1,1,72,96,0.1271758,"\int x^5 \text{erf}(b x) \, dx","Integrate[x^5*Erf[b*x],x]","\frac{e^{-b^2 x^2} \left(8 b^5 x^5+20 b^3 x^3+\sqrt{\pi } e^{b^2 x^2} \left(8 b^6 x^6-15\right) \text{erf}(b x)+30 b x\right)}{48 \sqrt{\pi } b^6}","-\frac{5 \text{erf}(b x)}{16 b^6}+\frac{x^5 e^{-b^2 x^2}}{6 \sqrt{\pi } b}+\frac{5 x e^{-b^2 x^2}}{8 \sqrt{\pi } b^5}+\frac{5 x^3 e^{-b^2 x^2}}{12 \sqrt{\pi } b^3}+\frac{1}{6} x^6 \text{erf}(b x)",1,"(30*b*x + 20*b^3*x^3 + 8*b^5*x^5 + E^(b^2*x^2)*Sqrt[Pi]*(-15 + 8*b^6*x^6)*Erf[b*x])/(48*b^6*E^(b^2*x^2)*Sqrt[Pi])","A",1
2,1,63,71,0.0259665,"\int x^3 \text{erf}(b x) \, dx","Integrate[x^3*Erf[b*x],x]","-\frac{3 \text{erf}(b x)}{16 b^4}+e^{-b^2 x^2} \left(\frac{3 x}{8 \sqrt{\pi } b^3}+\frac{x^3}{4 \sqrt{\pi } b}\right)+\frac{1}{4} x^4 \text{erf}(b x)","-\frac{3 \text{erf}(b x)}{16 b^4}+\frac{x^3 e^{-b^2 x^2}}{4 \sqrt{\pi } b}+\frac{3 x e^{-b^2 x^2}}{8 \sqrt{\pi } b^3}+\frac{1}{4} x^4 \text{erf}(b x)",1,"((3*x)/(8*b^3*Sqrt[Pi]) + x^3/(4*b*Sqrt[Pi]))/E^(b^2*x^2) - (3*Erf[b*x])/(16*b^4) + (x^4*Erf[b*x])/4","A",1
3,1,42,46,0.0427329,"\int x \text{erf}(b x) \, dx","Integrate[x*Erf[b*x],x]","\frac{1}{4} \left(\left(2 x^2-\frac{1}{b^2}\right) \text{erf}(b x)+\frac{2 x e^{-b^2 x^2}}{\sqrt{\pi } b}\right)","-\frac{\text{erf}(b x)}{4 b^2}+\frac{x e^{-b^2 x^2}}{2 \sqrt{\pi } b}+\frac{1}{2} x^2 \text{erf}(b x)",1,"((2*x)/(b*E^(b^2*x^2)*Sqrt[Pi]) + (-b^(-2) + 2*x^2)*Erf[b*x])/4","A",1
4,1,32,32,0.0841006,"\int \frac{\text{erf}(b x)}{x} \, dx","Integrate[Erf[b*x]/x,x]","\frac{2 b x \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-b^2 x^2\right)}{\sqrt{\pi }}","\frac{2 b x \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-b^2 x^2\right)}{\sqrt{\pi }}",1,"(2*b*x*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2}, -(b^2*x^2)])/Sqrt[Pi]","A",1
5,1,42,42,0.0501186,"\int \frac{\text{erf}(b x)}{x^3} \, dx","Integrate[Erf[b*x]/x^3,x]","b^2 (-\text{erf}(b x))-\frac{b e^{-b^2 x^2}}{\sqrt{\pi } x}-\frac{\text{erf}(b x)}{2 x^2}","b^2 (-\text{erf}(b x))-\frac{b e^{-b^2 x^2}}{\sqrt{\pi } x}-\frac{\text{erf}(b x)}{2 x^2}",1,"-(b/(E^(b^2*x^2)*Sqrt[Pi]*x)) - b^2*Erf[b*x] - Erf[b*x]/(2*x^2)","A",1
6,1,63,71,0.0193365,"\int \frac{\text{erf}(b x)}{x^5} \, dx","Integrate[Erf[b*x]/x^5,x]","\frac{1}{3} b^4 \text{erf}(b x)+e^{-b^2 x^2} \left(\frac{b^3}{3 \sqrt{\pi } x}-\frac{b}{6 \sqrt{\pi } x^3}\right)-\frac{\text{erf}(b x)}{4 x^4}","\frac{1}{3} b^4 \text{erf}(b x)-\frac{b e^{-b^2 x^2}}{6 \sqrt{\pi } x^3}+\frac{b^3 e^{-b^2 x^2}}{3 \sqrt{\pi } x}-\frac{\text{erf}(b x)}{4 x^4}",1,"(-1/6*b/(Sqrt[Pi]*x^3) + b^3/(3*Sqrt[Pi]*x))/E^(b^2*x^2) + (b^4*Erf[b*x])/3 - Erf[b*x]/(4*x^4)","A",1
7,1,73,96,0.0222572,"\int \frac{\text{erf}(b x)}{x^7} \, dx","Integrate[Erf[b*x]/x^7,x]","\frac{e^{-b^2 x^2} \left(-8 b^5 x^5+4 b^3 x^3-\sqrt{\pi } e^{b^2 x^2} \left(8 b^6 x^6+15\right) \text{erf}(b x)-6 b x\right)}{90 \sqrt{\pi } x^6}","-\frac{4}{45} b^6 \text{erf}(b x)-\frac{b e^{-b^2 x^2}}{15 \sqrt{\pi } x^5}-\frac{4 b^5 e^{-b^2 x^2}}{45 \sqrt{\pi } x}+\frac{2 b^3 e^{-b^2 x^2}}{45 \sqrt{\pi } x^3}-\frac{\text{erf}(b x)}{6 x^6}",1,"(-6*b*x + 4*b^3*x^3 - 8*b^5*x^5 - E^(b^2*x^2)*Sqrt[Pi]*(15 + 8*b^6*x^6)*Erf[b*x])/(90*E^(b^2*x^2)*Sqrt[Pi]*x^6)","A",1
8,1,72,109,0.0221253,"\int x^6 \text{erf}(b x) \, dx","Integrate[x^6*Erf[b*x],x]","\frac{e^{-b^2 x^2} \left(b^6 x^6+3 b^4 x^4+6 b^2 x^2+\sqrt{\pi } b^7 x^7 e^{b^2 x^2} \text{erf}(b x)+6\right)}{7 \sqrt{\pi } b^7}","\frac{x^6 e^{-b^2 x^2}}{7 \sqrt{\pi } b}+\frac{6 e^{-b^2 x^2}}{7 \sqrt{\pi } b^7}+\frac{6 x^2 e^{-b^2 x^2}}{7 \sqrt{\pi } b^5}+\frac{3 x^4 e^{-b^2 x^2}}{7 \sqrt{\pi } b^3}+\frac{1}{7} x^7 \text{erf}(b x)",1,"(6 + 6*b^2*x^2 + 3*b^4*x^4 + b^6*x^6 + b^7*E^(b^2*x^2)*Sqrt[Pi]*x^7*Erf[b*x])/(7*b^7*E^(b^2*x^2)*Sqrt[Pi])","A",1
9,1,66,84,0.0200641,"\int x^4 \text{erf}(b x) \, dx","Integrate[x^4*Erf[b*x],x]","e^{-b^2 x^2} \left(\frac{2}{5 \sqrt{\pi } b^5}+\frac{2 x^2}{5 \sqrt{\pi } b^3}+\frac{x^4}{5 \sqrt{\pi } b}\right)+\frac{1}{5} x^5 \text{erf}(b x)","\frac{x^4 e^{-b^2 x^2}}{5 \sqrt{\pi } b}+\frac{2 e^{-b^2 x^2}}{5 \sqrt{\pi } b^5}+\frac{2 x^2 e^{-b^2 x^2}}{5 \sqrt{\pi } b^3}+\frac{1}{5} x^5 \text{erf}(b x)",1,"(2/(5*b^5*Sqrt[Pi]) + (2*x^2)/(5*b^3*Sqrt[Pi]) + x^4/(5*b*Sqrt[Pi]))/E^(b^2*x^2) + (x^5*Erf[b*x])/5","A",1
10,1,41,59,0.0250115,"\int x^2 \text{erf}(b x) \, dx","Integrate[x^2*Erf[b*x],x]","\frac{1}{3} \left(\frac{e^{-b^2 x^2} \left(b^2 x^2+1\right)}{\sqrt{\pi } b^3}+x^3 \text{erf}(b x)\right)","\frac{x^2 e^{-b^2 x^2}}{3 \sqrt{\pi } b}+\frac{e^{-b^2 x^2}}{3 \sqrt{\pi } b^3}+\frac{1}{3} x^3 \text{erf}(b x)",1,"((1 + b^2*x^2)/(b^3*E^(b^2*x^2)*Sqrt[Pi]) + x^3*Erf[b*x])/3","A",1
11,1,26,26,0.008748,"\int \text{erf}(b x) \, dx","Integrate[Erf[b*x],x]","\frac{e^{-b^2 x^2}}{\sqrt{\pi } b}+x \text{erf}(b x)","\frac{e^{-b^2 x^2}}{\sqrt{\pi } b}+x \text{erf}(b x)",1,"1/(b*E^(b^2*x^2)*Sqrt[Pi]) + x*Erf[b*x]","A",1
12,1,26,26,0.014852,"\int \frac{\text{erf}(b x)}{x^2} \, dx","Integrate[Erf[b*x]/x^2,x]","\frac{b \text{Ei}\left(-b^2 x^2\right)}{\sqrt{\pi }}-\frac{\text{erf}(b x)}{x}","\frac{b \text{Ei}\left(-b^2 x^2\right)}{\sqrt{\pi }}-\frac{\text{erf}(b x)}{x}",1,"-(Erf[b*x]/x) + (b*ExpIntegralEi[-(b^2*x^2)])/Sqrt[Pi]","A",1
13,1,47,56,0.0547399,"\int \frac{\text{erf}(b x)}{x^4} \, dx","Integrate[Erf[b*x]/x^4,x]","-\frac{\frac{b x \left(b^2 x^2 \text{Ei}\left(-b^2 x^2\right)+e^{-b^2 x^2}\right)}{\sqrt{\pi }}+\text{erf}(b x)}{3 x^3}","-\frac{b e^{-b^2 x^2}}{3 \sqrt{\pi } x^2}-\frac{b^3 \text{Ei}\left(-b^2 x^2\right)}{3 \sqrt{\pi }}-\frac{\text{erf}(b x)}{3 x^3}",1,"-1/3*(Erf[b*x] + (b*x*(E^(-(b^2*x^2)) + b^2*x^2*ExpIntegralEi[-(b^2*x^2)]))/Sqrt[Pi])/x^3","A",1
14,1,62,81,0.0513247,"\int \frac{\text{erf}(b x)}{x^6} \, dx","Integrate[Erf[b*x]/x^6,x]","\frac{b x e^{-b^2 x^2} \left(b^2 x^2-1\right)+b^5 x^5 \text{Ei}\left(-b^2 x^2\right)-2 \sqrt{\pi } \text{erf}(b x)}{10 \sqrt{\pi } x^5}","-\frac{b e^{-b^2 x^2}}{10 \sqrt{\pi } x^4}+\frac{b^5 \text{Ei}\left(-b^2 x^2\right)}{10 \sqrt{\pi }}+\frac{b^3 e^{-b^2 x^2}}{10 \sqrt{\pi } x^2}-\frac{\text{erf}(b x)}{5 x^5}",1,"((b*x*(-1 + b^2*x^2))/E^(b^2*x^2) - 2*Sqrt[Pi]*Erf[b*x] + b^5*x^5*ExpIntegralEi[-(b^2*x^2)])/(10*Sqrt[Pi]*x^5)","A",1
15,1,248,289,0.3124874,"\int (c+d x)^3 \text{erf}(a+b x) \, dx","Integrate[(c + d*x)^3*Erf[a + b*x],x]","\frac{e^{-(a+b x)^2} \left(2 b d^2 \left(8 \left(a^2+1\right) c+\left(2 a^2+3\right) d x\right)-2 a \left(2 a^2+5\right) d^3-\sqrt{\pi } e^{(a+b x)^2} \text{erf}(a+b x) \left(4 a^4 d^3-16 a^3 b c d^2+12 a^2 \left(2 b^2 c^2 d+d^3\right)-8 a \left(2 b^3 c^3+3 b c d^2\right)-4 b^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)+12 b^2 c^2 d+3 d^3\right)-4 a b^2 d \left(6 c^2+4 c d x+d^2 x^2\right)+4 b^3 \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right)}{16 \sqrt{\pi } b^4}","\frac{d^2 e^{-(a+b x)^2} (a+b x)^2 (b c-a d)}{\sqrt{\pi } b^4}+\frac{d^2 e^{-(a+b x)^2} (b c-a d)}{\sqrt{\pi } b^4}-\frac{(b c-a d)^4 \text{erf}(a+b x)}{4 b^4 d}-\frac{3 d (b c-a d)^2 \text{erf}(a+b x)}{4 b^4}+\frac{e^{-(a+b x)^2} (b c-a d)^3}{\sqrt{\pi } b^4}+\frac{3 d e^{-(a+b x)^2} (a+b x) (b c-a d)^2}{2 \sqrt{\pi } b^4}-\frac{3 d^3 \text{erf}(a+b x)}{16 b^4}+\frac{d^3 e^{-(a+b x)^2} (a+b x)^3}{4 \sqrt{\pi } b^4}+\frac{3 d^3 e^{-(a+b x)^2} (a+b x)}{8 \sqrt{\pi } b^4}+\frac{(c+d x)^4 \text{erf}(a+b x)}{4 d}",1,"(-2*a*(5 + 2*a^2)*d^3 + 2*b*d^2*(8*(1 + a^2)*c + (3 + 2*a^2)*d*x) - 4*a*b^2*d*(6*c^2 + 4*c*d*x + d^2*x^2) + 4*b^3*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) - E^(a + b*x)^2*Sqrt[Pi]*(12*b^2*c^2*d - 16*a^3*b*c*d^2 + 3*d^3 + 4*a^4*d^3 - 8*a*(2*b^3*c^3 + 3*b*c*d^2) + 12*a^2*(2*b^2*c^2*d + d^3) - 4*b^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3))*Erf[a + b*x])/(16*b^4*E^(a + b*x)^2*Sqrt[Pi])","A",1
16,1,138,192,0.2325021,"\int (c+d x)^2 \text{erf}(a+b x) \, dx","Integrate[(c + d*x)^2*Erf[a + b*x],x]","\frac{\frac{2 e^{-(a+b x)^2} \left(\left(a^2+1\right) d^2-a b d (3 c+d x)+b^2 \left(3 c^2+3 c d x+d^2 x^2\right)\right)}{\sqrt{\pi }}+\text{erf}(a+b x) \left(2 a^3 d^2-6 a^2 b c d+3 a \left(2 b^2 c^2+d^2\right)+2 b^3 x \left(3 c^2+3 c d x+d^2 x^2\right)-3 b c d\right)}{6 b^3}","-\frac{(b c-a d)^3 \text{erf}(a+b x)}{3 b^3 d}-\frac{d (b c-a d) \text{erf}(a+b x)}{2 b^3}+\frac{e^{-(a+b x)^2} (b c-a d)^2}{\sqrt{\pi } b^3}+\frac{d e^{-(a+b x)^2} (a+b x) (b c-a d)}{\sqrt{\pi } b^3}+\frac{d^2 e^{-(a+b x)^2} (a+b x)^2}{3 \sqrt{\pi } b^3}+\frac{d^2 e^{-(a+b x)^2}}{3 \sqrt{\pi } b^3}+\frac{(c+d x)^3 \text{erf}(a+b x)}{3 d}",1,"((2*((1 + a^2)*d^2 - a*b*d*(3*c + d*x) + b^2*(3*c^2 + 3*c*d*x + d^2*x^2)))/(E^(a + b*x)^2*Sqrt[Pi]) + (-3*b*c*d - 6*a^2*b*c*d + 2*a^3*d^2 + 3*a*(2*b^2*c^2 + d^2) + 2*b^3*x*(3*c^2 + 3*c*d*x + d^2*x^2))*Erf[a + b*x])/(6*b^3)","A",1
17,1,88,118,0.1023521,"\int (c+d x) \text{erf}(a+b x) \, dx","Integrate[(c + d*x)*Erf[a + b*x],x]","\frac{e^{-(a+b x)^2} \left(-\sqrt{\pi } e^{(a+b x)^2} \text{erf}(a+b x) \left(2 a^2 d-4 a b c-4 b^2 c x-2 b^2 d x^2+d\right)-2 a d+4 b c+2 b d x\right)}{4 \sqrt{\pi } b^2}","-\frac{(b c-a d)^2 \text{erf}(a+b x)}{2 b^2 d}+\frac{e^{-(a+b x)^2} (b c-a d)}{\sqrt{\pi } b^2}-\frac{d \text{erf}(a+b x)}{4 b^2}+\frac{d e^{-(a+b x)^2} (a+b x)}{2 \sqrt{\pi } b^2}+\frac{(c+d x)^2 \text{erf}(a+b x)}{2 d}",1,"(4*b*c - 2*a*d + 2*b*d*x - E^(a + b*x)^2*Sqrt[Pi]*(-4*a*b*c + d + 2*a^2*d - 4*b^2*c*x - 2*b^2*d*x^2)*Erf[a + b*x])/(4*b^2*E^(a + b*x)^2*Sqrt[Pi])","A",1
18,1,35,36,0.0512062,"\int \text{erf}(a+b x) \, dx","Integrate[Erf[a + b*x],x]","\left(\frac{a}{b}+x\right) \text{erf}(a+b x)+\frac{e^{-(a+b x)^2}}{\sqrt{\pi } b}","\frac{(a+b x) \text{erf}(a+b x)}{b}+\frac{e^{-(a+b x)^2}}{\sqrt{\pi } b}",1,"1/(b*E^(a + b*x)^2*Sqrt[Pi]) + (a/b + x)*Erf[a + b*x]","A",1
19,0,0,17,1.3707897,"\int \frac{\text{erf}(a+b x)}{c+d x} \, dx","Integrate[Erf[a + b*x]/(c + d*x),x]","\int \frac{\text{erf}(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{erf}(a+b x)}{c+d x},x\right)",0,"Integrate[Erf[a + b*x]/(c + d*x), x]","A",-1
20,0,0,52,0.3408579,"\int \frac{\text{erf}(a+b x)}{(c+d x)^2} \, dx","Integrate[Erf[a + b*x]/(c + d*x)^2,x]","\int \frac{\text{erf}(a+b x)}{(c+d x)^2} \, dx","\frac{2 b \text{Int}\left(\frac{e^{-(a+b x)^2}}{c+d x},x\right)}{\sqrt{\pi } d}-\frac{\text{erf}(a+b x)}{d (c+d x)}",0,"Integrate[Erf[a + b*x]/(c + d*x)^2, x]","A",-1
21,0,0,107,0.5764762,"\int \frac{\text{erf}(a+b x)}{(c+d x)^3} \, dx","Integrate[Erf[a + b*x]/(c + d*x)^3,x]","\int \frac{\text{erf}(a+b x)}{(c+d x)^3} \, dx","\frac{2 b^2 (b c-a d) \text{Int}\left(\frac{e^{-(a+b x)^2}}{c+d x},x\right)}{\sqrt{\pi } d^3}-\frac{b^2 \text{erf}(a+b x)}{d^3}-\frac{b e^{-(a+b x)^2}}{\sqrt{\pi } d^2 (c+d x)}-\frac{\text{erf}(a+b x)}{2 d (c+d x)^2}",0,"Integrate[Erf[a + b*x]/(c + d*x)^3, x]","A",-1
22,1,106,178,0.0486363,"\int x^5 \text{erf}(b x)^2 \, dx","Integrate[x^5*Erf[b*x]^2,x]","\frac{e^{-2 b^2 x^2} \left(8 b^4 x^4+28 b^2 x^2+\pi  e^{2 b^2 x^2} \left(8 b^6 x^6-15\right) \text{erf}(b x)^2+4 \sqrt{\pi } b x e^{b^2 x^2} \left(4 b^4 x^4+10 b^2 x^2+15\right) \text{erf}(b x)+44\right)}{48 \pi  b^6}","-\frac{5 \text{erf}(b x)^2}{16 b^6}+\frac{x^5 e^{-b^2 x^2} \text{erf}(b x)}{3 \sqrt{\pi } b}+\frac{x^4 e^{-2 b^2 x^2}}{6 \pi  b^2}+\frac{11 e^{-2 b^2 x^2}}{12 \pi  b^6}+\frac{5 x e^{-b^2 x^2} \text{erf}(b x)}{4 \sqrt{\pi } b^5}+\frac{7 x^2 e^{-2 b^2 x^2}}{12 \pi  b^4}+\frac{5 x^3 e^{-b^2 x^2} \text{erf}(b x)}{6 \sqrt{\pi } b^3}+\frac{1}{6} x^6 \text{erf}(b x)^2",1,"(44 + 28*b^2*x^2 + 8*b^4*x^4 + 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(15 + 10*b^2*x^2 + 4*b^4*x^4)*Erf[b*x] + E^(2*b^2*x^2)*Pi*(-15 + 8*b^6*x^6)*Erf[b*x]^2)/(48*b^6*E^(2*b^2*x^2)*Pi)","A",1
23,1,90,126,0.0420529,"\int x^3 \text{erf}(b x)^2 \, dx","Integrate[x^3*Erf[b*x]^2,x]","\frac{e^{-2 b^2 x^2} \left(4 \sqrt{\pi } b x e^{b^2 x^2} \left(2 b^2 x^2+3\right) \text{erf}(b x)+4 b^2 x^2+\pi  e^{2 b^2 x^2} \left(4 b^4 x^4-3\right) \text{erf}(b x)^2+8\right)}{16 \pi  b^4}","-\frac{3 \text{erf}(b x)^2}{16 b^4}+\frac{x^3 e^{-b^2 x^2} \text{erf}(b x)}{2 \sqrt{\pi } b}+\frac{x^2 e^{-2 b^2 x^2}}{4 \pi  b^2}+\frac{e^{-2 b^2 x^2}}{2 \pi  b^4}+\frac{3 x e^{-b^2 x^2} \text{erf}(b x)}{4 \sqrt{\pi } b^3}+\frac{1}{4} x^4 \text{erf}(b x)^2",1,"(8 + 4*b^2*x^2 + 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(3 + 2*b^2*x^2)*Erf[b*x] + E^(2*b^2*x^2)*Pi*(-3 + 4*b^4*x^4)*Erf[b*x]^2)/(16*b^4*E^(2*b^2*x^2)*Pi)","A",1
24,1,64,71,0.0496721,"\int x \text{erf}(b x)^2 \, dx","Integrate[x*Erf[b*x]^2,x]","\frac{\pi  \left(2 b^2 x^2-1\right) \text{erf}(b x)^2+4 \sqrt{\pi } b x e^{-b^2 x^2} \text{erf}(b x)+2 e^{-2 b^2 x^2}}{4 \pi  b^2}","\frac{x e^{-b^2 x^2} \text{erf}(b x)}{\sqrt{\pi } b}-\frac{\text{erf}(b x)^2}{4 b^2}+\frac{e^{-2 b^2 x^2}}{2 \pi  b^2}+\frac{1}{2} x^2 \text{erf}(b x)^2",1,"(2/E^(2*b^2*x^2) + (4*b*Sqrt[Pi]*x*Erf[b*x])/E^(b^2*x^2) + Pi*(-1 + 2*b^2*x^2)*Erf[b*x]^2)/(4*b^2*Pi)","A",1
25,0,0,13,0.0283925,"\int \frac{\text{erf}(b x)^2}{x} \, dx","Integrate[Erf[b*x]^2/x,x]","\int \frac{\text{erf}(b x)^2}{x} \, dx","\text{Int}\left(\frac{\text{erf}(b x)^2}{x},x\right)",0,"Integrate[Erf[b*x]^2/x, x]","A",-1
26,1,63,67,0.0276547,"\int \frac{\text{erf}(b x)^2}{x^3} \, dx","Integrate[Erf[b*x]^2/x^3,x]","-\frac{2 b e^{-b^2 x^2} \text{erf}(b x)}{\sqrt{\pi } x}+\left(-b^2-\frac{1}{2 x^2}\right) \text{erf}(b x)^2+\frac{2 b^2 \text{Ei}\left(-2 b^2 x^2\right)}{\pi }","-\frac{2 b e^{-b^2 x^2} \text{erf}(b x)}{\sqrt{\pi } x}+b^2 \left(-\text{erf}(b x)^2\right)+\frac{2 b^2 \text{Ei}\left(-2 b^2 x^2\right)}{\pi }-\frac{\text{erf}(b x)^2}{2 x^2}",1,"(-2*b*Erf[b*x])/(E^(b^2*x^2)*Sqrt[Pi]*x) + (-b^2 - 1/(2*x^2))*Erf[b*x]^2 + (2*b^2*ExpIntegralEi[-2*b^2*x^2])/Pi","A",1
27,1,97,125,0.0853665,"\int \frac{\text{erf}(b x)^2}{x^5} \, dx","Integrate[Erf[b*x]^2/x^5,x]","\frac{\left(4 b^4 x^4-3\right) \text{erf}(b x)^2+\frac{4 b x e^{-b^2 x^2} \left(2 b^2 x^2-1\right) \text{erf}(b x)}{\sqrt{\pi }}-\frac{4 b^2 x^2 \left(4 b^2 x^2 \text{Ei}\left(-2 b^2 x^2\right)+e^{-2 b^2 x^2}\right)}{\pi }}{12 x^4}","\frac{1}{3} b^4 \text{erf}(b x)^2-\frac{b e^{-b^2 x^2} \text{erf}(b x)}{3 \sqrt{\pi } x^3}-\frac{b^2 e^{-2 b^2 x^2}}{3 \pi  x^2}-\frac{4 b^4 \text{Ei}\left(-2 b^2 x^2\right)}{3 \pi }+\frac{2 b^3 e^{-b^2 x^2} \text{erf}(b x)}{3 \sqrt{\pi } x}-\frac{\text{erf}(b x)^2}{4 x^4}",1,"((4*b*x*(-1 + 2*b^2*x^2)*Erf[b*x])/(E^(b^2*x^2)*Sqrt[Pi]) + (-3 + 4*b^4*x^4)*Erf[b*x]^2 - (4*b^2*x^2*(E^(-2*b^2*x^2) + 4*b^2*x^2*ExpIntegralEi[-2*b^2*x^2]))/Pi)/(12*x^4)","A",1
28,1,133,177,0.0492401,"\int \frac{\text{erf}(b x)^2}{x^7} \, dx","Integrate[Erf[b*x]^2/x^7,x]","\frac{e^{-2 b^2 x^2} \left(20 b^4 x^4-6 b^2 x^2-\pi  e^{2 b^2 x^2} \left(8 b^6 x^6+15\right) \text{erf}(b x)^2+56 b^6 x^6 e^{2 b^2 x^2} \text{Ei}\left(-2 b^2 x^2\right)-4 \sqrt{\pi } b x e^{b^2 x^2} \left(4 b^4 x^4-2 b^2 x^2+3\right) \text{erf}(b x)\right)}{90 \pi  x^6}","-\frac{4}{45} b^6 \text{erf}(b x)^2-\frac{2 b e^{-b^2 x^2} \text{erf}(b x)}{15 \sqrt{\pi } x^5}-\frac{b^2 e^{-2 b^2 x^2}}{15 \pi  x^4}+\frac{28 b^6 \text{Ei}\left(-2 b^2 x^2\right)}{45 \pi }-\frac{8 b^5 e^{-b^2 x^2} \text{erf}(b x)}{45 \sqrt{\pi } x}+\frac{2 b^4 e^{-2 b^2 x^2}}{9 \pi  x^2}+\frac{4 b^3 e^{-b^2 x^2} \text{erf}(b x)}{45 \sqrt{\pi } x^3}-\frac{\text{erf}(b x)^2}{6 x^6}",1,"(-6*b^2*x^2 + 20*b^4*x^4 - 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(3 - 2*b^2*x^2 + 4*b^4*x^4)*Erf[b*x] - E^(2*b^2*x^2)*Pi*(15 + 8*b^6*x^6)*Erf[b*x]^2 + 56*b^6*E^(2*b^2*x^2)*x^6*ExpIntegralEi[-2*b^2*x^2])/(90*E^(2*b^2*x^2)*Pi*x^6)","A",1
29,1,106,165,0.1091513,"\int x^4 \text{erf}(b x)^2 \, dx","Integrate[x^4*Erf[b*x]^2,x]","\frac{16 \pi  b^5 x^5 \text{erf}(b x)^2+4 b x e^{-2 b^2 x^2} \left(4 b^2 x^2+11\right)+32 \sqrt{\pi } e^{-b^2 x^2} \left(b^4 x^4+2 b^2 x^2+2\right) \text{erf}(b x)-43 \sqrt{2 \pi } \text{erf}\left(\sqrt{2} b x\right)}{80 \pi  b^5}","-\frac{43 \text{erf}\left(\sqrt{2} b x\right)}{40 \sqrt{2 \pi } b^5}+\frac{2 x^4 e^{-b^2 x^2} \text{erf}(b x)}{5 \sqrt{\pi } b}+\frac{x^3 e^{-2 b^2 x^2}}{5 \pi  b^2}+\frac{4 e^{-b^2 x^2} \text{erf}(b x)}{5 \sqrt{\pi } b^5}+\frac{11 x e^{-2 b^2 x^2}}{20 \pi  b^4}+\frac{4 x^2 e^{-b^2 x^2} \text{erf}(b x)}{5 \sqrt{\pi } b^3}+\frac{1}{5} x^5 \text{erf}(b x)^2",1,"((4*b*x*(11 + 4*b^2*x^2))/E^(2*b^2*x^2) + (32*Sqrt[Pi]*(2 + 2*b^2*x^2 + b^4*x^4)*Erf[b*x])/E^(b^2*x^2) + 16*b^5*Pi*x^5*Erf[b*x]^2 - 43*Sqrt[2*Pi]*Erf[Sqrt[2]*b*x])/(80*b^5*Pi)","A",1
30,1,88,113,0.0742508,"\int x^2 \text{erf}(b x)^2 \, dx","Integrate[x^2*Erf[b*x]^2,x]","\frac{4 \pi  b^3 x^3 \text{erf}(b x)^2+8 \sqrt{\pi } e^{-b^2 x^2} \left(b^2 x^2+1\right) \text{erf}(b x)+4 b x e^{-2 b^2 x^2}-5 \sqrt{2 \pi } \text{erf}\left(\sqrt{2} b x\right)}{12 \pi  b^3}","-\frac{5 \text{erf}\left(\sqrt{2} b x\right)}{6 \sqrt{2 \pi } b^3}+\frac{2 x^2 e^{-b^2 x^2} \text{erf}(b x)}{3 \sqrt{\pi } b}+\frac{x e^{-2 b^2 x^2}}{3 \pi  b^2}+\frac{2 e^{-b^2 x^2} \text{erf}(b x)}{3 \sqrt{\pi } b^3}+\frac{1}{3} x^3 \text{erf}(b x)^2",1,"((4*b*x)/E^(2*b^2*x^2) + (8*Sqrt[Pi]*(1 + b^2*x^2)*Erf[b*x])/E^(b^2*x^2) + 4*b^3*Pi*x^3*Erf[b*x]^2 - 5*Sqrt[2*Pi]*Erf[Sqrt[2]*b*x])/(12*b^3*Pi)","A",1
31,1,56,56,0.030702,"\int \text{erf}(b x)^2 \, dx","Integrate[Erf[b*x]^2,x]","\frac{2 e^{-b^2 x^2} \text{erf}(b x)}{\sqrt{\pi } b}+x \text{erf}(b x)^2-\frac{\sqrt{\frac{2}{\pi }} \text{erf}\left(\sqrt{2} b x\right)}{b}","\frac{2 e^{-b^2 x^2} \text{erf}(b x)}{\sqrt{\pi } b}+x \text{erf}(b x)^2-\frac{\sqrt{\frac{2}{\pi }} \text{erf}\left(\sqrt{2} b x\right)}{b}",1,"(2*Erf[b*x])/(b*E^(b^2*x^2)*Sqrt[Pi]) + x*Erf[b*x]^2 - (Sqrt[2/Pi]*Erf[Sqrt[2]*b*x])/b","A",1
32,0,0,13,0.0384391,"\int \frac{\text{erf}(b x)^2}{x^2} \, dx","Integrate[Erf[b*x]^2/x^2,x]","\int \frac{\text{erf}(b x)^2}{x^2} \, dx","\text{Int}\left(\frac{\text{erf}(b x)^2}{x^2},x\right)",0,"Integrate[Erf[b*x]^2/x^2, x]","A",-1
33,0,0,13,0.0472332,"\int \frac{\text{erf}(b x)^2}{x^4} \, dx","Integrate[Erf[b*x]^2/x^4,x]","\int \frac{\text{erf}(b x)^2}{x^4} \, dx","\text{Int}\left(\frac{\text{erf}(b x)^2}{x^4},x\right)",0,"Integrate[Erf[b*x]^2/x^4, x]","A",-1
34,0,0,13,0.0387125,"\int \frac{\text{erf}(b x)^2}{x^6} \, dx","Integrate[Erf[b*x]^2/x^6,x]","\int \frac{\text{erf}(b x)^2}{x^6} \, dx","\text{Int}\left(\frac{\text{erf}(b x)^2}{x^6},x\right)",0,"Integrate[Erf[b*x]^2/x^6, x]","A",-1
35,1,226,375,1.1008433,"\int (c+d x)^2 \text{erf}(a+b x)^2 \, dx","Integrate[(c + d*x)^2*Erf[a + b*x]^2,x]","\frac{\frac{8 e^{-(a+b x)^2} \text{erf}(a+b x) \left(\left(a^2+1\right) d^2-a b d (3 c+d x)+b^2 \left(3 c^2+3 c d x+d^2 x^2\right)\right)}{\sqrt{\pi }}-\sqrt{\frac{2}{\pi }} \left(\left(12 a^2+5\right) d^2-24 a b c d+12 b^2 c^2\right) \text{erf}\left(\sqrt{2} (a+b x)\right)+2 \text{erf}(a+b x)^2 \left(2 a^3 d^2-6 a^2 b c d+3 a \left(2 b^2 c^2+d^2\right)+2 b^3 x \left(3 c^2+3 c d x+d^2 x^2\right)-3 b c d\right)+\frac{4 d e^{-2 (a+b x)^2} (-2 a d+3 b c+b d x)}{\pi }}{12 b^3}","\frac{d (a+b x)^2 (b c-a d) \text{erf}(a+b x)^2}{b^3}+\frac{(a+b x) (b c-a d)^2 \text{erf}(a+b x)^2}{b^3}+\frac{2 d e^{-(a+b x)^2} (a+b x) (b c-a d) \text{erf}(a+b x)}{\sqrt{\pi } b^3}-\frac{d (b c-a d) \text{erf}(a+b x)^2}{2 b^3}+\frac{2 e^{-(a+b x)^2} (b c-a d)^2 \text{erf}(a+b x)}{\sqrt{\pi } b^3}-\frac{\sqrt{\frac{2}{\pi }} (b c-a d)^2 \text{erf}\left(\sqrt{2} (a+b x)\right)}{b^3}+\frac{d e^{-2 (a+b x)^2} (b c-a d)}{\pi  b^3}+\frac{d^2 (a+b x)^3 \text{erf}(a+b x)^2}{3 b^3}+\frac{2 d^2 e^{-(a+b x)^2} (a+b x)^2 \text{erf}(a+b x)}{3 \sqrt{\pi } b^3}+\frac{2 d^2 e^{-(a+b x)^2} \text{erf}(a+b x)}{3 \sqrt{\pi } b^3}-\frac{5 d^2 \text{erf}\left(\sqrt{2} (a+b x)\right)}{6 \sqrt{2 \pi } b^3}+\frac{d^2 e^{-2 (a+b x)^2} (a+b x)}{3 \pi  b^3}",1,"((4*d*(3*b*c - 2*a*d + b*d*x))/(E^(2*(a + b*x)^2)*Pi) + (8*((1 + a^2)*d^2 - a*b*d*(3*c + d*x) + b^2*(3*c^2 + 3*c*d*x + d^2*x^2))*Erf[a + b*x])/(E^(a + b*x)^2*Sqrt[Pi]) + 2*(-3*b*c*d - 6*a^2*b*c*d + 2*a^3*d^2 + 3*a*(2*b^2*c^2 + d^2) + 2*b^3*x*(3*c^2 + 3*c*d*x + d^2*x^2))*Erf[a + b*x]^2 - (12*b^2*c^2 - 24*a*b*c*d + (5 + 12*a^2)*d^2)*Sqrt[2/Pi]*Erf[Sqrt[2]*(a + b*x)])/(12*b^3)","A",1
36,1,132,188,0.3982767,"\int (c+d x) \text{erf}(a+b x)^2 \, dx","Integrate[(c + d*x)*Erf[a + b*x]^2,x]","\frac{\pi  \text{erf}(a+b x)^2 \left(-2 a^2 d+4 a b c+4 b^2 c x+2 b^2 d x^2-d\right)+4 \sqrt{\pi } e^{-(a+b x)^2} \text{erf}(a+b x) (-a d+2 b c+b d x)+4 \sqrt{2 \pi } (a d-b c) \text{erf}\left(\sqrt{2} (a+b x)\right)+2 d e^{-2 (a+b x)^2}}{4 \pi  b^2}","\frac{(a+b x) (b c-a d) \text{erf}(a+b x)^2}{b^2}+\frac{2 e^{-(a+b x)^2} (b c-a d) \text{erf}(a+b x)}{\sqrt{\pi } b^2}-\frac{\sqrt{\frac{2}{\pi }} (b c-a d) \text{erf}\left(\sqrt{2} (a+b x)\right)}{b^2}+\frac{d (a+b x)^2 \text{erf}(a+b x)^2}{2 b^2}-\frac{d \text{erf}(a+b x)^2}{4 b^2}+\frac{d e^{-(a+b x)^2} (a+b x) \text{erf}(a+b x)}{\sqrt{\pi } b^2}+\frac{d e^{-2 (a+b x)^2}}{2 \pi  b^2}",1,"((2*d)/E^(2*(a + b*x)^2) + (4*Sqrt[Pi]*(2*b*c - a*d + b*d*x)*Erf[a + b*x])/E^(a + b*x)^2 + Pi*(4*a*b*c - d - 2*a^2*d + 4*b^2*c*x + 2*b^2*d*x^2)*Erf[a + b*x]^2 + 4*(-(b*c) + a*d)*Sqrt[2*Pi]*Erf[Sqrt[2]*(a + b*x)])/(4*b^2*Pi)","A",1
37,1,66,71,0.0124778,"\int \text{erf}(a+b x)^2 \, dx","Integrate[Erf[a + b*x]^2,x]","\frac{(a+b x) \text{erf}(a+b x)^2+\frac{2 e^{-(a+b x)^2} \text{erf}(a+b x)}{\sqrt{\pi }}-\sqrt{\frac{2}{\pi }} \text{erf}\left(\sqrt{2} (a+b x)\right)}{b}","\frac{(a+b x) \text{erf}(a+b x)^2}{b}+\frac{2 e^{-(a+b x)^2} \text{erf}(a+b x)}{\sqrt{\pi } b}-\frac{\sqrt{\frac{2}{\pi }} \text{erf}\left(\sqrt{2} (a+b x)\right)}{b}",1,"((2*Erf[a + b*x])/(E^(a + b*x)^2*Sqrt[Pi]) + (a + b*x)*Erf[a + b*x]^2 - Sqrt[2/Pi]*Erf[Sqrt[2]*(a + b*x)])/b","A",1
38,0,0,19,0.0585967,"\int \frac{\text{erf}(a+b x)^2}{c+d x} \, dx","Integrate[Erf[a + b*x]^2/(c + d*x),x]","\int \frac{\text{erf}(a+b x)^2}{c+d x} \, dx","\text{Int}\left(\frac{\text{erf}(a+b x)^2}{c+d x},x\right)",0,"Integrate[Erf[a + b*x]^2/(c + d*x), x]","A",-1
39,0,0,19,0.1151801,"\int \frac{\text{erf}(a+b x)^2}{(c+d x)^2} \, dx","Integrate[Erf[a + b*x]^2/(c + d*x)^2,x]","\int \frac{\text{erf}(a+b x)^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{erf}(a+b x)^2}{(c+d x)^2},x\right)",0,"Integrate[Erf[a + b*x]^2/(c + d*x)^2, x]","A",-1
40,1,88,102,0.3529276,"\int x^2 \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^2*Erf[d*(a + b*Log[c*x^n])],x]","\frac{1}{3} \left(x^3 \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-x^3 \text{erf}\left(a d+b d \log \left(c x^n\right)-\frac{3}{2 b d n}\right) \exp \left(-\frac{3 \left(\frac{4 a b n-\frac{3}{d^2}}{b^2}+4 n \log \left(c x^n\right)\right)}{4 n^2}\right)\right)","\frac{1}{3} x^3 \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-\frac{1}{3} x^3 \left(c x^n\right)^{-3/n} e^{\frac{9-12 a b d^2 n}{4 b^2 d^2 n^2}} \text{erf}\left(\frac{2 a b d^2+2 b^2 d^2 \log \left(c x^n\right)-\frac{3}{n}}{2 b d}\right)",1,"(x^3*Erf[d*(a + b*Log[c*x^n])] - (x^3*Erf[a*d - 3/(2*b*d*n) + b*d*Log[c*x^n]])/E^((3*((-3/d^2 + 4*a*b*n)/b^2 + 4*n*Log[c*x^n]))/(4*n^2)))/3","A",1
