\right)-8 \text{Li}_3\left(i e^{\frac{1}{2} (c+d x)}\right)\right)}{d^3 \sqrt{a (\cosh (c+d x)+1)}}","\frac{16 i \text{Li}_3\left(-i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}-\frac{16 i \text{Li}_3\left(i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^3 \sqrt{a \cosh (c+d x)+a}}-\frac{8 i x \text{Li}_2\left(-i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{8 i x \text{Li}_2\left(i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \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,"((2*I)*Cosh[(c + d*x)/2]*(d^2*x^2*Log[1 - I*E^((c + d*x)/2)] - d^2*x^2*Log[1 + I*E^((c + d*x)/2)] - 4*d*x*PolyLog[2, (-I)*E^((c + d*x)/2)] + 4*d*x*PolyLog[2, I*E^((c + d*x)/2)] + 8*PolyLog[3, (-I)*E^((c + d*x)/2)] - 8*PolyLog[3, I*E^((c + d*x)/2)]))/(d^3*Sqrt[a*(1 + Cosh[c + d*x])])","A",1
141,1,117,157,0.7073344,"\int \frac{x}{\sqrt{a+a \cosh (c+d x)}} \, dx","Integrate[x/Sqrt[a + a*Cosh[c + d*x]],x]","\frac{4 \cosh \left(\frac{1}{2} (c+d x)\right) \left(-i \text{Li}_2\left(-i \left(\cosh \left(\frac{1}{2} (c+d x)\right)+\sinh \left(\frac{1}{2} (c+d x)\right)\right)\right)+i \text{Li}_2\left(i \left(\cosh \left(\frac{1}{2} (c+d x)\right)+\sinh \left(\frac{1}{2} (c+d x)\right)\right)\right)+d x \tan ^{-1}\left(\sinh \left(\frac{1}{2} (c+d x)\right)+\cosh \left(\frac{1}{2} (c+d x)\right)\right)\right)}{d^2 \sqrt{a (\cosh (c+d x)+1)}}","-\frac{4 i \text{Li}_2\left(-i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\frac{c}{2}+\frac{d x}{2}\right)}{d^2 \sqrt{a \cosh (c+d x)+a}}+\frac{4 i \text{Li}_2\left(i e^{\frac{c}{2}+\frac{d x}{2}}\right) \cosh \left(\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*Cosh[(c + d*x)/2]*(d*x*ArcTan[Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2]] - I*PolyLog[2, (-I)*(Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2])] + I*PolyLog[2, I*(Cosh[(c + d*x)/2] + Sinh[(c + d*x)/2])]))/(d^2*Sqrt[a*(1 + Cosh[c + d*x])])","A",0
142,0,0,21,2.992245,"\int \frac{1}{x \sqrt{a+a \cosh (c+d x)}} \, dx","Integrate[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,"Integrate[1/(x*Sqrt[a + a*Cosh[c + d*x]]), x]","A",-1
143,0,0,21,1.7555066,"\int \frac{1}{x^2 \sqrt{a+a \cosh (c+d x)}} \, dx","Integrate[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,"Integrate[1/(x^2*Sqrt[a + a*Cosh[c + d*x]]), x]","A",-1
144,1,716,402,2.9725906,"\int \frac{x^3}{(a+a \cosh (x))^{3/2}} \, dx","Integrate[x^3/(a + a*Cosh[x])^(3/2),x]","-\frac{i \cosh \left(\frac{x}{2}\right) \left(48 x^2 \text{Li}_2\left(-i e^{x/2}\right) \cosh ^2\left(\frac{x}{2}\right)-48 \left(-x^2-2 i \pi  x+\pi ^2+8\right) \text{Li}_2\left(-i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+96 i \pi  x \text{Li}_2\left(i e^{x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+192 x \text{Li}_3\left(-i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)-192 x \text{Li}_3\left(-i e^{x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+384 \text{Li}_2\left(i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)-48 \pi ^2 \text{Li}_2\left(i e^{x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+192 i \pi  \text{Li}_3\left(-i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)-192 i \pi  \text{Li}_3\left(i e^{x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+384 \text{Li}_4\left(-i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+384 \text{Li}_4\left(-i e^{x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+x^4 \left(-\cosh ^2\left(\frac{x}{2}\right)\right)+8 i x^3 \sinh \left(\frac{x}{2}\right)-4 i \pi  x^3 \cosh ^2\left(\frac{x}{2}\right)-8 x^3 \log \left(1+i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+8 x^3 \log \left(1+i e^{x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+6 \pi ^2 x^2 \cosh ^2\left(\frac{x}{2}\right)+48 i x^2 \cosh \left(\frac{x}{2}\right)-24 i \pi  x^2 \log \left(1+i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+24 i \pi  x^2 \log \left(1-i e^{x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+4 i \pi ^3 x \cosh ^2\left(\frac{x}{2}\right)+7 \pi ^4 \cosh ^2\left(\frac{x}{2}\right)-192 x \log \left(1-i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+24 \pi ^2 x \log \left(1+i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+192 x \log \left(1+i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)-24 \pi ^2 x \log \left(1-i e^{x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+8 i \pi ^3 \log \left(1+i e^{-x/2}\right) \cosh ^2\left(\frac{x}{2}\right)-8 i \pi ^3 \log \left(1+i e^{x/2}\right) \cosh ^2\left(\frac{x}{2}\right)+8 i \pi ^3 \cosh ^2\left(\frac{x}{2}\right) \log \left(\tan \left(\frac{1}{4} (\pi +i x)\right)\right)\right)}{8 (a (\cosh (x)+1))^{3/2}}","-\frac{3 i x^2 \text{Li}_2\left(-i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{3 i x^2 \text{Li}_2\left(i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{12 i x \text{Li}_3\left(-i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{12 i x \text{Li}_3\left(i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{24 i \text{Li}_2\left(-i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{24 i \text{Li}_2\left(i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{24 i \text{Li}_4\left(-i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{24 i \text{Li}_4\left(i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{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{3 x^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,"((-1/8*I)*Cosh[x/2]*((48*I)*x^2*Cosh[x/2] + 7*Pi^4*Cosh[x/2]^2 + (4*I)*Pi^3*x*Cosh[x/2]^2 + 6*Pi^2*x^2*Cosh[x/2]^2 - (4*I)*Pi*x^3*Cosh[x/2]^2 - x^4*Cosh[x/2]^2 - 192*x*Cosh[x/2]^2*Log[1 - I/E^(x/2)] + (8*I)*Pi^3*Cosh[x/2]^2*Log[1 + I/E^(x/2)] + 192*x*Cosh[x/2]^2*Log[1 + I/E^(x/2)] + 24*Pi^2*x*Cosh[x/2]^2*Log[1 + I/E^(x/2)] - (24*I)*Pi*x^2*Cosh[x/2]^2*Log[1 + I/E^(x/2)] - 8*x^3*Cosh[x/2]^2*Log[1 + I/E^(x/2)] - 24*Pi^2*x*Cosh[x/2]^2*Log[1 - I*E^(x/2)] + (24*I)*Pi*x^2*Cosh[x/2]^2*Log[1 - I*E^(x/2)] - (8*I)*Pi^3*Cosh[x/2]^2*Log[1 + I*E^(x/2)] + 8*x^3*Cosh[x/2]^2*Log[1 + I*E^(x/2)] + (8*I)*Pi^3*Cosh[x/2]^2*Log[Tan[(Pi + I*x)/4]] - 48*(8 + Pi^2 - (2*I)*Pi*x - x^2)*Cosh[x/2]^2*PolyLog[2, (-I)/E^(x/2)] + 384*Cosh[x/2]^2*PolyLog[2, I/E^(x/2)] + 48*x^2*Cosh[x/2]^2*PolyLog[2, (-I)*E^(x/2)] - 48*Pi^2*Cosh[x/2]^2*PolyLog[2, I*E^(x/2)] + (96*I)*Pi*x*Cosh[x/2]^2*PolyLog[2, I*E^(x/2)] + (192*I)*Pi*Cosh[x/2]^2*PolyLog[3, (-I)/E^(x/2)] + 192*x*Cosh[x/2]^2*PolyLog[3, (-I)/E^(x/2)] - 192*x*Cosh[x/2]^2*PolyLog[3, (-I)*E^(x/2)] - (192*I)*Pi*Cosh[x/2]^2*PolyLog[3, I*E^(x/2)] + 384*Cosh[x/2]^2*PolyLog[4, (-I)/E^(x/2)] + 384*Cosh[x/2]^2*PolyLog[4, (-I)*E^(x/2)] + (8*I)*x^3*Sinh[x/2]))/(a*(1 + Cosh[x]))^(3/2)","A",1
145,1,214,248,0.9107402,"\int \frac{x^2}{(a+a \cosh (x))^{3/2}} \, dx","Integrate[x^2/(a + a*Cosh[x])^(3/2),x]","\frac{\cosh \left(\frac{x}{2}\right) \left(-4 i x \cosh ^2\left(\frac{x}{2}\right) \text{Li}_2\left(-i \left(\cosh \left(\frac{x}{2}\right)+\sinh \left(\frac{x}{2}\right)\right)\right)+4 i x \cosh ^2\left(\frac{x}{2}\right) \text{Li}_2\left(i \left(\cosh \left(\frac{x}{2}\right)+\sinh \left(\frac{x}{2}\right)\right)\right)+8 i \cosh ^2\left(\frac{x}{2}\right) \text{Li}_3\left(-i \left(\cosh \left(\frac{x}{2}\right)+\sinh \left(\frac{x}{2}\right)\right)\right)-8 i \cosh ^2\left(\frac{x}{2}\right) \text{Li}_3\left(i \left(\cosh \left(\frac{x}{2}\right)+\sinh \left(\frac{x}{2}\right)\right)\right)+x^2 \sinh \left(\frac{x}{2}\right)+2 x^2 \cosh ^2\left(\frac{x}{2}\right) \tan ^{-1}\left(\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)\right)+4 x \cosh \left(\frac{x}{2}\right)-16 \cosh ^2\left(\frac{x}{2}\right) \tan ^{-1}\left(\sinh \left(\frac{x}{2}\right)+\cosh \left(\frac{x}{2}\right)\right)\right)}{(a (\cosh (x)+1))^{3/2}}","-\frac{2 i x \text{Li}_2\left(-i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{2 i x \text{Li}_2\left(i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{4 i \text{Li}_3\left(-i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}-\frac{4 i \text{Li}_3\left(i e^{x/2}\right) \cosh \left(\frac{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,"(Cosh[x/2]*(4*x*Cosh[x/2] - 16*ArcTan[Cosh[x/2] + Sinh[x/2]]*Cosh[x/2]^2 + 2*x^2*ArcTan[Cosh[x/2] + Sinh[x/2]]*Cosh[x/2]^2 - (4*I)*x*Cosh[x/2]^2*PolyLog[2, (-I)*(Cosh[x/2] + Sinh[x/2])] + (4*I)*x*Cosh[x/2]^2*PolyLog[2, I*(Cosh[x/2] + Sinh[x/2])] + (8*I)*Cosh[x/2]^2*PolyLog[3, (-I)*(Cosh[x/2] + Sinh[x/2])] - (8*I)*Cosh[x/2]^2*PolyLog[3, I*(Cosh[x/2] + Sinh[x/2])] + x^2*Sinh[x/2]))/(a*(1 + Cosh[x]))^(3/2)","A",0
146,1,137,140,0.1072625,"\int \frac{x}{(a+a \cosh (x))^{3/2}} \, dx","Integrate[x/(a + a*Cosh[x])^(3/2),x]","\frac{2 \cosh ^3\left(\frac{x}{2}\right) \left(-i \left(\text{Li}_2\left(-i e^{-x/2}\right)-\text{Li}_2\left(i e^{-x/2}\right)\right)-\frac{1}{2} i x \left(\log \left(1-i e^{-x/2}\right)-\log \left(1+i e^{-x/2}\right)\right)\right)}{(a (\cosh (x)+1))^{3/2}}+\frac{2 \cosh ^2\left(\frac{x}{2}\right)}{(a (\cosh (x)+1))^{3/2}}+\frac{x \sinh \left(\frac{x}{2}\right) \cosh \left(\frac{x}{2}\right)}{(a (\cosh (x)+1))^{3/2}}","-\frac{i \text{Li}_2\left(-i e^{x/2}\right) \cosh \left(\frac{x}{2}\right)}{a \sqrt{a \cosh (x)+a}}+\frac{i \text{Li}_2\left(i e^{x/2}\right) \cosh \left(\frac{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,"(2*Cosh[x/2]^2)/(a*(1 + Cosh[x]))^(3/2) + (2*Cosh[x/2]^3*((-1/2*I)*x*(Log[1 - I/E^(x/2)] - Log[1 + I/E^(x/2)]) - I*(PolyLog[2, (-I)/E^(x/2)] - PolyLog[2, I/E^(x/2)])))/(a*(1 + Cosh[x]))^(3/2) + (x*Cosh[x/2]*Sinh[x/2])/(a*(1 + Cosh[x]))^(3/2)","A",1
147,0,0,17,8.9377013,"\int \frac{1}{x (a+a \cosh (x))^{3/2}} \, dx","Integrate[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,"Integrate[1/(x*(a + a*Cosh[x])^(3/2)), x]","A",-1
148,0,0,17,10.67556,"\int \frac{1}{x^2 (a+a \cosh (x))^{3/2}} \, dx","Integrate[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,"Integrate[1/(x^2*(a + a*Cosh[x])^(3/2)), x]","A",-1
149,0,0,21,2.7978277,"\int \frac{\sqrt[3]{a+a \cosh (c+d x)}}{x} \, dx","Integrate[(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,"Integrate[(a + a*Cosh[c + d*x])^(1/3)/x, x]","A",-1
150,0,0,23,6.5242808,"\int (c+d x)^m (a+a \cosh (e+f x))^n \, dx","Integrate[(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,"Integrate[(c + d*x)^m*(a + a*Cosh[e + f*x])^n, x]","A",-1
