1,1,31,34,0.0341997,"\int x^3 \sinh \left(a+b x^2\right) \, dx","Integrate[x^3*Sinh[a + b*x^2],x]","\frac{b x^2 \cosh \left(a+b x^2\right)-\sinh \left(a+b x^2\right)}{2 b^2}","\frac{x^2 \cosh \left(a+b x^2\right)}{2 b}-\frac{\sinh \left(a+b x^2\right)}{2 b^2}",1,"(b*x^2*Cosh[a + b*x^2] - Sinh[a + b*x^2])/(2*b^2)","A",1
2,1,67,69,0.0683563,"\int x^2 \sinh \left(a+b x^2\right) \, dx","Integrate[x^2*Sinh[a + b*x^2],x]","\frac{\sqrt{\pi } (\sinh (a)-\cosh (a)) \text{erf}\left(\sqrt{b} x\right)-\sqrt{\pi } (\sinh (a)+\cosh (a)) \text{erfi}\left(\sqrt{b} x\right)+4 \sqrt{b} x \cosh \left(a+b x^2\right)}{8 b^{3/2}}","-\frac{\sqrt{\pi } e^{-a} \text{erf}\left(\sqrt{b} x\right)}{8 b^{3/2}}-\frac{\sqrt{\pi } e^a \text{erfi}\left(\sqrt{b} x\right)}{8 b^{3/2}}+\frac{x \cosh \left(a+b x^2\right)}{2 b}",1,"(4*Sqrt[b]*x*Cosh[a + b*x^2] + Sqrt[Pi]*Erf[Sqrt[b]*x]*(-Cosh[a] + Sinh[a]) - Sqrt[Pi]*Erfi[Sqrt[b]*x]*(Cosh[a] + Sinh[a]))/(8*b^(3/2))","A",1
3,1,31,15,0.0098335,"\int x \sinh \left(a+b x^2\right) \, dx","Integrate[x*Sinh[a + b*x^2],x]","\frac{\sinh (a) \sinh \left(b x^2\right)}{2 b}+\frac{\cosh (a) \cosh \left(b x^2\right)}{2 b}","\frac{\cosh \left(a+b x^2\right)}{2 b}",1,"(Cosh[a]*Cosh[b*x^2])/(2*b) + (Sinh[a]*Sinh[b*x^2])/(2*b)","B",1
4,1,45,53,0.0363138,"\int \sinh \left(a+b x^2\right) \, dx","Integrate[Sinh[a + b*x^2],x]","\frac{\sqrt{\pi } \left((\sinh (a)-\cosh (a)) \text{erf}\left(\sqrt{b} x\right)+(\sinh (a)+\cosh (a)) \text{erfi}\left(\sqrt{b} x\right)\right)}{4 \sqrt{b}}","\frac{\sqrt{\pi } e^a \text{erfi}\left(\sqrt{b} x\right)}{4 \sqrt{b}}-\frac{\sqrt{\pi } e^{-a} \text{erf}\left(\sqrt{b} x\right)}{4 \sqrt{b}}",1,"(Sqrt[Pi]*(Erf[Sqrt[b]*x]*(-Cosh[a] + Sinh[a]) + Erfi[Sqrt[b]*x]*(Cosh[a] + Sinh[a])))/(4*Sqrt[b])","A",1
5,1,23,25,0.0144528,"\int \frac{\sinh \left(a+b x^2\right)}{x} \, dx","Integrate[Sinh[a + b*x^2]/x,x]","\frac{1}{2} \left(\sinh (a) \text{Chi}\left(b x^2\right)+\cosh (a) \text{Shi}\left(b x^2\right)\right)","\frac{1}{2} \sinh (a) \text{Chi}\left(b x^2\right)+\frac{1}{2} \cosh (a) \text{Shi}\left(b x^2\right)",1,"(CoshIntegral[b*x^2]*Sinh[a] + Cosh[a]*SinhIntegral[b*x^2])/2","A",1
6,1,70,66,0.0616916,"\int \frac{\sinh \left(a+b x^2\right)}{x^2} \, dx","Integrate[Sinh[a + b*x^2]/x^2,x]","\frac{\sqrt{\pi } \sqrt{b} x (\cosh (a)-\sinh (a)) \text{erf}\left(\sqrt{b} x\right)+\sqrt{\pi } \sqrt{b} x (\sinh (a)+\cosh (a)) \text{erfi}\left(\sqrt{b} x\right)-2 \sinh \left(a+b x^2\right)}{2 x}","\frac{1}{2} \sqrt{\pi } e^{-a} \sqrt{b} \text{erf}\left(\sqrt{b} x\right)+\frac{1}{2} \sqrt{\pi } e^a \sqrt{b} \text{erfi}\left(\sqrt{b} x\right)-\frac{\sinh \left(a+b x^2\right)}{x}",1,"(Sqrt[b]*Sqrt[Pi]*x*Erf[Sqrt[b]*x]*(Cosh[a] - Sinh[a]) + Sqrt[b]*Sqrt[Pi]*x*Erfi[Sqrt[b]*x]*(Cosh[a] + Sinh[a]) - 2*Sinh[a + b*x^2])/(2*x)","A",1
7,1,38,42,0.0419755,"\int \frac{\sinh \left(a+b x^2\right)}{x^3} \, dx","Integrate[Sinh[a + b*x^2]/x^3,x]","\frac{1}{2} \left(b \cosh (a) \text{Chi}\left(b x^2\right)+b \sinh (a) \text{Shi}\left(b x^2\right)-\frac{\sinh \left(a+b x^2\right)}{x^2}\right)","\frac{1}{2} b \cosh (a) \text{Chi}\left(b x^2\right)+\frac{1}{2} b \sinh (a) \text{Shi}\left(b x^2\right)-\frac{\sinh \left(a+b x^2\right)}{2 x^2}",1,"(b*Cosh[a]*CoshIntegral[b*x^2] - Sinh[a + b*x^2]/x^2 + b*Sinh[a]*SinhIntegral[b*x^2])/2","A",1
8,1,42,51,0.1042608,"\int x^3 \sinh ^2\left(a+b x^2\right) \, dx","Integrate[x^3*Sinh[a + b*x^2]^2,x]","-\frac{2 b x^2 \left(b x^2-\sinh \left(2 \left(a+b x^2\right)\right)\right)+\cosh \left(2 \left(a+b x^2\right)\right)}{16 b^2}","-\frac{\sinh ^2\left(a+b x^2\right)}{8 b^2}+\frac{x^2 \sinh \left(a+b x^2\right) \cosh \left(a+b x^2\right)}{4 b}-\frac{x^4}{8}",1,"-1/16*(Cosh[2*(a + b*x^2)] + 2*b*x^2*(b*x^2 - Sinh[2*(a + b*x^2)]))/b^2","A",1
9,1,101,99,0.2161269,"\int x^2 \sinh ^2\left(a+b x^2\right) \, dx","Integrate[x^2*Sinh[a + b*x^2]^2,x]","\frac{3 \sqrt{2 \pi } (\cosh (2 a)-\sinh (2 a)) \text{erf}\left(\sqrt{2} \sqrt{b} x\right)-3 \sqrt{2 \pi } (\sinh (2 a)+\cosh (2 a)) \text{erfi}\left(\sqrt{2} \sqrt{b} x\right)+8 \sqrt{b} x \left(3 \sinh \left(2 \left(a+b x^2\right)\right)-4 b x^2\right)}{192 b^{3/2}}","\frac{\sqrt{\frac{\pi }{2}} e^{-2 a} \text{erf}\left(\sqrt{2} \sqrt{b} x\right)}{32 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} e^{2 a} \text{erfi}\left(\sqrt{2} \sqrt{b} x\right)}{32 b^{3/2}}+\frac{x \sinh \left(2 a+2 b x^2\right)}{8 b}-\frac{x^3}{6}",1,"(3*Sqrt[2*Pi]*Erf[Sqrt[2]*Sqrt[b]*x]*(Cosh[2*a] - Sinh[2*a]) - 3*Sqrt[2*Pi]*Erfi[Sqrt[2]*Sqrt[b]*x]*(Cosh[2*a] + Sinh[2*a]) + 8*Sqrt[b]*x*(-4*b*x^2 + 3*Sinh[2*(a + b*x^2)]))/(192*b^(3/2))","A",1
10,1,27,31,0.0227378,"\int x \sinh ^2\left(a+b x^2\right) \, dx","Integrate[x*Sinh[a + b*x^2]^2,x]","\frac{\sinh \left(2 \left(a+b x^2\right)\right)-2 \left(a+b x^2\right)}{8 b}","\frac{\sinh \left(a+b x^2\right) \cosh \left(a+b x^2\right)}{4 b}-\frac{x^2}{4}",1,"(-2*(a + b*x^2) + Sinh[2*(a + b*x^2)])/(8*b)","A",1
11,1,86,78,0.069753,"\int \sinh ^2\left(a+b x^2\right) \, dx","Integrate[Sinh[a + b*x^2]^2,x]","\frac{\sqrt{\pi } (\cosh (2 a)-\sinh (2 a)) \text{erf}\left(\sqrt{2} \sqrt{b} x\right)+\sqrt{\pi } (\sinh (2 a)+\cosh (2 a)) \text{erfi}\left(\sqrt{2} \sqrt{b} x\right)-4 \sqrt{2} \sqrt{b} x}{8 \sqrt{2} \sqrt{b}}","\frac{\sqrt{\frac{\pi }{2}} e^{-2 a} \text{erf}\left(\sqrt{2} \sqrt{b} x\right)}{8 \sqrt{b}}+\frac{\sqrt{\frac{\pi }{2}} e^{2 a} \text{erfi}\left(\sqrt{2} \sqrt{b} x\right)}{8 \sqrt{b}}-\frac{x}{2}",1,"(-4*Sqrt[2]*Sqrt[b]*x + Sqrt[Pi]*Erf[Sqrt[2]*Sqrt[b]*x]*(Cosh[2*a] - Sinh[2*a]) + Sqrt[Pi]*Erfi[Sqrt[2]*Sqrt[b]*x]*(Cosh[2*a] + Sinh[2*a]))/(8*Sqrt[2]*Sqrt[b])","A",1
12,1,33,37,0.0199826,"\int \frac{\sinh ^2\left(a+b x^2\right)}{x} \, dx","Integrate[Sinh[a + b*x^2]^2/x,x]","\frac{1}{4} \left(\cosh (2 a) \text{Chi}\left(2 b x^2\right)+\sinh (2 a) \text{Shi}\left(2 b x^2\right)-2 \log (x)\right)","\frac{1}{4} \cosh (2 a) \text{Chi}\left(2 b x^2\right)+\frac{1}{4} \sinh (2 a) \text{Shi}\left(2 b x^2\right)-\frac{\log (x)}{2}",1,"(Cosh[2*a]*CoshIntegral[2*b*x^2] - 2*Log[x] + Sinh[2*a]*SinhIntegral[2*b*x^2])/4","A",1
13,1,94,88,0.2225252,"\int \frac{\sinh ^2\left(a+b x^2\right)}{x^2} \, dx","Integrate[Sinh[a + b*x^2]^2/x^2,x]","\frac{\sqrt{2 \pi } \sqrt{b} x (\sinh (2 a)-\cosh (2 a)) \text{erf}\left(\sqrt{2} \sqrt{b} x\right)+\sqrt{2 \pi } \sqrt{b} x (\sinh (2 a)+\cosh (2 a)) \text{erfi}\left(\sqrt{2} \sqrt{b} x\right)-4 \sinh ^2\left(a+b x^2\right)}{4 x}","-\frac{1}{2} \sqrt{\frac{\pi }{2}} e^{-2 a} \sqrt{b} \text{erf}\left(\sqrt{2} \sqrt{b} x\right)+\frac{1}{2} \sqrt{\frac{\pi }{2}} e^{2 a} \sqrt{b} \text{erfi}\left(\sqrt{2} \sqrt{b} x\right)-\frac{\sinh ^2\left(a+b x^2\right)}{x}",1,"(Sqrt[b]*Sqrt[2*Pi]*x*Erf[Sqrt[2]*Sqrt[b]*x]*(-Cosh[2*a] + Sinh[2*a]) + Sqrt[b]*Sqrt[2*Pi]*x*Erfi[Sqrt[2]*Sqrt[b]*x]*(Cosh[2*a] + Sinh[2*a]) - 4*Sinh[a + b*x^2]^2)/(4*x)","A",1
14,1,46,57,0.0903026,"\int \frac{\sinh ^2\left(a+b x^2\right)}{x^3} \, dx","Integrate[Sinh[a + b*x^2]^2/x^3,x]","\frac{1}{2} \left(b \sinh (2 a) \text{Chi}\left(2 b x^2\right)+b \cosh (2 a) \text{Shi}\left(2 b x^2\right)-\frac{\sinh ^2\left(a+b x^2\right)}{x^2}\right)","\frac{1}{2} b \sinh (2 a) \text{Chi}\left(2 b x^2\right)+\frac{1}{2} b \cosh (2 a) \text{Shi}\left(2 b x^2\right)-\frac{\cosh \left(2 \left(a+b x^2\right)\right)}{4 x^2}+\frac{1}{4 x^2}",1,"(b*CoshIntegral[2*b*x^2]*Sinh[2*a] - Sinh[a + b*x^2]^2/x^2 + b*Cosh[2*a]*SinhIntegral[2*b*x^2])/2","A",1
15,1,58,79,0.1269839,"\int x^3 \sinh ^3\left(a+b x^2\right) \, dx","Integrate[x^3*Sinh[a + b*x^2]^3,x]","-\frac{-27 \sinh \left(a+b x^2\right)+\sinh \left(3 \left(a+b x^2\right)\right)+27 b x^2 \cosh \left(a+b x^2\right)-3 b x^2 \cosh \left(3 \left(a+b x^2\right)\right)}{72 b^2}","-\frac{\sinh ^3\left(a+b x^2\right)}{18 b^2}+\frac{\sinh \left(a+b x^2\right)}{3 b^2}-\frac{x^2 \cosh \left(a+b x^2\right)}{3 b}+\frac{x^2 \sinh ^2\left(a+b x^2\right) \cosh \left(a+b x^2\right)}{6 b}",1,"-1/72*(27*b*x^2*Cosh[a + b*x^2] - 3*b*x^2*Cosh[3*(a + b*x^2)] - 27*Sinh[a + b*x^2] + Sinh[3*(a + b*x^2)])/b^2","A",1
16,1,184,160,0.3017677,"\int x^2 \sinh ^3\left(a+b x^2\right) \, dx","Integrate[x^2*Sinh[a + b*x^2]^3,x]","\frac{27 \sqrt{\pi } (\cosh (a)-\sinh (a)) \text{erf}\left(\sqrt{b} x\right)+\sqrt{3 \pi } (\sinh (3 a)-\cosh (3 a)) \text{erf}\left(\sqrt{3} \sqrt{b} x\right)+27 \sqrt{\pi } \sinh (a) \text{erfi}\left(\sqrt{b} x\right)-\sqrt{3 \pi } \sinh (3 a) \text{erfi}\left(\sqrt{3} \sqrt{b} x\right)+27 \sqrt{\pi } \cosh (a) \text{erfi}\left(\sqrt{b} x\right)-\sqrt{3 \pi } \cosh (3 a) \text{erfi}\left(\sqrt{3} \sqrt{b} x\right)-108 \sqrt{b} x \cosh \left(a+b x^2\right)+12 \sqrt{b} x \cosh \left(3 \left(a+b x^2\right)\right)}{288 b^{3/2}}","\frac{3 \sqrt{\pi } e^{-a} \text{erf}\left(\sqrt{b} x\right)}{32 b^{3/2}}-\frac{\sqrt{\frac{\pi }{3}} e^{-3 a} \text{erf}\left(\sqrt{3} \sqrt{b} x\right)}{96 b^{3/2}}+\frac{3 \sqrt{\pi } e^a \text{erfi}\left(\sqrt{b} x\right)}{32 b^{3/2}}-\frac{\sqrt{\frac{\pi }{3}} e^{3 a} \text{erfi}\left(\sqrt{3} \sqrt{b} x\right)}{96 b^{3/2}}-\frac{3 x \cosh \left(a+b x^2\right)}{8 b}+\frac{x \cosh \left(3 a+3 b x^2\right)}{24 b}",1,"(-108*Sqrt[b]*x*Cosh[a + b*x^2] + 12*Sqrt[b]*x*Cosh[3*(a + b*x^2)] + 27*Sqrt[Pi]*Cosh[a]*Erfi[Sqrt[b]*x] - Sqrt[3*Pi]*Cosh[3*a]*Erfi[Sqrt[3]*Sqrt[b]*x] + 27*Sqrt[Pi]*Erf[Sqrt[b]*x]*(Cosh[a] - Sinh[a]) + 27*Sqrt[Pi]*Erfi[Sqrt[b]*x]*Sinh[a] - Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[b]*x]*Sinh[3*a] + Sqrt[3*Pi]*Erf[Sqrt[3]*Sqrt[b]*x]*(-Cosh[3*a] + Sinh[3*a]))/(288*b^(3/2))","A",1
17,1,33,33,0.0125744,"\int x \sinh ^3\left(a+b x^2\right) \, dx","Integrate[x*Sinh[a + b*x^2]^3,x]","\frac{\cosh \left(3 \left(a+b x^2\right)\right)}{24 b}-\frac{3 \cosh \left(a+b x^2\right)}{8 b}","\frac{\cosh ^3\left(a+b x^2\right)}{6 b}-\frac{\cosh \left(a+b x^2\right)}{2 b}",1,"(-3*Cosh[a + b*x^2])/(8*b) + Cosh[3*(a + b*x^2)]/(24*b)","A",1