41,1,84,94,0.298042,"\int x \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x*Erf[d*(a + b*Log[c*x^n])],x]","\frac{1}{2} \left(x^2 \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-x^2 e^{-\frac{\frac{2 a b n-\frac{1}{d^2}}{b^2}+2 n \log \left(c x^n\right)}{n^2}} \text{erf}\left(a d+b d \log \left(c x^n\right)-\frac{1}{b d n}\right)\right)","\frac{1}{2} x^2 \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-\frac{1}{2} x^2 \left(c x^n\right)^{-2/n} e^{\frac{1-2 a b d^2 n}{b^2 d^2 n^2}} \text{erf}\left(\frac{a b d^2+b^2 d^2 \log \left(c x^n\right)-\frac{1}{n}}{b d}\right)",1,"(x^2*Erf[d*(a + b*Log[c*x^n])] - (x^2*Erf[a*d - 1/(b*d*n) + b*d*Log[c*x^n]])/E^(((-d^(-2) + 2*a*b*n)/b^2 + 2*n*Log[c*x^n])/n^2))/2","A",1
42,1,80,93,0.2626915,"\int \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[Erf[d*(a + b*Log[c*x^n])],x]","x \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-x \text{erf}\left(a d+b d \log \left(c x^n\right)-\frac{1}{2 b d n}\right) \exp \left(-\frac{\frac{4 a b n-\frac{1}{d^2}}{b^2}+4 n \log \left(c x^n\right)}{4 n^2}\right)","x \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-x \left(c x^n\right)^{-1/n} e^{\frac{1-4 a b d^2 n}{4 b^2 d^2 n^2}} \text{erf}\left(\frac{2 a b d^2+2 b^2 d^2 \log \left(c x^n\right)-\frac{1}{n}}{2 b d}\right)",1,"x*Erf[d*(a + b*Log[c*x^n])] - (x*Erf[a*d - 1/(2*b*d*n) + b*d*Log[c*x^n]])/E^(((-d^(-2) + 4*a*b*n)/b^2 + 4*n*Log[c*x^n])/(4*n^2))","A",1
43,1,79,65,0.148791,"\int \frac{\text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Integrate[Erf[d*(a + b*Log[c*x^n])]/x,x]","\frac{\frac{\left(c x^n\right)^{-2 a b d^2} e^{-d^2 \left(a^2+b^2 \log ^2\left(c x^n\right)\right)}}{\sqrt{\pi } b d}+\left(\frac{a}{b}+\log \left(c x^n\right)\right) \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{n}","\frac{e^{-d^2 \left(a+b \log \left(c x^n\right)\right)^2}}{\sqrt{\pi } b d n}+\frac{\left(a+b \log \left(c x^n\right)\right) \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{b n}",1,"(1/(b*d*E^(d^2*(a^2 + b^2*Log[c*x^n]^2))*Sqrt[Pi]*(c*x^n)^(2*a*b*d^2)) + Erf[d*(a + b*Log[c*x^n])]*(a/b + Log[c*x^n]))/n","A",1
44,1,80,92,0.2880757,"\int \frac{\text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Integrate[Erf[d*(a + b*Log[c*x^n])]/x^2,x]","\frac{e^{\frac{\frac{4 a b n+\frac{1}{d^2}}{b^2}+4 n \log \left(c x^n\right)}{4 n^2}} \text{erf}\left(a d+b d \log \left(c x^n\right)+\frac{1}{2 b d n}\right)-\text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x}","\frac{\left(c x^n\right)^{\frac{1}{n}} e^{\frac{a}{b n}+\frac{1}{4 b^2 d^2 n^2}} \text{erf}\left(\frac{2 a b d^2+2 b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}}{2 b d}\right)}{x}-\frac{\text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x}",1,"(-Erf[d*(a + b*Log[c*x^n])] + E^(((d^(-2) + 4*a*b*n)/b^2 + 4*n*Log[c*x^n])/(4*n^2))*Erf[a*d + 1/(2*b*d*n) + b*d*Log[c*x^n]])/x","A",1
45,1,77,95,0.2609802,"\int \frac{\text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Integrate[Erf[d*(a + b*Log[c*x^n])]/x^3,x]","\frac{e^{\frac{\frac{2 a b n+\frac{1}{d^2}}{b^2}+2 n \log \left(c x^n\right)}{n^2}} \text{erf}\left(a d+b d \log \left(c x^n\right)+\frac{1}{b d n}\right)-\text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}","\frac{\left(c x^n\right)^{2/n} e^{\frac{2 a b d^2 n+1}{b^2 d^2 n^2}} \text{erf}\left(\frac{a b d^2 n+b^2 d^2 n \log \left(c x^n\right)+1}{b d n}\right)}{2 x^2}-\frac{\text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}",1,"(-Erf[d*(a + b*Log[c*x^n])] + E^(((d^(-2) + 2*a*b*n)/b^2 + 2*n*Log[c*x^n])/n^2)*Erf[a*d + 1/(b*d*n) + b*d*Log[c*x^n]])/(2*x^2)","A",1
46,1,127,125,0.5634016,"\int (e x)^m \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Erf[d*(a + b*Log[c*x^n])],x]","\frac{(e x)^m \left(x \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-x^{-m} \text{erf}\left(a d-\frac{-2 b^2 d^2 n \log \left(c x^n\right)+m+1}{2 b d n}\right) \exp \left(\frac{(m+1) \left(-4 a b d^2 n-4 b^2 d^2 n \log \left(c x^n\right)+4 b^2 d^2 n^2 \log (x)+m+1\right)}{4 b^2 d^2 n^2}\right)\right)}{m+1}","\frac{x (e x)^m \left(c x^n\right)^{-\frac{m+1}{n}} \exp \left(\frac{(m+1) \left(-4 a b d^2 n+m+1\right)}{4 b^2 d^2 n^2}\right) \text{erf}\left(\frac{-2 a b d^2 n-2 b^2 d^2 n \log \left(c x^n\right)+m+1}{2 b d n}\right)}{m+1}+\frac{(e x)^{m+1} \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (m+1)}",1,"((e*x)^m*(x*Erf[d*(a + b*Log[c*x^n])] - (E^(((1 + m)*(1 + m - 4*a*b*d^2*n + 4*b^2*d^2*n^2*Log[x] - 4*b^2*d^2*n*Log[c*x^n]))/(4*b^2*d^2*n^2))*Erf[a*d - (1 + m - 2*b^2*d^2*n*Log[c*x^n])/(2*b*d*n)])/x^m))/(1 + m)","A",1
47,1,21,21,0.0092603,"\int e^{c-b^2 x^2} \text{erf}(b x)^2 \, dx","Integrate[E^(c - b^2*x^2)*Erf[b*x]^2,x]","\frac{\sqrt{\pi } e^c \text{erf}(b x)^3}{6 b}","\frac{\sqrt{\pi } e^c \text{erf}(b x)^3}{6 b}",1,"(E^c*Sqrt[Pi]*Erf[b*x]^3)/(6*b)","A",1
48,1,21,21,0.0051152,"\int e^{c-b^2 x^2} \text{erf}(b x) \, dx","Integrate[E^(c - b^2*x^2)*Erf[b*x],x]","\frac{\sqrt{\pi } e^c \text{erf}(b x)^2}{4 b}","\frac{\sqrt{\pi } e^c \text{erf}(b x)^2}{4 b}",1,"(E^c*Sqrt[Pi]*Erf[b*x]^2)/(4*b)","A",1
49,1,20,20,0.01065,"\int \frac{e^{c-b^2 x^2}}{\text{erf}(b x)} \, dx","Integrate[E^(c - b^2*x^2)/Erf[b*x],x]","\frac{\sqrt{\pi } e^c \log (\text{erf}(b x))}{2 b}","\frac{\sqrt{\pi } e^c \log (\text{erf}(b x))}{2 b}",1,"(E^c*Sqrt[Pi]*Log[Erf[b*x]])/(2*b)","A",1
50,1,21,21,0.0056495,"\int \frac{e^{c-b^2 x^2}}{\text{erf}(b x)^2} \, dx","Integrate[E^(c - b^2*x^2)/Erf[b*x]^2,x]","-\frac{\sqrt{\pi } e^c}{2 b \text{erf}(b x)}","-\frac{\sqrt{\pi } e^c}{2 b \text{erf}(b x)}",1,"-1/2*(E^c*Sqrt[Pi])/(b*Erf[b*x])","A",1
51,1,21,21,0.0057306,"\int \frac{e^{c-b^2 x^2}}{\text{erf}(b x)^3} \, dx","Integrate[E^(c - b^2*x^2)/Erf[b*x]^3,x]","-\frac{\sqrt{\pi } e^c}{4 b \text{erf}(b x)^2}","-\frac{\sqrt{\pi } e^c}{4 b \text{erf}(b x)^2}",1,"-1/4*(E^c*Sqrt[Pi])/(b*Erf[b*x]^2)","A",1
52,1,28,28,0.0135934,"\int e^{c-b^2 x^2} \text{erf}(b x)^n \, dx","Integrate[E^(c - b^2*x^2)*Erf[b*x]^n,x]","\frac{\sqrt{\pi } e^c \text{erf}(b x)^{n+1}}{2 b (n+1)}","\frac{\sqrt{\pi } e^c \text{erf}(b x)^{n+1}}{2 b (n+1)}",1,"(E^c*Sqrt[Pi]*Erf[b*x]^(1 + n))/(2*b*(1 + n))","A",1
53,1,138,285,0.4667378,"\int e^{c+d x^2} x^5 \text{erf}(b x) \, dx","Integrate[E^(c + d*x^2)*x^5*Erf[b*x],x]","\frac{e^c \left(\frac{2 b d x e^{x^2 \left(d-b^2\right)} \left(2 b^2 \left(d x^2-2\right)+d \left(7-2 d x^2\right)\right)}{\sqrt{\pi } \left(b^2-d\right)^2}+\frac{b \left(-8 b^4+20 b^2 d-15 d^2\right) \text{erfi}\left(x \sqrt{d-b^2}\right)}{\left(d-b^2\right)^{5/2}}+4 e^{d x^2} \left(d^2 x^4-2 d x^2+2\right) \text{erf}(b x)\right)}{8 d^3}","-\frac{b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{d^3 \sqrt{b^2-d}}+\frac{b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{2 d^2 \left(b^2-d\right)^{3/2}}-\frac{b x e^{c-x^2 \left(b^2-d\right)}}{\sqrt{\pi } d^2 \left(b^2-d\right)}-\frac{3 b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{8 d \left(b^2-d\right)^{5/2}}+\frac{3 b x e^{c-x^2 \left(b^2-d\right)}}{4 \sqrt{\pi } d \left(b^2-d\right)^2}+\frac{b x^3 e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } d \left(b^2-d\right)}+\frac{\text{erf}(b x) e^{c+d x^2}}{d^3}-\frac{x^2 \text{erf}(b x) e^{c+d x^2}}{d^2}+\frac{x^4 \text{erf}(b x) e^{c+d x^2}}{2 d}",1,"(E^c*((2*b*d*E^((-b^2 + d)*x^2)*x*(d*(7 - 2*d*x^2) + 2*b^2*(-2 + d*x^2)))/((b^2 - d)^2*Sqrt[Pi]) + 4*E^(d*x^2)*(2 - 2*d*x^2 + d^2*x^4)*Erf[b*x] + (b*(-8*b^4 + 20*b^2*d - 15*d^2)*Erfi[Sqrt[-b^2 + d]*x])/(-b^2 + d)^(5/2)))/(8*d^3)","A",1
54,1,99,155,0.3042117,"\int e^{c+d x^2} x^3 \text{erf}(b x) \, dx","Integrate[E^(c + d*x^2)*x^3*Erf[b*x],x]","\frac{e^c \left(\frac{b \left(3 d-2 b^2\right) \text{erfi}\left(x \sqrt{d-b^2}\right)}{\left(d-b^2\right)^{3/2}}+\frac{2 b d x e^{x^2 \left(d-b^2\right)}}{\sqrt{\pi } \left(b^2-d\right)}+2 e^{d x^2} \left(d x^2-1\right) \text{erf}(b x)\right)}{4 d^2}","\frac{b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{2 d^2 \sqrt{b^2-d}}-\frac{b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{4 d \left(b^2-d\right)^{3/2}}+\frac{b x e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } d \left(b^2-d\right)}-\frac{\text{erf}(b x) e^{c+d x^2}}{2 d^2}+\frac{x^2 \text{erf}(b x) e^{c+d x^2}}{2 d}",1,"(E^c*((2*b*d*E^((-b^2 + d)*x^2)*x)/((b^2 - d)*Sqrt[Pi]) + 2*E^(d*x^2)*(-1 + d*x^2)*Erf[b*x] + (b*(-2*b^2 + 3*d)*Erfi[Sqrt[-b^2 + d]*x])/(-b^2 + d)^(3/2)))/(4*d^2)","A",1
55,1,51,57,0.0458908,"\int e^{c+d x^2} x \text{erf}(b x) \, dx","Integrate[E^(c + d*x^2)*x*Erf[b*x],x]","\frac{e^c \left(e^{d x^2} \text{erf}(b x)-\frac{b \text{erfi}\left(x \sqrt{d-b^2}\right)}{\sqrt{d-b^2}}\right)}{2 d}","\frac{\text{erf}(b x) e^{c+d x^2}}{2 d}-\frac{b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{2 d \sqrt{b^2-d}}",1,"(E^c*(E^(d*x^2)*Erf[b*x] - (b*Erfi[Sqrt[-b^2 + d]*x])/Sqrt[-b^2 + d]))/(2*d)","A",1
56,0,0,20,0.1551965,"\int \frac{e^{c+d x^2} \text{erf}(b x)}{x} \, dx","Integrate[(E^(c + d*x^2)*Erf[b*x])/x,x]","\int \frac{e^{c+d x^2} \text{erf}(b x)}{x} \, dx","\text{Int}\left(\frac{\text{erf}(b x) e^{c+d x^2}}{x},x\right)",0,"Integrate[(E^(c + d*x^2)*Erf[b*x])/x, x]","A",-1
57,0,0,101,0.2075043,"\int \frac{e^{c+d x^2} \text{erf}(b x)}{x^3} \, dx","Integrate[(E^(c + d*x^2)*Erf[b*x])/x^3,x]","\int \frac{e^{c+d x^2} \text{erf}(b x)}{x^3} \, dx","d \text{Int}\left(\frac{\text{erf}(b x) e^{c+d x^2}}{x},x\right)+b e^c \left(-\sqrt{b^2-d}\right) \text{erf}\left(x \sqrt{b^2-d}\right)-\frac{b e^{c-x^2 \left(b^2-d\right)}}{\sqrt{\pi } x}-\frac{\text{erf}(b x) e^{c+d x^2}}{2 x^2}",0,"Integrate[(E^(c + d*x^2)*Erf[b*x])/x^3, x]","A",-1
58,0,0,231,0.2900039,"\int \frac{e^{c+d x^2} \text{erf}(b x)}{x^5} \, dx","Integrate[(E^(c + d*x^2)*Erf[b*x])/x^5,x]","\int \frac{e^{c+d x^2} \text{erf}(b x)}{x^5} \, dx","\frac{1}{2} d^2 \text{Int}\left(\frac{\text{erf}(b x) e^{c+d x^2}}{x},x\right)-\frac{1}{2} b e^c d \sqrt{b^2-d} \text{erf}\left(x \sqrt{b^2-d}\right)+\frac{1}{3} b e^c \left(b^2-d\right)^{3/2} \text{erf}\left(x \sqrt{b^2-d}\right)-\frac{b d e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } x}+\frac{b \left(b^2-d\right) e^{c-x^2 \left(b^2-d\right)}}{3 \sqrt{\pi } x}-\frac{b e^{c-x^2 \left(b^2-d\right)}}{6 \sqrt{\pi } x^3}-\frac{d \text{erf}(b x) e^{c+d x^2}}{4 x^2}-\frac{\text{erf}(b x) e^{c+d x^2}}{4 x^4}",0,"Integrate[(E^(c + d*x^2)*Erf[b*x])/x^5, x]","A",-1
59,0,0,186,0.3196595,"\int e^{c+d x^2} x^4 \text{erf}(b x) \, dx","Integrate[E^(c + d*x^2)*x^4*Erf[b*x],x]","\int e^{c+d x^2} x^4 \text{erf}(b x) \, dx","\frac{3 \text{Int}\left(\text{erf}(b x) e^{c+d x^2},x\right)}{4 d^2}-\frac{3 b e^{c-x^2 \left(b^2-d\right)}}{4 \sqrt{\pi } d^2 \left(b^2-d\right)}+\frac{b x^2 e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } d \left(b^2-d\right)}+\frac{b e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } d \left(b^2-d\right)^2}-\frac{3 x \text{erf}(b x) e^{c+d x^2}}{4 d^2}+\frac{x^3 \text{erf}(b x) e^{c+d x^2}}{2 d}",0,"Integrate[E^(c + d*x^2)*x^4*Erf[b*x], x]","A",-1
60,0,0,84,0.2276455,"\int e^{c+d x^2} x^2 \text{erf}(b x) \, dx","Integrate[E^(c + d*x^2)*x^2*Erf[b*x],x]","\int e^{c+d x^2} x^2 \text{erf}(b x) \, dx","-\frac{\text{Int}\left(\text{erf}(b x) e^{c+d x^2},x\right)}{2 d}+\frac{b e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } d \left(b^2-d\right)}+\frac{x \text{erf}(b x) e^{c+d x^2}}{2 d}",0,"Integrate[E^(c + d*x^2)*x^2*Erf[b*x], x]","A",-1
61,0,0,17,0.0248625,"\int e^{c+d x^2} \text{erf}(b x) \, dx","Integrate[E^(c + d*x^2)*Erf[b*x],x]","\int e^{c+d x^2} \text{erf}(b x) \, dx","\text{Int}\left(\text{erf}(b x) e^{c+d x^2},x\right)",0,"Integrate[E^(c + d*x^2)*Erf[b*x], x]","A",-1
62,0,0,62,0.2288289,"\int \frac{e^{c+d x^2} \text{erf}(b x)}{x^2} \, dx","Integrate[(E^(c + d*x^2)*Erf[b*x])/x^2,x]","\int \frac{e^{c+d x^2} \text{erf}(b x)}{x^2} \, dx","2 d \text{Int}\left(\text{erf}(b x) e^{c+d x^2},x\right)+\frac{b e^c \text{Ei}\left(-\left(\left(b^2-d\right) x^2\right)\right)}{\sqrt{\pi }}-\frac{\text{erf}(b x) e^{c+d x^2}}{x}",0,"Integrate[(E^(c + d*x^2)*Erf[b*x])/x^2, x]","A",-1
63,0,0,155,0.3413728,"\int \frac{e^{c+d x^2} \text{erf}(b x)}{x^4} \, dx","Integrate[(E^(c + d*x^2)*Erf[b*x])/x^4,x]","\int \frac{e^{c+d x^2} \text{erf}(b x)}{x^4} \, dx","\frac{4}{3} d^2 \text{Int}\left(\text{erf}(b x) e^{c+d x^2},x\right)+\frac{2 b e^c d \text{Ei}\left(-\left(\left(b^2-d\right) x^2\right)\right)}{3 \sqrt{\pi }}-\frac{b e^c \left(b^2-d\right) \text{Ei}\left(-\left(\left(b^2-d\right) x^2\right)\right)}{3 \sqrt{\pi }}-\frac{b e^{c-x^2 \left(b^2-d\right)}}{3 \sqrt{\pi } x^2}-\frac{2 d \text{erf}(b x) e^{c+d x^2}}{3 x}-\frac{\text{erf}(b x) e^{c+d x^2}}{3 x^3}",0,"Integrate[(E^(c + d*x^2)*Erf[b*x])/x^4, x]","A",-1
64,1,73,118,0.0509752,"\int e^{c+b^2 x^2} x^5 \text{erf}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^5*Erf[b*x],x]","\frac{e^c \left(-6 b^5 x^5+20 b^3 x^3+15 \sqrt{\pi } e^{b^2 x^2} \left(b^4 x^4-2 b^2 x^2+2\right) \text{erf}(b x)-60 b x\right)}{30 \sqrt{\pi } b^6}","-\frac{2 e^c x}{\sqrt{\pi } b^5}+\frac{2 e^c x^3}{3 \sqrt{\pi } b^3}+\frac{x^4 e^{b^2 x^2+c} \text{erf}(b x)}{2 b^2}+\frac{e^{b^2 x^2+c} \text{erf}(b x)}{b^6}-\frac{x^2 e^{b^2 x^2+c} \text{erf}(b x)}{b^4}-\frac{e^c x^5}{5 \sqrt{\pi } b}",1,"(E^c*(-60*b*x + 20*b^3*x^3 - 6*b^5*x^5 + 15*E^(b^2*x^2)*Sqrt[Pi]*(2 - 2*b^2*x^2 + b^4*x^4)*Erf[b*x]))/(30*b^6*Sqrt[Pi])","A",1
65,1,57,79,0.043855,"\int e^{c+b^2 x^2} x^3 \text{erf}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^3*Erf[b*x],x]","\frac{e^c \left(-2 b^3 x^3+3 \sqrt{\pi } e^{b^2 x^2} \left(b^2 x^2-1\right) \text{erf}(b x)+6 b x\right)}{6 \sqrt{\pi } b^4}","\frac{e^c x}{\sqrt{\pi } b^3}+\frac{x^2 e^{b^2 x^2+c} \text{erf}(b x)}{2 b^2}-\frac{e^{b^2 x^2+c} \text{erf}(b x)}{2 b^4}-\frac{e^c x^3}{3 \sqrt{\pi } b}",1,"(E^c*(6*b*x - 2*b^3*x^3 + 3*E^(b^2*x^2)*Sqrt[Pi]*(-1 + b^2*x^2)*Erf[b*x]))/(6*b^4*Sqrt[Pi])","A",1
66,1,34,37,0.0267956,"\int e^{c+b^2 x^2} x \text{erf}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x*Erf[b*x],x]","\frac{e^c \left(e^{b^2 x^2} \text{erf}(b x)-\frac{2 b x}{\sqrt{\pi }}\right)}{2 b^2}","\frac{e^{b^2 x^2+c} \text{erf}(b x)}{2 b^2}-\frac{e^c x}{\sqrt{\pi } b}",1,"(E^c*((-2*b*x)/Sqrt[Pi] + E^(b^2*x^2)*Erf[b*x]))/(2*b^2)","A",1
67,1,32,32,0.1381596,"\int \frac{e^{c+b^2 x^2} \text{erf}(b x)}{x} \, dx","Integrate[(E^(c + b^2*x^2)*Erf[b*x])/x,x]","\frac{2 b e^c x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}","\frac{2 b e^c x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}",1,"(2*b*E^c*x*HypergeometricPFQ[{1/2, 1}, {3/2, 3/2}, b^2*x^2])/Sqrt[Pi]","A",1
68,1,34,71,0.1271153,"\int \frac{e^{c+b^2 x^2} \text{erf}(b x)}{x^3} \, dx","Integrate[(E^(c + b^2*x^2)*Erf[b*x])/x^3,x]","-\frac{2 b e^c \, _2F_2\left(-\frac{1}{2},1;\frac{1}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi } x}","\frac{2 b^3 e^c x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}-\frac{e^{b^2 x^2+c} \text{erf}(b x)}{2 x^2}-\frac{b e^c}{\sqrt{\pi } x}",1,"(-2*b*E^c*HypergeometricPFQ[{-1/2, 1}, {1/2, 3/2}, b^2*x^2])/(Sqrt[Pi]*x)","A",1
69,1,36,115,0.1565642,"\int \frac{e^{c+b^2 x^2} \text{erf}(b x)}{x^5} \, dx","Integrate[(E^(c + b^2*x^2)*Erf[b*x])/x^5,x]","-\frac{2 b e^c \, _2F_2\left(-\frac{3}{2},1;-\frac{1}{2},\frac{3}{2};b^2 x^2\right)}{3 \sqrt{\pi } x^3}","\frac{b^5 e^c x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}-\frac{b^3 e^c}{2 \sqrt{\pi } x}-\frac{b^2 e^{b^2 x^2+c} \text{erf}(b x)}{4 x^2}-\frac{e^{b^2 x^2+c} \text{erf}(b x)}{4 x^4}-\frac{b e^c}{6 \sqrt{\pi } x^3}",1,"(-2*b*E^c*HypergeometricPFQ[{-3/2, 1}, {-1/2, 3/2}, b^2*x^2])/(3*Sqrt[Pi]*x^3)","A",1
70,1,100,119,0.33123,"\int e^{c+b^2 x^2} x^4 \text{erf}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^4*Erf[b*x],x]","\frac{e^c \left(-6 b^2 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)-2 b^4 x^4+2 \sqrt{\pi } b x e^{b^2 x^2} \left(2 b^2 x^2-3\right) \text{erf}(b x)+6 b^2 x^2+3 \pi  \text{erf}(b x) \text{erfi}(b x)\right)}{8 \sqrt{\pi } b^5}","\frac{3 e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{4 \sqrt{\pi } b^3}+\frac{3 e^c x^2}{4 \sqrt{\pi } b^3}+\frac{x^3 e^{b^2 x^2+c} \text{erf}(b x)}{2 b^2}-\frac{3 x e^{b^2 x^2+c} \text{erf}(b x)}{4 b^4}-\frac{e^c x^4}{4 \sqrt{\pi } b}",1,"(E^c*(6*b^2*x^2 - 2*b^4*x^4 + 2*b*E^(b^2*x^2)*Sqrt[Pi]*x*(-3 + 2*b^2*x^2)*Erf[b*x] + 3*Pi*Erf[b*x]*Erfi[b*x] - 6*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)]))/(8*b^5*Sqrt[Pi])","A",1
71,1,80,76,0.2235277,"\int e^{c+b^2 x^2} x^2 \text{erf}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^2*Erf[b*x],x]","\frac{e^c \left(2 b^2 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)+\text{erf}(b x) \left(2 \sqrt{\pi } b x e^{b^2 x^2}-\pi  \text{erfi}(b x)\right)-2 b^2 x^2\right)}{4 \sqrt{\pi } b^3}","-\frac{e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi } b}+\frac{x e^{b^2 x^2+c} \text{erf}(b x)}{2 b^2}-\frac{e^c x^2}{2 \sqrt{\pi } b}",1,"(E^c*(-2*b^2*x^2 + Erf[b*x]*(2*b*E^(b^2*x^2)*Sqrt[Pi]*x - Pi*Erfi[b*x]) + 2*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)]))/(4*b^3*Sqrt[Pi])","A",1
72,0,0,29,0.0292549,"\int e^{c+b^2 x^2} \text{erf}(b x) \, dx","Integrate[E^(c + b^2*x^2)*Erf[b*x],x]","\int e^{c+b^2 x^2} \text{erf}(b x) \, dx","\frac{b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{\sqrt{\pi }}",1,"Integrate[E^(c + b^2*x^2)*Erf[b*x], x]","F",-1
73,1,74,66,0.2338997,"\int \frac{e^{c+b^2 x^2} \text{erf}(b x)}{x^2} \, dx","Integrate[(E^(c + b^2*x^2)*Erf[b*x])/x^2,x]","\frac{e^c \left(-2 b^3 x^3 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)+\text{erf}(b x) \left(\pi  b x \text{erfi}(b x)-\sqrt{\pi } e^{b^2 x^2}\right)+2 b x \log (x)\right)}{\sqrt{\pi } x}","\frac{2 b^3 e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{\sqrt{\pi }}-\frac{e^{b^2 x^2+c} \text{erf}(b x)}{x}+\frac{2 b e^c \log (x)}{\sqrt{\pi }}",1,"(E^c*(Erf[b*x]*(-(E^(b^2*x^2)*Sqrt[Pi]) + b*Pi*x*Erfi[b*x]) - 2*b^3*x^3*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)] + 2*b*x*Log[x]))/(Sqrt[Pi]*x)","A",1
74,1,100,115,0.3802787,"\int \frac{e^{c+b^2 x^2} \text{erf}(b x)}{x^4} \, dx","Integrate[(E^(c + b^2*x^2)*Erf[b*x])/x^4,x]","-\frac{e^c \left(4 b^5 x^5 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)-2 \pi  b^3 x^3 \text{erf}(b x) \text{erfi}(b x)-4 b^3 x^3 \log (x)+\sqrt{\pi } e^{b^2 x^2} \left(2 b^2 x^2+1\right) \text{erf}(b x)+b x\right)}{3 \sqrt{\pi } x^3}","\frac{4 b^5 e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{3 \sqrt{\pi }}+\frac{4 b^3 e^c \log (x)}{3 \sqrt{\pi }}-\frac{2 b^2 e^{b^2 x^2+c} \text{erf}(b x)}{3 x}-\frac{e^{b^2 x^2+c} \text{erf}(b x)}{3 x^3}-\frac{b e^c}{3 \sqrt{\pi } x^2}",1,"-1/3*(E^c*(b*x + E^(b^2*x^2)*Sqrt[Pi]*(1 + 2*b^2*x^2)*Erf[b*x] - 2*b^3*Pi*x^3*Erf[b*x]*Erfi[b*x] + 4*b^5*x^5*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)] - 4*b^3*x^3*Log[x]))/(Sqrt[Pi]*x^3)","A",1
75,1,86,135,0.0783303,"\int e^{-b^2 x^2} x^5 \text{erf}(b x) \, dx","Integrate[(x^5*Erf[b*x])/E^(b^2*x^2),x]","\frac{-\frac{4 b x e^{-2 b^2 x^2} \left(4 b^2 x^2+11\right)}{\sqrt{\pi }}-32 e^{-b^2 x^2} \left(b^4 x^4+2 b^2 x^2+2\right) \text{erf}(b x)+43 \sqrt{2} \text{erf}\left(\sqrt{2} b x\right)}{64 b^6}","\frac{43 \text{erf}\left(\sqrt{2} b x\right)}{32 \sqrt{2} b^6}-\frac{x^4 e^{-b^2 x^2} \text{erf}(b x)}{2 b^2}-\frac{e^{-b^2 x^2} \text{erf}(b x)}{b^6}-\frac{11 x e^{-2 b^2 x^2}}{16 \sqrt{\pi } b^5}-\frac{x^2 e^{-b^2 x^2} \text{erf}(b x)}{b^4}-\frac{x^3 e^{-2 b^2 x^2}}{4 \sqrt{\pi } b^3}",1,"((-4*b*x*(11 + 4*b^2*x^2))/(E^(2*b^2*x^2)*Sqrt[Pi]) - (32*(2 + 2*b^2*x^2 + b^4*x^4)*Erf[b*x])/E^(b^2*x^2) + 43*Sqrt[2]*Erf[Sqrt[2]*b*x])/(64*b^6)","A",1
76,1,68,90,0.0593653,"\int e^{-b^2 x^2} x^3 \text{erf}(b x) \, dx","Integrate[(x^3*Erf[b*x])/E^(b^2*x^2),x]","\frac{-8 e^{-b^2 x^2} \left(b^2 x^2+1\right) \text{erf}(b x)-\frac{4 b x e^{-2 b^2 x^2}}{\sqrt{\pi }}+5 \sqrt{2} \text{erf}\left(\sqrt{2} b x\right)}{16 b^4}","\frac{5 \text{erf}\left(\sqrt{2} b x\right)}{8 \sqrt{2} b^4}-\frac{x^2 e^{-b^2 x^2} \text{erf}(b x)}{2 b^2}-\frac{e^{-b^2 x^2} \text{erf}(b x)}{2 b^4}-\frac{x e^{-2 b^2 x^2}}{4 \sqrt{\pi } b^3}",1,"((-4*b*x)/(E^(2*b^2*x^2)*Sqrt[Pi]) - (8*(1 + b^2*x^2)*Erf[b*x])/E^(b^2*x^2) + 5*Sqrt[2]*Erf[Sqrt[2]*b*x])/(16*b^4)","A",1
77,1,39,43,0.0180894,"\int e^{-b^2 x^2} x \text{erf}(b x) \, dx","Integrate[(x*Erf[b*x])/E^(b^2*x^2),x]","\frac{\sqrt{2} \text{erf}\left(\sqrt{2} b x\right)-2 e^{-b^2 x^2} \text{erf}(b x)}{4 b^2}","\frac{\text{erf}\left(\sqrt{2} b x\right)}{2 \sqrt{2} b^2}-\frac{e^{-b^2 x^2} \text{erf}(b x)}{2 b^2}",1,"((-2*Erf[b*x])/E^(b^2*x^2) + Sqrt[2]*Erf[Sqrt[2]*b*x])/(4*b^2)","A",1
78,0,0,21,0.0933914,"\int \frac{e^{-b^2 x^2} \text{erf}(b x)}{x} \, dx","Integrate[Erf[b*x]/(E^(b^2*x^2)*x),x]","\int \frac{e^{-b^2 x^2} \text{erf}(b x)}{x} \, dx","\text{Int}\left(\frac{e^{-b^2 x^2} \text{erf}(b x)}{x},x\right)",0,"Integrate[Erf[b*x]/(E^(b^2*x^2)*x), x]","A",-1
79,0,0,88,0.1429142,"\int \frac{e^{-b^2 x^2} \text{erf}(b x)}{x^3} \, dx","Integrate[Erf[b*x]/(E^(b^2*x^2)*x^3),x]","\int \frac{e^{-b^2 x^2} \text{erf}(b x)}{x^3} \, dx","-b^2 \text{Int}\left(\frac{e^{-b^2 x^2} \text{erf}(b x)}{x},x\right)-\frac{e^{-b^2 x^2} \text{erf}(b x)}{2 x^2}-\sqrt{2} b^2 \text{erf}\left(\sqrt{2} b x\right)-\frac{b e^{-2 b^2 x^2}}{\sqrt{\pi } x}",0,"Integrate[Erf[b*x]/(E^(b^2*x^2)*x^3), x]","A",-1
80,0,0,161,0.1712605,"\int \frac{e^{-b^2 x^2} \text{erf}(b x)}{x^5} \, dx","Integrate[Erf[b*x]/(E^(b^2*x^2)*x^5),x]","\int \frac{e^{-b^2 x^2} \text{erf}(b x)}{x^5} \, dx","\frac{1}{2} b^4 \text{Int}\left(\frac{e^{-b^2 x^2} \text{erf}(b x)}{x},x\right)+\frac{2}{3} \sqrt{2} b^4 \text{erf}\left(\sqrt{2} b x\right)+\frac{b^4 \text{erf}\left(\sqrt{2} b x\right)}{\sqrt{2}}+\frac{b^2 e^{-b^2 x^2} \text{erf}(b x)}{4 x^2}-\frac{e^{-b^2 x^2} \text{erf}(b x)}{4 x^4}-\frac{b e^{-2 b^2 x^2}}{6 \sqrt{\pi } x^3}+\frac{7 b^3 e^{-2 b^2 x^2}}{6 \sqrt{\pi } x}",0,"Integrate[Erf[b*x]/(E^(b^2*x^2)*x^5), x]","A",-1
81,1,85,112,0.0416455,"\int e^{-b^2 x^2} x^4 \text{erf}(b x) \, dx","Integrate[(x^4*Erf[b*x])/E^(b^2*x^2),x]","\frac{e^{-2 b^2 x^2} \left(3 \pi  e^{2 b^2 x^2} \text{erf}(b x)^2-4 \sqrt{\pi } b x e^{b^2 x^2} \left(2 b^2 x^2+3\right) \text{erf}(b x)-4 \left(b^2 x^2+2\right)\right)}{16 \sqrt{\pi } b^5}","\frac{3 \sqrt{\pi } \text{erf}(b x)^2}{16 b^5}-\frac{x^3 e^{-b^2 x^2} \text{erf}(b x)}{2 b^2}-\frac{e^{-2 b^2 x^2}}{2 \sqrt{\pi } b^5}-\frac{3 x e^{-b^2 x^2} \text{erf}(b x)}{4 b^4}-\frac{x^2 e^{-2 b^2 x^2}}{4 \sqrt{\pi } b^3}",1,"(-4*(2 + b^2*x^2) - 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(3 + 2*b^2*x^2)*Erf[b*x] + 3*E^(2*b^2*x^2)*Pi*Erf[b*x]^2)/(16*b^5*E^(2*b^2*x^2)*Sqrt[Pi])","A",1
82,1,56,63,0.0458824,"\int e^{-b^2 x^2} x^2 \text{erf}(b x) \, dx","Integrate[(x^2*Erf[b*x])/E^(b^2*x^2),x]","-\frac{4 b x e^{-b^2 x^2} \text{erf}(b x)+\frac{2 e^{-2 b^2 x^2}}{\sqrt{\pi }}-\sqrt{\pi } \text{erf}(b x)^2}{8 b^3}","\frac{\sqrt{\pi } \text{erf}(b x)^2}{8 b^3}-\frac{x e^{-b^2 x^2} \text{erf}(b x)}{2 b^2}-\frac{e^{-2 b^2 x^2}}{4 \sqrt{\pi } b^3}",1,"-1/8*(2/(E^(2*b^2*x^2)*Sqrt[Pi]) + (4*b*x*Erf[b*x])/E^(b^2*x^2) - Sqrt[Pi]*Erf[b*x]^2)/b^3","A",1
