1,1,12,12,0.0071482,"\int \frac{e^x}{4+6 e^x} \, dx","Integrate[E^x/(4 + 6*E^x),x]","\frac{1}{6} \log \left(3 e^x+2\right)","\frac{1}{6} \log \left(3 e^x+2\right)",1,"Log[2 + 3*E^x]/6","A",1
2,1,12,12,0.0059392,"\int \frac{e^x}{a+b e^x} \, dx","Integrate[E^x/(a + b*E^x),x]","\frac{\log \left(a+b e^x\right)}{b}","\frac{\log \left(a+b e^x\right)}{b}",1,"Log[a + b*E^x]/b","A",1
3,1,24,24,0.0126723,"\int \frac{e^{d x}}{a+b e^{c+d x}} \, dx","Integrate[E^(d*x)/(a + b*E^(c + d*x)),x]","\frac{e^{-c} \log \left(a+b e^{c+d x}\right)}{b d}","\frac{e^{-c} \log \left(a+b e^{c+d x}\right)}{b d}",1,"Log[a + b*E^(c + d*x)]/(b*d*E^c)","A",1
4,1,19,19,0.0065897,"\int \frac{e^{c+d x}}{a+b e^{c+d x}} \, dx","Integrate[E^(c + d*x)/(a + b*E^(c + d*x)),x]","\frac{\log \left(a+b e^{c+d x}\right)}{b d}","\frac{\log \left(a+b e^{c+d x}\right)}{b d}",1,"Log[a + b*E^(c + d*x)]/(b*d)","A",1
5,1,19,20,0.021199,"\int e^x \left(a+b e^x\right)^n \, dx","Integrate[E^x*(a + b*E^x)^n,x]","\frac{\left(a+b e^x\right)^{n+1}}{b n+b}","\frac{\left(a+b e^x\right)^{n+1}}{b (n+1)}",1,"(a + b*E^x)^(1 + n)/(b + b*n)","A",1
6,1,31,32,0.0358091,"\int e^{d x} \left(a+b e^{c+d x}\right)^n \, dx","Integrate[E^(d*x)*(a + b*E^(c + d*x))^n,x]","\frac{e^{-c} \left(a+b e^{c+d x}\right)^{n+1}}{b d n+b d}","\frac{e^{-c} \left(a+b e^{c+d x}\right)^{n+1}}{b d (n+1)}",1,"(a + b*E^(c + d*x))^(1 + n)/(E^c*(b*d + b*d*n))","A",1
7,1,26,27,0.025133,"\int e^{c+d x} \left(a+b e^{c+d x}\right)^n \, dx","Integrate[E^(c + d*x)*(a + b*E^(c + d*x))^n,x]","\frac{\left(a+b e^{c+d x}\right)^{n+1}}{b d n+b d}","\frac{\left(a+b e^{c+d x}\right)^{n+1}}{b d (n+1)}",1,"(a + b*E^(c + d*x))^(1 + n)/(b*d + b*d*n)","A",1
8,1,16,16,0.0061582,"\int \frac{F^x}{a+b F^x} \, dx","Integrate[F^x/(a + b*F^x),x]","\frac{\log \left(a+b F^x\right)}{b \log (F)}","\frac{\log \left(a+b F^x\right)}{b \log (F)}",1,"Log[a + b*F^x]/(b*Log[F])","A",1
9,1,28,28,0.0094657,"\int \frac{F^{d x}}{a+b F^{c+d x}} \, dx","Integrate[F^(d*x)/(a + b*F^(c + d*x)),x]","\frac{F^{-c} \log \left(a+b F^{c+d x}\right)}{b d \log (F)}","\frac{F^{-c} \log \left(a+b F^{c+d x}\right)}{b d \log (F)}",1,"Log[a + b*F^(c + d*x)]/(b*d*F^c*Log[F])","A",1
10,1,23,23,0.0056083,"\int \frac{F^{c+d x}}{a+b F^{c+d x}} \, dx","Integrate[F^(c + d*x)/(a + b*F^(c + d*x)),x]","\frac{\log \left(a+b F^{c+d x}\right)}{b d \log (F)}","\frac{\log \left(a+b F^{c+d x}\right)}{b d \log (F)}",1,"Log[a + b*F^(c + d*x)]/(b*d*Log[F])","A",1
11,1,24,24,0.0243421,"\int F^x \left(a+b F^x\right)^n \, dx","Integrate[F^x*(a + b*F^x)^n,x]","\frac{\left(a+b F^x\right)^{n+1}}{b n \log (F)+b \log (F)}","\frac{\left(a+b F^x\right)^{n+1}}{b (n+1) \log (F)}",1,"(a + b*F^x)^(1 + n)/(b*Log[F] + b*n*Log[F])","A",1
12,1,35,36,0.0442088,"\int F^{d x} \left(a+b F^{c+d x}\right)^n \, dx","Integrate[F^(d*x)*(a + b*F^(c + d*x))^n,x]","\frac{F^{-c} \left(a+b F^{c+d x}\right)^{n+1}}{b d n \log (F)+b d \log (F)}","\frac{F^{-c} \left(a+b F^{c+d x}\right)^{n+1}}{b d (n+1) \log (F)}",1,"(a + b*F^(c + d*x))^(1 + n)/(F^c*(b*d*Log[F] + b*d*n*Log[F]))","A",1
13,1,30,31,0.0310187,"\int F^{c+d x} \left(a+b F^{c+d x}\right)^n \, dx","Integrate[F^(c + d*x)*(a + b*F^(c + d*x))^n,x]","\frac{\left(a+b F^{c+d x}\right)^{n+1}}{b d n \log (F)+b d \log (F)}","\frac{\left(a+b F^{c+d x}\right)^{n+1}}{b d (n+1) \log (F)}",1,"(a + b*F^(c + d*x))^(1 + n)/(b*d*Log[F] + b*d*n*Log[F])","A",1
14,1,24,25,0.0697737,"\int \left(e^x\right)^n \left(a+b \left(e^x\right)^n\right)^p \, dx","Integrate[(E^x)^n*(a + b*(E^x)^n)^p,x]","\frac{\left(a+b \left(e^x\right)^n\right)^{p+1}}{b n p+b n}","\frac{\left(a+b \left(e^x\right)^n\right)^{p+1}}{b n (p+1)}",1,"(a + b*(E^x)^n)^(1 + p)/(b*n + b*n*p)","A",1
15,1,36,37,0.0442448,"\int e^{n x} \left(a+b \left(e^x\right)^n\right)^p \, dx","Integrate[E^(n*x)*(a + b*(E^x)^n)^p,x]","\frac{e^{n x} \left(e^x\right)^{-n} \left(a+b \left(e^x\right)^n\right)^{p+1}}{b n p+b n}","\frac{e^{n x} \left(e^x\right)^{-n} \left(a+b \left(e^x\right)^n\right)^{p+1}}{b n (p+1)}",1,"(E^(n*x)*(a + b*(E^x)^n)^(1 + p))/((E^x)^n*(b*n + b*n*p))","A",1
16,0,0,41,0.3110784,"\int \left(F^{e (c+d x)}\right)^n \left(a+b \left(F^{e (c+d x)}\right)^n\right)^p \, dx","Integrate[(F^(e*(c + d*x)))^n*(a + b*(F^(e*(c + d*x)))^n)^p,x]","\int \left(F^{e (c+d x)}\right)^n \left(a+b \left(F^{e (c+d x)}\right)^n\right)^p \, dx","\frac{\left(a+b \left(F^{e (c+d x)}\right)^n\right)^{p+1}}{b d e n (p+1) \log (F)}",1,"Integrate[(F^(e*(c + d*x)))^n*(a + b*(F^(e*(c + d*x)))^n)^p, x]","F",-1
17,0,0,80,0.3204423,"\int \left(a+b \left(F^{e (c+d x)}\right)^n\right)^p \left(G^{h (f+g x)}\right)^{\frac{d e n \log (F)}{g h \log (G)}} \, dx","Integrate[(a + b*(F^(e*(c + d*x)))^n)^p*(G^(h*(f + g*x)))^((d*e*n*Log[F])/(g*h*Log[G])),x]","\int \left(a+b \left(F^{e (c+d x)}\right)^n\right)^p \left(G^{h (f+g x)}\right)^{\frac{d e n \log (F)}{g h \log (G)}} \, dx","\frac{\left(F^{e (c+d x)}\right)^{-n} \left(a+b \left(F^{e (c+d x)}\right)^n\right)^{p+1} \left(G^{h (f+g x)}\right)^{\frac{d e n \log (F)}{g h \log (G)}}}{b d e n (p+1) \log (F)}",1,"Integrate[(a + b*(F^(e*(c + d*x)))^n)^p*(G^(h*(f + g*x)))^((d*e*n*Log[F])/(g*h*Log[G])), x]","F",-1
18,1,22,22,0.0165989,"\int \frac{e^{2 x}}{a+b e^x} \, dx","Integrate[E^(2*x)/(a + b*E^x),x]","\frac{e^x}{b}-\frac{a \log \left(a+b e^x\right)}{b^2}","\frac{e^x}{b}-\frac{a \log \left(a+b e^x\right)}{b^2}",1,"E^x/b - (a*Log[a + b*E^x])/b^2","A",1
19,1,24,27,0.0247059,"\int \frac{e^{2 x}}{\left(a+b e^x\right)^2} \, dx","Integrate[E^(2*x)/(a + b*E^x)^2,x]","\frac{\frac{a}{a+b e^x}+\log \left(a+b e^x\right)}{b^2}","\frac{a}{b^2 \left(a+b e^x\right)}+\frac{\log \left(a+b e^x\right)}{b^2}",1,"(a/(a + b*E^x) + Log[a + b*E^x])/b^2","A",1
20,1,21,21,0.0101993,"\int \frac{e^{2 x}}{\left(a+b e^x\right)^3} \, dx","Integrate[E^(2*x)/(a + b*E^x)^3,x]","\frac{e^{2 x}}{2 a \left(a+b e^x\right)^2}","\frac{e^{2 x}}{2 a \left(a+b e^x\right)^2}",1,"E^(2*x)/(2*a*(a + b*E^x)^2)","A",1
21,1,24,34,0.0225825,"\int \frac{e^{2 x}}{\left(a+b e^x\right)^4} \, dx","Integrate[E^(2*x)/(a + b*E^x)^4,x]","-\frac{a+3 b e^x}{6 b^2 \left(a+b e^x\right)^3}","\frac{a}{3 b^2 \left(a+b e^x\right)^3}-\frac{1}{2 b^2 \left(a+b e^x\right)^2}",1,"-1/6*(a + 3*b*E^x)/(b^2*(a + b*E^x)^3)","A",1
22,1,30,31,0.0158446,"\int \frac{e^{4 x}}{a+b e^{2 x}} \, dx","Integrate[E^(4*x)/(a + b*E^(2*x)),x]","\frac{1}{2} \left(\frac{e^{2 x}}{b}-\frac{a \log \left(a+b e^{2 x}\right)}{b^2}\right)","\frac{e^{2 x}}{2 b}-\frac{a \log \left(a+b e^{2 x}\right)}{2 b^2}",1,"(E^(2*x)/b - (a*Log[a + b*E^(2*x)])/b^2)/2","A",1
23,1,31,37,0.0253652,"\int \frac{e^{4 x}}{\left(a+b e^{2 x}\right)^2} \, dx","Integrate[E^(4*x)/(a + b*E^(2*x))^2,x]","\frac{\frac{a}{a+b e^{2 x}}+\log \left(a+b e^{2 x}\right)}{2 b^2}","\frac{a}{2 b^2 \left(a+b e^{2 x}\right)}+\frac{\log \left(a+b e^{2 x}\right)}{2 b^2}",1,"(a/(a + b*E^(2*x)) + Log[a + b*E^(2*x)])/(2*b^2)","A",1
24,1,23,23,0.0092526,"\int \frac{e^{4 x}}{\left(a+b e^{2 x}\right)^3} \, dx","Integrate[E^(4*x)/(a + b*E^(2*x))^3,x]","\frac{e^{4 x}}{4 a \left(a+b e^{2 x}\right)^2}","\frac{e^{4 x}}{4 a \left(a+b e^{2 x}\right)^2}",1,"E^(4*x)/(4*a*(a + b*E^(2*x))^2)","A",1
25,1,28,38,0.0186007,"\int \frac{e^{4 x}}{\left(a+b e^{2 x}\right)^4} \, dx","Integrate[E^(4*x)/(a + b*E^(2*x))^4,x]","-\frac{a+3 b e^{2 x}}{12 b^2 \left(a+b e^{2 x}\right)^3}","\frac{a}{6 b^2 \left(a+b e^{2 x}\right)^3}-\frac{1}{4 b^2 \left(a+b e^{2 x}\right)^2}",1,"-1/12*(a + 3*b*E^(2*x))/(b^2*(a + b*E^(2*x))^3)","A",1
26,1,31,42,0.0203461,"\int \frac{e^{4 x}}{\left(a+b e^{2 x}\right)^{2/3}} \, dx","Integrate[E^(4*x)/(a + b*E^(2*x))^(2/3),x]","\frac{3 \left(b e^{2 x}-3 a\right) \sqrt[3]{a+b e^{2 x}}}{8 b^2}","\frac{3 \left(a+b e^{2 x}\right)^{4/3}}{8 b^2}-\frac{3 a \sqrt[3]{a+b e^{2 x}}}{2 b^2}",1,"(3*(-3*a + b*E^(2*x))*(a + b*E^(2*x))^(1/3))/(8*b^2)","A",1
27,1,16,16,0.0085069,"\int e^{-n x} \left(a+b e^{n x}\right) \, dx","Integrate[(a + b*E^(n*x))/E^(n*x),x]","b x-\frac{a e^{-n x}}{n}","b x-\frac{a e^{-n x}}{n}",1,"-(a/(E^(n*x)*n)) + b*x","A",1
28,1,31,32,0.0191894,"\int e^{-n x} \left(a+b e^{n x}\right)^2 \, dx","Integrate[(a + b*E^(n*x))^2/E^(n*x),x]","\frac{a^2 \left(-e^{-n x}\right)+2 a b n x+b^2 e^{n x}}{n}","-\frac{a^2 e^{-n x}}{n}+2 a b x+\frac{b^2 e^{n x}}{n}",1,"(-(a^2/E^(n*x)) + b^2*E^(n*x) + 2*a*b*n*x)/n","A",1
29,1,48,52,0.0267846,"\int e^{-n x} \left(a+b e^{n x}\right)^3 \, dx","Integrate[(a + b*E^(n*x))^3/E^(n*x),x]","\frac{a^3 \left(-e^{-n x}\right)+3 a^2 b n x+3 a b^2 e^{n x}+\frac{1}{2} b^3 e^{2 n x}}{n}","-\frac{a^3 e^{-n x}}{n}+3 a^2 b x+\frac{3 a b^2 e^{n x}}{n}+\frac{b^3 e^{2 n x}}{2 n}",1,"(-(a^3/E^(n*x)) + 3*a*b^2*E^(n*x) + (b^3*E^(2*n*x))/2 + 3*a^2*b*n*x)/n","A",1
30,1,34,40,0.039239,"\int \frac{e^{-n x}}{a+b e^{n x}} \, dx","Integrate[1/(E^(n*x)*(a + b*E^(n*x))),x]","-\frac{-b \log \left(a+b e^{n x}\right)+a e^{-n x}+b n x}{a^2 n}","\frac{b \log \left(a+b e^{n x}\right)}{a^2 n}-\frac{b x}{a^2}-\frac{e^{-n x}}{a n}",1,"-((a/E^(n*x) + b*n*x - b*Log[a + b*E^(n*x)])/(a^2*n))","A",1
31,1,49,61,0.1136555,"\int \frac{e^{-n x}}{\left(a+b e^{n x}\right)^2} \, dx","Integrate[1/(E^(n*x)*(a + b*E^(n*x))^2),x]","-\frac{a \left(\frac{b}{a+b e^{n x}}+e^{-n x}\right)-2 b \log \left(a+b e^{n x}\right)+2 b n x}{a^3 n}","\frac{2 b \log \left(a+b e^{n x}\right)}{a^3 n}-\frac{2 b x}{a^3}-\frac{b}{a^2 n \left(a+b e^{n x}\right)}-\frac{e^{-n x}}{a^2 n}",1,"-((a*(E^(-(n*x)) + b/(a + b*E^(n*x))) + 2*b*n*x - 2*b*Log[a + b*E^(n*x)])/(a^3*n))","A",1
32,1,69,83,0.139363,"\int \frac{e^{-n x}}{\left(a+b e^{n x}\right)^3} \, dx","Integrate[1/(E^(n*x)*(a + b*E^(n*x))^3),x]","-\frac{\frac{a^2 b}{\left(a+b e^{n x}\right)^2}+\frac{4 a b}{a+b e^{n x}}-6 b \log \left(a+b e^{n x}\right)+2 a e^{-n x}+6 b n x}{2 a^4 n}","\frac{3 b \log \left(a+b e^{n x}\right)}{a^4 n}-\frac{3 b x}{a^4}-\frac{2 b}{a^3 n \left(a+b e^{n x}\right)}-\frac{e^{-n x}}{a^3 n}-\frac{b}{2 a^2 n \left(a+b e^{n x}\right)^2}",1,"-1/2*((2*a)/E^(n*x) + (a^2*b)/(a + b*E^(n*x))^2 + (4*a*b)/(a + b*E^(n*x)) + 6*b*n*x - 6*b*Log[a + b*E^(n*x)])/(a^4*n)","A",1
33,1,50,50,0.0264203,"\int \frac{f^{a+b x}}{c+d f^{e+2 b x}} \, dx","Integrate[f^(a + b*x)/(c + d*f^(e + 2*b*x)),x]","\frac{f^{a-\frac{e}{2}} \tan ^{-1}\left(\frac{\sqrt{d} f^{b x+\frac{e}{2}}}{\sqrt{c}}\right)}{b \sqrt{c} \sqrt{d} \log (f)}","\frac{f^{a-\frac{e}{2}} \tan ^{-1}\left(\frac{\sqrt{d} f^{b x+\frac{e}{2}}}{\sqrt{c}}\right)}{b \sqrt{c} \sqrt{d} \log (f)}",1,"(f^(a - e/2)*ArcTan[(Sqrt[d]*f^(e/2 + b*x))/Sqrt[c]])/(b*Sqrt[c]*Sqrt[d]*Log[f])","A",1
34,1,34,34,0.0186512,"\int \frac{f^{a+2 b x}}{c+d f^{e+2 b x}} \, dx","Integrate[f^(a + 2*b*x)/(c + d*f^(e + 2*b*x)),x]","\frac{f^{a-e} \log \left(d f^{2 b x+e}+c\right)}{2 b d \log (f)}","\frac{f^{a-e} \log \left(d f^{2 b x+e}+c\right)}{2 b d \log (f)}",1,"(f^(a - e)*Log[c + d*f^(e + 2*b*x)])/(2*b*d*Log[f])","A",1
35,1,67,88,0.0696704,"\int \frac{f^{a+3 b x}}{c+d f^{e+2 b x}} \, dx","Integrate[f^(a + 3*b*x)/(c + d*f^(e + 2*b*x)),x]","\frac{f^a \left(\frac{f^{b x-e}}{d}-\frac{\sqrt{c} f^{-3 e/2} \tan ^{-1}\left(\frac{\sqrt{d} f^{b x+\frac{e}{2}}}{\sqrt{c}}\right)}{d^{3/2}}\right)}{b \log (f)}","\frac{f^{\frac{1}{2} (2 a-3 e)+\frac{1}{2} (2 b x+e)}}{b d \log (f)}-\frac{\sqrt{c} f^{a-\frac{3 e}{2}} \tan ^{-1}\left(\frac{\sqrt{d} f^{\frac{1}{2} (2 b x+e)}}{\sqrt{c}}\right)}{b d^{3/2} \log (f)}",1,"(f^a*(f^(-e + b*x)/d - (Sqrt[c]*ArcTan[(Sqrt[d]*f^(e/2 + b*x))/Sqrt[c]])/(d^(3/2)*f^((3*e)/2))))/(b*Log[f])","A",1
36,1,48,61,0.0460054,"\int \frac{f^{a+4 b x}}{c+d f^{e+2 b x}} \, dx","Integrate[f^(a + 4*b*x)/(c + d*f^(e + 2*b*x)),x]","\frac{f^{a-2 e} \left(d f^{2 b x+e}-c \log \left(d f^{2 b x+e}+c\right)\right)}{2 b d^2 \log (f)}","\frac{f^{a+2 b x-e}}{2 b d \log (f)}-\frac{c f^{a-2 e} \log \left(d f^{2 b x+e}+c\right)}{2 b d^2 \log (f)}",1,"(f^(a - 2*e)*(d*f^(e + 2*b*x) - c*Log[c + d*f^(e + 2*b*x)]))/(2*b*d^2*Log[f])","A",1
37,1,86,127,0.0679595,"\int \frac{f^{a+5 b x}}{c+d f^{e+2 b x}} \, dx","Integrate[f^(a + 5*b*x)/(c + d*f^(e + 2*b*x)),x]","\frac{3 c^{3/2} f^{a-\frac{5 e}{2}} \tan ^{-1}\left(\frac{\sqrt{d} f^{b x+\frac{e}{2}}}{\sqrt{c}}\right)+\sqrt{d} f^{a+b x-2 e} \left(d f^{2 b x+e}-3 c\right)}{3 b d^{5/2} \log (f)}","\frac{c^{3/2} f^{a-\frac{5 e}{2}} \tan ^{-1}\left(\frac{\sqrt{d} f^{\frac{1}{2} (2 b x+e)}}{\sqrt{c}}\right)}{b d^{5/2} \log (f)}-\frac{c f^{\frac{1}{2} (2 a-5 e)+\frac{1}{2} (2 b x+e)}}{b d^2 \log (f)}+\frac{f^{\frac{1}{2} (2 a-5 e)+\frac{3}{2} (2 b x+e)}}{3 b d \log (f)}",1,"(Sqrt[d]*f^(a - 2*e + b*x)*(-3*c + d*f^(e + 2*b*x)) + 3*c^(3/2)*f^(a - (5*e)/2)*ArcTan[(Sqrt[d]*f^(e/2 + b*x))/Sqrt[c]])/(3*b*d^(5/2)*Log[f])","A",1
38,1,4,4,0.0030586,"\int \frac{e^x}{1+e^{2 x}} \, dx","Integrate[E^x/(1 + E^(2*x)),x]","\tan ^{-1}\left(e^x\right)","\tan ^{-1}\left(e^x\right)",1,"ArcTan[E^x]","A",1
39,1,4,4,0.003644,"\int \frac{e^x}{1-e^{2 x}} \, dx","Integrate[E^x/(1 - E^(2*x)),x]","\tanh ^{-1}\left(e^x\right)","\tanh ^{-1}\left(e^x\right)",1,"ArcTanh[E^x]","A",1
40,1,45,27,0.0350131,"\int \frac{e^x x}{1-e^{2 x}} \, dx","Integrate[(E^x*x)/(1 - E^(2*x)),x]","\frac{\text{Li}_2\left(-e^x\right)}{2}-\frac{\text{Li}_2\left(e^x\right)}{2}-\frac{1}{2} x \log \left(1-e^x\right)+\frac{1}{2} x \log \left(e^x+1\right)","\frac{\text{Li}_2\left(-e^x\right)}{2}-\frac{\text{Li}_2\left(e^x\right)}{2}+x \tanh ^{-1}\left(e^x\right)",1,"-1/2*(x*Log[1 - E^x]) + (x*Log[1 + E^x])/2 + PolyLog[2, -E^x]/2 - PolyLog[2, E^x]/2","A",1
41,1,60,40,0.0369833,"\int \frac{e^x x^2}{1-e^{2 x}} \, dx","Integrate[(E^x*x^2)/(1 - E^(2*x)),x]","x \text{Li}_2\left(-e^x\right)-x \text{Li}_2\left(e^x\right)-\text{Li}_3\left(-e^x\right)+\text{Li}_3\left(e^x\right)-\frac{1}{2} x^2 \log \left(1-e^x\right)+\frac{1}{2} x^2 \log \left(e^x+1\right)","x \text{Li}_2\left(-e^x\right)-x \text{Li}_2\left(e^x\right)-\text{Li}_3\left(-e^x\right)+\text{Li}_3\left(e^x\right)+x^2 \tanh ^{-1}\left(e^x\right)",1,"-1/2*(x^2*Log[1 - E^x]) + (x^2*Log[1 + E^x])/2 + x*PolyLog[2, -E^x] - x*PolyLog[2, E^x] - PolyLog[3, -E^x] + PolyLog[3, E^x]","A",1
42,1,89,69,0.046957,"\int \frac{e^x x^3}{1-e^{2 x}} \, dx","Integrate[(E^x*x^3)/(1 - E^(2*x)),x]","\frac{3}{2} x^2 \text{Li}_2\left(-e^x\right)-\frac{3}{2} x^2 \text{Li}_2\left(e^x\right)-3 x \text{Li}_3\left(-e^x\right)+3 x \text{Li}_3\left(e^x\right)+3 \text{Li}_4\left(-e^x\right)-3 \text{Li}_4\left(e^x\right)-\frac{1}{2} x^3 \log \left(1-e^x\right)+\frac{1}{2} x^3 \log \left(e^x+1\right)","\frac{3}{2} x^2 \text{Li}_2\left(-e^x\right)-\frac{3}{2} x^2 \text{Li}_2\left(e^x\right)-3 x \text{Li}_3\left(-e^x\right)+3 x \text{Li}_3\left(e^x\right)+3 \text{Li}_4\left(-e^x\right)-3 \text{Li}_4\left(e^x\right)+x^3 \tanh ^{-1}\left(e^x\right)",1,"-1/2*(x^3*Log[1 - E^x]) + (x^3*Log[1 + E^x])/2 + (3*x^2*PolyLog[2, -E^x])/2 - (3*x^2*PolyLog[2, E^x])/2 - 3*x*PolyLog[3, -E^x] + 3*x*PolyLog[3, E^x] + 3*PolyLog[4, -E^x] - 3*PolyLog[4, E^x]","A",1
43,1,30,30,0.0086962,"\int \frac{f^x}{a+b f^{2 x}} \, dx","Integrate[f^x/(a + b*f^(2*x)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (f)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"ArcTan[(Sqrt[b]*f^x)/Sqrt[a]]/(Sqrt[a]*Sqrt[b]*Log[f])","A",1
44,1,108,110,0.0692261,"\int \frac{f^x x}{a+b f^{2 x}} \, dx","Integrate[(f^x*x)/(a + b*f^(2*x)),x]","\frac{i \left(-\text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+\text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+x \log (f) \left(\log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-\log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)\right)\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}","-\frac{i \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{x \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"((I/2)*(x*Log[f]*(Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]] - Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]]) - PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]] + PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]]))/(Sqrt[a]*Sqrt[b]*Log[f]^2)","A",1
45,1,168,184,0.0544165,"\int \frac{f^x x^2}{a+b f^{2 x}} \, dx","Integrate[(f^x*x^2)/(a + b*f^(2*x)),x]","\frac{i \left(2 \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-2 \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-2 x \log (f) \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+2 x \log (f) \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+x^2 \log ^2(f) \log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-x^2 \log ^2(f) \log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)\right)}{2 \sqrt{a} \sqrt{b} \log ^3(f)}","\frac{i \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{i \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{i x \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i x \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{x^2 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"((I/2)*(x^2*Log[f]^2*Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]] - x^2*Log[f]^2*Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]] - 2*x*Log[f]*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]] + 2*x*Log[f]*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]] + 2*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]] - 2*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]]))/(Sqrt[a]*Sqrt[b]*Log[f]^3)","A",1
46,1,224,268,0.0538848,"\int \frac{f^x x^3}{a+b f^{2 x}} \, dx","Integrate[(f^x*x^3)/(a + b*f^(2*x)),x]","\frac{i \left(-3 x^2 \log ^2(f) \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+3 x^2 \log ^2(f) \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-6 \text{Li}_4\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+6 \text{Li}_4\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+6 x \log (f) \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-6 x \log (f) \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+x^3 \log ^3(f) \log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-x^3 \log ^3(f) \log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)\right)}{2 \sqrt{a} \sqrt{b} \log ^4(f)}","-\frac{3 i x^2 \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{3 i x^2 \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}-\frac{3 i \text{Li}_4\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{3 i \text{Li}_4\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{3 i x \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}+\frac{x^3 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"((I/2)*(x^3*Log[f]^3*Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]] - x^3*Log[f]^3*Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]] - 3*x^2*Log[f]^2*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]] + 3*x^2*Log[f]^2*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]] + 6*x*Log[f]*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]] - 6*x*Log[f]*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]] - 6*PolyLog[4, ((-I)*Sqrt[b]*f^x)/Sqrt[a]] + 6*PolyLog[4, (I*Sqrt[b]*f^x)/Sqrt[a]]))/(Sqrt[a]*Sqrt[b]*Log[f]^4)","A",1
47,1,53,59,0.0594125,"\int \frac{f^x}{\left(a+b f^{2 x}\right)^2} \, dx","Integrate[f^x/(a + b*f^(2*x))^2,x]","\frac{\frac{\tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}+\frac{f^x}{a^2+a b f^{2 x}}}{2 \log (f)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log (f)}+\frac{f^x}{2 a \log (f) \left(a+b f^{2 x}\right)}",1,"(f^x/(a^2 + a*b*f^(2*x)) + ArcTan[(Sqrt[b]*f^x)/Sqrt[a]]/(a^(3/2)*Sqrt[b]))/(2*Log[f])","A",1
48,1,271,172,0.151132,"\int \frac{f^x x}{\left(a+b f^{2 x}\right)^2} \, dx","Integrate[(f^x*x)/(a + b*f^(2*x))^2,x]","\frac{\frac{-\frac{i \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log ^2(f)}-\frac{i x \log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log (f)}+\frac{i x^2}{2 \sqrt{a}}}{2 \sqrt{b}}+\frac{\frac{i \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log ^2(f)}+\frac{i x \log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log (f)}-\frac{i x^2}{2 \sqrt{a}}}{2 \sqrt{b}}}{2 a}+\frac{x f^x}{2 a \log (f) \left(a+b f^{2 x}\right)}-\frac{\left(\frac{b f^{2 x}}{a}+1\right) \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f) \left(a+b f^{2 x}\right)}","-\frac{i \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{i \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} \log ^2(f)}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{x \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log (f)}+\frac{x f^x}{2 a \log (f) \left(a+b f^{2 x}\right)}",1,"-1/2*((1 + (b*f^(2*x))/a)*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*(a + b*f^(2*x))*Log[f]^2) + (f^x*x)/(2*a*(a + b*f^(2*x))*Log[f]) + ((((I/2)*x^2)/Sqrt[a] - (I*x*Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]) - (I*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]^2))/(2*Sqrt[b]) + (((-1/2*I)*x^2)/Sqrt[a] + (I*x*Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]) + (I*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]^2))/(2*Sqrt[b]))/(2*a)","A",1
49,1,477,333,0.1247234,"\int \frac{f^x x^2}{\left(a+b f^{2 x}\right)^2} \, dx","Integrate[(f^x*x^2)/(a + b*f^(2*x))^2,x]","-\frac{\frac{-\frac{i \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log ^2(f)}-\frac{i x \log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log (f)}+\frac{i x^2}{2 \sqrt{a}}}{2 \sqrt{b}}+\frac{\frac{i \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log ^2(f)}+\frac{i x \log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log (f)}-\frac{i x^2}{2 \sqrt{a}}}{2 \sqrt{b}}}{a \log (f)}+\frac{\frac{\frac{2 i \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log ^3(f)}-\frac{2 i x \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log ^2(f)}-\frac{i x^2 \log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log (f)}+\frac{i x^3}{3 \sqrt{a}}}{2 \sqrt{b}}+\frac{-\frac{2 i \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log ^3(f)}+\frac{2 i x \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log ^2(f)}+\frac{i x^2 \log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \log (f)}-\frac{i x^3}{3 \sqrt{a}}}{2 \sqrt{b}}}{2 a}+\frac{x^2 f^x}{2 a \log (f) \left(a+b f^{2 x}\right)}","\frac{i \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{i \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{i \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{i \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{i x \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{i x \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{x^2 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log (f)}-\frac{x \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b} \log ^2(f)}+\frac{x^2 f^x}{2 a \log (f) \left(a+b f^{2 x}\right)}",1,"(f^x*x^2)/(2*a*(a + b*f^(2*x))*Log[f]) - ((((I/2)*x^2)/Sqrt[a] - (I*x*Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]) - (I*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]^2))/(2*Sqrt[b]) + (((-1/2*I)*x^2)/Sqrt[a] + (I*x*Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]) + (I*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]^2))/(2*Sqrt[b]))/(a*Log[f]) + ((((I/3)*x^3)/Sqrt[a] - (I*x^2*Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]) - ((2*I)*x*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]^2) + ((2*I)*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]^3))/(2*Sqrt[b]) + (((-1/3*I)*x^3)/Sqrt[a] + (I*x^2*Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]) + ((2*I)*x*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]^2) - ((2*I)*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Log[f]^3))/(2*Sqrt[b]))/(2*a)","A",1
50,1,434,501,0.2677956,"\int \frac{f^x x^3}{\left(a+b f^{2 x}\right)^2} \, dx","Integrate[(f^x*x^3)/(a + b*f^(2*x))^2,x]","\frac{-\frac{6 i \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}+\frac{6 i \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}-\frac{6 i \text{Li}_4\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}+\frac{6 i \text{Li}_4\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}-\frac{3 i x \log (f) (x \log (f)-2) \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}+\frac{3 i x \log (f) (x \log (f)-2) \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}+\frac{6 i x \log (f) \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}-\frac{6 i x \log (f) \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}+\frac{i x^3 \log ^3(f) \log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}-\frac{i x^3 \log ^3(f) \log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}-\frac{3 i x^2 \log ^2(f) \log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}+\frac{3 i x^2 \log ^2(f) \log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}+\frac{2 \sqrt{a} x^3 f^x \log ^3(f)}{a+b f^{2 x}}}{4 a^{3/2} \log ^4(f)}","-\frac{3 i x^2 \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{3 i x^2 \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} \log ^2(f)}-\frac{3 i \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(f)}+\frac{3 i \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(f)}-\frac{3 i \text{Li}_4\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(f)}+\frac{3 i \text{Li}_4\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(f)}+\frac{3 i x \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{3 i x \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{x^3 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log (f)}-\frac{3 x^2 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{x^3 f^x}{2 a \log (f) \left(a+b f^{2 x}\right)}",1,"((2*Sqrt[a]*f^x*x^3*Log[f]^3)/(a + b*f^(2*x)) - ((3*I)*x^2*Log[f]^2*Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] + (I*x^3*Log[f]^3*Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] + ((3*I)*x^2*Log[f]^2*Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] - (I*x^3*Log[f]^3*Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] - ((3*I)*x*Log[f]*(-2 + x*Log[f])*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] + ((3*I)*x*Log[f]*(-2 + x*Log[f])*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] - ((6*I)*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] + ((6*I)*x*Log[f]*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] + ((6*I)*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] - ((6*I)*x*Log[f]*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] - ((6*I)*PolyLog[4, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b] + ((6*I)*PolyLog[4, (I*Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b])/(4*a^(3/2)*Log[f]^4)","A",1