18,1,136,125,0.1290552,"\int \sinh ^3\left(a+b x^2\right) \, dx","Integrate[Sinh[a + b*x^2]^3,x]","\frac{\sqrt{\frac{\pi }{3}} \left(3 \sqrt{3} (\cosh (a)-\sinh (a)) \text{erf}\left(\sqrt{b} x\right)+(\sinh (3 a)-\cosh (3 a)) \text{erf}\left(\sqrt{3} \sqrt{b} x\right)-3 \sqrt{3} \sinh (a) \text{erfi}\left(\sqrt{b} x\right)+\sinh (3 a) \text{erfi}\left(\sqrt{3} \sqrt{b} x\right)-3 \sqrt{3} \cosh (a) \text{erfi}\left(\sqrt{b} x\right)+\cosh (3 a) \text{erfi}\left(\sqrt{3} \sqrt{b} x\right)\right)}{16 \sqrt{b}}","\frac{3 \sqrt{\pi } e^{-a} \text{erf}\left(\sqrt{b} x\right)}{16 \sqrt{b}}-\frac{\sqrt{\frac{\pi }{3}} e^{-3 a} \text{erf}\left(\sqrt{3} \sqrt{b} x\right)}{16 \sqrt{b}}-\frac{3 \sqrt{\pi } e^a \text{erfi}\left(\sqrt{b} x\right)}{16 \sqrt{b}}+\frac{\sqrt{\frac{\pi }{3}} e^{3 a} \text{erfi}\left(\sqrt{3} \sqrt{b} x\right)}{16 \sqrt{b}}",1,"(Sqrt[Pi/3]*(-3*Sqrt[3]*Cosh[a]*Erfi[Sqrt[b]*x] + Cosh[3*a]*Erfi[Sqrt[3]*Sqrt[b]*x] + 3*Sqrt[3]*Erf[Sqrt[b]*x]*(Cosh[a] - Sinh[a]) - 3*Sqrt[3]*Erfi[Sqrt[b]*x]*Sinh[a] + Erfi[Sqrt[3]*Sqrt[b]*x]*Sinh[3*a] + Erf[Sqrt[3]*Sqrt[b]*x]*(-Cosh[3*a] + Sinh[3*a])))/(16*Sqrt[b])","A",1
19,1,49,55,0.0336525,"\int \frac{\sinh ^3\left(a+b x^2\right)}{x} \, dx","Integrate[Sinh[a + b*x^2]^3/x,x]","\frac{1}{8} \left(-3 \sinh (a) \text{Chi}\left(b x^2\right)+\sinh (3 a) \text{Chi}\left(3 b x^2\right)-3 \cosh (a) \text{Shi}\left(b x^2\right)+\cosh (3 a) \text{Shi}\left(3 b x^2\right)\right)","-\frac{3}{8} \sinh (a) \text{Chi}\left(b x^2\right)+\frac{1}{8} \sinh (3 a) \text{Chi}\left(3 b x^2\right)-\frac{3}{8} \cosh (a) \text{Shi}\left(b x^2\right)+\frac{1}{8} \cosh (3 a) \text{Shi}\left(3 b x^2\right)",1,"(-3*CoshIntegral[b*x^2]*Sinh[a] + CoshIntegral[3*b*x^2]*Sinh[3*a] - 3*Cosh[a]*SinhIntegral[b*x^2] + Cosh[3*a]*SinhIntegral[3*b*x^2])/8","A",1
20,1,204,136,0.3149235,"\int \frac{\sinh ^3\left(a+b x^2\right)}{x^2} \, dx","Integrate[Sinh[a + b*x^2]^3/x^2,x]","\frac{3 \sqrt{\pi } \sqrt{b} x (\sinh (a)-\cosh (a)) \text{erf}\left(\sqrt{b} x\right)+\sqrt{3 \pi } \sqrt{b} x (\cosh (3 a)-\sinh (3 a)) \text{erf}\left(\sqrt{3} \sqrt{b} x\right)-3 \sqrt{\pi } \sqrt{b} x \sinh (a) \text{erfi}\left(\sqrt{b} x\right)+\sqrt{3 \pi } \sqrt{b} x \sinh (3 a) \text{erfi}\left(\sqrt{3} \sqrt{b} x\right)-3 \sqrt{\pi } \sqrt{b} x \cosh (a) \text{erfi}\left(\sqrt{b} x\right)+\sqrt{3 \pi } \sqrt{b} x \cosh (3 a) \text{erfi}\left(\sqrt{3} \sqrt{b} x\right)+6 \sinh \left(a+b x^2\right)-2 \sinh \left(3 \left(a+b x^2\right)\right)}{8 x}","-\frac{3}{8} \sqrt{\pi } e^{-a} \sqrt{b} \text{erf}\left(\sqrt{b} x\right)+\frac{1}{8} \sqrt{3 \pi } e^{-3 a} \sqrt{b} \text{erf}\left(\sqrt{3} \sqrt{b} x\right)-\frac{3}{8} \sqrt{\pi } e^a \sqrt{b} \text{erfi}\left(\sqrt{b} x\right)+\frac{1}{8} \sqrt{3 \pi } e^{3 a} \sqrt{b} \text{erfi}\left(\sqrt{3} \sqrt{b} x\right)-\frac{\sinh ^3\left(a+b x^2\right)}{x}",1,"(-3*Sqrt[b]*Sqrt[Pi]*x*Cosh[a]*Erfi[Sqrt[b]*x] + Sqrt[b]*Sqrt[3*Pi]*x*Cosh[3*a]*Erfi[Sqrt[3]*Sqrt[b]*x] - 3*Sqrt[b]*Sqrt[Pi]*x*Erfi[Sqrt[b]*x]*Sinh[a] + 3*Sqrt[b]*Sqrt[Pi]*x*Erf[Sqrt[b]*x]*(-Cosh[a] + Sinh[a]) + Sqrt[b]*Sqrt[3*Pi]*x*Erf[Sqrt[3]*Sqrt[b]*x]*(Cosh[3*a] - Sinh[3*a]) + Sqrt[b]*Sqrt[3*Pi]*x*Erfi[Sqrt[3]*Sqrt[b]*x]*Sinh[3*a] + 6*Sinh[a + b*x^2] - 2*Sinh[3*(a + b*x^2)])/(8*x)","A",1
21,1,90,91,0.1181405,"\int \frac{\sinh ^3\left(a+b x^2\right)}{x^3} \, dx","Integrate[Sinh[a + b*x^2]^3/x^3,x]","-\frac{3 b x^2 \cosh (a) \text{Chi}\left(b x^2\right)-3 b x^2 \cosh (3 a) \text{Chi}\left(3 b x^2\right)+3 b x^2 \sinh (a) \text{Shi}\left(b x^2\right)-3 b x^2 \sinh (3 a) \text{Shi}\left(3 b x^2\right)-3 \sinh \left(a+b x^2\right)+\sinh \left(3 \left(a+b x^2\right)\right)}{8 x^2}","-\frac{3}{8} b \cosh (a) \text{Chi}\left(b x^2\right)+\frac{3}{8} b \cosh (3 a) \text{Chi}\left(3 b x^2\right)-\frac{3}{8} b \sinh (a) \text{Shi}\left(b x^2\right)+\frac{3}{8} b \sinh (3 a) \text{Shi}\left(3 b x^2\right)+\frac{3 \sinh \left(a+b x^2\right)}{8 x^2}-\frac{\sinh \left(3 \left(a+b x^2\right)\right)}{8 x^2}",1,"-1/8*(3*b*x^2*Cosh[a]*CoshIntegral[b*x^2] - 3*b*x^2*Cosh[3*a]*CoshIntegral[3*b*x^2] - 3*Sinh[a + b*x^2] + Sinh[3*(a + b*x^2)] + 3*b*x^2*Sinh[a]*SinhIntegral[b*x^2] - 3*b*x^2*Sinh[3*a]*SinhIntegral[3*b*x^2])/x^2","A",1
22,1,67,67,0.0247593,"\int x \sinh ^7\left(a+b x^2\right) \, dx","Integrate[x*Sinh[a + b*x^2]^7,x]","-\frac{35 \cosh \left(a+b x^2\right)}{128 b}+\frac{7 \cosh \left(3 \left(a+b x^2\right)\right)}{128 b}-\frac{7 \cosh \left(5 \left(a+b x^2\right)\right)}{640 b}+\frac{\cosh \left(7 \left(a+b x^2\right)\right)}{896 b}","\frac{\cosh ^7\left(a+b x^2\right)}{14 b}-\frac{3 \cosh ^5\left(a+b x^2\right)}{10 b}+\frac{\cosh ^3\left(a+b x^2\right)}{2 b}-\frac{\cosh \left(a+b x^2\right)}{2 b}",1,"(-35*Cosh[a + b*x^2])/(128*b) + (7*Cosh[3*(a + b*x^2)])/(128*b) - (7*Cosh[5*(a + b*x^2)])/(640*b) + Cosh[7*(a + b*x^2)]/(896*b)","A",1
23,0,0,19,2.505825,"\int (e x)^m \sinh ^p\left(a+b x^2\right) \, dx","Integrate[(e*x)^m*Sinh[a + b*x^2]^p,x]","\int (e x)^m \sinh ^p\left(a+b x^2\right) \, dx","\text{Int}\left((e x)^m \sinh ^p\left(a+b x^2\right),x\right)",0,"Integrate[(e*x)^m*Sinh[a + b*x^2]^p, x]","A",-1
24,1,735,214,12.5472489,"\int (e x)^m \sinh ^3\left(a+b x^2\right) \, dx","Integrate[(e*x)^m*Sinh[a + b*x^2]^3,x]","\frac{1}{16} 3^{\frac{1}{2}-\frac{m}{2}} x \sinh (a) \cosh ^2(a) \left(-b^2 x^4\right)^{\frac{1}{2} (-m-1)} (e x)^m \left(\left(-b x^2\right)^{\frac{m+1}{2}} \left(3^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},b x^2\right)-\Gamma \left(\frac{m+1}{2},3 b x^2\right)\right)-\left(b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-3 b x^2\right)+3^{\frac{m+1}{2}} \left(b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-b x^2\right)\right)-\frac{1}{16} 3^{\frac{1}{2}-\frac{m}{2}} x \sinh ^2(a) \cosh (a) \left(-b^2 x^4\right)^{\frac{1}{2} (-m-1)} (e x)^m \left(-\left(\left(-b x^2\right)^{\frac{m+1}{2}} \left(3^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},b x^2\right)+\Gamma \left(\frac{m+1}{2},3 b x^2\right)\right)\right)+\left(b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-3 b x^2\right)+3^{\frac{m+1}{2}} \left(b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-b x^2\right)\right)+\cosh ^3(a) x^{-m} (e x)^m \left(\frac{1}{8} \left(\frac{1}{2} 3^{\frac{1}{2} (-m-1)} x^{m+1} \left(b x^2\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},3 b x^2\right)-\frac{1}{2} 3^{\frac{1}{2} (-m-1)} x^{m+1} \left(-b x^2\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},-3 b x^2\right)\right)-\frac{3}{8} \left(\frac{1}{2} x^{m+1} \left(b x^2\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},b x^2\right)-\frac{1}{2} x^{m+1} \left(-b x^2\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},-b x^2\right)\right)\right)+\sinh ^3(a) x^{-m} (e x)^m \left(\frac{3}{8} \left(-\frac{1}{2} x^{m+1} \left(-b x^2\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},-b x^2\right)-\frac{1}{2} x^{m+1} \left(b x^2\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},b x^2\right)\right)+\frac{1}{8} \left(-\frac{1}{2} 3^{\frac{1}{2} (-m-1)} x^{m+1} \left(-b x^2\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},-3 b x^2\right)-\frac{1}{2} 3^{\frac{1}{2} (-m-1)} x^{m+1} \left(b x^2\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},3 b x^2\right)\right)\right)","-\frac{e^{3 a} 3^{-\frac{m}{2}-\frac{1}{2}} \left(-b x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},-3 b x^2\right)}{16 e}+\frac{3 e^a \left(-b x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},-b x^2\right)}{16 e}-\frac{3 e^{-a} \left(b x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},b x^2\right)}{16 e}+\frac{e^{-3 a} 3^{-\frac{m}{2}-\frac{1}{2}} \left(b x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},3 b x^2\right)}{16 e}",1,"((e*x)^m*Cosh[a]^3*((-3*(-1/2*(x^(1 + m)*(-(b*x^2))^((-1 - m)/2)*Gamma[(1 + m)/2, -(b*x^2)]) + (x^(1 + m)*(b*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, b*x^2])/2))/8 + (-1/2*(3^((-1 - m)/2)*x^(1 + m)*(-(b*x^2))^((-1 - m)/2)*Gamma[(1 + m)/2, -3*b*x^2]) + (3^((-1 - m)/2)*x^(1 + m)*(b*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, 3*b*x^2])/2)/8))/x^m + (3^(1/2 - m/2)*x*(e*x)^m*(-(b^2*x^4))^((-1 - m)/2)*Cosh[a]^2*(-((b*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, -3*b*x^2]) + 3^((1 + m)/2)*(b*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, -(b*x^2)] + (-(b*x^2))^((1 + m)/2)*(3^((1 + m)/2)*Gamma[(1 + m)/2, b*x^2] - Gamma[(1 + m)/2, 3*b*x^2]))*Sinh[a])/16 - (3^(1/2 - m/2)*x*(e*x)^m*(-(b^2*x^4))^((-1 - m)/2)*Cosh[a]*((b*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, -3*b*x^2] + 3^((1 + m)/2)*(b*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, -(b*x^2)] - (-(b*x^2))^((1 + m)/2)*(3^((1 + m)/2)*Gamma[(1 + m)/2, b*x^2] + Gamma[(1 + m)/2, 3*b*x^2]))*Sinh[a]^2)/16 + ((e*x)^m*((3*(-1/2*(x^(1 + m)*(-(b*x^2))^((-1 - m)/2)*Gamma[(1 + m)/2, -(b*x^2)]) - (x^(1 + m)*(b*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, b*x^2])/2))/8 + (-1/2*(3^((-1 - m)/2)*x^(1 + m)*(-(b*x^2))^((-1 - m)/2)*Gamma[(1 + m)/2, -3*b*x^2]) - (3^((-1 - m)/2)*x^(1 + m)*(b*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, 3*b*x^2])/2)/8)*Sinh[a]^3)/x^m","B",1
25,1,152,135,0.5791786,"\int (e x)^m \sinh ^2\left(a+b x^2\right) \, dx","Integrate[(e*x)^m*Sinh[a + b*x^2]^2,x]","-\frac{2^{\frac{1}{2} (-m-7)} x \left(-b^2 x^4\right)^{\frac{1}{2} (-m-1)} (e x)^m \left((m+1) (\cosh (2 a)-\sinh (2 a)) \left(-b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},2 b x^2\right)+(m+1) (\sinh (2 a)+\cosh (2 a)) \left(b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-2 b x^2\right)+2^{\frac{m+5}{2}} \left(-b^2 x^4\right)^{\frac{m+1}{2}}\right)}{m+1}","-\frac{e^{2 a} 2^{-\frac{m}{2}-\frac{7}{2}} \left(-b x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},-2 b x^2\right)}{e}-\frac{e^{-2 a} 2^{-\frac{m}{2}-\frac{7}{2}} \left(b x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},2 b x^2\right)}{e}-\frac{(e x)^{m+1}}{2 e (m+1)}",1,"-((2^((-7 - m)/2)*x*(e*x)^m*(-(b^2*x^4))^((-1 - m)/2)*(2^((5 + m)/2)*(-(b^2*x^4))^((1 + m)/2) + (1 + m)*(-(b*x^2))^((1 + m)/2)*Gamma[(1 + m)/2, 2*b*x^2]*(Cosh[2*a] - Sinh[2*a]) + (1 + m)*(b*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, -2*b*x^2]*(Cosh[2*a] + Sinh[2*a])))/(1 + m))","A",1
26,1,98,95,0.1531656,"\int (e x)^m \sinh \left(a+b x^2\right) \, dx","Integrate[(e*x)^m*Sinh[a + b*x^2],x]","-\frac{1}{4} x \left(-b^2 x^4\right)^{\frac{1}{2} (-m-1)} (e x)^m \left((\sinh (a)+\cosh (a)) \left(b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-b x^2\right)-(\cosh (a)-\sinh (a)) \left(-b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},b x^2\right)\right)","\frac{e^{-a} \left(b x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},b x^2\right)}{4 e}-\frac{e^a \left(-b x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},-b x^2\right)}{4 e}",1,"-1/4*(x*(e*x)^m*(-(b^2*x^4))^((-1 - m)/2)*(-((-(b*x^2))^((1 + m)/2)*Gamma[(1 + m)/2, b*x^2]*(Cosh[a] - Sinh[a])) + (b*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, -(b*x^2)]*(Cosh[a] + Sinh[a])))","A",1