83,1,18,18,0.0038079,"\int e^{-b^2 x^2} \text{erf}(b x) \, dx","Integrate[Erf[b*x]/E^(b^2*x^2),x]","\frac{\sqrt{\pi } \text{erf}(b x)^2}{4 b}","\frac{\sqrt{\pi } \text{erf}(b x)^2}{4 b}",1,"(Sqrt[Pi]*Erf[b*x]^2)/(4*b)","A",1
84,1,52,52,0.0168096,"\int \frac{e^{-b^2 x^2} \text{erf}(b x)}{x^2} \, dx","Integrate[Erf[b*x]/(E^(b^2*x^2)*x^2),x]","-\frac{e^{-b^2 x^2} \text{erf}(b x)}{x}+\frac{b \text{Ei}\left(-2 b^2 x^2\right)}{\sqrt{\pi }}-\frac{1}{2} \sqrt{\pi } b \text{erf}(b x)^2","-\frac{e^{-b^2 x^2} \text{erf}(b x)}{x}+\frac{b \text{Ei}\left(-2 b^2 x^2\right)}{\sqrt{\pi }}-\frac{1}{2} \sqrt{\pi } b \text{erf}(b x)^2",1,"-(Erf[b*x]/(E^(b^2*x^2)*x)) - (b*Sqrt[Pi]*Erf[b*x]^2)/2 + (b*ExpIntegralEi[-2*b^2*x^2])/Sqrt[Pi]","A",1
85,1,85,108,0.0728678,"\int \frac{e^{-b^2 x^2} \text{erf}(b x)}{x^4} \, dx","Integrate[Erf[b*x]/(E^(b^2*x^2)*x^4),x]","\frac{1}{3} \left(\sqrt{\pi } b^3 \text{erf}(b x)^2+\frac{e^{-b^2 x^2} \left(2 b^2 x^2-1\right) \text{erf}(b x)}{x^3}+\frac{b \left(-4 b^2 \text{Ei}\left(-2 b^2 x^2\right)-\frac{e^{-2 b^2 x^2}}{x^2}\right)}{\sqrt{\pi }}\right)","\frac{1}{3} \sqrt{\pi } b^3 \text{erf}(b x)^2+\frac{2 b^2 e^{-b^2 x^2} \text{erf}(b x)}{3 x}-\frac{e^{-b^2 x^2} \text{erf}(b x)}{3 x^3}-\frac{b e^{-2 b^2 x^2}}{3 \sqrt{\pi } x^2}-\frac{4 b^3 \text{Ei}\left(-2 b^2 x^2\right)}{3 \sqrt{\pi }}",1,"(((-1 + 2*b^2*x^2)*Erf[b*x])/(E^(b^2*x^2)*x^3) + b^3*Sqrt[Pi]*Erf[b*x]^2 + (b*(-(1/(E^(2*b^2*x^2)*x^2)) - 4*b^2*ExpIntegralEi[-2*b^2*x^2]))/Sqrt[Pi])/3","A",1
86,1,240,342,5.4459299,"\int e^{c+d x^2} x^3 \text{erf}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x^3*Erf[a + b*x],x]","\frac{e^c \left(-\frac{b d e^{-a^2-2 a b x+x^2 \left(d-b^2\right)} \left(\sqrt{\pi } \sqrt{b^2-d} \left(\left(2 a^2+1\right) b^2-d\right) e^{\frac{\left(a b+x \left(b^2-d\right)\right)^2}{b^2-d}} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)+2 \left(b^2-d\right) \left(a b+x \left(d-b^2\right)\right)\right)}{\sqrt{\pi } \left(b^2-d\right)^3}+\frac{2 b e^{\frac{a^2 d}{b^2-d}} \text{erfi}\left(\frac{x \left(d-b^2\right)-a b}{\sqrt{d-b^2}}\right)}{\sqrt{d-b^2}}+2 e^{d x^2} \left(d x^2-1\right) \text{erf}(a+b x)\right)}{4 d^2}","\frac{b e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{2 d^2 \sqrt{b^2-d}}-\frac{b e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{4 d \left(b^2-d\right)^{3/2}}-\frac{a b^2 e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)^2}+\frac{b x e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)}-\frac{a^2 b^3 e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{2 d \left(b^2-d\right)^{5/2}}-\frac{e^{c+d x^2} \text{erf}(a+b x)}{2 d^2}+\frac{x^2 e^{c+d x^2} \text{erf}(a+b x)}{2 d}",1,"(E^c*(2*E^(d*x^2)*(-1 + d*x^2)*Erf[a + b*x] - (b*d*E^(-a^2 - 2*a*b*x + (-b^2 + d)*x^2)*(2*(b^2 - d)*(a*b + (-b^2 + d)*x) + Sqrt[b^2 - d]*((1 + 2*a^2)*b^2 - d)*E^((a*b + (b^2 - d)*x)^2/(b^2 - d))*Sqrt[Pi]*Erf[(a*b + (b^2 - d)*x)/Sqrt[b^2 - d]]))/((b^2 - d)^3*Sqrt[Pi]) + (2*b*E^((a^2*d)/(b^2 - d))*Erfi[(-(a*b) + (-b^2 + d)*x)/Sqrt[-b^2 + d]])/Sqrt[-b^2 + d]))/(4*d^2)","A",1
87,1,82,86,0.1144819,"\int e^{c+d x^2} x \text{erf}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x*Erf[a + b*x],x]","\frac{e^c \left(e^{d x^2} \text{erf}(a+b x)-\frac{b e^{\frac{a^2 d}{b^2-d}} \text{erfi}\left(\frac{x \left(d-b^2\right)-a b}{\sqrt{d-b^2}}\right)}{\sqrt{d-b^2}}\right)}{2 d}","\frac{e^{c+d x^2} \text{erf}(a+b x)}{2 d}-\frac{b e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{2 d \sqrt{b^2-d}}",1,"(E^c*(E^(d*x^2)*Erf[a + b*x] - (b*E^((a^2*d)/(b^2 - d))*Erfi[(-(a*b) + (-b^2 + d)*x)/Sqrt[-b^2 + d]])/Sqrt[-b^2 + d]))/(2*d)","A",1
88,0,0,22,0.2388349,"\int \frac{e^{c+d x^2} \text{erf}(a+b x)}{x} \, dx","Integrate[(E^(c + d*x^2)*Erf[a + b*x])/x,x]","\int \frac{e^{c+d x^2} \text{erf}(a+b x)}{x} \, dx","\text{Int}\left(\frac{e^{c+d x^2} \text{erf}(a+b x)}{x},x\right)",0,"Integrate[(E^(c + d*x^2)*Erf[a + b*x])/x, x]","A",-1
89,0,0,185,0.4241891,"\int \frac{e^{c+d x^2} \text{erf}(a+b x)}{x^3} \, dx","Integrate[(E^(c + d*x^2)*Erf[a + b*x])/x^3,x]","\int \frac{e^{c+d x^2} \text{erf}(a+b x)}{x^3} \, dx","-\frac{2 a b^2 \text{Int}\left(\frac{e^{-a^2-2 a b x+x^2 \left(d-b^2\right)+c}}{x},x\right)}{\sqrt{\pi }}+d \text{Int}\left(\frac{e^{c+d x^2} \text{erf}(a+b x)}{x},x\right)-b \sqrt{b^2-d} e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)-\frac{b e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{\sqrt{\pi } x}-\frac{e^{c+d x^2} \text{erf}(a+b x)}{2 x^2}",0,"Integrate[(E^(c + d*x^2)*Erf[a + b*x])/x^3, x]","A",-1
90,0,0,527,0.5646499,"\int e^{c+d x^2} x^4 \text{erf}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x^4*Erf[a + b*x],x]","\int e^{c+d x^2} x^4 \text{erf}(a+b x) \, dx","\frac{3 \text{Int}\left(e^{c+d x^2} \text{erf}(a+b x),x\right)}{4 d^2}-\frac{3 a b^2 e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{4 d^2 \left(b^2-d\right)^{3/2}}-\frac{3 b e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{4 \sqrt{\pi } d^2 \left(b^2-d\right)}+\frac{3 a b^2 e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{4 d \left(b^2-d\right)^{5/2}}-\frac{a b^2 x e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)^2}+\frac{b x^2 e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)}+\frac{b e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)^2}+\frac{a^2 b^3 e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)^3}+\frac{a^3 b^4 e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{2 d \left(b^2-d\right)^{7/2}}-\frac{3 x e^{c+d x^2} \text{erf}(a+b x)}{4 d^2}+\frac{x^3 e^{c+d x^2} \text{erf}(a+b x)}{2 d}",0,"Integrate[E^(c + d*x^2)*x^4*Erf[a + b*x], x]","A",-1
91,0,0,164,0.4652102,"\int e^{c+d x^2} x^2 \text{erf}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x^2*Erf[a + b*x],x]","\int e^{c+d x^2} x^2 \text{erf}(a+b x) \, dx","-\frac{\text{Int}\left(e^{c+d x^2} \text{erf}(a+b x),x\right)}{2 d}+\frac{a b^2 e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{2 d \left(b^2-d\right)^{3/2}}+\frac{b e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)}+\frac{x e^{c+d x^2} \text{erf}(a+b x)}{2 d}",0,"Integrate[E^(c + d*x^2)*x^2*Erf[a + b*x], x]","A",-1
92,0,0,19,0.0508321,"\int e^{c+d x^2} \text{erf}(a+b x) \, dx","Integrate[E^(c + d*x^2)*Erf[a + b*x],x]","\int e^{c+d x^2} \text{erf}(a+b x) \, dx","\text{Int}\left(e^{c+d x^2} \text{erf}(a+b x),x\right)",0,"Integrate[E^(c + d*x^2)*Erf[a + b*x], x]","A",-1
93,0,0,83,0.4620415,"\int \frac{e^{c+d x^2} \text{erf}(a+b x)}{x^2} \, dx","Integrate[(E^(c + d*x^2)*Erf[a + b*x])/x^2,x]","\int \frac{e^{c+d x^2} \text{erf}(a+b x)}{x^2} \, dx","\frac{2 b \text{Int}\left(\frac{e^{-a^2-2 a b x+x^2 \left(d-b^2\right)+c}}{x},x\right)}{\sqrt{\pi }}+2 d \text{Int}\left(e^{c+d x^2} \text{erf}(a+b x),x\right)-\frac{e^{c+d x^2} \text{erf}(a+b x)}{x}",0,"Integrate[(E^(c + d*x^2)*Erf[a + b*x])/x^2, x]","A",-1
94,0,0,355,0.6300294,"\int \frac{e^{c+d x^2} \text{erf}(a+b x)}{x^4} \, dx","Integrate[(E^(c + d*x^2)*Erf[a + b*x])/x^4,x]","\int \frac{e^{c+d x^2} \text{erf}(a+b x)}{x^4} \, dx","-\frac{2 b \left(b^2-d\right) \text{Int}\left(\frac{e^{-a^2-2 a b x+x^2 \left(d-b^2\right)+c}}{x},x\right)}{3 \sqrt{\pi }}+\frac{4 b d \text{Int}\left(\frac{e^{-a^2-2 a b x+x^2 \left(d-b^2\right)+c}}{x},x\right)}{3 \sqrt{\pi }}+\frac{4 a^2 b^3 \text{Int}\left(\frac{e^{-a^2-2 a b x+x^2 \left(d-b^2\right)+c}}{x},x\right)}{3 \sqrt{\pi }}+\frac{4}{3} d^2 \text{Int}\left(e^{c+d x^2} \text{erf}(a+b x),x\right)+\frac{2}{3} a b^2 \sqrt{b^2-d} e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)+\frac{2 a b^2 e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{3 \sqrt{\pi } x}-\frac{b e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{3 \sqrt{\pi } x^2}-\frac{2 d e^{c+d x^2} \text{erf}(a+b x)}{3 x}-\frac{e^{c+d x^2} \text{erf}(a+b x)}{3 x^3}",0,"Integrate[(E^(c + d*x^2)*Erf[a + b*x])/x^4, x]","A",-1
95,1,62,62,0.1328244,"\int \left(\frac{e^{-b^2 x^2} \text{erf}(b x)}{x^3}+\frac{b^2 e^{-b^2 x^2} \text{erf}(b x)}{x}\right) \, dx","Integrate[Erf[b*x]/(E^(b^2*x^2)*x^3) + (b^2*Erf[b*x])/(E^(b^2*x^2)*x),x]","-\frac{e^{-b^2 x^2} \text{erf}(b x)}{2 x^2}-\sqrt{2} b^2 \text{erf}\left(\sqrt{2} b x\right)-\frac{b e^{-2 b^2 x^2}}{\sqrt{\pi } x}","-\frac{e^{-b^2 x^2} \text{erf}(b x)}{2 x^2}-\sqrt{2} b^2 \text{erf}\left(\sqrt{2} b x\right)-\frac{b e^{-2 b^2 x^2}}{\sqrt{\pi } x}",1,"-(b/(E^(2*b^2*x^2)*Sqrt[Pi]*x)) - Erf[b*x]/(2*E^(b^2*x^2)*x^2) - Sqrt[2]*b^2*Erf[Sqrt[2]*b*x]","A",1
96,1,69,66,0.0963437,"\int \text{erf}(b x) \sin \left(c+i b^2 x^2\right) \, dx","Integrate[Erf[b*x]*Sin[c + I*b^2*x^2],x]","\frac{(\cos (c)-i \sin (c)) \left(4 i b^2 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)+\pi  \text{erf}(b x)^2 (\sin (2 c)-i \cos (2 c))\right)}{8 \sqrt{\pi } b}","\frac{i b e^{-i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}-\frac{i \sqrt{\pi } e^{i c} \text{erf}(b x)^2}{8 b}",1,"((Cos[c] - I*Sin[c])*((4*I)*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2] + Pi*Erf[b*x]^2*((-I)*Cos[2*c] + Sin[2*c])))/(8*b*Sqrt[Pi])","A",1
97,1,67,66,0.0905957,"\int \text{erf}(b x) \sin \left(c-i b^2 x^2\right) \, dx","Integrate[Erf[b*x]*Sin[c - I*b^2*x^2],x]","\frac{(\sin (c)+i \cos (c)) \left(\pi  \text{erf}(b x)^2-4 b^2 x^2 (\cos (2 c)+i \sin (2 c)) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)\right)}{8 \sqrt{\pi } b}","\frac{i \sqrt{\pi } e^{-i c} \text{erf}(b x)^2}{8 b}-\frac{i b e^{i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}",1,"((I*Cos[c] + Sin[c])*(Pi*Erf[b*x]^2 - 4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*(Cos[2*c] + I*Sin[2*c])))/(8*b*Sqrt[Pi])","A",1
98,0,0,62,0.7704489,"\int \cos \left(c+i b^2 x^2\right) \text{erf}(b x) \, dx","Integrate[Cos[c + I*b^2*x^2]*Erf[b*x],x]","\int \cos \left(c+i b^2 x^2\right) \text{erf}(b x) \, dx","\frac{b e^{-i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}+\frac{\sqrt{\pi } e^{i c} \text{erf}(b x)^2}{8 b}",1,"Integrate[Cos[c + I*b^2*x^2]*Erf[b*x], x]","F",-1
99,0,0,62,0.7684515,"\int \cos \left(c-i b^2 x^2\right) \text{erf}(b x) \, dx","Integrate[Cos[c - I*b^2*x^2]*Erf[b*x],x]","\int \cos \left(c-i b^2 x^2\right) \text{erf}(b x) \, dx","\frac{b e^{i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}+\frac{\sqrt{\pi } e^{-i c} \text{erf}(b x)^2}{8 b}",1,"Integrate[Cos[c - I*b^2*x^2]*Erf[b*x], x]","F",-1
100,1,57,56,0.0605393,"\int \text{erf}(b x) \sinh \left(c+b^2 x^2\right) \, dx","Integrate[Erf[b*x]*Sinh[c + b^2*x^2],x]","\frac{4 b^2 x^2 (\sinh (c)+\cosh (c)) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)+\pi  \text{erf}(b x)^2 (\sinh (c)-\cosh (c))}{8 \sqrt{\pi } b}","\frac{b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}-\frac{\sqrt{\pi } e^{-c} \text{erf}(b x)^2}{8 b}",1,"(Pi*Erf[b*x]^2*(-Cosh[c] + Sinh[c]) + 4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*(Cosh[c] + Sinh[c]))/(8*b*Sqrt[Pi])","A",1
101,1,61,56,0.0694196,"\int \text{erf}(b x) \sinh \left(c-b^2 x^2\right) \, dx","Integrate[Erf[b*x]*Sinh[c - b^2*x^2],x]","\frac{(\cosh (c)-\sinh (c)) \left(\pi  \text{erf}(b x)^2 (\sinh (2 c)+\cosh (2 c))-4 b^2 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)\right)}{8 \sqrt{\pi } b}","\frac{\sqrt{\pi } e^c \text{erf}(b x)^2}{8 b}-\frac{b e^{-c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}",1,"((Cosh[c] - Sinh[c])*(-4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2] + Pi*Erf[b*x]^2*(Cosh[2*c] + Sinh[2*c])))/(8*b*Sqrt[Pi])","A",1
102,1,93,56,0.2996311,"\int \cosh \left(c+b^2 x^2\right) \text{erf}(b x) \, dx","Integrate[Cosh[c + b^2*x^2]*Erf[b*x],x]","\frac{4 b^2 x^2 \sinh (c) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)-4 b^2 x^2 \cosh (c) \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)+\pi  \text{erf}(b x) (\text{erf}(b x) (\cosh (c)-\sinh (c))+2 \cosh (c) \text{erfi}(b x))}{8 \sqrt{\pi } b}","\frac{b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}+\frac{\sqrt{\pi } e^{-c} \text{erf}(b x)^2}{8 b}",1,"(-4*b^2*x^2*Cosh[c]*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)] + Pi*Erf[b*x]*(2*Cosh[c]*Erfi[b*x] + Erf[b*x]*(Cosh[c] - Sinh[c])) + 4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*Sinh[c])/(8*b*Sqrt[Pi])","A",1
103,1,91,56,0.1079784,"\int \cosh \left(c-b^2 x^2\right) \text{erf}(b x) \, dx","Integrate[Cosh[c - b^2*x^2]*Erf[b*x],x]","\frac{-4 b^2 x^2 \sinh (c) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)-4 b^2 x^2 \cosh (c) \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)+\pi  \text{erf}(b x) (\text{erf}(b x) (\sinh (c)+\cosh (c))+2 \cosh (c) \text{erfi}(b x))}{8 \sqrt{\pi } b}","\frac{b e^{-c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}+\frac{\sqrt{\pi } e^c \text{erf}(b x)^2}{8 b}",1,"(-4*b^2*x^2*Cosh[c]*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)] - 4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*Sinh[c] + Pi*Erf[b*x]*(2*Cosh[c]*Erfi[b*x] + Erf[b*x]*(Cosh[c] + Sinh[c])))/(8*b*Sqrt[Pi])","A",1
104,1,62,96,0.0778079,"\int x^5 \text{erfc}(b x) \, dx","Integrate[x^5*Erfc[b*x],x]","\frac{1}{48} \left(\frac{15 \text{erf}(b x)}{b^6}-\frac{2 x e^{-b^2 x^2} \left(4 b^4 x^4+10 b^2 x^2+15\right)}{\sqrt{\pi } b^5}+8 x^6 \text{erfc}(b x)\right)","\frac{5 \text{erf}(b x)}{16 b^6}-\frac{x^5 e^{-b^2 x^2}}{6 \sqrt{\pi } b}-\frac{5 x e^{-b^2 x^2}}{8 \sqrt{\pi } b^5}-\frac{5 x^3 e^{-b^2 x^2}}{12 \sqrt{\pi } b^3}+\frac{1}{6} x^6 \text{erfc}(b x)",1,"((-2*x*(15 + 10*b^2*x^2 + 4*b^4*x^4))/(b^5*E^(b^2*x^2)*Sqrt[Pi]) + (15*Erf[b*x])/b^6 + 8*x^6*Erfc[b*x])/48","A",1
105,1,54,71,0.0637228,"\int x^3 \text{erfc}(b x) \, dx","Integrate[x^3*Erfc[b*x],x]","\frac{1}{16} \left(\frac{3 \text{erf}(b x)}{b^4}-\frac{2 x e^{-b^2 x^2} \left(2 b^2 x^2+3\right)}{\sqrt{\pi } b^3}+4 x^4 \text{erfc}(b x)\right)","\frac{3 \text{erf}(b x)}{16 b^4}-\frac{x^3 e^{-b^2 x^2}}{4 \sqrt{\pi } b}-\frac{3 x e^{-b^2 x^2}}{8 \sqrt{\pi } b^3}+\frac{1}{4} x^4 \text{erfc}(b x)",1,"((-2*x*(3 + 2*b^2*x^2))/(b^3*E^(b^2*x^2)*Sqrt[Pi]) + (3*Erf[b*x])/b^4 + 4*x^4*Erfc[b*x])/16","A",1
106,1,43,46,0.0566709,"\int x \text{erfc}(b x) \, dx","Integrate[x*Erfc[b*x],x]","\frac{1}{4} \left(\frac{\text{erf}(b x)}{b^2}+2 x \left(x \text{erfc}(b x)-\frac{e^{-b^2 x^2}}{\sqrt{\pi } b}\right)\right)","\frac{\text{erf}(b x)}{4 b^2}-\frac{x e^{-b^2 x^2}}{2 \sqrt{\pi } b}+\frac{1}{2} x^2 \text{erfc}(b x)",1,"(Erf[b*x]/b^2 + 2*x*(-(1/(b*E^(b^2*x^2)*Sqrt[Pi])) + x*Erfc[b*x]))/4","A",1
107,1,45,35,0.0346296,"\int \frac{\text{erfc}(b x)}{x} \, dx","Integrate[Erfc[b*x]/x,x]","\log (x) (\text{erf}(b x)+\text{erfc}(b x))-\frac{2 b x \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-b^2 x^2\right)}{\sqrt{\pi }}","\log (x)-\frac{2 b x \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-b^2 x^2\right)}{\sqrt{\pi }}",1,"(-2*b*x*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2}, -(b^2*x^2)])/Sqrt[Pi] + (Erf[b*x] + Erfc[b*x])*Log[x]","A",1
108,1,40,40,0.0480938,"\int \frac{\text{erfc}(b x)}{x^3} \, dx","Integrate[Erfc[b*x]/x^3,x]","b^2 \text{erf}(b x)+\frac{b e^{-b^2 x^2}}{\sqrt{\pi } x}-\frac{\text{erfc}(b x)}{2 x^2}","b^2 \text{erf}(b x)+\frac{b e^{-b^2 x^2}}{\sqrt{\pi } x}-\frac{\text{erfc}(b x)}{2 x^2}",1,"b/(E^(b^2*x^2)*Sqrt[Pi]*x) + b^2*Erf[b*x] - Erfc[b*x]/(2*x^2)","A",1
109,1,53,71,0.0429914,"\int \frac{\text{erfc}(b x)}{x^5} \, dx","Integrate[Erfc[b*x]/x^5,x]","\frac{1}{12} \left(-4 b^4 \text{erf}(b x)+\frac{2 e^{-b^2 x^2} \left(b-2 b^3 x^2\right)}{\sqrt{\pi } x^3}-\frac{3 \text{erfc}(b x)}{x^4}\right)","-\frac{1}{3} b^4 \text{erf}(b x)+\frac{b e^{-b^2 x^2}}{6 \sqrt{\pi } x^3}-\frac{b^3 e^{-b^2 x^2}}{3 \sqrt{\pi } x}-\frac{\text{erfc}(b x)}{4 x^4}",1,"((2*(b - 2*b^3*x^2))/(E^(b^2*x^2)*Sqrt[Pi]*x^3) - 4*b^4*Erf[b*x] - (3*Erfc[b*x])/x^4)/12","A",1
110,1,62,96,0.0632427,"\int \frac{\text{erfc}(b x)}{x^7} \, dx","Integrate[Erfc[b*x]/x^7,x]","\frac{1}{90} \left(8 b^6 \text{erf}(b x)+\frac{2 b e^{-b^2 x^2} \left(4 b^4 x^4-2 b^2 x^2+3\right)}{\sqrt{\pi } x^5}-\frac{15 \text{erfc}(b x)}{x^6}\right)","\frac{4}{45} b^6 \text{erf}(b x)+\frac{b e^{-b^2 x^2}}{15 \sqrt{\pi } x^5}+\frac{4 b^5 e^{-b^2 x^2}}{45 \sqrt{\pi } x}-\frac{2 b^3 e^{-b^2 x^2}}{45 \sqrt{\pi } x^3}-\frac{\text{erfc}(b x)}{6 x^6}",1,"((2*b*(3 - 2*b^2*x^2 + 4*b^4*x^4))/(E^(b^2*x^2)*Sqrt[Pi]*x^5) + 8*b^6*Erf[b*x] - (15*Erfc[b*x])/x^6)/90","A",1
111,1,73,109,0.0240355,"\int x^6 \text{erfc}(b x) \, dx","Integrate[x^6*Erfc[b*x],x]","\frac{e^{-b^2 x^2} \left(-b^6 x^6-3 b^4 x^4-6 b^2 x^2+\sqrt{\pi } b^7 x^7 e^{b^2 x^2} \text{erfc}(b x)-6\right)}{7 \sqrt{\pi } b^7}","-\frac{x^6 e^{-b^2 x^2}}{7 \sqrt{\pi } b}-\frac{6 e^{-b^2 x^2}}{7 \sqrt{\pi } b^7}-\frac{6 x^2 e^{-b^2 x^2}}{7 \sqrt{\pi } b^5}-\frac{3 x^4 e^{-b^2 x^2}}{7 \sqrt{\pi } b^3}+\frac{1}{7} x^7 \text{erfc}(b x)",1,"(-6 - 6*b^2*x^2 - 3*b^4*x^4 - b^6*x^6 + b^7*E^(b^2*x^2)*Sqrt[Pi]*x^7*Erfc[b*x])/(7*b^7*E^(b^2*x^2)*Sqrt[Pi])","A",1
112,1,66,84,0.0254677,"\int x^4 \text{erfc}(b x) \, dx","Integrate[x^4*Erfc[b*x],x]","e^{-b^2 x^2} \left(-\frac{2}{5 \sqrt{\pi } b^5}-\frac{2 x^2}{5 \sqrt{\pi } b^3}-\frac{x^4}{5 \sqrt{\pi } b}\right)+\frac{1}{5} x^5 \text{erfc}(b x)","-\frac{x^4 e^{-b^2 x^2}}{5 \sqrt{\pi } b}-\frac{2 e^{-b^2 x^2}}{5 \sqrt{\pi } b^5}-\frac{2 x^2 e^{-b^2 x^2}}{5 \sqrt{\pi } b^3}+\frac{1}{5} x^5 \text{erfc}(b x)",1,"(-2/(5*b^5*Sqrt[Pi]) - (2*x^2)/(5*b^3*Sqrt[Pi]) - x^4/(5*b*Sqrt[Pi]))/E^(b^2*x^2) + (x^5*Erfc[b*x])/5","A",1
113,1,42,59,0.0320494,"\int x^2 \text{erfc}(b x) \, dx","Integrate[x^2*Erfc[b*x],x]","\frac{1}{3} \left(x^3 \text{erfc}(b x)-\frac{e^{-b^2 x^2} \left(b^2 x^2+1\right)}{\sqrt{\pi } b^3}\right)","-\frac{x^2 e^{-b^2 x^2}}{3 \sqrt{\pi } b}-\frac{e^{-b^2 x^2}}{3 \sqrt{\pi } b^3}+\frac{1}{3} x^3 \text{erfc}(b x)",1,"(-((1 + b^2*x^2)/(b^3*E^(b^2*x^2)*Sqrt[Pi])) + x^3*Erfc[b*x])/3","A",1
114,1,27,27,0.0029257,"\int \text{erfc}(b x) \, dx","Integrate[Erfc[b*x],x]","x \text{erfc}(b x)-\frac{e^{-b^2 x^2}}{\sqrt{\pi } b}","x \text{erfc}(b x)-\frac{e^{-b^2 x^2}}{\sqrt{\pi } b}",1,"-(1/(b*E^(b^2*x^2)*Sqrt[Pi])) + x*Erfc[b*x]","A",1
115,1,27,27,0.014261,"\int \frac{\text{erfc}(b x)}{x^2} \, dx","Integrate[Erfc[b*x]/x^2,x]","-\frac{b \text{Ei}\left(-b^2 x^2\right)}{\sqrt{\pi }}-\frac{\text{erfc}(b x)}{x}","-\frac{b \text{Ei}\left(-b^2 x^2\right)}{\sqrt{\pi }}-\frac{\text{erfc}(b x)}{x}",1,"-(Erfc[b*x]/x) - (b*ExpIntegralEi[-(b^2*x^2)])/Sqrt[Pi]","A",1
116,1,49,56,0.0429441,"\int \frac{\text{erfc}(b x)}{x^4} \, dx","Integrate[Erfc[b*x]/x^4,x]","\frac{1}{3} \left(\frac{b \left(b^2 \text{Ei}\left(-b^2 x^2\right)+\frac{e^{-b^2 x^2}}{x^2}\right)}{\sqrt{\pi }}-\frac{\text{erfc}(b x)}{x^3}\right)","\frac{b e^{-b^2 x^2}}{3 \sqrt{\pi } x^2}+\frac{b^3 \text{Ei}\left(-b^2 x^2\right)}{3 \sqrt{\pi }}-\frac{\text{erfc}(b x)}{3 x^3}",1,"(-(Erfc[b*x]/x^3) + (b*(1/(E^(b^2*x^2)*x^2) + b^2*ExpIntegralEi[-(b^2*x^2)]))/Sqrt[Pi])/3","A",1
117,1,73,81,0.0226525,"\int \frac{\text{erfc}(b x)}{x^6} \, dx","Integrate[Erfc[b*x]/x^6,x]","-\frac{b^5 \text{Ei}\left(-b^2 x^2\right)}{10 \sqrt{\pi }}+e^{-b^2 x^2} \left(\frac{b}{10 \sqrt{\pi } x^4}-\frac{b^3}{10 \sqrt{\pi } x^2}\right)-\frac{\text{erfc}(b x)}{5 x^5}","\frac{b e^{-b^2 x^2}}{10 \sqrt{\pi } x^4}-\frac{b^5 \text{Ei}\left(-b^2 x^2\right)}{10 \sqrt{\pi }}-\frac{b^3 e^{-b^2 x^2}}{10 \sqrt{\pi } x^2}-\frac{\text{erfc}(b x)}{5 x^5}",1,"(b/(10*Sqrt[Pi]*x^4) - b^3/(10*Sqrt[Pi]*x^2))/E^(b^2*x^2) - Erfc[b*x]/(5*x^5) - (b^5*ExpIntegralEi[-(b^2*x^2)])/(10*Sqrt[Pi])","A",1
118,1,268,292,0.3897306,"\int (c+d x)^3 \text{erfc}(a+b x) \, dx","Integrate[(c + d*x)^3*Erfc[a + b*x],x]","\frac{e^{-(a+b x)^2} \left(-2 b d^2 \left(8 \left(a^2+1\right) c+\left(2 a^2+3\right) d x\right)+2 a \left(2 a^2+5\right) d^3+\sqrt{\pi } e^{(a+b x)^2} \left(4 a^4 d^3-16 a^3 b c d^2+12 a^2 \left(2 b^2 c^2 d+d^3\right)-8 a \left(2 b^3 c^3+3 b c d^2\right)+3 \left(4 b^2 c^2 d+d^3\right)\right) \text{erf}(a+b x)+4 \sqrt{\pi } b^4 x e^{(a+b x)^2} \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \text{erfc}(a+b x)+4 a b^2 d \left(6 c^2+4 c d x+d^2 x^2\right)-4 b^3 \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right)}{16 \sqrt{\pi } b^4}","-\frac{d^2 e^{-(a+b x)^2} (a+b x)^2 (b c-a d)}{\sqrt{\pi } b^4}-\frac{d^2 e^{-(a+b x)^2} (b c-a d)}{\sqrt{\pi } b^4}+\frac{(b c-a d)^4 \text{erf}(a+b x)}{4 b^4 d}+\frac{3 d (b c-a d)^2 \text{erf}(a+b x)}{4 b^4}-\frac{e^{-(a+b x)^2} (b c-a d)^3}{\sqrt{\pi } b^4}-\frac{3 d e^{-(a+b x)^2} (a+b x) (b c-a d)^2}{2 \sqrt{\pi } b^4}+\frac{3 d^3 \text{erf}(a+b x)}{16 b^4}-\frac{d^3 e^{-(a+b x)^2} (a+b x)^3}{4 \sqrt{\pi } b^4}-\frac{3 d^3 e^{-(a+b x)^2} (a+b x)}{8 \sqrt{\pi } b^4}+\frac{(c+d x)^4 \text{erfc}(a+b x)}{4 d}",1,"(2*a*(5 + 2*a^2)*d^3 - 2*b*d^2*(8*(1 + a^2)*c + (3 + 2*a^2)*d*x) + 4*a*b^2*d*(6*c^2 + 4*c*d*x + d^2*x^2) - 4*b^3*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) + (-16*a^3*b*c*d^2 + 4*a^4*d^3 - 8*a*(2*b^3*c^3 + 3*b*c*d^2) + 12*a^2*(2*b^2*c^2*d + d^3) + 3*(4*b^2*c^2*d + d^3))*E^(a + b*x)^2*Sqrt[Pi]*Erf[a + b*x] + 4*b^4*E^(a + b*x)^2*Sqrt[Pi]*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Erfc[a + b*x])/(16*b^4*E^(a + b*x)^2*Sqrt[Pi])","A",1
119,1,159,194,0.3130239,"\int (c+d x)^2 \text{erfc}(a+b x) \, dx","Integrate[(c + d*x)^2*Erfc[a + b*x],x]","\frac{\frac{2 e^{-(a+b x)^2} \left(-\left(a^2+1\right) d^2+\sqrt{\pi } b^3 x e^{(a+b x)^2} \left(3 c^2+3 c d x+d^2 x^2\right) \text{erfc}(a+b x)+a b d (3 c+d x)-b^2 \left(3 c^2+3 c d x+d^2 x^2\right)\right)}{\sqrt{\pi }}-\left(2 a^3 d^2-6 a^2 b c d+3 a \left(2 b^2 c^2+d^2\right)-3 b c d\right) \text{erf}(a+b x)}{6 b^3}","\frac{(b c-a d)^3 \text{erf}(a+b x)}{3 b^3 d}+\frac{d (b c-a d) \text{erf}(a+b x)}{2 b^3}-\frac{e^{-(a+b x)^2} (b c-a d)^2}{\sqrt{\pi } b^3}-\frac{d e^{-(a+b x)^2} (a+b x) (b c-a d)}{\sqrt{\pi } b^3}-\frac{d^2 e^{-(a+b x)^2} (a+b x)^2}{3 \sqrt{\pi } b^3}-\frac{d^2 e^{-(a+b x)^2}}{3 \sqrt{\pi } b^3}+\frac{(c+d x)^3 \text{erfc}(a+b x)}{3 d}",1,"(-((-3*b*c*d - 6*a^2*b*c*d + 2*a^3*d^2 + 3*a*(2*b^2*c^2 + d^2))*Erf[a + b*x]) + (2*(-((1 + a^2)*d^2) + a*b*d*(3*c + d*x) - b^2*(3*c^2 + 3*c*d*x + d^2*x^2) + b^3*E^(a + b*x)^2*Sqrt[Pi]*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Erfc[a + b*x]))/(E^(a + b*x)^2*Sqrt[Pi]))/(6*b^3)","A",1
120,1,104,119,0.1472014,"\int (c+d x) \text{erfc}(a+b x) \, dx","Integrate[(c + d*x)*Erfc[a + b*x],x]","\frac{e^{-(a+b x)^2} \left(\sqrt{\pi } e^{(a+b x)^2} \left(2 a^2 d-4 a b c+d\right) \text{erf}(a+b x)+2 \sqrt{\pi } b^2 x e^{(a+b x)^2} (2 c+d x) \text{erfc}(a+b x)+2 a d-4 b c-2 b d x\right)}{4 \sqrt{\pi } b^2}","\frac{(b c-a d)^2 \text{erf}(a+b x)}{2 b^2 d}-\frac{e^{-(a+b x)^2} (b c-a d)}{\sqrt{\pi } b^2}+\frac{d \text{erf}(a+b x)}{4 b^2}-\frac{d e^{-(a+b x)^2} (a+b x)}{2 \sqrt{\pi } b^2}+\frac{(c+d x)^2 \text{erfc}(a+b x)}{2 d}",1,"(-4*b*c + 2*a*d - 2*b*d*x + (-4*a*b*c + d + 2*a^2*d)*E^(a + b*x)^2*Sqrt[Pi]*Erf[a + b*x] + 2*b^2*E^(a + b*x)^2*Sqrt[Pi]*x*(2*c + d*x)*Erfc[a + b*x])/(4*b^2*E^(a + b*x)^2*Sqrt[Pi])","A",1
