1,1,25,25,0.0014223,"\int x^{100} \text{Gamma}(0,a x) \, dx","Integrate[x^100*Gamma[0, a*x],x]","\frac{1}{101} x^{101} \text{Gamma}(0,a x)-\frac{\text{Gamma}(101,a x)}{101 a^{101}}","\frac{1}{101} x^{101} \text{Gamma}(0,a x)-\frac{\text{Gamma}(101,a x)}{101 a^{101}}",1,"(x^101*Gamma[0, a*x])/101 - Gamma[101, a*x]/(101*a^101)","A",1
2,1,25,25,0.0011724,"\int x^2 \text{Gamma}(0,a x) \, dx","Integrate[x^2*Gamma[0, a*x],x]","\frac{1}{3} x^3 \text{Gamma}(0,a x)-\frac{\text{Gamma}(3,a x)}{3 a^3}","\frac{1}{3} x^3 \text{Gamma}(0,a x)-\frac{\text{Gamma}(3,a x)}{3 a^3}",1,"(x^3*Gamma[0, a*x])/3 - Gamma[3, a*x]/(3*a^3)","A",1
3,1,25,25,0.0010071,"\int x \text{Gamma}(0,a x) \, dx","Integrate[x*Gamma[0, a*x],x]","\frac{1}{2} x^2 \text{Gamma}(0,a x)-\frac{\text{Gamma}(2,a x)}{2 a^2}","\frac{1}{2} x^2 \text{Gamma}(0,a x)-\frac{\text{Gamma}(2,a x)}{2 a^2}",1,"(x^2*Gamma[0, a*x])/2 - Gamma[2, a*x]/(2*a^2)","A",1
4,1,19,19,0.0073849,"\int \text{Gamma}(0,a x) \, dx","Integrate[Gamma[0, a*x],x]","x \text{Gamma}(0,a x)-\frac{e^{-a x}}{a}","x \text{Gamma}(0,a x)-\frac{e^{-a x}}{a}",1,"-(1/(a*E^(a*x))) + x*Gamma[0, a*x]","A",1
5,1,66,32,0.1827433,"\int \frac{\text{Gamma}(0,a x)}{x} \, dx","Integrate[Gamma[0, a*x]/x,x]","a x \, _3F_3(1,1,1;2,2,2;-a x)+\log (a x) \text{Gamma}(0,a x)+\frac{1}{2} \log (x) (-2 \text{Gamma}(0,a x)-2 (\log (a x)+\gamma )+\log (x))+\text{Ei}(-a x) (\log (a x)-\log (x))","a x \, _3F_3(1,1,1;2,2,2;-a x)-\frac{1}{2} \log ^2(a x)-\gamma  \log (x)",1,"a*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, -(a*x)] + Gamma[0, a*x]*Log[a*x] + ExpIntegralEi[-(a*x)]*(-Log[x] + Log[a*x]) + (Log[x]*(-2*Gamma[0, a*x] + Log[x] - 2*(EulerGamma + Log[a*x])))/2","B",1
6,1,18,18,0.0011962,"\int \frac{\text{Gamma}(0,a x)}{x^2} \, dx","Integrate[Gamma[0, a*x]/x^2,x]","a \text{Gamma}(-1,a x)-\frac{\text{Gamma}(0,a x)}{x}","a \text{Gamma}(-1,a x)-\frac{\text{Gamma}(0,a x)}{x}",1,"a*Gamma[-1, a*x] - Gamma[0, a*x]/x","A",1
7,1,25,25,0.001338,"\int \frac{\text{Gamma}(0,a x)}{x^3} \, dx","Integrate[Gamma[0, a*x]/x^3,x]","\frac{1}{2} a^2 \text{Gamma}(-2,a x)-\frac{\text{Gamma}(0,a x)}{2 x^2}","\frac{1}{2} a^2 \text{Gamma}(-2,a x)-\frac{\text{Gamma}(0,a x)}{2 x^2}",1,"(a^2*Gamma[-2, a*x])/2 - Gamma[0, a*x]/(2*x^2)","A",1
8,1,25,25,0.0012731,"\int \frac{\text{Gamma}(0,a x)}{x^4} \, dx","Integrate[Gamma[0, a*x]/x^4,x]","\frac{1}{3} a^3 \text{Gamma}(-3,a x)-\frac{\text{Gamma}(0,a x)}{3 x^3}","\frac{1}{3} a^3 \text{Gamma}(-3,a x)-\frac{\text{Gamma}(0,a x)}{3 x^3}",1,"(a^3*Gamma[-3, a*x])/3 - Gamma[0, a*x]/(3*x^3)","A",1
9,1,32,52,0.0108926,"\int e^{-a x} x^3 \, dx","Integrate[x^3/E^(a*x),x]","-\frac{e^{-a x} \left(a^3 x^3+3 a^2 x^2+6 a x+6\right)}{a^4}","-\frac{6 e^{-a x}}{a^4}-\frac{6 x e^{-a x}}{a^3}-\frac{3 x^2 e^{-a x}}{a^2}-\frac{x^3 e^{-a x}}{a}",1,"-((6 + 6*a*x + 3*a^2*x^2 + a^3*x^3)/(a^4*E^(a*x)))","A",1
10,1,24,38,0.0102095,"\int e^{-a x} x^2 \, dx","Integrate[x^2/E^(a*x),x]","-\frac{e^{-a x} \left(a^2 x^2+2 a x+2\right)}{a^3}","-\frac{2 e^{-a x}}{a^3}-\frac{2 x e^{-a x}}{a^2}-\frac{x^2 e^{-a x}}{a}",1,"-((2 + 2*a*x + a^2*x^2)/(a^3*E^(a*x)))","A",1
11,1,16,24,0.0065874,"\int e^{-a x} x \, dx","Integrate[x/E^(a*x),x]","-\frac{e^{-a x} (a x+1)}{a^2}","-\frac{e^{-a x}}{a^2}-\frac{x e^{-a x}}{a}",1,"-((1 + a*x)/(a^2*E^(a*x)))","A",1
12,1,11,11,0.0070558,"\int e^{-a x} \, dx","Integrate[E^(-(a*x)),x]","-\frac{e^{-a x}}{a}","-\frac{e^{-a x}}{a}",1,"-(1/(a*E^(a*x)))","A",1
13,1,5,5,0.006584,"\int \frac{e^{-a x}}{x} \, dx","Integrate[1/(E^(a*x)*x),x]","\text{Ei}(-a x)","\text{Ei}(-a x)",1,"ExpIntegralEi[-(a*x)]","A",1
14,1,20,20,0.0169249,"\int \frac{e^{-a x}}{x^2} \, dx","Integrate[1/(E^(a*x)*x^2),x]","-a \text{Ei}(-a x)-\frac{e^{-a x}}{x}","-a \text{Ei}(-a x)-\frac{e^{-a x}}{x}",1,"-(1/(E^(a*x)*x)) - a*ExpIntegralEi[-(a*x)]","A",1
15,1,36,40,0.0158058,"\int \frac{e^{-a x}}{x^3} \, dx","Integrate[1/(E^(a*x)*x^3),x]","\frac{1}{2} a^2 \text{Ei}(-a x)+e^{-a x} \left(\frac{a}{2 x}-\frac{1}{2 x^2}\right)","\frac{1}{2} a^2 \text{Ei}(-a x)-\frac{e^{-a x}}{2 x^2}+\frac{a e^{-a x}}{2 x}",1,"(-1/(2*x^2) + a/(2*x))/E^(a*x) + (a^2*ExpIntegralEi[-(a*x)])/2","A",1
16,1,43,56,0.0194494,"\int \frac{e^{-a x}}{x^4} \, dx","Integrate[1/(E^(a*x)*x^4),x]","-\frac{e^{-a x} \left(a^3 x^3 e^{a x} \text{Ei}(-a x)+a^2 x^2-a x+2\right)}{6 x^3}","-\frac{1}{6} a^3 \text{Ei}(-a x)-\frac{a^2 e^{-a x}}{6 x}-\frac{e^{-a x}}{3 x^3}+\frac{a e^{-a x}}{6 x^2}",1,"-(2 - a*x + a^2*x^2 + a^3*E^(a*x)*x^3*ExpIntegralEi[-(a*x)])/(6*E^(a*x)*x^3)","A",1
17,1,25,25,0.0043302,"\int x^{100} \text{Gamma}(2,a x) \, dx","Integrate[x^100*Gamma[2, a*x],x]","\frac{1}{101} x^{101} \text{Gamma}(2,a x)-\frac{\text{Gamma}(103,a x)}{101 a^{101}}","\frac{1}{101} x^{101} \text{Gamma}(2,a x)-\frac{\text{Gamma}(103,a x)}{101 a^{101}}",1,"(x^101*Gamma[2, a*x])/101 - Gamma[103, a*x]/(101*a^101)","A",1
18,1,25,25,0.0016905,"\int x^2 \text{Gamma}(2,a x) \, dx","Integrate[x^2*Gamma[2, a*x],x]","\frac{1}{3} x^3 \text{Gamma}(2,a x)-\frac{\text{Gamma}(5,a x)}{3 a^3}","\frac{1}{3} x^3 \text{Gamma}(2,a x)-\frac{\text{Gamma}(5,a x)}{3 a^3}",1,"(x^3*Gamma[2, a*x])/3 - Gamma[5, a*x]/(3*a^3)","A",1
19,1,25,25,0.0010817,"\int x \text{Gamma}(2,a x) \, dx","Integrate[x*Gamma[2, a*x],x]","\frac{1}{2} x^2 \text{Gamma}(2,a x)-\frac{\text{Gamma}(4,a x)}{2 a^2}","\frac{1}{2} x^2 \text{Gamma}(2,a x)-\frac{\text{Gamma}(4,a x)}{2 a^2}",1,"(x^2*Gamma[2, a*x])/2 - Gamma[4, a*x]/(2*a^2)","A",1
20,1,30,18,0.0212769,"\int \text{Gamma}(2,a x) \, dx","Integrate[Gamma[2, a*x],x]","x \text{Gamma}(2,a x)+e^{-a x} \left(-a x^2-\frac{2}{a}-2 x\right)","x \text{Gamma}(2,a x)-\frac{\text{Gamma}(3,a x)}{a}",1,"(-2/a - 2*x - a*x^2)/E^(a*x) + x*Gamma[2, a*x]","A",1
21,1,41,14,0.0195493,"\int \frac{\text{Gamma}(2,a x)}{x} \, dx","Integrate[Gamma[2, a*x]/x,x]","\log (a x) \text{Gamma}(2,a x)+\text{Ei}(-a x)-e^{-a x}-e^{-a x} (a x+1) \log (a x)","\text{Ei}(-a x)-e^{-a x}",1,"-E^(-(a*x)) + ExpIntegralEi[-(a*x)] - ((1 + a*x)*Log[a*x])/E^(a*x) + Gamma[2, a*x]*Log[a*x]","B",1
22,1,19,19,0.0042444,"\int \frac{\text{Gamma}(2,a x)}{x^2} \, dx","Integrate[Gamma[2, a*x]/x^2,x]","a e^{-a x}-\frac{\text{Gamma}(2,a x)}{x}","a e^{-a x}-\frac{\text{Gamma}(2,a x)}{x}",1,"a/E^(a*x) - Gamma[2, a*x]/x","A",1
23,1,25,25,0.0017373,"\int \frac{\text{Gamma}(2,a x)}{x^3} \, dx","Integrate[Gamma[2, a*x]/x^3,x]","\frac{1}{2} a^2 \text{Gamma}(0,a x)-\frac{\text{Gamma}(2,a x)}{2 x^2}","\frac{1}{2} a^2 \text{Gamma}(0,a x)-\frac{\text{Gamma}(2,a x)}{2 x^2}",1,"(a^2*Gamma[0, a*x])/2 - Gamma[2, a*x]/(2*x^2)","A",1
24,1,25,25,0.0012953,"\int \frac{\text{Gamma}(2,a x)}{x^4} \, dx","Integrate[Gamma[2, a*x]/x^4,x]","\frac{1}{3} a^3 \text{Gamma}(-1,a x)-\frac{\text{Gamma}(2,a x)}{3 x^3}","\frac{1}{3} a^3 \text{Gamma}(-1,a x)-\frac{\text{Gamma}(2,a x)}{3 x^3}",1,"(a^3*Gamma[-1, a*x])/3 - Gamma[2, a*x]/(3*x^3)","A",1
25,1,25,25,0.0012572,"\int x^{100} \text{Gamma}(3,a x) \, dx","Integrate[x^100*Gamma[3, a*x],x]","\frac{1}{101} x^{101} \text{Gamma}(3,a x)-\frac{\text{Gamma}(104,a x)}{101 a^{101}}","\frac{1}{101} x^{101} \text{Gamma}(3,a x)-\frac{\text{Gamma}(104,a x)}{101 a^{101}}",1,"(x^101*Gamma[3, a*x])/101 - Gamma[104, a*x]/(101*a^101)","A",1
26,1,25,25,0.0012099,"\int x^2 \text{Gamma}(3,a x) \, dx","Integrate[x^2*Gamma[3, a*x],x]","\frac{1}{3} x^3 \text{Gamma}(3,a x)-\frac{\text{Gamma}(6,a x)}{3 a^3}","\frac{1}{3} x^3 \text{Gamma}(3,a x)-\frac{\text{Gamma}(6,a x)}{3 a^3}",1,"(x^3*Gamma[3, a*x])/3 - Gamma[6, a*x]/(3*a^3)","A",1
27,1,25,25,0.0011161,"\int x \text{Gamma}(3,a x) \, dx","Integrate[x*Gamma[3, a*x],x]","\frac{1}{2} x^2 \text{Gamma}(3,a x)-\frac{\text{Gamma}(5,a x)}{2 a^2}","\frac{1}{2} x^2 \text{Gamma}(3,a x)-\frac{\text{Gamma}(5,a x)}{2 a^2}",1,"(x^2*Gamma[3, a*x])/2 - Gamma[5, a*x]/(2*a^2)","A",1
28,1,38,18,0.0147569,"\int \text{Gamma}(3,a x) \, dx","Integrate[Gamma[3, a*x],x]","x \text{Gamma}(3,a x)+e^{-a x} \left(-a^2 x^3-3 a x^2-\frac{6}{a}-6 x\right)","x \text{Gamma}(3,a x)-\frac{\text{Gamma}(4,a x)}{a}",1,"(-6/a - 6*x - 3*a*x^2 - a^2*x^3)/E^(a*x) + x*Gamma[3, a*x]","B",1
29,1,56,23,0.0286517,"\int \frac{\text{Gamma}(3,a x)}{x} \, dx","Integrate[Gamma[3, a*x]/x,x]","\log (a x) \text{Gamma}(3,a x)-e^{-a x} \left(a^2 x^2+2 a x+2\right) \log (a x)+2 \text{Ei}(-a x)+e^{-a x} (-a x-3)","-\text{Gamma}(2,a x)+2 \text{Ei}(-a x)-2 e^{-a x}",1,"(-3 - a*x)/E^(a*x) + 2*ExpIntegralEi[-(a*x)] - ((2 + 2*a*x + a^2*x^2)*Log[a*x])/E^(a*x) + Gamma[3, a*x]*Log[a*x]","B",1
30,1,18,18,0.0013104,"\int \frac{\text{Gamma}(3,a x)}{x^2} \, dx","Integrate[Gamma[3, a*x]/x^2,x]","a \text{Gamma}(2,a x)-\frac{\text{Gamma}(3,a x)}{x}","a \text{Gamma}(2,a x)-\frac{\text{Gamma}(3,a x)}{x}",1,"a*Gamma[2, a*x] - Gamma[3, a*x]/x","A",1
31,1,26,26,0.0066315,"\int \frac{\text{Gamma}(3,a x)}{x^3} \, dx","Integrate[Gamma[3, a*x]/x^3,x]","\frac{1}{2} a^2 e^{-a x}-\frac{\text{Gamma}(3,a x)}{2 x^2}","\frac{1}{2} a^2 e^{-a x}-\frac{\text{Gamma}(3,a x)}{2 x^2}",1,"a^2/(2*E^(a*x)) - Gamma[3, a*x]/(2*x^2)","A",1
32,1,25,25,0.0012231,"\int \frac{\text{Gamma}(3,a x)}{x^4} \, dx","Integrate[Gamma[3, a*x]/x^4,x]","\frac{1}{3} a^3 \text{Gamma}(0,a x)-\frac{\text{Gamma}(3,a x)}{3 x^3}","\frac{1}{3} a^3 \text{Gamma}(0,a x)-\frac{\text{Gamma}(3,a x)}{3 x^3}",1,"(a^3*Gamma[0, a*x])/3 - Gamma[3, a*x]/(3*x^3)","A",1
33,1,25,25,0.0013403,"\int x^{100} \text{Gamma}(-1,a x) \, dx","Integrate[x^100*Gamma[-1, a*x],x]","\frac{1}{101} x^{101} \text{Gamma}(-1,a x)-\frac{\text{Gamma}(100,a x)}{101 a^{101}}","\frac{1}{101} x^{101} \text{Gamma}(-1,a x)-\frac{\text{Gamma}(100,a x)}{101 a^{101}}",1,"(x^101*Gamma[-1, a*x])/101 - Gamma[100, a*x]/(101*a^101)","A",1
34,1,25,25,0.0012152,"\int x^3 \text{Gamma}(-1,a x) \, dx","Integrate[x^3*Gamma[-1, a*x],x]","\frac{1}{4} x^4 \text{Gamma}(-1,a x)-\frac{\text{Gamma}(3,a x)}{4 a^4}","\frac{1}{4} x^4 \text{Gamma}(-1,a x)-\frac{\text{Gamma}(3,a x)}{4 a^4}",1,"(x^4*Gamma[-1, a*x])/4 - Gamma[3, a*x]/(4*a^4)","A",1
35,1,25,25,0.0011872,"\int x^2 \text{Gamma}(-1,a x) \, dx","Integrate[x^2*Gamma[-1, a*x],x]","\frac{1}{3} x^3 \text{Gamma}(-1,a x)-\frac{\text{Gamma}(2,a x)}{3 a^3}","\frac{1}{3} x^3 \text{Gamma}(-1,a x)-\frac{\text{Gamma}(2,a x)}{3 a^3}",1,"(x^3*Gamma[-1, a*x])/3 - Gamma[2, a*x]/(3*a^3)","A",1
36,1,26,26,0.0075328,"\int x \text{Gamma}(-1,a x) \, dx","Integrate[x*Gamma[-1, a*x],x]","\frac{1}{2} x^2 \text{Gamma}(-1,a x)-\frac{e^{-a x}}{2 a^2}","\frac{1}{2} x^2 \text{Gamma}(-1,a x)-\frac{e^{-a x}}{2 a^2}",1,"-1/(2*a^2*E^(a*x)) + (x^2*Gamma[-1, a*x])/2","A",1
37,1,17,18,0.0021202,"\int \text{Gamma}(-1,a x) \, dx","Integrate[Gamma[-1, a*x],x]","x \text{Gamma}(-1,a x)+\frac{\text{Ei}(-a x)}{a}","x \text{Gamma}(-1,a x)-\frac{\text{Gamma}(0,a x)}{a}",1,"ExpIntegralEi[-(a*x)]/a + x*Gamma[-1, a*x]","A",1
38,1,103,39,0.6647509,"\int \frac{\text{Gamma}(-1,a x)}{x} \, dx","Integrate[Gamma[-1, a*x]/x,x]","-a x \, _3F_3(1,1,1;2,2,2;-a x)+\log (x) \text{Gamma}(0,a x)+\log (a x) \text{Gamma}(-1,a x)+\text{Ei}(-a x) (-\log (a x)+\log (x)-1)-\frac{e^{-a x}}{a x}+\log (x) \log (a x)-\frac{e^{-a x} \log (a x)}{a x}-\frac{1}{2} \log ^2(x)+\gamma  \log (x)","-a x \, _3F_3(1,1,1;2,2,2;-a x)-\text{Gamma}(-1,a x)+\frac{1}{2} \log ^2(a x)+\gamma  \log (x)",1,"-(1/(a*E^(a*x)*x)) - a*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, -(a*x)] + EulerGamma*Log[x] + Gamma[0, a*x]*Log[x] - Log[x]^2/2 + ExpIntegralEi[-(a*x)]*(-1 + Log[x] - Log[a*x]) - Log[a*x]/(a*E^(a*x)*x) + Gamma[-1, a*x]*Log[a*x] + Log[x]*Log[a*x]","B",1
39,1,18,18,0.0012171,"\int \frac{\text{Gamma}(-1,a x)}{x^2} \, dx","Integrate[Gamma[-1, a*x]/x^2,x]","a \text{Gamma}(-2,a x)-\frac{\text{Gamma}(-1,a x)}{x}","a \text{Gamma}(-2,a x)-\frac{\text{Gamma}(-1,a x)}{x}",1,"a*Gamma[-2, a*x] - Gamma[-1, a*x]/x","A",1
40,1,25,25,0.0012782,"\int \frac{\text{Gamma}(-1,a x)}{x^3} \, dx","Integrate[Gamma[-1, a*x]/x^3,x]","\frac{1}{2} a^2 \text{Gamma}(-3,a x)-\frac{\text{Gamma}(-1,a x)}{2 x^2}","\frac{1}{2} a^2 \text{Gamma}(-3,a x)-\frac{\text{Gamma}(-1,a x)}{2 x^2}",1,"(a^2*Gamma[-3, a*x])/2 - Gamma[-1, a*x]/(2*x^2)","A",1
41,1,25,25,0.0012689,"\int \frac{\text{Gamma}(-1,a x)}{x^4} \, dx","Integrate[Gamma[-1, a*x]/x^4,x]","\frac{1}{3} a^3 \text{Gamma}(-4,a x)-\frac{\text{Gamma}(-1,a x)}{3 x^3}","\frac{1}{3} a^3 \text{Gamma}(-4,a x)-\frac{\text{Gamma}(-1,a x)}{3 x^3}",1,"(a^3*Gamma[-4, a*x])/3 - Gamma[-1, a*x]/(3*x^3)","A",1
42,1,25,25,0.0013259,"\int x^{100} \text{Gamma}(-2,a x) \, dx","Integrate[x^100*Gamma[-2, a*x],x]","\frac{1}{101} x^{101} \text{Gamma}(-2,a x)-\frac{\text{Gamma}(99,a x)}{101 a^{101}}","\frac{1}{101} x^{101} \text{Gamma}(-2,a x)-\frac{\text{Gamma}(99,a x)}{101 a^{101}}",1,"(x^101*Gamma[-2, a*x])/101 - Gamma[99, a*x]/(101*a^101)","A",1
43,1,25,25,0.0016525,"\int x^3 \text{Gamma}(-2,a x) \, dx","Integrate[x^3*Gamma[-2, a*x],x]","\frac{1}{4} x^4 \text{Gamma}(-2,a x)-\frac{\text{Gamma}(2,a x)}{4 a^4}","\frac{1}{4} x^4 \text{Gamma}(-2,a x)-\frac{\text{Gamma}(2,a x)}{4 a^4}",1,"(x^4*Gamma[-2, a*x])/4 - Gamma[2, a*x]/(4*a^4)","A",1
44,1,26,26,0.0082595,"\int x^2 \text{Gamma}(-2,a x) \, dx","Integrate[x^2*Gamma[-2, a*x],x]","\frac{1}{3} x^3 \text{Gamma}(-2,a x)-\frac{e^{-a x}}{3 a^3}","\frac{1}{3} x^3 \text{Gamma}(-2,a x)-\frac{e^{-a x}}{3 a^3}",1,"-1/(3*a^3*E^(a*x)) + (x^3*Gamma[-2, a*x])/3","A",1
45,1,25,25,0.0010689,"\int x \text{Gamma}(-2,a x) \, dx","Integrate[x*Gamma[-2, a*x],x]","\frac{1}{2} x^2 \text{Gamma}(-2,a x)-\frac{\text{Gamma}(0,a x)}{2 a^2}","\frac{1}{2} x^2 \text{Gamma}(-2,a x)-\frac{\text{Gamma}(0,a x)}{2 a^2}",1,"(x^2*Gamma[-2, a*x])/2 - Gamma[0, a*x]/(2*a^2)","A",1
46,1,32,18,0.0194147,"\int \text{Gamma}(-2,a x) \, dx","Integrate[Gamma[-2, a*x],x]","x \text{Gamma}(-2,a x)-\frac{e^{-a x}}{a^2 x}-\frac{\text{Ei}(-a x)}{a}","x \text{Gamma}(-2,a x)-\frac{\text{Gamma}(-1,a x)}{a}",1,"-(1/(a^2*E^(a*x)*x)) - ExpIntegralEi[-(a*x)]/a + x*Gamma[-2, a*x]","A",1
47,1,141,55,0.9519923,"\int \frac{\text{Gamma}(-2,a x)}{x} \, dx","Integrate[Gamma[-2, a*x]/x,x]","\frac{1}{4} \left(2 a x \, _3F_3(1,1,1;2,2,2;-a x)-2 \log (x) \text{Gamma}(0,a x)-\frac{e^{-a x}}{a^2 x^2}-\frac{2 e^{-a x} \log (a x)}{a^2 x^2}+\text{Ei}(-a x) (2 \log (a x)-2 \log (x)+3)+\frac{3 e^{-a x}}{a x}-2 \log (x) \log (a x)+\frac{2 e^{-a x} \log (a x)}{a x}+\log ^2(x)-2 \gamma  \log (x)\right)+\log (a x) \text{Gamma}(-2,a x)","\frac{1}{2} a x \, _3F_3(1,1,1;2,2,2;-a x)-\frac{1}{2} \text{Gamma}(-2,a x)+\frac{1}{2} \text{Gamma}(-1,a x)-\frac{1}{4} \log ^2(a x)-\frac{1}{2} \gamma  \log (x)",1,"Gamma[-2, a*x]*Log[a*x] + (-(1/(a^2*E^(a*x)*x^2)) + 3/(a*E^(a*x)*x) + 2*a*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, -(a*x)] - 2*EulerGamma*Log[x] - 2*Gamma[0, a*x]*Log[x] + Log[x]^2 - (2*Log[a*x])/(a^2*E^(a*x)*x^2) + (2*Log[a*x])/(a*E^(a*x)*x) - 2*Log[x]*Log[a*x] + ExpIntegralEi[-(a*x)]*(3 - 2*Log[x] + 2*Log[a*x]))/4","B",1
48,1,18,18,0.0012673,"\int \frac{\text{Gamma}(-2,a x)}{x^2} \, dx","Integrate[Gamma[-2, a*x]/x^2,x]","a \text{Gamma}(-3,a x)-\frac{\text{Gamma}(-2,a x)}{x}","a \text{Gamma}(-3,a x)-\frac{\text{Gamma}(-2,a x)}{x}",1,"a*Gamma[-3, a*x] - Gamma[-2, a*x]/x","A",1
49,1,25,25,0.0014292,"\int \frac{\text{Gamma}(-2,a x)}{x^3} \, dx","Integrate[Gamma[-2, a*x]/x^3,x]","\frac{1}{2} a^2 \text{Gamma}(-4,a x)-\frac{\text{Gamma}(-2,a x)}{2 x^2}","\frac{1}{2} a^2 \text{Gamma}(-4,a x)-\frac{\text{Gamma}(-2,a x)}{2 x^2}",1,"(a^2*Gamma[-4, a*x])/2 - Gamma[-2, a*x]/(2*x^2)","A",1
50,1,25,25,0.0013572,"\int \frac{\text{Gamma}(-2,a x)}{x^4} \, dx","Integrate[Gamma[-2, a*x]/x^4,x]","\frac{1}{3} a^3 \text{Gamma}(-5,a x)-\frac{\text{Gamma}(-2,a x)}{3 x^3}","\frac{1}{3} a^3 \text{Gamma}(-5,a x)-\frac{\text{Gamma}(-2,a x)}{3 x^3}",1,"(a^3*Gamma[-5, a*x])/3 - Gamma[-2, a*x]/(3*x^3)","A",1
51,1,25,25,0.0013252,"\int x^{100} \text{Gamma}(-3,a x) \, dx","Integrate[x^100*Gamma[-3, a*x],x]","\frac{1}{101} x^{101} \text{Gamma}(-3,a x)-\frac{\text{Gamma}(98,a x)}{101 a^{101}}","\frac{1}{101} x^{101} \text{Gamma}(-3,a x)-\frac{\text{Gamma}(98,a x)}{101 a^{101}}",1,"(x^101*Gamma[-3, a*x])/101 - Gamma[98, a*x]/(101*a^101)","A",1
