1,1,149,225,0.3076845,"\int x^2 \cosh \left(a+b x+c x^2\right) \, dx","Integrate[x^2*Cosh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } \left(b^2+2 c\right) \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\cosh \left(a-\frac{b^2}{4 c}\right)-\sinh \left(a-\frac{b^2}{4 c}\right)\right)+\sqrt{\pi } \left(b^2-2 c\right) \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\sinh \left(a-\frac{b^2}{4 c}\right)+\cosh \left(a-\frac{b^2}{4 c}\right)\right)+4 \sqrt{c} (2 c x-b) \sinh (a+x (b+c x))}{16 c^{5/2}}","\frac{\sqrt{\pi } b^2 e^{\frac{b^2}{4 c}-a} \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } e^{\frac{b^2}{4 c}-a} \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}+\frac{\sqrt{\pi } b^2 e^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{16 c^{5/2}}-\frac{\sqrt{\pi } e^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}-\frac{b \sinh \left(a+b x+c x^2\right)}{4 c^2}+\frac{x \sinh \left(a+b x+c x^2\right)}{2 c}",1,"((b^2 + 2*c)*Sqrt[Pi]*Erf[(b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a - b^2/(4*c)] - Sinh[a - b^2/(4*c)]) + (b^2 - 2*c)*Sqrt[Pi]*Erfi[(b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a - b^2/(4*c)] + Sinh[a - b^2/(4*c)]) + 4*Sqrt[c]*(-b + 2*c*x)*Sinh[a + x*(b + c*x)])/(16*c^(5/2))","A",1
2,1,130,111,0.1521972,"\int x \cosh \left(a+b x+c x^2\right) \, dx","Integrate[x*Cosh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } b \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\sinh \left(a-\frac{b^2}{4 c}\right)-\cosh \left(a-\frac{b^2}{4 c}\right)\right)-\sqrt{\pi } b \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\sinh \left(a-\frac{b^2}{4 c}\right)+\cosh \left(a-\frac{b^2}{4 c}\right)\right)+4 \sqrt{c} \sinh (a+x (b+c x))}{8 c^{3/2}}","-\frac{\sqrt{\pi } b e^{\frac{b^2}{4 c}-a} \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}-\frac{\sqrt{\pi } b e^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}+\frac{\sinh \left(a+b x+c x^2\right)}{2 c}",1,"(b*Sqrt[Pi]*Erf[(b + 2*c*x)/(2*Sqrt[c])]*(-Cosh[a - b^2/(4*c)] + Sinh[a - b^2/(4*c)]) - b*Sqrt[Pi]*Erfi[(b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a - b^2/(4*c)] + Sinh[a - b^2/(4*c)]) + 4*Sqrt[c]*Sinh[a + x*(b + c*x)])/(8*c^(3/2))","A",1
3,1,105,91,0.0670764,"\int \cosh \left(a+b x+c x^2\right) \, dx","Integrate[Cosh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } \left(\text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\cosh \left(a-\frac{b^2}{4 c}\right)-\sinh \left(a-\frac{b^2}{4 c}\right)\right)+\text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\sinh \left(a-\frac{b^2}{4 c}\right)+\cosh \left(a-\frac{b^2}{4 c}\right)\right)\right)}{4 \sqrt{c}}","\frac{\sqrt{\pi } e^{\frac{b^2}{4 c}-a} \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{\sqrt{\pi } e^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{4 \sqrt{c}}",1,"(Sqrt[Pi]*(Erf[(b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a - b^2/(4*c)] - Sinh[a - b^2/(4*c)]) + Erfi[(b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a - b^2/(4*c)] + Sinh[a - b^2/(4*c)])))/(4*Sqrt[c])","A",1
4,0,0,18,0.5955572,"\int \frac{\cosh \left(a+b x+c x^2\right)}{x} \, dx","Integrate[Cosh[a + b*x + c*x^2]/x,x]","\int \frac{\cosh \left(a+b x+c x^2\right)}{x} \, dx","\text{Int}\left(\frac{\cosh \left(a+b x+c x^2\right)}{x},x\right)",0,"Integrate[Cosh[a + b*x + c*x^2]/x, x]","A",-1