121,1,42,37,0.0462234,"\int \text{erfc}(a+b x) \, dx","Integrate[Erfc[a + b*x],x]","-\frac{a \text{erf}(a+b x)}{b}+x \text{erfc}(a+b x)-\frac{e^{-(a+b x)^2}}{\sqrt{\pi } b}","\frac{(a+b x) \text{erfc}(a+b x)}{b}-\frac{e^{-(a+b x)^2}}{\sqrt{\pi } b}",1,"-(1/(b*E^(a + b*x)^2*Sqrt[Pi])) - (a*Erf[a + b*x])/b + x*Erfc[a + b*x]","A",1
122,0,0,17,0.1362758,"\int \frac{\text{erfc}(a+b x)}{c+d x} \, dx","Integrate[Erfc[a + b*x]/(c + d*x),x]","\int \frac{\text{erfc}(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{erfc}(a+b x)}{c+d x},x\right)",0,"Integrate[Erfc[a + b*x]/(c + d*x), x]","A",-1
123,0,0,52,0.5439727,"\int \frac{\text{erfc}(a+b x)}{(c+d x)^2} \, dx","Integrate[Erfc[a + b*x]/(c + d*x)^2,x]","\int \frac{\text{erfc}(a+b x)}{(c+d x)^2} \, dx","-\frac{2 b \text{Int}\left(\frac{e^{-(a+b x)^2}}{c+d x},x\right)}{\sqrt{\pi } d}-\frac{\text{erfc}(a+b x)}{d (c+d x)}",0,"Integrate[Erfc[a + b*x]/(c + d*x)^2, x]","A",-1
124,0,0,105,1.2051765,"\int \frac{\text{erfc}(a+b x)}{(c+d x)^3} \, dx","Integrate[Erfc[a + b*x]/(c + d*x)^3,x]","\int \frac{\text{erfc}(a+b x)}{(c+d x)^3} \, dx","-\frac{2 b^2 (b c-a d) \text{Int}\left(\frac{e^{-(a+b x)^2}}{c+d x},x\right)}{\sqrt{\pi } d^3}+\frac{b^2 \text{erf}(a+b x)}{d^3}+\frac{b e^{-(a+b x)^2}}{\sqrt{\pi } d^2 (c+d x)}-\frac{\text{erfc}(a+b x)}{2 d (c+d x)^2}",0,"Integrate[Erfc[a + b*x]/(c + d*x)^3, x]","A",-1
125,1,173,178,0.4655409,"\int x^5 \text{erfc}(b x)^2 \, dx","Integrate[x^5*Erfc[b*x]^2,x]","\frac{1}{24} \left(\left(\frac{15}{b^6}-8 x^6\right) \text{erf}(b x)+\frac{e^{-2 b^2 x^2} \left(8 b^4 x^4-15 \pi  e^{2 b^2 x^2} \text{erf}(b x)^2+28 b^2 x^2+4 \sqrt{\pi } b x e^{b^2 x^2} \left(4 b^4 x^4+10 b^2 x^2+15\right) \text{erf}(b x)+44\right)}{2 \pi  b^6}-\frac{2 x e^{-b^2 x^2} \left(4 b^4 x^4+10 b^2 x^2+15\right)}{\sqrt{\pi } b^5}+4 x^6 \text{erf}(b x)^2+4 x^6\right)","-\frac{5 \text{erfc}(b x)^2}{16 b^6}-\frac{x^5 e^{-b^2 x^2} \text{erfc}(b x)}{3 \sqrt{\pi } b}+\frac{x^4 e^{-2 b^2 x^2}}{6 \pi  b^2}+\frac{11 e^{-2 b^2 x^2}}{12 \pi  b^6}-\frac{5 x e^{-b^2 x^2} \text{erfc}(b x)}{4 \sqrt{\pi } b^5}+\frac{7 x^2 e^{-2 b^2 x^2}}{12 \pi  b^4}-\frac{5 x^3 e^{-b^2 x^2} \text{erfc}(b x)}{6 \sqrt{\pi } b^3}+\frac{1}{6} x^6 \text{erfc}(b x)^2",1,"(4*x^6 - (2*x*(15 + 10*b^2*x^2 + 4*b^4*x^4))/(b^5*E^(b^2*x^2)*Sqrt[Pi]) + (15/b^6 - 8*x^6)*Erf[b*x] + 4*x^6*Erf[b*x]^2 + (44 + 28*b^2*x^2 + 8*b^4*x^4 + 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(15 + 10*b^2*x^2 + 4*b^4*x^4)*Erf[b*x] - 15*E^(2*b^2*x^2)*Pi*Erf[b*x]^2)/(2*b^6*E^(2*b^2*x^2)*Pi))/24","A",0
126,1,149,126,0.4327333,"\int x^3 \text{erfc}(b x)^2 \, dx","Integrate[x^3*Erfc[b*x]^2,x]","\frac{1}{8} \left(\left(\frac{3}{b^4}-4 x^4\right) \text{erf}(b x)+\frac{e^{-2 b^2 x^2} \left(4 \sqrt{\pi } b x e^{b^2 x^2} \left(2 b^2 x^2+3\right) \text{erf}(b x)-3 \pi  e^{2 b^2 x^2} \text{erf}(b x)^2+4 b^2 x^2+8\right)}{2 \pi  b^4}-\frac{2 x e^{-b^2 x^2} \left(2 b^2 x^2+3\right)}{\sqrt{\pi } b^3}+2 x^4 \text{erf}(b x)^2+2 x^4\right)","-\frac{3 \text{erfc}(b x)^2}{16 b^4}-\frac{x^3 e^{-b^2 x^2} \text{erfc}(b x)}{2 \sqrt{\pi } b}+\frac{x^2 e^{-2 b^2 x^2}}{4 \pi  b^2}+\frac{e^{-2 b^2 x^2}}{2 \pi  b^4}-\frac{3 x e^{-b^2 x^2} \text{erfc}(b x)}{4 \sqrt{\pi } b^3}+\frac{1}{4} x^4 \text{erfc}(b x)^2",1,"(2*x^4 - (2*x*(3 + 2*b^2*x^2))/(b^3*E^(b^2*x^2)*Sqrt[Pi]) + (3/b^4 - 4*x^4)*Erf[b*x] + 2*x^4*Erf[b*x]^2 + (8 + 4*b^2*x^2 + 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(3 + 2*b^2*x^2)*Erf[b*x] - 3*E^(2*b^2*x^2)*Pi*Erf[b*x]^2)/(2*b^4*E^(2*b^2*x^2)*Pi))/8","A",0
127,1,99,72,0.1631396,"\int x \text{erfc}(b x)^2 \, dx","Integrate[x*Erfc[b*x]^2,x]","\frac{\pi  \left(2 b^2 x^2-1\right) \text{erf}(b x)^2+\left(4 \sqrt{\pi } b x e^{-b^2 x^2}+\pi  \left(2-4 b^2 x^2\right)\right) \text{erf}(b x)+2 e^{-2 b^2 x^2} \left(\sqrt{\pi } b x e^{b^2 x^2}-1\right)^2}{4 \pi  b^2}","-\frac{x e^{-b^2 x^2} \text{erfc}(b x)}{\sqrt{\pi } b}-\frac{\text{erfc}(b x)^2}{4 b^2}+\frac{e^{-2 b^2 x^2}}{2 \pi  b^2}+\frac{1}{2} x^2 \text{erfc}(b x)^2",1,"((2*(-1 + b*E^(b^2*x^2)*Sqrt[Pi]*x)^2)/E^(2*b^2*x^2) + ((4*b*Sqrt[Pi]*x)/E^(b^2*x^2) + Pi*(2 - 4*b^2*x^2))*Erf[b*x] + Pi*(-1 + 2*b^2*x^2)*Erf[b*x]^2)/(4*b^2*Pi)","A",0
128,0,0,13,0.1665791,"\int \frac{\text{erfc}(b x)^2}{x} \, dx","Integrate[Erfc[b*x]^2/x,x]","\int \frac{\text{erfc}(b x)^2}{x} \, dx","\text{Int}\left(\frac{\text{erfc}(b x)^2}{x},x\right)",0,"Integrate[Erfc[b*x]^2/x, x]","A",-1
129,1,63,67,0.0426565,"\int \frac{\text{erfc}(b x)^2}{x^3} \, dx","Integrate[Erfc[b*x]^2/x^3,x]","\frac{2 b e^{-b^2 x^2} \text{erfc}(b x)}{\sqrt{\pi } x}+\left(-b^2-\frac{1}{2 x^2}\right) \text{erfc}(b x)^2+\frac{2 b^2 \text{Ei}\left(-2 b^2 x^2\right)}{\pi }","\frac{2 b e^{-b^2 x^2} \text{erfc}(b x)}{\sqrt{\pi } x}+b^2 \left(-\text{erfc}(b x)^2\right)+\frac{2 b^2 \text{Ei}\left(-2 b^2 x^2\right)}{\pi }-\frac{\text{erfc}(b x)^2}{2 x^2}",1,"(2*b*Erfc[b*x])/(E^(b^2*x^2)*Sqrt[Pi]*x) + (-b^2 - 1/(2*x^2))*Erfc[b*x]^2 + (2*b^2*ExpIntegralEi[-2*b^2*x^2])/Pi","A",1
130,1,97,125,0.0672956,"\int \frac{\text{erfc}(b x)^2}{x^5} \, dx","Integrate[Erfc[b*x]^2/x^5,x]","\frac{\left(4 b^4 x^4-3\right) \text{erfc}(b x)^2-\frac{4 b x e^{-b^2 x^2} \left(2 b^2 x^2-1\right) \text{erfc}(b x)}{\sqrt{\pi }}-\frac{4 b^2 x^2 \left(4 b^2 x^2 \text{Ei}\left(-2 b^2 x^2\right)+e^{-2 b^2 x^2}\right)}{\pi }}{12 x^4}","\frac{1}{3} b^4 \text{erfc}(b x)^2+\frac{b e^{-b^2 x^2} \text{erfc}(b x)}{3 \sqrt{\pi } x^3}-\frac{b^2 e^{-2 b^2 x^2}}{3 \pi  x^2}-\frac{4 b^4 \text{Ei}\left(-2 b^2 x^2\right)}{3 \pi }-\frac{2 b^3 e^{-b^2 x^2} \text{erfc}(b x)}{3 \sqrt{\pi } x}-\frac{\text{erfc}(b x)^2}{4 x^4}",1,"((-4*b*x*(-1 + 2*b^2*x^2)*Erfc[b*x])/(E^(b^2*x^2)*Sqrt[Pi]) + (-3 + 4*b^4*x^4)*Erfc[b*x]^2 - (4*b^2*x^2*(E^(-2*b^2*x^2) + 4*b^2*x^2*ExpIntegralEi[-2*b^2*x^2]))/Pi)/(12*x^4)","A",1
131,1,133,177,0.0389402,"\int \frac{\text{erfc}(b x)^2}{x^7} \, dx","Integrate[Erfc[b*x]^2/x^7,x]","\frac{e^{-2 b^2 x^2} \left(20 b^4 x^4-6 b^2 x^2-\pi  e^{2 b^2 x^2} \left(8 b^6 x^6+15\right) \text{erfc}(b x)^2+56 b^6 x^6 e^{2 b^2 x^2} \text{Ei}\left(-2 b^2 x^2\right)+4 \sqrt{\pi } b x e^{b^2 x^2} \left(4 b^4 x^4-2 b^2 x^2+3\right) \text{erfc}(b x)\right)}{90 \pi  x^6}","-\frac{4}{45} b^6 \text{erfc}(b x)^2+\frac{2 b e^{-b^2 x^2} \text{erfc}(b x)}{15 \sqrt{\pi } x^5}-\frac{b^2 e^{-2 b^2 x^2}}{15 \pi  x^4}+\frac{28 b^6 \text{Ei}\left(-2 b^2 x^2\right)}{45 \pi }+\frac{8 b^5 e^{-b^2 x^2} \text{erfc}(b x)}{45 \sqrt{\pi } x}+\frac{2 b^4 e^{-2 b^2 x^2}}{9 \pi  x^2}-\frac{4 b^3 e^{-b^2 x^2} \text{erfc}(b x)}{45 \sqrt{\pi } x^3}-\frac{\text{erfc}(b x)^2}{6 x^6}",1,"(-6*b^2*x^2 + 20*b^4*x^4 + 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(3 - 2*b^2*x^2 + 4*b^4*x^4)*Erfc[b*x] - E^(2*b^2*x^2)*Pi*(15 + 8*b^6*x^6)*Erfc[b*x]^2 + 56*b^6*E^(2*b^2*x^2)*x^6*ExpIntegralEi[-2*b^2*x^2])/(90*E^(2*b^2*x^2)*Pi*x^6)","A",1
132,1,108,165,0.1587921,"\int x^4 \text{erfc}(b x)^2 \, dx","Integrate[x^4*Erfc[b*x]^2,x]","\frac{4 \left(4 \pi  b^5 x^5 \text{erfc}(b x)^2+b x e^{-2 b^2 x^2} \left(4 b^2 x^2+11\right)-8 \sqrt{\pi } e^{-b^2 x^2} \left(b^4 x^4+2 b^2 x^2+2\right) \text{erfc}(b x)\right)-43 \sqrt{2 \pi } \text{erf}\left(\sqrt{2} b x\right)}{80 \pi  b^5}","-\frac{43 \text{erf}\left(\sqrt{2} b x\right)}{40 \sqrt{2 \pi } b^5}-\frac{2 x^4 e^{-b^2 x^2} \text{erfc}(b x)}{5 \sqrt{\pi } b}+\frac{x^3 e^{-2 b^2 x^2}}{5 \pi  b^2}-\frac{4 e^{-b^2 x^2} \text{erfc}(b x)}{5 \sqrt{\pi } b^5}+\frac{11 x e^{-2 b^2 x^2}}{20 \pi  b^4}-\frac{4 x^2 e^{-b^2 x^2} \text{erfc}(b x)}{5 \sqrt{\pi } b^3}+\frac{1}{5} x^5 \text{erfc}(b x)^2",1,"(-43*Sqrt[2*Pi]*Erf[Sqrt[2]*b*x] + 4*((b*x*(11 + 4*b^2*x^2))/E^(2*b^2*x^2) - (8*Sqrt[Pi]*(2 + 2*b^2*x^2 + b^4*x^4)*Erfc[b*x])/E^(b^2*x^2) + 4*b^5*Pi*x^5*Erfc[b*x]^2))/(80*b^5*Pi)","A",1
133,1,88,113,0.1043802,"\int x^2 \text{erfc}(b x)^2 \, dx","Integrate[x^2*Erfc[b*x]^2,x]","\frac{4 \pi  b^3 x^3 \text{erfc}(b x)^2-8 \sqrt{\pi } e^{-b^2 x^2} \left(b^2 x^2+1\right) \text{erfc}(b x)+4 b x e^{-2 b^2 x^2}-5 \sqrt{2 \pi } \text{erf}\left(\sqrt{2} b x\right)}{12 \pi  b^3}","-\frac{5 \text{erf}\left(\sqrt{2} b x\right)}{6 \sqrt{2 \pi } b^3}-\frac{2 x^2 e^{-b^2 x^2} \text{erfc}(b x)}{3 \sqrt{\pi } b}+\frac{x e^{-2 b^2 x^2}}{3 \pi  b^2}-\frac{2 e^{-b^2 x^2} \text{erfc}(b x)}{3 \sqrt{\pi } b^3}+\frac{1}{3} x^3 \text{erfc}(b x)^2",1,"((4*b*x)/E^(2*b^2*x^2) - 5*Sqrt[2*Pi]*Erf[Sqrt[2]*b*x] - (8*Sqrt[Pi]*(1 + b^2*x^2)*Erfc[b*x])/E^(b^2*x^2) + 4*b^3*Pi*x^3*Erfc[b*x]^2)/(12*b^3*Pi)","A",1
134,1,56,56,0.053805,"\int \text{erfc}(b x)^2 \, dx","Integrate[Erfc[b*x]^2,x]","-\frac{2 e^{-b^2 x^2} \text{erfc}(b x)}{\sqrt{\pi } b}-\frac{\sqrt{\frac{2}{\pi }} \text{erf}\left(\sqrt{2} b x\right)}{b}+x \text{erfc}(b x)^2","-\frac{2 e^{-b^2 x^2} \text{erfc}(b x)}{\sqrt{\pi } b}-\frac{\sqrt{\frac{2}{\pi }} \text{erf}\left(\sqrt{2} b x\right)}{b}+x \text{erfc}(b x)^2",1,"-((Sqrt[2/Pi]*Erf[Sqrt[2]*b*x])/b) - (2*Erfc[b*x])/(b*E^(b^2*x^2)*Sqrt[Pi]) + x*Erfc[b*x]^2","A",1
135,0,0,13,0.1765117,"\int \frac{\text{erfc}(b x)^2}{x^2} \, dx","Integrate[Erfc[b*x]^2/x^2,x]","\int \frac{\text{erfc}(b x)^2}{x^2} \, dx","\text{Int}\left(\frac{\text{erfc}(b x)^2}{x^2},x\right)",0,"Integrate[Erfc[b*x]^2/x^2, x]","A",-1
136,0,0,13,0.1290387,"\int \frac{\text{erfc}(b x)^2}{x^4} \, dx","Integrate[Erfc[b*x]^2/x^4,x]","\int \frac{\text{erfc}(b x)^2}{x^4} \, dx","\text{Int}\left(\frac{\text{erfc}(b x)^2}{x^4},x\right)",0,"Integrate[Erfc[b*x]^2/x^4, x]","A",-1
137,0,0,13,0.1824559,"\int \frac{\text{erfc}(b x)^2}{x^6} \, dx","Integrate[Erfc[b*x]^2/x^6,x]","\int \frac{\text{erfc}(b x)^2}{x^6} \, dx","\text{Int}\left(\frac{\text{erfc}(b x)^2}{x^6},x\right)",0,"Integrate[Erfc[b*x]^2/x^6, x]","A",-1
138,1,610,375,4.4756163,"\int (c+d x)^2 \text{erfc}(a+b x)^2 \, dx","Integrate[(c + d*x)^2*Erfc[a + b*x]^2,x]","\frac{d^2 \left(-12 \sqrt{2 \pi } a^2 \text{erf}\left(\sqrt{2} (a+b x)\right)+12 \pi  a^2 b x+12 \pi  a b^2 x^2+12 \pi  b x \text{erf}(a+b x)-12 \sqrt{2 \pi } b x (2 a+b x) \text{erf}\left(\sqrt{2} (a+b x)\right)+4 \pi  (a+b x)^3 \text{erf}(a+b x)^2+6 \pi  (a+b x) \text{erf}(a+b x)^2-8 \pi  (a+b x)^3 \text{erf}(a+b x)+8 \sqrt{\pi } e^{-(a+b x)^2} \left((a+b x)^2+1\right) \text{erf}(a+b x)+12 \pi  a \text{erf}(a+b x)-5 \sqrt{2 \pi } \text{erf}\left(\sqrt{2} (a+b x)\right)-12 \sqrt{\pi } E_{\frac{3}{2}}\left((a+b x)^2\right)-8 e^{-2 (a+b x)^2} (a+b x)-8 \sqrt{\pi } e^{-(a+b x)^2} \left((a+b x)^2+1\right)+24 \sqrt{\pi } e^{-(a+b x)^2}+4 \pi  b^3 x^3-36 \pi  b x\right)-12 \sqrt{\pi } b^2 (c+d x)^2 \left(\sqrt{2} \text{erf}\left(\sqrt{2} (a+b x)\right)+\text{erfc}(a+b x) \left(2 e^{-(a+b x)^2}-\sqrt{\pi } (a+b x) \text{erfc}(a+b x)\right)\right)+6 b d (c+d x) \left(-2 \pi  (a+b x)^2 \text{erf}(a+b x)^2+4 \pi  (a+b x)^2 \text{erf}(a+b x)-4 \sqrt{\pi } e^{-(a+b x)^2} (a+b x) \text{erf}(a+b x)+\pi  \text{erf}(a+b x)^2-2 \pi  \text{erf}(a+b x)+4 \sqrt{2 \pi } b x \text{erf}\left(\sqrt{2} (a+b x)\right)+4 \sqrt{2 \pi } a \text{erf}\left(\sqrt{2} (a+b x)\right)+2 \pi  (\text{erfc}(-a-b x) \text{erfc}(a+b x)+2)-4 \sqrt{\pi } (a+b x) E_{\frac{1}{2}}\left((a+b x)^2\right)-2 \pi  (a+b x)^2+4 \sqrt{\pi } e^{-(a+b x)^2} (a+b x)+2 e^{-2 (a+b x)^2}\right)}{12 \pi  b^3}","-\frac{\sqrt{\frac{2}{\pi }} (b c-a d)^2 \text{erf}\left(\sqrt{2} (a+b x)\right)}{b^3}+\frac{d (a+b x)^2 (b c-a d) \text{erfc}(a+b x)^2}{b^3}+\frac{(a+b x) (b c-a d)^2 \text{erfc}(a+b x)^2}{b^3}-\frac{2 d e^{-(a+b x)^2} (a+b x) (b c-a d) \text{erfc}(a+b x)}{\sqrt{\pi } b^3}-\frac{d (b c-a d) \text{erfc}(a+b x)^2}{2 b^3}-\frac{2 e^{-(a+b x)^2} (b c-a d)^2 \text{erfc}(a+b x)}{\sqrt{\pi } b^3}+\frac{d e^{-2 (a+b x)^2} (b c-a d)}{\pi  b^3}-\frac{5 d^2 \text{erf}\left(\sqrt{2} (a+b x)\right)}{6 \sqrt{2 \pi } b^3}+\frac{d^2 (a+b x)^3 \text{erfc}(a+b x)^2}{3 b^3}-\frac{2 d^2 e^{-(a+b x)^2} (a+b x)^2 \text{erfc}(a+b x)}{3 \sqrt{\pi } b^3}-\frac{2 d^2 e^{-(a+b x)^2} \text{erfc}(a+b x)}{3 \sqrt{\pi } b^3}+\frac{d^2 e^{-2 (a+b x)^2} (a+b x)}{3 \pi  b^3}",1,"(-12*b^2*Sqrt[Pi]*(c + d*x)^2*(Sqrt[2]*Erf[Sqrt[2]*(a + b*x)] + Erfc[a + b*x]*(2/E^(a + b*x)^2 - Sqrt[Pi]*(a + b*x)*Erfc[a + b*x])) + 6*b*d*(c + d*x)*(2/E^(2*(a + b*x)^2) + (4*Sqrt[Pi]*(a + b*x))/E^(a + b*x)^2 - 2*Pi*(a + b*x)^2 - 2*Pi*Erf[a + b*x] - (4*Sqrt[Pi]*(a + b*x)*Erf[a + b*x])/E^(a + b*x)^2 + 4*Pi*(a + b*x)^2*Erf[a + b*x] + Pi*Erf[a + b*x]^2 - 2*Pi*(a + b*x)^2*Erf[a + b*x]^2 + 4*a*Sqrt[2*Pi]*Erf[Sqrt[2]*(a + b*x)] + 4*b*Sqrt[2*Pi]*x*Erf[Sqrt[2]*(a + b*x)] + 2*Pi*(2 + Erfc[-a - b*x]*Erfc[a + b*x]) - 4*Sqrt[Pi]*(a + b*x)*ExpIntegralE[1/2, (a + b*x)^2]) + d^2*((24*Sqrt[Pi])/E^(a + b*x)^2 - 36*b*Pi*x + 12*a^2*b*Pi*x + 12*a*b^2*Pi*x^2 + 4*b^3*Pi*x^3 - (8*(a + b*x))/E^(2*(a + b*x)^2) - (8*Sqrt[Pi]*(1 + (a + b*x)^2))/E^(a + b*x)^2 + 12*a*Pi*Erf[a + b*x] + 12*b*Pi*x*Erf[a + b*x] - 8*Pi*(a + b*x)^3*Erf[a + b*x] + (8*Sqrt[Pi]*(1 + (a + b*x)^2)*Erf[a + b*x])/E^(a + b*x)^2 + 6*Pi*(a + b*x)*Erf[a + b*x]^2 + 4*Pi*(a + b*x)^3*Erf[a + b*x]^2 - 5*Sqrt[2*Pi]*Erf[Sqrt[2]*(a + b*x)] - 12*a^2*Sqrt[2*Pi]*Erf[Sqrt[2]*(a + b*x)] - 12*b*Sqrt[2*Pi]*x*(2*a + b*x)*Erf[Sqrt[2]*(a + b*x)] - 12*Sqrt[Pi]*ExpIntegralE[3/2, (a + b*x)^2]))/(12*b^3*Pi)","A",0
139,1,301,189,1.3588845,"\int (c+d x) \text{erfc}(a+b x)^2 \, dx","Integrate[(c + d*x)*Erfc[a + b*x]^2,x]","\frac{4 b (c+d x) \left(\text{erfc}(a+b x) \left((a+b x) \text{erfc}(a+b x)-\frac{2 e^{-(a+b x)^2}}{\sqrt{\pi }}\right)-\sqrt{\frac{2}{\pi }} \text{erf}\left(\sqrt{2} (a+b x)\right)\right)+\frac{d \left(-2 \pi  (a+b x)^2 \text{erf}(a+b x)^2+4 \pi  (a+b x)^2 \text{erf}(a+b x)-4 \sqrt{\pi } e^{-(a+b x)^2} (a+b x) \text{erf}(a+b x)+\pi  \text{erf}(a+b x)^2-2 \pi  \text{erf}(a+b x)+4 \sqrt{2 \pi } b x \text{erf}\left(\sqrt{2} (a+b x)\right)+4 \sqrt{2 \pi } a \text{erf}\left(\sqrt{2} (a+b x)\right)+2 \pi  (\text{erfc}(-a-b x) \text{erfc}(a+b x)+2)-4 \sqrt{\pi } (a+b x) E_{\frac{1}{2}}\left((a+b x)^2\right)-2 \pi  (a+b x)^2+4 \sqrt{\pi } e^{-(a+b x)^2} (a+b x)+2 e^{-2 (a+b x)^2}\right)}{\pi }}{4 b^2}","-\frac{\sqrt{\frac{2}{\pi }} (b c-a d) \text{erf}\left(\sqrt{2} (a+b x)\right)}{b^2}+\frac{(a+b x) (b c-a d) \text{erfc}(a+b x)^2}{b^2}-\frac{2 e^{-(a+b x)^2} (b c-a d) \text{erfc}(a+b x)}{\sqrt{\pi } b^2}+\frac{d (a+b x)^2 \text{erfc}(a+b x)^2}{2 b^2}-\frac{d \text{erfc}(a+b x)^2}{4 b^2}-\frac{d e^{-(a+b x)^2} (a+b x) \text{erfc}(a+b x)}{\sqrt{\pi } b^2}+\frac{d e^{-2 (a+b x)^2}}{2 \pi  b^2}",1,"(4*b*(c + d*x)*(-(Sqrt[2/Pi]*Erf[Sqrt[2]*(a + b*x)]) + Erfc[a + b*x]*(-2/(E^(a + b*x)^2*Sqrt[Pi]) + (a + b*x)*Erfc[a + b*x])) + (d*(2/E^(2*(a + b*x)^2) + (4*Sqrt[Pi]*(a + b*x))/E^(a + b*x)^2 - 2*Pi*(a + b*x)^2 - 2*Pi*Erf[a + b*x] - (4*Sqrt[Pi]*(a + b*x)*Erf[a + b*x])/E^(a + b*x)^2 + 4*Pi*(a + b*x)^2*Erf[a + b*x] + Pi*Erf[a + b*x]^2 - 2*Pi*(a + b*x)^2*Erf[a + b*x]^2 + 4*a*Sqrt[2*Pi]*Erf[Sqrt[2]*(a + b*x)] + 4*b*Sqrt[2*Pi]*x*Erf[Sqrt[2]*(a + b*x)] + 2*Pi*(2 + Erfc[-a - b*x]*Erfc[a + b*x]) - 4*Sqrt[Pi]*(a + b*x)*ExpIntegralE[1/2, (a + b*x)^2]))/Pi)/(4*b^2)","A",0
140,1,66,71,0.0142795,"\int \text{erfc}(a+b x)^2 \, dx","Integrate[Erfc[a + b*x]^2,x]","\frac{\text{erfc}(a+b x) \left((a+b x) \text{erfc}(a+b x)-\frac{2 e^{-(a+b x)^2}}{\sqrt{\pi }}\right)-\sqrt{\frac{2}{\pi }} \text{erf}\left(\sqrt{2} (a+b x)\right)}{b}","-\frac{\sqrt{\frac{2}{\pi }} \text{erf}\left(\sqrt{2} (a+b x)\right)}{b}+\frac{(a+b x) \text{erfc}(a+b x)^2}{b}-\frac{2 e^{-(a+b x)^2} \text{erfc}(a+b x)}{\sqrt{\pi } b}",1,"(-(Sqrt[2/Pi]*Erf[Sqrt[2]*(a + b*x)]) + Erfc[a + b*x]*(-2/(E^(a + b*x)^2*Sqrt[Pi]) + (a + b*x)*Erfc[a + b*x]))/b","A",1
141,0,0,19,0.5065705,"\int \frac{\text{erfc}(a+b x)^2}{c+d x} \, dx","Integrate[Erfc[a + b*x]^2/(c + d*x),x]","\int \frac{\text{erfc}(a+b x)^2}{c+d x} \, dx","\text{Int}\left(\frac{\text{erfc}(a+b x)^2}{c+d x},x\right)",0,"Integrate[Erfc[a + b*x]^2/(c + d*x), x]","A",-1
142,0,0,19,0.5001487,"\int \frac{\text{erfc}(a+b x)^2}{(c+d x)^2} \, dx","Integrate[Erfc[a + b*x]^2/(c + d*x)^2,x]","\int \frac{\text{erfc}(a+b x)^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{erfc}(a+b x)^2}{(c+d x)^2},x\right)",0,"Integrate[Erfc[a + b*x]^2/(c + d*x)^2, x]","A",-1
143,1,87,102,0.3371716,"\int x^2 \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^2*Erfc[d*(a + b*Log[c*x^n])],x]","\frac{1}{3} \left(x^3 \text{erf}\left(a d+b d \log \left(c x^n\right)-\frac{3}{2 b d n}\right) \exp \left(\frac{3 \left(\frac{\frac{3}{d^2}-4 a b n}{b^2}-4 n \log \left(c x^n\right)\right)}{4 n^2}\right)+x^3 \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)\right)","\frac{1}{3} x^3 \left(c x^n\right)^{-3/n} e^{\frac{9-12 a b d^2 n}{4 b^2 d^2 n^2}} \text{erf}\left(\frac{2 a b d^2+2 b^2 d^2 \log \left(c x^n\right)-\frac{3}{n}}{2 b d}\right)+\frac{1}{3} x^3 \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"(E^((3*((3/d^2 - 4*a*b*n)/b^2 - 4*n*Log[c*x^n]))/(4*n^2))*x^3*Erf[a*d - 3/(2*b*d*n) + b*d*Log[c*x^n]] + x^3*Erfc[d*(a + b*Log[c*x^n])])/3","A",1
144,1,80,94,0.2960484,"\int x \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x*Erfc[d*(a + b*Log[c*x^n])],x]","\frac{1}{2} \left(x^2 e^{\frac{\frac{\frac{1}{d^2}-2 a b n}{b^2}-2 n \log \left(c x^n\right)}{n^2}} \text{erf}\left(a d+b d \log \left(c x^n\right)-\frac{1}{b d n}\right)+x^2 \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)\right)","\frac{1}{2} x^2 \left(c x^n\right)^{-2/n} e^{\frac{1-2 a b d^2 n}{b^2 d^2 n^2}} \text{erf}\left(\frac{a b d^2+b^2 d^2 \log \left(c x^n\right)-\frac{1}{n}}{b d}\right)+\frac{1}{2} x^2 \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"(E^(((d^(-2) - 2*a*b*n)/b^2 - 2*n*Log[c*x^n])/n^2)*x^2*Erf[a*d - 1/(b*d*n) + b*d*Log[c*x^n]] + x^2*Erfc[d*(a + b*Log[c*x^n])])/2","A",1
145,1,77,92,0.2836942,"\int \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[Erfc[d*(a + b*Log[c*x^n])],x]","x e^{\frac{\frac{\frac{1}{d^2}-4 a b n}{b^2}-4 n \log \left(c x^n\right)}{4 n^2}} \text{erf}\left(a d+b d \log \left(c x^n\right)-\frac{1}{2 b d n}\right)+x \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)","x \left(c x^n\right)^{-1/n} e^{\frac{1-4 a b d^2 n}{4 b^2 d^2 n^2}} \text{erf}\left(\frac{2 a b d^2+2 b^2 d^2 \log \left(c x^n\right)-\frac{1}{n}}{2 b d}\right)+x \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"E^(((d^(-2) - 4*a*b*n)/b^2 - 4*n*Log[c*x^n])/(4*n^2))*x*Erf[a*d - 1/(2*b*d*n) + b*d*Log[c*x^n]] + x*Erfc[d*(a + b*Log[c*x^n])]","A",1
146,1,93,66,0.1341641,"\int \frac{\text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Integrate[Erfc[d*(a + b*Log[c*x^n])]/x,x]","\frac{-\frac{\left(c x^n\right)^{-2 a b d^2} e^{-d^2 \left(a^2+b^2 \log ^2\left(c x^n\right)\right)}}{\sqrt{\pi } b d}-\frac{a \text{erf}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{b}+\log \left(c x^n\right) \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{n}","\frac{\left(a+b \log \left(c x^n\right)\right) \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{e^{-d^2 \left(a+b \log \left(c x^n\right)\right)^2}}{\sqrt{\pi } b d n}",1,"(-(1/(b*d*E^(d^2*(a^2 + b^2*Log[c*x^n]^2))*Sqrt[Pi]*(c*x^n)^(2*a*b*d^2))) - (a*Erf[d*(a + b*Log[c*x^n])])/b + Erfc[d*(a + b*Log[c*x^n])]*Log[c*x^n])/n","A",1
147,1,81,93,0.2730422,"\int \frac{\text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Integrate[Erfc[d*(a + b*Log[c*x^n])]/x^2,x]","-\frac{\left(c x^n\right)^{\frac{1}{n}} e^{\frac{4 a b d^2 n+1}{4 b^2 d^2 n^2}} \text{erf}\left(a d+b d \log \left(c x^n\right)+\frac{1}{2 b d n}\right)+\text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x}","-\frac{\left(c x^n\right)^{\frac{1}{n}} e^{\frac{a}{b n}+\frac{1}{4 b^2 d^2 n^2}} \text{erf}\left(\frac{2 a b d^2+2 b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}}{2 b d}\right)}{x}-\frac{\text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x}",1,"-((E^((1 + 4*a*b*d^2*n)/(4*b^2*d^2*n^2))*(c*x^n)^n^(-1)*Erf[a*d + 1/(2*b*d*n) + b*d*Log[c*x^n]] + Erfc[d*(a + b*Log[c*x^n])])/x)","A",1
148,1,79,95,0.2631752,"\int \frac{\text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Integrate[Erfc[d*(a + b*Log[c*x^n])]/x^3,x]","-\frac{\left(c x^n\right)^{2/n} e^{\frac{2 a b d^2 n+1}{b^2 d^2 n^2}} \text{erf}\left(a d+b d \log \left(c x^n\right)+\frac{1}{b d n}\right)+\text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}","-\frac{\left(c x^n\right)^{2/n} e^{\frac{2 a b d^2 n+1}{b^2 d^2 n^2}} \text{erf}\left(\frac{a b d^2 n+b^2 d^2 n \log \left(c x^n\right)+1}{b d n}\right)}{2 x^2}-\frac{\text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}",1,"-1/2*(E^((1 + 2*a*b*d^2*n)/(b^2*d^2*n^2))*(c*x^n)^(2/n)*Erf[a*d + 1/(b*d*n) + b*d*Log[c*x^n]] + Erfc[d*(a + b*Log[c*x^n])])/x^2","A",1
149,1,126,126,0.5257881,"\int (e x)^m \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Erfc[d*(a + b*Log[c*x^n])],x]","\frac{(e x)^m \left(x^{-m} \text{erf}\left(a d-\frac{-2 b^2 d^2 n \log \left(c x^n\right)+m+1}{2 b d n}\right) \exp \left(\frac{(m+1) \left(-4 a b d^2 n-4 b^2 d^2 n \log \left(c x^n\right)+4 b^2 d^2 n^2 \log (x)+m+1\right)}{4 b^2 d^2 n^2}\right)+x \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)\right)}{m+1}","\frac{(e x)^{m+1} \text{erfc}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (m+1)}-\frac{x (e x)^m \left(c x^n\right)^{-\frac{m+1}{n}} \exp \left(\frac{(m+1) \left(-4 a b d^2 n+m+1\right)}{4 b^2 d^2 n^2}\right) \text{erf}\left(\frac{-2 a b d^2 n-2 b^2 d^2 n \log \left(c x^n\right)+m+1}{2 b d n}\right)}{m+1}",1,"((e*x)^m*((E^(((1 + m)*(1 + m - 4*a*b*d^2*n + 4*b^2*d^2*n^2*Log[x] - 4*b^2*d^2*n*Log[c*x^n]))/(4*b^2*d^2*n^2))*Erf[a*d - (1 + m - 2*b^2*d^2*n*Log[c*x^n])/(2*b*d*n)])/x^m + x*Erfc[d*(a + b*Log[c*x^n])]))/(1 + m)","A",1
150,1,21,21,0.0119,"\int e^{c-b^2 x^2} \text{erfc}(b x)^2 \, dx","Integrate[E^(c - b^2*x^2)*Erfc[b*x]^2,x]","-\frac{\sqrt{\pi } e^c \text{erfc}(b x)^3}{6 b}","-\frac{\sqrt{\pi } e^c \text{erfc}(b x)^3}{6 b}",1,"-1/6*(E^c*Sqrt[Pi]*Erfc[b*x]^3)/b","A",1
151,1,21,21,0.0057178,"\int e^{c-b^2 x^2} \text{erfc}(b x) \, dx","Integrate[E^(c - b^2*x^2)*Erfc[b*x],x]","-\frac{\sqrt{\pi } e^c \text{erfc}(b x)^2}{4 b}","-\frac{\sqrt{\pi } e^c \text{erfc}(b x)^2}{4 b}",1,"-1/4*(E^c*Sqrt[Pi]*Erfc[b*x]^2)/b","A",1
152,1,20,20,0.0165866,"\int \frac{e^{c-b^2 x^2}}{\text{erfc}(b x)} \, dx","Integrate[E^(c - b^2*x^2)/Erfc[b*x],x]","-\frac{\sqrt{\pi } e^c \log (\text{erfc}(b x))}{2 b}","-\frac{\sqrt{\pi } e^c \log (\text{erfc}(b x))}{2 b}",1,"-1/2*(E^c*Sqrt[Pi]*Log[Erfc[b*x]])/b","A",1
153,1,21,21,0.0099373,"\int \frac{e^{c-b^2 x^2}}{\text{erfc}(b x)^2} \, dx","Integrate[E^(c - b^2*x^2)/Erfc[b*x]^2,x]","\frac{\sqrt{\pi } e^c}{2 b \text{erfc}(b x)}","\frac{\sqrt{\pi } e^c}{2 b \text{erfc}(b x)}",1,"(E^c*Sqrt[Pi])/(2*b*Erfc[b*x])","A",1
154,1,21,21,0.0092416,"\int \frac{e^{c-b^2 x^2}}{\text{erfc}(b x)^3} \, dx","Integrate[E^(c - b^2*x^2)/Erfc[b*x]^3,x]","\frac{\sqrt{\pi } e^c}{4 b \text{erfc}(b x)^2}","\frac{\sqrt{\pi } e^c}{4 b \text{erfc}(b x)^2}",1,"(E^c*Sqrt[Pi])/(4*b*Erfc[b*x]^2)","A",1
155,1,28,28,0.0116992,"\int e^{c-b^2 x^2} \text{erfc}(b x)^n \, dx","Integrate[E^(c - b^2*x^2)*Erfc[b*x]^n,x]","-\frac{\sqrt{\pi } e^c \text{erfc}(b x)^{n+1}}{2 b (n+1)}","-\frac{\sqrt{\pi } e^c \text{erfc}(b x)^{n+1}}{2 b (n+1)}",1,"-1/2*(E^c*Sqrt[Pi]*Erfc[b*x]^(1 + n))/(b*(1 + n))","A",1
