1,1,31,34,0.0413171,"\int x^3 \cosh \left(a+b x^2\right) \, dx","Integrate[x^3*Cosh[a + b*x^2],x]","\frac{b x^2 \sinh \left(a+b x^2\right)-\cosh \left(a+b x^2\right)}{2 b^2}","\frac{x^2 \sinh \left(a+b x^2\right)}{2 b}-\frac{\cosh \left(a+b x^2\right)}{2 b^2}",1,"(-Cosh[a + b*x^2] + b*x^2*Sinh[a + b*x^2])/(2*b^2)","A",1
2,1,67,69,0.0758256,"\int x^2 \cosh \left(a+b x^2\right) \, dx","Integrate[x^2*Cosh[a + b*x^2],x]","\frac{\sqrt{\pi } (\cosh (a)-\sinh (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 \sinh \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 \sinh \left(a+b x^2\right)}{2 b}",1,"(Sqrt[Pi]*Erf[Sqrt[b]*x]*(Cosh[a] - Sinh[a]) - Sqrt[Pi]*Erfi[Sqrt[b]*x]*(Cosh[a] + Sinh[a]) + 4*Sqrt[b]*x*Sinh[a + b*x^2])/(8*b^(3/2))","A",1
3,1,31,15,0.0101369,"\int x \cosh \left(a+b x^2\right) \, dx","Integrate[x*Cosh[a + b*x^2],x]","\frac{\sinh (a) \cosh \left(b x^2\right)}{2 b}+\frac{\cosh (a) \sinh \left(b x^2\right)}{2 b}","\frac{\sinh \left(a+b x^2\right)}{2 b}",1,"(Cosh[b*x^2]*Sinh[a])/(2*b) + (Cosh[a]*Sinh[b*x^2])/(2*b)","B",1
4,1,45,53,0.031561,"\int \cosh \left(a+b x^2\right) \, dx","Integrate[Cosh[a + b*x^2],x]","\frac{\sqrt{\pi } \left((\cosh (a)-\sinh (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{erf}\left(\sqrt{b} x\right)}{4 \sqrt{b}}+\frac{\sqrt{\pi } e^a \text{erfi}\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
5,1,23,25,0.0155529,"\int \frac{\cosh \left(a+b x^2\right)}{x} \, dx","Integrate[Cosh[a + b*x^2]/x,x]","\frac{1}{2} \left(\cosh (a) \text{Chi}\left(b x^2\right)+\sinh (a) \text{Shi}\left(b x^2\right)\right)","\frac{1}{2} \cosh (a) \text{Chi}\left(b x^2\right)+\frac{1}{2} \sinh (a) \text{Shi}\left(b x^2\right)",1,"(Cosh[a]*CoshIntegral[b*x^2] + Sinh[a]*SinhIntegral[b*x^2])/2","A",1
6,1,70,66,0.0740239,"\int \frac{\cosh \left(a+b x^2\right)}{x^2} \, dx","Integrate[Cosh[a + b*x^2]/x^2,x]","\frac{\sqrt{\pi } \sqrt{b} x (\sinh (a)-\cosh (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 \cosh \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{\cosh \left(a+b x^2\right)}{x}",1,"(-2*Cosh[a + b*x^2] + 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*x)","A",1
7,1,38,42,0.0452132,"\int \frac{\cosh \left(a+b x^2\right)}{x^3} \, dx","Integrate[Cosh[a + b*x^2]/x^3,x]","\frac{1}{2} \left(b \sinh (a) \text{Chi}\left(b x^2\right)+b \cosh (a) \text{Shi}\left(b x^2\right)-\frac{\cosh \left(a+b x^2\right)}{x^2}\right)","\frac{1}{2} b \sinh (a) \text{Chi}\left(b x^2\right)+\frac{1}{2} b \cosh (a) \text{Shi}\left(b x^2\right)-\frac{\cosh \left(a+b x^2\right)}{2 x^2}",1,"(-(Cosh[a + b*x^2]/x^2) + b*CoshIntegral[b*x^2]*Sinh[a] + b*Cosh[a]*SinhIntegral[b*x^2])/2","A",1
8,1,40,51,0.10156,"\int x^3 \cosh ^2\left(a+b x^2\right) \, dx","Integrate[x^3*Cosh[a + b*x^2]^2,x]","-\frac{\cosh \left(2 \left(a+b x^2\right)\right)-2 b x^2 \left(\sinh \left(2 \left(a+b x^2\right)\right)+b x^2\right)}{16 b^2}","-\frac{\cosh ^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
9,1,101,99,0.2333548,"\int x^2 \cosh ^2\left(a+b x^2\right) \, dx","Integrate[x^2*Cosh[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
10,1,27,31,0.0234622,"\int x \cosh ^2\left(a+b x^2\right) \, dx","Integrate[x*Cosh[a + b*x^2]^2,x]","\frac{2 \left(a+b x^2\right)+\sinh \left(2 \left(a+b x^2\right)\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
11,1,86,78,0.0771121,"\int \cosh ^2\left(a+b x^2\right) \, dx","Integrate[Cosh[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
12,1,33,37,0.0219817,"\int \frac{\cosh ^2\left(a+b x^2\right)}{x} \, dx","Integrate[Cosh[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
13,1,94,88,0.2464118,"\int \frac{\cosh ^2\left(a+b x^2\right)}{x^2} \, dx","Integrate[Cosh[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 \cosh ^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{\cosh ^2\left(a+b x^2\right)}{x}",1,"(-4*Cosh[a + b*x^2]^2 + 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*x)","A",1
14,1,46,57,0.09934,"\int \frac{\cosh ^2\left(a+b x^2\right)}{x^3} \, dx","Integrate[Cosh[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{\cosh ^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,"(-(Cosh[a + b*x^2]^2/x^2) + b*CoshIntegral[2*b*x^2]*Sinh[2*a] + b*Cosh[2*a]*SinhIntegral[2*b*x^2])/2","A",1