5,1,132,107,8.2693385,"\int \left(\frac{\cosh \left(a+b x+c x^2\right)}{x^2}-\frac{b \sinh \left(a+b x+c x^2\right)}{x}\right) \, dx","Integrate[Cosh[a + b*x + c*x^2]/x^2 - (b*Sinh[a + b*x + c*x^2])/x,x]","\frac{\sqrt{\pi } \sqrt{c} x \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\sinh \left(a-\frac{b^2}{4 c}\right)-\cosh \left(a-\frac{b^2}{4 c}\right)\right)+\sqrt{\pi } \sqrt{c} x \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\sinh \left(a-\frac{b^2}{4 c}\right)+\cosh \left(a-\frac{b^2}{4 c}\right)\right)-2 \cosh (a+x (b+c x))}{2 x}","-\frac{1}{2} \sqrt{\pi } \sqrt{c} e^{\frac{b^2}{4 c}-a} \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)+\frac{1}{2} \sqrt{\pi } \sqrt{c} e^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)-\frac{\cosh \left(a+b x+c x^2\right)}{x}",1,"(-2*Cosh[a + x*(b + c*x)] + Sqrt[c]*Sqrt[Pi]*x*Erf[(b + 2*c*x)/(2*Sqrt[c])]*(-Cosh[a - b^2/(4*c)] + Sinh[a - b^2/(4*c)]) + Sqrt[c]*Sqrt[Pi]*x*Erfi[(b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a - b^2/(4*c)] + Sinh[a - b^2/(4*c)]))/(2*x)","A",1
6,1,152,227,0.3060336,"\int x^2 \cosh \left(a+b x-c x^2\right) \, dx","Integrate[x^2*Cosh[a + b*x - c*x^2],x]","\frac{\sqrt{\pi } \left(b^2+2 c\right) \text{erf}\left(\frac{2 c x-b}{2 \sqrt{c}}\right) \left(\sinh \left(a+\frac{b^2}{4 c}\right)+\cosh \left(a+\frac{b^2}{4 c}\right)\right)+\sqrt{\pi } \left(b^2-2 c\right) \text{erfi}\left(\frac{2 c x-b}{2 \sqrt{c}}\right) \left(\cosh \left(a+\frac{b^2}{4 c}\right)-\sinh \left(a+\frac{b^2}{4 c}\right)\right)-4 \sqrt{c} (b+2 c x) \sinh (a+x (b-c x))}{16 c^{5/2}}","-\frac{\sqrt{\pi } b^2 e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{16 c^{5/2}}-\frac{\sqrt{\pi } e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}-\frac{\sqrt{\pi } b^2 e^{-a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } e^{-a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}-\frac{b \sinh \left(a+b x-c x^2\right)}{4 c^2}-\frac{x \sinh \left(a+b x-c x^2\right)}{2 c}",1,"((b^2 - 2*c)*Sqrt[Pi]*Erfi[(-b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a + b^2/(4*c)] - Sinh[a + b^2/(4*c)]) + (b^2 + 2*c)*Sqrt[Pi]*Erf[(-b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a + b^2/(4*c)] + Sinh[a + b^2/(4*c)]) - 4*Sqrt[c]*(b + 2*c*x)*Sinh[a + x*(b - c*x)])/(16*c^(5/2))","A",1
7,1,134,112,0.1520865,"\int x \cosh \left(a+b x-c x^2\right) \, dx","Integrate[x*Cosh[a + b*x - c*x^2],x]","\frac{\sqrt{\pi } b \text{erf}\left(\frac{2 c x-b}{2 \sqrt{c}}\right) \left(\sinh \left(a+\frac{b^2}{4 c}\right)+\cosh \left(a+\frac{b^2}{4 c}\right)\right)+\sqrt{\pi } b \text{erfi}\left(\frac{2 c x-b}{2 \sqrt{c}}\right) \left(\cosh \left(a+\frac{b^2}{4 c}\right)-\sinh \left(a+\frac{b^2}{4 c}\right)\right)-4 \sqrt{c} \sinh (a+x (b-c x))}{8 c^{3/2}}","-\frac{\sqrt{\pi } b e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}-\frac{\sqrt{\pi } b e^{-a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}-\frac{\sinh \left(a+b x-c x^2\right)}{2 c}",1,"(b*Sqrt[Pi]*Erfi[(-b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a + b^2/(4*c)] - Sinh[a + b^2/(4*c)]) + b*Sqrt[Pi]*Erf[(-b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a + b^2/(4*c)] + Sinh[a + b^2/(4*c)]) - 4*Sqrt[c]*Sinh[a + x*(b - c*x)])/(8*c^(3/2))","A",1
8,1,109,91,0.0713106,"\int \cosh \left(a+b x-c x^2\right) \, dx","Integrate[Cosh[a + b*x - c*x^2],x]","\frac{\sqrt{\pi } \left(\text{erf}\left(\frac{2 c x-b}{2 \sqrt{c}}\right) \left(\sinh \left(a+\frac{b^2}{4 c}\right)+\cosh \left(a+\frac{b^2}{4 c}\right)\right)+\text{erfi}\left(\frac{2 c x-b}{2 \sqrt{c}}\right) \left(\cosh \left(a+\frac{b^2}{4 c}\right)-\sinh \left(a+\frac{b^2}{4 c}\right)\right)\right)}{4 \sqrt{c}}","-\frac{\sqrt{\pi } e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{4 \sqrt{c}}-\frac{\sqrt{\pi } e^{-a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{4 \sqrt{c}}",1,"(Sqrt[Pi]*(Erfi[(-b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a + b^2/(4*c)] - Sinh[a + b^2/(4*c)]) + Erf[(-b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a + b^2/(4*c)] + Sinh[a + b^2/(4*c)])))/(4*Sqrt[c])","A",1