151,1,429,402,2.4203149,"\int (c+d x)^m (a+a \cosh (e+f x))^3 \, dx","Integrate[(c + d*x)^m*(a + a*Cosh[e + f*x])^3,x]","-\frac{a^3 2^{-m-6} 3^{-m-1} e^{-3 \left(\frac{c f}{d}+e\right)} (c+d x)^m (\cosh (e+f x)+1)^3 \text{sech}^6\left(\frac{1}{2} (e+f x)\right) \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(2^m e^{\frac{3 c f}{d}} \left(d (m+1) e^{\frac{3 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{3 f (c+d x)}{d}\right)-20 e^{3 e} f 3^{m+1} (c+d x) \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^m\right)+d \left(-3^{m+2}\right) (m+1) e^{\frac{c f}{d}+5 e} \left(f \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)-d e^{6 e} 2^m (m+1) \left(\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,-\frac{3 f (c+d x)}{d}\right)-5 d 2^m 3^{m+2} (m+1) e^{\frac{2 c f}{d}+4 e} \left(\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)+5 d 2^m 3^{m+2} (m+1) e^{\frac{4 c f}{d}+2 e} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)+d 3^{m+2} (m+1) e^{\frac{5 c f}{d}+e} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)\right)}{d f (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} \Gamma \left(m+1,-\frac{3 f (c+d x)}{d}\right)}{8 f}+\frac{3 a^3 2^{-m-3} e^{2 e-\frac{2 c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)}{f}+\frac{15 a^3 e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{8 f}-\frac{15 a^3 e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{8 f}-\frac{3 a^3 2^{-m-3} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}-\frac{a^3 3^{-m-1} e^{\frac{3 c f}{d}-3 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{3 f (c+d x)}{d}\right)}{8 f}+\frac{5 a^3 (c+d x)^{m+1}}{2 d (m+1)}",1,"-((2^(-6 - m)*3^(-1 - m)*a^3*(c + d*x)^m*(1 + Cosh[e + f*x])^3*(-(2^m*d*E^(6*e)*(1 + m)*((f*(c + d*x))/d)^m*Gamma[1 + m, (-3*f*(c + d*x))/d]) - 3^(2 + m)*d*E^(5*e + (c*f)/d)*(1 + m)*(f*(c/d + x))^m*Gamma[1 + m, (-2*f*(c + d*x))/d] - 5*2^m*3^(2 + m)*d*E^(4*e + (2*c*f)/d)*(1 + m)*((f*(c + d*x))/d)^m*Gamma[1 + m, -((f*(c + d*x))/d)] + 5*2^m*3^(2 + m)*d*E^(2*e + (4*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (f*(c + d*x))/d] + 3^(2 + m)*d*E^(e + (5*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (2*f*(c + d*x))/d] + 2^m*E^((3*c*f)/d)*(-20*3^(1 + m)*E^(3*e)*f*(c + d*x)*(-((f^2*(c + d*x)^2)/d^2))^m + d*E^((3*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (3*f*(c + d*x))/d]))*Sech[(e + f*x)/2]^6)/(d*E^(3*(e + (c*f)/d))*f*(1 + m)*(-((f^2*(c + d*x)^2)/d^2))^m))","A",1
152,1,302,263,1.092732,"\int (c+d x)^m (a+a \cosh (e+f x))^2 \, dx","Integrate[(c + d*x)^m*(a + a*Cosh[e + f*x])^2,x]","-\frac{a^2 2^{-m-5} e^{-2 \left(\frac{c f}{d}+e\right)} (c+d x)^m (\cosh (e+f x)+1)^2 \text{sech}^4\left(\frac{1}{2} (e+f x)\right) \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(-3 f 2^{m+2} (c+d x) e^{2 \left(\frac{c f}{d}+e\right)} \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^m-d e^{4 e} (m+1) \left(f \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)-d 2^{m+3} (m+1) e^{\frac{c f}{d}+3 e} \left(f \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)+d 2^{m+3} (m+1) e^{\frac{3 c f}{d}+e} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)+d (m+1) e^{\frac{4 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)\right)}{d f (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} \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} \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} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{f}-\frac{a^2 2^{-m-3} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}+\frac{3 a^2 (c+d x)^{m+1}}{2 d (m+1)}",1,"-((2^(-5 - m)*a^2*(c + d*x)^m*(1 + Cosh[e + f*x])^2*(-3*2^(2 + m)*E^(2*(e + (c*f)/d))*f*(c + d*x)*(-((f^2*(c + d*x)^2)/d^2))^m - d*E^(4*e)*(1 + m)*(f*(c/d + x))^m*Gamma[1 + m, (-2*f*(c + d*x))/d] - 2^(3 + m)*d*E^(3*e + (c*f)/d)*(1 + m)*(f*(c/d + x))^m*Gamma[1 + m, -((f*(c + d*x))/d)] + 2^(3 + m)*d*E^(e + (3*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (f*(c + d*x))/d] + d*E^((4*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (2*f*(c + d*x))/d])*Sech[(e + f*x)/2]^4)/(d*E^(2*(e + (c*f)/d))*f*(1 + m)*(-((f^2*(c + d*x)^2)/d^2))^m))","A",1
153,1,189,131,0.3346956,"\int (c+d x)^m (a+a \cosh (e+f x)) \, dx","Integrate[(c + d*x)^m*(a + a*Cosh[e + f*x]),x]","-\frac{a e^{-\frac{c f}{d}-e} (c+d x)^m (\cosh (e+f x)+1) \text{sech}^2\left(\frac{1}{2} (e+f x)\right) \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(-2 f (c+d x) e^{\frac{c f}{d}+e} \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^m-d e^{2 e} (m+1) \left(f \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)+d (m+1) e^{\frac{2 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)\right)}{4 d f (m+1)}","\frac{a e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{2 f}-\frac{a e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{2 f}+\frac{a (c+d x)^{m+1}}{d (m+1)}",1,"-1/4*(a*E^(-e - (c*f)/d)*(c + d*x)^m*(1 + Cosh[e + f*x])*(-2*E^(e + (c*f)/d)*f*(c + d*x)*(-((f^2*(c + d*x)^2)/d^2))^m - d*E^(2*e)*(1 + m)*(f*(c/d + x))^m*Gamma[1 + m, -((f*(c + d*x))/d)] + d*E^((2*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (f*(c + d*x))/d])*Sech[(e + f*x)/2]^2)/(d*f*(1 + m)*(-((f^2*(c + d*x)^2)/d^2))^m)","A",1
154,0,0,23,5.2532354,"\int \frac{(c+d x)^m}{a+a \cosh (e+f x)} \, dx","Integrate[(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,"Integrate[(c + d*x)^m/(a + a*Cosh[e + f*x]), x]","A",-1
155,0,0,23,9.8720009,"\int \frac{(c+d x)^m}{(a+a \cosh (e+f x))^2} \, dx","Integrate[(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,"Integrate[(c + d*x)^m/(a + a*Cosh[e + f*x])^2, x]","A",-1