15,1,55,79,0.1868113,"\int x^3 \cosh ^3\left(a+b x^2\right) \, dx","Integrate[x^3*Cosh[a + b*x^2]^3,x]","-\frac{-3 b x^2 \left(9 \sinh \left(a+b x^2\right)+\sinh \left(3 \left(a+b x^2\right)\right)\right)+27 \cosh \left(a+b x^2\right)+\cosh \left(3 \left(a+b x^2\right)\right)}{72 b^2}","-\frac{\cosh ^3\left(a+b x^2\right)}{18 b^2}-\frac{\cosh \left(a+b x^2\right)}{3 b^2}+\frac{x^2 \sinh \left(a+b x^2\right)}{3 b}+\frac{x^2 \sinh \left(a+b x^2\right) \cosh ^2\left(a+b x^2\right)}{6 b}",1,"-1/72*(27*Cosh[a + b*x^2] + Cosh[3*(a + b*x^2)] - 3*b*x^2*(9*Sinh[a + b*x^2] + Sinh[3*(a + b*x^2)]))/b^2","A",1
16,1,184,160,0.3252916,"\int x^2 \cosh ^3\left(a+b x^2\right) \, dx","Integrate[x^2*Cosh[a + b*x^2]^3,x]","\frac{27 \sqrt{\pi } (\cosh (a)-\sinh (a)) \text{erf}\left(\sqrt{b} x\right)+\sqrt{3 \pi } (\cosh (3 a)-\sinh (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 \sinh \left(a+b x^2\right)+12 \sqrt{b} x \sinh \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 \sinh \left(a+b x^2\right)}{8 b}+\frac{x \sinh \left(3 a+3 b x^2\right)}{24 b}",1,"(-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]*Erf[Sqrt[3]*Sqrt[b]*x]*(Cosh[3*a] - Sinh[3*a]) - Sqrt[3*Pi]*Erfi[Sqrt[3]*Sqrt[b]*x]*Sinh[3*a] + 108*Sqrt[b]*x*Sinh[a + b*x^2] + 12*Sqrt[b]*x*Sinh[3*(a + b*x^2)])/(288*b^(3/2))","A",1
17,1,33,33,0.0092991,"\int x \cosh ^3\left(a+b x^2\right) \, dx","Integrate[x*Cosh[a + b*x^2]^3,x]","\frac{\sinh ^3\left(a+b x^2\right)}{6 b}+\frac{\sinh \left(a+b x^2\right)}{2 b}","\frac{\sinh ^3\left(a+b x^2\right)}{6 b}+\frac{\sinh \left(a+b x^2\right)}{2 b}",1,"Sinh[a + b*x^2]/(2*b) + Sinh[a + b*x^2]^3/(6*b)","A",1
18,1,136,125,0.1301841,"\int \cosh ^3\left(a+b x^2\right) \, dx","Integrate[Cosh[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)+(\cosh (3 a)-\sinh (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] + Erf[Sqrt[3]*Sqrt[b]*x]*(Cosh[3*a] - Sinh[3*a]) + Erfi[Sqrt[3]*Sqrt[b]*x]*Sinh[3*a]))/(16*Sqrt[b])","A",1
19,1,49,55,0.0373464,"\int \frac{\cosh ^3\left(a+b x^2\right)}{x} \, dx","Integrate[Cosh[a + b*x^2]^3/x,x]","\frac{1}{8} \left(3 \cosh (a) \text{Chi}\left(b x^2\right)+\cosh (3 a) \text{Chi}\left(3 b x^2\right)+3 \sinh (a) \text{Shi}\left(b x^2\right)+\sinh (3 a) \text{Shi}\left(3 b x^2\right)\right)","\frac{3}{8} \cosh (a) \text{Chi}\left(b x^2\right)+\frac{1}{8} \cosh (3 a) \text{Chi}\left(3 b x^2\right)+\frac{3}{8} \sinh (a) \text{Shi}\left(b x^2\right)+\frac{1}{8} \sinh (3 a) \text{Shi}\left(3 b x^2\right)",1,"(3*Cosh[a]*CoshIntegral[b*x^2] + Cosh[3*a]*CoshIntegral[3*b*x^2] + 3*Sinh[a]*SinhIntegral[b*x^2] + Sinh[3*a]*SinhIntegral[3*b*x^2])/8","A",1
20,1,204,136,0.38453,"\int \frac{\cosh ^3\left(a+b x^2\right)}{x^2} \, dx","Integrate[Cosh[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 (\sinh (3 a)-\cosh (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 \cosh \left(a+b x^2\right)-2 \cosh \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{\cosh ^3\left(a+b x^2\right)}{x}",1,"(-6*Cosh[a + b*x^2] - 2*Cosh[3*(a + b*x^2)] + 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*Erfi[Sqrt[3]*Sqrt[b]*x]*Sinh[3*a] + Sqrt[b]*Sqrt[3*Pi]*x*Erf[Sqrt[3]*Sqrt[b]*x]*(-Cosh[3*a] + Sinh[3*a]))/(8*x)","A",1
21,1,92,91,0.0889582,"\int \frac{\cosh ^3\left(a+b x^2\right)}{x^3} \, dx","Integrate[Cosh[a + b*x^2]^3/x^3,x]","\frac{3 b x^2 \sinh (a) \text{Chi}\left(b x^2\right)+3 b x^2 \sinh (3 a) \text{Chi}\left(3 b x^2\right)+3 b x^2 \cosh (a) \text{Shi}\left(b x^2\right)+3 b x^2 \cosh (3 a) \text{Shi}\left(3 b x^2\right)-3 \cosh \left(a+b x^2\right)-\cosh \left(3 \left(a+b x^2\right)\right)}{8 x^2}","\frac{3}{8} b \sinh (a) \text{Chi}\left(b x^2\right)+\frac{3}{8} b \sinh (3 a) \text{Chi}\left(3 b x^2\right)+\frac{3}{8} b \cosh (a) \text{Shi}\left(b x^2\right)+\frac{3}{8} b \cosh (3 a) \text{Shi}\left(3 b x^2\right)-\frac{3 \cosh \left(a+b x^2\right)}{8 x^2}-\frac{\cosh \left(3 \left(a+b x^2\right)\right)}{8 x^2}",1,"(-3*Cosh[a + b*x^2] - Cosh[3*(a + b*x^2)] + 3*b*x^2*CoshIntegral[b*x^2]*Sinh[a] + 3*b*x^2*CoshIntegral[3*b*x^2]*Sinh[3*a] + 3*b*x^2*Cosh[a]*SinhIntegral[b*x^2] + 3*b*x^2*Cosh[3*a]*SinhIntegral[3*b*x^2])/(8*x^2)","A",1
22,1,67,67,0.0279971,"\int x \cosh ^7\left(a+b x^2\right) \, dx","Integrate[x*Cosh[a + b*x^2]^7,x]","\frac{\sinh ^7\left(a+b x^2\right)}{14 b}+\frac{3 \sinh ^5\left(a+b x^2\right)}{10 b}+\frac{\sinh ^3\left(a+b x^2\right)}{2 b}+\frac{\sinh \left(a+b x^2\right)}{2 b}","\frac{\sinh ^7\left(a+b x^2\right)}{14 b}+\frac{3 \sinh ^5\left(a+b x^2\right)}{10 b}+\frac{\sinh ^3\left(a+b x^2\right)}{2 b}+\frac{\sinh \left(a+b x^2\right)}{2 b}",1,"Sinh[a + b*x^2]/(2*b) + Sinh[a + b*x^2]^3/(2*b) + (3*Sinh[a + b*x^2]^5)/(10*b) + Sinh[a + b*x^2]^7/(14*b)","A",1