9,0,0,19,1.2824659,"\int \frac{\cosh \left(a+b x-c x^2\right)}{x} \, dx","Integrate[Cosh[a + b*x - c*x^2]/x,x]","\int \frac{\cosh \left(a+b x-c x^2\right)}{x} \, dx","\text{Int}\left(\frac{\cosh \left(a+b x-c x^2\right)}{x},x\right)",0,"Integrate[Cosh[a + b*x - c*x^2]/x, x]","A",-1
10,1,136,108,9.9239698,"\int \left(\frac{\cosh \left(a+b x-c x^2\right)}{x^2}-\frac{b \sinh \left(a+b x-c x^2\right)}{x}\right) \, dx","Integrate[Cosh[a + b*x - c*x^2]/x^2 - (b*Sinh[a + b*x - c*x^2])/x,x]","\frac{1}{2} \left(-\sqrt{\pi } \sqrt{c} \text{erf}\left(\frac{2 c x-b}{2 \sqrt{c}}\right) \left(\sinh \left(a+\frac{b^2}{4 c}\right)+\cosh \left(a+\frac{b^2}{4 c}\right)\right)+\sqrt{\pi } \sqrt{c} \text{erfi}\left(\frac{2 c x-b}{2 \sqrt{c}}\right) \left(\cosh \left(a+\frac{b^2}{4 c}\right)-\sinh \left(a+\frac{b^2}{4 c}\right)\right)-\frac{2 \cosh (a+x (b-c x))}{x}\right)","\frac{1}{2} \sqrt{\pi } \sqrt{c} e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)-\frac{1}{2} \sqrt{\pi } \sqrt{c} e^{-a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)-\frac{\cosh \left(a+b x-c x^2\right)}{x}",1,"((-2*Cosh[a + x*(b - c*x)])/x + Sqrt[c]*Sqrt[Pi]*Erfi[(-b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a + b^2/(4*c)] - Sinh[a + b^2/(4*c)]) - Sqrt[c]*Sqrt[Pi]*Erf[(-b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a + b^2/(4*c)] + Sinh[a + b^2/(4*c)]))/2","A",1
11,1,72,66,0.1671468,"\int x^2 \cosh \left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[x^2*Cosh[1/4 + x + x^2],x]","\frac{1}{16} \left(3 \sqrt{\pi } \text{erf}\left(x+\frac{1}{2}\right)-\sqrt{\pi } \text{erfi}\left(x+\frac{1}{2}\right)+\frac{2 (2 x-1) \left(\left(1+\sqrt{e}\right) \sinh (x (x+1))+\left(\sqrt{e}-1\right) \cosh (x (x+1))\right)}{\sqrt[4]{e}}\right)","-\frac{3}{16} \sqrt{\pi } \text{erf}\left(\frac{1}{2} (-2 x-1)\right)-\frac{1}{16} \sqrt{\pi } \text{erfi}\left(\frac{1}{2} (2 x+1)\right)+\frac{1}{2} x \sinh \left(x^2+x+\frac{1}{4}\right)-\frac{1}{4} \sinh \left(x^2+x+\frac{1}{4}\right)",1,"(3*Sqrt[Pi]*Erf[1/2 + x] - Sqrt[Pi]*Erfi[1/2 + x] + (2*(-1 + 2*x)*((-1 + Sqrt[E])*Cosh[x*(1 + x)] + (1 + Sqrt[E])*Sinh[x*(1 + x)]))/E^(1/4))/16","A",1
12,1,76,52,0.0789182,"\int x \cosh \left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[x*Cosh[1/4 + x + x^2],x]","\frac{-\sqrt[4]{e} \sqrt{\pi } \text{erf}\left(x+\frac{1}{2}\right)-\sqrt[4]{e} \sqrt{\pi } \text{erfi}\left(x+\frac{1}{2}\right)+2 \left(1+\sqrt{e}\right) \sinh (x (x+1))+2 \left(\sqrt{e}-1\right) \cosh (x (x+1))}{8 \sqrt[4]{e}}","\frac{1}{8} \sqrt{\pi } \text{erf}\left(\frac{1}{2} (-2 x-1)\right)-\frac{1}{8} \sqrt{\pi } \text{erfi}\left(\frac{1}{2} (2 x+1)\right)+\frac{1}{2} \sinh \left(x^2+x+\frac{1}{4}\right)",1,"(2*(-1 + Sqrt[E])*Cosh[x*(1 + x)] - E^(1/4)*Sqrt[Pi]*Erf[1/2 + x] - E^(1/4)*Sqrt[Pi]*Erfi[1/2 + x] + 2*(1 + Sqrt[E])*Sinh[x*(1 + x)])/(8*E^(1/4))","A",1
13,1,22,39,0.0250395,"\int \cosh \left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[Cosh[1/4 + x + x^2],x]","\frac{1}{4} \sqrt{\pi } \left(\text{erf}\left(x+\frac{1}{2}\right)+\text{erfi}\left(x+\frac{1}{2}\right)\right)","\frac{1}{4} \sqrt{\pi } \text{erfi}\left(\frac{1}{2} (2 x+1)\right)-\frac{1}{4} \sqrt{\pi } \text{erf}\left(\frac{1}{2} (-2 x-1)\right)",1,"(Sqrt[Pi]*(Erf[1/2 + x] + Erfi[1/2 + x]))/4","A",1