51,1,68,84,0.0514112,"\int \frac{f^x}{\left(a+b f^{2 x}\right)^3} \, dx","Integrate[f^x/(a + b*f^(2*x))^3,x]","\frac{\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{b}}+\frac{\sqrt{a} f^x \left(5 a+3 b f^{2 x}\right)}{\left(a+b f^{2 x}\right)^2}}{8 a^{5/2} \log (f)}","\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log (f)}+\frac{3 f^x}{8 a^2 \log (f) \left(a+b f^{2 x}\right)}+\frac{f^x}{4 a \log (f) \left(a+b f^{2 x}\right)^2}",1,"((Sqrt[a]*f^x*(5*a + 3*b*f^(2*x)))/(a + b*f^(2*x))^2 + (3*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/Sqrt[b])/(8*a^(5/2)*Log[f])","A",1
52,1,184,223,0.3148492,"\int \frac{f^x x}{\left(a+b f^{2 x}\right)^3} \, dx","Integrate[(f^x*x)/(a + b*f^(2*x))^3,x]","\frac{\frac{6 i \left(-\text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+\text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+x \log (f) \left(\log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-\log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)\right)\right)}{\sqrt{a} \sqrt{b}}-\frac{16 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}+\frac{8 a x f^x \log (f)}{\left(a+b f^{2 x}\right)^2}+\frac{4 f^x (3 x \log (f)-1)}{a+b f^{2 x}}}{32 a^2 \log ^2(f)}","-\frac{3 i \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b} \log ^2(f)}+\frac{3 i \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b} \log ^2(f)}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b} \log ^2(f)}+\frac{3 x \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log (f)}-\frac{f^x}{8 a^2 \log ^2(f) \left(a+b f^{2 x}\right)}+\frac{3 x f^x}{8 a^2 \log (f) \left(a+b f^{2 x}\right)}+\frac{x f^x}{4 a \log (f) \left(a+b f^{2 x}\right)^2}",1,"((-16*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]) + (8*a*f^x*x*Log[f])/(a + b*f^(2*x))^2 + (4*f^x*(-1 + 3*x*Log[f]))/(a + b*f^(2*x)) + ((6*I)*(x*Log[f]*(Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]] - Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]]) - PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]] + PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]]))/(Sqrt[a]*Sqrt[b]))/(32*a^2*Log[f]^2)","A",1
53,1,353,420,0.5038581,"\int \frac{f^x x^2}{\left(a+b f^{2 x}\right)^3} \, dx","Integrate[(f^x*x^2)/(a + b*f^(2*x))^3,x]","\frac{\frac{3 i \left(2 \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-2 \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-2 x \log (f) \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+2 x \log (f) \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+x^2 \log ^2(f) \log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-x^2 \log ^2(f) \log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)\right)}{\sqrt{a} \sqrt{b}}-\frac{8 i \left(-\text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+\text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)+x \log (f) \left(\log \left(1-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)-\log \left(1+\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)\right)\right)}{\sqrt{a} \sqrt{b}}+\frac{4 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}+\frac{4 a x^2 f^x \log ^2(f)}{\left(a+b f^{2 x}\right)^2}+\frac{2 x f^x \log (f) (3 x \log (f)-2)}{a+b f^{2 x}}}{16 a^2 \log ^3(f)}","\frac{i \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b} \log ^3(f)}-\frac{i \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b} \log ^3(f)}+\frac{3 i \text{Li}_3\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^3(f)}-\frac{3 i \text{Li}_3\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{Li}_2\left(-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^2(f)}+\frac{3 i x \text{Li}_2\left(\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^2(f)}+\frac{3 x^2 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log (f)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b} \log ^3(f)}-\frac{x \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{a^{5/2} \sqrt{b} \log ^2(f)}+\frac{3 x^2 f^x}{8 a^2 \log (f) \left(a+b f^{2 x}\right)}-\frac{x f^x}{4 a^2 \log ^2(f) \left(a+b f^{2 x}\right)}+\frac{x^2 f^x}{4 a \log (f) \left(a+b f^{2 x}\right)^2}",1,"((4*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]) + (4*a*f^x*x^2*Log[f]^2)/(a + b*f^(2*x))^2 + (2*f^x*x*Log[f]*(-2 + 3*x*Log[f]))/(a + b*f^(2*x)) - ((8*I)*(x*Log[f]*(Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]] - Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]]) - PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]] + PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]]))/(Sqrt[a]*Sqrt[b]) + ((3*I)*(x^2*Log[f]^2*Log[1 - (I*Sqrt[b]*f^x)/Sqrt[a]] - x^2*Log[f]^2*Log[1 + (I*Sqrt[b]*f^x)/Sqrt[a]] - 2*x*Log[f]*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]] + 2*x*Log[f]*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]] + 2*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]] - 2*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]]))/(Sqrt[a]*Sqrt[b]))/(16*a^2*Log[f]^3)","A",1
54,1,30,30,0.0079404,"\int \frac{1}{b f^{-x}+a f^x} \, dx","Integrate[(b/f^x + a*f^x)^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log (f)}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"ArcTan[(Sqrt[a]*f^x)/Sqrt[b]]/(Sqrt[a]*Sqrt[b]*Log[f])","A",1
55,1,108,110,0.0636434,"\int \frac{x}{b f^{-x}+a f^x} \, dx","Integrate[x/(b/f^x + a*f^x),x]","\frac{i \left(-\text{Li}_2\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)+\text{Li}_2\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)+x \log (f) \left(\log \left(1-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)-\log \left(1+\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)\right)\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}","-\frac{i \text{Li}_2\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i \text{Li}_2\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{x \tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"((I/2)*(x*Log[f]*(Log[1 - (I*Sqrt[a]*f^x)/Sqrt[b]] - Log[1 + (I*Sqrt[a]*f^x)/Sqrt[b]]) - PolyLog[2, ((-I)*Sqrt[a]*f^x)/Sqrt[b]] + PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]]))/(Sqrt[a]*Sqrt[b]*Log[f]^2)","A",1
56,1,168,184,0.0502434,"\int \frac{x^2}{b f^{-x}+a f^x} \, dx","Integrate[x^2/(b/f^x + a*f^x),x]","\frac{i \left(2 \text{Li}_3\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)-2 \text{Li}_3\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)-2 x \log (f) \text{Li}_2\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)+2 x \log (f) \text{Li}_2\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)+x^2 \log ^2(f) \log \left(1-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)-x^2 \log ^2(f) \log \left(1+\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)\right)}{2 \sqrt{a} \sqrt{b} \log ^3(f)}","\frac{i \text{Li}_3\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{i \text{Li}_3\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{i x \text{Li}_2\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i x \text{Li}_2\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{x^2 \tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"((I/2)*(x^2*Log[f]^2*Log[1 - (I*Sqrt[a]*f^x)/Sqrt[b]] - x^2*Log[f]^2*Log[1 + (I*Sqrt[a]*f^x)/Sqrt[b]] - 2*x*Log[f]*PolyLog[2, ((-I)*Sqrt[a]*f^x)/Sqrt[b]] + 2*x*Log[f]*PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]] + 2*PolyLog[3, ((-I)*Sqrt[a]*f^x)/Sqrt[b]] - 2*PolyLog[3, (I*Sqrt[a]*f^x)/Sqrt[b]]))/(Sqrt[a]*Sqrt[b]*Log[f]^3)","A",1
57,1,224,268,0.0539573,"\int \frac{x^3}{b f^{-x}+a f^x} \, dx","Integrate[x^3/(b/f^x + a*f^x),x]","\frac{i \left(-3 x^2 \log ^2(f) \text{Li}_2\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)+3 x^2 \log ^2(f) \text{Li}_2\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)-6 \text{Li}_4\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)+6 \text{Li}_4\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)+6 x \log (f) \text{Li}_3\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)-6 x \log (f) \text{Li}_3\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)+x^3 \log ^3(f) \log \left(1-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)-x^3 \log ^3(f) \log \left(1+\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)\right)}{2 \sqrt{a} \sqrt{b} \log ^4(f)}","-\frac{3 i x^2 \text{Li}_2\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{3 i x^2 \text{Li}_2\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}-\frac{3 i \text{Li}_4\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{3 i \text{Li}_4\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{3 i x \text{Li}_3\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{Li}_3\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}+\frac{x^3 \tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"((I/2)*(x^3*Log[f]^3*Log[1 - (I*Sqrt[a]*f^x)/Sqrt[b]] - x^3*Log[f]^3*Log[1 + (I*Sqrt[a]*f^x)/Sqrt[b]] - 3*x^2*Log[f]^2*PolyLog[2, ((-I)*Sqrt[a]*f^x)/Sqrt[b]] + 3*x^2*Log[f]^2*PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]] + 6*x*Log[f]*PolyLog[3, ((-I)*Sqrt[a]*f^x)/Sqrt[b]] - 6*x*Log[f]*PolyLog[3, (I*Sqrt[a]*f^x)/Sqrt[b]] - 6*PolyLog[4, ((-I)*Sqrt[a]*f^x)/Sqrt[b]] + 6*PolyLog[4, (I*Sqrt[a]*f^x)/Sqrt[b]]))/(Sqrt[a]*Sqrt[b]*Log[f]^4)","A",1
58,1,23,22,0.0204613,"\int \frac{1}{\left(b f^{-x}+a f^x\right)^2} \, dx","Integrate[(b/f^x + a*f^x)^(-2),x]","-\frac{1}{2 a^2 f^{2 x} \log (f)+2 a b \log (f)}","-\frac{1}{2 a \log (f) \left(a f^{2 x}+b\right)}",1,"-(2*a*b*Log[f] + 2*a^2*f^(2*x)*Log[f])^(-1)","A",1
59,1,48,63,0.059536,"\int \frac{x}{\left(b f^{-x}+a f^x\right)^2} \, dx","Integrate[x/(b/f^x + a*f^x)^2,x]","\frac{\frac{2 x f^{2 x} \log (f)}{a f^{2 x}+b}-\frac{\log \left(a f^{2 x}+b\right)}{a}}{4 b \log ^2(f)}","-\frac{\log \left(a f^{2 x}+b\right)}{4 a b \log ^2(f)}-\frac{x}{2 a \log (f) \left(a f^{2 x}+b\right)}+\frac{x}{2 a b \log (f)}",1,"((2*f^(2*x)*x*Log[f])/(b + a*f^(2*x)) - Log[b + a*f^(2*x)]/a)/(4*b*Log[f]^2)","A",1
60,1,90,98,0.0650594,"\int \frac{x^2}{\left(b f^{-x}+a f^x\right)^2} \, dx","Integrate[x^2/(b/f^x + a*f^x)^2,x]","\frac{2 x \log (f) \left(a x f^{2 x} \log (f)-\left(a f^{2 x}+b\right) \log \left(\frac{a f^{2 x}}{b}+1\right)\right)-\left(a f^{2 x}+b\right) \text{Li}_2\left(-\frac{a f^{2 x}}{b}\right)}{4 a b \log ^3(f) \left(a f^{2 x}+b\right)}","-\frac{\text{Li}_2\left(-\frac{a f^{2 x}}{b}\right)}{4 a b \log ^3(f)}-\frac{x^2}{2 a \log (f) \left(a f^{2 x}+b\right)}-\frac{x \log \left(\frac{a f^{2 x}}{b}+1\right)}{2 a b \log ^2(f)}+\frac{x^2}{2 a b \log (f)}",1,"(2*x*Log[f]*(a*f^(2*x)*x*Log[f] - (b + a*f^(2*x))*Log[1 + (a*f^(2*x))/b]) - (b + a*f^(2*x))*PolyLog[2, -((a*f^(2*x))/b)])/(4*a*b*(b + a*f^(2*x))*Log[f]^3)","A",1
61,1,124,128,0.0850228,"\int \frac{x^3}{\left(b f^{-x}+a f^x\right)^2} \, dx","Integrate[x^3/(b/f^x + a*f^x)^2,x]","\frac{3 \left(\frac{\text{Li}_3\left(-\frac{a f^{2 x}}{b}\right)}{4 b \log ^3(f)}-\frac{x \text{Li}_2\left(-\frac{a f^{2 x}}{b}\right)}{2 b \log ^2(f)}-\frac{x^2 \log \left(\frac{a f^{2 x}}{b}+1\right)}{2 b \log (f)}+\frac{x^3}{3 b}\right)}{2 a \log (f)}-\frac{x^3}{2 a \log (f) \left(a f^{2 x}+b\right)}","\frac{3 \text{Li}_3\left(-\frac{a f^{2 x}}{b}\right)}{8 a b \log ^4(f)}-\frac{3 x \text{Li}_2\left(-\frac{a f^{2 x}}{b}\right)}{4 a b \log ^3(f)}-\frac{x^3}{2 a \log (f) \left(a f^{2 x}+b\right)}-\frac{3 x^2 \log \left(\frac{a f^{2 x}}{b}+1\right)}{4 a b \log ^2(f)}+\frac{x^3}{2 a b \log (f)}",1,"-1/2*x^3/(a*(b + a*f^(2*x))*Log[f]) + (3*(x^3/(3*b) - (x^2*Log[1 + (a*f^(2*x))/b])/(2*b*Log[f]) - (x*PolyLog[2, -((a*f^(2*x))/b)])/(2*b*Log[f]^2) + PolyLog[3, -((a*f^(2*x))/b)]/(4*b*Log[f]^3)))/(2*a*Log[f])","A",1
62,1,70,87,0.0544861,"\int \frac{1}{\left(b f^{-x}+a f^x\right)^3} \, dx","Integrate[(b/f^x + a*f^x)^(-3),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)+\frac{\sqrt{a} \sqrt{b} f^x \left(a f^{2 x}-b\right)}{\left(a f^{2 x}+b\right)^2}}{8 a^{3/2} b^{3/2} \log (f)}","\frac{\tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log (f)}+\frac{f^x}{8 a b \log (f) \left(a f^{2 x}+b\right)}-\frac{f^x}{4 a \log (f) \left(a f^{2 x}+b\right)^2}",1,"((Sqrt[a]*Sqrt[b]*f^x*(-b + a*f^(2*x)))/(b + a*f^(2*x))^2 + ArcTan[(Sqrt[a]*f^x)/Sqrt[b]])/(8*a^(3/2)*b^(3/2)*Log[f])","A",1
63,1,209,196,0.2195255,"\int \frac{x}{\left(b f^{-x}+a f^x\right)^3} \, dx","Integrate[x/(b/f^x + a*f^x)^3,x]","\frac{-\frac{i \text{Li}_2\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{b^{3/2}}+\frac{i \text{Li}_2\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{b^{3/2}}+\frac{i x \log (f) \log \left(1-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{b^{3/2}}-\frac{i x \log (f) \log \left(1+\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{b^{3/2}}+\frac{2 \sqrt{a} f^x}{a b f^{2 x}+b^2}+\frac{2 \sqrt{a} x f^x \log (f)}{a b f^{2 x}+b^2}-\frac{4 \sqrt{a} x f^x \log (f)}{\left(a f^{2 x}+b\right)^2}}{16 a^{3/2} \log ^2(f)}","-\frac{i \text{Li}_2\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{16 a^{3/2} b^{3/2} \log ^2(f)}+\frac{i \text{Li}_2\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{16 a^{3/2} b^{3/2} \log ^2(f)}+\frac{x \tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log (f)}+\frac{f^x}{8 a b \log ^2(f) \left(a f^{2 x}+b\right)}+\frac{x f^x}{8 a b \log (f) \left(a f^{2 x}+b\right)}-\frac{x f^x}{4 a \log (f) \left(a f^{2 x}+b\right)^2}",1,"((2*Sqrt[a]*f^x)/(b^2 + a*b*f^(2*x)) - (4*Sqrt[a]*f^x*x*Log[f])/(b + a*f^(2*x))^2 + (2*Sqrt[a]*f^x*x*Log[f])/(b^2 + a*b*f^(2*x)) + (I*x*Log[f]*Log[1 - (I*Sqrt[a]*f^x)/Sqrt[b]])/b^(3/2) - (I*x*Log[f]*Log[1 + (I*Sqrt[a]*f^x)/Sqrt[b]])/b^(3/2) - (I*PolyLog[2, ((-I)*Sqrt[a]*f^x)/Sqrt[b]])/b^(3/2) + (I*PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]])/b^(3/2))/(16*a^(3/2)*Log[f]^2)","A",1
64,1,254,316,0.51879,"\int \frac{x^2}{\left(b f^{-x}+a f^x\right)^3} \, dx","Integrate[x^2/(b/f^x + a*f^x)^3,x]","\frac{\frac{3 i \left(2 \text{Li}_3\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)-2 \text{Li}_3\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)-2 x \log (f) \text{Li}_2\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)+2 x \log (f) \text{Li}_2\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)+x^2 \log ^2(f) \log \left(1-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)-x^2 \log ^2(f) \log \left(1+\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)\right)}{b^{3/2}}-\frac{12 \tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{b^{3/2}}-\frac{12 \sqrt{a} x^2 f^x \log ^2(f)}{\left(a f^{2 x}+b\right)^2}+\frac{6 \sqrt{a} x f^x \log (f) (x \log (f)+2)}{b \left(a f^{2 x}+b\right)}}{48 a^{3/2} \log ^3(f)}","\frac{i \text{Li}_3\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^3(f)}-\frac{i \text{Li}_3\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^3(f)}-\frac{i x \text{Li}_2\left(-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^2(f)}+\frac{i x \text{Li}_2\left(\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^2(f)}+\frac{x^2 \tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log (f)}-\frac{\tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{4 a^{3/2} b^{3/2} \log ^3(f)}+\frac{x^2 f^x}{8 a b \log (f) \left(a f^{2 x}+b\right)}-\frac{x^2 f^x}{4 a \log (f) \left(a f^{2 x}+b\right)^2}+\frac{x f^x}{4 a b \log ^2(f) \left(a f^{2 x}+b\right)}",1,"((-12*ArcTan[(Sqrt[a]*f^x)/Sqrt[b]])/b^(3/2) - (12*Sqrt[a]*f^x*x^2*Log[f]^2)/(b + a*f^(2*x))^2 + (6*Sqrt[a]*f^x*x*Log[f]*(2 + x*Log[f]))/(b*(b + a*f^(2*x))) + ((3*I)*(x^2*Log[f]^2*Log[1 - (I*Sqrt[a]*f^x)/Sqrt[b]] - x^2*Log[f]^2*Log[1 + (I*Sqrt[a]*f^x)/Sqrt[b]] - 2*x*Log[f]*PolyLog[2, ((-I)*Sqrt[a]*f^x)/Sqrt[b]] + 2*x*Log[f]*PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]] + 2*PolyLog[3, ((-I)*Sqrt[a]*f^x)/Sqrt[b]] - 2*PolyLog[3, (I*Sqrt[a]*f^x)/Sqrt[b]]))/b^(3/2))/(48*a^(3/2)*Log[f]^3)","A",1
65,1,93,95,0.0657093,"\int f^{a+b x+c x^2} g^{d+e x+f x^2} \, dx","Integrate[f^(a + b*x + c*x^2)*g^(d + e*x + f*x^2),x]","\frac{\sqrt{\pi } f^a g^d \exp \left(-\frac{(b \log (f)+e \log (g))^2}{4 (c \log (f)+f \log (g))}\right) \text{erfi}\left(\frac{\log (f) (b+2 c x)+\log (g) (e+2 f x)}{2 \sqrt{c \log (f)+f \log (g)}}\right)}{2 \sqrt{c \log (f)+f \log (g)}}","\frac{\sqrt{\pi } f^a g^d \exp \left(-\frac{(b \log (f)+e \log (g))^2}{4 (c \log (f)+f \log (g))}\right) \text{erfi}\left(\frac{b \log (f)+2 x (c \log (f)+f \log (g))+e \log (g)}{2 \sqrt{c \log (f)+f \log (g)}}\right)}{2 \sqrt{c \log (f)+f \log (g)}}",1,"(f^a*g^d*Sqrt[Pi]*Erfi[((b + 2*c*x)*Log[f] + (e + 2*f*x)*Log[g])/(2*Sqrt[c*Log[f] + f*Log[g]])])/(2*E^((b*Log[f] + e*Log[g])^2/(4*(c*Log[f] + f*Log[g])))*Sqrt[c*Log[f] + f*Log[g]])","A",1
66,1,92,106,0.0468151,"\int F^{e (c+d x)} \left(a+b G^{h (f+g x)}\right)^n \, dx","Integrate[F^(e*(c + d*x))*(a + b*G^(h*(f + g*x)))^n,x]","\frac{F^{e (c+d x)} \left(a+b G^{h (f+g x)}\right)^{n+1} \, _2F_1\left(1,n+\frac{d e \log (F)}{g h \log (G)}+1;\frac{d e \log (F)}{g h \log (G)}+1;-\frac{b G^{h (f+g x)}}{a}\right)}{a d e \log (F)}","\frac{F^{e (c+d x)} \left(a+b G^{h (f+g x)}\right)^n \left(\frac{b G^{h (f+g x)}}{a}+1\right)^{-n} \, _2F_1\left(-n,\frac{d e \log (F)}{g h \log (G)};\frac{d e \log (F)}{g h \log (G)}+1;-\frac{b G^{h (f+g x)}}{a}\right)}{d e \log (F)}",1,"(F^(e*(c + d*x))*(a + b*G^(h*(f + g*x)))^(1 + n)*Hypergeometric2F1[1, 1 + n + (d*e*Log[F])/(g*h*Log[G]), 1 + (d*e*Log[F])/(g*h*Log[G]), -((b*G^(h*(f + g*x)))/a)])/(a*d*e*Log[F])","A",0
67,1,75,75,0.1663151,"\int \frac{F^{e (c+d x)} H^{t (r+s x)}}{a+b F^{e (c+d x)}} \, dx","Integrate[(F^(e*(c + d*x))*H^(t*(r + s*x)))/(a + b*F^(e*(c + d*x))),x]","-\frac{H^{t (r+s x)} \left(\, _2F_1\left(1,\frac{s t \log (H)}{d e \log (F)};\frac{s t \log (H)}{d e \log (F)}+1;-\frac{b F^{e (c+d x)}}{a}\right)-1\right)}{b s t \log (H)}","\frac{H^{t (r+s x)} \, _2F_1\left(1,-\frac{s t \log (H)}{d e \log (F)};1-\frac{s t \log (H)}{d e \log (F)};-\frac{a F^{-e (c+d x)}}{b}\right)}{b s t \log (H)}",1,"-((H^(t*(r + s*x))*(-1 + Hypergeometric2F1[1, (s*t*Log[H])/(d*e*Log[F]), 1 + (s*t*Log[H])/(d*e*Log[F]), -((b*F^(e*(c + d*x)))/a)]))/(b*s*t*Log[H]))","A",1
68,1,84,85,0.1496284,"\int \frac{F^{e (f+d x)} H^{t (r+s x)}}{a+b F^{e (c+d x)}} \, dx","Integrate[(F^(e*(f + d*x))*H^(t*(r + s*x)))/(a + b*F^(e*(c + d*x))),x]","-\frac{F^{e (f-c)} H^{t (r+s x)} \left(\, _2F_1\left(1,\frac{s t \log (H)}{d e \log (F)};\frac{s t \log (H)}{d e \log (F)}+1;-\frac{b F^{e (c+d x)}}{a}\right)-1\right)}{b s t \log (H)}","\frac{F^{-e (c-f)} H^{t (r+s x)} \, _2F_1\left(1,-\frac{s t \log (H)}{d e \log (F)};1-\frac{s t \log (H)}{d e \log (F)};-\frac{a F^{-e (c+d x)}}{b}\right)}{b s t \log (H)}",1,"-((F^(e*(-c + f))*H^(t*(r + s*x))*(-1 + Hypergeometric2F1[1, (s*t*Log[H])/(d*e*Log[F]), 1 + (s*t*Log[H])/(d*e*Log[F]), -((b*F^(e*(c + d*x)))/a)]))/(b*s*t*Log[H]))","A",1
69,1,46,46,0.0123151,"\int f^{a+b x^2} x^m \, dx","Integrate[f^(a + b*x^2)*x^m,x]","-\frac{1}{2} f^a x^{m+1} \left(-b x^2 \log (f)\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},-b x^2 \log (f)\right)","-\frac{1}{2} f^a x^{m+1} \left(-b x^2 \log (f)\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},-b x^2 \log (f)\right)",1,"-1/2*(f^a*x^(1 + m)*Gamma[(1 + m)/2, -(b*x^2*Log[f])]*(-(b*x^2*Log[f]))^((-1 - m)/2))","A",1
70,1,24,78,0.0031732,"\int f^{a+b x^2} x^{11} \, dx","Integrate[f^(a + b*x^2)*x^11,x]","-\frac{f^a \Gamma \left(6,-b x^2 \log (f)\right)}{2 b^6 \log ^6(f)}","-\frac{f^{a+b x^2} \left(-b^5 x^{10} \log ^5(f)+5 b^4 x^8 \log ^4(f)-20 b^3 x^6 \log ^3(f)+60 b^2 x^4 \log ^2(f)-120 b x^2 \log (f)+120\right)}{2 b^6 \log ^6(f)}",1,"-1/2*(f^a*Gamma[6, -(b*x^2*Log[f])])/(b^6*Log[f]^6)","C",1
71,1,24,65,0.0030743,"\int f^{a+b x^2} x^9 \, dx","Integrate[f^(a + b*x^2)*x^9,x]","\frac{f^a \Gamma \left(5,-b x^2 \log (f)\right)}{2 b^5 \log ^5(f)}","\frac{f^{a+b x^2} \left(b^4 x^8 \log ^4(f)-4 b^3 x^6 \log ^3(f)+12 b^2 x^4 \log ^2(f)-24 b x^2 \log (f)+24\right)}{2 b^5 \log ^5(f)}",1,"(f^a*Gamma[5, -(b*x^2*Log[f])])/(2*b^5*Log[f]^5)","C",1
72,1,53,86,0.0115585,"\int f^{a+b x^2} x^7 \, dx","Integrate[f^(a + b*x^2)*x^7,x]","\frac{f^{a+b x^2} \left(b^3 x^6 \log ^3(f)-3 b^2 x^4 \log ^2(f)+6 b x^2 \log (f)-6\right)}{2 b^4 \log ^4(f)}","-\frac{3 f^{a+b x^2}}{b^4 \log ^4(f)}+\frac{3 x^2 f^{a+b x^2}}{b^3 \log ^3(f)}-\frac{3 x^4 f^{a+b x^2}}{2 b^2 \log ^2(f)}+\frac{x^6 f^{a+b x^2}}{2 b \log (f)}",1,"(f^(a + b*x^2)*(-6 + 6*b*x^2*Log[f] - 3*b^2*x^4*Log[f]^2 + b^3*x^6*Log[f]^3))/(2*b^4*Log[f]^4)","A",1
73,1,41,62,0.0085249,"\int f^{a+b x^2} x^5 \, dx","Integrate[f^(a + b*x^2)*x^5,x]","\frac{f^{a+b x^2} \left(b^2 x^4 \log ^2(f)-2 b x^2 \log (f)+2\right)}{2 b^3 \log ^3(f)}","\frac{f^{a+b x^2}}{b^3 \log ^3(f)}-\frac{x^2 f^{a+b x^2}}{b^2 \log ^2(f)}+\frac{x^4 f^{a+b x^2}}{2 b \log (f)}",1,"(f^(a + b*x^2)*(2 - 2*b*x^2*Log[f] + b^2*x^4*Log[f]^2))/(2*b^3*Log[f]^3)","A",1
74,1,29,44,0.0071056,"\int f^{a+b x^2} x^3 \, dx","Integrate[f^(a + b*x^2)*x^3,x]","\frac{f^{a+b x^2} \left(b x^2 \log (f)-1\right)}{2 b^2 \log ^2(f)}","\frac{x^2 f^{a+b x^2}}{2 b \log (f)}-\frac{f^{a+b x^2}}{2 b^2 \log ^2(f)}",1,"(f^(a + b*x^2)*(-1 + b*x^2*Log[f]))/(2*b^2*Log[f]^2)","A",1
75,1,20,20,0.0024195,"\int f^{a+b x^2} x \, dx","Integrate[f^(a + b*x^2)*x,x]","\frac{f^{a+b x^2}}{2 b \log (f)}","\frac{f^{a+b x^2}}{2 b \log (f)}",1,"f^(a + b*x^2)/(2*b*Log[f])","A",1
76,1,15,15,0.0020819,"\int \frac{f^{a+b x^2}}{x} \, dx","Integrate[f^(a + b*x^2)/x,x]","\frac{1}{2} f^a \text{Ei}\left(b x^2 \log (f)\right)","\frac{1}{2} f^a \text{Ei}\left(b x^2 \log (f)\right)",1,"(f^a*ExpIntegralEi[b*x^2*Log[f]])/2","A",1
77,1,32,35,0.0097732,"\int \frac{f^{a+b x^2}}{x^3} \, dx","Integrate[f^(a + b*x^2)/x^3,x]","\frac{1}{2} f^a \left(b \log (f) \text{Ei}\left(b x^2 \log (f)\right)-\frac{f^{b x^2}}{x^2}\right)","\frac{1}{2} b f^a \log (f) \text{Ei}\left(b x^2 \log (f)\right)-\frac{f^{a+b x^2}}{2 x^2}",1,"(f^a*(-(f^(b*x^2)/x^2) + b*ExpIntegralEi[b*x^2*Log[f]]*Log[f]))/2","A",1
78,1,48,58,0.0186981,"\int \frac{f^{a+b x^2}}{x^5} \, dx","Integrate[f^(a + b*x^2)/x^5,x]","\frac{f^a \left(b^2 x^4 \log ^2(f) \text{Ei}\left(b x^2 \log (f)\right)-f^{b x^2} \left(b x^2 \log (f)+1\right)\right)}{4 x^4}","\frac{1}{4} b^2 f^a \log ^2(f) \text{Ei}\left(b x^2 \log (f)\right)-\frac{b \log (f) f^{a+b x^2}}{4 x^2}-\frac{f^{a+b x^2}}{4 x^4}",1,"(f^a*(b^2*x^4*ExpIntegralEi[b*x^2*Log[f]]*Log[f]^2 - f^(b*x^2)*(1 + b*x^2*Log[f])))/(4*x^4)","A",1
79,1,59,81,0.0235644,"\int \frac{f^{a+b x^2}}{x^7} \, dx","Integrate[f^(a + b*x^2)/x^7,x]","\frac{f^a \left(b^3 x^6 \log ^3(f) \text{Ei}\left(b x^2 \log (f)\right)-f^{b x^2} \left(b^2 x^4 \log ^2(f)+b x^2 \log (f)+2\right)\right)}{12 x^6}","\frac{1}{12} b^3 f^a \log ^3(f) \text{Ei}\left(b x^2 \log (f)\right)-\frac{b^2 \log ^2(f) f^{a+b x^2}}{12 x^2}-\frac{f^{a+b x^2}}{6 x^6}-\frac{b \log (f) f^{a+b x^2}}{12 x^4}",1,"(f^a*(b^3*x^6*ExpIntegralEi[b*x^2*Log[f]]*Log[f]^3 - f^(b*x^2)*(2 + b*x^2*Log[f] + b^2*x^4*Log[f]^2)))/(12*x^6)","A",1
80,1,24,24,0.0025482,"\int \frac{f^{a+b x^2}}{x^9} \, dx","Integrate[f^(a + b*x^2)/x^9,x]","-\frac{1}{2} b^4 f^a \log ^4(f) \Gamma \left(-4,-b x^2 \log (f)\right)","-\frac{1}{2} b^4 f^a \log ^4(f) \Gamma \left(-4,-b x^2 \log (f)\right)",1,"-1/2*(b^4*f^a*Gamma[-4, -(b*x^2*Log[f])]*Log[f]^4)","A",1
81,1,24,24,0.0025015,"\int \frac{f^{a+b x^2}}{x^{11}} \, dx","Integrate[f^(a + b*x^2)/x^11,x]","\frac{1}{2} b^5 f^a \log ^5(f) \Gamma \left(-5,-b x^2 \log (f)\right)","\frac{1}{2} b^5 f^a \log ^5(f) \Gamma \left(-5,-b x^2 \log (f)\right)",1,"(b^5*f^a*Gamma[-5, -(b*x^2*Log[f])]*Log[f]^5)/2","A",1
82,1,34,34,0.0063401,"\int f^{a+b x^2} x^{12} \, dx","Integrate[f^(a + b*x^2)*x^12,x]","-\frac{x^{13} f^a \Gamma \left(\frac{13}{2},-b x^2 \log (f)\right)}{2 \left(-b x^2 \log (f)\right)^{13/2}}","-\frac{x^{13} f^a \Gamma \left(\frac{13}{2},-b x^2 \log (f)\right)}{2 \left(-b x^2 \log (f)\right)^{13/2}}",1,"-1/2*(f^a*x^13*Gamma[13/2, -(b*x^2*Log[f])])/(-(b*x^2*Log[f]))^(13/2)","A",1
83,1,34,34,0.0060768,"\int f^{a+b x^2} x^{10} \, dx","Integrate[f^(a + b*x^2)*x^10,x]","-\frac{x^{11} f^a \Gamma \left(\frac{11}{2},-b x^2 \log (f)\right)}{2 \left(-b x^2 \log (f)\right)^{11/2}}","-\frac{x^{11} f^a \Gamma \left(\frac{11}{2},-b x^2 \log (f)\right)}{2 \left(-b x^2 \log (f)\right)^{11/2}}",1,"-1/2*(f^a*x^11*Gamma[11/2, -(b*x^2*Log[f])])/(-(b*x^2*Log[f]))^(11/2)","A",1
84,1,95,128,0.0433347,"\int f^{a+b x^2} x^8 \, dx","Integrate[f^(a + b*x^2)*x^8,x]","\frac{f^a \left(2 \sqrt{b} x \sqrt{\log (f)} f^{b x^2} \left(8 b^3 x^6 \log ^3(f)-28 b^2 x^4 \log ^2(f)+70 b x^2 \log (f)-105\right)+105 \sqrt{\pi } \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)\right)}{32 b^{9/2} \log ^{\frac{9}{2}}(f)}","\frac{105 \sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)}{32 b^{9/2} \log ^{\frac{9}{2}}(f)}-\frac{105 x f^{a+b x^2}}{16 b^4 \log ^4(f)}+\frac{35 x^3 f^{a+b x^2}}{8 b^3 \log ^3(f)}-\frac{7 x^5 f^{a+b x^2}}{4 b^2 \log ^2(f)}+\frac{x^7 f^{a+b x^2}}{2 b \log (f)}",1,"(f^a*(105*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]] + 2*Sqrt[b]*f^(b*x^2)*x*Sqrt[Log[f]]*(-105 + 70*b*x^2*Log[f] - 28*b^2*x^4*Log[f]^2 + 8*b^3*x^6*Log[f]^3)))/(32*b^(9/2)*Log[f]^(9/2))","A",1
