1,1,67,67,0.0381443,"\int F^{c (a+b x)} (d+e x)^m \, dx","Integrate[F^(c*(a + b*x))*(d + e*x)^m,x]","\frac{(d+e x)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-m} \Gamma \left(m+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}","\frac{(d+e x)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-m} \Gamma \left(m+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}",1,"(F^(c*(a - (b*d)/e))*(d + e*x)^m*Gamma[1 + m, -((b*c*(d + e*x)*Log[F])/e)])/(b*c*Log[F]*(-((b*c*(d + e*x)*Log[F])/e))^m)","A",1
2,1,100,141,0.1261766,"\int F^{c (a+b x)} (d+e x)^4 \, dx","Integrate[F^(c*(a + b*x))*(d + e*x)^4,x]","\frac{F^{c (a+b x)} \left(b^4 c^4 \log ^4(F) (d+e x)^4-4 b^3 c^3 e \log ^3(F) (d+e x)^3+12 b^2 c^2 e^2 \log ^2(F) (d+e x)^2-24 b c e^3 \log (F) (d+e x)+24 e^4\right)}{b^5 c^5 \log ^5(F)}","\frac{24 e^4 F^{c (a+b x)}}{b^5 c^5 \log ^5(F)}-\frac{24 e^3 (d+e x) F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}+\frac{12 e^2 (d+e x)^2 F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{4 e (d+e x)^3 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{(d+e x)^4 F^{c (a+b x)}}{b c \log (F)}",1,"(F^(c*(a + b*x))*(24*e^4 - 24*b*c*e^3*(d + e*x)*Log[F] + 12*b^2*c^2*e^2*(d + e*x)^2*Log[F]^2 - 4*b^3*c^3*e*(d + e*x)^3*Log[F]^3 + b^4*c^4*(d + e*x)^4*Log[F]^4))/(b^5*c^5*Log[F]^5)","A",1
3,1,78,110,0.0857759,"\int F^{c (a+b x)} (d+e x)^3 \, dx","Integrate[F^(c*(a + b*x))*(d + e*x)^3,x]","\frac{F^{c (a+b x)} \left(b^3 c^3 \log ^3(F) (d+e x)^3-3 b^2 c^2 e \log ^2(F) (d+e x)^2+6 b c e^2 \log (F) (d+e x)-6 e^3\right)}{b^4 c^4 \log ^4(F)}","-\frac{6 e^3 F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}+\frac{6 e^2 (d+e x) F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{3 e (d+e x)^2 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{(d+e x)^3 F^{c (a+b x)}}{b c \log (F)}",1,"(F^(c*(a + b*x))*(-6*e^3 + 6*b*c*e^2*(d + e*x)*Log[F] - 3*b^2*c^2*e*(d + e*x)^2*Log[F]^2 + b^3*c^3*(d + e*x)^3*Log[F]^3))/(b^4*c^4*Log[F]^4)","A",1
4,1,56,79,0.0678683,"\int F^{c (a+b x)} (d+e x)^2 \, dx","Integrate[F^(c*(a + b*x))*(d + e*x)^2,x]","\frac{F^{c (a+b x)} \left(b^2 c^2 \log ^2(F) (d+e x)^2-2 b c e \log (F) (d+e x)+2 e^2\right)}{b^3 c^3 \log ^3(F)}","\frac{2 e^2 F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{2 e (d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{(d+e x)^2 F^{c (a+b x)}}{b c \log (F)}",1,"(F^(c*(a + b*x))*(2*e^2 - 2*b*c*e*(d + e*x)*Log[F] + b^2*c^2*(d + e*x)^2*Log[F]^2))/(b^3*c^3*Log[F]^3)","A",1
5,1,34,48,0.0383299,"\int F^{c (a+b x)} (d+e x) \, dx","Integrate[F^(c*(a + b*x))*(d + e*x),x]","\frac{F^{c (a+b x)} (b c \log (F) (d+e x)-e)}{b^2 c^2 \log ^2(F)}","\frac{(d+e x) F^{c (a+b x)}}{b c \log (F)}-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}",1,"(F^(c*(a + b*x))*(-e + b*c*(d + e*x)*Log[F]))/(b^2*c^2*Log[F]^2)","A",1
6,1,21,20,0.0049286,"\int F^{c (a+b x)} \, dx","Integrate[F^(c*(a + b*x)),x]","\frac{F^{a c+b c x}}{b c \log (F)}","\frac{F^{c (a+b x)}}{b c \log (F)}",1,"F^(a*c + b*c*x)/(b*c*Log[F])","A",1
7,1,31,31,0.0419025,"\int \frac{F^{c (a+b x)}}{d+e x} \, dx","Integrate[F^(c*(a + b*x))/(d + e*x),x]","\frac{F^{c \left(a-\frac{b d}{e}\right)} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)}{e}","\frac{F^{c \left(a-\frac{b d}{e}\right)} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)}{e}",1,"(F^(c*(a - (b*d)/e))*ExpIntegralEi[(b*c*(d + e*x)*Log[F])/e])/e","A",1
8,1,55,57,0.1191774,"\int \frac{F^{c (a+b x)}}{(d+e x)^2} \, dx","Integrate[F^(c*(a + b*x))/(d + e*x)^2,x]","\frac{F^{a c} \left(b c \log (F) F^{-\frac{b c d}{e}} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)-\frac{e F^{b c x}}{d+e x}\right)}{e^2}","\frac{b c \log (F) F^{c \left(a-\frac{b d}{e}\right)} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)}{e^2}-\frac{F^{c (a+b x)}}{e (d+e x)}",1,"(F^(a*c)*(-((e*F^(b*c*x))/(d + e*x)) + (b*c*ExpIntegralEi[(b*c*(d + e*x)*Log[F])/e]*Log[F])/F^((b*c*d)/e)))/e^2","A",1
9,1,88,95,0.1534061,"\int \frac{F^{c (a+b x)}}{(d+e x)^3} \, dx","Integrate[F^(c*(a + b*x))/(d + e*x)^3,x]","\frac{F^{c \left(a-\frac{b d}{e}\right)} \left(b^2 c^2 \log ^2(F) (d+e x)^2 \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)-e F^{\frac{b c (d+e x)}{e}} (b c \log (F) (d+e x)+e)\right)}{2 e^3 (d+e x)^2}","\frac{b^2 c^2 \log ^2(F) F^{c \left(a-\frac{b d}{e}\right)} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)}{2 e^3}-\frac{b c \log (F) F^{c (a+b x)}}{2 e^2 (d+e x)}-\frac{F^{c (a+b x)}}{2 e (d+e x)^2}",1,"(F^(c*(a - (b*d)/e))*(b^2*c^2*(d + e*x)^2*ExpIntegralEi[(b*c*(d + e*x)*Log[F])/e]*Log[F]^2 - e*F^((b*c*(d + e*x))/e)*(e + b*c*(d + e*x)*Log[F])))/(2*e^3*(d + e*x)^2)","A",1
10,1,99,128,0.1939833,"\int \frac{F^{c (a+b x)}}{(d+e x)^4} \, dx","Integrate[F^(c*(a + b*x))/(d + e*x)^4,x]","\frac{F^{a c} \left(b^3 c^3 \log ^3(F) F^{-\frac{b c d}{e}} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)-\frac{e F^{b c x} \left(b^2 c^2 \log ^2(F) (d+e x)^2+b c e \log (F) (d+e x)+2 e^2\right)}{(d+e x)^3}\right)}{6 e^4}","\frac{b^3 c^3 \log ^3(F) F^{c \left(a-\frac{b d}{e}\right)} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)}{6 e^4}-\frac{b^2 c^2 \log ^2(F) F^{c (a+b x)}}{6 e^3 (d+e x)}-\frac{b c \log (F) F^{c (a+b x)}}{6 e^2 (d+e x)^2}-\frac{F^{c (a+b x)}}{3 e (d+e x)^3}",1,"(F^(a*c)*((b^3*c^3*ExpIntegralEi[(b*c*(d + e*x)*Log[F])/e]*Log[F]^3)/F^((b*c*d)/e) - (e*F^(b*c*x)*(2*e^2 + b*c*e*(d + e*x)*Log[F] + b^2*c^2*(d + e*x)^2*Log[F]^2))/(d + e*x)^3))/(6*e^4)","A",1
11,1,121,161,0.1643771,"\int \frac{F^{c (a+b x)}}{(d+e x)^5} \, dx","Integrate[F^(c*(a + b*x))/(d + e*x)^5,x]","\frac{F^{a c} \left(b^4 c^4 \log ^4(F) F^{-\frac{b c d}{e}} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)-\frac{e F^{b c x} \left(b^3 c^3 \log ^3(F) (d+e x)^3+b^2 c^2 e \log ^2(F) (d+e x)^2+2 b c e^2 \log (F) (d+e x)+6 e^3\right)}{(d+e x)^4}\right)}{24 e^5}","\frac{b^4 c^4 \log ^4(F) F^{c \left(a-\frac{b d}{e}\right)} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)}{24 e^5}-\frac{b^3 c^3 \log ^3(F) F^{c (a+b x)}}{24 e^4 (d+e x)}-\frac{b^2 c^2 \log ^2(F) F^{c (a+b x)}}{24 e^3 (d+e x)^2}-\frac{b c \log (F) F^{c (a+b x)}}{12 e^2 (d+e x)^3}-\frac{F^{c (a+b x)}}{4 e (d+e x)^4}",1,"(F^(a*c)*((b^4*c^4*ExpIntegralEi[(b*c*(d + e*x)*Log[F])/e]*Log[F]^4)/F^((b*c*d)/e) - (e*F^(b*c*x)*(6*e^3 + 2*b*c*e^2*(d + e*x)*Log[F] + b^2*c^2*e*(d + e*x)^2*Log[F]^2 + b^3*c^3*(d + e*x)^3*Log[F]^3))/(d + e*x)^4))/(24*e^5)","A",1
12,1,100,141,0.0619024,"\int F^{c (a+b x)} \left(d^4+4 d^3 e x+6 d^2 e^2 x^2+4 d e^3 x^3+e^4 x^4\right) \, dx","Integrate[F^(c*(a + b*x))*(d^4 + 4*d^3*e*x + 6*d^2*e^2*x^2 + 4*d*e^3*x^3 + e^4*x^4),x]","\frac{F^{c (a+b x)} \left(b^4 c^4 \log ^4(F) (d+e x)^4-4 b^3 c^3 e \log ^3(F) (d+e x)^3+12 b^2 c^2 e^2 \log ^2(F) (d+e x)^2-24 b c e^3 \log (F) (d+e x)+24 e^4\right)}{b^5 c^5 \log ^5(F)}","\frac{24 e^4 F^{c (a+b x)}}{b^5 c^5 \log ^5(F)}-\frac{24 e^3 (d+e x) F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}+\frac{12 e^2 (d+e x)^2 F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{4 e (d+e x)^3 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{(d+e x)^4 F^{c (a+b x)}}{b c \log (F)}",1,"(F^(c*(a + b*x))*(24*e^4 - 24*b*c*e^3*(d + e*x)*Log[F] + 12*b^2*c^2*e^2*(d + e*x)^2*Log[F]^2 - 4*b^3*c^3*e*(d + e*x)^3*Log[F]^3 + b^4*c^4*(d + e*x)^4*Log[F]^4))/(b^5*c^5*Log[F]^5)","A",1
13,1,78,110,0.0792926,"\int F^{c (a+b x)} \left(d^3+3 d^2 e x+3 d e^2 x^2+e^3 x^3\right) \, dx","Integrate[F^(c*(a + b*x))*(d^3 + 3*d^2*e*x + 3*d*e^2*x^2 + e^3*x^3),x]","\frac{F^{c (a+b x)} \left(b^3 c^3 \log ^3(F) (d+e x)^3-3 b^2 c^2 e \log ^2(F) (d+e x)^2+6 b c e^2 \log (F) (d+e x)-6 e^3\right)}{b^4 c^4 \log ^4(F)}","-\frac{6 e^3 F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}+\frac{6 e^2 (d+e x) F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{3 e (d+e x)^2 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{(d+e x)^3 F^{c (a+b x)}}{b c \log (F)}",1,"(F^(c*(a + b*x))*(-6*e^3 + 6*b*c*e^2*(d + e*x)*Log[F] - 3*b^2*c^2*e*(d + e*x)^2*Log[F]^2 + b^3*c^3*(d + e*x)^3*Log[F]^3))/(b^4*c^4*Log[F]^4)","A",1
14,1,56,79,0.0368529,"\int F^{c (a+b x)} \left(d^2+2 d e x+e^2 x^2\right) \, dx","Integrate[F^(c*(a + b*x))*(d^2 + 2*d*e*x + e^2*x^2),x]","\frac{F^{c (a+b x)} \left(b^2 c^2 \log ^2(F) (d+e x)^2-2 b c e \log (F) (d+e x)+2 e^2\right)}{b^3 c^3 \log ^3(F)}","\frac{2 e^2 F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{2 e (d+e x) F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{(d+e x)^2 F^{c (a+b x)}}{b c \log (F)}",1,"(F^(c*(a + b*x))*(2*e^2 - 2*b*c*e*(d + e*x)*Log[F] + b^2*c^2*(d + e*x)^2*Log[F]^2))/(b^3*c^3*Log[F]^3)","A",1
15,1,55,57,0.0610075,"\int \frac{F^{c (a+b x)}}{d^2+2 d e x+e^2 x^2} \, dx","Integrate[F^(c*(a + b*x))/(d^2 + 2*d*e*x + e^2*x^2),x]","\frac{F^{a c} \left(b c \log (F) F^{-\frac{b c d}{e}} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)-\frac{e F^{b c x}}{d+e x}\right)}{e^2}","\frac{b c \log (F) F^{c \left(a-\frac{b d}{e}\right)} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)}{e^2}-\frac{F^{c (a+b x)}}{e (d+e x)}",1,"(F^(a*c)*(-((e*F^(b*c*x))/(d + e*x)) + (b*c*ExpIntegralEi[(b*c*(d + e*x)*Log[F])/e]*Log[F])/F^((b*c*d)/e)))/e^2","A",1