156,1,138,283,0.4482552,"\int e^{c+d x^2} x^5 \text{erfc}(b x) \, dx","Integrate[E^(c + d*x^2)*x^5*Erfc[b*x],x]","\frac{e^c \left(\frac{2 b d x e^{x^2 \left(d-b^2\right)} \left(b^2 \left(4-2 d x^2\right)+d \left(2 d x^2-7\right)\right)}{\sqrt{\pi } \left(b^2-d\right)^2}+\frac{b \left(8 b^4-20 b^2 d+15 d^2\right) \text{erfi}\left(x \sqrt{d-b^2}\right)}{\left(d-b^2\right)^{5/2}}+4 e^{d x^2} \left(d^2 x^4-2 d x^2+2\right) \text{erfc}(b x)\right)}{8 d^3}","\frac{b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{d^3 \sqrt{b^2-d}}-\frac{b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{2 d^2 \left(b^2-d\right)^{3/2}}+\frac{b x e^{c-x^2 \left(b^2-d\right)}}{\sqrt{\pi } d^2 \left(b^2-d\right)}+\frac{3 b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{8 d \left(b^2-d\right)^{5/2}}-\frac{3 b x e^{c-x^2 \left(b^2-d\right)}}{4 \sqrt{\pi } d \left(b^2-d\right)^2}-\frac{b x^3 e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } d \left(b^2-d\right)}+\frac{\text{erfc}(b x) e^{c+d x^2}}{d^3}-\frac{x^2 \text{erfc}(b x) e^{c+d x^2}}{d^2}+\frac{x^4 \text{erfc}(b x) e^{c+d x^2}}{2 d}",1,"(E^c*((2*b*d*E^((-b^2 + d)*x^2)*x*(b^2*(4 - 2*d*x^2) + d*(-7 + 2*d*x^2)))/((b^2 - d)^2*Sqrt[Pi]) + 4*E^(d*x^2)*(2 - 2*d*x^2 + d^2*x^4)*Erfc[b*x] + (b*(8*b^4 - 20*b^2*d + 15*d^2)*Erfi[Sqrt[-b^2 + d]*x])/(-b^2 + d)^(5/2)))/(8*d^3)","A",1
157,1,99,155,0.3429096,"\int e^{c+d x^2} x^3 \text{erfc}(b x) \, dx","Integrate[E^(c + d*x^2)*x^3*Erfc[b*x],x]","\frac{e^c \left(\frac{2 b d x e^{x^2 \left(d-b^2\right)}}{\sqrt{\pi } \left(d-b^2\right)}+\frac{\left(2 b^3-3 b d\right) \text{erfi}\left(x \sqrt{d-b^2}\right)}{\left(d-b^2\right)^{3/2}}+2 e^{d x^2} \left(d x^2-1\right) \text{erfc}(b x)\right)}{4 d^2}","-\frac{b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{2 d^2 \sqrt{b^2-d}}+\frac{b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{4 d \left(b^2-d\right)^{3/2}}-\frac{b x e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } d \left(b^2-d\right)}-\frac{\text{erfc}(b x) e^{c+d x^2}}{2 d^2}+\frac{x^2 \text{erfc}(b x) e^{c+d x^2}}{2 d}",1,"(E^c*((2*b*d*E^((-b^2 + d)*x^2)*x)/((-b^2 + d)*Sqrt[Pi]) + 2*E^(d*x^2)*(-1 + d*x^2)*Erfc[b*x] + ((2*b^3 - 3*b*d)*Erfi[Sqrt[-b^2 + d]*x])/(-b^2 + d)^(3/2)))/(4*d^2)","A",1
158,1,50,57,0.0579085,"\int e^{c+d x^2} x \text{erfc}(b x) \, dx","Integrate[E^(c + d*x^2)*x*Erfc[b*x],x]","\frac{e^c \left(\frac{b \text{erfi}\left(x \sqrt{d-b^2}\right)}{\sqrt{d-b^2}}+e^{d x^2} \text{erfc}(b x)\right)}{2 d}","\frac{b e^c \text{erf}\left(x \sqrt{b^2-d}\right)}{2 d \sqrt{b^2-d}}+\frac{\text{erfc}(b x) e^{c+d x^2}}{2 d}",1,"(E^c*(E^(d*x^2)*Erfc[b*x] + (b*Erfi[Sqrt[-b^2 + d]*x])/Sqrt[-b^2 + d]))/(2*d)","A",1
159,0,0,20,0.6230366,"\int \frac{e^{c+d x^2} \text{erfc}(b x)}{x} \, dx","Integrate[(E^(c + d*x^2)*Erfc[b*x])/x,x]","\int \frac{e^{c+d x^2} \text{erfc}(b x)}{x} \, dx","\text{Int}\left(\frac{\text{erfc}(b x) e^{c+d x^2}}{x},x\right)",0,"Integrate[(E^(c + d*x^2)*Erfc[b*x])/x, x]","A",-1
160,0,0,99,0.7836804,"\int \frac{e^{c+d x^2} \text{erfc}(b x)}{x^3} \, dx","Integrate[(E^(c + d*x^2)*Erfc[b*x])/x^3,x]","\int \frac{e^{c+d x^2} \text{erfc}(b x)}{x^3} \, dx","d \text{Int}\left(\frac{\text{erfc}(b x) e^{c+d x^2}}{x},x\right)+b e^c \sqrt{b^2-d} \text{erf}\left(x \sqrt{b^2-d}\right)+\frac{b e^{c-x^2 \left(b^2-d\right)}}{\sqrt{\pi } x}-\frac{\text{erfc}(b x) e^{c+d x^2}}{2 x^2}",0,"Integrate[(E^(c + d*x^2)*Erfc[b*x])/x^3, x]","A",-1
161,0,0,231,0.8137415,"\int \frac{e^{c+d x^2} \text{erfc}(b x)}{x^5} \, dx","Integrate[(E^(c + d*x^2)*Erfc[b*x])/x^5,x]","\int \frac{e^{c+d x^2} \text{erfc}(b x)}{x^5} \, dx","\frac{1}{2} d^2 \text{Int}\left(\frac{\text{erfc}(b x) e^{c+d x^2}}{x},x\right)+\frac{1}{2} b e^c d \sqrt{b^2-d} \text{erf}\left(x \sqrt{b^2-d}\right)-\frac{1}{3} b e^c \left(b^2-d\right)^{3/2} \text{erf}\left(x \sqrt{b^2-d}\right)+\frac{b d e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } x}-\frac{b \left(b^2-d\right) e^{c-x^2 \left(b^2-d\right)}}{3 \sqrt{\pi } x}+\frac{b e^{c-x^2 \left(b^2-d\right)}}{6 \sqrt{\pi } x^3}-\frac{d \text{erfc}(b x) e^{c+d x^2}}{4 x^2}-\frac{\text{erfc}(b x) e^{c+d x^2}}{4 x^4}",0,"Integrate[(E^(c + d*x^2)*Erfc[b*x])/x^5, x]","A",-1
162,0,0,186,0.9529122,"\int e^{c+d x^2} x^4 \text{erfc}(b x) \, dx","Integrate[E^(c + d*x^2)*x^4*Erfc[b*x],x]","\int e^{c+d x^2} x^4 \text{erfc}(b x) \, dx","\frac{3 \text{Int}\left(\text{erfc}(b x) e^{c+d x^2},x\right)}{4 d^2}+\frac{3 b e^{c-x^2 \left(b^2-d\right)}}{4 \sqrt{\pi } d^2 \left(b^2-d\right)}-\frac{b x^2 e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } d \left(b^2-d\right)}-\frac{b e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } d \left(b^2-d\right)^2}-\frac{3 x \text{erfc}(b x) e^{c+d x^2}}{4 d^2}+\frac{x^3 \text{erfc}(b x) e^{c+d x^2}}{2 d}",0,"Integrate[E^(c + d*x^2)*x^4*Erfc[b*x], x]","A",-1
163,0,0,84,0.8336906,"\int e^{c+d x^2} x^2 \text{erfc}(b x) \, dx","Integrate[E^(c + d*x^2)*x^2*Erfc[b*x],x]","\int e^{c+d x^2} x^2 \text{erfc}(b x) \, dx","-\frac{\text{Int}\left(\text{erfc}(b x) e^{c+d x^2},x\right)}{2 d}-\frac{b e^{c-x^2 \left(b^2-d\right)}}{2 \sqrt{\pi } d \left(b^2-d\right)}+\frac{x \text{erfc}(b x) e^{c+d x^2}}{2 d}",0,"Integrate[E^(c + d*x^2)*x^2*Erfc[b*x], x]","A",-1
164,0,0,17,0.0349133,"\int e^{c+d x^2} \text{erfc}(b x) \, dx","Integrate[E^(c + d*x^2)*Erfc[b*x],x]","\int e^{c+d x^2} \text{erfc}(b x) \, dx","\text{Int}\left(\text{erfc}(b x) e^{c+d x^2},x\right)",0,"Integrate[E^(c + d*x^2)*Erfc[b*x], x]","A",-1
165,0,0,63,0.8595543,"\int \frac{e^{c+d x^2} \text{erfc}(b x)}{x^2} \, dx","Integrate[(E^(c + d*x^2)*Erfc[b*x])/x^2,x]","\int \frac{e^{c+d x^2} \text{erfc}(b x)}{x^2} \, dx","2 d \text{Int}\left(\text{erfc}(b x) e^{c+d x^2},x\right)-\frac{b e^c \text{Ei}\left(-\left(\left(b^2-d\right) x^2\right)\right)}{\sqrt{\pi }}-\frac{\text{erfc}(b x) e^{c+d x^2}}{x}",0,"Integrate[(E^(c + d*x^2)*Erfc[b*x])/x^2, x]","A",-1
166,0,0,155,1.015736,"\int \frac{e^{c+d x^2} \text{erfc}(b x)}{x^4} \, dx","Integrate[(E^(c + d*x^2)*Erfc[b*x])/x^4,x]","\int \frac{e^{c+d x^2} \text{erfc}(b x)}{x^4} \, dx","\frac{4}{3} d^2 \text{Int}\left(\text{erfc}(b x) e^{c+d x^2},x\right)-\frac{2 b e^c d \text{Ei}\left(-\left(\left(b^2-d\right) x^2\right)\right)}{3 \sqrt{\pi }}+\frac{b e^c \left(b^2-d\right) \text{Ei}\left(-\left(\left(b^2-d\right) x^2\right)\right)}{3 \sqrt{\pi }}+\frac{b e^{c-x^2 \left(b^2-d\right)}}{3 \sqrt{\pi } x^2}-\frac{2 d \text{erfc}(b x) e^{c+d x^2}}{3 x}-\frac{\text{erfc}(b x) e^{c+d x^2}}{3 x^3}",0,"Integrate[(E^(c + d*x^2)*Erfc[b*x])/x^4, x]","A",-1
167,1,73,118,0.0453428,"\int e^{c+b^2 x^2} x^5 \text{erfc}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^5*Erfc[b*x],x]","\frac{e^c \left(6 b^5 x^5-20 b^3 x^3+15 \sqrt{\pi } e^{b^2 x^2} \left(b^4 x^4-2 b^2 x^2+2\right) \text{erfc}(b x)+60 b x\right)}{30 \sqrt{\pi } b^6}","\frac{2 e^c x}{\sqrt{\pi } b^5}-\frac{2 e^c x^3}{3 \sqrt{\pi } b^3}+\frac{x^4 e^{b^2 x^2+c} \text{erfc}(b x)}{2 b^2}+\frac{e^{b^2 x^2+c} \text{erfc}(b x)}{b^6}-\frac{x^2 e^{b^2 x^2+c} \text{erfc}(b x)}{b^4}+\frac{e^c x^5}{5 \sqrt{\pi } b}",1,"(E^c*(60*b*x - 20*b^3*x^3 + 6*b^5*x^5 + 15*E^(b^2*x^2)*Sqrt[Pi]*(2 - 2*b^2*x^2 + b^4*x^4)*Erfc[b*x]))/(30*b^6*Sqrt[Pi])","A",1
168,1,58,80,0.0343782,"\int e^{c+b^2 x^2} x^3 \text{erfc}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^3*Erfc[b*x],x]","\frac{e^c \left(3 \sqrt{\pi } e^{b^2 x^2} \left(b^2 x^2-1\right) \text{erfc}(b x)+2 b x \left(b^2 x^2-3\right)\right)}{6 \sqrt{\pi } b^4}","-\frac{e^c x}{\sqrt{\pi } b^3}+\frac{x^2 e^{b^2 x^2+c} \text{erfc}(b x)}{2 b^2}-\frac{e^{b^2 x^2+c} \text{erfc}(b x)}{2 b^4}+\frac{e^c x^3}{3 \sqrt{\pi } b}",1,"(E^c*(2*b*x*(-3 + b^2*x^2) + 3*E^(b^2*x^2)*Sqrt[Pi]*(-1 + b^2*x^2)*Erfc[b*x]))/(6*b^4*Sqrt[Pi])","A",1
169,1,36,36,0.0212451,"\int e^{c+b^2 x^2} x \text{erfc}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x*Erfc[b*x],x]","\frac{e^{b^2 x^2+c} \text{erfc}(b x)}{2 b^2}+\frac{e^c x}{\sqrt{\pi } b}","\frac{e^{b^2 x^2+c} \text{erfc}(b x)}{2 b^2}+\frac{e^c x}{\sqrt{\pi } b}",1,"(E^c*x)/(b*Sqrt[Pi]) + (E^(c + b^2*x^2)*Erfc[b*x])/(2*b^2)","A",1
170,1,45,48,0.1881262,"\int \frac{e^{c+b^2 x^2} \text{erfc}(b x)}{x} \, dx","Integrate[(E^(c + b^2*x^2)*Erfc[b*x])/x,x]","\frac{1}{2} e^c \left(\text{Ei}\left(b^2 x^2\right)-\frac{4 b x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}\right)","\frac{1}{2} e^c \text{Ei}\left(b^2 x^2\right)-\frac{2 b e^c x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}",1,"(E^c*(ExpIntegralEi[b^2*x^2] - (4*b*x*HypergeometricPFQ[{1/2, 1}, {3/2, 3/2}, b^2*x^2])/Sqrt[Pi]))/2","A",1
171,1,65,88,0.2243914,"\int \frac{e^{c+b^2 x^2} \text{erfc}(b x)}{x^3} \, dx","Integrate[(E^(c + b^2*x^2)*Erfc[b*x])/x^3,x]","-\frac{e^c \left(-\frac{4 b x \, _2F_2\left(-\frac{1}{2},1;\frac{1}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}-b^2 x^2 \text{Ei}\left(b^2 x^2\right)+e^{b^2 x^2}\right)}{2 x^2}","-\frac{2 b^3 e^c x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}-\frac{e^{b^2 x^2+c} \text{erfc}(b x)}{2 x^2}+\frac{1}{2} b^2 e^c \text{Ei}\left(b^2 x^2\right)+\frac{b e^c}{\sqrt{\pi } x}",1,"-1/2*(E^c*(E^(b^2*x^2) - b^2*x^2*ExpIntegralEi[b^2*x^2] - (4*b*x*HypergeometricPFQ[{-1/2, 1}, {1/2, 3/2}, b^2*x^2])/Sqrt[Pi]))/x^2","A",0
172,1,83,134,0.2579049,"\int \frac{e^{c+b^2 x^2} \text{erfc}(b x)}{x^5} \, dx","Integrate[(E^(c + b^2*x^2)*Erfc[b*x])/x^5,x]","-\frac{e^c \left(3 \sqrt{\pi } \left(e^{b^2 x^2} \left(b^2 x^2+1\right)-b^4 x^4 \text{Ei}\left(b^2 x^2\right)\right)-8 b x \, _2F_2\left(-\frac{3}{2},1;-\frac{1}{2},\frac{3}{2};b^2 x^2\right)\right)}{12 \sqrt{\pi } x^4}","-\frac{b^5 e^c x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}+\frac{b^3 e^c}{2 \sqrt{\pi } x}-\frac{b^2 e^{b^2 x^2+c} \text{erfc}(b x)}{4 x^2}-\frac{e^{b^2 x^2+c} \text{erfc}(b x)}{4 x^4}+\frac{1}{4} b^4 e^c \text{Ei}\left(b^2 x^2\right)+\frac{b e^c}{6 \sqrt{\pi } x^3}",1,"-1/12*(E^c*(3*Sqrt[Pi]*(E^(b^2*x^2)*(1 + b^2*x^2) - b^4*x^4*ExpIntegralEi[b^2*x^2]) - 8*b*x*HypergeometricPFQ[{-3/2, 1}, {-1/2, 3/2}, b^2*x^2]))/(Sqrt[Pi]*x^4)","A",0
173,1,147,138,0.2962429,"\int e^{c+b^2 x^2} x^4 \text{erfc}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^4*Erfc[b*x],x]","-\frac{e^c \left(-6 b^2 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)-2 b^4 x^4+2 \sqrt{\pi } b x e^{b^2 x^2} \left(2 b^2 x^2-3\right) \text{erf}(b x)+6 b^2 x^2+6 \sqrt{\pi } b x e^{b^2 x^2}-4 \sqrt{\pi } b^3 x^3 e^{b^2 x^2}+3 \pi  \text{erf}(b x) \text{erfi}(b x)-3 \pi  \text{erfi}(b x)\right)}{8 \sqrt{\pi } b^5}","-\frac{3 e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{4 \sqrt{\pi } b^3}+\frac{3 \sqrt{\pi } e^c \text{erfi}(b x)}{8 b^5}-\frac{3 e^c x^2}{4 \sqrt{\pi } b^3}+\frac{x^3 e^{b^2 x^2+c} \text{erfc}(b x)}{2 b^2}-\frac{3 x e^{b^2 x^2+c} \text{erfc}(b x)}{4 b^4}+\frac{e^c x^4}{4 \sqrt{\pi } b}",1,"-1/8*(E^c*(6*b*E^(b^2*x^2)*Sqrt[Pi]*x + 6*b^2*x^2 - 4*b^3*E^(b^2*x^2)*Sqrt[Pi]*x^3 - 2*b^4*x^4 + 2*b*E^(b^2*x^2)*Sqrt[Pi]*x*(-3 + 2*b^2*x^2)*Erf[b*x] - 3*Pi*Erfi[b*x] + 3*Pi*Erf[b*x]*Erfi[b*x] - 6*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)]))/(b^5*Sqrt[Pi])","A",0
174,1,104,95,0.3386468,"\int e^{c+b^2 x^2} x^2 \text{erfc}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^2*Erfc[b*x],x]","-\frac{e^c \left(2 b^2 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)+\text{erf}(b x) \left(2 \sqrt{\pi } b x e^{b^2 x^2}-\pi  \text{erfi}(b x)\right)-2 b^2 x^2-2 \sqrt{\pi } b x e^{b^2 x^2}+\pi  \text{erfi}(b x)\right)}{4 \sqrt{\pi } b^3}","\frac{e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi } b}-\frac{\sqrt{\pi } e^c \text{erfi}(b x)}{4 b^3}+\frac{x e^{b^2 x^2+c} \text{erfc}(b x)}{2 b^2}+\frac{e^c x^2}{2 \sqrt{\pi } b}",1,"-1/4*(E^c*(-2*b*E^(b^2*x^2)*Sqrt[Pi]*x - 2*b^2*x^2 + Pi*Erfi[b*x] + Erf[b*x]*(2*b*E^(b^2*x^2)*Sqrt[Pi]*x - Pi*Erfi[b*x]) + 2*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)]))/(b^3*Sqrt[Pi])","A",0
175,0,0,50,0.1106236,"\int e^{c+b^2 x^2} \text{erfc}(b x) \, dx","Integrate[E^(c + b^2*x^2)*Erfc[b*x],x]","\int e^{c+b^2 x^2} \text{erfc}(b x) \, dx","\frac{\sqrt{\pi } e^c \text{erfi}(b x)}{2 b}-\frac{b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{\sqrt{\pi }}",1,"Integrate[E^(c + b^2*x^2)*Erfc[b*x], x]","F",-1
176,1,99,80,0.3085747,"\int \frac{e^{c+b^2 x^2} \text{erfc}(b x)}{x^2} \, dx","Integrate[(E^(c + b^2*x^2)*Erfc[b*x])/x^2,x]","-\frac{e^c \left(-2 b^3 x^3 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)+\text{erf}(b x) \left(\pi  b x \text{erfi}(b x)-\sqrt{\pi } e^{b^2 x^2}\right)+\sqrt{\pi } e^{b^2 x^2}-\pi  b x \text{erfi}(b x)+2 b x \log (x)\right)}{\sqrt{\pi } x}","-\frac{2 b^3 e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{\sqrt{\pi }}-\frac{e^{b^2 x^2+c} \text{erfc}(b x)}{x}+\sqrt{\pi } b e^c \text{erfi}(b x)-\frac{2 b e^c \log (x)}{\sqrt{\pi }}",1,"-((E^c*(E^(b^2*x^2)*Sqrt[Pi] - b*Pi*x*Erfi[b*x] + Erf[b*x]*(-(E^(b^2*x^2)*Sqrt[Pi]) + b*Pi*x*Erfi[b*x]) - 2*b^3*x^3*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)] + 2*b*x*Log[x]))/(Sqrt[Pi]*x))","A",0
177,1,151,134,0.2387528,"\int \frac{e^{c+b^2 x^2} \text{erfc}(b x)}{x^4} \, dx","Integrate[(E^(c + b^2*x^2)*Erfc[b*x])/x^4,x]","\frac{e^c \left(4 b^5 x^5 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)-2 \pi  b^3 x^3 \text{erf}(b x) \text{erfi}(b x)+2 \pi  b^3 x^3 \text{erfi}(b x)-4 b^3 x^3 \log (x)+\sqrt{\pi } e^{b^2 x^2} \left(2 b^2 x^2+1\right) \text{erf}(b x)-2 \sqrt{\pi } b^2 x^2 e^{b^2 x^2}-\sqrt{\pi } e^{b^2 x^2}+b x\right)}{3 \sqrt{\pi } x^3}","-\frac{4 b^5 e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{3 \sqrt{\pi }}+\frac{2}{3} \sqrt{\pi } b^3 e^c \text{erfi}(b x)-\frac{4 b^3 e^c \log (x)}{3 \sqrt{\pi }}-\frac{2 b^2 e^{b^2 x^2+c} \text{erfc}(b x)}{3 x}-\frac{e^{b^2 x^2+c} \text{erfc}(b x)}{3 x^3}+\frac{b e^c}{3 \sqrt{\pi } x^2}",1,"(E^c*(-(E^(b^2*x^2)*Sqrt[Pi]) + b*x - 2*b^2*E^(b^2*x^2)*Sqrt[Pi]*x^2 + E^(b^2*x^2)*Sqrt[Pi]*(1 + 2*b^2*x^2)*Erf[b*x] + 2*b^3*Pi*x^3*Erfi[b*x] - 2*b^3*Pi*x^3*Erf[b*x]*Erfi[b*x] + 4*b^5*x^5*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)] - 4*b^3*x^3*Log[x]))/(3*Sqrt[Pi]*x^3)","A",0
178,1,87,135,0.1667559,"\int e^{-b^2 x^2} x^5 \text{erfc}(b x) \, dx","Integrate[(x^5*Erfc[b*x])/E^(b^2*x^2),x]","\frac{4 e^{-2 b^2 x^2} \left(\frac{b x \left(4 b^2 x^2+11\right)}{\sqrt{\pi }}-8 e^{b^2 x^2} \left(b^4 x^4+2 b^2 x^2+2\right) \text{erfc}(b x)\right)-43 \sqrt{2} \text{erf}\left(\sqrt{2} b x\right)}{64 b^6}","-\frac{43 \text{erf}\left(\sqrt{2} b x\right)}{32 \sqrt{2} b^6}-\frac{x^4 e^{-b^2 x^2} \text{erfc}(b x)}{2 b^2}-\frac{e^{-b^2 x^2} \text{erfc}(b x)}{b^6}+\frac{11 x e^{-2 b^2 x^2}}{16 \sqrt{\pi } b^5}-\frac{x^2 e^{-b^2 x^2} \text{erfc}(b x)}{b^4}+\frac{x^3 e^{-2 b^2 x^2}}{4 \sqrt{\pi } b^3}",1,"(-43*Sqrt[2]*Erf[Sqrt[2]*b*x] + (4*((b*x*(11 + 4*b^2*x^2))/Sqrt[Pi] - 8*E^(b^2*x^2)*(2 + 2*b^2*x^2 + b^4*x^4)*Erfc[b*x]))/E^(2*b^2*x^2))/(64*b^6)","A",1
179,1,69,90,0.0938836,"\int e^{-b^2 x^2} x^3 \text{erfc}(b x) \, dx","Integrate[(x^3*Erfc[b*x])/E^(b^2*x^2),x]","\frac{4 e^{-2 b^2 x^2} \left(\frac{b x}{\sqrt{\pi }}-2 e^{b^2 x^2} \left(b^2 x^2+1\right) \text{erfc}(b x)\right)-5 \sqrt{2} \text{erf}\left(\sqrt{2} b x\right)}{16 b^4}","-\frac{5 \text{erf}\left(\sqrt{2} b x\right)}{8 \sqrt{2} b^4}-\frac{x^2 e^{-b^2 x^2} \text{erfc}(b x)}{2 b^2}-\frac{e^{-b^2 x^2} \text{erfc}(b x)}{2 b^4}+\frac{x e^{-2 b^2 x^2}}{4 \sqrt{\pi } b^3}",1,"(-5*Sqrt[2]*Erf[Sqrt[2]*b*x] + (4*((b*x)/Sqrt[Pi] - 2*E^(b^2*x^2)*(1 + b^2*x^2)*Erfc[b*x]))/E^(2*b^2*x^2))/(16*b^4)","A",1
180,1,39,43,0.023328,"\int e^{-b^2 x^2} x \text{erfc}(b x) \, dx","Integrate[(x*Erfc[b*x])/E^(b^2*x^2),x]","-\frac{2 e^{-b^2 x^2} \text{erfc}(b x)+\sqrt{2} \text{erf}\left(\sqrt{2} b x\right)}{4 b^2}","-\frac{\text{erf}\left(\sqrt{2} b x\right)}{2 \sqrt{2} b^2}-\frac{e^{-b^2 x^2} \text{erfc}(b x)}{2 b^2}",1,"-1/4*(Sqrt[2]*Erf[Sqrt[2]*b*x] + (2*Erfc[b*x])/E^(b^2*x^2))/b^2","A",1
181,0,0,21,0.1679911,"\int \frac{e^{-b^2 x^2} \text{erfc}(b x)}{x} \, dx","Integrate[Erfc[b*x]/(E^(b^2*x^2)*x),x]","\int \frac{e^{-b^2 x^2} \text{erfc}(b x)}{x} \, dx","\text{Int}\left(\frac{e^{-b^2 x^2} \text{erfc}(b x)}{x},x\right)",0,"Integrate[Erfc[b*x]/(E^(b^2*x^2)*x), x]","A",-1
182,0,0,86,0.3008215,"\int \frac{e^{-b^2 x^2} \text{erfc}(b x)}{x^3} \, dx","Integrate[Erfc[b*x]/(E^(b^2*x^2)*x^3),x]","\int \frac{e^{-b^2 x^2} \text{erfc}(b x)}{x^3} \, dx","-b^2 \text{Int}\left(\frac{e^{-b^2 x^2} \text{erfc}(b x)}{x},x\right)+\sqrt{2} b^2 \text{erf}\left(\sqrt{2} b x\right)-\frac{e^{-b^2 x^2} \text{erfc}(b x)}{2 x^2}+\frac{b e^{-2 b^2 x^2}}{\sqrt{\pi } x}",0,"Integrate[Erfc[b*x]/(E^(b^2*x^2)*x^3), x]","A",-1
183,0,0,162,0.2848534,"\int \frac{e^{-b^2 x^2} \text{erfc}(b x)}{x^5} \, dx","Integrate[Erfc[b*x]/(E^(b^2*x^2)*x^5),x]","\int \frac{e^{-b^2 x^2} \text{erfc}(b x)}{x^5} \, dx","\frac{1}{2} b^4 \text{Int}\left(\frac{e^{-b^2 x^2} \text{erfc}(b x)}{x},x\right)-\frac{2}{3} \sqrt{2} b^4 \text{erf}\left(\sqrt{2} b x\right)-\frac{b^4 \text{erf}\left(\sqrt{2} b x\right)}{\sqrt{2}}+\frac{b^2 e^{-b^2 x^2} \text{erfc}(b x)}{4 x^2}-\frac{e^{-b^2 x^2} \text{erfc}(b x)}{4 x^4}+\frac{b e^{-2 b^2 x^2}}{6 \sqrt{\pi } x^3}-\frac{7 b^3 e^{-2 b^2 x^2}}{6 \sqrt{\pi } x}",0,"Integrate[Erfc[b*x]/(E^(b^2*x^2)*x^5), x]","A",-1
184,1,112,112,0.1809243,"\int e^{-b^2 x^2} x^4 \text{erfc}(b x) \, dx","Integrate[(x^4*Erfc[b*x])/E^(b^2*x^2),x]","-\frac{-4 \sqrt{\pi } b x e^{-b^2 x^2} \left(2 b^2 x^2+3\right) \text{erf}(b x)-4 e^{-2 b^2 x^2} \left(b^2 x^2+2\right)+4 \sqrt{\pi } b x e^{-b^2 x^2} \left(2 b^2 x^2+3\right)+3 \pi  \text{erf}(b x)^2-6 \pi  \text{erf}(b x)}{16 \sqrt{\pi } b^5}","-\frac{3 \sqrt{\pi } \text{erfc}(b x)^2}{16 b^5}-\frac{x^3 e^{-b^2 x^2} \text{erfc}(b x)}{2 b^2}+\frac{e^{-2 b^2 x^2}}{2 \sqrt{\pi } b^5}-\frac{3 x e^{-b^2 x^2} \text{erfc}(b x)}{4 b^4}+\frac{x^2 e^{-2 b^2 x^2}}{4 \sqrt{\pi } b^3}",1,"-1/16*((-4*(2 + b^2*x^2))/E^(2*b^2*x^2) + (4*b*Sqrt[Pi]*x*(3 + 2*b^2*x^2))/E^(b^2*x^2) - 6*Pi*Erf[b*x] - (4*b*Sqrt[Pi]*x*(3 + 2*b^2*x^2)*Erf[b*x])/E^(b^2*x^2) + 3*Pi*Erf[b*x]^2)/(b^5*Sqrt[Pi])","A",0
185,1,79,63,0.1501374,"\int e^{-b^2 x^2} x^2 \text{erfc}(b x) \, dx","Integrate[(x^2*Erfc[b*x])/E^(b^2*x^2),x]","\frac{\left(4 b x e^{-b^2 x^2}+2 \sqrt{\pi }\right) \text{erf}(b x)+2 e^{-2 b^2 x^2} \left(\frac{1}{\sqrt{\pi }}-2 b x e^{b^2 x^2}\right)-\sqrt{\pi } \text{erf}(b x)^2}{8 b^3}","-\frac{\sqrt{\pi } \text{erfc}(b x)^2}{8 b^3}-\frac{x e^{-b^2 x^2} \text{erfc}(b x)}{2 b^2}+\frac{e^{-2 b^2 x^2}}{4 \sqrt{\pi } b^3}",1,"((2*(1/Sqrt[Pi] - 2*b*E^(b^2*x^2)*x))/E^(2*b^2*x^2) + (2*Sqrt[Pi] + (4*b*x)/E^(b^2*x^2))*Erf[b*x] - Sqrt[Pi]*Erf[b*x]^2)/(8*b^3)","A",0
186,1,18,18,0.0094134,"\int e^{-b^2 x^2} \text{erfc}(b x) \, dx","Integrate[Erfc[b*x]/E^(b^2*x^2),x]","-\frac{\sqrt{\pi } \text{erfc}(b x)^2}{4 b}","-\frac{\sqrt{\pi } \text{erfc}(b x)^2}{4 b}",1,"-1/4*(Sqrt[Pi]*Erfc[b*x]^2)/b","A",1
187,1,53,53,0.0219632,"\int \frac{e^{-b^2 x^2} \text{erfc}(b x)}{x^2} \, dx","Integrate[Erfc[b*x]/(E^(b^2*x^2)*x^2),x]","-\frac{e^{-b^2 x^2} \text{erfc}(b x)}{x}-\frac{b \text{Ei}\left(-2 b^2 x^2\right)}{\sqrt{\pi }}+\frac{1}{2} \sqrt{\pi } b \text{erfc}(b x)^2","-\frac{e^{-b^2 x^2} \text{erfc}(b x)}{x}-\frac{b \text{Ei}\left(-2 b^2 x^2\right)}{\sqrt{\pi }}+\frac{1}{2} \sqrt{\pi } b \text{erfc}(b x)^2",1,"-(Erfc[b*x]/(E^(b^2*x^2)*x)) + (b*Sqrt[Pi]*Erfc[b*x]^2)/2 - (b*ExpIntegralEi[-2*b^2*x^2])/Sqrt[Pi]","A",1
188,1,85,108,0.0667482,"\int \frac{e^{-b^2 x^2} \text{erfc}(b x)}{x^4} \, dx","Integrate[Erfc[b*x]/(E^(b^2*x^2)*x^4),x]","\frac{1}{3} \left(-\sqrt{\pi } b^3 \text{erfc}(b x)^2+\frac{e^{-b^2 x^2} \left(2 b^2 x^2-1\right) \text{erfc}(b x)}{x^3}+\frac{b \left(4 b^2 \text{Ei}\left(-2 b^2 x^2\right)+\frac{e^{-2 b^2 x^2}}{x^2}\right)}{\sqrt{\pi }}\right)","-\frac{1}{3} \sqrt{\pi } b^3 \text{erfc}(b x)^2+\frac{2 b^2 e^{-b^2 x^2} \text{erfc}(b x)}{3 x}-\frac{e^{-b^2 x^2} \text{erfc}(b x)}{3 x^3}+\frac{b e^{-2 b^2 x^2}}{3 \sqrt{\pi } x^2}+\frac{4 b^3 \text{Ei}\left(-2 b^2 x^2\right)}{3 \sqrt{\pi }}",1,"(((-1 + 2*b^2*x^2)*Erfc[b*x])/(E^(b^2*x^2)*x^3) - b^3*Sqrt[Pi]*Erfc[b*x]^2 + (b*(1/(E^(2*b^2*x^2)*x^2) + 4*b^2*ExpIntegralEi[-2*b^2*x^2]))/Sqrt[Pi])/3","A",1
189,1,256,342,2.6168704,"\int e^{c+d x^2} x^3 \text{erfc}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x^3*Erfc[a + b*x],x]","-\frac{e^c \left(-\frac{b d e^{-a^2-2 a b x+x^2 \left(d-b^2\right)} \left(\sqrt{\pi } \sqrt{b^2-d} \left(\left(2 a^2+1\right) b^2-d\right) e^{\frac{\left(a b+x \left(b^2-d\right)\right)^2}{b^2-d}} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)+2 \left(b^2-d\right) \left(a b+x \left(d-b^2\right)\right)\right)}{\sqrt{\pi } \left(b^2-d\right)^3}+\frac{2 b e^{\frac{a^2 d}{b^2-d}} \text{erfi}\left(\frac{x \left(d-b^2\right)-a b}{\sqrt{d-b^2}}\right)}{\sqrt{d-b^2}}+2 e^{d x^2} \left(d x^2-1\right) \text{erf}(a+b x)-2 e^{d x^2} \left(d x^2-1\right)\right)}{4 d^2}","-\frac{b e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{2 d^2 \sqrt{b^2-d}}+\frac{b e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{4 d \left(b^2-d\right)^{3/2}}+\frac{a b^2 e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)^2}-\frac{b x e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)}+\frac{a^2 b^3 e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{2 d \left(b^2-d\right)^{5/2}}-\frac{e^{c+d x^2} \text{erfc}(a+b x)}{2 d^2}+\frac{x^2 e^{c+d x^2} \text{erfc}(a+b x)}{2 d}",1,"-1/4*(E^c*(-2*E^(d*x^2)*(-1 + d*x^2) + 2*E^(d*x^2)*(-1 + d*x^2)*Erf[a + b*x] - (b*d*E^(-a^2 - 2*a*b*x + (-b^2 + d)*x^2)*(2*(b^2 - d)*(a*b + (-b^2 + d)*x) + Sqrt[b^2 - d]*((1 + 2*a^2)*b^2 - d)*E^((a*b + (b^2 - d)*x)^2/(b^2 - d))*Sqrt[Pi]*Erf[(a*b + (b^2 - d)*x)/Sqrt[b^2 - d]]))/((b^2 - d)^3*Sqrt[Pi]) + (2*b*E^((a^2*d)/(b^2 - d))*Erfi[(-(a*b) + (-b^2 + d)*x)/Sqrt[-b^2 + d]])/Sqrt[-b^2 + d]))/d^2","A",0
190,1,81,86,0.1183875,"\int e^{c+d x^2} x \text{erfc}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x*Erfc[a + b*x],x]","\frac{e^c \left(\frac{b e^{\frac{a^2 d}{b^2-d}} \text{erfi}\left(\frac{x \left(d-b^2\right)-a b}{\sqrt{d-b^2}}\right)}{\sqrt{d-b^2}}+e^{d x^2} \text{erfc}(a+b x)\right)}{2 d}","\frac{b e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{2 d \sqrt{b^2-d}}+\frac{e^{c+d x^2} \text{erfc}(a+b x)}{2 d}",1,"(E^c*(E^(d*x^2)*Erfc[a + b*x] + (b*E^((a^2*d)/(b^2 - d))*Erfi[(-(a*b) + (-b^2 + d)*x)/Sqrt[-b^2 + d]])/Sqrt[-b^2 + d]))/(2*d)","A",1
191,0,0,22,0.7723866,"\int \frac{e^{c+d x^2} \text{erfc}(a+b x)}{x} \, dx","Integrate[(E^(c + d*x^2)*Erfc[a + b*x])/x,x]","\int \frac{e^{c+d x^2} \text{erfc}(a+b x)}{x} \, dx","\text{Int}\left(\frac{e^{c+d x^2} \text{erfc}(a+b x)}{x},x\right)",0,"Integrate[(E^(c + d*x^2)*Erfc[a + b*x])/x, x]","A",-1
