1,1,82,124,0.1608134,"\int x^3 (a+b x) \cosh (c+d x) \, dx","Integrate[x^3*(a + b*x)*Cosh[c + d*x],x]","\frac{\left(a d^2 x \left(d^2 x^2+6\right)+b \left(d^4 x^4+12 d^2 x^2+24\right)\right) \sinh (c+d x)-d \left(3 a \left(d^2 x^2+2\right)+4 b x \left(d^2 x^2+6\right)\right) \cosh (c+d x)}{d^5}","-\frac{6 a \cosh (c+d x)}{d^4}+\frac{6 a x \sinh (c+d x)}{d^3}-\frac{3 a x^2 \cosh (c+d x)}{d^2}+\frac{a x^3 \sinh (c+d x)}{d}+\frac{24 b \sinh (c+d x)}{d^5}-\frac{24 b x \cosh (c+d x)}{d^4}+\frac{12 b x^2 \sinh (c+d x)}{d^3}-\frac{4 b x^3 \cosh (c+d x)}{d^2}+\frac{b x^4 \sinh (c+d x)}{d}",1,"(-(d*(3*a*(2 + d^2*x^2) + 4*b*x*(6 + d^2*x^2))*Cosh[c + d*x]) + (a*d^2*x*(6 + d^2*x^2) + b*(24 + 12*d^2*x^2 + d^4*x^4))*Sinh[c + d*x])/d^5","A",1
2,1,65,94,0.1368749,"\int x^2 (a+b x) \cosh (c+d x) \, dx","Integrate[x^2*(a + b*x)*Cosh[c + d*x],x]","\frac{d \left(a \left(d^2 x^2+2\right)+b x \left(d^2 x^2+6\right)\right) \sinh (c+d x)-\left(2 a d^2 x+3 b \left(d^2 x^2+2\right)\right) \cosh (c+d x)}{d^4}","\frac{2 a \sinh (c+d x)}{d^3}-\frac{2 a x \cosh (c+d x)}{d^2}+\frac{a x^2 \sinh (c+d x)}{d}-\frac{6 b \cosh (c+d x)}{d^4}+\frac{6 b x \sinh (c+d x)}{d^3}-\frac{3 b x^2 \cosh (c+d x)}{d^2}+\frac{b x^3 \sinh (c+d x)}{d}",1,"(-((2*a*d^2*x + 3*b*(2 + d^2*x^2))*Cosh[c + d*x]) + d*(a*(2 + d^2*x^2) + b*x*(6 + d^2*x^2))*Sinh[c + d*x])/d^4","A",1
3,1,45,64,0.0971156,"\int x (a+b x) \cosh (c+d x) \, dx","Integrate[x*(a + b*x)*Cosh[c + d*x],x]","\frac{\left(a d^2 x+b \left(d^2 x^2+2\right)\right) \sinh (c+d x)-d (a+2 b x) \cosh (c+d x)}{d^3}","-\frac{a \cosh (c+d x)}{d^2}+\frac{a x \sinh (c+d x)}{d}+\frac{2 b \sinh (c+d x)}{d^3}-\frac{2 b x \cosh (c+d x)}{d^2}+\frac{b x^2 \sinh (c+d x)}{d}",1,"(-(d*(a + 2*b*x)*Cosh[c + d*x]) + (a*d^2*x + b*(2 + d^2*x^2))*Sinh[c + d*x])/d^3","A",1
4,1,27,28,0.0553056,"\int (a+b x) \cosh (c+d x) \, dx","Integrate[(a + b*x)*Cosh[c + d*x],x]","\frac{d (a+b x) \sinh (c+d x)-b \cosh (c+d x)}{d^2}","\frac{(a+b x) \sinh (c+d x)}{d}-\frac{b \cosh (c+d x)}{d^2}",1,"(-(b*Cosh[c + d*x]) + d*(a + b*x)*Sinh[c + d*x])/d^2","A",1
5,1,39,28,0.028525,"\int \frac{(a+b x) \cosh (c+d x)}{x} \, dx","Integrate[((a + b*x)*Cosh[c + d*x])/x,x]","a \cosh (c) \text{Chi}(d x)+a \sinh (c) \text{Shi}(d x)+\frac{b \sinh (c) \cosh (d x)}{d}+\frac{b \cosh (c) \sinh (d x)}{d}","a \cosh (c) \text{Chi}(d x)+a \sinh (c) \text{Shi}(d x)+\frac{b \sinh (c+d x)}{d}",1,"a*Cosh[c]*CoshIntegral[d*x] + (b*Cosh[d*x]*Sinh[c])/d + (b*Cosh[c]*Sinh[d*x])/d + a*Sinh[c]*SinhIntegral[d*x]","A",1
6,1,59,47,0.1362467,"\int \frac{(a+b x) \cosh (c+d x)}{x^2} \, dx","Integrate[((a + b*x)*Cosh[c + d*x])/x^2,x]","a d (\sinh (c) \text{Chi}(d x)+\cosh (c) \text{Shi}(d x))-\frac{a \sinh (c) \sinh (d x)}{x}-\frac{a \cosh (c) \cosh (d x)}{x}+b \cosh (c) \text{Chi}(d x)+b \sinh (c) \text{Shi}(d x)","a d \sinh (c) \text{Chi}(d x)+a d \cosh (c) \text{Shi}(d x)-\frac{a \cosh (c+d x)}{x}+b \cosh (c) \text{Chi}(d x)+b \sinh (c) \text{Shi}(d x)",1,"-((a*Cosh[c]*Cosh[d*x])/x) + b*Cosh[c]*CoshIntegral[d*x] - (a*Sinh[c]*Sinh[d*x])/x + b*Sinh[c]*SinhIntegral[d*x] + a*d*(CoshIntegral[d*x]*Sinh[c] + Cosh[c]*SinhIntegral[d*x])","A",1
7,1,78,88,0.1655489,"\int \frac{(a+b x) \cosh (c+d x)}{x^3} \, dx","Integrate[((a + b*x)*Cosh[c + d*x])/x^3,x]","\frac{d x^2 \text{Chi}(d x) (a d \cosh (c)+2 b \sinh (c))+d x^2 \text{Shi}(d x) (a d \sinh (c)+2 b \cosh (c))-a d x \sinh (c+d x)-a \cosh (c+d x)-2 b x \cosh (c+d x)}{2 x^2}","\frac{1}{2} a d^2 \cosh (c) \text{Chi}(d x)+\frac{1}{2} a d^2 \sinh (c) \text{Shi}(d x)-\frac{a \cosh (c+d x)}{2 x^2}-\frac{a d \sinh (c+d x)}{2 x}+b d \sinh (c) \text{Chi}(d x)+b d \cosh (c) \text{Shi}(d x)-\frac{b \cosh (c+d x)}{x}",1,"(-(a*Cosh[c + d*x]) - 2*b*x*Cosh[c + d*x] + d*x^2*CoshIntegral[d*x]*(a*d*Cosh[c] + 2*b*Sinh[c]) - a*d*x*Sinh[c + d*x] + d*x^2*(2*b*Cosh[c] + a*d*Sinh[c])*SinhIntegral[d*x])/(2*x^2)","A",1
8,1,110,132,0.2922766,"\int \frac{(a+b x) \cosh (c+d x)}{x^4} \, dx","Integrate[((a + b*x)*Cosh[c + d*x])/x^4,x]","-\frac{-d^2 x^3 \text{Chi}(d x) (a d \sinh (c)+3 b \cosh (c))-d^2 x^3 \text{Shi}(d x) (a d \cosh (c)+3 b \sinh (c))+a d^2 x^2 \cosh (c+d x)+a d x \sinh (c+d x)+2 a \cosh (c+d x)+3 b d x^2 \sinh (c+d x)+3 b x \cosh (c+d x)}{6 x^3}","\frac{1}{6} a d^3 \sinh (c) \text{Chi}(d x)+\frac{1}{6} a d^3 \cosh (c) \text{Shi}(d x)-\frac{a d^2 \cosh (c+d x)}{6 x}-\frac{a \cosh (c+d x)}{3 x^3}-\frac{a d \sinh (c+d x)}{6 x^2}+\frac{1}{2} b d^2 \cosh (c) \text{Chi}(d x)+\frac{1}{2} b d^2 \sinh (c) \text{Shi}(d x)-\frac{b \cosh (c+d x)}{2 x^2}-\frac{b d \sinh (c+d x)}{2 x}",1,"-1/6*(2*a*Cosh[c + d*x] + 3*b*x*Cosh[c + d*x] + a*d^2*x^2*Cosh[c + d*x] - d^2*x^3*CoshIntegral[d*x]*(3*b*Cosh[c] + a*d*Sinh[c]) + a*d*x*Sinh[c + d*x] + 3*b*d*x^2*Sinh[c + d*x] - d^2*x^3*(a*d*Cosh[c] + 3*b*Sinh[c])*SinhIntegral[d*x])/x^3","A",1
9,1,140,166,0.3496439,"\int \frac{(a+b x) \cosh (c+d x)}{x^5} \, dx","Integrate[((a + b*x)*Cosh[c + d*x])/x^5,x]","-\frac{-d^3 x^4 \text{Chi}(d x) (a d \cosh (c)+4 b \sinh (c))-d^3 x^4 \text{Shi}(d x) (a d \sinh (c)+4 b \cosh (c))+a d^3 x^3 \sinh (c+d x)+a d^2 x^2 \cosh (c+d x)+2 a d x \sinh (c+d x)+6 a \cosh (c+d x)+4 b d^2 x^3 \cosh (c+d x)+4 b d x^2 \sinh (c+d x)+8 b x \cosh (c+d x)}{24 x^4}","\frac{1}{24} a d^4 \cosh (c) \text{Chi}(d x)+\frac{1}{24} a d^4 \sinh (c) \text{Shi}(d x)-\frac{a d^3 \sinh (c+d x)}{24 x}-\frac{a d^2 \cosh (c+d x)}{24 x^2}-\frac{a \cosh (c+d x)}{4 x^4}-\frac{a d \sinh (c+d x)}{12 x^3}+\frac{1}{6} b d^3 \sinh (c) \text{Chi}(d x)+\frac{1}{6} b d^3 \cosh (c) \text{Shi}(d x)-\frac{b d^2 \cosh (c+d x)}{6 x}-\frac{b \cosh (c+d x)}{3 x^3}-\frac{b d \sinh (c+d x)}{6 x^2}",1,"-1/24*(6*a*Cosh[c + d*x] + 8*b*x*Cosh[c + d*x] + a*d^2*x^2*Cosh[c + d*x] + 4*b*d^2*x^3*Cosh[c + d*x] - d^3*x^4*CoshIntegral[d*x]*(a*d*Cosh[c] + 4*b*Sinh[c]) + 2*a*d*x*Sinh[c + d*x] + 4*b*d*x^2*Sinh[c + d*x] + a*d^3*x^3*Sinh[c + d*x] - d^3*x^4*(4*b*Cosh[c] + a*d*Sinh[c])*SinhIntegral[d*x])/x^4","A",1
10,1,100,184,0.2768826,"\int x^2 (a+b x)^2 \cosh (c+d x) \, dx","Integrate[x^2*(a + b*x)^2*Cosh[c + d*x],x]","\frac{\left(a^2 d^2 \left(d^2 x^2+2\right)+2 a b d^2 x \left(d^2 x^2+6\right)+b^2 \left(d^4 x^4+12 d^2 x^2+24\right)\right) \sinh (c+d x)-2 d (a+2 b x) \left(a d^2 x+b \left(d^2 x^2+6\right)\right) \cosh (c+d x)}{d^5}","\frac{2 a^2 \sinh (c+d x)}{d^3}-\frac{2 a^2 x \cosh (c+d x)}{d^2}+\frac{a^2 x^2 \sinh (c+d x)}{d}-\frac{12 a b \cosh (c+d x)}{d^4}+\frac{12 a b x \sinh (c+d x)}{d^3}-\frac{6 a b x^2 \cosh (c+d x)}{d^2}+\frac{2 a b x^3 \sinh (c+d x)}{d}+\frac{24 b^2 \sinh (c+d x)}{d^5}-\frac{24 b^2 x \cosh (c+d x)}{d^4}+\frac{12 b^2 x^2 \sinh (c+d x)}{d^3}-\frac{4 b^2 x^3 \cosh (c+d x)}{d^2}+\frac{b^2 x^4 \sinh (c+d x)}{d}",1,"(-2*d*(a + 2*b*x)*(a*d^2*x + b*(6 + d^2*x^2))*Cosh[c + d*x] + (a^2*d^2*(2 + d^2*x^2) + 2*a*b*d^2*x*(6 + d^2*x^2) + b^2*(24 + 12*d^2*x^2 + d^4*x^4))*Sinh[c + d*x])/d^5","A",1
11,1,87,134,0.2168845,"\int x (a+b x)^2 \cosh (c+d x) \, dx","Integrate[x*(a + b*x)^2*Cosh[c + d*x],x]","\frac{d \left(a^2 d^2 x+2 a b \left(d^2 x^2+2\right)+b^2 x \left(d^2 x^2+6\right)\right) \sinh (c+d x)-\left(a^2 d^2+4 a b d^2 x+3 b^2 \left(d^2 x^2+2\right)\right) \cosh (c+d x)}{d^4}","-\frac{a^2 \cosh (c+d x)}{d^2}+\frac{a^2 x \sinh (c+d x)}{d}+\frac{4 a b \sinh (c+d x)}{d^3}-\frac{4 a b x \cosh (c+d x)}{d^2}+\frac{2 a b x^2 \sinh (c+d x)}{d}-\frac{6 b^2 \cosh (c+d x)}{d^4}+\frac{6 b^2 x \sinh (c+d x)}{d^3}-\frac{3 b^2 x^2 \cosh (c+d x)}{d^2}+\frac{b^2 x^3 \sinh (c+d x)}{d}",1,"(-((a^2*d^2 + 4*a*b*d^2*x + 3*b^2*(2 + d^2*x^2))*Cosh[c + d*x]) + d*(a^2*d^2*x + 2*a*b*(2 + d^2*x^2) + b^2*x*(6 + d^2*x^2))*Sinh[c + d*x])/d^4","A",1
12,1,56,49,0.1535169,"\int (a+b x)^2 \cosh (c+d x) \, dx","Integrate[(a + b*x)^2*Cosh[c + d*x],x]","\frac{\left(a^2 d^2+2 a b d^2 x+b^2 \left(d^2 x^2+2\right)\right) \sinh (c+d x)-2 b d (a+b x) \cosh (c+d x)}{d^3}","-\frac{2 b (a+b x) \cosh (c+d x)}{d^2}+\frac{(a+b x)^2 \sinh (c+d x)}{d}+\frac{2 b^2 \sinh (c+d x)}{d^3}",1,"(-2*b*d*(a + b*x)*Cosh[c + d*x] + (a^2*d^2 + 2*a*b*d^2*x + b^2*(2 + d^2*x^2))*Sinh[c + d*x])/d^3","A",1
13,1,51,62,0.2501821,"\int \frac{(a+b x)^2 \cosh (c+d x)}{x} \, dx","Integrate[((a + b*x)^2*Cosh[c + d*x])/x,x]","a^2 \cosh (c) \text{Chi}(d x)+a^2 \sinh (c) \text{Shi}(d x)+\frac{b (d (2 a+b x) \sinh (c+d x)-b \cosh (c+d x))}{d^2}","a^2 \cosh (c) \text{Chi}(d x)+a^2 \sinh (c) \text{Shi}(d x)+\frac{2 a b \sinh (c+d x)}{d}-\frac{b^2 \cosh (c+d x)}{d^2}+\frac{b^2 x \sinh (c+d x)}{d}",1,"a^2*Cosh[c]*CoshIntegral[d*x] + (b*(-(b*Cosh[c + d*x]) + d*(2*a + b*x)*Sinh[c + d*x]))/d^2 + a^2*Sinh[c]*SinhIntegral[d*x]","A",1
14,1,62,70,0.24519,"\int \frac{(a+b x)^2 \cosh (c+d x)}{x^2} \, dx","Integrate[((a + b*x)^2*Cosh[c + d*x])/x^2,x]","-\frac{a^2 \cosh (c+d x)}{x}+a \text{Chi}(d x) (a d \sinh (c)+2 b \cosh (c))+a \text{Shi}(d x) (a d \cosh (c)+2 b \sinh (c))+\frac{b^2 \sinh (c+d x)}{d}","a^2 d \sinh (c) \text{Chi}(d x)+a^2 d \cosh (c) \text{Shi}(d x)-\frac{a^2 \cosh (c+d x)}{x}+2 a b \cosh (c) \text{Chi}(d x)+2 a b \sinh (c) \text{Shi}(d x)+\frac{b^2 \sinh (c+d x)}{d}",1,"-((a^2*Cosh[c + d*x])/x) + a*CoshIntegral[d*x]*(2*b*Cosh[c] + a*d*Sinh[c]) + (b^2*Sinh[c + d*x])/d + a*(a*d*Cosh[c] + 2*b*Sinh[c])*SinhIntegral[d*x]","A",1
15,1,93,121,0.3985959,"\int \frac{(a+b x)^2 \cosh (c+d x)}{x^3} \, dx","Integrate[((a + b*x)^2*Cosh[c + d*x])/x^3,x]","\frac{1}{2} \left(\text{Chi}(d x) \left(\cosh (c) \left(a^2 d^2+2 b^2\right)+4 a b d \sinh (c)\right)+\text{Shi}(d x) \left(\sinh (c) \left(a^2 d^2+2 b^2\right)+4 a b d \cosh (c)\right)-\frac{a ((a+4 b x) \cosh (c+d x)+a d x \sinh (c+d x))}{x^2}\right)","\frac{1}{2} a^2 d^2 \cosh (c) \text{Chi}(d x)+\frac{1}{2} a^2 d^2 \sinh (c) \text{Shi}(d x)-\frac{a^2 \cosh (c+d x)}{2 x^2}-\frac{a^2 d \sinh (c+d x)}{2 x}+2 a b d \sinh (c) \text{Chi}(d x)+2 a b d \cosh (c) \text{Shi}(d x)-\frac{2 a b \cosh (c+d x)}{x}+b^2 \cosh (c) \text{Chi}(d x)+b^2 \sinh (c) \text{Shi}(d x)",1,"(CoshIntegral[d*x]*((2*b^2 + a^2*d^2)*Cosh[c] + 4*a*b*d*Sinh[c]) - (a*((a + 4*b*x)*Cosh[c + d*x] + a*d*x*Sinh[c + d*x]))/x^2 + (4*a*b*d*Cosh[c] + (2*b^2 + a^2*d^2)*Sinh[c])*SinhIntegral[d*x])/2","A",1
16,1,154,172,0.4865648,"\int \frac{(a+b x)^2 \cosh (c+d x)}{x^4} \, dx","Integrate[((a + b*x)^2*Cosh[c + d*x])/x^4,x]","-\frac{-d x^3 \text{Chi}(d x) \left(\sinh (c) \left(a^2 d^2+6 b^2\right)+6 a b d \cosh (c)\right)-d x^3 \text{Shi}(d x) \left(a^2 d^2 \cosh (c)+6 a b d \sinh (c)+6 b^2 \cosh (c)\right)+a^2 d^2 x^2 \cosh (c+d x)+a^2 d x \sinh (c+d x)+2 a^2 \cosh (c+d x)+6 a b d x^2 \sinh (c+d x)+6 a b x \cosh (c+d x)+6 b^2 x^2 \cosh (c+d x)}{6 x^3}","\frac{1}{6} a^2 d^3 \sinh (c) \text{Chi}(d x)+\frac{1}{6} a^2 d^3 \cosh (c) \text{Shi}(d x)-\frac{a^2 d^2 \cosh (c+d x)}{6 x}-\frac{a^2 \cosh (c+d x)}{3 x^3}-\frac{a^2 d \sinh (c+d x)}{6 x^2}+a b d^2 \cosh (c) \text{Chi}(d x)+a b d^2 \sinh (c) \text{Shi}(d x)-\frac{a b \cosh (c+d x)}{x^2}-\frac{a b d \sinh (c+d x)}{x}+b^2 d \sinh (c) \text{Chi}(d x)+b^2 d \cosh (c) \text{Shi}(d x)-\frac{b^2 \cosh (c+d x)}{x}",1,"-1/6*(2*a^2*Cosh[c + d*x] + 6*a*b*x*Cosh[c + d*x] + 6*b^2*x^2*Cosh[c + d*x] + a^2*d^2*x^2*Cosh[c + d*x] - d*x^3*CoshIntegral[d*x]*(6*a*b*d*Cosh[c] + (6*b^2 + a^2*d^2)*Sinh[c]) + a^2*d*x*Sinh[c + d*x] + 6*a*b*d*x^2*Sinh[c + d*x] - d*x^3*(6*b^2*Cosh[c] + a^2*d^2*Cosh[c] + 6*a*b*d*Sinh[c])*SinhIntegral[d*x])/x^3","A",1
17,1,206,248,0.5860422,"\int \frac{(a+b x)^2 \cosh (c+d x)}{x^5} \, dx","Integrate[((a + b*x)^2*Cosh[c + d*x])/x^5,x]","-\frac{-d^2 x^4 \text{Chi}(d x) \left(\cosh (c) \left(a^2 d^2+12 b^2\right)+8 a b d \sinh (c)\right)-d^2 x^4 \text{Shi}(d x) \left(a^2 d^2 \sinh (c)+8 a b d \cosh (c)+12 b^2 \sinh (c)\right)+a^2 d^3 x^3 \sinh (c+d x)+a^2 d^2 x^2 \cosh (c+d x)+2 a^2 d x \sinh (c+d x)+6 a^2 \cosh (c+d x)+8 a b d^2 x^3 \cosh (c+d x)+8 a b d x^2 \sinh (c+d x)+16 a b x \cosh (c+d x)+12 b^2 d x^3 \sinh (c+d x)+12 b^2 x^2 \cosh (c+d x)}{24 x^4}","\frac{1}{24} a^2 d^4 \cosh (c) \text{Chi}(d x)+\frac{1}{24} a^2 d^4 \sinh (c) \text{Shi}(d x)-\frac{a^2 d^3 \sinh (c+d x)}{24 x}-\frac{a^2 d^2 \cosh (c+d x)}{24 x^2}-\frac{a^2 \cosh (c+d x)}{4 x^4}-\frac{a^2 d \sinh (c+d x)}{12 x^3}+\frac{1}{3} a b d^3 \sinh (c) \text{Chi}(d x)+\frac{1}{3} a b d^3 \cosh (c) \text{Shi}(d x)-\frac{a b d^2 \cosh (c+d x)}{3 x}-\frac{2 a b \cosh (c+d x)}{3 x^3}-\frac{a b d \sinh (c+d x)}{3 x^2}+\frac{1}{2} b^2 d^2 \cosh (c) \text{Chi}(d x)+\frac{1}{2} b^2 d^2 \sinh (c) \text{Shi}(d x)-\frac{b^2 \cosh (c+d x)}{2 x^2}-\frac{b^2 d \sinh (c+d x)}{2 x}",1,"-1/24*(6*a^2*Cosh[c + d*x] + 16*a*b*x*Cosh[c + d*x] + 12*b^2*x^2*Cosh[c + d*x] + a^2*d^2*x^2*Cosh[c + d*x] + 8*a*b*d^2*x^3*Cosh[c + d*x] - d^2*x^4*CoshIntegral[d*x]*((12*b^2 + a^2*d^2)*Cosh[c] + 8*a*b*d*Sinh[c]) + 2*a^2*d*x*Sinh[c + d*x] + 8*a*b*d*x^2*Sinh[c + d*x] + 12*b^2*d*x^3*Sinh[c + d*x] + a^2*d^3*x^3*Sinh[c + d*x] - d^2*x^4*(8*a*b*d*Cosh[c] + 12*b^2*Sinh[c] + a^2*d^2*Sinh[c])*SinhIntegral[d*x])/x^4","A",1
18,1,159,219,0.6515255,"\int \frac{x^4 \cosh (c+d x)}{a+b x} \, dx","Integrate[(x^4*Cosh[c + d*x])/(a + b*x),x]","\frac{a^4 d^4 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)+a^4 d^4 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-b \left(b \left(a^2 d^2-2 a b d^2 x+3 b^2 \left(d^2 x^2+2\right)\right) \cosh (c+d x)+d \left(a^3 d^2-a^2 b d^2 x+a b^2 \left(d^2 x^2+2\right)-b^3 x \left(d^2 x^2+6\right)\right) \sinh (c+d x)\right)}{b^5 d^4}","\frac{a^4 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^5}+\frac{a^4 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^5}-\frac{a^3 \sinh (c+d x)}{b^4 d}-\frac{a^2 \cosh (c+d x)}{b^3 d^2}+\frac{a^2 x \sinh (c+d x)}{b^3 d}-\frac{2 a \sinh (c+d x)}{b^2 d^3}+\frac{2 a x \cosh (c+d x)}{b^2 d^2}-\frac{a x^2 \sinh (c+d x)}{b^2 d}-\frac{6 \cosh (c+d x)}{b d^4}+\frac{6 x \sinh (c+d x)}{b d^3}-\frac{3 x^2 \cosh (c+d x)}{b d^2}+\frac{x^3 \sinh (c+d x)}{b d}",1,"(a^4*d^4*Cosh[c - (a*d)/b]*CoshIntegral[d*(a/b + x)] - b*(b*(a^2*d^2 - 2*a*b*d^2*x + 3*b^2*(2 + d^2*x^2))*Cosh[c + d*x] + d*(a^3*d^2 - a^2*b*d^2*x + a*b^2*(2 + d^2*x^2) - b^3*x*(6 + d^2*x^2))*Sinh[c + d*x]) + a^4*d^4*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/(b^5*d^4)","A",1
19,1,118,150,0.4511526,"\int \frac{x^3 \cosh (c+d x)}{a+b x} \, dx","Integrate[(x^3*Cosh[c + d*x])/(a + b*x),x]","\frac{-a^3 d^3 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)-a^3 d^3 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+b \left(\left(a^2 d^2-a b d^2 x+b^2 \left(d^2 x^2+2\right)\right) \sinh (c+d x)+b d (a-2 b x) \cosh (c+d x)\right)}{b^4 d^3}","-\frac{a^3 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{a^3 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^4}+\frac{a^2 \sinh (c+d x)}{b^3 d}+\frac{a \cosh (c+d x)}{b^2 d^2}-\frac{a x \sinh (c+d x)}{b^2 d}+\frac{2 \sinh (c+d x)}{b d^3}-\frac{2 x \cosh (c+d x)}{b d^2}+\frac{x^2 \sinh (c+d x)}{b d}",1,"(-(a^3*d^3*Cosh[c - (a*d)/b]*CoshIntegral[d*(a/b + x)]) + b*(b*d*(a - 2*b*x)*Cosh[c + d*x] + (a^2*d^2 - a*b*d^2*x + b^2*(2 + d^2*x^2))*Sinh[c + d*x]) - a^3*d^3*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/(b^4*d^3)","A",1
20,1,89,100,0.3082032,"\int \frac{x^2 \cosh (c+d x)}{a+b x} \, dx","Integrate[(x^2*Cosh[c + d*x])/(a + b*x),x]","\frac{a^2 d^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)+a^2 d^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+b (d (b x-a) \sinh (c+d x)-b \cosh (c+d x))}{b^3 d^2}","\frac{a^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{a^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^3}-\frac{a \sinh (c+d x)}{b^2 d}-\frac{\cosh (c+d x)}{b d^2}+\frac{x \sinh (c+d x)}{b d}",1,"(a^2*d^2*Cosh[c - (a*d)/b]*CoshIntegral[d*(a/b + x)] + b*(-(b*Cosh[c + d*x]) + d*(-a + b*x)*Sinh[c + d*x]) + a^2*d^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/(b^3*d^2)","A",1
21,1,64,68,0.1467531,"\int \frac{x \cosh (c+d x)}{a+b x} \, dx","Integrate[(x*Cosh[c + d*x])/(a + b*x),x]","\frac{-a d \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)-a d \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+b \sinh (c+d x)}{b^2 d}","-\frac{a \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^2}-\frac{a \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^2}+\frac{\sinh (c+d x)}{b d}",1,"(-(a*d*Cosh[c - (a*d)/b]*CoshIntegral[d*(a/b + x)]) + b*Sinh[c + d*x] - a*d*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/(b^2*d)","A",1
22,1,49,51,0.0648518,"\int \frac{\cosh (c+d x)}{a+b x} \, dx","Integrate[Cosh[c + d*x]/(a + b*x),x]","\frac{\cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)+\sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b}","\frac{\cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b}+\frac{\sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b}",1,"(Cosh[c - (a*d)/b]*CoshIntegral[(a*d)/b + d*x] + Sinh[c - (a*d)/b]*SinhIntegral[(a*d)/b + d*x])/b","A",1
23,1,63,73,0.1499452,"\int \frac{\cosh (c+d x)}{x (a+b x)} \, dx","Integrate[Cosh[c + d*x]/(x*(a + b*x)),x]","\frac{-\cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)-\sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+\cosh (c) \text{Chi}(d x)+\sinh (c) \text{Shi}(d x)}{a}","-\frac{\cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a}-\frac{\sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a}+\frac{\cosh (c) \text{Chi}(d x)}{a}+\frac{\sinh (c) \text{Shi}(d x)}{a}",1,"(Cosh[c]*CoshIntegral[d*x] - Cosh[c - (a*d)/b]*CoshIntegral[d*(a/b + x)] + Sinh[c]*SinhIntegral[d*x] - Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/a","A",1
24,1,101,113,0.4013247,"\int \frac{\cosh (c+d x)}{x^2 (a+b x)} \, dx","Integrate[Cosh[c + d*x]/(x^2*(a + b*x)),x]","\frac{b x \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)+\text{Chi}(d x) (a d x \sinh (c)-b x \cosh (c))+b x \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+a d x \cosh (c) \text{Shi}(d x)-a \cosh (c+d x)-b x \sinh (c) \text{Shi}(d x)}{a^2 x}","-\frac{b \cosh (c) \text{Chi}(d x)}{a^2}+\frac{b \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^2}-\frac{b \sinh (c) \text{Shi}(d x)}{a^2}+\frac{b \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^2}+\frac{d \sinh (c) \text{Chi}(d x)}{a}+\frac{d \cosh (c) \text{Shi}(d x)}{a}-\frac{\cosh (c+d x)}{a x}",1,"(-(a*Cosh[c + d*x]) + b*x*Cosh[c - (a*d)/b]*CoshIntegral[d*(a/b + x)] + CoshIntegral[d*x]*(-(b*x*Cosh[c]) + a*d*x*Sinh[c]) + a*d*x*Cosh[c]*SinhIntegral[d*x] - b*x*Sinh[c]*SinhIntegral[d*x] + b*x*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/(a^2*x)","A",1
25,1,178,190,0.4989609,"\int \frac{\cosh (c+d x)}{x^3 (a+b x)} \, dx","Integrate[Cosh[c + d*x]/(x^3*(a + b*x)),x]","\frac{x^2 \text{Chi}(d x) \left(\cosh (c) \left(a^2 d^2+2 b^2\right)-2 a b d \sinh (c)\right)+a^2 d^2 x^2 \sinh (c) \text{Shi}(d x)-a^2 d x \sinh (c+d x)+a^2 (-\cosh (c+d x))-2 b^2 x^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)-2 b^2 x^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-2 a b d x^2 \cosh (c) \text{Shi}(d x)+2 a b x \cosh (c+d x)+2 b^2 x^2 \sinh (c) \text{Shi}(d x)}{2 a^3 x^2}","\frac{b^2 \cosh (c) \text{Chi}(d x)}{a^3}-\frac{b^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^3}+\frac{b^2 \sinh (c) \text{Shi}(d x)}{a^3}-\frac{b^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^3}-\frac{b d \sinh (c) \text{Chi}(d x)}{a^2}-\frac{b d \cosh (c) \text{Shi}(d x)}{a^2}+\frac{b \cosh (c+d x)}{a^2 x}+\frac{d^2 \cosh (c) \text{Chi}(d x)}{2 a}+\frac{d^2 \sinh (c) \text{Shi}(d x)}{2 a}-\frac{\cosh (c+d x)}{2 a x^2}-\frac{d \sinh (c+d x)}{2 a x}",1,"(-(a^2*Cosh[c + d*x]) + 2*a*b*x*Cosh[c + d*x] - 2*b^2*x^2*Cosh[c - (a*d)/b]*CoshIntegral[d*(a/b + x)] + x^2*CoshIntegral[d*x]*((2*b^2 + a^2*d^2)*Cosh[c] - 2*a*b*d*Sinh[c]) - a^2*d*x*Sinh[c + d*x] - 2*a*b*d*x^2*Cosh[c]*SinhIntegral[d*x] + 2*b^2*x^2*Sinh[c]*SinhIntegral[d*x] + a^2*d^2*x^2*Sinh[c]*SinhIntegral[d*x] - 2*b^2*x^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/(2*a^3*x^2)","A",1
26,1,173,231,1.2628437,"\int \frac{x^4 \cosh (c+d x)}{(a+b x)^2} \, dx","Integrate[(x^4*Cosh[c + d*x])/(a + b*x)^2,x]","\frac{a^3 \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(a d \sinh \left(c-\frac{a d}{b}\right)-4 b \cosh \left(c-\frac{a d}{b}\right)\right)+a^3 \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right) \left(a d \cosh \left(c-\frac{a d}{b}\right)-4 b \sinh \left(c-\frac{a d}{b}\right)\right)+\frac{b^2 \left(3 a^2 d^2-2 a b d^2 x+b^2 \left(d^2 x^2+2\right)\right) \sinh (c+d x)}{d^3}-\frac{b \left(a^4 d^2-2 a^2 b^2+2 b^4 x^2\right) \cosh (c+d x)}{d^2 (a+b x)}}{b^6}","\frac{a^4 d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^6}+\frac{a^4 d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^6}-\frac{a^4 \cosh (c+d x)}{b^5 (a+b x)}-\frac{4 a^3 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^5}-\frac{4 a^3 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^5}+\frac{3 a^2 \sinh (c+d x)}{b^4 d}+\frac{2 a \cosh (c+d x)}{b^3 d^2}-\frac{2 a x \sinh (c+d x)}{b^3 d}+\frac{2 \sinh (c+d x)}{b^2 d^3}-\frac{2 x \cosh (c+d x)}{b^2 d^2}+\frac{x^2 \sinh (c+d x)}{b^2 d}",1,"(-((b*(-2*a^2*b^2 + a^4*d^2 + 2*b^4*x^2)*Cosh[c + d*x])/(d^2*(a + b*x))) + a^3*CoshIntegral[d*(a/b + x)]*(-4*b*Cosh[c - (a*d)/b] + a*d*Sinh[c - (a*d)/b]) + (b^2*(3*a^2*d^2 - 2*a*b*d^2*x + b^2*(2 + d^2*x^2))*Sinh[c + d*x])/d^3 + a^3*(a*d*Cosh[c - (a*d)/b] - 4*b*Sinh[c - (a*d)/b])*SinhIntegral[d*(a/b + x)])/b^6","A",1