156,1,123,89,0.511015,"\int (c+d x)^3 (a+b \cosh (e+f x)) \, dx","Integrate[(c + d*x)^3*(a + b*Cosh[e + f*x]),x]","\frac{1}{4} a x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)-\frac{3 b d \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \cosh (e+f x)}{f^4}+\frac{b (c+d x) \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+6\right)\right) \sinh (e+f x)}{f^3}","\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*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3))/4 - (3*b*d*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Cosh[e + f*x])/f^4 + (b*(c + d*x)*(c^2*f^2 + 2*c*d*f^2*x + d^2*(6 + f^2*x^2))*Sinh[e + f*x])/f^3","A",1
157,1,83,67,0.3463058,"\int (c+d x)^2 (a+b \cosh (e+f x)) \, dx","Integrate[(c + d*x)^2*(a + b*Cosh[e + f*x]),x]","\frac{1}{3} a x \left(3 c^2+3 c d x+d^2 x^2\right)+\frac{b \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \sinh (e+f x)}{f^3}-\frac{2 b d (c+d x) \cosh (e+f x)}{f^2}","\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*x*(3*c^2 + 3*c*d*x + d^2*x^2))/3 - (2*b*d*(c + d*x)*Cosh[e + f*x])/f^2 + (b*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Sinh[e + f*x])/f^3","A",1
158,1,46,45,0.1153315,"\int (c+d x) (a+b \cosh (e+f x)) \, dx","Integrate[(c + d*x)*(a + b*Cosh[e + f*x]),x]","\frac{f (a f x (2 c+d x)+2 b (c+d x) \sinh (e+f x))-2 b d \cosh (e+f x)}{2 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,"(-2*b*d*Cosh[e + f*x] + f*(a*f*x*(2*c + d*x) + 2*b*(c + d*x)*Sinh[e + f*x]))/(2*f^2)","A",1
159,1,57,64,0.1466535,"\int \frac{a+b \cosh (e+f x)}{c+d x} \, dx","Integrate[(a + b*Cosh[e + f*x])/(c + d*x),x]","\frac{a \log (c+d x)+b \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+b \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)}{d}","\frac{a \log (c+d x)}{d}+\frac{b \text{Chi}\left(x f+\frac{c f}{d}\right) \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[f*(c/d + x)] + a*Log[c + d*x] + b*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)])/d","A",1
160,1,71,87,0.4185972,"\int \frac{a+b \cosh (e+f x)}{(c+d x)^2} \, dx","Integrate[(a + b*Cosh[e + f*x])/(c + d*x)^2,x]","\frac{-\frac{d (a+b \cosh (e+f x))}{c+d x}+b f \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+b f \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)}{d^2}","-\frac{a}{d (c+d x)}+\frac{b f \text{Chi}\left(x f+\frac{c f}{d}\right) \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,"(-((d*(a + b*Cosh[e + f*x]))/(c + d*x)) + b*f*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] + b*f*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)])/d^2","A",1
161,1,95,123,0.634551,"\int \frac{a+b \cosh (e+f x)}{(c+d x)^3} \, dx","Integrate[(a + b*Cosh[e + f*x])/(c + d*x)^3,x]","\frac{-\frac{d (a d+b f (c+d x) \sinh (e+f x)+b d \cosh (e+f x))}{(c+d x)^2}+b f^2 \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+b f^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)}{2 d^3}","-\frac{a}{2 d (c+d x)^2}+\frac{b f^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \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,"(b*f^2*Cosh[e - (c*f)/d]*CoshIntegral[f*(c/d + x)] - (d*(a*d + b*d*Cosh[e + f*x] + b*f*(c + d*x)*Sinh[e + f*x]))/(c + d*x)^2 + b*f^2*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)])/(2*d^3)","A",1
162,1,232,250,1.5246221,"\int (c+d x)^3 (a+b \cosh (e+f x))^2 \, dx","Integrate[(c + d*x)^3*(a + b*Cosh[e + f*x])^2,x]","\frac{2 f \left(f^3 x \left(2 a^2+b^2\right) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)+16 a b (c+d x) \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+6\right)\right) \sinh (e+f x)+b^2 (c+d x) \left(2 c^2 f^2+4 c d f^2 x+d^2 \left(2 f^2 x^2+3\right)\right) \sinh (2 (e+f x))\right)-96 a b d \left(c^2 f^2+2 c d f^2 x+d^2 \left(f^2 x^2+2\right)\right) \cosh (e+f x)-3 b^2 d \left(2 c^2 f^2+4 c d f^2 x+d^2 \left(2 f^2 x^2+1\right)\right) \cosh (2 (e+f x))}{16 f^4}","\frac{a^2 (c+d x)^4}{4 d}+\frac{12 a b d^2 (c+d x) \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,"(-96*a*b*d*(c^2*f^2 + 2*c*d*f^2*x + d^2*(2 + f^2*x^2))*Cosh[e + f*x] - 3*b^2*d*(2*c^2*f^2 + 4*c*d*f^2*x + d^2*(1 + 2*f^2*x^2))*Cosh[2*(e + f*x)] + 2*f*((2*a^2 + b^2)*f^3*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) + 16*a*b*(c + d*x)*(c^2*f^2 + 2*c*d*f^2*x + d^2*(6 + f^2*x^2))*Sinh[e + f*x] + b^2*(c + d*x)*(2*c^2*f^2 + 4*c*d*f^2*x + d^2*(3 + 2*f^2*x^2))*Sinh[2*(e + f*x)]))/(16*f^4)","A",1
163,1,252,182,1.0453175,"\int (c+d x)^2 (a+b \cosh (e+f x))^2 \, dx","Integrate[(c + d*x)^2*(a + b*Cosh[e + f*x])^2,x]","\frac{1}{24} \left(24 a^2 c^2 x+24 a^2 c d x^2+8 a^2 d^2 x^3+\frac{48 a b c^2 \sinh (e+f x)}{f}-\frac{96 a b d (c+d x) \cosh (e+f x)}{f^2}+\frac{96 a b c d x \sinh (e+f x)}{f}+\frac{96 a b d^2 \sinh (e+f x)}{f^3}+\frac{48 a b d^2 x^2 \sinh (e+f x)}{f}+\frac{6 b^2 c^2 \sinh (2 (e+f x))}{f}+12 b^2 c^2 x-\frac{6 b^2 d (c+d x) \cosh (2 (e+f x))}{f^2}+\frac{12 b^2 c d x \sinh (2 (e+f x))}{f}+12 b^2 c d x^2+\frac{3 b^2 d^2 \sinh (2 (e+f x))}{f^3}+\frac{6 b^2 d^2 x^2 \sinh (2 (e+f x))}{f}+4 b^2 d^2 x^3\right)","\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,"(24*a^2*c^2*x + 12*b^2*c^2*x + 24*a^2*c*d*x^2 + 12*b^2*c*d*x^2 + 8*a^2*d^2*x^3 + 4*b^2*d^2*x^3 - (96*a*b*d*(c + d*x)*Cosh[e + f*x])/f^2 - (6*b^2*d*(c + d*x)*Cosh[2*(e + f*x)])/f^2 + (96*a*b*d^2*Sinh[e + f*x])/f^3 + (48*a*b*c^2*Sinh[e + f*x])/f + (96*a*b*c*d*x*Sinh[e + f*x])/f + (48*a*b*d^2*x^2*Sinh[e + f*x])/f + (3*b^2*d^2*Sinh[2*(e + f*x)])/f^3 + (6*b^2*c^2*Sinh[2*(e + f*x)])/f + (12*b^2*c*d*x*Sinh[2*(e + f*x)])/f + (6*b^2*d^2*x^2*Sinh[2*(e + f*x)])/f)/24","A",1