16,1,88,95,0.0504406,"\int \frac{F^{c (a+b x)}}{d^3+3 d^2 e x+3 d e^2 x^2+e^3 x^3} \, dx","Integrate[F^(c*(a + b*x))/(d^3 + 3*d^2*e*x + 3*d*e^2*x^2 + e^3*x^3),x]","\frac{F^{c \left(a-\frac{b d}{e}\right)} \left(b^2 c^2 \log ^2(F) (d+e x)^2 \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)-e F^{\frac{b c (d+e x)}{e}} (b c \log (F) (d+e x)+e)\right)}{2 e^3 (d+e x)^2}","\frac{b^2 c^2 \log ^2(F) F^{c \left(a-\frac{b d}{e}\right)} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)}{2 e^3}-\frac{b c \log (F) F^{c (a+b x)}}{2 e^2 (d+e x)}-\frac{F^{c (a+b x)}}{2 e (d+e x)^2}",1,"(F^(c*(a - (b*d)/e))*(b^2*c^2*(d + e*x)^2*ExpIntegralEi[(b*c*(d + e*x)*Log[F])/e]*Log[F]^2 - e*F^((b*c*(d + e*x))/e)*(e + b*c*(d + e*x)*Log[F])))/(2*e^3*(d + e*x)^2)","A",1
17,1,99,128,0.0440268,"\int \frac{F^{c (a+b x)}}{d^4+4 d^3 e x+6 d^2 e^2 x^2+4 d e^3 x^3+e^4 x^4} \, dx","Integrate[F^(c*(a + b*x))/(d^4 + 4*d^3*e*x + 6*d^2*e^2*x^2 + 4*d*e^3*x^3 + e^4*x^4),x]","\frac{F^{a c} \left(b^3 c^3 \log ^3(F) F^{-\frac{b c d}{e}} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)-\frac{e F^{b c x} \left(b^2 c^2 \log ^2(F) (d+e x)^2+b c e \log (F) (d+e x)+2 e^2\right)}{(d+e x)^3}\right)}{6 e^4}","\frac{b^3 c^3 \log ^3(F) F^{c \left(a-\frac{b d}{e}\right)} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)}{6 e^4}-\frac{b^2 c^2 \log ^2(F) F^{c (a+b x)}}{6 e^3 (d+e x)}-\frac{b c \log (F) F^{c (a+b x)}}{6 e^2 (d+e x)^2}-\frac{F^{c (a+b x)}}{3 e (d+e x)^3}",1,"(F^(a*c)*((b^3*c^3*ExpIntegralEi[(b*c*(d + e*x)*Log[F])/e]*Log[F]^3)/F^((b*c*d)/e) - (e*F^(b*c*x)*(2*e^2 + b*c*e*(d + e*x)*Log[F] + b^2*c^2*(d + e*x)^2*Log[F]^2))/(d + e*x)^3))/(6*e^4)","A",1
18,1,121,161,0.0316852,"\int \frac{F^{c (a+b x)}}{d^5+5 d^4 e x+10 d^3 e^2 x^2+10 d^2 e^3 x^3+5 d e^4 x^4+e^5 x^5} \, dx","Integrate[F^(c*(a + b*x))/(d^5 + 5*d^4*e*x + 10*d^3*e^2*x^2 + 10*d^2*e^3*x^3 + 5*d*e^4*x^4 + e^5*x^5),x]","\frac{F^{a c} \left(b^4 c^4 \log ^4(F) F^{-\frac{b c d}{e}} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)-\frac{e F^{b c x} \left(b^3 c^3 \log ^3(F) (d+e x)^3+b^2 c^2 e \log ^2(F) (d+e x)^2+2 b c e^2 \log (F) (d+e x)+6 e^3\right)}{(d+e x)^4}\right)}{24 e^5}","\frac{b^4 c^4 \log ^4(F) F^{c \left(a-\frac{b d}{e}\right)} \text{Ei}\left(\frac{b c (d+e x) \log (F)}{e}\right)}{24 e^5}-\frac{b^3 c^3 \log ^3(F) F^{c (a+b x)}}{24 e^4 (d+e x)}-\frac{b^2 c^2 \log ^2(F) F^{c (a+b x)}}{24 e^3 (d+e x)^2}-\frac{b c \log (F) F^{c (a+b x)}}{12 e^2 (d+e x)^3}-\frac{F^{c (a+b x)}}{4 e (d+e x)^4}",1,"(F^(a*c)*((b^4*c^4*ExpIntegralEi[(b*c*(d + e*x)*Log[F])/e]*Log[F]^4)/F^((b*c*d)/e) - (e*F^(b*c*x)*(6*e^3 + 2*b*c*e^2*(d + e*x)*Log[F] + b^2*c^2*e*(d + e*x)^2*Log[F]^2 + b^3*c^3*(d + e*x)^3*Log[F]^3))/(d + e*x)^4))/(24*e^5)","A",1
19,1,72,72,0.0124051,"\int F^{c (a+b x)} \left((d+e x)^n\right)^m \, dx","Integrate[F^(c*(a + b*x))*((d + e*x)^n)^m,x]","\frac{\left((d+e x)^n\right)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-m n} \Gamma \left(m n+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}","\frac{\left((d+e x)^n\right)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-m n} \Gamma \left(m n+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}",1,"(F^(c*(a - (b*d)/e))*((d + e*x)^n)^m*Gamma[1 + m*n, -((b*c*(d + e*x)*Log[F])/e)])/(b*c*Log[F]*(-((b*c*(d + e*x)*Log[F])/e))^(m*n))","A",1
20,1,71,71,0.0148551,"\int F^{c (a+b x)} \left(d^4+4 d^3 e x+6 d^2 e^2 x^2+4 d e^3 x^3+e^4 x^4\right)^m \, dx","Integrate[F^(c*(a + b*x))*(d^4 + 4*d^3*e*x + 6*d^2*e^2*x^2 + 4*d*e^3*x^3 + e^4*x^4)^m,x]","\frac{\left((d+e x)^4\right)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-4 m} \Gamma \left(4 m+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}","\frac{\left((d+e x)^4\right)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-4 m} \Gamma \left(4 m+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}",1,"(F^(c*(a - (b*d)/e))*((d + e*x)^4)^m*Gamma[1 + 4*m, -((b*c*(d + e*x)*Log[F])/e)])/(b*c*Log[F]*(-((b*c*(d + e*x)*Log[F])/e))^(4*m))","A",1
21,1,71,71,0.0137519,"\int F^{c (a+b x)} \left(d^3+3 d^2 e x+3 d e^2 x^2+e^3 x^3\right)^m \, dx","Integrate[F^(c*(a + b*x))*(d^3 + 3*d^2*e*x + 3*d*e^2*x^2 + e^3*x^3)^m,x]","\frac{\left((d+e x)^3\right)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-3 m} \Gamma \left(3 m+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}","\frac{\left((d+e x)^3\right)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-3 m} \Gamma \left(3 m+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}",1,"(F^(c*(a - (b*d)/e))*((d + e*x)^3)^m*Gamma[1 + 3*m, -((b*c*(d + e*x)*Log[F])/e)])/(b*c*Log[F]*(-((b*c*(d + e*x)*Log[F])/e))^(3*m))","A",1
22,1,71,71,0.0143268,"\int F^{c (a+b x)} \left(d^2+2 d e x+e^2 x^2\right)^m \, dx","Integrate[F^(c*(a + b*x))*(d^2 + 2*d*e*x + e^2*x^2)^m,x]","\frac{\left((d+e x)^2\right)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-2 m} \Gamma \left(2 m+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}","\frac{\left((d+e x)^2\right)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-2 m} \Gamma \left(2 m+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}",1,"(F^(c*(a - (b*d)/e))*((d + e*x)^2)^m*Gamma[1 + 2*m, -((b*c*(d + e*x)*Log[F])/e)])/(b*c*Log[F]*(-((b*c*(d + e*x)*Log[F])/e))^(2*m))","A",1
23,1,67,67,0.0121971,"\int F^{c (a+b x)} (d+e x)^m \, dx","Integrate[F^(c*(a + b*x))*(d + e*x)^m,x]","\frac{(d+e x)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-m} \Gamma \left(m+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}","\frac{(d+e x)^m F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{-m} \Gamma \left(m+1,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}",1,"(F^(c*(a - (b*d)/e))*(d + e*x)^m*Gamma[1 + m, -((b*c*(d + e*x)*Log[F])/e)])/(b*c*Log[F]*(-((b*c*(d + e*x)*Log[F])/e))^m)","A",1
24,1,69,69,0.0137317,"\int F^{c (a+b x)} (d+e x)^{-m} \, dx","Integrate[F^(c*(a + b*x))/(d + e*x)^m,x]","\frac{(d+e x)^{-m} F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^m \Gamma \left(1-m,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}","\frac{(d+e x)^{-m} F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^m \Gamma \left(1-m,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}",1,"(F^(c*(a - (b*d)/e))*Gamma[1 - m, -((b*c*(d + e*x)*Log[F])/e)]*(-((b*c*(d + e*x)*Log[F])/e))^m)/(b*c*(d + e*x)^m*Log[F])","A",1
25,1,73,73,0.0108557,"\int F^{c (a+b x)} \left(d^2+2 d e x+e^2 x^2\right)^{-m} \, dx","Integrate[F^(c*(a + b*x))/(d^2 + 2*d*e*x + e^2*x^2)^m,x]","\frac{\left((d+e x)^2\right)^{-m} F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{2 m} \Gamma \left(1-2 m,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}","\frac{\left((d+e x)^2\right)^{-m} F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{2 m} \Gamma \left(1-2 m,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}",1,"(F^(c*(a - (b*d)/e))*Gamma[1 - 2*m, -((b*c*(d + e*x)*Log[F])/e)]*(-((b*c*(d + e*x)*Log[F])/e))^(2*m))/(b*c*((d + e*x)^2)^m*Log[F])","A",1
26,1,73,73,0.0116949,"\int F^{c (a+b x)} \left(d^3+3 d^2 e x+3 d e^2 x^2+e^3 x^3\right)^{-m} \, dx","Integrate[F^(c*(a + b*x))/(d^3 + 3*d^2*e*x + 3*d*e^2*x^2 + e^3*x^3)^m,x]","\frac{\left((d+e x)^3\right)^{-m} F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{3 m} \Gamma \left(1-3 m,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}","\frac{\left((d+e x)^3\right)^{-m} F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{3 m} \Gamma \left(1-3 m,-\frac{b c (d+e x) \log (F)}{e}\right)}{b c \log (F)}",1,"(F^(c*(a - (b*d)/e))*Gamma[1 - 3*m, -((b*c*(d + e*x)*Log[F])/e)]*(-((b*c*(d + e*x)*Log[F])/e))^(3*m))/(b*c*((d + e*x)^3)^m*Log[F])","A",1
27,1,15,15,0.0036062,"\int F^{2+5 x} \, dx","Integrate[F^(2 + 5*x),x]","\frac{F^{5 x+2}}{5 \log (F)}","\frac{F^{5 x+2}}{5 \log (F)}",1,"F^(2 + 5*x)/(5*Log[F])","A",1
28,1,15,15,0.0034274,"\int F^{a+b x} \, dx","Integrate[F^(a + b*x),x]","\frac{F^{a+b x}}{b \log (F)}","\frac{F^{a+b x}}{b \log (F)}",1,"F^(a + b*x)/(b*Log[F])","A",1
29,1,19,19,0.0047309,"\int 10^{2+5 x} \, dx","Integrate[10^(2 + 5*x),x]","\frac{2^{5 x+2} 5^{5 x+1}}{\log (10)}","\frac{2^{5 x+2} 5^{5 x+1}}{\log (10)}",1,"(2^(2 + 5*x)*5^(1 + 5*x))/Log[10]","A",1
30,1,36,131,0.0065376,"\int F^{a+b x} x^{7/2} \, dx","Integrate[F^(a + b*x)*x^(7/2),x]","\frac{F^a \sqrt{-b x \log (F)} \Gamma \left(\frac{9}{2},-b x \log (F)\right)}{b^5 \sqrt{x} \log ^5(F)}","\frac{105 \sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right)}{16 b^{9/2} \log ^{\frac{9}{2}}(F)}-\frac{105 \sqrt{x} F^{a+b x}}{8 b^4 \log ^4(F)}+\frac{35 x^{3/2} F^{a+b x}}{4 b^3 \log ^3(F)}-\frac{7 x^{5/2} F^{a+b x}}{2 b^2 \log ^2(F)}+\frac{x^{7/2} F^{a+b x}}{b \log (F)}",1,"(F^a*Gamma[9/2, -(b*x*Log[F])]*Sqrt[-(b*x*Log[F])])/(b^5*Sqrt[x]*Log[F]^5)","A",1
31,1,36,108,0.0069747,"\int F^{a+b x} x^{5/2} \, dx","Integrate[F^(a + b*x)*x^(5/2),x]","\frac{\sqrt{x} F^a \Gamma \left(\frac{7}{2},-b x \log (F)\right)}{b^3 \log ^3(F) \sqrt{-b x \log (F)}}","-\frac{15 \sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right)}{8 b^{7/2} \log ^{\frac{7}{2}}(F)}+\frac{15 \sqrt{x} F^{a+b x}}{4 b^3 \log ^3(F)}-\frac{5 x^{3/2} F^{a+b x}}{2 b^2 \log ^2(F)}+\frac{x^{5/2} F^{a+b x}}{b \log (F)}",1,"(F^a*Sqrt[x]*Gamma[7/2, -(b*x*Log[F])])/(b^3*Log[F]^3*Sqrt[-(b*x*Log[F])])","A",1