52,1,26,26,0.007867,"\int x^3 \text{Gamma}(-3,a x) \, dx","Integrate[x^3*Gamma[-3, a*x],x]","\frac{1}{4} x^4 \text{Gamma}(-3,a x)-\frac{e^{-a x}}{4 a^4}","\frac{1}{4} x^4 \text{Gamma}(-3,a x)-\frac{e^{-a x}}{4 a^4}",1,"-1/(4*a^4*E^(a*x)) + (x^4*Gamma[-3, a*x])/4","A",1
53,1,25,25,0.0021865,"\int x^2 \text{Gamma}(-3,a x) \, dx","Integrate[x^2*Gamma[-3, a*x],x]","\frac{1}{3} x^3 \text{Gamma}(-3,a x)-\frac{\text{Gamma}(0,a x)}{3 a^3}","\frac{1}{3} x^3 \text{Gamma}(-3,a x)-\frac{\text{Gamma}(0,a x)}{3 a^3}",1,"(x^3*Gamma[-3, a*x])/3 - Gamma[0, a*x]/(3*a^3)","A",1
54,1,25,25,0.0010158,"\int x \text{Gamma}(-3,a x) \, dx","Integrate[x*Gamma[-3, a*x],x]","\frac{1}{2} x^2 \text{Gamma}(-3,a x)-\frac{\text{Gamma}(-1,a x)}{2 a^2}","\frac{1}{2} x^2 \text{Gamma}(-3,a x)-\frac{\text{Gamma}(-1,a x)}{2 a^2}",1,"(x^2*Gamma[-3, a*x])/2 - Gamma[-1, a*x]/(2*a^2)","A",1
55,1,40,18,0.0242067,"\int \text{Gamma}(-3,a x) \, dx","Integrate[Gamma[-3, a*x],x]","\frac{1}{2} \left(2 x \text{Gamma}(-3,a x)+\frac{e^{-a x} (a x-1)}{a^3 x^2}+\frac{\text{Ei}(-a x)}{a}\right)","x \text{Gamma}(-3,a x)-\frac{\text{Gamma}(-2,a x)}{a}",1,"((-1 + a*x)/(a^3*E^(a*x)*x^2) + ExpIntegralEi[-(a*x)]/a + 2*x*Gamma[-3, a*x])/2","B",1
56,1,175,64,0.8511321,"\int \frac{\text{Gamma}(-3,a x)}{x} \, dx","Integrate[Gamma[-3, a*x]/x,x]","\frac{-6 a^4 x \, _3F_3(1,1,1;2,2,2;-a x)+6 a^3 \log (x) \text{Gamma}(0,a x)+a^3 (6 \log (x)-11) \text{Ei}(-a x)-3 a^3 \log ^2(x)+6 \gamma  a^3 \log (x)+6 a^3 \log (x) \log (a x)-\frac{11 a^2 e^{-a x}}{x}-\frac{6 e^{-a x} \left(a^3 x^3 e^{a x} \text{Ei}(-a x)+a^2 x^2-a x+2\right) \log (a x)}{x^3}-\frac{4 e^{-a x}}{x^3}+\frac{5 a e^{-a x}}{x^2}}{36 a^3}+\log (a x) \text{Gamma}(-3,a x)","-\frac{1}{6} a x \, _3F_3(1,1,1;2,2,2;-a x)-\frac{1}{3} \text{Gamma}(-3,a x)+\frac{1}{6} \text{Gamma}(-2,a x)-\frac{1}{6} \text{Gamma}(-1,a x)+\frac{1}{12} \log ^2(a x)+\frac{1}{6} \gamma  \log (x)",1,"Gamma[-3, a*x]*Log[a*x] + (-4/(E^(a*x)*x^3) + (5*a)/(E^(a*x)*x^2) - (11*a^2)/(E^(a*x)*x) - 6*a^4*x*HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, -(a*x)] + 6*a^3*EulerGamma*Log[x] + 6*a^3*Gamma[0, a*x]*Log[x] - 3*a^3*Log[x]^2 + a^3*ExpIntegralEi[-(a*x)]*(-11 + 6*Log[x]) - (6*(2 - a*x + a^2*x^2 + a^3*E^(a*x)*x^3*ExpIntegralEi[-(a*x)])*Log[a*x])/(E^(a*x)*x^3) + 6*a^3*Log[x]*Log[a*x])/(36*a^3)","B",1
57,1,18,18,0.0012301,"\int \frac{\text{Gamma}(-3,a x)}{x^2} \, dx","Integrate[Gamma[-3, a*x]/x^2,x]","a \text{Gamma}(-4,a x)-\frac{\text{Gamma}(-3,a x)}{x}","a \text{Gamma}(-4,a x)-\frac{\text{Gamma}(-3,a x)}{x}",1,"a*Gamma[-4, a*x] - Gamma[-3, a*x]/x","A",1
58,1,25,25,0.0014596,"\int \frac{\text{Gamma}(-3,a x)}{x^3} \, dx","Integrate[Gamma[-3, a*x]/x^3,x]","\frac{1}{2} a^2 \text{Gamma}(-5,a x)-\frac{\text{Gamma}(-3,a x)}{2 x^2}","\frac{1}{2} a^2 \text{Gamma}(-5,a x)-\frac{\text{Gamma}(-3,a x)}{2 x^2}",1,"(a^2*Gamma[-5, a*x])/2 - Gamma[-3, a*x]/(2*x^2)","A",1
59,1,25,25,0.0015731,"\int \frac{\text{Gamma}(-3,a x)}{x^4} \, dx","Integrate[Gamma[-3, a*x]/x^4,x]","\frac{1}{3} a^3 \text{Gamma}(-6,a x)-\frac{\text{Gamma}(-3,a x)}{3 x^3}","\frac{1}{3} a^3 \text{Gamma}(-6,a x)-\frac{\text{Gamma}(-3,a x)}{3 x^3}",1,"(a^3*Gamma[-6, a*x])/3 - Gamma[-3, a*x]/(3*x^3)","A",1
60,1,29,29,0.0013361,"\int x^{100} \text{Gamma}\left(\frac{1}{2},a x\right) \, dx","Integrate[x^100*Gamma[1/2, a*x],x]","\frac{1}{101} x^{101} \text{Gamma}\left(\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{203}{2},a x\right)}{101 a^{101}}","\frac{1}{101} x^{101} \text{Gamma}\left(\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{203}{2},a x\right)}{101 a^{101}}",1,"(x^101*Gamma[1/2, a*x])/101 - Gamma[203/2, a*x]/(101*a^101)","A",1
61,1,29,29,0.0012697,"\int x^2 \text{Gamma}\left(\frac{1}{2},a x\right) \, dx","Integrate[x^2*Gamma[1/2, a*x],x]","\frac{1}{3} x^3 \text{Gamma}\left(\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{7}{2},a x\right)}{3 a^3}","\frac{1}{3} x^3 \text{Gamma}\left(\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{7}{2},a x\right)}{3 a^3}",1,"(x^3*Gamma[1/2, a*x])/3 - Gamma[7/2, a*x]/(3*a^3)","A",1
62,1,29,29,0.0010492,"\int x \text{Gamma}\left(\frac{1}{2},a x\right) \, dx","Integrate[x*Gamma[1/2, a*x],x]","\frac{1}{2} x^2 \text{Gamma}\left(\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{5}{2},a x\right)}{2 a^2}","\frac{1}{2} x^2 \text{Gamma}\left(\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{5}{2},a x\right)}{2 a^2}",1,"(x^2*Gamma[1/2, a*x])/2 - Gamma[5/2, a*x]/(2*a^2)","A",1
63,1,50,22,0.0379352,"\int \text{Gamma}\left(\frac{1}{2},a x\right) \, dx","Integrate[Gamma[1/2, a*x],x]","x \text{Gamma}\left(\frac{1}{2},a x\right)+\frac{2 \left(\frac{1}{4} \sqrt{\pi } \text{Erf}\left(\sqrt{a x}\right)-\frac{1}{2} e^{-a x} \sqrt{a x}\right)}{a}","x \text{Gamma}\left(\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{a}",1,"(2*(-Sqrt[a*x]/(2*E^(a*x)) + (Sqrt[Pi]*Erf[Sqrt[a*x]])/4))/a + x*Gamma[1/2, a*x]","B",1
64,1,56,37,0.0624439,"\int \frac{\text{Gamma}\left(\frac{1}{2},a x\right)}{x} \, dx","Integrate[Gamma[1/2, a*x]/x,x]","\log (a x) \left(\text{Gamma}\left(\frac{1}{2},a x\right)+\sqrt{\pi } \text{Erf}\left(\sqrt{a x}\right)\right)-4 \sqrt{a x} \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-a x\right)","\sqrt{\pi } \log (x)-4 \sqrt{a x} \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-a x\right)",1,"-4*Sqrt[a*x]*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2}, -(a*x)] + (Sqrt[Pi]*Erf[Sqrt[a*x]] + Gamma[1/2, a*x])*Log[a*x]","A",0
65,1,22,22,0.0012675,"\int \frac{\text{Gamma}\left(\frac{1}{2},a x\right)}{x^2} \, dx","Integrate[Gamma[1/2, a*x]/x^2,x]","a \text{Gamma}\left(-\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{1}{2},a x\right)}{x}","a \text{Gamma}\left(-\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{1}{2},a x\right)}{x}",1,"a*Gamma[-1/2, a*x] - Gamma[1/2, a*x]/x","A",1
66,1,29,29,0.0016766,"\int \frac{\text{Gamma}\left(\frac{1}{2},a x\right)}{x^3} \, dx","Integrate[Gamma[1/2, a*x]/x^3,x]","\frac{1}{2} a^2 \text{Gamma}\left(-\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{1}{2},a x\right)}{2 x^2}","\frac{1}{2} a^2 \text{Gamma}\left(-\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{1}{2},a x\right)}{2 x^2}",1,"(a^2*Gamma[-3/2, a*x])/2 - Gamma[1/2, a*x]/(2*x^2)","A",1
67,1,29,29,0.0030628,"\int \frac{\text{Gamma}\left(\frac{1}{2},a x\right)}{x^4} \, dx","Integrate[Gamma[1/2, a*x]/x^4,x]","\frac{1}{3} a^3 \text{Gamma}\left(-\frac{5}{2},a x\right)-\frac{\text{Gamma}\left(\frac{1}{2},a x\right)}{3 x^3}","\frac{1}{3} a^3 \text{Gamma}\left(-\frac{5}{2},a x\right)-\frac{\text{Gamma}\left(\frac{1}{2},a x\right)}{3 x^3}",1,"(a^3*Gamma[-5/2, a*x])/3 - Gamma[1/2, a*x]/(3*x^3)","A",1
68,1,29,29,0.0012691,"\int x^{100} \text{Gamma}\left(\frac{3}{2},a x\right) \, dx","Integrate[x^100*Gamma[3/2, a*x],x]","\frac{1}{101} x^{101} \text{Gamma}\left(\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{205}{2},a x\right)}{101 a^{101}}","\frac{1}{101} x^{101} \text{Gamma}\left(\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{205}{2},a x\right)}{101 a^{101}}",1,"(x^101*Gamma[3/2, a*x])/101 - Gamma[205/2, a*x]/(101*a^101)","A",1
69,1,29,29,0.0011605,"\int x^2 \text{Gamma}\left(\frac{3}{2},a x\right) \, dx","Integrate[x^2*Gamma[3/2, a*x],x]","\frac{1}{3} x^3 \text{Gamma}\left(\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{9}{2},a x\right)}{3 a^3}","\frac{1}{3} x^3 \text{Gamma}\left(\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{9}{2},a x\right)}{3 a^3}",1,"(x^3*Gamma[3/2, a*x])/3 - Gamma[9/2, a*x]/(3*a^3)","A",1
70,1,29,29,0.0009883,"\int x \text{Gamma}\left(\frac{3}{2},a x\right) \, dx","Integrate[x*Gamma[3/2, a*x],x]","\frac{1}{2} x^2 \text{Gamma}\left(\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{7}{2},a x\right)}{2 a^2}","\frac{1}{2} x^2 \text{Gamma}\left(\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{7}{2},a x\right)}{2 a^2}",1,"(x^2*Gamma[3/2, a*x])/2 - Gamma[7/2, a*x]/(2*a^2)","A",1
71,1,54,22,0.0960617,"\int \text{Gamma}\left(\frac{3}{2},a x\right) \, dx","Integrate[Gamma[3/2, a*x],x]","x \text{Gamma}\left(\frac{3}{2},a x\right)+\frac{3 \sqrt{\pi } \text{Erf}\left(\sqrt{a x}\right)-2 e^{-a x} \sqrt{a x} (2 a x+3)}{4 a}","x \text{Gamma}\left(\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{5}{2},a x\right)}{a}",1,"((-2*Sqrt[a*x]*(3 + 2*a*x))/E^(a*x) + 3*Sqrt[Pi]*Erf[Sqrt[a*x]])/(4*a) + x*Gamma[3/2, a*x]","B",1
72,1,78,42,0.402701,"\int \frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{x} \, dx","Integrate[Gamma[3/2, a*x]/x,x]","\frac{1}{2} \log (a x) \left(2 \text{Gamma}\left(\frac{3}{2},a x\right)+\sqrt{\pi } \text{Erf}\left(\sqrt{a x}\right)-2 e^{-a x} \sqrt{a x}\right)-\frac{4}{9} (a x)^{3/2} \, _2F_2\left(\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};-a x\right)","\frac{1}{2} \sqrt{\pi } \log (x)-\frac{4}{9} (a x)^{3/2} \, _2F_2\left(\frac{3}{2},\frac{3}{2};\frac{5}{2},\frac{5}{2};-a x\right)",1,"(-4*(a*x)^(3/2)*HypergeometricPFQ[{3/2, 3/2}, {5/2, 5/2}, -(a*x)])/9 + (((-2*Sqrt[a*x])/E^(a*x) + Sqrt[Pi]*Erf[Sqrt[a*x]] + 2*Gamma[3/2, a*x])*Log[a*x])/2","A",1
73,1,22,22,0.0013305,"\int \frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{x^2} \, dx","Integrate[Gamma[3/2, a*x]/x^2,x]","a \text{Gamma}\left(\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{x}","a \text{Gamma}\left(\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{x}",1,"a*Gamma[1/2, a*x] - Gamma[3/2, a*x]/x","A",1
74,1,29,29,0.0013302,"\int \frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{x^3} \, dx","Integrate[Gamma[3/2, a*x]/x^3,x]","\frac{1}{2} a^2 \text{Gamma}\left(-\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{2 x^2}","\frac{1}{2} a^2 \text{Gamma}\left(-\frac{1}{2},a x\right)-\frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{2 x^2}",1,"(a^2*Gamma[-1/2, a*x])/2 - Gamma[3/2, a*x]/(2*x^2)","A",1
75,1,29,29,0.0012402,"\int \frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{x^4} \, dx","Integrate[Gamma[3/2, a*x]/x^4,x]","\frac{1}{3} a^3 \text{Gamma}\left(-\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{3 x^3}","\frac{1}{3} a^3 \text{Gamma}\left(-\frac{3}{2},a x\right)-\frac{\text{Gamma}\left(\frac{3}{2},a x\right)}{3 x^3}",1,"(a^3*Gamma[-3/2, a*x])/3 - Gamma[3/2, a*x]/(3*x^3)","A",1
76,1,39,51,0.0219625,"\int (d x)^m \text{Gamma}(3,b x) \, dx","Integrate[(d*x)^m*Gamma[3, b*x],x]","\frac{(d x)^m \left(b x \text{Gamma}(3,b x)-(b x)^{-m} \text{Gamma}(m+4,b x)\right)}{b (m+1)}","\frac{(d x)^{m+1} \text{Gamma}(3,b x)}{d (m+1)}-\frac{(b x)^{-m} (d x)^m \text{Gamma}(m+4,b x)}{b (m+1)}",1,"((d*x)^m*(b*x*Gamma[3, b*x] - Gamma[4 + m, b*x]/(b*x)^m))/(b*(1 + m))","A",1
77,1,39,51,0.0206228,"\int (d x)^m \text{Gamma}(2,b x) \, dx","Integrate[(d*x)^m*Gamma[2, b*x],x]","\frac{(d x)^m \left(b x \text{Gamma}(2,b x)-(b x)^{-m} \text{Gamma}(m+3,b x)\right)}{b (m+1)}","\frac{(d x)^{m+1} \text{Gamma}(2,b x)}{d (m+1)}-\frac{(b x)^{-m} (d x)^m \text{Gamma}(m+3,b x)}{b (m+1)}",1,"((d*x)^m*(b*x*Gamma[2, b*x] - Gamma[3 + m, b*x]/(b*x)^m))/(b*(1 + m))","A",1
78,1,24,24,0.004833,"\int e^{-b x} (d x)^m \, dx","Integrate[(d*x)^m/E^(b*x),x]","-\frac{(b x)^{-m} (d x)^m \text{Gamma}(m+1,b x)}{b}","-\frac{(b x)^{-m} (d x)^m \text{Gamma}(m+1,b x)}{b}",1,"-(((d*x)^m*Gamma[1 + m, b*x])/(b*(b*x)^m))","A",1
79,1,39,51,0.0203746,"\int (d x)^m \text{Gamma}(0,b x) \, dx","Integrate[(d*x)^m*Gamma[0, b*x],x]","\frac{(d x)^m \left(b x \text{Gamma}(0,b x)-(b x)^{-m} \text{Gamma}(m+1,b x)\right)}{b (m+1)}","\frac{(d x)^{m+1} \text{Gamma}(0,b x)}{d (m+1)}-\frac{(b x)^{-m} (d x)^m \text{Gamma}(m+1,b x)}{b (m+1)}",1,"((d*x)^m*(b*x*Gamma[0, b*x] - Gamma[1 + m, b*x]/(b*x)^m))/(b*(1 + m))","A",1
80,1,37,49,0.0174927,"\int (d x)^m \text{Gamma}(-1,b x) \, dx","Integrate[(d*x)^m*Gamma[-1, b*x],x]","\frac{(d x)^m \left(b x \text{Gamma}(-1,b x)-(b x)^{-m} \text{Gamma}(m,b x)\right)}{b (m+1)}","\frac{(d x)^{m+1} \text{Gamma}(-1,b x)}{d (m+1)}-\frac{(b x)^{-m} (d x)^m \text{Gamma}(m,b x)}{b (m+1)}",1,"((d*x)^m*(b*x*Gamma[-1, b*x] - Gamma[m, b*x]/(b*x)^m))/(b*(1 + m))","A",1
81,1,39,51,0.0172699,"\int (d x)^m \text{Gamma}(-2,b x) \, dx","Integrate[(d*x)^m*Gamma[-2, b*x],x]","\frac{(d x)^m \left(b x \text{Gamma}(-2,b x)-(b x)^{-m} \text{Gamma}(m-1,b x)\right)}{b (m+1)}","\frac{(d x)^{m+1} \text{Gamma}(-2,b x)}{d (m+1)}-\frac{(b x)^{-m} (d x)^m \text{Gamma}(m-1,b x)}{b (m+1)}",1,"((d*x)^m*(b*x*Gamma[-2, b*x] - Gamma[-1 + m, b*x]/(b*x)^m))/(b*(1 + m))","A",1
82,1,24,28,0.0433425,"\int x^m \text{Gamma}(n,x) \, dx","Integrate[x^m*Gamma[n, x],x]","\frac{x^{m+1} \text{Gamma}(n,x)-\text{Gamma}(m+n+1,x)}{m+1}","\frac{x^{m+1} \text{Gamma}(n,x)}{m+1}-\frac{\text{Gamma}(m+n+1,x)}{m+1}",1,"(x^(1 + m)*Gamma[n, x] - Gamma[1 + m + n, x])/(1 + m)","A",1
83,1,38,45,0.0162884,"\int x^m \text{Gamma}(n,b x) \, dx","Integrate[x^m*Gamma[n, b*x],x]","\frac{x^m \left(b x \text{Gamma}(n,b x)-(b x)^{-m} \text{Gamma}(m+n+1,b x)\right)}{b (m+1)}","\frac{x^{m+1} \text{Gamma}(n,b x)}{m+1}-\frac{x^m (b x)^{-m} \text{Gamma}(m+n+1,b x)}{b (m+1)}",1,"(x^m*(b*x*Gamma[n, b*x] - Gamma[1 + m + n, b*x]/(b*x)^m))/(b*(1 + m))","A",1
84,1,34,43,0.0309134,"\int (d x)^m \text{Gamma}(n,x) \, dx","Integrate[(d*x)^m*Gamma[n, x],x]","\frac{x^{-m} (d x)^m \left(x^{m+1} \text{Gamma}(n,x)-\text{Gamma}(m+n+1,x)\right)}{m+1}","\frac{(d x)^{m+1} \text{Gamma}(n,x)}{d (m+1)}-\frac{x^{-m} (d x)^m \text{Gamma}(m+n+1,x)}{m+1}",1,"((d*x)^m*(x^(1 + m)*Gamma[n, x] - Gamma[1 + m + n, x]))/((1 + m)*x^m)","A",1
85,1,40,52,0.0142325,"\int (d x)^m \text{Gamma}(n,b x) \, dx","Integrate[(d*x)^m*Gamma[n, b*x],x]","\frac{(d x)^m \left(b x \text{Gamma}(n,b x)-(b x)^{-m} \text{Gamma}(m+n+1,b x)\right)}{b (m+1)}","\frac{(d x)^{m+1} \text{Gamma}(n,b x)}{d (m+1)}-\frac{(b x)^{-m} (d x)^m \text{Gamma}(m+n+1,b x)}{b (m+1)}",1,"((d*x)^m*(b*x*Gamma[n, b*x] - Gamma[1 + m + n, b*x]/(b*x)^m))/(b*(1 + m))","A",1
86,1,27,27,0.0014561,"\int x^{100} \text{Gamma}(n,a x) \, dx","Integrate[x^100*Gamma[n, a*x],x]","\frac{1}{101} x^{101} \text{Gamma}(n,a x)-\frac{\text{Gamma}(n+101,a x)}{101 a^{101}}","\frac{1}{101} x^{101} \text{Gamma}(n,a x)-\frac{\text{Gamma}(n+101,a x)}{101 a^{101}}",1,"(x^101*Gamma[n, a*x])/101 - Gamma[101 + n, a*x]/(101*a^101)","A",1
87,1,27,27,0.0012424,"\int x^2 \text{Gamma}(n,a x) \, dx","Integrate[x^2*Gamma[n, a*x],x]","\frac{1}{3} x^3 \text{Gamma}(n,a x)-\frac{\text{Gamma}(n+3,a x)}{3 a^3}","\frac{1}{3} x^3 \text{Gamma}(n,a x)-\frac{\text{Gamma}(n+3,a x)}{3 a^3}",1,"(x^3*Gamma[n, a*x])/3 - Gamma[3 + n, a*x]/(3*a^3)","A",1
88,1,27,27,0.0009408,"\int x \text{Gamma}(n,a x) \, dx","Integrate[x*Gamma[n, a*x],x]","\frac{1}{2} x^2 \text{Gamma}(n,a x)-\frac{\text{Gamma}(n+2,a x)}{2 a^2}","\frac{1}{2} x^2 \text{Gamma}(n,a x)-\frac{\text{Gamma}(n+2,a x)}{2 a^2}",1,"(x^2*Gamma[n, a*x])/2 - Gamma[2 + n, a*x]/(2*a^2)","A",1
89,1,20,20,0.0205356,"\int \text{Gamma}(n,a x) \, dx","Integrate[Gamma[n, a*x],x]","x \text{Gamma}(n,a x)-\frac{\text{Gamma}(n+1,a x)}{a}","x \text{Gamma}(n,a x)-\frac{\text{Gamma}(n+1,a x)}{a}",1,"x*Gamma[n, a*x] - Gamma[1 + n, a*x]/a","A",1
90,1,41,31,0.1571698,"\int \frac{\text{Gamma}(n,a x)}{x} \, dx","Integrate[Gamma[n, a*x]/x,x]","\log (x) (\text{Gamma}(n,a x)+\text{Gamma}(n,0,a x))-\frac{(a x)^n \, _2F_2(n,n;n+1,n+1;-a x)}{n^2}","\text{Gamma}(n) \log (x)-\frac{(a x)^n \, _2F_2(n,n;n+1,n+1;-a x)}{n^2}",1,"-(((a*x)^n*HypergeometricPFQ[{n, n}, {1 + n, 1 + n}, -(a*x)])/n^2) + (Gamma[n, a*x] + Gamma[n, 0, a*x])*Log[x]","A",1
91,1,20,20,0.0012743,"\int \frac{\text{Gamma}(n,a x)}{x^2} \, dx","Integrate[Gamma[n, a*x]/x^2,x]","a \text{Gamma}(n-1,a x)-\frac{\text{Gamma}(n,a x)}{x}","a \text{Gamma}(n-1,a x)-\frac{\text{Gamma}(n,a x)}{x}",1,"a*Gamma[-1 + n, a*x] - Gamma[n, a*x]/x","A",1