14,0,0,16,7.6310114,"\int \frac{\cosh \left(\frac{1}{4}+x+x^2\right)}{x} \, dx","Integrate[Cosh[1/4 + x + x^2]/x,x]","\int \frac{\cosh \left(\frac{1}{4}+x+x^2\right)}{x} \, dx","\text{Int}\left(\frac{\cosh \left(x^2+x+\frac{1}{4}\right)}{x},x\right)",0,"Integrate[Cosh[1/4 + x + x^2]/x, x]","A",-1
15,0,0,69,9.9464277,"\int \frac{\cosh \left(\frac{1}{4}+x+x^2\right)}{x^2} \, dx","Integrate[Cosh[1/4 + x + x^2]/x^2,x]","\int \frac{\cosh \left(\frac{1}{4}+x+x^2\right)}{x^2} \, dx","\text{Int}\left(\frac{\sinh \left(x^2+x+\frac{1}{4}\right)}{x},x\right)+\frac{1}{2} \sqrt{\pi } \text{erf}\left(\frac{1}{2} (-2 x-1)\right)+\frac{1}{2} \sqrt{\pi } \text{erfi}\left(\frac{1}{2} (2 x+1)\right)-\frac{\cosh \left(x^2+x+\frac{1}{4}\right)}{x}",0,"Integrate[Cosh[1/4 + x + x^2]/x^2, x]","A",-1
16,1,176,268,0.7950149,"\int x^2 \cosh ^2\left(a+b x+c x^2\right) \, dx","Integrate[x^2*Cosh[a + b*x + c*x^2]^2,x]","\frac{3 \sqrt{2 \pi } \left(b^2+c\right) \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right) \left(\cosh \left(2 a-\frac{b^2}{2 c}\right)-\sinh \left(2 a-\frac{b^2}{2 c}\right)\right)+3 \sqrt{2 \pi } \left(b^2-c\right) \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right) \left(\sinh \left(2 a-\frac{b^2}{2 c}\right)+\cosh \left(2 a-\frac{b^2}{2 c}\right)\right)+4 \sqrt{c} \left(8 c^2 x^3-3 (b-2 c x) \sinh (2 (a+x (b+c x)))\right)}{192 c^{5/2}}","\frac{\sqrt{\frac{\pi }{2}} e^{\frac{b^2}{2 c}-2 a} \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} b^2 e^{\frac{b^2}{2 c}-2 a} \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{5/2}}-\frac{\sqrt{\frac{\pi }{2}} e^{2 a-\frac{b^2}{2 c}} \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} b^2 e^{2 a-\frac{b^2}{2 c}} \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{5/2}}-\frac{b \sinh \left(2 a+2 b x+2 c x^2\right)}{16 c^2}+\frac{x \sinh \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{x^3}{6}",1,"(3*(b^2 + c)*Sqrt[2*Pi]*Erf[(b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a - b^2/(2*c)] - Sinh[2*a - b^2/(2*c)]) + 3*(b^2 - c)*Sqrt[2*Pi]*Erfi[(b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a - b^2/(2*c)] + Sinh[2*a - b^2/(2*c)]) + 4*Sqrt[c]*(8*c^2*x^3 - 3*(b - 2*c*x)*Sinh[2*(a + x*(b + c*x))]))/(192*c^(5/2))","A",1
17,1,155,136,0.4163614,"\int x \cosh ^2\left(a+b x+c x^2\right) \, dx","Integrate[x*Cosh[a + b*x + c*x^2]^2,x]","\frac{\sqrt{2 \pi } b \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right) \left(\sinh \left(2 a-\frac{b^2}{2 c}\right)-\cosh \left(2 a-\frac{b^2}{2 c}\right)\right)-\sqrt{2 \pi } b \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right) \left(\sinh \left(2 a-\frac{b^2}{2 c}\right)+\cosh \left(2 a-\frac{b^2}{2 c}\right)\right)+4 \sqrt{c} \left(\sinh (2 (a+x (b+c x)))+2 c x^2\right)}{32 c^{3/2}}","-\frac{\sqrt{\frac{\pi }{2}} b e^{\frac{b^2}{2 c}-2 a} \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{16 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} b e^{2 a-\frac{b^2}{2 c}} \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{16 c^{3/2}}+\frac{\sinh \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{x^2}{4}",1,"(b*Sqrt[2*Pi]*Erf[(b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(-Cosh[2*a - b^2/(2*c)] + Sinh[2*a - b^2/(2*c)]) - b*Sqrt[2*Pi]*Erfi[(b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a - b^2/(2*c)] + Sinh[2*a - b^2/(2*c)]) + 4*Sqrt[c]*(2*c*x^2 + Sinh[2*(a + x*(b + c*x))]))/(32*c^(3/2))","A",1