27,1,156,182,0.9564865,"\int \frac{x^3 \cosh (c+d x)}{(a+b x)^2} \, dx","Integrate[(x^3*Cosh[c + d*x])/(a + b*x)^2,x]","\frac{a^2 \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(3 b \cosh \left(c-\frac{a d}{b}\right)-a d \sinh \left(c-\frac{a d}{b}\right)\right)-a^2 \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right) \left(a d \cosh \left(c-\frac{a d}{b}\right)-3 b \sinh \left(c-\frac{a d}{b}\right)\right)+\frac{b \left(\left(a^3 d^2-a b^2-b^3 x\right) \cosh (c+d x)+b d \left(-2 a^2-a b x+b^2 x^2\right) \sinh (c+d x)\right)}{d^2 (a+b x)}}{b^5}","-\frac{a^3 d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^5}-\frac{a^3 d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^5}+\frac{a^3 \cosh (c+d x)}{b^4 (a+b x)}+\frac{3 a^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^4}+\frac{3 a^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{2 a \sinh (c+d x)}{b^3 d}-\frac{\cosh (c+d x)}{b^2 d^2}+\frac{x \sinh (c+d x)}{b^2 d}",1,"(a^2*CoshIntegral[d*(a/b + x)]*(3*b*Cosh[c - (a*d)/b] - a*d*Sinh[c - (a*d)/b]) + (b*((-(a*b^2) + a^3*d^2 - b^3*x)*Cosh[c + d*x] + b*d*(-2*a^2 - a*b*x + b^2*x^2)*Sinh[c + d*x]))/(d^2*(a + b*x)) - a^2*(a*d*Cosh[c - (a*d)/b] - 3*b*Sinh[c - (a*d)/b])*SinhIntegral[d*(a/b + x)])/b^5","A",1
28,1,115,147,0.7129304,"\int \frac{x^2 \cosh (c+d x)}{(a+b x)^2} \, dx","Integrate[(x^2*Cosh[c + d*x])/(a + b*x)^2,x]","\frac{b \left(\frac{b \sinh (c+d x)}{d}-\frac{a^2 \cosh (c+d x)}{a+b x}\right)+a \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(a d \sinh \left(c-\frac{a d}{b}\right)-2 b \cosh \left(c-\frac{a d}{b}\right)\right)+a \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right) \left(a d \cosh \left(c-\frac{a d}{b}\right)-2 b \sinh \left(c-\frac{a d}{b}\right)\right)}{b^4}","\frac{a^2 d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^4}+\frac{a^2 d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{a^2 \cosh (c+d x)}{b^3 (a+b x)}-\frac{2 a \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^3}-\frac{2 a \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{\sinh (c+d x)}{b^2 d}",1,"(a*CoshIntegral[d*(a/b + x)]*(-2*b*Cosh[c - (a*d)/b] + a*d*Sinh[c - (a*d)/b]) + b*(-((a^2*Cosh[c + d*x])/(a + b*x)) + (b*Sinh[c + d*x])/d) + a*(a*d*Cosh[c - (a*d)/b] - 2*b*Sinh[c - (a*d)/b])*SinhIntegral[d*(a/b + x)])/b^4","A",1
29,1,97,125,0.4428257,"\int \frac{x \cosh (c+d x)}{(a+b x)^2} \, dx","Integrate[(x*Cosh[c + d*x])/(a + b*x)^2,x]","\frac{\text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(b \cosh \left(c-\frac{a d}{b}\right)-a d \sinh \left(c-\frac{a d}{b}\right)\right)+\text{Shi}\left(d \left(\frac{a}{b}+x\right)\right) \left(b \sinh \left(c-\frac{a d}{b}\right)-a d \cosh \left(c-\frac{a d}{b}\right)\right)+\frac{a b \cosh (c+d x)}{a+b x}}{b^3}","-\frac{a d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^3}-\frac{a d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{\cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^2}+\frac{\sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^2}+\frac{a \cosh (c+d x)}{b^2 (a+b x)}",1,"((a*b*Cosh[c + d*x])/(a + b*x) + CoshIntegral[d*(a/b + x)]*(b*Cosh[c - (a*d)/b] - a*d*Sinh[c - (a*d)/b]) + (-(a*d*Cosh[c - (a*d)/b]) + b*Sinh[c - (a*d)/b])*SinhIntegral[d*(a/b + x)])/b^3","A",1
30,1,65,71,0.2110678,"\int \frac{\cosh (c+d x)}{(a+b x)^2} \, dx","Integrate[Cosh[c + d*x]/(a + b*x)^2,x]","\frac{d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)+d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-\frac{b \cosh (c+d x)}{a+b x}}{b^2}","\frac{d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^2}+\frac{d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^2}-\frac{\cosh (c+d x)}{b (a+b x)}",1,"(-((b*Cosh[c + d*x])/(a + b*x)) + d*CoshIntegral[d*(a/b + x)]*Sinh[c - (a*d)/b] + d*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/b^2","A",1
31,1,139,150,1.2115957,"\int \frac{\cosh (c+d x)}{x (a+b x)^2} \, dx","Integrate[Cosh[c + d*x]/(x*(a + b*x)^2),x]","\frac{-\frac{\text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(a d \sinh \left(c-\frac{a d}{b}\right)+b \cosh \left(c-\frac{a d}{b}\right)\right)}{b}-\sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-\frac{a d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)}{b}+\frac{a \sinh (c) \sinh (d x)}{a+b x}+\frac{a \cosh (c) \cosh (d x)}{a+b x}+\cosh (c) \text{Chi}(d x)+\sinh (c) \text{Shi}(d x)}{a^2}","-\frac{\cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^2}-\frac{\sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^2}+\frac{\cosh (c) \text{Chi}(d x)}{a^2}+\frac{\sinh (c) \text{Shi}(d x)}{a^2}-\frac{d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a b}-\frac{d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a b}+\frac{\cosh (c+d x)}{a (a+b x)}",1,"((a*Cosh[c]*Cosh[d*x])/(a + b*x) + Cosh[c]*CoshIntegral[d*x] - (CoshIntegral[d*(a/b + x)]*(b*Cosh[c - (a*d)/b] + a*d*Sinh[c - (a*d)/b]))/b + (a*Sinh[c]*Sinh[d*x])/(a + b*x) + Sinh[c]*SinhIntegral[d*x] - (a*d*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/b - Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/a^2","A",1
32,1,183,186,1.4203726,"\int \frac{\cosh (c+d x)}{x^2 (a+b x)^2} \, dx","Integrate[Cosh[c + d*x]/(x^2*(a + b*x)^2),x]","\frac{a d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)+2 b \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)+2 b \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+a d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-\frac{a \sinh (c) (a+2 b x) \sinh (d x)}{x (a+b x)}-\frac{a \cosh (c) (a+2 b x) \cosh (d x)}{x (a+b x)}+a d \sinh (c) \text{Chi}(d x)+a d \cosh (c) \text{Shi}(d x)-2 b \cosh (c) \text{Chi}(d x)-2 b \sinh (c) \text{Shi}(d x)}{a^3}","-\frac{2 b \cosh (c) \text{Chi}(d x)}{a^3}+\frac{2 b \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^3}-\frac{2 b \sinh (c) \text{Shi}(d x)}{a^3}+\frac{2 b \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^3}+\frac{d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^2}+\frac{d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^2}-\frac{b \cosh (c+d x)}{a^2 (a+b x)}+\frac{d \sinh (c) \text{Chi}(d x)}{a^2}+\frac{d \cosh (c) \text{Shi}(d x)}{a^2}-\frac{\cosh (c+d x)}{a^2 x}",1,"(-((a*(a + 2*b*x)*Cosh[c]*Cosh[d*x])/(x*(a + b*x))) - 2*b*Cosh[c]*CoshIntegral[d*x] + 2*b*Cosh[c - (a*d)/b]*CoshIntegral[d*(a/b + x)] + a*d*CoshIntegral[d*x]*Sinh[c] + a*d*CoshIntegral[d*(a/b + x)]*Sinh[c - (a*d)/b] - (a*(a + 2*b*x)*Sinh[c]*Sinh[d*x])/(x*(a + b*x)) + a*d*Cosh[c]*SinhIntegral[d*x] - 2*b*Sinh[c]*SinhIntegral[d*x] + a*d*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 2*b*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/a^3","A",1
33,1,236,264,1.0474339,"\int \frac{x^3 \cosh (c+d x)}{(a+b x)^3} \, dx","Integrate[(x^3*Cosh[c + d*x])/(a + b*x)^3,x]","-\frac{a d (a+b x)^2 \left(\text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(\left(a^2 d^2+6 b^2\right) \cosh \left(c-\frac{a d}{b}\right)-6 a b d \sinh \left(c-\frac{a d}{b}\right)\right)+\text{Shi}\left(d \left(\frac{a}{b}+x\right)\right) \left(\left(a^2 d^2+6 b^2\right) \sinh \left(c-\frac{a d}{b}\right)-6 a b d \cosh \left(c-\frac{a d}{b}\right)\right)\right)+b \cosh (d x) \left(a^2 b d \cosh (c) (5 a+6 b x)-\sinh (c) (a+b x) \left(a^3 d^2+2 a b^2+2 b^3 x\right)\right)-b \sinh (d x) \left(\cosh (c) (a+b x) \left(a^3 d^2+2 a b^2+2 b^3 x\right)-a^2 b d \sinh (c) (5 a+6 b x)\right)}{2 b^6 d (a+b x)^2}","-\frac{a^3 d^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{2 b^6}-\frac{a^3 d^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{2 b^6}+\frac{a^3 d \sinh (c+d x)}{2 b^5 (a+b x)}+\frac{a^3 \cosh (c+d x)}{2 b^4 (a+b x)^2}+\frac{3 a^2 d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^5}+\frac{3 a^2 d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^5}-\frac{3 a^2 \cosh (c+d x)}{b^4 (a+b x)}-\frac{3 a \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{3 a \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^4}+\frac{\sinh (c+d x)}{b^3 d}",1,"-1/2*(b*Cosh[d*x]*(a^2*b*d*(5*a + 6*b*x)*Cosh[c] - (a + b*x)*(2*a*b^2 + a^3*d^2 + 2*b^3*x)*Sinh[c]) - b*((a + b*x)*(2*a*b^2 + a^3*d^2 + 2*b^3*x)*Cosh[c] - a^2*b*d*(5*a + 6*b*x)*Sinh[c])*Sinh[d*x] + a*d*(a + b*x)^2*(CoshIntegral[d*(a/b + x)]*((6*b^2 + a^2*d^2)*Cosh[c - (a*d)/b] - 6*a*b*d*Sinh[c - (a*d)/b]) + (-6*a*b*d*Cosh[c - (a*d)/b] + (6*b^2 + a^2*d^2)*Sinh[c - (a*d)/b])*SinhIntegral[d*(a/b + x)]))/(b^6*d*(a + b*x)^2)","A",1
34,1,153,241,0.9733466,"\int \frac{x^2 \cosh (c+d x)}{(a+b x)^3} \, dx","Integrate[(x^2*Cosh[c + d*x])/(a + b*x)^3,x]","\frac{\text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(\left(a^2 d^2+2 b^2\right) \cosh \left(c-\frac{a d}{b}\right)-4 a b d \sinh \left(c-\frac{a d}{b}\right)\right)+\text{Shi}\left(d \left(\frac{a}{b}+x\right)\right) \left(\left(a^2 d^2+2 b^2\right) \sinh \left(c-\frac{a d}{b}\right)-4 a b d \cosh \left(c-\frac{a d}{b}\right)\right)-\frac{a b (a d (a+b x) \sinh (c+d x)-b (3 a+4 b x) \cosh (c+d x))}{(a+b x)^2}}{2 b^5}","\frac{a^2 d^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{2 b^5}+\frac{a^2 d^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{2 b^5}-\frac{a^2 d \sinh (c+d x)}{2 b^4 (a+b x)}-\frac{a^2 \cosh (c+d x)}{2 b^3 (a+b x)^2}-\frac{2 a d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^4}-\frac{2 a d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^4}+\frac{\cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{\sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{2 a \cosh (c+d x)}{b^3 (a+b x)}",1,"(CoshIntegral[d*(a/b + x)]*((2*b^2 + a^2*d^2)*Cosh[c - (a*d)/b] - 4*a*b*d*Sinh[c - (a*d)/b]) - (a*b*(-(b*(3*a + 4*b*x)*Cosh[c + d*x]) + a*d*(a + b*x)*Sinh[c + d*x]))/(a + b*x)^2 + (-4*a*b*d*Cosh[c - (a*d)/b] + (2*b^2 + a^2*d^2)*Sinh[c - (a*d)/b])*SinhIntegral[d*(a/b + x)])/(2*b^5)","A",1
35,1,158,178,0.5971795,"\int \frac{x \cosh (c+d x)}{(a+b x)^3} \, dx","Integrate[(x*Cosh[c + d*x])/(a + b*x)^3,x]","-\frac{d (a+b x)^2 \left(\text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(a d \cosh \left(c-\frac{a d}{b}\right)-2 b \sinh \left(c-\frac{a d}{b}\right)\right)+\text{Shi}\left(d \left(\frac{a}{b}+x\right)\right) \left(a d \sinh \left(c-\frac{a d}{b}\right)-2 b \cosh \left(c-\frac{a d}{b}\right)\right)\right)+b \cosh (d x) (b \cosh (c) (a+2 b x)-a d \sinh (c) (a+b x))-b \sinh (d x) (a d \cosh (c) (a+b x)-b \sinh (c) (a+2 b x))}{2 b^4 (a+b x)^2}","-\frac{a d^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{2 b^4}-\frac{a d^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{2 b^4}+\frac{d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{b^3}+\frac{a d \sinh (c+d x)}{2 b^3 (a+b x)}-\frac{\cosh (c+d x)}{b^2 (a+b x)}+\frac{a \cosh (c+d x)}{2 b^2 (a+b x)^2}",1,"-1/2*(b*Cosh[d*x]*(b*(a + 2*b*x)*Cosh[c] - a*d*(a + b*x)*Sinh[c]) - b*(a*d*(a + b*x)*Cosh[c] - b*(a + 2*b*x)*Sinh[c])*Sinh[d*x] + d*(a + b*x)^2*(CoshIntegral[d*(a/b + x)]*(a*d*Cosh[c - (a*d)/b] - 2*b*Sinh[c - (a*d)/b]) + (-2*b*Cosh[c - (a*d)/b] + a*d*Sinh[c - (a*d)/b])*SinhIntegral[d*(a/b + x)]))/(b^4*(a + b*x)^2)","A",1
36,1,88,104,0.5114779,"\int \frac{\cosh (c+d x)}{(a+b x)^3} \, dx","Integrate[Cosh[c + d*x]/(a + b*x)^3,x]","\frac{d^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right)+d^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-\frac{b (d (a+b x) \sinh (c+d x)+b \cosh (c+d x))}{(a+b x)^2}}{2 b^3}","\frac{d^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{2 b^3}+\frac{d^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{2 b^3}-\frac{d \sinh (c+d x)}{2 b^2 (a+b x)}-\frac{\cosh (c+d x)}{2 b (a+b x)^2}",1,"(d^2*Cosh[c - (a*d)/b]*CoshIntegral[d*(a/b + x)] - (b*(b*Cosh[c + d*x] + d*(a + b*x)*Sinh[c + d*x]))/(a + b*x)^2 + d^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/(2*b^3)","A",1
37,1,451,262,1.3760579,"\int \frac{\cosh (c+d x)}{x (a+b x)^3} \, dx","Integrate[Cosh[c + d*x]/(x*(a + b*x)^3),x]","-\frac{a^4 d^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+2 a^3 b d^2 x \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+2 a^3 b d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-a^3 b d \sinh (c+d x)+(a+b x)^2 \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(\left(a^2 d^2+2 b^2\right) \cosh \left(c-\frac{a d}{b}\right)+2 a b d \sinh \left(c-\frac{a d}{b}\right)\right)+a^2 b^2 d^2 x^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-2 a^2 b^2 \sinh (c) \text{Shi}(d x)+2 a^2 b^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+4 a^2 b^2 d x \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-a^2 b^2 d x \sinh (c+d x)-3 a^2 b^2 \cosh (c+d x)+2 b^4 x^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+2 a b^3 d x^2 \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-4 a b^3 x \sinh (c) \text{Shi}(d x)+4 a b^3 x \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-2 a b^3 x \cosh (c+d x)-2 b^2 \cosh (c) (a+b x)^2 \text{Chi}(d x)-2 b^4 x^2 \sinh (c) \text{Shi}(d x)}{2 a^3 b^2 (a+b x)^2}","-\frac{\cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^3}-\frac{\sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^3}+\frac{\cosh (c) \text{Chi}(d x)}{a^3}+\frac{\sinh (c) \text{Shi}(d x)}{a^3}-\frac{d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^2 b}-\frac{d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^2 b}+\frac{\cosh (c+d x)}{a^2 (a+b x)}-\frac{d^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{2 a b^2}-\frac{d^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{2 a b^2}+\frac{d \sinh (c+d x)}{2 a b (a+b x)}+\frac{\cosh (c+d x)}{2 a (a+b x)^2}",1,"-1/2*(-3*a^2*b^2*Cosh[c + d*x] - 2*a*b^3*x*Cosh[c + d*x] - 2*b^2*(a + b*x)^2*Cosh[c]*CoshIntegral[d*x] + (a + b*x)^2*CoshIntegral[d*(a/b + x)]*((2*b^2 + a^2*d^2)*Cosh[c - (a*d)/b] + 2*a*b*d*Sinh[c - (a*d)/b]) - a^3*b*d*Sinh[c + d*x] - a^2*b^2*d*x*Sinh[c + d*x] - 2*a^2*b^2*Sinh[c]*SinhIntegral[d*x] - 4*a*b^3*x*Sinh[c]*SinhIntegral[d*x] - 2*b^4*x^2*Sinh[c]*SinhIntegral[d*x] + 2*a^3*b*d*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 4*a^2*b^2*d*x*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 2*a*b^3*d*x^2*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 2*a^2*b^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + a^4*d^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 4*a*b^3*x*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 2*a^3*b*d^2*x*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 2*b^4*x^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + a^2*b^2*d^2*x^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/(a^3*b^2*(a + b*x)^2)","A",1
38,1,541,298,1.571997,"\int \frac{\cosh (c+d x)}{x^2 (a+b x)^3} \, dx","Integrate[Cosh[c + d*x]/(x^2*(a + b*x)^3),x]","\frac{a^4 d^2 x \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+2 a^3 b d^2 x^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+2 a^3 b d x \cosh (c) \text{Shi}(d x)+4 a^3 b d x \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-a^3 b d x \sinh (c+d x)-2 a^3 b \cosh (c+d x)+x (a+b x)^2 \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(\left(a^2 d^2+6 b^2\right) \cosh \left(c-\frac{a d}{b}\right)+4 a b d \sinh \left(c-\frac{a d}{b}\right)\right)+a^2 b^2 d^2 x^3 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+4 a^2 b^2 d x^2 \cosh (c) \text{Shi}(d x)+8 a^2 b^2 d x^2 \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-6 a^2 b^2 x \sinh (c) \text{Shi}(d x)+6 a^2 b^2 x \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-a^2 b^2 d x^2 \sinh (c+d x)-9 a^2 b^2 x \cosh (c+d x)+6 b^4 x^3 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+2 a b^3 d x^3 \cosh (c) \text{Shi}(d x)+4 a b^3 d x^3 \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-12 a b^3 x^2 \sinh (c) \text{Shi}(d x)+12 a b^3 x^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-6 a b^3 x^2 \cosh (c+d x)+2 b x (a+b x)^2 \text{Chi}(d x) (a d \sinh (c)-3 b \cosh (c))-6 b^4 x^3 \sinh (c) \text{Shi}(d x)}{2 a^4 b x (a+b x)^2}","-\frac{3 b \cosh (c) \text{Chi}(d x)}{a^4}+\frac{3 b \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^4}-\frac{3 b \sinh (c) \text{Shi}(d x)}{a^4}+\frac{3 b \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^4}+\frac{2 d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^3}+\frac{2 d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^3}-\frac{2 b \cosh (c+d x)}{a^3 (a+b x)}+\frac{d \sinh (c) \text{Chi}(d x)}{a^3}+\frac{d \cosh (c) \text{Shi}(d x)}{a^3}-\frac{\cosh (c+d x)}{a^3 x}+\frac{d^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{2 a^2 b}+\frac{d^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{2 a^2 b}-\frac{d \sinh (c+d x)}{2 a^2 (a+b x)}-\frac{b \cosh (c+d x)}{2 a^2 (a+b x)^2}",1,"(-2*a^3*b*Cosh[c + d*x] - 9*a^2*b^2*x*Cosh[c + d*x] - 6*a*b^3*x^2*Cosh[c + d*x] + 2*b*x*(a + b*x)^2*CoshIntegral[d*x]*(-3*b*Cosh[c] + a*d*Sinh[c]) + x*(a + b*x)^2*CoshIntegral[d*(a/b + x)]*((6*b^2 + a^2*d^2)*Cosh[c - (a*d)/b] + 4*a*b*d*Sinh[c - (a*d)/b]) - a^3*b*d*x*Sinh[c + d*x] - a^2*b^2*d*x^2*Sinh[c + d*x] + 2*a^3*b*d*x*Cosh[c]*SinhIntegral[d*x] + 4*a^2*b^2*d*x^2*Cosh[c]*SinhIntegral[d*x] + 2*a*b^3*d*x^3*Cosh[c]*SinhIntegral[d*x] - 6*a^2*b^2*x*Sinh[c]*SinhIntegral[d*x] - 12*a*b^3*x^2*Sinh[c]*SinhIntegral[d*x] - 6*b^4*x^3*Sinh[c]*SinhIntegral[d*x] + 4*a^3*b*d*x*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 8*a^2*b^2*d*x^2*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 4*a*b^3*d*x^3*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 6*a^2*b^2*x*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + a^4*d^2*x*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 12*a*b^3*x^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 2*a^3*b*d^2*x^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 6*b^4*x^3*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + a^2*b^2*d^2*x^3*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/(2*a^4*b*x*(a + b*x)^2)","A",1
39,1,627,377,1.8687503,"\int \frac{\cosh (c+d x)}{x^3 (a+b x)^3} \, dx","Integrate[Cosh[c + d*x]/(x^3*(a + b*x)^3),x]","-\frac{a^4 d^2 x^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-a^4 d^2 x^2 \sinh (c) \text{Shi}(d x)+a^4 d x \sinh (c+d x)+a^4 \cosh (c+d x)-2 a^3 b d^2 x^3 \sinh (c) \text{Shi}(d x)+2 a^3 b d^2 x^3 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+6 a^3 b d x^2 \cosh (c) \text{Shi}(d x)+6 a^3 b d x^2 \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+a^3 b d x^2 \sinh (c+d x)-4 a^3 b x \cosh (c+d x)-x^2 (a+b x)^2 \text{Chi}(d x) \left(\cosh (c) \left(a^2 d^2+12 b^2\right)-6 a b d \sinh (c)\right)+x^2 (a+b x)^2 \text{Chi}\left(d \left(\frac{a}{b}+x\right)\right) \left(\left(a^2 d^2+12 b^2\right) \cosh \left(c-\frac{a d}{b}\right)+6 a b d \sinh \left(c-\frac{a d}{b}\right)\right)-a^2 b^2 d^2 x^4 \sinh (c) \text{Shi}(d x)+a^2 b^2 d^2 x^4 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+12 a^2 b^2 d x^3 \cosh (c) \text{Shi}(d x)+12 a^2 b^2 d x^3 \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-12 a^2 b^2 x^2 \sinh (c) \text{Shi}(d x)+12 a^2 b^2 x^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-18 a^2 b^2 x^2 \cosh (c+d x)+12 b^4 x^4 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)+6 a b^3 d x^4 \cosh (c) \text{Shi}(d x)+6 a b^3 d x^4 \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-24 a b^3 x^3 \sinh (c) \text{Shi}(d x)+24 a b^3 x^3 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(d \left(\frac{a}{b}+x\right)\right)-12 a b^3 x^3 \cosh (c+d x)-12 b^4 x^4 \sinh (c) \text{Shi}(d x)}{2 a^5 x^2 (a+b x)^2}","\frac{6 b^2 \cosh (c) \text{Chi}(d x)}{a^5}-\frac{6 b^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^5}+\frac{6 b^2 \sinh (c) \text{Shi}(d x)}{a^5}-\frac{6 b^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^5}+\frac{3 b^2 \cosh (c+d x)}{a^4 (a+b x)}-\frac{3 b d \sinh (c) \text{Chi}(d x)}{a^4}-\frac{3 b d \sinh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{a^4}-\frac{3 b d \cosh (c) \text{Shi}(d x)}{a^4}-\frac{3 b d \cosh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{a^4}+\frac{3 b \cosh (c+d x)}{a^4 x}+\frac{b^2 \cosh (c+d x)}{2 a^3 (a+b x)^2}-\frac{d^2 \cosh \left(c-\frac{a d}{b}\right) \text{Chi}\left(x d+\frac{a d}{b}\right)}{2 a^3}-\frac{d^2 \sinh \left(c-\frac{a d}{b}\right) \text{Shi}\left(x d+\frac{a d}{b}\right)}{2 a^3}+\frac{b d \sinh (c+d x)}{2 a^3 (a+b x)}+\frac{d^2 \cosh (c) \text{Chi}(d x)}{2 a^3}+\frac{d^2 \sinh (c) \text{Shi}(d x)}{2 a^3}-\frac{\cosh (c+d x)}{2 a^3 x^2}-\frac{d \sinh (c+d x)}{2 a^3 x}",1,"-1/2*(a^4*Cosh[c + d*x] - 4*a^3*b*x*Cosh[c + d*x] - 18*a^2*b^2*x^2*Cosh[c + d*x] - 12*a*b^3*x^3*Cosh[c + d*x] - x^2*(a + b*x)^2*CoshIntegral[d*x]*((12*b^2 + a^2*d^2)*Cosh[c] - 6*a*b*d*Sinh[c]) + x^2*(a + b*x)^2*CoshIntegral[d*(a/b + x)]*((12*b^2 + a^2*d^2)*Cosh[c - (a*d)/b] + 6*a*b*d*Sinh[c - (a*d)/b]) + a^4*d*x*Sinh[c + d*x] + a^3*b*d*x^2*Sinh[c + d*x] + 6*a^3*b*d*x^2*Cosh[c]*SinhIntegral[d*x] + 12*a^2*b^2*d*x^3*Cosh[c]*SinhIntegral[d*x] + 6*a*b^3*d*x^4*Cosh[c]*SinhIntegral[d*x] - 12*a^2*b^2*x^2*Sinh[c]*SinhIntegral[d*x] - a^4*d^2*x^2*Sinh[c]*SinhIntegral[d*x] - 24*a*b^3*x^3*Sinh[c]*SinhIntegral[d*x] - 2*a^3*b*d^2*x^3*Sinh[c]*SinhIntegral[d*x] - 12*b^4*x^4*Sinh[c]*SinhIntegral[d*x] - a^2*b^2*d^2*x^4*Sinh[c]*SinhIntegral[d*x] + 6*a^3*b*d*x^2*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 12*a^2*b^2*d*x^3*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 6*a*b^3*d*x^4*Cosh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 12*a^2*b^2*x^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + a^4*d^2*x^2*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 24*a*b^3*x^3*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 2*a^3*b*d^2*x^3*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + 12*b^4*x^4*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)] + a^2*b^2*d^2*x^4*Sinh[c - (a*d)/b]*SinhIntegral[d*(a/b + x)])/(a^5*x^2*(a + b*x)^2)","A",1