192,0,0,183,1.0310598,"\int \frac{e^{c+d x^2} \text{erfc}(a+b x)}{x^3} \, dx","Integrate[(E^(c + d*x^2)*Erfc[a + b*x])/x^3,x]","\int \frac{e^{c+d x^2} \text{erfc}(a+b x)}{x^3} \, dx","\frac{2 a b^2 \text{Int}\left(\frac{e^{-a^2-2 a b x+x^2 \left(d-b^2\right)+c}}{x},x\right)}{\sqrt{\pi }}+d \text{Int}\left(\frac{e^{c+d x^2} \text{erfc}(a+b x)}{x},x\right)+b \sqrt{b^2-d} e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)+\frac{b e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{\sqrt{\pi } x}-\frac{e^{c+d x^2} \text{erfc}(a+b x)}{2 x^2}",0,"Integrate[(E^(c + d*x^2)*Erfc[a + b*x])/x^3, x]","A",-1
193,0,0,527,1.1950553,"\int e^{c+d x^2} x^4 \text{erfc}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x^4*Erfc[a + b*x],x]","\int e^{c+d x^2} x^4 \text{erfc}(a+b x) \, dx","\frac{3 \text{Int}\left(e^{c+d x^2} \text{erfc}(a+b x),x\right)}{4 d^2}+\frac{3 a b^2 e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{4 d^2 \left(b^2-d\right)^{3/2}}+\frac{3 b e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{4 \sqrt{\pi } d^2 \left(b^2-d\right)}-\frac{3 a b^2 e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{4 d \left(b^2-d\right)^{5/2}}+\frac{a b^2 x e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)^2}-\frac{b x^2 e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)}-\frac{b e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)^2}-\frac{a^2 b^3 e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)^3}-\frac{a^3 b^4 e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{2 d \left(b^2-d\right)^{7/2}}-\frac{3 x e^{c+d x^2} \text{erfc}(a+b x)}{4 d^2}+\frac{x^3 e^{c+d x^2} \text{erfc}(a+b x)}{2 d}",0,"Integrate[E^(c + d*x^2)*x^4*Erfc[a + b*x], x]","A",-1
194,0,0,164,1.0037201,"\int e^{c+d x^2} x^2 \text{erfc}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x^2*Erfc[a + b*x],x]","\int e^{c+d x^2} x^2 \text{erfc}(a+b x) \, dx","-\frac{\text{Int}\left(e^{c+d x^2} \text{erfc}(a+b x),x\right)}{2 d}-\frac{a b^2 e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)}{2 d \left(b^2-d\right)^{3/2}}-\frac{b e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{2 \sqrt{\pi } d \left(b^2-d\right)}+\frac{x e^{c+d x^2} \text{erfc}(a+b x)}{2 d}",0,"Integrate[E^(c + d*x^2)*x^2*Erfc[a + b*x], x]","A",-1
195,0,0,19,0.0436174,"\int e^{c+d x^2} \text{erfc}(a+b x) \, dx","Integrate[E^(c + d*x^2)*Erfc[a + b*x],x]","\int e^{c+d x^2} \text{erfc}(a+b x) \, dx","\text{Int}\left(e^{c+d x^2} \text{erfc}(a+b x),x\right)",0,"Integrate[E^(c + d*x^2)*Erfc[a + b*x], x]","A",-1
196,0,0,83,1.0881989,"\int \frac{e^{c+d x^2} \text{erfc}(a+b x)}{x^2} \, dx","Integrate[(E^(c + d*x^2)*Erfc[a + b*x])/x^2,x]","\int \frac{e^{c+d x^2} \text{erfc}(a+b x)}{x^2} \, dx","-\frac{2 b \text{Int}\left(\frac{e^{-a^2-2 a b x+x^2 \left(d-b^2\right)+c}}{x},x\right)}{\sqrt{\pi }}+2 d \text{Int}\left(e^{c+d x^2} \text{erfc}(a+b x),x\right)-\frac{e^{c+d x^2} \text{erfc}(a+b x)}{x}",0,"Integrate[(E^(c + d*x^2)*Erfc[a + b*x])/x^2, x]","A",-1
197,0,0,355,1.2989108,"\int \frac{e^{c+d x^2} \text{erfc}(a+b x)}{x^4} \, dx","Integrate[(E^(c + d*x^2)*Erfc[a + b*x])/x^4,x]","\int \frac{e^{c+d x^2} \text{erfc}(a+b x)}{x^4} \, dx","\frac{2 b \left(b^2-d\right) \text{Int}\left(\frac{e^{-a^2-2 a b x+x^2 \left(d-b^2\right)+c}}{x},x\right)}{3 \sqrt{\pi }}-\frac{4 b d \text{Int}\left(\frac{e^{-a^2-2 a b x+x^2 \left(d-b^2\right)+c}}{x},x\right)}{3 \sqrt{\pi }}-\frac{4 a^2 b^3 \text{Int}\left(\frac{e^{-a^2-2 a b x+x^2 \left(d-b^2\right)+c}}{x},x\right)}{3 \sqrt{\pi }}+\frac{4}{3} d^2 \text{Int}\left(e^{c+d x^2} \text{erfc}(a+b x),x\right)-\frac{2}{3} a b^2 \sqrt{b^2-d} e^{\frac{a^2 d}{b^2-d}+c} \text{erf}\left(\frac{a b+x \left(b^2-d\right)}{\sqrt{b^2-d}}\right)-\frac{2 a b^2 e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{3 \sqrt{\pi } x}+\frac{b e^{-a^2-2 a b x-x^2 \left(b^2-d\right)+c}}{3 \sqrt{\pi } x^2}-\frac{2 d e^{c+d x^2} \text{erfc}(a+b x)}{3 x}-\frac{e^{c+d x^2} \text{erfc}(a+b x)}{3 x^3}",0,"Integrate[(E^(c + d*x^2)*Erfc[a + b*x])/x^4, x]","A",-1
198,1,60,60,0.0964005,"\int \left(\frac{e^{-b^2 x^2} \text{erfc}(b x)}{x^3}+\frac{b^2 e^{-b^2 x^2} \text{erfc}(b x)}{x}\right) \, dx","Integrate[Erfc[b*x]/(E^(b^2*x^2)*x^3) + (b^2*Erfc[b*x])/(E^(b^2*x^2)*x),x]","\sqrt{2} b^2 \text{erf}\left(\sqrt{2} b x\right)-\frac{e^{-b^2 x^2} \text{erfc}(b x)}{2 x^2}+\frac{b e^{-2 b^2 x^2}}{\sqrt{\pi } x}","\sqrt{2} b^2 \text{erf}\left(\sqrt{2} b x\right)-\frac{e^{-b^2 x^2} \text{erfc}(b x)}{2 x^2}+\frac{b e^{-2 b^2 x^2}}{\sqrt{\pi } x}",1,"b/(E^(2*b^2*x^2)*Sqrt[Pi]*x) + Sqrt[2]*b^2*Erf[Sqrt[2]*b*x] - Erfc[b*x]/(2*E^(b^2*x^2)*x^2)","A",1
199,1,94,91,0.6683751,"\int \text{erfc}(b x) \sin \left(c+i b^2 x^2\right) \, dx","Integrate[Erfc[b*x]*Sin[c + I*b^2*x^2],x]","\frac{(\sin (c)+i \cos (c)) \left(-4 b^2 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)+\pi  \left(\text{erf}(b x)^2 (\cos (2 c)+i \sin (2 c))-2 \text{erf}(b x) (\cos (2 c)+i \sin (2 c))+2 \text{erfi}(b x)\right)\right)}{8 \sqrt{\pi } b}","-\frac{i b e^{-i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}+\frac{i \sqrt{\pi } e^{i c} \text{erfc}(b x)^2}{8 b}+\frac{i \sqrt{\pi } e^{-i c} \text{erfi}(b x)}{4 b}",1,"((I*Cos[c] + Sin[c])*(-4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2] + Pi*(2*Erfi[b*x] - 2*Erf[b*x]*(Cos[2*c] + I*Sin[2*c]) + Erf[b*x]^2*(Cos[2*c] + I*Sin[2*c]))))/(8*b*Sqrt[Pi])","A",0
200,1,101,91,0.5456046,"\int \text{erfc}(b x) \sin \left(c-i b^2 x^2\right) \, dx","Integrate[Erfc[b*x]*Sin[c - I*b^2*x^2],x]","\frac{1}{2} i \left(\frac{b x^2 (\cos (c)+i \sin (c)) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{\sqrt{\pi }}-\frac{\sqrt{\pi } \left(\text{erf}(b x)^2 (\cos (c)-i \sin (c))-2 \text{erf}(b x) (\cos (c)-i \sin (c))+2 \text{erfi}(b x) (\cos (c)+i \sin (c))\right)}{4 b}\right)","\frac{i b e^{i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}-\frac{i \sqrt{\pi } e^{-i c} \text{erfc}(b x)^2}{8 b}-\frac{i \sqrt{\pi } e^{i c} \text{erfi}(b x)}{4 b}",1,"(I/2)*(-1/4*(Sqrt[Pi]*(-2*Erf[b*x]*(Cos[c] - I*Sin[c]) + Erf[b*x]^2*(Cos[c] - I*Sin[c]) + 2*Erfi[b*x]*(Cos[c] + I*Sin[c])))/b + (b*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*(Cos[c] + I*Sin[c]))/Sqrt[Pi])","A",0
201,0,0,85,1.7405086,"\int \cos \left(c+i b^2 x^2\right) \text{erfc}(b x) \, dx","Integrate[Cos[c + I*b^2*x^2]*Erfc[b*x],x]","\int \cos \left(c+i b^2 x^2\right) \text{erfc}(b x) \, dx","-\frac{b e^{-i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}-\frac{\sqrt{\pi } e^{i c} \text{erfc}(b x)^2}{8 b}+\frac{\sqrt{\pi } e^{-i c} \text{erfi}(b x)}{4 b}",1,"Integrate[Cos[c + I*b^2*x^2]*Erfc[b*x], x]","F",-1
202,0,0,85,1.6629016,"\int \cos \left(c-i b^2 x^2\right) \text{erfc}(b x) \, dx","Integrate[Cos[c - I*b^2*x^2]*Erfc[b*x],x]","\int \cos \left(c-i b^2 x^2\right) \text{erfc}(b x) \, dx","-\frac{b e^{i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}-\frac{\sqrt{\pi } e^{-i c} \text{erfc}(b x)^2}{8 b}+\frac{\sqrt{\pi } e^{i c} \text{erfi}(b x)}{4 b}",1,"Integrate[Cos[c - I*b^2*x^2]*Erfc[b*x], x]","F",-1
203,1,83,75,0.2015589,"\int \text{erfc}(b x) \sinh \left(c+b^2 x^2\right) \, dx","Integrate[Erfc[b*x]*Sinh[c + b^2*x^2],x]","\frac{\pi  \left(\text{erf}(b x)^2 (\cosh (c)-\sinh (c))-2 \text{erf}(b x) (\cosh (c)-\sinh (c))+2 \text{erfi}(b x) (\sinh (c)+\cosh (c))\right)-4 b^2 x^2 (\sinh (c)+\cosh (c)) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{8 \sqrt{\pi } b}","-\frac{b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}+\frac{\sqrt{\pi } e^{-c} \text{erfc}(b x)^2}{8 b}+\frac{\sqrt{\pi } e^c \text{erfi}(b x)}{4 b}",1,"(-4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*(Cosh[c] + Sinh[c]) + Pi*(-2*Erf[b*x]*(Cosh[c] - Sinh[c]) + Erf[b*x]^2*(Cosh[c] - Sinh[c]) + 2*Erfi[b*x]*(Cosh[c] + Sinh[c])))/(8*b*Sqrt[Pi])","A",0
204,1,84,77,0.1788863,"\int \text{erfc}(b x) \sinh \left(c-b^2 x^2\right) \, dx","Integrate[Erfc[b*x]*Sinh[c - b^2*x^2],x]","-\frac{(\cosh (c)-\sinh (c)) \left(\pi  \left(\text{erf}(b x)^2 (\sinh (2 c)+\cosh (2 c))-2 \text{erf}(b x) (\sinh (2 c)+\cosh (2 c))+2 \text{erfi}(b x)\right)-4 b^2 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)\right)}{8 \sqrt{\pi } b}","\frac{b e^{-c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}-\frac{\sqrt{\pi } e^c \text{erfc}(b x)^2}{8 b}-\frac{\sqrt{\pi } e^{-c} \text{erfi}(b x)}{4 b}",1,"-1/8*((Cosh[c] - Sinh[c])*(-4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2] + Pi*(2*Erfi[b*x] - 2*Erf[b*x]*(Cosh[2*c] + Sinh[2*c]) + Erf[b*x]^2*(Cosh[2*c] + Sinh[2*c]))))/(b*Sqrt[Pi])","A",0
205,1,114,75,0.1337244,"\int \cosh \left(c+b^2 x^2\right) \text{erfc}(b x) \, dx","Integrate[Cosh[c + b^2*x^2]*Erfc[b*x],x]","\frac{-4 b^2 x^2 \sinh (c) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)+4 b^2 x^2 \cosh (c) \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)+\pi  \left(-2 \text{erf}(b x) (\cosh (c) \text{erfi}(b x)+\sinh (c)-\cosh (c))+\text{erf}(b x)^2 (\sinh (c)-\cosh (c))+2 \text{erfi}(b x) (\sinh (c)+\cosh (c))\right)}{8 \sqrt{\pi } b}","-\frac{b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}-\frac{\sqrt{\pi } e^{-c} \text{erfc}(b x)^2}{8 b}+\frac{\sqrt{\pi } e^c \text{erfi}(b x)}{4 b}",1,"(4*b^2*x^2*Cosh[c]*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)] - 4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*Sinh[c] + Pi*(Erf[b*x]^2*(-Cosh[c] + Sinh[c]) + 2*Erfi[b*x]*(Cosh[c] + Sinh[c]) - 2*Erf[b*x]*(-Cosh[c] + Cosh[c]*Erfi[b*x] + Sinh[c])))/(8*b*Sqrt[Pi])","A",0
206,1,117,77,0.1319076,"\int \cosh \left(c-b^2 x^2\right) \text{erfc}(b x) \, dx","Integrate[Cosh[c - b^2*x^2]*Erfc[b*x],x]","\frac{4 b^2 x^2 \sinh (c) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)+4 b^2 x^2 \cosh (c) \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)-\pi  \left(2 \text{erf}(b x) (\cosh (c) \text{erfi}(b x)-\sinh (c)-\cosh (c))+\text{erf}(b x)^2 (\sinh (c)+\cosh (c))+2 \text{erfi}(b x) (\sinh (c)-\cosh (c))\right)}{8 \sqrt{\pi } b}","-\frac{b e^{-c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{2 \sqrt{\pi }}-\frac{\sqrt{\pi } e^c \text{erfc}(b x)^2}{8 b}+\frac{\sqrt{\pi } e^{-c} \text{erfi}(b x)}{4 b}",1,"(4*b^2*x^2*Cosh[c]*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)] + 4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*Sinh[c] - Pi*(2*Erf[b*x]*(-Cosh[c] + Cosh[c]*Erfi[b*x] - Sinh[c]) + 2*Erfi[b*x]*(-Cosh[c] + Sinh[c]) + Erf[b*x]^2*(Cosh[c] + Sinh[c])))/(8*b*Sqrt[Pi])","A",0
207,1,64,93,0.0394859,"\int x^5 \text{erfi}(b x) \, dx","Integrate[x^5*Erfi[b*x],x]","\frac{\sqrt{\pi } \left(8 b^6 x^6+15\right) \text{erfi}(b x)-2 b x e^{b^2 x^2} \left(4 b^4 x^4-10 b^2 x^2+15\right)}{48 \sqrt{\pi } b^6}","\frac{5 \text{erfi}(b x)}{16 b^6}-\frac{x^5 e^{b^2 x^2}}{6 \sqrt{\pi } b}-\frac{5 x e^{b^2 x^2}}{8 \sqrt{\pi } b^5}+\frac{5 x^3 e^{b^2 x^2}}{12 \sqrt{\pi } b^3}+\frac{1}{6} x^6 \text{erfi}(b x)",1,"(-2*b*E^(b^2*x^2)*x*(15 - 10*b^2*x^2 + 4*b^4*x^4) + Sqrt[Pi]*(15 + 8*b^6*x^6)*Erfi[b*x])/(48*b^6*Sqrt[Pi])","A",1
208,1,51,69,0.0365689,"\int x^3 \text{erfi}(b x) \, dx","Integrate[x^3*Erfi[b*x],x]","\frac{\left(4 b^4 x^4-3\right) \text{erfi}(b x)-\frac{2 b x e^{b^2 x^2} \left(2 b^2 x^2-3\right)}{\sqrt{\pi }}}{16 b^4}","-\frac{3 \text{erfi}(b x)}{16 b^4}-\frac{x^3 e^{b^2 x^2}}{4 \sqrt{\pi } b}+\frac{3 x e^{b^2 x^2}}{8 \sqrt{\pi } b^3}+\frac{1}{4} x^4 \text{erfi}(b x)",1,"((-2*b*E^(b^2*x^2)*x*(-3 + 2*b^2*x^2))/Sqrt[Pi] + (-3 + 4*b^4*x^4)*Erfi[b*x])/(16*b^4)","A",1
209,1,39,45,0.0362938,"\int x \text{erfi}(b x) \, dx","Integrate[x*Erfi[b*x],x]","\frac{1}{4} \left(\left(\frac{1}{b^2}+2 x^2\right) \text{erfi}(b x)-\frac{2 x e^{b^2 x^2}}{\sqrt{\pi } b}\right)","\frac{\text{erfi}(b x)}{4 b^2}-\frac{x e^{b^2 x^2}}{2 \sqrt{\pi } b}+\frac{1}{2} x^2 \text{erfi}(b x)",1,"((-2*E^(b^2*x^2)*x)/(b*Sqrt[Pi]) + (b^(-2) + 2*x^2)*Erfi[b*x])/4","A",1
210,1,31,31,0.0244462,"\int \frac{\text{erfi}(b x)}{x} \, dx","Integrate[Erfi[b*x]/x,x]","\frac{2 b x \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}","\frac{2 b x \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};b^2 x^2\right)}{\sqrt{\pi }}",1,"(2*b*x*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2}, b^2*x^2])/Sqrt[Pi]","A",1
211,1,37,40,0.0288347,"\int \frac{\text{erfi}(b x)}{x^3} \, dx","Integrate[Erfi[b*x]/x^3,x]","\left(b^2-\frac{1}{2 x^2}\right) \text{erfi}(b x)-\frac{b e^{b^2 x^2}}{\sqrt{\pi } x}","b^2 \text{erfi}(b x)-\frac{b e^{b^2 x^2}}{\sqrt{\pi } x}-\frac{\text{erfi}(b x)}{2 x^2}",1,"-((b*E^(b^2*x^2))/(Sqrt[Pi]*x)) + (b^2 - 1/(2*x^2))*Erfi[b*x]","A",1
212,1,51,69,0.0411011,"\int \frac{\text{erfi}(b x)}{x^5} \, dx","Integrate[Erfi[b*x]/x^5,x]","\frac{\left(4 b^4 x^4-3\right) \text{erfi}(b x)-\frac{2 b x e^{b^2 x^2} \left(2 b^2 x^2+1\right)}{\sqrt{\pi }}}{12 x^4}","\frac{1}{3} b^4 \text{erfi}(b x)-\frac{b e^{b^2 x^2}}{6 \sqrt{\pi } x^3}-\frac{b^3 e^{b^2 x^2}}{3 \sqrt{\pi } x}-\frac{\text{erfi}(b x)}{4 x^4}",1,"((-2*b*E^(b^2*x^2)*x*(1 + 2*b^2*x^2))/Sqrt[Pi] + (-3 + 4*b^4*x^4)*Erfi[b*x])/(12*x^4)","A",1
213,1,64,93,0.0266479,"\int \frac{\text{erfi}(b x)}{x^7} \, dx","Integrate[Erfi[b*x]/x^7,x]","\frac{\sqrt{\pi } \left(8 b^6 x^6-15\right) \text{erfi}(b x)-2 b x e^{b^2 x^2} \left(4 b^4 x^4+2 b^2 x^2+3\right)}{90 \sqrt{\pi } x^6}","\frac{4}{45} b^6 \text{erfi}(b x)-\frac{b e^{b^2 x^2}}{15 \sqrt{\pi } x^5}-\frac{4 b^5 e^{b^2 x^2}}{45 \sqrt{\pi } x}-\frac{2 b^3 e^{b^2 x^2}}{45 \sqrt{\pi } x^3}-\frac{\text{erfi}(b x)}{6 x^6}",1,"(-2*b*E^(b^2*x^2)*x*(3 + 2*b^2*x^2 + 4*b^4*x^4) + Sqrt[Pi]*(-15 + 8*b^6*x^6)*Erfi[b*x])/(90*Sqrt[Pi]*x^6)","A",1
214,1,57,105,0.0488517,"\int x^6 \text{erfi}(b x) \, dx","Integrate[x^6*Erfi[b*x],x]","\frac{1}{7} \left(\frac{e^{b^2 x^2} \left(-b^6 x^6+3 b^4 x^4-6 b^2 x^2+6\right)}{\sqrt{\pi } b^7}+x^7 \text{erfi}(b x)\right)","-\frac{x^6 e^{b^2 x^2}}{7 \sqrt{\pi } b}+\frac{6 e^{b^2 x^2}}{7 \sqrt{\pi } b^7}-\frac{6 x^2 e^{b^2 x^2}}{7 \sqrt{\pi } b^5}+\frac{3 x^4 e^{b^2 x^2}}{7 \sqrt{\pi } b^3}+\frac{1}{7} x^7 \text{erfi}(b x)",1,"((E^(b^2*x^2)*(6 - 6*b^2*x^2 + 3*b^4*x^4 - b^6*x^6))/(b^7*Sqrt[Pi]) + x^7*Erfi[b*x])/7","A",1
215,1,49,81,0.0294285,"\int x^4 \text{erfi}(b x) \, dx","Integrate[x^4*Erfi[b*x],x]","\frac{1}{5} \left(x^5 \text{erfi}(b x)-\frac{e^{b^2 x^2} \left(b^4 x^4-2 b^2 x^2+2\right)}{\sqrt{\pi } b^5}\right)","-\frac{x^4 e^{b^2 x^2}}{5 \sqrt{\pi } b}-\frac{2 e^{b^2 x^2}}{5 \sqrt{\pi } b^5}+\frac{2 x^2 e^{b^2 x^2}}{5 \sqrt{\pi } b^3}+\frac{1}{5} x^5 \text{erfi}(b x)",1,"(-((E^(b^2*x^2)*(2 - 2*b^2*x^2 + b^4*x^4))/(b^5*Sqrt[Pi])) + x^5*Erfi[b*x])/5","A",1
216,1,41,57,0.0359238,"\int x^2 \text{erfi}(b x) \, dx","Integrate[x^2*Erfi[b*x],x]","\frac{1}{3} \left(\frac{e^{b^2 x^2} \left(1-b^2 x^2\right)}{\sqrt{\pi } b^3}+x^3 \text{erfi}(b x)\right)","-\frac{x^2 e^{b^2 x^2}}{3 \sqrt{\pi } b}+\frac{e^{b^2 x^2}}{3 \sqrt{\pi } b^3}+\frac{1}{3} x^3 \text{erfi}(b x)",1,"((E^(b^2*x^2)*(1 - b^2*x^2))/(b^3*Sqrt[Pi]) + x^3*Erfi[b*x])/3","A",1
217,1,26,26,0.0065191,"\int \text{erfi}(b x) \, dx","Integrate[Erfi[b*x],x]","x \text{erfi}(b x)-\frac{e^{b^2 x^2}}{\sqrt{\pi } b}","x \text{erfi}(b x)-\frac{e^{b^2 x^2}}{\sqrt{\pi } b}",1,"-(E^(b^2*x^2)/(b*Sqrt[Pi])) + x*Erfi[b*x]","A",1
218,1,25,25,0.0197359,"\int \frac{\text{erfi}(b x)}{x^2} \, dx","Integrate[Erfi[b*x]/x^2,x]","\frac{b \text{Ei}\left(b^2 x^2\right)}{\sqrt{\pi }}-\frac{\text{erfi}(b x)}{x}","\frac{b \text{Ei}\left(b^2 x^2\right)}{\sqrt{\pi }}-\frac{\text{erfi}(b x)}{x}",1,"-(Erfi[b*x]/x) + (b*ExpIntegralEi[b^2*x^2])/Sqrt[Pi]","A",1
219,1,50,54,0.0226034,"\int \frac{\text{erfi}(b x)}{x^4} \, dx","Integrate[Erfi[b*x]/x^4,x]","-\frac{\frac{b x e^{b^2 x^2}}{\sqrt{\pi }}-\frac{b^3 x^3 \text{Ei}\left(b^2 x^2\right)}{\sqrt{\pi }}+\text{erfi}(b x)}{3 x^3}","-\frac{b e^{b^2 x^2}}{3 \sqrt{\pi } x^2}+\frac{b^3 \text{Ei}\left(b^2 x^2\right)}{3 \sqrt{\pi }}-\frac{\text{erfi}(b x)}{3 x^3}",1,"-1/3*((b*E^(b^2*x^2)*x)/Sqrt[Pi] + Erfi[b*x] - (b^3*x^3*ExpIntegralEi[b^2*x^2])/Sqrt[Pi])/x^3","A",1
220,1,61,78,0.0320165,"\int \frac{\text{erfi}(b x)}{x^6} \, dx","Integrate[Erfi[b*x]/x^6,x]","\frac{-b x e^{b^2 x^2} \left(b^2 x^2+1\right)+b^5 x^5 \text{Ei}\left(b^2 x^2\right)-2 \sqrt{\pi } \text{erfi}(b x)}{10 \sqrt{\pi } x^5}","-\frac{b e^{b^2 x^2}}{10 \sqrt{\pi } x^4}+\frac{b^5 \text{Ei}\left(b^2 x^2\right)}{10 \sqrt{\pi }}-\frac{b^3 e^{b^2 x^2}}{10 \sqrt{\pi } x^2}-\frac{\text{erfi}(b x)}{5 x^5}",1,"(-(b*E^(b^2*x^2)*x*(1 + b^2*x^2)) - 2*Sqrt[Pi]*Erfi[b*x] + b^5*x^5*ExpIntegralEi[b^2*x^2])/(10*Sqrt[Pi]*x^5)","A",1
221,1,237,279,0.333741,"\int (c+d x)^3 \text{erfi}(a+b x) \, dx","Integrate[(c + d*x)^3*Erfi[a + b*x],x]","\frac{\sqrt{\pi } \text{erfi}(a+b x) \left(-4 a^4 d^3+16 a^3 b c d^2+12 a^2 d \left(d^2-2 b^2 c^2\right)+8 a \left(2 b^3 c^3-3 b c d^2\right)+4 b^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)+12 b^2 c^2 d-3 d^3\right)-2 e^{(a+b x)^2} \left(b d^2 \left(8 \left(a^2-1\right) c+\left(2 a^2-3\right) d x\right)+a \left(5-2 a^2\right) d^3-2 a b^2 d \left(6 c^2+4 c d x+d^2 x^2\right)+2 b^3 \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right)}{16 \sqrt{\pi } b^4}","-\frac{d^2 e^{(a+b x)^2} (a+b x)^2 (b c-a d)}{\sqrt{\pi } b^4}+\frac{d^2 e^{(a+b x)^2} (b c-a d)}{\sqrt{\pi } b^4}-\frac{(b c-a d)^4 \text{erfi}(a+b x)}{4 b^4 d}+\frac{3 d (b c-a d)^2 \text{erfi}(a+b x)}{4 b^4}-\frac{e^{(a+b x)^2} (b c-a d)^3}{\sqrt{\pi } b^4}-\frac{3 d e^{(a+b x)^2} (a+b x) (b c-a d)^2}{2 \sqrt{\pi } b^4}-\frac{3 d^3 \text{erfi}(a+b x)}{16 b^4}-\frac{d^3 e^{(a+b x)^2} (a+b x)^3}{4 \sqrt{\pi } b^4}+\frac{3 d^3 e^{(a+b x)^2} (a+b x)}{8 \sqrt{\pi } b^4}+\frac{(c+d x)^4 \text{erfi}(a+b x)}{4 d}",1,"(-2*E^(a + b*x)^2*(a*(5 - 2*a^2)*d^3 + b*d^2*(8*(-1 + a^2)*c + (-3 + 2*a^2)*d*x) - 2*a*b^2*d*(6*c^2 + 4*c*d*x + d^2*x^2) + 2*b^3*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)) + Sqrt[Pi]*(12*b^2*c^2*d + 16*a^3*b*c*d^2 - 3*d^3 - 4*a^4*d^3 + 12*a^2*d*(-2*b^2*c^2 + d^2) + 8*a*(2*b^3*c^3 - 3*b*c*d^2) + 4*b^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3))*Erfi[a + b*x])/(16*b^4*Sqrt[Pi])","A",1
222,1,142,186,0.2070298,"\int (c+d x)^2 \text{erfi}(a+b x) \, dx","Integrate[(c + d*x)^2*Erfi[a + b*x],x]","\frac{\sqrt{\pi } \text{erfi}(a+b x) \left(2 a^3 d^2-6 a^2 b c d+a \left(6 b^2 c^2-3 d^2\right)+2 b^3 x \left(3 c^2+3 c d x+d^2 x^2\right)+3 b c d\right)-2 e^{(a+b x)^2} \left(\left(a^2-1\right) d^2-a b d (3 c+d x)+b^2 \left(3 c^2+3 c d x+d^2 x^2\right)\right)}{6 \sqrt{\pi } b^3}","-\frac{(b c-a d)^3 \text{erfi}(a+b x)}{3 b^3 d}+\frac{d (b c-a d) \text{erfi}(a+b x)}{2 b^3}-\frac{e^{(a+b x)^2} (b c-a d)^2}{\sqrt{\pi } b^3}-\frac{d e^{(a+b x)^2} (a+b x) (b c-a d)}{\sqrt{\pi } b^3}-\frac{d^2 e^{(a+b x)^2} (a+b x)^2}{3 \sqrt{\pi } b^3}+\frac{d^2 e^{(a+b x)^2}}{3 \sqrt{\pi } b^3}+\frac{(c+d x)^3 \text{erfi}(a+b x)}{3 d}",1,"(-2*E^(a + b*x)^2*((-1 + a^2)*d^2 - a*b*d*(3*c + d*x) + b^2*(3*c^2 + 3*c*d*x + d^2*x^2)) + Sqrt[Pi]*(3*b*c*d - 6*a^2*b*c*d + 2*a^3*d^2 + a*(6*b^2*c^2 - 3*d^2) + 2*b^3*x*(3*c^2 + 3*c*d*x + d^2*x^2))*Erfi[a + b*x])/(6*b^3*Sqrt[Pi])","A",1
223,1,78,115,0.0905514,"\int (c+d x) \text{erfi}(a+b x) \, dx","Integrate[(c + d*x)*Erfi[a + b*x],x]","\frac{\sqrt{\pi } \text{erfi}(a+b x) \left(-2 a^2 d+4 a b c+4 b^2 c x+2 b^2 d x^2+d\right)-2 e^{(a+b x)^2} (-a d+2 b c+b d x)}{4 \sqrt{\pi } b^2}","-\frac{(b c-a d)^2 \text{erfi}(a+b x)}{2 b^2 d}-\frac{e^{(a+b x)^2} (b c-a d)}{\sqrt{\pi } b^2}+\frac{d \text{erfi}(a+b x)}{4 b^2}-\frac{d e^{(a+b x)^2} (a+b x)}{2 \sqrt{\pi } b^2}+\frac{(c+d x)^2 \text{erfi}(a+b x)}{2 d}",1,"(-2*E^(a + b*x)^2*(2*b*c - a*d + b*d*x) + Sqrt[Pi]*(4*a*b*c + d - 2*a^2*d + 4*b^2*c*x + 2*b^2*d*x^2)*Erfi[a + b*x])/(4*b^2*Sqrt[Pi])","A",1
224,1,33,35,0.04698,"\int \text{erfi}(a+b x) \, dx","Integrate[Erfi[a + b*x],x]","\frac{(a+b x) \text{erfi}(a+b x)-\frac{e^{(a+b x)^2}}{\sqrt{\pi }}}{b}","\frac{(a+b x) \text{erfi}(a+b x)}{b}-\frac{e^{(a+b x)^2}}{\sqrt{\pi } b}",1,"(-(E^(a + b*x)^2/Sqrt[Pi]) + (a + b*x)*Erfi[a + b*x])/b","A",1
225,0,0,17,1.2647989,"\int \frac{\text{erfi}(a+b x)}{c+d x} \, dx","Integrate[Erfi[a + b*x]/(c + d*x),x]","\int \frac{\text{erfi}(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{erfi}(a+b x)}{c+d x},x\right)",0,"Integrate[Erfi[a + b*x]/(c + d*x), x]","A",-1
226,0,0,50,0.3568751,"\int \frac{\text{erfi}(a+b x)}{(c+d x)^2} \, dx","Integrate[Erfi[a + b*x]/(c + d*x)^2,x]","\int \frac{\text{erfi}(a+b x)}{(c+d x)^2} \, dx","\frac{2 b \text{Int}\left(\frac{e^{(a+b x)^2}}{c+d x},x\right)}{\sqrt{\pi } d}-\frac{\text{erfi}(a+b x)}{d (c+d x)}",0,"Integrate[Erfi[a + b*x]/(c + d*x)^2, x]","A",-1
227,0,0,102,0.6418144,"\int \frac{\text{erfi}(a+b x)}{(c+d x)^3} \, dx","Integrate[Erfi[a + b*x]/(c + d*x)^3,x]","\int \frac{\text{erfi}(a+b x)}{(c+d x)^3} \, dx","-\frac{2 b^2 (b c-a d) \text{Int}\left(\frac{e^{(a+b x)^2}}{c+d x},x\right)}{\sqrt{\pi } d^3}+\frac{b^2 \text{erfi}(a+b x)}{d^3}-\frac{b e^{(a+b x)^2}}{\sqrt{\pi } d^2 (c+d x)}-\frac{\text{erfi}(a+b x)}{2 d (c+d x)^2}",0,"Integrate[Erfi[a + b*x]/(c + d*x)^3, x]","A",-1
228,1,99,175,0.0492193,"\int x^5 \text{erfi}(b x)^2 \, dx","Integrate[x^5*Erfi[b*x]^2,x]","\frac{\pi  \left(8 b^6 x^6+15\right) \text{erfi}(b x)^2-4 \sqrt{\pi } b x e^{b^2 x^2} \left(4 b^4 x^4-10 b^2 x^2+15\right) \text{erfi}(b x)+4 e^{2 b^2 x^2} \left(2 b^4 x^4-7 b^2 x^2+11\right)}{48 \pi  b^6}","\frac{5 \text{erfi}(b x)^2}{16 b^6}-\frac{x^5 e^{b^2 x^2} \text{erfi}(b x)}{3 \sqrt{\pi } b}+\frac{x^4 e^{2 b^2 x^2}}{6 \pi  b^2}+\frac{11 e^{2 b^2 x^2}}{12 \pi  b^6}-\frac{5 x e^{b^2 x^2} \text{erfi}(b x)}{4 \sqrt{\pi } b^5}-\frac{7 x^2 e^{2 b^2 x^2}}{12 \pi  b^4}+\frac{5 x^3 e^{b^2 x^2} \text{erfi}(b x)}{6 \sqrt{\pi } b^3}+\frac{1}{6} x^6 \text{erfi}(b x)^2",1,"(4*E^(2*b^2*x^2)*(11 - 7*b^2*x^2 + 2*b^4*x^4) - 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(15 - 10*b^2*x^2 + 4*b^4*x^4)*Erfi[b*x] + Pi*(15 + 8*b^6*x^6)*Erfi[b*x]^2)/(48*b^6*Pi)","A",1
229,1,82,124,0.0321998,"\int x^3 \text{erfi}(b x)^2 \, dx","Integrate[x^3*Erfi[b*x]^2,x]","\frac{\pi  \left(4 b^4 x^4-3\right) \text{erfi}(b x)^2-4 \sqrt{\pi } b x e^{b^2 x^2} \left(2 b^2 x^2-3\right) \text{erfi}(b x)+4 e^{2 b^2 x^2} \left(b^2 x^2-2\right)}{16 \pi  b^4}","-\frac{3 \text{erfi}(b x)^2}{16 b^4}-\frac{x^3 e^{b^2 x^2} \text{erfi}(b x)}{2 \sqrt{\pi } b}+\frac{x^2 e^{2 b^2 x^2}}{4 \pi  b^2}-\frac{e^{2 b^2 x^2}}{2 \pi  b^4}+\frac{3 x e^{b^2 x^2} \text{erfi}(b x)}{4 \sqrt{\pi } b^3}+\frac{1}{4} x^4 \text{erfi}(b x)^2",1,"(4*E^(2*b^2*x^2)*(-2 + b^2*x^2) - 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(-3 + 2*b^2*x^2)*Erfi[b*x] + Pi*(-3 + 4*b^4*x^4)*Erfi[b*x]^2)/(16*b^4*Pi)","A",1
230,1,63,71,0.0206207,"\int x \text{erfi}(b x)^2 \, dx","Integrate[x*Erfi[b*x]^2,x]","\frac{\left(2 \pi  b^2 x^2+\pi \right) \text{erfi}(b x)^2-4 \sqrt{\pi } b x e^{b^2 x^2} \text{erfi}(b x)+2 e^{2 b^2 x^2}}{4 \pi  b^2}","-\frac{x e^{b^2 x^2} \text{erfi}(b x)}{\sqrt{\pi } b}+\frac{\text{erfi}(b x)^2}{4 b^2}+\frac{e^{2 b^2 x^2}}{2 \pi  b^2}+\frac{1}{2} x^2 \text{erfi}(b x)^2",1,"(2*E^(2*b^2*x^2) - 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*Erfi[b*x] + (Pi + 2*b^2*Pi*x^2)*Erfi[b*x]^2)/(4*b^2*Pi)","A",1
231,0,0,13,0.0335142,"\int \frac{\text{erfi}(b x)^2}{x} \, dx","Integrate[Erfi[b*x]^2/x,x]","\int \frac{\text{erfi}(b x)^2}{x} \, dx","\text{Int}\left(\frac{\text{erfi}(b x)^2}{x},x\right)",0,"Integrate[Erfi[b*x]^2/x, x]","A",-1