23,1,8,8,0.0028636,"\int x^2 \cosh \left(x^3\right) \, dx","Integrate[x^2*Cosh[x^3],x]","\frac{\sinh \left(x^3\right)}{3}","\frac{\sinh \left(x^3\right)}{3}",1,"Sinh[x^3]/3","A",1
24,1,8,8,0.0048552,"\int \frac{\cosh \left(\frac{1}{x^5}\right)}{x^6} \, dx","Integrate[Cosh[x^(-5)]/x^6,x]","-\frac{1}{5} \sinh \left(\frac{1}{x^5}\right)","-\frac{1}{5} \sinh \left(\frac{1}{x^5}\right)",1,"-1/5*Sinh[x^(-5)]","A",1
25,1,33,33,0.0288587,"\int \cosh \left(a+\frac{b}{x}\right) \, dx","Integrate[Cosh[a + b/x],x]","-b \sinh (a) \text{Chi}\left(\frac{b}{x}\right)-b \cosh (a) \text{Shi}\left(\frac{b}{x}\right)+x \cosh \left(a+\frac{b}{x}\right)","-b \sinh (a) \text{Chi}\left(\frac{b}{x}\right)-b \cosh (a) \text{Shi}\left(\frac{b}{x}\right)+x \cosh \left(a+\frac{b}{x}\right)",1,"x*Cosh[a + b/x] - b*CoshIntegral[b/x]*Sinh[a] - b*Cosh[a]*SinhIntegral[b/x]","A",1
26,1,21,21,0.0109523,"\int \frac{\cosh \left(a+\frac{b}{x}\right)}{x} \, dx","Integrate[Cosh[a + b/x]/x,x]","-\cosh (a) \text{Chi}\left(\frac{b}{x}\right)-\sinh (a) \text{Shi}\left(\frac{b}{x}\right)","-\cosh (a) \text{Chi}\left(\frac{b}{x}\right)-\sinh (a) \text{Shi}\left(\frac{b}{x}\right)",1,"-(Cosh[a]*CoshIntegral[b/x]) - Sinh[a]*SinhIntegral[b/x]","A",1
27,1,13,13,0.0047046,"\int \frac{\cosh \left(a+\frac{b}{x}\right)}{x^2} \, dx","Integrate[Cosh[a + b/x]/x^2,x]","-\frac{\sinh \left(a+\frac{b}{x}\right)}{b}","-\frac{\sinh \left(a+\frac{b}{x}\right)}{b}",1,"-(Sinh[a + b/x]/b)","A",1
28,1,29,29,0.0297904,"\int \frac{\cosh \left(a+\frac{b}{x}\right)}{x^3} \, dx","Integrate[Cosh[a + b/x]/x^3,x]","\frac{x \cosh \left(a+\frac{b}{x}\right)-b \sinh \left(a+\frac{b}{x}\right)}{b^2 x}","\frac{\cosh \left(a+\frac{b}{x}\right)}{b^2}-\frac{\sinh \left(a+\frac{b}{x}\right)}{b x}",1,"(x*Cosh[a + b/x] - b*Sinh[a + b/x])/(b^2*x)","A",1
29,1,39,46,0.0506804,"\int \frac{\cosh \left(a+\frac{b}{x}\right)}{x^4} \, dx","Integrate[Cosh[a + b/x]/x^4,x]","\frac{2 b x \cosh \left(a+\frac{b}{x}\right)-\left(b^2+2 x^2\right) \sinh \left(a+\frac{b}{x}\right)}{b^3 x^2}","-\frac{2 \sinh \left(a+\frac{b}{x}\right)}{b^3}+\frac{2 \cosh \left(a+\frac{b}{x}\right)}{b^2 x}-\frac{\sinh \left(a+\frac{b}{x}\right)}{b x^2}",1,"(2*b*x*Cosh[a + b/x] - (b^2 + 2*x^2)*Sinh[a + b/x])/(b^3*x^2)","A",1
30,1,71,67,0.087696,"\int \cosh \left(a+\frac{b}{x^2}\right) \, dx","Integrate[Cosh[a + b/x^2],x]","\frac{1}{2} \sqrt{\pi } \sqrt{b} (\cosh (a)-\sinh (a)) \text{erf}\left(\frac{\sqrt{b}}{x}\right)-\frac{1}{2} \sqrt{\pi } \sqrt{b} (\sinh (a)+\cosh (a)) \text{erfi}\left(\frac{\sqrt{b}}{x}\right)+x \cosh \left(a+\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 \cosh \left(a+\frac{b}{x^2}\right)",1,"x*Cosh[a + b/x^2] + (Sqrt[b]*Sqrt[Pi]*Erf[Sqrt[b]/x]*(Cosh[a] - Sinh[a]))/2 - (Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[b]/x]*(Cosh[a] + Sinh[a]))/2","A",1
31,1,25,25,0.016735,"\int \frac{\cosh \left(a+\frac{b}{x^2}\right)}{x} \, dx","Integrate[Cosh[a + b/x^2]/x,x]","\frac{1}{2} \left(-\cosh (a) \text{Chi}\left(\frac{b}{x^2}\right)-\sinh (a) \text{Shi}\left(\frac{b}{x^2}\right)\right)","-\frac{1}{2} \cosh (a) \text{Chi}\left(\frac{b}{x^2}\right)-\frac{1}{2} \sinh (a) \text{Shi}\left(\frac{b}{x^2}\right)",1,"(-(Cosh[a]*CoshIntegral[b/x^2]) - Sinh[a]*SinhIntegral[b/x^2])/2","A",1
32,1,49,57,0.0383928,"\int \frac{\cosh \left(a+\frac{b}{x^2}\right)}{x^2} \, dx","Integrate[Cosh[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,"-1/4*(Sqrt[Pi]*(Erf[Sqrt[b]/x]*(Cosh[a] - Sinh[a]) + Erfi[Sqrt[b]/x]*(Cosh[a] + Sinh[a])))/Sqrt[b]","A",1
33,1,15,15,0.0049323,"\int \frac{\cosh \left(a+\frac{b}{x^2}\right)}{x^3} \, dx","Integrate[Cosh[a + b/x^2]/x^3,x]","-\frac{\sinh \left(a+\frac{b}{x^2}\right)}{2 b}","-\frac{\sinh \left(a+\frac{b}{x^2}\right)}{2 b}",1,"-1/2*Sinh[a + b/x^2]/b","A",1
34,1,74,75,0.0763308,"\int \frac{\cosh \left(a+\frac{b}{x^2}\right)}{x^4} \, dx","Integrate[Cosh[a + b/x^2]/x^4,x]","\frac{\sqrt{\pi } x (\sinh (a)-\cosh (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} \sinh \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{\sinh \left(a+\frac{b}{x^2}\right)}{2 b x}",1,"(Sqrt[Pi]*x*Erf[Sqrt[b]/x]*(-Cosh[a] + Sinh[a]) + Sqrt[Pi]*x*Erfi[Sqrt[b]/x]*(Cosh[a] + Sinh[a]) - 4*Sqrt[b]*Sinh[a + b/x^2])/(8*b^(3/2)*x)","A",1