18,1,140,110,0.1482758,"\int \cosh ^2\left(a+b x+c x^2\right) \, dx","Integrate[Cosh[a + b*x + c*x^2]^2,x]","\frac{\sqrt{\pi } \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right) \left(\cosh \left(2 a-\frac{b^2}{2 c}\right)-\sinh \left(2 a-\frac{b^2}{2 c}\right)\right)+\sqrt{\pi } \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right) \left(\sinh \left(2 a-\frac{b^2}{2 c}\right)+\cosh \left(2 a-\frac{b^2}{2 c}\right)\right)+4 \sqrt{2} \sqrt{c} x}{8 \sqrt{2} \sqrt{c}}","\frac{\sqrt{\frac{\pi }{2}} e^{\frac{b^2}{2 c}-2 a} \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{c}}+\frac{\sqrt{\frac{\pi }{2}} e^{2 a-\frac{b^2}{2 c}} \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{c}}+\frac{x}{2}",1,"(4*Sqrt[2]*Sqrt[c]*x + Sqrt[Pi]*Erf[(b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a - b^2/(2*c)] - Sinh[2*a - b^2/(2*c)]) + Sqrt[Pi]*Erfi[(b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a - b^2/(2*c)] + Sinh[2*a - b^2/(2*c)]))/(8*Sqrt[2]*Sqrt[c])","A",1
19,0,0,33,35.2463045,"\int \frac{\cosh ^2\left(a+b x+c x^2\right)}{x} \, dx","Integrate[Cosh[a + b*x + c*x^2]^2/x,x]","\int \frac{\cosh ^2\left(a+b x+c x^2\right)}{x} \, dx","\frac{1}{2} \text{Int}\left(\frac{\cosh \left(2 a+2 b x+2 c x^2\right)}{x},x\right)+\frac{\log (x)}{2}",0,"Integrate[Cosh[a + b*x + c*x^2]^2/x, x]","A",-1
20,1,181,268,0.7687861,"\int x^2 \cosh ^2\left(a+b x-c x^2\right) \, dx","Integrate[x^2*Cosh[a + b*x - c*x^2]^2,x]","\frac{3 \sqrt{2 \pi } \left(b^2+c\right) \text{erf}\left(\frac{2 c x-b}{\sqrt{2} \sqrt{c}}\right) \left(\sinh \left(2 a+\frac{b^2}{2 c}\right)+\cosh \left(2 a+\frac{b^2}{2 c}\right)\right)+3 \sqrt{2 \pi } \left(b^2-c\right) \text{erfi}\left(\frac{2 c x-b}{\sqrt{2} \sqrt{c}}\right) \left(\cosh \left(2 a+\frac{b^2}{2 c}\right)-\sinh \left(2 a+\frac{b^2}{2 c}\right)\right)+4 \sqrt{c} \left(8 c^2 x^3-3 (b+2 c x) \sinh (2 (a+x (b-c x)))\right)}{192 c^{5/2}}","-\frac{\sqrt{\frac{\pi }{2}} e^{2 a+\frac{b^2}{2 c}} \text{erf}\left(\frac{b-2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} b^2 e^{2 a+\frac{b^2}{2 c}} \text{erf}\left(\frac{b-2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} e^{-2 a-\frac{b^2}{2 c}} \text{erfi}\left(\frac{b-2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} b^2 e^{-2 a-\frac{b^2}{2 c}} \text{erfi}\left(\frac{b-2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{5/2}}-\frac{b \sinh \left(2 a+2 b x-2 c x^2\right)}{16 c^2}-\frac{x \sinh \left(2 a+2 b x-2 c x^2\right)}{8 c}+\frac{x^3}{6}",1,"(3*(b^2 - c)*Sqrt[2*Pi]*Erfi[(-b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a + b^2/(2*c)] - Sinh[2*a + b^2/(2*c)]) + 3*(b^2 + c)*Sqrt[2*Pi]*Erf[(-b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a + b^2/(2*c)] + Sinh[2*a + b^2/(2*c)]) + 4*Sqrt[c]*(8*c^2*x^3 - 3*(b + 2*c*x)*Sinh[2*(a + x*(b - c*x))]))/(192*c^(5/2))","A",1
21,1,161,136,0.4122813,"\int x \cosh ^2\left(a+b x-c x^2\right) \, dx","Integrate[x*Cosh[a + b*x - c*x^2]^2,x]","\frac{\sqrt{2 \pi } b \text{erf}\left(\frac{2 c x-b}{\sqrt{2} \sqrt{c}}\right) \left(\sinh \left(2 a+\frac{b^2}{2 c}\right)+\cosh \left(2 a+\frac{b^2}{2 c}\right)\right)+\sqrt{2 \pi } b \text{erfi}\left(\frac{2 c x-b}{\sqrt{2} \sqrt{c}}\right) \left(\cosh \left(2 a+\frac{b^2}{2 c}\right)-\sinh \left(2 a+\frac{b^2}{2 c}\right)\right)+4 \sqrt{c} \left(2 c x^2-\sinh (2 (a+x (b-c x)))\right)}{32 c^{3/2}}","-\frac{\sqrt{\frac{\pi }{2}} b e^{2 a+\frac{b^2}{2 c}} \text{erf}\left(\frac{b-2 