232,1,60,65,0.0320673,"\int \frac{\text{erfi}(b x)^2}{x^3} \, dx","Integrate[Erfi[b*x]^2/x^3,x]","-\frac{2 b e^{b^2 x^2} \text{erfi}(b x)}{\sqrt{\pi } x}+\left(b^2-\frac{1}{2 x^2}\right) \text{erfi}(b x)^2+\frac{2 b^2 \text{Ei}\left(2 b^2 x^2\right)}{\pi }","-\frac{2 b e^{b^2 x^2} \text{erfi}(b x)}{\sqrt{\pi } x}+b^2 \text{erfi}(b x)^2+\frac{2 b^2 \text{Ei}\left(2 b^2 x^2\right)}{\pi }-\frac{\text{erfi}(b x)^2}{2 x^2}",1,"(-2*b*E^(b^2*x^2)*Erfi[b*x])/(Sqrt[Pi]*x) + (b^2 - 1/(2*x^2))*Erfi[b*x]^2 + (2*b^2*ExpIntegralEi[2*b^2*x^2])/Pi","A",1
233,1,97,123,0.0364573,"\int \frac{\text{erfi}(b x)^2}{x^5} \, dx","Integrate[Erfi[b*x]^2/x^5,x]","\frac{\pi  \left(4 b^4 x^4-3\right) \text{erfi}(b x)^2-4 \sqrt{\pi } b x e^{b^2 x^2} \left(2 b^2 x^2+1\right) \text{erfi}(b x)-4 b^2 x^2 \left(e^{2 b^2 x^2}-4 b^2 x^2 \text{Ei}\left(2 b^2 x^2\right)\right)}{12 \pi  x^4}","\frac{1}{3} b^4 \text{erfi}(b x)^2-\frac{b e^{b^2 x^2} \text{erfi}(b x)}{3 \sqrt{\pi } x^3}-\frac{b^2 e^{2 b^2 x^2}}{3 \pi  x^2}+\frac{4 b^4 \text{Ei}\left(2 b^2 x^2\right)}{3 \pi }-\frac{2 b^3 e^{b^2 x^2} \text{erfi}(b x)}{3 \sqrt{\pi } x}-\frac{\text{erfi}(b x)^2}{4 x^4}",1,"(-4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(1 + 2*b^2*x^2)*Erfi[b*x] + Pi*(-3 + 4*b^4*x^4)*Erfi[b*x]^2 - 4*b^2*x^2*(E^(2*b^2*x^2) - 4*b^2*x^2*ExpIntegralEi[2*b^2*x^2]))/(12*Pi*x^4)","A",1
234,1,114,174,0.0432808,"\int \frac{\text{erfi}(b x)^2}{x^7} \, dx","Integrate[Erfi[b*x]^2/x^7,x]","\frac{\pi  \left(8 b^6 x^6-15\right) \text{erfi}(b x)^2-2 b^2 x^2 e^{2 b^2 x^2} \left(10 b^2 x^2+3\right)+56 b^6 x^6 \text{Ei}\left(2 b^2 x^2\right)-4 \sqrt{\pi } b x e^{b^2 x^2} \left(4 b^4 x^4+2 b^2 x^2+3\right) \text{erfi}(b x)}{90 \pi  x^6}","\frac{4}{45} b^6 \text{erfi}(b x)^2-\frac{2 b e^{b^2 x^2} \text{erfi}(b x)}{15 \sqrt{\pi } x^5}-\frac{b^2 e^{2 b^2 x^2}}{15 \pi  x^4}+\frac{28 b^6 \text{Ei}\left(2 b^2 x^2\right)}{45 \pi }-\frac{8 b^5 e^{b^2 x^2} \text{erfi}(b x)}{45 \sqrt{\pi } x}-\frac{2 b^4 e^{2 b^2 x^2}}{9 \pi  x^2}-\frac{4 b^3 e^{b^2 x^2} \text{erfi}(b x)}{45 \sqrt{\pi } x^3}-\frac{\text{erfi}(b x)^2}{6 x^6}",1,"(-2*b^2*E^(2*b^2*x^2)*x^2*(3 + 10*b^2*x^2) - 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(3 + 2*b^2*x^2 + 4*b^4*x^4)*Erfi[b*x] + Pi*(-15 + 8*b^6*x^6)*Erfi[b*x]^2 + 56*b^6*x^6*ExpIntegralEi[2*b^2*x^2])/(90*Pi*x^6)","A",1
235,1,105,162,0.0506655,"\int x^4 \text{erfi}(b x)^2 \, dx","Integrate[x^4*Erfi[b*x]^2,x]","\frac{16 \pi  b^5 x^5 \text{erfi}(b x)^2+4 b x e^{2 b^2 x^2} \left(4 b^2 x^2-11\right)-32 \sqrt{\pi } e^{b^2 x^2} \left(b^4 x^4-2 b^2 x^2+2\right) \text{erfi}(b x)+43 \sqrt{2 \pi } \text{erfi}\left(\sqrt{2} b x\right)}{80 \pi  b^5}","\frac{43 \text{erfi}\left(\sqrt{2} b x\right)}{40 \sqrt{2 \pi } b^5}-\frac{2 x^4 e^{b^2 x^2} \text{erfi}(b x)}{5 \sqrt{\pi } b}+\frac{x^3 e^{2 b^2 x^2}}{5 \pi  b^2}-\frac{4 e^{b^2 x^2} \text{erfi}(b x)}{5 \sqrt{\pi } b^5}-\frac{11 x e^{2 b^2 x^2}}{20 \pi  b^4}+\frac{4 x^2 e^{b^2 x^2} \text{erfi}(b x)}{5 \sqrt{\pi } b^3}+\frac{1}{5} x^5 \text{erfi}(b x)^2",1,"(4*b*E^(2*b^2*x^2)*x*(-11 + 4*b^2*x^2) - 32*E^(b^2*x^2)*Sqrt[Pi]*(2 - 2*b^2*x^2 + b^4*x^4)*Erfi[b*x] + 16*b^5*Pi*x^5*Erfi[b*x]^2 + 43*Sqrt[2*Pi]*Erfi[Sqrt[2]*b*x])/(80*b^5*Pi)","A",1
236,1,87,111,0.0315259,"\int x^2 \text{erfi}(b x)^2 \, dx","Integrate[x^2*Erfi[b*x]^2,x]","\frac{4 \pi  b^3 x^3 \text{erfi}(b x)^2-8 \sqrt{\pi } e^{b^2 x^2} \left(b^2 x^2-1\right) \text{erfi}(b x)+4 b x e^{2 b^2 x^2}-5 \sqrt{2 \pi } \text{erfi}\left(\sqrt{2} b x\right)}{12 \pi  b^3}","-\frac{5 \text{erfi}\left(\sqrt{2} b x\right)}{6 \sqrt{2 \pi } b^3}-\frac{2 x^2 e^{b^2 x^2} \text{erfi}(b x)}{3 \sqrt{\pi } b}+\frac{x e^{2 b^2 x^2}}{3 \pi  b^2}+\frac{2 e^{b^2 x^2} \text{erfi}(b x)}{3 \sqrt{\pi } b^3}+\frac{1}{3} x^3 \text{erfi}(b x)^2",1,"(4*b*E^(2*b^2*x^2)*x - 8*E^(b^2*x^2)*Sqrt[Pi]*(-1 + b^2*x^2)*Erfi[b*x] + 4*b^3*Pi*x^3*Erfi[b*x]^2 - 5*Sqrt[2*Pi]*Erfi[Sqrt[2]*b*x])/(12*b^3*Pi)","A",1
237,1,54,54,0.0213553,"\int \text{erfi}(b x)^2 \, dx","Integrate[Erfi[b*x]^2,x]","-\frac{2 e^{b^2 x^2} \text{erfi}(b x)}{\sqrt{\pi } b}+x \text{erfi}(b x)^2+\frac{\sqrt{\frac{2}{\pi }} \text{erfi}\left(\sqrt{2} b x\right)}{b}","-\frac{2 e^{b^2 x^2} \text{erfi}(b x)}{\sqrt{\pi } b}+x \text{erfi}(b x)^2+\frac{\sqrt{\frac{2}{\pi }} \text{erfi}\left(\sqrt{2} b x\right)}{b}",1,"(-2*E^(b^2*x^2)*Erfi[b*x])/(b*Sqrt[Pi]) + x*Erfi[b*x]^2 + (Sqrt[2/Pi]*Erfi[Sqrt[2]*b*x])/b","A",1
238,0,0,13,0.0381902,"\int \frac{\text{erfi}(b x)^2}{x^2} \, dx","Integrate[Erfi[b*x]^2/x^2,x]","\int \frac{\text{erfi}(b x)^2}{x^2} \, dx","\text{Int}\left(\frac{\text{erfi}(b x)^2}{x^2},x\right)",0,"Integrate[Erfi[b*x]^2/x^2, x]","A",-1
239,0,0,13,0.0394647,"\int \frac{\text{erfi}(b x)^2}{x^4} \, dx","Integrate[Erfi[b*x]^2/x^4,x]","\int \frac{\text{erfi}(b x)^2}{x^4} \, dx","\text{Int}\left(\frac{\text{erfi}(b x)^2}{x^4},x\right)",0,"Integrate[Erfi[b*x]^2/x^4, x]","A",-1
240,0,0,13,0.039661,"\int \frac{\text{erfi}(b x)^2}{x^6} \, dx","Integrate[Erfi[b*x]^2/x^6,x]","\int \frac{\text{erfi}(b x)^2}{x^6} \, dx","\text{Int}\left(\frac{\text{erfi}(b x)^2}{x^6},x\right)",0,"Integrate[Erfi[b*x]^2/x^6, x]","A",-1
241,0,0,366,0.8613185,"\int (c+d x)^2 \text{erfi}(a+b x)^2 \, dx","Integrate[(c + d*x)^2*Erfi[a + b*x]^2,x]","\int (c+d x)^2 \text{erfi}(a+b x)^2 \, dx","\frac{d (a+b x)^2 (b c-a d) \text{erfi}(a+b x)^2}{b^3}+\frac{(a+b x) (b c-a d)^2 \text{erfi}(a+b x)^2}{b^3}-\frac{2 d e^{(a+b x)^2} (a+b x) (b c-a d) \text{erfi}(a+b x)}{\sqrt{\pi } b^3}+\frac{d (b c-a d) \text{erfi}(a+b x)^2}{2 b^3}-\frac{2 e^{(a+b x)^2} (b c-a d)^2 \text{erfi}(a+b x)}{\sqrt{\pi } b^3}+\frac{\sqrt{\frac{2}{\pi }} (b c-a d)^2 \text{erfi}\left(\sqrt{2} (a+b x)\right)}{b^3}+\frac{d e^{2 (a+b x)^2} (b c-a d)}{\pi  b^3}+\frac{d^2 (a+b x)^3 \text{erfi}(a+b x)^2}{3 b^3}-\frac{2 d^2 e^{(a+b x)^2} (a+b x)^2 \text{erfi}(a+b x)}{3 \sqrt{\pi } b^3}+\frac{2 d^2 e^{(a+b x)^2} \text{erfi}(a+b x)}{3 \sqrt{\pi } b^3}-\frac{5 d^2 \text{erfi}\left(\sqrt{2} (a+b x)\right)}{6 \sqrt{2 \pi } b^3}+\frac{d^2 e^{2 (a+b x)^2} (a+b x)}{3 \pi  b^3}",1,"Integrate[(c + d*x)^2*Erfi[a + b*x]^2, x]","F",-1
242,1,128,184,0.1819401,"\int (c+d x) \text{erfi}(a+b x)^2 \, dx","Integrate[(c + d*x)*Erfi[a + b*x]^2,x]","\frac{\pi  \text{erfi}(a+b x)^2 \left(-2 a^2 d+4 a b c+4 b^2 c x+2 b^2 d x^2+d\right)-4 \sqrt{\pi } e^{(a+b x)^2} \text{erfi}(a+b x) (-a d+2 b c+b d x)+4 \sqrt{2 \pi } (b c-a d) \text{erfi}\left(\sqrt{2} (a+b x)\right)+2 d e^{2 (a+b x)^2}}{4 \pi  b^2}","\frac{(a+b x) (b c-a d) \text{erfi}(a+b x)^2}{b^2}-\frac{2 e^{(a+b x)^2} (b c-a d) \text{erfi}(a+b x)}{\sqrt{\pi } b^2}+\frac{\sqrt{\frac{2}{\pi }} (b c-a d) \text{erfi}\left(\sqrt{2} (a+b x)\right)}{b^2}+\frac{d (a+b x)^2 \text{erfi}(a+b x)^2}{2 b^2}+\frac{d \text{erfi}(a+b x)^2}{4 b^2}-\frac{d e^{(a+b x)^2} (a+b x) \text{erfi}(a+b x)}{\sqrt{\pi } b^2}+\frac{d e^{2 (a+b x)^2}}{2 \pi  b^2}",1,"(2*d*E^(2*(a + b*x)^2) - 4*E^(a + b*x)^2*Sqrt[Pi]*(2*b*c - a*d + b*d*x)*Erfi[a + b*x] + Pi*(4*a*b*c + d - 2*a^2*d + 4*b^2*c*x + 2*b^2*d*x^2)*Erfi[a + b*x]^2 + 4*(b*c - a*d)*Sqrt[2*Pi]*Erfi[Sqrt[2]*(a + b*x)])/(4*b^2*Pi)","A",1
243,1,64,68,0.056823,"\int \text{erfi}(a+b x)^2 \, dx","Integrate[Erfi[a + b*x]^2,x]","\frac{\sqrt{\pi } (a+b x) \text{erfi}(a+b x)^2-2 e^{(a+b x)^2} \text{erfi}(a+b x)+\sqrt{2} \text{erfi}\left(\sqrt{2} (a+b x)\right)}{\sqrt{\pi } b}","\frac{(a+b x) \text{erfi}(a+b x)^2}{b}-\frac{2 e^{(a+b x)^2} \text{erfi}(a+b x)}{\sqrt{\pi } b}+\frac{\sqrt{\frac{2}{\pi }} \text{erfi}\left(\sqrt{2} (a+b x)\right)}{b}",1,"(-2*E^(a + b*x)^2*Erfi[a + b*x] + Sqrt[Pi]*(a + b*x)*Erfi[a + b*x]^2 + Sqrt[2]*Erfi[Sqrt[2]*(a + b*x)])/(b*Sqrt[Pi])","A",1
244,0,0,19,0.0642102,"\int \frac{\text{erfi}(a+b x)^2}{c+d x} \, dx","Integrate[Erfi[a + b*x]^2/(c + d*x),x]","\int \frac{\text{erfi}(a+b x)^2}{c+d x} \, dx","\text{Int}\left(\frac{\text{erfi}(a+b x)^2}{c+d x},x\right)",0,"Integrate[Erfi[a + b*x]^2/(c + d*x), x]","A",-1
245,0,0,19,0.116162,"\int \frac{\text{erfi}(a+b x)^2}{(c+d x)^2} \, dx","Integrate[Erfi[a + b*x]^2/(c + d*x)^2,x]","\int \frac{\text{erfi}(a+b x)^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{erfi}(a+b x)^2}{(c+d x)^2},x\right)",0,"Integrate[Erfi[a + b*x]^2/(c + d*x)^2, x]","A",-1
246,1,90,102,0.3633984,"\int x^2 \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^2*Erfi[d*(a + b*Log[c*x^n])],x]","\frac{1}{3} \left(x^3 \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-x^3 \left(c x^n\right)^{-3/n} e^{-\frac{3 \left(4 a b d^2 n+3\right)}{4 b^2 d^2 n^2}} \text{erfi}\left(a d+b d \log \left(c x^n\right)+\frac{3}{2 b d n}\right)\right)","\frac{1}{3} x^3 \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-\frac{1}{3} x^3 \left(c x^n\right)^{-3/n} e^{-\frac{3 \left(4 a b d^2 n+3\right)}{4 b^2 d^2 n^2}} \text{erfi}\left(\frac{2 a b d^2+2 b^2 d^2 \log \left(c x^n\right)+\frac{3}{n}}{2 b d}\right)",1,"(x^3*Erfi[d*(a + b*Log[c*x^n])] - (x^3*Erfi[a*d + 3/(2*b*d*n) + b*d*Log[c*x^n]])/(E^((3*(3 + 4*a*b*d^2*n))/(4*b^2*d^2*n^2))*(c*x^n)^(3/n)))/3","A",1
247,1,81,93,0.3588761,"\int x \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x*Erfi[d*(a + b*Log[c*x^n])],x]","\frac{1}{2} \left(x^2 \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-x^2 e^{-\frac{\frac{2 a b n+\frac{1}{d^2}}{b^2}+2 n \log \left(c x^n\right)}{n^2}} \text{erfi}\left(a d+b d \log \left(c x^n\right)+\frac{1}{b d n}\right)\right)","\frac{1}{2} x^2 \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-\frac{1}{2} x^2 \left(c x^n\right)^{-2/n} e^{-\frac{2 a b d^2 n+1}{b^2 d^2 n^2}} \text{erfi}\left(\frac{a b d^2+b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}}{b d}\right)",1,"(x^2*Erfi[d*(a + b*Log[c*x^n])] - (x^2*Erfi[a*d + 1/(b*d*n) + b*d*Log[c*x^n]])/E^(((d^(-2) + 2*a*b*n)/b^2 + 2*n*Log[c*x^n])/n^2))/2","A",1
248,1,78,91,0.3593916,"\int \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[Erfi[d*(a + b*Log[c*x^n])],x]","x \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-x \text{erfi}\left(a d+b d \log \left(c x^n\right)+\frac{1}{2 b d n}\right) \exp \left(-\frac{\frac{4 a b n+\frac{1}{d^2}}{b^2}+4 n \log \left(c x^n\right)}{4 n^2}\right)","x \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-x \left(c x^n\right)^{-1/n} e^{-\frac{4 a b d^2 n+1}{4 b^2 d^2 n^2}} \text{erfi}\left(\frac{2 a b d^2+2 b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}}{2 b d}\right)",1,"x*Erfi[d*(a + b*Log[c*x^n])] - (x*Erfi[a*d + 1/(2*b*d*n) + b*d*Log[c*x^n]])/E^(((d^(-2) + 4*a*b*n)/b^2 + 4*n*Log[c*x^n])/(4*n^2))","A",1
249,1,83,64,0.1294504,"\int \frac{\text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Integrate[Erfi[d*(a + b*Log[c*x^n])]/x,x]","\frac{\sqrt{\pi } d \left(a+b \log \left(c x^n\right)\right) \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-\left(c x^n\right)^{2 a b d^2} e^{d^2 \left(a^2+b^2 \log ^2\left(c x^n\right)\right)}}{\sqrt{\pi } b d n}","\frac{\left(a+b \log \left(c x^n\right)\right) \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{e^{\left(a d+b d \log \left(c x^n\right)\right)^2}}{\sqrt{\pi } b d n}",1,"(-(E^(d^2*(a^2 + b^2*Log[c*x^n]^2))*(c*x^n)^(2*a*b*d^2)) + d*Sqrt[Pi]*Erfi[d*(a + b*Log[c*x^n])]*(a + b*Log[c*x^n]))/(b*d*n*Sqrt[Pi])","A",1
250,1,82,94,0.3111843,"\int \frac{\text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Integrate[Erfi[d*(a + b*Log[c*x^n])]/x^2,x]","\frac{\left(c x^n\right)^{\frac{1}{n}} e^{\frac{4 a b d^2 n-1}{4 b^2 d^2 n^2}} \text{erfi}\left(a d+b d \log \left(c x^n\right)-\frac{1}{2 b d n}\right)-\text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x}","\frac{\left(c x^n\right)^{\frac{1}{n}} e^{\frac{a}{b n}-\frac{1}{4 b^2 d^2 n^2}} \text{erfi}\left(\frac{2 a b d^2+2 b^2 d^2 \log \left(c x^n\right)-\frac{1}{n}}{2 b d}\right)}{x}-\frac{\text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x}",1,"(-Erfi[d*(a + b*Log[c*x^n])] + E^((-1 + 4*a*b*d^2*n)/(4*b^2*d^2*n^2))*(c*x^n)^n^(-1)*Erfi[a*d - 1/(2*b*d*n) + b*d*Log[c*x^n]])/x","A",1
251,1,80,95,0.2993359,"\int \frac{\text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Integrate[Erfi[d*(a + b*Log[c*x^n])]/x^3,x]","\frac{e^{\frac{\frac{2 a b n-\frac{1}{d^2}}{b^2}+2 n \log \left(c x^n\right)}{n^2}} \text{erfi}\left(a d+b d \log \left(c x^n\right)-\frac{1}{b d n}\right)-\text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}","\frac{\left(c x^n\right)^{2/n} e^{-\frac{1-2 a b d^2 n}{b^2 d^2 n^2}} \text{erfi}\left(\frac{a b d^2+b^2 d^2 \log \left(c x^n\right)-\frac{1}{n}}{b d}\right)}{2 x^2}-\frac{\text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}",1,"(-Erfi[d*(a + b*Log[c*x^n])] + E^(((-d^(-2) + 2*a*b*n)/b^2 + 2*n*Log[c*x^n])/n^2)*Erfi[a*d - 1/(b*d*n) + b*d*Log[c*x^n]])/(2*x^2)","A",1
252,1,126,126,0.535692,"\int (e x)^m \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Erfi[d*(a + b*Log[c*x^n])],x]","\frac{(e x)^m \left(x \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)-x^{-m} \text{erfi}\left(\frac{2 a b d^2 n+m+1}{2 b d n}+b d \log \left(c x^n\right)\right) \exp \left(-\frac{(m+1) \left(4 a b d^2 n+4 b^2 d^2 n \log \left(c x^n\right)-4 b^2 d^2 n^2 \log (x)+m+1\right)}{4 b^2 d^2 n^2}\right)\right)}{m+1}","\frac{(e x)^{m+1} \text{erfi}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (m+1)}-\frac{x (e x)^m \left(c x^n\right)^{-\frac{m+1}{n}} \exp \left(-\frac{(m+1) \left(4 a b d^2 n+m+1\right)}{4 b^2 d^2 n^2}\right) \text{erfi}\left(\frac{2 a b d^2 n+2 b^2 d^2 n \log \left(c x^n\right)+m+1}{2 b d n}\right)}{m+1}",1,"((e*x)^m*(x*Erfi[d*(a + b*Log[c*x^n])] - Erfi[(1 + m + 2*a*b*d^2*n)/(2*b*d*n) + b*d*Log[c*x^n]]/(E^(((1 + m)*(1 + m + 4*a*b*d^2*n - 4*b^2*d^2*n^2*Log[x] + 4*b^2*d^2*n*Log[c*x^n]))/(4*b^2*d^2*n^2))*x^m)))/(1 + m)","A",1
253,1,21,21,0.0071594,"\int e^{c+b^2 x^2} \text{erfi}(b x)^2 \, dx","Integrate[E^(c + b^2*x^2)*Erfi[b*x]^2,x]","\frac{\sqrt{\pi } e^c \text{erfi}(b x)^3}{6 b}","\frac{\sqrt{\pi } e^c \text{erfi}(b x)^3}{6 b}",1,"(E^c*Sqrt[Pi]*Erfi[b*x]^3)/(6*b)","A",1
254,1,21,21,0.0063272,"\int e^{c+b^2 x^2} \text{erfi}(b x) \, dx","Integrate[E^(c + b^2*x^2)*Erfi[b*x],x]","\frac{\sqrt{\pi } e^c \text{erfi}(b x)^2}{4 b}","\frac{\sqrt{\pi } e^c \text{erfi}(b x)^2}{4 b}",1,"(E^c*Sqrt[Pi]*Erfi[b*x]^2)/(4*b)","A",1
255,1,20,20,0.0118394,"\int \frac{e^{c+b^2 x^2}}{\text{erfi}(b x)} \, dx","Integrate[E^(c + b^2*x^2)/Erfi[b*x],x]","\frac{\sqrt{\pi } e^c \log (\text{erfi}(b x))}{2 b}","\frac{\sqrt{\pi } e^c \log (\text{erfi}(b x))}{2 b}",1,"(E^c*Sqrt[Pi]*Log[Erfi[b*x]])/(2*b)","A",1
256,1,21,21,0.0067902,"\int \frac{e^{c+b^2 x^2}}{\text{erfi}(b x)^2} \, dx","Integrate[E^(c + b^2*x^2)/Erfi[b*x]^2,x]","-\frac{\sqrt{\pi } e^c}{2 b \text{erfi}(b x)}","-\frac{\sqrt{\pi } e^c}{2 b \text{erfi}(b x)}",1,"-1/2*(E^c*Sqrt[Pi])/(b*Erfi[b*x])","A",1
257,1,21,21,0.0058069,"\int \frac{e^{c+b^2 x^2}}{\text{erfi}(b x)^3} \, dx","Integrate[E^(c + b^2*x^2)/Erfi[b*x]^3,x]","-\frac{\sqrt{\pi } e^c}{4 b \text{erfi}(b x)^2}","-\frac{\sqrt{\pi } e^c}{4 b \text{erfi}(b x)^2}",1,"-1/4*(E^c*Sqrt[Pi])/(b*Erfi[b*x]^2)","A",1
258,1,28,28,0.0166705,"\int e^{c+b^2 x^2} \text{erfi}(b x)^n \, dx","Integrate[E^(c + b^2*x^2)*Erfi[b*x]^n,x]","\frac{\sqrt{\pi } e^c \text{erfi}(b x)^{n+1}}{2 b (n+1)}","\frac{\sqrt{\pi } e^c \text{erfi}(b x)^{n+1}}{2 b (n+1)}",1,"(E^c*Sqrt[Pi]*Erfi[b*x]^(1 + n))/(2*b*(1 + n))","A",1
259,1,131,257,0.3417123,"\int e^{c+d x^2} x^5 \text{erfi}(b x) \, dx","Integrate[E^(c + d*x^2)*x^5*Erfi[b*x],x]","\frac{e^c \left(-\frac{2 b d x e^{x^2 \left(b^2+d\right)} \left(2 b^2 \left(d x^2-2\right)+d \left(2 d x^2-7\right)\right)}{\sqrt{\pi } \left(b^2+d\right)^2}-\frac{b \left(8 b^4+20 b^2 d+15 d^2\right) \text{erfi}\left(x \sqrt{b^2+d}\right)}{\left(b^2+d\right)^{5/2}}+4 e^{d x^2} \left(d^2 x^4-2 d x^2+2\right) \text{erfi}(b x)\right)}{8 d^3}","-\frac{b e^c \text{erfi}\left(x \sqrt{b^2+d}\right)}{d^3 \sqrt{b^2+d}}-\frac{b e^c \text{erfi}\left(x \sqrt{b^2+d}\right)}{2 d^2 \left(b^2+d\right)^{3/2}}+\frac{b x e^{x^2 \left(b^2+d\right)+c}}{\sqrt{\pi } d^2 \left(b^2+d\right)}-\frac{3 b e^c \text{erfi}\left(x \sqrt{b^2+d}\right)}{8 d \left(b^2+d\right)^{5/2}}+\frac{3 b x e^{x^2 \left(b^2+d\right)+c}}{4 \sqrt{\pi } d \left(b^2+d\right)^2}-\frac{b x^3 e^{x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)}+\frac{\text{erfi}(b x) e^{c+d x^2}}{d^3}-\frac{x^2 \text{erfi}(b x) e^{c+d x^2}}{d^2}+\frac{x^4 \text{erfi}(b x) e^{c+d x^2}}{2 d}",1,"(E^c*((-2*b*d*E^((b^2 + d)*x^2)*x*(2*b^2*(-2 + d*x^2) + d*(-7 + 2*d*x^2)))/((b^2 + d)^2*Sqrt[Pi]) + 4*E^(d*x^2)*(2 - 2*d*x^2 + d^2*x^4)*Erfi[b*x] - (b*(8*b^4 + 20*b^2*d + 15*d^2)*Erfi[Sqrt[b^2 + d]*x])/(b^2 + d)^(5/2)))/(8*d^3)","A",1
260,1,91,142,0.2201018,"\int e^{c+d x^2} x^3 \text{erfi}(b x) \, dx","Integrate[E^(c + d*x^2)*x^3*Erfi[b*x],x]","\frac{e^c \left(-\frac{2 b d x e^{x^2 \left(b^2+d\right)}}{\sqrt{\pi } \left(b^2+d\right)}+\frac{\left(2 b^3+3 b d\right) \text{erfi}\left(x \sqrt{b^2+d}\right)}{\left(b^2+d\right)^{3/2}}+2 e^{d x^2} \left(d x^2-1\right) \text{erfi}(b x)\right)}{4 d^2}","\frac{b e^c \text{erfi}\left(x \sqrt{b^2+d}\right)}{2 d^2 \sqrt{b^2+d}}+\frac{b e^c \text{erfi}\left(x \sqrt{b^2+d}\right)}{4 d \left(b^2+d\right)^{3/2}}-\frac{b x e^{x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)}-\frac{\text{erfi}(b x) e^{c+d x^2}}{2 d^2}+\frac{x^2 \text{erfi}(b x) e^{c+d x^2}}{2 d}",1,"(E^c*((-2*b*d*E^((b^2 + d)*x^2)*x)/((b^2 + d)*Sqrt[Pi]) + 2*E^(d*x^2)*(-1 + d*x^2)*Erfi[b*x] + ((2*b^3 + 3*b*d)*Erfi[Sqrt[b^2 + d]*x])/(b^2 + d)^(3/2)))/(4*d^2)","A",1
261,1,47,53,0.0257929,"\int e^{c+d x^2} x \text{erfi}(b x) \, dx","Integrate[E^(c + d*x^2)*x*Erfi[b*x],x]","\frac{e^c \left(e^{d x^2} \text{erfi}(b x)-\frac{b \text{erfi}\left(x \sqrt{b^2+d}\right)}{\sqrt{b^2+d}}\right)}{2 d}","\frac{\text{erfi}(b x) e^{c+d x^2}}{2 d}-\frac{b e^c \text{erfi}\left(x \sqrt{b^2+d}\right)}{2 d \sqrt{b^2+d}}",1,"(E^c*(E^(d*x^2)*Erfi[b*x] - (b*Erfi[Sqrt[b^2 + d]*x])/Sqrt[b^2 + d]))/(2*d)","A",1
262,0,0,20,0.1495416,"\int \frac{e^{c+d x^2} \text{erfi}(b x)}{x} \, dx","Integrate[(E^(c + d*x^2)*Erfi[b*x])/x,x]","\int \frac{e^{c+d x^2} \text{erfi}(b x)}{x} \, dx","\text{Int}\left(\frac{\text{erfi}(b x) e^{c+d x^2}}{x},x\right)",0,"Integrate[(E^(c + d*x^2)*Erfi[b*x])/x, x]","A",-1
263,0,0,93,0.2491392,"\int \frac{e^{c+d x^2} \text{erfi}(b x)}{x^3} \, dx","Integrate[(E^(c + d*x^2)*Erfi[b*x])/x^3,x]","\int \frac{e^{c+d x^2} \text{erfi}(b x)}{x^3} \, dx","d \text{Int}\left(\frac{\text{erfi}(b x) e^{c+d x^2}}{x},x\right)+b e^c \sqrt{b^2+d} \text{erfi}\left(x \sqrt{b^2+d}\right)-\frac{b e^{x^2 \left(b^2+d\right)+c}}{\sqrt{\pi } x}-\frac{\text{erfi}(b x) e^{c+d x^2}}{2 x^2}",0,"Integrate[(E^(c + d*x^2)*Erfi[b*x])/x^3, x]","A",-1
264,0,0,212,0.3034865,"\int \frac{e^{c+d x^2} \text{erfi}(b x)}{x^5} \, dx","Integrate[(E^(c + d*x^2)*Erfi[b*x])/x^5,x]","\int \frac{e^{c+d x^2} \text{erfi}(b x)}{x^5} \, dx","\frac{1}{2} d^2 \text{Int}\left(\frac{\text{erfi}(b x) e^{c+d x^2}}{x},x\right)+\frac{1}{2} b e^c d \sqrt{b^2+d} \text{erfi}\left(x \sqrt{b^2+d}\right)+\frac{1}{3} b e^c \left(b^2+d\right)^{3/2} \text{erfi}\left(x \sqrt{b^2+d}\right)-\frac{b d e^{x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } x}-\frac{b \left(b^2+d\right) e^{x^2 \left(b^2+d\right)+c}}{3 \sqrt{\pi } x}-\frac{b e^{x^2 \left(b^2+d\right)+c}}{6 \sqrt{\pi } x^3}-\frac{d \text{erfi}(b x) e^{c+d x^2}}{4 x^2}-\frac{\text{erfi}(b x) e^{c+d x^2}}{4 x^4}",0,"Integrate[(E^(c + d*x^2)*Erfi[b*x])/x^5, x]","A",-1
265,0,0,171,0.2819179,"\int e^{c+d x^2} x^4 \text{erfi}(b x) \, dx","Integrate[E^(c + d*x^2)*x^4*Erfi[b*x],x]","\int e^{c+d x^2} x^4 \text{erfi}(b x) \, dx","\frac{3 \text{Int}\left(\text{erfi}(b x) e^{c+d x^2},x\right)}{4 d^2}+\frac{3 b e^{x^2 \left(b^2+d\right)+c}}{4 \sqrt{\pi } d^2 \left(b^2+d\right)}-\frac{b x^2 e^{x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)}+\frac{b e^{x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)^2}-\frac{3 x \text{erfi}(b x) e^{c+d x^2}}{4 d^2}+\frac{x^3 \text{erfi}(b x) e^{c+d x^2}}{2 d}",0,"Integrate[E^(c + d*x^2)*x^4*Erfi[b*x], x]","A",-1
266,0,0,79,0.2158923,"\int e^{c+d x^2} x^2 \text{erfi}(b x) \, dx","Integrate[E^(c + d*x^2)*x^2*Erfi[b*x],x]","\int e^{c+d x^2} x^2 \text{erfi}(b x) \, dx","-\frac{\text{Int}\left(\text{erfi}(b x) e^{c+d x^2},x\right)}{2 d}-\frac{b e^{x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)}+\frac{x \text{erfi}(b x) e^{c+d x^2}}{2 d}",0,"Integrate[E^(c + d*x^2)*x^2*Erfi[b*x], x]","A",-1
267,0,0,17,0.0366564,"\int e^{c+d x^2} \text{erfi}(b x) \, dx","Integrate[E^(c + d*x^2)*Erfi[b*x],x]","\int e^{c+d x^2} \text{erfi}(b x) \, dx","\text{Int}\left(\text{erfi}(b x) e^{c+d x^2},x\right)",0,"Integrate[E^(c + d*x^2)*Erfi[b*x], x]","A",-1
268,0,0,59,0.20811,"\int \frac{e^{c+d x^2} \text{erfi}(b x)}{x^2} \, dx","Integrate[(E^(c + d*x^2)*Erfi[b*x])/x^2,x]","\int \frac{e^{c+d x^2} \text{erfi}(b x)}{x^2} \, dx","2 d \text{Int}\left(\text{erfi}(b x) e^{c+d x^2},x\right)+\frac{b e^c \text{Ei}\left(\left(b^2+d\right) x^2\right)}{\sqrt{\pi }}-\frac{\text{erfi}(b x) e^{c+d x^2}}{x}",0,"Integrate[(E^(c + d*x^2)*Erfi[b*x])/x^2, x]","A",-1
269,0,0,144,0.3212462,"\int \frac{e^{c+d x^2} \text{erfi}(b x)}{x^4} \, dx","Integrate[(E^(c + d*x^2)*Erfi[b*x])/x^4,x]","\int \frac{e^{c+d x^2} \text{erfi}(b x)}{x^4} \, dx","\frac{4}{3} d^2 \text{Int}\left(\text{erfi}(b x) e^{c+d x^2},x\right)+\frac{2 b e^c d \text{Ei}\left(\left(b^2+d\right) x^2\right)}{3 \sqrt{\pi }}+\frac{b e^c \left(b^2+d\right) \text{Ei}\left(\left(b^2+d\right) x^2\right)}{3 \sqrt{\pi }}-\frac{b e^{x^2 \left(b^2+d\right)+c}}{3 \sqrt{\pi } x^2}-\frac{2 d \text{erfi}(b x) e^{c+d x^2}}{3 x}-\frac{\text{erfi}(b x) e^{c+d x^2}}{3 x^3}",0,"Integrate[(E^(c + d*x^2)*Erfi[b*x])/x^4, x]","A",-1
270,1,68,107,0.052319,"\int e^{-b^2 x^2} x^5 \text{erfi}(b x) \, dx","Integrate[(x^5*Erfi[b*x])/E^(b^2*x^2),x]","\frac{\frac{6 b^5 x^5+20 b^3 x^3+60 b x}{\sqrt{\pi }}-15 e^{-b^2 x^2} \left(b^4 x^4+2 b^2 x^2+2\right) \text{erfi}(b x)}{30 b^6}","\frac{2 x}{\sqrt{\pi } b^5}+\frac{2 x^3}{3 \sqrt{\pi } b^3}-\frac{x^4 e^{-b^2 x^2} \text{erfi}(b x)}{2 b^2}-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{b^6}-\frac{x^2 e^{-b^2 x^2} \text{erfi}(b x)}{b^4}+\frac{x^5}{5 \sqrt{\pi } b}",1,"((60*b*x + 20*b^3*x^3 + 6*b^5*x^5)/Sqrt[Pi] - (15*(2 + 2*b^2*x^2 + b^4*x^4)*Erfi[b*x])/E^(b^2*x^2))/(30*b^6)","A",1
271,1,51,71,0.0344674,"\int e^{-b^2 x^2} x^3 \text{erfi}(b x) \, dx","Integrate[(x^3*Erfi[b*x])/E^(b^2*x^2),x]","\frac{\frac{2 b x \left(b^2 x^2+3\right)}{\sqrt{\pi }}-3 e^{-b^2 x^2} \left(b^2 x^2+1\right) \text{erfi}(b x)}{6 b^4}","\frac{x}{\sqrt{\pi } b^3}-\frac{x^2 e^{-b^2 x^2} \text{erfi}(b x)}{2 b^2}-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{2 b^4}+\frac{x^3}{3 \sqrt{\pi } b}",1,"((2*b*x*(3 + b^2*x^2))/Sqrt[Pi] - (3*(1 + b^2*x^2)*Erfi[b*x])/E^(b^2*x^2))/(6*b^4)","A",1