85,1,83,105,0.0354125,"\int f^{a+b x^2} x^6 \, dx","Integrate[f^(a + b*x^2)*x^6,x]","\frac{f^a \left(2 \sqrt{b} x \sqrt{\log (f)} f^{b x^2} \left(4 b^2 x^4 \log ^2(f)-10 b x^2 \log (f)+15\right)-15 \sqrt{\pi } \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)\right)}{16 b^{7/2} \log ^{\frac{7}{2}}(f)}","-\frac{15 \sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)}{16 b^{7/2} \log ^{\frac{7}{2}}(f)}+\frac{15 x f^{a+b x^2}}{8 b^3 \log ^3(f)}-\frac{5 x^3 f^{a+b x^2}}{4 b^2 \log ^2(f)}+\frac{x^5 f^{a+b x^2}}{2 b \log (f)}",1,"(f^a*(-15*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]] + 2*Sqrt[b]*f^(b*x^2)*x*Sqrt[Log[f]]*(15 - 10*b*x^2*Log[f] + 4*b^2*x^4*Log[f]^2)))/(16*b^(7/2)*Log[f]^(7/2))","A",1
86,1,71,82,0.0273324,"\int f^{a+b x^2} x^4 \, dx","Integrate[f^(a + b*x^2)*x^4,x]","\frac{f^a \left(3 \sqrt{\pi } \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)+2 \sqrt{b} x \sqrt{\log (f)} f^{b x^2} \left(2 b x^2 \log (f)-3\right)\right)}{8 b^{5/2} \log ^{\frac{5}{2}}(f)}","\frac{3 \sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)}{8 b^{5/2} \log ^{\frac{5}{2}}(f)}-\frac{3 x f^{a+b x^2}}{4 b^2 \log ^2(f)}+\frac{x^3 f^{a+b x^2}}{2 b \log (f)}",1,"(f^a*(3*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]] + 2*Sqrt[b]*f^(b*x^2)*x*Sqrt[Log[f]]*(-3 + 2*b*x^2*Log[f])))/(8*b^(5/2)*Log[f]^(5/2))","A",1
87,1,59,59,0.0234778,"\int f^{a+b x^2} x^2 \, dx","Integrate[f^(a + b*x^2)*x^2,x]","\frac{x f^{a+b x^2}}{2 b \log (f)}-\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)}{4 b^{3/2} \log ^{\frac{3}{2}}(f)}","\frac{x f^{a+b x^2}}{2 b \log (f)}-\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)}{4 b^{3/2} \log ^{\frac{3}{2}}(f)}",1,"-1/4*(f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]])/(b^(3/2)*Log[f]^(3/2)) + (f^(a + b*x^2)*x)/(2*b*Log[f])","A",1
88,1,37,37,0.0047116,"\int f^{a+b x^2} \, dx","Integrate[f^(a + b*x^2),x]","\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)}{2 \sqrt{b} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)}{2 \sqrt{b} \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]])/(2*Sqrt[b]*Sqrt[Log[f]])","A",1
89,1,49,49,0.0148509,"\int \frac{f^{a+b x^2}}{x^2} \, dx","Integrate[f^(a + b*x^2)/x^2,x]","\sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)-\frac{f^{a+b x^2}}{x}","\sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)-\frac{f^{a+b x^2}}{x}",1,"-(f^(a + b*x^2)/x) + Sqrt[b]*f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]]*Sqrt[Log[f]]","A",1
90,1,62,73,0.0438898,"\int \frac{f^{a+b x^2}}{x^4} \, dx","Integrate[f^(a + b*x^2)/x^4,x]","\frac{1}{3} f^a \left(2 \sqrt{\pi } b^{3/2} \log ^{\frac{3}{2}}(f) \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)-\frac{f^{b x^2} \left(2 b x^2 \log (f)+1\right)}{x^3}\right)","\frac{2}{3} \sqrt{\pi } b^{3/2} f^a \log ^{\frac{3}{2}}(f) \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)-\frac{2 b \log (f) f^{a+b x^2}}{3 x}-\frac{f^{a+b x^2}}{3 x^3}",1,"(f^a*(2*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]]*Log[f]^(3/2) - (f^(b*x^2)*(1 + 2*b*x^2*Log[f]))/x^3))/3","A",1
91,1,77,96,0.035506,"\int \frac{f^{a+b x^2}}{x^6} \, dx","Integrate[f^(a + b*x^2)/x^6,x]","\frac{f^a \left(4 \sqrt{\pi } b^{5/2} x^5 \log ^{\frac{5}{2}}(f) \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)-f^{b x^2} \left(4 b^2 x^4 \log ^2(f)+2 b x^2 \log (f)+3\right)\right)}{15 x^5}","\frac{4}{15} \sqrt{\pi } b^{5/2} f^a \log ^{\frac{5}{2}}(f) \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)-\frac{4 b^2 \log ^2(f) f^{a+b x^2}}{15 x}-\frac{f^{a+b x^2}}{5 x^5}-\frac{2 b \log (f) f^{a+b x^2}}{15 x^3}",1,"(f^a*(4*b^(5/2)*Sqrt[Pi]*x^5*Erfi[Sqrt[b]*x*Sqrt[Log[f]]]*Log[f]^(5/2) - f^(b*x^2)*(3 + 2*b*x^2*Log[f] + 4*b^2*x^4*Log[f]^2)))/(15*x^5)","A",1
92,1,89,119,0.0425622,"\int \frac{f^{a+b x^2}}{x^8} \, dx","Integrate[f^(a + b*x^2)/x^8,x]","\frac{f^a \left(8 \sqrt{\pi } b^{7/2} x^7 \log ^{\frac{7}{2}}(f) \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)-f^{b x^2} \left(8 b^3 x^6 \log ^3(f)+4 b^2 x^4 \log ^2(f)+6 b x^2 \log (f)+15\right)\right)}{105 x^7}","\frac{8}{105} \sqrt{\pi } b^{7/2} f^a \log ^{\frac{7}{2}}(f) \text{erfi}\left(\sqrt{b} x \sqrt{\log (f)}\right)-\frac{8 b^3 \log ^3(f) f^{a+b x^2}}{105 x}-\frac{4 b^2 \log ^2(f) f^{a+b x^2}}{105 x^3}-\frac{f^{a+b x^2}}{7 x^7}-\frac{2 b \log (f) f^{a+b x^2}}{35 x^5}",1,"(f^a*(8*b^(7/2)*Sqrt[Pi]*x^7*Erfi[Sqrt[b]*x*Sqrt[Log[f]]]*Log[f]^(7/2) - f^(b*x^2)*(15 + 6*b*x^2*Log[f] + 4*b^2*x^4*Log[f]^2 + 8*b^3*x^6*Log[f]^3)))/(105*x^7)","A",1
93,1,34,34,0.0060767,"\int \frac{f^{a+b x^2}}{x^{10}} \, dx","Integrate[f^(a + b*x^2)/x^10,x]","-\frac{f^a \left(-b x^2 \log (f)\right)^{9/2} \Gamma \left(-\frac{9}{2},-b x^2 \log (f)\right)}{2 x^9}","-\frac{f^a \left(-b x^2 \log (f)\right)^{9/2} \Gamma \left(-\frac{9}{2},-b x^2 \log (f)\right)}{2 x^9}",1,"-1/2*(f^a*Gamma[-9/2, -(b*x^2*Log[f])]*(-(b*x^2*Log[f]))^(9/2))/x^9","A",1
94,1,34,34,0.0055716,"\int \frac{f^{a+b x^2}}{x^{12}} \, dx","Integrate[f^(a + b*x^2)/x^12,x]","-\frac{f^a \left(-b x^2 \log (f)\right)^{11/2} \Gamma \left(-\frac{11}{2},-b x^2 \log (f)\right)}{2 x^{11}}","-\frac{f^a \left(-b x^2 \log (f)\right)^{11/2} \Gamma \left(-\frac{11}{2},-b x^2 \log (f)\right)}{2 x^{11}}",1,"-1/2*(f^a*Gamma[-11/2, -(b*x^2*Log[f])]*(-(b*x^2*Log[f]))^(11/2))/x^11","A",1
95,1,46,46,0.0117114,"\int f^{a+b x^3} x^m \, dx","Integrate[f^(a + b*x^3)*x^m,x]","-\frac{1}{3} f^a x^{m+1} \left(-b x^3 \log (f)\right)^{\frac{1}{3} (-m-1)} \Gamma \left(\frac{m+1}{3},-b x^3 \log (f)\right)","-\frac{1}{3} f^a x^{m+1} \left(-b x^3 \log (f)\right)^{\frac{1}{3} (-m-1)} \Gamma \left(\frac{m+1}{3},-b x^3 \log (f)\right)",1,"-1/3*(f^a*x^(1 + m)*Gamma[(1 + m)/3, -(b*x^3*Log[f])]*(-(b*x^3*Log[f]))^((-1 - m)/3))","A",1
96,1,24,78,0.0032526,"\int f^{a+b x^3} x^{17} \, dx","Integrate[f^(a + b*x^3)*x^17,x]","-\frac{f^a \Gamma \left(6,-b x^3 \log (f)\right)}{3 b^6 \log ^6(f)}","-\frac{f^{a+b x^3} \left(-b^5 x^{15} \log ^5(f)+5 b^4 x^{12} \log ^4(f)-20 b^3 x^9 \log ^3(f)+60 b^2 x^6 \log ^2(f)-120 b x^3 \log (f)+120\right)}{3 b^6 \log ^6(f)}",1,"-1/3*(f^a*Gamma[6, -(b*x^3*Log[f])])/(b^6*Log[f]^6)","C",1
97,1,24,65,0.003096,"\int f^{a+b x^3} x^{14} \, dx","Integrate[f^(a + b*x^3)*x^14,x]","\frac{f^a \Gamma \left(5,-b x^3 \log (f)\right)}{3 b^5 \log ^5(f)}","\frac{f^{a+b x^3} \left(b^4 x^{12} \log ^4(f)-4 b^3 x^9 \log ^3(f)+12 b^2 x^6 \log ^2(f)-24 b x^3 \log (f)+24\right)}{3 b^5 \log ^5(f)}",1,"(f^a*Gamma[5, -(b*x^3*Log[f])])/(3*b^5*Log[f]^5)","C",1
98,1,53,84,0.0113845,"\int f^{a+b x^3} x^{11} \, dx","Integrate[f^(a + b*x^3)*x^11,x]","\frac{f^{a+b x^3} \left(b^3 x^9 \log ^3(f)-3 b^2 x^6 \log ^2(f)+6 b x^3 \log (f)-6\right)}{3 b^4 \log ^4(f)}","-\frac{2 f^{a+b x^3}}{b^4 \log ^4(f)}+\frac{2 x^3 f^{a+b x^3}}{b^3 \log ^3(f)}-\frac{x^6 f^{a+b x^3}}{b^2 \log ^2(f)}+\frac{x^9 f^{a+b x^3}}{3 b \log (f)}",1,"(f^(a + b*x^3)*(-6 + 6*b*x^3*Log[f] - 3*b^2*x^6*Log[f]^2 + b^3*x^9*Log[f]^3))/(3*b^4*Log[f]^4)","A",1
99,1,41,67,0.0093527,"\int f^{a+b x^3} x^8 \, dx","Integrate[f^(a + b*x^3)*x^8,x]","\frac{f^{a+b x^3} \left(b^2 x^6 \log ^2(f)-2 b x^3 \log (f)+2\right)}{3 b^3 \log ^3(f)}","\frac{2 f^{a+b x^3}}{3 b^3 \log ^3(f)}-\frac{2 x^3 f^{a+b x^3}}{3 b^2 \log ^2(f)}+\frac{x^6 f^{a+b x^3}}{3 b \log (f)}",1,"(f^(a + b*x^3)*(2 - 2*b*x^3*Log[f] + b^2*x^6*Log[f]^2))/(3*b^3*Log[f]^3)","A",1
100,1,29,44,0.0070841,"\int f^{a+b x^3} x^5 \, dx","Integrate[f^(a + b*x^3)*x^5,x]","\frac{f^{a+b x^3} \left(b x^3 \log (f)-1\right)}{3 b^2 \log ^2(f)}","\frac{x^3 f^{a+b x^3}}{3 b \log (f)}-\frac{f^{a+b x^3}}{3 b^2 \log ^2(f)}",1,"(f^(a + b*x^3)*(-1 + b*x^3*Log[f]))/(3*b^2*Log[f]^2)","A",1
101,1,20,20,0.0026501,"\int f^{a+b x^3} x^2 \, dx","Integrate[f^(a + b*x^3)*x^2,x]","\frac{f^{a+b x^3}}{3 b \log (f)}","\frac{f^{a+b x^3}}{3 b \log (f)}",1,"f^(a + b*x^3)/(3*b*Log[f])","A",1
102,1,15,15,0.0021105,"\int \frac{f^{a+b x^3}}{x} \, dx","Integrate[f^(a + b*x^3)/x,x]","\frac{1}{3} f^a \text{Ei}\left(b x^3 \log (f)\right)","\frac{1}{3} f^a \text{Ei}\left(b x^3 \log (f)\right)",1,"(f^a*ExpIntegralEi[b*x^3*Log[f]])/3","A",1
103,1,32,35,0.009584,"\int \frac{f^{a+b x^3}}{x^4} \, dx","Integrate[f^(a + b*x^3)/x^4,x]","\frac{1}{3} f^a \left(b \log (f) \text{Ei}\left(b x^3 \log (f)\right)-\frac{f^{b x^3}}{x^3}\right)","\frac{1}{3} b f^a \log (f) \text{Ei}\left(b x^3 \log (f)\right)-\frac{f^{a+b x^3}}{3 x^3}",1,"(f^a*(-(f^(b*x^3)/x^3) + b*ExpIntegralEi[b*x^3*Log[f]]*Log[f]))/3","A",1
104,1,48,58,0.0190748,"\int \frac{f^{a+b x^3}}{x^7} \, dx","Integrate[f^(a + b*x^3)/x^7,x]","\frac{f^a \left(b^2 x^6 \log ^2(f) \text{Ei}\left(b x^3 \log (f)\right)-f^{b x^3} \left(b x^3 \log (f)+1\right)\right)}{6 x^6}","\frac{1}{6} b^2 f^a \log ^2(f) \text{Ei}\left(b x^3 \log (f)\right)-\frac{b \log (f) f^{a+b x^3}}{6 x^3}-\frac{f^{a+b x^3}}{6 x^6}",1,"(f^a*(b^2*x^6*ExpIntegralEi[b*x^3*Log[f]]*Log[f]^2 - f^(b*x^3)*(1 + b*x^3*Log[f])))/(6*x^6)","A",1
105,1,59,81,0.0243592,"\int \frac{f^{a+b x^3}}{x^{10}} \, dx","Integrate[f^(a + b*x^3)/x^10,x]","\frac{f^a \left(b^3 x^9 \log ^3(f) \text{Ei}\left(b x^3 \log (f)\right)-f^{b x^3} \left(b^2 x^6 \log ^2(f)+b x^3 \log (f)+2\right)\right)}{18 x^9}","\frac{1}{18} b^3 f^a \log ^3(f) \text{Ei}\left(b x^3 \log (f)\right)-\frac{b^2 \log ^2(f) f^{a+b x^3}}{18 x^3}-\frac{f^{a+b x^3}}{9 x^9}-\frac{b \log (f) f^{a+b x^3}}{18 x^6}",1,"(f^a*(b^3*x^9*ExpIntegralEi[b*x^3*Log[f]]*Log[f]^3 - f^(b*x^3)*(2 + b*x^3*Log[f] + b^2*x^6*Log[f]^2)))/(18*x^9)","A",1
106,1,24,24,0.002488,"\int \frac{f^{a+b x^3}}{x^{13}} \, dx","Integrate[f^(a + b*x^3)/x^13,x]","-\frac{1}{3} b^4 f^a \log ^4(f) \Gamma \left(-4,-b x^3 \log (f)\right)","-\frac{1}{3} b^4 f^a \log ^4(f) \Gamma \left(-4,-b x^3 \log (f)\right)",1,"-1/3*(b^4*f^a*Gamma[-4, -(b*x^3*Log[f])]*Log[f]^4)","A",1
107,1,24,24,0.0025766,"\int \frac{f^{a+b x^3}}{x^{16}} \, dx","Integrate[f^(a + b*x^3)/x^16,x]","\frac{1}{3} b^5 f^a \log ^5(f) \Gamma \left(-5,-b x^3 \log (f)\right)","\frac{1}{3} b^5 f^a \log ^5(f) \Gamma \left(-5,-b x^3 \log (f)\right)",1,"(b^5*f^a*Gamma[-5, -(b*x^3*Log[f])]*Log[f]^5)/3","A",1
108,1,34,34,0.0058863,"\int f^{a+b x^3} x^4 \, dx","Integrate[f^(a + b*x^3)*x^4,x]","-\frac{x^5 f^a \Gamma \left(\frac{5}{3},-b x^3 \log (f)\right)}{3 \left(-b x^3 \log (f)\right)^{5/3}}","-\frac{x^5 f^a \Gamma \left(\frac{5}{3},-b x^3 \log (f)\right)}{3 \left(-b x^3 \log (f)\right)^{5/3}}",1,"-1/3*(f^a*x^5*Gamma[5/3, -(b*x^3*Log[f])])/(-(b*x^3*Log[f]))^(5/3)","A",1
109,1,34,34,0.0056849,"\int f^{a+b x^3} x^3 \, dx","Integrate[f^(a + b*x^3)*x^3,x]","-\frac{x^4 f^a \Gamma \left(\frac{4}{3},-b x^3 \log (f)\right)}{3 \left(-b x^3 \log (f)\right)^{4/3}}","-\frac{x^4 f^a \Gamma \left(\frac{4}{3},-b x^3 \log (f)\right)}{3 \left(-b x^3 \log (f)\right)^{4/3}}",1,"-1/3*(f^a*x^4*Gamma[4/3, -(b*x^3*Log[f])])/(-(b*x^3*Log[f]))^(4/3)","A",1
110,1,34,34,0.0051581,"\int f^{a+b x^3} x \, dx","Integrate[f^(a + b*x^3)*x,x]","-\frac{x^2 f^a \Gamma \left(\frac{2}{3},-b x^3 \log (f)\right)}{3 \left(-b x^3 \log (f)\right)^{2/3}}","-\frac{x^2 f^a \Gamma \left(\frac{2}{3},-b x^3 \log (f)\right)}{3 \left(-b x^3 \log (f)\right)^{2/3}}",1,"-1/3*(f^a*x^2*Gamma[2/3, -(b*x^3*Log[f])])/(-(b*x^3*Log[f]))^(2/3)","A",1
111,1,32,32,0.0043266,"\int f^{a+b x^3} \, dx","Integrate[f^(a + b*x^3),x]","-\frac{x f^a \Gamma \left(\frac{1}{3},-b x^3 \log (f)\right)}{3 \sqrt[3]{-b x^3 \log (f)}}","-\frac{x f^a \Gamma \left(\frac{1}{3},-b x^3 \log (f)\right)}{3 \sqrt[3]{-b x^3 \log (f)}}",1,"-1/3*(f^a*x*Gamma[1/3, -(b*x^3*Log[f])])/(-(b*x^3*Log[f]))^(1/3)","A",1
112,1,34,34,0.003836,"\int \frac{f^{a+b x^3}}{x^2} \, dx","Integrate[f^(a + b*x^3)/x^2,x]","-\frac{f^a \sqrt[3]{-b x^3 \log (f)} \Gamma \left(-\frac{1}{3},-b x^3 \log (f)\right)}{3 x}","-\frac{f^a \sqrt[3]{-b x^3 \log (f)} \Gamma \left(-\frac{1}{3},-b x^3 \log (f)\right)}{3 x}",1,"-1/3*(f^a*Gamma[-1/3, -(b*x^3*Log[f])]*(-(b*x^3*Log[f]))^(1/3))/x","A",1
113,1,34,34,0.0040194,"\int \frac{f^{a+b x^3}}{x^3} \, dx","Integrate[f^(a + b*x^3)/x^3,x]","-\frac{f^a \left(-b x^3 \log (f)\right)^{2/3} \Gamma \left(-\frac{2}{3},-b x^3 \log (f)\right)}{3 x^2}","-\frac{f^a \left(-b x^3 \log (f)\right)^{2/3} \Gamma \left(-\frac{2}{3},-b x^3 \log (f)\right)}{3 x^2}",1,"-1/3*(f^a*Gamma[-2/3, -(b*x^3*Log[f])]*(-(b*x^3*Log[f]))^(2/3))/x^2","A",1
114,1,11,11,0.002049,"\int e^{4 x^3} x^2 \, dx","Integrate[E^(4*x^3)*x^2,x]","\frac{e^{4 x^3}}{12}","\frac{e^{4 x^3}}{12}",1,"E^(4*x^3)/12","A",1
115,1,35,35,0.0076044,"\int f^{a+\frac{b}{x}} x^m \, dx","Integrate[f^(a + b/x)*x^m,x]","f^a x^{m+1} \left(-\frac{b \log (f)}{x}\right)^{m+1} \Gamma \left(-m-1,-\frac{b \log (f)}{x}\right)","f^a x^{m+1} \left(-\frac{b \log (f)}{x}\right)^{m+1} \Gamma \left(-m-1,-\frac{b \log (f)}{x}\right)",1,"f^a*x^(1 + m)*Gamma[-1 - m, -((b*Log[f])/x)]*(-((b*Log[f])/x))^(1 + m)","A",1
116,1,22,22,0.0023939,"\int f^{a+\frac{b}{x}} x^4 \, dx","Integrate[f^(a + b/x)*x^4,x]","-b^5 f^a \log ^5(f) \Gamma \left(-5,-\frac{b \log (f)}{x}\right)","-b^5 f^a \log ^5(f) \Gamma \left(-5,-\frac{b \log (f)}{x}\right)",1,"-(b^5*f^a*Gamma[-5, -((b*Log[f])/x)]*Log[f]^5)","A",1
117,1,21,21,0.0024589,"\int f^{a+\frac{b}{x}} x^3 \, dx","Integrate[f^(a + b/x)*x^3,x]","b^4 f^a \log ^4(f) \Gamma \left(-4,-\frac{b \log (f)}{x}\right)","b^4 f^a \log ^4(f) \Gamma \left(-4,-\frac{b \log (f)}{x}\right)",1,"b^4*f^a*Gamma[-4, -((b*Log[f])/x)]*Log[f]^4","A",1
118,1,53,79,0.0247323,"\int f^{a+\frac{b}{x}} x^2 \, dx","Integrate[f^(a + b/x)*x^2,x]","\frac{1}{6} f^a \left(x f^{b/x} \left(b^2 \log ^2(f)+b x \log (f)+2 x^2\right)-b^3 \log ^3(f) \text{Ei}\left(\frac{b \log (f)}{x}\right)\right)","-\frac{1}{6} b^3 f^a \log ^3(f) \text{Ei}\left(\frac{b \log (f)}{x}\right)+\frac{1}{6} b^2 x \log ^2(f) f^{a+\frac{b}{x}}+\frac{1}{3} x^3 f^{a+\frac{b}{x}}+\frac{1}{6} b x^2 \log (f) f^{a+\frac{b}{x}}",1,"(f^a*(-(b^3*ExpIntegralEi[(b*Log[f])/x]*Log[f]^3) + f^(b/x)*x*(2*x^2 + b*x*Log[f] + b^2*Log[f]^2)))/6","A",1
119,1,40,56,0.0187783,"\int f^{a+\frac{b}{x}} x \, dx","Integrate[f^(a + b/x)*x,x]","\frac{1}{2} f^a \left(x f^{b/x} (b \log (f)+x)-b^2 \log ^2(f) \text{Ei}\left(\frac{b \log (f)}{x}\right)\right)","-\frac{1}{2} b^2 f^a \log ^2(f) \text{Ei}\left(\frac{b \log (f)}{x}\right)+\frac{1}{2} x^2 f^{a+\frac{b}{x}}+\frac{1}{2} b x \log (f) f^{a+\frac{b}{x}}",1,"(f^a*(-(b^2*ExpIntegralEi[(b*Log[f])/x]*Log[f]^2) + f^(b/x)*x*(x + b*Log[f])))/2","A",1
120,1,28,28,0.0074401,"\int f^{a+\frac{b}{x}} \, dx","Integrate[f^(a + b/x),x]","x f^{a+\frac{b}{x}}-b f^a \log (f) \text{Ei}\left(\frac{b \log (f)}{x}\right)","x f^{a+\frac{b}{x}}-b f^a \log (f) \text{Ei}\left(\frac{b \log (f)}{x}\right)",1,"f^(a + b/x)*x - b*f^a*ExpIntegralEi[(b*Log[f])/x]*Log[f]","A",1
121,1,13,13,0.0021987,"\int \frac{f^{a+\frac{b}{x}}}{x} \, dx","Integrate[f^(a + b/x)/x,x]","-f^a \text{Ei}\left(\frac{b \log (f)}{x}\right)","-f^a \text{Ei}\left(\frac{b \log (f)}{x}\right)",1,"-(f^a*ExpIntegralEi[(b*Log[f])/x])","A",1
122,1,18,18,0.0034378,"\int \frac{f^{a+\frac{b}{x}}}{x^2} \, dx","Integrate[f^(a + b/x)/x^2,x]","-\frac{f^{a+\frac{b}{x}}}{b \log (f)}","-\frac{f^{a+\frac{b}{x}}}{b \log (f)}",1,"-(f^(a + b/x)/(b*Log[f]))","A",1
123,1,27,39,0.0062909,"\int \frac{f^{a+\frac{b}{x}}}{x^3} \, dx","Integrate[f^(a + b/x)/x^3,x]","\frac{f^{a+\frac{b}{x}} (x-b \log (f))}{b^2 x \log ^2(f)}","\frac{f^{a+\frac{b}{x}}}{b^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x}}}{b x \log (f)}",1,"(f^(a + b/x)*(x - b*Log[f]))/(b^2*x*Log[f]^2)","A",1
124,1,41,61,0.0083717,"\int \frac{f^{a+\frac{b}{x}}}{x^4} \, dx","Integrate[f^(a + b/x)/x^4,x]","-\frac{f^{a+\frac{b}{x}} \left(b^2 \log ^2(f)-2 b x \log (f)+2 x^2\right)}{b^3 x^2 \log ^3(f)}","-\frac{2 f^{a+\frac{b}{x}}}{b^3 \log ^3(f)}+\frac{2 f^{a+\frac{b}{x}}}{b^2 x \log ^2(f)}-\frac{f^{a+\frac{b}{x}}}{b x^2 \log (f)}",1,"-((f^(a + b/x)*(2*x^2 - 2*b*x*Log[f] + b^2*Log[f]^2))/(b^3*x^2*Log[f]^3))","A",1
125,1,53,82,0.0104996,"\int \frac{f^{a+\frac{b}{x}}}{x^5} \, dx","Integrate[f^(a + b/x)/x^5,x]","\frac{f^{a+\frac{b}{x}} \left(-b^3 \log ^3(f)+3 b^2 x \log ^2(f)-6 b x^2 \log (f)+6 x^3\right)}{b^4 x^3 \log ^4(f)}","\frac{6 f^{a+\frac{b}{x}}}{b^4 \log ^4(f)}-\frac{6 f^{a+\frac{b}{x}}}{b^3 x \log ^3(f)}+\frac{3 f^{a+\frac{b}{x}}}{b^2 x^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x}}}{b x^3 \log (f)}",1,"(f^(a + b/x)*(6*x^3 - 6*b*x^2*Log[f] + 3*b^2*x*Log[f]^2 - b^3*Log[f]^3))/(b^4*x^3*Log[f]^4)","A",1
126,1,22,65,0.0027889,"\int \frac{f^{a+\frac{b}{x}}}{x^6} \, dx","Integrate[f^(a + b/x)/x^6,x]","-\frac{f^a \Gamma \left(5,-\frac{b \log (f)}{x}\right)}{b^5 \log ^5(f)}","-\frac{f^{a+\frac{b}{x}} \left(b^4 \log ^4(f)-4 b^3 x \log ^3(f)+12 b^2 x^2 \log ^2(f)-24 b x^3 \log (f)+24 x^4\right)}{b^5 x^4 \log ^5(f)}",1,"-((f^a*Gamma[5, -((b*Log[f])/x)])/(b^5*Log[f]^5))","C",1
127,1,21,77,0.0028624,"\int \frac{f^{a+\frac{b}{x}}}{x^7} \, dx","Integrate[f^(a + b/x)/x^7,x]","\frac{f^a \Gamma \left(6,-\frac{b \log (f)}{x}\right)}{b^6 \log ^6(f)}","\frac{f^{a+\frac{b}{x}} \left(-b^5 \log ^5(f)+5 b^4 x \log ^4(f)-20 b^3 x^2 \log ^3(f)+60 b^2 x^3 \log ^2(f)-120 b x^4 \log (f)+120 x^5\right)}{b^6 x^5 \log ^6(f)}",1,"(f^a*Gamma[6, -((b*Log[f])/x)])/(b^6*Log[f]^6)","C",1
128,1,46,46,0.0110854,"\int f^{a+\frac{b}{x^2}} x^m \, dx","Integrate[f^(a + b/x^2)*x^m,x]","\frac{1}{2} f^a x^{m+1} \left(-\frac{b \log (f)}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),-\frac{b \log (f)}{x^2}\right)","\frac{1}{2} f^a x^{m+1} \left(-\frac{b \log (f)}{x^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),-\frac{b \log (f)}{x^2}\right)",1,"(f^a*x^(1 + m)*Gamma[(-1 - m)/2, -((b*Log[f])/x^2)]*(-((b*Log[f])/x^2))^((1 + m)/2))/2","A",1
129,1,24,24,0.0025571,"\int f^{a+\frac{b}{x^2}} x^9 \, dx","Integrate[f^(a + b/x^2)*x^9,x]","-\frac{1}{2} b^5 f^a \log ^5(f) \Gamma \left(-5,-\frac{b \log (f)}{x^2}\right)","-\frac{1}{2} b^5 f^a \log ^5(f) \Gamma \left(-5,-\frac{b \log (f)}{x^2}\right)",1,"-1/2*(b^5*f^a*Gamma[-5, -((b*Log[f])/x^2)]*Log[f]^5)","A",1
130,1,24,24,0.0025611,"\int f^{a+\frac{b}{x^2}} x^7 \, dx","Integrate[f^(a + b/x^2)*x^7,x]","\frac{1}{2} b^4 f^a \log ^4(f) \Gamma \left(-4,-\frac{b \log (f)}{x^2}\right)","\frac{1}{2} b^4 f^a \log ^4(f) \Gamma \left(-4,-\frac{b \log (f)}{x^2}\right)",1,"(b^4*f^a*Gamma[-4, -((b*Log[f])/x^2)]*Log[f]^4)/2","A",1
131,1,57,81,0.0210676,"\int f^{a+\frac{b}{x^2}} x^5 \, dx","Integrate[f^(a + b/x^2)*x^5,x]","\frac{1}{12} f^a \left(x^2 f^{\frac{b}{x^2}} \left(b^2 \log ^2(f)+b x^2 \log (f)+2 x^4\right)-b^3 \log ^3(f) \text{Ei}\left(\frac{b \log (f)}{x^2}\right)\right)","-\frac{1}{12} b^3 f^a \log ^3(f) \text{Ei}\left(\frac{b \log (f)}{x^2}\right)+\frac{1}{12} b^2 x^2 \log ^2(f) f^{a+\frac{b}{x^2}}+\frac{1}{6} x^6 f^{a+\frac{b}{x^2}}+\frac{1}{12} b x^4 \log (f) f^{a+\frac{b}{x^2}}",1,"(f^a*(-(b^3*ExpIntegralEi[(b*Log[f])/x^2]*Log[f]^3) + f^(b/x^2)*x^2*(2*x^4 + b*x^2*Log[f] + b^2*Log[f]^2)))/12","A",1
132,1,44,58,0.0146552,"\int f^{a+\frac{b}{x^2}} x^3 \, dx","Integrate[f^(a + b/x^2)*x^3,x]","\frac{1}{4} f^a \left(x^2 f^{\frac{b}{x^2}} \left(b \log (f)+x^2\right)-b^2 \log ^2(f) \text{Ei}\left(\frac{b \log (f)}{x^2}\right)\right)","-\frac{1}{4} b^2 f^a \log ^2(f) \text{Ei}\left(\frac{b \log (f)}{x^2}\right)+\frac{1}{4} b x^2 \log (f) f^{a+\frac{b}{x^2}}+\frac{1}{4} x^4 f^{a+\frac{b}{x^2}}",1,"(f^a*(-(b^2*ExpIntegralEi[(b*Log[f])/x^2]*Log[f]^2) + f^(b/x^2)*x^2*(x^2 + b*Log[f])))/4","A",1
133,1,32,35,0.0053501,"\int f^{a+\frac{b}{x^2}} x \, dx","Integrate[f^(a + b/x^2)*x,x]","\frac{1}{2} f^a \left(x^2 f^{\frac{b}{x^2}}-b \log (f) \text{Ei}\left(\frac{b \log (f)}{x^2}\right)\right)","\frac{1}{2} x^2 f^{a+\frac{b}{x^2}}-\frac{1}{2} b f^a \log (f) \text{Ei}\left(\frac{b \log (f)}{x^2}\right)",1,"(f^a*(f^(b/x^2)*x^2 - b*ExpIntegralEi[(b*Log[f])/x^2]*Log[f]))/2","A",1
134,1,15,15,0.0024104,"\int \frac{f^{a+\frac{b}{x^2}}}{x} \, dx","Integrate[f^(a + b/x^2)/x,x]","-\frac{1}{2} f^a \text{Ei}\left(\frac{b \log (f)}{x^2}\right)","-\frac{1}{2} f^a \text{Ei}\left(\frac{b \log (f)}{x^2}\right)",1,"-1/2*(f^a*ExpIntegralEi[(b*Log[f])/x^2])","A",1
135,1,20,20,0.0038875,"\int \frac{f^{a+\frac{b}{x^2}}}{x^3} \, dx","Integrate[f^(a + b/x^2)/x^3,x]","-\frac{f^{a+\frac{b}{x^2}}}{2 b \log (f)}","-\frac{f^{a+\frac{b}{x^2}}}{2 b \log (f)}",1,"-1/2*f^(a + b/x^2)/(b*Log[f])","A",1
136,1,32,44,0.0076315,"\int \frac{f^{a+\frac{b}{x^2}}}{x^5} \, dx","Integrate[f^(a + b/x^2)/x^5,x]","\frac{f^{a+\frac{b}{x^2}} \left(x^2-b \log (f)\right)}{2 b^2 x^2 \log ^2(f)}","\frac{f^{a+\frac{b}{x^2}}}{2 b^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^2 \log (f)}",1,"(f^(a + b/x^2)*(x^2 - b*Log[f]))/(2*b^2*x^2*Log[f]^2)","A",1
137,1,45,62,0.008892,"\int \frac{f^{a+\frac{b}{x^2}}}{x^7} \, dx","Integrate[f^(a + b/x^2)/x^7,x]","-\frac{f^{a+\frac{b}{x^2}} \left(b^2 \log ^2(f)-2 b x^2 \log (f)+2 x^4\right)}{2 b^3 x^4 \log ^3(f)}","-\frac{f^{a+\frac{b}{x^2}}}{b^3 \log ^3(f)}+\frac{f^{a+\frac{b}{x^2}}}{b^2 x^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^4 \log (f)}",1,"-1/2*(f^(a + b/x^2)*(2*x^4 - 2*b*x^2*Log[f] + b^2*Log[f]^2))/(b^3*x^4*Log[f]^3)","A",1
138,1,58,86,0.0106022,"\int \frac{f^{a+\frac{b}{x^2}}}{x^9} \, dx","Integrate[f^(a + b/x^2)/x^9,x]","\frac{f^{a+\frac{b}{x^2}} \left(-b^3 \log ^3(f)+3 b^2 x^2 \log ^2(f)-6 b x^4 \log (f)+6 x^6\right)}{2 b^4 x^6 \log ^4(f)}","\frac{3 f^{a+\frac{b}{x^2}}}{b^4 \log ^4(f)}-\frac{3 f^{a+\frac{b}{x^2}}}{b^3 x^2 \log ^3(f)}+\frac{3 f^{a+\frac{b}{x^2}}}{2 b^2 x^4 \log ^2(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^6 \log (f)}",1,"(f^(a + b/x^2)*(6*x^6 - 6*b*x^4*Log[f] + 3*b^2*x^2*Log[f]^2 - b^3*Log[f]^3))/(2*b^4*x^6*Log[f]^4)","A",1
139,1,24,69,0.0029519,"\int \frac{f^{a+\frac{b}{x^2}}}{x^{11}} \, dx","Integrate[f^(a + b/x^2)/x^11,x]","-\frac{f^a \Gamma \left(5,-\frac{b \log (f)}{x^2}\right)}{2 b^5 \log ^5(f)}","-\frac{f^{a+\frac{b}{x^2}} \left(b^4 \log ^4(f)-4 b^3 x^2 \log ^3(f)+12 b^2 x^4 \log ^2(f)-24 b x^6 \log (f)+24 x^8\right)}{2 b^5 x^8 \log ^5(f)}",1,"-1/2*(f^a*Gamma[5, -((b*Log[f])/x^2)])/(b^5*Log[f]^5)","C",1
140,1,24,82,0.0029319,"\int \frac{f^{a+\frac{b}{x^2}}}{x^{13}} \, dx","Integrate[f^(a + b/x^2)/x^13,x]","\frac{f^a \Gamma \left(6,-\frac{b \log (f)}{x^2}\right)}{2 b^6 \log ^6(f)}","\frac{f^{a+\frac{b}{x^2}} \left(-b^5 \log ^5(f)+5 b^4 x^2 \log ^4(f)-20 b^3 x^4 \log ^3(f)+60 b^2 x^6 \log ^2(f)-120 b x^8 \log (f)+120 x^{10}\right)}{2 b^6 x^{10} \log ^6(f)}",1,"(f^a*Gamma[6, -((b*Log[f])/x^2)])/(2*b^6*Log[f]^6)","C",1
141,1,34,34,0.0043266,"\int f^{a+\frac{b}{x^2}} x^{10} \, dx","Integrate[f^(a + b/x^2)*x^10,x]","\frac{1}{2} x^{11} f^a \left(-\frac{b \log (f)}{x^2}\right)^{11/2} \Gamma \left(-\frac{11}{2},-\frac{b \log (f)}{x^2}\right)","\frac{1}{2} x^{11} f^a \left(-\frac{b \log (f)}{x^2}\right)^{11/2} \Gamma \left(-\frac{11}{2},-\frac{b \log (f)}{x^2}\right)",1,"(f^a*x^11*Gamma[-11/2, -((b*Log[f])/x^2)]*(-((b*Log[f])/x^2))^(11/2))/2","A",1
142,1,34,34,0.0043455,"\int f^{a+\frac{b}{x^2}} x^8 \, dx","Integrate[f^(a + b/x^2)*x^8,x]","\frac{1}{2} x^9 f^a \left(-\frac{b \log (f)}{x^2}\right)^{9/2} \Gamma \left(-\frac{9}{2},-\frac{b \log (f)}{x^2}\right)","\frac{1}{2} x^9 f^a \left(-\frac{b \log (f)}{x^2}\right)^{9/2} \Gamma \left(-\frac{9}{2},-\frac{b \log (f)}{x^2}\right)",1,"(f^a*x^9*Gamma[-9/2, -((b*Log[f])/x^2)]*(-((b*Log[f])/x^2))^(9/2))/2","A",1
143,1,86,119,0.0374628,"\int f^{a+\frac{b}{x^2}} x^6 \, dx","Integrate[f^(a + b/x^2)*x^6,x]","\frac{1}{105} f^a \left(x f^{\frac{b}{x^2}} \left(8 b^3 \log ^3(f)+4 b^2 x^2 \log ^2(f)+6 b x^4 \log (f)+15 x^6\right)-8 \sqrt{\pi } b^{7/2} \log ^{\frac{7}{2}}(f) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)\right)","-\frac{8}{105} \sqrt{\pi } b^{7/2} f^a \log ^{\frac{7}{2}}(f) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)+\frac{8}{105} b^3 x \log ^3(f) f^{a+\frac{b}{x^2}}+\frac{4}{105} b^2 x^3 \log ^2(f) f^{a+\frac{b}{x^2}}+\frac{1}{7} x^7 f^{a+\frac{b}{x^2}}+\frac{2}{35} b x^5 \log (f) f^{a+\frac{b}{x^2}}",1,"(f^a*(-8*b^(7/2)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x]*Log[f]^(7/2) + f^(b/x^2)*x*(15*x^6 + 6*b*x^4*Log[f] + 4*b^2*x^2*Log[f]^2 + 8*b^3*Log[f]^3)))/105","A",1
144,1,74,96,0.0322968,"\int f^{a+\frac{b}{x^2}} x^4 \, dx","Integrate[f^(a + b/x^2)*x^4,x]","\frac{1}{15} f^a \left(x f^{\frac{b}{x^2}} \left(4 b^2 \log ^2(f)+2 b x^2 \log (f)+3 x^4\right)-4 \sqrt{\pi } b^{5/2} \log ^{\frac{5}{2}}(f) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)\right)","-\frac{4}{15} \sqrt{\pi } b^{5/2} f^a \log ^{\frac{5}{2}}(f) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)+\frac{4}{15} b^2 x \log ^2(f) f^{a+\frac{b}{x^2}}+\frac{1}{5} x^5 f^{a+\frac{b}{x^2}}+\frac{2}{15} b x^3 \log (f) f^{a+\frac{b}{x^2}}",1,"(f^a*(-4*b^(5/2)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x]*Log[f]^(5/2) + f^(b/x^2)*x*(3*x^4 + 2*b*x^2*Log[f] + 4*b^2*Log[f]^2)))/15","A",1
145,1,60,73,0.0252162,"\int f^{a+\frac{b}{x^2}} x^2 \, dx","Integrate[f^(a + b/x^2)*x^2,x]","\frac{1}{3} f^a \left(x f^{\frac{b}{x^2}} \left(2 b \log (f)+x^2\right)-2 \sqrt{\pi } b^{3/2} \log ^{\frac{3}{2}}(f) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)\right)","-\frac{2}{3} \sqrt{\pi } b^{3/2} f^a \log ^{\frac{3}{2}}(f) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)+\frac{2}{3} b x \log (f) f^{a+\frac{b}{x^2}}+\frac{1}{3} x^3 f^{a+\frac{b}{x^2}}",1,"(f^a*(-2*b^(3/2)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x]*Log[f]^(3/2) + f^(b/x^2)*x*(x^2 + 2*b*Log[f])))/3","A",1
146,1,49,49,0.0112804,"\int f^{a+\frac{b}{x^2}} \, dx","Integrate[f^(a + b/x^2),x]","x f^{a+\frac{b}{x^2}}-\sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)","x f^{a+\frac{b}{x^2}}-\sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)",1,"f^(a + b/x^2)*x - Sqrt[b]*f^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x]*Sqrt[Log[f]]","A",1