164,1,96,116,0.8929547,"\int (c+d x) (a+b \cosh (e+f x))^2 \, dx","Integrate[(c + d*x)*(a + b*Cosh[e + f*x])^2,x]","-\frac{2 \left(2 a^2+b^2\right) (e+f x) (d (e-f x)-2 c f)-16 a b f (c+d x) \sinh (e+f x)+16 a b d \cosh (e+f x)-2 b^2 f (c+d x) \sinh (2 (e+f x))+b^2 d \cosh (2 (e+f x))}{8 f^2}","\frac{a^2 (c+d x)^2}{2 d}+\frac{2 a b (c+d x) \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,"-1/8*(2*(2*a^2 + b^2)*(e + f*x)*(-2*c*f + d*(e - f*x)) + 16*a*b*d*Cosh[e + f*x] + b^2*d*Cosh[2*(e + f*x)] - 16*a*b*f*(c + d*x)*Sinh[e + f*x] - 2*b^2*f*(c + d*x)*Sinh[2*(e + f*x)])/f^2","A",1
165,1,133,156,0.3100478,"\int \frac{(a+b \cosh (e+f x))^2}{c+d x} \, dx","Integrate[(a + b*Cosh[e + f*x])^2/(c + d*x),x]","\frac{2 a^2 \log (c+d x)+4 a b \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)+4 a b \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+b^2 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)+b^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+b^2 \log (c+d x)}{2 d}","\frac{a^2 \log (c+d x)}{d}+\frac{2 a b \text{Chi}\left(x f+\frac{c f}{d}\right) \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,"(4*a*b*Cosh[e - (c*f)/d]*CoshIntegral[f*(c/d + x)] + b^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*f*(c + d*x))/d] + 2*a^2*Log[c + d*x] + b^2*Log[c + d*x] + 4*a*b*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + b^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d])/(2*d)","A",1
166,1,233,183,0.7957601,"\int \frac{(a+b \cosh (e+f x))^2}{(c+d x)^2} \, dx","Integrate[(a + b*Cosh[e + f*x])^2/(c + d*x)^2,x]","\frac{-2 a^2 d+4 a b f (c+d x) \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \sinh \left(e-\frac{c f}{d}\right)+4 a b c f \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+4 a b d f x \cosh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-4 a b d \cosh (e+f x)+2 b^2 f (c+d x) \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \sinh \left(2 e-\frac{2 c f}{d}\right)+2 b^2 c f \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+2 b^2 d f x \cosh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-b^2 d \cosh (2 (e+f x))-b^2 d}{2 d^2 (c+d x)}","-\frac{a^2}{d (c+d x)}+\frac{2 a b f \text{Chi}\left(x f+\frac{c f}{d}\right) \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,"(-2*a^2*d - b^2*d - 4*a*b*d*Cosh[e + f*x] - b^2*d*Cosh[2*(e + f*x)] + 2*b^2*f*(c + d*x)*CoshIntegral[(2*f*(c + d*x))/d]*Sinh[2*e - (2*c*f)/d] + 4*a*b*f*(c + d*x)*CoshIntegral[f*(c/d + x)]*Sinh[e - (c*f)/d] + 4*a*b*c*f*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 4*a*b*d*f*x*Cosh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] + 2*b^2*c*f*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] + 2*b^2*d*f*x*Cosh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d])/(2*d^2*(c + d*x))","A",1
167,1,394,242,1.3197619,"\int \frac{(a+b \cosh (e+f x))^2}{(c+d x)^3} \, dx","Integrate[(a + b*Cosh[e + f*x])^2/(c + d*x)^3,x]","-\frac{2 a^2 d^2-4 a b c^2 f^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-4 a b f^2 (c+d x)^2 \text{Chi}\left(f \left(\frac{c}{d}+x\right)\right) \cosh \left(e-\frac{c f}{d}\right)-4 a b d^2 f^2 x^2 \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)-8 a b c d f^2 x \sinh \left(e-\frac{c f}{d}\right) \text{Shi}\left(f \left(\frac{c}{d}+x\right)\right)+4 a b c d f \sinh (e+f x)+4 a b d^2 f x \sinh (e+f x)+4 a b d^2 \cosh (e+f x)-4 b^2 c^2 f^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-4 b^2 f^2 (c+d x)^2 \text{Chi}\left(\frac{2 f (c+d x)}{d}\right) \cosh \left(2 e-\frac{2 c f}{d}\right)-4 b^2 d^2 f^2 x^2 \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)-8 b^2 c d f^2 x \sinh \left(2 e-\frac{2 c f}{d}\right) \text{Shi}\left(\frac{2 f (c+d x)}{d}\right)+2 b^2 c d f \sinh (2 (e+f x))+2 b^2 d^2 f x \sinh (2 (e+f x))+b^2 d^2 \cosh (2 (e+f x))+b^2 d^2}{4 d^3 (c+d x)^2}","-\frac{a^2}{2 d (c+d x)^2}+\frac{a b f^2 \text{Chi}\left(x f+\frac{c f}{d}\right) \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,"-1/4*(2*a^2*d^2 + b^2*d^2 + 4*a*b*d^2*Cosh[e + f*x] + b^2*d^2*Cosh[2*(e + f*x)] - 4*a*b*f^2*(c + d*x)^2*Cosh[e - (c*f)/d]*CoshIntegral[f*(c/d + x)] - 4*b^2*f^2*(c + d*x)^2*Cosh[2*e - (2*c*f)/d]*CoshIntegral[(2*f*(c + d*x))/d] + 4*a*b*c*d*f*Sinh[e + f*x] + 4*a*b*d^2*f*x*Sinh[e + f*x] + 2*b^2*c*d*f*Sinh[2*(e + f*x)] + 2*b^2*d^2*f*x*Sinh[2*(e + f*x)] - 4*a*b*c^2*f^2*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] - 8*a*b*c*d*f^2*x*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] - 4*a*b*d^2*f^2*x^2*Sinh[e - (c*f)/d]*SinhIntegral[f*(c/d + x)] - 4*b^2*c^2*f^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] - 8*b^2*c*d*f^2*x*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d] - 4*b^2*d^2*f^2*x^2*Sinh[2*e - (2*c*f)/d]*SinhIntegral[(2*f*(c + d*x))/d])/(d^3*(c + d*x)^2)","A",1