92,1,27,27,0.0023069,"\int \frac{\text{Gamma}(n,a x)}{x^3} \, dx","Integrate[Gamma[n, a*x]/x^3,x]","\frac{1}{2} a^2 \text{Gamma}(n-2,a x)-\frac{\text{Gamma}(n,a x)}{2 x^2}","\frac{1}{2} a^2 \text{Gamma}(n-2,a x)-\frac{\text{Gamma}(n,a x)}{2 x^2}",1,"(a^2*Gamma[-2 + n, a*x])/2 - Gamma[n, a*x]/(2*x^2)","A",1
93,1,27,27,0.0012143,"\int \frac{\text{Gamma}(n,a x)}{x^4} \, dx","Integrate[Gamma[n, a*x]/x^4,x]","\frac{1}{3} a^3 \text{Gamma}(n-3,a x)-\frac{\text{Gamma}(n,a x)}{3 x^3}","\frac{1}{3} a^3 \text{Gamma}(n-3,a x)-\frac{\text{Gamma}(n,a x)}{3 x^3}",1,"(a^3*Gamma[-3 + n, a*x])/3 - Gamma[n, a*x]/(3*x^3)","A",1
94,1,24,24,0.001334,"\int x^{100} \text{Gamma}(n,2 x) \, dx","Integrate[x^100*Gamma[n, 2*x],x]","\frac{1}{101} x^{101} \text{Gamma}(n,2 x)-\frac{\text{Gamma}(n+101,2 x)}{256065421246102339102334047485952}","\frac{1}{101} x^{101} \text{Gamma}(n,2 x)-\frac{\text{Gamma}(n+101,2 x)}{256065421246102339102334047485952}",1,"(x^101*Gamma[n, 2*x])/101 - Gamma[101 + n, 2*x]/256065421246102339102334047485952","A",1
95,1,24,24,0.0085011,"\int x^2 \text{Gamma}(n,2 x) \, dx","Integrate[x^2*Gamma[n, 2*x],x]","\frac{1}{3} x^3 \text{Gamma}(n,2 x)-\frac{1}{24} \text{Gamma}(n+3,2 x)","\frac{1}{3} x^3 \text{Gamma}(n,2 x)-\frac{1}{24} \text{Gamma}(n+3,2 x)",1,"(x^3*Gamma[n, 2*x])/3 - Gamma[3 + n, 2*x]/24","A",1
96,1,24,24,0.0010187,"\int x \text{Gamma}(n,2 x) \, dx","Integrate[x*Gamma[n, 2*x],x]","\frac{1}{2} x^2 \text{Gamma}(n,2 x)-\frac{1}{8} \text{Gamma}(n+2,2 x)","\frac{1}{2} x^2 \text{Gamma}(n,2 x)-\frac{1}{8} \text{Gamma}(n+2,2 x)",1,"(x^2*Gamma[n, 2*x])/2 - Gamma[2 + n, 2*x]/8","A",1
97,1,19,19,0.008399,"\int \text{Gamma}(n,2 x) \, dx","Integrate[Gamma[n, 2*x],x]","x \text{Gamma}(n,2 x)-\frac{1}{2} \text{Gamma}(n+1,2 x)","x \text{Gamma}(n,2 x)-\frac{1}{2} \text{Gamma}(n+1,2 x)",1,"x*Gamma[n, 2*x] - Gamma[1 + n, 2*x]/2","A",1
98,1,43,31,0.1180862,"\int \frac{\text{Gamma}(n,2 x)}{x} \, dx","Integrate[Gamma[n, 2*x]/x,x]","\log (2 x) (\text{Gamma}(n,2 x)+\text{Gamma}(n,0,2 x))-\frac{2^n x^n \, _2F_2(n,n;n+1,n+1;-2 x)}{n^2}","\text{Gamma}(n) \log (x)-\frac{2^n x^n \, _2F_2(n,n;n+1,n+1;-2 x)}{n^2}",1,"-((2^n*x^n*HypergeometricPFQ[{n, n}, {1 + n, 1 + n}, -2*x])/n^2) + (Gamma[n, 2*x] + Gamma[n, 0, 2*x])*Log[2*x]","A",1
99,1,20,20,0.0012513,"\int \frac{\text{Gamma}(n,2 x)}{x^2} \, dx","Integrate[Gamma[n, 2*x]/x^2,x]","2 \text{Gamma}(n-1,2 x)-\frac{\text{Gamma}(n,2 x)}{x}","2 \text{Gamma}(n-1,2 x)-\frac{\text{Gamma}(n,2 x)}{x}",1,"2*Gamma[-1 + n, 2*x] - Gamma[n, 2*x]/x","A",1
100,1,22,22,0.001419,"\int \frac{\text{Gamma}(n,2 x)}{x^3} \, dx","Integrate[Gamma[n, 2*x]/x^3,x]","2 \text{Gamma}(n-2,2 x)-\frac{\text{Gamma}(n,2 x)}{2 x^2}","2 \text{Gamma}(n-2,2 x)-\frac{\text{Gamma}(n,2 x)}{2 x^2}",1,"2*Gamma[-2 + n, 2*x] - Gamma[n, 2*x]/(2*x^2)","A",1
101,1,24,24,0.0012447,"\int \frac{\text{Gamma}(n,2 x)}{x^4} \, dx","Integrate[Gamma[n, 2*x]/x^4,x]","\frac{8}{3} \text{Gamma}(n-3,2 x)-\frac{\text{Gamma}(n,2 x)}{3 x^3}","\frac{8}{3} \text{Gamma}(n-3,2 x)-\frac{\text{Gamma}(n,2 x)}{3 x^3}",1,"(8*Gamma[-3 + n, 2*x])/3 - Gamma[n, 2*x]/(3*x^3)","A",1
102,1,299,194,0.1834427,"\int (c+d x)^3 \text{Gamma}(0,a+b x) \, dx","Integrate[(c + d*x)^3*Gamma[0, a + b*x],x]","\frac{e^{-a-b x} \left(b^4 x e^{a+b x} \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \text{Gamma}(0,a+b x)+a^3 d^3-4 a^2 b c d^2-a^2 b d^3 x-a^2 d^3+a e^{a+b x} \left(a^3 d^3-4 a^2 b c d^2+6 a b^2 c^2 d-4 b^3 c^3\right) \text{Ei}(-a-b x)+6 a b^2 c^2 d+4 a b^2 c d^2 x+a b^2 d^3 x^2+4 a b c d^2+2 a b d^3 x+2 a d^3-4 b^3 c^3-6 b^3 c^2 d x-4 b^3 c d^2 x^2-b^3 d^3 x^3-6 b^2 c^2 d-8 b^2 c d^2 x-3 b^2 d^3 x^2-8 b c d^2-6 b d^3 x-6 d^3\right)}{4 b^4}","-\frac{d^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(4,\frac{b (c+d x)}{d}\right)}{4 b^4}-\frac{d^2 e^{\frac{b c}{d}-a} (b c-a d) \text{Gamma}\left(3,\frac{b (c+d x)}{d}\right)}{4 b^4}-\frac{(b c-a d)^4 \text{Gamma}(0,a+b x)}{4 b^4 d}-\frac{d e^{\frac{b c}{d}-a} (b c-a d)^2 \text{Gamma}\left(2,\frac{b (c+d x)}{d}\right)}{4 b^4}+\frac{(c+d x)^4 \text{Gamma}(0,a+b x)}{4 d}-\frac{e^{-a-b x} (b c-a d)^3}{4 b^4}",1,"(E^(-a - b*x)*(-4*b^3*c^3 - 6*b^2*c^2*d + 6*a*b^2*c^2*d - 8*b*c*d^2 + 4*a*b*c*d^2 - 4*a^2*b*c*d^2 - 6*d^3 + 2*a*d^3 - a^2*d^3 + a^3*d^3 - 6*b^3*c^2*d*x - 8*b^2*c*d^2*x + 4*a*b^2*c*d^2*x - 6*b*d^3*x + 2*a*b*d^3*x - a^2*b*d^3*x - 4*b^3*c*d^2*x^2 - 3*b^2*d^3*x^2 + a*b^2*d^3*x^2 - b^3*d^3*x^3 + a*(-4*b^3*c^3 + 6*a*b^2*c^2*d - 4*a^2*b*c*d^2 + a^3*d^3)*E^(a + b*x)*ExpIntegralEi[-a - b*x] + b^4*E^(a + b*x)*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Gamma[0, a + b*x]))/(4*b^4)","A",1
103,1,166,150,0.1391632,"\int (c+d x)^2 \text{Gamma}(0,a+b x) \, dx","Integrate[(c + d*x)^2*Gamma[0, a + b*x],x]","\frac{e^{-a-b x} \left(b^3 x e^{a+b x} \left(3 c^2+3 c d x+d^2 x^2\right) \text{Gamma}(0,a+b x)-a e^{a+b x} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right) \text{Ei}(-a-b x)-a^2 d^2+3 a b c d+a b d^2 x+a d^2-3 b^2 c^2-3 b^2 c d x-b^2 d^2 x^2-3 b c d-2 b d^2 x-2 d^2\right)}{3 b^3}","-\frac{d^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(3,\frac{b (c+d x)}{d}\right)}{3 b^3}-\frac{(b c-a d)^3 \text{Gamma}(0,a+b x)}{3 b^3 d}-\frac{d e^{\frac{b c}{d}-a} (b c-a d) \text{Gamma}\left(2,\frac{b (c+d x)}{d}\right)}{3 b^3}+\frac{(c+d x)^3 \text{Gamma}(0,a+b x)}{3 d}-\frac{e^{-a-b x} (b c-a d)^2}{3 b^3}",1,"(E^(-a - b*x)*(-3*b^2*c^2 - 3*b*c*d + 3*a*b*c*d - 2*d^2 + a*d^2 - a^2*d^2 - 3*b^2*c*d*x - 2*b*d^2*x + a*b*d^2*x - b^2*d^2*x^2 - a*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*E^(a + b*x)*ExpIntegralEi[-a - b*x] + b^3*E^(a + b*x)*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Gamma[0, a + b*x]))/(3*b^3)","A",1
104,1,85,106,0.0700383,"\int (c+d x) \text{Gamma}(0,a+b x) \, dx","Integrate[(c + d*x)*Gamma[0, a + b*x],x]","\frac{e^{-a-b x} \left(b^2 x e^{a+b x} (2 c+d x) \text{Gamma}(0,a+b x)+a e^{a+b x} (a d-2 b c) \text{Ei}(-a-b x)+a d-2 b c-b d x-d\right)}{2 b^2}","-\frac{(b c-a d)^2 \text{Gamma}(0,a+b x)}{2 b^2 d}-\frac{d e^{\frac{b c}{d}-a} \text{Gamma}\left(2,\frac{b (c+d x)}{d}\right)}{2 b^2}+\frac{(c+d x)^2 \text{Gamma}(0,a+b x)}{2 d}-\frac{e^{-a-b x} (b c-a d)}{2 b^2}",1,"(E^(-a - b*x)*(-2*b*c - d + a*d - b*d*x + a*(-2*b*c + a*d)*E^(a + b*x)*ExpIntegralEi[-a - b*x] + b^2*E^(a + b*x)*x*(2*c + d*x)*Gamma[0, a + b*x]))/(2*b^2)","A",1
105,1,40,32,0.0389496,"\int \text{Gamma}(0,a+b x) \, dx","Integrate[Gamma[0, a + b*x],x]","x \text{Gamma}(0,a+b x)-\frac{a \text{Ei}(-a-b x)}{b}-\frac{e^{-a-b x}}{b}","\frac{(a+b x) \text{Gamma}(0,a+b x)}{b}-\frac{e^{-a-b x}}{b}",1,"-(E^(-a - b*x)/b) - (a*ExpIntegralEi[-a - b*x])/b + x*Gamma[0, a + b*x]","A",1
106,0,0,18,0.3396345,"\int \frac{\text{Gamma}(0,a+b x)}{c+d x} \, dx","Integrate[Gamma[0, a + b*x]/(c + d*x),x]","\int \frac{\text{Gamma}(0,a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{Gamma}(0,a+b x)}{c+d x},x\right)",0,"Integrate[Gamma[0, a + b*x]/(c + d*x), x]","F",-1
107,1,78,82,0.1982789,"\int \frac{\text{Gamma}(0,a+b x)}{(c+d x)^2} \, dx","Integrate[Gamma[0, a + b*x]/(c + d*x)^2,x]","\frac{-\frac{\text{Gamma}(0,a+b x)}{c+d x}+\frac{b \text{Ei}(-a-b x)}{a d-b c}+\frac{b e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{b c-a d}}{d}","\frac{b \text{Gamma}(0,a+b x)}{d (b c-a d)}-\frac{\text{Gamma}(0,a+b x)}{d (c+d x)}-\frac{b e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{d (b c-a d)}",1,"((b*ExpIntegralEi[-a - b*x])/(-(b*c) + a*d) + (b*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(b*c - a*d) - Gamma[0, a + b*x]/(c + d*x))/d","A",1
108,1,124,137,0.8488684,"\int \frac{\text{Gamma}(0,a+b x)}{(c+d x)^3} \, dx","Integrate[Gamma[0, a + b*x]/(c + d*x)^3,x]","-\frac{\frac{d \left(\text{Gamma}(0,a+b x)+\frac{b e^{-a-b x} (c+d x)}{b c-a d}\right)}{(c+d x)^2}+\frac{b^2 d \text{Ei}(-a-b x)}{(b c-a d)^2}+\frac{b^2 (b c-(a+1) d) e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{(b c-a d)^2}}{2 d^2}","-\frac{b^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{2 d^2 (b c-a d)}+\frac{b^2 \text{Gamma}(0,a+b x)}{2 d (b c-a d)^2}-\frac{b^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{2 d (b c-a d)^2}-\frac{\text{Gamma}(0,a+b x)}{2 d (c+d x)^2}",1,"-((b^2*d*ExpIntegralEi[-a - b*x])/(b*c - a*d)^2 + (b^2*(b*c - (1 + a)*d)*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(b*c - a*d)^2 + (d*((b*E^(-a - b*x)*(c + d*x))/(b*c - a*d) + Gamma[0, a + b*x]))/(c + d*x)^2)/(2*d^2)","A",1
109,1,204,181,1.0454748,"\int \frac{\text{Gamma}(0,a+b x)}{(c+d x)^4} \, dx","Integrate[Gamma[0, a + b*x]/(c + d*x)^4,x]","\frac{-\frac{2 d^2 \text{Gamma}(0,a+b x)}{(c+d x)^3}+\frac{2 b^3 d^2 \text{Ei}(-a-b x)}{(a d-b c)^3}+\frac{2 b^3 d^2 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{(b c-a d)^3}+\frac{e^{-a-b x} \left(b^3 (c+d x)^2 (b c-(a+2) d) e^{b \left(\frac{c}{d}+x\right)} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+b d \left(-b d ((a+3) c+(a+2) d x)+a d^2+b^2 c (c+d x)\right)\right)}{(c+d x)^2 (b c-a d)^2}}{6 d^3}","-\frac{b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(-2,\frac{b (c+d x)}{d}\right)}{3 d^3 (b c-a d)}-\frac{b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{3 d^2 (b c-a d)^2}+\frac{b^3 \text{Gamma}(0,a+b x)}{3 d (b c-a d)^3}-\frac{b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{3 d (b c-a d)^3}-\frac{\text{Gamma}(0,a+b x)}{3 d (c+d x)^3}",1,"((2*b^3*d^2*ExpIntegralEi[-a - b*x])/(-(b*c) + a*d)^3 + (2*b^3*d^2*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(b*c - a*d)^3 + (E^(-a - b*x)*(b*d*(a*d^2 + b^2*c*(c + d*x) - b*d*((3 + a)*c + (2 + a)*d*x)) + b^3*(b*c - (2 + a)*d)*E^(b*(c/d + x))*(c + d*x)^2*ExpIntegralEi[-((b*(c + d*x))/d)]))/((b*c - a*d)^2*(c + d*x)^2) - (2*d^2*Gamma[0, a + b*x])/(c + d*x)^3)/(6*d^3)","A",1
110,1,71,112,0.0991972,"\int e^{-a-b x} (c+d x)^4 \, dx","Integrate[E^(-a - b*x)*(c + d*x)^4,x]","\frac{e^{-a-b x} \left(-b^4 (c+d x)^4-4 b^3 d (c+d x)^3-12 b^2 d^2 (c+d x)^2-24 b d^3 (c+d x)-24 d^4\right)}{b^5}","-\frac{24 d^4 e^{-a-b x}}{b^5}-\frac{24 d^3 e^{-a-b x} (c+d x)}{b^4}-\frac{12 d^2 e^{-a-b x} (c+d x)^2}{b^3}-\frac{4 d e^{-a-b x} (c+d x)^3}{b^2}-\frac{e^{-a-b x} (c+d x)^4}{b}",1,"(E^(-a - b*x)*(-24*d^4 - 24*b*d^3*(c + d*x) - 12*b^2*d^2*(c + d*x)^2 - 4*b^3*d*(c + d*x)^3 - b^4*(c + d*x)^4))/b^5","A",1
111,1,56,87,0.0746062,"\int e^{-a-b x} (c+d x)^3 \, dx","Integrate[E^(-a - b*x)*(c + d*x)^3,x]","\frac{e^{-a-b x} \left(-b^3 (c+d x)^3-3 b^2 d (c+d x)^2-6 b d^2 (c+d x)-6 d^3\right)}{b^4}","-\frac{6 d^3 e^{-a-b x}}{b^4}-\frac{6 d^2 e^{-a-b x} (c+d x)}{b^3}-\frac{3 d e^{-a-b x} (c+d x)^2}{b^2}-\frac{e^{-a-b x} (c+d x)^3}{b}",1,"(E^(-a - b*x)*(-6*d^3 - 6*b*d^2*(c + d*x) - 3*b^2*d*(c + d*x)^2 - b^3*(c + d*x)^3))/b^4","A",1
112,1,41,62,0.0519798,"\int e^{-a-b x} (c+d x)^2 \, dx","Integrate[E^(-a - b*x)*(c + d*x)^2,x]","\frac{e^{-a-b x} \left(-b^2 (c+d x)^2-2 b d (c+d x)-2 d^2\right)}{b^3}","-\frac{2 d^2 e^{-a-b x}}{b^3}-\frac{2 d e^{-a-b x} (c+d x)}{b^2}-\frac{e^{-a-b x} (c+d x)^2}{b}",1,"(E^(-a - b*x)*(-2*d^2 - 2*b*d*(c + d*x) - b^2*(c + d*x)^2))/b^3","A",1
113,1,24,37,0.0310945,"\int e^{-a-b x} (c+d x) \, dx","Integrate[E^(-a - b*x)*(c + d*x),x]","-\frac{e^{-a-b x} (b (c+d x)+d)}{b^2}","-\frac{d e^{-a-b x}}{b^2}-\frac{e^{-a-b x} (c+d x)}{b}",1,"-((E^(-a - b*x)*(d + b*(c + d*x)))/b^2)","A",1
114,1,15,15,0.0041567,"\int e^{-a-b x} \, dx","Integrate[E^(-a - b*x),x]","-\frac{e^{-a-b x}}{b}","-\frac{e^{-a-b x}}{b}",1,"-(E^(-a - b*x)/b)","A",1
115,1,29,28,0.0241712,"\int \frac{e^{-a-b x}}{c+d x} \, dx","Integrate[E^(-a - b*x)/(c + d*x),x]","\frac{e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b c}{d}-b x\right)}{d}","\frac{e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d}",1,"(E^(-a + (b*c)/d)*ExpIntegralEi[-((b*c)/d) - b*x])/d","A",1
116,1,54,53,0.0770844,"\int \frac{e^{-a-b x}}{(c+d x)^2} \, dx","Integrate[E^(-a - b*x)/(c + d*x)^2,x]","-\frac{b e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b c}{d}-b x\right)}{d^2}-\frac{e^{-a-b x}}{d (c+d x)}","-\frac{b e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^2}-\frac{e^{-a-b x}}{d (c+d x)}",1,"-(E^(-a - b*x)/(d*(c + d*x))) - (b*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*c)/d) - b*x])/d^2","A",1
117,1,72,84,0.1027958,"\int \frac{e^{-a-b x}}{(c+d x)^3} \, dx","Integrate[E^(-a - b*x)/(c + d*x)^3,x]","\frac{e^{-a-b x} \left(b^2 (c+d x)^2 e^{b \left(\frac{c}{d}+x\right)} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+d (b (c+d x)-d)\right)}{2 d^3 (c+d x)^2}","\frac{b^2 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{2 d^3}+\frac{b e^{-a-b x}}{2 d^2 (c+d x)}-\frac{e^{-a-b x}}{2 d (c+d x)^2}",1,"(E^(-a - b*x)*(d*(-d + b*(c + d*x)) + b^2*E^(b*(c/d + x))*(c + d*x)^2*ExpIntegralEi[-((b*(c + d*x))/d)]))/(2*d^3*(c + d*x)^2)","A",1
118,1,88,111,0.112894,"\int \frac{e^{-a-b x}}{(c+d x)^4} \, dx","Integrate[E^(-a - b*x)/(c + d*x)^4,x]","\frac{e^{-a-b x} \left(-b^3 (c+d x)^3 e^{b \left(\frac{c}{d}+x\right)} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)-b^2 d (c+d x)^2+b d^2 (c+d x)-2 d^3\right)}{6 d^4 (c+d x)^3}","-\frac{b^3 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{6 d^4}-\frac{b^2 e^{-a-b x}}{6 d^3 (c+d x)}+\frac{b e^{-a-b x}}{6 d^2 (c+d x)^2}-\frac{e^{-a-b x}}{3 d (c+d x)^3}",1,"(E^(-a - b*x)*(-2*d^3 + b*d^2*(c + d*x) - b^2*d*(c + d*x)^2 - b^3*E^(b*(c/d + x))*(c + d*x)^3*ExpIntegralEi[-((b*(c + d*x))/d)]))/(6*d^4*(c + d*x)^3)","A",1
119,1,223,98,0.1824133,"\int (c+d x)^3 \text{Gamma}(2,a+b x) \, dx","Integrate[(c + d*x)^3*Gamma[2, a + b*x],x]","\frac{e^{-a-b x} \left(b^4 x e^{a+b x} \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \text{Gamma}(2,a+b x)-b^4 x \left(4 (a+2) c^3+6 (a+3) c^2 d x+4 (a+4) c d^2 x^2+(a+5) d^3 x^3\right)-4 b^3 (c+d x)^2 ((a+2) c+(a+5) d x)-12 b^2 d (c+d x) ((a+3) c+(a+5) d x)-24 b d^2 ((a+4) c+(a+5) d x)-24 (a+5) d^3+b^5 \left(-x^2\right) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right)}{4 b^4}","-\frac{d^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(6,\frac{b (c+d x)}{d}\right)}{4 b^4}+\frac{d^2 (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(5,\frac{b (c+d x)}{d}\right)}{4 b^4}+\frac{(c+d x)^4 \text{Gamma}(2,a+b x)}{4 d}",1,"(E^(-a - b*x)*(-24*(5 + a)*d^3 - 4*b^3*(c + d*x)^2*((2 + a)*c + (5 + a)*d*x) - 12*b^2*d*(c + d*x)*((3 + a)*c + (5 + a)*d*x) - 24*b*d^2*((4 + a)*c + (5 + a)*d*x) - b^5*x^2*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) - b^4*x*(4*(2 + a)*c^3 + 6*(3 + a)*c^2*d*x + 4*(4 + a)*c*d^2*x^2 + (5 + a)*d^3*x^3) + b^4*E^(a + b*x)*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Gamma[2, a + b*x]))/(4*b^4)","B",1
120,1,160,96,0.1461436,"\int (c+d x)^2 \text{Gamma}(2,a+b x) \, dx","Integrate[(c + d*x)^2*Gamma[2, a + b*x],x]","\frac{e^{-a-b x} \left(b^3 x e^{a+b x} \left(3 c^2+3 c d x+d^2 x^2\right) \text{Gamma}(2,a+b x)-b^3 x \left(3 (a+2) c^2+3 (a+3) c d x+(a+4) d^2 x^2\right)-3 b^2 (c+d x) ((a+2) c+(a+4) d x)-6 b d ((a+3) c+(a+4) d x)-6 (a+4) d^2+b^4 \left(-x^2\right) \left(3 c^2+3 c d x+d^2 x^2\right)\right)}{3 b^3}","-\frac{d^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(5,\frac{b (c+d x)}{d}\right)}{3 b^3}+\frac{d (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(4,\frac{b (c+d x)}{d}\right)}{3 b^3}+\frac{(c+d x)^3 \text{Gamma}(2,a+b x)}{3 d}",1,"(E^(-a - b*x)*(-6*(4 + a)*d^2 - 3*b^2*(c + d*x)*((2 + a)*c + (4 + a)*d*x) - 6*b*d*((3 + a)*c + (4 + a)*d*x) - b^4*x^2*(3*c^2 + 3*c*d*x + d^2*x^2) - b^3*x*(3*(2 + a)*c^2 + 3*(3 + a)*c*d*x + (4 + a)*d^2*x^2) + b^3*E^(a + b*x)*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Gamma[2, a + b*x]))/(3*b^3)","A",1