147,1,39,39,0.0060069,"\int \frac{f^{a+\frac{b}{x^2}}}{x^2} \, dx","Integrate[f^(a + b/x^2)/x^2,x]","-\frac{\sqrt{\pi } f^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)}{2 \sqrt{b} \sqrt{\log (f)}}","-\frac{\sqrt{\pi } f^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)}{2 \sqrt{b} \sqrt{\log (f)}}",1,"-1/2*(f^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x])/(Sqrt[b]*Sqrt[Log[f]])","A",1
148,1,63,63,0.0188047,"\int \frac{f^{a+\frac{b}{x^2}}}{x^4} \, dx","Integrate[f^(a + b/x^2)/x^4,x]","\frac{\sqrt{\pi } f^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)}{4 b^{3/2} \log ^{\frac{3}{2}}(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x \log (f)}","\frac{\sqrt{\pi } f^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)}{4 b^{3/2} \log ^{\frac{3}{2}}(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x \log (f)}",1,"(f^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x])/(4*b^(3/2)*Log[f]^(3/2)) - f^(a + b/x^2)/(2*b*x*Log[f])","A",1
149,1,74,86,0.0516043,"\int \frac{f^{a+\frac{b}{x^2}}}{x^6} \, dx","Integrate[f^(a + b/x^2)/x^6,x]","\frac{f^{a+\frac{b}{x^2}} \left(3 x^2-2 b \log (f)\right)}{4 b^2 x^3 \log ^2(f)}-\frac{3 \sqrt{\pi } f^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)}{8 b^{5/2} \log ^{\frac{5}{2}}(f)}","-\frac{3 \sqrt{\pi } f^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)}{8 b^{5/2} \log ^{\frac{5}{2}}(f)}+\frac{3 f^{a+\frac{b}{x^2}}}{4 b^2 x \log ^2(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^3 \log (f)}",1,"(-3*f^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x])/(8*b^(5/2)*Log[f]^(5/2)) + (f^(a + b/x^2)*(3*x^2 - 2*b*Log[f]))/(4*b^2*x^3*Log[f]^2)","A",1
150,1,86,109,0.055236,"\int \frac{f^{a+\frac{b}{x^2}}}{x^8} \, dx","Integrate[f^(a + b/x^2)/x^8,x]","\frac{15 \sqrt{\pi } f^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)}{16 b^{7/2} \log ^{\frac{7}{2}}(f)}-\frac{f^{a+\frac{b}{x^2}} \left(4 b^2 \log ^2(f)-10 b x^2 \log (f)+15 x^4\right)}{8 b^3 x^5 \log ^3(f)}","\frac{15 \sqrt{\pi } f^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)}{16 b^{7/2} \log ^{\frac{7}{2}}(f)}-\frac{15 f^{a+\frac{b}{x^2}}}{8 b^3 x \log ^3(f)}+\frac{5 f^{a+\frac{b}{x^2}}}{4 b^2 x^3 \log ^2(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^5 \log (f)}",1,"(15*f^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x])/(16*b^(7/2)*Log[f]^(7/2)) - (f^(a + b/x^2)*(15*x^4 - 10*b*x^2*Log[f] + 4*b^2*Log[f]^2))/(8*b^3*x^5*Log[f]^3)","A",1
151,1,100,132,0.0882034,"\int \frac{f^{a+\frac{b}{x^2}}}{x^{10}} \, dx","Integrate[f^(a + b/x^2)/x^10,x]","\frac{f^a \left(\frac{2 \sqrt{b} \sqrt{\log (f)} f^{\frac{b}{x^2}} \left(-8 b^3 \log ^3(f)+28 b^2 x^2 \log ^2(f)-70 b x^4 \log (f)+105 x^6\right)}{x^7}-105 \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)\right)}{32 b^{9/2} \log ^{\frac{9}{2}}(f)}","-\frac{105 \sqrt{\pi } f^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (f)}}{x}\right)}{32 b^{9/2} \log ^{\frac{9}{2}}(f)}+\frac{105 f^{a+\frac{b}{x^2}}}{16 b^4 x \log ^4(f)}-\frac{35 f^{a+\frac{b}{x^2}}}{8 b^3 x^3 \log ^3(f)}+\frac{7 f^{a+\frac{b}{x^2}}}{4 b^2 x^5 \log ^2(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^7 \log (f)}",1,"(f^a*(-105*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x] + (2*Sqrt[b]*f^(b/x^2)*Sqrt[Log[f]]*(105*x^6 - 70*b*x^4*Log[f] + 28*b^2*x^2*Log[f]^2 - 8*b^3*Log[f]^3))/x^7))/(32*b^(9/2)*Log[f]^(9/2))","A",1
152,1,34,34,0.0054483,"\int \frac{f^{a+\frac{b}{x^2}}}{x^{12}} \, dx","Integrate[f^(a + b/x^2)/x^12,x]","\frac{f^a \Gamma \left(\frac{11}{2},-\frac{b \log (f)}{x^2}\right)}{2 x^{11} \left(-\frac{b \log (f)}{x^2}\right)^{11/2}}","\frac{f^a \Gamma \left(\frac{11}{2},-\frac{b \log (f)}{x^2}\right)}{2 x^{11} \left(-\frac{b \log (f)}{x^2}\right)^{11/2}}",1,"(f^a*Gamma[11/2, -((b*Log[f])/x^2)])/(2*x^11*(-((b*Log[f])/x^2))^(11/2))","A",1
153,1,34,34,0.0060892,"\int \frac{f^{a+\frac{b}{x^2}}}{x^{14}} \, dx","Integrate[f^(a + b/x^2)/x^14,x]","\frac{f^a \Gamma \left(\frac{13}{2},-\frac{b \log (f)}{x^2}\right)}{2 x^{13} \left(-\frac{b \log (f)}{x^2}\right)^{13/2}}","\frac{f^a \Gamma \left(\frac{13}{2},-\frac{b \log (f)}{x^2}\right)}{2 x^{13} \left(-\frac{b \log (f)}{x^2}\right)^{13/2}}",1,"(f^a*Gamma[13/2, -((b*Log[f])/x^2)])/(2*x^13*(-((b*Log[f])/x^2))^(13/2))","A",1
154,1,46,46,0.0112895,"\int f^{a+\frac{b}{x^3}} x^m \, dx","Integrate[f^(a + b/x^3)*x^m,x]","\frac{1}{3} f^a x^{m+1} \left(-\frac{b \log (f)}{x^3}\right)^{\frac{m+1}{3}} \Gamma \left(\frac{1}{3} (-m-1),-\frac{b \log (f)}{x^3}\right)","\frac{1}{3} f^a x^{m+1} \left(-\frac{b \log (f)}{x^3}\right)^{\frac{m+1}{3}} \Gamma \left(\frac{1}{3} (-m-1),-\frac{b \log (f)}{x^3}\right)",1,"(f^a*x^(1 + m)*Gamma[(-1 - m)/3, -((b*Log[f])/x^3)]*(-((b*Log[f])/x^3))^((1 + m)/3))/3","A",1
155,1,24,24,0.002703,"\int f^{a+\frac{b}{x^3}} x^{14} \, dx","Integrate[f^(a + b/x^3)*x^14,x]","-\frac{1}{3} b^5 f^a \log ^5(f) \Gamma \left(-5,-\frac{b \log (f)}{x^3}\right)","-\frac{1}{3} b^5 f^a \log ^5(f) \Gamma \left(-5,-\frac{b \log (f)}{x^3}\right)",1,"-1/3*(b^5*f^a*Gamma[-5, -((b*Log[f])/x^3)]*Log[f]^5)","A",1
156,1,24,24,0.0025765,"\int f^{a+\frac{b}{x^3}} x^{11} \, dx","Integrate[f^(a + b/x^3)*x^11,x]","\frac{1}{3} b^4 f^a \log ^4(f) \Gamma \left(-4,-\frac{b \log (f)}{x^3}\right)","\frac{1}{3} b^4 f^a \log ^4(f) \Gamma \left(-4,-\frac{b \log (f)}{x^3}\right)",1,"(b^4*f^a*Gamma[-4, -((b*Log[f])/x^3)]*Log[f]^4)/3","A",1
157,1,57,81,0.0207136,"\int f^{a+\frac{b}{x^3}} x^8 \, dx","Integrate[f^(a + b/x^3)*x^8,x]","\frac{1}{18} f^a \left(x^3 f^{\frac{b}{x^3}} \left(b^2 \log ^2(f)+b x^3 \log (f)+2 x^6\right)-b^3 \log ^3(f) \text{Ei}\left(\frac{b \log (f)}{x^3}\right)\right)","-\frac{1}{18} b^3 f^a \log ^3(f) \text{Ei}\left(\frac{b \log (f)}{x^3}\right)+\frac{1}{18} b^2 x^3 \log ^2(f) f^{a+\frac{b}{x^3}}+\frac{1}{9} x^9 f^{a+\frac{b}{x^3}}+\frac{1}{18} b x^6 \log (f) f^{a+\frac{b}{x^3}}",1,"(f^a*(-(b^3*ExpIntegralEi[(b*Log[f])/x^3]*Log[f]^3) + f^(b/x^3)*x^3*(2*x^6 + b*x^3*Log[f] + b^2*Log[f]^2)))/18","A",1
158,1,44,58,0.0150494,"\int f^{a+\frac{b}{x^3}} x^5 \, dx","Integrate[f^(a + b/x^3)*x^5,x]","\frac{1}{6} f^a \left(x^3 f^{\frac{b}{x^3}} \left(b \log (f)+x^3\right)-b^2 \log ^2(f) \text{Ei}\left(\frac{b \log (f)}{x^3}\right)\right)","-\frac{1}{6} b^2 f^a \log ^2(f) \text{Ei}\left(\frac{b \log (f)}{x^3}\right)+\frac{1}{6} b x^3 \log (f) f^{a+\frac{b}{x^3}}+\frac{1}{6} x^6 f^{a+\frac{b}{x^3}}",1,"(f^a*(-(b^2*ExpIntegralEi[(b*Log[f])/x^3]*Log[f]^2) + f^(b/x^3)*x^3*(x^3 + b*Log[f])))/6","A",1
159,1,32,35,0.0055861,"\int f^{a+\frac{b}{x^3}} x^2 \, dx","Integrate[f^(a + b/x^3)*x^2,x]","\frac{1}{3} f^a \left(x^3 f^{\frac{b}{x^3}}-b \log (f) \text{Ei}\left(\frac{b \log (f)}{x^3}\right)\right)","\frac{1}{3} x^3 f^{a+\frac{b}{x^3}}-\frac{1}{3} b f^a \log (f) \text{Ei}\left(\frac{b \log (f)}{x^3}\right)",1,"(f^a*(f^(b/x^3)*x^3 - b*ExpIntegralEi[(b*Log[f])/x^3]*Log[f]))/3","A",1
160,1,15,15,0.0021822,"\int \frac{f^{a+\frac{b}{x^3}}}{x} \, dx","Integrate[f^(a + b/x^3)/x,x]","-\frac{1}{3} f^a \text{Ei}\left(\frac{b \log (f)}{x^3}\right)","-\frac{1}{3} f^a \text{Ei}\left(\frac{b \log (f)}{x^3}\right)",1,"-1/3*(f^a*ExpIntegralEi[(b*Log[f])/x^3])","A",1
161,1,20,20,0.0037906,"\int \frac{f^{a+\frac{b}{x^3}}}{x^4} \, dx","Integrate[f^(a + b/x^3)/x^4,x]","-\frac{f^{a+\frac{b}{x^3}}}{3 b \log (f)}","-\frac{f^{a+\frac{b}{x^3}}}{3 b \log (f)}",1,"-1/3*f^(a + b/x^3)/(b*Log[f])","A",1
162,1,32,44,0.0070196,"\int \frac{f^{a+\frac{b}{x^3}}}{x^7} \, dx","Integrate[f^(a + b/x^3)/x^7,x]","\frac{f^{a+\frac{b}{x^3}} \left(x^3-b \log (f)\right)}{3 b^2 x^3 \log ^2(f)}","\frac{f^{a+\frac{b}{x^3}}}{3 b^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x^3}}}{3 b x^3 \log (f)}",1,"(f^(a + b/x^3)*(x^3 - b*Log[f]))/(3*b^2*x^3*Log[f]^2)","A",1
163,1,45,67,0.0092909,"\int \frac{f^{a+\frac{b}{x^3}}}{x^{10}} \, dx","Integrate[f^(a + b/x^3)/x^10,x]","-\frac{f^{a+\frac{b}{x^3}} \left(b^2 \log ^2(f)-2 b x^3 \log (f)+2 x^6\right)}{3 b^3 x^6 \log ^3(f)}","-\frac{2 f^{a+\frac{b}{x^3}}}{3 b^3 \log ^3(f)}+\frac{2 f^{a+\frac{b}{x^3}}}{3 b^2 x^3 \log ^2(f)}-\frac{f^{a+\frac{b}{x^3}}}{3 b x^6 \log (f)}",1,"-1/3*(f^(a + b/x^3)*(2*x^6 - 2*b*x^3*Log[f] + b^2*Log[f]^2))/(b^3*x^6*Log[f]^3)","A",1
164,1,58,83,0.0104926,"\int \frac{f^{a+\frac{b}{x^3}}}{x^{13}} \, dx","Integrate[f^(a + b/x^3)/x^13,x]","\frac{f^{a+\frac{b}{x^3}} \left(-b^3 \log ^3(f)+3 b^2 x^3 \log ^2(f)-6 b x^6 \log (f)+6 x^9\right)}{3 b^4 x^9 \log ^4(f)}","\frac{2 f^{a+\frac{b}{x^3}}}{b^4 \log ^4(f)}-\frac{2 f^{a+\frac{b}{x^3}}}{b^3 x^3 \log ^3(f)}+\frac{f^{a+\frac{b}{x^3}}}{b^2 x^6 \log ^2(f)}-\frac{f^{a+\frac{b}{x^3}}}{3 b x^9 \log (f)}",1,"(f^(a + b/x^3)*(6*x^9 - 6*b*x^6*Log[f] + 3*b^2*x^3*Log[f]^2 - b^3*Log[f]^3))/(3*b^4*x^9*Log[f]^4)","A",1
165,1,24,69,0.0028831,"\int \frac{f^{a+\frac{b}{x^3}}}{x^{16}} \, dx","Integrate[f^(a + b/x^3)/x^16,x]","-\frac{f^a \Gamma \left(5,-\frac{b \log (f)}{x^3}\right)}{3 b^5 \log ^5(f)}","-\frac{f^{a+\frac{b}{x^3}} \left(b^4 \log ^4(f)-4 b^3 x^3 \log ^3(f)+12 b^2 x^6 \log ^2(f)-24 b x^9 \log (f)+24 x^{12}\right)}{3 b^5 x^{12} \log ^5(f)}",1,"-1/3*(f^a*Gamma[5, -((b*Log[f])/x^3)])/(b^5*Log[f]^5)","C",1
166,1,24,82,0.0031683,"\int \frac{f^{a+\frac{b}{x^3}}}{x^{19}} \, dx","Integrate[f^(a + b/x^3)/x^19,x]","\frac{f^a \Gamma \left(6,-\frac{b \log (f)}{x^3}\right)}{3 b^6 \log ^6(f)}","\frac{f^{a+\frac{b}{x^3}} \left(-b^5 \log ^5(f)+5 b^4 x^3 \log ^4(f)-20 b^3 x^6 \log ^3(f)+60 b^2 x^9 \log ^2(f)-120 b x^{12} \log (f)+120 x^{15}\right)}{3 b^6 x^{15} \log ^6(f)}",1,"(f^a*Gamma[6, -((b*Log[f])/x^3)])/(3*b^6*Log[f]^6)","C",1
167,1,34,34,0.004197,"\int f^{a+\frac{b}{x^3}} x^4 \, dx","Integrate[f^(a + b/x^3)*x^4,x]","\frac{1}{3} x^5 f^a \left(-\frac{b \log (f)}{x^3}\right)^{5/3} \Gamma \left(-\frac{5}{3},-\frac{b \log (f)}{x^3}\right)","\frac{1}{3} x^5 f^a \left(-\frac{b \log (f)}{x^3}\right)^{5/3} \Gamma \left(-\frac{5}{3},-\frac{b \log (f)}{x^3}\right)",1,"(f^a*x^5*Gamma[-5/3, -((b*Log[f])/x^3)]*(-((b*Log[f])/x^3))^(5/3))/3","A",1
168,1,34,34,0.0037994,"\int f^{a+\frac{b}{x^3}} x^3 \, dx","Integrate[f^(a + b/x^3)*x^3,x]","\frac{1}{3} x^4 f^a \left(-\frac{b \log (f)}{x^3}\right)^{4/3} \Gamma \left(-\frac{4}{3},-\frac{b \log (f)}{x^3}\right)","\frac{1}{3} x^4 f^a \left(-\frac{b \log (f)}{x^3}\right)^{4/3} \Gamma \left(-\frac{4}{3},-\frac{b \log (f)}{x^3}\right)",1,"(f^a*x^4*Gamma[-4/3, -((b*Log[f])/x^3)]*(-((b*Log[f])/x^3))^(4/3))/3","A",1
169,1,34,34,0.0038592,"\int f^{a+\frac{b}{x^3}} x \, dx","Integrate[f^(a + b/x^3)*x,x]","\frac{1}{3} x^2 f^a \left(-\frac{b \log (f)}{x^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{b \log (f)}{x^3}\right)","\frac{1}{3} x^2 f^a \left(-\frac{b \log (f)}{x^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{b \log (f)}{x^3}\right)",1,"(f^a*x^2*Gamma[-2/3, -((b*Log[f])/x^3)]*(-((b*Log[f])/x^3))^(2/3))/3","A",1
170,1,32,32,0.0033926,"\int f^{a+\frac{b}{x^3}} \, dx","Integrate[f^(a + b/x^3),x]","\frac{1}{3} x f^a \sqrt[3]{-\frac{b \log (f)}{x^3}} \Gamma \left(-\frac{1}{3},-\frac{b \log (f)}{x^3}\right)","\frac{1}{3} x f^a \sqrt[3]{-\frac{b \log (f)}{x^3}} \Gamma \left(-\frac{1}{3},-\frac{b \log (f)}{x^3}\right)",1,"(f^a*x*Gamma[-1/3, -((b*Log[f])/x^3)]*(-((b*Log[f])/x^3))^(1/3))/3","A",1
171,1,34,34,0.0059363,"\int \frac{f^{a+\frac{b}{x^3}}}{x^2} \, dx","Integrate[f^(a + b/x^3)/x^2,x]","\frac{f^a \Gamma \left(\frac{1}{3},-\frac{b \log (f)}{x^3}\right)}{3 x \sqrt[3]{-\frac{b \log (f)}{x^3}}}","\frac{f^a \Gamma \left(\frac{1}{3},-\frac{b \log (f)}{x^3}\right)}{3 x \sqrt[3]{-\frac{b \log (f)}{x^3}}}",1,"(f^a*Gamma[1/3, -((b*Log[f])/x^3)])/(3*x*(-((b*Log[f])/x^3))^(1/3))","A",1
172,1,34,34,0.0053402,"\int \frac{f^{a+\frac{b}{x^3}}}{x^3} \, dx","Integrate[f^(a + b/x^3)/x^3,x]","\frac{f^a \Gamma \left(\frac{2}{3},-\frac{b \log (f)}{x^3}\right)}{3 x^2 \left(-\frac{b \log (f)}{x^3}\right)^{2/3}}","\frac{f^a \Gamma \left(\frac{2}{3},-\frac{b \log (f)}{x^3}\right)}{3 x^2 \left(-\frac{b \log (f)}{x^3}\right)^{2/3}}",1,"(f^a*Gamma[2/3, -((b*Log[f])/x^3)])/(3*x^2*(-((b*Log[f])/x^3))^(2/3))","A",1
173,1,34,34,0.0054636,"\int \frac{f^{a+\frac{b}{x^3}}}{x^5} \, dx","Integrate[f^(a + b/x^3)/x^5,x]","\frac{f^a \Gamma \left(\frac{4}{3},-\frac{b \log (f)}{x^3}\right)}{3 x^4 \left(-\frac{b \log (f)}{x^3}\right)^{4/3}}","\frac{f^a \Gamma \left(\frac{4}{3},-\frac{b \log (f)}{x^3}\right)}{3 x^4 \left(-\frac{b \log (f)}{x^3}\right)^{4/3}}",1,"(f^a*Gamma[4/3, -((b*Log[f])/x^3)])/(3*x^4*(-((b*Log[f])/x^3))^(4/3))","A",1
174,1,46,46,0.0129021,"\int f^{a+b x^n} x^m \, dx","Integrate[f^(a + b*x^n)*x^m,x]","-\frac{f^a x^{m+1} \left(-b \log (f) x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-b x^n \log (f)\right)}{n}","-\frac{f^a x^{m+1} \left(-b \log (f) x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-b x^n \log (f)\right)}{n}",1,"-((f^a*x^(1 + m)*Gamma[(1 + m)/n, -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^((1 + m)/n)))","A",1
175,1,39,39,0.0069946,"\int f^{a+b x^n} x^3 \, dx","Integrate[f^(a + b*x^n)*x^3,x]","-\frac{x^4 f^a \left(-b \log (f) x^n\right)^{-4/n} \Gamma \left(\frac{4}{n},-b x^n \log (f)\right)}{n}","-\frac{x^4 f^a \left(-b \log (f) x^n\right)^{-4/n} \Gamma \left(\frac{4}{n},-b x^n \log (f)\right)}{n}",1,"-((f^a*x^4*Gamma[4/n, -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^(4/n)))","A",1
176,1,39,39,0.00626,"\int f^{a+b x^n} x^2 \, dx","Integrate[f^(a + b*x^n)*x^2,x]","-\frac{x^3 f^a \left(-b \log (f) x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-b x^n \log (f)\right)}{n}","-\frac{x^3 f^a \left(-b \log (f) x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-b x^n \log (f)\right)}{n}",1,"-((f^a*x^3*Gamma[3/n, -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^(3/n)))","A",1
177,1,39,39,0.0060992,"\int f^{a+b x^n} x \, dx","Integrate[f^(a + b*x^n)*x,x]","-\frac{x^2 f^a \left(-b \log (f) x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-b x^n \log (f)\right)}{n}","-\frac{x^2 f^a \left(-b \log (f) x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-b x^n \log (f)\right)}{n}",1,"-((f^a*x^2*Gamma[2/n, -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^(2/n)))","A",1
178,1,35,35,0.0048587,"\int f^{a+b x^n} \, dx","Integrate[f^(a + b*x^n),x]","-\frac{x f^a \left(-b \log (f) x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-b x^n \log (f)\right)}{n}","-\frac{x f^a \left(-b \log (f) x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-b x^n \log (f)\right)}{n}",1,"-((f^a*x*Gamma[n^(-1), -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^n^(-1)))","A",1
179,1,15,15,0.0026902,"\int \frac{f^{a+b x^n}}{x} \, dx","Integrate[f^(a + b*x^n)/x,x]","\frac{f^a \text{Ei}\left(b x^n \log (f)\right)}{n}","\frac{f^a \text{Ei}\left(b x^n \log (f)\right)}{n}",1,"(f^a*ExpIntegralEi[b*x^n*Log[f]])/n","A",1
180,1,37,37,0.0040769,"\int \frac{f^{a+b x^n}}{x^2} \, dx","Integrate[f^(a + b*x^n)/x^2,x]","-\frac{f^a \left(-b \log (f) x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-b x^n \log (f)\right)}{n x}","-\frac{f^a \left(-b \log (f) x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-b x^n \log (f)\right)}{n x}",1,"-((f^a*Gamma[-n^(-1), -(b*x^n*Log[f])]*(-(b*x^n*Log[f]))^n^(-1))/(n*x))","A",1
181,1,39,39,0.0043593,"\int \frac{f^{a+b x^n}}{x^3} \, dx","Integrate[f^(a + b*x^n)/x^3,x]","-\frac{f^a \left(-b \log (f) x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},-b x^n \log (f)\right)}{n x^2}","-\frac{f^a \left(-b \log (f) x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},-b x^n \log (f)\right)}{n x^2}",1,"-((f^a*Gamma[-2/n, -(b*x^n*Log[f])]*(-(b*x^n*Log[f]))^(2/n))/(n*x^2))","A",1
182,1,39,39,0.004298,"\int \frac{f^{a+b x^n}}{x^4} \, dx","Integrate[f^(a + b*x^n)/x^4,x]","-\frac{f^a \left(-b \log (f) x^n\right)^{3/n} \Gamma \left(-\frac{3}{n},-b x^n \log (f)\right)}{n x^3}","-\frac{f^a \left(-b \log (f) x^n\right)^{3/n} \Gamma \left(-\frac{3}{n},-b x^n \log (f)\right)}{n x^3}",1,"-((f^a*Gamma[-3/n, -(b*x^n*Log[f])]*(-(b*x^n*Log[f]))^(3/n))/(n*x^3))","A",1
183,1,24,71,0.0041557,"\int f^{a+b x^n} x^{-1+3 n} \, dx","Integrate[f^(a + b*x^n)*x^(-1 + 3*n),x]","\frac{f^a \Gamma \left(3,-b x^n \log (f)\right)}{b^3 n \log ^3(f)}","\frac{2 f^{a+b x^n}}{b^3 n \log ^3(f)}-\frac{2 x^n f^{a+b x^n}}{b^2 n \log ^2(f)}+\frac{x^{2 n} f^{a+b x^n}}{b n \log (f)}",1,"(f^a*Gamma[3, -(b*x^n*Log[f])])/(b^3*n*Log[f]^3)","C",1
184,1,25,45,0.0059855,"\int f^{a+b x^n} x^{-1+2 n} \, dx","Integrate[f^(a + b*x^n)*x^(-1 + 2*n),x]","-\frac{f^a \Gamma \left(2,-b x^n \log (f)\right)}{b^2 n \log ^2(f)}","\frac{x^n f^{a+b x^n}}{b n \log (f)}-\frac{f^{a+b x^n}}{b^2 n \log ^2(f)}",1,"-((f^a*Gamma[2, -(b*x^n*Log[f])])/(b^2*n*Log[f]^2))","C",1
185,1,20,20,0.0047662,"\int f^{a+b x^n} x^{-1+n} \, dx","Integrate[f^(a + b*x^n)*x^(-1 + n),x]","\frac{f^{a+b x^n}}{b n \log (f)}","\frac{f^{a+b x^n}}{b n \log (f)}",1,"f^(a + b*x^n)/(b*n*Log[f])","A",1
186,1,15,15,0.0029062,"\int \frac{f^{a+b x^n}}{x} \, dx","Integrate[f^(a + b*x^n)/x,x]","\frac{f^a \text{Ei}\left(b x^n \log (f)\right)}{n}","\frac{f^a \text{Ei}\left(b x^n \log (f)\right)}{n}",1,"(f^a*ExpIntegralEi[b*x^n*Log[f]])/n","A",1
187,1,20,38,0.0037051,"\int f^{a+b x^n} x^{-1-n} \, dx","Integrate[f^(a + b*x^n)*x^(-1 - n),x]","\frac{b f^a \log (f) \Gamma \left(-1,-b x^n \log (f)\right)}{n}","\frac{b f^a \log (f) \text{Ei}\left(b x^n \log (f)\right)}{n}-\frac{x^{-n} f^{a+b x^n}}{n}",1,"(b*f^a*Gamma[-1, -(b*x^n*Log[f])]*Log[f])/n","A",1
188,1,25,71,0.0043315,"\int f^{a+b x^n} x^{-1-2 n} \, dx","Integrate[f^(a + b*x^n)*x^(-1 - 2*n),x]","-\frac{b^2 f^a \log ^2(f) \Gamma \left(-2,-b x^n \log (f)\right)}{n}","\frac{b^2 f^a \log ^2(f) \text{Ei}\left(b x^n \log (f)\right)}{2 n}-\frac{x^{-2 n} f^{a+b x^n}}{2 n}-\frac{b \log (f) x^{-n} f^{a+b x^n}}{2 n}",1,"-((b^2*f^a*Gamma[-2, -(b*x^n*Log[f])]*Log[f]^2)/n)","A",1
189,1,39,104,0.010975,"\int f^{a+b x^n} x^{-1+\frac{5 n}{2}} \, dx","Integrate[f^(a + b*x^n)*x^(-1 + (5*n)/2),x]","-\frac{f^a x^{5 n/2} \Gamma \left(\frac{5}{2},-b x^n \log (f)\right)}{n \left(-b \log (f) x^n\right)^{5/2}}","\frac{3 \sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} \sqrt{\log (f)} x^{n/2}\right)}{4 b^{5/2} n \log ^{\frac{5}{2}}(f)}-\frac{3 x^{n/2} f^{a+b x^n}}{2 b^2 n \log ^2(f)}+\frac{x^{3 n/2} f^{a+b x^n}}{b n \log (f)}",1,"-((f^a*x^((5*n)/2)*Gamma[5/2, -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^(5/2)))","A",1
190,1,39,74,0.0090954,"\int f^{a+b x^n} x^{-1+\frac{3 n}{2}} \, dx","Integrate[f^(a + b*x^n)*x^(-1 + (3*n)/2),x]","-\frac{f^a x^{3 n/2} \Gamma \left(\frac{3}{2},-b x^n \log (f)\right)}{n \left(-b \log (f) x^n\right)^{3/2}}","\frac{x^{n/2} f^{a+b x^n}}{b n \log (f)}-\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} \sqrt{\log (f)} x^{n/2}\right)}{2 b^{3/2} n \log ^{\frac{3}{2}}(f)}",1,"-((f^a*x^((3*n)/2)*Gamma[3/2, -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^(3/2)))","A",1
191,1,43,43,0.0090893,"\int f^{a+b x^n} x^{-1+\frac{n}{2}} \, dx","Integrate[f^(a + b*x^n)*x^(-1 + n/2),x]","\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} \sqrt{\log (f)} x^{n/2}\right)}{\sqrt{b} n \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^a \text{erfi}\left(\sqrt{b} \sqrt{\log (f)} x^{n/2}\right)}{\sqrt{b} n \sqrt{\log (f)}}",1,"(f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x^(n/2)*Sqrt[Log[f]]])/(Sqrt[b]*n*Sqrt[Log[f]])","A",1
192,1,39,66,0.0074431,"\int f^{a+b x^n} x^{-1-\frac{n}{2}} \, dx","Integrate[f^(a + b*x^n)*x^(-1 - n/2),x]","-\frac{f^a x^{-n/2} \sqrt{-b \log (f) x^n} \Gamma \left(-\frac{1}{2},-b x^n \log (f)\right)}{n}","\frac{2 \sqrt{\pi } \sqrt{b} f^a \sqrt{\log (f)} \text{erfi}\left(\sqrt{b} \sqrt{\log (f)} x^{n/2}\right)}{n}-\frac{2 x^{-n/2} f^{a+b x^n}}{n}",1,"-((f^a*Gamma[-1/2, -(b*x^n*Log[f])]*Sqrt[-(b*x^n*Log[f])])/(n*x^(n/2)))","A",1
193,1,39,96,0.0079492,"\int f^{a+b x^n} x^{-1-\frac{3 n}{2}} \, dx","Integrate[f^(a + b*x^n)*x^(-1 - (3*n)/2),x]","-\frac{f^a x^{-3 n/2} \left(-b \log (f) x^n\right)^{3/2} \Gamma \left(-\frac{3}{2},-b x^n \log (f)\right)}{n}","\frac{4 \sqrt{\pi } b^{3/2} f^a \log ^{\frac{3}{2}}(f) \text{erfi}\left(\sqrt{b} \sqrt{\log (f)} x^{n/2}\right)}{3 n}-\frac{2 x^{-3 n/2} f^{a+b x^n}}{3 n}-\frac{4 b \log (f) x^{-n/2} f^{a+b x^n}}{3 n}",1,"-((f^a*Gamma[-3/2, -(b*x^n*Log[f])]*(-(b*x^n*Log[f]))^(3/2))/(n*x^((3*n)/2)))","A",1
194,1,11,16,0.0054379,"\int e^{-0.1 x} x \, dx","Integrate[x/E^(0.1*x),x]","e^{-0.1 x} (-10. x-100.)","-10. e^{-0.1 x} x-100. e^{-0.1 x}",1,"(-99.99999999999999 - 10.*x)/E^(0.1*x)","A",1
195,1,96,203,0.1103498,"\int f^{c (a+b x)^2} x^3 \, dx","Integrate[f^(c*(a + b*x)^2)*x^3,x]","\frac{2 f^{c (a+b x)^2} \left(c \log (f) \left(a^2-a b x+b^2 x^2\right)-1\right)+\sqrt{\pi } a \sqrt{c} \sqrt{\log (f)} \left(3-2 a^2 c \log (f)\right) \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)}{4 b^4 c^2 \log ^2(f)}","-\frac{\sqrt{\pi } a^3 \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)}{2 b^4 \sqrt{c} \sqrt{\log (f)}}+\frac{3 a^2 f^{c (a+b x)^2}}{2 b^4 c \log (f)}+\frac{3 \sqrt{\pi } a \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)}{4 b^4 c^{3/2} \log ^{\frac{3}{2}}(f)}-\frac{f^{c (a+b x)^2}}{2 b^4 c^2 \log ^2(f)}+\frac{(a+b x)^2 f^{c (a+b x)^2}}{2 b^4 c \log (f)}-\frac{3 a (a+b x) f^{c (a+b x)^2}}{2 b^4 c \log (f)}",1,"(a*Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]]*Sqrt[Log[f]]*(3 - 2*a^2*c*Log[f]) + 2*f^(c*(a + b*x)^2)*(-1 + c*(a^2 - a*b*x + b^2*x^2)*Log[f]))/(4*b^4*c^2*Log[f]^2)","A",1
196,1,83,140,0.0689381,"\int f^{c (a+b x)^2} x^2 \, dx","Integrate[f^(c*(a + b*x)^2)*x^2,x]","\frac{\sqrt{\pi } \left(2 a^2 c \log (f)-1\right) \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)-2 \sqrt{c} \sqrt{\log (f)} (a-b x) f^{c (a+b x)^2}}{4 b^3 c^{3/2} \log ^{\frac{3}{2}}(f)}","\frac{\sqrt{\pi } a^2 \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)}{2 b^3 \sqrt{c} \sqrt{\log (f)}}-\frac{\sqrt{\pi } \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)}{4 b^3 c^{3/2} \log ^{\frac{3}{2}}(f)}+\frac{(a+b x) f^{c (a+b x)^2}}{2 b^3 c \log (f)}-\frac{a f^{c (a+b x)^2}}{b^3 c \log (f)}",1,"(-2*Sqrt[c]*f^(c*(a + b*x)^2)*(a - b*x)*Sqrt[Log[f]] + Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]]*(-1 + 2*a^2*c*Log[f]))/(4*b^3*c^(3/2)*Log[f]^(3/2))","A",1
197,1,63,68,0.0295942,"\int f^{c (a+b x)^2} x \, dx","Integrate[f^(c*(a + b*x)^2)*x,x]","\frac{f^{c (a+b x)^2}-\sqrt{\pi } a \sqrt{c} \sqrt{\log (f)} \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)}{2 b^2 c \log (f)}","\frac{f^{c (a+b x)^2}}{2 b^2 c \log (f)}-\frac{\sqrt{\pi } a \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)}{2 b^2 \sqrt{c} \sqrt{\log (f)}}",1,"(f^(c*(a + b*x)^2) - a*Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]]*Sqrt[Log[f]])/(2*b^2*c*Log[f])","A",1
198,1,41,41,0.0041664,"\int f^{c (a+b x)^2} \, dx","Integrate[f^(c*(a + b*x)^2),x]","\frac{\sqrt{\pi } \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)}{2 b \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)}{2 b \sqrt{c} \sqrt{\log (f)}}",1,"(Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]])/(2*b*Sqrt[c]*Sqrt[Log[f]])","A",1
199,0,0,18,0.1223745,"\int \frac{f^{c (a+b x)^2}}{x} \, dx","Integrate[f^(c*(a + b*x)^2)/x,x]","\int \frac{f^{c (a+b x)^2}}{x} \, dx","\text{Int}\left(\frac{f^{c (a+b x)^2}}{x},x\right)",0,"Integrate[f^(c*(a + b*x)^2)/x, x]","A",-1
200,0,0,78,0.3199282,"\int \frac{f^{c (a+b x)^2}}{x^2} \, dx","Integrate[f^(c*(a + b*x)^2)/x^2,x]","\int \frac{f^{c (a+b x)^2}}{x^2} \, dx","2 a b c \log (f) \text{Int}\left(\frac{f^{c (a+b x)^2}}{x},x\right)+\sqrt{\pi } b \sqrt{c} \sqrt{\log (f)} \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)-\frac{f^{c (a+b x)^2}}{x}",0,"Integrate[f^(c*(a + b*x)^2)/x^2, x]","A",-1
201,0,0,137,0.4283345,"\int \frac{f^{c (a+b x)^2}}{x^3} \, dx","Integrate[f^(c*(a + b*x)^2)/x^3,x]","\int \frac{f^{c (a+b x)^2}}{x^3} \, dx","2 a^2 b^2 c^2 \log ^2(f) \text{Int}\left(\frac{f^{c (a+b x)^2}}{x},x\right)+b^2 c \log (f) \text{Int}\left(\frac{f^{c (a+b x)^2}}{x},x\right)+\sqrt{\pi } a b^2 c^{3/2} \log ^{\frac{3}{2}}(f) \text{erfi}\left(\sqrt{c} \sqrt{\log (f)} (a+b x)\right)-\frac{f^{c (a+b x)^2}}{2 x^2}-\frac{a b c \log (f) f^{c (a+b x)^2}}{x}",0,"Integrate[f^(c*(a + b*x)^2)/x^3, x]","A",-1
202,1,111,120,0.20379,"\int f^{c (a+b x)^3} x^2 \, dx","Integrate[f^(c*(a + b*x)^3)*x^2,x]","\frac{-\frac{a^2 (a+b x) \Gamma \left(\frac{1}{3},-c (a+b x)^3 \log (f)\right)}{\sqrt[3]{-c \log (f) (a+b x)^3}}+\frac{f^{c (a+b x)^3}}{c \log (f)}+\frac{2 a (a+b x)^2 \Gamma \left(\frac{2}{3},-c (a+b x)^3 \log (f)\right)}{\left(-c \log (f) (a+b x)^3\right)^{2/3}}}{3 b^3}","-\frac{a^2 (a+b x) \Gamma \left(\frac{1}{3},-c (a+b x)^3 \log (f)\right)}{3 b^3 \sqrt[3]{-c \log (f) (a+b x)^3}}+\frac{f^{c (a+b x)^3}}{3 b^3 c \log (f)}+\frac{2 a (a+b x)^2 \Gamma \left(\frac{2}{3},-c (a+b x)^3 \log (f)\right)}{3 b^3 \left(-c \log (f) (a+b x)^3\right)^{2/3}}",1,"(f^(c*(a + b*x)^3)/(c*Log[f]) + (2*a*(a + b*x)^2*Gamma[2/3, -(c*(a + b*x)^3*Log[f])])/(-(c*(a + b*x)^3*Log[f]))^(2/3) - (a^2*(a + b*x)*Gamma[1/3, -(c*(a + b*x)^3*Log[f])])/(-(c*(a + b*x)^3*Log[f]))^(1/3))/(3*b^3)","A",1
203,1,86,92,0.0533532,"\int f^{c (a+b x)^3} x \, dx","Integrate[f^(c*(a + b*x)^3)*x,x]","-\frac{(a+b x) \left((a+b x) \Gamma \left(\frac{2}{3},-c (a+b x)^3 \log (f)\right)-a \sqrt[3]{-c \log (f) (a+b x)^3} \Gamma \left(\frac{1}{3},-c (a+b x)^3 \log (f)\right)\right)}{3 b^2 \left(-c \log (f) (a+b x)^3\right)^{2/3}}","\frac{a (a+b x) \Gamma \left(\frac{1}{3},-c (a+b x)^3 \log (f)\right)}{3 b^2 \sqrt[3]{-c \log (f) (a+b x)^3}}-\frac{(a+b x)^2 \Gamma \left(\frac{2}{3},-c (a+b x)^3 \log (f)\right)}{3 b^2 \left(-c \log (f) (a+b x)^3\right)^{2/3}}",1,"-1/3*((a + b*x)*((a + b*x)*Gamma[2/3, -(c*(a + b*x)^3*Log[f])] - a*Gamma[1/3, -(c*(a + b*x)^3*Log[f])]*(-(c*(a + b*x)^3*Log[f]))^(1/3)))/(b^2*(-(c*(a + b*x)^3*Log[f]))^(2/3))","A",1