168,1,384,436,1.6171606,"\int \frac{(c+d x)^3}{a+b \cosh (e+f x)} \, dx","Integrate[(c + d*x)^3/(a + b*Cosh[e + f*x]),x]","\frac{\frac{3 d \left(f^2 (c+d x)^2 \text{Li}_2\left(\frac{b (\cosh (e+f x)+\sinh (e+f x))}{\sqrt{a^2-b^2}-a}\right)-2 d f (c+d x) \text{Li}_3\left(\frac{b (\cosh (e+f x)+\sinh (e+f x))}{\sqrt{a^2-b^2}-a}\right)+2 d^2 \text{Li}_4\left(\frac{b (\cosh (e+f x)+\sinh (e+f x))}{\sqrt{a^2-b^2}-a}\right)\right)}{f^3}-\frac{3 d \left(f^2 (c+d x)^2 \text{Li}_2\left(-\frac{b (\cosh (e+f x)+\sinh (e+f x))}{a+\sqrt{a^2-b^2}}\right)-2 d f (c+d x) \text{Li}_3\left(-\frac{b (\cosh (e+f x)+\sinh (e+f x))}{a+\sqrt{a^2-b^2}}\right)+2 d^2 \text{Li}_4\left(-\frac{b (\cosh (e+f x)+\sinh (e+f x))}{a+\sqrt{a^2-b^2}}\right)\right)}{f^3}+(c+d x)^3 \log \left(\frac{b (\sinh (e+f x)+\cosh (e+f x))}{a-\sqrt{a^2-b^2}}+1\right)-(c+d x)^3 \log \left(\frac{b (\sinh (e+f x)+\cosh (e+f x))}{\sqrt{a^2-b^2}+a}+1\right)}{f \sqrt{a^2-b^2}}","-\frac{6 d^2 (c+d x) \text{Li}_3\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \sqrt{a^2-b^2}}+\frac{6 d^2 (c+d x) \text{Li}_3\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^3 \sqrt{a^2-b^2}}+\frac{3 d (c+d x)^2 \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}-\frac{3 d (c+d x)^2 \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}+\frac{(c+d x)^3 \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}+1\right)}{f \sqrt{a^2-b^2}}-\frac{(c+d x)^3 \log \left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}+a}+1\right)}{f \sqrt{a^2-b^2}}+\frac{6 d^3 \text{Li}_4\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right)}{f^4 \sqrt{a^2-b^2}}-\frac{6 d^3 \text{Li}_4\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^4 \sqrt{a^2-b^2}}",1,"((c + d*x)^3*Log[1 + (b*(Cosh[e + f*x] + Sinh[e + f*x]))/(a - Sqrt[a^2 - b^2])] - (c + d*x)^3*Log[1 + (b*(Cosh[e + f*x] + Sinh[e + f*x]))/(a + Sqrt[a^2 - b^2])] + (3*d*(f^2*(c + d*x)^2*PolyLog[2, (b*(Cosh[e + f*x] + Sinh[e + f*x]))/(-a + Sqrt[a^2 - b^2])] - 2*d*f*(c + d*x)*PolyLog[3, (b*(Cosh[e + f*x] + Sinh[e + f*x]))/(-a + Sqrt[a^2 - b^2])] + 2*d^2*PolyLog[4, (b*(Cosh[e + f*x] + Sinh[e + f*x]))/(-a + Sqrt[a^2 - b^2])]))/f^3 - (3*d*(f^2*(c + d*x)^2*PolyLog[2, -((b*(Cosh[e + f*x] + Sinh[e + f*x]))/(a + Sqrt[a^2 - b^2]))] - 2*d*f*(c + d*x)*PolyLog[3, -((b*(Cosh[e + f*x] + Sinh[e + f*x]))/(a + Sqrt[a^2 - b^2]))] + 2*d^2*PolyLog[4, -((b*(Cosh[e + f*x] + Sinh[e + f*x]))/(a + Sqrt[a^2 - b^2]))]))/f^3)/(Sqrt[a^2 - b^2]*f)","A",1
169,1,247,320,1.0543269,"\int \frac{(c+d x)^2}{a+b \cosh (e+f x)} \, dx","Integrate[(c + d*x)^2/(a + b*Cosh[e + f*x]),x]","\frac{\frac{2 d \left(f (c+d x) \text{Li}_2\left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}-a}\right)-d \text{Li}_3\left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}-a}\right)\right)}{f^2}-\frac{2 d \left(f (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)-d \text{Li}_3\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)\right)}{f^2}+(c+d x)^2 \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}+1\right)-(c+d x)^2 \log \left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}+a}+1\right)}{f \sqrt{a^2-b^2}}","\frac{2 d (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}-\frac{2 d (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}+\frac{(c+d x)^2 \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}+1\right)}{f \sqrt{a^2-b^2}}-\frac{(c+d x)^2 \log \left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}+a}+1\right)}{f \sqrt{a^2-b^2}}-\frac{2 d^2 \text{Li}_3\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \sqrt{a^2-b^2}}+\frac{2 d^2 \text{Li}_3\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^3 \sqrt{a^2-b^2}}",1,"((c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 - b^2])] - (c + d*x)^2*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 - b^2])] + (2*d*(f*(c + d*x)*PolyLog[2, (b*E^(e + f*x))/(-a + Sqrt[a^2 - b^2])] - d*PolyLog[3, (b*E^(e + f*x))/(-a + Sqrt[a^2 - b^2])]))/f^2 - (2*d*(f*(c + d*x)*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 - b^2]))] - d*PolyLog[3, -((b*E^(e + f*x))/(a + Sqrt[a^2 - b^2]))]))/f^2)/(Sqrt[a^2 - b^2]*f)","A",1
170,1,152,203,0.9638412,"\int \frac{c+d x}{a+b \cosh (e+f x)} \, dx","Integrate[(c + d*x)/(a + b*Cosh[e + f*x]),x]","\frac{f (c+d x) \left(\log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}+1\right)-\log \left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}+a}+1\right)\right)+d \text{Li}_2\left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}-a}\right)-d \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}","\frac{(c+d x) \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}+1\right)}{f \sqrt{a^2-b^2}}-\frac{(c+d x) \log \left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}+a}+1\right)}{f \sqrt{a^2-b^2}}+\frac{d \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}-\frac{d \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^2 \sqrt{a^2-b^2}}",1,"(f*(c + d*x)*(Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 - b^2])] - Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 - b^2])]) + d*PolyLog[2, (b*E^(e + f*x))/(-a + Sqrt[a^2 - b^2])] - d*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 - b^2]))])/(Sqrt[a^2 - b^2]*f^2)","A",1
171,0,0,23,0.9725076,"\int \frac{1}{(c+d x) (a+b \cosh (e+f x))} \, dx","Integrate[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,"Integrate[1/((c + d*x)*(a + b*Cosh[e + f*x])), x]","A",-1
172,0,0,23,1.0234163,"\int \frac{1}{(c+d x)^2 (a+b \cosh (e+f x))} \, dx","Integrate[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,"Integrate[1/((c + d*x)^2*(a + b*Cosh[e + f*x])), x]","A",-1