121,1,99,93,0.0928061,"\int (c+d x) \text{Gamma}(2,a+b x) \, dx","Integrate[(c + d*x)*Gamma[2, a + b*x],x]","\frac{e^{-a-b x} \left(b^2 x e^{a+b x} (2 c+d x) \text{Gamma}(2,a+b x)-b^2 x (2 (a+2) c+(a+3) d x)-2 b ((a+2) c+(a+3) d x)-2 (a+3) d+b^3 \left(-x^2\right) (2 c+d x)\right)}{2 b^2}","\frac{(b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(3,\frac{b (c+d x)}{d}\right)}{2 b^2}-\frac{d e^{\frac{b c}{d}-a} \text{Gamma}\left(4,\frac{b (c+d x)}{d}\right)}{2 b^2}+\frac{(c+d x)^2 \text{Gamma}(2,a+b x)}{2 d}",1,"(E^(-a - b*x)*(-2*(3 + a)*d - b^3*x^2*(2*c + d*x) - 2*b*((2 + a)*c + (3 + a)*d*x) - b^2*x*(2*(2 + a)*c + (3 + a)*d*x) + b^2*E^(a + b*x)*x*(2*c + d*x)*Gamma[2, a + b*x]))/(2*b^2)","A",1
122,1,53,29,0.0257461,"\int \text{Gamma}(2,a+b x) \, dx","Integrate[Gamma[2, a + b*x],x]","x \text{Gamma}(2,a+b x)+e^{-b x} \left(e^{-a} (-b) x^2-\frac{(a+2) e^{-a}}{b}-(a+2) e^{-a} x\right)","\frac{(a+b x) \text{Gamma}(2,a+b x)}{b}-\frac{\text{Gamma}(3,a+b x)}{b}",1,"(-((2 + a)/(b*E^a)) - ((2 + a)*x)/E^a - (b*x^2)/E^a)/E^(b*x) + x*Gamma[2, a + b*x]","A",1
123,0,0,81,0.3649937,"\int \frac{\text{Gamma}(2,a+b x)}{c+d x} \, dx","Integrate[Gamma[2, a + b*x]/(c + d*x),x]","\int \frac{\text{Gamma}(2,a+b x)}{c+d x} \, dx","-\frac{(b c-a d) e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^2}+\frac{e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d}-\frac{e^{-a-b x}}{d}",1,"Integrate[Gamma[2, a + b*x]/(c + d*x), x]","A",-1
124,1,87,73,0.0945127,"\int \frac{\text{Gamma}(2,a+b x)}{(c+d x)^2} \, dx","Integrate[Gamma[2, a + b*x]/(c + d*x)^2,x]","\frac{e^{-a-b x} \left(d \left(b (c+d x)-d e^{a+b x} \text{Gamma}(2,a+b x)\right)+b (c+d x) (b c-a d) e^{b \left(\frac{c}{d}+x\right)} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)\right)}{d^3 (c+d x)}","-\frac{b (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{d^3}-\frac{\text{Gamma}(2,a+b x)}{d (c+d x)}+\frac{b e^{-a-b x}}{d^2}",1,"(E^(-a - b*x)*(b*(b*c - a*d)*E^(b*(c/d + x))*(c + d*x)*ExpIntegralEi[-((b*(c + d*x))/d)] + d*(b*(c + d*x) - d*E^(a + b*x)*Gamma[2, a + b*x])))/(d^3*(c + d*x))","A",1
125,1,94,98,0.1949464,"\int \frac{\text{Gamma}(2,a+b x)}{(c+d x)^3} \, dx","Integrate[Gamma[2, a + b*x]/(c + d*x)^3,x]","\frac{\frac{d \left(d^2 (-\text{Gamma}(2,a+b x))-b e^{-a-b x} (c+d x) (b c-a d)\right)}{(c+d x)^2}-b^2 (-a d+b c+d) e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{2 d^4}","-\frac{b^2 (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{2 d^4}+\frac{b^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{2 d^3}-\frac{\text{Gamma}(2,a+b x)}{2 d (c+d x)^2}",1,"(-(b^2*(b*c + d - a*d)*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)]) + (d*(-(b*(b*c - a*d)*E^(-a - b*x)*(c + d*x)) - d^2*Gamma[2, a + b*x]))/(c + d*x)^2)/(2*d^4)","A",1
126,1,117,98,0.3029653,"\int \frac{\text{Gamma}(2,a+b x)}{(c+d x)^4} \, dx","Integrate[Gamma[2, a + b*x]/(c + d*x)^4,x]","\frac{\frac{d \left(b e^{-a-b x} (c+d x) \left(b d (-a c-(a-2) d x+c)+a d^2+b^2 c (c+d x)\right)-2 d^3 \text{Gamma}(2,a+b x)\right)}{(c+d x)^3}+b^3 (b c-(a-2) d) e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{6 d^5}","-\frac{b^3 (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(-2,\frac{b (c+d x)}{d}\right)}{3 d^5}+\frac{b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{3 d^4}-\frac{\text{Gamma}(2,a+b x)}{3 d (c+d x)^3}",1,"(b^3*(b*c - (-2 + a)*d)*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + (d*(b*E^(-a - b*x)*(c + d*x)*(a*d^2 + b^2*c*(c + d*x) + b*d*(c - a*c - (-2 + a)*d*x)) - 2*d^3*Gamma[2, a + b*x]))/(c + d*x)^3)/(6*d^5)","A",1
127,1,191,98,0.2770666,"\int \frac{\text{Gamma}(2,a+b x)}{(c+d x)^5} \, dx","Integrate[Gamma[2, a + b*x]/(c + d*x)^5,x]","-\frac{\frac{6 d^5 \text{Gamma}(2,a+b x)}{(c+d x)^4}+b^5 c e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)-a b^4 d e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+3 b^4 d e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+\frac{b d e^{-a-b x} \left(b^2 (c+d x)^2 (b c-(a-3) d)+2 d^2 (b c-a d)-b d (c+d x) (b c-(a-3) d)\right)}{(c+d x)^3}}{24 d^6}","-\frac{b^4 (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(-3,\frac{b (c+d x)}{d}\right)}{4 d^6}+\frac{b^4 e^{\frac{b c}{d}-a} \text{Gamma}\left(-2,\frac{b (c+d x)}{d}\right)}{4 d^5}-\frac{\text{Gamma}(2,a+b x)}{4 d (c+d x)^4}",1,"-((b*d*E^(-a - b*x)*(2*d^2*(b*c - a*d) - b*d*(b*c - (-3 + a)*d)*(c + d*x) + b^2*(b*c - (-3 + a)*d)*(c + d*x)^2))/(c + d*x)^3 + b^5*c*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + 3*b^4*d*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - a*b^4*d*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + (6*d^5*Gamma[2, a + b*x])/(c + d*x)^4)/(24*d^6)","A",1
128,1,361,140,0.2700388,"\int (c+d x)^3 \text{Gamma}(3,a+b x) \, dx","Integrate[(c + d*x)^3*Gamma[3, a + b*x],x]","\frac{e^{-a-b x} \left(b^4 x e^{a+b x} \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \text{Gamma}(3,a+b x)-b^4 x \left(4 \left(a^2+4 a+6\right) c^3+6 \left(a^2+6 a+12\right) c^2 d x+4 \left(a^2+8 a+20\right) c d^2 x^2+\left(a^2+10 a+30\right) d^3 x^3\right)-4 b^3 (c+d x) \left(\left(a^2+4 a+6\right) c^2+2 \left(a^2+7 a+15\right) c d x+\left(a^2+10 a+30\right) d^2 x^2\right)-12 b^2 d \left(\left(a^2+6 a+12\right) c^2+2 \left(a^2+8 a+20\right) c d x+\left(a^2+10 a+30\right) d^2 x^2\right)-24 b d^2 \left(\left(a^2+8 a+20\right) c+\left(a^2+10 a+30\right) d x\right)-24 \left(a^2+10 a+30\right) d^3-2 b^5 x^2 \left((4 a+6) c^3+6 (a+2) c^2 d x+2 (2 a+5) c d^2 x^2+(a+3) d^3 x^3\right)+b^6 \left(-x^3\right) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right)}{4 b^4}","-\frac{d^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(7,\frac{b (c+d x)}{d}\right)}{4 b^4}+\frac{d^2 (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(6,\frac{b (c+d x)}{d}\right)}{2 b^4}-\frac{d (b c-a d)^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(5,\frac{b (c+d x)}{d}\right)}{4 b^4}+\frac{(c+d x)^4 \text{Gamma}(3,a+b x)}{4 d}",1,"(E^(-a - b*x)*(-24*(30 + 10*a + a^2)*d^3 - 24*b*d^2*((20 + 8*a + a^2)*c + (30 + 10*a + a^2)*d*x) - 4*b^3*(c + d*x)*((6 + 4*a + a^2)*c^2 + 2*(15 + 7*a + a^2)*c*d*x + (30 + 10*a + a^2)*d^2*x^2) - 12*b^2*d*((12 + 6*a + a^2)*c^2 + 2*(20 + 8*a + a^2)*c*d*x + (30 + 10*a + a^2)*d^2*x^2) - b^6*x^3*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3) - 2*b^5*x^2*((6 + 4*a)*c^3 + 6*(2 + a)*c^2*d*x + 2*(5 + 2*a)*c*d^2*x^2 + (3 + a)*d^3*x^3) - b^4*x*(4*(6 + 4*a + a^2)*c^3 + 6*(12 + 6*a + a^2)*c^2*d*x + 4*(20 + 8*a + a^2)*c*d^2*x^2 + (30 + 10*a + a^2)*d^3*x^3) + b^4*E^(a + b*x)*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Gamma[3, a + b*x]))/(4*b^4)","B",1
129,1,252,137,0.2001782,"\int (c+d x)^2 \text{Gamma}(3,a+b x) \, dx","Integrate[(c + d*x)^2*Gamma[3, a + b*x],x]","\frac{e^{-a-b x} \left(b^3 x e^{a+b x} \left(3 c^2+3 c d x+d^2 x^2\right) \text{Gamma}(3,a+b x)-b^3 x \left(3 \left(a^2+4 a+6\right) c^2+3 \left(a^2+6 a+12\right) c d x+\left(a^2+8 a+20\right) d^2 x^2\right)-3 b^2 \left(\left(a^2+4 a+6\right) c^2+2 \left(a^2+6 a+12\right) c d x+\left(a^2+8 a+20\right) d^2 x^2\right)-6 b d \left(\left(a^2+6 a+12\right) c+\left(a^2+8 a+20\right) d x\right)-6 \left(a^2+8 a+20\right) d^2-b^4 x^2 \left((6 a+9) c^2+6 (a+2) c d x+(2 a+5) d^2 x^2\right)+b^5 \left(-x^3\right) \left(3 c^2+3 c d x+d^2 x^2\right)\right)}{3 b^3}","-\frac{d^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(6,\frac{b (c+d x)}{d}\right)}{3 b^3}-\frac{(b c-a d)^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(4,\frac{b (c+d x)}{d}\right)}{3 b^3}+\frac{2 d (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(5,\frac{b (c+d x)}{d}\right)}{3 b^3}+\frac{(c+d x)^3 \text{Gamma}(3,a+b x)}{3 d}",1,"(E^(-a - b*x)*(-6*(20 + 8*a + a^2)*d^2 - 6*b*d*((12 + 6*a + a^2)*c + (20 + 8*a + a^2)*d*x) - b^5*x^3*(3*c^2 + 3*c*d*x + d^2*x^2) - b^4*x^2*((9 + 6*a)*c^2 + 6*(2 + a)*c*d*x + (5 + 2*a)*d^2*x^2) - 3*b^2*((6 + 4*a + a^2)*c^2 + 2*(12 + 6*a + a^2)*c*d*x + (20 + 8*a + a^2)*d^2*x^2) - b^3*x*(3*(6 + 4*a + a^2)*c^2 + 3*(12 + 6*a + a^2)*c*d*x + (20 + 8*a + a^2)*d^2*x^2) + b^3*E^(a + b*x)*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Gamma[3, a + b*x]))/(3*b^3)","A",1
130,1,146,84,0.0966295,"\int (c+d x) \text{Gamma}(3,a+b x) \, dx","Integrate[(c + d*x)*Gamma[3, a + b*x],x]","\frac{e^{-a-b x} \left(b^2 x e^{a+b x} (2 c+d x) \text{Gamma}(3,a+b x)-b^2 x \left(2 \left(a^2+4 a+6\right) c+\left(a^2+6 a+12\right) d x\right)-2 b \left(\left(a^2+4 a+6\right) c+\left(a^2+6 a+12\right) d x\right)-2 \left(a^2+6 a+12\right) d-2 b^3 x^2 ((2 a+3) c+(a+2) d x)+b^4 \left(-x^3\right) (2 c+d x)\right)}{2 b^2}","-\frac{(b c-a d)^2 \text{Gamma}(3,a+b x)}{2 b^2 d}-\frac{(b c-a d) \text{Gamma}(4,a+b x)}{b^2}-\frac{d \text{Gamma}(5,a+b x)}{2 b^2}+\frac{(c+d x)^2 \text{Gamma}(3,a+b x)}{2 d}",1,"(E^(-a - b*x)*(-2*(12 + 6*a + a^2)*d - b^4*x^3*(2*c + d*x) - 2*b^3*x^2*((3 + 2*a)*c + (2 + a)*d*x) - 2*b*((6 + 4*a + a^2)*c + (12 + 6*a + a^2)*d*x) - b^2*x*(2*(6 + 4*a + a^2)*c + (12 + 6*a + a^2)*d*x) + b^2*E^(a + b*x)*x*(2*c + d*x)*Gamma[3, a + b*x]))/(2*b^2)","A",1
131,1,81,29,0.0325986,"\int \text{Gamma}(3,a+b x) \, dx","Integrate[Gamma[3, a + b*x],x]","x \text{Gamma}(3,a+b x)+e^{-b x} \left(-\frac{\left(a^2+4 a+6\right) e^{-a}}{b}-\left(a^2+4 a+6\right) e^{-a} x+e^{-a} \left(-b^2\right) x^3-(2 a+3) e^{-a} b x^2\right)","\frac{(a+b x) \text{Gamma}(3,a+b x)}{b}-\frac{\text{Gamma}(4,a+b x)}{b}",1,"(-((6 + 4*a + a^2)/(b*E^a)) - ((6 + 4*a + a^2)*x)/E^a - ((3 + 2*a)*b*x^2)/E^a - (b^2*x^3)/E^a)/E^(b*x) + x*Gamma[3, a + b*x]","B",1
132,0,0,162,0.5408387,"\int \frac{\text{Gamma}(3,a+b x)}{c+d x} \, dx","Integrate[Gamma[3, a + b*x]/(c + d*x),x]","\int \frac{\text{Gamma}(3,a+b x)}{c+d x} \, dx","\frac{e^{\frac{b c}{d}-a} (b c-a d)^2 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^3}-\frac{2 e^{\frac{b c}{d}-a} (b c-a d) \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^2}+\frac{e^{-a-b x} (b c-a d)}{d^2}+\frac{2 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d}-\frac{3 e^{-a-b x}}{d}-\frac{e^{-a-b x} (a+b x)}{d}",1,"Integrate[Gamma[3, a + b*x]/(c + d*x), x]","A",-1
133,1,88,95,0.1901602,"\int \frac{\text{Gamma}(3,a+b x)}{(c+d x)^2} \, dx","Integrate[Gamma[3, a + b*x]/(c + d*x)^2,x]","\frac{-\frac{d^3 \text{Gamma}(3,a+b x)}{c+d x}-b (b c-a d)^2 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+b d e^{-a-b x} (2 a d-b c+b d x+d)}{d^4}","\frac{b e^{\frac{b c}{d}-a} (b c-a d)^2 \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{d^4}-\frac{\text{Gamma}(3,a+b x)}{d (c+d x)}+\frac{b \text{Gamma}(2,a+b x)}{d^2}-\frac{b e^{-a-b x} (b c-a d)}{d^3}",1,"(b*d*E^(-a - b*x)*(-(b*c) + d + 2*a*d + b*d*x) - b*(b*c - a*d)^2*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - (d^3*Gamma[3, a + b*x])/(c + d*x))/d^4","A",1
134,1,126,126,0.3199144,"\int \frac{\text{Gamma}(3,a+b x)}{(c+d x)^3} \, dx","Integrate[Gamma[3, a + b*x]/(c + d*x)^3,x]","\frac{\frac{d \left(b e^{-a-b x} (c+d x) \left(a^2 d^2+b d (-2 a c+c+d x)+b^2 c^2\right)-d^3 \text{Gamma}(3,a+b x)\right)}{(c+d x)^2}+b^2 \left(-2 (a-1) b c d+(a-2) a d^2+b^2 c^2\right) e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{2 d^5}","\frac{b^2 (b c-a d)^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{2 d^5}-\frac{b^2 (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{d^4}-\frac{\text{Gamma}(3,a+b x)}{2 d (c+d x)^2}+\frac{b^2 e^{-a-b x}}{2 d^3}",1,"(b^2*(b^2*c^2 - 2*(-1 + a)*b*c*d + (-2 + a)*a*d^2)*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + (d*(b*E^(-a - b*x)*(c + d*x)*(b^2*c^2 + a^2*d^2 + b*d*(c - 2*a*c + d*x)) - d^3*Gamma[3, a + b*x]))/(c + d*x)^2)/(2*d^5)","A",1
135,1,145,142,0.416196,"\int \frac{\text{Gamma}(3,a+b x)}{(c+d x)^4} \, dx","Integrate[Gamma[3, a + b*x]/(c + d*x)^4,x]","\frac{\frac{d \left(-2 d^4 \text{Gamma}(3,a+b x)-b e^{-a-b x} (c+d x) (b c-a d) \left(-b d ((a-3) c+(a-4) d x)+a d^2+b^2 c (c+d x)\right)\right)}{(c+d x)^3}-b^3 \left(\left(a^2-4 a+2\right) d^2-2 (a-2) b c d+b^2 c^2\right) e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{6 d^6}","\frac{b^3 (b c-a d)^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(-2,\frac{b (c+d x)}{d}\right)}{3 d^6}-\frac{2 b^3 (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{3 d^5}+\frac{b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{3 d^4}-\frac{\text{Gamma}(3,a+b x)}{3 d (c+d x)^3}",1,"(-(b^3*(b^2*c^2 - 2*(-2 + a)*b*c*d + (2 - 4*a + a^2)*d^2)*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)]) + (d*(-(b*(b*c - a*d)*E^(-a - b*x)*(c + d*x)*(a*d^2 + b^2*c*(c + d*x) - b*d*((-3 + a)*c + (-4 + a)*d*x))) - 2*d^4*Gamma[3, a + b*x]))/(c + d*x)^3)/(6*d^6)","A",1
136,1,328,142,0.3281406,"\int \frac{\text{Gamma}(3,a+b x)}{(c+d x)^5} \, dx","Integrate[Gamma[3, a + b*x]/(c + d*x)^5,x]","\frac{-\frac{6 d^6 \text{Gamma}(3,a+b x)}{(c+d x)^4}+a^2 b^4 d^2 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+\frac{b d e^{-a-b x} \left(b^2 (c+d x)^2 \left(\left(a^2-6 a+6\right) d^2-2 (a-3) b c d+b^2 c^2\right)-b d (c+d x) \left(-2 (a-3) b c d+(a-6) a d^2+b^2 c^2\right)+2 d^2 (b c-a d)^2\right)}{(c+d x)^3}+b^6 c^2 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)-2 a b^5 c d e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+6 b^5 c d e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)-6 a b^4 d^2 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+6 b^4 d^2 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{24 d^7}","\frac{b^4 (b c-a d)^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(-3,\frac{b (c+d x)}{d}\right)}{4 d^7}-\frac{b^4 (b c-a d) e^{\frac{b c}{d}-a} \text{Gamma}\left(-2,\frac{b (c+d x)}{d}\right)}{2 d^6}+\frac{b^4 e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{4 d^5}-\frac{\text{Gamma}(3,a+b x)}{4 d (c+d x)^4}",1,"((b*d*E^(-a - b*x)*(2*d^2*(b*c - a*d)^2 - b*d*(b^2*c^2 - 2*(-3 + a)*b*c*d + (-6 + a)*a*d^2)*(c + d*x) + b^2*(b^2*c^2 - 2*(-3 + a)*b*c*d + (6 - 6*a + a^2)*d^2)*(c + d*x)^2))/(c + d*x)^3 + b^6*c^2*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + 6*b^5*c*d*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - 2*a*b^5*c*d*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + 6*b^4*d^2*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - 6*a*b^4*d^2*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + a^2*b^4*d^2*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - (6*d^6*Gamma[3, a + b*x])/(c + d*x)^4)/(24*d^7)","B",1
137,1,282,139,0.7317404,"\int (c+d x)^3 \text{Gamma}(-1,a+b x) \, dx","Integrate[(c + d*x)^3*Gamma[-1, a + b*x],x]","\frac{\frac{e^{-a-b x} \left(b^4 x e^{a+b x} (a+b x) \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \text{Gamma}(-1,a+b x)+a^4 \left(-d^3\right)+a^3 d^2 (4 b c-3 d)+a^2 d \left(-6 b^2 c^2+b d (8 c-d x)+2 d^2\right)+a \left(4 b^3 c^3+b^2 d \left(-6 c^2+4 c d x+d^2 x^2\right)-4 b c d^2-2 d^3\right)-b d x \left(b^2 \left(6 c^2+4 c d x+d^2 x^2\right)+2 b d (2 c+d x)+2 d^2\right)\right)}{a+b x}+\left(-a^3 (a+4) d^3+4 a^2 (a+3) b c d^2+4 (a+1) b^3 c^3-6 a (a+2) b^2 c^2 d\right) \text{Ei}(-a-b x)}{4 b^4}","-\frac{d^2 (b c-a d) \text{Gamma}(2,a+b x)}{b^4}-\frac{(b c-a d)^4 \text{Gamma}(-1,a+b x)}{4 b^4 d}-\frac{(b c-a d)^3 \text{Gamma}(0,a+b x)}{b^4}-\frac{d^3 \text{Gamma}(3,a+b x)}{4 b^4}+\frac{(c+d x)^4 \text{Gamma}(-1,a+b x)}{4 d}-\frac{3 d e^{-a-b x} (b c-a d)^2}{2 b^4}",1,"((4*(1 + a)*b^3*c^3 - 6*a*(2 + a)*b^2*c^2*d + 4*a^2*(3 + a)*b*c*d^2 - a^3*(4 + a)*d^3)*ExpIntegralEi[-a - b*x] + (E^(-a - b*x)*(a^3*(4*b*c - 3*d)*d^2 - a^4*d^3 + a^2*d*(-6*b^2*c^2 + 2*d^2 + b*d*(8*c - d*x)) + a*(4*b^3*c^3 - 4*b*c*d^2 - 2*d^3 + b^2*d*(-6*c^2 + 4*c*d*x + d^2*x^2)) - b*d*x*(2*d^2 + 2*b*d*(2*c + d*x) + b^2*(6*c^2 + 4*c*d*x + d^2*x^2)) + b^4*E^(a + b*x)*x*(a + b*x)*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Gamma[-1, a + b*x]))/(a + b*x))/(4*b^4)","B",1