32,1,36,85,0.0062411,"\int F^{a+b x} x^{3/2} \, dx","Integrate[F^(a + b*x)*x^(3/2),x]","\frac{F^a \sqrt{-b x \log (F)} \Gamma \left(\frac{5}{2},-b x \log (F)\right)}{b^3 \sqrt{x} \log ^3(F)}","\frac{3 \sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right)}{4 b^{5/2} \log ^{\frac{5}{2}}(F)}-\frac{3 \sqrt{x} F^{a+b x}}{2 b^2 \log ^2(F)}+\frac{x^{3/2} F^{a+b x}}{b \log (F)}",1,"(F^a*Gamma[5/2, -(b*x*Log[F])]*Sqrt[-(b*x*Log[F])])/(b^3*Sqrt[x]*Log[F]^3)","A",1
33,1,30,62,0.008503,"\int F^{a+b x} \sqrt{x} \, dx","Integrate[F^(a + b*x)*Sqrt[x],x]","-\frac{x^{3/2} F^a \Gamma \left(\frac{3}{2},-b x \log (F)\right)}{(-b x \log (F))^{3/2}}","\frac{\sqrt{x} F^{a+b x}}{b \log (F)}-\frac{\sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right)}{2 b^{3/2} \log ^{\frac{3}{2}}(F)}",1,"-((F^a*x^(3/2)*Gamma[3/2, -(b*x*Log[F])])/(-(b*x*Log[F]))^(3/2))","A",1
34,1,30,38,0.0069777,"\int \frac{F^{a+b x}}{\sqrt{x}} \, dx","Integrate[F^(a + b*x)/Sqrt[x],x]","-\frac{\sqrt{x} F^a \Gamma \left(\frac{1}{2},-b x \log (F)\right)}{\sqrt{-b x \log (F)}}","\frac{\sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right)}{\sqrt{b} \sqrt{\log (F)}}",1,"-((F^a*Sqrt[x]*Gamma[1/2, -(b*x*Log[F])])/Sqrt[-(b*x*Log[F])])","A",1
35,1,38,54,0.0155476,"\int \frac{F^{a+b x}}{x^{3/2}} \, dx","Integrate[F^(a + b*x)/x^(3/2),x]","-\frac{2 F^a \left(F^{b x}-\sqrt{-b x \log (F)} \Gamma \left(\frac{1}{2},-b x \log (F)\right)\right)}{\sqrt{x}}","2 \sqrt{\pi } \sqrt{b} F^a \sqrt{\log (F)} \text{erfi}\left(\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right)-\frac{2 F^{a+b x}}{\sqrt{x}}",1,"(-2*F^a*(F^(b*x) - Gamma[1/2, -(b*x*Log[F])]*Sqrt[-(b*x*Log[F])]))/Sqrt[x]","A",1
36,1,49,77,0.0387285,"\int \frac{F^{a+b x}}{x^{5/2}} \, dx","Integrate[F^(a + b*x)/x^(5/2),x]","-\frac{2 F^a \left(F^{b x} (2 b x \log (F)+1)+2 (-b x \log (F))^{3/2} \Gamma \left(\frac{1}{2},-b x \log (F)\right)\right)}{3 x^{3/2}}","\frac{4}{3} \sqrt{\pi } b^{3/2} F^a \log ^{\frac{3}{2}}(F) \text{erfi}\left(\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right)-\frac{2 F^{a+b x}}{3 x^{3/2}}-\frac{4 b \log (F) F^{a+b x}}{3 \sqrt{x}}",1,"(-2*F^a*(2*Gamma[1/2, -(b*x*Log[F])]*(-(b*x*Log[F]))^(3/2) + F^(b*x)*(1 + 2*b*x*Log[F])))/(3*x^(3/2))","A",1
37,1,61,100,0.0522198,"\int \frac{F^{a+b x}}{x^{7/2}} \, dx","Integrate[F^(a + b*x)/x^(7/2),x]","-\frac{2 F^a \left(F^{b x} \left(4 b^2 x^2 \log ^2(F)+2 b x \log (F)+3\right)-4 (-b x \log (F))^{5/2} \Gamma \left(\frac{1}{2},-b x \log (F)\right)\right)}{15 x^{5/2}}","\frac{8}{15} \sqrt{\pi } b^{5/2} F^a \log ^{\frac{5}{2}}(F) \text{erfi}\left(\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right)-\frac{8 b^2 \log ^2(F) F^{a+b x}}{15 \sqrt{x}}-\frac{2 F^{a+b x}}{5 x^{5/2}}-\frac{4 b \log (F) F^{a+b x}}{15 x^{3/2}}",1,"(-2*F^a*(-4*Gamma[1/2, -(b*x*Log[F])]*(-(b*x*Log[F]))^(5/2) + F^(b*x)*(3 + 2*b*x*Log[F] + 4*b^2*x^2*Log[F]^2)))/(15*x^(5/2))","A",1
38,1,73,123,0.0639416,"\int \frac{F^{a+b x}}{x^{9/2}} \, dx","Integrate[F^(a + b*x)/x^(9/2),x]","-\frac{2 F^a \left(F^{b x} \left(8 b^3 x^3 \log ^3(F)+4 b^2 x^2 \log ^2(F)+6 b x \log (F)+15\right)+8 (-b x \log (F))^{7/2} \Gamma \left(\frac{1}{2},-b x \log (F)\right)\right)}{105 x^{7/2}}","\frac{16}{105} \sqrt{\pi } b^{7/2} F^a \log ^{\frac{7}{2}}(F) \text{erfi}\left(\sqrt{b} \sqrt{x} \sqrt{\log (F)}\right)-\frac{16 b^3 \log ^3(F) F^{a+b x}}{105 \sqrt{x}}-\frac{8 b^2 \log ^2(F) F^{a+b x}}{105 x^{3/2}}-\frac{2 F^{a+b x}}{7 x^{7/2}}-\frac{4 b \log (F) F^{a+b x}}{35 x^{5/2}}",1,"(-2*F^a*(8*Gamma[1/2, -(b*x*Log[F])]*(-(b*x*Log[F]))^(7/2) + F^(b*x)*(15 + 6*b*x*Log[F] + 4*b^2*x^2*Log[F]^2 + 8*b^3*x^3*Log[F]^3)))/(105*x^(7/2))","A",1
39,1,72,208,0.0281851,"\int F^{c (a+b x)} (d+e x)^{7/2} \, dx","Integrate[F^(c*(a + b*x))*(d + e*x)^(7/2),x]","\frac{e^4 F^{c \left(a-\frac{b d}{e}\right)} \sqrt{-\frac{b c \log (F) (d+e x)}{e}} \Gamma \left(\frac{9}{2},-\frac{b c (d+e x) \log (F)}{e}\right)}{b^5 c^5 \log ^5(F) \sqrt{d+e x}}","\frac{105 \sqrt{\pi } e^{7/2} F^{c \left(a-\frac{b d}{e}\right)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c} \sqrt{\log (F)} \sqrt{d+e x}}{\sqrt{e}}\right)}{16 b^{9/2} c^{9/2} \log ^{\frac{9}{2}}(F)}-\frac{105 e^3 \sqrt{d+e x} F^{c (a+b x)}}{8 b^4 c^4 \log ^4(F)}+\frac{35 e^2 (d+e x)^{3/2} F^{c (a+b x)}}{4 b^3 c^3 \log ^3(F)}-\frac{7 e (d+e x)^{5/2} F^{c (a+b x)}}{2 b^2 c^2 \log ^2(F)}+\frac{(d+e x)^{7/2} F^{c (a+b x)}}{b c \log (F)}",1,"(e^4*F^(c*(a - (b*d)/e))*Gamma[9/2, -((b*c*(d + e*x)*Log[F])/e)]*Sqrt[-((b*c*(d + e*x)*Log[F])/e)])/(b^5*c^5*Sqrt[d + e*x]*Log[F]^5)","A",1
40,1,72,173,0.0253882,"\int F^{c (a+b x)} (d+e x)^{5/2} \, dx","Integrate[F^(c*(a + b*x))*(d + e*x)^(5/2),x]","\frac{e^2 \sqrt{d+e x} F^{c \left(a-\frac{b d}{e}\right)} \Gamma \left(\frac{7}{2},-\frac{b c (d+e x) \log (F)}{e}\right)}{b^3 c^3 \log ^3(F) \sqrt{-\frac{b c \log (F) (d+e x)}{e}}}","-\frac{15 \sqrt{\pi } e^{5/2} F^{c \left(a-\frac{b d}{e}\right)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c} \sqrt{\log (F)} \sqrt{d+e x}}{\sqrt{e}}\right)}{8 b^{7/2} c^{7/2} \log ^{\frac{7}{2}}(F)}+\frac{15 e^2 \sqrt{d+e x} F^{c (a+b x)}}{4 b^3 c^3 \log ^3(F)}-\frac{5 e (d+e x)^{3/2} F^{c (a+b x)}}{2 b^2 c^2 \log ^2(F)}+\frac{(d+e x)^{5/2} F^{c (a+b x)}}{b c \log (F)}",1,"(e^2*F^(c*(a - (b*d)/e))*Sqrt[d + e*x]*Gamma[7/2, -((b*c*(d + e*x)*Log[F])/e)])/(b^3*c^3*Log[F]^3*Sqrt[-((b*c*(d + e*x)*Log[F])/e)])","A",1
41,1,63,138,0.0742183,"\int F^{c (a+b x)} (d+e x)^{3/2} \, dx","Integrate[F^(c*(a + b*x))*(d + e*x)^(3/2),x]","-\frac{(d+e x)^{5/2} F^{c \left(a-\frac{b d}{e}\right)} \Gamma \left(\frac{5}{2},-\frac{b c (d+e x) \log (F)}{e}\right)}{e \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{5/2}}","\frac{3 \sqrt{\pi } e^{3/2} F^{c \left(a-\frac{b d}{e}\right)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c} \sqrt{\log (F)} \sqrt{d+e x}}{\sqrt{e}}\right)}{4 b^{5/2} c^{5/2} \log ^{\frac{5}{2}}(F)}-\frac{3 e \sqrt{d+e x} F^{c (a+b x)}}{2 b^2 c^2 \log ^2(F)}+\frac{(d+e x)^{3/2} F^{c (a+b x)}}{b c \log (F)}",1,"-((F^(c*(a - (b*d)/e))*(d + e*x)^(5/2)*Gamma[5/2, -((b*c*(d + e*x)*Log[F])/e)])/(e*(-((b*c*(d + e*x)*Log[F])/e))^(5/2)))","A",1
42,1,63,105,0.0391139,"\int F^{c (a+b x)} \sqrt{d+e x} \, dx","Integrate[F^(c*(a + b*x))*Sqrt[d + e*x],x]","-\frac{(d+e x)^{3/2} F^{c \left(a-\frac{b d}{e}\right)} \Gamma \left(\frac{3}{2},-\frac{b c (d+e x) \log (F)}{e}\right)}{e \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{3/2}}","\frac{\sqrt{d+e x} F^{c (a+b x)}}{b c \log (F)}-\frac{\sqrt{\pi } \sqrt{e} F^{c \left(a-\frac{b d}{e}\right)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c} \sqrt{\log (F)} \sqrt{d+e x}}{\sqrt{e}}\right)}{2 b^{3/2} c^{3/2} \log ^{\frac{3}{2}}(F)}",1,"-((F^(c*(a - (b*d)/e))*(d + e*x)^(3/2)*Gamma[3/2, -((b*c*(d + e*x)*Log[F])/e)])/(e*(-((b*c*(d + e*x)*Log[F])/e))^(3/2)))","A",1
43,1,63,72,0.0286529,"\int \frac{F^{c (a+b x)}}{\sqrt{d+e x}} \, dx","Integrate[F^(c*(a + b*x))/Sqrt[d + e*x],x]","-\frac{\sqrt{d+e x} F^{c \left(a-\frac{b d}{e}\right)} \Gamma \left(\frac{1}{2},-\frac{b c (d+e x) \log (F)}{e}\right)}{e \sqrt{-\frac{b c \log (F) (d+e x)}{e}}}","\frac{\sqrt{\pi } F^{c \left(a-\frac{b d}{e}\right)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c} \sqrt{\log (F)} \sqrt{d+e x}}{\sqrt{e}}\right)}{\sqrt{b} \sqrt{c} \sqrt{e} \sqrt{\log (F)}}",1,"-((F^(c*(a - (b*d)/e))*Sqrt[d + e*x]*Gamma[1/2, -((b*c*(d + e*x)*Log[F])/e)])/(e*Sqrt[-((b*c*(d + e*x)*Log[F])/e)]))","A",1
44,1,75,97,0.0779373,"\int \frac{F^{c (a+b x)}}{(d+e x)^{3/2}} \, dx","Integrate[F^(c*(a + b*x))/(d + e*x)^(3/2),x]","-\frac{2 \left(F^{c (a+b x)}-F^{c \left(a-\frac{b d}{e}\right)} \sqrt{-\frac{b c \log (F) (d+e x)}{e}} \Gamma \left(\frac{1}{2},-\frac{b c (d+e x) \log (F)}{e}\right)\right)}{e \sqrt{d+e x}}","\frac{2 \sqrt{\pi } \sqrt{b} \sqrt{c} \sqrt{\log (F)} F^{c \left(a-\frac{b d}{e}\right)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c} \sqrt{\log (F)} \sqrt{d+e x}}{\sqrt{e}}\right)}{e^{3/2}}-\frac{2 F^{c (a+b x)}}{e \sqrt{d+e x}}",1,"(-2*(F^(c*(a + b*x)) - F^(c*(a - (b*d)/e))*Gamma[1/2, -((b*c*(d + e*x)*Log[F])/e)]*Sqrt[-((b*c*(d + e*x)*Log[F])/e)]))/(e*Sqrt[d + e*x])","A",1
45,1,92,130,0.2370043,"\int \frac{F^{c (a+b x)}}{(d+e x)^{5/2}} \, dx","Integrate[F^(c*(a + b*x))/(d + e*x)^(5/2),x]","-\frac{2 \left(F^{c (a+b x)} (2 b c \log (F) (d+e x)+e)+2 e F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{b c (d+e x) \log (F)}{e}\right)\right)}{3 e^2 (d+e x)^{3/2}}","\frac{4 \sqrt{\pi } b^{3/2} c^{3/2} \log ^{\frac{3}{2}}(F) F^{c \left(a-\frac{b d}{e}\right)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c} \sqrt{\log (F)} \sqrt{d+e x}}{\sqrt{e}}\right)}{3 e^{5/2}}-\frac{4 b c \log (F) F^{c (a+b x)}}{3 e^2 \sqrt{d+e x}}-\frac{2 F^{c (a+b x)}}{3 e (d+e x)^{3/2}}",1,"(-2*(2*e*F^(c*(a - (b*d)/e))*Gamma[1/2, -((b*c*(d + e*x)*Log[F])/e)]*(-((b*c*(d + e*x)*Log[F])/e))^(3/2) + F^(c*(a + b*x))*(e + 2*b*c*(d + e*x)*Log[F])))/(3*e^2*(d + e*x)^(3/2))","A",1