27,0,0,26,2.9646369,"\int (e x)^m \text{csch}\left(a+b x^2\right) \, dx","Integrate[(e*x)^m*Csch[a + b*x^2],x]","\int (e x)^m \text{csch}\left(a+b x^2\right) \, dx","x^{-m} (e x)^m \text{Int}\left(x^m \text{csch}\left(a+b x^2\right),x\right)",0,"Integrate[(e*x)^m*Csch[a + b*x^2], x]","A",-1
28,1,15,15,0.007846,"\int x^3 \sinh \left(a+b x^4\right) \, dx","Integrate[x^3*Sinh[a + b*x^4],x]","\frac{\cosh \left(a+b x^4\right)}{4 b}","\frac{\cosh \left(a+b x^4\right)}{4 b}",1,"Cosh[a + b*x^4]/(4*b)","A",1
29,1,70,78,0.0665903,"\int x^2 \sinh \left(a+\frac{b}{x}\right) \, dx","Integrate[x^2*Sinh[a + b/x],x]","\frac{1}{6} \left(b^3 (-\cosh (a)) \text{Chi}\left(\frac{b}{x}\right)-b^3 \sinh (a) \text{Shi}\left(\frac{b}{x}\right)+x \left(b^2 \sinh \left(a+\frac{b}{x}\right)+2 x^2 \sinh \left(a+\frac{b}{x}\right)+b x \cosh \left(a+\frac{b}{x}\right)\right)\right)","-\frac{1}{6} b^3 \cosh (a) \text{Chi}\left(\frac{b}{x}\right)-\frac{1}{6} b^3 \sinh (a) \text{Shi}\left(\frac{b}{x}\right)+\frac{1}{6} b^2 x \sinh \left(a+\frac{b}{x}\right)+\frac{1}{3} x^3 \sinh \left(a+\frac{b}{x}\right)+\frac{1}{6} b x^2 \cosh \left(a+\frac{b}{x}\right)",1,"(-(b^3*Cosh[a]*CoshIntegral[b/x]) + x*(b*x*Cosh[a + b/x] + b^2*Sinh[a + b/x] + 2*x^2*Sinh[a + b/x]) - b^3*Sinh[a]*SinhIntegral[b/x])/6","A",1
30,1,54,60,0.0464837,"\int x \sinh \left(a+\frac{b}{x}\right) \, dx","Integrate[x*Sinh[a + b/x],x]","\frac{1}{2} \left(b^2 \sinh (a) \left(-\text{Chi}\left(\frac{b}{x}\right)\right)-b^2 \cosh (a) \text{Shi}\left(\frac{b}{x}\right)+x \left(x \sinh \left(a+\frac{b}{x}\right)+b \cosh \left(a+\frac{b}{x}\right)\right)\right)","-\frac{1}{2} b^2 \sinh (a) \text{Chi}\left(\frac{b}{x}\right)-\frac{1}{2} b^2 \cosh (a) \text{Shi}\left(\frac{b}{x}\right)+\frac{1}{2} x^2 \sinh \left(a+\frac{b}{x}\right)+\frac{1}{2} b x \cosh \left(a+\frac{b}{x}\right)",1,"(-(b^2*CoshIntegral[b/x]*Sinh[a]) + x*(b*Cosh[a + b/x] + x*Sinh[a + b/x]) - b^2*Cosh[a]*SinhIntegral[b/x])/2","A",1
31,1,33,33,0.0200472,"\int \sinh \left(a+\frac{b}{x}\right) \, dx","Integrate[Sinh[a + b/x],x]","-b \cosh (a) \text{Chi}\left(\frac{b}{x}\right)-b \sinh (a) \text{Shi}\left(\frac{b}{x}\right)+x \sinh \left(a+\frac{b}{x}\right)","-b \cosh (a) \text{Chi}\left(\frac{b}{x}\right)-b \sinh (a) \text{Shi}\left(\frac{b}{x}\right)+x \sinh \left(a+\frac{b}{x}\right)",1,"-(b*Cosh[a]*CoshIntegral[b/x]) + x*Sinh[a + b/x] - b*Sinh[a]*SinhIntegral[b/x]","A",1
32,1,21,21,0.0096586,"\int \frac{\sinh \left(a+\frac{b}{x}\right)}{x} \, dx","Integrate[Sinh[a + b/x]/x,x]","\sinh (a) \left(-\text{Chi}\left(\frac{b}{x}\right)\right)-\cosh (a) \text{Shi}\left(\frac{b}{x}\right)","\sinh (a) \left(-\text{Chi}\left(\frac{b}{x}\right)\right)-\cosh (a) \text{Shi}\left(\frac{b}{x}\right)",1,"-(CoshIntegral[b/x]*Sinh[a]) - Cosh[a]*SinhIntegral[b/x]","A",1
33,1,13,13,0.0043897,"\int \frac{\sinh \left(a+\frac{b}{x}\right)}{x^2} \, dx","Integrate[Sinh[a + b/x]/x^2,x]","-\frac{\cosh \left(a+\frac{b}{x}\right)}{b}","-\frac{\cosh \left(a+\frac{b}{x}\right)}{b}",1,"-(Cosh[a + b/x]/b)","A",1
34,1,29,29,0.0276424,"\int \frac{\sinh \left(a+\frac{b}{x}\right)}{x^3} \, dx","Integrate[Sinh[a + b/x]/x^3,x]","\frac{x \sinh \left(a+\frac{b}{x}\right)-b \cosh \left(a+\frac{b}{x}\right)}{b^2 x}","\frac{\sinh \left(a+\frac{b}{x}\right)}{b^2}-\frac{\cosh \left(a+\frac{b}{x}\right)}{b x}",1,"(-(b*Cosh[a + b/x]) + x*Sinh[a + b/x])/(b^2*x)","A",1
35,1,39,46,0.0483332,"\int \frac{\sinh \left(a+\frac{b}{x}\right)}{x^4} \, dx","Integrate[Sinh[a + b/x]/x^4,x]","\frac{2 b x \sinh \left(a+\frac{b}{x}\right)-\left(b^2+2 x^2\right) \cosh \left(a+\frac{b}{x}\right)}{b^3 x^2}","-\frac{2 \cosh \left(a+\frac{b}{x}\right)}{b^3}+\frac{2 \sinh \left(a+\frac{b}{x}\right)}{b^2 x}-\frac{\cosh \left(a+\frac{b}{x}\right)}{b x^2}",1,"(-((b^2 + 2*x^2)*Cosh[a + b/x]) + 2*b*x*Sinh[a + b/x])/(b^3*x^2)","A",1
36,1,48,62,0.0645728,"\int \frac{\sinh \left(a+\frac{b}{x}\right)}{x^5} \, dx","Integrate[Sinh[a + b/x]/x^5,x]","\frac{3 x \left(b^2+2 x^2\right) \sinh \left(a+\frac{b}{x}\right)-b \left(b^2+6 x^2\right) \cosh \left(a+\frac{b}{x}\right)}{b^4 x^3}","\frac{6 \sinh \left(a+\frac{b}{x}\right)}{b^4}-\frac{6 \cosh \left(a+\frac{b}{x}\right)}{b^3 x}+\frac{3 \sinh \left(a+\frac{b}{x}\right)}{b^2 x^2}-\frac{\cosh \left(a+\frac{b}{x}\right)}{b x^3}",1,"(-(b*(b^2 + 6*x^2)*Cosh[a + b/x]) + 3*x*(b^2 + 2*x^2)*Sinh[a + b/x])/(b^4*x^3)","A",1
37,-1,0,146,180.0013924,"\int (e x)^m \sinh ^3\left(a+\frac{b}{x}\right) \, dx","Integrate[(e*x)^m*Sinh[a + b/x]^3,x]","\text{\$Aborted}","-\frac{1}{8} e^{3 a} b 3^{m+1} \left(-\frac{b}{x}\right)^m (e x)^m \Gamma \left(-m-1,-\frac{3 b}{x}\right)+\frac{3}{8} e^a b \left(-\frac{b}{x}\right)^m (e x)^m \Gamma \left(-m-1,-\frac{b}{x}\right)+\frac{3}{8} e^{-a} b \left(\frac{b}{x}\right)^m (e x)^m \Gamma \left(-m-1,\frac{b}{x}\right)-\frac{1}{8} e^{-3 a} b 3^{m+1} \left(\frac{b}{x}\right)^m (e x)^m \Gamma \left(-m-1,\frac{3 b}{x}\right)",1,"$Aborted","F",-1
38,1,88,90,0.2556996,"\int (e x)^m \sinh ^2\left(a+\frac{b}{x}\right) \, dx","Integrate[(e*x)^m*Sinh[a + b/x]^2,x]","-\frac{(e x)^m \left(b 2^m (m+1) (\sinh (a)+\cosh (a))^2 \left(-\frac{b}{x}\right)^m \Gamma \left(-m-1,-\frac{2 b}{x}\right)-b 2^m (m+1) (\cosh (a)-\sinh (a))^2 \left(\frac{b}{x}\right)^m \Gamma \left(-m-1,\frac{2 b}{x}\right)+x\right)}{2 (m+1)}","-e^{2 a} b 2^{m-1} \left(-\frac{b}{x}\right)^m (e x)^m \Gamma \left(-m-1,-\frac{2 b}{x}\right)+e^{-2 a} b 2^{m-1} \left(\frac{b}{x}\right)^m (e x)^m \Gamma \left(-m-1,\frac{2 b}{x}\right)-\frac{x (e x)^m}{2 (m+1)}",1,"-1/2*((e*x)^m*(x - 2^m*b*(1 + m)*(b/x)^m*Gamma[-1 - m, (2*b)/x]*(Cosh[a] - Sinh[a])^2 + 2^m*b*(1 + m)*(-(b/x))^m*Gamma[-1 - m, (-2*b)/x]*(Cosh[a] + Sinh[a])^2))/(1 + m)","A",1
39,1,63,67,0.0874432,"\int (e x)^m \sinh \left(a+\frac{b}{x}\right) \, dx","Integrate[(e*x)^m*Sinh[a + b/x],x]","-\frac{1}{2} b (e x)^m \left((\sinh (a)+\cosh (a)) \left(-\frac{b}{x}\right)^m \Gamma \left(-m-1,-\frac{b}{x}\right)+(\cosh (a)-\sinh (a)) \left(\frac{b}{x}\right)^m \Gamma \left(-m-1,\frac{b}{x}\right)\right)","-\frac{1}{2} e^a b \left(-\frac{b}{x}\right)^m (e x)^m \Gamma \left(-m-1,-\frac{b}{x}\right)-\frac{1}{2} e^{-a} b \left(\frac{b}{x}\right)^m (e x)^m \Gamma \left(-m-1,\frac{b}{x}\right)",1,"-1/2*(b*(e*x)^m*((b/x)^m*Gamma[-1 - m, b/x]*(Cosh[a] - Sinh[a]) + (-(b/x))^m*Gamma[-1 - m, -(b/x)]*(Cosh[a] + Sinh[a])))","A",1
40,0,0,26,3.4183714,"\int (e x)^m \text{csch}\left(a+\frac{b}{x}\right) \, dx","Integrate[(e*x)^m*Csch[a + b/x],x]","\int (e x)^m \text{csch}\left(a+\frac{b}{x}\right) \, dx","x^{-m} (e x)^m \text{Int}\left(x^m \text{csch}\left(a+\frac{b}{x}\right),x\right)",0,"Integrate[(e*x)^m*Csch[a + b/x], x]","A",-1
41,1,102,104,0.1115234,"\int x^4 \sinh \left(a+\frac{b}{x^2}\right) \, dx","Integrate[x^4*Sinh[a + b/x^2],x]","\frac{1}{15} \left(2 \sqrt{\pi } b^{5/2} (\sinh (a)-\cosh (a)) \text{erf}\left(\frac{\sqrt{b}}{x}\right)-2 \sqrt{\pi } b^{5/2} (\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{\sqrt{b}}{x}\right)+4 b^2 x \sinh \left(a+\frac{b}{x^2}\right)+3 x^5 \sinh \left(a+\frac{b}{x^2}\right)+2 b x^3 \cosh \left(a+\frac{b}{x^2}\right)\right)","-\frac{2}{15} \sqrt{\pi } e^{-a} b^{5/2} \text{erf}\left(\frac{\sqrt{b}}{x}\right)-\frac{2}{15} \sqrt{\pi } e^a b^{5/2} \text{erfi}\left(\frac{\sqrt{b}}{x}\right)+\frac{4}{15} b^2 x \sinh \left(a+\frac{b}{x^2}\right)+\frac{1}{5} x^5 \sinh \left(a+\frac{b}{x^2}\right)+\frac{2}{15} b x^3 \cosh \left(a+\frac{b}{x^2}\right)",1,"(2*b*x^3*Cosh[a + b/x^2] + 2*b^(5/2)*Sqrt[Pi]*Erf[Sqrt[b]/x]*(-Cosh[a] + Sinh[a]) - 2*b^(5/2)*Sqrt[Pi]*Erfi[Sqrt[b]/x]*(Cosh[a] + Sinh[a]) + 4*b^2*x*Sinh[a + b/x^2] + 3*x^5*Sinh[a + b/x^2])/15","A",1
42,1,56,62,0.0435215,"\int x^3 \sinh \left(a+\frac{b}{x^2}\right) \, dx","Integrate[x^3*Sinh[a + b/x^2],x]","\frac{1}{4} \left(-b^2 \sinh (a) \text{Chi}\left(\frac{b}{x^2}\right)-b^2 \cosh (a) \text{Shi}\left(\frac{b}{x^2}\right)+b x^2 \cosh \left(a+\frac{b}{x^2}\right)+x^4 \sinh \left(a+\frac{b}{x^2}\right)\right)","-\frac{1}{4} b^2 \sinh (a) \text{Chi}\left(\frac{b}{x^2}\right)-\frac{1}{4} b^2 \cosh (a) \text{Shi}\left(\frac{b}{x^2}\right)+\frac{1}{4} b x^2 \cosh \left(a+\frac{b}{x^2}\right)+\frac{1}{4} x^4 \sinh \left(a+\frac{b}{x^2}\right)",1,"(b*x^2*Cosh[a + b/x^2] - b^2*CoshIntegral[b/x^2]*Sinh[a] + x^4*Sinh[a + b/x^2] - b^2*Cosh[a]*SinhIntegral[b/x^2])/4","A",1
43,1,84,86,0.0880144,"\int x^2 \sinh \left(a+\frac{b}{x^2}\right) \, dx","Integrate[x^2*Sinh[a + b/x^2],x]","\frac{1}{3} \left(\sqrt{\pi } b^{3/2} (\cosh (a)-\sinh (a)) \text{erf}\left(\frac{\sqrt{b}}{x}\right)-\sqrt{\pi } b^{3/2} (\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{\sqrt{b}}{x}\right)+2 b x \cosh \left(a+\frac{b}{x^2}\right)+x^3 \sinh \left(a+\frac{b}{x^2}\right)\right)","\frac{1}{3} \sqrt{\pi } e^{-a} b^{3/2} \text{erf}\left(\frac{\sqrt{b}}{x}\right)-\frac{1}{3} \sqrt{\pi } e^a b^{3/2} \text{erfi}\left(\frac{\sqrt{b}}{x}\right)+\frac{2}{3} b x \cosh \left(a+\frac{b}{x^2}\right)+\frac{1}{3} x^3 \sinh \left(a+\frac{b}{x^2}\right)",1,"(2*b*x*Cosh[a + b/x^2] + b^(3/2)*Sqrt[Pi]*Erf[Sqrt[b]/x]*(Cosh[a] - Sinh[a]) - b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[b]/x]*(Cosh[a] + Sinh[a]) + x^3*Sinh[a + b/x^2])/3","A",1
44,1,39,42,0.02621,"\int x \sinh \left(a+\frac{b}{x^2}\right) \, dx","Integrate[x*Sinh[a + b/x^2],x]","\frac{1}{2} \left(-b \cosh (a) \text{Chi}\left(\frac{b}{x^2}\right)-b \sinh (a) \text{Shi}\left(\frac{b}{x^2}\right)+x^2 \sinh \left(a+\frac{b}{x^2}\right)\right)","-\frac{1}{2} b \cosh (a) \text{Chi}\left(\frac{b}{x^2}\right)-\frac{1}{2} b \sinh (a) \text{Shi}\left(\frac{b}{x^2}\right)+\frac{1}{2} x^2 \sinh \left(a+\frac{b}{x^2}\right)",1,"(-(b*Cosh[a]*CoshIntegral[b/x^2]) + x^2*Sinh[a + b/x^2] - b*Sinh[a]*SinhIntegral[b/x^2])/2","A",1