204,1,44,44,0.0097646,"\int f^{c (a+b x)^3} \, dx","Integrate[f^(c*(a + b*x)^3),x]","-\frac{(a+b x) \Gamma \left(\frac{1}{3},-c (a+b x)^3 \log (f)\right)}{3 b \sqrt[3]{-c \log (f) (a+b x)^3}}","-\frac{(a+b x) \Gamma \left(\frac{1}{3},-c (a+b x)^3 \log (f)\right)}{3 b \sqrt[3]{-c \log (f) (a+b x)^3}}",1,"-1/3*((a + b*x)*Gamma[1/3, -(c*(a + b*x)^3*Log[f])])/(b*(-(c*(a + b*x)^3*Log[f]))^(1/3))","A",1
205,0,0,18,0.3020614,"\int \frac{f^{c (a+b x)^3}}{x} \, dx","Integrate[f^(c*(a + b*x)^3)/x,x]","\int \frac{f^{c (a+b x)^3}}{x} \, dx","\text{Int}\left(\frac{f^{c (a+b x)^3}}{x},x\right)",0,"Integrate[f^(c*(a + b*x)^3)/x, x]","A",-1
206,0,0,133,1.1077887,"\int \frac{f^{c (a+b x)^3}}{x^2} \, dx","Integrate[f^(c*(a + b*x)^3)/x^2,x]","\int \frac{f^{c (a+b x)^3}}{x^2} \, dx","3 a^2 b c \log (f) \text{Int}\left(\frac{f^{c (a+b x)^3}}{x},x\right)-\frac{f^{c (a+b x)^3}}{x}-\frac{a b c \log (f) (a+b x) \Gamma \left(\frac{1}{3},-c (a+b x)^3 \log (f)\right)}{\sqrt[3]{-c \log (f) (a+b x)^3}}-\frac{b c \log (f) (a+b x)^2 \Gamma \left(\frac{2}{3},-c (a+b x)^3 \log (f)\right)}{\left(-c \log (f) (a+b x)^3\right)^{2/3}}",0,"Integrate[f^(c*(a + b*x)^3)/x^2, x]","A",-1
207,0,0,263,1.4776315,"\int \frac{f^{c (a+b x)^3}}{x^3} \, dx","Integrate[f^(c*(a + b*x)^3)/x^3,x]","\int \frac{f^{c (a+b x)^3}}{x^3} \, dx","\frac{9}{2} a^4 b^2 c^2 \log ^2(f) \text{Int}\left(\frac{f^{c (a+b x)^3}}{x},x\right)+3 a b^2 c \log (f) \text{Int}\left(\frac{f^{c (a+b x)^3}}{x},x\right)-\frac{3 a^3 b^2 c^2 \log ^2(f) (a+b x) \Gamma \left(\frac{1}{3},-c (a+b x)^3 \log (f)\right)}{2 \sqrt[3]{-c \log (f) (a+b x)^3}}-\frac{3 a^2 b^2 c^2 \log ^2(f) (a+b x)^2 \Gamma \left(\frac{2}{3},-c (a+b x)^3 \log (f)\right)}{2 \left(-c \log (f) (a+b x)^3\right)^{2/3}}-\frac{3 a^2 b c \log (f) f^{c (a+b x)^3}}{2 x}-\frac{b^2 c \log (f) (a+b x) \Gamma \left(\frac{1}{3},-c (a+b x)^3 \log (f)\right)}{2 \sqrt[3]{-c \log (f) (a+b x)^3}}-\frac{f^{c (a+b x)^3}}{2 x^2}",0,"Integrate[f^(c*(a + b*x)^3)/x^3, x]","A",-1
208,1,164,183,0.1788249,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^4 \, dx","Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^4,x]","\frac{-\left(a^4 (a+b x) \sqrt[3]{-(a+b x)^3} \Gamma \left(\frac{1}{3},-(a+b x)^3\right)\right)+4 a^3 (a+b x)^2 \Gamma \left(\frac{2}{3},-(a+b x)^3\right)+6 a^2 e^{(a+b x)^3} \left(-(a+b x)^3\right)^{2/3}-4 a (a+b x) \sqrt[3]{-(a+b x)^3} \Gamma \left(\frac{4}{3},-(a+b x)^3\right)+(a+b x)^2 \Gamma \left(\frac{5}{3},-(a+b x)^3\right)}{3 b^5 \left(-(a+b x)^3\right)^{2/3}}","-\frac{a^4 (a+b x) \Gamma \left(\frac{1}{3},-(a+b x)^3\right)}{3 b^5 \sqrt[3]{-(a+b x)^3}}+\frac{4 a^3 (a+b x)^2 \Gamma \left(\frac{2}{3},-(a+b x)^3\right)}{3 b^5 \left(-(a+b x)^3\right)^{2/3}}+\frac{2 a^2 e^{(a+b x)^3}}{b^5}-\frac{(a+b x)^5 \Gamma \left(\frac{5}{3},-(a+b x)^3\right)}{3 b^5 \left(-(a+b x)^3\right)^{5/3}}+\frac{4 a (a+b x)^4 \Gamma \left(\frac{4}{3},-(a+b x)^3\right)}{3 b^5 \left(-(a+b x)^3\right)^{4/3}}",1,"(6*a^2*E^(a + b*x)^3*(-(a + b*x)^3)^(2/3) - a^4*(a + b*x)*(-(a + b*x)^3)^(1/3)*Gamma[1/3, -(a + b*x)^3] + 4*a^3*(a + b*x)^2*Gamma[2/3, -(a + b*x)^3] - 4*a*(a + b*x)*(-(a + b*x)^3)^(1/3)*Gamma[4/3, -(a + b*x)^3] + (a + b*x)^2*Gamma[5/3, -(a + b*x)^3])/(3*b^5*(-(a + b*x)^3)^(2/3))","A",1
209,1,138,138,0.1415328,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^3 \, dx","Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^3,x]","\frac{a^3 (a+b x) \Gamma \left(\frac{1}{3},-(a+b x)^3\right)}{3 b^4 \sqrt[3]{-(a+b x)^3}}-\frac{a^2 (a+b x)^2 \Gamma \left(\frac{2}{3},-(a+b x)^3\right)}{b^4 \left(-(a+b x)^3\right)^{2/3}}-\frac{a e^{(a+b x)^3}}{b^4}-\frac{(a+b x)^4 \Gamma \left(\frac{4}{3},-(a+b x)^3\right)}{3 b^4 \left(-(a+b x)^3\right)^{4/3}}","\frac{a^3 (a+b x) \Gamma \left(\frac{1}{3},-(a+b x)^3\right)}{3 b^4 \sqrt[3]{-(a+b x)^3}}-\frac{a^2 (a+b x)^2 \Gamma \left(\frac{2}{3},-(a+b x)^3\right)}{b^4 \left(-(a+b x)^3\right)^{2/3}}-\frac{a e^{(a+b x)^3}}{b^4}-\frac{(a+b x)^4 \Gamma \left(\frac{4}{3},-(a+b x)^3\right)}{3 b^4 \left(-(a+b x)^3\right)^{4/3}}",1,"-((a*E^(a + b*x)^3)/b^4) + (a^3*(a + b*x)*Gamma[1/3, -(a + b*x)^3])/(3*b^4*(-(a + b*x)^3)^(1/3)) - (a^2*(a + b*x)^2*Gamma[2/3, -(a + b*x)^3])/(b^4*(-(a + b*x)^3)^(2/3)) - ((a + b*x)^4*Gamma[4/3, -(a + b*x)^3])/(3*b^4*(-(a + b*x)^3)^(4/3))","A",1
210,1,89,99,0.0832287,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^2 \, dx","Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^2,x]","\frac{-\frac{a^2 (a+b x) \Gamma \left(\frac{1}{3},-(a+b x)^3\right)}{\sqrt[3]{-(a+b x)^3}}+e^{(a+b x)^3}+\frac{2 a (a+b x)^2 \Gamma \left(\frac{2}{3},-(a+b x)^3\right)}{\left(-(a+b x)^3\right)^{2/3}}}{3 b^3}","-\frac{a^2 (a+b x) \Gamma \left(\frac{1}{3},-(a+b x)^3\right)}{3 b^3 \sqrt[3]{-(a+b x)^3}}+\frac{e^{(a+b x)^3}}{3 b^3}+\frac{2 a (a+b x)^2 \Gamma \left(\frac{2}{3},-(a+b x)^3\right)}{3 b^3 \left(-(a+b x)^3\right)^{2/3}}",1,"(E^(a + b*x)^3 - (a^2*(a + b*x)*Gamma[1/3, -(a + b*x)^3])/(-(a + b*x)^3)^(1/3) + (2*a*(a + b*x)^2*Gamma[2/3, -(a + b*x)^3])/(-(a + b*x)^3)^(2/3))/(3*b^3)","A",1
211,1,74,80,0.0324508,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x \, dx","Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x,x]","\frac{(a+b x) \left(a \sqrt[3]{-(a+b x)^3} \Gamma \left(\frac{1}{3},-(a+b x)^3\right)-(a+b x) \Gamma \left(\frac{2}{3},-(a+b x)^3\right)\right)}{3 b^2 \left(-(a+b x)^3\right)^{2/3}}","\frac{a (a+b x) \Gamma \left(\frac{1}{3},-(a+b x)^3\right)}{3 b^2 \sqrt[3]{-(a+b x)^3}}-\frac{(a+b x)^2 \Gamma \left(\frac{2}{3},-(a+b x)^3\right)}{3 b^2 \left(-(a+b x)^3\right)^{2/3}}",1,"((a + b*x)*(a*(-(a + b*x)^3)^(1/3)*Gamma[1/3, -(a + b*x)^3] - (a + b*x)*Gamma[2/3, -(a + b*x)^3]))/(3*b^2*(-(a + b*x)^3)^(2/3))","A",1
212,1,38,38,0.0055663,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} \, dx","Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3),x]","-\frac{(a+b x) \Gamma \left(\frac{1}{3},-(a+b x)^3\right)}{3 b \sqrt[3]{-(a+b x)^3}}","-\frac{(a+b x) \Gamma \left(\frac{1}{3},-(a+b x)^3\right)}{3 b \sqrt[3]{-(a+b x)^3}}",1,"-1/3*((a + b*x)*Gamma[1/3, -(a + b*x)^3])/(b*(-(a + b*x)^3)^(1/3))","A",1
213,0,0,36,0.2446489,"\int \frac{e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx","Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)/x,x]","\int \frac{e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx","\text{Int}\left(\frac{e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x},x\right)",0,"Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)/x, x]","A",-1
214,0,0,36,0.1900804,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx","Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^m,x]","\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx","\text{Int}\left(x^m e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3},x\right)",0,"Integrate[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^m, x]","A",-1
215,1,26,40,0.0121242,"\int e^{\sqrt{5+3 x}} \, dx","Integrate[E^Sqrt[5 + 3*x],x]","\frac{2}{3} e^{\sqrt{3 x+5}} \left(\sqrt{3 x+5}-1\right)","\frac{2}{3} e^{\sqrt{3 x+5}} \sqrt{3 x+5}-\frac{2}{3} e^{\sqrt{3 x+5}}",1,"(2*E^Sqrt[5 + 3*x]*(-1 + Sqrt[5 + 3*x]))/3","A",1
216,1,241,291,0.2020333,"\int f^{\frac{c}{a+b x}} x^4 \, dx","Integrate[f^(c/(a + b*x))*x^4,x]","\frac{a \left(24 a^4-154 a^3 c \log (f)+102 a^2 c^2 \log ^2(f)-19 a c^3 \log ^3(f)+c^4 \log ^4(f)\right) f^{\frac{c}{a+b x}}}{120 b^5}+\frac{b x f^{\frac{c}{a+b x}} \left(2 c^2 \log ^2(f) \left(43 a^2-7 a b x+b^2 x^2\right)+2 c \log (f) \left(-48 a^3+18 a^2 b x-8 a b^2 x^2+3 b^3 x^3\right)+c^3 \log ^3(f) (b x-18 a)+24 b^4 x^4+c^4 \log ^4(f)\right)-c \log (f) \left(120 a^4-240 a^3 c \log (f)+120 a^2 c^2 \log ^2(f)-20 a c^3 \log ^3(f)+c^4 \log ^4(f)\right) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{120 b^5}","-\frac{a^4 c \log (f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^5}+\frac{a^4 (a+b x) f^{\frac{c}{a+b x}}}{b^5}+\frac{2 a^3 c^2 \log ^2(f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^5}-\frac{2 a^3 (a+b x)^2 f^{\frac{c}{a+b x}}}{b^5}-\frac{2 a^3 c \log (f) (a+b x) f^{\frac{c}{a+b x}}}{b^5}-\frac{a^2 c^3 \log ^3(f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^5}+\frac{a^2 c^2 \log ^2(f) (a+b x) f^{\frac{c}{a+b x}}}{b^5}+\frac{2 a^2 (a+b x)^3 f^{\frac{c}{a+b x}}}{b^5}+\frac{a^2 c \log (f) (a+b x)^2 f^{\frac{c}{a+b x}}}{b^5}-\frac{c^5 \log ^5(f) \Gamma \left(-5,-\frac{c \log (f)}{a+b x}\right)}{b^5}-\frac{4 a c^4 \log ^4(f) \Gamma \left(-4,-\frac{c \log (f)}{a+b x}\right)}{b^5}",1,"(a*f^(c/(a + b*x))*(24*a^4 - 154*a^3*c*Log[f] + 102*a^2*c^2*Log[f]^2 - 19*a*c^3*Log[f]^3 + c^4*Log[f]^4))/(120*b^5) + (-(c*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]*(120*a^4 - 240*a^3*c*Log[f] + 120*a^2*c^2*Log[f]^2 - 20*a*c^3*Log[f]^3 + c^4*Log[f]^4)) + b*f^(c/(a + b*x))*x*(24*b^4*x^4 + 2*c*(-48*a^3 + 18*a^2*b*x - 8*a*b^2*x^2 + 3*b^3*x^3)*Log[f] + 2*c^2*(43*a^2 - 7*a*b*x + b^2*x^2)*Log[f]^2 + c^3*(-18*a + b*x)*Log[f]^3 + c^4*Log[f]^4))/(120*b^5)","A",1
217,1,179,269,0.2003136,"\int f^{\frac{c}{a+b x}} x^3 \, dx","Integrate[f^(c/(a + b*x))*x^3,x]","\frac{b x f^{\frac{c}{a+b x}} \left(2 c \log (f) \left(9 a^2-3 a b x+b^2 x^2\right)+c^2 \log ^2(f) (b x-10 a)+6 b^3 x^3+c^3 \log ^3(f)\right)+c \log (f) \left(24 a^3-36 a^2 c \log (f)+12 a c^2 \log ^2(f)-c^3 \log ^3(f)\right) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{24 b^4}-\frac{a \left(6 a^3-26 a^2 c \log (f)+11 a c^2 \log ^2(f)-c^3 \log ^3(f)\right) f^{\frac{c}{a+b x}}}{24 b^4}","\frac{a^3 c \log (f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^4}-\frac{a^3 (a+b x) f^{\frac{c}{a+b x}}}{b^4}-\frac{3 a^2 c^2 \log ^2(f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{2 b^4}+\frac{3 a^2 (a+b x)^2 f^{\frac{c}{a+b x}}}{2 b^4}+\frac{3 a^2 c \log (f) (a+b x) f^{\frac{c}{a+b x}}}{2 b^4}+\frac{c^4 \log ^4(f) \Gamma \left(-4,-\frac{c \log (f)}{a+b x}\right)}{b^4}+\frac{a c^3 \log ^3(f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{2 b^4}-\frac{a c^2 \log ^2(f) (a+b x) f^{\frac{c}{a+b x}}}{2 b^4}-\frac{a (a+b x)^3 f^{\frac{c}{a+b x}}}{b^4}-\frac{a c \log (f) (a+b x)^2 f^{\frac{c}{a+b x}}}{2 b^4}",1,"-1/24*(a*f^(c/(a + b*x))*(6*a^3 - 26*a^2*c*Log[f] + 11*a*c^2*Log[f]^2 - c^3*Log[f]^3))/b^4 + (c*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]*(24*a^3 - 36*a^2*c*Log[f] + 12*a*c^2*Log[f]^2 - c^3*Log[f]^3) + b*f^(c/(a + b*x))*x*(6*b^3*x^3 + 2*c*(9*a^2 - 3*a*b*x + b^2*x^2)*Log[f] + c^2*(-10*a + b*x)*Log[f]^2 + c^3*Log[f]^3))/(24*b^4)","A",1
218,1,128,229,0.1271633,"\int f^{\frac{c}{a+b x}} x^2 \, dx","Integrate[f^(c/(a + b*x))*x^2,x]","\frac{a \left(2 a^2-5 a c \log (f)+c^2 \log ^2(f)\right) f^{\frac{c}{a+b x}}}{6 b^3}+\frac{b x f^{\frac{c}{a+b x}} \left(\log (f) (b c x-4 a c)+2 b^2 x^2+c^2 \log ^2(f)\right)-c \log (f) \left(6 a^2-6 a c \log (f)+c^2 \log ^2(f)\right) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{6 b^3}","-\frac{a^2 c \log (f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^3}+\frac{a^2 (a+b x) f^{\frac{c}{a+b x}}}{b^3}-\frac{c^3 \log ^3(f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{6 b^3}+\frac{a c^2 \log ^2(f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^3}+\frac{c^2 \log ^2(f) (a+b x) f^{\frac{c}{a+b x}}}{6 b^3}+\frac{(a+b x)^3 f^{\frac{c}{a+b x}}}{3 b^3}-\frac{a (a+b x)^2 f^{\frac{c}{a+b x}}}{b^3}+\frac{c \log (f) (a+b x)^2 f^{\frac{c}{a+b x}}}{6 b^3}-\frac{a c \log (f) (a+b x) f^{\frac{c}{a+b x}}}{b^3}",1,"(a*f^(c/(a + b*x))*(2*a^2 - 5*a*c*Log[f] + c^2*Log[f]^2))/(6*b^3) + (-(c*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]*(6*a^2 - 6*a*c*Log[f] + c^2*Log[f]^2)) + b*f^(c/(a + b*x))*x*(2*b^2*x^2 + (-4*a*c + b*c*x)*Log[f] + c^2*Log[f]^2))/(6*b^3)","A",1
219,1,82,120,0.0692995,"\int f^{\frac{c}{a+b x}} x \, dx","Integrate[f^(c/(a + b*x))*x,x]","\frac{c \log (f) (2 a-c \log (f)) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)+b x f^{\frac{c}{a+b x}} (b x+c \log (f))}{2 b^2}-\frac{a (a-c \log (f)) f^{\frac{c}{a+b x}}}{2 b^2}","-\frac{c^2 \log ^2(f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{2 b^2}+\frac{a c \log (f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^2}+\frac{(a+b x)^2 f^{\frac{c}{a+b x}}}{2 b^2}-\frac{a (a+b x) f^{\frac{c}{a+b x}}}{b^2}+\frac{c \log (f) (a+b x) f^{\frac{c}{a+b x}}}{2 b^2}",1,"-1/2*(a*f^(c/(a + b*x))*(a - c*Log[f]))/b^2 + (c*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]*(2*a - c*Log[f]) + b*f^(c/(a + b*x))*x*(b*x + c*Log[f]))/(2*b^2)","A",1
220,1,41,41,0.0160538,"\int f^{\frac{c}{a+b x}} \, dx","Integrate[f^(c/(a + b*x)),x]","\frac{(a+b x) f^{\frac{c}{a+b x}}}{b}-\frac{c \log (f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b}","\frac{(a+b x) f^{\frac{c}{a+b x}}}{b}-\frac{c \log (f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b}",1,"(f^(c/(a + b*x))*(a + b*x))/b - (c*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f])/b","A",1
221,1,41,41,0.0346472,"\int \frac{f^{\frac{c}{a+b x}}}{x} \, dx","Integrate[f^(c/(a + b*x))/x,x]","f^{\frac{c}{a}} \text{Ei}\left(-\frac{b c x \log (f)}{a^2+b x a}\right)-\text{Ei}\left(\frac{c \log (f)}{a+b x}\right)","f^{\frac{c}{a}} \text{Ei}\left(-\frac{b c x \log (f)}{a (a+b x)}\right)-\text{Ei}\left(\frac{c \log (f)}{a+b x}\right)",1,"-ExpIntegralEi[(c*Log[f])/(a + b*x)] + f^(c/a)*ExpIntegralEi[-((b*c*x*Log[f])/(a^2 + a*b*x))]","A",1
222,1,68,68,0.1095728,"\int \frac{f^{\frac{c}{a+b x}}}{x^2} \, dx","Integrate[f^(c/(a + b*x))/x^2,x]","-\frac{b c \log (f) f^{\frac{c}{a}} \text{Ei}\left(-\frac{b c x \log (f)}{a^2+b x a}\right)}{a^2}-\frac{b f^{\frac{c}{a+b x}}}{a}-\frac{f^{\frac{c}{a+b x}}}{x}","-\frac{b c \log (f) f^{\frac{c}{a}} \text{Ei}\left(-\frac{b c x \log (f)}{a (a+b x)}\right)}{a^2}-\frac{b f^{\frac{c}{a+b x}}}{a}-\frac{f^{\frac{c}{a+b x}}}{x}",1,"-((b*f^(c/(a + b*x)))/a) - f^(c/(a + b*x))/x - (b*c*f^(c/a)*ExpIntegralEi[-((b*c*x*Log[f])/(a^2 + a*b*x))]*Log[f])/a^2","A",1
223,1,115,166,0.1936018,"\int \frac{f^{\frac{c}{a+b x}}}{x^3} \, dx","Integrate[f^(c/(a + b*x))/x^3,x]","\frac{b^2 (2 a+c \log (f)) f^{\frac{c}{a+b x}}}{2 a^3}+\frac{b^2 c \log (f) f^{\frac{c}{a}} (2 a+c \log (f)) \text{Ei}\left(-\frac{b c x \log (f)}{a^2+b x a}\right)-\frac{a^2 f^{\frac{c}{a+b x}} \left(a^2+b^2 x^2-b c x \log (f)\right)}{x^2}}{2 a^4}","\frac{b^2 c^2 \log ^2(f) f^{\frac{c}{a}} \text{Ei}\left(-\frac{b c x \log (f)}{a (a+b x)}\right)}{2 a^4}+\frac{b^2 c \log (f) f^{\frac{c}{a}} \text{Ei}\left(-\frac{b c x \log (f)}{a (a+b x)}\right)}{a^3}+\frac{b^2 c \log (f) f^{\frac{c}{a+b x}}}{2 a^3}+\frac{b^2 f^{\frac{c}{a+b x}}}{2 a^2}+\frac{b c \log (f) f^{\frac{c}{a+b x}}}{2 a^2 x}-\frac{f^{\frac{c}{a+b x}}}{2 x^2}",1,"(b^2*f^(c/(a + b*x))*(2*a + c*Log[f]))/(2*a^3) + (b^2*c*f^(c/a)*ExpIntegralEi[-((b*c*x*Log[f])/(a^2 + a*b*x))]*Log[f]*(2*a + c*Log[f]) - (a^2*f^(c/(a + b*x))*(a^2 + b^2*x^2 - b*c*x*Log[f]))/x^2)/(2*a^4)","A",1
224,1,195,415,0.2219226,"\int f^{\frac{c}{(a+b x)^2}} x^4 \, dx","Integrate[f^(c/(a + b*x)^2)*x^4,x]","\frac{a \left(3 a^4+47 a^2 c \log (f)+4 c^2 \log ^2(f)\right) f^{\frac{c}{(a+b x)^2}}}{15 b^5}+\frac{b x f^{\frac{c}{(a+b x)^2}} \left(c \log (f) \left(36 a^2-9 a b x+2 b^2 x^2\right)+3 b^4 x^4+4 c^2 \log ^2(f)\right)+15 a c \log (f) \left(2 a^2+c \log (f)\right) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)-\sqrt{\pi } \sqrt{c} \sqrt{\log (f)} \left(15 a^4+60 a^2 c \log (f)+4 c^2 \log ^2(f)\right) \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{15 b^5}","-\frac{\sqrt{\pi } a^4 \sqrt{c} \sqrt{\log (f)} \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{b^5}+\frac{a^4 (a+b x) f^{\frac{c}{(a+b x)^2}}}{b^5}+\frac{2 a^3 c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)}{b^5}-\frac{2 a^3 (a+b x)^2 f^{\frac{c}{(a+b x)^2}}}{b^5}-\frac{4 \sqrt{\pi } a^2 c^{3/2} \log ^{\frac{3}{2}}(f) \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{b^5}+\frac{2 a^2 (a+b x)^3 f^{\frac{c}{(a+b x)^2}}}{b^5}+\frac{4 a^2 c \log (f) (a+b x) f^{\frac{c}{(a+b x)^2}}}{b^5}-\frac{4 \sqrt{\pi } c^{5/2} \log ^{\frac{5}{2}}(f) \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{15 b^5}+\frac{a c^2 \log ^2(f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)}{b^5}+\frac{4 c^2 \log ^2(f) (a+b x) f^{\frac{c}{(a+b x)^2}}}{15 b^5}+\frac{(a+b x)^5 f^{\frac{c}{(a+b x)^2}}}{5 b^5}-\frac{a (a+b x)^4 f^{\frac{c}{(a+b x)^2}}}{b^5}+\frac{2 c \log (f) (a+b x)^3 f^{\frac{c}{(a+b x)^2}}}{15 b^5}-\frac{a c \log (f) (a+b x)^2 f^{\frac{c}{(a+b x)^2}}}{b^5}",1,"(a*f^(c/(a + b*x)^2)*(3*a^4 + 47*a^2*c*Log[f] + 4*c^2*Log[f]^2))/(15*b^5) + (15*a*c*ExpIntegralEi[(c*Log[f])/(a + b*x)^2]*Log[f]*(2*a^2 + c*Log[f]) - Sqrt[c]*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Sqrt[Log[f]]*(15*a^4 + 60*a^2*c*Log[f] + 4*c^2*Log[f]^2) + b*f^(c/(a + b*x)^2)*x*(3*b^4*x^4 + c*(36*a^2 - 9*a*b*x + 2*b^2*x^2)*Log[f] + 4*c^2*Log[f]^2))/(15*b^5)","A",1
225,1,148,291,0.1495295,"\int f^{\frac{c}{(a+b x)^2}} x^3 \, dx","Integrate[f^(c/(a + b*x)^2)*x^3,x]","\frac{4 \sqrt{\pi } a \sqrt{c} \sqrt{\log (f)} \left(a^2+2 c \log (f)\right) \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)-c \log (f) \left(6 a^2+c \log (f)\right) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)+b x f^{\frac{c}{(a+b x)^2}} \left(-6 a c \log (f)+b^3 x^3+b c x \log (f)\right)}{4 b^4}-\frac{a^2 \left(a^2+7 c \log (f)\right) f^{\frac{c}{(a+b x)^2}}}{4 b^4}","\frac{\sqrt{\pi } a^3 \sqrt{c} \sqrt{\log (f)} \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{b^4}-\frac{a^3 (a+b x) f^{\frac{c}{(a+b x)^2}}}{b^4}-\frac{3 a^2 c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)}{2 b^4}+\frac{3 a^2 (a+b x)^2 f^{\frac{c}{(a+b x)^2}}}{2 b^4}+\frac{2 \sqrt{\pi } a c^{3/2} \log ^{\frac{3}{2}}(f) \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{b^4}-\frac{c^2 \log ^2(f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)}{4 b^4}+\frac{(a+b x)^4 f^{\frac{c}{(a+b x)^2}}}{4 b^4}-\frac{a (a+b x)^3 f^{\frac{c}{(a+b x)^2}}}{b^4}+\frac{c \log (f) (a+b x)^2 f^{\frac{c}{(a+b x)^2}}}{4 b^4}-\frac{2 a c \log (f) (a+b x) f^{\frac{c}{(a+b x)^2}}}{b^4}",1,"-1/4*(a^2*f^(c/(a + b*x)^2)*(a^2 + 7*c*Log[f]))/b^4 + (-(c*ExpIntegralEi[(c*Log[f])/(a + b*x)^2]*Log[f]*(6*a^2 + c*Log[f])) + 4*a*Sqrt[c]*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Sqrt[Log[f]]*(a^2 + 2*c*Log[f]) + b*f^(c/(a + b*x)^2)*x*(b^3*x^3 - 6*a*c*Log[f] + b*c*x*Log[f]))/(4*b^4)","A",1
226,1,131,206,0.1153574,"\int f^{\frac{c}{(a+b x)^2}} x^2 \, dx","Integrate[f^(c/(a + b*x)^2)*x^2,x]","\frac{a \left(a^2+2 c \log (f)\right) f^{\frac{c}{(a+b x)^2}}}{3 b^3}+\frac{-\sqrt{\pi } \sqrt{c} \sqrt{\log (f)} \left(3 a^2+2 c \log (f)\right) \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)+b x f^{\frac{c}{(a+b x)^2}} \left(b^2 x^2+2 c \log (f)\right)+3 a c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)}{3 b^3}","-\frac{\sqrt{\pi } a^2 \sqrt{c} \sqrt{\log (f)} \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{b^3}+\frac{a^2 (a+b x) f^{\frac{c}{(a+b x)^2}}}{b^3}-\frac{2 \sqrt{\pi } c^{3/2} \log ^{\frac{3}{2}}(f) \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{3 b^3}+\frac{a c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)}{b^3}+\frac{(a+b x)^3 f^{\frac{c}{(a+b x)^2}}}{3 b^3}-\frac{a (a+b x)^2 f^{\frac{c}{(a+b x)^2}}}{b^3}+\frac{2 c \log (f) (a+b x) f^{\frac{c}{(a+b x)^2}}}{3 b^3}",1,"(a*f^(c/(a + b*x)^2)*(a^2 + 2*c*Log[f]))/(3*b^3) + (3*a*c*ExpIntegralEi[(c*Log[f])/(a + b*x)^2]*Log[f] - Sqrt[c]*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Sqrt[Log[f]]*(3*a^2 + 2*c*Log[f]) + b*f^(c/(a + b*x)^2)*x*(b^2*x^2 + 2*c*Log[f]))/(3*b^3)","A",1
227,1,89,111,0.0538801,"\int f^{\frac{c}{(a+b x)^2}} x \, dx","Integrate[f^(c/(a + b*x)^2)*x,x]","\frac{\left(b^2 x^2-a^2\right) f^{\frac{c}{(a+b x)^2}}+2 \sqrt{\pi } a \sqrt{c} \sqrt{\log (f)} \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)-c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)}{2 b^2}","\frac{\sqrt{\pi } a \sqrt{c} \sqrt{\log (f)} \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{b^2}-\frac{c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)}{2 b^2}+\frac{(a+b x)^2 f^{\frac{c}{(a+b x)^2}}}{2 b^2}-\frac{a (a+b x) f^{\frac{c}{(a+b x)^2}}}{b^2}",1,"(f^(c/(a + b*x)^2)*(-a^2 + b^2*x^2) + 2*a*Sqrt[c]*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Sqrt[Log[f]] - c*ExpIntegralEi[(c*Log[f])/(a + b*x)^2]*Log[f])/(2*b^2)","A",1
228,1,62,62,0.0210247,"\int f^{\frac{c}{(a+b x)^2}} \, dx","Integrate[f^(c/(a + b*x)^2),x]","\frac{(a+b x) f^{\frac{c}{(a+b x)^2}}}{b}-\frac{\sqrt{\pi } \sqrt{c} \sqrt{\log (f)} \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{b}","\frac{(a+b x) f^{\frac{c}{(a+b x)^2}}}{b}-\frac{\sqrt{\pi } \sqrt{c} \sqrt{\log (f)} \text{erfi}\left(\frac{\sqrt{c} \sqrt{\log (f)}}{a+b x}\right)}{b}",1,"(f^(c/(a + b*x)^2)*(a + b*x))/b - (Sqrt[c]*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Sqrt[Log[f]])/b","A",1
229,0,0,18,0.0723283,"\int \frac{f^{\frac{c}{(a+b x)^2}}}{x} \, dx","Integrate[f^(c/(a + b*x)^2)/x,x]","\int \frac{f^{\frac{c}{(a+b x)^2}}}{x} \, dx","\text{Int}\left(\frac{f^{\frac{c}{(a+b x)^2}}}{x},x\right)",0,"Integrate[f^(c/(a + b*x)^2)/x, x]","A",-1
230,0,0,18,0.2346202,"\int \frac{f^{\frac{c}{(a+b x)^2}}}{x^2} \, dx","Integrate[f^(c/(a + b*x)^2)/x^2,x]","\int \frac{f^{\frac{c}{(a+b x)^2}}}{x^2} \, dx","\text{Int}\left(\frac{f^{\frac{c}{(a+b x)^2}}}{x^2},x\right)",0,"Integrate[f^(c/(a + b*x)^2)/x^2, x]","A",-1
231,0,0,18,0.2928767,"\int \frac{f^{\frac{c}{(a+b x)^2}}}{x^3} \, dx","Integrate[f^(c/(a + b*x)^2)/x^3,x]","\int \frac{f^{\frac{c}{(a+b x)^2}}}{x^3} \, dx","\text{Int}\left(\frac{f^{\frac{c}{(a+b x)^2}}}{x^3},x\right)",0,"Integrate[f^(c/(a + b*x)^2)/x^3, x]","A",-1
232,1,219,239,0.193298,"\int f^{\frac{c}{(a+b x)^3}} x^4 \, dx","Integrate[f^(c/(a + b*x)^3)*x^4,x]","\frac{a^4 (a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)-4 a^3 (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{c \log (f)}{(a+b x)^3}\right)-6 a^2 c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^3}\right)+6 a^2 (a+b x)^3 f^{\frac{c}{(a+b x)^3}}+(a+b x)^5 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{5/3} \Gamma \left(-\frac{5}{3},-\frac{c \log (f)}{(a+b x)^3}\right)+4 a c \log (f) (a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{4}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^5}","\frac{a^4 (a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^5}-\frac{4 a^3 (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^5}-\frac{2 a^2 c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^3}\right)}{b^5}+\frac{2 a^2 (a+b x)^3 f^{\frac{c}{(a+b x)^3}}}{b^5}+\frac{(a+b x)^5 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{5/3} \Gamma \left(-\frac{5}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^5}-\frac{4 a (a+b x)^4 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{4/3} \Gamma \left(-\frac{4}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^5}",1,"(6*a^2*f^(c/(a + b*x)^3)*(a + b*x)^3 - 6*a^2*c*ExpIntegralEi[(c*Log[f])/(a + b*x)^3]*Log[f] + a^4*(a + b*x)*Gamma[-1/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(1/3) + 4*a*c*(a + b*x)*Gamma[-4/3, -((c*Log[f])/(a + b*x)^3)]*Log[f]*(-((c*Log[f])/(a + b*x)^3))^(1/3) - 4*a^3*(a + b*x)^2*Gamma[-2/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(2/3) + (a + b*x)^5*Gamma[-5/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(5/3))/(3*b^5)","A",1
233,1,167,184,0.371546,"\int f^{\frac{c}{(a+b x)^3}} x^3 \, dx","Integrate[f^(c/(a + b*x)^3)*x^3,x]","\frac{3 a c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^3}\right)-(a+b x) \left(a^3 \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)+3 a (a+b x) \left((a+b x) f^{\frac{c}{(a+b x)^3}}-a \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{c \log (f)}{(a+b x)^3}\right)\right)+c \log (f) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{4}{3},-\frac{c \log (f)}{(a+b x)^3}\right)\right)}{3 b^4}","-\frac{a^3 (a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^4}+\frac{a^2 (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{b^4}+\frac{a c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^3}\right)}{b^4}-\frac{a (a+b x)^3 f^{\frac{c}{(a+b x)^3}}}{b^4}+\frac{(a+b x)^4 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{4/3} \Gamma \left(-\frac{4}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^4}",1,"(3*a*c*ExpIntegralEi[(c*Log[f])/(a + b*x)^3]*Log[f] - (a + b*x)*(a^3*Gamma[-1/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(1/3) + c*Gamma[-4/3, -((c*Log[f])/(a + b*x)^3)]*Log[f]*(-((c*Log[f])/(a + b*x)^3))^(1/3) + 3*a*(a + b*x)*(f^(c/(a + b*x)^3)*(a + b*x) - a*Gamma[-2/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(2/3))))/(3*b^4)","A",1
234,1,127,142,0.0671244,"\int f^{\frac{c}{(a+b x)^3}} x^2 \, dx","Integrate[f^(c/(a + b*x)^3)*x^2,x]","\frac{a^2 (a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)-c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^3}\right)+(a+b x)^3 f^{\frac{c}{(a+b x)^3}}-2 a (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^3}","\frac{a^2 (a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^3}-\frac{c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^3}+\frac{(a+b x)^3 f^{\frac{c}{(a+b x)^3}}}{3 b^3}-\frac{2 a (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^3}",1,"(f^(c/(a + b*x)^3)*(a + b*x)^3 - c*ExpIntegralEi[(c*Log[f])/(a + b*x)^3]*Log[f] + a^2*(a + b*x)*Gamma[-1/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(1/3) - 2*a*(a + b*x)^2*Gamma[-2/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(2/3))/(3*b^3)","A",1