138,1,171,118,0.3339639,"\int (c+d x)^2 \text{Gamma}(-1,a+b x) \, dx","Integrate[(c + d*x)^2*Gamma[-1, a + b*x],x]","\frac{\frac{e^{-a-b x} \left(b^3 x e^{a+b x} (a+b x) \left(3 c^2+3 c d x+d^2 x^2\right) \text{Gamma}(-1,a+b x)+a^3 d^2+a^2 d (2 d-3 b c)+a \left(3 b^2 c^2+b d (d x-3 c)-d^2\right)-b d x (3 b c+b d x+d)\right)}{a+b x}+\left(a^2 (a+3) d^2+3 (a+1) b^2 c^2-3 a (a+2) b c d\right) \text{Ei}(-a-b x)}{3 b^3}","-\frac{(b c-a d)^3 \text{Gamma}(-1,a+b x)}{3 b^3 d}-\frac{(b c-a d)^2 \text{Gamma}(0,a+b x)}{b^3}-\frac{e^{-a} d^2 \text{Gamma}(2,b x)}{3 b^3}+\frac{(c+d x)^3 \text{Gamma}(-1,a+b x)}{3 d}-\frac{d e^{-a-b x} (3 b c-2 a d)}{3 b^3}",1,"((3*(1 + a)*b^2*c^2 - 3*a*(2 + a)*b*c*d + a^2*(3 + a)*d^2)*ExpIntegralEi[-a - b*x] + (E^(-a - b*x)*(a^3*d^2 + a^2*d*(-3*b*c + 2*d) - b*d*x*(3*b*c + d + b*d*x) + a*(3*b^2*c^2 - d^2 + b*d*(-3*c + d*x)) + b^3*E^(a + b*x)*x*(a + b*x)*(3*c^2 + 3*c*d*x + d^2*x^2)*Gamma[-1, a + b*x]))/(a + b*x))/(3*b^3)","A",1
139,1,113,87,0.1110494,"\int (c+d x) \text{Gamma}(-1,a+b x) \, dx","Integrate[(c + d*x)*Gamma[-1, a + b*x],x]","\frac{e^{-a-b x} \left(b^2 x e^{a+b x} (a+b x) (2 c+d x) \text{Gamma}(-1,a+b x)+a^2 (-d)+e^{a+b x} (a+b x) (2 (a+1) b c-a (a+2) d) \text{Ei}(-a-b x)+2 a b c-a d-b d x\right)}{2 b^2 (a+b x)}","-\frac{(b c-a d)^2 \text{Gamma}(-1,a+b x)}{2 b^2 d}-\frac{(b c-a d) \text{Gamma}(0,a+b x)}{b^2}+\frac{(c+d x)^2 \text{Gamma}(-1,a+b x)}{2 d}-\frac{d e^{-a-b x}}{2 b^2}",1,"(E^(-a - b*x)*(2*a*b*c - a*d - a^2*d - b*d*x + (2*(1 + a)*b*c - a*(2 + a)*d)*E^(a + b*x)*(a + b*x)*ExpIntegralEi[-a - b*x] + b^2*E^(a + b*x)*x*(a + b*x)*(2*c + d*x)*Gamma[-1, a + b*x]))/(2*b^2*(a + b*x))","A",1
140,1,48,29,0.0684718,"\int \text{Gamma}(-1,a+b x) \, dx","Integrate[Gamma[-1, a + b*x],x]","x \text{Gamma}(-1,a+b x)+\frac{(a+1) \text{Ei}(-a-b x)}{b}+\frac{a e^{-a-b x}}{b (a+b x)}","\frac{(a+b x) \text{Gamma}(-1,a+b x)}{b}-\frac{\text{Gamma}(0,a+b x)}{b}",1,"(a*E^(-a - b*x))/(b*(a + b*x)) + ((1 + a)*ExpIntegralEi[-a - b*x])/b + x*Gamma[-1, a + b*x]","A",1
141,0,0,18,0.5932058,"\int \frac{\text{Gamma}(-1,a+b x)}{c+d x} \, dx","Integrate[Gamma[-1, a + b*x]/(c + d*x),x]","\int \frac{\text{Gamma}(-1,a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{Gamma}(-1,a+b x)}{c+d x},x\right)",0,"Integrate[Gamma[-1, a + b*x]/(c + d*x), x]","F",-1
142,1,121,98,0.5111137,"\int \frac{\text{Gamma}(-1,a+b x)}{(c+d x)^2} \, dx","Integrate[Gamma[-1, a + b*x]/(c + d*x)^2,x]","\frac{\frac{b e^{-a-b x}}{(a+b x) (b c-a d)}-\frac{\text{Gamma}(-1,a+b x)}{c+d x}}{d}+\frac{b (-a d+b c+d) \text{Ei}(-a-b x)}{d (b c-a d)^2}-\frac{b e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{(b c-a d)^2}","\frac{b \text{Gamma}(-1,a+b x)}{d (b c-a d)}-\frac{\text{Gamma}(-1,a+b x)}{d (c+d x)}-\frac{b \text{Gamma}(0,a+b x)}{(b c-a d)^2}+\frac{b e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{(b c-a d)^2}",1,"(b*(b*c + d - a*d)*ExpIntegralEi[-a - b*x])/(d*(b*c - a*d)^2) - (b*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(b*c - a*d)^2 + ((b*E^(-a - b*x))/((b*c - a*d)*(a + b*x)) - Gamma[-1, a + b*x]/(c + d*x))/d","A",1
143,1,174,153,1.0010134,"\int \frac{\text{Gamma}(-1,a+b x)}{(c+d x)^3} \, dx","Integrate[Gamma[-1, a + b*x]/(c + d*x)^3,x]","\frac{1}{2} \left(-\frac{\text{Gamma}(-1,a+b x)}{d (c+d x)^2}+\frac{b^2 ((a-2) d-b c) \text{Ei}(-a-b x)}{d (a d-b c)^3}+\frac{b^2 (b c-(a+2) d) e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d (b c-a d)^3}+\frac{b^2 e^{-a-b x}}{d (a+b x) (b c-a d)^2}+\frac{b e^{-a-b x}}{(c+d x) (b c-a d)^2}\right)","\frac{b^2 \text{Gamma}(-1,a+b x)}{2 d (b c-a d)^2}+\frac{b^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{2 d (b c-a d)^2}-\frac{b^2 \text{Gamma}(0,a+b x)}{(b c-a d)^3}+\frac{b^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{(b c-a d)^3}-\frac{\text{Gamma}(-1,a+b x)}{2 d (c+d x)^2}",1,"((b^2*E^(-a - b*x))/(d*(b*c - a*d)^2*(a + b*x)) + (b*E^(-a - b*x))/((b*c - a*d)^2*(c + d*x)) + (b^2*(-(b*c) + (-2 + a)*d)*ExpIntegralEi[-a - b*x])/(d*(-(b*c) + a*d)^3) + (b^2*(b*c - (2 + a)*d)*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(d*(b*c - a*d)^3) - Gamma[-1, a + b*x]/(d*(c + d*x)^2))/2","A",1
144,0,0,197,1.1821424,"\int \frac{\text{Gamma}(-1,a+b x)}{(c+d x)^4} \, dx","Integrate[Gamma[-1, a + b*x]/(c + d*x)^4,x]","\int \frac{\text{Gamma}(-1,a+b x)}{(c+d x)^4} \, dx","\frac{b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(-2,\frac{b (c+d x)}{d}\right)}{3 d^2 (b c-a d)^2}+\frac{b^3 \text{Gamma}(-1,a+b x)}{3 d (b c-a d)^3}+\frac{2 b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{3 d (b c-a d)^3}-\frac{b^3 \text{Gamma}(0,a+b x)}{(b c-a d)^4}+\frac{b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{(b c-a d)^4}-\frac{\text{Gamma}(-1,a+b x)}{3 d (c+d x)^3}",1,"Integrate[Gamma[-1, a + b*x]/(c + d*x)^4, x]","A",-1
145,1,398,145,0.7351181,"\int (c+d x)^3 \text{Gamma}(-2,a+b x) \, dx","Integrate[(c + d*x)^3*Gamma[-2, a + b*x],x]","\frac{1}{8} \left(2 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \text{Gamma}(-2,a+b x)+\frac{a^4 d^3 \text{Ei}(-a-b x)}{b^4}+\frac{8 a^3 d^3 \text{Ei}(-a-b x)}{b^4}-\frac{4 a^3 c d^2 \text{Ei}(-a-b x)}{b^3}+\frac{12 a^2 d^3 \text{Ei}(-a-b x)}{b^4}-\frac{24 a^2 c d^2 \text{Ei}(-a-b x)}{b^3}+\frac{6 a^2 c^2 d \text{Ei}(-a-b x)}{b^2}+\frac{e^{-a-b x} \left(\frac{a^3 (a+8) d^3-4 a^2 (a+6) b c d^2-4 (a+2) b^3 c^3+6 a (a+4) b^2 c^2 d}{a+b x}-\frac{a \left(a^3 d^3-4 a^2 b c d^2+6 a b^2 c^2 d-4 b^3 c^3\right)}{(a+b x)^2}+2 d^2 ((3 a-1) d-4 b c)-2 b d^3 x\right)}{b^4}-\frac{24 a c d^2 \text{Ei}(-a-b x)}{b^3}+\frac{24 a c^2 d \text{Ei}(-a-b x)}{b^2}+\frac{12 c^2 d \text{Ei}(-a-b x)}{b^2}-\frac{4 a c^3 \text{Ei}(-a-b x)}{b}-\frac{8 c^3 \text{Ei}(-a-b x)}{b}\right)","-\frac{(b c-a d)^4 \text{Gamma}(-2,a+b x)}{4 b^4 d}-\frac{(b c-a d)^3 \text{Gamma}(-1,a+b x)}{b^4}-\frac{3 d (b c-a d)^2 \text{Gamma}(0,a+b x)}{2 b^4}-\frac{e^{-a} d^3 \text{Gamma}(2,b x)}{4 b^4}+\frac{(c+d x)^4 \text{Gamma}(-2,a+b x)}{4 d}-\frac{d^2 e^{-a-b x} (4 b c-3 a d)}{4 b^4}",1,"((E^(-a - b*x)*(2*d^2*(-4*b*c + (-1 + 3*a)*d) - 2*b*d^3*x - (a*(-4*b^3*c^3 + 6*a*b^2*c^2*d - 4*a^2*b*c*d^2 + a^3*d^3))/(a + b*x)^2 + (-4*(2 + a)*b^3*c^3 + 6*a*(4 + a)*b^2*c^2*d - 4*a^2*(6 + a)*b*c*d^2 + a^3*(8 + a)*d^3)/(a + b*x)))/b^4 - (8*c^3*ExpIntegralEi[-a - b*x])/b - (4*a*c^3*ExpIntegralEi[-a - b*x])/b + (12*c^2*d*ExpIntegralEi[-a - b*x])/b^2 + (24*a*c^2*d*ExpIntegralEi[-a - b*x])/b^2 + (6*a^2*c^2*d*ExpIntegralEi[-a - b*x])/b^2 - (24*a*c*d^2*ExpIntegralEi[-a - b*x])/b^3 - (24*a^2*c*d^2*ExpIntegralEi[-a - b*x])/b^3 - (4*a^3*c*d^2*ExpIntegralEi[-a - b*x])/b^3 + (12*a^2*d^3*ExpIntegralEi[-a - b*x])/b^4 + (8*a^3*d^3*ExpIntegralEi[-a - b*x])/b^4 + (a^4*d^3*ExpIntegralEi[-a - b*x])/b^4 + 2*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Gamma[-2, a + b*x])/8","B",1
146,1,229,112,0.4423011,"\int (c+d x)^2 \text{Gamma}(-2,a+b x) \, dx","Integrate[(c + d*x)^2*Gamma[-2, a + b*x],x]","\frac{\frac{e^{-a-b x} \left(2 b^3 x e^{a+b x} (a+b x)^2 \left(3 c^2+3 c d x+d^2 x^2\right) \text{Gamma}(-2,a+b x)+a^4 \left(-d^2\right)-a^3 d (-3 b c+b d x+5 d)+a^2 \left(-3 b^2 c (c-d x)+3 b d (3 c-2 d x)-2 d^2\right)-a b \left(3 b^2 c^2 x+3 b c (c-4 d x)+4 d^2 x\right)-2 b^2 x \left(3 b c^2+d^2 x\right)\right)}{(a+b x)^2}-\left(-3 \left(a^2+4 a+2\right) b c d+a \left(a^2+6 a+6\right) d^2+3 (a+2) b^2 c^2\right) \text{Ei}(-a-b x)}{6 b^3}","-\frac{(b c-a d)^3 \text{Gamma}(-2,a+b x)}{3 b^3 d}-\frac{(b c-a d)^2 \text{Gamma}(-1,a+b x)}{b^3}-\frac{d (b c-a d) \text{Gamma}(0,a+b x)}{b^3}+\frac{(c+d x)^3 \text{Gamma}(-2,a+b x)}{3 d}-\frac{d^2 e^{-a-b x}}{3 b^3}",1,"(-((3*(2 + a)*b^2*c^2 - 3*(2 + 4*a + a^2)*b*c*d + a*(6 + 6*a + a^2)*d^2)*ExpIntegralEi[-a - b*x]) + (E^(-a - b*x)*(-(a^4*d^2) - a^3*d*(-3*b*c + 5*d + b*d*x) - 2*b^2*x*(3*b*c^2 + d^2*x) - a*b*(3*b^2*c^2*x + 4*d^2*x + 3*b*c*(c - 4*d*x)) + a^2*(-2*d^2 + 3*b*d*(3*c - 2*d*x) - 3*b^2*c*(c - d*x)) + 2*b^3*E^(a + b*x)*x*(a + b*x)^2*(3*c^2 + 3*c*d*x + d^2*x^2)*Gamma[-2, a + b*x]))/(a + b*x)^2)/(6*b^3)","B",1
147,1,142,84,0.2314781,"\int (c+d x) \text{Gamma}(-2,a+b x) \, dx","Integrate[(c + d*x)*Gamma[-2, a + b*x],x]","\frac{\frac{e^{-a-b x} \left(2 b^2 x e^{a+b x} (a+b x)^2 (2 c+d x) \text{Gamma}(-2,a+b x)+a^3 d-2 a^2 b c+a^2 b d x+3 a^2 d-2 a b^2 c x-2 a b c+4 a b d x-4 b^2 c x\right)}{(a+b x)^2}-\left(2 (a+2) b c-\left(a^2+4 a+2\right) d\right) \text{Ei}(-a-b x)}{4 b^2}","-\frac{(b c-a d)^2 \text{Gamma}(-2,a+b x)}{2 b^2 d}-\frac{(b c-a d) \text{Gamma}(-1,a+b x)}{b^2}-\frac{d \text{Gamma}(0,a+b x)}{2 b^2}+\frac{(c+d x)^2 \text{Gamma}(-2,a+b x)}{2 d}",1,"(-((2*(2 + a)*b*c - (2 + 4*a + a^2)*d)*ExpIntegralEi[-a - b*x]) + (E^(-a - b*x)*(-2*a*b*c - 2*a^2*b*c + 3*a^2*d + a^3*d - 4*b^2*c*x - 2*a*b^2*c*x + 4*a*b*d*x + a^2*b*d*x + 2*b^2*E^(a + b*x)*x*(a + b*x)^2*(2*c + d*x)*Gamma[-2, a + b*x]))/(a + b*x)^2)/(4*b^2)","A",1
148,1,77,29,0.0798809,"\int \text{Gamma}(-2,a+b x) \, dx","Integrate[Gamma[-2, a + b*x],x]","x \text{Gamma}(-2,a+b x)-\frac{a \text{Ei}(-a-b x)}{2 b}-\frac{\text{Ei}(-a-b x)}{b}+\frac{e^{-a-b x} (a-(a+2) (a+b x))}{2 b (a+b x)^2}","\frac{(a+b x) \text{Gamma}(-2,a+b x)}{b}-\frac{\text{Gamma}(-1,a+b x)}{b}",1,"(E^(-a - b*x)*(a - (2 + a)*(a + b*x)))/(2*b*(a + b*x)^2) - ExpIntegralEi[-a - b*x]/b - (a*ExpIntegralEi[-a - b*x])/(2*b) + x*Gamma[-2, a + b*x]","B",1
149,0,0,18,1.1212243,"\int \frac{\text{Gamma}(-2,a+b x)}{c+d x} \, dx","Integrate[Gamma[-2, a + b*x]/(c + d*x),x]","\int \frac{\text{Gamma}(-2,a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{Gamma}(-2,a+b x)}{c+d x},x\right)",0,"Integrate[Gamma[-2, a + b*x]/(c + d*x), x]","F",-1
150,1,178,120,0.4756338,"\int \frac{\text{Gamma}(-2,a+b x)}{(c+d x)^2} \, dx","Integrate[Gamma[-2, a + b*x]/(c + d*x)^2,x]","-\frac{\text{Gamma}(-2,a+b x)}{d (c+d x)}-\frac{b e^{-a-b x} \left(e^{a+b x} (a+b x)^2 (b c-(a-2) d) \text{Ei}(-a-b x)+(a-1) b c-(a-2) b d x-(a-3) a d+b^2 c x\right)}{2 d (a+b x)^2 (b c-a d)^2}+\frac{b d \text{Ei}(-a-b x)}{(a d-b c)^3}-\frac{b d e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b c}{d}-b x\right)}{(a d-b c)^3}","\frac{b \text{Gamma}(-2,a+b x)}{d (b c-a d)}-\frac{\text{Gamma}(-2,a+b x)}{d (c+d x)}-\frac{b \text{Gamma}(-1,a+b x)}{(b c-a d)^2}+\frac{b d \text{Gamma}(0,a+b x)}{(b c-a d)^3}-\frac{b d e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{(b c-a d)^3}",1,"(b*d*ExpIntegralEi[-a - b*x])/(-(b*c) + a*d)^3 - (b*E^(-a - b*x)*((-1 + a)*b*c - (-3 + a)*a*d + b^2*c*x - (-2 + a)*b*d*x + (b*c - (-2 + a)*d)*E^(a + b*x)*(a + b*x)^2*ExpIntegralEi[-a - b*x]))/(2*d*(b*c - a*d)^2*(a + b*x)^2) - (b*d*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*c)/d) - b*x])/(-(b*c) + a*d)^3 - Gamma[-2, a + b*x]/(d*(c + d*x))","A",1
151,1,237,179,0.885322,"\int \frac{\text{Gamma}(-2,a+b x)}{(c+d x)^3} \, dx","Integrate[Gamma[-2, a + b*x]/(c + d*x)^3,x]","\frac{1}{2} \left(-\frac{\text{Gamma}(-2,a+b x)}{d (c+d x)^2}-\frac{3 b^2 d \text{Ei}(-a-b x)}{(b c-a d)^4}-\frac{b^2 (b c-(a+3) d) e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{(b c-a d)^4}+\frac{b^2 e^{-a-b x}}{2 d (a+b x)^2 (b c-a d)^2}+\frac{b d e^{-a-b x}}{(c+d x) (a d-b c)^3}\right)-\frac{b^2 e^{-a-b x} (b c-(a-4) d) \left(e^{a+b x} (a+b x) \text{Ei}(-a-b x)+1\right)}{4 d (a+b x) (b c-a d)^3}","\frac{b^2 \text{Gamma}(-2,a+b x)}{2 d (b c-a d)^2}-\frac{b^2 \text{Gamma}(-1,a+b x)}{(b c-a d)^3}-\frac{b^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{2 (b c-a d)^3}+\frac{3 b^2 d \text{Gamma}(0,a+b x)}{2 (b c-a d)^4}-\frac{3 b^2 d e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{2 (b c-a d)^4}-\frac{\text{Gamma}(-2,a+b x)}{2 d (c+d x)^2}",1,"-(b^2*(b*c - (-4 + a)*d)*E^(-a - b*x)*(1 + E^(a + b*x)*(a + b*x)*ExpIntegralEi[-a - b*x]))/(4*d*(b*c - a*d)^3*(a + b*x)) + ((b^2*E^(-a - b*x))/(2*d*(b*c - a*d)^2*(a + b*x)^2) + (b*d*E^(-a - b*x))/((-(b*c) + a*d)^3*(c + d*x)) - (3*b^2*d*ExpIntegralEi[-a - b*x])/(b*c - a*d)^4 - (b^2*(b*c - (3 + a)*d)*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(b*c - a*d)^4 - Gamma[-2, a + b*x]/(d*(c + d*x)^2))/2","A",1
152,0,0,217,2.0541197,"\int \frac{\text{Gamma}(-2,a+b x)}{(c+d x)^4} \, dx","Integrate[Gamma[-2, a + b*x]/(c + d*x)^4,x]","\int \frac{\text{Gamma}(-2,a+b x)}{(c+d x)^4} \, dx","\frac{b^3 \text{Gamma}(-2,a+b x)}{3 d (b c-a d)^3}-\frac{b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(-2,\frac{b (c+d x)}{d}\right)}{3 d (b c-a d)^3}-\frac{b^3 \text{Gamma}(-1,a+b x)}{(b c-a d)^4}-\frac{b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{(b c-a d)^4}+\frac{2 b^3 d \text{Gamma}(0,a+b x)}{(b c-a d)^5}-\frac{2 b^3 d e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{(b c-a d)^5}-\frac{\text{Gamma}(-2,a+b x)}{3 d (c+d x)^3}",1,"Integrate[Gamma[-2, a + b*x]/(c + d*x)^4, x]","A",-1
153,1,482,139,0.6841066,"\int (c+d x)^3 \text{Gamma}(-3,a+b x) \, dx","Integrate[(c + d*x)^3*Gamma[-3, a + b*x],x]","\frac{1}{24} \left(6 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right) \text{Gamma}(-3,a+b x)-\frac{a^4 d^3 \text{Ei}(-a-b x)}{b^4}-\frac{12 a^3 d^3 \text{Ei}(-a-b x)}{b^4}+\frac{4 a^3 c d^2 \text{Ei}(-a-b x)}{b^3}-\frac{36 a^2 d^3 \text{Ei}(-a-b x)}{b^4}+\frac{36 a^2 c d^2 \text{Ei}(-a-b x)}{b^3}-\frac{6 a^2 c^2 d \text{Ei}(-a-b x)}{b^2}+\frac{e^{-a-b x} \left(\frac{-6 \left(a^2+6 a+6\right) b^2 c^2 d+4 a \left(a^2+9 a+18\right) b c d^2-a^2 (a+6)^2 d^3+4 (a+3) b^3 c^3}{a+b x}+\frac{a^3 (a+12) d^3-4 a^2 (a+9) b c d^2-4 (a+3) b^3 c^3+6 a (a+6) b^2 c^2 d}{(a+b x)^2}-\frac{2 a \left(a^3 d^3-4 a^2 b c d^2+6 a b^2 c^2 d-4 b^3 c^3\right)}{(a+b x)^3}-6 d^3\right)}{b^4}-\frac{24 a d^3 \text{Ei}(-a-b x)}{b^4}+\frac{72 a c d^2 \text{Ei}(-a-b x)}{b^3}+\frac{24 c d^2 \text{Ei}(-a-b x)}{b^3}-\frac{36 a c^2 d \text{Ei}(-a-b x)}{b^2}-\frac{36 c^2 d \text{Ei}(-a-b x)}{b^2}+\frac{4 a c^3 \text{Ei}(-a-b x)}{b}+\frac{12 c^3 \text{Ei}(-a-b x)}{b}\right)","-\frac{d^2 (b c-a d) \text{Gamma}(0,a+b x)}{b^4}-\frac{(b c-a d)^4 \text{Gamma}(-3,a+b x)}{4 b^4 d}-\frac{(b c-a d)^3 \text{Gamma}(-2,a+b x)}{b^4}-\frac{3 d (b c-a d)^2 \text{Gamma}(-1,a+b x)}{2 b^4}+\frac{(c+d x)^4 \text{Gamma}(-3,a+b x)}{4 d}-\frac{d^3 e^{-a-b x}}{4 b^4}",1,"((E^(-a - b*x)*(-6*d^3 - (2*a*(-4*b^3*c^3 + 6*a*b^2*c^2*d - 4*a^2*b*c*d^2 + a^3*d^3))/(a + b*x)^3 + (-4*(3 + a)*b^3*c^3 + 6*a*(6 + a)*b^2*c^2*d - 4*a^2*(9 + a)*b*c*d^2 + a^3*(12 + a)*d^3)/(a + b*x)^2 + (4*(3 + a)*b^3*c^3 - 6*(6 + 6*a + a^2)*b^2*c^2*d + 4*a*(18 + 9*a + a^2)*b*c*d^2 - a^2*(6 + a)^2*d^3)/(a + b*x)))/b^4 + (12*c^3*ExpIntegralEi[-a - b*x])/b + (4*a*c^3*ExpIntegralEi[-a - b*x])/b - (36*c^2*d*ExpIntegralEi[-a - b*x])/b^2 - (36*a*c^2*d*ExpIntegralEi[-a - b*x])/b^2 - (6*a^2*c^2*d*ExpIntegralEi[-a - b*x])/b^2 + (24*c*d^2*ExpIntegralEi[-a - b*x])/b^3 + (72*a*c*d^2*ExpIntegralEi[-a - b*x])/b^3 + (36*a^2*c*d^2*ExpIntegralEi[-a - b*x])/b^3 + (4*a^3*c*d^2*ExpIntegralEi[-a - b*x])/b^3 - (24*a*d^3*ExpIntegralEi[-a - b*x])/b^4 - (36*a^2*d^3*ExpIntegralEi[-a - b*x])/b^4 - (12*a^3*d^3*ExpIntegralEi[-a - b*x])/b^4 - (a^4*d^3*ExpIntegralEi[-a - b*x])/b^4 + 6*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3)*Gamma[-3, a + b*x])/24","B",1
154,1,351,109,0.5682163,"\int (c+d x)^2 \text{Gamma}(-3,a+b x) \, dx","Integrate[(c + d*x)^2*Gamma[-3, a + b*x],x]","\frac{1}{18} \left(6 x \left(3 c^2+3 c d x+d^2 x^2\right) \text{Gamma}(-3,a+b x)+\frac{a^3 d^2 \text{Ei}(-a-b x)}{b^3}+\frac{9 a^2 d^2 \text{Ei}(-a-b x)}{b^3}-\frac{3 a^2 c d \text{Ei}(-a-b x)}{b^2}+\frac{2 a e^{-a-b x} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3 (a+b x)^3}+\frac{e^{-a-b x} \left(-3 \left(a^2+6 a+6\right) b c d+a \left(a^2+9 a+18\right) d^2+3 (a+3) b^2 c^2\right)}{b^3 (a+b x)}+\frac{e^{-a-b x} \left(-a^2 (a+9) d^2-3 (a+3) b^2 c^2+3 a (a+6) b c d\right)}{b^3 (a+b x)^2}+\frac{18 a d^2 \text{Ei}(-a-b x)}{b^3}+\frac{6 d^2 \text{Ei}(-a-b x)}{b^3}-\frac{18 a c d \text{Ei}(-a-b x)}{b^2}-\frac{18 c d \text{Ei}(-a-b x)}{b^2}+\frac{3 a c^2 \text{Ei}(-a-b x)}{b}+\frac{9 c^2 \text{Ei}(-a-b x)}{b}\right)","-\frac{(b c-a d)^3 \text{Gamma}(-3,a+b x)}{3 b^3 d}-\frac{(b c-a d)^2 \text{Gamma}(-2,a+b x)}{b^3}-\frac{d (b c-a d) \text{Gamma}(-1,a+b x)}{b^3}-\frac{d^2 \text{Gamma}(0,a+b x)}{3 b^3}+\frac{(c+d x)^3 \text{Gamma}(-3,a+b x)}{3 d}",1,"((2*a*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*E^(-a - b*x))/(b^3*(a + b*x)^3) + ((-3*(3 + a)*b^2*c^2 + 3*a*(6 + a)*b*c*d - a^2*(9 + a)*d^2)*E^(-a - b*x))/(b^3*(a + b*x)^2) + ((3*(3 + a)*b^2*c^2 - 3*(6 + 6*a + a^2)*b*c*d + a*(18 + 9*a + a^2)*d^2)*E^(-a - b*x))/(b^3*(a + b*x)) + (9*c^2*ExpIntegralEi[-a - b*x])/b + (3*a*c^2*ExpIntegralEi[-a - b*x])/b - (18*c*d*ExpIntegralEi[-a - b*x])/b^2 - (18*a*c*d*ExpIntegralEi[-a - b*x])/b^2 - (3*a^2*c*d*ExpIntegralEi[-a - b*x])/b^2 + (6*d^2*ExpIntegralEi[-a - b*x])/b^3 + (18*a*d^2*ExpIntegralEi[-a - b*x])/b^3 + (9*a^2*d^2*ExpIntegralEi[-a - b*x])/b^3 + (a^3*d^2*ExpIntegralEi[-a - b*x])/b^3 + 6*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Gamma[-3, a + b*x])/18","B",1