35,1,77,67,0.0777863,"\int \cosh \left(a+b x^n\right) \, dx","Integrate[Cosh[a + b*x^n],x]","-\frac{x \left(-b^2 x^{2 n}\right)^{-1/n} \left((\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)\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,"-1/2*(x*((-(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])))/(n*(-(b^2*x^(2*n)))^n^(-1))","A",1
36,1,23,25,0.0281867,"\int \frac{\cosh \left(a+b x^n\right)}{x} \, dx","Integrate[Cosh[a + b*x^n]/x,x]","\frac{\cosh (a) \text{Chi}\left(b x^n\right)+\sinh (a) \text{Shi}\left(b x^n\right)}{n}","\frac{\cosh (a) \text{Chi}\left(b x^n\right)}{n}+\frac{\sinh (a) \text{Shi}\left(b x^n\right)}{n}",1,"(Cosh[a]*CoshIntegral[b*x^n] + Sinh[a]*SinhIntegral[b*x^n])/n","A",1
37,1,81,89,0.1271029,"\int \cosh ^2\left(a+b x^n\right) \, dx","Integrate[Cosh[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
38,1,36,43,0.035549,"\int \frac{\cosh ^2\left(a+b x^n\right)}{x} \, dx","Integrate[Cosh[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)+n \log (x)}{2 n}","\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,"(Cosh[2*a]*CoshIntegral[2*b*x^n] + n*Log[x] + Sinh[2*a]*SinhIntegral[2*b*x^n])/(2*n)","A",1
39,1,138,150,0.6546031,"\int \cosh ^3\left(a+b x^n\right) \, dx","Integrate[Cosh[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(e^{2 a} 3^{\frac{1}{n}+1} \Gamma \left(\frac{1}{n},b x^n\right)+\Gamma \left(\frac{1}{n},3 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,"-1/8*(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])))/(3^n^(-1)*E^(3*a)*n*(-(b^2*x^(2*n)))^n^(-1))","A",1
40,1,52,67,0.0595357,"\int \frac{\cosh ^3\left(a+b x^n\right)}{x} \, dx","Integrate[Cosh[a + b*x^n]^3/x,x]","\frac{3 \cosh (a) \text{Chi}\left(b x^n\right)+\cosh (3 a) \text{Chi}\left(3 b x^n\right)+3 \sinh (a) \text{Shi}\left(b x^n\right)+\sinh (3 a) \text{Shi}\left(3 b x^n\right)}{4 n}","\frac{3 \cosh (a) \text{Chi}\left(b x^n\right)}{4 n}+\frac{\cosh (3 a) \text{Chi}\left(3 b x^n\right)}{4 n}+\frac{3 \sinh (a) \text{Shi}\left(b x^n\right)}{4 n}+\frac{\sinh (3 a) \text{Shi}\left(3 b x^n\right)}{4 n}",1,"(3*Cosh[a]*CoshIntegral[b*x^n] + Cosh[3*a]*CoshIntegral[3*b*x^n] + 3*Sinh[a]*SinhIntegral[b*x^n] + Sinh[3*a]*SinhIntegral[3*b*x^n])/(4*n)","A",1
41,0,0,21,5.7485965,"\int (e x)^m \left(b \cosh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^m*(b*Cosh[c + d*x^n])^p,x]","\int (e x)^m \left(b \cosh \left(c+d x^n\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(b \cosh \left(c+d x^n\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(b*Cosh[c + d*x^n])^p, x]","A",-1
42,0,0,23,8.5409537,"\int (e x)^m \left(a+b \cosh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^m*(a + b*Cosh[c + d*x^n])^p,x]","\int (e x)^m \left(a+b \cosh \left(c+d x^n\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(a+b \cosh \left(c+d x^n\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(a + b*Cosh[c + d*x^n])^p, x]","A",-1
43,1,94,95,0.1461628,"\int (e x)^{-1+n} \left(b \cosh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + n)*(b*Cosh[c + d*x^n])^p,x]","-\frac{x^{-n} (e x)^n \sinh \left(2 \left(c+d x^n\right)\right) \left(b \cosh \left(c+d x^n\right)\right)^p \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};\cosh ^2\left(d x^n+c\right)\right)}{2 d e n (p+1) \sqrt{-\sinh ^2\left(c+d x^n\right)}}","-\frac{x^{-n} (e x)^n \sinh \left(c+d x^n\right) \left(b \cosh \left(c+d x^n\right)\right)^{p+1} \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};\cosh ^2\left(d x^n+c\right)\right)}{b d e n (p+1) \sqrt{-\sinh ^2\left(c+d x^n\right)}}",1,"-1/2*((e*x)^n*(b*Cosh[c + d*x^n])^p*Hypergeometric2F1[1/2, (1 + p)/2, (3 + p)/2, Cosh[c + d*x^n]^2]*Sinh[2*(c + d*x^n)])/(d*e*n*(1 + p)*x^n*Sqrt[-Sinh[c + d*x^n]^2])","A",1
44,0,0,39,6.1937743,"\int (e x)^{-1+2 n} \left(b \cosh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + 2*n)*(b*Cosh[c + d*x^n])^p,x]","\int (e x)^{-1+2 n} \left(b \cosh \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 \cosh \left(c+d x^n\right)\right)^p,x\right)}{e}",0,"Integrate[(e*x)^(-1 + 2*n)*(b*Cosh[c + d*x^n])^p, x]","A",-1