45,1,70,67,0.0668902,"\int \sinh \left(a+\frac{b}{x^2}\right) \, dx","Integrate[Sinh[a + b/x^2],x]","-\frac{1}{2} \sqrt{\pi } \sqrt{b} \left((\cosh (a)-\sinh (a)) \text{erf}\left(\frac{\sqrt{b}}{x}\right)+(\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{\sqrt{b}}{x}\right)\right)+x \sinh (a) \cosh \left(\frac{b}{x^2}\right)+x \cosh (a) \sinh \left(\frac{b}{x^2}\right)","-\frac{1}{2} \sqrt{\pi } e^{-a} \sqrt{b} \text{erf}\left(\frac{\sqrt{b}}{x}\right)-\frac{1}{2} \sqrt{\pi } e^a \sqrt{b} \text{erfi}\left(\frac{\sqrt{b}}{x}\right)+x \sinh \left(a+\frac{b}{x^2}\right)",1,"x*Cosh[b/x^2]*Sinh[a] - (Sqrt[b]*Sqrt[Pi]*(Erf[Sqrt[b]/x]*(Cosh[a] - Sinh[a]) + Erfi[Sqrt[b]/x]*(Cosh[a] + Sinh[a])))/2 + x*Cosh[a]*Sinh[b/x^2]","A",1
46,1,25,25,0.014605,"\int \frac{\sinh \left(a+\frac{b}{x^2}\right)}{x} \, dx","Integrate[Sinh[a + b/x^2]/x,x]","\frac{1}{2} \left(\sinh (a) \left(-\text{Chi}\left(\frac{b}{x^2}\right)\right)-\cosh (a) \text{Shi}\left(\frac{b}{x^2}\right)\right)","-\frac{1}{2} \sinh (a) \text{Chi}\left(\frac{b}{x^2}\right)-\frac{1}{2} \cosh (a) \text{Shi}\left(\frac{b}{x^2}\right)",1,"(-(CoshIntegral[b/x^2]*Sinh[a]) - Cosh[a]*SinhIntegral[b/x^2])/2","A",1
47,1,50,57,0.0343379,"\int \frac{\sinh \left(a+\frac{b}{x^2}\right)}{x^2} \, dx","Integrate[Sinh[a + b/x^2]/x^2,x]","\frac{\sqrt{\pi } \left((\cosh (a)-\sinh (a)) \text{erf}\left(\frac{\sqrt{b}}{x}\right)-(\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{\sqrt{b}}{x}\right)\right)}{4 \sqrt{b}}","\frac{\sqrt{\pi } e^{-a} \text{erf}\left(\frac{\sqrt{b}}{x}\right)}{4 \sqrt{b}}-\frac{\sqrt{\pi } e^a \text{erfi}\left(\frac{\sqrt{b}}{x}\right)}{4 \sqrt{b}}",1,"(Sqrt[Pi]*(Erf[Sqrt[b]/x]*(Cosh[a] - Sinh[a]) - Erfi[Sqrt[b]/x]*(Cosh[a] + Sinh[a])))/(4*Sqrt[b])","A",1
48,1,15,15,0.0048193,"\int \frac{\sinh \left(a+\frac{b}{x^2}\right)}{x^3} \, dx","Integrate[Sinh[a + b/x^2]/x^3,x]","-\frac{\cosh \left(a+\frac{b}{x^2}\right)}{2 b}","-\frac{\cosh \left(a+\frac{b}{x^2}\right)}{2 b}",1,"-1/2*Cosh[a + b/x^2]/b","A",1
49,1,74,75,0.073276,"\int \frac{\sinh \left(a+\frac{b}{x^2}\right)}{x^4} \, dx","Integrate[Sinh[a + b/x^2]/x^4,x]","\frac{\sqrt{\pi } x (\cosh (a)-\sinh (a)) \text{erf}\left(\frac{\sqrt{b}}{x}\right)+\sqrt{\pi } x (\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{\sqrt{b}}{x}\right)-4 \sqrt{b} \cosh \left(a+\frac{b}{x^2}\right)}{8 b^{3/2} x}","\frac{\sqrt{\pi } e^{-a} \text{erf}\left(\frac{\sqrt{b}}{x}\right)}{8 b^{3/2}}+\frac{\sqrt{\pi } e^a \text{erfi}\left(\frac{\sqrt{b}}{x}\right)}{8 b^{3/2}}-\frac{\cosh \left(a+\frac{b}{x^2}\right)}{2 b x}",1,"(-4*Sqrt[b]*Cosh[a + b/x^2] + Sqrt[Pi]*x*Erf[Sqrt[b]/x]*(Cosh[a] - Sinh[a]) + Sqrt[Pi]*x*Erfi[Sqrt[b]/x]*(Cosh[a] + Sinh[a]))/(8*b^(3/2)*x)","A",1
50,1,34,34,0.0295363,"\int \frac{\sinh \left(a+\frac{b}{x^2}\right)}{x^5} \, dx","Integrate[Sinh[a + b/x^2]/x^5,x]","\frac{x^2 \sinh \left(a+\frac{b}{x^2}\right)-b \cosh \left(a+\frac{b}{x^2}\right)}{2 b^2 x^2}","\frac{\sinh \left(a+\frac{b}{x^2}\right)}{2 b^2}-\frac{\cosh \left(a+\frac{b}{x^2}\right)}{2 b x^2}",1,"(-(b*Cosh[a + b/x^2]) + x^2*Sinh[a + b/x^2])/(2*b^2*x^2)","A",1
51,1,97,93,0.1232851,"\int \frac{\sinh \left(a+\frac{b}{x^2}\right)}{x^6} \, dx","Integrate[Sinh[a + b/x^2]/x^6,x]","\frac{3 \sqrt{\pi } x^3 (\cosh (a)-\sinh (a)) \text{erf}\left(\frac{\sqrt{b}}{x}\right)-3 \sqrt{\pi } x^3 (\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{\sqrt{b}}{x}\right)+4 \sqrt{b} \left(3 x^2 \sinh \left(a+\frac{b}{x^2}\right)-2 b \cosh \left(a+\frac{b}{x^2}\right)\right)}{16 b^{5/2} x^3}","\frac{3 \sqrt{\pi } e^{-a} \text{erf}\left(\frac{\sqrt{b}}{x}\right)}{16 b^{5/2}}-\frac{3 \sqrt{\pi } e^a \text{erfi}\left(\frac{\sqrt{b}}{x}\right)}{16 b^{5/2}}+\frac{3 \sinh \left(a+\frac{b}{x^2}\right)}{4 b^2 x}-\frac{\cosh \left(a+\frac{b}{x^2}\right)}{2 b x^3}",1,"(3*Sqrt[Pi]*x^3*Erf[Sqrt[b]/x]*(Cosh[a] - Sinh[a]) - 3*Sqrt[Pi]*x^3*Erfi[Sqrt[b]/x]*(Cosh[a] + Sinh[a]) + 4*Sqrt[b]*(-2*b*Cosh[a + b/x^2] + 3*x^2*Sinh[a + b/x^2]))/(16*b^(5/2)*x^3)","A",1
52,1,44,47,0.0498856,"\int \frac{\sinh \left(a+\frac{b}{x^2}\right)}{x^7} \, dx","Integrate[Sinh[a + b/x^2]/x^7,x]","\frac{2 b x^2 \sinh \left(a+\frac{b}{x^2}\right)-\left(b^2+2 x^4\right) \cosh \left(a+\frac{b}{x^2}\right)}{2 b^3 x^4}","-\frac{\cosh \left(a+\frac{b}{x^2}\right)}{b^3}+\frac{\sinh \left(a+\frac{b}{x^2}\right)}{b^2 x^2}-\frac{\cosh \left(a+\frac{b}{x^2}\right)}{2 b x^4}",1,"(-((b^2 + 2*x^4)*Cosh[a + b/x^2]) + 2*b*x^2*Sinh[a + b/x^2])/(2*b^3*x^4)","A",1
53,1,1039,194,24.2938983,"\int (e x)^m \sinh ^3\left(a+\frac{b}{x^2}\right) \, dx","Integrate[(e*x)^m*Sinh[a + b/x^2]^3,x]","(e x)^m \left(\frac{3}{8} \left(\frac{1}{2} x^{m+1} \Gamma \left(\frac{1}{2} (-m-1),-\frac{b}{x^2}\right) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}}+\frac{1}{2} \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} x^{m+1} \Gamma \left(\frac{1}{2} (-m-1),\frac{b}{x^2}\right)\right)+\frac{1}{8} \left(\frac{1}{2} 3^{\frac{m+1}{2}} x^{m+1} \Gamma \left(\frac{1}{2} (-m-1),-\frac{3 b}{x^2}\right) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}}+\frac{1}{2} 3^{\frac{m+1}{2}} \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} x^{m+1} \Gamma \left(\frac{1}{2} (-m-1),\frac{3 b}{x^2}\right)\right)\right) \sinh ^3(a) x^{-m}+(e x)^m \cosh ^3(a) \left(\frac{1}{8} \left(\frac{1}{2} 3^{\frac{m+1}{2}} \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}} x^{m+1} \Gamma \left(\frac{1}{2} (-m-1),-\frac{3 b}{x^2}\right)-\frac{1}{2} 3^{\frac{m+1}{2}} \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} x^{m+1} \Gamma \left(\frac{1}{2} (-m-1),\frac{3 b}{x^2}\right)\right)-\frac{3}{8} \left(\frac{1}{2} \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}} x^{m+1} \Gamma \left(\frac{1}{2} (-m-1),-\frac{b}{x^2}\right)-\frac{1}{2} \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} x^{m+1} \Gamma \left(\frac{1}{2} (-m-1),\frac{b}{x^2}\right)\right)\right) x^{-m}+\frac{3}{16} (e x)^m \cosh ^2(a) \left(-3^{\frac{m+1}{2}} m \Gamma \left(\frac{1}{2} (-m-1),-\frac{3 b}{x^2}\right) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}}+m \Gamma \left(\frac{1}{2} (-m-1),-\frac{b}{x^2}\right) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}}-2\ 3^{\frac{m+1}{2}} \Gamma \left(\frac{1-m}{2},-\frac{3 b}{x^2}\right) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}}+2 \Gamma \left(\frac{1-m}{2},-\frac{b}{x^2}\right) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}}-4 \cosh \left(\frac{b}{x^2}\right)+4 \cosh \left(\frac{3 b}{x^2}\right)+m \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),\frac{b}{x^2}\right)-3^{\frac{m+1}{2}} m \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),\frac{3 b}{x^2}\right)+2 \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1-m}{2},\frac{b}{x^2}\right)-2\ 3^{\frac{m+1}{2}} \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1-m}{2},\frac{3 b}{x^2}\right)\right) \sinh (a) x+\frac{3}{16} (e x)^m \cosh (a) \sinh ^2(a) \left(-3^{\frac{m+1}{2}} m \Gamma \left(\frac{1}{2} (-m-1),-\frac{3 b}{x^2}\right) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}}-m \Gamma \left(\frac{1}{2} (-m-1),-\frac{b}{x^2}\right) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}}-2\ 3^{\frac{m+1}{2}} \Gamma \left(\frac{1-m}{2},-\frac{3 b}{x^2}\right) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}}-2 \Gamma \left(\frac{1-m}{2},-\frac{b}{x^2}\right) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}}+m \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),\frac{b}{x^2}\right)+3^{\frac{m+1}{2}} m \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),\frac{3 b}{x^2}\right)+2 \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1-m}{2},\frac{b}{x^2}\right)+2\ 3^{\frac{m+1}{2}} \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1-m}{2},\frac{3 b}{x^2}\right)+4 \sinh \left(\frac{b}{x^2}\right)+4 \sinh \left(\frac{3 b}{x^2}\right)\right) x","\frac{1}{16} e^{3 a} 3^{\frac{m+1}{2}} x \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}} (e x)^m \Gamma \left(\frac{1}{2} (-m-1),-\frac{3 b}{x^2}\right)-\frac{3}{16} e^a x \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}} (e x)^m \Gamma \left(\frac{1}{2} (-m-1),-\frac{b}{x^2}\right)+\frac{3}{16} e^{-a} x \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} (e x)^m \Gamma \left(\frac{1}{2} (-m-1),\frac{b}{x^2}\right)-\frac{1}{16} e^{-3 a} 3^{\frac{m+1}{2}} x \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} (e x)^m \Gamma \left(\frac{1}{2} (-m-1),\frac{3 b}{x^2}\right)",1,"((e*x)^m*Cosh[a]^3*((-3*(((-(b/x^2))^((1 + m)/2)*x^(1 + m)*Gamma[(-1 - m)/2, -(b/x^2)])/2 - ((b/x^2)^((1 + m)/2)*x^(1 + m)*Gamma[(-1 - m)/2, b/x^2])/2))/8 + ((3^((1 + m)/2)*(-(b/x^2))^((1 + m)/2)*x^(1 + m)*Gamma[(-1 - m)/2, (-3*b)/x^2])/2 - (3^((1 + m)/2)*(b/x^2)^((1 + m)/2)*x^(1 + m)*Gamma[(-1 - m)/2, (3*b)/x^2])/2)/8))/x^m + (3*x*(e*x)^m*Cosh[a]^2*(-4*Cosh[b/x^2] + 4*Cosh[(3*b)/x^2] - 3^((1 + m)/2)*m*(-(b/x^2))^((1 + m)/2)*Gamma[(-1 - m)/2, (-3*b)/x^2] + m*(-(b/x^2))^((1 + m)/2)*Gamma[(-1 - m)/2, -(b/x^2)] + m*(b/x^2)^((1 + m)/2)*Gamma[(-1 - m)/2, b/x^2] - 3^((1 + m)/2)*m*(b/x^2)^((1 + m)/2)*Gamma[(-1 - m)/2, (3*b)/x^2] - 2*3^((1 + m)/2)*(-(b/x^2))^((1 + m)/2)*Gamma[(1 - m)/2, (-3*b)/x^2] + 2*(-(b/x^2))^((1 + m)/2)*Gamma[(1 - m)/2, -(b/x^2)] + 2*(b/x^2)^((1 + m)/2)*Gamma[(1 - m)/2, b/x^2] - 2*3^((1 + m)/2)*(b/x^2)^((1 + m)/2)*Gamma[(1 - m)/2, (3*b)/x^2])*Sinh[a])/16 + ((e*x)^m*((3*(((-(b/x^2))^((1 + m)/2)*x^(1 + m)*Gamma[(-1 - m)/2, -(b/x^2)])/2 + ((b/x^2)^((1 + m)/2)*x^(1 + m)*Gamma[(-1 - m)/2, b/x^2])/2))/8 + ((3^((1 + m)/2)*(-(b/x^2))^((1 + m)/2)*x^(1 + m)*Gamma[(-1 - m)/2, (-3*b)/x^2])/2 + (3^((1 + m)/2)*(b/x^2)^((1 + m)/2)*x^(1 + m)*Gamma[(-1 - m)/2, (3*b)/x^2])/2)/8)*Sinh[a]^3)/x^m + (3*x*(e*x)^m*Cosh[a]*Sinh[a]^2*(-(3^((1 + m)/2)*m*(-(b/x^2))^((1 + m)/2)*Gamma[(-1 - m)/2, (-3*b)/x^2]) - m*(-(b/x^2))^((1 + m)/2)*Gamma[(-1 - m)/2, -(b/x^2)] + m*(b/x^2)^((1 + m)/2)*Gamma[(-1 - m)/2, b/x^2] + 3^((1 + m)/2)*m*(b/x^2)^((1 + m)/2)*Gamma[(-1 - m)/2, (3*b)/x^2] - 2*3^((1 + m)/2)*(-(b/x^2))^((1 + m)/2)*Gamma[(1 - m)/2, (-3*b)/x^2] - 2*(-(b/x^2))^((1 + m)/2)*Gamma[(1 - m)/2, -(b/x^2)] + 2*(b/x^2)^((1 + m)/2)*Gamma[(1 - m)/2, b/x^2] + 2*3^((1 + m)/2)*(b/x^2)^((1 + m)/2)*Gamma[(1 - m)/2, (3*b)/x^2] + 4*Sinh[b/x^2] + 4*Sinh[(3*b)/x^2]))/16","B",1