c x}{\sqrt{2} \sqrt{c}}\right)}{16 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} b e^{-2 a-\frac{b^2}{2 c}} \text{erfi}\left(\frac{b-2 c x}{\sqrt{2} \sqrt{c}}\right)}{16 c^{3/2}}-\frac{\sinh \left(2 a+2 b x-2 c x^2\right)}{8 c}+\frac{x^2}{4}",1,"(b*Sqrt[2*Pi]*Erfi[(-b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a + b^2/(2*c)] - Sinh[2*a + b^2/(2*c)]) + b*Sqrt[2*Pi]*Erf[(-b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a + b^2/(2*c)] + Sinh[2*a + b^2/(2*c)]) + 4*Sqrt[c]*(2*c*x^2 - Sinh[2*(a + x*(b - c*x))]))/(32*c^(3/2))","A",1
22,1,144,110,0.1483191,"\int \cosh ^2\left(a+b x-c x^2\right) \, dx","Integrate[Cosh[a + b*x - c*x^2]^2,x]","\frac{\sqrt{\pi } \text{erf}\left(\frac{2 c x-b}{\sqrt{2} \sqrt{c}}\right) \left(\sinh \left(2 a+\frac{b^2}{2 c}\right)+\cosh \left(2 a+\frac{b^2}{2 c}\right)\right)+\sqrt{\pi } \text{erfi}\left(\frac{2 c x-b}{\sqrt{2} \sqrt{c}}\right) \left(\cosh \left(2 a+\frac{b^2}{2 c}\right)-\sinh \left(2 a+\frac{b^2}{2 c}\right)\right)+4 \sqrt{2} \sqrt{c} x}{8 \sqrt{2} \sqrt{c}}","-\frac{\sqrt{\frac{\pi }{2}} e^{2 a+\frac{b^2}{2 c}} \text{erf}\left(\frac{b-2 c x}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{c}}-\frac{\sqrt{\frac{\pi }{2}} e^{-2 a-\frac{b^2}{2 c}} \text{erfi}\left(\frac{b-2 c x}{\sqrt{2} \sqrt{c}}\right)}{8 \sqrt{c}}+\frac{x}{2}",1,"(4*Sqrt[2]*Sqrt[c]*x + Sqrt[Pi]*Erfi[(-b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a + b^2/(2*c)] - Sinh[2*a + b^2/(2*c)]) + Sqrt[Pi]*Erf[(-b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a + b^2/(2*c)] + Sinh[2*a + b^2/(2*c)]))/(8*Sqrt[2]*Sqrt[c])","A",1
23,0,0,33,37.1117306,"\int \frac{\cosh ^2\left(a+b x-c x^2\right)}{x} \, dx","Integrate[Cosh[a + b*x - c*x^2]^2/x,x]","\int \frac{\cosh ^2\left(a+b x-c x^2\right)}{x} \, dx","\frac{1}{2} \text{Int}\left(\frac{\cosh \left(2 a+2 b x-2 c x^2\right)}{x},x\right)+\frac{\log (x)}{2}",0,"Integrate[Cosh[a + b*x - c*x^2]^2/x, x]","A",-1
24,1,99,68,0.2189711,"\int x^2 \cosh ^2\left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[x^2*Cosh[1/4 + x + x^2]^2,x]","\frac{3 \sqrt{2 e \pi } \text{erf}\left(\frac{2 x+1}{\sqrt{2}}\right)+16 \sqrt{e} x^3+6 e x \sinh (2 x (x+1))+6 x \sinh (2 x (x+1))-3 e \sinh (2 x (x+1))-3 \sinh (2 x (x+1))+3 (e-1) (2 x-1) \cosh (2 x (x+1))}{96 \sqrt{e}}","\frac{1}{16} \sqrt{\frac{\pi }{2}} \text{erf}\left(\frac{2 x+1}{\sqrt{2}}\right)+\frac{x^3}{6}+\frac{1}{8} x \sinh \left(2 x^2+2 x+\frac{1}{2}\right)-\frac{1}{16} \sinh \left(2 x^2+2 x+\frac{1}{2}\right)",1,"(16*Sqrt[E]*x^3 + 3*(-1 + E)*(-1 + 2*x)*Cosh[2*x*(1 + x)] + 3*Sqrt[2*E*Pi]*Erf[(1 + 2*x)/Sqrt[2]] - 3*Sinh[2*x*(1 + x)] - 3*E*Sinh[2*x*(1 + x)] + 6*x*Sinh[2*x*(1 + x)] + 6*E*x*Sinh[2*x*(1 + x)])/(96*Sqrt[E])","A",1
25,1,88,75,0.2136615,"\int x \cosh ^2\left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[x*Cosh[1/4 + x + x^2]^2,x]","\frac{-\sqrt{2 e \pi } \text{erf}\left(\frac{2 x+1}{\sqrt{2}}\right)-\sqrt{2 e \pi } \text{erfi}\left(\frac{2 x+1}{\sqrt{2}}\right)+8 \sqrt{e} x^2+2 (1+e) \sinh (2 x (x+1))+2 (e-1) \cosh (2 x (x+1))}{32 \sqrt{e}}","-\frac{1}{16} \sqrt{\frac{\pi }{2}} \text{erf}\left(\frac{2 x+1}{\sqrt{2}}\right)-\frac{1}{16} \sqrt{\frac{\pi }{2}} \text{erfi}\left(\frac{2 x+1}{\sqrt{2}}\right)+\frac{x^2}{4}+\frac{1}{8} \sinh \left(2 x^2+2 x+\frac{1}{2}\right)",1,"(8*Sqrt[E]*x^2 + 2*(-1 + E)*Cosh[2*x*(1 + x)] - Sqrt[2*E*Pi]*Erf[(1 + 2*x)/Sqrt[2]] - Sqrt[2*E*Pi]*Erfi[(1 + 2*x)/Sqrt[2]] + 2*(1 + E)*Sinh[2*x*(1 + x)])/(32*Sqrt[E])","A",1