40,1,92,139,0.1696101,"\int x^3 \left(a+b x^2\right) \cosh (c+d x) \, dx","Integrate[x^3*(a + b*x^2)*Cosh[c + d*x],x]","\frac{d x \left(a d^2 \left(d^2 x^2+6\right)+b \left(d^4 x^4+20 d^2 x^2+120\right)\right) \sinh (c+d x)-\left(3 a d^2 \left(d^2 x^2+2\right)+5 b \left(d^4 x^4+12 d^2 x^2+24\right)\right) \cosh (c+d x)}{d^6}","-\frac{6 a \cosh (c+d x)}{d^4}+\frac{6 a x \sinh (c+d x)}{d^3}-\frac{3 a x^2 \cosh (c+d x)}{d^2}+\frac{a x^3 \sinh (c+d x)}{d}-\frac{120 b \cosh (c+d x)}{d^6}+\frac{120 b x \sinh (c+d x)}{d^5}-\frac{60 b x^2 \cosh (c+d x)}{d^4}+\frac{20 b x^3 \sinh (c+d x)}{d^3}-\frac{5 b x^4 \cosh (c+d x)}{d^2}+\frac{b x^5 \sinh (c+d x)}{d}",1,"(-((3*a*d^2*(2 + d^2*x^2) + 5*b*(24 + 12*d^2*x^2 + d^4*x^4))*Cosh[c + d*x]) + d*x*(a*d^2*(6 + d^2*x^2) + b*(120 + 20*d^2*x^2 + d^4*x^4))*Sinh[c + d*x])/d^6","A",1
41,1,74,109,0.1382329,"\int x^2 \left(a+b x^2\right) \cosh (c+d x) \, dx","Integrate[x^2*(a + b*x^2)*Cosh[c + d*x],x]","\frac{\left(a d^2 \left(d^2 x^2+2\right)+b \left(d^4 x^4+12 d^2 x^2+24\right)\right) \sinh (c+d x)-2 d x \left(a d^2+2 b \left(d^2 x^2+6\right)\right) \cosh (c+d x)}{d^5}","\frac{2 a \sinh (c+d x)}{d^3}-\frac{2 a x \cosh (c+d x)}{d^2}+\frac{a x^2 \sinh (c+d x)}{d}+\frac{24 b \sinh (c+d x)}{d^5}-\frac{24 b x \cosh (c+d x)}{d^4}+\frac{12 b x^2 \sinh (c+d x)}{d^3}-\frac{4 b x^3 \cosh (c+d x)}{d^2}+\frac{b x^4 \sinh (c+d x)}{d}",1,"(-2*d*x*(a*d^2 + 2*b*(6 + d^2*x^2))*Cosh[c + d*x] + (a*d^2*(2 + d^2*x^2) + b*(24 + 12*d^2*x^2 + d^4*x^4))*Sinh[c + d*x])/d^5","A",1
42,1,57,79,0.1217198,"\int x \left(a+b x^2\right) \cosh (c+d x) \, dx","Integrate[x*(a + b*x^2)*Cosh[c + d*x],x]","\frac{d x \left(a d^2+b \left(d^2 x^2+6\right)\right) \sinh (c+d x)-\left(a d^2+3 b \left(d^2 x^2+2\right)\right) \cosh (c+d x)}{d^4}","-\frac{a \cosh (c+d x)}{d^2}+\frac{a x \sinh (c+d x)}{d}-\frac{6 b \cosh (c+d x)}{d^4}+\frac{6 b x \sinh (c+d x)}{d^3}-\frac{3 b x^2 \cosh (c+d x)}{d^2}+\frac{b x^3 \sinh (c+d x)}{d}",1,"(-((a*d^2 + 3*b*(2 + d^2*x^2))*Cosh[c + d*x]) + d*x*(a*d^2 + b*(6 + d^2*x^2))*Sinh[c + d*x])/d^4","A",1
43,1,40,51,0.0744482,"\int \left(a+b x^2\right) \cosh (c+d x) \, dx","Integrate[(a + b*x^2)*Cosh[c + d*x],x]","\frac{\left(a d^2+b \left(d^2 x^2+2\right)\right) \sinh (c+d x)-2 b d x \cosh (c+d x)}{d^3}","\frac{a \sinh (c+d x)}{d}+\frac{2 b \sinh (c+d x)}{d^3}-\frac{2 b x \cosh (c+d x)}{d^2}+\frac{b x^2 \sinh (c+d x)}{d}",1,"(-2*b*d*x*Cosh[c + d*x] + (a*d^2 + b*(2 + d^2*x^2))*Sinh[c + d*x])/d^3","A",1
44,1,55,41,0.1189165,"\int \frac{\left(a+b x^2\right) \cosh (c+d x)}{x} \, dx","Integrate[((a + b*x^2)*Cosh[c + d*x])/x,x]","a \cosh (c) \text{Chi}(d x)+a \sinh (c) \text{Shi}(d x)+\frac{b \cosh (d x) (d x \sinh (c)-\cosh (c))}{d^2}+\frac{b \sinh (d x) (d x \cosh (c)-\sinh (c))}{d^2}","a \cosh (c) \text{Chi}(d x)+a \sinh (c) \text{Shi}(d x)-\frac{b \cosh (c+d x)}{d^2}+\frac{b x \sinh (c+d x)}{d}",1,"a*Cosh[c]*CoshIntegral[d*x] + (b*Cosh[d*x]*(-Cosh[c] + d*x*Sinh[c]))/d^2 + (b*(d*x*Cosh[c] - Sinh[c])*Sinh[d*x])/d^2 + a*Sinh[c]*SinhIntegral[d*x]","A",1
45,1,42,42,0.090905,"\int \frac{\left(a+b x^2\right) \cosh (c+d x)}{x^2} \, dx","Integrate[((a + b*x^2)*Cosh[c + d*x])/x^2,x]","a d \sinh (c) \text{Chi}(d x)+a d \cosh (c) \text{Shi}(d x)-\frac{a \cosh (c+d x)}{x}+\frac{b \sinh (c+d x)}{d}","a d \sinh (c) \text{Chi}(d x)+a d \cosh (c) \text{Shi}(d x)-\frac{a \cosh (c+d x)}{x}+\frac{b \sinh (c+d x)}{d}",1,"-((a*Cosh[c + d*x])/x) + a*d*CoshIntegral[d*x]*Sinh[c] + (b*Sinh[c + d*x])/d + a*d*Cosh[c]*SinhIntegral[d*x]","A",1
46,1,80,74,0.1600396,"\int \frac{\left(a+b x^2\right) \cosh (c+d x)}{x^3} \, dx","Integrate[((a + b*x^2)*Cosh[c + d*x])/x^3,x]","\frac{1}{2} a d^2 (\cosh (c) \text{Chi}(d x)+\sinh (c) \text{Shi}(d x))-\frac{a \cosh (d x) (d x \sinh (c)+\cosh (c))}{2 x^2}-\frac{a \sinh (d x) (d x \cosh (c)+\sinh (c))}{2 x^2}+b \cosh (c) \text{Chi}(d x)+b \sinh (c) \text{Shi}(d x)","\frac{1}{2} a d^2 \cosh (c) \text{Chi}(d x)+\frac{1}{2} a d^2 \sinh (c) \text{Shi}(d x)-\frac{a \cosh (c+d x)}{2 x^2}-\frac{a d \sinh (c+d x)}{2 x}+b \cosh (c) \text{Chi}(d x)+b \sinh (c) \text{Shi}(d x)",1,"b*Cosh[c]*CoshIntegral[d*x] - (a*Cosh[d*x]*(Cosh[c] + d*x*Sinh[c]))/(2*x^2) - (a*(d*x*Cosh[c] + Sinh[c])*Sinh[d*x])/(2*x^2) + b*Sinh[c]*SinhIntegral[d*x] + (a*d^2*(Cosh[c]*CoshIntegral[d*x] + Sinh[c]*SinhIntegral[d*x]))/2","A",1
47,1,95,105,0.2373435,"\int \frac{\left(a+b x^2\right) \cosh (c+d x)}{x^4} \, dx","Integrate[((a + b*x^2)*Cosh[c + d*x])/x^4,x]","-\frac{-d x^3 \sinh (c) \left(a d^2+6 b\right) \text{Chi}(d x)-d x^3 \cosh (c) \left(a d^2+6 b\right) \text{Shi}(d x)+a d^2 x^2 \cosh (c+d x)+a d x \sinh (c+d x)+2 a \cosh (c+d x)+6 b x^2 \cosh (c+d x)}{6 x^3}","\frac{1}{6} a d^3 \sinh (c) \text{Chi}(d x)+\frac{1}{6} a d^3 \cosh (c) \text{Shi}(d x)-\frac{a d^2 \cosh (c+d x)}{6 x}-\frac{a \cosh (c+d x)}{3 x^3}-\frac{a d \sinh (c+d x)}{6 x^2}+b d \sinh (c) \text{Chi}(d x)+b d \cosh (c) \text{Shi}(d x)-\frac{b \cosh (c+d x)}{x}",1,"-1/6*(2*a*Cosh[c + d*x] + 6*b*x^2*Cosh[c + d*x] + a*d^2*x^2*Cosh[c + d*x] - d*(6*b + a*d^2)*x^3*CoshIntegral[d*x]*Sinh[c] + a*d*x*Sinh[c + d*x] - d*(6*b + a*d^2)*x^3*Cosh[c]*SinhIntegral[d*x])/x^3","A",1
48,1,127,149,0.285585,"\int \frac{\left(a+b x^2\right) \cosh (c+d x)}{x^5} \, dx","Integrate[((a + b*x^2)*Cosh[c + d*x])/x^5,x]","-\frac{-d^2 x^4 \cosh (c) \left(a d^2+12 b\right) \text{Chi}(d x)-d^2 x^4 \sinh (c) \left(a d^2+12 b\right) \text{Shi}(d x)+a d^3 x^3 \sinh (c+d x)+a d^2 x^2 \cosh (c+d x)+2 a d x \sinh (c+d x)+6 a \cosh (c+d x)+12 b d x^3 \sinh (c+d x)+12 b x^2 \cosh (c+d x)}{24 x^4}","\frac{1}{24} a d^4 \cosh (c) \text{Chi}(d x)+\frac{1}{24} a d^4 \sinh (c) \text{Shi}(d x)-\frac{a d^3 \sinh (c+d x)}{24 x}-\frac{a d^2 \cosh (c+d x)}{24 x^2}-\frac{a \cosh (c+d x)}{4 x^4}-\frac{a d \sinh (c+d x)}{12 x^3}+\frac{1}{2} b d^2 \cosh (c) \text{Chi}(d x)+\frac{1}{2} b d^2 \sinh (c) \text{Shi}(d x)-\frac{b \cosh (c+d x)}{2 x^2}-\frac{b d \sinh (c+d x)}{2 x}",1,"-1/24*(6*a*Cosh[c + d*x] + 12*b*x^2*Cosh[c + d*x] + a*d^2*x^2*Cosh[c + d*x] - d^2*(12*b + a*d^2)*x^4*Cosh[c]*CoshIntegral[d*x] + 2*a*d*x*Sinh[c + d*x] + 12*b*d*x^3*Sinh[c + d*x] + a*d^3*x^3*Sinh[c + d*x] - d^2*(12*b + a*d^2)*x^4*Sinh[c]*SinhIntegral[d*x])/x^4","A",1
49,1,138,234,0.3491445,"\int x^2 \left(a+b x^2\right)^2 \cosh (c+d x) \, dx","Integrate[x^2*(a + b*x^2)^2*Cosh[c + d*x],x]","\frac{\left(a^2 d^4 \left(d^2 x^2+2\right)+2 a b d^2 \left(d^4 x^4+12 d^2 x^2+24\right)+b^2 \left(d^6 x^6+30 d^4 x^4+360 d^2 x^2+720\right)\right) \sinh (c+d x)-2 d x \left(a^2 d^4+4 a b d^2 \left(d^2 x^2+6\right)+3 b^2 \left(d^4 x^4+20 d^2 x^2+120\right)\right) \cosh (c+d x)}{d^7}","\frac{2 a^2 \sinh (c+d x)}{d^3}-\frac{2 a^2 x \cosh (c+d x)}{d^2}+\frac{a^2 x^2 \sinh (c+d x)}{d}+\frac{48 a b \sinh (c+d x)}{d^5}-\frac{48 a b x \cosh (c+d x)}{d^4}+\frac{24 a b x^2 \sinh (c+d x)}{d^3}-\frac{8 a b x^3 \cosh (c+d x)}{d^2}+\frac{2 a b x^4 \sinh (c+d x)}{d}+\frac{720 b^2 \sinh (c+d x)}{d^7}-\frac{720 b^2 x \cosh (c+d x)}{d^6}+\frac{360 b^2 x^2 \sinh (c+d x)}{d^5}-\frac{120 b^2 x^3 \cosh (c+d x)}{d^4}+\frac{30 b^2 x^4 \sinh (c+d x)}{d^3}-\frac{6 b^2 x^5 \cosh (c+d x)}{d^2}+\frac{b^2 x^6 \sinh (c+d x)}{d}",1,"(-2*d*x*(a^2*d^4 + 4*a*b*d^2*(6 + d^2*x^2) + 3*b^2*(120 + 20*d^2*x^2 + d^4*x^4))*Cosh[c + d*x] + (a^2*d^4*(2 + d^2*x^2) + 2*a*b*d^2*(24 + 12*d^2*x^2 + d^4*x^4) + b^2*(720 + 360*d^2*x^2 + 30*d^4*x^4 + d^6*x^6))*Sinh[c + d*x])/d^7","A",1
50,1,113,184,0.2480112,"\int x \left(a+b x^2\right)^2 \cosh (c+d x) \, dx","Integrate[x*(a + b*x^2)^2*Cosh[c + d*x],x]","\frac{d x \left(a^2 d^4+2 a b d^2 \left(d^2 x^2+6\right)+b^2 \left(d^4 x^4+20 d^2 x^2+120\right)\right) \sinh (c+d x)-\left(a^2 d^4+6 a b d^2 \left(d^2 x^2+2\right)+5 b^2 \left(d^4 x^4+12 d^2 x^2+24\right)\right) \cosh (c+d x)}{d^6}","-\frac{a^2 \cosh (c+d x)}{d^2}+\frac{a^2 x \sinh (c+d x)}{d}-\frac{12 a b \cosh (c+d x)}{d^4}+\frac{12 a b x \sinh (c+d x)}{d^3}-\frac{6 a b x^2 \cosh (c+d x)}{d^2}+\frac{2 a b x^3 \sinh (c+d x)}{d}-\frac{120 b^2 \cosh (c+d x)}{d^6}+\frac{120 b^2 x \sinh (c+d x)}{d^5}-\frac{60 b^2 x^2 \cosh (c+d x)}{d^4}+\frac{20 b^2 x^3 \sinh (c+d x)}{d^3}-\frac{5 b^2 x^4 \cosh (c+d x)}{d^2}+\frac{b^2 x^5 \sinh (c+d x)}{d}",1,"(-((a^2*d^4 + 6*a*b*d^2*(2 + d^2*x^2) + 5*b^2*(24 + 12*d^2*x^2 + d^4*x^4))*Cosh[c + d*x]) + d*x*(a^2*d^4 + 2*a*b*d^2*(6 + d^2*x^2) + b^2*(120 + 20*d^2*x^2 + d^4*x^4))*Sinh[c + d*x])/d^6","A",1
51,1,85,136,0.1972427,"\int \left(a+b x^2\right)^2 \cosh (c+d x) \, dx","Integrate[(a + b*x^2)^2*Cosh[c + d*x],x]","\frac{\left(a^2 d^4+2 a b d^2 \left(d^2 x^2+2\right)+b^2 \left(d^4 x^4+12 d^2 x^2+24\right)\right) \sinh (c+d x)-4 b d x \left(a d^2+b \left(d^2 x^2+6\right)\right) \cosh (c+d x)}{d^5}","\frac{a^2 \sinh (c+d x)}{d}+\frac{4 a b \sinh (c+d x)}{d^3}-\frac{4 a b x \cosh (c+d x)}{d^2}+\frac{2 a b x^2 \sinh (c+d x)}{d}+\frac{24 b^2 \sinh (c+d x)}{d^5}-\frac{24 b^2 x \cosh (c+d x)}{d^4}+\frac{12 b^2 x^2 \sinh (c+d x)}{d^3}-\frac{4 b^2 x^3 \cosh (c+d x)}{d^2}+\frac{b^2 x^4 \sinh (c+d x)}{d}",1,"(-4*b*d*x*(a*d^2 + b*(6 + d^2*x^2))*Cosh[c + d*x] + (a^2*d^4 + 2*a*b*d^2*(2 + d^2*x^2) + b^2*(24 + 12*d^2*x^2 + d^4*x^4))*Sinh[c + d*x])/d^5","A",1
52,1,82,110,0.3896023,"\int \frac{\left(a+b x^2\right)^2 \cosh (c+d x)}{x} \, dx","Integrate[((a + b*x^2)^2*Cosh[c + d*x])/x,x]","a^2 \cosh (c) \text{Chi}(d x)+a^2 \sinh (c) \text{Shi}(d x)-\frac{b \left(2 a d^2+3 b \left(d^2 x^2+2\right)\right) \cosh (c+d x)}{d^4}+\frac{b x \left(2 a d^2+b \left(d^2 x^2+6\right)\right) \sinh (c+d x)}{d^3}","a^2 \cosh (c) \text{Chi}(d x)+a^2 \sinh (c) \text{Shi}(d x)-\frac{2 a b \cosh (c+d x)}{d^2}+\frac{2 a b x \sinh (c+d x)}{d}-\frac{6 b^2 \cosh (c+d x)}{d^4}+\frac{6 b^2 x \sinh (c+d x)}{d^3}-\frac{3 b^2 x^2 \cosh (c+d x)}{d^2}+\frac{b^2 x^3 \sinh (c+d x)}{d}",1,"-((b*(2*a*d^2 + 3*b*(2 + d^2*x^2))*Cosh[c + d*x])/d^4) + a^2*Cosh[c]*CoshIntegral[d*x] + (b*x*(2*a*d^2 + b*(6 + d^2*x^2))*Sinh[c + d*x])/d^3 + a^2*Sinh[c]*SinhIntegral[d*x]","A",1
53,1,95,95,0.281255,"\int \frac{\left(a+b x^2\right)^2 \cosh (c+d x)}{x^2} \, dx","Integrate[((a + b*x^2)^2*Cosh[c + d*x])/x^2,x]","a^2 d \sinh (c) \text{Chi}(d x)+a^2 d \cosh (c) \text{Shi}(d x)-\frac{a^2 \cosh (c+d x)}{x}+\frac{2 a b \sinh (c+d x)}{d}+\frac{2 b^2 \sinh (c+d x)}{d^3}-\frac{2 b^2 x \cosh (c+d x)}{d^2}+\frac{b^2 x^2 \sinh (c+d x)}{d}","a^2 d \sinh (c) \text{Chi}(d x)+a^2 d \cosh (c) \text{Shi}(d x)-\frac{a^2 \cosh (c+d x)}{x}+\frac{2 a b \sinh (c+d x)}{d}+\frac{2 b^2 \sinh (c+d x)}{d^3}-\frac{2 b^2 x \cosh (c+d x)}{d^2}+\frac{b^2 x^2 \sinh (c+d x)}{d}",1,"-((a^2*Cosh[c + d*x])/x) - (2*b^2*x*Cosh[c + d*x])/d^2 + a^2*d*CoshIntegral[d*x]*Sinh[c] + (2*b^2*Sinh[c + d*x])/d^3 + (2*a*b*Sinh[c + d*x])/d + (b^2*x^2*Sinh[c + d*x])/d + a^2*d*Cosh[c]*SinhIntegral[d*x]","A",1
54,1,97,114,0.3956596,"\int \frac{\left(a+b x^2\right)^2 \cosh (c+d x)}{x^3} \, dx","Integrate[((a + b*x^2)^2*Cosh[c + d*x])/x^3,x]","\frac{1}{2} \left(-\frac{a^2 \cosh (c+d x)}{x^2}-\frac{a^2 d \sinh (c+d x)}{x}+a \cosh (c) \left(a d^2+4 b\right) \text{Chi}(d x)+a \sinh (c) \left(a d^2+4 b\right) \text{Shi}(d x)-\frac{2 b^2 \cosh (c+d x)}{d^2}+\frac{2 b^2 x \sinh (c+d x)}{d}\right)","\frac{1}{2} a^2 d^2 \cosh (c) \text{Chi}(d x)+\frac{1}{2} a^2 d^2 \sinh (c) \text{Shi}(d x)-\frac{a^2 \cosh (c+d x)}{2 x^2}-\frac{a^2 d \sinh (c+d x)}{2 x}+2 a b \cosh (c) \text{Chi}(d x)+2 a b \sinh (c) \text{Shi}(d x)-\frac{b^2 \cosh (c+d x)}{d^2}+\frac{b^2 x \sinh (c+d x)}{d}",1,"((-2*b^2*Cosh[c + d*x])/d^2 - (a^2*Cosh[c + d*x])/x^2 + a*(4*b + a*d^2)*Cosh[c]*CoshIntegral[d*x] - (a^2*d*Sinh[c + d*x])/x + (2*b^2*x*Sinh[c + d*x])/d + a*(4*b + a*d^2)*Sinh[c]*SinhIntegral[d*x])/2","A",1
55,1,114,133,0.436212,"\int \frac{\left(a+b x^2\right)^2 \cosh (c+d x)}{x^4} \, dx","Integrate[((a + b*x^2)^2*Cosh[c + d*x])/x^4,x]","\frac{1}{6} \left(-\frac{a^2 d^2 \cosh (c+d x)}{x}-\frac{2 a^2 \cosh (c+d x)}{x^3}-\frac{a^2 d \sinh (c+d x)}{x^2}+a d \sinh (c) \left(a d^2+12 b\right) \text{Chi}(d x)+a d \cosh (c) \left(a d^2+12 b\right) \text{Shi}(d x)-\frac{12 a b \cosh (c+d x)}{x}+\frac{6 b^2 \sinh (c+d x)}{d}\right)","\frac{1}{6} a^2 d^3 \sinh (c) \text{Chi}(d x)+\frac{1}{6} a^2 d^3 \cosh (c) \text{Shi}(d x)-\frac{a^2 d^2 \cosh (c+d x)}{6 x}-\frac{a^2 \cosh (c+d x)}{3 x^3}-\frac{a^2 d \sinh (c+d x)}{6 x^2}+2 a b d \sinh (c) \text{Chi}(d x)+2 a b d \cosh (c) \text{Shi}(d x)-\frac{2 a b \cosh (c+d x)}{x}+\frac{b^2 \sinh (c+d x)}{d}",1,"((-2*a^2*Cosh[c + d*x])/x^3 - (12*a*b*Cosh[c + d*x])/x - (a^2*d^2*Cosh[c + d*x])/x + a*d*(12*b + a*d^2)*CoshIntegral[d*x]*Sinh[c] + (6*b^2*Sinh[c + d*x])/d - (a^2*d*Sinh[c + d*x])/x^2 + a*d*(12*b + a*d^2)*Cosh[c]*SinhIntegral[d*x])/6","A",1
56,1,124,175,0.4875207,"\int \frac{\left(a+b x^2\right)^2 \cosh (c+d x)}{x^5} \, dx","Integrate[((a + b*x^2)^2*Cosh[c + d*x])/x^5,x]","\frac{x^4 \cosh (c) \left(a^2 d^4+24 a b d^2+24 b^2\right) \text{Chi}(d x)+x^4 \sinh (c) \left(a^2 d^4+24 a b d^2+24 b^2\right) \text{Shi}(d x)-a \left(d x \left(a d^2 x^2+2 a+24 b x^2\right) \sinh (c+d x)+\left(a d^2 x^2+6 a+24 b x^2\right) \cosh (c+d x)\right)}{24 x^4}","\frac{1}{24} a^2 d^4 \cosh (c) \text{Chi}(d x)+\frac{1}{24} a^2 d^4 \sinh (c) \text{Shi}(d x)-\frac{a^2 d^3 \sinh (c+d x)}{24 x}-\frac{a^2 d^2 \cosh (c+d x)}{24 x^2}-\frac{a^2 \cosh (c+d x)}{4 x^4}-\frac{a^2 d \sinh (c+d x)}{12 x^3}+a b d^2 \cosh (c) \text{Chi}(d x)+a b d^2 \sinh (c) \text{Shi}(d x)-\frac{a b \cosh (c+d x)}{x^2}-\frac{a b d \sinh (c+d x)}{x}+b^2 \cosh (c) \text{Chi}(d x)+b^2 \sinh (c) \text{Shi}(d x)",1,"((24*b^2 + 24*a*b*d^2 + a^2*d^4)*x^4*Cosh[c]*CoshIntegral[d*x] - a*((6*a + 24*b*x^2 + a*d^2*x^2)*Cosh[c + d*x] + d*x*(2*a + 24*b*x^2 + a*d^2*x^2)*Sinh[c + d*x]) + (24*b^2 + 24*a*b*d^2 + a^2*d^4)*x^4*Sinh[c]*SinhIntegral[d*x])/(24*x^4)","A",1
57,1,274,273,0.4543246,"\int \frac{x^4 \cosh (c+d x)}{a+b x^2} \, dx","Integrate[(x^4*Cosh[c + d*x])/(a + b*x^2),x]","\frac{i a^{3/2} d^3 \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-i a^{3/2} d^3 \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-a^{3/2} d^3 \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-a^{3/2} d^3 \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-2 a \sqrt{b} d^2 \sinh (c+d x)+2 b^{3/2} d^2 x^2 \sinh (c+d x)+4 b^{3/2} \sinh (c+d x)-4 b^{3/2} d x \cosh (c+d x)}{2 b^{5/2} d^3}","\frac{(-a)^{3/2} \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{5/2}}-\frac{(-a)^{3/2} \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^{5/2}}-\frac{(-a)^{3/2} \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{5/2}}-\frac{(-a)^{3/2} \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^{5/2}}-\frac{a \sinh (c+d x)}{b^2 d}+\frac{2 \sinh (c+d x)}{b d^3}-\frac{2 x \cosh (c+d x)}{b d^2}+\frac{x^2 \sinh (c+d x)}{b d}",1,"(-4*b^(3/2)*d*x*Cosh[c + d*x] + I*a^(3/2)*d^3*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] - I*a^(3/2)*d^3*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + 4*b^(3/2)*Sinh[c + d*x] - 2*a*Sqrt[b]*d^2*Sinh[c + d*x] + 2*b^(3/2)*d^2*x^2*Sinh[c + d*x] - a^(3/2)*d^3*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - a^(3/2)*d^3*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(2*b^(5/2)*d^3)","C",0
58,1,210,209,0.3901568,"\int \frac{x^3 \cosh (c+d x)}{a+b x^2} \, dx","Integrate[(x^3*Cosh[c + d*x])/(a + b*x^2),x]","-\frac{a d^2 \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+a d^2 \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+i a d^2 \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-i a d^2 \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-2 b d x \sinh (c+d x)+2 b \cosh (c+d x)}{2 b^2 d^2}","-\frac{a \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}-\frac{a \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^2}+\frac{a \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}-\frac{a \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^2}-\frac{\cosh (c+d x)}{b d^2}+\frac{x \sinh (c+d x)}{b d}",1,"-1/2*(2*b*Cosh[c + d*x] + a*d^2*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + a*d^2*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - 2*b*d*x*Sinh[c + d*x] + I*a*d^2*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - I*a*d^2*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(b^2*d^2)","C",0
59,1,213,226,0.2703173,"\int \frac{x^2 \cosh (c+d x)}{a+b x^2} \, dx","Integrate[(x^2*Cosh[c + d*x])/(a + b*x^2),x]","\frac{-i \sqrt{a} d \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+i \sqrt{a} d \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sqrt{a} d \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\sqrt{a} d \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+2 \sqrt{b} \sinh (c+d x)}{2 b^{3/2} d}","\frac{\sqrt{-a} \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{3/2}}-\frac{\sqrt{-a} \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^{3/2}}-\frac{\sqrt{-a} \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^{3/2}}-\frac{\sqrt{-a} \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^{3/2}}+\frac{\sinh (c+d x)}{b d}",1,"((-I)*Sqrt[a]*d*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + I*Sqrt[a]*d*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + 2*Sqrt[b]*Sinh[c + d*x] + Sqrt[a]*d*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + Sqrt[a]*d*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(2*b^(3/2)*d)","C",0
60,1,171,177,0.1863788,"\int \frac{x \cosh (c+d x)}{a+b x^2} \, dx","Integrate[(x*Cosh[c + d*x])/(a + b*x^2),x]","\frac{\cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+i \left(\sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-\sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)}{2 b}","\frac{\cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b}+\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b}-\frac{\sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b}+\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b}",1,"(Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + I*(Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]))/(2*b)","C",0
61,1,180,213,0.2052496,"\int \frac{\cosh (c+d x)}{a+b x^2} \, dx","Integrate[Cosh[c + d*x]/(a + b*x^2),x]","\frac{i \left(\cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-\cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+i \left(\sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{2 \sqrt{a} \sqrt{b}}","\frac{\cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 \sqrt{-a} \sqrt{b}}-\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 \sqrt{-a} \sqrt{b}}-\frac{\sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 \sqrt{-a} \sqrt{b}}-\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 \sqrt{-a} \sqrt{b}}",1,"((I/2)*(Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] - Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + I*(Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/(Sqrt[a]*Sqrt[b])","C",0