54,1,122,117,0.8285476,"\int (e x)^m \sinh ^2\left(a+\frac{b}{x^2}\right) \, dx","Integrate[(e*x)^m*Sinh[a + b/x^2]^2,x]","\frac{x (e x)^m \left(2^{\frac{m+1}{2}} (m+1) (\sinh (2 a)+\cosh (2 a)) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),-\frac{2 b}{x^2}\right)+2^{\frac{m+1}{2}} (m+1) (\cosh (2 a)-\sinh (2 a)) \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),\frac{2 b}{x^2}\right)-4\right)}{8 (m+1)}","e^{2 a} 2^{\frac{m-5}{2}} x \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}} (e x)^m \Gamma \left(\frac{1}{2} (-m-1),-\frac{2 b}{x^2}\right)+e^{-2 a} 2^{\frac{m-5}{2}} x \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} (e x)^m \Gamma \left(\frac{1}{2} (-m-1),\frac{2 b}{x^2}\right)-\frac{x (e x)^m}{2 (m+1)}",1,"(x*(e*x)^m*(-4 + 2^((1 + m)/2)*(1 + m)*(b/x^2)^((1 + m)/2)*Gamma[(-1 - m)/2, (2*b)/x^2]*(Cosh[2*a] - Sinh[2*a]) + 2^((1 + m)/2)*(1 + m)*(-(b/x^2))^((1 + m)/2)*Gamma[(-1 - m)/2, (-2*b)/x^2]*(Cosh[2*a] + Sinh[2*a])))/(8*(1 + m))","A",1
55,1,84,87,0.1435628,"\int (e x)^m \sinh \left(a+\frac{b}{x^2}\right) \, dx","Integrate[(e*x)^m*Sinh[a + b/x^2],x]","\frac{1}{4} x (e x)^m \left((\sinh (a)+\cosh (a)) \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),-\frac{b}{x^2}\right)-(\cosh (a)-\sinh (a)) \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),\frac{b}{x^2}\right)\right)","\frac{1}{4} e^a x \left(-\frac{b}{x^2}\right)^{\frac{m+1}{2}} (e x)^m \Gamma \left(\frac{1}{2} (-m-1),-\frac{b}{x^2}\right)-\frac{1}{4} e^{-a} x \left(\frac{b}{x^2}\right)^{\frac{m+1}{2}} (e x)^m \Gamma \left(\frac{1}{2} (-m-1),\frac{b}{x^2}\right)",1,"(x*(e*x)^m*(-((b/x^2)^((1 + m)/2)*Gamma[(-1 - m)/2, b/x^2]*(Cosh[a] - Sinh[a])) + (-(b/x^2))^((1 + m)/2)*Gamma[(-1 - m)/2, -(b/x^2)]*(Cosh[a] + Sinh[a])))/4","A",1
56,0,0,26,3.3968776,"\int (e x)^m \text{csch}\left(a+\frac{b}{x^2}\right) \, dx","Integrate[(e*x)^m*Csch[a + b/x^2],x]","\int (e x)^m \text{csch}\left(a+\frac{b}{x^2}\right) \, dx","x^{-m} (e x)^m \text{Int}\left(x^m \text{csch}\left(a+\frac{b}{x^2}\right),x\right)",0,"Integrate[(e*x)^m*Csch[a + b/x^2], x]","A",-1
57,1,8,8,0.003013,"\int \frac{\sinh \left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[Sinh[Sqrt[x]]/Sqrt[x],x]","2 \cosh \left(\sqrt{x}\right)","2 \cosh \left(\sqrt{x}\right)",1,"2*Cosh[Sqrt[x]]","A",1
58,1,88,75,0.0984172,"\int x^2 \sinh \left(a+b x^n\right) \, dx","Integrate[x^2*Sinh[a + b*x^n],x]","-\frac{x^3 \left(-b^2 x^{2 n}\right)^{-3/n} \left((\sinh (a)+\cosh (a)) \left(b x^n\right)^{3/n} \Gamma \left(\frac{3}{n},-b x^n\right)-(\cosh (a)-\sinh (a)) \left(-b x^n\right)^{3/n} \Gamma \left(\frac{3}{n},b x^n\right)\right)}{2 n}","\frac{e^{-a} x^3 \left(b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},b x^n\right)}{2 n}-\frac{e^a x^3 \left(-b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-b x^n\right)}{2 n}",1,"-1/2*(x^3*(-((-(b*x^n))^(3/n)*Gamma[3/n, b*x^n]*(Cosh[a] - Sinh[a])) + (b*x^n)^(3/n)*Gamma[3/n, -(b*x^n)]*(Cosh[a] + Sinh[a])))/(n*(-(b^2*x^(2*n)))^(3/n))","A",1
59,1,88,75,0.0852281,"\int x \sinh \left(a+b x^n\right) \, dx","Integrate[x*Sinh[a + b*x^n],x]","-\frac{x^2 \left(-b^2 x^{2 n}\right)^{-2/n} \left((\sinh (a)+\cosh (a)) \left(b x^n\right)^{2/n} \Gamma \left(\frac{2}{n},-b x^n\right)-(\cosh (a)-\sinh (a)) \left(-b x^n\right)^{2/n} \Gamma \left(\frac{2}{n},b x^n\right)\right)}{2 n}","\frac{e^{-a} x^2 \left(b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},b x^n\right)}{2 n}-\frac{e^a x^2 \left(-b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-b x^n\right)}{2 n}",1,"-1/2*(x^2*(-((-(b*x^n))^(2/n)*Gamma[2/n, b*x^n]*(Cosh[a] - Sinh[a])) + (b*x^n)^(2/n)*Gamma[2/n, -(b*x^n)]*(Cosh[a] + Sinh[a])))/(n*(-(b^2*x^(2*n)))^(2/n))","A",1
60,1,79,67,0.0821754,"\int \sinh \left(a+b x^n\right) \, dx","Integrate[Sinh[a + b*x^n],x]","\frac{\left(-b^2 x^{2 n}\right)^{-1/n} \left(x (\cosh (a)-\sinh (a)) \left(-b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},b x^n\right)-x (\sinh (a)+\cosh (a)) \left(b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-b x^n\right)\right)}{2 n}","\frac{e^{-a} x \left(b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},b x^n\right)}{2 n}-\frac{e^a x \left(-b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-b x^n\right)}{2 n}",1,"(x*(-(b*x^n))^n^(-1)*Gamma[n^(-1), b*x^n]*(Cosh[a] - Sinh[a]) - x*(b*x^n)^n^(-1)*Gamma[n^(-1), -(b*x^n)]*(Cosh[a] + Sinh[a]))/(2*n*(-(b^2*x^(2*n)))^n^(-1))","A",1
61,1,23,25,0.0266183,"\int \frac{\sinh \left(a+b x^n\right)}{x} \, dx","Integrate[Sinh[a + b*x^n]/x,x]","\frac{\sinh (a) \text{Chi}\left(b x^n\right)+\cosh (a) \text{Shi}\left(b x^n\right)}{n}","\frac{\sinh (a) \text{Chi}\left(b x^n\right)}{n}+\frac{\cosh (a) \text{Shi}\left(b x^n\right)}{n}",1,"(CoshIntegral[b*x^n]*Sinh[a] + Cosh[a]*SinhIntegral[b*x^n])/n","A",1
62,1,68,71,0.0705954,"\int \frac{\sinh \left(a+b x^n\right)}{x^2} \, dx","Integrate[Sinh[a + b*x^n]/x^2,x]","\frac{(\cosh (a)-\sinh (a)) \left(b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},b x^n\right)-(\sinh (a)+\cosh (a)) \left(-b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-b x^n\right)}{2 n x}","\frac{e^{-a} \left(b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},b x^n\right)}{2 n x}-\frac{e^a \left(-b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-b x^n\right)}{2 n x}",1,"((b*x^n)^n^(-1)*Gamma[-n^(-1), b*x^n]*(Cosh[a] - Sinh[a]) - (-(b*x^n))^n^(-1)*Gamma[-n^(-1), -(b*x^n)]*(Cosh[a] + Sinh[a]))/(2*n*x)","A",1
63,1,72,75,0.0760029,"\int \frac{\sinh \left(a+b x^n\right)}{x^3} \, dx","Integrate[Sinh[a + b*x^n]/x^3,x]","\frac{(\cosh (a)-\sinh (a)) \left(b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},b x^n\right)-(\sinh (a)+\cosh (a)) \left(-b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},-b x^n\right)}{2 n x^2}","\frac{e^{-a} \left(b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},b x^n\right)}{2 n x^2}-\frac{e^a \left(-b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},-b x^n\right)}{2 n x^2}",1,"((b*x^n)^(2/n)*Gamma[-2/n, b*x^n]*(Cosh[a] - Sinh[a]) - (-(b*x^n))^(2/n)*Gamma[-2/n, -(b*x^n)]*(Cosh[a] + Sinh[a]))/(2*n*x^2)","A",1
64,1,89,99,1.5091611,"\int x^2 \sinh ^2\left(a+b x^n\right) \, dx","Integrate[x^2*Sinh[a + b*x^n]^2,x]","-\frac{x^3 \left(3 e^{2 a} 8^{-1/n} \left(-b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-2 b x^n\right)+3 e^{-2 a} 8^{-1/n} \left(b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},2 b x^n\right)+2 n\right)}{12 n}","-\frac{e^{2 a} 2^{-\frac{3}{n}-2} x^3 \left(-b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-2 b x^n\right)}{n}-\frac{e^{-2 a} 2^{-\frac{3}{n}-2} x^3 \left(b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},2 b x^n\right)}{n}-\frac{x^3}{6}",1,"-1/12*(x^3*(2*n + (3*E^(2*a)*Gamma[3/n, -2*b*x^n])/(8^n^(-1)*(-(b*x^n))^(3/n)) + (3*Gamma[3/n, 2*b*x^n])/(8^n^(-1)*E^(2*a)*(b*x^n)^(3/n))))/n","A",1
65,1,85,99,1.3075674,"\int x \sinh ^2\left(a+b x^n\right) \, dx","Integrate[x*Sinh[a + b*x^n]^2,x]","-\frac{x^2 \left(e^{2 a} 4^{-1/n} \left(-b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-2 b x^n\right)+e^{-2 a} 4^{-1/n} \left(b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},2 b x^n\right)+n\right)}{4 n}","-\frac{e^{2 a} 4^{-\frac{1}{n}-1} x^2 \left(-b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-2 b x^n\right)}{n}-\frac{e^{-2 a} 4^{-\frac{1}{n}-1} x^2 \left(b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},2 b x^n\right)}{n}-\frac{x^2}{4}",1,"-1/4*(x^2*(n + (E^(2*a)*Gamma[2/n, -2*b*x^n])/(4^n^(-1)*(-(b*x^n))^(2/n)) + Gamma[2/n, 2*b*x^n]/(4^n^(-1)*E^(2*a)*(b*x^n)^(2/n))))/n","A",1
66,1,81,89,1.1128163,"\int \sinh ^2\left(a+b x^n\right) \, dx","Integrate[Sinh[a + b*x^n]^2,x]","-\frac{x \left(e^{2 a} 2^{-1/n} \left(-b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 b x^n\right)+e^{-2 a} 2^{-1/n} \left(b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 b x^n\right)+2 n\right)}{4 n}","-\frac{e^{2 a} 2^{-\frac{1}{n}-2} x \left(-b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 b x^n\right)}{n}-\frac{e^{-2 a} 2^{-\frac{1}{n}-2} x \left(b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 b x^n\right)}{n}-\frac{x}{2}",1,"-1/4*(x*(2*n + (E^(2*a)*Gamma[n^(-1), -2*b*x^n])/(2^n^(-1)*(-(b*x^n))^n^(-1)) + Gamma[n^(-1), 2*b*x^n]/(2^n^(-1)*E^(2*a)*(b*x^n)^n^(-1))))/n","A",1
67,1,39,43,0.0352448,"\int \frac{\sinh ^2\left(a+b x^n\right)}{x} \, dx","Integrate[Sinh[a + b*x^n]^2/x,x]","\frac{\cosh (2 a) \text{Chi}\left(2 b x^n\right)+\sinh (2 a) \text{Shi}\left(2 b x^n\right)}{2 n}-\frac{\log (x)}{2}","\frac{\cosh (2 a) \text{Chi}\left(2 b x^n\right)}{2 n}+\frac{\sinh (2 a) \text{Shi}\left(2 b x^n\right)}{2 n}-\frac{\log (x)}{2}",1,"-1/2*Log[x] + (Cosh[2*a]*CoshIntegral[2*b*x^n] + Sinh[2*a]*SinhIntegral[2*b*x^n])/(2*n)","A",1
68,1,79,91,1.4282269,"\int \frac{\sinh ^2\left(a+b x^n\right)}{x^2} \, dx","Integrate[Sinh[a + b*x^n]^2/x^2,x]","-\frac{e^{2 a} 2^{\frac{1}{n}} \left(-b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-2 b x^n\right)+e^{-2 a} 2^{\frac{1}{n}} \left(b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},2 b x^n\right)-2 n}{4 n x}","-\frac{e^{2 a} 2^{\frac{1}{n}-2} \left(-b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-2 b x^n\right)}{n x}-\frac{e^{-2 a} 2^{\frac{1}{n}-2} \left(b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},2 b x^n\right)}{n x}+\frac{1}{2 x}",1,"-1/4*(-2*n + 2^n^(-1)*E^(2*a)*(-(b*x^n))^n^(-1)*Gamma[-n^(-1), -2*b*x^n] + (2^n^(-1)*(b*x^n)^n^(-1)*Gamma[-n^(-1), 2*b*x^n])/E^(2*a))/(n*x)","A",1
69,1,161,166,1.5384056,"\int x^2 \sinh ^3\left(a+b x^n\right) \, dx","Integrate[x^2*Sinh[a + b*x^n]^3,x]","-\frac{e^{-3 a} 27^{-1/n} x^3 \left(-b^2 x^{2 n}\right)^{-3/n} \left(\left(-b x^n\right)^{3/n} \left(e^{2 a} 3^{\frac{n+3}{n}} \Gamma \left(\frac{3}{n},b x^n\right)-\Gamma \left(\frac{3}{n},3 b x^n\right)\right)+e^{6 a} \left(b x^n\right)^{3/n} \Gamma \left(\frac{3}{n},-3 b x^n\right)-e^{4 a} 3^{\frac{n+3}{n}} \left(b x^n\right)^{3/n} \Gamma \left(\frac{3}{n},-b x^n\right)\right)}{8 n}","-\frac{e^{3 a} 3^{-3/n} x^3 \left(-b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-3 b x^n\right)}{8 n}+\frac{3 e^a x^3 \left(-b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-b x^n\right)}{8 n}-\frac{3 e^{-a} x^3 \left(b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},b x^n\right)}{8 n}+\frac{e^{-3 a} 3^{-3/n} x^3 \left(b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},3 b x^n\right)}{8 n}",1,"-1/8*(x^3*(E^(6*a)*(b*x^n)^(3/n)*Gamma[3/n, -3*b*x^n] - 3^((3 + n)/n)*E^(4*a)*(b*x^n)^(3/n)*Gamma[3/n, -(b*x^n)] + (-(b*x^n))^(3/n)*(3^((3 + n)/n)*E^(2*a)*Gamma[3/n, b*x^n] - Gamma[3/n, 3*b*x^n])))/(27^n^(-1)*E^(3*a)*n*(-(b^2*x^(2*n)))^(3/n))","A",1