155,1,270,84,0.2073108,"\int (c+d x) \text{Gamma}(-3,a+b x) \, dx","Integrate[(c + d*x)*Gamma[-3, a + b*x],x]","c x \text{Gamma}(-3,a+b x)+\frac{1}{2} d x^2 \text{Gamma}(-3,a+b x)-\frac{a^2 d \text{Ei}(-a-b x)}{12 b^2}+d e^{-b x} \left(-\frac{e^{-a} a^2}{6 b^2 (a+b x)^3}-\frac{\left(a^2+6 a+6\right) e^{-a}}{12 b^2 (a+b x)}+\frac{(a+6) e^{-a} a}{12 b^2 (a+b x)^2}\right)-\frac{a d \text{Ei}(-a-b x)}{2 b^2}-\frac{d \text{Ei}(-a-b x)}{2 b^2}+\frac{a c \text{Ei}(-a-b x)}{6 b}+\frac{c \text{Ei}(-a-b x)}{2 b}+c e^{-b x} \left(\frac{e^{-a} a}{3 b (a+b x)^3}+\frac{(a+3) e^{-a}}{6 b (a+b x)}-\frac{(a+3) e^{-a}}{6 b (a+b x)^2}\right)","-\frac{(b c-a d)^2 \text{Gamma}(-3,a+b x)}{2 b^2 d}-\frac{(b c-a d) \text{Gamma}(-2,a+b x)}{b^2}-\frac{d \text{Gamma}(-1,a+b x)}{2 b^2}+\frac{(c+d x)^2 \text{Gamma}(-3,a+b x)}{2 d}",1,"(d*(-a^2/(6*b^2*E^a*(a + b*x)^3) + (a*(6 + a))/(12*b^2*E^a*(a + b*x)^2) - (6 + 6*a + a^2)/(12*b^2*E^a*(a + b*x))))/E^(b*x) + (c*(a/(3*b*E^a*(a + b*x)^3) - (3 + a)/(6*b*E^a*(a + b*x)^2) + (3 + a)/(6*b*E^a*(a + b*x))))/E^(b*x) + (c*ExpIntegralEi[-a - b*x])/(2*b) + (a*c*ExpIntegralEi[-a - b*x])/(6*b) - (d*ExpIntegralEi[-a - b*x])/(2*b^2) - (a*d*ExpIntegralEi[-a - b*x])/(2*b^2) - (a^2*d*ExpIntegralEi[-a - b*x])/(12*b^2) + c*x*Gamma[-3, a + b*x] + (d*x^2*Gamma[-3, a + b*x])/2","B",1
156,1,89,29,0.0605488,"\int \text{Gamma}(-3,a+b x) \, dx","Integrate[Gamma[-3, a + b*x],x]","\frac{1}{6} \left(6 x \text{Gamma}(-3,a+b x)+\frac{a \text{Ei}(-a-b x)}{b}+\frac{3 \text{Ei}(-a-b x)}{b}+\frac{e^{-a-b x} \left((a+3) (a+b x)^2-(a+3) (a+b x)+2 a\right)}{b (a+b x)^3}\right)","\frac{(a+b x) \text{Gamma}(-3,a+b x)}{b}-\frac{\text{Gamma}(-2,a+b x)}{b}",1,"((E^(-a - b*x)*(2*a - (3 + a)*(a + b*x) + (3 + a)*(a + b*x)^2))/(b*(a + b*x)^3) + (3*ExpIntegralEi[-a - b*x])/b + (a*ExpIntegralEi[-a - b*x])/b + 6*x*Gamma[-3, a + b*x])/6","B",1
157,0,0,18,0.4442457,"\int \frac{\text{Gamma}(-3,a+b x)}{c+d x} \, dx","Integrate[Gamma[-3, a + b*x]/(c + d*x),x]","\int \frac{\text{Gamma}(-3,a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{Gamma}(-3,a+b x)}{c+d x},x\right)",0,"Integrate[Gamma[-3, a + b*x]/(c + d*x), x]","F",-1
158,1,395,144,1.6297259,"\int \frac{\text{Gamma}(-3,a+b x)}{(c+d x)^2} \, dx","Integrate[Gamma[-3, a + b*x]/(c + d*x)^2,x]","-\frac{\text{Gamma}(-3,a+b x)}{d (c+d x)}+\frac{b \left(\left((a+b x)^3 \text{Ei}(-a-b x)+e^{-a-b x} \left((a+b x)^2-a-b x+2\right)\right) \left(3 a^2 d^2+3 a b d (d x-c)+b^2 \left(c^2-c d x+d^2 x^2\right)\right)-d e^{-a-b x} (a+b x) \left(-a^2-e^{a+b x} (a+b x)^2 (a+b x+3) \text{Ei}(-a-b x)-2 a (b x+1)-b^2 x^2-2 b x+1\right) (b (c-2 d x)-3 a d)+d^2 e^{-a-b x} (a+b x)^2 \left(a^2+e^{a+b x} \left(a^3+3 a^2 (b x+2)+3 a \left(b^2 x^2+4 b x+2\right)+b x \left(b^2 x^2+6 b x+6\right)\right) \text{Ei}(-a-b x)+a (2 b x+5)+b^2 x^2+5 b x+2\right)\right)}{6 d (a+b x)^3 (b c-a d)^3}+\frac{b d^2 \text{Ei}(-a-b x)}{(a d-b c)^4}-\frac{b d^2 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b c}{d}-b x\right)}{(a d-b c)^4}","-\frac{b d^2 \text{Gamma}(0,a+b x)}{(b c-a d)^4}+\frac{b d^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{(b c-a d)^4}+\frac{b d \text{Gamma}(-1,a+b x)}{(b c-a d)^3}-\frac{b \text{Gamma}(-2,a+b x)}{(b c-a d)^2}+\frac{b \text{Gamma}(-3,a+b x)}{d (b c-a d)}-\frac{\text{Gamma}(-3,a+b x)}{d (c+d x)}",1,"(b*d^2*ExpIntegralEi[-a - b*x])/(-(b*c) + a*d)^4 + (b*((3*a^2*d^2 + 3*a*b*d*(-c + d*x) + b^2*(c^2 - c*d*x + d^2*x^2))*(E^(-a - b*x)*(2 - a - b*x + (a + b*x)^2) + (a + b*x)^3*ExpIntegralEi[-a - b*x]) - d*E^(-a - b*x)*(a + b*x)*(-3*a*d + b*(c - 2*d*x))*(1 - a^2 - 2*b*x - b^2*x^2 - 2*a*(1 + b*x) - E^(a + b*x)*(a + b*x)^2*(3 + a + b*x)*ExpIntegralEi[-a - b*x]) + d^2*E^(-a - b*x)*(a + b*x)^2*(2 + a^2 + 5*b*x + b^2*x^2 + a*(5 + 2*b*x) + E^(a + b*x)*(a^3 + 3*a^2*(2 + b*x) + 3*a*(2 + 4*b*x + b^2*x^2) + b*x*(6 + 6*b*x + b^2*x^2))*ExpIntegralEi[-a - b*x])))/(6*d*(b*c - a*d)^3*(a + b*x)^3) - (b*d^2*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*c)/d) - b*x])/(-(b*c) + a*d)^4 - Gamma[-3, a + b*x]/(d*(c + d*x))","B",1
159,1,877,205,8.8174873,"\int \frac{\text{Gamma}(-3,a+b x)}{(c+d x)^3} \, dx","Integrate[Gamma[-3, a + b*x]/(c + d*x)^3,x]","\frac{1}{12} \left(\frac{2 \left(\frac{e^{-a-b x} \left((a+3) (a+b x)^2-(a+3) (a+b x)+2 a\right)}{b (a+b x)^3}+\frac{a \text{Ei}(-a-b x)}{b}+\frac{3 \text{Ei}(-a-b x)}{b}+6 x \text{Gamma}(-3,a+b x)\right)}{(c+d x)^3}+d \left(\frac{c^3 \text{Ei}(-a-b x) b^5}{d^2 (b c-a d)^5}+\frac{6 c^2 \text{Ei}(-a-b x) b^4}{d (b c-a d)^5}+\frac{3 a c^2 \text{Ei}(-a-b x) b^4}{d (a d-b c)^5}+\frac{3 a^2 c \text{Ei}(-a-b x) b^3}{(b c-a d)^5}-\frac{12 a c \text{Ei}(-a-b x) b^3}{(b c-a d)^5}+\frac{18 c \text{Ei}(-a-b x) b^3}{(b c-a d)^5}+\frac{6 c e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right) b^3}{(b c-a d)^5}+\frac{24 d \text{Ei}(-a-b x) b^2}{(b c-a d)^5}+\frac{a^3 d \text{Ei}(-a-b x) b^2}{(a d-b c)^5}-\frac{6 a^2 d \text{Ei}(-a-b x) b^2}{(a d-b c)^5}+\frac{18 a d \text{Ei}(-a-b x) b^2}{(a d-b c)^5}-\frac{24 d e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right) b^2}{(b c-a d)^5}+\frac{6 a d e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right) b^2}{(a d-b c)^5}+e^{-a-b x} \left(-\frac{\left(b^3 c^3-5 a b^2 d c^2+a (7 a-6) b d^2 c-3 a \left(a^2-2 a+8\right) d^3\right) b^2}{d^2 (a d-b c)^5 (a+b x)}-\frac{\left(b^2 c^2-4 a b d c+3 (a-4) a d^2\right) b^2}{d^2 (b c-a d)^4 (a+b x)^2}-\frac{2 (b c-3 a d) b^2}{d^2 (a d-b c)^3 (a+b x)^3}+\frac{2 \left(d^2 a^3+(a+3) b^2 c^2+\left(-2 a^2-3 a+12\right) b c d\right) b}{(b c-a d)^5 (c+d x)}+\frac{2 \left((a+3) b^2 c^2-2 \left(a^2+2 a-3\right) b d c+a^2 (a+1) d^2\right)}{(b c-a d)^4 (c+d x)^2}+\frac{2 \left((a+3) b^2 c^2+\left(-2 a^2-5 a+3\right) b d c+a \left(a^2+2 a-1\right) d^2\right)}{(b c-a d)^3 (c+d x)^3 b}\right)-\frac{6 (c+3 d x) \text{Gamma}(-3,a+b x)}{d^2 (c+d x)^3}-\frac{2 (a+3) \text{Ei}(-a-b x)}{d (c+d x)^3 b}\right)\right)","-\frac{2 b^2 d^2 \text{Gamma}(0,a+b x)}{(b c-a d)^5}+\frac{2 b^2 d^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{(b c-a d)^5}+\frac{b^2 \text{Gamma}(-3,a+b x)}{2 d (b c-a d)^2}-\frac{b^2 \text{Gamma}(-2,a+b x)}{(b c-a d)^3}+\frac{3 b^2 d \text{Gamma}(-1,a+b x)}{2 (b c-a d)^4}+\frac{b^2 d e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{2 (b c-a d)^4}-\frac{\text{Gamma}(-3,a+b x)}{2 d (c+d x)^2}",1,"((2*((E^(-a - b*x)*(2*a - (3 + a)*(a + b*x) + (3 + a)*(a + b*x)^2))/(b*(a + b*x)^3) + (3*ExpIntegralEi[-a - b*x])/b + (a*ExpIntegralEi[-a - b*x])/b + 6*x*Gamma[-3, a + b*x]))/(c + d*x)^3 + d*(E^(-a - b*x)*((-2*b^2*(b*c - 3*a*d))/(d^2*(-(b*c) + a*d)^3*(a + b*x)^3) - (b^2*(b^2*c^2 - 4*a*b*c*d + 3*(-4 + a)*a*d^2))/(d^2*(b*c - a*d)^4*(a + b*x)^2) - (b^2*(b^3*c^3 - 5*a*b^2*c^2*d + a*(-6 + 7*a)*b*c*d^2 - 3*a*(8 - 2*a + a^2)*d^3))/(d^2*(-(b*c) + a*d)^5*(a + b*x)) + (2*((3 + a)*b^2*c^2 + (3 - 5*a - 2*a^2)*b*c*d + a*(-1 + 2*a + a^2)*d^2))/(b*(b*c - a*d)^3*(c + d*x)^3) + (2*((3 + a)*b^2*c^2 - 2*(-3 + 2*a + a^2)*b*c*d + a^2*(1 + a)*d^2))/((b*c - a*d)^4*(c + d*x)^2) + (2*b*((3 + a)*b^2*c^2 + (12 - 3*a - 2*a^2)*b*c*d + a^3*d^2))/((b*c - a*d)^5*(c + d*x))) + (18*b^3*c*ExpIntegralEi[-a - b*x])/(b*c - a*d)^5 - (12*a*b^3*c*ExpIntegralEi[-a - b*x])/(b*c - a*d)^5 + (3*a^2*b^3*c*ExpIntegralEi[-a - b*x])/(b*c - a*d)^5 + (b^5*c^3*ExpIntegralEi[-a - b*x])/(d^2*(b*c - a*d)^5) + (6*b^4*c^2*ExpIntegralEi[-a - b*x])/(d*(b*c - a*d)^5) + (24*b^2*d*ExpIntegralEi[-a - b*x])/(b*c - a*d)^5 + (3*a*b^4*c^2*ExpIntegralEi[-a - b*x])/(d*(-(b*c) + a*d)^5) + (18*a*b^2*d*ExpIntegralEi[-a - b*x])/(-(b*c) + a*d)^5 - (6*a^2*b^2*d*ExpIntegralEi[-a - b*x])/(-(b*c) + a*d)^5 + (a^3*b^2*d*ExpIntegralEi[-a - b*x])/(-(b*c) + a*d)^5 - (2*(3 + a)*ExpIntegralEi[-a - b*x])/(b*d*(c + d*x)^3) + (6*b^3*c*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(b*c - a*d)^5 - (24*b^2*d*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(b*c - a*d)^5 + (6*a*b^2*d*E^(-a + (b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(-(b*c) + a*d)^5 - (6*(c + 3*d*x)*Gamma[-3, a + b*x])/(d^2*(c + d*x)^3)))/12","B",1
160,0,0,248,3.3659344,"\int \frac{\text{Gamma}(-3,a+b x)}{(c+d x)^4} \, dx","Integrate[Gamma[-3, a + b*x]/(c + d*x)^4,x]","\int \frac{\text{Gamma}(-3,a+b x)}{(c+d x)^4} \, dx","-\frac{10 b^3 d^2 \text{Gamma}(0,a+b x)}{3 (b c-a d)^6}+\frac{10 b^3 d^2 e^{\frac{b c}{d}-a} \text{Gamma}\left(0,\frac{b (c+d x)}{d}\right)}{3 (b c-a d)^6}+\frac{b^3 \text{Gamma}(-3,a+b x)}{3 d (b c-a d)^3}-\frac{b^3 \text{Gamma}(-2,a+b x)}{(b c-a d)^4}+\frac{b^3 e^{\frac{b c}{d}-a} \text{Gamma}\left(-2,\frac{b (c+d x)}{d}\right)}{3 (b c-a d)^4}+\frac{2 b^3 d \text{Gamma}(-1,a+b x)}{(b c-a d)^5}+\frac{4 b^3 d e^{\frac{b c}{d}-a} \text{Gamma}\left(-1,\frac{b (c+d x)}{d}\right)}{3 (b c-a d)^5}-\frac{\text{Gamma}(-3,a+b x)}{3 d (c+d x)^3}",1,"Integrate[Gamma[-3, a + b*x]/(c + d*x)^4, x]","A",-1
161,1,134,80,0.1555858,"\int x^{5/2} \text{Gamma}(2,a+b x) \, dx","Integrate[x^(5/2)*Gamma[2, a + b*x],x]","\frac{e^{-a} \left(105 \sqrt{\pi } (2 a+9) \text{Erf}\left(\sqrt{b} \sqrt{x}\right)-2 \sqrt{b} \sqrt{x} e^{-b x} \left(-16 b^3 x^3 e^{a+b x} \text{Gamma}(2,a+b x)+2 a \left(8 b^3 x^3+28 b^2 x^2+70 b x+105\right)+16 b^4 x^4+72 b^3 x^3+252 b^2 x^2+630 b x+945\right)\right)}{112 b^{7/2}}","-\frac{2 a e^{-a} \sqrt{x} \text{Gamma}\left(\frac{9}{2},b x\right)}{7 b^3 \sqrt{b x}}-\frac{2 e^{-a} \sqrt{x} \text{Gamma}\left(\frac{11}{2},b x\right)}{7 b^3 \sqrt{b x}}+\frac{2}{7} x^{7/2} \text{Gamma}(2,a+b x)",1,"(105*(9 + 2*a)*Sqrt[Pi]*Erf[Sqrt[b]*Sqrt[x]] - (2*Sqrt[b]*Sqrt[x]*(945 + 630*b*x + 252*b^2*x^2 + 72*b^3*x^3 + 16*b^4*x^4 + 2*a*(105 + 70*b*x + 28*b^2*x^2 + 8*b^3*x^3) - 16*b^3*E^(a + b*x)*x^3*Gamma[2, a + b*x]))/E^(b*x))/(112*b^(7/2)*E^a)","A",1
162,1,117,80,0.1515117,"\int x^{3/2} \text{Gamma}(2,a+b x) \, dx","Integrate[x^(3/2)*Gamma[2, a + b*x],x]","\frac{e^{-a} \left(15 \sqrt{\pi } (2 a+7) \text{Erf}\left(\sqrt{b} \sqrt{x}\right)-2 \sqrt{b} \sqrt{x} e^{-b x} \left(-8 b^2 x^2 e^{a+b x} \text{Gamma}(2,a+b x)+a \left(8 b^2 x^2+20 b x+30\right)+8 b^3 x^3+28 b^2 x^2+70 b x+105\right)\right)}{40 b^{5/2}}","-\frac{2 a e^{-a} \sqrt{x} \text{Gamma}\left(\frac{7}{2},b x\right)}{5 b^2 \sqrt{b x}}-\frac{2 e^{-a} \sqrt{x} \text{Gamma}\left(\frac{9}{2},b x\right)}{5 b^2 \sqrt{b x}}+\frac{2}{5} x^{5/2} \text{Gamma}(2,a+b x)",1,"(15*(7 + 2*a)*Sqrt[Pi]*Erf[Sqrt[b]*Sqrt[x]] - (2*Sqrt[b]*Sqrt[x]*(105 + 70*b*x + 28*b^2*x^2 + 8*b^3*x^3 + a*(30 + 20*b*x + 8*b^2*x^2) - 8*b^2*E^(a + b*x)*x^2*Gamma[2, a + b*x]))/E^(b*x))/(40*b^(5/2)*E^a)","A",1
163,1,97,80,0.1161923,"\int \sqrt{x} \text{Gamma}(2,a+b x) \, dx","Integrate[Sqrt[x]*Gamma[2, a + b*x],x]","\frac{e^{-a} \left(3 \sqrt{\pi } (2 a+5) \text{Erf}\left(\sqrt{b} \sqrt{x}\right)-2 \sqrt{b} \sqrt{x} e^{-b x} \left(-4 b x e^{a+b x} \text{Gamma}(2,a+b x)+4 a b x+6 a+4 b^2 x^2+10 b x+15\right)\right)}{12 b^{3/2}}","\frac{2}{3} x^{3/2} \text{Gamma}(2,a+b x)-\frac{2 a e^{-a} \sqrt{x} \text{Gamma}\left(\frac{5}{2},b x\right)}{3 b \sqrt{b x}}-\frac{2 e^{-a} \sqrt{x} \text{Gamma}\left(\frac{7}{2},b x\right)}{3 b \sqrt{b x}}",1,"(3*(5 + 2*a)*Sqrt[Pi]*Erf[Sqrt[b]*Sqrt[x]] - (2*Sqrt[b]*Sqrt[x]*(15 + 6*a + 10*b*x + 4*a*b*x + 4*b^2*x^2 - 4*b*E^(a + b*x)*x*Gamma[2, a + b*x]))/E^(b*x))/(12*b^(3/2)*E^a)","A",1
164,1,76,68,0.0903819,"\int \frac{\text{Gamma}(2,a+b x)}{\sqrt{x}} \, dx","Integrate[Gamma[2, a + b*x]/Sqrt[x],x]","\frac{1}{2} e^{-a} \left(\frac{\sqrt{\pi } (2 a+3) \text{Erf}\left(\sqrt{b} \sqrt{x}\right)}{\sqrt{b}}-2 \sqrt{x} e^{-b x} \left(-2 e^{a+b x} \text{Gamma}(2,a+b x)+2 a+2 b x+3\right)\right)","-\frac{2 a e^{-a} \sqrt{x} \text{Gamma}\left(\frac{3}{2},b x\right)}{\sqrt{b x}}+2 \sqrt{x} \text{Gamma}(2,a+b x)-\frac{2 e^{-a} \sqrt{x} \text{Gamma}\left(\frac{5}{2},b x\right)}{\sqrt{b x}}",1,"(((3 + 2*a)*Sqrt[Pi]*Erf[Sqrt[b]*Sqrt[x]])/Sqrt[b] - (2*Sqrt[x]*(3 + 2*a + 2*b*x - 2*E^(a + b*x)*Gamma[2, a + b*x]))/E^(b*x))/(2*E^a)","A",1
165,1,65,69,0.0967023,"\int \frac{\text{Gamma}(2,a+b x)}{x^{3/2}} \, dx","Integrate[Gamma[2, a + b*x]/x^(3/2),x]","\frac{2 \left(b x e^{-a-b x}-\text{Gamma}(2,a+b x)\right)}{\sqrt{x}}-\sqrt{\pi } (2 a+1) e^{-a} \sqrt{b} \text{Erf}\left(\sqrt{b} \sqrt{x}\right)","\frac{2 a e^{-a} \sqrt{b x} \text{Gamma}\left(\frac{1}{2},b x\right)}{\sqrt{x}}+\frac{2 e^{-a} b \sqrt{x} \text{Gamma}\left(\frac{3}{2},b x\right)}{\sqrt{b x}}-\frac{2 \text{Gamma}(2,a+b x)}{\sqrt{x}}",1,"-(((1 + 2*a)*Sqrt[b]*Sqrt[Pi]*Erf[Sqrt[b]*Sqrt[x]])/E^a) + (2*(b*E^(-a - b*x)*x - Gamma[2, a + b*x]))/Sqrt[x]","A",1
166,1,69,76,0.1325849,"\int \frac{\text{Gamma}(2,a+b x)}{x^{5/2}} \, dx","Integrate[Gamma[2, a + b*x]/x^(5/2),x]","\frac{2}{3} \left(\frac{2 a b x e^{-a-b x}-\text{Gamma}(2,a+b x)}{x^{3/2}}+\sqrt{\pi } (2 a-1) e^{-a} b^{3/2} \text{Erf}\left(\sqrt{b} \sqrt{x}\right)\right)","-\frac{2 \text{Gamma}(2,a+b x)}{3 x^{3/2}}+\frac{2 a e^{-a} b \sqrt{b x} \text{Gamma}\left(-\frac{1}{2},b x\right)}{3 \sqrt{x}}+\frac{2 e^{-a} b \sqrt{b x} \text{Gamma}\left(\frac{1}{2},b x\right)}{3 \sqrt{x}}",1,"(2*(((-1 + 2*a)*b^(3/2)*Sqrt[Pi]*Erf[Sqrt[b]*Sqrt[x]])/E^a + (2*a*b*E^(-a - b*x)*x - Gamma[2, a + b*x])/x^(3/2)))/3","A",1
167,1,80,80,0.1698991,"\int \frac{\text{Gamma}(2,a+b x)}{x^{7/2}} \, dx","Integrate[Gamma[2, a + b*x]/x^(7/2),x]","\frac{2}{15} \left(\frac{2 b x e^{-a-b x} (-2 a b x+a+3 b x)-3 \text{Gamma}(2,a+b x)}{x^{5/2}}-2 \sqrt{\pi } (2 a-3) e^{-a} b^{5/2} \text{Erf}\left(\sqrt{b} \sqrt{x}\right)\right)","\frac{2 a e^{-a} b^2 \sqrt{b x} \text{Gamma}\left(-\frac{3}{2},b x\right)}{5 \sqrt{x}}+\frac{2 e^{-a} b^2 \sqrt{b x} \text{Gamma}\left(-\frac{1}{2},b x\right)}{5 \sqrt{x}}-\frac{2 \text{Gamma}(2,a+b x)}{5 x^{5/2}}",1,"(2*((-2*(-3 + 2*a)*b^(5/2)*Sqrt[Pi]*Erf[Sqrt[b]*Sqrt[x]])/E^a + (2*b*E^(-a - b*x)*x*(a + 3*b*x - 2*a*b*x) - 3*Gamma[2, a + b*x])/x^(5/2)))/15","A",1
168,1,96,80,0.1968461,"\int \frac{\text{Gamma}(2,a+b x)}{x^{9/2}} \, dx","Integrate[Gamma[2, a + b*x]/x^(9/2),x]","\frac{2}{105} \left(\frac{2 b x e^{-a-b x} \left(a \left(4 b^2 x^2-2 b x+3\right)+5 b x (1-2 b x)\right)-15 \text{Gamma}(2,a+b x)}{x^{7/2}}+4 \sqrt{\pi } (2 a-5) e^{-a} b^{7/2} \text{Erf}\left(\sqrt{b} \sqrt{x}\right)\right)","\frac{2 a e^{-a} b^3 \sqrt{b x} \text{Gamma}\left(-\frac{5}{2},b x\right)}{7 \sqrt{x}}+\frac{2 e^{-a} b^3 \sqrt{b x} \text{Gamma}\left(-\frac{3}{2},b x\right)}{7 \sqrt{x}}-\frac{2 \text{Gamma}(2,a+b x)}{7 x^{7/2}}",1,"(2*((4*(-5 + 2*a)*b^(7/2)*Sqrt[Pi]*Erf[Sqrt[b]*Sqrt[x]])/E^a + (2*b*E^(-a - b*x)*x*(5*b*x*(1 - 2*b*x) + a*(3 - 2*b*x + 4*b^2*x^2)) - 15*Gamma[2, a + b*x])/x^(7/2)))/105","A",1
169,0,0,16,2.8860262,"\int x^{3/2} \text{Gamma}(-2,a+b x) \, dx","Integrate[x^(3/2)*Gamma[-2, a + b*x],x]","\int x^{3/2} \text{Gamma}(-2,a+b x) \, dx","\text{Int}\left(x^{3/2} \text{Gamma}(-2,a+b x),x\right)",0,"Integrate[x^(3/2)*Gamma[-2, a + b*x], x]","F",-1
170,0,0,16,2.405933,"\int \sqrt{x} \text{Gamma}(-2,a+b x) \, dx","Integrate[Sqrt[x]*Gamma[-2, a + b*x],x]","\int \sqrt{x} \text{Gamma}(-2,a+b x) \, dx","\text{Int}\left(\sqrt{x} \text{Gamma}(-2,a+b x),x\right)",0,"Integrate[Sqrt[x]*Gamma[-2, a + b*x], x]","F",-1
171,0,0,16,2.3966164,"\int \frac{\text{Gamma}(-2,a+b x)}{\sqrt{x}} \, dx","Integrate[Gamma[-2, a + b*x]/Sqrt[x],x]","\int \frac{\text{Gamma}(-2,a+b x)}{\sqrt{x}} \, dx","\text{Int}\left(\frac{\text{Gamma}(-2,a+b x)}{\sqrt{x}},x\right)",0,"Integrate[Gamma[-2, a + b*x]/Sqrt[x], x]","F",-1