173,1,11178,823,27.1962289,"\int \frac{(c+d x)^3}{(a+b \cosh (e+f x))^2} \, dx","Integrate[(c + d*x)^3/(a + b*Cosh[e + f*x])^2,x]","\text{Result too large to show}","-\frac{6 \text{Li}_3\left(-\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{Li}_3\left(-\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{Li}_4\left(-\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{Li}_4\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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{Li}_3\left(-\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{Li}_3\left(-\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{Li}_2\left(-\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{Li}_2\left(-\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,"Result too large to show","B",0
174,1,6018,593,22.8033449,"\int \frac{(c+d x)^2}{(a+b \cosh (e+f x))^2} \, dx","Integrate[(c + d*x)^2/(a + b*Cosh[e + f*x])^2,x]","\text{Result too large to show}","\frac{2 a d (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}-\frac{2 a d (c+d x) \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}+\frac{2 d (c+d x) \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}+1\right)}{f^2 \left(a^2-b^2\right)}+\frac{2 d (c+d x) \log \left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}+a}+1\right)}{f^2 \left(a^2-b^2\right)}+\frac{a (c+d x)^2 \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}+1\right)}{f \left(a^2-b^2\right)^{3/2}}-\frac{a (c+d x)^2 \log \left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}+a}+1\right)}{f \left(a^2-b^2\right)^{3/2}}-\frac{b (c+d x)^2 \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 d^2 \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \left(a^2-b^2\right)}+\frac{2 d^2 \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^3 \left(a^2-b^2\right)}-\frac{2 a d^2 \text{Li}_3\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right)}{f^3 \left(a^2-b^2\right)^{3/2}}+\frac{2 a d^2 \text{Li}_3\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^3 \left(a^2-b^2\right)^{3/2}}",1,"Result too large to show","B",0
175,1,509,274,5.0376478,"\int \frac{c+d x}{(a+b \cosh (e+f x))^2} \, dx","Integrate[(c + d*x)/(a + b*Cosh[e + f*x])^2,x]","\frac{\frac{\left(a^2-b^2\right) \left(2 a c f \sqrt{b^2-a^2} \tanh ^{-1}\left(\frac{a+b e^{e+f x}}{\sqrt{a^2-b^2}}\right)-a d \sqrt{b^2-a^2} \text{Li}_2\left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}-a}\right)+a d \sqrt{b^2-a^2} \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)+d \sqrt{-\left(a^2-b^2\right)^2} (e+f x)-a d \sqrt{b^2-a^2} (e+f x) \log \left(\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}+1\right)+a d \sqrt{b^2-a^2} (e+f x) \log \left(\frac{b e^{e+f x}}{\sqrt{a^2-b^2}+a}+1\right)-d \sqrt{-\left(a^2-b^2\right)^2} \log \left(2 a e^{e+f x}+b e^{2 (e+f x)}+b\right)-2 a d \sqrt{a^2-b^2} \tan ^{-1}\left(\frac{a+b e^{e+f x}}{\sqrt{b^2-a^2}}\right)-2 a d \sqrt{b^2-a^2} \tanh ^{-1}\left(\frac{a+b e^{e+f x}}{\sqrt{a^2-b^2}}\right)-2 a d e \sqrt{b^2-a^2} \tanh ^{-1}\left(\frac{a+b e^{e+f x}}{\sqrt{a^2-b^2}}\right)\right)}{\left(-\left(a^2-b^2\right)^2\right)^{3/2}}-\frac{b f (c+d x) \sinh (e+f x)}{(a-b) (a+b) (a+b \cosh (e+f x))}}{f^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{a d \text{Li}_2\left(-\frac{b e^{e+f x}}{a-\sqrt{a^2-b^2}}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}-\frac{a d \text{Li}_2\left(-\frac{b e^{e+f x}}{a+\sqrt{a^2-b^2}}\right)}{f^2 \left(a^2-b^2\right)^{3/2}}+\frac{d \log (a+b \cosh (e+f x))}{f^2 \left(a^2-b^2\right)}",1,"(((a^2 - b^2)*(Sqrt[-(a^2 - b^2)^2]*d*(e + f*x) - 2*a*Sqrt[a^2 - b^2]*d*ArcTan[(a + b*E^(e + f*x))/Sqrt[-a^2 + b^2]] - 2*a*Sqrt[-a^2 + b^2]*d*ArcTanh[(a + b*E^(e + f*x))/Sqrt[a^2 - b^2]] - 2*a*Sqrt[-a^2 + b^2]*d*e*ArcTanh[(a + b*E^(e + f*x))/Sqrt[a^2 - b^2]] + 2*a*Sqrt[-a^2 + b^2]*c*f*ArcTanh[(a + b*E^(e + f*x))/Sqrt[a^2 - b^2]] - a*Sqrt[-a^2 + b^2]*d*(e + f*x)*Log[1 + (b*E^(e + f*x))/(a - Sqrt[a^2 - b^2])] + a*Sqrt[-a^2 + b^2]*d*(e + f*x)*Log[1 + (b*E^(e + f*x))/(a + Sqrt[a^2 - b^2])] - Sqrt[-(a^2 - b^2)^2]*d*Log[b + 2*a*E^(e + f*x) + b*E^(2*(e + f*x))] - a*Sqrt[-a^2 + b^2]*d*PolyLog[2, (b*E^(e + f*x))/(-a + Sqrt[a^2 - b^2])] + a*Sqrt[-a^2 + b^2]*d*PolyLog[2, -((b*E^(e + f*x))/(a + Sqrt[a^2 - b^2]))]))/(-(a^2 - b^2)^2)^(3/2) - (b*f*(c + d*x)*Sinh[e + f*x])/((a - b)*(a + b)*(a + b*Cosh[e + f*x])))/f^2","A",0
176,0,0,23,51.5337008,"\int \frac{1}{(c+d x) (a+b \cosh (e+f x))^2} \, dx","Integrate[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,"Integrate[1/((c + d*x)*(a + b*Cosh[e + f*x])^2), x]","A",-1
177,0,0,23,54.9576364,"\int \frac{1}{(c+d x)^2 (a+b \cosh (e+f x))^2} \, dx","Integrate[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,"Integrate[1/((c + d*x)^2*(a + b*Cosh[e + f*x])^2), x]","A",-1
178,0,0,23,4.5309073,"\int (c+d x)^m (a+b \cosh (e+f x))^n \, dx","Integrate[(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,"Integrate[(c + d*x)^m*(a + b*Cosh[e + f*x])^n, x]","A",-1