235,1,86,92,0.0690675,"\int f^{\frac{c}{(a+b x)^3}} x \, dx","Integrate[f^(c/(a + b*x)^3)*x,x]","\frac{(a+b x) \left((a+b x) \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{c \log (f)}{(a+b x)^3}\right)-a \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)\right)}{3 b^2}","\frac{(a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^2}-\frac{a (a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^2}",1,"((a + b*x)*(-(a*Gamma[-1/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(1/3)) + (a + b*x)*Gamma[-2/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(2/3)))/(3*b^2)","A",1
236,1,44,44,0.0083256,"\int f^{\frac{c}{(a+b x)^3}} \, dx","Integrate[f^(c/(a + b*x)^3),x]","\frac{(a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b}","\frac{(a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \Gamma \left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b}",1,"((a + b*x)*Gamma[-1/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(1/3))/(3*b)","A",1
237,0,0,18,0.061777,"\int \frac{f^{\frac{c}{(a+b x)^3}}}{x} \, dx","Integrate[f^(c/(a + b*x)^3)/x,x]","\int \frac{f^{\frac{c}{(a+b x)^3}}}{x} \, dx","\text{Int}\left(\frac{f^{\frac{c}{(a+b x)^3}}}{x},x\right)",0,"Integrate[f^(c/(a + b*x)^3)/x, x]","A",-1
238,0,0,18,0.2917053,"\int \frac{f^{\frac{c}{(a+b x)^3}}}{x^2} \, dx","Integrate[f^(c/(a + b*x)^3)/x^2,x]","\int \frac{f^{\frac{c}{(a+b x)^3}}}{x^2} \, dx","\text{Int}\left(\frac{f^{\frac{c}{(a+b x)^3}}}{x^2},x\right)",0,"Integrate[f^(c/(a + b*x)^3)/x^2, x]","A",-1
239,0,0,18,0.0367493,"\int \frac{f^{\frac{c}{(a+b x)^3}}}{x^3} \, dx","Integrate[f^(c/(a + b*x)^3)/x^3,x]","\int \frac{f^{\frac{c}{(a+b x)^3}}}{x^3} \, dx","\text{Int}\left(\frac{f^{\frac{c}{(a+b x)^3}}}{x^3},x\right)",0,"Integrate[f^(c/(a + b*x)^3)/x^3, x]","A",-1
240,0,0,18,0.24594,"\int f^{c (a+b x)^3} x^m \, dx","Integrate[f^(c*(a + b*x)^3)*x^m,x]","\int f^{c (a+b x)^3} x^m \, dx","\text{Int}\left(x^m f^{c (a+b x)^3},x\right)",0,"Integrate[f^(c*(a + b*x)^3)*x^m, x]","A",-1
241,0,0,29,0.1476401,"\int f^{c (a+b x)^2} x^m \, dx","Integrate[f^(c*(a + b*x)^2)*x^m,x]","\int f^{c (a+b x)^2} x^m \, dx","\text{Int}\left(x^m f^{a^2 c+2 a b c x+b^2 c x^2},x\right)",0,"Integrate[f^(c*(a + b*x)^2)*x^m, x]","A",-1
242,1,36,41,0.0146879,"\int f^{c (a+b x)} x^m \, dx","Integrate[f^(c*(a + b*x))*x^m,x]","x^{m+1} \left(-f^{a c}\right) (-b c x \log (f))^{-m-1} \Gamma (m+1,-b c x \log (f))","\frac{x^m f^{a c} (-b c x \log (f))^{-m} \Gamma (m+1,-b c x \log (f))}{b c \log (f)}",1,"-(f^(a*c)*x^(1 + m)*Gamma[1 + m, -(b*c*x*Log[f])]*(-(b*c*x*Log[f]))^(-1 - m))","A",1
243,0,0,18,0.0458962,"\int f^{\frac{c}{a+b x}} x^m \, dx","Integrate[f^(c/(a + b*x))*x^m,x]","\int f^{\frac{c}{a+b x}} x^m \, dx","\text{Int}\left(x^m f^{\frac{c}{a+b x}},x\right)",0,"Integrate[f^(c/(a + b*x))*x^m, x]","A",-1
244,0,0,18,0.0884518,"\int f^{\frac{c}{(a+b x)^2}} x^m \, dx","Integrate[f^(c/(a + b*x)^2)*x^m,x]","\int f^{\frac{c}{(a+b x)^2}} x^m \, dx","\text{Int}\left(x^m f^{\frac{c}{(a+b x)^2}},x\right)",0,"Integrate[f^(c/(a + b*x)^2)*x^m, x]","A",-1
245,0,0,18,0.0802906,"\int f^{\frac{c}{(a+b x)^3}} x^m \, dx","Integrate[f^(c/(a + b*x)^3)*x^m,x]","\int f^{\frac{c}{(a+b x)^3}} x^m \, dx","\text{Int}\left(x^m f^{\frac{c}{(a+b x)^3}},x\right)",0,"Integrate[f^(c/(a + b*x)^3)*x^m, x]","A",-1
246,0,0,18,0.0541461,"\int f^{c (a+b x)^n} x^m \, dx","Integrate[f^(c*(a + b*x)^n)*x^m,x]","\int f^{c (a+b x)^n} x^m \, dx","\text{Int}\left(x^m f^{c (a+b x)^n},x\right)",0,"Integrate[f^(c*(a + b*x)^n)*x^m, x]","A",-1
247,1,183,207,0.1603436,"\int f^{c (a+b x)^n} x^3 \, dx","Integrate[f^(c*(a + b*x)^n)*x^3,x]","-\frac{(a+b x) \left(-c \log (f) (a+b x)^n\right)^{-4/n} \left((a+b x)^3 \Gamma \left(\frac{4}{n},-c (a+b x)^n \log (f)\right)-a \left(-c \log (f) (a+b x)^n\right)^{\frac{1}{n}} \left(a \left(-c \log (f) (a+b x)^n\right)^{\frac{1}{n}} \left(a \left(-c \log (f) (a+b x)^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-c (a+b x)^n \log (f)\right)-3 (a+b x) \Gamma \left(\frac{2}{n},-c (a+b x)^n \log (f)\right)\right)+3 (a+b x)^2 \Gamma \left(\frac{3}{n},-c (a+b x)^n \log (f)\right)\right)\right)}{b^4 n}","\frac{a^3 (a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-c (a+b x)^n \log (f)\right)}{b^4 n}-\frac{3 a^2 (a+b x)^2 \left(-c \log (f) (a+b x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-c (a+b x)^n \log (f)\right)}{b^4 n}-\frac{(a+b x)^4 \left(-c \log (f) (a+b x)^n\right)^{-4/n} \Gamma \left(\frac{4}{n},-c (a+b x)^n \log (f)\right)}{b^4 n}+\frac{3 a (a+b x)^3 \left(-c \log (f) (a+b x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-c (a+b x)^n \log (f)\right)}{b^4 n}",1,"-(((a + b*x)*((a + b*x)^3*Gamma[4/n, -(c*(a + b*x)^n*Log[f])] - a*(-(c*(a + b*x)^n*Log[f]))^n^(-1)*(3*(a + b*x)^2*Gamma[3/n, -(c*(a + b*x)^n*Log[f])] + a*(-(c*(a + b*x)^n*Log[f]))^n^(-1)*(-3*(a + b*x)*Gamma[2/n, -(c*(a + b*x)^n*Log[f])] + a*Gamma[n^(-1), -(c*(a + b*x)^n*Log[f])]*(-(c*(a + b*x)^n*Log[f]))^n^(-1)))))/(b^4*n*(-(c*(a + b*x)^n*Log[f]))^(4/n)))","A",1
248,1,136,154,0.0831392,"\int f^{c (a+b x)^n} x^2 \, dx","Integrate[f^(c*(a + b*x)^n)*x^2,x]","-\frac{(a+b x) \left(-c \log (f) (a+b x)^n\right)^{-3/n} \left(a \left(-c \log (f) (a+b x)^n\right)^{\frac{1}{n}} \left(a \left(-c \log (f) (a+b x)^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-c (a+b x)^n \log (f)\right)-2 (a+b x) \Gamma \left(\frac{2}{n},-c (a+b x)^n \log (f)\right)\right)+(a+b x)^2 \Gamma \left(\frac{3}{n},-c (a+b x)^n \log (f)\right)\right)}{b^3 n}","-\frac{a^2 (a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-c (a+b x)^n \log (f)\right)}{b^3 n}-\frac{(a+b x)^3 \left(-c \log (f) (a+b x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-c (a+b x)^n \log (f)\right)}{b^3 n}+\frac{2 a (a+b x)^2 \left(-c \log (f) (a+b x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-c (a+b x)^n \log (f)\right)}{b^3 n}",1,"-(((a + b*x)*((a + b*x)^2*Gamma[3/n, -(c*(a + b*x)^n*Log[f])] + a*(-(c*(a + b*x)^n*Log[f]))^n^(-1)*(-2*(a + b*x)*Gamma[2/n, -(c*(a + b*x)^n*Log[f])] + a*Gamma[n^(-1), -(c*(a + b*x)^n*Log[f])]*(-(c*(a + b*x)^n*Log[f]))^n^(-1))))/(b^3*n*(-(c*(a + b*x)^n*Log[f]))^(3/n)))","A",1
249,1,91,99,0.0375935,"\int f^{c (a+b x)^n} x \, dx","Integrate[f^(c*(a + b*x)^n)*x,x]","-\frac{(a+b x) \left(-c \log (f) (a+b x)^n\right)^{-2/n} \left((a+b x) \Gamma \left(\frac{2}{n},-c (a+b x)^n \log (f)\right)-a \left(-c \log (f) (a+b x)^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-c (a+b x)^n \log (f)\right)\right)}{b^2 n}","\frac{a (a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-c (a+b x)^n \log (f)\right)}{b^2 n}-\frac{(a+b x)^2 \left(-c \log (f) (a+b x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-c (a+b x)^n \log (f)\right)}{b^2 n}",1,"-(((a + b*x)*((a + b*x)*Gamma[2/n, -(c*(a + b*x)^n*Log[f])] - a*Gamma[n^(-1), -(c*(a + b*x)^n*Log[f])]*(-(c*(a + b*x)^n*Log[f]))^n^(-1)))/(b^2*n*(-(c*(a + b*x)^n*Log[f]))^(2/n)))","A",1
250,1,47,47,0.0067542,"\int f^{c (a+b x)^n} \, dx","Integrate[f^(c*(a + b*x)^n),x]","-\frac{(a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-c (a+b x)^n \log (f)\right)}{b n}","-\frac{(a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-c (a+b x)^n \log (f)\right)}{b n}",1,"-(((a + b*x)*Gamma[n^(-1), -(c*(a + b*x)^n*Log[f])])/(b*n*(-(c*(a + b*x)^n*Log[f]))^n^(-1)))","A",1
251,0,0,18,0.0421328,"\int \frac{f^{c (a+b x)^n}}{x} \, dx","Integrate[f^(c*(a + b*x)^n)/x,x]","\int \frac{f^{c (a+b x)^n}}{x} \, dx","\text{Int}\left(\frac{f^{c (a+b x)^n}}{x},x\right)",0,"Integrate[f^(c*(a + b*x)^n)/x, x]","A",-1
252,0,0,18,0.0335551,"\int \frac{f^{c (a+b x)^n}}{x^2} \, dx","Integrate[f^(c*(a + b*x)^n)/x^2,x]","\int \frac{f^{c (a+b x)^n}}{x^2} \, dx","\text{Int}\left(\frac{f^{c (a+b x)^n}}{x^2},x\right)",0,"Integrate[f^(c*(a + b*x)^n)/x^2, x]","A",-1
253,0,0,18,0.0360995,"\int \frac{f^{c (a+b x)^n}}{x^3} \, dx","Integrate[f^(c*(a + b*x)^n)/x^3,x]","\int \frac{f^{c (a+b x)^n}}{x^3} \, dx","\text{Int}\left(\frac{f^{c (a+b x)^n}}{x^3},x\right)",0,"Integrate[f^(c*(a + b*x)^n)/x^3, x]","A",-1
254,1,61,61,0.0375052,"\int F^{a+b (c+d x)^2} (c+d x)^m \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^m,x]","-\frac{F^a (c+d x)^{m+1} \left(-b \log (F) (c+d x)^2\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},-b (c+d x)^2 \log (F)\right)}{2 d}","-\frac{F^a (c+d x)^{m+1} \left(-b \log (F) (c+d x)^2\right)^{\frac{1}{2} (-m-1)} \Gamma \left(\frac{m+1}{2},-b (c+d x)^2 \log (F)\right)}{2 d}",1,"-1/2*(F^a*(c + d*x)^(1 + m)*Gamma[(1 + m)/2, -(b*(c + d*x)^2*Log[F])]*(-(b*(c + d*x)^2*Log[F]))^((-1 - m)/2))/d","A",1
255,1,31,105,0.0085779,"\int F^{a+b (c+d x)^2} (c+d x)^{11} \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^11,x]","-\frac{F^a \Gamma \left(6,-b (c+d x)^2 \log (F)\right)}{2 b^6 d \log ^6(F)}","-\frac{F^{a+b (c+d x)^2} \left(-b^5 \log ^5(F) (c+d x)^{10}+5 b^4 \log ^4(F) (c+d x)^8-20 b^3 \log ^3(F) (c+d x)^6+60 b^2 \log ^2(F) (c+d x)^4-120 b \log (F) (c+d x)^2+120\right)}{2 b^6 d \log ^6(F)}",1,"-1/2*(F^a*Gamma[6, -(b*(c + d*x)^2*Log[F])])/(b^6*d*Log[F]^6)","C",1
256,1,31,88,0.0094313,"\int F^{a+b (c+d x)^2} (c+d x)^9 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^9,x]","\frac{F^a \Gamma \left(5,-b (c+d x)^2 \log (F)\right)}{2 b^5 d \log ^5(F)}","\frac{F^{a+b (c+d x)^2} \left(b^4 \log ^4(F) (c+d x)^8-4 b^3 \log ^3(F) (c+d x)^6+12 b^2 \log ^2(F) (c+d x)^4-24 b \log (F) (c+d x)^2+24\right)}{2 b^5 d \log ^5(F)}",1,"(F^a*Gamma[5, -(b*(c + d*x)^2*Log[F])])/(2*b^5*d*Log[F]^5)","C",1
257,1,72,126,0.0434191,"\int F^{a+b (c+d x)^2} (c+d x)^7 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^7,x]","\frac{F^{a+b (c+d x)^2} \left(b^3 \log ^3(F) (c+d x)^6-3 b^2 \log ^2(F) (c+d x)^4+6 b \log (F) (c+d x)^2-6\right)}{2 b^4 d \log ^4(F)}","-\frac{3 F^{a+b (c+d x)^2}}{b^4 d \log ^4(F)}+\frac{3 (c+d x)^2 F^{a+b (c+d x)^2}}{b^3 d \log ^3(F)}-\frac{3 (c+d x)^4 F^{a+b (c+d x)^2}}{2 b^2 d \log ^2(F)}+\frac{(c+d x)^6 F^{a+b (c+d x)^2}}{2 b d \log (F)}",1,"(F^(a + b*(c + d*x)^2)*(-6 + 6*b*(c + d*x)^2*Log[F] - 3*b^2*(c + d*x)^4*Log[F]^2 + b^3*(c + d*x)^6*Log[F]^3))/(2*b^4*d*Log[F]^4)","A",1
258,1,56,91,0.0334435,"\int F^{a+b (c+d x)^2} (c+d x)^5 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^5,x]","\frac{F^{a+b (c+d x)^2} \left(b^2 \log ^2(F) (c+d x)^4-2 b \log (F) (c+d x)^2+2\right)}{2 b^3 d \log ^3(F)}","\frac{F^{a+b (c+d x)^2}}{b^3 d \log ^3(F)}-\frac{(c+d x)^2 F^{a+b (c+d x)^2}}{b^2 d \log ^2(F)}+\frac{(c+d x)^4 F^{a+b (c+d x)^2}}{2 b d \log (F)}",1,"(F^(a + b*(c + d*x)^2)*(2 - 2*b*(c + d*x)^2*Log[F] + b^2*(c + d*x)^4*Log[F]^2))/(2*b^3*d*Log[F]^3)","A",1
259,1,40,62,0.0222623,"\int F^{a+b (c+d x)^2} (c+d x)^3 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^3,x]","\frac{F^{a+b (c+d x)^2} \left(b \log (F) (c+d x)^2-1\right)}{2 b^2 d \log ^2(F)}","\frac{(c+d x)^2 F^{a+b (c+d x)^2}}{2 b d \log (F)}-\frac{F^{a+b (c+d x)^2}}{2 b^2 d \log ^2(F)}",1,"(F^(a + b*(c + d*x)^2)*(-1 + b*(c + d*x)^2*Log[F]))/(2*b^2*d*Log[F]^2)","A",1
260,1,27,27,0.0064465,"\int F^{a+b (c+d x)^2} (c+d x) \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x),x]","\frac{F^{a+b (c+d x)^2}}{2 b d \log (F)}","\frac{F^{a+b (c+d x)^2}}{2 b d \log (F)}",1,"F^(a + b*(c + d*x)^2)/(2*b*d*Log[F])","A",1
261,1,22,22,0.0059832,"\int \frac{F^{a+b (c+d x)^2}}{c+d x} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x),x]","\frac{F^a \text{Ei}\left(b (c+d x)^2 \log (F)\right)}{2 d}","\frac{F^a \text{Ei}\left(b (c+d x)^2 \log (F)\right)}{2 d}",1,"(F^a*ExpIntegralEi[b*(c + d*x)^2*Log[F]])/(2*d)","A",1
262,1,47,53,0.0393216,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^3} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^3,x]","\frac{F^a \left(b \log (F) \text{Ei}\left(b (c+d x)^2 \log (F)\right)-\frac{F^{b (c+d x)^2}}{(c+d x)^2}\right)}{2 d}","\frac{b F^a \log (F) \text{Ei}\left(b (c+d x)^2 \log (F)\right)}{2 d}-\frac{F^{a+b (c+d x)^2}}{2 d (c+d x)^2}",1,"(F^a*(-(F^(b*(c + d*x)^2)/(c + d*x)^2) + b*ExpIntegralEi[b*(c + d*x)^2*Log[F]]*Log[F]))/(2*d)","A",1
263,1,64,87,0.0742279,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^5} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^5,x]","\frac{F^a \left(b^2 \log ^2(F) \text{Ei}\left(b (c+d x)^2 \log (F)\right)-\frac{F^{b (c+d x)^2} \left(b \log (F) (c+d x)^2+1\right)}{(c+d x)^4}\right)}{4 d}","\frac{b^2 F^a \log ^2(F) \text{Ei}\left(b (c+d x)^2 \log (F)\right)}{4 d}-\frac{F^{a+b (c+d x)^2}}{4 d (c+d x)^4}-\frac{b \log (F) F^{a+b (c+d x)^2}}{4 d (c+d x)^2}",1,"(F^a*(b^2*ExpIntegralEi[b*(c + d*x)^2*Log[F]]*Log[F]^2 - (F^(b*(c + d*x)^2)*(1 + b*(c + d*x)^2*Log[F]))/(c + d*x)^4))/(4*d)","A",1
264,1,79,121,0.0889975,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^7} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^7,x]","\frac{F^a \left(b^3 \log ^3(F) \text{Ei}\left(b (c+d x)^2 \log (F)\right)-\frac{F^{b (c+d x)^2} \left(b^2 \log ^2(F) (c+d x)^4+b \log (F) (c+d x)^2+2\right)}{(c+d x)^6}\right)}{12 d}","\frac{b^3 F^a \log ^3(F) \text{Ei}\left(b (c+d x)^2 \log (F)\right)}{12 d}-\frac{b^2 \log ^2(F) F^{a+b (c+d x)^2}}{12 d (c+d x)^2}-\frac{F^{a+b (c+d x)^2}}{6 d (c+d x)^6}-\frac{b \log (F) F^{a+b (c+d x)^2}}{12 d (c+d x)^4}",1,"(F^a*(b^3*ExpIntegralEi[b*(c + d*x)^2*Log[F]]*Log[F]^3 - (F^(b*(c + d*x)^2)*(2 + b*(c + d*x)^2*Log[F] + b^2*(c + d*x)^4*Log[F]^2))/(c + d*x)^6))/(12*d)","A",1
265,1,31,31,0.0069335,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^9} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^9,x]","-\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-b (c+d x)^2 \log (F)\right)}{2 d}","-\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-b (c+d x)^2 \log (F)\right)}{2 d}",1,"-1/2*(b^4*F^a*Gamma[-4, -(b*(c + d*x)^2*Log[F])]*Log[F]^4)/d","A",1
266,1,31,31,0.0070332,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^{11}} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^11,x]","\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-b (c+d x)^2 \log (F)\right)}{2 d}","\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-b (c+d x)^2 \log (F)\right)}{2 d}",1,"(b^5*F^a*Gamma[-5, -(b*(c + d*x)^2*Log[F])]*Log[F]^5)/(2*d)","A",1
267,1,49,49,0.0274397,"\int F^{a+b (c+d x)^2} (c+d x)^{12} \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^12,x]","-\frac{F^a (c+d x)^{13} \Gamma \left(\frac{13}{2},-b (c+d x)^2 \log (F)\right)}{2 d \left(-b \log (F) (c+d x)^2\right)^{13/2}}","-\frac{F^a (c+d x)^{13} \Gamma \left(\frac{13}{2},-b (c+d x)^2 \log (F)\right)}{2 d \left(-b \log (F) (c+d x)^2\right)^{13/2}}",1,"-1/2*(F^a*(c + d*x)^13*Gamma[13/2, -(b*(c + d*x)^2*Log[F])])/(d*(-(b*(c + d*x)^2*Log[F]))^(13/2))","A",1
268,1,49,49,0.025366,"\int F^{a+b (c+d x)^2} (c+d x)^{10} \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^10,x]","-\frac{F^a (c+d x)^{11} \Gamma \left(\frac{11}{2},-b (c+d x)^2 \log (F)\right)}{2 d \left(-b \log (F) (c+d x)^2\right)^{11/2}}","-\frac{F^a (c+d x)^{11} \Gamma \left(\frac{11}{2},-b (c+d x)^2 \log (F)\right)}{2 d \left(-b \log (F) (c+d x)^2\right)^{11/2}}",1,"-1/2*(F^a*(c + d*x)^11*Gamma[11/2, -(b*(c + d*x)^2*Log[F])])/(d*(-(b*(c + d*x)^2*Log[F]))^(11/2))","A",1
269,1,153,179,0.3803959,"\int F^{a+b (c+d x)^2} (c+d x)^8 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^8,x]","\frac{F^a \left(\frac{105 \sqrt{\pi } \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{b^{7/2} \log ^{\frac{7}{2}}(F)}-\frac{210 (c+d x) F^{b (c+d x)^2}}{b^3 \log ^3(F)}+\frac{140 (c+d x)^3 F^{b (c+d x)^2}}{b^2 \log ^2(F)}+16 (c+d x)^7 F^{b (c+d x)^2}-\frac{56 (c+d x)^5 F^{b (c+d x)^2}}{b \log (F)}\right)}{32 b d \log (F)}","\frac{105 \sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{32 b^{9/2} d \log ^{\frac{9}{2}}(F)}-\frac{105 (c+d x) F^{a+b (c+d x)^2}}{16 b^4 d \log ^4(F)}+\frac{35 (c+d x)^3 F^{a+b (c+d x)^2}}{8 b^3 d \log ^3(F)}-\frac{7 (c+d x)^5 F^{a+b (c+d x)^2}}{4 b^2 d \log ^2(F)}+\frac{(c+d x)^7 F^{a+b (c+d x)^2}}{2 b d \log (F)}",1,"(F^a*(16*F^(b*(c + d*x)^2)*(c + d*x)^7 + (105*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(b^(7/2)*Log[F]^(7/2)) - (210*F^(b*(c + d*x)^2)*(c + d*x))/(b^3*Log[F]^3) + (140*F^(b*(c + d*x)^2)*(c + d*x)^3)/(b^2*Log[F]^2) - (56*F^(b*(c + d*x)^2)*(c + d*x)^5)/(b*Log[F])))/(32*b*d*Log[F])","A",1
270,1,126,145,0.1477178,"\int F^{a+b (c+d x)^2} (c+d x)^6 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^6,x]","\frac{F^a \left(-\frac{15 \sqrt{\pi } \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{b^{5/2} \log ^{\frac{5}{2}}(F)}+\frac{30 (c+d x) F^{b (c+d x)^2}}{b^2 \log ^2(F)}+8 (c+d x)^5 F^{b (c+d x)^2}-\frac{20 (c+d x)^3 F^{b (c+d x)^2}}{b \log (F)}\right)}{16 b d \log (F)}","-\frac{15 \sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{16 b^{7/2} d \log ^{\frac{7}{2}}(F)}+\frac{15 (c+d x) F^{a+b (c+d x)^2}}{8 b^3 d \log ^3(F)}-\frac{5 (c+d x)^3 F^{a+b (c+d x)^2}}{4 b^2 d \log ^2(F)}+\frac{(c+d x)^5 F^{a+b (c+d x)^2}}{2 b d \log (F)}",1,"(F^a*(8*F^(b*(c + d*x)^2)*(c + d*x)^5 - (15*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(b^(5/2)*Log[F]^(5/2)) + (30*F^(b*(c + d*x)^2)*(c + d*x))/(b^2*Log[F]^2) - (20*F^(b*(c + d*x)^2)*(c + d*x)^3)/(b*Log[F])))/(16*b*d*Log[F])","A",1
271,1,90,111,0.0956075,"\int F^{a+b (c+d x)^2} (c+d x)^4 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^4,x]","\frac{F^a \left(3 \sqrt{\pi } \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)+2 \sqrt{b} \sqrt{\log (F)} (c+d x) F^{b (c+d x)^2} \left(2 b \log (F) (c+d x)^2-3\right)\right)}{8 b^{5/2} d \log ^{\frac{5}{2}}(F)}","\frac{3 \sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{8 b^{5/2} d \log ^{\frac{5}{2}}(F)}-\frac{3 (c+d x) F^{a+b (c+d x)^2}}{4 b^2 d \log ^2(F)}+\frac{(c+d x)^3 F^{a+b (c+d x)^2}}{2 b d \log (F)}",1,"(F^a*(3*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]] + 2*Sqrt[b]*F^(b*(c + d*x)^2)*(c + d*x)*Sqrt[Log[F]]*(-3 + 2*b*(c + d*x)^2*Log[F])))/(8*b^(5/2)*d*Log[F]^(5/2))","A",1
272,1,77,77,0.0461793,"\int F^{a+b (c+d x)^2} (c+d x)^2 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(c + d*x)^2,x]","\frac{(c+d x) F^{a+b (c+d x)^2}}{2 b d \log (F)}-\frac{\sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{4 b^{3/2} d \log ^{\frac{3}{2}}(F)}","\frac{(c+d x) F^{a+b (c+d x)^2}}{2 b d \log (F)}-\frac{\sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{4 b^{3/2} d \log ^{\frac{3}{2}}(F)}",1,"-1/4*(F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(b^(3/2)*d*Log[F]^(3/2)) + (F^(a + b*(c + d*x)^2)*(c + d*x))/(2*b*d*Log[F])","A",1
273,1,44,44,0.0062542,"\int F^{a+b (c+d x)^2} \, dx","Integrate[F^(a + b*(c + d*x)^2),x]","\frac{\sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 \sqrt{b} d \sqrt{\log (F)}}","\frac{\sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 \sqrt{b} d \sqrt{\log (F)}}",1,"(F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(2*Sqrt[b]*d*Sqrt[Log[F]])","A",1
274,1,63,67,0.0458505,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^2} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^2,x]","\frac{F^a \left(\sqrt{\pi } \sqrt{b} \sqrt{\log (F)} \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)-\frac{F^{b (c+d x)^2}}{c+d x}\right)}{d}","\frac{\sqrt{\pi } \sqrt{b} F^a \sqrt{\log (F)} \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{d}-\frac{F^{a+b (c+d x)^2}}{d (c+d x)}",1,"(F^a*(-(F^(b*(c + d*x)^2)/(c + d*x)) + Sqrt[b]*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Sqrt[Log[F]]))/d","A",1
275,1,81,102,0.1031734,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^4} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^4,x]","\frac{F^a \left(2 \sqrt{\pi } b^{3/2} \log ^{\frac{3}{2}}(F) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)-\frac{F^{b (c+d x)^2} \left(2 b \log (F) (c+d x)^2+1\right)}{(c+d x)^3}\right)}{3 d}","\frac{2 \sqrt{\pi } b^{3/2} F^a \log ^{\frac{3}{2}}(F) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{3 d}-\frac{F^{a+b (c+d x)^2}}{3 d (c+d x)^3}-\frac{2 b \log (F) F^{a+b (c+d x)^2}}{3 d (c+d x)}",1,"(F^a*(2*b^(3/2)*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Log[F]^(3/2) - (F^(b*(c + d*x)^2)*(1 + 2*b*(c + d*x)^2*Log[F]))/(c + d*x)^3))/(3*d)","A",1
276,1,97,136,0.1200595,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^6} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^6,x]","\frac{F^a \left(4 \sqrt{\pi } b^{5/2} \log ^{\frac{5}{2}}(F) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)-\frac{F^{b (c+d x)^2} \left(4 b^2 \log ^2(F) (c+d x)^4+2 b \log (F) (c+d x)^2+3\right)}{(c+d x)^5}\right)}{15 d}","\frac{4 \sqrt{\pi } b^{5/2} F^a \log ^{\frac{5}{2}}(F) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{15 d}-\frac{4 b^2 \log ^2(F) F^{a+b (c+d x)^2}}{15 d (c+d x)}-\frac{F^{a+b (c+d x)^2}}{5 d (c+d x)^5}-\frac{2 b \log (F) F^{a+b (c+d x)^2}}{15 d (c+d x)^3}",1,"(F^a*(4*b^(5/2)*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Log[F]^(5/2) - (F^(b*(c + d*x)^2)*(3 + 2*b*(c + d*x)^2*Log[F] + 4*b^2*(c + d*x)^4*Log[F]^2))/(c + d*x)^5))/(15*d)","A",1
277,1,112,170,0.1463231,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^8} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^8,x]","\frac{F^a \left(8 \sqrt{\pi } b^{7/2} \log ^{\frac{7}{2}}(F) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)+\frac{F^{b (c+d x)^2} \left(-8 b^3 \log ^3(F) (c+d x)^6-4 b^2 \log ^2(F) (c+d x)^4-6 b \log (F) (c+d x)^2-15\right)}{(c+d x)^7}\right)}{105 d}","\frac{8 \sqrt{\pi } b^{7/2} F^a \log ^{\frac{7}{2}}(F) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{105 d}-\frac{8 b^3 \log ^3(F) F^{a+b (c+d x)^2}}{105 d (c+d x)}-\frac{4 b^2 \log ^2(F) F^{a+b (c+d x)^2}}{105 d (c+d x)^3}-\frac{F^{a+b (c+d x)^2}}{7 d (c+d x)^7}-\frac{2 b \log (F) F^{a+b (c+d x)^2}}{35 d (c+d x)^5}",1,"(F^a*(8*b^(7/2)*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Log[F]^(7/2) + (F^(b*(c + d*x)^2)*(-15 - 6*b*(c + d*x)^2*Log[F] - 4*b^2*(c + d*x)^4*Log[F]^2 - 8*b^3*(c + d*x)^6*Log[F]^3))/(c + d*x)^7))/(105*d)","A",1
278,1,49,49,0.0310982,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^{10}} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^10,x]","-\frac{F^a \left(-b \log (F) (c+d x)^2\right)^{9/2} \Gamma \left(-\frac{9}{2},-b (c+d x)^2 \log (F)\right)}{2 d (c+d x)^9}","-\frac{F^a \left(-b \log (F) (c+d x)^2\right)^{9/2} \Gamma \left(-\frac{9}{2},-b (c+d x)^2 \log (F)\right)}{2 d (c+d x)^9}",1,"-1/2*(F^a*Gamma[-9/2, -(b*(c + d*x)^2*Log[F])]*(-(b*(c + d*x)^2*Log[F]))^(9/2))/(d*(c + d*x)^9)","A",1
279,1,49,49,0.0309341,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^{12}} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(c + d*x)^12,x]","-\frac{F^a \left(-b \log (F) (c+d x)^2\right)^{11/2} \Gamma \left(-\frac{11}{2},-b (c+d x)^2 \log (F)\right)}{2 d (c+d x)^{11}}","-\frac{F^a \left(-b \log (F) (c+d x)^2\right)^{11/2} \Gamma \left(-\frac{11}{2},-b (c+d x)^2 \log (F)\right)}{2 d (c+d x)^{11}}",1,"-1/2*(F^a*Gamma[-11/2, -(b*(c + d*x)^2*Log[F])]*(-(b*(c + d*x)^2*Log[F]))^(11/2))/(d*(c + d*x)^11)","A",1
280,1,61,61,0.0418707,"\int F^{a+b (c+d x)^3} (c+d x)^m \, dx","Integrate[F^(a + b*(c + d*x)^3)*(c + d*x)^m,x]","-\frac{F^a (c+d x)^{m+1} \left(-b \log (F) (c+d x)^3\right)^{\frac{1}{3} (-m-1)} \Gamma \left(\frac{m+1}{3},-b (c+d x)^3 \log (F)\right)}{3 d}","-\frac{F^a (c+d x)^{m+1} \left(-b \log (F) (c+d x)^3\right)^{\frac{1}{3} (-m-1)} \Gamma \left(\frac{m+1}{3},-b (c+d x)^3 \log (F)\right)}{3 d}",1,"-1/3*(F^a*(c + d*x)^(1 + m)*Gamma[(1 + m)/3, -(b*(c + d*x)^3*Log[F])]*(-(b*(c + d*x)^3*Log[F]))^((-1 - m)/3))/d","A",1
281,1,31,105,0.0105146,"\int F^{a+b (c+d x)^3} (c+d x)^{17} \, dx","Integrate[F^(a + b*(c + d*x)^3)*(c + d*x)^17,x]","-\frac{F^a \Gamma \left(6,-b (c+d x)^3 \log (F)\right)}{3 b^6 d \log ^6(F)}","-\frac{F^{a+b (c+d x)^3} \left(-b^5 \log ^5(F) (c+d x)^{15}+5 b^4 \log ^4(F) (c+d x)^{12}-20 b^3 \log ^3(F) (c+d x)^9+60 b^2 \log ^2(F) (c+d x)^6-120 b \log (F) (c+d x)^3+120\right)}{3 b^6 d \log ^6(F)}",1,"-1/3*(F^a*Gamma[6, -(b*(c + d*x)^3*Log[F])])/(b^6*d*Log[F]^6)","C",1
282,1,31,88,0.0100053,"\int F^{a+b (c+d x)^3} (c+d x)^{14} \, dx","Integrate[F^(a + b*(c + d*x)^3)*(c + d*x)^14,x]","\frac{F^a \Gamma \left(5,-b (c+d x)^3 \log (F)\right)}{3 b^5 d \log ^5(F)}","\frac{F^{a+b (c+d x)^3} \left(b^4 \log ^4(F) (c+d x)^{12}-4 b^3 \log ^3(F) (c+d x)^9+12 b^2 \log ^2(F) (c+d x)^6-24 b \log (F) (c+d x)^3+24\right)}{3 b^5 d \log ^5(F)}",1,"(F^a*Gamma[5, -(b*(c + d*x)^3*Log[F])])/(3*b^5*d*Log[F]^5)","C",1
283,1,75,124,0.0638457,"\int F^{a+b (c+d x)^3} (c+d x)^{11} \, dx","Integrate[F^(a + b*(c + d*x)^3)*(c + d*x)^11,x]","\frac{F^{a+b (c+d x)^3} \left(b^3 \log ^3(F) (c+d x)^9-3 b^2 \log ^2(F) (c+d x)^6-6 \left(1-b \log (F) (c+d x)^3\right)\right)}{3 b^4 d \log ^4(F)}","-\frac{2 F^{a+b (c+d x)^3}}{b^4 d \log ^4(F)}+\frac{2 (c+d x)^3 F^{a+b (c+d x)^3}}{b^3 d \log ^3(F)}-\frac{(c+d x)^6 F^{a+b (c+d x)^3}}{b^2 d \log ^2(F)}+\frac{(c+d x)^9 F^{a+b (c+d x)^3}}{3 b d \log (F)}",1,"(F^(a + b*(c + d*x)^3)*(-3*b^2*(c + d*x)^6*Log[F]^2 + b^3*(c + d*x)^9*Log[F]^3 - 6*(1 - b*(c + d*x)^3*Log[F])))/(3*b^4*d*Log[F]^4)","A",1
284,1,56,96,0.0422169,"\int F^{a+b (c+d x)^3} (c+d x)^8 \, dx","Integrate[F^(a + b*(c + d*x)^3)*(c + d*x)^8,x]","\frac{F^{a+b (c+d x)^3} \left(b^2 \log ^2(F) (c+d x)^6-2 b \log (F) (c+d x)^3+2\right)}{3 b^3 d \log ^3(F)}","\frac{2 F^{a+b (c+d x)^3}}{3 b^3 d \log ^3(F)}-\frac{2 (c+d x)^3 F^{a+b (c+d x)^3}}{3 b^2 d \log ^2(F)}+\frac{(c+d x)^6 F^{a+b (c+d x)^3}}{3 b d \log (F)}",1,"(F^(a + b*(c + d*x)^3)*(2 - 2*b*(c + d*x)^3*Log[F] + b^2*(c + d*x)^6*Log[F]^2))/(3*b^3*d*Log[F]^3)","A",1
285,1,40,62,0.0260611,"\int F^{a+b (c+d x)^3} (c+d x)^5 \, dx","Integrate[F^(a + b*(c + d*x)^3)*(c + d*x)^5,x]","\frac{F^{a+b (c+d x)^3} \left(b \log (F) (c+d x)^3-1\right)}{3 b^2 d \log ^2(F)}","\frac{(c+d x)^3 F^{a+b (c+d x)^3}}{3 b d \log (F)}-\frac{F^{a+b (c+d x)^3}}{3 b^2 d \log ^2(F)}",1,"(F^(a + b*(c + d*x)^3)*(-1 + b*(c + d*x)^3*Log[F]))/(3*b^2*d*Log[F]^2)","A",1
286,1,27,27,0.008431,"\int F^{a+b (c+d x)^3} (c+d x)^2 \, dx","Integrate[F^(a + b*(c + d*x)^3)*(c + d*x)^2,x]","\frac{F^{a+b (c+d x)^3}}{3 b d \log (F)}","\frac{F^{a+b (c+d x)^3}}{3 b d \log (F)}",1,"F^(a + b*(c + d*x)^3)/(3*b*d*Log[F])","A",1