46,1,118,165,0.1392059,"\int \frac{F^{c (a+b x)}}{(d+e x)^{7/2}} \, dx","Integrate[F^(c*(a + b*x))/(d + e*x)^(7/2),x]","\frac{2 \left(-2 b c \log (F) (d+e x) \left(F^{c (a+b x)} (2 b c \log (F) (d+e x)+e)+2 e F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{b c (d+e x) \log (F)}{e}\right)\right)-3 e^2 F^{c (a+b x)}\right)}{15 e^3 (d+e x)^{5/2}}","\frac{8 \sqrt{\pi } b^{5/2} c^{5/2} \log ^{\frac{5}{2}}(F) F^{c \left(a-\frac{b d}{e}\right)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c} \sqrt{\log (F)} \sqrt{d+e x}}{\sqrt{e}}\right)}{15 e^{7/2}}-\frac{8 b^2 c^2 \log ^2(F) F^{c (a+b x)}}{15 e^3 \sqrt{d+e x}}-\frac{4 b c \log (F) F^{c (a+b x)}}{15 e^2 (d+e x)^{3/2}}-\frac{2 F^{c (a+b x)}}{5 e (d+e x)^{5/2}}",1,"(2*(-3*e^2*F^(c*(a + b*x)) - 2*b*c*(d + e*x)*Log[F]*(2*e*F^(c*(a - (b*d)/e))*Gamma[1/2, -((b*c*(d + e*x)*Log[F])/e)]*(-((b*c*(d + e*x)*Log[F])/e))^(3/2) + F^(c*(a + b*x))*(e + 2*b*c*(d + e*x)*Log[F]))))/(15*e^3*(d + e*x)^(5/2))","A",1
47,1,144,200,0.1678011,"\int \frac{F^{c (a+b x)}}{(d+e x)^{9/2}} \, dx","Integrate[F^(c*(a + b*x))/(d + e*x)^(9/2),x]","\frac{2 \left(2 b c \log (F) (d+e x) \left(-2 b c \log (F) (d+e x) \left(F^{c (a+b x)} (2 b c \log (F) (d+e x)+e)+2 e F^{c \left(a-\frac{b d}{e}\right)} \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{3/2} \Gamma \left(\frac{1}{2},-\frac{b c (d+e x) \log (F)}{e}\right)\right)-3 e^2 F^{c (a+b x)}\right)-15 e^3 F^{c (a+b x)}\right)}{105 e^4 (d+e x)^{7/2}}","\frac{16 \sqrt{\pi } b^{7/2} c^{7/2} \log ^{\frac{7}{2}}(F) F^{c \left(a-\frac{b d}{e}\right)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{c} \sqrt{\log (F)} \sqrt{d+e x}}{\sqrt{e}}\right)}{105 e^{9/2}}-\frac{16 b^3 c^3 \log ^3(F) F^{c (a+b x)}}{105 e^4 \sqrt{d+e x}}-\frac{8 b^2 c^2 \log ^2(F) F^{c (a+b x)}}{105 e^3 (d+e x)^{3/2}}-\frac{4 b c \log (F) F^{c (a+b x)}}{35 e^2 (d+e x)^{5/2}}-\frac{2 F^{c (a+b x)}}{7 e (d+e x)^{7/2}}",1,"(2*(-15*e^3*F^(c*(a + b*x)) + 2*b*c*(d + e*x)*Log[F]*(-3*e^2*F^(c*(a + b*x)) - 2*b*c*(d + e*x)*Log[F]*(2*e*F^(c*(a - (b*d)/e))*Gamma[1/2, -((b*c*(d + e*x)*Log[F])/e)]*(-((b*c*(d + e*x)*Log[F])/e))^(3/2) + F^(c*(a + b*x))*(e + 2*b*c*(d + e*x)*Log[F])))))/(105*e^4*(d + e*x)^(7/2))","A",1
48,1,24,151,0.004795,"\int e^{-b x} x^{13/2} \, dx","Integrate[x^(13/2)/E^(b*x),x]","-\frac{\sqrt{b x} \Gamma \left(\frac{15}{2},b x\right)}{b^8 \sqrt{x}}","\frac{135135 \sqrt{\pi } \text{erf}\left(\sqrt{b} \sqrt{x}\right)}{128 b^{15/2}}-\frac{135135 \sqrt{x} e^{-b x}}{64 b^7}-\frac{45045 x^{3/2} e^{-b x}}{32 b^6}-\frac{9009 x^{5/2} e^{-b x}}{16 b^5}-\frac{1287 x^{7/2} e^{-b x}}{8 b^4}-\frac{143 x^{9/2} e^{-b x}}{4 b^3}-\frac{13 x^{11/2} e^{-b x}}{2 b^2}-\frac{x^{13/2} e^{-b x}}{b}",1,"-((Sqrt[b*x]*Gamma[15/2, b*x])/(b^8*Sqrt[x]))","A",1
49,1,63,71,0.0790801,"\int F^{c (a+b x)} (d+e x)^{4/3} \, dx","Integrate[F^(c*(a + b*x))*(d + e*x)^(4/3),x]","-\frac{(d+e x)^{7/3} F^{c \left(a-\frac{b d}{e}\right)} \Gamma \left(\frac{7}{3},-\frac{b c (d+e x) \log (F)}{e}\right)}{e \left(-\frac{b c \log (F) (d+e x)}{e}\right)^{7/3}}","-\frac{e \sqrt[3]{d+e x} F^{c \left(a-\frac{b d}{e}\right)} \Gamma \left(\frac{7}{3},-\frac{b c (d+e x) \log (F)}{e}\right)}{b^2 c^2 \log ^2(F) \sqrt[3]{-\frac{b c \log (F) (d+e x)}{e}}}",1,"-((F^(c*(a - (b*d)/e))*(d + e*x)^(7/3)*Gamma[7/3, -((b*c*(d + e*x)*Log[F])/e)])/(e*(-((b*c*(d + e*x)*Log[F])/e))^(7/3)))","A",1
50,1,78,98,0.1384265,"\int \left(F^{c (a+b x)}\right)^n (d+e x)^{4/3} \, dx","Integrate[(F^(c*(a + b*x)))^n*(d + e*x)^(4/3),x]","-\frac{(d+e x)^{7/3} \left(F^{c (a+b x)}\right)^n F^{-\frac{b c n (d+e x)}{e}} \Gamma \left(\frac{7}{3},-\frac{b c n (d+e x) \log (F)}{e}\right)}{e \left(-\frac{b c n \log (F) (d+e x)}{e}\right)^{7/3}}","-\frac{e \sqrt[3]{d+e x} \left(F^{c (a+b x)}\right)^n F^{c n \left(a-\frac{b d}{e}\right)-c n (a+b x)} \Gamma \left(\frac{7}{3},-\frac{b c n (d+e x) \log (F)}{e}\right)}{b^2 c^2 n^2 \log ^2(F) \sqrt[3]{-\frac{b c n \log (F) (d+e x)}{e}}}",1,"-(((F^(c*(a + b*x)))^n*(d + e*x)^(7/3)*Gamma[7/3, -((b*c*n*(d + e*x)*Log[F])/e)])/(e*F^((b*c*n*(d + e*x))/e)*(-((b*c*n*(d + e*x)*Log[F])/e))^(7/3)))","A",1
51,1,34,48,0.0285586,"\int F^{c (a+b x)} (d+e x) \, dx","Integrate[F^(c*(a + b*x))*(d + e*x),x]","\frac{F^{c (a+b x)} (b c \log (F) (d+e x)-e)}{b^2 c^2 \log ^2(F)}","\frac{(d+e x) F^{c (a+b x)}}{b c \log (F)}-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}",1,"(F^(c*(a + b*x))*(-e + b*c*(d + e*x)*Log[F]))/(b^2*c^2*Log[F]^2)","A",1
52,1,56,135,0.0786121,"\int F^{c (a+b x)} \left(d+e x+f x^2\right) \, dx","Integrate[F^(c*(a + b*x))*(d + e*x + f*x^2),x]","\frac{F^{c (a+b x)} \left(b^2 c^2 \log ^2(F) (d+x (e+f x))-b c \log (F) (e+2 f x)+2 f\right)}{b^3 c^3 \log ^3(F)}","\frac{2 f F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{2 f x F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{d F^{c (a+b x)}}{b c \log (F)}+\frac{e x F^{c (a+b x)}}{b c \log (F)}+\frac{f x^2 F^{c (a+b x)}}{b c \log (F)}",1,"(F^(c*(a + b*x))*(2*f - b*c*(e + 2*f*x)*Log[F] + b^2*c^2*(d + x*(e + f*x))*Log[F]^2))/(b^3*c^3*Log[F]^3)","A",1
53,1,84,229,0.1156124,"\int F^{c (a+b x)} \left(d+e x+f x^2+g x^3\right) \, dx","Integrate[F^(c*(a + b*x))*(d + e*x + f*x^2 + g*x^3),x]","\frac{F^{c (a+b x)} \left(b^3 c^3 \log ^3(F) (d+x (e+x (f+g x)))-b^2 c^2 \log ^2(F) (e+x (2 f+3 g x))+2 b c \log (F) (f+3 g x)-6 g\right)}{b^4 c^4 \log ^4(F)}","-\frac{6 g F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}+\frac{2 f F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}+\frac{6 g x F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{2 f x F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{3 g x^2 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{d F^{c (a+b x)}}{b c \log (F)}+\frac{e x F^{c (a+b x)}}{b c \log (F)}+\frac{f x^2 F^{c (a+b x)}}{b c \log (F)}+\frac{g x^3 F^{c (a+b x)}}{b c \log (F)}",1,"(F^(c*(a + b*x))*(-6*g + 2*b*c*(f + 3*g*x)*Log[F] - b^2*c^2*(e + x*(2*f + 3*g*x))*Log[F]^2 + b^3*c^3*(d + x*(e + x*(f + g*x)))*Log[F]^3))/(b^4*c^4*Log[F]^4)","A",1
54,1,117,348,0.1790761,"\int F^{c (a+b x)} \left(d+e x+f x^2+g x^3+h x^4\right) \, dx","Integrate[F^(c*(a + b*x))*(d + e*x + f*x^2 + g*x^3 + h*x^4),x]","\frac{F^{c (a+b x)} \left(b^4 c^4 \log ^4(F) (d+x (e+x (f+x (g+h x))))-b^3 c^3 \log ^3(F) \left(e+x \left(2 f+3 g x+4 h x^2\right)\right)+2 b^2 c^2 \log ^2(F) (f+3 x (g+2 h x))-6 b c \log (F) (g+4 h x)+24 h\right)}{b^5 c^5 \log ^5(F)}","\frac{24 h F^{c (a+b x)}}{b^5 c^5 \log ^5(F)}-\frac{6 g F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}-\frac{24 h x F^{c (a+b x)}}{b^4 c^4 \log ^4(F)}+\frac{2 f F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}+\frac{6 g x F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}+\frac{12 h x^2 F^{c (a+b x)}}{b^3 c^3 \log ^3(F)}-\frac{e F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{2 f x F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{3 g x^2 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}-\frac{4 h x^3 F^{c (a+b x)}}{b^2 c^2 \log ^2(F)}+\frac{d F^{c (a+b x)}}{b c \log (F)}+\frac{e x F^{c (a+b x)}}{b c \log (F)}+\frac{f x^2 F^{c (a+b x)}}{b c \log (F)}+\frac{g x^3 F^{c (a+b x)}}{b c \log (F)}+\frac{h x^4 F^{c (a+b x)}}{b c \log (F)}",1,"(F^(c*(a + b*x))*(24*h - 6*b*c*(g + 4*h*x)*Log[F] + 2*b^2*c^2*(f + 3*x*(g + 2*h*x))*Log[F]^2 - b^3*c^3*(e + x*(2*f + 3*g*x + 4*h*x^2))*Log[F]^3 + b^4*c^4*(d + x*(e + x*(f + x*(g + h*x))))*Log[F]^4))/(b^5*c^5*Log[F]^5)","A",1
55,1,61,116,0.0591203,"\int e^{-a-b x} x^m (a+b x)^3 \, dx","Integrate[E^(-a - b*x)*x^m*(a + b*x)^3,x]","-\frac{e^{-a} x^m (b x)^{-m} \left(a^3 \Gamma (m+1,b x)+3 a^2 \Gamma (m+2,b x)+3 a \Gamma (m+3,b x)+\Gamma (m+4,b x)\right)}{b}","-\frac{a^3 e^{-a} x^m (b x)^{-m} \Gamma (m+1,b x)}{b}-\frac{3 a^2 e^{-a} x^m (b x)^{-m} \Gamma (m+2,b x)}{b}-\frac{3 a e^{-a} x^m (b x)^{-m} \Gamma (m+3,b x)}{b}-\frac{e^{-a} x^m (b x)^{-m} \Gamma (m+4,b x)}{b}",1,"-((x^m*(a^3*Gamma[1 + m, b*x] + 3*a^2*Gamma[2 + m, b*x] + 3*a*Gamma[3 + m, b*x] + Gamma[4 + m, b*x]))/(b*E^a*(b*x)^m))","A",1
56,1,121,397,0.3574176,"\int e^{-a-b x} x^3 (a+b x)^3 \, dx","Integrate[E^(-a - b*x)*x^3*(a + b*x)^3,x]","e^{-a-b x} \left(-3 \left(a^2+5 a+10\right) x^4-\frac{6 \left(a^3+12 a^2+60 a+120\right)}{b^4}-\frac{6 \left(a^3+12 a^2+60 a+120\right) x}{b^3}-\frac{3 \left(a^3+12 a^2+60 a+120\right) x^2}{b^2}-\frac{\left(a^3+12 a^2+60 a+120\right) x^3}{b}-3 (a+2) b x^5-b^2 x^6\right)","-\frac{6 a^3 e^{-a-b x}}{b^4}-\frac{6 a^3 x e^{-a-b x}}{b^3}-\frac{3 a^3 x^2 e^{-a-b x}}{b^2}-\frac{a^3 x^3 e^{-a-b x}}{b}-\frac{72 a^2 e^{-a-b x}}{b^4}-\frac{72 a^2 x e^{-a-b x}}{b^3}-\frac{36 a^2 x^2 e^{-a-b x}}{b^2}-3 a^2 x^4 e^{-a-b x}-\frac{12 a^2 x^3 e^{-a-b x}}{b}-\frac{360 a e^{-a-b x}}{b^4}-\frac{720 e^{-a-b x}}{b^4}-\frac{360 a x e^{-a-b x}}{b^3}-\frac{720 x e^{-a-b x}}{b^3}-b^2 x^6 e^{-a-b x}-\frac{180 a x^2 e^{-a-b x}}{b^2}-\frac{360 x^2 e^{-a-b x}}{b^2}-3 a b x^5 e^{-a-b x}-6 b x^5 e^{-a-b x}-15 a x^4 e^{-a-b x}-30 x^4 e^{-a-b x}-\frac{60 a x^3 e^{-a-b x}}{b}-\frac{120 x^3 e^{-a-b x}}{b}",1,"E^(-a - b*x)*((-6*(120 + 60*a + 12*a^2 + a^3))/b^4 - (6*(120 + 60*a + 12*a^2 + a^3)*x)/b^3 - (3*(120 + 60*a + 12*a^2 + a^3)*x^2)/b^2 - ((120 + 60*a + 12*a^2 + a^3)*x^3)/b - 3*(10 + 5*a + a^2)*x^4 - 3*(2 + a)*b*x^5 - b^2*x^6)","A",1