172,0,0,16,2.3557033,"\int \frac{\text{Gamma}(-2,a+b x)}{x^{3/2}} \, dx","Integrate[Gamma[-2, a + b*x]/x^(3/2),x]","\int \frac{\text{Gamma}(-2,a+b x)}{x^{3/2}} \, dx","\text{Int}\left(\frac{\text{Gamma}(-2,a+b x)}{x^{3/2}},x\right)",0,"Integrate[Gamma[-2, a + b*x]/x^(3/2), x]","F",-1
173,1,119,80,0.1389663,"\int x^{4/3} \text{Gamma}(2,a+b x) \, dx","Integrate[x^(4/3)*Gamma[2, a + b*x],x]","-\frac{\sqrt[3]{x} e^{-a-b x} \left(3 \sqrt[3]{b x} \left(-27 b^2 x^2 e^{a+b x} \text{Gamma}(2,a+b x)+3 a \left(9 b^2 x^2+21 b x+28\right)+27 b^3 x^3+90 b^2 x^2+210 b x+280\right)+28 (3 a+10) e^{b x} \text{Gamma}\left(\frac{1}{3},b x\right)\right)}{189 b^2 \sqrt[3]{b x}}","-\frac{3 a e^{-a} \sqrt[3]{x} \text{Gamma}\left(\frac{10}{3},b x\right)}{7 b^2 \sqrt[3]{b x}}-\frac{3 e^{-a} \sqrt[3]{x} \text{Gamma}\left(\frac{13}{3},b x\right)}{7 b^2 \sqrt[3]{b x}}+\frac{3}{7} x^{7/3} \text{Gamma}(2,a+b x)",1,"-(E^(-a - b*x)*x^(1/3)*(28*(10 + 3*a)*E^(b*x)*Gamma[1/3, b*x] + 3*(b*x)^(1/3)*(280 + 210*b*x + 90*b^2*x^2 + 27*b^3*x^3 + 3*a*(28 + 21*b*x + 9*b^2*x^2) - 27*b^2*E^(a + b*x)*x^2*Gamma[2, a + b*x])))/(189*b^2*(b*x)^(1/3))","A",1
174,1,95,80,0.1280682,"\int x^{2/3} \text{Gamma}(2,a+b x) \, dx","Integrate[x^(2/3)*Gamma[2, a + b*x],x]","-\frac{x^{5/3} e^{-a-b x} \left(3 (b x)^{2/3} \left(-9 b x e^{a+b x} \text{Gamma}(2,a+b x)+9 a b x+15 a+9 b^2 x^2+24 b x+40\right)+10 (3 a+8) e^{b x} \text{Gamma}\left(\frac{2}{3},b x\right)\right)}{45 (b x)^{5/3}}","\frac{3}{5} x^{5/3} \text{Gamma}(2,a+b x)-\frac{3 a e^{-a} x^{2/3} \text{Gamma}\left(\frac{8}{3},b x\right)}{5 b (b x)^{2/3}}-\frac{3 e^{-a} x^{2/3} \text{Gamma}\left(\frac{11}{3},b x\right)}{5 b (b x)^{2/3}}",1,"-(E^(-a - b*x)*x^(5/3)*(10*(8 + 3*a)*E^(b*x)*Gamma[2/3, b*x] + 3*(b*x)^(2/3)*(40 + 15*a + 24*b*x + 9*a*b*x + 9*b^2*x^2 - 9*b*E^(a + b*x)*x*Gamma[2, a + b*x])))/(45*(b*x)^(5/3))","A",1
175,1,95,80,0.1254718,"\int \sqrt[3]{x} \text{Gamma}(2,a+b x) \, dx","Integrate[x^(1/3)*Gamma[2, a + b*x],x]","-\frac{x^{4/3} e^{-a-b x} \left(3 \sqrt[3]{b x} \left(-9 b x e^{a+b x} \text{Gamma}(2,a+b x)+9 a b x+12 a+9 b^2 x^2+21 b x+28\right)+4 (3 a+7) e^{b x} \text{Gamma}\left(\frac{1}{3},b x\right)\right)}{36 (b x)^{4/3}}","\frac{3}{4} x^{4/3} \text{Gamma}(2,a+b x)-\frac{3 a e^{-a} \sqrt[3]{x} \text{Gamma}\left(\frac{7}{3},b x\right)}{4 b \sqrt[3]{b x}}-\frac{3 e^{-a} \sqrt[3]{x} \text{Gamma}\left(\frac{10}{3},b x\right)}{4 b \sqrt[3]{b x}}",1,"-(E^(-a - b*x)*x^(4/3)*(4*(7 + 3*a)*E^(b*x)*Gamma[1/3, b*x] + 3*(b*x)^(1/3)*(28 + 12*a + 21*b*x + 9*a*b*x + 9*b^2*x^2 - 9*b*E^(a + b*x)*x*Gamma[2, a + b*x])))/(36*(b*x)^(4/3))","A",1
176,1,80,74,0.1019711,"\int \frac{\text{Gamma}(2,a+b x)}{\sqrt[3]{x}} \, dx","Integrate[Gamma[2, a + b*x]/x^(1/3),x]","-\frac{x^{2/3} e^{-a-b x} \left(2 (3 a+5) e^{b x} \text{Gamma}\left(\frac{2}{3},b x\right)+3 (b x)^{2/3} \left(-3 e^{a+b x} \text{Gamma}(2,a+b x)+3 a+3 b x+5\right)\right)}{6 (b x)^{2/3}}","-\frac{3 a e^{-a} x^{2/3} \text{Gamma}\left(\frac{5}{3},b x\right)}{2 (b x)^{2/3}}+\frac{3}{2} x^{2/3} \text{Gamma}(2,a+b x)-\frac{3 e^{-a} x^{2/3} \text{Gamma}\left(\frac{8}{3},b x\right)}{2 (b x)^{2/3}}",1,"-(E^(-a - b*x)*x^(2/3)*(2*(5 + 3*a)*E^(b*x)*Gamma[2/3, b*x] + 3*(b*x)^(2/3)*(5 + 3*a + 3*b*x - 3*E^(a + b*x)*Gamma[2, a + b*x])))/(6*(b*x)^(2/3))","A",1
177,1,69,68,0.1187162,"\int \frac{\text{Gamma}(2,a+b x)}{x^{2/3}} \, dx","Integrate[Gamma[2, a + b*x]/x^(2/3),x]","\frac{1}{3} e^{-a} \sqrt[3]{x} \left(-\frac{(3 a+4) \text{Gamma}\left(\frac{1}{3},b x\right)}{\sqrt[3]{b x}}-3 e^{-b x} \left(-3 e^{a+b x} \text{Gamma}(2,a+b x)+3 a+3 b x+4\right)\right)","-\frac{3 a e^{-a} \sqrt[3]{x} \text{Gamma}\left(\frac{4}{3},b x\right)}{\sqrt[3]{b x}}+3 \sqrt[3]{x} \text{Gamma}(2,a+b x)-\frac{3 e^{-a} \sqrt[3]{x} \text{Gamma}\left(\frac{7}{3},b x\right)}{\sqrt[3]{b x}}",1,"(x^(1/3)*(-(((4 + 3*a)*Gamma[1/3, b*x])/(b*x)^(1/3)) - (3*(4 + 3*a + 3*b*x - 3*E^(a + b*x)*Gamma[2, a + b*x]))/E^(b*x)))/(3*E^a)","A",1
178,1,54,69,0.1189136,"\int \frac{\text{Gamma}(2,a+b x)}{x^{4/3}} \, dx","Integrate[Gamma[2, a + b*x]/x^(4/3),x]","\frac{e^{-a} \left((3 a+2) \sqrt[3]{b x} \text{Gamma}\left(\frac{2}{3},b x\right)-3 e^a \text{Gamma}(2,a+b x)+3 b x e^{-b x}\right)}{\sqrt[3]{x}}","\frac{3 e^{-a} b x^{2/3} \text{Gamma}\left(\frac{5}{3},b x\right)}{(b x)^{2/3}}+\frac{3 a e^{-a} \sqrt[3]{b x} \text{Gamma}\left(\frac{2}{3},b x\right)}{\sqrt[3]{x}}-\frac{3 \text{Gamma}(2,a+b x)}{\sqrt[3]{x}}",1,"((3*b*x)/E^(b*x) + (2 + 3*a)*(b*x)^(1/3)*Gamma[2/3, b*x] - 3*E^a*Gamma[2, a + b*x])/(E^a*x^(1/3))","A",1
179,1,147,221,0.5139788,"\int (c+d x)^m \text{Gamma}(3,a+b x) \, dx","Integrate[(c + d*x)^m*Gamma[3, a + b*x],x]","\frac{e^{-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \left(e^a b d (c+d x) \text{Gamma}(3,a+b x) \left(b \left(\frac{c}{d}+x\right)\right)^m-e^{\frac{b c}{d}} \left((b c-a d)^2 \text{Gamma}\left(m+2,\frac{b (c+d x)}{d}\right)+d \left((2 a d-2 b c) \text{Gamma}\left(m+3,\frac{b (c+d x)}{d}\right)+d \text{Gamma}\left(m+4,\frac{b (c+d x)}{d}\right)\right)\right)\right)}{b d^2 (m+1)}","-\frac{(b c-a d)^2 e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+2,\frac{b (c+d x)}{d}\right)}{b d^2 (m+1)}+\frac{2 (b c-a d) e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+3,\frac{b (c+d x)}{d}\right)}{b d (m+1)}-\frac{e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+4,\frac{b (c+d x)}{d}\right)}{b (m+1)}+\frac{(c+d x)^{m+1} \text{Gamma}(3,a+b x)}{d (m+1)}",1,"((c + d*x)^m*(b*d*E^a*(b*(c/d + x))^m*(c + d*x)*Gamma[3, a + b*x] - E^((b*c)/d)*((b*c - a*d)^2*Gamma[2 + m, (b*(c + d*x))/d] + d*((-2*b*c + 2*a*d)*Gamma[3 + m, (b*(c + d*x))/d] + d*Gamma[4 + m, (b*(c + d*x))/d]))))/(b*d^2*E^a*(1 + m)*((b*(c + d*x))/d)^m)","A",1
180,1,117,150,0.2769594,"\int (c+d x)^m \text{Gamma}(2,a+b x) \, dx","Integrate[(c + d*x)^m*Gamma[2, a + b*x],x]","\frac{e^{-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \left(e^a b (c+d x) \text{Gamma}(2,a+b x) \left(b \left(\frac{c}{d}+x\right)\right)^m+e^{\frac{b c}{d}} \left((b c-a d) \text{Gamma}\left(m+2,\frac{b (c+d x)}{d}\right)-d \text{Gamma}\left(m+3,\frac{b (c+d x)}{d}\right)\right)\right)}{b d (m+1)}","\frac{(b c-a d) e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+2,\frac{b (c+d x)}{d}\right)}{b d (m+1)}-\frac{e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+3,\frac{b (c+d x)}{d}\right)}{b (m+1)}+\frac{(c+d x)^{m+1} \text{Gamma}(2,a+b x)}{d (m+1)}",1,"((c + d*x)^m*(b*E^a*(b*(c/d + x))^m*(c + d*x)*Gamma[2, a + b*x] + E^((b*c)/d)*((b*c - a*d)*Gamma[2 + m, (b*(c + d*x))/d] - d*Gamma[3 + m, (b*(c + d*x))/d])))/(b*d*E^a*(1 + m)*((b*(c + d*x))/d)^m)","A",1
181,1,52,52,0.007932,"\int e^{-a-b x} (c+d x)^m \, dx","Integrate[E^(-a - b*x)*(c + d*x)^m,x]","-\frac{e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{b (c+d x)}{d}\right)}{b}","-\frac{e^{\frac{b c}{d}-a} (c+d x)^m \left(\frac{b (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,\frac{b (c+d x)}{d}\right)}{b}",1,"-((E^(-a + (b*c)/d)*(c + d*x)^m*Gamma[1 + m, (b*(c + d*x))/d])/(b*((b*(c + d*x))/d)^m))","A",1
182,0,0,18,0.385412,"\int (c+d x)^m \text{Gamma}(0,a+b x) \, dx","Integrate[(c + d*x)^m*Gamma[0, a + b*x],x]","\int (c+d x)^m \text{Gamma}(0,a+b x) \, dx","\text{Int}\left((c+d x)^m \text{Gamma}(0,a+b x),x\right)",0,"Integrate[(c + d*x)^m*Gamma[0, a + b*x], x]","F",-1
183,0,0,18,0.4450015,"\int (c+d x)^m \text{Gamma}(-1,a+b x) \, dx","Integrate[(c + d*x)^m*Gamma[-1, a + b*x],x]","\int (c+d x)^m \text{Gamma}(-1,a+b x) \, dx","\text{Int}\left((c+d x)^m \text{Gamma}(-1,a+b x),x\right)",0,"Integrate[(c + d*x)^m*Gamma[-1, a + b*x], x]","F",-1
184,0,0,18,0.643324,"\int (c+d x)^m \text{Gamma}(-2,a+b x) \, dx","Integrate[(c + d*x)^m*Gamma[-2, a + b*x],x]","\int (c+d x)^m \text{Gamma}(-2,a+b x) \, dx","\text{Int}\left((c+d x)^m \text{Gamma}(-2,a+b x),x\right)",0,"Integrate[(c + d*x)^m*Gamma[-2, a + b*x], x]","F",-1
185,0,0,18,1.0634367,"\int (c+d x)^m \text{Gamma}(-3,a+b x) \, dx","Integrate[(c + d*x)^m*Gamma[-3, a + b*x],x]","\int (c+d x)^m \text{Gamma}(-3,a+b x) \, dx","\text{Int}\left((c+d x)^m \text{Gamma}(-3,a+b x),x\right)",0,"Integrate[(c + d*x)^m*Gamma[-3, a + b*x], x]","F",-1
186,0,0,14,0.3396364,"\int x^m \text{Gamma}(n,a+b x) \, dx","Integrate[x^m*Gamma[n, a + b*x],x]","\int x^m \text{Gamma}(n,a+b x) \, dx","\text{Int}\left(x^m \text{Gamma}(n,a+b x),x\right)",0,"Integrate[x^m*Gamma[n, a + b*x], x]","F",-1
187,0,0,18,0.5336461,"\int (c+d x)^m \text{Gamma}(n,a+b x) \, dx","Integrate[(c + d*x)^m*Gamma[n, a + b*x],x]","\int (c+d x)^m \text{Gamma}(n,a+b x) \, dx","\text{Int}\left((c+d x)^m \text{Gamma}(n,a+b x),x\right)",0,"Integrate[(c + d*x)^m*Gamma[n, a + b*x], x]","F",-1
188,1,217,169,0.4430347,"\int (c+d x)^4 \text{Gamma}(n,a+b x) \, dx","Integrate[(c + d*x)^4*Gamma[n, a + b*x],x]","\frac{\left(a^5 d^4-5 a^4 b c d^3+10 a^3 b^2 c^2 d^2-10 a^2 b^3 c^3 d+5 a b^4 c^4+b^5 x \left(5 c^4+10 c^3 d x+10 c^2 d^2 x^2+5 c d^3 x^3+d^4 x^4\right)\right) \text{Gamma}(n,a+b x)-5 (b c-a d)^4 \text{Gamma}(n+1,a+b x)+d \left(-10 (b c-a d)^3 \text{Gamma}(n+2,a+b x)-d \left(10 (b c-a d)^2 \text{Gamma}(n+3,a+b x)+d (5 (b c-a d) \text{Gamma}(n+4,a+b x)+d \text{Gamma}(n+5,a+b x))\right)\right)}{5 b^5}","-\frac{d^3 (b c-a d) \text{Gamma}(n+4,a+b x)}{b^5}-\frac{2 d^2 (b c-a d)^2 \text{Gamma}(n+3,a+b x)}{b^5}-\frac{(b c-a d)^5 \text{Gamma}(n,a+b x)}{5 b^5 d}-\frac{(b c-a d)^4 \text{Gamma}(n+1,a+b x)}{b^5}-\frac{2 d (b c-a d)^3 \text{Gamma}(n+2,a+b x)}{b^5}-\frac{d^4 \text{Gamma}(n+5,a+b x)}{5 b^5}+\frac{(c+d x)^5 \text{Gamma}(n,a+b x)}{5 d}",1,"((5*a*b^4*c^4 - 10*a^2*b^3*c^3*d + 10*a^3*b^2*c^2*d^2 - 5*a^4*b*c*d^3 + a^5*d^4 + b^5*x*(5*c^4 + 10*c^3*d*x + 10*c^2*d^2*x^2 + 5*c*d^3*x^3 + d^4*x^4))*Gamma[n, a + b*x] - 5*(b*c - a*d)^4*Gamma[1 + n, a + b*x] + d*(-10*(b*c - a*d)^3*Gamma[2 + n, a + b*x] - d*(10*(b*c - a*d)^2*Gamma[3 + n, a + b*x] + d*(5*(b*c - a*d)*Gamma[4 + n, a + b*x] + d*Gamma[5 + n, a + b*x]))))/(5*b^5)","A",1
189,1,169,144,0.2794159,"\int (c+d x)^3 \text{Gamma}(n,a+b x) \, dx","Integrate[(c + d*x)^3*Gamma[n, a + b*x],x]","\frac{\left(a^4 \left(-d^3\right)+4 a^3 b c d^2-6 a^2 b^2 c^2 d+4 a b^3 c^3+b^4 x \left(4 c^3+6 c^2 d x+4 c d^2 x^2+d^3 x^3\right)\right) \text{Gamma}(n,a+b x)-4 (b c-a d)^3 \text{Gamma}(n+1,a+b x)-d \left(6 (b c-a d)^2 \text{Gamma}(n+2,a+b x)+d (4 (b c-a d) \text{Gamma}(n+3,a+b x)+d \text{Gamma}(n+4,a+b x))\right)}{4 b^4}","-\frac{d^2 (b c-a d) \text{Gamma}(n+3,a+b x)}{b^4}-\frac{(b c-a d)^4 \text{Gamma}(n,a+b x)}{4 b^4 d}-\frac{(b c-a d)^3 \text{Gamma}(n+1,a+b x)}{b^4}-\frac{3 d (b c-a d)^2 \text{Gamma}(n+2,a+b x)}{2 b^4}-\frac{d^3 \text{Gamma}(n+4,a+b x)}{4 b^4}+\frac{(c+d x)^4 \text{Gamma}(n,a+b x)}{4 d}",1,"((4*a*b^3*c^3 - 6*a^2*b^2*c^2*d + 4*a^3*b*c*d^2 - a^4*d^3 + b^4*x*(4*c^3 + 6*c^2*d*x + 4*c*d^2*x^2 + d^3*x^3))*Gamma[n, a + b*x] - 4*(b*c - a*d)^3*Gamma[1 + n, a + b*x] - d*(6*(b*c - a*d)^2*Gamma[2 + n, a + b*x] + d*(4*(b*c - a*d)*Gamma[3 + n, a + b*x] + d*Gamma[4 + n, a + b*x])))/(4*b^4)","A",1
190,1,119,115,0.1764225,"\int (c+d x)^2 \text{Gamma}(n,a+b x) \, dx","Integrate[(c + d*x)^2*Gamma[n, a + b*x],x]","\frac{\left(a^3 d^2-3 a^2 b c d+3 a b^2 c^2+b^3 x \left(3 c^2+3 c d x+d^2 x^2\right)\right) \text{Gamma}(n,a+b x)-3 (b c-a d)^2 \text{Gamma}(n+1,a+b x)+d ((3 a d-3 b c) \text{Gamma}(n+2,a+b x)-d \text{Gamma}(n+3,a+b x))}{3 b^3}","-\frac{(b c-a d)^3 \text{Gamma}(n,a+b x)}{3 b^3 d}-\frac{(b c-a d)^2 \text{Gamma}(n+1,a+b x)}{b^3}-\frac{d (b c-a d) \text{Gamma}(n+2,a+b x)}{b^3}-\frac{d^2 \text{Gamma}(n+3,a+b x)}{3 b^3}+\frac{(c+d x)^3 \text{Gamma}(n,a+b x)}{3 d}",1,"((3*a*b^2*c^2 - 3*a^2*b*c*d + a^3*d^2 + b^3*x*(3*c^2 + 3*c*d*x + d^2*x^2))*Gamma[n, a + b*x] - 3*(b*c - a*d)^2*Gamma[1 + n, a + b*x] + d*((-3*b*c + 3*a*d)*Gamma[2 + n, a + b*x] - d*Gamma[3 + n, a + b*x]))/(3*b^3)","A",1
191,1,65,88,0.1466642,"\int (c+d x) \text{Gamma}(n,a+b x) \, dx","Integrate[(c + d*x)*Gamma[n, a + b*x],x]","-\frac{(a+b x) (a d-b (2 c+d x)) \text{Gamma}(n,a+b x)+2 (b c-a d) \text{Gamma}(n+1,a+b x)+d \text{Gamma}(n+2,a+b x)}{2 b^2}","-\frac{(b c-a d)^2 \text{Gamma}(n,a+b x)}{2 b^2 d}-\frac{(b c-a d) \text{Gamma}(n+1,a+b x)}{b^2}-\frac{d \text{Gamma}(n+2,a+b x)}{2 b^2}+\frac{(c+d x)^2 \text{Gamma}(n,a+b x)}{2 d}",1,"-((a + b*x)*(a*d - b*(2*c + d*x))*Gamma[n, a + b*x] + 2*(b*c - a*d)*Gamma[1 + n, a + b*x] + d*Gamma[2 + n, a + b*x])/(2*b^2)","A",1
192,1,36,31,0.0331477,"\int \text{Gamma}(n,a+b x) \, dx","Integrate[Gamma[n, a + b*x],x]","x \text{Gamma}(n,a+b x)+\frac{a \text{Gamma}(n,a+b x)}{b}-\frac{\text{Gamma}(n+1,a+b x)}{b}","\frac{(a+b x) \text{Gamma}(n,a+b x)}{b}-\frac{\text{Gamma}(n+1,a+b x)}{b}",1,"(a*Gamma[n, a + b*x])/b + x*Gamma[n, a + b*x] - Gamma[1 + n, a + b*x]/b","A",1
193,0,0,18,0.4589227,"\int \frac{\text{Gamma}(n,a+b x)}{c+d x} \, dx","Integrate[Gamma[n, a + b*x]/(c + d*x),x]","\int \frac{\text{Gamma}(n,a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{Gamma}(n,a+b x)}{c+d x},x\right)",0,"Integrate[Gamma[n, a + b*x]/(c + d*x), x]","F",-1
194,0,0,18,0.3055987,"\int \frac{\text{Gamma}(n,a+b x)}{(c+d x)^2} \, dx","Integrate[Gamma[n, a + b*x]/(c + d*x)^2,x]","\int \frac{\text{Gamma}(n,a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{Gamma}(n,a+b x)}{(c+d x)^2},x\right)",0,"Integrate[Gamma[n, a + b*x]/(c + d*x)^2, x]","F",-1
195,0,0,18,0.4102215,"\int \frac{\text{Gamma}(n,a+b x)}{(c+d x)^3} \, dx","Integrate[Gamma[n, a + b*x]/(c + d*x)^3,x]","\int \frac{\text{Gamma}(n,a+b x)}{(c+d x)^3} \, dx","\text{Int}\left(\frac{\text{Gamma}(n,a+b x)}{(c+d x)^3},x\right)",0,"Integrate[Gamma[n, a + b*x]/(c + d*x)^3, x]","F",-1
196,1,112,121,0.3629136,"\int x^2 \text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^2*Gamma[p, d*(a + b*Log[c*x^n])],x]","\frac{1}{3} x^3 \left(\text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)-e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(\frac{(b d n-3) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,\frac{(b d n-3) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)\right)","\frac{1}{3} x^3 \text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)-\frac{1}{3} x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(-\frac{(3-b d n) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,-\frac{(3-b d n) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)",1,"(x^3*(Gamma[p, d*(a + b*Log[c*x^n])] - (Gamma[p, ((-3 + b*d*n)*(a + b*Log[c*x^n]))/(b*n)]*(d*(a + b*Log[c*x^n]))^p)/(E^((3*a)/(b*n))*(c*x^n)^(3/n)*(((-3 + b*d*n)*(a + b*Log[c*x^n]))/(b*n))^p)))/3","A",1
197,1,112,121,0.3847723,"\int x \text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x*Gamma[p, d*(a + b*Log[c*x^n])],x]","\frac{1}{2} x^2 \left(\text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)-e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(\frac{(b d n-2) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,\frac{(b d n-2) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)\right)","\frac{1}{2} x^2 \text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)-\frac{1}{2} x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(-\frac{(2-b d n) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,-\frac{(2-b d n) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)",1,"(x^2*(Gamma[p, d*(a + b*Log[c*x^n])] - (Gamma[p, ((-2 + b*d*n)*(a + b*Log[c*x^n]))/(b*n)]*(d*(a + b*Log[c*x^n]))^p)/(E^((2*a)/(b*n))*(c*x^n)^(2/n)*(((-2 + b*d*n)*(a + b*Log[c*x^n]))/(b*n))^p)))/2","A",1
198,1,107,112,0.3238847,"\int \text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[Gamma[p, d*(a + b*Log[c*x^n])],x]","x \left(\text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)-e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(\frac{(b d n-1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,\frac{(b d n-1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)\right)","x \text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)-x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(-\frac{(1-b d n) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,-\frac{(1-b d n) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)",1,"x*(Gamma[p, d*(a + b*Log[c*x^n])] - (Gamma[p, ((-1 + b*d*n)*(a + b*Log[c*x^n]))/(b*n)]*(d*(a + b*Log[c*x^n]))^p)/(E^(a/(b*n))*(c*x^n)^n^(-1)*(((-1 + b*d*n)*(a + b*Log[c*x^n]))/(b*n))^p))","A",1