70,1,161,166,1.5987325,"\int x \sinh ^3\left(a+b x^n\right) \, dx","Integrate[x*Sinh[a + b*x^n]^3,x]","-\frac{e^{-3 a} 9^{-1/n} x^2 \left(-b^2 x^{2 n}\right)^{-2/n} \left(\left(-b x^n\right)^{2/n} \left(e^{2 a} 3^{\frac{n+2}{n}} \Gamma \left(\frac{2}{n},b x^n\right)-\Gamma \left(\frac{2}{n},3 b x^n\right)\right)+e^{6 a} \left(b x^n\right)^{2/n} \Gamma \left(\frac{2}{n},-3 b x^n\right)-e^{4 a} 3^{\frac{n+2}{n}} \left(b x^n\right)^{2/n} \Gamma \left(\frac{2}{n},-b x^n\right)\right)}{8 n}","-\frac{e^{3 a} 9^{-1/n} x^2 \left(-b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-3 b x^n\right)}{8 n}+\frac{3 e^a x^2 \left(-b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-b x^n\right)}{8 n}-\frac{3 e^{-a} x^2 \left(b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},b x^n\right)}{8 n}+\frac{e^{-3 a} 9^{-1/n} x^2 \left(b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},3 b x^n\right)}{8 n}",1,"-1/8*(x^2*(E^(6*a)*(b*x^n)^(2/n)*Gamma[2/n, -3*b*x^n] - 3^((2 + n)/n)*E^(4*a)*(b*x^n)^(2/n)*Gamma[2/n, -(b*x^n)] + (-(b*x^n))^(2/n)*(3^((2 + n)/n)*E^(2*a)*Gamma[2/n, b*x^n] - Gamma[2/n, 3*b*x^n])))/(9^n^(-1)*E^(3*a)*n*(-(b^2*x^(2*n)))^(2/n))","A",1
71,1,140,150,1.2113062,"\int \sinh ^3\left(a+b x^n\right) \, dx","Integrate[Sinh[a + b*x^n]^3,x]","\frac{e^{-3 a} 3^{-1/n} x \left(-b^2 x^{2 n}\right)^{-1/n} \left(\left(-b x^n\right)^{\frac{1}{n}} \left(\Gamma \left(\frac{1}{n},3 b x^n\right)-e^{2 a} 3^{\frac{1}{n}+1} \Gamma \left(\frac{1}{n},b x^n\right)\right)-e^{6 a} \left(b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-3 b x^n\right)+e^{4 a} 3^{\frac{1}{n}+1} \left(b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-b x^n\right)\right)}{8 n}","-\frac{e^{3 a} 3^{-1/n} x \left(-b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-3 b x^n\right)}{8 n}+\frac{3 e^a x \left(-b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-b x^n\right)}{8 n}-\frac{3 e^{-a} x \left(b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},b x^n\right)}{8 n}+\frac{e^{-3 a} 3^{-1/n} x \left(b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},3 b x^n\right)}{8 n}",1,"(x*(-(E^(6*a)*(b*x^n)^n^(-1)*Gamma[n^(-1), -3*b*x^n]) + 3^(1 + n^(-1))*E^(4*a)*(b*x^n)^n^(-1)*Gamma[n^(-1), -(b*x^n)] + (-(b*x^n))^n^(-1)*(-(3^(1 + n^(-1))*E^(2*a)*Gamma[n^(-1), b*x^n]) + Gamma[n^(-1), 3*b*x^n])))/(8*3^n^(-1)*E^(3*a)*n*(-(b^2*x^(2*n)))^n^(-1))","A",1
72,1,52,67,0.0616103,"\int \frac{\sinh ^3\left(a+b x^n\right)}{x} \, dx","Integrate[Sinh[a + b*x^n]^3/x,x]","\frac{-3 \sinh (a) \text{Chi}\left(b x^n\right)+\sinh (3 a) \text{Chi}\left(3 b x^n\right)-3 \cosh (a) \text{Shi}\left(b x^n\right)+\cosh (3 a) \text{Shi}\left(3 b x^n\right)}{4 n}","-\frac{3 \sinh (a) \text{Chi}\left(b x^n\right)}{4 n}+\frac{\sinh (3 a) \text{Chi}\left(3 b x^n\right)}{4 n}-\frac{3 \cosh (a) \text{Shi}\left(b x^n\right)}{4 n}+\frac{\cosh (3 a) \text{Shi}\left(3 b x^n\right)}{4 n}",1,"(-3*CoshIntegral[b*x^n]*Sinh[a] + CoshIntegral[3*b*x^n]*Sinh[3*a] - 3*Cosh[a]*SinhIntegral[b*x^n] + Cosh[3*a]*SinhIntegral[3*b*x^n])/(4*n)","A",1
73,1,126,154,1.4077506,"\int \frac{\sinh ^3\left(a+b x^n\right)}{x^2} \, dx","Integrate[Sinh[a + b*x^n]^3/x^2,x]","\frac{e^{-3 a} \left(e^{6 a} \left(-3^{\frac{1}{n}}\right) \left(-b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-3 b x^n\right)+3 e^{4 a} \left(-b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-b x^n\right)+\left(b x^n\right)^{\frac{1}{n}} \left(3^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},3 b x^n\right)-3 e^{2 a} \Gamma \left(-\frac{1}{n},b x^n\right)\right)\right)}{8 n x}","-\frac{e^{3 a} 3^{\frac{1}{n}} \left(-b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-3 b x^n\right)}{8 n x}+\frac{3 e^a \left(-b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-b x^n\right)}{8 n x}-\frac{3 e^{-a} \left(b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},b x^n\right)}{8 n x}+\frac{e^{-3 a} 3^{\frac{1}{n}} \left(b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},3 b x^n\right)}{8 n x}",1,"(-(3^n^(-1)*E^(6*a)*(-(b*x^n))^n^(-1)*Gamma[-n^(-1), -3*b*x^n]) + 3*E^(4*a)*(-(b*x^n))^n^(-1)*Gamma[-n^(-1), -(b*x^n)] + (b*x^n)^n^(-1)*(-3*E^(2*a)*Gamma[-n^(-1), b*x^n] + 3^n^(-1)*Gamma[-n^(-1), 3*b*x^n]))/(8*E^(3*a)*n*x)","A",1
74,0,0,21,5.4057702,"\int (e x)^m \left(b \sinh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^m*(b*Sinh[c + d*x^n])^p,x]","\int (e x)^m \left(b \sinh \left(c+d x^n\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(b \sinh \left(c+d x^n\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(b*Sinh[c + d*x^n])^p, x]","A",-1
75,0,0,23,8.0763275,"\int (e x)^m \left(a+b \sinh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^m*(a + b*Sinh[c + d*x^n])^p,x]","\int (e x)^m \left(a+b \sinh \left(c+d x^n\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(a+b \sinh \left(c+d x^n\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(a + b*Sinh[c + d*x^n])^p, x]","A",-1
76,1,93,94,0.1351789,"\int (e x)^{-1+n} \left(b \sinh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + n)*(b*Sinh[c + d*x^n])^p,x]","-\frac{x^{-n} (e x)^n \sinh \left(2 \left(c+d x^n\right)\right) \left(-\sinh ^2\left(c+d x^n\right)\right)^{\frac{1}{2} (-p-1)} \left(b \sinh \left(c+d x^n\right)\right)^p \, _2F_1\left(\frac{1}{2},\frac{1-p}{2};\frac{3}{2};\cosh ^2\left(d x^n+c\right)\right)}{2 d e n}","\frac{x^{-n} (e x)^n \cosh \left(c+d x^n\right) \left(b \sinh \left(c+d x^n\right)\right)^{p+1} \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};-\sinh ^2\left(d x^n+c\right)\right)}{b d e n (p+1) \sqrt{\cosh ^2\left(c+d x^n\right)}}",1,"-1/2*((e*x)^n*Hypergeometric2F1[1/2, (1 - p)/2, 3/2, Cosh[c + d*x^n]^2]*(b*Sinh[c + d*x^n])^p*(-Sinh[c + d*x^n]^2)^((-1 - p)/2)*Sinh[2*(c + d*x^n)])/(d*e*n*x^n)","A",1
77,0,0,39,5.8954186,"\int (e x)^{-1+2 n} \left(b \sinh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + 2*n)*(b*Sinh[c + d*x^n])^p,x]","\int (e x)^{-1+2 n} \left(b \sinh \left(c+d x^n\right)\right)^p \, dx","\frac{x^{-2 n} (e x)^{2 n} \text{Int}\left(x^{2 n-1} \left(b \sinh \left(c+d x^n\right)\right)^p,x\right)}{e}",0,"Integrate[(e*x)^(-1 + 2*n)*(b*Sinh[c + d*x^n])^p, x]","A",-1
78,1,167,150,0.4105148,"\int (e x)^{-1+n} \left(a+b \sinh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + n)*(a + b*Sinh[c + d*x^n])^p,x]","\frac{x^{-n} (e x)^n \text{sech}\left(c+d x^n\right) \sqrt{\frac{b \left(1-i \sinh \left(c+d x^n\right)\right)}{b+i a}} \sqrt{\frac{b \left(1+i \sinh \left(c+d x^n\right)\right)}{b-i a}} \left(a+b \sinh \left(c+d x^n\right)\right)^{p+1} F_1\left(p+1;\frac{1}{2},\frac{1}{2};p+2;\frac{a+b \sinh \left(d x^n+c\right)}{a+i b},\frac{a+b \sinh \left(d x^n+c\right)}{a-i b}\right)}{b d e n (p+1)}","\frac{i \sqrt{2} x^{-n} (e x)^n \cosh \left(c+d x^n\right) \left(a+b \sinh \left(c+d x^n\right)\right)^p \left(\frac{a+b \sinh \left(c+d x^n\right)}{a-i b}\right)^{-p} F_1\left(\frac{1}{2};\frac{1}{2},-p;\frac{3}{2};\frac{1}{2} \left(1-i \sinh \left(d x^n+c\right)\right),\frac{b \left(1-i \sinh \left(d x^n+c\right)\right)}{i a+b}\right)}{d e n \sqrt{1+i \sinh \left(c+d x^n\right)}}",1,"((e*x)^n*AppellF1[1 + p, 1/2, 1/2, 2 + p, (a + b*Sinh[c + d*x^n])/(a + I*b), (a + b*Sinh[c + d*x^n])/(a - I*b)]*Sech[c + d*x^n]*Sqrt[(b*(1 - I*Sinh[c + d*x^n]))/(I*a + b)]*Sqrt[(b*(1 + I*Sinh[c + d*x^n]))/((-I)*a + b)]*(a + b*Sinh[c + d*x^n])^(1 + p))/(b*d*e*n*(1 + p)*x^n)","A",0
79,0,0,41,8.4472663,"\int (e x)^{-1+2 n} \left(a+b \sinh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + 2*n)*(a + b*Sinh[c + d*x^n])^p,x]","\int (e x)^{-1+2 n} \left(a+b \sinh \left(c+d x^n\right)\right)^p \, dx","\frac{x^{-2 n} (e x)^{2 n} \text{Int}\left(x^{2 n-1} \left(a+b \sinh \left(c+d x^n\right)\right)^p,x\right)}{e}",0,"Integrate[(e*x)^(-1 + 2*n)*(a + b*Sinh[c + d*x^n])^p, x]","A",-1
80,1,185,220,2.1511831,"\int (e x)^m \sinh ^3\left(a+b x^n\right) \, dx","Integrate[(e*x)^m*Sinh[a + b*x^n]^3,x]","\frac{e^{-3 a} x 3^{-\frac{m+1}{n}} (e x)^m \left(-b^2 x^{2 n}\right)^{-\frac{m+1}{n}} \left(\left(-b x^n\right)^{\frac{m+1}{n}} \left(\Gamma \left(\frac{m+1}{n},3 b x^n\right)-e^{2 a} 3^{\frac{m+n+1}{n}} \Gamma \left(\frac{m+1}{n},b x^n\right)\right)-e^{6 a} \left(b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-3 b x^n\right)+e^{4 a} 3^{\frac{m+n+1}{n}} \left(b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-b x^n\right)\right)}{8 n}","-\frac{e^{3 a} 3^{-\frac{m+1}{n}} (e x)^{m+1} \left(-b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-3 b x^n\right)}{8 e n}+\frac{3 e^a (e x)^{m+1} \left(-b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-b x^n\right)}{8 e n}-\frac{3 e^{-a} (e x)^{m+1} \left(b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},b x^n\right)}{8 e n}+\frac{e^{-3 a} 3^{-\frac{m+1}{n}} (e x)^{m+1} \left(b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},3 b x^n\right)}{8 e n}",1,"(x*(e*x)^m*(-(E^(6*a)*(b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, -3*b*x^n]) + 3^((1 + m + n)/n)*E^(4*a)*(b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, -(b*x^n)] + (-(b*x^n))^((1 + m)/n)*(-(3^((1 + m + n)/n)*E^(2*a)*Gamma[(1 + m)/n, b*x^n]) + Gamma[(1 + m)/n, 3*b*x^n])))/(8*3^((1 + m)/n)*E^(3*a)*n*(-(b^2*x^(2*n)))^((1 + m)/n))","A",1
81,1,117,143,1.9984181,"\int (e x)^m \sinh ^2\left(a+b x^n\right) \, dx","Integrate[(e*x)^m*Sinh[a + b*x^n]^2,x]","-\frac{x (e x)^m \left(e^{2 a} (m+1) 2^{-\frac{m+1}{n}} \left(-b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-2 b x^n\right)+e^{-2 a} (m+1) 2^{-\frac{m+1}{n}} \left(b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},2 b x^n\right)+2 n\right)}{4 (m+1) n}","-\frac{e^{2 a} 2^{-\frac{m+2 n+1}{n}} (e x)^{m+1} \left(-b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-2 b x^n\right)}{e n}-\frac{e^{-2 a} 2^{-\frac{m+2 n+1}{n}} (e x)^{m+1} \left(b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},2 b x^n\right)}{e n}-\frac{(e x)^{m+1}}{2 e (m+1)}",1,"-1/4*(x*(e*x)^m*(2*n + (E^(2*a)*(1 + m)*Gamma[(1 + m)/n, -2*b*x^n])/(2^((1 + m)/n)*(-(b*x^n))^((1 + m)/n)) + ((1 + m)*Gamma[(1 + m)/n, 2*b*x^n])/(2^((1 + m)/n)*E^(2*a)*(b*x^n)^((1 + m)/n))))/((1 + m)*n)","A",1