287,1,22,22,0.0068459,"\int \frac{F^{a+b (c+d x)^3}}{c+d x} \, dx","Integrate[F^(a + b*(c + d*x)^3)/(c + d*x),x]","\frac{F^a \text{Ei}\left(b (c+d x)^3 \log (F)\right)}{3 d}","\frac{F^a \text{Ei}\left(b (c+d x)^3 \log (F)\right)}{3 d}",1,"(F^a*ExpIntegralEi[b*(c + d*x)^3*Log[F]])/(3*d)","A",1
288,1,47,53,0.0312043,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^4} \, dx","Integrate[F^(a + b*(c + d*x)^3)/(c + d*x)^4,x]","\frac{F^a \left(b \log (F) \text{Ei}\left(b (c+d x)^3 \log (F)\right)-\frac{F^{b (c+d x)^3}}{(c+d x)^3}\right)}{3 d}","\frac{b F^a \log (F) \text{Ei}\left(b (c+d x)^3 \log (F)\right)}{3 d}-\frac{F^{a+b (c+d x)^3}}{3 d (c+d x)^3}",1,"(F^a*(-(F^(b*(c + d*x)^3)/(c + d*x)^3) + b*ExpIntegralEi[b*(c + d*x)^3*Log[F]]*Log[F]))/(3*d)","A",1
289,1,64,87,0.0760585,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^7} \, dx","Integrate[F^(a + b*(c + d*x)^3)/(c + d*x)^7,x]","\frac{F^a \left(b^2 \log ^2(F) \text{Ei}\left(b (c+d x)^3 \log (F)\right)-\frac{F^{b (c+d x)^3} \left(b \log (F) (c+d x)^3+1\right)}{(c+d x)^6}\right)}{6 d}","\frac{b^2 F^a \log ^2(F) \text{Ei}\left(b (c+d x)^3 \log (F)\right)}{6 d}-\frac{F^{a+b (c+d x)^3}}{6 d (c+d x)^6}-\frac{b \log (F) F^{a+b (c+d x)^3}}{6 d (c+d x)^3}",1,"(F^a*(b^2*ExpIntegralEi[b*(c + d*x)^3*Log[F]]*Log[F]^2 - (F^(b*(c + d*x)^3)*(1 + b*(c + d*x)^3*Log[F]))/(c + d*x)^6))/(6*d)","A",1
290,1,80,121,0.100323,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^{10}} \, dx","Integrate[F^(a + b*(c + d*x)^3)/(c + d*x)^10,x]","\frac{F^a \left(b^3 \log ^3(F) \text{Ei}\left(b (c+d x)^3 \log (F)\right)+\frac{F^{b (c+d x)^3} \left(-b^2 \log ^2(F) (c+d x)^6-b \log (F) (c+d x)^3-2\right)}{(c+d x)^9}\right)}{18 d}","\frac{b^3 F^a \log ^3(F) \text{Ei}\left(b (c+d x)^3 \log (F)\right)}{18 d}-\frac{b^2 \log ^2(F) F^{a+b (c+d x)^3}}{18 d (c+d x)^3}-\frac{F^{a+b (c+d x)^3}}{9 d (c+d x)^9}-\frac{b \log (F) F^{a+b (c+d x)^3}}{18 d (c+d x)^6}",1,"(F^a*(b^3*ExpIntegralEi[b*(c + d*x)^3*Log[F]]*Log[F]^3 + (F^(b*(c + d*x)^3)*(-2 - b*(c + d*x)^3*Log[F] - b^2*(c + d*x)^6*Log[F]^2))/(c + d*x)^9))/(18*d)","A",1
291,1,31,31,0.008044,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^{13}} \, dx","Integrate[F^(a + b*(c + d*x)^3)/(c + d*x)^13,x]","-\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-b (c+d x)^3 \log (F)\right)}{3 d}","-\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-b (c+d x)^3 \log (F)\right)}{3 d}",1,"-1/3*(b^4*F^a*Gamma[-4, -(b*(c + d*x)^3*Log[F])]*Log[F]^4)/d","A",1
292,1,31,31,0.0078521,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^{16}} \, dx","Integrate[F^(a + b*(c + d*x)^3)/(c + d*x)^16,x]","\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-b (c+d x)^3 \log (F)\right)}{3 d}","\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-b (c+d x)^3 \log (F)\right)}{3 d}",1,"(b^5*F^a*Gamma[-5, -(b*(c + d*x)^3*Log[F])]*Log[F]^5)/(3*d)","A",1
293,1,49,49,0.0262953,"\int F^{a+b (c+d x)^3} (c+d x)^3 \, dx","Integrate[F^(a + b*(c + d*x)^3)*(c + d*x)^3,x]","-\frac{F^a (c+d x)^4 \Gamma \left(\frac{4}{3},-b (c+d x)^3 \log (F)\right)}{3 d \left(-b \log (F) (c+d x)^3\right)^{4/3}}","-\frac{F^a (c+d x)^4 \Gamma \left(\frac{4}{3},-b (c+d x)^3 \log (F)\right)}{3 d \left(-b \log (F) (c+d x)^3\right)^{4/3}}",1,"-1/3*(F^a*(c + d*x)^4*Gamma[4/3, -(b*(c + d*x)^3*Log[F])])/(d*(-(b*(c + d*x)^3*Log[F]))^(4/3))","A",1
294,1,49,49,0.0233114,"\int F^{a+b (c+d x)^3} (c+d x) \, dx","Integrate[F^(a + b*(c + d*x)^3)*(c + d*x),x]","-\frac{F^a (c+d x)^2 \Gamma \left(\frac{2}{3},-b (c+d x)^3 \log (F)\right)}{3 d \left(-b \log (F) (c+d x)^3\right)^{2/3}}","-\frac{F^a (c+d x)^2 \Gamma \left(\frac{2}{3},-b (c+d x)^3 \log (F)\right)}{3 d \left(-b \log (F) (c+d x)^3\right)^{2/3}}",1,"-1/3*(F^a*(c + d*x)^2*Gamma[2/3, -(b*(c + d*x)^3*Log[F])])/(d*(-(b*(c + d*x)^3*Log[F]))^(2/3))","A",1
295,1,47,47,0.0168127,"\int F^{a+b (c+d x)^3} \, dx","Integrate[F^(a + b*(c + d*x)^3),x]","-\frac{F^a (c+d x) \Gamma \left(\frac{1}{3},-b (c+d x)^3 \log (F)\right)}{3 d \sqrt[3]{-b \log (F) (c+d x)^3}}","-\frac{F^a (c+d x) \Gamma \left(\frac{1}{3},-b (c+d x)^3 \log (F)\right)}{3 d \sqrt[3]{-b \log (F) (c+d x)^3}}",1,"-1/3*(F^a*(c + d*x)*Gamma[1/3, -(b*(c + d*x)^3*Log[F])])/(d*(-(b*(c + d*x)^3*Log[F]))^(1/3))","A",1
296,1,49,49,0.0159943,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^2} \, dx","Integrate[F^(a + b*(c + d*x)^3)/(c + d*x)^2,x]","-\frac{F^a \sqrt[3]{-b \log (F) (c+d x)^3} \Gamma \left(-\frac{1}{3},-b (c+d x)^3 \log (F)\right)}{3 d (c+d x)}","-\frac{F^a \sqrt[3]{-b \log (F) (c+d x)^3} \Gamma \left(-\frac{1}{3},-b (c+d x)^3 \log (F)\right)}{3 d (c+d x)}",1,"-1/3*(F^a*Gamma[-1/3, -(b*(c + d*x)^3*Log[F])]*(-(b*(c + d*x)^3*Log[F]))^(1/3))/(d*(c + d*x))","A",1
297,1,49,49,0.0164512,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^3} \, dx","Integrate[F^(a + b*(c + d*x)^3)/(c + d*x)^3,x]","-\frac{F^a \left(-b \log (F) (c+d x)^3\right)^{2/3} \Gamma \left(-\frac{2}{3},-b (c+d x)^3 \log (F)\right)}{3 d (c+d x)^2}","-\frac{F^a \left(-b \log (F) (c+d x)^3\right)^{2/3} \Gamma \left(-\frac{2}{3},-b (c+d x)^3 \log (F)\right)}{3 d (c+d x)^2}",1,"-1/3*(F^a*Gamma[-2/3, -(b*(c + d*x)^3*Log[F])]*(-(b*(c + d*x)^3*Log[F]))^(2/3))/(d*(c + d*x)^2)","A",1
298,1,49,49,0.0239186,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^5} \, dx","Integrate[F^(a + b*(c + d*x)^3)/(c + d*x)^5,x]","-\frac{F^a \left(-b \log (F) (c+d x)^3\right)^{4/3} \Gamma \left(-\frac{4}{3},-b (c+d x)^3 \log (F)\right)}{3 d (c+d x)^4}","-\frac{F^a \left(-b \log (F) (c+d x)^3\right)^{4/3} \Gamma \left(-\frac{4}{3},-b (c+d x)^3 \log (F)\right)}{3 d (c+d x)^4}",1,"-1/3*(F^a*Gamma[-4/3, -(b*(c + d*x)^3*Log[F])]*(-(b*(c + d*x)^3*Log[F]))^(4/3))/(d*(c + d*x)^4)","A",1
299,1,42,64,0.0338197,"\int f^{a+b \sqrt{c+d x}} \, dx","Integrate[f^(a + b*Sqrt[c + d*x]),x]","\frac{2 f^{a+b \sqrt{c+d x}} \left(b \log (f) \sqrt{c+d x}-1\right)}{b^2 d \log ^2(f)}","\frac{2 \sqrt{c+d x} f^{a+b \sqrt{c+d x}}}{b d \log (f)}-\frac{2 f^{a+b \sqrt{c+d x}}}{b^2 d \log ^2(f)}",1,"(2*f^(a + b*Sqrt[c + d*x])*(-1 + b*Sqrt[c + d*x]*Log[f]))/(b^2*d*Log[f]^2)","A",1
300,1,60,100,0.0428769,"\int f^{a+b \sqrt[3]{c+d x}} \, dx","Integrate[f^(a + b*(c + d*x)^(1/3)),x]","\frac{3 f^{a+b \sqrt[3]{c+d x}} \left(b^2 \log ^2(f) (c+d x)^{2/3}-2 b \log (f) \sqrt[3]{c+d x}+2\right)}{b^3 d \log ^3(f)}","\frac{6 f^{a+b \sqrt[3]{c+d x}}}{b^3 d \log ^3(f)}-\frac{6 \sqrt[3]{c+d x} f^{a+b \sqrt[3]{c+d x}}}{b^2 d \log ^2(f)}+\frac{3 (c+d x)^{2/3} f^{a+b \sqrt[3]{c+d x}}}{b d \log (f)}",1,"(3*f^(a + b*(c + d*x)^(1/3))*(2 - 2*b*(c + d*x)^(1/3)*Log[f] + b^2*(c + d*x)^(2/3)*Log[f]^2))/(b^3*d*Log[f]^3)","A",1
301,1,50,50,0.0186541,"\int F^{a+\frac{b}{c+d x}} (c+d x)^m \, dx","Integrate[F^(a + b/(c + d*x))*(c + d*x)^m,x]","\frac{F^a (c+d x)^{m+1} \left(-\frac{b \log (F)}{c+d x}\right)^{m+1} \Gamma \left(-m-1,-\frac{b \log (F)}{c+d x}\right)}{d}","\frac{F^a (c+d x)^{m+1} \left(-\frac{b \log (F)}{c+d x}\right)^{m+1} \Gamma \left(-m-1,-\frac{b \log (F)}{c+d x}\right)}{d}",1,"(F^a*(c + d*x)^(1 + m)*Gamma[-1 - m, -((b*Log[F])/(c + d*x))]*(-((b*Log[F])/(c + d*x)))^(1 + m))/d","A",1
302,1,29,29,0.0065644,"\int F^{a+\frac{b}{c+d x}} (c+d x)^4 \, dx","Integrate[F^(a + b/(c + d*x))*(c + d*x)^4,x]","-\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-\frac{b \log (F)}{c+d x}\right)}{d}","-\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-\frac{b \log (F)}{c+d x}\right)}{d}",1,"-((b^5*F^a*Gamma[-5, -((b*Log[F])/(c + d*x))]*Log[F]^5)/d)","A",1
303,1,28,28,0.0060409,"\int F^{a+\frac{b}{c+d x}} (c+d x)^3 \, dx","Integrate[F^(a + b/(c + d*x))*(c + d*x)^3,x]","\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-\frac{b \log (F)}{c+d x}\right)}{d}","\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-\frac{b \log (F)}{c+d x}\right)}{d}",1,"(b^4*F^a*Gamma[-4, -((b*Log[F])/(c + d*x))]*Log[F]^4)/d","A",1
304,1,76,119,0.0712956,"\int F^{a+\frac{b}{c+d x}} (c+d x)^2 \, dx","Integrate[F^(a + b/(c + d*x))*(c + d*x)^2,x]","\frac{F^a \left((c+d x) F^{\frac{b}{c+d x}} \left(b^2 \log ^2(F)+b \log (F) (c+d x)+2 (c+d x)^2\right)-b^3 \log ^3(F) \text{Ei}\left(\frac{b \log (F)}{c+d x}\right)\right)}{6 d}","-\frac{b^3 F^a \log ^3(F) \text{Ei}\left(\frac{b \log (F)}{c+d x}\right)}{6 d}+\frac{b^2 \log ^2(F) (c+d x) F^{a+\frac{b}{c+d x}}}{6 d}+\frac{(c+d x)^3 F^{a+\frac{b}{c+d x}}}{3 d}+\frac{b \log (F) (c+d x)^2 F^{a+\frac{b}{c+d x}}}{6 d}",1,"(F^a*(-(b^3*ExpIntegralEi[(b*Log[F])/(c + d*x)]*Log[F]^3) + F^(b/(c + d*x))*(c + d*x)*(2*(c + d*x)^2 + b*(c + d*x)*Log[F] + b^2*Log[F]^2)))/(6*d)","A",1
305,1,58,85,0.0469366,"\int F^{a+\frac{b}{c+d x}} (c+d x) \, dx","Integrate[F^(a + b/(c + d*x))*(c + d*x),x]","\frac{F^a \left((c+d x) F^{\frac{b}{c+d x}} (b \log (F)+c+d x)-b^2 \log ^2(F) \text{Ei}\left(\frac{b \log (F)}{c+d x}\right)\right)}{2 d}","-\frac{b^2 F^a \log ^2(F) \text{Ei}\left(\frac{b \log (F)}{c+d x}\right)}{2 d}+\frac{(c+d x)^2 F^{a+\frac{b}{c+d x}}}{2 d}+\frac{b \log (F) (c+d x) F^{a+\frac{b}{c+d x}}}{2 d}",1,"(F^a*(-(b^2*ExpIntegralEi[(b*Log[F])/(c + d*x)]*Log[F]^2) + F^(b/(c + d*x))*(c + d*x)*(c + d*x + b*Log[F])))/(2*d)","A",1
306,1,42,46,0.025159,"\int F^{a+\frac{b}{c+d x}} \, dx","Integrate[F^(a + b/(c + d*x)),x]","\frac{F^a \left((c+d x) F^{\frac{b}{c+d x}}-b \log (F) \text{Ei}\left(\frac{b \log (F)}{c+d x}\right)\right)}{d}","\frac{(c+d x) F^{a+\frac{b}{c+d x}}}{d}-\frac{b F^a \log (F) \text{Ei}\left(\frac{b \log (F)}{c+d x}\right)}{d}",1,"(F^a*(F^(b/(c + d*x))*(c + d*x) - b*ExpIntegralEi[(b*Log[F])/(c + d*x)]*Log[F]))/d","A",1
307,1,20,20,0.0048808,"\int \frac{F^{a+\frac{b}{c+d x}}}{c+d x} \, dx","Integrate[F^(a + b/(c + d*x))/(c + d*x),x]","-\frac{F^a \text{Ei}\left(\frac{b \log (F)}{c+d x}\right)}{d}","-\frac{F^a \text{Ei}\left(\frac{b \log (F)}{c+d x}\right)}{d}",1,"-((F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)])/d)","A",1
308,1,25,25,0.0066634,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^2} \, dx","Integrate[F^(a + b/(c + d*x))/(c + d*x)^2,x]","-\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F)}","-\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F)}",1,"-(F^(a + b/(c + d*x))/(b*d*Log[F]))","A",1
309,1,41,57,0.017798,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^3} \, dx","Integrate[F^(a + b/(c + d*x))/(c + d*x)^3,x]","\frac{F^{a+\frac{b}{c+d x}} (-b \log (F)+c+d x)}{b^2 d \log ^2(F) (c+d x)}","\frac{F^{a+\frac{b}{c+d x}}}{b^2 d \log ^2(F)}-\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F) (c+d x)}",1,"(F^(a + b/(c + d*x))*(c + d*x - b*Log[F]))/(b^2*d*(c + d*x)*Log[F]^2)","A",1
310,1,60,90,0.0252829,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^4} \, dx","Integrate[F^(a + b/(c + d*x))/(c + d*x)^4,x]","-\frac{F^{a+\frac{b}{c+d x}} \left(b^2 \log ^2(F)-2 b \log (F) (c+d x)+2 (c+d x)^2\right)}{b^3 d \log ^3(F) (c+d x)^2}","-\frac{2 F^{a+\frac{b}{c+d x}}}{b^3 d \log ^3(F)}+\frac{2 F^{a+\frac{b}{c+d x}}}{b^2 d \log ^2(F) (c+d x)}-\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F) (c+d x)^2}",1,"-((F^(a + b/(c + d*x))*(2*(c + d*x)^2 - 2*b*(c + d*x)*Log[F] + b^2*Log[F]^2))/(b^3*d*(c + d*x)^2*Log[F]^3))","A",1
311,1,76,122,0.0354446,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^5} \, dx","Integrate[F^(a + b/(c + d*x))/(c + d*x)^5,x]","\frac{F^{a+\frac{b}{c+d x}} \left(-b^3 \log ^3(F)+3 b^2 \log ^2(F) (c+d x)-6 b \log (F) (c+d x)^2+6 (c+d x)^3\right)}{b^4 d \log ^4(F) (c+d x)^3}","\frac{6 F^{a+\frac{b}{c+d x}}}{b^4 d \log ^4(F)}-\frac{6 F^{a+\frac{b}{c+d x}}}{b^3 d \log ^3(F) (c+d x)}+\frac{3 F^{a+\frac{b}{c+d x}}}{b^2 d \log ^2(F) (c+d x)^2}-\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F) (c+d x)^3}",1,"(F^(a + b/(c + d*x))*(6*(c + d*x)^3 - 6*b*(c + d*x)^2*Log[F] + 3*b^2*(c + d*x)*Log[F]^2 - b^3*Log[F]^3))/(b^4*d*(c + d*x)^3*Log[F]^4)","A",1
312,1,29,92,0.0063117,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^6} \, dx","Integrate[F^(a + b/(c + d*x))/(c + d*x)^6,x]","-\frac{F^a \Gamma \left(5,-\frac{b \log (F)}{c+d x}\right)}{b^5 d \log ^5(F)}","-\frac{F^{a+\frac{b}{c+d x}} \left(b^4 \log ^4(F)-4 b^3 \log ^3(F) (c+d x)+12 b^2 \log ^2(F) (c+d x)^2-24 b \log (F) (c+d x)^3+24 (c+d x)^4\right)}{b^5 d \log ^5(F) (c+d x)^4}",1,"-((F^a*Gamma[5, -((b*Log[F])/(c + d*x))])/(b^5*d*Log[F]^5))","C",1
313,1,28,108,0.006491,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^7} \, dx","Integrate[F^(a + b/(c + d*x))/(c + d*x)^7,x]","\frac{F^a \Gamma \left(6,-\frac{b \log (F)}{c+d x}\right)}{b^6 d \log ^6(F)}","\frac{F^{a+\frac{b}{c+d x}} \left(-b^5 \log ^5(F)+5 b^4 \log ^4(F) (c+d x)-20 b^3 \log ^3(F) (c+d x)^2+60 b^2 \log ^2(F) (c+d x)^3-120 b \log (F) (c+d x)^4+120 (c+d x)^5\right)}{b^6 d \log ^6(F) (c+d x)^5}",1,"(F^a*Gamma[6, -((b*Log[F])/(c + d*x))])/(b^6*d*Log[F]^6)","C",1
314,1,61,61,0.0354135,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^m \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^m,x]","\frac{F^a (c+d x)^{m+1} \left(-\frac{b \log (F)}{(c+d x)^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}","\frac{F^a (c+d x)^{m+1} \left(-\frac{b \log (F)}{(c+d x)^2}\right)^{\frac{m+1}{2}} \Gamma \left(\frac{1}{2} (-m-1),-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}",1,"(F^a*(c + d*x)^(1 + m)*Gamma[(-1 - m)/2, -((b*Log[F])/(c + d*x)^2)]*(-((b*Log[F])/(c + d*x)^2))^((1 + m)/2))/(2*d)","A",1
315,1,31,31,0.0082152,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^9 \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^9,x]","-\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}","-\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}",1,"-1/2*(b^5*F^a*Gamma[-5, -((b*Log[F])/(c + d*x)^2)]*Log[F]^5)/d","A",1
316,1,31,31,0.0076269,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^7 \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^7,x]","\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}","\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}",1,"(b^4*F^a*Gamma[-4, -((b*Log[F])/(c + d*x)^2)]*Log[F]^4)/(2*d)","A",1
317,1,96,121,0.171444,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^5 \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^5,x]","\frac{F^a \left(b \log (F) \left(b \log (F) \left((c+d x)^2 F^{\frac{b}{(c+d x)^2}}-b \log (F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^2}\right)\right)+(c+d x)^4 F^{\frac{b}{(c+d x)^2}}\right)+2 (c+d x)^6 F^{\frac{b}{(c+d x)^2}}\right)}{12 d}","-\frac{b^3 F^a \log ^3(F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^2}\right)}{12 d}+\frac{b^2 \log ^2(F) (c+d x)^2 F^{a+\frac{b}{(c+d x)^2}}}{12 d}+\frac{(c+d x)^6 F^{a+\frac{b}{(c+d x)^2}}}{6 d}+\frac{b \log (F) (c+d x)^4 F^{a+\frac{b}{(c+d x)^2}}}{12 d}",1,"(F^a*(2*F^(b/(c + d*x)^2)*(c + d*x)^6 + b*Log[F]*(F^(b/(c + d*x)^2)*(c + d*x)^4 + b*Log[F]*(F^(b/(c + d*x)^2)*(c + d*x)^2 - b*ExpIntegralEi[(b*Log[F])/(c + d*x)^2]*Log[F]))))/(12*d)","A",1
318,1,71,87,0.0438802,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^3 \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^3,x]","\frac{F^a \left(b \log (F) \left((c+d x)^2 F^{\frac{b}{(c+d x)^2}}-b \log (F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^2}\right)\right)+(c+d x)^4 F^{\frac{b}{(c+d x)^2}}\right)}{4 d}","-\frac{b^2 F^a \log ^2(F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^2}\right)}{4 d}+\frac{(c+d x)^4 F^{a+\frac{b}{(c+d x)^2}}}{4 d}+\frac{b \log (F) (c+d x)^2 F^{a+\frac{b}{(c+d x)^2}}}{4 d}",1,"(F^a*(F^(b/(c + d*x)^2)*(c + d*x)^4 + b*Log[F]*(F^(b/(c + d*x)^2)*(c + d*x)^2 - b*ExpIntegralEi[(b*Log[F])/(c + d*x)^2]*Log[F])))/(4*d)","A",1
319,1,47,53,0.0238436,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x) \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x),x]","\frac{F^a \left((c+d x)^2 F^{\frac{b}{(c+d x)^2}}-b \log (F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^2}\right)\right)}{2 d}","\frac{(c+d x)^2 F^{a+\frac{b}{(c+d x)^2}}}{2 d}-\frac{b F^a \log (F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}",1,"(F^a*(F^(b/(c + d*x)^2)*(c + d*x)^2 - b*ExpIntegralEi[(b*Log[F])/(c + d*x)^2]*Log[F]))/(2*d)","A",1
320,1,22,22,0.0061428,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{c+d x} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x),x]","-\frac{F^a \text{Ei}\left(\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}","-\frac{F^a \text{Ei}\left(\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}",1,"-1/2*(F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)^2])/d","A",1
321,1,27,27,0.009428,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^3} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^3,x]","-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F)}","-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F)}",1,"-1/2*F^(a + b/(c + d*x)^2)/(b*d*Log[F])","A",1
322,1,47,62,0.0250205,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^5} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^5,x]","\frac{F^{a+\frac{b}{(c+d x)^2}} \left((c+d x)^2-b \log (F)\right)}{2 b^2 d \log ^2(F) (c+d x)^2}","\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b^2 d \log ^2(F)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^2}",1,"(F^(a + b/(c + d*x)^2)*((c + d*x)^2 - b*Log[F]))/(2*b^2*d*(c + d*x)^2*Log[F]^2)","A",1
323,1,64,91,0.0339002,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^7} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^7,x]","-\frac{F^{a+\frac{b}{(c+d x)^2}} \left(b^2 \log ^2(F)-2 b \log (F) (c+d x)^2+2 (c+d x)^4\right)}{2 b^3 d \log ^3(F) (c+d x)^4}","-\frac{F^{a+\frac{b}{(c+d x)^2}}}{b^3 d \log ^3(F)}+\frac{F^{a+\frac{b}{(c+d x)^2}}}{b^2 d \log ^2(F) (c+d x)^2}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^4}",1,"-1/2*(F^(a + b/(c + d*x)^2)*(2*(c + d*x)^4 - 2*b*(c + d*x)^2*Log[F] + b^2*Log[F]^2))/(b^3*d*(c + d*x)^4*Log[F]^3)","A",1
324,1,81,126,0.044663,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^9} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^9,x]","\frac{F^{a+\frac{b}{(c+d x)^2}} \left(-b^3 \log ^3(F)+3 b^2 \log ^2(F) (c+d x)^2-6 b \log (F) (c+d x)^4+6 (c+d x)^6\right)}{2 b^4 d \log ^4(F) (c+d x)^6}","\frac{3 F^{a+\frac{b}{(c+d x)^2}}}{b^4 d \log ^4(F)}-\frac{3 F^{a+\frac{b}{(c+d x)^2}}}{b^3 d \log ^3(F) (c+d x)^2}+\frac{3 F^{a+\frac{b}{(c+d x)^2}}}{2 b^2 d \log ^2(F) (c+d x)^4}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^6}",1,"(F^(a + b/(c + d*x)^2)*(6*(c + d*x)^6 - 6*b*(c + d*x)^4*Log[F] + 3*b^2*(c + d*x)^2*Log[F]^2 - b^3*Log[F]^3))/(2*b^4*d*(c + d*x)^6*Log[F]^4)","A",1
325,1,31,96,0.007161,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{11}} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^11,x]","-\frac{F^a \Gamma \left(5,-\frac{b \log (F)}{(c+d x)^2}\right)}{2 b^5 d \log ^5(F)}","-\frac{F^{a+\frac{b}{(c+d x)^2}} \left(b^4 \log ^4(F)-4 b^3 \log ^3(F) (c+d x)^2+12 b^2 \log ^2(F) (c+d x)^4-24 b \log (F) (c+d x)^6+24 (c+d x)^8\right)}{2 b^5 d \log ^5(F) (c+d x)^8}",1,"-1/2*(F^a*Gamma[5, -((b*Log[F])/(c + d*x)^2)])/(b^5*d*Log[F]^5)","C",1
326,1,31,113,0.0072026,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{13}} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^13,x]","\frac{F^a \Gamma \left(6,-\frac{b \log (F)}{(c+d x)^2}\right)}{2 b^6 d \log ^6(F)}","\frac{F^{a+\frac{b}{(c+d x)^2}} \left(-b^5 \log ^5(F)+5 b^4 \log ^4(F) (c+d x)^2-20 b^3 \log ^3(F) (c+d x)^4+60 b^2 \log ^2(F) (c+d x)^6-120 b \log (F) (c+d x)^8+120 (c+d x)^{10}\right)}{2 b^6 d \log ^6(F) (c+d x)^{10}}",1,"(F^a*Gamma[6, -((b*Log[F])/(c + d*x)^2)])/(2*b^6*d*Log[F]^6)","C",1
327,1,49,49,0.0294888,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^{10} \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^10,x]","\frac{F^a (c+d x)^{11} \left(-\frac{b \log (F)}{(c+d x)^2}\right)^{11/2} \Gamma \left(-\frac{11}{2},-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}","\frac{F^a (c+d x)^{11} \left(-\frac{b \log (F)}{(c+d x)^2}\right)^{11/2} \Gamma \left(-\frac{11}{2},-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}",1,"(F^a*(c + d*x)^11*Gamma[-11/2, -((b*Log[F])/(c + d*x)^2)]*(-((b*Log[F])/(c + d*x)^2))^(11/2))/(2*d)","A",1
328,1,49,49,0.0268192,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^8 \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^8,x]","\frac{F^a (c+d x)^9 \left(-\frac{b \log (F)}{(c+d x)^2}\right)^{9/2} \Gamma \left(-\frac{9}{2},-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}","\frac{F^a (c+d x)^9 \left(-\frac{b \log (F)}{(c+d x)^2}\right)^{9/2} \Gamma \left(-\frac{9}{2},-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}",1,"(F^a*(c + d*x)^9*Gamma[-9/2, -((b*Log[F])/(c + d*x)^2)]*(-((b*Log[F])/(c + d*x)^2))^(9/2))/(2*d)","A",1
329,1,113,170,0.1296587,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^6 \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^6,x]","\frac{F^a \left((c+d x) F^{\frac{b}{(c+d x)^2}} \left(8 b^3 \log ^3(F)+4 b^2 \log ^2(F) (c+d x)^2+6 b \log (F) (c+d x)^4+15 (c+d x)^6\right)-8 \sqrt{\pi } b^{7/2} \log ^{\frac{7}{2}}(F) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)\right)}{105 d}","-\frac{8 \sqrt{\pi } b^{7/2} F^a \log ^{\frac{7}{2}}(F) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{105 d}+\frac{8 b^3 \log ^3(F) (c+d x) F^{a+\frac{b}{(c+d x)^2}}}{105 d}+\frac{4 b^2 \log ^2(F) (c+d x)^3 F^{a+\frac{b}{(c+d x)^2}}}{105 d}+\frac{(c+d x)^7 F^{a+\frac{b}{(c+d x)^2}}}{7 d}+\frac{2 b \log (F) (c+d x)^5 F^{a+\frac{b}{(c+d x)^2}}}{35 d}",1,"(F^a*(-8*b^(7/2)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)]*Log[F]^(7/2) + F^(b/(c + d*x)^2)*(c + d*x)*(15*(c + d*x)^6 + 6*b*(c + d*x)^4*Log[F] + 4*b^2*(c + d*x)^2*Log[F]^2 + 8*b^3*Log[F]^3)))/(105*d)","A",1
330,1,97,136,0.0995409,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^4 \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^4,x]","\frac{F^a \left((c+d x) F^{\frac{b}{(c+d x)^2}} \left(4 b^2 \log ^2(F)+2 b \log (F) (c+d x)^2+3 (c+d x)^4\right)-4 \sqrt{\pi } b^{5/2} \log ^{\frac{5}{2}}(F) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)\right)}{15 d}","-\frac{4 \sqrt{\pi } b^{5/2} F^a \log ^{\frac{5}{2}}(F) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{15 d}+\frac{4 b^2 \log ^2(F) (c+d x) F^{a+\frac{b}{(c+d x)^2}}}{15 d}+\frac{(c+d x)^5 F^{a+\frac{b}{(c+d x)^2}}}{5 d}+\frac{2 b \log (F) (c+d x)^3 F^{a+\frac{b}{(c+d x)^2}}}{15 d}",1,"(F^a*(-4*b^(5/2)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)]*Log[F]^(5/2) + F^(b/(c + d*x)^2)*(c + d*x)*(3*(c + d*x)^4 + 2*b*(c + d*x)^2*Log[F] + 4*b^2*Log[F]^2)))/(15*d)","A",1
331,1,79,102,0.0785378,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^2 \, dx","Integrate[F^(a + b/(c + d*x)^2)*(c + d*x)^2,x]","\frac{F^a \left((c+d x) F^{\frac{b}{(c+d x)^2}} \left(2 b \log (F)+(c+d x)^2\right)-2 \sqrt{\pi } b^{3/2} \log ^{\frac{3}{2}}(F) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)\right)}{3 d}","-\frac{2 \sqrt{\pi } b^{3/2} F^a \log ^{\frac{3}{2}}(F) \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{3 d}+\frac{(c+d x)^3 F^{a+\frac{b}{(c+d x)^2}}}{3 d}+\frac{2 b \log (F) (c+d x) F^{a+\frac{b}{(c+d x)^2}}}{3 d}",1,"(F^a*(-2*b^(3/2)*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)]*Log[F]^(3/2) + F^(b/(c + d*x)^2)*(c + d*x)*((c + d*x)^2 + 2*b*Log[F])))/(3*d)","A",1
332,1,63,67,0.0353358,"\int F^{a+\frac{b}{(c+d x)^2}} \, dx","Integrate[F^(a + b/(c + d*x)^2),x]","\frac{F^a \left((c+d x) F^{\frac{b}{(c+d x)^2}}-\sqrt{\pi } \sqrt{b} \sqrt{\log (F)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)\right)}{d}","\frac{(c+d x) F^{a+\frac{b}{(c+d x)^2}}}{d}-\frac{\sqrt{\pi } \sqrt{b} F^a \sqrt{\log (F)} \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{d}",1,"(F^a*(F^(b/(c + d*x)^2)*(c + d*x) - Sqrt[b]*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)]*Sqrt[Log[F]]))/d","A",1
333,1,46,46,0.0093193,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^2} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^2,x]","-\frac{\sqrt{\pi } F^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{2 \sqrt{b} d \sqrt{\log (F)}}","-\frac{\sqrt{\pi } F^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{2 \sqrt{b} d \sqrt{\log (F)}}",1,"-1/2*(F^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)])/(Sqrt[b]*d*Sqrt[Log[F]])","A",1
334,1,81,81,0.0485874,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^4} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^4,x]","\frac{\sqrt{\pi } F^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{4 b^{3/2} d \log ^{\frac{3}{2}}(F)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)}","\frac{\sqrt{\pi } F^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{4 b^{3/2} d \log ^{\frac{3}{2}}(F)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)}",1,"(F^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)])/(4*b^(3/2)*d*Log[F]^(3/2)) - F^(a + b/(c + d*x)^2)/(2*b*d*(c + d*x)*Log[F])","A",1
335,1,95,115,0.0958691,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^6} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^6,x]","\frac{F^a \left(-3 \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)-\frac{2 \sqrt{b} \sqrt{\log (F)} F^{\frac{b}{(c+d x)^2}} \left(2 b \log (F)-3 (c+d x)^2\right)}{(c+d x)^3}\right)}{8 b^{5/2} d \log ^{\frac{5}{2}}(F)}","-\frac{3 \sqrt{\pi } F^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{8 b^{5/2} d \log ^{\frac{5}{2}}(F)}+\frac{3 F^{a+\frac{b}{(c+d x)^2}}}{4 b^2 d \log ^2(F) (c+d x)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^3}",1,"(F^a*(-3*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)] - (2*Sqrt[b]*F^(b/(c + d*x)^2)*Sqrt[Log[F]]*(-3*(c + d*x)^2 + 2*b*Log[F]))/(c + d*x)^3))/(8*b^(5/2)*d*Log[F]^(5/2))","A",1