62,1,187,197,0.334445,"\int \frac{\cosh (c+d x)}{x \left(a+b x^2\right)} \, dx","Integrate[Cosh[c + d*x]/(x*(a + b*x^2)),x]","-\frac{\cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+i \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-i \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-2 \cosh (c) \text{Chi}(d x)-2 \sinh (c) \text{Shi}(d x)}{2 a}","-\frac{\cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a}-\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a}+\frac{\sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a}-\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a}+\frac{\cosh (c) \text{Chi}(d x)}{a}+\frac{\sinh (c) \text{Shi}(d x)}{a}",1,"-1/2*(-2*Cosh[c]*CoshIntegral[d*x] + Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - 2*Sinh[c]*SinhIntegral[d*x] + I*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - I*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/a","C",0
63,1,243,249,0.3800694,"\int \frac{\cosh (c+d x)}{x^2 \left(a+b x^2\right)} \, dx","Integrate[Cosh[c + d*x]/(x^2*(a + b*x^2)),x]","\frac{-i \sqrt{b} x \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+i \sqrt{b} x \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sqrt{b} x \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\sqrt{b} x \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+2 \sqrt{a} d x \sinh (c) \text{Chi}(d x)+2 \sqrt{a} d x \cosh (c) \text{Shi}(d x)-2 \sqrt{a} \cosh (c+d x)}{2 a^{3/2} x}","\frac{\sqrt{b} \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 (-a)^{3/2}}-\frac{\sqrt{b} \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 (-a)^{3/2}}-\frac{\sqrt{b} \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 (-a)^{3/2}}-\frac{\sqrt{b} \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 (-a)^{3/2}}+\frac{d \sinh (c) \text{Chi}(d x)}{a}+\frac{d \cosh (c) \text{Shi}(d x)}{a}-\frac{\cosh (c+d x)}{a x}",1,"(-2*Sqrt[a]*Cosh[c + d*x] - I*Sqrt[b]*x*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + I*Sqrt[b]*x*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + 2*Sqrt[a]*d*x*CoshIntegral[d*x]*Sinh[c] + 2*Sqrt[a]*d*x*Cosh[c]*SinhIntegral[d*x] + Sqrt[b]*x*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + Sqrt[b]*x*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(2*a^(3/2)*x)","C",0
64,1,257,270,0.5685384,"\int \frac{\cosh (c+d x)}{x^3 \left(a+b x^2\right)} \, dx","Integrate[Cosh[c + d*x]/(x^3*(a + b*x^2)),x]","\frac{-\left(x^2 \cosh (c) \left(2 b-a d^2\right) \text{Chi}(d x)\right)+b x^2 \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+b x^2 \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+i b x^2 \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-i b x^2 \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+a d^2 x^2 \sinh (c) \text{Shi}(d x)-a d x \sinh (c+d x)-a \cosh (c+d x)-2 b x^2 \sinh (c) \text{Shi}(d x)}{2 a^2 x^2}","-\frac{b \cosh (c) \text{Chi}(d x)}{a^2}+\frac{b \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}+\frac{b \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^2}-\frac{b \sinh (c) \text{Shi}(d x)}{a^2}-\frac{b \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}+\frac{b \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^2}+\frac{d^2 \cosh (c) \text{Chi}(d x)}{2 a}+\frac{d^2 \sinh (c) \text{Shi}(d x)}{2 a}-\frac{\cosh (c+d x)}{2 a x^2}-\frac{d \sinh (c+d x)}{2 a x}",1,"(-(a*Cosh[c + d*x]) - (2*b - a*d^2)*x^2*Cosh[c]*CoshIntegral[d*x] + b*x^2*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + b*x^2*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - a*d*x*Sinh[c + d*x] - 2*b*x^2*Sinh[c]*SinhIntegral[d*x] + a*d^2*x^2*Sinh[c]*SinhIntegral[d*x] + I*b*x^2*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - I*b*x^2*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(2*a^2*x^2)","C",0
65,1,621,449,1.6259451,"\int \frac{x^4 \cosh (c+d x)}{\left(a+b x^2\right)^2} \, dx","Integrate[(x^4*Cosh[c + d*x])/(a + b*x^2)^2,x]","\frac{-\frac{3 \sqrt{a} \sinh (c) \left(\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{\sqrt{b}}-\frac{a d \sinh (c) \left(\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{b}-\frac{3 i \sqrt{a} \cosh (c) \left(\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{\sqrt{b}}+\frac{i a d \cosh (c) \left(\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)\right)\right)}{b}+2 \cosh (d x) \left(\frac{a x \cosh (c)}{a+b x^2}+\frac{2 \sinh (c)}{d}\right)+2 \sinh (d x) \left(\frac{a x \sinh (c)}{a+b x^2}+\frac{2 \cosh (c)}{d}\right)}{4 b^2}","\frac{3 \sqrt{-a} \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}-\frac{3 \sqrt{-a} \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^{5/2}}-\frac{3 \sqrt{-a} \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}-\frac{3 \sqrt{-a} \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^{5/2}}-\frac{a d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^3}-\frac{a d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^3}+\frac{a d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^3}-\frac{a d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^3}-\frac{x^3 \cosh (c+d x)}{2 b \left(a+b x^2\right)}+\frac{\sinh (c+d x)}{b^2 d}+\frac{x \cosh (c+d x)}{2 b^2}",1,"(2*Cosh[d*x]*((a*x*Cosh[c])/(a + b*x^2) + (2*Sinh[c])/d) + 2*((2*Cosh[c])/d + (a*x*Sinh[c])/(a + b*x^2))*Sinh[d*x] - ((3*I)*Sqrt[a]*Cosh[c]*(Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] - Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sin[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/Sqrt[b] + (I*a*d*Cosh[c]*(CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] - CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] + Cos[(Sqrt[a]*d)/Sqrt[b]]*(-SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/b - (3*Sqrt[a]*Sinh[c]*(CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] + CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] - Cos[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/Sqrt[b] - (a*d*Sinh[c]*(Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sin[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/b)/(4*b^2)","C",0
66,1,582,431,0.7944202,"\int \frac{x^3 \cosh (c+d x)}{\left(a+b x^2\right)^2} \, dx","Integrate[(x^3*Cosh[c + d*x])/(a + b*x^2)^2,x]","\frac{a^{3/2} d \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+a^{3/2} d \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+2 i b^{3/2} x^2 \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-2 i b^{3/2} x^2 \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\left(a+b x^2\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(2 \sqrt{b} \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)-i \sqrt{a} d \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)+\left(a+b x^2\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(i \sqrt{a} d \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)+2 \sqrt{b} \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)+\sqrt{a} b d x^2 \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\sqrt{a} b d x^2 \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+2 i a \sqrt{b} \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-2 i a \sqrt{b} \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+2 a \sqrt{b} \cosh (c+d x)}{4 b^{5/2} \left(a+b x^2\right)}","-\frac{\sqrt{-a} d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^{5/2}}+\frac{\sqrt{-a} d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}-\frac{\sqrt{-a} d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^{5/2}}-\frac{\sqrt{-a} d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^{5/2}}+\frac{\cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}+\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^2}-\frac{\sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 b^2}+\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 b^2}-\frac{x^2 \cosh (c+d x)}{2 b \left(a+b x^2\right)}+\frac{\cosh (c+d x)}{2 b^2}",1,"(2*a*Sqrt[b]*Cosh[c + d*x] + (a + b*x^2)*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*(2*Sqrt[b]*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]] - I*Sqrt[a]*d*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]) + (a + b*x^2)*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*(2*Sqrt[b]*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]] + I*Sqrt[a]*d*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]) + a^(3/2)*d*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + Sqrt[a]*b*d*x^2*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + (2*I)*a*Sqrt[b]*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + (2*I)*b^(3/2)*x^2*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + a^(3/2)*d*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sqrt[a]*b*d*x^2*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - (2*I)*a*Sqrt[b]*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - (2*I)*b^(3/2)*x^2*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(4*b^(5/2)*(a + b*x^2))","C",0
67,1,364,416,1.0643581,"\int \frac{x^2 \cosh (c+d x)}{\left(a+b x^2\right)^2} \, dx","Integrate[(x^2*Cosh[c + d*x])/(a + b*x^2)^2,x]","\frac{\left(a+b x^2\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\sqrt{a} d \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)+i \sqrt{b} \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)+\left(a+b x^2\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\sqrt{a} d \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)-i \sqrt{b} \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)+\left(a+b x^2\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right) \left(i \sqrt{a} d \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)-\sqrt{b} \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)-\left(a+b x^2\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\sqrt{b} \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)+i \sqrt{a} d \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)-2 \sqrt{a} b x \cosh (c+d x)}{4 \sqrt{a} b^2 \left(a+b x^2\right)}","\frac{\cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}-\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 \sqrt{-a} b^{3/2}}-\frac{\sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}-\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 \sqrt{-a} b^{3/2}}+\frac{d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^2}+\frac{d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^2}-\frac{d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 b^2}+\frac{d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 b^2}-\frac{x \cosh (c+d x)}{2 b \left(a+b x^2\right)}",1,"(-2*Sqrt[a]*b*x*Cosh[c + d*x] + (a + b*x^2)*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*(I*Sqrt[b]*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]] + Sqrt[a]*d*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]) + (a + b*x^2)*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*((-I)*Sqrt[b]*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]] + Sqrt[a]*d*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]) + (a + b*x^2)*(I*Sqrt[a]*d*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]] - Sqrt[b]*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]])*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - (a + b*x^2)*(I*Sqrt[a]*d*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]] + Sqrt[b]*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]])*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(4*Sqrt[a]*b^2*(a + b*x^2))","C",0
68,1,239,239,0.5335083,"\int \frac{x \cosh (c+d x)}{\left(a+b x^2\right)^2} \, dx","Integrate[(x*Cosh[c + d*x])/(a + b*x^2)^2,x]","\frac{i \left(d \left(a+b x^2\right) \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-d \left(a+b x^2\right) \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+i \left(d \left(a+b x^2\right) \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+d \left(a+b x^2\right) \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+2 \sqrt{a} \sqrt{b} \cosh (c+d x)\right)\right)}{4 \sqrt{a} b^{3/2} \left(a+b x^2\right)}","-\frac{d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 \sqrt{-a} b^{3/2}}+\frac{d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}-\frac{d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 \sqrt{-a} b^{3/2}}-\frac{d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 \sqrt{-a} b^{3/2}}-\frac{\cosh (c+d x)}{2 b \left(a+b x^2\right)}",1,"((I/4)*(d*(a + b*x^2)*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]] - d*(a + b*x^2)*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]] + I*(2*Sqrt[a]*Sqrt[b]*Cosh[c + d*x] + d*(a + b*x^2)*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + d*(a + b*x^2)*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/(Sqrt[a]*b^(3/2)*(a + b*x^2))","C",0
69,1,590,476,0.7402018,"\int \frac{\cosh (c+d x)}{\left(a+b x^2\right)^2} \, dx","Integrate[Cosh[c + d*x]/(a + b*x^2)^2,x]","\frac{-i a^{3/2} d \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+i a^{3/2} d \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-b^{3/2} x^2 \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-b^{3/2} x^2 \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\left(a+b x^2\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\sqrt{a} d \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)-i \sqrt{b} \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)-\left(a+b x^2\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\sqrt{a} d \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)+i \sqrt{b} \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)-i \sqrt{a} b d x^2 \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+i \sqrt{a} b d x^2 \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-a \sqrt{b} \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-a \sqrt{b} \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+2 \sqrt{a} b x \cosh (c+d x)}{4 a^{3/2} b \left(a+b x^2\right)}","-\frac{d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 a b}-\frac{d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a b}-\frac{\cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{\sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a b}-\frac{d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 a b}-\frac{\cosh (c+d x)}{4 a \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\cosh (c+d x)}{4 a \sqrt{b} \left(\sqrt{-a}+\sqrt{b} x\right)}",1,"(2*Sqrt[a]*b*x*Cosh[c + d*x] - (a + b*x^2)*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*((-I)*Sqrt[b]*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]] + Sqrt[a]*d*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]) - (a + b*x^2)*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*(I*Sqrt[b]*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]] + Sqrt[a]*d*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]) - I*a^(3/2)*d*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - I*Sqrt[a]*b*d*x^2*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - a*Sqrt[b]*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - b^(3/2)*x^2*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + I*a^(3/2)*d*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + I*Sqrt[a]*b*d*x^2*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - a*Sqrt[b]*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - b^(3/2)*x^2*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(4*a^(3/2)*b*(a + b*x^2))","C",0
70,1,501,435,1.3333754,"\int \frac{\cosh (c+d x)}{x \left(a+b x^2\right)^2} \, dx","Integrate[Cosh[c + d*x]/(x*(a + b*x^2)^2),x]","\frac{\frac{\sqrt{a} d \left(-i \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+i \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)}{2 \sqrt{b}}+i \sinh (c) \left(\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)\right)\right)-\cosh (c) \left(\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)+\frac{a \sinh (c) \sinh (d x)}{a+b x^2}+\frac{a \cosh (c) \cosh (d x)}{a+b x^2}+2 (\cosh (c) \text{Chi}(d x)+\sinh (c) \text{Shi}(d x))}{2 a^2}","-\frac{\cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}-\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^2}+\frac{\sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^2}-\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^2}+\frac{\cosh (c) \text{Chi}(d x)}{a^2}+\frac{\sinh (c) \text{Shi}(d x)}{a^2}-\frac{d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}-\frac{d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{3/2} \sqrt{b}}-\frac{d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{3/2} \sqrt{b}}+\frac{\cosh (c+d x)}{2 a \left(a+b x^2\right)}",1,"((a*Cosh[c]*Cosh[d*x])/(a + b*x^2) + (a*Sinh[c]*Sinh[d*x])/(a + b*x^2) + 2*(Cosh[c]*CoshIntegral[d*x] + Sinh[c]*SinhIntegral[d*x]) + (Sqrt[a]*d*((-I)*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]] + I*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]] + Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]))/(2*Sqrt[b]) + I*Sinh[c]*(CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] - CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] + Cos[(Sqrt[a]*d)/Sqrt[b]]*(-SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])) - Cosh[c]*(Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sin[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/(2*a^2)","C",0
71,1,675,500,1.0913292,"\int \frac{\cosh (c+d x)}{x^2 \left(a+b x^2\right)^2} \, dx","Integrate[Cosh[c + d*x]/(x^2*(a + b*x^2)^2),x]","\frac{i a^{3/2} d x \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-i a^{3/2} d x \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+4 a^{3/2} d x \sinh (c) \text{Chi}(d x)+4 a^{3/2} d x \cosh (c) \text{Shi}(d x)-4 a^{3/2} \cosh (c+d x)+3 b^{3/2} x^3 \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+3 b^{3/2} x^3 \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+4 \sqrt{a} b d x^3 \sinh (c) \text{Chi}(d x)+x \left(a+b x^2\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\sqrt{a} d \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)-3 i \sqrt{b} \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)+x \left(a+b x^2\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\sqrt{a} d \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)+3 i \sqrt{b} \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)+4 \sqrt{a} b d x^3 \cosh (c) \text{Shi}(d x)+i \sqrt{a} b d x^3 \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-i \sqrt{a} b d x^3 \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+3 a \sqrt{b} x \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+3 a \sqrt{b} x \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-6 \sqrt{a} b x^2 \cosh (c+d x)}{4 a^{5/2} x \left(a+b x^2\right)}","\frac{d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 a^2}+\frac{d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a^2}-\frac{d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 a^2}+\frac{d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 a^2}+\frac{\sqrt{b} \cosh (c+d x)}{4 a^2 \left(\sqrt{-a}-\sqrt{b} x\right)}-\frac{\sqrt{b} \cosh (c+d x)}{4 a^2 \left(\sqrt{-a}+\sqrt{b} x\right)}+\frac{d \sinh (c) \text{Chi}(d x)}{a^2}+\frac{d \cosh (c) \text{Shi}(d x)}{a^2}-\frac{\cosh (c+d x)}{a^2 x}-\frac{3 \sqrt{b} \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{5/2}}+\frac{3 \sqrt{b} \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{5/2}}+\frac{3 \sqrt{b} \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{4 (-a)^{5/2}}+\frac{3 \sqrt{b} \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{4 (-a)^{5/2}}",1,"(-4*a^(3/2)*Cosh[c + d*x] - 6*Sqrt[a]*b*x^2*Cosh[c + d*x] + 4*a^(3/2)*d*x*CoshIntegral[d*x]*Sinh[c] + 4*Sqrt[a]*b*d*x^3*CoshIntegral[d*x]*Sinh[c] + x*(a + b*x^2)*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*((-3*I)*Sqrt[b]*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]] + Sqrt[a]*d*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]) + x*(a + b*x^2)*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*((3*I)*Sqrt[b]*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]] + Sqrt[a]*d*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]) + 4*a^(3/2)*d*x*Cosh[c]*SinhIntegral[d*x] + 4*Sqrt[a]*b*d*x^3*Cosh[c]*SinhIntegral[d*x] + I*a^(3/2)*d*x*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + I*Sqrt[a]*b*d*x^3*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + 3*a*Sqrt[b]*x*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + 3*b^(3/2)*x^3*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - I*a^(3/2)*d*x*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - I*Sqrt[a]*b*d*x^3*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + 3*a*Sqrt[b]*x*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + 3*b^(3/2)*x^3*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(4*a^(5/2)*x*(a + b*x^2))","C",0