272,1,32,32,0.0208026,"\int e^{-b^2 x^2} x \text{erfi}(b x) \, dx","Integrate[(x*Erfi[b*x])/E^(b^2*x^2),x]","\frac{x}{\sqrt{\pi } b}-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{2 b^2}","\frac{x}{\sqrt{\pi } b}-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{2 b^2}",1,"x/(b*Sqrt[Pi]) - Erfi[b*x]/(2*b^2*E^(b^2*x^2))","A",1
273,1,30,30,0.020823,"\int \frac{e^{-b^2 x^2} \text{erfi}(b x)}{x} \, dx","Integrate[Erfi[b*x]/(E^(b^2*x^2)*x),x]","\frac{2 b x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};-b^2 x^2\right)}{\sqrt{\pi }}","\frac{2 b x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};-b^2 x^2\right)}{\sqrt{\pi }}",1,"(2*b*x*HypergeometricPFQ[{1/2, 1}, {3/2, 3/2}, -(b^2*x^2)])/Sqrt[Pi]","A",1
274,1,32,65,0.0229846,"\int \frac{e^{-b^2 x^2} \text{erfi}(b x)}{x^3} \, dx","Integrate[Erfi[b*x]/(E^(b^2*x^2)*x^3),x]","-\frac{2 b \, _2F_2\left(-\frac{1}{2},1;\frac{1}{2},\frac{3}{2};-b^2 x^2\right)}{\sqrt{\pi } x}","-\frac{2 b^3 x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};-b^2 x^2\right)}{\sqrt{\pi }}-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{2 x^2}-\frac{b}{\sqrt{\pi } x}",1,"(-2*b*HypergeometricPFQ[{-1/2, 1}, {1/2, 3/2}, -(b^2*x^2)])/(Sqrt[Pi]*x)","A",1
275,1,34,105,0.0280699,"\int \frac{e^{-b^2 x^2} \text{erfi}(b x)}{x^5} \, dx","Integrate[Erfi[b*x]/(E^(b^2*x^2)*x^5),x]","-\frac{2 b \, _2F_2\left(-\frac{3}{2},1;-\frac{1}{2},\frac{3}{2};-b^2 x^2\right)}{3 \sqrt{\pi } x^3}","\frac{b^5 x \, _2F_2\left(\frac{1}{2},1;\frac{3}{2},\frac{3}{2};-b^2 x^2\right)}{\sqrt{\pi }}+\frac{b^3}{2 \sqrt{\pi } x}+\frac{b^2 e^{-b^2 x^2} \text{erfi}(b x)}{4 x^2}-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{4 x^4}-\frac{b}{6 \sqrt{\pi } x^3}",1,"(-2*b*HypergeometricPFQ[{-3/2, 1}, {-1/2, 3/2}, -(b^2*x^2)])/(3*Sqrt[Pi]*x^3)","A",1
276,1,52,148,0.0253643,"\int e^{-b^2 x^2} x^6 \text{erfi}(b x) \, dx","Integrate[(x^6*Erfi[b*x])/E^(b^2*x^2),x]","\frac{x^2 \left(-9 \, _2F_2\left(1,1;-\frac{3}{2},2;-b^2 x^2\right)+4 b^4 x^4+3 b^2 x^2+9\right)}{24 \sqrt{\pi } b^5}","\frac{15 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{8 \sqrt{\pi } b^5}+\frac{15 x^2}{8 \sqrt{\pi } b^5}+\frac{5 x^4}{8 \sqrt{\pi } b^3}-\frac{x^5 e^{-b^2 x^2} \text{erfi}(b x)}{2 b^2}-\frac{15 x e^{-b^2 x^2} \text{erfi}(b x)}{8 b^6}-\frac{5 x^3 e^{-b^2 x^2} \text{erfi}(b x)}{4 b^4}+\frac{x^6}{6 \sqrt{\pi } b}",1,"(x^2*(9 + 3*b^2*x^2 + 4*b^4*x^4 - 9*HypergeometricPFQ[{1, 1}, {-3/2, 2}, -(b^2*x^2)]))/(24*b^5*Sqrt[Pi])","A",0
277,1,43,109,0.0341278,"\int e^{-b^2 x^2} x^4 \text{erfi}(b x) \, dx","Integrate[(x^4*Erfi[b*x])/E^(b^2*x^2),x]","\frac{x^2 \left(-\, _2F_2\left(1,1;-\frac{1}{2},2;-b^2 x^2\right)+b^2 x^2+1\right)}{4 \sqrt{\pi } b^3}","\frac{3 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{4 \sqrt{\pi } b^3}+\frac{3 x^2}{4 \sqrt{\pi } b^3}-\frac{x^3 e^{-b^2 x^2} \text{erfi}(b x)}{2 b^2}-\frac{3 x e^{-b^2 x^2} \text{erfi}(b x)}{4 b^4}+\frac{x^4}{4 \sqrt{\pi } b}",1,"(x^2*(1 + b^2*x^2 - HypergeometricPFQ[{1, 1}, {-1/2, 2}, -(b^2*x^2)]))/(4*b^3*Sqrt[Pi])","A",0
278,1,36,70,0.0182722,"\int e^{-b^2 x^2} x^2 \text{erfi}(b x) \, dx","Integrate[(x^2*Erfi[b*x])/E^(b^2*x^2),x]","\frac{x^2 \left(1-\, _2F_2\left(1,1;\frac{1}{2},2;-b^2 x^2\right)\right)}{2 \sqrt{\pi } b}","\frac{x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{2 \sqrt{\pi } b}-\frac{x e^{-b^2 x^2} \text{erfi}(b x)}{2 b^2}+\frac{x^2}{2 \sqrt{\pi } b}",1,"(x^2*(1 - HypergeometricPFQ[{1, 1}, {1/2, 2}, -(b^2*x^2)]))/(2*b*Sqrt[Pi])","A",0
279,1,27,27,0.0103512,"\int e^{-b^2 x^2} \text{erfi}(b x) \, dx","Integrate[Erfi[b*x]/E^(b^2*x^2),x]","\frac{b x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{\sqrt{\pi }}","\frac{b x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{\sqrt{\pi }}",1,"(b*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, -(b^2*x^2)])/Sqrt[Pi]","A",1
280,1,26,60,0.0231797,"\int \frac{e^{-b^2 x^2} \text{erfi}(b x)}{x^2} \, dx","Integrate[Erfi[b*x]/(E^(b^2*x^2)*x^2),x]","-\frac{1}{2} b G_{2,3}^{2,1}\left(b^2 x^2|\begin{array}{c} 0,1 \\ 0,0,-\frac{1}{2} \\\end{array}\right)","-\frac{2 b^3 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{\sqrt{\pi }}-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{x}+\frac{2 b \log (x)}{\sqrt{\pi }}",1,"-1/2*(b*MeijerG[{{0}, {1}}, {{0, 0}, {-1/2}}, b^2*x^2])","C",0
281,1,29,105,0.0193666,"\int \frac{e^{-b^2 x^2} \text{erfi}(b x)}{x^4} \, dx","Integrate[Erfi[b*x]/(E^(b^2*x^2)*x^4),x]","-\frac{b G_{2,3}^{2,1}\left(b^2 x^2|\begin{array}{c} 0,2 \\ 0,1,-\frac{1}{2} \\\end{array}\right)}{2 x^2}","\frac{4 b^5 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{3 \sqrt{\pi }}-\frac{4 b^3 \log (x)}{3 \sqrt{\pi }}+\frac{2 b^2 e^{-b^2 x^2} \text{erfi}(b x)}{3 x}-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{3 x^3}-\frac{b}{3 \sqrt{\pi } x^2}",1,"-1/2*(b*MeijerG[{{0}, {2}}, {{0, 1}, {-1/2}}, b^2*x^2])/x^2","C",0
282,1,29,144,0.030951,"\int \frac{e^{-b^2 x^2} \text{erfi}(b x)}{x^6} \, dx","Integrate[Erfi[b*x]/(E^(b^2*x^2)*x^6),x]","-\frac{b G_{2,3}^{2,1}\left(b^2 x^2|\begin{array}{c} 0,3 \\ 0,2,-\frac{1}{2} \\\end{array}\right)}{2 x^4}","-\frac{8 b^7 x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{15 \sqrt{\pi }}+\frac{8 b^5 \log (x)}{15 \sqrt{\pi }}+\frac{2 b^3}{15 \sqrt{\pi } x^2}-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{5 x^5}+\frac{2 b^2 e^{-b^2 x^2} \text{erfi}(b x)}{15 x^3}-\frac{4 b^4 e^{-b^2 x^2} \text{erfi}(b x)}{15 x}-\frac{b}{10 \sqrt{\pi } x^4}",1,"-1/2*(b*MeijerG[{{0}, {3}}, {{0, 2}, {-1/2}}, b^2*x^2])/x^4","C",0
283,1,95,144,0.0808359,"\int e^{c+b^2 x^2} x^5 \text{erfi}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^5*Erfi[b*x],x]","\frac{e^c \left(-4 b x e^{2 b^2 x^2} \left(4 b^2 x^2-11\right)+32 \sqrt{\pi } e^{b^2 x^2} \left(b^4 x^4-2 b^2 x^2+2\right) \text{erfi}(b x)-43 \sqrt{2 \pi } \text{erfi}\left(\sqrt{2} b x\right)\right)}{64 \sqrt{\pi } b^6}","-\frac{43 e^c \text{erfi}\left(\sqrt{2} b x\right)}{32 \sqrt{2} b^6}+\frac{x^4 e^{b^2 x^2+c} \text{erfi}(b x)}{2 b^2}+\frac{e^{b^2 x^2+c} \text{erfi}(b x)}{b^6}+\frac{11 x e^{2 b^2 x^2+c}}{16 \sqrt{\pi } b^5}-\frac{x^2 e^{b^2 x^2+c} \text{erfi}(b x)}{b^4}-\frac{x^3 e^{2 b^2 x^2+c}}{4 \sqrt{\pi } b^3}",1,"(E^c*(-4*b*E^(2*b^2*x^2)*x*(-11 + 4*b^2*x^2) + 32*E^(b^2*x^2)*Sqrt[Pi]*(2 - 2*b^2*x^2 + b^4*x^4)*Erfi[b*x] - 43*Sqrt[2*Pi]*Erfi[Sqrt[2]*b*x]))/(64*b^6*Sqrt[Pi])","A",1
284,1,77,97,0.0527015,"\int e^{c+b^2 x^2} x^3 \text{erfi}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^3*Erfi[b*x],x]","\frac{e^c \left(8 \sqrt{\pi } e^{b^2 x^2} \left(b^2 x^2-1\right) \text{erfi}(b x)-4 b x e^{2 b^2 x^2}+5 \sqrt{2 \pi } \text{erfi}\left(\sqrt{2} b x\right)\right)}{16 \sqrt{\pi } b^4}","\frac{5 e^c \text{erfi}\left(\sqrt{2} b x\right)}{8 \sqrt{2} b^4}+\frac{x^2 e^{b^2 x^2+c} \text{erfi}(b x)}{2 b^2}-\frac{e^{b^2 x^2+c} \text{erfi}(b x)}{2 b^4}-\frac{x e^{2 b^2 x^2+c}}{4 \sqrt{\pi } b^3}",1,"(E^c*(-4*b*E^(2*b^2*x^2)*x + 8*E^(b^2*x^2)*Sqrt[Pi]*(-1 + b^2*x^2)*Erfi[b*x] + 5*Sqrt[2*Pi]*Erfi[Sqrt[2]*b*x]))/(16*b^4*Sqrt[Pi])","A",1
285,1,42,47,0.0127606,"\int e^{c+b^2 x^2} x \text{erfi}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x*Erfi[b*x],x]","\frac{e^c \left(2 e^{b^2 x^2} \text{erfi}(b x)-\sqrt{2} \text{erfi}\left(\sqrt{2} b x\right)\right)}{4 b^2}","\frac{e^{b^2 x^2+c} \text{erfi}(b x)}{2 b^2}-\frac{e^c \text{erfi}\left(\sqrt{2} b x\right)}{2 \sqrt{2} b^2}",1,"(E^c*(2*E^(b^2*x^2)*Erfi[b*x] - Sqrt[2]*Erfi[Sqrt[2]*b*x]))/(4*b^2)","A",1
286,0,0,22,0.0870592,"\int \frac{e^{c+b^2 x^2} \text{erfi}(b x)}{x} \, dx","Integrate[(E^(c + b^2*x^2)*Erfi[b*x])/x,x]","\int \frac{e^{c+b^2 x^2} \text{erfi}(b x)}{x} \, dx","\text{Int}\left(\frac{e^{b^2 x^2+c} \text{erfi}(b x)}{x},x\right)",0,"Integrate[(E^(c + b^2*x^2)*Erfi[b*x])/x, x]","A",-1
287,0,0,93,0.1746848,"\int \frac{e^{c+b^2 x^2} \text{erfi}(b x)}{x^3} \, dx","Integrate[(E^(c + b^2*x^2)*Erfi[b*x])/x^3,x]","\int \frac{e^{c+b^2 x^2} \text{erfi}(b x)}{x^3} \, dx","b^2 \text{Int}\left(\frac{e^{b^2 x^2+c} \text{erfi}(b x)}{x},x\right)-\frac{e^{b^2 x^2+c} \text{erfi}(b x)}{2 x^2}+\sqrt{2} b^2 e^c \text{erfi}\left(\sqrt{2} b x\right)-\frac{b e^{2 b^2 x^2+c}}{\sqrt{\pi } x}",0,"Integrate[(E^(c + b^2*x^2)*Erfi[b*x])/x^3, x]","A",-1
288,0,0,174,0.2216671,"\int \frac{e^{c+b^2 x^2} \text{erfi}(b x)}{x^5} \, dx","Integrate[(E^(c + b^2*x^2)*Erfi[b*x])/x^5,x]","\int \frac{e^{c+b^2 x^2} \text{erfi}(b x)}{x^5} \, dx","\frac{1}{2} b^4 \text{Int}\left(\frac{e^{b^2 x^2+c} \text{erfi}(b x)}{x},x\right)+\frac{2}{3} \sqrt{2} b^4 e^c \text{erfi}\left(\sqrt{2} b x\right)+\frac{b^4 e^c \text{erfi}\left(\sqrt{2} b x\right)}{\sqrt{2}}-\frac{b^2 e^{b^2 x^2+c} \text{erfi}(b x)}{4 x^2}-\frac{e^{b^2 x^2+c} \text{erfi}(b x)}{4 x^4}-\frac{b e^{2 b^2 x^2+c}}{6 \sqrt{\pi } x^3}-\frac{7 b^3 e^{2 b^2 x^2+c}}{6 \sqrt{\pi } x}",0,"Integrate[(E^(c + b^2*x^2)*Erfi[b*x])/x^5, x]","A",-1
289,1,78,121,0.0523948,"\int e^{c+b^2 x^2} x^4 \text{erfi}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^4*Erfi[b*x],x]","\frac{e^c \left(4 \sqrt{\pi } b x e^{b^2 x^2} \left(2 b^2 x^2-3\right) \text{erfi}(b x)-4 e^{2 b^2 x^2} \left(b^2 x^2-2\right)+3 \pi  \text{erfi}(b x)^2\right)}{16 \sqrt{\pi } b^5}","\frac{3 \sqrt{\pi } e^c \text{erfi}(b x)^2}{16 b^5}+\frac{x^3 e^{b^2 x^2+c} \text{erfi}(b x)}{2 b^2}+\frac{e^{2 b^2 x^2+c}}{2 \sqrt{\pi } b^5}-\frac{3 x e^{b^2 x^2+c} \text{erfi}(b x)}{4 b^4}-\frac{x^2 e^{2 b^2 x^2+c}}{4 \sqrt{\pi } b^3}",1,"(E^c*(-4*E^(2*b^2*x^2)*(-2 + b^2*x^2) + 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*(-3 + 2*b^2*x^2)*Erfi[b*x] + 3*Pi*Erfi[b*x]^2))/(16*b^5*Sqrt[Pi])","A",1
290,1,58,69,0.0161163,"\int e^{c+b^2 x^2} x^2 \text{erfi}(b x) \, dx","Integrate[E^(c + b^2*x^2)*x^2*Erfi[b*x],x]","-\frac{e^c \left(-4 \sqrt{\pi } b x e^{b^2 x^2} \text{erfi}(b x)+2 e^{2 b^2 x^2}+\pi  \text{erfi}(b x)^2\right)}{8 \sqrt{\pi } b^3}","-\frac{\sqrt{\pi } e^c \text{erfi}(b x)^2}{8 b^3}+\frac{x e^{b^2 x^2+c} \text{erfi}(b x)}{2 b^2}-\frac{e^{2 b^2 x^2+c}}{4 \sqrt{\pi } b^3}",1,"-1/8*(E^c*(2*E^(2*b^2*x^2) - 4*b*E^(b^2*x^2)*Sqrt[Pi]*x*Erfi[b*x] + Pi*Erfi[b*x]^2))/(b^3*Sqrt[Pi])","A",1
291,1,21,21,0.0049016,"\int e^{c+b^2 x^2} \text{erfi}(b x) \, dx","Integrate[E^(c + b^2*x^2)*Erfi[b*x],x]","\frac{\sqrt{\pi } e^c \text{erfi}(b x)^2}{4 b}","\frac{\sqrt{\pi } e^c \text{erfi}(b x)^2}{4 b}",1,"(E^c*Sqrt[Pi]*Erfi[b*x]^2)/(4*b)","A",1
292,1,56,59,0.0311944,"\int \frac{e^{c+b^2 x^2} \text{erfi}(b x)}{x^2} \, dx","Integrate[(E^(c + b^2*x^2)*Erfi[b*x])/x^2,x]","\frac{1}{2} e^c \left(-\frac{2 e^{b^2 x^2} \text{erfi}(b x)}{x}+\frac{2 b \text{Ei}\left(2 b^2 x^2\right)}{\sqrt{\pi }}+\sqrt{\pi } b \text{erfi}(b x)^2\right)","-\frac{e^{b^2 x^2+c} \text{erfi}(b x)}{x}+\frac{b e^c \text{Ei}\left(2 b^2 x^2\right)}{\sqrt{\pi }}+\frac{1}{2} \sqrt{\pi } b e^c \text{erfi}(b x)^2",1,"(E^c*((-2*E^(b^2*x^2)*Erfi[b*x])/x + b*Sqrt[Pi]*Erfi[b*x]^2 + (2*b*ExpIntegralEi[2*b^2*x^2])/Sqrt[Pi]))/2","A",1
293,1,91,118,0.0428164,"\int \frac{e^{c+b^2 x^2} \text{erfi}(b x)}{x^4} \, dx","Integrate[(E^(c + b^2*x^2)*Erfi[b*x])/x^4,x]","-\frac{e^c \left(\pi  \left(-b^3\right) x^3 \text{erfi}(b x)^2+\sqrt{\pi } e^{b^2 x^2} \left(2 b^2 x^2+1\right) \text{erfi}(b x)+b x \left(e^{2 b^2 x^2}-4 b^2 x^2 \text{Ei}\left(2 b^2 x^2\right)\right)\right)}{3 \sqrt{\pi } x^3}","\frac{1}{3} \sqrt{\pi } b^3 e^c \text{erfi}(b x)^2-\frac{2 b^2 e^{b^2 x^2+c} \text{erfi}(b x)}{3 x}-\frac{e^{b^2 x^2+c} \text{erfi}(b x)}{3 x^3}-\frac{b e^{2 b^2 x^2+c}}{3 \sqrt{\pi } x^2}+\frac{4 b^3 e^c \text{Ei}\left(2 b^2 x^2\right)}{3 \sqrt{\pi }}",1,"-1/3*(E^c*(E^(b^2*x^2)*Sqrt[Pi]*(1 + 2*b^2*x^2)*Erfi[b*x] - b^3*Pi*x^3*Erfi[b*x]^2 + b*x*(E^(2*b^2*x^2) - 4*b^2*x^2*ExpIntegralEi[2*b^2*x^2])))/(Sqrt[Pi]*x^3)","A",1
294,1,206,304,2.5475675,"\int e^{c+d x^2} x^3 \text{erfi}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x^3*Erfi[a + b*x],x]","\frac{e^c \left(\frac{2 b e^{\frac{a^2 d}{b^2+d}} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)}{\sqrt{b^2+d}}-\frac{b d e^{\frac{a^2 d}{b^2+d}} \left(\sqrt{\pi } \sqrt{b^2+d} \left(\left(2 a^2-1\right) b^2-d\right) \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)+2 \left(b^2+d\right) e^{\frac{\left(a b+x \left(b^2+d\right)\right)^2}{b^2+d}} \left(x \left(b^2+d\right)-a b\right)\right)}{\sqrt{\pi } \left(b^2+d\right)^3}+2 e^{d x^2} \left(d x^2-1\right) \text{erfi}(a+b x)\right)}{4 d^2}","\frac{b e^{\frac{a^2 d}{b^2+d}+c} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)}{2 d^2 \sqrt{b^2+d}}+\frac{b e^{\frac{a^2 d}{b^2+d}+c} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)}{4 d \left(b^2+d\right)^{3/2}}+\frac{a b^2 e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)^2}-\frac{b x e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)}-\frac{a^2 b^3 e^{\frac{a^2 d}{b^2+d}+c} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)}{2 d \left(b^2+d\right)^{5/2}}-\frac{e^{c+d x^2} \text{erfi}(a+b x)}{2 d^2}+\frac{x^2 e^{c+d x^2} \text{erfi}(a+b x)}{2 d}",1,"(E^c*(2*E^(d*x^2)*(-1 + d*x^2)*Erfi[a + b*x] + (2*b*E^((a^2*d)/(b^2 + d))*Erfi[(a*b + (b^2 + d)*x)/Sqrt[b^2 + d]])/Sqrt[b^2 + d] - (b*d*E^((a^2*d)/(b^2 + d))*(2*(b^2 + d)*E^((a*b + (b^2 + d)*x)^2/(b^2 + d))*(-(a*b) + (b^2 + d)*x) + ((-1 + 2*a^2)*b^2 - d)*Sqrt[b^2 + d]*Sqrt[Pi]*Erfi[(a*b + (b^2 + d)*x)/Sqrt[b^2 + d]]))/((b^2 + d)^3*Sqrt[Pi])))/(4*d^2)","A",1
295,1,73,78,0.0739529,"\int e^{c+d x^2} x \text{erfi}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x*Erfi[a + b*x],x]","\frac{e^c \left(e^{d x^2} \text{erfi}(a+b x)-\frac{b e^{\frac{a^2 d}{b^2+d}} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)}{\sqrt{b^2+d}}\right)}{2 d}","\frac{e^{c+d x^2} \text{erfi}(a+b x)}{2 d}-\frac{b e^{\frac{a^2 d}{b^2+d}+c} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)}{2 d \sqrt{b^2+d}}",1,"(E^c*(E^(d*x^2)*Erfi[a + b*x] - (b*E^((a^2*d)/(b^2 + d))*Erfi[(a*b + (b^2 + d)*x)/Sqrt[b^2 + d]])/Sqrt[b^2 + d]))/(2*d)","A",1
296,0,0,22,0.19912,"\int \frac{e^{c+d x^2} \text{erfi}(a+b x)}{x} \, dx","Integrate[(E^(c + d*x^2)*Erfi[a + b*x])/x,x]","\int \frac{e^{c+d x^2} \text{erfi}(a+b x)}{x} \, dx","\text{Int}\left(\frac{e^{c+d x^2} \text{erfi}(a+b x)}{x},x\right)",0,"Integrate[(E^(c + d*x^2)*Erfi[a + b*x])/x, x]","A",-1
297,0,0,167,0.3666155,"\int \frac{e^{c+d x^2} \text{erfi}(a+b x)}{x^3} \, dx","Integrate[(E^(c + d*x^2)*Erfi[a + b*x])/x^3,x]","\int \frac{e^{c+d x^2} \text{erfi}(a+b x)}{x^3} \, dx","\frac{2 a b^2 \text{Int}\left(\frac{e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{x},x\right)}{\sqrt{\pi }}+d \text{Int}\left(\frac{e^{c+d x^2} \text{erfi}(a+b x)}{x},x\right)+b \sqrt{b^2+d} e^{\frac{a^2 d}{b^2+d}+c} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)-\frac{b e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{\sqrt{\pi } x}-\frac{e^{c+d x^2} \text{erfi}(a+b x)}{2 x^2}",0,"Integrate[(E^(c + d*x^2)*Erfi[a + b*x])/x^3, x]","A",-1
298,0,0,468,0.5752841,"\int e^{c+d x^2} x^4 \text{erfi}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x^4*Erfi[a + b*x],x]","\int e^{c+d x^2} x^4 \text{erfi}(a+b x) \, dx","\frac{3 \text{Int}\left(e^{c+d x^2} \text{erfi}(a+b x),x\right)}{4 d^2}-\frac{3 a b^2 e^{\frac{a^2 d}{b^2+d}+c} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)}{4 d^2 \left(b^2+d\right)^{3/2}}+\frac{3 b e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{4 \sqrt{\pi } d^2 \left(b^2+d\right)}-\frac{3 a b^2 e^{\frac{a^2 d}{b^2+d}+c} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)}{4 d \left(b^2+d\right)^{5/2}}+\frac{a b^2 x e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)^2}-\frac{b x^2 e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)}+\frac{b e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)^2}-\frac{a^2 b^3 e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)^3}+\frac{a^3 b^4 e^{\frac{a^2 d}{b^2+d}+c} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)}{2 d \left(b^2+d\right)^{7/2}}-\frac{3 x e^{c+d x^2} \text{erfi}(a+b x)}{4 d^2}+\frac{x^3 e^{c+d x^2} \text{erfi}(a+b x)}{2 d}",0,"Integrate[E^(c + d*x^2)*x^4*Erfi[a + b*x], x]","A",-1
299,0,0,149,0.4217438,"\int e^{c+d x^2} x^2 \text{erfi}(a+b x) \, dx","Integrate[E^(c + d*x^2)*x^2*Erfi[a + b*x],x]","\int e^{c+d x^2} x^2 \text{erfi}(a+b x) \, dx","-\frac{\text{Int}\left(e^{c+d x^2} \text{erfi}(a+b x),x\right)}{2 d}+\frac{a b^2 e^{\frac{a^2 d}{b^2+d}+c} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)}{2 d \left(b^2+d\right)^{3/2}}-\frac{b e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{2 \sqrt{\pi } d \left(b^2+d\right)}+\frac{x e^{c+d x^2} \text{erfi}(a+b x)}{2 d}",0,"Integrate[E^(c + d*x^2)*x^2*Erfi[a + b*x], x]","A",-1
300,0,0,19,0.0384554,"\int e^{c+d x^2} \text{erfi}(a+b x) \, dx","Integrate[E^(c + d*x^2)*Erfi[a + b*x],x]","\int e^{c+d x^2} \text{erfi}(a+b x) \, dx","\text{Int}\left(e^{c+d x^2} \text{erfi}(a+b x),x\right)",0,"Integrate[E^(c + d*x^2)*Erfi[a + b*x], x]","A",-1
301,0,0,79,0.3955668,"\int \frac{e^{c+d x^2} \text{erfi}(a+b x)}{x^2} \, dx","Integrate[(E^(c + d*x^2)*Erfi[a + b*x])/x^2,x]","\int \frac{e^{c+d x^2} \text{erfi}(a+b x)}{x^2} \, dx","\frac{2 b \text{Int}\left(\frac{e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{x},x\right)}{\sqrt{\pi }}+2 d \text{Int}\left(e^{c+d x^2} \text{erfi}(a+b x),x\right)-\frac{e^{c+d x^2} \text{erfi}(a+b x)}{x}",0,"Integrate[(E^(c + d*x^2)*Erfi[a + b*x])/x^2, x]","A",-1
302,0,0,323,0.5803095,"\int \frac{e^{c+d x^2} \text{erfi}(a+b x)}{x^4} \, dx","Integrate[(E^(c + d*x^2)*Erfi[a + b*x])/x^4,x]","\int \frac{e^{c+d x^2} \text{erfi}(a+b x)}{x^4} \, dx","\frac{4 b d \text{Int}\left(\frac{e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{x},x\right)}{3 \sqrt{\pi }}+\frac{2 b \left(b^2+d\right) \text{Int}\left(\frac{e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{x},x\right)}{3 \sqrt{\pi }}+\frac{4 a^2 b^3 \text{Int}\left(\frac{e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{x},x\right)}{3 \sqrt{\pi }}+\frac{4}{3} d^2 \text{Int}\left(e^{c+d x^2} \text{erfi}(a+b x),x\right)+\frac{2}{3} a b^2 \sqrt{b^2+d} e^{\frac{a^2 d}{b^2+d}+c} \text{erfi}\left(\frac{a b+x \left(b^2+d\right)}{\sqrt{b^2+d}}\right)-\frac{2 a b^2 e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{3 \sqrt{\pi } x}-\frac{b e^{a^2+2 a b x+x^2 \left(b^2+d\right)+c}}{3 \sqrt{\pi } x^2}-\frac{2 d e^{c+d x^2} \text{erfi}(a+b x)}{3 x}-\frac{e^{c+d x^2} \text{erfi}(a+b x)}{3 x^3}",0,"Integrate[(E^(c + d*x^2)*Erfi[a + b*x])/x^4, x]","A",-1
303,1,33,33,0.0557197,"\int \left(\frac{e^{-b^2 x^2} \text{erfi}(b x)}{x^3}+\frac{b^2 e^{-b^2 x^2} \text{erfi}(b x)}{x}\right) \, dx","Integrate[Erfi[b*x]/(E^(b^2*x^2)*x^3) + (b^2*Erfi[b*x])/(E^(b^2*x^2)*x),x]","-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{2 x^2}-\frac{b}{\sqrt{\pi } x}","-\frac{e^{-b^2 x^2} \text{erfi}(b x)}{2 x^2}-\frac{b}{\sqrt{\pi } x}",1,"-(b/(Sqrt[Pi]*x)) - Erfi[b*x]/(2*E^(b^2*x^2)*x^2)","A",1
304,0,0,67,0.659272,"\int \text{erfi}(b x) \sin \left(c+i b^2 x^2\right) \, dx","Integrate[Erfi[b*x]*Sin[c + I*b^2*x^2],x]","\int \text{erfi}(b x) \sin \left(c+i b^2 x^2\right) \, dx","\frac{i \sqrt{\pi } e^{-i c} \text{erfi}(b x)^2}{8 b}-\frac{i b e^{i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{2 \sqrt{\pi }}",1,"Integrate[Erfi[b*x]*Sin[c + I*b^2*x^2], x]","F",-1
305,0,0,67,0.7106839,"\int \text{erfi}(b x) \sin \left(c-i b^2 x^2\right) \, dx","Integrate[Erfi[b*x]*Sin[c - I*b^2*x^2],x]","\int \text{erfi}(b x) \sin \left(c-i b^2 x^2\right) \, dx","\frac{i b e^{-i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{2 \sqrt{\pi }}-\frac{i \sqrt{\pi } e^{i c} \text{erfi}(b x)^2}{8 b}",1,"Integrate[Erfi[b*x]*Sin[c - I*b^2*x^2], x]","F",-1
306,0,0,63,0.5402663,"\int \cos \left(c+i b^2 x^2\right) \text{erfi}(b x) \, dx","Integrate[Cos[c + I*b^2*x^2]*Erfi[b*x],x]","\int \cos \left(c+i b^2 x^2\right) \text{erfi}(b x) \, dx","\frac{b e^{i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{2 \sqrt{\pi }}+\frac{\sqrt{\pi } e^{-i c} \text{erfi}(b x)^2}{8 b}",1,"Integrate[Cos[c + I*b^2*x^2]*Erfi[b*x], x]","F",-1
307,0,0,63,0.5096741,"\int \cos \left(c-i b^2 x^2\right) \text{erfi}(b x) \, dx","Integrate[Cos[c - I*b^2*x^2]*Erfi[b*x],x]","\int \cos \left(c-i b^2 x^2\right) \text{erfi}(b x) \, dx","\frac{b e^{-i c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{2 \sqrt{\pi }}+\frac{\sqrt{\pi } e^{i c} \text{erfi}(b x)^2}{8 b}",1,"Integrate[Cos[c - I*b^2*x^2]*Erfi[b*x], x]","F",-1
308,1,74,57,1.5603181,"\int \text{erfi}(b x) \sinh \left(c+b^2 x^2\right) \, dx","Integrate[Erfi[b*x]*Sinh[c + b^2*x^2],x]","\frac{4 b^2 x^2 (\cosh (c)-\sinh (c)) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)+\pi  \text{erfi}(b x) (\text{erfi}(b x) (\sinh (c)+\cosh (c))-2 \text{erf}(b x) (\cosh (c)-\sinh (c)))}{8 \sqrt{\pi } b}","\frac{\sqrt{\pi } e^c \text{erfi}(b x)^2}{8 b}-\frac{b e^{-c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{2 \sqrt{\pi }}",1,"(4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*(Cosh[c] - Sinh[c]) + Pi*Erfi[b*x]*(-2*Erf[b*x]*(Cosh[c] - Sinh[c]) + Erfi[b*x]*(Cosh[c] + Sinh[c])))/(8*b*Sqrt[Pi])","A",1
309,1,72,57,0.9731409,"\int \text{erfi}(b x) \sinh \left(c-b^2 x^2\right) \, dx","Integrate[Erfi[b*x]*Sinh[c - b^2*x^2],x]","\frac{\pi  \text{erfi}(b x) (2 \text{erf}(b x) (\sinh (c)+\cosh (c))+\text{erfi}(b x) (\sinh (c)-\cosh (c)))-4 b^2 x^2 (\sinh (c)+\cosh (c)) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{8 \sqrt{\pi } b}","\frac{b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{2 \sqrt{\pi }}-\frac{\sqrt{\pi } e^{-c} \text{erfi}(b x)^2}{8 b}",1,"(-4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*(Cosh[c] + Sinh[c]) + Pi*Erfi[b*x]*(Erfi[b*x]*(-Cosh[c] + Sinh[c]) + 2*Erf[b*x]*(Cosh[c] + Sinh[c])))/(8*b*Sqrt[Pi])","A",1
310,1,74,57,12.9525922,"\int \cosh \left(c+b^2 x^2\right) \text{erfi}(b x) \, dx","Integrate[Cosh[c + b^2*x^2]*Erfi[b*x],x]","\frac{4 b^2 x^2 (\sinh (c)-\cosh (c)) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)+\pi  \text{erfi}(b x) (2 \text{erf}(b x) (\cosh (c)-\sinh (c))+\text{erfi}(b x) (\sinh (c)+\cosh (c)))}{8 \sqrt{\pi } b}","\frac{b e^{-c} x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{2 \sqrt{\pi }}+\frac{\sqrt{\pi } e^c \text{erfi}(b x)^2}{8 b}",1,"(4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*(-Cosh[c] + Sinh[c]) + Pi*Erfi[b*x]*(2*Erf[b*x]*(Cosh[c] - Sinh[c]) + Erfi[b*x]*(Cosh[c] + Sinh[c])))/(8*b*Sqrt[Pi])","A",1
311,1,72,57,1.9582497,"\int \cosh \left(c-b^2 x^2\right) \text{erfi}(b x) \, dx","Integrate[Cosh[c - b^2*x^2]*Erfi[b*x],x]","\frac{\pi  \text{erfi}(b x) (2 \text{erf}(b x) (\sinh (c)+\cosh (c))+\text{erfi}(b x) (\cosh (c)-\sinh (c)))-4 b^2 x^2 (\sinh (c)+\cosh (c)) \, _2F_2\left(1,1;\frac{3}{2},2;b^2 x^2\right)}{8 \sqrt{\pi } b}","\frac{b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-b^2 x^2\right)}{2 \sqrt{\pi }}+\frac{\sqrt{\pi } e^{-c} \text{erfi}(b x)^2}{8 b}",1,"(-4*b^2*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, b^2*x^2]*(Cosh[c] + Sinh[c]) + Pi*Erfi[b*x]*(Erfi[b*x]*(Cosh[c] - Sinh[c]) + 2*Erf[b*x]*(Cosh[c] + Sinh[c])))/(8*b*Sqrt[Pi])","A",1