199,1,55,61,0.4369961,"\int \frac{\text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Integrate[Gamma[p, d*(a + b*Log[c*x^n])]/x,x]","\frac{d \left(a+b \log \left(c x^n\right)\right) \text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)-\text{Gamma}\left(p+1,d \left(a+b \log \left(c x^n\right)\right)\right)}{b d n}","\frac{\left(a+b \log \left(c x^n\right)\right) \text{Gamma}\left(p,a d+b d \log \left(c x^n\right)\right)}{b n}-\frac{\text{Gamma}\left(p+1,a d+b d \log \left(c x^n\right)\right)}{b d n}",1,"(-Gamma[1 + p, d*(a + b*Log[c*x^n])] + d*Gamma[p, d*(a + b*Log[c*x^n])]*(a + b*Log[c*x^n]))/(b*d*n)","A",1
200,1,107,109,0.2732166,"\int \frac{\text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Integrate[Gamma[p, d*(a + b*Log[c*x^n])]/x^2,x]","\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(\frac{(b d n+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,\frac{(b d n+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)-\text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)}{x}","\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(\frac{(b d n+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,\frac{(b d n+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x}-\frac{\text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)}{x}",1,"(-Gamma[p, d*(a + b*Log[c*x^n])] + (E^(a/(b*n))*(c*x^n)^n^(-1)*Gamma[p, ((1 + b*d*n)*(a + b*Log[c*x^n]))/(b*n)]*(d*(a + b*Log[c*x^n]))^p)/(((1 + b*d*n)*(a + b*Log[c*x^n]))/(b*n))^p)/x","A",1
201,1,113,117,0.2972694,"\int \frac{\text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Integrate[Gamma[p, d*(a + b*Log[c*x^n])]/x^3,x]","\frac{e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(\frac{(b d n+2) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,\frac{(b d n+2) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)-\text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}","\frac{e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(\frac{(b d n+2) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,\frac{(b d n+2) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{2 x^2}-\frac{\text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}",1,"(-Gamma[p, d*(a + b*Log[c*x^n])] + (E^((2*a)/(b*n))*(c*x^n)^(2/n)*Gamma[p, ((2 + b*d*n)*(a + b*Log[c*x^n]))/(b*n)]*(d*(a + b*Log[c*x^n]))^p)/(((2 + b*d*n)*(a + b*Log[c*x^n]))/(b*n))^p)/(2*x^2)","A",1
202,1,136,148,0.614731,"\int (e x)^m \text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*Gamma[p, d*(a + b*Log[c*x^n])],x]","\frac{(e x)^m \left(x \text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)-x^{-m} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \exp \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)-b n \log (x)\right)}{b n}\right) \left(\frac{(b d n-m-1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,\frac{(b d n-m-1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)\right)}{m+1}","\frac{(e x)^{m+1} \text{Gamma}\left(p,d \left(a+b \log \left(c x^n\right)\right)\right)}{e (m+1)}-\frac{(e x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(d \left(a+b \log \left(c x^n\right)\right)\right)^p \left(-\frac{(-b d n+m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p,-\frac{(-b d n+m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{e (m+1)}",1,"((e*x)^m*(x*Gamma[p, d*(a + b*Log[c*x^n])] - (Gamma[p, ((-1 - m + b*d*n)*(a + b*Log[c*x^n]))/(b*n)]*(d*(a + b*Log[c*x^n]))^p)/(E^(((1 + m)*(a - b*n*Log[x] + b*Log[c*x^n]))/(b*n))*x^m*(((-1 - m + b*d*n)*(a + b*Log[c*x^n]))/(b*n))^p)))/(1 + m)","A",1
203,1,69,74,0.1057898,"\int (c+d x)^3 \text{log$\Gamma $}(a+b x) \, dx","Integrate[(c + d*x)^3*LogGamma[a + b*x],x]","\frac{b (c+d x) \left(b (c+d x) (b (c+d x) \psi ^{(-2)}(a+b x)-3 d \psi ^{(-3)}(a+b x))+6 d^2 \psi ^{(-4)}(a+b x)\right)-6 d^3 \psi ^{(-5)}(a+b x)}{b^4}","-\frac{6 d^3 \psi ^{(-5)}(a+b x)}{b^4}+\frac{6 d^2 (c+d x) \psi ^{(-4)}(a+b x)}{b^3}-\frac{3 d (c+d x)^2 \psi ^{(-3)}(a+b x)}{b^2}+\frac{(c+d x)^3 \psi ^{(-2)}(a+b x)}{b}",1,"(-6*d^3*PolyGamma[-5, a + b*x] + b*(c + d*x)*(6*d^2*PolyGamma[-4, a + b*x] + b*(c + d*x)*(-3*d*PolyGamma[-3, a + b*x] + b*(c + d*x)*PolyGamma[-2, a + b*x])))/b^4","A",1
204,1,49,52,0.0415827,"\int (c+d x)^2 \text{log$\Gamma $}(a+b x) \, dx","Integrate[(c + d*x)^2*LogGamma[a + b*x],x]","\frac{b (c+d x) (b (c+d x) \psi ^{(-2)}(a+b x)-2 d \psi ^{(-3)}(a+b x))+2 d^2 \psi ^{(-4)}(a+b x)}{b^3}","\frac{2 d^2 \psi ^{(-4)}(a+b x)}{b^3}-\frac{2 d (c+d x) \psi ^{(-3)}(a+b x)}{b^2}+\frac{(c+d x)^2 \psi ^{(-2)}(a+b x)}{b}",1,"(2*d^2*PolyGamma[-4, a + b*x] + b*(c + d*x)*(-2*d*PolyGamma[-3, a + b*x] + b*(c + d*x)*PolyGamma[-2, a + b*x]))/b^3","A",1
205,1,40,30,0.0146265,"\int (c+d x) \text{log$\Gamma $}(a+b x) \, dx","Integrate[(c + d*x)*LogGamma[a + b*x],x]","\frac{c \psi ^{(-2)}(a+b x)}{b}+\frac{d \left(x \psi ^{(-2)}(a+b x)-\frac{\psi ^{(-3)}(a+b x)}{b}\right)}{b}","\frac{(c+d x) \psi ^{(-2)}(a+b x)}{b}-\frac{d \psi ^{(-3)}(a+b x)}{b^2}",1,"(c*PolyGamma[-2, a + b*x])/b + (d*(-(PolyGamma[-3, a + b*x]/b) + x*PolyGamma[-2, a + b*x]))/b","A",1
206,1,11,11,0.0042961,"\int \text{log$\Gamma $}(a+b x) \, dx","Integrate[LogGamma[a + b*x],x]","\frac{\psi ^{(-2)}(a+b x)}{b}","\frac{\psi ^{(-2)}(a+b x)}{b}",1,"PolyGamma[-2, a + b*x]/b","A",1
207,0,0,17,0.0617511,"\int \frac{\text{log$\Gamma $}(a+b x)}{c+d x} \, dx","Integrate[LogGamma[a + b*x]/(c + d*x),x]","\int \frac{\text{log$\Gamma $}(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{log$\Gamma $}(a+b x)}{c+d x},x\right)",0,"Integrate[LogGamma[a + b*x]/(c + d*x), x]","F",-1
208,0,0,17,0.0587492,"\int \frac{\text{log$\Gamma $}(a+b x)}{(c+d x)^2} \, dx","Integrate[LogGamma[a + b*x]/(c + d*x)^2,x]","\int \frac{\text{log$\Gamma $}(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{log$\Gamma $}(a+b x)}{(c+d x)^2},x\right)",0,"Integrate[LogGamma[a + b*x]/(c + d*x)^2, x]","F",-1
209,0,0,19,0.1757512,"\int (c+d x)^{3/2} \text{log$\Gamma $}(a+b x) \, dx","Integrate[(c + d*x)^(3/2)*LogGamma[a + b*x],x]","\int (c+d x)^{3/2} \text{log$\Gamma $}(a+b x) \, dx","\text{Int}\left((c+d x)^{3/2} \text{log$\Gamma $}(a+b x),x\right)",0,"Integrate[(c + d*x)^(3/2)*LogGamma[a + b*x], x]","F",-1
210,0,0,19,0.1961969,"\int \sqrt{c+d x} \text{log$\Gamma $}(a+b x) \, dx","Integrate[Sqrt[c + d*x]*LogGamma[a + b*x],x]","\int \sqrt{c+d x} \text{log$\Gamma $}(a+b x) \, dx","\text{Int}\left(\sqrt{c+d x} \text{log$\Gamma $}(a+b x),x\right)",0,"Integrate[Sqrt[c + d*x]*LogGamma[a + b*x], x]","F",-1
211,0,0,19,0.176531,"\int \frac{\text{log$\Gamma $}(a+b x)}{\sqrt{c+d x}} \, dx","Integrate[LogGamma[a + b*x]/Sqrt[c + d*x],x]","\int \frac{\text{log$\Gamma $}(a+b x)}{\sqrt{c+d x}} \, dx","\text{Int}\left(\frac{\text{log$\Gamma $}(a+b x)}{\sqrt{c+d x}},x\right)",0,"Integrate[LogGamma[a + b*x]/Sqrt[c + d*x], x]","F",-1
212,1,115,93,0.1373689,"\int (c+d x)^2 \log (\Gamma (a+b x)) \, dx","Integrate[(c + d*x)^2*Log[Gamma[a + b*x]],x]","\frac{b^3 (-x) \left(3 c^2+3 c d x+d^2 x^2\right) \text{log$\Gamma $}(a+b x)+b \left(b \left(b x \left(3 c^2+3 c d x+d^2 x^2\right) \log (\Gamma (a+b x))+3 (c+d x)^2 \psi ^{(-2)}(a+b x)\right)-6 d (c+d x) \psi ^{(-3)}(a+b x)\right)+6 d^2 \psi ^{(-4)}(a+b x)}{3 b^3}","\frac{2 d^2 \psi ^{(-4)}(a+b x)}{b^3}-\frac{2 d (c+d x) \psi ^{(-3)}(a+b x)}{b^2}-\frac{(c+d x)^3 \text{log$\Gamma $}(a+b x)}{3 d}+\frac{(c+d x)^2 \psi ^{(-2)}(a+b x)}{b}+\frac{(c+d x)^3 \log (\Gamma (a+b x))}{3 d}",1,"(-(b^3*x*(3*c^2 + 3*c*d*x + d^2*x^2)*LogGamma[a + b*x]) + 6*d^2*PolyGamma[-4, a + b*x] + b*(-6*d*(c + d*x)*PolyGamma[-3, a + b*x] + b*(b*x*(3*c^2 + 3*c*d*x + d^2*x^2)*Log[Gamma[a + b*x]] + 3*(c + d*x)^2*PolyGamma[-2, a + b*x])))/(3*b^3)","A",1
213,1,104,71,0.0514302,"\int (c+d x) \log (\Gamma (a+b x)) \, dx","Integrate[(c + d*x)*Log[Gamma[a + b*x]],x]","\frac{1}{2} d \left(-\frac{2 \psi ^{(-3)}(a+b x)}{b^2}+x^2 (-\text{log$\Gamma $}(a+b x))+\frac{2 x \psi ^{(-2)}(a+b x)}{b}\right)-\frac{c (a+b x) \text{log$\Gamma $}(a+b x)}{b}+\frac{c \psi ^{(-2)}(a+b x)}{b}+\frac{c (a+b x) \log (\Gamma (a+b x))}{b}+\frac{1}{2} d x^2 \log (\Gamma (a+b x))","-\frac{d \psi ^{(-3)}(a+b x)}{b^2}-\frac{(c+d x)^2 \text{log$\Gamma $}(a+b x)}{2 d}+\frac{(c+d x) \psi ^{(-2)}(a+b x)}{b}+\frac{(c+d x)^2 \log (\Gamma (a+b x))}{2 d}",1,"(d*x^2*Log[Gamma[a + b*x]])/2 + (c*(a + b*x)*Log[Gamma[a + b*x]])/b - (c*(a + b*x)*LogGamma[a + b*x])/b + (c*PolyGamma[-2, a + b*x])/b + (d*(-(x^2*LogGamma[a + b*x]) - (2*PolyGamma[-3, a + b*x])/b^2 + (2*x*PolyGamma[-2, a + b*x])/b))/2","A",1
214,1,38,30,0.0191725,"\int \log (\Gamma (a+b x)) \, dx","Integrate[Log[Gamma[a + b*x]],x]","\frac{-(a+b x) \text{log$\Gamma $}(a+b x)+\psi ^{(-2)}(a+b x)+(a+b x) \log (\Gamma (a+b x))}{b}","-x \text{log$\Gamma $}(a+b x)+\frac{\psi ^{(-2)}(a+b x)}{b}+x \log (\Gamma (a+b x))",1,"((a + b*x)*Log[Gamma[a + b*x]] - (a + b*x)*LogGamma[a + b*x] + PolyGamma[-2, a + b*x])/b","A",1
215,0,0,44,0.0412694,"\int \frac{\log (\Gamma (a+b x))}{c+d x} \, dx","Integrate[Log[Gamma[a + b*x]]/(c + d*x),x]","\int \frac{\log (\Gamma (a+b x))}{c+d x} \, dx","\text{Int}\left(\frac{\text{log$\Gamma $}(a+b x)}{c+d x},x\right)+\frac{\log (c+d x) (\log (\Gamma (a+b x))-\text{log$\Gamma $}(a+b x))}{d}",0,"Integrate[Log[Gamma[a + b*x]]/(c + d*x), x]","F",-1
216,0,0,43,0.1058824,"\int \frac{\log (\Gamma (a+b x))}{(c+d x)^2} \, dx","Integrate[Log[Gamma[a + b*x]]/(c + d*x)^2,x]","\int \frac{\log (\Gamma (a+b x))}{(c+d x)^2} \, dx","\frac{b \text{Int}\left(\frac{\psi ^{(0)}(a+b x)}{c+d x},x\right)}{d}-\frac{\log (\Gamma (a+b x))}{d (c+d x)}",0,"Integrate[Log[Gamma[a + b*x]]/(c + d*x)^2, x]","F",-1
217,0,0,18,0.0912897,"\int (c+d x)^m \psi ^{(n)}(a+b x) \, dx","Integrate[(c + d*x)^m*PolyGamma[n, a + b*x],x]","\int (c+d x)^m \psi ^{(n)}(a+b x) \, dx","\text{Int}\left((c+d x)^m \psi ^{(n)}(a+b x),x\right)",0,"Integrate[(c + d*x)^m*PolyGamma[n, a + b*x], x]","F",-1
218,1,77,82,0.1053594,"\int (c+d x)^3 \psi ^{(n)}(a+b x) \, dx","Integrate[(c + d*x)^3*PolyGamma[n, a + b*x],x]","\frac{b (c+d x) \left(b (c+d x) (b (c+d x) \psi ^{(n-1)}(a+b x)-3 d \psi ^{(n-2)}(a+b x))+6 d^2 \psi ^{(n-3)}(a+b x)\right)-6 d^3 \psi ^{(n-4)}(a+b x)}{b^4}","-\frac{6 d^3 \psi ^{(n-4)}(a+b x)}{b^4}+\frac{6 d^2 (c+d x) \psi ^{(n-3)}(a+b x)}{b^3}-\frac{3 d (c+d x)^2 \psi ^{(n-2)}(a+b x)}{b^2}+\frac{(c+d x)^3 \psi ^{(n-1)}(a+b x)}{b}",1,"(-6*d^3*PolyGamma[-4 + n, a + b*x] + b*(c + d*x)*(6*d^2*PolyGamma[-3 + n, a + b*x] + b*(c + d*x)*(-3*d*PolyGamma[-2 + n, a + b*x] + b*(c + d*x)*PolyGamma[-1 + n, a + b*x])))/b^4","A",1
219,1,55,58,0.0488536,"\int (c+d x)^2 \psi ^{(n)}(a+b x) \, dx","Integrate[(c + d*x)^2*PolyGamma[n, a + b*x],x]","\frac{b (c+d x) (b (c+d x) \psi ^{(n-1)}(a+b x)-2 d \psi ^{(n-2)}(a+b x))+2 d^2 \psi ^{(n-3)}(a+b x)}{b^3}","\frac{2 d^2 \psi ^{(n-3)}(a+b x)}{b^3}-\frac{2 d (c+d x) \psi ^{(n-2)}(a+b x)}{b^2}+\frac{(c+d x)^2 \psi ^{(n-1)}(a+b x)}{b}",1,"(2*d^2*PolyGamma[-3 + n, a + b*x] + b*(c + d*x)*(-2*d*PolyGamma[-2 + n, a + b*x] + b*(c + d*x)*PolyGamma[-1 + n, a + b*x]))/b^3","A",1
220,1,46,34,0.0120068,"\int (c+d x) \psi ^{(n)}(a+b x) \, dx","Integrate[(c + d*x)*PolyGamma[n, a + b*x],x]","\frac{c \psi ^{(n-1)}(a+b x)}{b}+\frac{d \left(x \psi ^{(n-1)}(a+b x)-\frac{\psi ^{(n-2)}(a+b x)}{b}\right)}{b}","\frac{(c+d x) \psi ^{(n-1)}(a+b x)}{b}-\frac{d \psi ^{(n-2)}(a+b x)}{b^2}",1,"(c*PolyGamma[-1 + n, a + b*x])/b + (d*(-(PolyGamma[-2 + n, a + b*x]/b) + x*PolyGamma[-1 + n, a + b*x]))/b","A",1
221,1,13,13,0.0032534,"\int \psi ^{(n)}(a+b x) \, dx","Integrate[PolyGamma[n, a + b*x],x]","\frac{\psi ^{(n-1)}(a+b x)}{b}","\frac{\psi ^{(n-1)}(a+b x)}{b}",1,"PolyGamma[-1 + n, a + b*x]/b","A",1
222,0,0,18,0.0566742,"\int \frac{\psi ^{(n)}(a+b x)}{c+d x} \, dx","Integrate[PolyGamma[n, a + b*x]/(c + d*x),x]","\int \frac{\psi ^{(n)}(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\psi ^{(n)}(a+b x)}{c+d x},x\right)",0,"Integrate[PolyGamma[n, a + b*x]/(c + d*x), x]","F",-1
223,0,0,45,0.0509638,"\int \frac{\psi ^{(n)}(a+b x)}{(c+d x)^2} \, dx","Integrate[PolyGamma[n, a + b*x]/(c + d*x)^2,x]","\int \frac{\psi ^{(n)}(a+b x)}{(c+d x)^2} \, dx","\frac{b \text{Int}\left(\frac{\psi ^{(n+1)}(a+b x)}{c+d x},x\right)}{d}-\frac{\psi ^{(n)}(a+b x)}{d (c+d x)}",0,"Integrate[PolyGamma[n, a + b*x]/(c + d*x)^2, x]","F",-1
224,0,0,76,0.0583951,"\int \frac{\psi ^{(n)}(a+b x)}{(c+d x)^3} \, dx","Integrate[PolyGamma[n, a + b*x]/(c + d*x)^3,x]","\int \frac{\psi ^{(n)}(a+b x)}{(c+d x)^3} \, dx","\frac{b^2 \text{Int}\left(\frac{\psi ^{(n+2)}(a+b x)}{c+d x},x\right)}{2 d^2}-\frac{b \psi ^{(n+1)}(a+b x)}{2 d^2 (c+d x)}-\frac{\psi ^{(n)}(a+b x)}{2 d (c+d x)^2}",0,"Integrate[PolyGamma[n, a + b*x]/(c + d*x)^3, x]","F",-1
225,0,0,81,0.1756389,"\int (c+d x)^{3/2} \psi ^{(n)}(a+b x) \, dx","Integrate[(c + d*x)^(3/2)*PolyGamma[n, a + b*x],x]","\int (c+d x)^{3/2} \psi ^{(n)}(a+b x) \, dx","\frac{3 d^2 \text{Int}\left(\frac{\psi ^{(n-2)}(a+b x)}{\sqrt{c+d x}},x\right)}{4 b^2}-\frac{3 d \sqrt{c+d x} \psi ^{(n-2)}(a+b x)}{2 b^2}+\frac{(c+d x)^{3/2} \psi ^{(n-1)}(a+b x)}{b}",0,"Integrate[(c + d*x)^(3/2)*PolyGamma[n, a + b*x], x]","F",-1
226,0,0,53,0.1979542,"\int \sqrt{c+d x} \psi ^{(n)}(a+b x) \, dx","Integrate[Sqrt[c + d*x]*PolyGamma[n, a + b*x],x]","\int \sqrt{c+d x} \psi ^{(n)}(a+b x) \, dx","\frac{\sqrt{c+d x} \psi ^{(n-1)}(a+b x)}{b}-\frac{d \text{Int}\left(\frac{\psi ^{(n-1)}(a+b x)}{\sqrt{c+d x}},x\right)}{2 b}",0,"Integrate[Sqrt[c + d*x]*PolyGamma[n, a + b*x], x]","F",-1
227,0,0,20,0.2010335,"\int \frac{\psi ^{(n)}(a+b x)}{\sqrt{c+d x}} \, dx","Integrate[PolyGamma[n, a + b*x]/Sqrt[c + d*x],x]","\int \frac{\psi ^{(n)}(a+b x)}{\sqrt{c+d x}} \, dx","\text{Int}\left(\frac{\psi ^{(n)}(a+b x)}{\sqrt{c+d x}},x\right)",0,"Integrate[PolyGamma[n, a + b*x]/Sqrt[c + d*x], x]","F",-1
228,0,0,50,0.1473304,"\int \frac{\psi ^{(n)}(a+b x)}{(c+d x)^{3/2}} \, dx","Integrate[PolyGamma[n, a + b*x]/(c + d*x)^(3/2),x]","\int \frac{\psi ^{(n)}(a+b x)}{(c+d x)^{3/2}} \, dx","\frac{2 b \text{Int}\left(\frac{\psi ^{(n+1)}(a+b x)}{\sqrt{c+d x}},x\right)}{d}-\frac{2 \psi ^{(n)}(a+b x)}{d \sqrt{c+d x}}",0,"Integrate[PolyGamma[n, a + b*x]/(c + d*x)^(3/2), x]","F",-1
229,1,40,39,0.0107053,"\int x^2 \psi ^{(1)}(a+b x) \, dx","Integrate[x^2*PolyGamma[1, a + b*x],x]","\frac{\frac{2 \psi ^{(-2)}(a+b x)}{b^2}-\frac{2 x \text{log$\Gamma $}(a+b x)}{b}+x^2 \psi ^{(0)}(a+b x)}{b}","\frac{2 \psi ^{(-2)}(a+b x)}{b^3}-\frac{2 x \text{log$\Gamma $}(a+b x)}{b^2}+\frac{x^2 \psi ^{(0)}(a+b x)}{b}",1,"((-2*x*LogGamma[a + b*x])/b + (2*PolyGamma[-2, a + b*x])/b^2 + x^2*PolyGamma[0, a + b*x])/b","A",1
230,1,12,12,0.030609,"\int \left(\frac{\psi ^{(1)}(a+b x)}{x^2}-\frac{b \psi ^{(2)}(a+b x)}{x}\right) \, dx","Integrate[PolyGamma[1, a + b*x]/x^2 - (b*PolyGamma[2, a + b*x])/x,x]","-\frac{\psi ^{(1)}(a+b x)}{x}","-\frac{\psi ^{(1)}(a+b x)}{x}",1,"-(PolyGamma[1, a + b*x]/x)","A",1
231,1,12,12,0.0284268,"\int \left(\frac{\psi ^{(n)}(a+b x)}{x^2}-\frac{b \psi ^{(1+n)}(a+b x)}{x}\right) \, dx","Integrate[PolyGamma[n, a + b*x]/x^2 - (b*PolyGamma[1 + n, a + b*x])/x,x]","-\frac{\psi ^{(n)}(a+b x)}{x}","-\frac{\psi ^{(n)}(a+b x)}{x}",1,"-(PolyGamma[n, a + b*x]/x)","A",1
232,1,15,15,0.0111213,"\int \Gamma (a+b x)^n \psi ^{(0)}(a+b x) \, dx","Integrate[Gamma[a + b*x]^n*PolyGamma[0, a + b*x],x]","\frac{\Gamma (a+b x)^n}{b n}","\frac{\Gamma (a+b x)^n}{b n}",1,"Gamma[a + b*x]^n/(b*n)","A",1
233,1,15,15,0.0112374,"\int ((a+b x)!)^n \psi ^{(0)}(1+a+b x) \, dx","Integrate[(a + b*x)!^n*PolyGamma[0, 1 + a + b*x],x]","\frac{((a+b x)!)^n}{b n}","\frac{((a+b x)!)^n}{b n}",1,"(a + b*x)!^n/(b*n)","A",1