57,1,130,318,0.2102778,"\int e^{-a-b x} x^2 (a+b x)^3 \, dx","Integrate[E^(-a - b*x)*x^2*(a + b*x)^3,x]","e^{-b x} \left(-\left(3 a^2+12 a+20\right) e^{-a} x^3-\frac{2 \left(a^3+9 a^2+36 a+60\right) e^{-a}}{b^3}-\frac{2 \left(a^3+9 a^2+36 a+60\right) e^{-a} x}{b^2}-\frac{\left(a^3+9 a^2+36 a+60\right) e^{-a} x^2}{b}+e^{-a} \left(-b^2\right) x^5-(3 a+5) e^{-a} b x^4\right)","-\frac{2 a^3 e^{-a-b x}}{b^3}-\frac{2 a^3 x e^{-a-b x}}{b^2}-\frac{a^3 x^2 e^{-a-b x}}{b}-\frac{18 a^2 e^{-a-b x}}{b^3}-\frac{18 a^2 x e^{-a-b x}}{b^2}-3 a^2 x^3 e^{-a-b x}-\frac{9 a^2 x^2 e^{-a-b x}}{b}-\frac{72 a e^{-a-b x}}{b^3}-\frac{120 e^{-a-b x}}{b^3}-b^2 x^5 e^{-a-b x}-\frac{72 a x e^{-a-b x}}{b^2}-\frac{120 x e^{-a-b x}}{b^2}-3 a b x^4 e^{-a-b x}-5 b x^4 e^{-a-b x}-12 a x^3 e^{-a-b x}-20 x^3 e^{-a-b x}-\frac{36 a x^2 e^{-a-b x}}{b}-\frac{60 x^2 e^{-a-b x}}{b}",1,"((-2*(60 + 36*a + 9*a^2 + a^3))/(b^3*E^a) - (2*(60 + 36*a + 9*a^2 + a^3)*x)/(b^2*E^a) - ((60 + 36*a + 9*a^2 + a^3)*x^2)/(b*E^a) - ((20 + 12*a + 3*a^2)*x^3)/E^a - ((5 + 3*a)*b*x^4)/E^a - (b^2*x^5)/E^a)/E^(b*x)","A",1
58,1,96,184,0.1329751,"\int e^{-a-b x} x (a+b x)^3 \, dx","Integrate[E^(-a - b*x)*x*(a + b*x)^3,x]","\frac{e^{-a-b x} \left(-a^3 (b x+1)-3 a^2 \left(b^2 x^2+2 b x+2\right)-3 a \left(b^3 x^3+3 b^2 x^2+6 b x+6\right)-b^4 x^4-4 b^3 x^3-12 b^2 x^2-24 b x-24\right)}{b^2}","-\frac{e^{-a-b x} (a+b x)^4}{b^2}+\frac{a e^{-a-b x} (a+b x)^3}{b^2}-\frac{4 e^{-a-b x} (a+b x)^3}{b^2}+\frac{3 a e^{-a-b x} (a+b x)^2}{b^2}-\frac{12 e^{-a-b x} (a+b x)^2}{b^2}+\frac{6 a e^{-a-b x} (a+b x)}{b^2}-\frac{24 e^{-a-b x} (a+b x)}{b^2}+\frac{6 a e^{-a-b x}}{b^2}-\frac{24 e^{-a-b x}}{b^2}",1,"(E^(-a - b*x)*(-24 - 24*b*x - 12*b^2*x^2 - 4*b^3*x^3 - b^4*x^4 - a^3*(1 + b*x) - 3*a^2*(2 + 2*b*x + b^2*x^2) - 3*a*(6 + 6*b*x + 3*b^2*x^2 + b^3*x^3)))/b^2","A",1
59,1,41,80,0.0484563,"\int e^{-a-b x} (a+b x)^3 \, dx","Integrate[E^(-a - b*x)*(a + b*x)^3,x]","\frac{e^{-a-b x} \left(-(a+b x)^3-3 (a+b x)^2-6 (a+b x)-6\right)}{b}","-\frac{e^{-a-b x} (a+b x)^3}{b}-\frac{3 e^{-a-b x} (a+b x)^2}{b}-\frac{6 e^{-a-b x} (a+b x)}{b}-\frac{6 e^{-a-b x}}{b}",1,"(E^(-a - b*x)*(-6 - 6*(a + b*x) - 3*(a + b*x)^2 - (a + b*x)^3))/b","A",1
60,1,52,102,0.0551892,"\int \frac{e^{-a-b x} (a+b x)^3}{x} \, dx","Integrate[(E^(-a - b*x)*(a + b*x)^3)/x,x]","e^{-a-b x} \left(a^3 e^{b x} \text{Ei}(-b x)-3 a^2-3 a (b x+1)-b^2 x^2-2 b x-2\right)","e^{-a} a^3 \text{Ei}(-b x)-3 a^2 e^{-a-b x}-b^2 x^2 e^{-a-b x}-3 a e^{-a-b x}-3 a b x e^{-a-b x}-2 e^{-a-b x}-2 b x e^{-a-b x}",1,"E^(-a - b*x)*(-2 - 3*a^2 - 2*b*x - b^2*x^2 - 3*a*(1 + b*x) + a^3*E^(b*x)*ExpIntegralEi[-(b*x)])","A",1
61,1,54,94,0.0696959,"\int \frac{e^{-a-b x} (a+b x)^3}{x^2} \, dx","Integrate[(E^(-a - b*x)*(a + b*x)^3)/x^2,x]","\frac{e^{-a-b x} \left(-a^3-(a-3) a^2 b x e^{b x} \text{Ei}(-b x)-3 a b x-b x (b x+1)\right)}{x}","e^{-a} a^3 (-b) \text{Ei}(-b x)-\frac{a^3 e^{-a-b x}}{x}+3 e^{-a} a^2 b \text{Ei}(-b x)-b^2 x e^{-a-b x}-3 a b e^{-a-b x}-b e^{-a-b x}",1,"(E^(-a - b*x)*(-a^3 - 3*a*b*x - b*x*(1 + b*x) - (-3 + a)*a^2*b*E^(b*x)*x*ExpIntegralEi[-(b*x)]))/x","A",1
62,1,68,130,0.0768137,"\int \frac{e^{-a-b x} (a+b x)^3}{x^3} \, dx","Integrate[(E^(-a - b*x)*(a + b*x)^3)/x^3,x]","\frac{e^{-a-b x} \left(a^3 (b x-1)+\left(a^2-6 a+6\right) a b^2 x^2 e^{b x} \text{Ei}(-b x)-6 a^2 b x-2 b^2 x^2\right)}{2 x^2}","\frac{1}{2} e^{-a} a^3 b^2 \text{Ei}(-b x)-\frac{a^3 e^{-a-b x}}{2 x^2}+\frac{a^3 b e^{-a-b x}}{2 x}-3 e^{-a} a^2 b^2 \text{Ei}(-b x)-\frac{3 a^2 b e^{-a-b x}}{x}+3 e^{-a} a b^2 \text{Ei}(-b x)-b^2 e^{-a-b x}",1,"(E^(-a - b*x)*(-6*a^2*b*x - 2*b^2*x^2 + a^3*(-1 + b*x) + a*(6 - 6*a + a^2)*b^2*E^(b*x)*x^2*ExpIntegralEi[-(b*x)]))/(2*x^2)","A",1
63,1,81,198,0.112854,"\int \frac{e^{-a-b x} (a+b x)^3}{x^4} \, dx","Integrate[(E^(-a - b*x)*(a + b*x)^3)/x^4,x]","\frac{1}{6} e^{-a} \left(-\frac{a e^{-b x} \left(a^2 \left(b^2 x^2-b x+2\right)-9 a b x (b x-1)+18 b^2 x^2\right)}{x^3}-\left(\left(a^3-9 a^2+18 a-6\right) b^3 \text{Ei}(-b x)\right)\right)","-\frac{1}{6} e^{-a} a^3 b^3 \text{Ei}(-b x)-\frac{a^3 b^2 e^{-a-b x}}{6 x}-\frac{a^3 e^{-a-b x}}{3 x^3}+\frac{a^3 b e^{-a-b x}}{6 x^2}+\frac{3}{2} e^{-a} a^2 b^3 \text{Ei}(-b x)+\frac{3 a^2 b^2 e^{-a-b x}}{2 x}-\frac{3 a^2 b e^{-a-b x}}{2 x^2}-3 e^{-a} a b^3 \text{Ei}(-b x)+e^{-a} b^3 \text{Ei}(-b x)-\frac{3 a b^2 e^{-a-b x}}{x}",1,"(-((a*(18*b^2*x^2 - 9*a*b*x*(-1 + b*x) + a^2*(2 - b*x + b^2*x^2)))/(E^(b*x)*x^3)) - (-6 + 18*a - 9*a^2 + a^3)*b^3*ExpIntegralEi[-(b*x)])/(6*E^a)","A",1
64,1,86,139,0.1259525,"\int F^{a+b (c+d x)} x^m (e+f x)^2 \, dx","Integrate[F^(a + b*(c + d*x))*x^m*(e + f*x)^2,x]","\frac{x^m F^{a+b c} (-b d x \log (F))^{-m} \left(b d e \log (F) (b d e \log (F) \Gamma (m+1,-b d x \log (F))-2 f \Gamma (m+2,-b d x \log (F)))+f^2 \Gamma (m+3,-b d x \log (F))\right)}{b^3 d^3 \log ^3(F)}","\frac{f^2 x^m F^{a+b c} (-b d x \log (F))^{-m} \Gamma (m+3,-b d x \log (F))}{b^3 d^3 \log ^3(F)}-\frac{2 e f x^m F^{a+b c} (-b d x \log (F))^{-m} \Gamma (m+2,-b d x \log (F))}{b^2 d^2 \log ^2(F)}+\frac{e^2 x^m F^{a+b c} (-b d x \log (F))^{-m} \Gamma (m+1,-b d x \log (F))}{b d \log (F)}",1,"(F^(a + b*c)*x^m*(f^2*Gamma[3 + m, -(b*d*x*Log[F])] + b*d*e*Log[F]*(-2*f*Gamma[2 + m, -(b*d*x*Log[F])] + b*d*e*Gamma[1 + m, -(b*d*x*Log[F])]*Log[F])))/(b^3*d^3*Log[F]^3*(-(b*d*x*Log[F]))^m)","A",1
65,1,159,414,0.1251671,"\int F^{a+b (c+d x)} x^3 (e+f x)^2 \, dx","Integrate[F^(a + b*(c + d*x))*x^3*(e + f*x)^2,x]","\frac{F^{a+b (c+d x)} \left(b^5 d^5 x^3 \log ^5(F) (e+f x)^2-b^4 d^4 x^2 \log ^4(F) \left(3 e^2+8 e f x+5 f^2 x^2\right)+2 b^3 d^3 x \log ^3(F) \left(3 e^2+12 e f x+10 f^2 x^2\right)-6 b^2 d^2 \log ^2(F) \left(e^2+8 e f x+10 f^2 x^2\right)+24 b d f \log (F) (2 e+5 f x)-120 f^2\right)}{b^6 d^6 \log ^6(F)}","-\frac{120 f^2 F^{a+b c+b d x}}{b^6 d^6 \log ^6(F)}+\frac{48 e f F^{a+b c+b d x}}{b^5 d^5 \log ^5(F)}+\frac{120 f^2 x F^{a+b c+b d x}}{b^5 d^5 \log ^5(F)}-\frac{6 e^2 F^{a+b c+b d x}}{b^4 d^4 \log ^4(F)}-\frac{48 e f x F^{a+b c+b d x}}{b^4 d^4 \log ^4(F)}-\frac{60 f^2 x^2 F^{a+b c+b d x}}{b^4 d^4 \log ^4(F)}+\frac{6 e^2 x F^{a+b c+b d x}}{b^3 d^3 \log ^3(F)}+\frac{24 e f x^2 F^{a+b c+b d x}}{b^3 d^3 \log ^3(F)}+\frac{20 f^2 x^3 F^{a+b c+b d x}}{b^3 d^3 \log ^3(F)}-\frac{3 e^2 x^2 F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}-\frac{8 e f x^3 F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}-\frac{5 f^2 x^4 F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}+\frac{e^2 x^3 F^{a+b c+b d x}}{b d \log (F)}+\frac{2 e f x^4 F^{a+b c+b d x}}{b d \log (F)}+\frac{f^2 x^5 F^{a+b c+b d x}}{b d \log (F)}",1,"(F^(a + b*(c + d*x))*(-120*f^2 + 24*b*d*f*(2*e + 5*f*x)*Log[F] - 6*b^2*d^2*(e^2 + 8*e*f*x + 10*f^2*x^2)*Log[F]^2 + 2*b^3*d^3*x*(3*e^2 + 12*e*f*x + 10*f^2*x^2)*Log[F]^3 - b^4*d^4*x^2*(3*e^2 + 8*e*f*x + 5*f^2*x^2)*Log[F]^4 + b^5*d^5*x^3*(e + f*x)^2*Log[F]^5))/(b^6*d^6*Log[F]^6)","A",1
66,1,121,328,0.2462168,"\int F^{a+b (c+d x)} x^2 (e+f x)^2 \, dx","Integrate[F^(a + b*(c + d*x))*x^2*(e + f*x)^2,x]","\frac{F^{a+b (c+d x)} \left(b^4 d^4 x^2 \log ^4(F) (e+f x)^2-2 b^3 d^3 x \log ^3(F) \left(e^2+3 e f x+2 f^2 x^2\right)+2 b^2 d^2 \log ^2(F) \left(e^2+6 e f x+6 f^2 x^2\right)-12 b d f \log (F) (e+2 f x)+24 f^2\right)}{b^5 d^5 \log ^5(F)}","\frac{24 f^2 F^{a+b c+b d x}}{b^5 d^5 \log ^5(F)}-\frac{12 e f F^{a+b c+b d x}}{b^4 d^4 \log ^4(F)}-\frac{24 f^2 x F^{a+b c+b d x}}{b^4 d^4 \log ^4(F)}+\frac{2 e^2 F^{a+b c+b d x}}{b^3 d^3 \log ^3(F)}+\frac{12 e f x F^{a+b c+b d x}}{b^3 d^3 \log ^3(F)}+\frac{12 f^2 x^2 F^{a+b c+b d x}}{b^3 d^3 \log ^3(F)}-\frac{2 e^2 x F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}-\frac{6 e f x^2 F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}-\frac{4 f^2 x^3 F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}+\frac{e^2 x^2 F^{a+b c+b d x}}{b d \log (F)}+\frac{2 e f x^3 F^{a+b c+b d x}}{b d \log (F)}+\frac{f^2 x^4 F^{a+b c+b d x}}{b d \log (F)}",1,"(F^(a + b*(c + d*x))*(24*f^2 - 12*b*d*f*(e + 2*f*x)*Log[F] + 2*b^2*d^2*(e^2 + 6*e*f*x + 6*f^2*x^2)*Log[F]^2 - 2*b^3*d^3*x*(e^2 + 3*e*f*x + 2*f^2*x^2)*Log[F]^3 + b^4*d^4*x^2*(e + f*x)^2*Log[F]^4))/(b^5*d^5*Log[F]^5)","A",1
67,1,91,242,0.1539061,"\int F^{a+b (c+d x)} x (e+f x)^2 \, dx","Integrate[F^(a + b*(c + d*x))*x*(e + f*x)^2,x]","\frac{F^{a+b (c+d x)} \left(b^3 d^3 x \log ^3(F) (e+f x)^2-b^2 d^2 \log ^2(F) \left(e^2+4 e f x+3 f^2 x^2\right)+2 b d f \log (F) (2 e+3 f x)-6 f^2\right)}{b^4 d^4 \log ^4(F)}","-\frac{6 f^2 F^{a+b c+b d x}}{b^4 d^4 \log ^4(F)}+\frac{4 e f F^{a+b c+b d x}}{b^3 d^3 \log ^3(F)}+\frac{6 f^2 x F^{a+b c+b d x}}{b^3 d^3 \log ^3(F)}-\frac{e^2 F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}-\frac{4 e f x F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}-\frac{3 f^2 x^2 F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}+\frac{e^2 x F^{a+b c+b d x}}{b d \log (F)}+\frac{2 e f x^2 F^{a+b c+b d x}}{b d \log (F)}+\frac{f^2 x^3 F^{a+b c+b d x}}{b d \log (F)}",1,"(F^(a + b*(c + d*x))*(-6*f^2 + 2*b*d*f*(2*e + 3*f*x)*Log[F] - b^2*d^2*(e^2 + 4*e*f*x + 3*f^2*x^2)*Log[F]^2 + b^3*d^3*x*(e + f*x)^2*Log[F]^3))/(b^4*d^4*Log[F]^4)","A",1
68,1,58,85,0.0718087,"\int F^{a+b (c+d x)} (e+f x)^2 \, dx","Integrate[F^(a + b*(c + d*x))*(e + f*x)^2,x]","\frac{F^{a+b (c+d x)} \left(b^2 d^2 \log ^2(F) (e+f x)^2-2 b d f \log (F) (e+f x)+2 f^2\right)}{b^3 d^3 \log ^3(F)}","\frac{2 f^2 F^{a+b c+b d x}}{b^3 d^3 \log ^3(F)}-\frac{2 f (e+f x) F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}+\frac{(e+f x)^2 F^{a+b c+b d x}}{b d \log (F)}",1,"(F^(a + b*(c + d*x))*(2*f^2 - 2*b*d*f*(e + f*x)*Log[F] + b^2*d^2*(e + f*x)^2*Log[F]^2))/(b^3*d^3*Log[F]^3)","A",1