45,1,148,131,0.3832061,"\int (e x)^{-1+n} \left(a+b \cosh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + n)*(a + b*Cosh[c + d*x^n])^p,x]","\frac{x^{-n} (e x)^n \text{csch}\left(c+d x^n\right) \sqrt{-\frac{b \left(\cosh \left(c+d x^n\right)-1\right)}{a+b}} \sqrt{\frac{b \left(\cosh \left(c+d x^n\right)+1\right)}{b-a}} \left(a+b \cosh \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 \cosh \left(d x^n+c\right)}{a+b},\frac{a+b \cosh \left(d x^n+c\right)}{a-b}\right)}{b d e n (p+1)}","\frac{\sqrt{2} x^{-n} (e x)^n \sinh \left(c+d x^n\right) \left(a+b \cosh \left(c+d x^n\right)\right)^p \left(\frac{a+b \cosh \left(c+d x^n\right)}{a+b}\right)^{-p} F_1\left(\frac{1}{2};\frac{1}{2},-p;\frac{3}{2};\frac{1}{2} \left(1-\cosh \left(d x^n+c\right)\right),\frac{b \left(1-\cosh \left(d x^n+c\right)\right)}{a+b}\right)}{d e n \sqrt{\cosh \left(c+d x^n\right)+1}}",1,"((e*x)^n*AppellF1[1 + p, 1/2, 1/2, 2 + p, (a + b*Cosh[c + d*x^n])/(a + b), (a + b*Cosh[c + d*x^n])/(a - b)]*Sqrt[-((b*(-1 + Cosh[c + d*x^n]))/(a + b))]*Sqrt[(b*(1 + Cosh[c + d*x^n]))/(-a + b)]*(a + b*Cosh[c + d*x^n])^(1 + p)*Csch[c + d*x^n])/(b*d*e*n*(1 + p)*x^n)","A",0
46,0,0,41,8.7969463,"\int (e x)^{-1+2 n} \left(a+b \cosh \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + 2*n)*(a + b*Cosh[c + d*x^n])^p,x]","\int (e x)^{-1+2 n} \left(a+b \cosh \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 \cosh \left(c+d x^n\right)\right)^p,x\right)}{e}",0,"Integrate[(e*x)^(-1 + 2*n)*(a + b*Cosh[c + d*x^n])^p, x]","A",-1
47,1,100,89,0.1876969,"\int x^m \cosh \left(a+b x^n\right) \, dx","Integrate[x^m*Cosh[a + b*x^n],x]","-\frac{x^{m+1} \left(-b^2 x^{2 n}\right)^{-\frac{m+1}{n}} \left((\cosh (a)-\sinh (a)) \left(-b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},b x^n\right)+(\sinh (a)+\cosh (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 x^{m+1} \left(-b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-b x^n\right)}{2 n}-\frac{e^{-a} x^{m+1} \left(b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},b x^n\right)}{2 n}",1,"-1/2*(x^(1 + 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
48,1,116,128,0.2733622,"\int x^m \cosh ^2\left(a+b x^n\right) \, dx","Integrate[x^m*Cosh[a + b*x^n]^2,x]","-\frac{x^{m+1} \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}} x^{m+1} \left(-b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-2 b x^n\right)}{n}-\frac{e^{-2 a} 2^{-\frac{m+2 n+1}{n}} x^{m+1} \left(b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},2 b x^n\right)}{n}+\frac{x^{m+1}}{2 (m+1)}",1,"-1/4*(x^(1 + 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
49,1,182,200,1.0815596,"\int x^m \cosh ^3\left(a+b x^n\right) \, dx","Integrate[x^m*Cosh[a + b*x^n]^3,x]","-\frac{e^{-3 a} 3^{-\frac{m+1}{n}} x^{m+1} \left(-b^2 x^{2 n}\right)^{-\frac{m+1}{n}} \left(\left(-b x^n\right)^{\frac{m+1}{n}} \left(e^{2 a} 3^{\frac{m+n+1}{n}} \Gamma \left(\frac{m+1}{n},b x^n\right)+\Gamma \left(\frac{m+1}{n},3 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}} x^{m+1} \left(-b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-3 b x^n\right)}{8 n}-\frac{3 e^a x^{m+1} \left(-b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-b x^n\right)}{8 n}-\frac{3 e^{-a} x^{m+1} \left(b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},b x^n\right)}{8 n}-\frac{e^{-3 a} 3^{-\frac{m+1}{n}} x^{m+1} \left(b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},3 b x^n\right)}{8 n}",1,"-1/8*(x^(1 + 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])))/(3^((1 + m)/n)*E^(3*a)*n*(-(b^2*x^(2*n)))^((1 + m)/n))","A",1
50,1,46,45,0.0683244,"\int x^{-1-n} \cosh \left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Cosh[a + b*x^n],x]","\frac{x^{-n} \left(b \sinh (a) x^n \text{Chi}\left(b x^n\right)+b \cosh (a) x^n \text{Shi}\left(b x^n\right)-\cosh \left(a+b x^n\right)\right)}{n}","\frac{b \sinh (a) \text{Chi}\left(b x^n\right)}{n}+\frac{b \cosh (a) \text{Shi}\left(b x^n\right)}{n}-\frac{x^{-n} \cosh \left(a+b x^n\right)}{n}",1,"(-Cosh[a + b*x^n] + b*x^n*CoshIntegral[b*x^n]*Sinh[a] + b*x^n*Cosh[a]*SinhIntegral[b*x^n])/(n*x^n)","A",1
51,1,54,67,0.1391072,"\int x^{-1-n} \cosh ^2\left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Cosh[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)-\cosh ^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,"(-Cosh[a + b*x^n]^2 + b*x^n*CoshIntegral[2*b*x^n]*Sinh[2*a] + b*x^n*Cosh[2*a]*SinhIntegral[2*b*x^n])/(n*x^n)","A",1