72,1,648,476,1.9666878,"\int \frac{x^3 \cosh (c+d x)}{\left(a+b x^2\right)^3} \, dx","Integrate[(x^3*Cosh[c + d*x])/(a + b*x^2)^3,x]","\frac{-\frac{i d^2 \sinh (c) \left(\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)\right)\right)}{b}+\frac{d^2 \cosh (c) \left(\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{b}+\frac{3 i d \sinh (c) \left(\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{\sqrt{a} \sqrt{b}}+\frac{3 d \cosh (c) \left(\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{\sqrt{a} \sqrt{b}}-\frac{2 \cosh (d x) \left(d x \sinh (c) \left(a+b x^2\right)+2 \cosh (c) \left(a+2 b x^2\right)\right)}{\left(a+b x^2\right)^2}-\frac{2 \sinh (d x) \left(d x \cosh (c) \left(a+b x^2\right)+2 \sinh (c) \left(a+2 b x^2\right)\right)}{\left(a+b x^2\right)^2}}{16 b^2}","-\frac{3 d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 \sqrt{-a} b^{5/2}}+\frac{3 d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}-\frac{3 d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}-\frac{3 d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 \sqrt{-a} b^{5/2}}+\frac{d^2 \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 b^3}+\frac{d^2 \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 b^3}-\frac{d^2 \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 b^3}+\frac{d^2 \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 b^3}-\frac{d x \sinh (c+d x)}{8 b^2 \left(a+b x^2\right)}-\frac{\cosh (c+d x)}{4 b^2 \left(a+b x^2\right)}-\frac{x^2 \cosh (c+d x)}{4 b \left(a+b x^2\right)^2}",1,"((-2*Cosh[d*x]*(2*(a + 2*b*x^2)*Cosh[c] + d*x*(a + b*x^2)*Sinh[c]))/(a + b*x^2)^2 - (2*(d*x*(a + b*x^2)*Cosh[c] + 2*(a + 2*b*x^2)*Sinh[c])*Sinh[d*x])/(a + b*x^2)^2 + ((3*I)*d*Sinh[c]*(Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] - Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sin[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/(Sqrt[a]*Sqrt[b]) - (I*d^2*Sinh[c]*(CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] - CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] + Cos[(Sqrt[a]*d)/Sqrt[b]]*(-SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/b + (3*d*Cosh[c]*(CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] + CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] - Cos[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/(Sqrt[a]*Sqrt[b]) + (d^2*Cosh[c]*(Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sin[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/b)/(16*b^2)","C",0
73,1,932,746,2.6714893,"\int \frac{x^2 \cosh (c+d x)}{\left(a+b x^2\right)^3} \, dx","Integrate[(x^2*Cosh[c + d*x])/(a + b*x^2)^3,x]","\frac{\frac{2 \sqrt{a} b^2 \cosh (c) \cosh (d x) x^3}{\left(b x^2+a\right)^2}+\frac{2 \sqrt{a} b^2 \sinh (c) \sinh (d x) x^3}{\left(b x^2+a\right)^2}-\frac{2 a^{3/2} b d \cosh (d x) \sinh (c) x^2}{\left(b x^2+a\right)^2}-\frac{2 a^{3/2} b d \cosh (c) \sinh (d x) x^2}{\left(b x^2+a\right)^2}-\frac{2 a^{3/2} b \cosh (c) \cosh (d x) x}{\left(b x^2+a\right)^2}-\frac{2 a^{3/2} b \sinh (c) \sinh (d x) x}{\left(b x^2+a\right)^2}-\frac{2 a^{5/2} d \cosh (d x) \sinh (c)}{\left(b x^2+a\right)^2}+\frac{i \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\left(a d^2+b\right) \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)+i \sqrt{a} \sqrt{b} d \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)}{\sqrt{b}}-\frac{i \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\left(a d^2+b\right) \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)-i \sqrt{a} \sqrt{b} d \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)}{\sqrt{b}}-\frac{2 a^{5/2} d \cosh (c) \sinh (d x)}{\left(b x^2+a\right)^2}-i \sqrt{a} d \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \cosh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\frac{i a d^2 \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)}{\sqrt{b}}+i \sqrt{b} \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-\frac{a d^2 \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)}{\sqrt{b}}-\sqrt{b} \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-\sqrt{a} d \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+i \sqrt{a} d \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \cosh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\frac{i a d^2 \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{\sqrt{b}}-i \sqrt{b} \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\frac{a d^2 \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{\sqrt{b}}-\sqrt{b} \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\sqrt{a} d \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{16 a^{3/2} b^2}","\frac{d^2 \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}-\frac{d^2 \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 \sqrt{-a} b^{5/2}}-\frac{\cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}+\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d^2 \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 \sqrt{-a} b^{5/2}}-\frac{d^2 \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 \sqrt{-a} b^{5/2}}+\frac{\sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}+\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{\cosh (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\cosh (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}+\sqrt{b} x\right)}-\frac{d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a b^2}-\frac{d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}+\frac{d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}-\frac{d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a b^2}-\frac{d \sinh (c+d x)}{8 b^2 \left(a+b x^2\right)}-\frac{x \cosh (c+d x)}{4 b \left(a+b x^2\right)^2}",1,"((-2*a^(3/2)*b*x*Cosh[c]*Cosh[d*x])/(a + b*x^2)^2 + (2*Sqrt[a]*b^2*x^3*Cosh[c]*Cosh[d*x])/(a + b*x^2)^2 - (2*a^(5/2)*d*Cosh[d*x]*Sinh[c])/(a + b*x^2)^2 - (2*a^(3/2)*b*d*x^2*Cosh[d*x]*Sinh[c])/(a + b*x^2)^2 + (I*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*((b + a*d^2)*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]] + I*Sqrt[a]*Sqrt[b]*d*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]))/Sqrt[b] - (I*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*((b + a*d^2)*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]] - I*Sqrt[a]*Sqrt[b]*d*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]))/Sqrt[b] - (2*a^(5/2)*d*Cosh[c]*Sinh[d*x])/(a + b*x^2)^2 - (2*a^(3/2)*b*d*x^2*Cosh[c]*Sinh[d*x])/(a + b*x^2)^2 - (2*a^(3/2)*b*x*Sinh[c]*Sinh[d*x])/(a + b*x^2)^2 + (2*Sqrt[a]*b^2*x^3*Sinh[c]*Sinh[d*x])/(a + b*x^2)^2 - I*Sqrt[a]*d*Cos[(Sqrt[a]*d)/Sqrt[b]]*Cosh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + I*Sqrt[b]*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + (I*a*d^2*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x])/Sqrt[b] - Sqrt[b]*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - (a*d^2*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x])/Sqrt[b] - Sqrt[a]*d*Sin[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + I*Sqrt[a]*d*Cos[(Sqrt[a]*d)/Sqrt[b]]*Cosh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - I*Sqrt[b]*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - (I*a*d^2*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/Sqrt[b] - Sqrt[b]*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - (a*d^2*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/Sqrt[b] - Sqrt[a]*d*Sin[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(16*a^(3/2)*b^2)","C",0
74,1,637,512,1.8473019,"\int \frac{x \cosh (c+d x)}{\left(a+b x^2\right)^3} \, dx","Integrate[(x*Cosh[c + d*x])/(a + b*x^2)^3,x]","\frac{\frac{i d^2 \sinh (c) \left(\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)\right)\right)}{b}-\frac{d^2 \cosh (c) \left(\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{b}+\frac{i d \sinh (c) \left(\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{\sqrt{a} \sqrt{b}}+\frac{d \cosh (c) \left(\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{\sqrt{a} \sqrt{b}}+\frac{2 \cosh (d x) \left(d x \sinh (c) \left(a+b x^2\right)-2 a \cosh (c)\right)}{\left(a+b x^2\right)^2}+\frac{2 \sinh (d x) \left(d x \cosh (c) \left(a+b x^2\right)-2 a \sinh (c)\right)}{\left(a+b x^2\right)^2}}{16 a b}","\frac{d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}+\frac{d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{3/2} b^{3/2}}+\frac{d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{3/2} b^{3/2}}-\frac{d \sinh (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{d \sinh (c+d x)}{16 a b^{3/2} \left(\sqrt{-a}+\sqrt{b} x\right)}-\frac{d^2 \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}-\frac{d^2 \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a b^2}+\frac{d^2 \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a b^2}-\frac{d^2 \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a b^2}-\frac{\cosh (c+d x)}{4 b \left(a+b x^2\right)^2}",1,"((2*Cosh[d*x]*(-2*a*Cosh[c] + d*x*(a + b*x^2)*Sinh[c]))/(a + b*x^2)^2 + (2*(d*x*(a + b*x^2)*Cosh[c] - 2*a*Sinh[c])*Sinh[d*x])/(a + b*x^2)^2 + (I*d*Sinh[c]*(Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] - Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sin[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/(Sqrt[a]*Sqrt[b]) + (I*d^2*Sinh[c]*(CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] - CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] + Cos[(Sqrt[a]*d)/Sqrt[b]]*(-SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/b + (d*Cosh[c]*(CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] + CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] - Cos[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/(Sqrt[a]*Sqrt[b]) - (d^2*Cosh[c]*(Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sin[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/b)/(16*a*b)","C",0
75,1,933,856,2.6005155,"\int \frac{\cosh (c+d x)}{\left(a+b x^2\right)^3} \, dx","Integrate[Cosh[c + d*x]/(a + b*x^2)^3,x]","\frac{\frac{6 b^{5/2} \cosh (c) \cosh (d x) x^3}{\left(b x^2+a\right)^2}+\frac{6 b^{5/2} \sinh (c) \sinh (d x) x^3}{\left(b x^2+a\right)^2}+\frac{2 a b^{3/2} d \cosh (d x) \sinh (c) x^2}{\left(b x^2+a\right)^2}+\frac{2 a b^{3/2} d \cosh (c) \sinh (d x) x^2}{\left(b x^2+a\right)^2}+\frac{10 a b^{3/2} \cosh (c) \cosh (d x) x}{\left(b x^2+a\right)^2}+\frac{10 a b^{3/2} \sinh (c) \sinh (d x) x}{\left(b x^2+a\right)^2}+\frac{2 a^2 \sqrt{b} d \cosh (d x) \sinh (c)}{\left(b x^2+a\right)^2}+\frac{\text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(i \left(3 b-a d^2\right) \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)-3 \sqrt{a} \sqrt{b} d \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)}{\sqrt{a}}+\frac{i \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\left(a d^2-3 b\right) \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)+3 i \sqrt{a} \sqrt{b} d \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)}{\sqrt{a}}+\frac{2 a^2 \sqrt{b} d \cosh (c) \sinh (d x)}{\left(b x^2+a\right)^2}-3 i \sqrt{b} d \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \cosh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-i \sqrt{a} d^2 \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\frac{3 i b \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)}{\sqrt{a}}+\sqrt{a} d^2 \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-\frac{3 b \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)}{\sqrt{a}}-3 \sqrt{b} d \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+3 i \sqrt{b} d \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \cosh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+i \sqrt{a} d^2 \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\frac{3 i b \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{\sqrt{a}}+\sqrt{a} d^2 \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\frac{3 b \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{\sqrt{a}}-3 \sqrt{b} d \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{16 a^2 b^{3/2}}","\frac{\cosh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d^2}{16 (-a)^{3/2} b^{3/2}}-\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{3/2} b^{3/2}}-\frac{\sinh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d^2}{16 (-a)^{3/2} b^{3/2}}-\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{3/2} b^{3/2}}-\frac{3 \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^2 b}-\frac{3 \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) \sinh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^2 b}+\frac{\sinh (c+d x) d}{16 (-a)^{3/2} b \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\sinh (c+d x) d}{16 (-a)^{3/2} b \left(\sqrt{b} x+\sqrt{-a}\right)}+\frac{3 \cosh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d}{16 a^2 b}-\frac{3 \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^2 b}-\frac{3 \cosh (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{3 \cosh (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{b} x+\sqrt{-a}\right)}-\frac{\cosh (c+d x)}{16 (-a)^{3/2} \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)^2}+\frac{\cosh (c+d x)}{16 (-a)^{3/2} \sqrt{b} \left(\sqrt{b} x+\sqrt{-a}\right)^2}+\frac{3 \cosh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{3 \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{3 \sinh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{3 \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}",1,"((10*a*b^(3/2)*x*Cosh[c]*Cosh[d*x])/(a + b*x^2)^2 + (6*b^(5/2)*x^3*Cosh[c]*Cosh[d*x])/(a + b*x^2)^2 + (2*a^2*Sqrt[b]*d*Cosh[d*x]*Sinh[c])/(a + b*x^2)^2 + (2*a*b^(3/2)*d*x^2*Cosh[d*x]*Sinh[c])/(a + b*x^2)^2 + (CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*(I*(3*b - a*d^2)*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]] - 3*Sqrt[a]*Sqrt[b]*d*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]))/Sqrt[a] + (I*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*((-3*b + a*d^2)*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]] + (3*I)*Sqrt[a]*Sqrt[b]*d*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]))/Sqrt[a] + (2*a^2*Sqrt[b]*d*Cosh[c]*Sinh[d*x])/(a + b*x^2)^2 + (2*a*b^(3/2)*d*x^2*Cosh[c]*Sinh[d*x])/(a + b*x^2)^2 + (10*a*b^(3/2)*x*Sinh[c]*Sinh[d*x])/(a + b*x^2)^2 + (6*b^(5/2)*x^3*Sinh[c]*Sinh[d*x])/(a + b*x^2)^2 - (3*I)*Sqrt[b]*d*Cos[(Sqrt[a]*d)/Sqrt[b]]*Cosh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + ((3*I)*b*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x])/Sqrt[a] - I*Sqrt[a]*d^2*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - (3*b*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x])/Sqrt[a] + Sqrt[a]*d^2*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - 3*Sqrt[b]*d*Sin[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + (3*I)*Sqrt[b]*d*Cos[(Sqrt[a]*d)/Sqrt[b]]*Cosh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - ((3*I)*b*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/Sqrt[a] + I*Sqrt[a]*d^2*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - (3*b*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/Sqrt[a] + Sqrt[a]*d^2*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - 3*Sqrt[b]*d*Sin[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(16*a^2*b^(3/2))","C",0
76,1,1046,730,2.6138604,"\int \frac{\cosh (c+d x)}{x \left(a+b x^2\right)^3} \, dx","Integrate[Cosh[c + d*x]/(x*(a + b*x^2)^3),x]","\frac{\frac{16 b^2 \sinh (c) \text{Shi}(d x) x^4}{\left(b x^2+a\right)^2}-\frac{2 a b d \sinh (c+d x) x^3}{\left(b x^2+a\right)^2}+\frac{8 a b \cosh (c+d x) x^2}{\left(b x^2+a\right)^2}+\frac{32 a b \sinh (c) \text{Shi}(d x) x^2}{\left(b x^2+a\right)^2}-\frac{2 a^2 d \sinh (c+d x) x}{\left(b x^2+a\right)^2}+\frac{12 a^2 \cosh (c+d x)}{\left(b x^2+a\right)^2}+16 \cosh (c) \text{Chi}(d x)+\frac{a d^2 \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \cosh (c) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{b}-8 \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \cosh (c) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\frac{5 \sqrt{a} d \cosh (c) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right)}{\sqrt{b}}+\frac{5 i \sqrt{a} d \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c)}{\sqrt{b}}+\frac{i a d^2 \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c)}{b}-8 i \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c)-\frac{\text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\left(8 b-a d^2\right) \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)+5 i \sqrt{a} \sqrt{b} d \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)}{b}+\frac{16 a^2 \sinh (c) \text{Shi}(d x)}{\left(b x^2+a\right)^2}+\frac{5 \sqrt{a} d \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \cosh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)}{\sqrt{b}}+\frac{a d^2 \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)}{b}-8 \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\frac{i a d^2 \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)}{b}-8 i \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-\frac{5 i \sqrt{a} d \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)}{\sqrt{b}}+\frac{5 \sqrt{a} d \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \cosh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{\sqrt{b}}+\frac{a d^2 \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{b}-8 \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\frac{i a d^2 \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{b}+8 i \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\frac{5 i \sqrt{a} d \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{\sqrt{b}}}{16 a^3}","-\frac{\cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^3}-\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^3}+\frac{\sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^3}-\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^3}+\frac{\cosh (c) \text{Chi}(d x)}{a^3}+\frac{\sinh (c) \text{Shi}(d x)}{a^3}+\frac{d^2 \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^2 b}+\frac{d^2 \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a^2 b}-\frac{d^2 \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^2 b}+\frac{d^2 \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a^2 b}+\frac{\cosh (c+d x)}{2 a^2 \left(a+b x^2\right)}+\frac{d \sinh (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{-a}-\sqrt{b} x\right)}-\frac{d \sinh (c+d x)}{16 a^2 \sqrt{b} \left(\sqrt{-a}+\sqrt{b} x\right)}+\frac{5 d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}-\frac{5 d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{5/2} \sqrt{b}}+\frac{5 d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{5/2} \sqrt{b}}+\frac{5 d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{5/2} \sqrt{b}}+\frac{\cosh (c+d x)}{4 a \left(a+b x^2\right)^2}",1,"((12*a^2*Cosh[c + d*x])/(a + b*x^2)^2 + (8*a*b*x^2*Cosh[c + d*x])/(a + b*x^2)^2 + 16*Cosh[c]*CoshIntegral[d*x] - 8*Cos[(Sqrt[a]*d)/Sqrt[b]]*Cosh[c]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + (a*d^2*Cos[(Sqrt[a]*d)/Sqrt[b]]*Cosh[c]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/b - (5*Sqrt[a]*d*Cosh[c]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]])/Sqrt[b] + ((5*I)*Sqrt[a]*d*Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sinh[c])/Sqrt[b] - (8*I)*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c] + (I*a*d^2*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c])/b - (CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*((8*b - a*d^2)*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]] + (5*I)*Sqrt[a]*Sqrt[b]*d*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]))/b - (2*a^2*d*x*Sinh[c + d*x])/(a + b*x^2)^2 - (2*a*b*d*x^3*Sinh[c + d*x])/(a + b*x^2)^2 + (16*a^2*Sinh[c]*SinhIntegral[d*x])/(a + b*x^2)^2 + (32*a*b*x^2*Sinh[c]*SinhIntegral[d*x])/(a + b*x^2)^2 + (16*b^2*x^4*Sinh[c]*SinhIntegral[d*x])/(a + b*x^2)^2 + (5*Sqrt[a]*d*Cos[(Sqrt[a]*d)/Sqrt[b]]*Cosh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x])/Sqrt[b] - 8*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + (a*d^2*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x])/b - (8*I)*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + (I*a*d^2*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x])/b - ((5*I)*Sqrt[a]*d*Sin[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x])/Sqrt[b] + (5*Sqrt[a]*d*Cos[(Sqrt[a]*d)/Sqrt[b]]*Cosh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/Sqrt[b] - 8*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + (a*d^2*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/b + (8*I)*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - (I*a*d^2*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/b + ((5*I)*Sqrt[a]*d*Sin[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/Sqrt[b])/(16*a^3)","C",0