179,1,447,543,1.7384186,"\int (c+d x)^m (a+b \cosh (e+f x))^3 \, dx","Integrate[(c + d*x)^m*(a + b*Cosh[e + f*x])^3,x]","\frac{2^{-m-3} 3^{-m-1} e^{-3 \left(\frac{c f}{d}+e\right)} (c+d x)^m \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^{-m} \left(b d 2^m 3^{m+2} (m+1) \left(4 a^2+b^2\right) e^{\frac{2 c f}{d}+4 e} \left(\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)-e^{\frac{3 c f}{d}} \left(b d 2^m 3^{m+2} (m+1) \left(4 a^2+b^2\right) e^{\frac{c f}{d}+2 e} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)+2^m \left(b^3 d (m+1) e^{\frac{3 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{3 f (c+d x)}{d}\right)-4 a e^{3 e} f 3^{m+1} \left(2 a^2+3 b^2\right) (c+d x) \left(-\frac{f^2 (c+d x)^2}{d^2}\right)^m\right)+a b^2 d 3^{m+2} (m+1) e^{\frac{2 c f}{d}+e} \left(-\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)\right)+a b^2 d 3^{m+2} (m+1) e^{\frac{c f}{d}+5 e} \left(f \left(\frac{c}{d}+x\right)\right)^m \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)+b^3 d e^{6 e} 2^m (m+1) \left(\frac{f (c+d x)}{d}\right)^m \Gamma \left(m+1,-\frac{3 f (c+d x)}{d}\right)\right)}{d f (m+1)}","\frac{a^3 (c+d x)^{m+1}}{d (m+1)}+\frac{3 a^2 b e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{2 f}-\frac{3 a^2 b e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{2 f}+\frac{3 a b^2 2^{-m-3} e^{2 e-\frac{2 c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)}{f}-\frac{3 a b^2 2^{-m-3} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}+\frac{3 a b^2 (c+d x)^{m+1}}{2 d (m+1)}+\frac{b^3 3^{-m-1} e^{3 e-\frac{3 c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{3 f (c+d x)}{d}\right)}{8 f}+\frac{3 b^3 e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{8 f}-\frac{3 b^3 e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{8 f}-\frac{b^3 3^{-m-1} e^{\frac{3 c f}{d}-3 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{3 f (c+d x)}{d}\right)}{8 f}",1,"(2^(-3 - m)*3^(-1 - m)*(c + d*x)^m*(2^m*b^3*d*E^(6*e)*(1 + m)*((f*(c + d*x))/d)^m*Gamma[1 + m, (-3*f*(c + d*x))/d] + 3^(2 + m)*a*b^2*d*E^(5*e + (c*f)/d)*(1 + m)*(f*(c/d + x))^m*Gamma[1 + m, (-2*f*(c + d*x))/d] + 2^m*3^(2 + m)*b*(4*a^2 + b^2)*d*E^(4*e + (2*c*f)/d)*(1 + m)*((f*(c + d*x))/d)^m*Gamma[1 + m, -((f*(c + d*x))/d)] - E^((3*c*f)/d)*(2^m*3^(2 + m)*b*(4*a^2 + b^2)*d*E^(2*e + (c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (f*(c + d*x))/d] + 3^(2 + m)*a*b^2*d*E^(e + (2*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (2*f*(c + d*x))/d] + 2^m*(-4*3^(1 + m)*a*(2*a^2 + 3*b^2)*E^(3*e)*f*(c + d*x)*(-((f^2*(c + d*x)^2)/d^2))^m + b^3*d*E^((3*c*f)/d)*(1 + m)*(-((f*(c + d*x))/d))^m*Gamma[1 + m, (3*f*(c + d*x))/d]))))/(d*E^(3*(e + (c*f)/d))*f*(1 + m)*(-((f^2*(c + d*x)^2)/d^2))^m)","A",1
180,1,254,282,0.8049551,"\int (c+d x)^m (a+b \cosh (e+f x))^2 \, dx","Integrate[(c + d*x)^m*(a + b*Cosh[e + f*x])^2,x]","\frac{(c+d x)^m \left(8 a^2 f (c+d x)+8 a b d (m+1) e^{e-\frac{c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)-8 a b d (m+1) e^{\frac{c f}{d}-e} \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)+b^2 d 2^{-m} (m+1) e^{2 e-\frac{2 c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)-b^2 d 2^{-m} (m+1) e^{\frac{2 c f}{d}-2 e} \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)+4 b^2 f (c+d x)\right)}{8 d f (m+1)}","\frac{a^2 (c+d x)^{m+1}}{d (m+1)}+\frac{a b e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{f}-\frac{a b e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{f}+\frac{b^2 2^{-m-3} e^{2 e-\frac{2 c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{2 f (c+d x)}{d}\right)}{f}-\frac{b^2 2^{-m-3} e^{\frac{2 c f}{d}-2 e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{2 f (c+d x)}{d}\right)}{f}+\frac{b^2 (c+d x)^{m+1}}{2 d (m+1)}",1,"((c + d*x)^m*(8*a^2*f*(c + d*x) + 4*b^2*f*(c + d*x) + (b^2*d*E^(2*e - (2*c*f)/d)*(1 + m)*Gamma[1 + m, (-2*f*(c + d*x))/d])/(2^m*(-((f*(c + d*x))/d))^m) + (8*a*b*d*E^(e - (c*f)/d)*(1 + m)*Gamma[1 + m, -((f*(c + d*x))/d)])/(-((f*(c + d*x))/d))^m - (8*a*b*d*E^(-e + (c*f)/d)*(1 + m)*Gamma[1 + m, (f*(c + d*x))/d])/((f*(c + d*x))/d)^m - (b^2*d*E^(-2*e + (2*c*f)/d)*(1 + m)*Gamma[1 + m, (2*f*(c + d*x))/d])/(2^m*((f*(c + d*x))/d)^m)))/(8*d*f*(1 + m))","A",1
181,1,119,131,0.1843399,"\int (c+d x)^m (a+b \cosh (e+f x)) \, dx","Integrate[(c + d*x)^m*(a + b*Cosh[e + f*x]),x]","\frac{1}{2} (c+d x)^m \left(\frac{2 a (c+d x)}{d (m+1)}-\frac{b e^{\frac{c f}{d}-e} \left(f \left(\frac{c}{d}+x\right)\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{f}+\frac{b e^{e-\frac{c f}{d}} \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{f}\right)","\frac{a (c+d x)^{m+1}}{d (m+1)}+\frac{b e^{e-\frac{c f}{d}} (c+d x)^m \left(-\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,-\frac{f (c+d x)}{d}\right)}{2 f}-\frac{b e^{\frac{c f}{d}-e} (c+d x)^m \left(\frac{f (c+d x)}{d}\right)^{-m} \Gamma \left(m+1,\frac{f (c+d x)}{d}\right)}{2 f}",1,"((c + d*x)^m*((2*a*(c + d*x))/(d*(1 + m)) + (b*E^(e - (c*f)/d)*Gamma[1 + m, -((f*(c + d*x))/d)])/(f*(-((f*(c + d*x))/d))^m) - (b*E^(-e + (c*f)/d)*Gamma[1 + m, (f*(c + d*x))/d])/(f*(f*(c/d + x))^m)))/2","A",1
182,0,0,23,1.2030197,"\int \frac{(c+d x)^m}{a+b \cosh (e+f x)} \, dx","Integrate[(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,"Integrate[(c + d*x)^m/(a + b*Cosh[e + f*x]), x]","A",-1
183,0,0,23,5.5752705,"\int \frac{(c+d x)^m}{(a+b \cosh (e+f x))^2} \, dx","Integrate[(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,"Integrate[(c + d*x)^m/(a + b*Cosh[e + f*x])^2, x]","A",-1