82,1,102,99,0.1816178,"\int (e x)^m \sinh \left(a+b x^n\right) \, dx","Integrate[(e*x)^m*Sinh[a + b*x^n],x]","-\frac{x (e x)^m \left(-b^2 x^{2 n}\right)^{-\frac{m+1}{n}} \left((\sinh (a)+\cosh (a)) \left(b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-b x^n\right)-(\cosh (a)-\sinh (a)) \left(-b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},b x^n\right)\right)}{2 n}","\frac{e^{-a} (e x)^{m+1} \left(b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},b x^n\right)}{2 e n}-\frac{e^a (e x)^{m+1} \left(-b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-b x^n\right)}{2 e n}",1,"-1/2*(x*(e*x)^m*(-((-(b*x^n))^((1 + m)/n)*Gamma[(1 + m)/n, b*x^n]*(Cosh[a] - Sinh[a])) + (b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, -(b*x^n)]*(Cosh[a] + Sinh[a])))/(n*(-(b^2*x^(2*n)))^((1 + m)/n))","A",1
83,0,0,28,24.3373014,"\int (e x)^m \text{csch}^2\left(a+b x^n\right) \, dx","Integrate[(e*x)^m*Csch[a + b*x^n]^2,x]","\int (e x)^m \text{csch}^2\left(a+b x^n\right) \, dx","x^{-m} (e x)^m \text{Int}\left(x^m \text{csch}^2\left(a+b x^n\right),x\right)",0,"Integrate[(e*x)^m*Csch[a + b*x^n]^2, x]","A",-1
84,1,46,45,0.0666812,"\int x^{-1-n} \sinh \left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Sinh[a + b*x^n],x]","\frac{x^{-n} \left(b \cosh (a) x^n \text{Chi}\left(b x^n\right)+b \sinh (a) x^n \text{Shi}\left(b x^n\right)-\sinh \left(a+b x^n\right)\right)}{n}","\frac{b \cosh (a) \text{Chi}\left(b x^n\right)}{n}+\frac{b \sinh (a) \text{Shi}\left(b x^n\right)}{n}-\frac{x^{-n} \sinh \left(a+b x^n\right)}{n}",1,"(b*x^n*Cosh[a]*CoshIntegral[b*x^n] - Sinh[a + b*x^n] + b*x^n*Sinh[a]*SinhIntegral[b*x^n])/(n*x^n)","A",1
85,1,54,67,0.1377692,"\int x^{-1-n} \sinh ^2\left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Sinh[a + b*x^n]^2,x]","\frac{x^{-n} \left(b \sinh (2 a) x^n \text{Chi}\left(2 b x^n\right)+b \cosh (2 a) x^n \text{Shi}\left(2 b x^n\right)-\sinh ^2\left(a+b x^n\right)\right)}{n}","\frac{b \sinh (2 a) \text{Chi}\left(2 b x^n\right)}{n}+\frac{b \cosh (2 a) \text{Shi}\left(2 b x^n\right)}{n}-\frac{x^{-n} \cosh \left(2 \left(a+b x^n\right)\right)}{2 n}+\frac{x^{-n}}{2 n}",1,"(b*x^n*CoshIntegral[2*b*x^n]*Sinh[2*a] - Sinh[a + b*x^n]^2 + b*x^n*Cosh[2*a]*SinhIntegral[2*b*x^n])/(n*x^n)","A",1
86,1,95,113,0.2187793,"\int x^{-1-n} \sinh ^3\left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Sinh[a + b*x^n]^3,x]","-\frac{x^{-n} \left(3 b \cosh (a) x^n \text{Chi}\left(b x^n\right)-3 b \cosh (3 a) x^n \text{Chi}\left(3 b x^n\right)+3 b \sinh (a) x^n \text{Shi}\left(b x^n\right)-3 b \sinh (3 a) x^n \text{Shi}\left(3 b x^n\right)-3 \sinh \left(a+b x^n\right)+\sinh \left(3 \left(a+b x^n\right)\right)\right)}{4 n}","-\frac{3 b \cosh (a) \text{Chi}\left(b x^n\right)}{4 n}+\frac{3 b \cosh (3 a) \text{Chi}\left(3 b x^n\right)}{4 n}-\frac{3 b \sinh (a) \text{Shi}\left(b x^n\right)}{4 n}+\frac{3 b \sinh (3 a) \text{Shi}\left(3 b x^n\right)}{4 n}+\frac{3 x^{-n} \sinh \left(a+b x^n\right)}{4 n}-\frac{x^{-n} \sinh \left(3 \left(a+b x^n\right)\right)}{4 n}",1,"-1/4*(3*b*x^n*Cosh[a]*CoshIntegral[b*x^n] - 3*b*x^n*Cosh[3*a]*CoshIntegral[3*b*x^n] - 3*Sinh[a + b*x^n] + Sinh[3*(a + b*x^n)] + 3*b*x^n*Sinh[a]*SinhIntegral[b*x^n] - 3*b*x^n*Sinh[3*a]*SinhIntegral[3*b*x^n])/(n*x^n)","A",1
87,1,60,71,1.5771424,"\int x^{-1+\frac{n}{2}} \sinh \left(a+b x^n\right) \, dx","Integrate[x^(-1 + n/2)*Sinh[a + b*x^n],x]","\frac{\sqrt{\pi } \left((\sinh (a)-\cosh (a)) \text{erf}\left(\sqrt{b} x^{n/2}\right)+(\sinh (a)+\cosh (a)) \text{erfi}\left(\sqrt{b} x^{n/2}\right)\right)}{2 \sqrt{b} n}","\frac{\sqrt{\pi } e^a \text{erfi}\left(\sqrt{b} x^{n/2}\right)}{2 \sqrt{b} n}-\frac{\sqrt{\pi } e^{-a} \text{erf}\left(\sqrt{b} x^{n/2}\right)}{2 \sqrt{b} n}",1,"(Sqrt[Pi]*(Erf[Sqrt[b]*x^(n/2)]*(-Cosh[a] + Sinh[a]) + Erfi[Sqrt[b]*x^(n/2)]*(Cosh[a] + Sinh[a])))/(2*Sqrt[b]*n)","A",1
88,1,63,113,0.1381256,"\int x^2 \sinh \left((a+b x)^2\right) \, dx","Integrate[x^2*Sinh[(a + b*x)^2],x]","\frac{-\sqrt{\pi } \left(2 a^2+1\right) \text{erf}(a+b x)+\sqrt{\pi } \left(2 a^2-1\right) \text{erfi}(a+b x)-4 (a-b x) \cosh \left((a+b x)^2\right)}{8 b^3}","-\frac{\sqrt{\pi } a^2 \text{erf}(a+b x)}{4 b^3}+\frac{\sqrt{\pi } a^2 \text{erfi}(a+b x)}{4 b^3}-\frac{\sqrt{\pi } \text{erf}(a+b x)}{8 b^3}-\frac{\sqrt{\pi } \text{erfi}(a+b x)}{8 b^3}-\frac{a \cosh \left((a+b x)^2\right)}{b^3}+\frac{(a+b x) \cosh \left((a+b x)^2\right)}{2 b^3}",1,"(-4*(a - b*x)*Cosh[(a + b*x)^2] - (1 + 2*a^2)*Sqrt[Pi]*Erf[a + b*x] + (-1 + 2*a^2)*Sqrt[Pi]*Erfi[a + b*x])/(8*b^3)","A",1
89,1,44,54,0.0280433,"\int x \sinh \left((a+b x)^2\right) \, dx","Integrate[x*Sinh[(a + b*x)^2],x]","\frac{\cosh \left((a+b x)^2\right)}{2 b^2}-\frac{\sqrt{\pi } a (\text{erfi}(a+b x)-\text{erf}(a+b x))}{4 b^2}","\frac{\sqrt{\pi } a \text{erf}(a+b x)}{4 b^2}-\frac{\sqrt{\pi } a \text{erfi}(a+b x)}{4 b^2}+\frac{\cosh \left((a+b x)^2\right)}{2 b^2}",1,"Cosh[(a + b*x)^2]/(2*b^2) - (a*Sqrt[Pi]*(-Erf[a + b*x] + Erfi[a + b*x]))/(4*b^2)","A",1
90,1,27,37,0.0046164,"\int \sinh \left((a+b x)^2\right) \, dx","Integrate[Sinh[(a + b*x)^2],x]","\frac{\sqrt{\pi } (\text{erfi}(a+b x)-\text{erf}(a+b x))}{4 b}","\frac{\sqrt{\pi } \text{erfi}(a+b x)}{4 b}-\frac{\sqrt{\pi } \text{erf}(a+b x)}{4 b}",1,"(Sqrt[Pi]*(-Erf[a + b*x] + Erfi[a + b*x]))/(4*b)","A",1
91,0,0,20,9.9825655,"\int \frac{\sinh \left((a+b x)^2\right)}{x} \, dx","Integrate[Sinh[(a + b*x)^2]/x,x]","\int \frac{\sinh \left((a+b x)^2\right)}{x} \, dx","b \text{Int}\left(\frac{\sinh \left((a+b x)^2\right)}{b x},x\right)",0,"Integrate[Sinh[(a + b*x)^2]/x, x]","A",-1
92,0,0,15,13.4056686,"\int \frac{\sinh \left((a+b x)^2\right)}{x^2} \, dx","Integrate[Sinh[(a + b*x)^2]/x^2,x]","\int \frac{\sinh \left((a+b x)^2\right)}{x^2} \, dx","\text{Int}\left(\frac{\sinh \left((a+b x)^2\right)}{x^2},x\right)",0,"Integrate[Sinh[(a + b*x)^2]/x^2, x]","A",-1
93,1,104,346,1.3015131,"\int x^2 \sinh \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[x^2*Sinh[a + b*Sqrt[c + d*x]],x]","\frac{2 b \sqrt{c+d x} \left(b^4 d^2 x^2+4 b^2 (2 c+5 d x)+120\right) \cosh \left(a+b \sqrt{c+d x}\right)-2 \left(b^4 d x (4 c+5 d x)+12 b^2 (4 c+5 d x)+120\right) \sinh \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}","-\frac{240 \sinh \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}+\frac{240 \sqrt{c+d x} \cosh \left(a+b \sqrt{c+d x}\right)}{b^5 d^3}-\frac{120 (c+d x) \sinh \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{24 c \sinh \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{40 (c+d x)^{3/2} \cosh \left(a+b \sqrt{c+d x}\right)}{b^3 d^3}-\frac{24 c \sqrt{c+d x} \cosh \left(a+b \sqrt{c+d x}\right)}{b^3 d^3}-\frac{2 c^2 \sinh \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{10 (c+d x)^2 \sinh \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}+\frac{12 c (c+d x) \sinh \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}+\frac{2 c^2 \sqrt{c+d x} \cosh \left(a+b \sqrt{c+d x}\right)}{b d^3}+\frac{2 (c+d x)^{5/2} \cosh \left(a+b \sqrt{c+d x}\right)}{b d^3}-\frac{4 c (c+d x)^{3/2} \cosh \left(a+b \sqrt{c+d x}\right)}{b d^3}",1,"(2*b*Sqrt[c + d*x]*(120 + b^4*d^2*x^2 + 4*b^2*(2*c + 5*d*x))*Cosh[a + b*Sqrt[c + d*x]] - 2*(120 + 12*b^2*(4*c + 5*d*x) + b^4*d*x*(4*c + 5*d*x))*Sinh[a + b*Sqrt[c + d*x]])/(b^6*d^3)","A",1
94,1,72,167,0.2069126,"\int x \sinh \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[x*Sinh[a + b*Sqrt[c + d*x]],x]","\frac{2 b \left(b^2 d x+6\right) \sqrt{c+d x} \cosh \left(a+b \sqrt{c+d x}\right)-2 \left(b^2 (2 c+3 d x)+6\right) \sinh \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}","-\frac{12 \sinh \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}+\frac{12 \sqrt{c+d x} \cosh \left(a+b \sqrt{c+d x}\right)}{b^3 d^2}-\frac{6 (c+d x) \sinh \left(a+b \sqrt{c+d x}\right)}{b^2 d^2}+\frac{2 c \sinh \left(a+b \sqrt{c+d x}\right)}{b^2 d^2}+\frac{2 (c+d x)^{3/2} \cosh \left(a+b \sqrt{c+d x}\right)}{b d^2}-\frac{2 c \sqrt{c+d x} \cosh \left(a+b \sqrt{c+d x}\right)}{b d^2}",1,"(2*b*Sqrt[c + d*x]*(6 + b^2*d*x)*Cosh[a + b*Sqrt[c + d*x]] - 2*(6 + b^2*(2*c + 3*d*x))*Sinh[a + b*Sqrt[c + d*x]])/(b^4*d^2)","A",1
95,1,50,54,0.0630328,"\int \sinh \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[Sinh[a + b*Sqrt[c + d*x]],x]","\frac{2 \left(b \sqrt{c+d x} \cosh \left(a+b \sqrt{c+d x}\right)-\sinh \left(a+b \sqrt{c+d x}\right)\right)}{b^2 d}","\frac{2 \sqrt{c+d x} \cosh \left(a+b \sqrt{c+d x}\right)}{b d}-\frac{2 \sinh \left(a+b \sqrt{c+d x}\right)}{b^2 d}",1,"(2*(b*Sqrt[c + d*x]*Cosh[a + b*Sqrt[c + d*x]] - Sinh[a + b*Sqrt[c + d*x]]))/(b^2*d)","A",1
96,1,130,124,0.9889061,"\int \frac{\sinh \left(a+b \sqrt{c+d x}\right)}{x} \, dx","Integrate[Sinh[a + b*Sqrt[c + d*x]]/x,x]","\frac{1}{2} e^{-a-b \sqrt{c}} \left(e^{2 \left(a+b \sqrt{c}\right)} \text{Ei}\left(b \left(\sqrt{c+d x}-\sqrt{c}\right)\right)+e^{2 a} \text{Ei}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)-\text{Ei}\left(b \left(\sqrt{c}-\sqrt{c+d x}\right)\right)-e^{2 b \sqrt{c}} \text{Ei}\left(-b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)\right)","\sinh \left(a-b \sqrt{c}\right) \text{Chi}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)+\sinh \left(a+b \sqrt{c}\right) \text{Chi}\left(b \left(\sqrt{c}-\sqrt{c+d x}\right)\right)-\cosh \left(a+b \sqrt{c}\right) \text{Shi}\left(b \left(\sqrt{c}-\sqrt{c+d x}\right)\right)+\cosh \left(a-b \sqrt{c}\right) \text{Shi}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)",1,"(E^(-a - b*Sqrt[c])*(-ExpIntegralEi[b*(Sqrt[c] - Sqrt[c + d*x])] + E^(2*(a + b*Sqrt[c]))*ExpIntegralEi[b*(-Sqrt[c] + Sqrt[c + d*x])] - E^(2*b*Sqrt[c])*ExpIntegralEi[-(b*(Sqrt[c] + Sqrt[c + d*x]))] + E^(2*a)*ExpIntegralEi[b*(Sqrt[c] + Sqrt[c + d*x])]))/2","A",1