77,1,1009,874,2.9449499,"\int \frac{\cosh (c+d x)}{x^2 \left(a+b x^2\right)^3} \, dx","Integrate[Cosh[c + d*x]/(x^2*(a + b*x^2)^3),x]","\frac{-\frac{30 \sqrt{a} b^2 \cosh (c) \cosh (d x) x^3}{\left(b x^2+a\right)^2}-\frac{30 \sqrt{a} b^2 \sinh (c) \sinh (d x) x^3}{\left(b x^2+a\right)^2}-\frac{2 a^{3/2} b d \cosh (d x) \sinh (c) x^2}{\left(b x^2+a\right)^2}-\frac{2 a^{3/2} b d \cosh (c) \sinh (d x) x^2}{\left(b x^2+a\right)^2}-\frac{50 a^{3/2} b \cosh (c) \cosh (d x) x}{\left(b x^2+a\right)^2}-\frac{50 a^{3/2} b \sinh (c) \sinh (d x) x}{\left(b x^2+a\right)^2}-\frac{2 a^{5/2} d \cosh (d x) \sinh (c)}{\left(b x^2+a\right)^2}+16 \sqrt{a} d \text{Chi}(d x) \sinh (c)+\frac{\text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(7 \sqrt{a} \sqrt{b} d \sinh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)-i \left(15 b-a d^2\right) \cosh \left(c-\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)}{\sqrt{b}}+\frac{\text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(i \left(15 b-a d^2\right) \cosh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)+7 \sqrt{a} \sqrt{b} d \sinh \left(c+\frac{i \sqrt{a} d}{\sqrt{b}}\right)\right)}{\sqrt{b}}-\frac{2 a^{5/2} d \cosh (c) \sinh (d x)}{\left(b x^2+a\right)^2}+16 \sqrt{a} d \cosh (c) \text{Shi}(d x)+7 i \sqrt{a} d \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \cosh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\frac{i a d^2 \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)}{\sqrt{b}}-15 i \sqrt{b} \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-\frac{a d^2 \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)}{\sqrt{b}}+15 \sqrt{b} \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+7 \sqrt{a} d \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-7 i \sqrt{a} d \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \cosh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\frac{i a d^2 \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{\sqrt{b}}+15 i \sqrt{b} \cosh (c) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\frac{a d^2 \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)}{\sqrt{b}}+15 \sqrt{b} \cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+7 \sqrt{a} d \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \sinh (c) \text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\frac{16 a^{5/2} \cosh (c) \cosh (d x)}{\left(b x^2+a\right)^2 x}-\frac{16 a^{5/2} \sinh (c) \sinh (d x)}{\left(b x^2+a\right)^2 x}}{16 a^{7/2}}","\frac{\cosh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d^2}{16 (-a)^{5/2} \sqrt{b}}-\frac{\cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{5/2} \sqrt{b}}-\frac{\sinh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d^2}{16 (-a)^{5/2} \sqrt{b}}-\frac{\sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d^2}{16 (-a)^{5/2} \sqrt{b}}+\frac{\text{Chi}(d x) \sinh (c) d}{a^3}+\frac{7 \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^3}+\frac{7 \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) \sinh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^3}+\frac{\sinh (c+d x) d}{16 (-a)^{5/2} \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\sinh (c+d x) d}{16 (-a)^{5/2} \left(\sqrt{b} x+\sqrt{-a}\right)}+\frac{\cosh (c) \text{Shi}(d x) d}{a^3}-\frac{7 \cosh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right) d}{16 a^3}+\frac{7 \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right) d}{16 a^3}-\frac{\cosh (c+d x)}{a^3 x}+\frac{7 \sqrt{b} \cosh (c+d x)}{16 a^3 \left(\sqrt{-a}-\sqrt{b} x\right)}-\frac{7 \sqrt{b} \cosh (c+d x)}{16 a^3 \left(\sqrt{b} x+\sqrt{-a}\right)}-\frac{\sqrt{b} \cosh (c+d x)}{16 (-a)^{5/2} \left(\sqrt{-a}-\sqrt{b} x\right)^2}+\frac{\sqrt{b} \cosh (c+d x)}{16 (-a)^{5/2} \left(\sqrt{b} x+\sqrt{-a}\right)^2}+\frac{15 \sqrt{b} \cosh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{7/2}}-\frac{15 \sqrt{b} \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}-\frac{15 \sqrt{b} \sinh \left(c+\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{7/2}}-\frac{15 \sqrt{b} \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}",1,"((-16*a^(5/2)*Cosh[c]*Cosh[d*x])/(x*(a + b*x^2)^2) - (50*a^(3/2)*b*x*Cosh[c]*Cosh[d*x])/(a + b*x^2)^2 - (30*Sqrt[a]*b^2*x^3*Cosh[c]*Cosh[d*x])/(a + b*x^2)^2 - (2*a^(5/2)*d*Cosh[d*x]*Sinh[c])/(a + b*x^2)^2 - (2*a^(3/2)*b*d*x^2*Cosh[d*x]*Sinh[c])/(a + b*x^2)^2 + 16*Sqrt[a]*d*CoshIntegral[d*x]*Sinh[c] + (CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*((-I)*(15*b - a*d^2)*Cosh[c - (I*Sqrt[a]*d)/Sqrt[b]] + 7*Sqrt[a]*Sqrt[b]*d*Sinh[c - (I*Sqrt[a]*d)/Sqrt[b]]))/Sqrt[b] + (CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*(I*(15*b - a*d^2)*Cosh[c + (I*Sqrt[a]*d)/Sqrt[b]] + 7*Sqrt[a]*Sqrt[b]*d*Sinh[c + (I*Sqrt[a]*d)/Sqrt[b]]))/Sqrt[b] - (2*a^(5/2)*d*Cosh[c]*Sinh[d*x])/(a + b*x^2)^2 - (2*a^(3/2)*b*d*x^2*Cosh[c]*Sinh[d*x])/(a + b*x^2)^2 - (16*a^(5/2)*Sinh[c]*Sinh[d*x])/(x*(a + b*x^2)^2) - (50*a^(3/2)*b*x*Sinh[c]*Sinh[d*x])/(a + b*x^2)^2 - (30*Sqrt[a]*b^2*x^3*Sinh[c]*Sinh[d*x])/(a + b*x^2)^2 + 16*Sqrt[a]*d*Cosh[c]*SinhIntegral[d*x] + (7*I)*Sqrt[a]*d*Cos[(Sqrt[a]*d)/Sqrt[b]]*Cosh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - (15*I)*Sqrt[b]*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + (I*a*d^2*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x])/Sqrt[b] + 15*Sqrt[b]*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - (a*d^2*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x])/Sqrt[b] + 7*Sqrt[a]*d*Sin[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - (7*I)*Sqrt[a]*d*Cos[(Sqrt[a]*d)/Sqrt[b]]*Cosh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + (15*I)*Sqrt[b]*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - (I*a*d^2*Cosh[c]*Sin[(Sqrt[a]*d)/Sqrt[b]]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/Sqrt[b] + 15*Sqrt[b]*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] - (a*d^2*Cos[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/Sqrt[b] + 7*Sqrt[a]*d*Sin[(Sqrt[a]*d)/Sqrt[b]]*Sinh[c]*SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])/(16*a^(7/2))","C",0
78,1,998,791,4.0203309,"\int \frac{\cosh (c+d x)}{x^3 \left(a+b x^2\right)^3} \, dx","Integrate[Cosh[c + d*x]/(x^3*(a + b*x^2)^3),x]","-\frac{-i a \sinh (c) \left(\text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right)-\text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)\right)\right) d^2+a \cosh (c) \left(\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right) d^2-9 i \sqrt{a} \sqrt{b} \sinh (c) \left(\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)-\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)-\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right) d-9 \sqrt{a} \sqrt{b} \cosh (c) \left(\text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right)+\text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right)-\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right) d+\frac{2 a \cosh (d x) \left(2 \left(6 b^2 x^4+9 a b x^2+2 a^2\right) \cosh (c)+d x \left(3 b^2 x^4+7 a b x^2+4 a^2\right) \sinh (c)\right)}{x^2 \left(b x^2+a\right)^2}+\frac{2 a \left(d x \left(3 b^2 x^4+7 a b x^2+4 a^2\right) \cosh (c)+2 \left(6 b^2 x^4+9 a b x^2+2 a^2\right) \sinh (c)\right) \sinh (d x)}{x^2 \left(b x^2+a\right)^2}+8 \left(6 b-a d^2\right) (\cosh (c) \text{Chi}(d x)+\sinh (c) \text{Shi}(d x))+24 i b \sinh (c) \left(\text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right)-\text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right) \sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)-\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)\right)\right)-24 b \cosh (c) \left(\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i d x-\frac{\sqrt{a} d}{\sqrt{b}}\right)+\cos \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \text{Ci}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)+\sin \left(\frac{\sqrt{a} d}{\sqrt{b}}\right) \left(\text{Si}\left(\frac{\sqrt{a} d}{\sqrt{b}}-i d x\right)+\text{Si}\left(i x d+\frac{\sqrt{a} d}{\sqrt{b}}\right)\right)\right)}{16 a^4}","-\frac{3 b \cosh (c) \text{Chi}(d x)}{a^4}+\frac{3 b \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^4}+\frac{3 b \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^4}-\frac{3 b \sinh (c) \text{Shi}(d x)}{a^4}-\frac{3 b \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{2 a^4}+\frac{3 b \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{2 a^4}-\frac{d^2 \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^3}-\frac{d^2 \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a^3}+\frac{d^2 \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 a^3}-\frac{d^2 \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 a^3}-\frac{b \cosh (c+d x)}{a^3 \left(a+b x^2\right)}-\frac{\sqrt{b} d \sinh (c+d x)}{16 a^3 \left(\sqrt{-a}-\sqrt{b} x\right)}+\frac{\sqrt{b} d \sinh (c+d x)}{16 a^3 \left(\sqrt{-a}+\sqrt{b} x\right)}+\frac{d^2 \cosh (c) \text{Chi}(d x)}{2 a^3}+\frac{d^2 \sinh (c) \text{Shi}(d x)}{2 a^3}-\frac{\cosh (c+d x)}{2 a^3 x^2}-\frac{d \sinh (c+d x)}{2 a^3 x}-\frac{b \cosh (c+d x)}{4 a^2 \left(a+b x^2\right)^2}+\frac{9 \sqrt{b} d \sinh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Chi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}-\frac{9 \sqrt{b} d \sinh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Chi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{7/2}}+\frac{9 \sqrt{b} d \cosh \left(\frac{\sqrt{-a} d}{\sqrt{b}}+c\right) \text{Shi}\left(\frac{\sqrt{-a} d}{\sqrt{b}}-d x\right)}{16 (-a)^{7/2}}+\frac{9 \sqrt{b} d \cosh \left(c-\frac{\sqrt{-a} d}{\sqrt{b}}\right) \text{Shi}\left(x d+\frac{\sqrt{-a} d}{\sqrt{b}}\right)}{16 (-a)^{7/2}}",1,"-1/16*((2*a*Cosh[d*x]*(2*(2*a^2 + 9*a*b*x^2 + 6*b^2*x^4)*Cosh[c] + d*x*(4*a^2 + 7*a*b*x^2 + 3*b^2*x^4)*Sinh[c]))/(x^2*(a + b*x^2)^2) + (2*a*(d*x*(4*a^2 + 7*a*b*x^2 + 3*b^2*x^4)*Cosh[c] + 2*(2*a^2 + 9*a*b*x^2 + 6*b^2*x^4)*Sinh[c])*Sinh[d*x])/(x^2*(a + b*x^2)^2) + 8*(6*b - a*d^2)*(Cosh[c]*CoshIntegral[d*x] + Sinh[c]*SinhIntegral[d*x]) - (9*I)*Sqrt[a]*Sqrt[b]*d*Sinh[c]*(Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] - Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sin[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] - SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])) + (24*I)*b*Sinh[c]*(CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] - CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] + Cos[(Sqrt[a]*d)/Sqrt[b]]*(-SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])) - I*a*d^2*Sinh[c]*(CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] - CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] + Cos[(Sqrt[a]*d)/Sqrt[b]]*(-SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])) - 9*Sqrt[a]*Sqrt[b]*d*Cosh[c]*(CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] + CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x]*Sin[(Sqrt[a]*d)/Sqrt[b]] - Cos[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])) - 24*b*Cosh[c]*(Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sin[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])) + a*d^2*Cosh[c]*(Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[-((Sqrt[a]*d)/Sqrt[b]) + I*d*x] + Cos[(Sqrt[a]*d)/Sqrt[b]]*CosIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x] + Sin[(Sqrt[a]*d)/Sqrt[b]]*(SinIntegral[(Sqrt[a]*d)/Sqrt[b] - I*d*x] + SinIntegral[(Sqrt[a]*d)/Sqrt[b] + I*d*x])))/a^4","C",0
79,1,100,154,0.185471,"\int x^3 \left(a+b x^3\right) \cosh (c+d x) \, dx","Integrate[x^3*(a + b*x^3)*Cosh[c + d*x],x]","\frac{\left(a d^4 x \left(d^2 x^2+6\right)+b \left(d^6 x^6+30 d^4 x^4+360 d^2 x^2+720\right)\right) \sinh (c+d x)-3 d \left(a d^2 \left(d^2 x^2+2\right)+2 b x \left(d^4 x^4+20 d^2 x^2+120\right)\right) \cosh (c+d x)}{d^7}","-\frac{6 a \cosh (c+d x)}{d^4}+\frac{6 a x \sinh (c+d x)}{d^3}-\frac{3 a x^2 \cosh (c+d x)}{d^2}+\frac{a x^3 \sinh (c+d x)}{d}+\frac{720 b \sinh (c+d x)}{d^7}-\frac{720 b x \cosh (c+d x)}{d^6}+\frac{360 b x^2 \sinh (c+d x)}{d^5}-\frac{120 b x^3 \cosh (c+d x)}{d^4}+\frac{30 b x^4 \sinh (c+d x)}{d^3}-\frac{6 b x^5 \cosh (c+d x)}{d^2}+\frac{b x^6 \sinh (c+d x)}{d}",1,"(-3*d*(a*d^2*(2 + d^2*x^2) + 2*b*x*(120 + 20*d^2*x^2 + d^4*x^4))*Cosh[c + d*x] + (a*d^4*x*(6 + d^2*x^2) + b*(720 + 360*d^2*x^2 + 30*d^4*x^4 + d^6*x^6))*Sinh[c + d*x])/d^7","A",1
80,1,84,124,0.1474732,"\int x^2 \left(a+b x^3\right) \cosh (c+d x) \, dx","Integrate[x^2*(a + b*x^3)*Cosh[c + d*x],x]","\frac{d \left(a d^2 \left(d^2 x^2+2\right)+b x \left(d^4 x^4+20 d^2 x^2+120\right)\right) \sinh (c+d x)-\left(2 a d^4 x+5 b \left(d^4 x^4+12 d^2 x^2+24\right)\right) \cosh (c+d x)}{d^6}","\frac{2 a \sinh (c+d x)}{d^3}-\frac{2 a x \cosh (c+d x)}{d^2}+\frac{a x^2 \sinh (c+d x)}{d}-\frac{120 b \cosh (c+d x)}{d^6}+\frac{120 b x \sinh (c+d x)}{d^5}-\frac{60 b x^2 \cosh (c+d x)}{d^4}+\frac{20 b x^3 \sinh (c+d x)}{d^3}-\frac{5 b x^4 \cosh (c+d x)}{d^2}+\frac{b x^5 \sinh (c+d x)}{d}",1,"(-((2*a*d^4*x + 5*b*(24 + 12*d^2*x^2 + d^4*x^4))*Cosh[c + d*x]) + d*(a*d^2*(2 + d^2*x^2) + b*x*(120 + 20*d^2*x^2 + d^4*x^4))*Sinh[c + d*x])/d^6","A",1
81,1,66,94,0.1242596,"\int x \left(a+b x^3\right) \cosh (c+d x) \, dx","Integrate[x*(a + b*x^3)*Cosh[c + d*x],x]","\frac{\left(a d^4 x+b \left(d^4 x^4+12 d^2 x^2+24\right)\right) \sinh (c+d x)-d \left(a d^2+4 b x \left(d^2 x^2+6\right)\right) \cosh (c+d x)}{d^5}","-\frac{a \cosh (c+d x)}{d^2}+\frac{a x \sinh (c+d x)}{d}+\frac{24 b \sinh (c+d x)}{d^5}-\frac{24 b x \cosh (c+d x)}{d^4}+\frac{12 b x^2 \sinh (c+d x)}{d^3}-\frac{4 b x^3 \cosh (c+d x)}{d^2}+\frac{b x^4 \sinh (c+d x)}{d}",1,"(-(d*(a*d^2 + 4*b*x*(6 + d^2*x^2))*Cosh[c + d*x]) + (a*d^4*x + b*(24 + 12*d^2*x^2 + d^4*x^4))*Sinh[c + d*x])/d^5","A",1
82,1,49,66,0.0970034,"\int \left(a+b x^3\right) \cosh (c+d x) \, dx","Integrate[(a + b*x^3)*Cosh[c + d*x],x]","\frac{d \left(a d^2+b x \left(d^2 x^2+6\right)\right) \sinh (c+d x)-3 b \left(d^2 x^2+2\right) \cosh (c+d x)}{d^4}","\frac{a \sinh (c+d x)}{d}-\frac{6 b \cosh (c+d x)}{d^4}+\frac{6 b x \sinh (c+d x)}{d^3}-\frac{3 b x^2 \cosh (c+d x)}{d^2}+\frac{b x^3 \sinh (c+d x)}{d}",1,"(-3*b*(2 + d^2*x^2)*Cosh[c + d*x] + d*(a*d^2 + b*x*(6 + d^2*x^2))*Sinh[c + d*x])/d^4","A",1
83,1,49,56,0.1823307,"\int \frac{\left(a+b x^3\right) \cosh (c+d x)}{x} \, dx","Integrate[((a + b*x^3)*Cosh[c + d*x])/x,x]","a \cosh (c) \text{Chi}(d x)+a \sinh (c) \text{Shi}(d x)+\frac{b \left(\left(d^2 x^2+2\right) \sinh (c+d x)-2 d x \cosh (c+d x)\right)}{d^3}","a \cosh (c) \text{Chi}(d x)+a \sinh (c) \text{Shi}(d x)+\frac{2 b \sinh (c+d x)}{d^3}-\frac{2 b x \cosh (c+d x)}{d^2}+\frac{b x^2 \sinh (c+d x)}{d}",1,"a*Cosh[c]*CoshIntegral[d*x] + (b*(-2*d*x*Cosh[c + d*x] + (2 + d^2*x^2)*Sinh[c + d*x]))/d^3 + a*Sinh[c]*SinhIntegral[d*x]","A",1
84,1,55,55,0.1415892,"\int \frac{\left(a+b x^3\right) \cosh (c+d x)}{x^2} \, dx","Integrate[((a + b*x^3)*Cosh[c + d*x])/x^2,x]","a d \sinh (c) \text{Chi}(d x)+a d \cosh (c) \text{Shi}(d x)-\frac{a \cosh (c+d x)}{x}-\frac{b \cosh (c+d x)}{d^2}+\frac{b x \sinh (c+d x)}{d}","a d \sinh (c) \text{Chi}(d x)+a d \cosh (c) \text{Shi}(d x)-\frac{a \cosh (c+d x)}{x}-\frac{b \cosh (c+d x)}{d^2}+\frac{b x \sinh (c+d x)}{d}",1,"-((b*Cosh[c + d*x])/d^2) - (a*Cosh[c + d*x])/x + a*d*CoshIntegral[d*x]*Sinh[c] + (b*x*Sinh[c + d*x])/d + a*d*Cosh[c]*SinhIntegral[d*x]","A",1
85,1,86,69,0.1476837,"\int \frac{\left(a+b x^3\right) \cosh (c+d x)}{x^3} \, dx","Integrate[((a + b*x^3)*Cosh[c + d*x])/x^3,x]","\frac{1}{2} a d^2 (\cosh (c) \text{Chi}(d x)+\sinh (c) \text{Shi}(d x))-\frac{a \cosh (d x) (d x \sinh (c)+\cosh (c))}{2 x^2}-\frac{a \sinh (d x) (d x \cosh (c)+\sinh (c))}{2 x^2}+\frac{b \sinh (c) \cosh (d x)}{d}+\frac{b \cosh (c) \sinh (d x)}{d}","\frac{1}{2} a d^2 \cosh (c) \text{Chi}(d x)+\frac{1}{2} a d^2 \sinh (c) \text{Shi}(d x)-\frac{a \cosh (c+d x)}{2 x^2}-\frac{a d \sinh (c+d x)}{2 x}+\frac{b \sinh (c+d x)}{d}",1,"(b*Cosh[d*x]*Sinh[c])/d - (a*Cosh[d*x]*(Cosh[c] + d*x*Sinh[c]))/(2*x^2) + (b*Cosh[c]*Sinh[d*x])/d - (a*(d*x*Cosh[c] + Sinh[c])*Sinh[d*x])/(2*x^2) + (a*d^2*(Cosh[c]*CoshIntegral[d*x] + Sinh[c]*SinhIntegral[d*x]))/2","A",1
86,1,73,91,0.262659,"\int \frac{\left(a+b x^3\right) \cosh (c+d x)}{x^4} \, dx","Integrate[((a + b*x^3)*Cosh[c + d*x])/x^4,x]","\frac{1}{6} \left(\text{Chi}(d x) \left(a d^3 \sinh (c)+6 b \cosh (c)\right)+\text{Shi}(d x) \left(a d^3 \cosh (c)+6 b \sinh (c)\right)-\frac{a \left(\left(d^2 x^2+2\right) \cosh (c+d x)+d x \sinh (c+d x)\right)}{x^3}\right)","\frac{1}{6} a d^3 \sinh (c) \text{Chi}(d x)+\frac{1}{6} a d^3 \cosh (c) \text{Shi}(d x)-\frac{a d^2 \cosh (c+d x)}{6 x}-\frac{a \cosh (c+d x)}{3 x^3}-\frac{a d \sinh (c+d x)}{6 x^2}+b \cosh (c) \text{Chi}(d x)+b \sinh (c) \text{Shi}(d x)",1,"(CoshIntegral[d*x]*(6*b*Cosh[c] + a*d^3*Sinh[c]) - (a*((2 + d^2*x^2)*Cosh[c + d*x] + d*x*Sinh[c + d*x]))/x^3 + (a*d^3*Cosh[c] + 6*b*Sinh[c])*SinhIntegral[d*x])/6","A",1
87,1,139,234,0.3204034,"\int x \left(a+b x^3\right)^2 \cosh (c+d x) \, dx","Integrate[x*(a + b*x^3)^2*Cosh[c + d*x],x]","\frac{d \left(a^2 d^6 x+2 a b d^2 \left(d^4 x^4+12 d^2 x^2+24\right)+b^2 x \left(d^6 x^6+42 d^4 x^4+840 d^2 x^2+5040\right)\right) \sinh (c+d x)-\left(a^2 d^6+8 a b d^4 x \left(d^2 x^2+6\right)+7 b^2 \left(d^6 x^6+30 d^4 x^4+360 d^2 x^2+720\right)\right) \cosh (c+d x)}{d^8}","-\frac{a^2 \cosh (c+d x)}{d^2}+\frac{a^2 x \sinh (c+d x)}{d}+\frac{48 a b \sinh (c+d x)}{d^5}-\frac{48 a b x \cosh (c+d x)}{d^4}+\frac{24 a b x^2 \sinh (c+d x)}{d^3}-\frac{8 a b x^3 \cosh (c+d x)}{d^2}+\frac{2 a b x^4 \sinh (c+d x)}{d}-\frac{5040 b^2 \cosh (c+d x)}{d^8}+\frac{5040 b^2 x \sinh (c+d x)}{d^7}-\frac{2520 b^2 x^2 \cosh (c+d x)}{d^6}+\frac{840 b^2 x^3 \sinh (c+d x)}{d^5}-\frac{210 b^2 x^4 \cosh (c+d x)}{d^4}+\frac{42 b^2 x^5 \sinh (c+d x)}{d^3}-\frac{7 b^2 x^6 \cosh (c+d x)}{d^2}+\frac{b^2 x^7 \sinh (c+d x)}{d}",1,"(-((a^2*d^6 + 8*a*b*d^4*x*(6 + d^2*x^2) + 7*b^2*(720 + 360*d^2*x^2 + 30*d^4*x^4 + d^6*x^6))*Cosh[c + d*x]) + d*(a^2*d^6*x + 2*a*b*d^2*(24 + 12*d^2*x^2 + d^4*x^4) + b^2*x*(5040 + 840*d^2*x^2 + 42*d^4*x^4 + d^6*x^6))*Sinh[c + d*x])/d^8","A",1
88,1,111,186,0.2443065,"\int \left(a+b x^3\right)^2 \cosh (c+d x) \, dx","Integrate[(a + b*x^3)^2*Cosh[c + d*x],x]","\frac{\left(a^2 d^6+2 a b d^4 x \left(d^2 x^2+6\right)+b^2 \left(d^6 x^6+30 d^4 x^4+360 d^2 x^2+720\right)\right) \sinh (c+d x)-6 b d \left(a d^2 \left(d^2 x^2+2\right)+b x \left(d^4 x^4+20 d^2 x^2+120\right)\right) \cosh (c+d x)}{d^7}","\frac{a^2 \sinh (c+d x)}{d}-\frac{12 a b \cosh (c+d x)}{d^4}+\frac{12 a b x \sinh (c+d x)}{d^3}-\frac{6 a b x^2 \cosh (c+d x)}{d^2}+\frac{2 a b x^3 \sinh (c+d x)}{d}+\frac{720 b^2 \sinh (c+d x)}{d^7}-\frac{720 b^2 x \cosh (c+d x)}{d^6}+\frac{360 b^2 x^2 \sinh (c+d x)}{d^5}-\frac{120 b^2 x^3 \cosh (c+d x)}{d^4}+\frac{30 b^2 x^4 \sinh (c+d x)}{d^3}-\frac{6 b^2 x^5 \cosh (c+d x)}{d^2}+\frac{b^2 x^6 \sinh (c+d x)}{d}",1,"(-6*b*d*(a*d^2*(2 + d^2*x^2) + b*x*(120 + 20*d^2*x^2 + d^4*x^4))*Cosh[c + d*x] + (a^2*d^6 + 2*a*b*d^4*x*(6 + d^2*x^2) + b^2*(720 + 360*d^2*x^2 + 30*d^4*x^4 + d^6*x^6))*Sinh[c + d*x])/d^7","A",1
89,1,108,160,0.5150867,"\int \frac{\left(a+b x^3\right)^2 \cosh (c+d x)}{x} \, dx","Integrate[((a + b*x^3)^2*Cosh[c + d*x])/x,x]","a^2 \cosh (c) \text{Chi}(d x)+a^2 \sinh (c) \text{Shi}(d x)-\frac{b \left(4 a d^4 x+5 b \left(d^4 x^4+12 d^2 x^2+24\right)\right) \cosh (c+d x)}{d^6}+\frac{b \left(2 a d^2 \left(d^2 x^2+2\right)+b x \left(d^4 x^4+20 d^2 x^2+120\right)\right) \sinh (c+d x)}{d^5}","a^2 \cosh (c) \text{Chi}(d x)+a^2 \sinh (c) \text{Shi}(d x)+\frac{4 a b \sinh (c+d x)}{d^3}-\frac{4 a b x \cosh (c+d x)}{d^2}+\frac{2 a b x^2 \sinh (c+d x)}{d}-\frac{120 b^2 \cosh (c+d x)}{d^6}+\frac{120 b^2 x \sinh (c+d x)}{d^5}-\frac{60 b^2 x^2 \cosh (c+d x)}{d^4}+\frac{20 b^2 x^3 \sinh (c+d x)}{d^3}-\frac{5 b^2 x^4 \cosh (c+d x)}{d^2}+\frac{b^2 x^5 \sinh (c+d x)}{d}",1,"-((b*(4*a*d^4*x + 5*b*(24 + 12*d^2*x^2 + d^4*x^4))*Cosh[c + d*x])/d^6) + a^2*Cosh[c]*CoshIntegral[d*x] + (b*(2*a*d^2*(2 + d^2*x^2) + b*x*(120 + 20*d^2*x^2 + d^4*x^4))*Sinh[c + d*x])/d^5 + a^2*Sinh[c]*SinhIntegral[d*x]","A",1