26,1,48,56,0.076826,"\int \cosh ^2\left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[Cosh[1/4 + x + x^2]^2,x]","\frac{1}{16} \left(\sqrt{2 \pi } \text{erf}\left(\frac{2 x+1}{\sqrt{2}}\right)+\sqrt{2 \pi } \text{erfi}\left(\frac{2 x+1}{\sqrt{2}}\right)+8 x\right)","\frac{1}{8} \sqrt{\frac{\pi }{2}} \text{erf}\left(\frac{2 x+1}{\sqrt{2}}\right)+\frac{1}{8} \sqrt{\frac{\pi }{2}} \text{erfi}\left(\frac{2 x+1}{\sqrt{2}}\right)+\frac{x}{2}",1,"(8*x + Sqrt[2*Pi]*Erf[(1 + 2*x)/Sqrt[2]] + Sqrt[2*Pi]*Erfi[(1 + 2*x)/Sqrt[2]])/16","A",1
27,0,0,31,11.106897,"\int \frac{\cosh ^2\left(\frac{1}{4}+x+x^2\right)}{x} \, dx","Integrate[Cosh[1/4 + x + x^2]^2/x,x]","\int \frac{\cosh ^2\left(\frac{1}{4}+x+x^2\right)}{x} \, dx","\frac{1}{2} \text{Int}\left(\frac{\cosh \left(2 x^2+2 x+\frac{1}{2}\right)}{x},x\right)+\frac{\log (x)}{2}",0,"Integrate[Cosh[1/4 + x + x^2]^2/x, x]","A",-1
28,1,194,261,0.5546207,"\int (d+e x)^2 \cosh \left(a+b x+c x^2\right) \, dx","Integrate[(d + e*x)^2*Cosh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } \left(b^2 e^2+2 c e (e-2 b d)+4 c^2 d^2\right) \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\cosh \left(a-\frac{b^2}{4 c}\right)-\sinh \left(a-\frac{b^2}{4 c}\right)\right)+\sqrt{\pi } \left(b^2 e^2-2 c e (2 b d+e)+4 c^2 d^2\right) \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\sinh \left(a-\frac{b^2}{4 c}\right)+\cosh \left(a-\frac{b^2}{4 c}\right)\right)+4 \sqrt{c} e \sinh (a+x (b+c x)) (-b e+4 c d+2 c e x)}{16 c^{5/2}}","\frac{\sqrt{\pi } e^{\frac{b^2}{4 c}-a} (2 c d-b e)^2 \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } e^{a-\frac{b^2}{4 c}} (2 c d-b e)^2 \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } e^2 e^{\frac{b^2}{4 c}-a} \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}-\frac{\sqrt{\pi } e^2 e^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}+\frac{e (2 c d-b e) \sinh \left(a+b x+c x^2\right)}{4 c^2}+\frac{e (d+e x) \sinh \left(a+b x+c x^2\right)}{2 c}",1,"((4*c^2*d^2 + b^2*e^2 + 2*c*e*(-2*b*d + e))*Sqrt[Pi]*Erf[(b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a - b^2/(4*c)] - Sinh[a - b^2/(4*c)]) + (4*c^2*d^2 + b^2*e^2 - 2*c*e*(2*b*d + e))*Sqrt[Pi]*Erfi[(b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a - b^2/(4*c)] + Sinh[a - b^2/(4*c)]) + 4*Sqrt[c]*e*(4*c*d - b*e + 2*c*e*x)*Sinh[a + x*(b + c*x)])/(16*c^(5/2))","A",1
29,1,146,128,0.2449159,"\int (d+e x) \cosh \left(a+b x+c x^2\right) \, dx","Integrate[(d + e*x)*Cosh[a + b*x + c*x^2],x]","\frac{\sqrt{\pi } (2 c d-b e) \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\cosh \left(a-\frac{b^2}{4 c}\right)-\sinh \left(a-\frac{b^2}{4 c}\right)\right)+\sqrt{\pi } (2 c d-b e) \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right) \left(\sinh \left(a-\frac{b^2}{4 c}\right)+\cosh \left(a-\frac{b^2}{4 c}\right)\right)+4 \sqrt{c} e \sinh (a+x (b+c x))}{8 c^{3/2}}","\frac{\sqrt{\pi } e^{\frac{b^2}{4 c}-a} (2 c d-b e) \text{erf}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}+\frac{\sqrt{\pi } e^{a-\frac{b^2}{4 c}} (2 c d-b e) \text{erfi}\left(\frac{b+2 c x}{2 \sqrt{c}}\right)}{8 c^{3/2}}+\frac{e \sinh \left(a+b x+c x^2\right)}{2 c}",1,"((2*c*d - b*e)*Sqrt[Pi]*Erf[(b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a - b^2/(4*c)] - Sinh[a - b^2/(4*c)]) + (2*c*d - b*e)*Sqrt[Pi]*Erfi[(b + 2*c*x)/(2*Sqrt[c])]*(Cosh[a - b^2/(4*c)] + Sinh[a - b^2/(4*c)]) + 4*Sqrt[c]*e*Sinh[a + x*(b + c*x)])/(8*c^(3/2))","A",1