52,1,97,113,0.1805011,"\int x^{-1-n} \cosh ^3\left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Cosh[a + b*x^n]^3,x]","\frac{x^{-n} \left(3 b \sinh (a) x^n \text{Chi}\left(b x^n\right)+3 b \sinh (3 a) x^n \text{Chi}\left(3 b x^n\right)+3 b \cosh (a) x^n \text{Shi}\left(b x^n\right)+3 b \cosh (3 a) x^n \text{Shi}\left(3 b x^n\right)-3 \cosh \left(a+b x^n\right)-\cosh \left(3 \left(a+b x^n\right)\right)\right)}{4 n}","\frac{3 b \sinh (a) \text{Chi}\left(b x^n\right)}{4 n}+\frac{3 b \sinh (3 a) \text{Chi}\left(3 b x^n\right)}{4 n}+\frac{3 b \cosh (a) \text{Shi}\left(b x^n\right)}{4 n}+\frac{3 b \cosh (3 a) \text{Shi}\left(3 b x^n\right)}{4 n}-\frac{3 x^{-n} \cosh \left(a+b x^n\right)}{4 n}-\frac{x^{-n} \cosh \left(3 \left(a+b x^n\right)\right)}{4 n}",1,"(-3*Cosh[a + b*x^n] - Cosh[3*(a + b*x^n)] + 3*b*x^n*CoshIntegral[b*x^n]*Sinh[a] + 3*b*x^n*CoshIntegral[3*b*x^n]*Sinh[3*a] + 3*b*x^n*Cosh[a]*SinhIntegral[b*x^n] + 3*b*x^n*Cosh[3*a]*SinhIntegral[3*b*x^n])/(4*n*x^n)","A",1
53,1,60,71,0.7821326,"\int x^{-1+\frac{n}{2}} \cosh \left(a+b x^n\right) \, dx","Integrate[x^(-1 + n/2)*Cosh[a + b*x^n],x]","\frac{\sqrt{\pi } \left((\cosh (a)-\sinh (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{erf}\left(\sqrt{b} x^{n/2}\right)}{2 \sqrt{b} n}+\frac{\sqrt{\pi } e^a \text{erfi}\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
54,1,62,113,0.1421569,"\int x^2 \cosh \left((a+b x)^2\right) \, dx","Integrate[x^2*Cosh[(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) \sinh \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 \sinh \left((a+b x)^2\right)}{b^3}+\frac{(a+b x) \sinh \left((a+b x)^2\right)}{2 b^3}",1,"((1 + 2*a^2)*Sqrt[Pi]*Erf[a + b*x] + (-1 + 2*a^2)*Sqrt[Pi]*Erfi[a + b*x] - 4*(a - b*x)*Sinh[(a + b*x)^2])/(8*b^3)","A",1
55,1,39,54,0.030753,"\int x \cosh \left((a+b x)^2\right) \, dx","Integrate[x*Cosh[(a + b*x)^2],x]","\frac{2 \sinh \left((a+b x)^2\right)-\sqrt{\pi } a (\text{erf}(a+b x)+\text{erfi}(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{\sinh \left((a+b x)^2\right)}{2 b^2}",1,"(-(a*Sqrt[Pi]*(Erf[a + b*x] + Erfi[a + b*x])) + 2*Sinh[(a + b*x)^2])/(4*b^2)","A",1
56,1,25,37,0.0042205,"\int \cosh \left((a+b x)^2\right) \, dx","Integrate[Cosh[(a + b*x)^2],x]","\frac{\sqrt{\pi } (\text{erf}(a+b x)+\text{erfi}(a+b x))}{4 b}","\frac{\sqrt{\pi } \text{erf}(a+b x)}{4 b}+\frac{\sqrt{\pi } \text{erfi}(a+b x)}{4 b}",1,"(Sqrt[Pi]*(Erf[a + b*x] + Erfi[a + b*x]))/(4*b)","A",1
57,0,0,20,1.5853837,"\int \frac{\cosh \left((a+b x)^2\right)}{x} \, dx","Integrate[Cosh[(a + b*x)^2]/x,x]","\int \frac{\cosh \left((a+b x)^2\right)}{x} \, dx","b \text{Int}\left(\frac{\cosh \left((a+b x)^2\right)}{b x},x\right)",0,"Integrate[Cosh[(a + b*x)^2]/x, x]","A",-1
58,0,0,15,11.05202,"\int \frac{\cosh \left((a+b x)^2\right)}{x^2} \, dx","Integrate[Cosh[(a + b*x)^2]/x^2,x]","\int \frac{\cosh \left((a+b x)^2\right)}{x^2} \, dx","\text{Int}\left(\frac{\cosh \left((a+b x)^2\right)}{x^2},x\right)",0,"Integrate[Cosh[(a + b*x)^2]/x^2, x]","A",-1
59,1,104,346,0.5355263,"\int x^2 \cosh \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[x^2*Cosh[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) \sinh \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) \cosh \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}","-\frac{240 \cosh \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}+\frac{240 \sqrt{c+d x} \sinh \left(a+b \sqrt{c+d x}\right)}{b^5 d^3}-\frac{120 (c+d x) \cosh \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{24 c \cosh \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{40 (c+d x)^{3/2} \sinh \left(a+b \sqrt{c+d x}\right)}{b^3 d^3}-\frac{24 c \sqrt{c+d x} \sinh \left(a+b \sqrt{c+d x}\right)}{b^3 d^3}-\frac{2 c^2 \cosh \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{10 (c+d x)^2 \cosh \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}+\frac{12 c (c+d x) \cosh \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}+\frac{2 c^2 \sqrt{c+d x} \sinh \left(a+b \sqrt{c+d x}\right)}{b d^3}+\frac{2 (c+d x)^{5/2} \sinh \left(a+b \sqrt{c+d x}\right)}{b d^3}-\frac{4 c (c+d x)^{3/2} \sinh \left(a+b \sqrt{c+d x}\right)}{b d^3}",1,"(-2*(120 + 12*b^2*(4*c + 5*d*x) + b^4*d*x*(4*c + 5*d*x))*Cosh[a + b*Sqrt[c + d*x]] + 2*b*Sqrt[c + d*x]*(120 + b^4*d^2*x^2 + 4*b^2*(2*c + 5*d*x))*Sinh[a + b*Sqrt[c + d*x]])/(b^6*d^3)","A",1
60,1,72,167,0.2108797,"\int x \cosh \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[x*Cosh[a + b*Sqrt[c + d*x]],x]","\frac{2 b \left(b^2 d x+6\right) \sqrt{c+d x} \sinh \left(a+b \sqrt{c+d x}\right)-2 \left(b^2 (2 c+3 d x)+6\right) \cosh \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}","-\frac{12 \cosh \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}+\frac{12 \sqrt{c+d x} \sinh \left(a+b \sqrt{c+d x}\right)}{b^3 d^2}-\frac{6 (c+d x) \cosh \left(a+b \sqrt{c+d x}\right)}{b^2 d^2}+\frac{2 c \cosh \left(a+b \sqrt{c+d x}\right)}{b^2 d^2}+\frac{2 (c+d x)^{3/2} \sinh \left(a+b \sqrt{c+d x}\right)}{b d^2}-\frac{2 c \sqrt{c+d x} \sinh \left(a+b \sqrt{c+d x}\right)}{b d^2}",1,"(-2*(6 + b^2*(2*c + 3*d*x))*Cosh[a + b*Sqrt[c + d*x]] + 2*b*Sqrt[c + d*x]*(6 + b^2*d*x)*Sinh[a + b*Sqrt[c + d*x]])/(b^4*d^2)","A",1