90,1,143,143,0.3774339,"\int \frac{\left(a+b x^3\right)^2 \cosh (c+d x)}{x^2} \, dx","Integrate[((a + b*x^3)^2*Cosh[c + d*x])/x^2,x]","a^2 d \sinh (c) \text{Chi}(d x)+a^2 d \cosh (c) \text{Shi}(d x)-\frac{a^2 \cosh (c+d x)}{x}-\frac{2 a b \cosh (c+d x)}{d^2}+\frac{2 a b x \sinh (c+d x)}{d}+\frac{24 b^2 \sinh (c+d x)}{d^5}-\frac{24 b^2 x \cosh (c+d x)}{d^4}+\frac{12 b^2 x^2 \sinh (c+d x)}{d^3}-\frac{4 b^2 x^3 \cosh (c+d x)}{d^2}+\frac{b^2 x^4 \sinh (c+d x)}{d}","a^2 d \sinh (c) \text{Chi}(d x)+a^2 d \cosh (c) \text{Shi}(d x)-\frac{a^2 \cosh (c+d x)}{x}-\frac{2 a b \cosh (c+d x)}{d^2}+\frac{2 a b x \sinh (c+d x)}{d}+\frac{24 b^2 \sinh (c+d x)}{d^5}-\frac{24 b^2 x \cosh (c+d x)}{d^4}+\frac{12 b^2 x^2 \sinh (c+d x)}{d^3}-\frac{4 b^2 x^3 \cosh (c+d x)}{d^2}+\frac{b^2 x^4 \sinh (c+d x)}{d}",1,"(-2*a*b*Cosh[c + d*x])/d^2 - (a^2*Cosh[c + d*x])/x - (24*b^2*x*Cosh[c + d*x])/d^4 - (4*b^2*x^3*Cosh[c + d*x])/d^2 + a^2*d*CoshIntegral[d*x]*Sinh[c] + (24*b^2*Sinh[c + d*x])/d^5 + (2*a*b*x*Sinh[c + d*x])/d + (12*b^2*x^2*Sinh[c + d*x])/d^3 + (b^2*x^4*Sinh[c + d*x])/d + a^2*d*Cosh[c]*SinhIntegral[d*x]","A",1
91,1,136,141,0.3756088,"\int \frac{\left(a+b x^3\right)^2 \cosh (c+d x)}{x^3} \, dx","Integrate[((a + b*x^3)^2*Cosh[c + d*x])/x^3,x]","\frac{1}{2} \left(a^2 d^2 \cosh (c) \text{Chi}(d x)+a^2 d^2 \sinh (c) \text{Shi}(d x)-\frac{a^2 \cosh (c+d x)}{x^2}-\frac{a^2 d \sinh (c+d x)}{x}+\frac{4 a b \sinh (c+d x)}{d}-\frac{12 b^2 \cosh (c+d x)}{d^4}+\frac{12 b^2 x \sinh (c+d x)}{d^3}-\frac{6 b^2 x^2 \cosh (c+d x)}{d^2}+\frac{2 b^2 x^3 \sinh (c+d x)}{d}\right)","\frac{1}{2} a^2 d^2 \cosh (c) \text{Chi}(d x)+\frac{1}{2} a^2 d^2 \sinh (c) \text{Shi}(d x)-\frac{a^2 \cosh (c+d x)}{2 x^2}-\frac{a^2 d \sinh (c+d x)}{2 x}+\frac{2 a b \sinh (c+d x)}{d}-\frac{6 b^2 \cosh (c+d x)}{d^4}+\frac{6 b^2 x \sinh (c+d x)}{d^3}-\frac{3 b^2 x^2 \cosh (c+d x)}{d^2}+\frac{b^2 x^3 \sinh (c+d x)}{d}",1,"((-12*b^2*Cosh[c + d*x])/d^4 - (a^2*Cosh[c + d*x])/x^2 - (6*b^2*x^2*Cosh[c + d*x])/d^2 + a^2*d^2*Cosh[c]*CoshIntegral[d*x] + (4*a*b*Sinh[c + d*x])/d - (a^2*d*Sinh[c + d*x])/x + (12*b^2*x*Sinh[c + d*x])/d^3 + (2*b^2*x^3*Sinh[c + d*x])/d + a^2*d^2*Sinh[c]*SinhIntegral[d*x])/2","A",1
92,1,135,150,0.6328427,"\int \frac{\left(a+b x^3\right)^2 \cosh (c+d x)}{x^4} \, dx","Integrate[((a + b*x^3)^2*Cosh[c + d*x])/x^4,x]","\frac{1}{6} \left(-\frac{a^2 d^2 \cosh (c+d x)}{x}-\frac{2 a^2 \cosh (c+d x)}{x^3}-\frac{a^2 d \sinh (c+d x)}{x^2}+a \text{Chi}(d x) \left(a d^3 \sinh (c)+12 b \cosh (c)\right)+a \text{Shi}(d x) \left(a d^3 \cosh (c)+12 b \sinh (c)\right)+\frac{12 b^2 \sinh (c+d x)}{d^3}-\frac{12 b^2 x \cosh (c+d x)}{d^2}+\frac{6 b^2 x^2 \sinh (c+d x)}{d}\right)","\frac{1}{6} a^2 d^3 \sinh (c) \text{Chi}(d x)+\frac{1}{6} a^2 d^3 \cosh (c) \text{Shi}(d x)-\frac{a^2 d^2 \cosh (c+d x)}{6 x}-\frac{a^2 \cosh (c+d x)}{3 x^3}-\frac{a^2 d \sinh (c+d x)}{6 x^2}+2 a b \cosh (c) \text{Chi}(d x)+2 a b \sinh (c) \text{Shi}(d x)+\frac{2 b^2 \sinh (c+d x)}{d^3}-\frac{2 b^2 x \cosh (c+d x)}{d^2}+\frac{b^2 x^2 \sinh (c+d x)}{d}",1,"((-2*a^2*Cosh[c + d*x])/x^3 - (a^2*d^2*Cosh[c + d*x])/x - (12*b^2*x*Cosh[c + d*x])/d^2 + a*CoshIntegral[d*x]*(12*b*Cosh[c] + a*d^3*Sinh[c]) + (12*b^2*Sinh[c + d*x])/d^3 - (a^2*d*Sinh[c + d*x])/x^2 + (6*b^2*x^2*Sinh[c + d*x])/d + a*(a*d^3*Cosh[c] + 12*b*Sinh[c])*SinhIntegral[d*x])/6","A",1
93,1,150,167,0.5756899,"\int \frac{\left(a+b x^3\right)^2 \cosh (c+d x)}{x^5} \, dx","Integrate[((a + b*x^3)^2*Cosh[c + d*x])/x^5,x]","\frac{1}{24} \left(-\frac{a^2 d^3 \sinh (c+d x)}{x}-\frac{a^2 d^2 \cosh (c+d x)}{x^2}-\frac{6 a^2 \cosh (c+d x)}{x^4}-\frac{2 a^2 d \sinh (c+d x)}{x^3}+a d \text{Chi}(d x) \left(a d^3 \cosh (c)+48 b \sinh (c)\right)+a d \text{Shi}(d x) \left(a d^3 \sinh (c)+48 b \cosh (c)\right)-\frac{48 a b \cosh (c+d x)}{x}-\frac{24 b^2 \cosh (c+d x)}{d^2}+\frac{24 b^2 x \sinh (c+d x)}{d}\right)","\frac{1}{24} a^2 d^4 \cosh (c) \text{Chi}(d x)+\frac{1}{24} a^2 d^4 \sinh (c) \text{Shi}(d x)-\frac{a^2 d^3 \sinh (c+d x)}{24 x}-\frac{a^2 d^2 \cosh (c+d x)}{24 x^2}-\frac{a^2 \cosh (c+d x)}{4 x^4}-\frac{a^2 d \sinh (c+d x)}{12 x^3}+2 a b d \sinh (c) \text{Chi}(d x)+2 a b d \cosh (c) \text{Shi}(d x)-\frac{2 a b \cosh (c+d x)}{x}-\frac{b^2 \cosh (c+d x)}{d^2}+\frac{b^2 x \sinh (c+d x)}{d}",1,"((-24*b^2*Cosh[c + d*x])/d^2 - (6*a^2*Cosh[c + d*x])/x^4 - (a^2*d^2*Cosh[c + d*x])/x^2 - (48*a*b*Cosh[c + d*x])/x + a*d*CoshIntegral[d*x]*(a*d^3*Cosh[c] + 48*b*Sinh[c]) - (2*a^2*d*Sinh[c + d*x])/x^3 - (a^2*d^3*Sinh[c + d*x])/x + (24*b^2*x*Sinh[c + d*x])/d + a*d*(48*b*Cosh[c] + a*d^3*Sinh[c])*SinhIntegral[d*x])/24","A",1
94,1,213,373,0.5107909,"\int \frac{x^4 \cosh (c+d x)}{a+b x^3} \, dx","Integrate[(x^4*Cosh[c + d*x])/(a + b*x^3),x]","-\frac{a d^2 \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}}\&\right]+a d^2 \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}}\&\right]+6 b (\cosh (c+d x)-d x \sinh (c+d x))}{6 b^2 d^2}","\frac{(-1)^{2/3} a^{2/3} \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{5/3}}-\frac{\sqrt[3]{-1} a^{2/3} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{5/3}}+\frac{a^{2/3} \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{5/3}}-\frac{(-1)^{2/3} a^{2/3} \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{5/3}}+\frac{a^{2/3} \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{5/3}}-\frac{\sqrt[3]{-1} a^{2/3} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{5/3}}-\frac{\cosh (c+d x)}{b d^2}+\frac{x \sinh (c+d x)}{b d}",1,"-1/6*(a*d^2*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1 & ] + a*d^2*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1 & ] + 6*b*(Cosh[c + d*x] - d*x*Sinh[c + d*x]))/(b^2*d^2)","C",1
95,1,198,358,0.2835465,"\int \frac{x^3 \cosh (c+d x)}{a+b x^3} \, dx","Integrate[(x^3*Cosh[c + d*x])/(a + b*x^3),x]","-\frac{a d \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+a d \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]-6 b \sinh (c+d x)}{6 b^2 d}","\frac{\sqrt[3]{-1} \sqrt[3]{a} \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{a} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{4/3}}-\frac{\sqrt[3]{a} \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{a} \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b^{4/3}}-\frac{\sqrt[3]{a} \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{a} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b^{4/3}}+\frac{\sinh (c+d x)}{b d}",1,"-1/6*(a*d*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1^2 & ] + a*d*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1^2 & ] - 6*b*Sinh[c + d*x])/(b^2*d)","C",1
96,1,170,283,0.2404952,"\int \frac{x^2 \cosh (c+d x)}{a+b x^3} \, dx","Integrate[(x^2*Cosh[c + d*x])/(a + b*x^3),x]","\frac{\text{RootSum}\left[\text{$\#$1}^3 b+a\&,-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))\&\right]+\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))\&\right]}{6 b}","\frac{\cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b}+\frac{\cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b}+\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b}-\frac{\sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 b}+\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b}+\frac{\sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 b}",1,"(RootSum[a + b*#1^3 & , Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] & ] + RootSum[a + b*#1^3 & , Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] & ])/(6*b)","C",1
97,1,180,345,0.2233074,"\int \frac{x \cosh (c+d x)}{a+b x^3} \, dx","Integrate[(x*Cosh[c + d*x])/(a + b*x^3),x]","\frac{\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}}\&\right]+\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}}\&\right]}{6 b}","-\frac{(-1)^{2/3} \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{\sqrt[3]{-1} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{(-1)^{2/3} \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 \sqrt[3]{a} b^{2/3}}-\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 \sqrt[3]{a} b^{2/3}}+\frac{\sqrt[3]{-1} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 \sqrt[3]{a} b^{2/3}}",1,"(RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1 & ] + RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1 & ])/(6*b)","C",1
98,1,180,345,0.1362263,"\int \frac{\cosh (c+d x)}{a+b x^3} \, dx","Integrate[Cosh[c + d*x]/(a + b*x^3),x]","\frac{\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]}{6 b}","-\frac{\sqrt[3]{-1} \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\sqrt[3]{-1} \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{2/3} \sqrt[3]{b}}+\frac{(-1)^{2/3} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{2/3} \sqrt[3]{b}}",1,"(RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1^2 & ] + RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1^2 & ])/(6*b)","C",1
99,1,186,303,0.2829639,"\int \frac{\cosh (c+d x)}{x \left(a+b x^3\right)} \, dx","Integrate[Cosh[c + d*x]/(x*(a + b*x^3)),x]","-\frac{\text{RootSum}\left[\text{$\#$1}^3 b+a\&,-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))\&\right]+\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))\&\right]-6 \cosh (c) \text{Chi}(d x)-6 \sinh (c) \text{Shi}(d x)}{6 a}","-\frac{\cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a}-\frac{\cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a}-\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a}+\frac{\sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a}-\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a}-\frac{\sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a}+\frac{\cosh (c) \text{Chi}(d x)}{a}+\frac{\sinh (c) \text{Shi}(d x)}{a}",1,"-1/6*(-6*Cosh[c]*CoshIntegral[d*x] + RootSum[a + b*#1^3 & , Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] & ] + RootSum[a + b*#1^3 & , Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] & ] - 6*Sinh[c]*SinhIntegral[d*x])/a","C",1
100,1,215,381,0.434775,"\int \frac{\cosh (c+d x)}{x^2 \left(a+b x^3\right)} \, dx","Integrate[Cosh[c + d*x]/(x^2*(a + b*x^3)),x]","-\frac{x \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}}\&\right]+x \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}}\&\right]-6 d x \sinh (c) \text{Chi}(d x)-6 d x \cosh (c) \text{Shi}(d x)+6 \cosh (c+d x)}{6 a x}","\frac{(-1)^{2/3} \sqrt[3]{b} \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{4/3}}+\frac{\sqrt[3]{b} \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{b} \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{4/3}}+\frac{\sqrt[3]{b} \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{4/3}}-\frac{\sqrt[3]{-1} \sqrt[3]{b} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{4/3}}+\frac{d \sinh (c) \text{Chi}(d x)}{a}+\frac{d \cosh (c) \text{Shi}(d x)}{a}-\frac{\cosh (c+d x)}{a x}",1,"-1/6*(6*Cosh[c + d*x] + x*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1 & ] + x*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1 & ] - 6*d*x*CoshIntegral[d*x]*Sinh[c] - 6*d*x*Cosh[c]*SinhIntegral[d*x])/(a*x)","C",1
101,1,237,410,0.4073904,"\int \frac{\cosh (c+d x)}{x^3 \left(a+b x^3\right)} \, dx","Integrate[Cosh[c + d*x]/(x^3*(a + b*x^3)),x]","-\frac{x^2 \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+x^2 \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]-3 d^2 x^2 \cosh (c) \text{Chi}(d x)-3 d^2 x^2 \sinh (c) \text{Shi}(d x)+3 d x \sinh (c+d x)+3 \cosh (c+d x)}{6 a x^2}","\frac{\sqrt[3]{-1} b^{2/3} \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{5/3}}-\frac{(-1)^{2/3} b^{2/3} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{5/3}}-\frac{b^{2/3} \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{5/3}}-\frac{\sqrt[3]{-1} b^{2/3} \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^{5/3}}-\frac{b^{2/3} \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{5/3}}-\frac{(-1)^{2/3} b^{2/3} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^{5/3}}+\frac{d^2 \cosh (c) \text{Chi}(d x)}{2 a}+\frac{d^2 \sinh (c) \text{Shi}(d x)}{2 a}-\frac{\cosh (c+d x)}{2 a x^2}-\frac{d \sinh (c+d x)}{2 a x}",1,"-1/6*(3*Cosh[c + d*x] - 3*d^2*x^2*Cosh[c]*CoshIntegral[d*x] + x^2*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1^2 & ] + x^2*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1^2 & ] + 3*d*x*Sinh[c + d*x] - 3*d^2*x^2*Sinh[c]*SinhIntegral[d*x])/(a*x^2)","C",1
102,1,363,718,0.3672408,"\int \frac{x^3 \cosh (c+d x)}{\left(a+b x^3\right)^2} \, dx","Integrate[(x^3*Cosh[c + d*x])/(a + b*x^3)^2,x]","\frac{-\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]-\frac{6 b x \cosh (c+d x)}{a+b x^3}}{18 b^2}","-\frac{\sqrt[3]{-1} \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}+\frac{(-1)^{2/3} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}+\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}+\frac{\sqrt[3]{-1} \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}+\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}+\frac{(-1)^{2/3} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}-\frac{d \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{(-1)^{2/3} d \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 \sqrt[3]{a} b^{5/3}}+\frac{\sqrt[3]{-1} d \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 \sqrt[3]{a} b^{5/3}}+\frac{(-1)^{2/3} d \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{d \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 \sqrt[3]{a} b^{5/3}}+\frac{\sqrt[3]{-1} d \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 \sqrt[3]{a} b^{5/3}}-\frac{x \cosh (c+d x)}{3 b \left(a+b x^3\right)}",1,"((-6*b*x*Cosh[c + d*x])/(a + b*x^3) - RootSum[a + b*#1^3 & , (-(Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]) + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] - Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 - d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 - d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1)/#1^2 & ] + RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 + d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 + d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1)/#1^2 & ])/(18*b^2)","C",1
103,1,203,373,0.1781061,"\int \frac{x^2 \cosh (c+d x)}{\left(a+b x^3\right)^2} \, dx","Integrate[(x^2*Cosh[c + d*x])/(a + b*x^3)^2,x]","\frac{-d \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+d \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]-\frac{6 b \cosh (c+d x)}{a+b x^3}}{18 b^2}","\frac{d \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}-\frac{\sqrt[3]{-1} d \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}+\frac{(-1)^{2/3} d \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}+\frac{\sqrt[3]{-1} d \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{2/3} b^{4/3}}+\frac{d \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}+\frac{(-1)^{2/3} d \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{2/3} b^{4/3}}-\frac{\cosh (c+d x)}{3 b \left(a+b x^3\right)}",1,"((-6*b*Cosh[c + d*x])/(a + b*x^3) - d*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1^2 & ] + d*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1^2 & ])/(18*b^2)","C",1
104,1,387,695,0.2035068,"\int \frac{x \cosh (c+d x)}{\left(a+b x^3\right)^2} \, dx","Integrate[(x*Cosh[c + d*x])/(a + b*x^3)^2,x]","\frac{\left(a+b x^3\right) \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}}\&\right]-\left(a+b x^3\right) \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}}\&\right]+6 b x^2 \cosh (c+d x)}{18 a b \left(a+b x^3\right)}","-\frac{(-1)^{2/3} \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}+\frac{\sqrt[3]{-1} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}-\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}+\frac{(-1)^{2/3} \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}-\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}+\frac{\sqrt[3]{-1} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}-\frac{d \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a b}-\frac{d \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a b}-\frac{d \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a b}+\frac{d \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a b}-\frac{d \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a b}-\frac{d \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a b}-\frac{\cosh (c+d x)}{3 b x \left(a+b x^3\right)}+\frac{\cosh (c+d x)}{3 a b x}",1,"(6*b*x^2*Cosh[c + d*x] + (a + b*x^3)*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 - d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 - d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1)/#1 & ] - (a + b*x^3)*RootSum[a + b*#1^3 & , (-(Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]) - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] - Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 + d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 + d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1)/#1 & ])/(18*a*b*(a + b*x^3))","C",0
105,1,387,739,0.2104392,"\int \frac{\cosh (c+d x)}{\left(a+b x^3\right)^2} \, dx","Integrate[Cosh[c + d*x]/(a + b*x^3)^2,x]","\frac{\left(a+b x^3\right) \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]-\left(a+b x^3\right) \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+6 b x \cosh (c+d x)}{18 a b \left(a+b x^3\right)}","\frac{d \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}+\frac{(-1)^{2/3} d \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}-\frac{\sqrt[3]{-1} d \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}-\frac{(-1)^{2/3} d \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{4/3} b^{2/3}}+\frac{d \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}-\frac{\sqrt[3]{-1} d \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{4/3} b^{2/3}}-\frac{2 \sqrt[3]{-1} \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 (-1)^{2/3} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \sqrt[3]{-1} \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{2 (-1)^{2/3} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{\cosh (c+d x)}{3 a b x^2}-\frac{\cosh (c+d x)}{3 b x^2 \left(a+b x^3\right)}",1,"(6*b*x*Cosh[c + d*x] + (a + b*x^3)*RootSum[a + b*#1^3 & , (2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - 2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - 2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + 2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 - d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 - d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1)/#1^2 & ] - (a + b*x^3)*RootSum[a + b*#1^3 & , (-2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - 2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - 2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] - 2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 + d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 + d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1)/#1^2 & ])/(18*a*b*(a + b*x^3))","C",1
106,1,411,697,0.8261552,"\int \frac{\cosh (c+d x)}{x \left(a+b x^3\right)^2} \, dx","Integrate[Cosh[c + d*x]/(x*(a + b*x^3)^2),x]","\frac{-3 \text{RootSum}\left[\text{$\#$1}^3 b+a\&,-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))\&\right]-3 \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))\&\right]+\frac{a d \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]}{b}-\frac{a d \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]}{b}+\frac{6 a \sinh (c) \sinh (d x)}{a+b x^3}+\frac{6 a \cosh (c) \cosh (d x)}{a+b x^3}+18 \cosh (c) \text{Chi}(d x)+18 \sinh (c) \text{Shi}(d x)}{18 a^2}","-\frac{d \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}+\frac{\sqrt[3]{-1} d \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{(-1)^{2/3} d \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{\sqrt[3]{-1} d \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{d \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{(-1)^{2/3} d \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{9 a^{5/3} \sqrt[3]{b}}-\frac{\cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^2}-\frac{\cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^2}-\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^2}+\frac{\sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{3 a^2}-\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^2}-\frac{\sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{3 a^2}+\frac{\cosh (c) \text{Chi}(d x)}{a^2}+\frac{\sinh (c) \text{Shi}(d x)}{a^2}-\frac{\cosh (c+d x)}{3 b x^3 \left(a+b x^3\right)}+\frac{\cosh (c+d x)}{3 a b x^3}",1,"((6*a*Cosh[c]*Cosh[d*x])/(a + b*x^3) + 18*Cosh[c]*CoshIntegral[d*x] - 3*RootSum[a + b*#1^3 & , Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] & ] - 3*RootSum[a + b*#1^3 & , Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] & ] + (a*d*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1^2 & ])/b - (a*d*RootSum[a + b*#1^3 & , (Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + Sinh[c + d*#1]*SinhIntegral[d*(x - #1)])/#1^2 & ])/b + (6*a*Sinh[c]*Sinh[d*x])/(a + b*x^3) + 18*Sinh[c]*SinhIntegral[d*x])/(18*a^2)","C",1