97,1,199,182,3.0924067,"\int \frac{\sinh \left(a+b \sqrt{c+d x}\right)}{x^2} \, dx","Integrate[Sinh[a + b*Sqrt[c + d*x]]/x^2,x]","\frac{e^{-a} \left(b d x e^{-b \sqrt{c}} \text{Ei}\left(b \left(\sqrt{c}-\sqrt{c+d x}\right)\right)-b d x e^{b \sqrt{c}} \text{Ei}\left(-b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)+2 \sqrt{c} e^{-b \sqrt{c+d x}}\right)+e^a \left(b d x e^{b \sqrt{c}} \text{Ei}\left(b \left(\sqrt{c+d x}-\sqrt{c}\right)\right)-b d x e^{-b \sqrt{c}} \text{Ei}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)-2 \sqrt{c} e^{b \sqrt{c+d x}}\right)}{4 \sqrt{c} x}","\frac{b d \cosh \left(a+b \sqrt{c}\right) \text{Chi}\left(b \left(\sqrt{c}-\sqrt{c+d x}\right)\right)}{2 \sqrt{c}}-\frac{b d \cosh \left(a-b \sqrt{c}\right) \text{Chi}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)}{2 \sqrt{c}}-\frac{b d \sinh \left(a+b \sqrt{c}\right) \text{Shi}\left(b \left(\sqrt{c}-\sqrt{c+d x}\right)\right)}{2 \sqrt{c}}-\frac{b d \sinh \left(a-b \sqrt{c}\right) \text{Shi}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)}{2 \sqrt{c}}-\frac{\sinh \left(a+b \sqrt{c+d x}\right)}{x}",1,"(((2*Sqrt[c])/E^(b*Sqrt[c + d*x]) + (b*d*x*ExpIntegralEi[b*(Sqrt[c] - Sqrt[c + d*x])])/E^(b*Sqrt[c]) - b*d*E^(b*Sqrt[c])*x*ExpIntegralEi[-(b*(Sqrt[c] + Sqrt[c + d*x]))])/E^a + E^a*(-2*Sqrt[c]*E^(b*Sqrt[c + d*x]) + b*d*E^(b*Sqrt[c])*x*ExpIntegralEi[b*(-Sqrt[c] + Sqrt[c + d*x])] - (b*d*x*ExpIntegralEi[b*(Sqrt[c] + Sqrt[c + d*x])])/E^(b*Sqrt[c])))/(4*Sqrt[c]*x)","A",1
98,1,378,537,2.9023562,"\int x^2 \sinh \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[x^2*Sinh[a + b*(c + d*x)^(1/3)],x]","\frac{3 \left((\sinh (a)+\cosh (a)) \left(b^8 d^2 x^2 (c+d x)^{2/3}-2 b^7 d x \sqrt[3]{c+d x} (3 c+4 d x)+2 b^6 \left(9 c^2+36 c d x+28 d^2 x^2\right)-24 b^5 (c+d x)^{2/3} (9 c+14 d x)+240 b^4 \sqrt[3]{c+d x} (6 c+7 d x)-240 b^3 (27 c+28 d x)+20160 b^2 (c+d x)^{2/3}-40320 b \sqrt[3]{c+d x}+40320\right) \left(\sinh \left(b \sqrt[3]{c+d x}\right)+\cosh \left(b \sqrt[3]{c+d x}\right)\right)+\left(b^8 d^2 x^2 (c+d x)^{2/3}+2 b^7 d x \sqrt[3]{c+d x} (3 c+4 d x)+2 b^6 \left(9 c^2+36 c d x+28 d^2 x^2\right)+24 b^5 (c+d x)^{2/3} (9 c+14 d x)+240 b^4 \sqrt[3]{c+d x} (6 c+7 d x)+240 b^3 (27 c+28 d x)+20160 b^2 (c+d x)^{2/3}+40320 b \sqrt[3]{c+d x}+40320\right) \left(\cosh \left(a+b \sqrt[3]{c+d x}\right)-\sinh \left(a+b \sqrt[3]{c+d x}\right)\right)\right)}{2 b^9 d^3}","\frac{120960 \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^9 d^3}-\frac{120960 \sqrt[3]{c+d x} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^8 d^3}+\frac{60480 (c+d x)^{2/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^7 d^3}-\frac{20160 (c+d x) \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}+\frac{720 c \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}+\frac{5040 (c+d x)^{4/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^3}-\frac{720 c \sqrt[3]{c+d x} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^3}-\frac{1008 (c+d x)^{5/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}+\frac{360 c (c+d x)^{2/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}+\frac{6 c^2 \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}+\frac{168 (c+d x)^2 \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}-\frac{120 c (c+d x) \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}-\frac{6 c^2 \sqrt[3]{c+d x} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}-\frac{24 (c+d x)^{7/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}+\frac{30 c (c+d x)^{4/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}+\frac{3 c^2 (c+d x)^{2/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}+\frac{3 (c+d x)^{8/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}-\frac{6 c (c+d x)^{5/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}",1,"(3*((40320 - 40320*b*(c + d*x)^(1/3) + 20160*b^2*(c + d*x)^(2/3) + b^8*d^2*x^2*(c + d*x)^(2/3) - 2*b^7*d*x*(c + d*x)^(1/3)*(3*c + 4*d*x) + 240*b^4*(c + d*x)^(1/3)*(6*c + 7*d*x) - 24*b^5*(c + d*x)^(2/3)*(9*c + 14*d*x) - 240*b^3*(27*c + 28*d*x) + 2*b^6*(9*c^2 + 36*c*d*x + 28*d^2*x^2))*(Cosh[a] + Sinh[a])*(Cosh[b*(c + d*x)^(1/3)] + Sinh[b*(c + d*x)^(1/3)]) + (40320 + 40320*b*(c + d*x)^(1/3) + 20160*b^2*(c + d*x)^(2/3) + b^8*d^2*x^2*(c + d*x)^(2/3) + 2*b^7*d*x*(c + d*x)^(1/3)*(3*c + 4*d*x) + 240*b^4*(c + d*x)^(1/3)*(6*c + 7*d*x) + 24*b^5*(c + d*x)^(2/3)*(9*c + 14*d*x) + 240*b^3*(27*c + 28*d*x) + 2*b^6*(9*c^2 + 36*c*d*x + 28*d^2*x^2))*(Cosh[a + b*(c + d*x)^(1/3)] - Sinh[a + b*(c + d*x)^(1/3)])))/(2*b^9*d^3)","A",1
99,1,118,261,0.3483396,"\int x \sinh \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[x*Sinh[a + b*(c + d*x)^(1/3)],x]","\frac{3 b \left(b^4 d x (c+d x)^{2/3}+2 b^2 (9 c+10 d x)+120 \sqrt[3]{c+d x}\right) \cosh \left(a+b \sqrt[3]{c+d x}\right)-3 \left(b^4 \sqrt[3]{c+d x} (3 c+5 d x)+60 b^2 (c+d x)^{2/3}+120\right) \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^2}","-\frac{360 \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^2}+\frac{360 \sqrt[3]{c+d x} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^2}-\frac{180 (c+d x)^{2/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^2}+\frac{60 (c+d x) \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^2}-\frac{6 c \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^2}-\frac{15 (c+d x)^{4/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^2}+\frac{6 c \sqrt[3]{c+d x} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^2}+\frac{3 (c+d x)^{5/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b d^2}-\frac{3 c (c+d x)^{2/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b d^2}",1,"(3*b*(120*(c + d*x)^(1/3) + b^4*d*x*(c + d*x)^(2/3) + 2*b^2*(9*c + 10*d*x))*Cosh[a + b*(c + d*x)^(1/3)] - 3*(120 + 60*b^2*(c + d*x)^(2/3) + b^4*(c + d*x)^(1/3)*(3*c + 5*d*x))*Sinh[a + b*(c + d*x)^(1/3)])/(b^6*d^2)","A",1
100,1,65,85,0.0857406,"\int \sinh \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[Sinh[a + b*(c + d*x)^(1/3)],x]","\frac{3 \left(b^2 (c+d x)^{2/3}+2\right) \cosh \left(a+b \sqrt[3]{c+d x}\right)-6 b \sqrt[3]{c+d x} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}","\frac{6 \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}-\frac{6 \sqrt[3]{c+d x} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d}+\frac{3 (c+d x)^{2/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b d}",1,"(3*(2 + b^2*(c + d*x)^(2/3))*Cosh[a + b*(c + d*x)^(1/3)] - 6*b*(c + d*x)^(1/3)*Sinh[a + b*(c + d*x)^(1/3)])/(b^3*d)","A",1
101,1,233,232,0.069781,"\int \frac{\sinh \left(a+b \sqrt[3]{c+d x}\right)}{x} \, dx","Integrate[Sinh[a + b*(c + d*x)^(1/3)]/x,x]","\frac{1}{2} \left(\text{RootSum}\left[c-\text{$\#$1}^3\&,\sinh (\text{$\#$1} b+a) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\cosh (\text{$\#$1} b+a) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\sinh (\text{$\#$1} b+a) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\cosh (\text{$\#$1} b+a) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)\&\right]-\text{RootSum}\left[c-\text{$\#$1}^3\&,-\sinh (\text{$\#$1} b+a) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\cosh (\text{$\#$1} b+a) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\sinh (\text{$\#$1} b+a) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)-\cosh (\text{$\#$1} b+a) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)\&\right]\right)","\sinh \left(a+b \sqrt[3]{c}\right) \text{Chi}\left(b \left(\sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)+\sinh \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Chi}\left(b \left(\sqrt[3]{-1} \sqrt[3]{c}+\sqrt[3]{c+d x}\right)\right)+\sinh \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Chi}\left(-b \left((-1)^{2/3} \sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)-\cosh \left(a+b \sqrt[3]{c}\right) \text{Shi}\left(b \left(\sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)-\cosh \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Shi}\left(b \left((-1)^{2/3} \sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)+\cosh \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Shi}\left(b \left(\sqrt[3]{-1} \sqrt[3]{c}+\sqrt[3]{c+d x}\right)\right)",1,"(-RootSum[c - #1^3 & , Cosh[a + b*#1]*CoshIntegral[b*((c + d*x)^(1/3) - #1)] - CoshIntegral[b*((c + d*x)^(1/3) - #1)]*Sinh[a + b*#1] - Cosh[a + b*#1]*SinhIntegral[b*((c + d*x)^(1/3) - #1)] + Sinh[a + b*#1]*SinhIntegral[b*((c + d*x)^(1/3) - #1)] & ] + RootSum[c - #1^3 & , Cosh[a + b*#1]*CoshIntegral[b*((c + d*x)^(1/3) - #1)] + CoshIntegral[b*((c + d*x)^(1/3) - #1)]*Sinh[a + b*#1] + Cosh[a + b*#1]*SinhIntegral[b*((c + d*x)^(1/3) - #1)] + Sinh[a + b*#1]*SinhIntegral[b*((c + d*x)^(1/3) - #1)] & ])/2","C",1
102,1,210,329,1.8491352,"\int \frac{\sinh \left(a+b \sqrt[3]{c+d x}\right)}{x^2} \, dx","Integrate[Sinh[a + b*(c + d*x)^(1/3)]/x^2,x]","\frac{e^{-a} \left(b d x \text{RootSum}\left[c-\text{$\#$1}^3\&,\frac{-\sinh (\text{$\#$1} b) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\cosh (\text{$\#$1} b) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\sinh (\text{$\#$1} b) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)-\cosh (\text{$\#$1} b) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)}{\text{$\#$1}^2}\&\right]-3 e^{2 a+b \sqrt[3]{c+d x}}+3 e^{-b \sqrt[3]{c+d x}}\right)+b d x \text{RootSum}\left[c-\text{$\#$1}^3\&,\frac{e^{\text{$\#$1} b+a} \text{Ei}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)}{\text{$\#$1}^2}\&\right]}{6 x}","\frac{b d \cosh \left(a+b \sqrt[3]{c}\right) \text{Chi}\left(b \left(\sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)}{3 c^{2/3}}+\frac{(-1)^{2/3} b d \cosh \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Chi}\left(-b \left((-1)^{2/3} \sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)}{3 c^{2/3}}-\frac{\sqrt[3]{-1} b d \cosh \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Chi}\left(b \left(\sqrt[3]{-1} \sqrt[3]{c}+\sqrt[3]{c+d x}\right)\right)}{3 c^{2/3}}-\frac{b d \sinh \left(a+b \sqrt[3]{c}\right) \text{Shi}\left(b \left(\sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)}{3 c^{2/3}}-\frac{(-1)^{2/3} b d \sinh \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Shi}\left(b \left((-1)^{2/3} \sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)}{3 c^{2/3}}-\frac{\sqrt[3]{-1} b d \sinh \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Shi}\left(b \left(\sqrt[3]{-1} \sqrt[3]{c}+\sqrt[3]{c+d x}\right)\right)}{3 c^{2/3}}-\frac{\sinh \left(a+b \sqrt[3]{c+d x}\right)}{x}",1,"(b*d*x*RootSum[c - #1^3 & , (E^(a + b*#1)*ExpIntegralEi[b*((c + d*x)^(1/3) - #1)])/#1^2 & ] + (3/E^(b*(c + d*x)^(1/3)) - 3*E^(2*a + b*(c + d*x)^(1/3)) + b*d*x*RootSum[c - #1^3 & , (Cosh[b*#1]*CoshIntegral[b*((c + d*x)^(1/3) - #1)] - CoshIntegral[b*((c + d*x)^(1/3) - #1)]*Sinh[b*#1] - Cosh[b*#1]*SinhIntegral[b*((c + d*x)^(1/3) - #1)] + Sinh[b*#1]*SinhIntegral[b*((c + d*x)^(1/3) - #1)])/#1^2 & ])/E^a)/(6*x)","C",1