61,1,50,54,0.0675234,"\int \cosh \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[Cosh[a + b*Sqrt[c + d*x]],x]","\frac{2 \left(b \sqrt{c+d x} \sinh \left(a+b \sqrt{c+d x}\right)-\cosh \left(a+b \sqrt{c+d x}\right)\right)}{b^2 d}","\frac{2 \sqrt{c+d x} \sinh \left(a+b \sqrt{c+d x}\right)}{b d}-\frac{2 \cosh \left(a+b \sqrt{c+d x}\right)}{b^2 d}",1,"(2*(-Cosh[a + b*Sqrt[c + d*x]] + b*Sqrt[c + d*x]*Sinh[a + b*Sqrt[c + d*x]]))/(b^2*d)","A",1
62,1,127,124,0.5258985,"\int \frac{\cosh \left(a+b \sqrt{c+d x}\right)}{x} \, dx","Integrate[Cosh[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)","\cosh \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{Chi}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)-\sinh \left(a+b \sqrt{c}\right) \text{Shi}\left(b \left(\sqrt{c}-\sqrt{c+d x}\right)\right)+\sinh \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
63,1,199,182,1.8768694,"\int \frac{\cosh \left(a+b \sqrt{c+d x}\right)}{x^2} \, dx","Integrate[Cosh[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 \sinh \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{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{Shi}\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{Shi}\left(b \left(\sqrt{c}+\sqrt{c+d x}\right)\right)}{2 \sqrt{c}}-\frac{\cosh \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
64,1,381,537,0.7486707,"\int x^2 \cosh \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[x^2*Cosh[a + b*(c + d*x)^(1/3)],x]","\frac{3 (\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(3 \sinh \left(a+b \sqrt[3]{c+d x}\right)-3 \cosh \left(a+b \sqrt[3]{c+d x}\right)\right)}{2 b^9 d^3}","\frac{120960 \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^9 d^3}-\frac{120960 \sqrt[3]{c+d x} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^8 d^3}+\frac{60480 (c+d x)^{2/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^7 d^3}-\frac{20160 (c+d x) \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}+\frac{720 c \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}+\frac{5040 (c+d x)^{4/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^3}-\frac{720 c \sqrt[3]{c+d x} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^3}-\frac{1008 (c+d x)^{5/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}+\frac{360 c (c+d x)^{2/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}+\frac{6 c^2 \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}+\frac{168 (c+d x)^2 \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}-\frac{120 c (c+d x) \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}-\frac{6 c^2 \sqrt[3]{c+d x} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}-\frac{24 (c+d x)^{7/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}+\frac{30 c (c+d x)^{4/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}+\frac{3 c^2 (c+d x)^{2/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}+\frac{3 (c+d x)^{8/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}-\frac{6 c (c+d x)^{5/3} \sinh \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))*(-3*Cosh[a + b*(c + d*x)^(1/3)] + 3*Sinh[a + b*(c + d*x)^(1/3)]))/(2*b^9*d^3)","A",1
65,1,118,261,0.428414,"\int x \cosh \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[x*Cosh[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) \sinh \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) \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^2}","-\frac{360 \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^2}+\frac{360 \sqrt[3]{c+d x} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^2}-\frac{180 (c+d x)^{2/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^2}+\frac{60 (c+d x) \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^2}-\frac{6 c \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^2}-\frac{15 (c+d x)^{4/3} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^2}+\frac{6 c \sqrt[3]{c+d x} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^2}+\frac{3 (c+d x)^{5/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b d^2}-\frac{3 c (c+d x)^{2/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b d^2}",1,"(-3*(120 + 60*b^2*(c + d*x)^(2/3) + b^4*(c + d*x)^(1/3)*(3*c + 5*d*x))*Cosh[a + b*(c + d*x)^(1/3)] + 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))*Sinh[a + b*(c + d*x)^(1/3)])/(b^6*d^2)","A",1