107,1,397,784,0.6771715,"\int \frac{x^5 \cosh (c+d x)}{\left(a+b x^3\right)^3} \, dx","Integrate[(x^5*Cosh[c + d*x])/(a + b*x^3)^3,x]","\frac{d \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{4 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-4 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-4 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+4 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+d \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{4 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+4 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+4 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+4 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]-\frac{6 b \left(d x \left(a+b x^3\right) \sinh (c+d x)+3 \left(a+2 b x^3\right) \cosh (c+d x)\right)}{\left(a+b x^3\right)^2}}{108 b^3}","\frac{2 d \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{2/3} b^{7/3}}-\frac{2 \sqrt[3]{-1} d \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{2/3} b^{7/3}}+\frac{2 (-1)^{2/3} d \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{2/3} b^{7/3}}+\frac{2 \sqrt[3]{-1} d \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{2/3} b^{7/3}}+\frac{2 d \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{2/3} b^{7/3}}+\frac{2 (-1)^{2/3} d \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{2/3} b^{7/3}}-\frac{(-1)^{2/3} d^2 \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 \sqrt[3]{a} b^{8/3}}+\frac{\sqrt[3]{-1} d^2 \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 \sqrt[3]{a} b^{8/3}}-\frac{d^2 \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 \sqrt[3]{a} b^{8/3}}+\frac{(-1)^{2/3} d^2 \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 \sqrt[3]{a} b^{8/3}}-\frac{d^2 \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 \sqrt[3]{a} b^{8/3}}+\frac{\sqrt[3]{-1} d^2 \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 \sqrt[3]{a} b^{8/3}}-\frac{d x \sinh (c+d x)}{18 b^2 \left(a+b x^3\right)}-\frac{\cosh (c+d x)}{6 b^2 \left(a+b x^3\right)}-\frac{x^3 \cosh (c+d x)}{6 b \left(a+b x^3\right)^2}",1,"(d*RootSum[a + b*#1^3 & , (-4*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + 4*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + 4*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] - 4*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 - d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 - d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1)/#1^2 & ] + d*RootSum[a + b*#1^3 & , (4*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + 4*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + 4*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + 4*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 + d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 + d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1)/#1^2 & ] - (6*b*(3*(a + 2*b*x^3)*Cosh[c + d*x] + d*x*(a + b*x^3)*Sinh[c + d*x]))/(a + b*x^3)^2)/(108*b^3)","C",1
108,1,675,1105,0.5770047,"\int \frac{x^4 \cosh (c+d x)}{\left(a+b x^3\right)^3} \, dx","Integrate[(x^4*Cosh[c + d*x])/(a + b*x^3)^3,x]","\frac{\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-2 \text{$\#$1}^2 b d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+2 \text{$\#$1}^2 b d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+2 \text{$\#$1}^2 b d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \text{$\#$1}^2 b d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-a d^2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+a d^2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+a d^2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-a d^2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \text{$\#$1} b \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+2 \text{$\#$1} b \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+2 \text{$\#$1} b \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \text{$\#$1} b \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]-\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{2 \text{$\#$1}^2 b d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+2 \text{$\#$1}^2 b d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+2 \text{$\#$1}^2 b d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+2 \text{$\#$1}^2 b d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-a d^2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-a d^2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-a d^2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-a d^2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \text{$\#$1} b \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-2 \text{$\#$1} b \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-2 \text{$\#$1} b \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \text{$\#$1} b \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+\frac{6 b \cosh (d x) \left(b x^2 \cosh (c) \left(2 b x^3-a\right)-a d \sinh (c) \left(a+b x^3\right)\right)}{\left(a+b x^3\right)^2}+\frac{6 b \sinh (d x) \left(b x^2 \sinh (c) \left(2 b x^3-a\right)-a d \cosh (c) \left(a+b x^3\right)\right)}{\left(a+b x^3\right)^2}}{108 a b^3}","-\frac{\sqrt[3]{-1} \cosh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d^2}{54 a^{2/3} b^{7/3}}+\frac{(-1)^{2/3} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{2/3} b^{7/3}}+\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{2/3} b^{7/3}}+\frac{\sqrt[3]{-1} \sinh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d^2}{54 a^{2/3} b^{7/3}}+\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{2/3} b^{7/3}}+\frac{(-1)^{2/3} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{2/3} b^{7/3}}-\frac{\text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a b^2}-\frac{\text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sinh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a b^2}-\frac{\text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a b^2}-\frac{\sinh (c+d x) d}{18 b^2 \left(b x^3+a\right)}+\frac{\cosh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{27 a b^2}-\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a b^2}-\frac{\cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a b^2}+\frac{\cosh (c+d x)}{9 a b^2 x}-\frac{\cosh (c+d x)}{9 b^2 x \left(b x^3+a\right)}-\frac{x^2 \cosh (c+d x)}{6 b \left(b x^3+a\right)^2}-\frac{(-1)^{2/3} \cosh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{4/3} b^{5/3}}+\frac{\sqrt[3]{-1} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{4/3} b^{5/3}}-\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{4/3} b^{5/3}}+\frac{(-1)^{2/3} \sinh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{4/3} b^{5/3}}-\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{4/3} b^{5/3}}+\frac{\sqrt[3]{-1} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{4/3} b^{5/3}}",1,"(RootSum[a + b*#1^3 & , (a*d^2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - a*d^2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - a*d^2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + a*d^2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + 2*b*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 - 2*b*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 - 2*b*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + 2*b*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + 2*b*d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1^2 - 2*b*d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1^2 - 2*b*d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2 + 2*b*d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2)/#1^2 & ] - RootSum[a + b*#1^3 & , (-(a*d^2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]) - a*d^2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - a*d^2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] - a*d^2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] - 2*b*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 - 2*b*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 - 2*b*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 - 2*b*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + 2*b*d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1^2 + 2*b*d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1^2 + 2*b*d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2 + 2*b*d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2)/#1^2 & ] + (6*b*Cosh[d*x]*(b*x^2*(-a + 2*b*x^3)*Cosh[c] - a*d*(a + b*x^3)*Sinh[c]))/(a + b*x^3)^2 + (6*b*(-(a*d*(a + b*x^3)*Cosh[c]) + b*x^2*(-a + 2*b*x^3)*Sinh[c])*Sinh[d*x])/(a + b*x^3)^2)/(108*a*b^3)","C",1
109,1,429,776,0.705445,"\int \frac{x^3 \cosh (c+d x)}{\left(a+b x^3\right)^3} \, dx","Integrate[(x^3*Cosh[c + d*x])/(a + b*x^3)^3,x]","-\frac{\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-\text{$\#$1}^2 d^2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1}^2 d^2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1}^2 d^2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\text{$\#$1}^2 d^2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{\text{$\#$1}^2 d^2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1}^2 d^2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1}^2 d^2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1}^2 d^2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]-\frac{6 b x \left(d x \left(a+b x^3\right) \sinh (c+d x)+\left(b x^3-2 a\right) \cosh (c+d x)\right)}{\left(a+b x^3\right)^2}}{108 a b^2}","-\frac{\sqrt[3]{-1} \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}+\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}+\frac{\sqrt[3]{-1} \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}+\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}-\frac{d^2 \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a b^2}-\frac{d^2 \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a b^2}-\frac{d^2 \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a b^2}+\frac{d^2 \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a b^2}-\frac{d^2 \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a b^2}-\frac{d^2 \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a b^2}-\frac{d \sinh (c+d x)}{18 b^2 x \left(a+b x^3\right)}+\frac{\cosh (c+d x)}{18 a b^2 x^2}-\frac{\cosh (c+d x)}{18 b^2 x^2 \left(a+b x^3\right)}+\frac{d \sinh (c+d x)}{18 a b^2 x}-\frac{x \cosh (c+d x)}{6 b \left(a+b x^3\right)^2}",1,"-1/108*(RootSum[a + b*#1^3 & , (-2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + 2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + 2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] - 2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d^2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1^2 - d^2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1^2 - d^2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2 + d^2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2)/#1^2 & ] + RootSum[a + b*#1^3 & , (-2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - 2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - 2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] - 2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d^2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1^2 + d^2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1^2 + d^2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2 + d^2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2)/#1^2 & ] - (6*b*x*((-2*a + b*x^3)*Cosh[c + d*x] + d*x*(a + b*x^3)*Sinh[c + d*x]))/(a + b*x^3)^2)/(a*b^2)","C",1
110,1,423,781,0.457701,"\int \frac{x^2 \cosh (c+d x)}{\left(a+b x^3\right)^3} \, dx","Integrate[(x^2*Cosh[c + d*x])/(a + b*x^3)^3,x]","-\frac{d \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+d \text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+\text{$\#$1} d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]-\frac{6 b \cosh (d x) \left(d x \sinh (c) \left(a+b x^3\right)-3 a \cosh (c)\right)}{\left(a+b x^3\right)^2}-\frac{6 b \sinh (d x) \left(d x \cosh (c) \left(a+b x^3\right)-3 a \sinh (c)\right)}{\left(a+b x^3\right)^2}}{108 a b^2}","\frac{(-1)^{2/3} d^2 \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a^{4/3} b^{5/3}}-\frac{\sqrt[3]{-1} d^2 \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a^{4/3} b^{5/3}}+\frac{d^2 \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a^{4/3} b^{5/3}}+\frac{d \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}-\frac{\sqrt[3]{-1} d \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} d \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}-\frac{(-1)^{2/3} d^2 \sinh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{54 a^{4/3} b^{5/3}}+\frac{d^2 \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a^{4/3} b^{5/3}}-\frac{\sqrt[3]{-1} d^2 \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{54 a^{4/3} b^{5/3}}+\frac{\sqrt[3]{-1} d \cosh \left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}+c\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{5/3} b^{4/3}}+\frac{d \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}+\frac{(-1)^{2/3} d \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{5/3} b^{4/3}}+\frac{d \sinh (c+d x)}{18 a b^2 x^2}-\frac{d \sinh (c+d x)}{18 b^2 x^2 \left(a+b x^3\right)}-\frac{\cosh (c+d x)}{6 b \left(a+b x^3\right)^2}",1,"-1/108*(d*RootSum[a + b*#1^3 & , (2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - 2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - 2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + 2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 - d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 - d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1)/#1^2 & ] + d*RootSum[a + b*#1^3 & , (-2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] - 2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] - 2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] - 2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 + d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 + d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1)/#1^2 & ] - (6*b*Cosh[d*x]*(-3*a*Cosh[c] + d*x*(a + b*x^3)*Sinh[c]))/(a + b*x^3)^2 - (6*b*(d*x*(a + b*x^3)*Cosh[c] - 3*a*Sinh[c])*Sinh[d*x])/(a + b*x^3)^2)/(a*b^2)","C",1
111,1,669,1147,0.5017573,"\int \frac{x \cosh (c+d x)}{\left(a+b x^3\right)^3} \, dx","Integrate[(x*Cosh[c + d*x])/(a + b*x^3)^3,x]","\frac{\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{-4 \text{$\#$1}^2 b d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+4 \text{$\#$1}^2 b d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+4 \text{$\#$1}^2 b d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-4 \text{$\#$1}^2 b d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+a d^2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-a d^2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-a d^2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+a d^2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-4 \text{$\#$1} b \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+4 \text{$\#$1} b \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+4 \text{$\#$1} b \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-4 \text{$\#$1} b \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]-\text{RootSum}\left[\text{$\#$1}^3 b+a\&,\frac{4 \text{$\#$1}^2 b d \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+4 \text{$\#$1}^2 b d \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+4 \text{$\#$1}^2 b d \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+4 \text{$\#$1}^2 b d \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+a d^2 \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+a d^2 \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))+a d^2 \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))+a d^2 \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-4 \text{$\#$1} b \sinh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-4 \text{$\#$1} b \cosh (\text{$\#$1} d+c) \text{Chi}(d (x-\text{$\#$1}))-4 \text{$\#$1} b \sinh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))-4 \text{$\#$1} b \cosh (\text{$\#$1} d+c) \text{Shi}(d (x-\text{$\#$1}))}{\text{$\#$1}^2}\&\right]+\frac{6 b \cosh (d x) \left(a d \sinh (c) \left(a+b x^3\right)+b x^2 \cosh (c) \left(7 a+4 b x^3\right)\right)}{\left(a+b x^3\right)^2}+\frac{6 b \sinh (d x) \left(a d \cosh (c) \left(a+b x^3\right)+b x^2 \sinh (c) \left(7 a+4 b x^3\right)\right)}{\left(a+b x^3\right)^2}}{108 a^2 b^2}","\frac{\sqrt[3]{-1} \cosh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d^2}{54 a^{5/3} b^{4/3}}-\frac{(-1)^{2/3} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}-\frac{\cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}-\frac{\sqrt[3]{-1} \sinh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d^2}{54 a^{5/3} b^{4/3}}-\frac{\sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}-\frac{(-1)^{2/3} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d^2}{54 a^{5/3} b^{4/3}}-\frac{2 \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}-\frac{2 \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) \sinh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}-\frac{2 \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}-\frac{\sinh (c+d x) d}{18 b^2 x^3 \left(b x^3+a\right)}+\frac{\sinh (c+d x) d}{18 a b^2 x^3}+\frac{2 \cosh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right) d}{27 a^2 b}-\frac{2 \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}-\frac{2 \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) d}{27 a^2 b}+\frac{2 \cosh (c+d x)}{9 a^2 b x}+\frac{\cosh (c+d x)}{18 b^2 x^4 \left(b x^3+a\right)}-\frac{\cosh (c+d x)}{6 b x \left(b x^3+a\right)^2}-\frac{\cosh (c+d x)}{18 a b^2 x^4}-\frac{2 (-1)^{2/3} \cosh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{7/3} b^{2/3}}+\frac{2 \sqrt[3]{-1} \cosh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(-x d-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}-\frac{2 \cosh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Chi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}+\frac{2 (-1)^{2/3} \sinh \left(c+\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(\frac{\sqrt[3]{-1} \sqrt[3]{a} d}{\sqrt[3]{b}}-d x\right)}{27 a^{7/3} b^{2/3}}-\frac{2 \sinh \left(c-\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{\sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}+\frac{2 \sqrt[3]{-1} \sinh \left(c-\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right) \text{Shi}\left(x d+\frac{(-1)^{2/3} \sqrt[3]{a} d}{\sqrt[3]{b}}\right)}{27 a^{7/3} b^{2/3}}",1,"(RootSum[a + b*#1^3 & , (-(a*d^2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]) + a*d^2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + a*d^2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] - a*d^2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] + 4*b*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 - 4*b*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 - 4*b*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + 4*b*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + 4*b*d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1^2 - 4*b*d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1^2 - 4*b*d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2 + 4*b*d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2)/#1^2 & ] - RootSum[a + b*#1^3 & , (a*d^2*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)] + a*d^2*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1] + a*d^2*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)] + a*d^2*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)] - 4*b*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1 - 4*b*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1 - 4*b*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 - 4*b*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1 + 4*b*d*Cosh[c + d*#1]*CoshIntegral[d*(x - #1)]*#1^2 + 4*b*d*CoshIntegral[d*(x - #1)]*Sinh[c + d*#1]*#1^2 + 4*b*d*Cosh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2 + 4*b*d*Sinh[c + d*#1]*SinhIntegral[d*(x - #1)]*#1^2)/#1^2 & ] + (6*b*Cosh[d*x]*(b*x^2*(7*a + 4*b*x^3)*Cosh[c] + a*d*(a + b*x^3)*Sinh[c]))/(a + b*x^3)^2 + (6*b*(a*d*(a + b*x^3)*Cosh[c] + b*x^2*(7*a + 4*b*x^3)*Sinh[c])*Sinh[d*x])/(a + b*x^3)^2)/(108*a^2*b^2)","C",1