69,1,54,96,0.1290082,"\int \frac{F^{a+b (c+d x)} (e+f x)^2}{x} \, dx","Integrate[(F^(a + b*(c + d*x))*(e + f*x)^2)/x,x]","F^{a+b c} \left(\frac{f F^{b d x} (b d \log (F) (2 e+f x)-f)}{b^2 d^2 \log ^2(F)}+e^2 \text{Ei}(b d x \log (F))\right)","-\frac{f^2 F^{a+b c+b d x}}{b^2 d^2 \log ^2(F)}+e^2 F^{a+b c} \text{Ei}(b d x \log (F))+\frac{2 e f F^{a+b c+b d x}}{b d \log (F)}+\frac{f^2 x F^{a+b c+b d x}}{b d \log (F)}",1,"F^(a + b*c)*(e^2*ExpIntegralEi[b*d*x*Log[F]] + (f*F^(b*d*x)*(-f + b*d*(2*e + f*x)*Log[F]))/(b^2*d^2*Log[F]^2))","A",1
70,1,58,85,0.1549621,"\int \frac{F^{a+b (c+d x)} (e+f x)^2}{x^2} \, dx","Integrate[(F^(a + b*(c + d*x))*(e + f*x)^2)/x^2,x]","F^{a+b c} \left(F^{b d x} \left(\frac{f^2}{b d \log (F)}-\frac{e^2}{x}\right)+e (b d e \log (F)+2 f) \text{Ei}(b d x \log (F))\right)","b d e^2 \log (F) F^{a+b c} \text{Ei}(b d x \log (F))-\frac{e^2 F^{a+b c+b d x}}{x}+2 e f F^{a+b c} \text{Ei}(b d x \log (F))+\frac{f^2 F^{a+b c+b d x}}{b d \log (F)}",1,"F^(a + b*c)*(F^(b*d*x)*(-(e^2/x) + f^2/(b*d*Log[F])) + e*ExpIntegralEi[b*d*x*Log[F]]*(2*f + b*d*e*Log[F]))","A",1
71,1,76,136,0.1531752,"\int \frac{F^{a+b (c+d x)} (e+f x)^2}{x^3} \, dx","Integrate[(F^(a + b*(c + d*x))*(e + f*x)^2)/x^3,x]","\frac{F^{a+b c} \left(x^2 \left(b^2 d^2 e^2 \log ^2(F)+4 b d e f \log (F)+2 f^2\right) \text{Ei}(b d x \log (F))-e F^{b d x} (b d e x \log (F)+e+4 f x)\right)}{2 x^2}","\frac{1}{2} b^2 d^2 e^2 \log ^2(F) F^{a+b c} \text{Ei}(b d x \log (F))-\frac{e^2 F^{a+b c+b d x}}{2 x^2}-\frac{b d e^2 \log (F) F^{a+b c+b d x}}{2 x}+2 b d e f \log (F) F^{a+b c} \text{Ei}(b d x \log (F))-\frac{2 e f F^{a+b c+b d x}}{x}+f^2 F^{a+b c} \text{Ei}(b d x \log (F))",1,"(F^(a + b*c)*(-(e*F^(b*d*x)*(e + 4*f*x + b*d*e*x*Log[F])) + x^2*ExpIntegralEi[b*d*x*Log[F]]*(2*f^2 + 4*b*d*e*f*Log[F] + b^2*d^2*e^2*Log[F]^2)))/(2*x^2)","A",1
72,1,116,217,0.2293414,"\int \frac{F^{a+b (c+d x)} (e+f x)^2}{x^4} \, dx","Integrate[(F^(a + b*(c + d*x))*(e + f*x)^2)/x^4,x]","\frac{F^{a+b c} \left(b d x^3 \log (F) \left(b^2 d^2 e^2 \log ^2(F)+6 b d e f \log (F)+6 f^2\right) \text{Ei}(b d x \log (F))-F^{b d x} \left(b^2 d^2 e^2 x^2 \log ^2(F)+b d e x \log (F) (e+6 f x)+2 \left(e^2+3 e f x+3 f^2 x^2\right)\right)\right)}{6 x^3}","\frac{1}{6} b^3 d^3 e^2 \log ^3(F) F^{a+b c} \text{Ei}(b d x \log (F))-\frac{b^2 d^2 e^2 \log ^2(F) F^{a+b c+b d x}}{6 x}+b^2 d^2 e f \log ^2(F) F^{a+b c} \text{Ei}(b d x \log (F))-\frac{e^2 F^{a+b c+b d x}}{3 x^3}-\frac{b d e^2 \log (F) F^{a+b c+b d x}}{6 x^2}-\frac{e f F^{a+b c+b d x}}{x^2}-\frac{b d e f \log (F) F^{a+b c+b d x}}{x}+b d f^2 \log (F) F^{a+b c} \text{Ei}(b d x \log (F))-\frac{f^2 F^{a+b c+b d x}}{x}",1,"(F^(a + b*c)*(b*d*x^3*ExpIntegralEi[b*d*x*Log[F]]*Log[F]*(6*f^2 + 6*b*d*e*f*Log[F] + b^2*d^2*e^2*Log[F]^2) - F^(b*d*x)*(2*(e^2 + 3*e*f*x + 3*f^2*x^2) + b*d*e*x*(e + 6*f*x)*Log[F] + b^2*d^2*e^2*x^2*Log[F]^2)))/(6*x^3)","A",1
73,1,156,321,0.3023508,"\int \frac{F^{a+b (c+d x)} (e+f x)^2}{x^5} \, dx","Integrate[(F^(a + b*(c + d*x))*(e + f*x)^2)/x^5,x]","\frac{F^{a+b c} \left(b^2 d^2 x^4 \log ^2(F) \left(b^2 d^2 e^2 \log ^2(F)+8 b d e f \log (F)+12 f^2\right) \text{Ei}(b d x \log (F))-F^{b d x} \left(b^3 d^3 e^2 x^3 \log ^3(F)+b^2 d^2 e x^2 \log ^2(F) (e+8 f x)+2 b d x \log (F) \left(e^2+4 e f x+6 f^2 x^2\right)+2 \left(3 e^2+8 e f x+6 f^2 x^2\right)\right)\right)}{24 x^4}","\frac{1}{24} b^4 d^4 e^2 \log ^4(F) F^{a+b c} \text{Ei}(b d x \log (F))-\frac{b^3 d^3 e^2 \log ^3(F) F^{a+b c+b d x}}{24 x}+\frac{1}{3} b^3 d^3 e f \log ^3(F) F^{a+b c} \text{Ei}(b d x \log (F))-\frac{b^2 d^2 e^2 \log ^2(F) F^{a+b c+b d x}}{24 x^2}-\frac{b^2 d^2 e f \log ^2(F) F^{a+b c+b d x}}{3 x}+\frac{1}{2} b^2 d^2 f^2 \log ^2(F) F^{a+b c} \text{Ei}(b d x \log (F))-\frac{e^2 F^{a+b c+b d x}}{4 x^4}-\frac{b d e^2 \log (F) F^{a+b c+b d x}}{12 x^3}-\frac{2 e f F^{a+b c+b d x}}{3 x^3}-\frac{b d e f \log (F) F^{a+b c+b d x}}{3 x^2}-\frac{f^2 F^{a+b c+b d x}}{2 x^2}-\frac{b d f^2 \log (F) F^{a+b c+b d x}}{2 x}",1,"(F^(a + b*c)*(b^2*d^2*x^4*ExpIntegralEi[b*d*x*Log[F]]*Log[F]^2*(12*f^2 + 8*b*d*e*f*Log[F] + b^2*d^2*e^2*Log[F]^2) - F^(b*d*x)*(2*(3*e^2 + 8*e*f*x + 6*f^2*x^2) + 2*b*d*x*(e^2 + 4*e*f*x + 6*f^2*x^2)*Log[F] + b^2*d^2*e*x^2*(e + 8*f*x)*Log[F]^2 + b^3*d^3*e^2*x^3*Log[F]^3)))/(24*x^4)","A",1
74,1,458,754,0.7184769,"\int e^{-a-b x} (a+b x)^4 (c+d x)^3 \, dx","Integrate[E^(-a - b*x)*(a + b*x)^4*(c + d*x)^3,x]","\frac{e^{-a-b x} \left(-6 b^5 x^2 (c+d x) \left(\left(a^2+2 a+2\right) c^2+2 \left(a^2+3 a+4\right) c d x+\left(a^2+4 a+7\right) d^2 x^2\right)-2 b^4 x \left(2 \left(a^3+3 a^2+6 a+6\right) c^3+3 \left(2 a^3+9 a^2+24 a+30\right) c^2 d x+6 \left(a^3+6 a^2+20 a+30\right) c d^2 x^2+\left(2 a^3+15 a^2+60 a+105\right) d^3 x^3\right)-b^3 \left(\left(a^4+4 a^3+12 a^2+24 a+24\right) c^3+3 \left(a^4+8 a^3+36 a^2+96 a+120\right) c^2 d x+3 \left(a^4+12 a^3+72 a^2+240 a+360\right) c d^2 x^2+\left(a^4+16 a^3+120 a^2+480 a+840\right) d^3 x^3\right)-3 b^2 d \left(\left(a^4+8 a^3+36 a^2+96 a+120\right) c^2+2 \left(a^4+12 a^3+72 a^2+240 a+360\right) c d x+\left(a^4+16 a^3+120 a^2+480 a+840\right) d^2 x^2\right)-6 b d^2 \left(\left(a^4+12 a^3+72 a^2+240 a+360\right) c+\left(a^4+16 a^3+120 a^2+480 a+840\right) d x\right)-6 \left(a^4+16 a^3+120 a^2+480 a+840\right) d^3-b^6 x^3 (c+d x)^2 (4 (a+1) c+(4 a+7) d x)+b^7 \left(-x^4\right) (c+d x)^3\right)}{b^4}","-\frac{3 d^2 e^{-a-b x} (a+b x)^6 (b c-a d)}{b^4}-\frac{18 d^2 e^{-a-b x} (a+b x)^5 (b c-a d)}{b^4}-\frac{90 d^2 e^{-a-b x} (a+b x)^4 (b c-a d)}{b^4}-\frac{360 d^2 e^{-a-b x} (a+b x)^3 (b c-a d)}{b^4}-\frac{1080 d^2 e^{-a-b x} (a+b x)^2 (b c-a d)}{b^4}-\frac{2160 d^2 e^{-a-b x} (a+b x) (b c-a d)}{b^4}-\frac{2160 d^2 e^{-a-b x} (b c-a d)}{b^4}-\frac{3 d e^{-a-b x} (a+b x)^5 (b c-a d)^2}{b^4}-\frac{e^{-a-b x} (a+b x)^4 (b c-a d)^3}{b^4}-\frac{15 d e^{-a-b x} (a+b x)^4 (b c-a d)^2}{b^4}-\frac{4 e^{-a-b x} (a+b x)^3 (b c-a d)^3}{b^4}-\frac{60 d e^{-a-b x} (a+b x)^3 (b c-a d)^2}{b^4}-\frac{12 e^{-a-b x} (a+b x)^2 (b c-a d)^3}{b^4}-\frac{180 d e^{-a-b x} (a+b x)^2 (b c-a d)^2}{b^4}-\frac{24 e^{-a-b x} (a+b x) (b c-a d)^3}{b^4}-\frac{360 d e^{-a-b x} (a+b x) (b c-a d)^2}{b^4}-\frac{24 e^{-a-b x} (b c-a d)^3}{b^4}-\frac{360 d e^{-a-b x} (b c-a d)^2}{b^4}-\frac{d^3 e^{-a-b x} (a+b x)^7}{b^4}-\frac{7 d^3 e^{-a-b x} (a+b x)^6}{b^4}-\frac{42 d^3 e^{-a-b x} (a+b x)^5}{b^4}-\frac{210 d^3 e^{-a-b x} (a+b x)^4}{b^4}-\frac{840 d^3 e^{-a-b x} (a+b x)^3}{b^4}-\frac{2520 d^3 e^{-a-b x} (a+b x)^2}{b^4}-\frac{5040 d^3 e^{-a-b x} (a+b x)}{b^4}-\frac{5040 d^3 e^{-a-b x}}{b^4}",1,"(E^(-a - b*x)*(-6*(840 + 480*a + 120*a^2 + 16*a^3 + a^4)*d^3 - b^7*x^4*(c + d*x)^3 - b^6*x^3*(c + d*x)^2*(4*(1 + a)*c + (7 + 4*a)*d*x) - 6*b*d^2*((360 + 240*a + 72*a^2 + 12*a^3 + a^4)*c + (840 + 480*a + 120*a^2 + 16*a^3 + a^4)*d*x) - 6*b^5*x^2*(c + d*x)*((2 + 2*a + a^2)*c^2 + 2*(4 + 3*a + a^2)*c*d*x + (7 + 4*a + a^2)*d^2*x^2) - 3*b^2*d*((120 + 96*a + 36*a^2 + 8*a^3 + a^4)*c^2 + 2*(360 + 240*a + 72*a^2 + 12*a^3 + a^4)*c*d*x + (840 + 480*a + 120*a^2 + 16*a^3 + a^4)*d^2*x^2) - 2*b^4*x*(2*(6 + 6*a + 3*a^2 + a^3)*c^3 + 3*(30 + 24*a + 9*a^2 + 2*a^3)*c^2*d*x + 6*(30 + 20*a + 6*a^2 + a^3)*c*d^2*x^2 + (105 + 60*a + 15*a^2 + 2*a^3)*d^3*x^3) - b^3*((24 + 24*a + 12*a^2 + 4*a^3 + a^4)*c^3 + 3*(120 + 96*a + 36*a^2 + 8*a^3 + a^4)*c^2*d*x + 3*(360 + 240*a + 72*a^2 + 12*a^3 + a^4)*c*d^2*x^2 + (840 + 480*a + 120*a^2 + 16*a^3 + a^4)*d^3*x^3)))/b^4","A",1
75,1,320,495,0.4698495,"\int e^{-a-b x} (a+b x)^4 (c+d x)^2 \, dx","Integrate[E^(-a - b*x)*(a + b*x)^4*(c + d*x)^2,x]","\frac{e^{-a-b x} \left(-2 b^4 x^2 \left(3 \left(a^2+2 a+2\right) c^2+2 \left(3 a^2+8 a+10\right) c d x+\left(3 a^2+10 a+15\right) d^2 x^2\right)-4 b^3 x \left(\left(a^3+3 a^2+6 a+6\right) c^2+\left(2 a^3+9 a^2+24 a+30\right) c d x+\left(a^3+6 a^2+20 a+30\right) d^2 x^2\right)-b^2 \left(\left(a^4+4 a^3+12 a^2+24 a+24\right) c^2+2 \left(a^4+8 a^3+36 a^2+96 a+120\right) c d x+\left(a^4+12 a^3+72 a^2+240 a+360\right) d^2 x^2\right)-2 b d \left(\left(a^4+8 a^3+36 a^2+96 a+120\right) c+\left(a^4+12 a^3+72 a^2+240 a+360\right) d x\right)-2 \left(a^4+12 a^3+72 a^2+240 a+360\right) d^2-2 b^5 x^3 (c+d x) (2 (a+1) c+(2 a+3) d x)+b^6 \left(-x^4\right) (c+d x)^2\right)}{b^3}","-\frac{2 d e^{-a-b x} (a+b x)^5 (b c-a d)}{b^3}-\frac{e^{-a-b x} (a+b x)^4 (b c-a d)^2}{b^3}-\frac{10 d e^{-a-b x} (a+b x)^4 (b c-a d)}{b^3}-\frac{4 e^{-a-b x} (a+b x)^3 (b c-a d)^2}{b^3}-\frac{40 d e^{-a-b x} (a+b x)^3 (b c-a d)}{b^3}-\frac{12 e^{-a-b x} (a+b x)^2 (b c-a d)^2}{b^3}-\frac{120 d e^{-a-b x} (a+b x)^2 (b c-a d)}{b^3}-\frac{24 e^{-a-b x} (a+b x) (b c-a d)^2}{b^3}-\frac{240 d e^{-a-b x} (a+b x) (b c-a d)}{b^3}-\frac{24 e^{-a-b x} (b c-a d)^2}{b^3}-\frac{240 d e^{-a-b x} (b c-a d)}{b^3}-\frac{d^2 e^{-a-b x} (a+b x)^6}{b^3}-\frac{6 d^2 e^{-a-b x} (a+b x)^5}{b^3}-\frac{30 d^2 e^{-a-b x} (a+b x)^4}{b^3}-\frac{120 d^2 e^{-a-b x} (a+b x)^3}{b^3}-\frac{360 d^2 e^{-a-b x} (a+b x)^2}{b^3}-\frac{720 d^2 e^{-a-b x} (a+b x)}{b^3}-\frac{720 d^2 e^{-a-b x}}{b^3}",1,"(E^(-a - b*x)*(-2*(360 + 240*a + 72*a^2 + 12*a^3 + a^4)*d^2 - b^6*x^4*(c + d*x)^2 - 2*b^5*x^3*(c + d*x)*(2*(1 + a)*c + (3 + 2*a)*d*x) - 2*b*d*((120 + 96*a + 36*a^2 + 8*a^3 + a^4)*c + (360 + 240*a + 72*a^2 + 12*a^3 + a^4)*d*x) - 2*b^4*x^2*(3*(2 + 2*a + a^2)*c^2 + 2*(10 + 8*a + 3*a^2)*c*d*x + (15 + 10*a + 3*a^2)*d^2*x^2) - 4*b^3*x*((6 + 6*a + 3*a^2 + a^3)*c^2 + (30 + 24*a + 9*a^2 + 2*a^3)*c*d*x + (30 + 20*a + 6*a^2 + a^3)*d^2*x^2) - b^2*((24 + 24*a + 12*a^2 + 4*a^3 + a^4)*c^2 + 2*(120 + 96*a + 36*a^2 + 8*a^3 + a^4)*c*d*x + (360 + 240*a + 72*a^2 + 12*a^3 + a^4)*d^2*x^2)))/b^3","A",1