66,1,65,85,0.0895238,"\int \cosh \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[Cosh[a + b*(c + d*x)^(1/3)],x]","\frac{3 \left(b^2 (c+d x)^{2/3}+2\right) \sinh \left(a+b \sqrt[3]{c+d x}\right)-6 b \sqrt[3]{c+d x} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}","\frac{6 \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}-\frac{6 \sqrt[3]{c+d x} \cosh \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d}+\frac{3 (c+d x)^{2/3} \sinh \left(a+b \sqrt[3]{c+d x}\right)}{b d}",1,"(-6*b*(c + d*x)^(1/3)*Cosh[a + b*(c + d*x)^(1/3)] + 3*(2 + b^2*(c + d*x)^(2/3))*Sinh[a + b*(c + d*x)^(1/3)])/(b^3*d)","A",1
67,1,231,232,0.0721634,"\int \frac{\cosh \left(a+b \sqrt[3]{c+d x}\right)}{x} \, dx","Integrate[Cosh[a + b*(c + d*x)^(1/3)]/x,x]","\frac{1}{2} \left(\text{RootSum}\left[c-\text{$\#$1}^3\&,-\sinh (\text{$\#$1} b+a) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\cosh (\text{$\#$1} b+a) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\sinh (\text{$\#$1} b+a) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)-\cosh (\text{$\#$1} b+a) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)\&\right]+\text{RootSum}\left[c-\text{$\#$1}^3\&,\sinh (\text{$\#$1} b+a) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\cosh (\text{$\#$1} b+a) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\sinh (\text{$\#$1} b+a) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\cosh (\text{$\#$1} b+a) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)\&\right]\right)","\cosh \left(a+b \sqrt[3]{c}\right) \text{Chi}\left(b \left(\sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)+\cosh \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Chi}\left(-b \left((-1)^{2/3} \sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)+\cosh \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Chi}\left(b \left(\sqrt[3]{-1} \sqrt[3]{c}+\sqrt[3]{c+d x}\right)\right)-\sinh \left(a+b \sqrt[3]{c}\right) \text{Shi}\left(b \left(\sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)-\sinh \left(a+(-1)^{2/3} b \sqrt[3]{c}\right) \text{Shi}\left(b \left((-1)^{2/3} \sqrt[3]{c}-\sqrt[3]{c+d x}\right)\right)+\sinh \left(a-\sqrt[3]{-1} b \sqrt[3]{c}\right) \text{Shi}\left(b \left(\sqrt[3]{-1} \sqrt[3]{c}+\sqrt[3]{c+d x}\right)\right)",1,"(RootSum[c - #1^3 & , Cosh[a + b*#1]*CoshIntegral[b*((c + d*x)^(1/3) - #1)] - CoshIntegral[b*((c + d*x)^(1/3) - #1)]*Sinh[a + b*#1] - Cosh[a + b*#1]*SinhIntegral[b*((c + d*x)^(1/3) - #1)] + Sinh[a + b*#1]*SinhIntegral[b*((c + d*x)^(1/3) - #1)] & ] + RootSum[c - #1^3 & , Cosh[a + b*#1]*CoshIntegral[b*((c + d*x)^(1/3) - #1)] + CoshIntegral[b*((c + d*x)^(1/3) - #1)]*Sinh[a + b*#1] + Cosh[a + b*#1]*SinhIntegral[b*((c + d*x)^(1/3) - #1)] + Sinh[a + b*#1]*SinhIntegral[b*((c + d*x)^(1/3) - #1)] & ])/2","C",1
68,1,211,329,0.5481426,"\int \frac{\cosh \left(a+b \sqrt[3]{c+d x}\right)}{x^2} \, dx","Integrate[Cosh[a + b*(c + d*x)^(1/3)]/x^2,x]","\frac{e^{-a} \left(-b d x \text{RootSum}\left[c-\text{$\#$1}^3\&,\frac{-\sinh (\text{$\#$1} b) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\cosh (\text{$\#$1} b) \text{Chi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)+\sinh (\text{$\#$1} b) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)-\cosh (\text{$\#$1} b) \text{Shi}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)}{\text{$\#$1}^2}\&\right]-3 e^{-b \sqrt[3]{c+d x}} \left(e^{2 \left(a+b \sqrt[3]{c+d x}\right)}+1\right)\right)+b d x \text{RootSum}\left[c-\text{$\#$1}^3\&,\frac{e^{\text{$\#$1} b+a} \text{Ei}\left(b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)}{\text{$\#$1}^2}\&\right]}{6 x}","\frac{b d \sinh \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{\sqrt[3]{-1} b d \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)}{3 c^{2/3}}+\frac{(-1)^{2/3} b d \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)}{3 c^{2/3}}-\frac{b d \cosh \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 \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)}{3 c^{2/3}}-\frac{\sqrt[3]{-1} b d \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)}{3 c^{2/3}}-\frac{\cosh \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*(1 + E^(2*(a + b*(c + d*x)^(1/3)))))/E^(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