30,0,0,22,2.6128415,"\int \frac{\cosh \left(a+b x+c x^2\right)}{d+e x} \, dx","Integrate[Cosh[a + b*x + c*x^2]/(d + e*x),x]","\int \frac{\cosh \left(a+b x+c x^2\right)}{d+e x} \, dx","\text{Int}\left(\frac{\cosh \left(a+b x+c x^2\right)}{d+e x},x\right)",0,"Integrate[Cosh[a + b*x + c*x^2]/(d + e*x), x]","A",-1
31,1,240,311,1.4161842,"\int (d+e x)^2 \cosh ^2\left(a+b x+c x^2\right) \, dx","Integrate[(d + e*x)^2*Cosh[a + b*x + c*x^2]^2,x]","\frac{3 \sqrt{2 \pi } \left(b^2 e^2+c e (e-4 b d)+4 c^2 d^2\right) \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right) \left(\cosh \left(2 a-\frac{b^2}{2 c}\right)-\sinh \left(2 a-\frac{b^2}{2 c}\right)\right)+3 \sqrt{2 \pi } \left(b^2 e^2-c e (4 b d+e)+4 c^2 d^2\right) \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right) \left(\sinh \left(2 a-\frac{b^2}{2 c}\right)+\cosh \left(2 a-\frac{b^2}{2 c}\right)\right)+4 \sqrt{c} \left(3 e \sinh (2 (a+x (b+c x))) (-b e+4 c d+2 c e x)+8 c^2 x \left(3 d^2+3 d e x+e^2 x^2\right)\right)}{192 c^{5/2}}","\frac{\sqrt{\frac{\pi }{2}} e^{\frac{b^2}{2 c}-2 a} (2 c d-b e)^2 \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} e^{2 a-\frac{b^2}{2 c}} (2 c d-b e)^2 \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} e^2 e^{\frac{b^2}{2 c}-2 a} \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} e^2 e^{2 a-\frac{b^2}{2 c}} \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{32 c^{3/2}}+\frac{e (2 c d-b e) \sinh \left(2 a+2 b x+2 c x^2\right)}{16 c^2}+\frac{e (d+e x) \sinh \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{(d+e x)^3}{6 e}",1,"(3*(4*c^2*d^2 + b^2*e^2 + c*e*(-4*b*d + e))*Sqrt[2*Pi]*Erf[(b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a - b^2/(2*c)] - Sinh[2*a - b^2/(2*c)]) + 3*(4*c^2*d^2 + b^2*e^2 - c*e*(4*b*d + e))*Sqrt[2*Pi]*Erfi[(b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a - b^2/(2*c)] + Sinh[2*a - b^2/(2*c)]) + 4*Sqrt[c]*(8*c^2*x*(3*d^2 + 3*d*e*x + e^2*x^2) + 3*e*(4*c*d - b*e + 2*c*e*x)*Sinh[2*(a + x*(b + c*x))]))/(192*c^(5/2))","A",1
32,1,177,160,0.6836101,"\int (d+e x) \cosh ^2\left(a+b x+c x^2\right) \, dx","Integrate[(d + e*x)*Cosh[a + b*x + c*x^2]^2,x]","\frac{\sqrt{2 \pi } (2 c d-b e) \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right) \left(\cosh \left(2 a-\frac{b^2}{2 c}\right)-\sinh \left(2 a-\frac{b^2}{2 c}\right)\right)+\sqrt{2 \pi } (2 c d-b e) \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right) \left(\sinh \left(2 a-\frac{b^2}{2 c}\right)+\cosh \left(2 a-\frac{b^2}{2 c}\right)\right)+4 \sqrt{c} (e \sinh (2 (a+x (b+c x)))+2 c x (2 d+e x))}{32 c^{3/2}}","\frac{\sqrt{\frac{\pi }{2}} e^{\frac{b^2}{2 c}-2 a} (2 c d-b e) \text{erf}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{16 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} e^{2 a-\frac{b^2}{2 c}} (2 c d-b e) \text{erfi}\left(\frac{b+2 c x}{\sqrt{2} \sqrt{c}}\right)}{16 c^{3/2}}+\frac{e \sinh \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{(d+e x)^2}{4 e}",1,"((2*c*d - b*e)*Sqrt[2*Pi]*Erf[(b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a - b^2/(2*c)] - Sinh[2*a - b^2/(2*c)]) + (2*c*d - b*e)*Sqrt[2*Pi]*Erfi[(b + 2*c*x)/(Sqrt[2]*Sqrt[c])]*(Cosh[2*a - b^2/(2*c)] + Sinh[2*a - b^2/(2*c)]) + 4*Sqrt[c]*(2*c*x*(2*d + e*x) + e*Sinh[2*(a + x*(b + c*x))]))/(32*c^(3/2))","A",1
33,0,0,44,8.9424714,"\int \frac{\cosh ^2\left(a+b x+c x^2\right)}{d+e x} \, dx","Integrate[Cosh[a + b*x + c*x^2]^2/(d + e*x),x]","\int \frac{\cosh ^2\left(a+b x+c x^2\right)}{d+e x} \, dx","\frac{1}{2} \text{Int}\left(\frac{\cosh \left(2 a+2 b x+2 c x^2\right)}{d+e x},x\right)+\frac{\log (d+e x)}{2 e}",0,"Integrate[Cosh[a + b*x + c*x^2]^2/(d + e*x), x]","A",-1