76,1,191,271,0.2656027,"\int e^{-a-b x} (a+b x)^4 (c+d x) \, dx","Integrate[E^(-a - b*x)*(a + b*x)^4*(c + d*x),x]","\frac{e^{-a-b x} \left(-2 b^3 x^2 \left(3 \left(a^2+2 a+2\right) c+\left(3 a^2+8 a+10\right) d x\right)-2 b^2 x \left(2 \left(a^3+3 a^2+6 a+6\right) c+\left(2 a^3+9 a^2+24 a+30\right) d x\right)-b \left(\left(a^4+4 a^3+12 a^2+24 a+24\right) c+\left(a^4+8 a^3+36 a^2+96 a+120\right) d x\right)-\left(a^4+8 a^3+36 a^2+96 a+120\right) d-b^4 x^3 (4 (a+1) c+(4 a+5) d x)+b^5 \left(-x^4\right) (c+d x)\right)}{b^2}","-\frac{e^{-a-b x} (a+b x)^4 (b c-a d)}{b^2}-\frac{4 e^{-a-b x} (a+b x)^3 (b c-a d)}{b^2}-\frac{12 e^{-a-b x} (a+b x)^2 (b c-a d)}{b^2}-\frac{24 e^{-a-b x} (a+b x) (b c-a d)}{b^2}-\frac{24 e^{-a-b x} (b c-a d)}{b^2}-\frac{d e^{-a-b x} (a+b x)^5}{b^2}-\frac{5 d e^{-a-b x} (a+b x)^4}{b^2}-\frac{20 d e^{-a-b x} (a+b x)^3}{b^2}-\frac{60 d e^{-a-b x} (a+b x)^2}{b^2}-\frac{120 d e^{-a-b x} (a+b x)}{b^2}-\frac{120 d e^{-a-b x}}{b^2}",1,"(E^(-a - b*x)*(-((120 + 96*a + 36*a^2 + 8*a^3 + a^4)*d) - b^5*x^4*(c + d*x) - b^4*x^3*(4*(1 + a)*c + (5 + 4*a)*d*x) - 2*b^3*x^2*(3*(2 + 2*a + a^2)*c + (10 + 8*a + 3*a^2)*d*x) - 2*b^2*x*(2*(6 + 6*a + 3*a^2 + a^3)*c + (30 + 24*a + 9*a^2 + 2*a^3)*d*x) - b*((24 + 24*a + 12*a^2 + 4*a^3 + a^4)*c + (120 + 96*a + 36*a^2 + 8*a^3 + a^4)*d*x)))/b^2","A",1
77,1,50,102,0.0655934,"\int e^{-a-b x} (a+b x)^4 \, dx","Integrate[E^(-a - b*x)*(a + b*x)^4,x]","\frac{e^{-a-b x} \left(-(a+b x)^4-4 (a+b x)^3-12 (a+b x)^2-24 (a+b x)-24\right)}{b}","-\frac{e^{-a-b x} (a+b x)^4}{b}-\frac{4 e^{-a-b x} (a+b x)^3}{b}-\frac{12 e^{-a-b x} (a+b x)^2}{b}-\frac{24 e^{-a-b x} (a+b x)}{b}-\frac{24 e^{-a-b x}}{b}",1,"(E^(-a - b*x)*(-24 - 24*(a + b*x) - 12*(a + b*x)^2 - 4*(a + b*x)^3 - (a + b*x)^4))/b","A",1
78,1,175,277,0.3086194,"\int \frac{e^{-a-b x} (a+b x)^4}{c+d x} \, dx","Integrate[(E^(-a - b*x)*(a + b*x)^4)/(c + d*x),x]","\frac{e^{-a-b x} \left((b c-a d)^4 e^{b \left(\frac{c}{d}+x\right)} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)-d \left(2 b d^2 \left(\left(3 a^2+4 a+3\right) d x-\left(3 a^2+2 a+1\right) c\right)+2 \left(2 a^3+3 a^2+4 a+3\right) d^3+b^2 d \left((4 a+1) c^2-2 (2 a+1) c d x+(4 a+3) d^2 x^2\right)+b^3 \left(-c^3+c^2 d x-c d^2 x^2+d^3 x^3\right)\right)\right)}{d^5}","\frac{e^{\frac{b c}{d}-a} (b c-a d)^4 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^5}+\frac{e^{-a-b x} (b c-a d)^3}{d^4}-\frac{e^{-a-b x} (b c-a d)^2}{d^3}-\frac{e^{-a-b x} (a+b x) (b c-a d)^2}{d^3}+\frac{2 e^{-a-b x} (b c-a d)}{d^2}+\frac{e^{-a-b x} (a+b x)^2 (b c-a d)}{d^2}+\frac{2 e^{-a-b x} (a+b x) (b c-a d)}{d^2}-\frac{6 e^{-a-b x}}{d}-\frac{e^{-a-b x} (a+b x)^3}{d}-\frac{3 e^{-a-b x} (a+b x)^2}{d}-\frac{6 e^{-a-b x} (a+b x)}{d}",1,"(E^(-a - b*x)*(-(d*(2*(3 + 4*a + 3*a^2 + 2*a^3)*d^3 + 2*b*d^2*(-((1 + 2*a + 3*a^2)*c) + (3 + 4*a + 3*a^2)*d*x) + b^2*d*((1 + 4*a)*c^2 - 2*(1 + 2*a)*c*d*x + (3 + 4*a)*d^2*x^2) + b^3*(-c^3 + c^2*d*x - c*d^2*x^2 + d^3*x^3))) + (b*c - a*d)^4*E^(b*(c/d + x))*ExpIntegralEi[-((b*(c + d*x))/d)]))/d^5","A",1
79,1,163,258,0.4404113,"\int \frac{e^{-a-b x} (a+b x)^4}{(c+d x)^2} \, dx","Integrate[(E^(-a - b*x)*(a + b*x)^4)/(c + d*x)^2,x]","\frac{e^{-a} \left(-\frac{d e^{-b x} \left(b d (c+d x) \left(2 \left(3 a^2+2 a+1\right) d^2-2 (4 a+1) b c d+3 b^2 c^2\right)-2 b^2 d^2 x (c+d x) (b c-(2 a+1) d)+(b c-a d)^4+b^3 d^3 x^2 (c+d x)\right)}{c+d x}-b e^{\frac{b c}{d}} (b c-(a-4) d) (b c-a d)^3 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)\right)}{d^6}","-\frac{b^3 e^{-a-b x} (c+d x)^2}{d^4}+\frac{4 b^2 e^{-a-b x} (c+d x) (b c-a d)}{d^4}-\frac{2 b^2 e^{-a-b x} (c+d x)}{d^3}-\frac{b e^{\frac{b c}{d}-a} (b c-a d)^4 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^6}-\frac{4 b e^{\frac{b c}{d}-a} (b c-a d)^3 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^5}-\frac{e^{-a-b x} (b c-a d)^4}{d^5 (c+d x)}-\frac{6 b e^{-a-b x} (b c-a d)^2}{d^4}+\frac{4 b e^{-a-b x} (b c-a d)}{d^3}-\frac{2 b e^{-a-b x}}{d^2}",1,"(-((d*((b*c - a*d)^4 + b*d*(3*b^2*c^2 - 2*(1 + 4*a)*b*c*d + 2*(1 + 2*a + 3*a^2)*d^2)*(c + d*x) - 2*b^2*d^2*(b*c - (1 + 2*a)*d)*x*(c + d*x) + b^3*d^3*x^2*(c + d*x)))/(E^(b*x)*(c + d*x))) - b*(b*c - (-4 + a)*d)*(b*c - a*d)^3*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(d^6*E^a)","A",1
80,1,267,294,0.6594258,"\int \frac{e^{-a-b x} (a+b x)^4}{(c+d x)^3} \, dx","Integrate[(E^(-a - b*x)*(a + b*x)^4)/(c + d*x)^3,x]","\frac{e^{-a} \left(b^2 e^{\frac{b c}{d}} \left(\left(a^2-8 a+12\right) d^2-2 (a-4) b c d+b^2 c^2\right) (b c-a d)^2 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+\frac{d e^{-b x} \left(-a^4 d^5+a^3 b d^4 ((a-4) c+(a-8) d x)+2 b^3 d^2 \left(\left(3 a^2-10 a+3\right) c^3+\left(3 a^2-12 a+5\right) c^2 d x+c d^2 x^2-d^3 x^3\right)-2 b^2 d^3 \left(\left(2 a^3-9 a^2+4 a+1\right) c^2+2 \left(a^3-6 a^2+4 a+1\right) c d x+(4 a+1) d^2 x^2\right)+b^4 c^3 d ((7-4 a) c-4 (a-2) d x)+b^5 c^4 (c+d x)\right)}{(c+d x)^2}\right)}{2 d^7}","-\frac{b^3 x e^{-a-b x}}{d^3}+\frac{b^2 e^{\frac{b c}{d}-a} (b c-a d)^4 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{2 d^7}+\frac{4 b^2 e^{\frac{b c}{d}-a} (b c-a d)^3 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^6}+\frac{6 b^2 e^{\frac{b c}{d}-a} (b c-a d)^2 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^5}+\frac{b^2 e^{-a-b x} (3 b c-4 a d)}{d^4}-\frac{b^2 e^{-a-b x}}{d^3}+\frac{b e^{-a-b x} (b c-a d)^4}{2 d^6 (c+d x)}-\frac{e^{-a-b x} (b c-a d)^4}{2 d^5 (c+d x)^2}+\frac{4 b e^{-a-b x} (b c-a d)^3}{d^5 (c+d x)}",1,"((d*(-(a^4*d^5) + b^5*c^4*(c + d*x) + a^3*b*d^4*((-4 + a)*c + (-8 + a)*d*x) + b^4*c^3*d*((7 - 4*a)*c - 4*(-2 + a)*d*x) - 2*b^2*d^3*((1 + 4*a - 9*a^2 + 2*a^3)*c^2 + 2*(1 + 4*a - 6*a^2 + a^3)*c*d*x + (1 + 4*a)*d^2*x^2) + 2*b^3*d^2*((3 - 10*a + 3*a^2)*c^3 + (5 - 12*a + 3*a^2)*c^2*d*x + c*d^2*x^2 - d^3*x^3)))/(E^(b*x)*(c + d*x)^2) + b^2*(b*c - a*d)^2*(b^2*c^2 - 2*(-4 + a)*b*c*d + (12 - 8*a + a^2)*d^2)*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(2*d^7*E^a)","A",1
81,1,389,396,0.8167918,"\int \frac{e^{-a-b x} (a+b x)^4}{(c+d x)^4} \, dx","Integrate[(E^(-a - b*x)*(a + b*x)^4)/(c + d*x)^4,x]","\frac{e^{-a} \left(-\left(b^3 e^{\frac{b c}{d}} \left(6 \left(a^2-6 a+6\right) b^2 c^2 d^2-4 \left(a^3-9 a^2+18 a-6\right) b c d^3+a \left(a^3-12 a^2+36 a-24\right) d^4-4 (a-3) b^3 c^3 d+b^4 c^4\right) \text{Ei}\left(-\frac{b (c+d x)}{d}\right)\right)-\frac{d e^{-b x} \left(2 a^4 d^6-a^3 b d^5 ((a-4) c+(a-12) d x)+2 b^4 c^2 d^2 \left(\left(3 a^2-16 a+13\right) c^2+2 \left(3 a^2-17 a+15\right) c d x+3 \left(a^2-6 a+6\right) d^2 x^2\right)+a^2 b^2 d^4 \left(\left(a^2-8 a+12\right) c^2+2 \left(a^2-10 a+18\right) c d x+(a-6)^2 d^2 x^2\right)+2 b^3 d^3 \left(\left(-2 a^3+15 a^2-22 a+3\right) c^3+\left(-4 a^3+33 a^2-54 a+9\right) c^2 d x+\left(-2 a^3+18 a^2-36 a+9\right) c d^2 x^2+3 d^3 x^3\right)-b^5 c^3 d (c+d x) ((4 a-11) c+4 (a-3) d x)+b^6 c^4 (c+d x)^2\right)}{(c+d x)^3}\right)}{6 d^8}","-\frac{b^3 e^{\frac{b c}{d}-a} (b c-a d)^4 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{6 d^8}-\frac{2 b^3 e^{\frac{b c}{d}-a} (b c-a d)^3 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^7}-\frac{6 b^3 e^{\frac{b c}{d}-a} (b c-a d)^2 \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^6}-\frac{4 b^3 e^{\frac{b c}{d}-a} (b c-a d) \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^5}-\frac{b^3 e^{-a-b x}}{d^4}-\frac{b^2 e^{-a-b x} (b c-a d)^4}{6 d^7 (c+d x)}-\frac{2 b^2 e^{-a-b x} (b c-a d)^3}{d^6 (c+d x)}-\frac{6 b^2 e^{-a-b x} (b c-a d)^2}{d^5 (c+d x)}+\frac{b e^{-a-b x} (b c-a d)^4}{6 d^6 (c+d x)^2}-\frac{e^{-a-b x} (b c-a d)^4}{3 d^5 (c+d x)^3}+\frac{2 b e^{-a-b x} (b c-a d)^3}{d^5 (c+d x)^2}",1,"(-((d*(2*a^4*d^6 + b^6*c^4*(c + d*x)^2 - a^3*b*d^5*((-4 + a)*c + (-12 + a)*d*x) - b^5*c^3*d*(c + d*x)*((-11 + 4*a)*c + 4*(-3 + a)*d*x) + a^2*b^2*d^4*((12 - 8*a + a^2)*c^2 + 2*(18 - 10*a + a^2)*c*d*x + (-6 + a)^2*d^2*x^2) + 2*b^4*c^2*d^2*((13 - 16*a + 3*a^2)*c^2 + 2*(15 - 17*a + 3*a^2)*c*d*x + 3*(6 - 6*a + a^2)*d^2*x^2) + 2*b^3*d^3*((3 - 22*a + 15*a^2 - 2*a^3)*c^3 + (9 - 54*a + 33*a^2 - 4*a^3)*c^2*d*x + (9 - 36*a + 18*a^2 - 2*a^3)*c*d^2*x^2 + 3*d^3*x^3)))/(E^(b*x)*(c + d*x)^3)) - b^3*(b^4*c^4 - 4*(-3 + a)*b^3*c^3*d + 6*(6 - 6*a + a^2)*b^2*c^2*d^2 - 4*(-6 + 18*a - 9*a^2 + a^3)*b*c*d^3 + a*(-24 + 36*a - 12*a^2 + a^3)*d^4)*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(6*d^8*E^a)","A",1
82,1,669,557,0.7403097,"\int \frac{e^{-a-b x} (a+b x)^4}{(c+d x)^5} \, dx","Integrate[(E^(-a - b*x)*(a + b*x)^4)/(c + d*x)^5,x]","\frac{e^{-a} \left(a^4 b^4 d^4 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)-4 a^3 b^5 c d^3 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)-16 a^3 b^4 d^4 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+6 a^2 b^6 c^2 d^2 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+48 a^2 b^5 c d^3 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+72 a^2 b^4 d^4 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+\frac{d e^{-b x} \left(-b^2 d (c+d x)^2 \left(\left(a^2-16 a+72\right) d^2-2 (a-8) b c d+b^2 c^2\right) (b c-a d)^2+b^3 (c+d x)^3 \left(6 \left(a^2-8 a+12\right) b^2 c^2 d^2-4 \left(a^3-12 a^2+36 a-24\right) b c d^3+a \left(a^3-16 a^2+72 a-96\right) d^4-4 (a-4) b^3 c^3 d+b^4 c^4\right)-6 d^3 (b c-a d)^4+2 b d^2 (c+d x) (b c-(a-16) d) (b c-a d)^3\right)}{(c+d x)^4}-4 a b^7 c^3 d e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)-48 a b^6 c^2 d^2 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)-144 a b^5 c d^3 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)-96 a b^4 d^4 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+b^8 c^4 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+16 b^7 c^3 d e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+72 b^6 c^2 d^2 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+96 b^5 c d^3 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)+24 b^4 d^4 e^{\frac{b c}{d}} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)\right)}{24 d^9}","\frac{b^4 (b c-a d)^4 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{24 d^9}+\frac{2 b^4 (b c-a d)^3 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{3 d^8}+\frac{3 b^4 (b c-a d)^2 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^7}+\frac{4 b^4 (b c-a d) e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^6}+\frac{b^4 e^{\frac{b c}{d}-a} \text{Ei}\left(-\frac{b (c+d x)}{d}\right)}{d^5}+\frac{b^3 e^{-a-b x} (b c-a d)^4}{24 d^8 (c+d x)}+\frac{2 b^3 e^{-a-b x} (b c-a d)^3}{3 d^7 (c+d x)}+\frac{3 b^3 e^{-a-b x} (b c-a d)^2}{d^6 (c+d x)}+\frac{4 b^3 e^{-a-b x} (b c-a d)}{d^5 (c+d x)}-\frac{b^2 e^{-a-b x} (b c-a d)^4}{24 d^7 (c+d x)^2}-\frac{2 b^2 e^{-a-b x} (b c-a d)^3}{3 d^6 (c+d x)^2}-\frac{3 b^2 e^{-a-b x} (b c-a d)^2}{d^5 (c+d x)^2}+\frac{b e^{-a-b x} (b c-a d)^4}{12 d^6 (c+d x)^3}+\frac{4 b e^{-a-b x} (b c-a d)^3}{3 d^5 (c+d x)^3}-\frac{e^{-a-b x} (b c-a d)^4}{4 d^5 (c+d x)^4}",1,"((d*(-6*d^3*(b*c - a*d)^4 + 2*b*d^2*(b*c - (-16 + a)*d)*(b*c - a*d)^3*(c + d*x) - b^2*d*(b*c - a*d)^2*(b^2*c^2 - 2*(-8 + a)*b*c*d + (72 - 16*a + a^2)*d^2)*(c + d*x)^2 + b^3*(b^4*c^4 - 4*(-4 + a)*b^3*c^3*d + 6*(12 - 8*a + a^2)*b^2*c^2*d^2 - 4*(-24 + 36*a - 12*a^2 + a^3)*b*c*d^3 + a*(-96 + 72*a - 16*a^2 + a^3)*d^4)*(c + d*x)^3))/(E^(b*x)*(c + d*x)^4) + b^8*c^4*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + 16*b^7*c^3*d*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - 4*a*b^7*c^3*d*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + 72*b^6*c^2*d^2*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - 48*a*b^6*c^2*d^2*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + 6*a^2*b^6*c^2*d^2*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + 96*b^5*c*d^3*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - 144*a*b^5*c*d^3*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + 48*a^2*b^5*c*d^3*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - 4*a^3*b^5*c*d^3*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + 24*b^4*d^4*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - 96*a*b^4*d^4*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + 72*a^2*b^4*d^4*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] - 16*a^3*b^4*d^4*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)] + a^4*b^4*d^4*E^((b*c)/d)*ExpIntegralEi[-((b*(c + d*x))/d)])/(24*d^9*E^a)","A",1
83,1,24,24,0.3853341,"\int F^{c (a+b x)} x^m \log ^n(d x) (e+e n+e (1+m+b c x \log (F)) \log (d x)) \, dx","Integrate[F^(c*(a + b*x))*x^m*Log[d*x]^n*(e + e*n + e*(1 + m + b*c*x*Log[F])*Log[d*x]),x]","e x^{m+1} \log ^{n+1}(d x) F^{c (a+b x)}","e x^{m+1} \log ^{n+1}(d x) F^{c (a+b x)}",1,"e*F^(c*(a + b*x))*x^(1 + m)*Log[d*x]^(1 + n)","A",1
84,1,23,22,0.3108262,"\int F^{c (a+b x)} x^2 \log ^n(d x) (e+e n+e (3+b c x \log (F)) \log (d x)) \, dx","Integrate[F^(c*(a + b*x))*x^2*Log[d*x]^n*(e + e*n + e*(3 + b*c*x*Log[F])*Log[d*x]),x]","e x^3 \log ^{n+1}(d x) F^{a c+b c x}","e x^3 \log ^{n+1}(d x) F^{c (a+b x)}",1,"e*F^(a*c + b*c*x)*x^3*Log[d*x]^(1 + n)","A",1
85,1,23,22,0.2746572,"\int F^{c (a+b x)} x \log ^n(d x) (e+e n+e (2+b c x \log (F)) \log (d x)) \, dx","Integrate[F^(c*(a + b*x))*x*Log[d*x]^n*(e + e*n + e*(2 + b*c*x*Log[F])*Log[d*x]),x]","e x^2 \log ^{n+1}(d x) F^{a c+b c x}","e x^2 \log ^{n+1}(d x) F^{c (a+b x)}",1,"e*F^(a*c + b*c*x)*x^2*Log[d*x]^(1 + n)","A",1
86,1,21,20,0.1802148,"\int F^{c (a+b x)} \log ^n(d x) (e+e n+e (1+b c x \log (F)) \log (d x)) \, dx","Integrate[F^(c*(a + b*x))*Log[d*x]^n*(e + e*n + e*(1 + b*c*x*Log[F])*Log[d*x]),x]","e x \log ^{n+1}(d x) F^{a c+b c x}","e x \log ^{n+1}(d x) F^{c (a+b x)}",1,"e*F^(a*c + b*c*x)*x*Log[d*x]^(1 + n)","A",1
87,1,19,19,0.0335737,"\int \frac{F^{c (a+b x)} \log ^n(d x) (e+e n+b c e x \log (F) \log (d x))}{x} \, dx","Integrate[(F^(c*(a + b*x))*Log[d*x]^n*(e + e*n + b*c*e*x*Log[F]*Log[d*x]))/x,x]","e \log ^{n+1}(d x) F^{c (a+b x)}","e \log ^{n+1}(d x) F^{c (a+b x)}",1,"e*F^(c*(a + b*x))*Log[d*x]^(1 + n)","A",1
88,1,23,22,0.3471459,"\int \frac{F^{c (a+b x)} \log ^n(d x) (e+e n+e (-1+b c x \log (F)) \log (d x))}{x^2} \, dx","Integrate[(F^(c*(a + b*x))*Log[d*x]^n*(e + e*n + e*(-1 + b*c*x*Log[F])*Log[d*x]))/x^2,x]","\frac{e \log ^{n+1}(d x) F^{a c+b c x}}{x}","\frac{e \log ^{n+1}(d x) F^{c (a+b x)}}{x}",1,"(e*F^(a*c + b*c*x)*Log[d*x]^(1 + n))/x","A",1
89,1,23,22,0.3370705,"\int \frac{F^{c (a+b x)} \log ^n(d x) (e+e n+e (-2+b c x \log (F)) \log (d x))}{x^3} \, dx","Integrate[(F^(c*(a + b*x))*Log[d*x]^n*(e + e*n + e*(-2 + b*c*x*Log[F])*Log[d*x]))/x^3,x]","\frac{e \log ^{n+1}(d x) F^{a c+b c x}}{x^2}","\frac{e \log ^{n+1}(d x) F^{c (a+b x)}}{x^2}",1,"(e*F^(a*c + b*c*x)*Log[d*x]^(1 + n))/x^2","A",1
90,1,45,91,0.0219725,"\int \sqrt{e^{a+b x}} x^4 \, dx","Integrate[Sqrt[E^(a + b*x)]*x^4,x]","\frac{2 \left(b^4 x^4-8 b^3 x^3+48 b^2 x^2-192 b x+384\right) \sqrt{e^{a+b x}}}{b^5}","\frac{768 \sqrt{e^{a+b x}}}{b^5}-\frac{384 x \sqrt{e^{a+b x}}}{b^4}+\frac{96 x^2 \sqrt{e^{a+b x}}}{b^3}-\frac{16 x^3 \sqrt{e^{a+b x}}}{b^2}+\frac{2 x^4 \sqrt{e^{a+b x}}}{b}",1,"(2*Sqrt[E^(a + b*x)]*(384 - 192*b*x + 48*b^2*x^2 - 8*b^3*x^3 + b^4*x^4))/b^5","A",1
91,1,37,72,0.0141465,"\int \sqrt{e^{a+b x}} x^3 \, dx","Integrate[Sqrt[E^(a + b*x)]*x^3,x]","\frac{2 \left(b^3 x^3-6 b^2 x^2+24 b x-48\right) \sqrt{e^{a+b x}}}{b^4}","-\frac{96 \sqrt{e^{a+b x}}}{b^4}+\frac{48 x \sqrt{e^{a+b x}}}{b^3}-\frac{12 x^2 \sqrt{e^{a+b x}}}{b^2}+\frac{2 x^3 \sqrt{e^{a+b x}}}{b}",1,"(2*Sqrt[E^(a + b*x)]*(-48 + 24*b*x - 6*b^2*x^2 + b^3*x^3))/b^4","A",1
92,1,29,53,0.0134643,"\int \sqrt{e^{a+b x}} x^2 \, dx","Integrate[Sqrt[E^(a + b*x)]*x^2,x]","\frac{2 \left(b^2 x^2-4 b x+8\right) \sqrt{e^{a+b x}}}{b^3}","\frac{16 \sqrt{e^{a+b x}}}{b^3}-\frac{8 x \sqrt{e^{a+b x}}}{b^2}+\frac{2 x^2 \sqrt{e^{a+b x}}}{b}",1,"(2*Sqrt[E^(a + b*x)]*(8 - 4*b*x + b^2*x^2))/b^3","A",1
93,1,21,34,0.0103595,"\int \sqrt{e^{a+b x}} x \, dx","Integrate[Sqrt[E^(a + b*x)]*x,x]","\frac{2 (b x-2) \sqrt{e^{a+b x}}}{b^2}","\frac{2 x \sqrt{e^{a+b x}}}{b}-\frac{4 \sqrt{e^{a+b x}}}{b^2}",1,"(2*Sqrt[E^(a + b*x)]*(-2 + b*x))/b^2","A",1
94,1,16,16,0.0053766,"\int \sqrt{e^{a+b x}} \, dx","Integrate[Sqrt[E^(a + b*x)],x]","\frac{2 \sqrt{e^{a+b x}}}{b}","\frac{2 \sqrt{e^{a+b x}}}{b}",1,"(2*Sqrt[E^(a + b*x)])/b","A",1
95,1,27,27,0.0156642,"\int \frac{\sqrt{e^{a+b x}}}{x} \, dx","Integrate[Sqrt[E^(a + b*x)]/x,x]","e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \text{Ei}\left(\frac{b x}{2}\right)","e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \text{Ei}\left(\frac{b x}{2}\right)",1,"(Sqrt[E^(a + b*x)]*ExpIntegralEi[(b*x)/2])/E^((b*x)/2)","A",1
96,1,47,48,0.0278296,"\int \frac{\sqrt{e^{a+b x}}}{x^2} \, dx","Integrate[Sqrt[E^(a + b*x)]/x^2,x]","\frac{e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \left(b x \text{Ei}\left(\frac{b x}{2}\right)-2 e^{\frac{b x}{2}}\right)}{2 x}","\frac{1}{2} b e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \text{Ei}\left(\frac{b x}{2}\right)-\frac{\sqrt{e^{a+b x}}}{x}",1,"(Sqrt[E^(a + b*x)]*(-2*E^((b*x)/2) + b*x*ExpIntegralEi[(b*x)/2]))/(2*E^((b*x)/2)*x)","A",1
97,1,56,71,0.0487004,"\int \frac{\sqrt{e^{a+b x}}}{x^3} \, dx","Integrate[Sqrt[E^(a + b*x)]/x^3,x]","\frac{e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \left(b^2 x^2 \text{Ei}\left(\frac{b x}{2}\right)-2 e^{\frac{b x}{2}} (b x+2)\right)}{8 x^2}","\frac{1}{8} b^2 e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \text{Ei}\left(\frac{b x}{2}\right)-\frac{\sqrt{e^{a+b x}}}{2 x^2}-\frac{b \sqrt{e^{a+b x}}}{4 x}",1,"(Sqrt[E^(a + b*x)]*(-2*E^((b*x)/2)*(2 + b*x) + b^2*x^2*ExpIntegralEi[(b*x)/2]))/(8*E^((b*x)/2)*x^2)","A",1
98,1,64,92,0.0643666,"\int \frac{\sqrt{e^{a+b x}}}{x^4} \, dx","Integrate[Sqrt[E^(a + b*x)]/x^4,x]","\frac{e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \left(b^3 x^3 \text{Ei}\left(\frac{b x}{2}\right)-2 e^{\frac{b x}{2}} \left(b^2 x^2+2 b x+8\right)\right)}{48 x^3}","\frac{1}{48} b^3 e^{-\frac{b x}{2}} \sqrt{e^{a+b x}} \text{Ei}\left(\frac{b x}{2}\right)-\frac{b^2 \sqrt{e^{a+b x}}}{24 x}-\frac{\sqrt{e^{a+b x}}}{3 x^3}-\frac{b \sqrt{e^{a+b x}}}{12 x^2}",1,"(Sqrt[E^(a + b*x)]*(-2*E^((b*x)/2)*(8 + 2*b*x + b^2*x^2) + b^3*x^3*ExpIntegralEi[(b*x)/2]))/(48*E^((b*x)/2)*x^3)","A",1