336,1,111,149,0.1311782,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^8} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^8,x]","\frac{F^a \left(15 \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)-\frac{2 \sqrt{b} \sqrt{\log (F)} F^{\frac{b}{(c+d x)^2}} \left(4 b^2 \log ^2(F)-10 b \log (F) (c+d x)^2+15 (c+d x)^4\right)}{(c+d x)^5}\right)}{16 b^{7/2} d \log ^{\frac{7}{2}}(F)}","\frac{15 \sqrt{\pi } F^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{16 b^{7/2} d \log ^{\frac{7}{2}}(F)}-\frac{15 F^{a+\frac{b}{(c+d x)^2}}}{8 b^3 d \log ^3(F) (c+d x)}+\frac{5 F^{a+\frac{b}{(c+d x)^2}}}{4 b^2 d \log ^2(F) (c+d x)^3}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^5}",1,"(F^a*(15*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)] - (2*Sqrt[b]*F^(b/(c + d*x)^2)*Sqrt[Log[F]]*(15*(c + d*x)^4 - 10*b*(c + d*x)^2*Log[F] + 4*b^2*Log[F]^2))/(c + d*x)^5))/(16*b^(7/2)*d*Log[F]^(7/2))","A",1
337,1,127,183,0.1591277,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{10}} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^10,x]","\frac{F^a \left(\frac{2 \sqrt{b} \sqrt{\log (F)} F^{\frac{b}{(c+d x)^2}} \left(-8 b^3 \log ^3(F)+28 b^2 \log ^2(F) (c+d x)^2-70 b \log (F) (c+d x)^4+105 (c+d x)^6\right)}{(c+d x)^7}-105 \sqrt{\pi } \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)\right)}{32 b^{9/2} d \log ^{\frac{9}{2}}(F)}","-\frac{105 \sqrt{\pi } F^a \text{erfi}\left(\frac{\sqrt{b} \sqrt{\log (F)}}{c+d x}\right)}{32 b^{9/2} d \log ^{\frac{9}{2}}(F)}+\frac{105 F^{a+\frac{b}{(c+d x)^2}}}{16 b^4 d \log ^4(F) (c+d x)}-\frac{35 F^{a+\frac{b}{(c+d x)^2}}}{8 b^3 d \log ^3(F) (c+d x)^3}+\frac{7 F^{a+\frac{b}{(c+d x)^2}}}{4 b^2 d \log ^2(F) (c+d x)^5}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^7}",1,"(F^a*(-105*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)] + (2*Sqrt[b]*F^(b/(c + d*x)^2)*Sqrt[Log[F]]*(105*(c + d*x)^6 - 70*b*(c + d*x)^4*Log[F] + 28*b^2*(c + d*x)^2*Log[F]^2 - 8*b^3*Log[F]^3))/(c + d*x)^7))/(32*b^(9/2)*d*Log[F]^(9/2))","A",1
338,1,49,49,0.0385921,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{12}} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^12,x]","\frac{F^a \Gamma \left(\frac{11}{2},-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d (c+d x)^{11} \left(-\frac{b \log (F)}{(c+d x)^2}\right)^{11/2}}","\frac{F^a \Gamma \left(\frac{11}{2},-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d (c+d x)^{11} \left(-\frac{b \log (F)}{(c+d x)^2}\right)^{11/2}}",1,"(F^a*Gamma[11/2, -((b*Log[F])/(c + d*x)^2)])/(2*d*(c + d*x)^11*(-((b*Log[F])/(c + d*x)^2))^(11/2))","A",1
339,1,49,49,0.0261972,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{14}} \, dx","Integrate[F^(a + b/(c + d*x)^2)/(c + d*x)^14,x]","\frac{F^a \Gamma \left(\frac{13}{2},-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d (c+d x)^{13} \left(-\frac{b \log (F)}{(c+d x)^2}\right)^{13/2}}","\frac{F^a \Gamma \left(\frac{13}{2},-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d (c+d x)^{13} \left(-\frac{b \log (F)}{(c+d x)^2}\right)^{13/2}}",1,"(F^a*Gamma[13/2, -((b*Log[F])/(c + d*x)^2)])/(2*d*(c + d*x)^13*(-((b*Log[F])/(c + d*x)^2))^(13/2))","A",1
340,1,61,61,0.0395204,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^m \, dx","Integrate[F^(a + b/(c + d*x)^3)*(c + d*x)^m,x]","\frac{F^a (c+d x)^{m+1} \left(-\frac{b \log (F)}{(c+d x)^3}\right)^{\frac{m+1}{3}} \Gamma \left(\frac{1}{3} (-m-1),-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}","\frac{F^a (c+d x)^{m+1} \left(-\frac{b \log (F)}{(c+d x)^3}\right)^{\frac{m+1}{3}} \Gamma \left(\frac{1}{3} (-m-1),-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}",1,"(F^a*(c + d*x)^(1 + m)*Gamma[(-1 - m)/3, -((b*Log[F])/(c + d*x)^3)]*(-((b*Log[F])/(c + d*x)^3))^((1 + m)/3))/(3*d)","A",1
341,1,31,31,0.0103415,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^{14} \, dx","Integrate[F^(a + b/(c + d*x)^3)*(c + d*x)^14,x]","-\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}","-\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}",1,"-1/3*(b^5*F^a*Gamma[-5, -((b*Log[F])/(c + d*x)^3)]*Log[F]^5)/d","A",1
342,1,31,31,0.0095604,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^{11} \, dx","Integrate[F^(a + b/(c + d*x)^3)*(c + d*x)^11,x]","\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}","\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}",1,"(b^4*F^a*Gamma[-4, -((b*Log[F])/(c + d*x)^3)]*Log[F]^4)/(3*d)","A",1
343,1,96,121,0.2095924,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^8 \, dx","Integrate[F^(a + b/(c + d*x)^3)*(c + d*x)^8,x]","\frac{F^a \left(b \log (F) \left(b \log (F) \left((c+d x)^3 F^{\frac{b}{(c+d x)^3}}-b \log (F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^3}\right)\right)+(c+d x)^6 F^{\frac{b}{(c+d x)^3}}\right)+2 (c+d x)^9 F^{\frac{b}{(c+d x)^3}}\right)}{18 d}","-\frac{b^3 F^a \log ^3(F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^3}\right)}{18 d}+\frac{b^2 \log ^2(F) (c+d x)^3 F^{a+\frac{b}{(c+d x)^3}}}{18 d}+\frac{(c+d x)^9 F^{a+\frac{b}{(c+d x)^3}}}{9 d}+\frac{b \log (F) (c+d x)^6 F^{a+\frac{b}{(c+d x)^3}}}{18 d}",1,"(F^a*(2*F^(b/(c + d*x)^3)*(c + d*x)^9 + b*Log[F]*(F^(b/(c + d*x)^3)*(c + d*x)^6 + b*Log[F]*(F^(b/(c + d*x)^3)*(c + d*x)^3 - b*ExpIntegralEi[(b*Log[F])/(c + d*x)^3]*Log[F]))))/(18*d)","A",1
344,1,71,87,0.0620814,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^5 \, dx","Integrate[F^(a + b/(c + d*x)^3)*(c + d*x)^5,x]","\frac{F^a \left(b \log (F) \left((c+d x)^3 F^{\frac{b}{(c+d x)^3}}-b \log (F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^3}\right)\right)+(c+d x)^6 F^{\frac{b}{(c+d x)^3}}\right)}{6 d}","-\frac{b^2 F^a \log ^2(F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^3}\right)}{6 d}+\frac{(c+d x)^6 F^{a+\frac{b}{(c+d x)^3}}}{6 d}+\frac{b \log (F) (c+d x)^3 F^{a+\frac{b}{(c+d x)^3}}}{6 d}",1,"(F^a*(F^(b/(c + d*x)^3)*(c + d*x)^6 + b*Log[F]*(F^(b/(c + d*x)^3)*(c + d*x)^3 - b*ExpIntegralEi[(b*Log[F])/(c + d*x)^3]*Log[F])))/(6*d)","A",1
345,1,47,53,0.044572,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^2 \, dx","Integrate[F^(a + b/(c + d*x)^3)*(c + d*x)^2,x]","\frac{F^a \left((c+d x)^3 F^{\frac{b}{(c+d x)^3}}-b \log (F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^3}\right)\right)}{3 d}","\frac{(c+d x)^3 F^{a+\frac{b}{(c+d x)^3}}}{3 d}-\frac{b F^a \log (F) \text{Ei}\left(\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}",1,"(F^a*(F^(b/(c + d*x)^3)*(c + d*x)^3 - b*ExpIntegralEi[(b*Log[F])/(c + d*x)^3]*Log[F]))/(3*d)","A",1
346,1,22,22,0.0073751,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{c+d x} \, dx","Integrate[F^(a + b/(c + d*x)^3)/(c + d*x),x]","-\frac{F^a \text{Ei}\left(\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}","-\frac{F^a \text{Ei}\left(\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}",1,"-1/3*(F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)^3])/d","A",1
347,1,27,27,0.0120196,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^4} \, dx","Integrate[F^(a + b/(c + d*x)^3)/(c + d*x)^4,x]","-\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F)}","-\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F)}",1,"-1/3*F^(a + b/(c + d*x)^3)/(b*d*Log[F])","A",1
348,1,47,62,0.0299047,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^7} \, dx","Integrate[F^(a + b/(c + d*x)^3)/(c + d*x)^7,x]","\frac{F^{a+\frac{b}{(c+d x)^3}} \left((c+d x)^3-b \log (F)\right)}{3 b^2 d \log ^2(F) (c+d x)^3}","\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b^2 d \log ^2(F)}-\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F) (c+d x)^3}",1,"(F^(a + b/(c + d*x)^3)*((c + d*x)^3 - b*Log[F]))/(3*b^2*d*(c + d*x)^3*Log[F]^2)","A",1
349,1,64,96,0.0452809,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^{10}} \, dx","Integrate[F^(a + b/(c + d*x)^3)/(c + d*x)^10,x]","-\frac{F^{a+\frac{b}{(c+d x)^3}} \left(b^2 \log ^2(F)-2 b \log (F) (c+d x)^3+2 (c+d x)^6\right)}{3 b^3 d \log ^3(F) (c+d x)^6}","-\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{3 b^3 d \log ^3(F)}+\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{3 b^2 d \log ^2(F) (c+d x)^3}-\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F) (c+d x)^6}",1,"-1/3*(F^(a + b/(c + d*x)^3)*(2*(c + d*x)^6 - 2*b*(c + d*x)^3*Log[F] + b^2*Log[F]^2))/(b^3*d*(c + d*x)^6*Log[F]^3)","A",1
350,1,73,123,0.049448,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^{13}} \, dx","Integrate[F^(a + b/(c + d*x)^3)/(c + d*x)^13,x]","\frac{F^{a+\frac{b}{(c+d x)^3}} \left(-\frac{b^3 \log ^3(F)}{(c+d x)^9}+\frac{3 b^2 \log ^2(F)}{(c+d x)^6}-\frac{6 b \log (F)}{(c+d x)^3}+6\right)}{3 b^4 d \log ^4(F)}","\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{b^4 d \log ^4(F)}-\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{b^3 d \log ^3(F) (c+d x)^3}+\frac{F^{a+\frac{b}{(c+d x)^3}}}{b^2 d \log ^2(F) (c+d x)^6}-\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F) (c+d x)^9}",1,"(F^(a + b/(c + d*x)^3)*(6 - (6*b*Log[F])/(c + d*x)^3 + (3*b^2*Log[F]^2)/(c + d*x)^6 - (b^3*Log[F]^3)/(c + d*x)^9))/(3*b^4*d*Log[F]^4)","A",1
351,1,31,96,0.009294,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^{16}} \, dx","Integrate[F^(a + b/(c + d*x)^3)/(c + d*x)^16,x]","-\frac{F^a \Gamma \left(5,-\frac{b \log (F)}{(c+d x)^3}\right)}{3 b^5 d \log ^5(F)}","-\frac{F^{a+\frac{b}{(c+d x)^3}} \left(b^4 \log ^4(F)-4 b^3 \log ^3(F) (c+d x)^3+12 b^2 \log ^2(F) (c+d x)^6-24 b \log (F) (c+d x)^9+24 (c+d x)^{12}\right)}{3 b^5 d \log ^5(F) (c+d x)^{12}}",1,"-1/3*(F^a*Gamma[5, -((b*Log[F])/(c + d*x)^3)])/(b^5*d*Log[F]^5)","C",1
352,1,31,113,0.0090696,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^{19}} \, dx","Integrate[F^(a + b/(c + d*x)^3)/(c + d*x)^19,x]","\frac{F^a \Gamma \left(6,-\frac{b \log (F)}{(c+d x)^3}\right)}{3 b^6 d \log ^6(F)}","\frac{F^{a+\frac{b}{(c+d x)^3}} \left(-b^5 \log ^5(F)+5 b^4 \log ^4(F) (c+d x)^3-20 b^3 \log ^3(F) (c+d x)^6+60 b^2 \log ^2(F) (c+d x)^9-120 b \log (F) (c+d x)^{12}+120 (c+d x)^{15}\right)}{3 b^6 d \log ^6(F) (c+d x)^{15}}",1,"(F^a*Gamma[6, -((b*Log[F])/(c + d*x)^3)])/(3*b^6*d*Log[F]^6)","C",1
353,1,49,49,0.0328411,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^3 \, dx","Integrate[F^(a + b/(c + d*x)^3)*(c + d*x)^3,x]","\frac{F^a (c+d x)^4 \left(-\frac{b \log (F)}{(c+d x)^3}\right)^{4/3} \Gamma \left(-\frac{4}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}","\frac{F^a (c+d x)^4 \left(-\frac{b \log (F)}{(c+d x)^3}\right)^{4/3} \Gamma \left(-\frac{4}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}",1,"(F^a*(c + d*x)^4*Gamma[-4/3, -((b*Log[F])/(c + d*x)^3)]*(-((b*Log[F])/(c + d*x)^3))^(4/3))/(3*d)","A",1
354,1,49,49,0.0302465,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x) \, dx","Integrate[F^(a + b/(c + d*x)^3)*(c + d*x),x]","\frac{F^a (c+d x)^2 \left(-\frac{b \log (F)}{(c+d x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}","\frac{F^a (c+d x)^2 \left(-\frac{b \log (F)}{(c+d x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}",1,"(F^a*(c + d*x)^2*Gamma[-2/3, -((b*Log[F])/(c + d*x)^3)]*(-((b*Log[F])/(c + d*x)^3))^(2/3))/(3*d)","A",1
355,1,47,47,0.0134707,"\int F^{a+\frac{b}{(c+d x)^3}} \, dx","Integrate[F^(a + b/(c + d*x)^3),x]","\frac{F^a (c+d x) \sqrt[3]{-\frac{b \log (F)}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}","\frac{F^a (c+d x) \sqrt[3]{-\frac{b \log (F)}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}",1,"(F^a*(c + d*x)*Gamma[-1/3, -((b*Log[F])/(c + d*x)^3)]*(-((b*Log[F])/(c + d*x)^3))^(1/3))/(3*d)","A",1
356,1,49,49,0.0308686,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^2} \, dx","Integrate[F^(a + b/(c + d*x)^3)/(c + d*x)^2,x]","\frac{F^a \Gamma \left(\frac{1}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d (c+d x) \sqrt[3]{-\frac{b \log (F)}{(c+d x)^3}}}","\frac{F^a \Gamma \left(\frac{1}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d (c+d x) \sqrt[3]{-\frac{b \log (F)}{(c+d x)^3}}}",1,"(F^a*Gamma[1/3, -((b*Log[F])/(c + d*x)^3)])/(3*d*(c + d*x)*(-((b*Log[F])/(c + d*x)^3))^(1/3))","A",1
357,1,49,49,0.0287814,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^3} \, dx","Integrate[F^(a + b/(c + d*x)^3)/(c + d*x)^3,x]","\frac{F^a \Gamma \left(\frac{2}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d (c+d x)^2 \left(-\frac{b \log (F)}{(c+d x)^3}\right)^{2/3}}","\frac{F^a \Gamma \left(\frac{2}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d (c+d x)^2 \left(-\frac{b \log (F)}{(c+d x)^3}\right)^{2/3}}",1,"(F^a*Gamma[2/3, -((b*Log[F])/(c + d*x)^3)])/(3*d*(c + d*x)^2*(-((b*Log[F])/(c + d*x)^3))^(2/3))","A",1
358,1,49,49,0.0366211,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^5} \, dx","Integrate[F^(a + b/(c + d*x)^3)/(c + d*x)^5,x]","\frac{F^a \Gamma \left(\frac{4}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d (c+d x)^4 \left(-\frac{b \log (F)}{(c+d x)^3}\right)^{4/3}}","\frac{F^a \Gamma \left(\frac{4}{3},-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d (c+d x)^4 \left(-\frac{b \log (F)}{(c+d x)^3}\right)^{4/3}}",1,"(F^a*Gamma[4/3, -((b*Log[F])/(c + d*x)^3)])/(3*d*(c + d*x)^4*(-((b*Log[F])/(c + d*x)^3))^(4/3))","A",1
359,1,61,61,0.021886,"\int F^{a+b (c+d x)^n} (c+d x)^m \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^m,x]","-\frac{F^a (c+d x)^{m+1} \left(-b \log (F) (c+d x)^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-b (c+d x)^n \log (F)\right)}{d n}","-\frac{F^a (c+d x)^{m+1} \left(-b \log (F) (c+d x)^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-b (c+d x)^n \log (F)\right)}{d n}",1,"-((F^a*(c + d*x)^(1 + m)*Gamma[(1 + m)/n, -(b*(c + d*x)^n*Log[F])])/(d*n*(-(b*(c + d*x)^n*Log[F]))^((1 + m)/n)))","A",1
360,1,54,54,0.0163512,"\int F^{a+b (c+d x)^n} (c+d x)^3 \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^3,x]","-\frac{F^a (c+d x)^4 \left(-b \log (F) (c+d x)^n\right)^{-4/n} \Gamma \left(\frac{4}{n},-b (c+d x)^n \log (F)\right)}{d n}","-\frac{F^a (c+d x)^4 \left(-b \log (F) (c+d x)^n\right)^{-4/n} \Gamma \left(\frac{4}{n},-b (c+d x)^n \log (F)\right)}{d n}",1,"-((F^a*(c + d*x)^4*Gamma[4/n, -(b*(c + d*x)^n*Log[F])])/(d*n*(-(b*(c + d*x)^n*Log[F]))^(4/n)))","A",1
361,1,54,54,0.0161677,"\int F^{a+b (c+d x)^n} (c+d x)^2 \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^2,x]","-\frac{F^a (c+d x)^3 \left(-b \log (F) (c+d x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-b (c+d x)^n \log (F)\right)}{d n}","-\frac{F^a (c+d x)^3 \left(-b \log (F) (c+d x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-b (c+d x)^n \log (F)\right)}{d n}",1,"-((F^a*(c + d*x)^3*Gamma[3/n, -(b*(c + d*x)^n*Log[F])])/(d*n*(-(b*(c + d*x)^n*Log[F]))^(3/n)))","A",1
362,1,54,54,0.0128447,"\int F^{a+b (c+d x)^n} (c+d x) \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x),x]","-\frac{F^a (c+d x)^2 \left(-b \log (F) (c+d x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-b (c+d x)^n \log (F)\right)}{d n}","-\frac{F^a (c+d x)^2 \left(-b \log (F) (c+d x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-b (c+d x)^n \log (F)\right)}{d n}",1,"-((F^a*(c + d*x)^2*Gamma[2/n, -(b*(c + d*x)^n*Log[F])])/(d*n*(-(b*(c + d*x)^n*Log[F]))^(2/n)))","A",1
363,1,50,50,0.0093329,"\int F^{a+b (c+d x)^n} \, dx","Integrate[F^(a + b*(c + d*x)^n),x]","-\frac{F^a (c+d x) \left(-b \log (F) (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-b (c+d x)^n \log (F)\right)}{d n}","-\frac{F^a (c+d x) \left(-b \log (F) (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-b (c+d x)^n \log (F)\right)}{d n}",1,"-((F^a*(c + d*x)*Gamma[n^(-1), -(b*(c + d*x)^n*Log[F])])/(d*n*(-(b*(c + d*x)^n*Log[F]))^n^(-1)))","A",1
364,1,22,22,0.0047462,"\int \frac{F^{a+b (c+d x)^n}}{c+d x} \, dx","Integrate[F^(a + b*(c + d*x)^n)/(c + d*x),x]","\frac{F^a \text{Ei}\left(b (c+d x)^n \log (F)\right)}{d n}","\frac{F^a \text{Ei}\left(b (c+d x)^n \log (F)\right)}{d n}",1,"(F^a*ExpIntegralEi[b*(c + d*x)^n*Log[F]])/(d*n)","A",1
365,1,52,52,0.0128248,"\int \frac{F^{a+b (c+d x)^n}}{(c+d x)^2} \, dx","Integrate[F^(a + b*(c + d*x)^n)/(c + d*x)^2,x]","-\frac{F^a \left(-b \log (F) (c+d x)^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-b (c+d x)^n \log (F)\right)}{d n (c+d x)}","-\frac{F^a \left(-b \log (F) (c+d x)^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-b (c+d x)^n \log (F)\right)}{d n (c+d x)}",1,"-((F^a*Gamma[-n^(-1), -(b*(c + d*x)^n*Log[F])]*(-(b*(c + d*x)^n*Log[F]))^n^(-1))/(d*n*(c + d*x)))","A",1
366,1,54,54,0.0106418,"\int \frac{F^{a+b (c+d x)^n}}{(c+d x)^3} \, dx","Integrate[F^(a + b*(c + d*x)^n)/(c + d*x)^3,x]","-\frac{F^a \left(-b \log (F) (c+d x)^n\right)^{2/n} \Gamma \left(-\frac{2}{n},-b (c+d x)^n \log (F)\right)}{d n (c+d x)^2}","-\frac{F^a \left(-b \log (F) (c+d x)^n\right)^{2/n} \Gamma \left(-\frac{2}{n},-b (c+d x)^n \log (F)\right)}{d n (c+d x)^2}",1,"-((F^a*Gamma[-2/n, -(b*(c + d*x)^n*Log[F])]*(-(b*(c + d*x)^n*Log[F]))^(2/n))/(d*n*(c + d*x)^2))","A",1
367,1,54,54,0.0103534,"\int \frac{F^{a+b (c+d x)^n}}{(c+d x)^4} \, dx","Integrate[F^(a + b*(c + d*x)^n)/(c + d*x)^4,x]","-\frac{F^a \left(-b \log (F) (c+d x)^n\right)^{3/n} \Gamma \left(-\frac{3}{n},-b (c+d x)^n \log (F)\right)}{d n (c+d x)^3}","-\frac{F^a \left(-b \log (F) (c+d x)^n\right)^{3/n} \Gamma \left(-\frac{3}{n},-b (c+d x)^n \log (F)\right)}{d n (c+d x)^3}",1,"-((F^a*Gamma[-3/n, -(b*(c + d*x)^n*Log[F])]*(-(b*(c + d*x)^n*Log[F]))^(3/n))/(d*n*(c + d*x)^3))","A",1
368,1,32,114,0.0067304,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+6 n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 6*n),x]","-\frac{F^a \Gamma \left(6,-b (c+d x)^n \log (F)\right)}{b^6 d n \log ^6(F)}","-\frac{F^{a+b (c+d x)^n} \left(-b^5 \log ^5(F) (c+d x)^{5 n}+5 b^4 \log ^4(F) (c+d x)^{4 n}-20 b^3 \log ^3(F) (c+d x)^{3 n}+60 b^2 \log ^2(F) (c+d x)^{2 n}-120 b \log (F) (c+d x)^n+120\right)}{b^6 d n \log ^6(F)}",1,"-((F^a*Gamma[6, -(b*(c + d*x)^n*Log[F])])/(b^6*d*n*Log[F]^6))","C",1
369,1,31,94,0.0070114,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+5 n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 5*n),x]","\frac{F^a \Gamma \left(5,-b (c+d x)^n \log (F)\right)}{b^5 d n \log ^5(F)}","\frac{F^{a+b (c+d x)^n} \left(b^4 \log ^4(F) (c+d x)^{4 n}-4 b^3 \log ^3(F) (c+d x)^{3 n}+12 b^2 \log ^2(F) (c+d x)^{2 n}-24 b \log (F) (c+d x)^n+24\right)}{b^5 d n \log ^5(F)}",1,"(F^a*Gamma[5, -(b*(c + d*x)^n*Log[F])])/(b^5*d*n*Log[F]^5)","C",1
370,1,32,137,0.0065961,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+4 n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 4*n),x]","-\frac{F^a \Gamma \left(4,-b (c+d x)^n \log (F)\right)}{b^4 d n \log ^4(F)}","-\frac{6 F^{a+b (c+d x)^n}}{b^4 d n \log ^4(F)}+\frac{6 (c+d x)^n F^{a+b (c+d x)^n}}{b^3 d n \log ^3(F)}-\frac{3 (c+d x)^{2 n} F^{a+b (c+d x)^n}}{b^2 d n \log ^2(F)}+\frac{(c+d x)^{3 n} F^{a+b (c+d x)^n}}{b d n \log (F)}",1,"-((F^a*Gamma[4, -(b*(c + d*x)^n*Log[F])])/(b^4*d*n*Log[F]^4))","C",1
371,1,31,100,0.0065198,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+3 n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 3*n),x]","\frac{F^a \Gamma \left(3,-b (c+d x)^n \log (F)\right)}{b^3 d n \log ^3(F)}","\frac{2 F^{a+b (c+d x)^n}}{b^3 d n \log ^3(F)}-\frac{2 (c+d x)^n F^{a+b (c+d x)^n}}{b^2 d n \log ^2(F)}+\frac{(c+d x)^{2 n} F^{a+b (c+d x)^n}}{b d n \log (F)}",1,"(F^a*Gamma[3, -(b*(c + d*x)^n*Log[F])])/(b^3*d*n*Log[F]^3)","C",1
372,1,32,63,0.0065413,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+2 n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 2*n),x]","-\frac{F^a \Gamma \left(2,-b (c+d x)^n \log (F)\right)}{b^2 d n \log ^2(F)}","\frac{(c+d x)^n F^{a+b (c+d x)^n}}{b d n \log (F)}-\frac{F^{a+b (c+d x)^n}}{b^2 d n \log ^2(F)}",1,"-((F^a*Gamma[2, -(b*(c + d*x)^n*Log[F])])/(b^2*d*n*Log[F]^2))","C",1
373,1,27,27,0.0076673,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + n),x]","\frac{F^{a+b (c+d x)^n}}{b d n \log (F)}","\frac{F^{a+b (c+d x)^n}}{b d n \log (F)}",1,"F^(a + b*(c + d*x)^n)/(b*d*n*Log[F])","A",1
374,1,22,22,0.00191,"\int \frac{F^{a+b (c+d x)^n}}{c+d x} \, dx","Integrate[F^(a + b*(c + d*x)^n)/(c + d*x),x]","\frac{F^a \text{Ei}\left(b (c+d x)^n \log (F)\right)}{d n}","\frac{F^a \text{Ei}\left(b (c+d x)^n \log (F)\right)}{d n}",1,"(F^a*ExpIntegralEi[b*(c + d*x)^n*Log[F]])/(d*n)","A",1
375,1,27,56,0.0067269,"\int F^{a+b (c+d x)^n} (c+d x)^{-1-n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 - n),x]","\frac{b F^a \log (F) \Gamma \left(-1,-b (c+d x)^n \log (F)\right)}{d n}","\frac{b F^a \log (F) \text{Ei}\left(b (c+d x)^n \log (F)\right)}{d n}-\frac{(c+d x)^{-n} F^{a+b (c+d x)^n}}{d n}",1,"(b*F^a*Gamma[-1, -(b*(c + d*x)^n*Log[F])]*Log[F])/(d*n)","A",1
376,1,32,100,0.0069667,"\int F^{a+b (c+d x)^n} (c+d x)^{-1-2 n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 - 2*n),x]","-\frac{b^2 F^a \log ^2(F) \Gamma \left(-2,-b (c+d x)^n \log (F)\right)}{d n}","\frac{b^2 F^a \log ^2(F) \text{Ei}\left(b (c+d x)^n \log (F)\right)}{2 d n}-\frac{(c+d x)^{-2 n} F^{a+b (c+d x)^n}}{2 d n}-\frac{b \log (F) (c+d x)^{-n} F^{a+b (c+d x)^n}}{2 d n}",1,"-((b^2*F^a*Gamma[-2, -(b*(c + d*x)^n*Log[F])]*Log[F]^2)/(d*n))","A",1
377,1,31,139,0.0072904,"\int F^{a+b (c+d x)^n} (c+d x)^{-1-3 n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 - 3*n),x]","\frac{b^3 F^a \log ^3(F) \Gamma \left(-3,-b (c+d x)^n \log (F)\right)}{d n}","\frac{b^3 F^a \log ^3(F) \text{Ei}\left(b (c+d x)^n \log (F)\right)}{6 d n}-\frac{b^2 \log ^2(F) (c+d x)^{-n} F^{a+b (c+d x)^n}}{6 d n}-\frac{(c+d x)^{-3 n} F^{a+b (c+d x)^n}}{3 d n}-\frac{b \log (F) (c+d x)^{-2 n} F^{a+b (c+d x)^n}}{6 d n}",1,"(b^3*F^a*Gamma[-3, -(b*(c + d*x)^n*Log[F])]*Log[F]^3)/(d*n)","A",1
378,1,32,32,0.0070088,"\int F^{a+b (c+d x)^n} (c+d x)^{-1-4 n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 - 4*n),x]","-\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-b (c+d x)^n \log (F)\right)}{d n}","-\frac{b^4 F^a \log ^4(F) \Gamma \left(-4,-b (c+d x)^n \log (F)\right)}{d n}",1,"-((b^4*F^a*Gamma[-4, -(b*(c + d*x)^n*Log[F])]*Log[F]^4)/(d*n))","A",1
379,1,31,31,0.0069284,"\int F^{a+b (c+d x)^n} (c+d x)^{-1-5 n} \, dx","Integrate[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 - 5*n),x]","\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-b (c+d x)^n \log (F)\right)}{d n}","\frac{b^5 F^a \log ^5(F) \Gamma \left(-5,-b (c+d x)^n \log (F)\right)}{d n}",1,"(b^5*F^a*Gamma[-5, -(b*(c + d*x)^n*Log[F])]*Log[F]^5)/(d*n)","A",1
380,1,47,47,0.0119252,"\int F^{c (a+b x)^n} (a+b x)^{-1+\frac{n}{2}} \, dx","Integrate[F^(c*(a + b*x)^n)*(a + b*x)^(-1 + n/2),x]","\frac{\sqrt{\pi } \text{erfi}\left(\sqrt{c} \sqrt{\log (F)} (a+b x)^{n/2}\right)}{b \sqrt{c} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } \text{erfi}\left(\sqrt{c} \sqrt{\log (F)} (a+b x)^{n/2}\right)}{b \sqrt{c} n \sqrt{\log (F)}}",1,"(Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)^(n/2)*Sqrt[Log[F]]])/(b*Sqrt[c]*n*Sqrt[Log[F]])","A",1
381,1,47,47,0.007511,"\int F^{-c (a+b x)^n} (a+b x)^{-1+\frac{n}{2}} \, dx","Integrate[(a + b*x)^(-1 + n/2)/F^(c*(a + b*x)^n),x]","\frac{\sqrt{\pi } \text{erf}\left(\sqrt{c} \sqrt{\log (F)} (a+b x)^{n/2}\right)}{b \sqrt{c} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } \text{erf}\left(\sqrt{c} \sqrt{\log (F)} (a+b x)^{n/2}\right)}{b \sqrt{c} n \sqrt{\log (F)}}",1,"(Sqrt[Pi]*Erf[Sqrt[c]*(a + b*x)^(n/2)*Sqrt[Log[F]]])/(b*Sqrt[c]*n*Sqrt[Log[F]])","A",1
382,1,412,518,0.6236133,"\int F^{a+b (c+d x)^2} (e+f x)^5 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(e + f*x)^5,x]","\frac{F^a \left(4 \sqrt{\pi } b^{3/2} \log ^{\frac{3}{2}}(F) (d e-c f)^5 \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)+\frac{15 f^4 (c f-d e) \left(2 \sqrt{b} \sqrt{\log (F)} (c+d x) F^{b (c+d x)^2}-\sqrt{\pi } \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)\right)}{\sqrt{b} \sqrt{\log (F)}}+20 \sqrt{\pi } \sqrt{b} f^2 \sqrt{\log (F)} (c f-d e)^3 \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)+20 b f^4 \log (F) (c+d x)^3 (d e-c f) F^{b (c+d x)^2}-40 f^3 (d e-c f)^2 F^{b (c+d x)^2}+40 b f^3 \log (F) (c+d x)^2 (d e-c f)^2 F^{b (c+d x)^2}+40 b f^2 \log (F) (c+d x) (d e-c f)^3 F^{b (c+d x)^2}+20 b f \log (F) (d e-c f)^4 F^{b (c+d x)^2}+4 b f^5 \log (F) (c+d x)^4 F^{b (c+d x)^2}+\frac{8 f^5 F^{b (c+d x)^2} \left(1-b \log (F) (c+d x)^2\right)}{b \log (F)}\right)}{8 b^2 d^6 \log ^2(F)}","\frac{15 \sqrt{\pi } f^4 F^a (d e-c f) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{8 b^{5/2} d^6 \log ^{\frac{5}{2}}(F)}-\frac{5 \sqrt{\pi } f^2 F^a (d e-c f)^3 \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 b^{3/2} d^6 \log ^{\frac{3}{2}}(F)}+\frac{f^5 F^{a+b (c+d x)^2}}{b^3 d^6 \log ^3(F)}-\frac{15 f^4 (c+d x) (d e-c f) F^{a+b (c+d x)^2}}{4 b^2 d^6 \log ^2(F)}-\frac{5 f^3 (d e-c f)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(F)}-\frac{f^5 (c+d x)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(F)}+\frac{\sqrt{\pi } F^a (d e-c f)^5 \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 \sqrt{b} d^6 \sqrt{\log (F)}}+\frac{5 f^4 (c+d x)^3 (d e-c f) F^{a+b (c+d x)^2}}{2 b d^6 \log (F)}+\frac{5 f^3 (c+d x)^2 (d e-c f)^2 F^{a+b (c+d x)^2}}{b d^6 \log (F)}+\frac{5 f^2 (c+d x) (d e-c f)^3 F^{a+b (c+d x)^2}}{b d^6 \log (F)}+\frac{5 f (d e-c f)^4 F^{a+b (c+d x)^2}}{2 b d^6 \log (F)}+\frac{f^5 (c+d x)^4 F^{a+b (c+d x)^2}}{2 b d^6 \log (F)}",1,"(F^a*(-40*f^3*(d*e - c*f)^2*F^(b*(c + d*x)^2) + (15*f^4*(-(d*e) + c*f)*(-(Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]) + 2*Sqrt[b]*F^(b*(c + d*x)^2)*(c + d*x)*Sqrt[Log[F]]))/(Sqrt[b]*Sqrt[Log[F]]) + 20*Sqrt[b]*f^2*(-(d*e) + c*f)^3*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Sqrt[Log[F]] + 20*b*f*(d*e - c*f)^4*F^(b*(c + d*x)^2)*Log[F] + 40*b*f^2*(d*e - c*f)^3*F^(b*(c + d*x)^2)*(c + d*x)*Log[F] + 40*b*f^3*(d*e - c*f)^2*F^(b*(c + d*x)^2)*(c + d*x)^2*Log[F] + 20*b*f^4*(d*e - c*f)*F^(b*(c + d*x)^2)*(c + d*x)^3*Log[F] + 4*b*f^5*F^(b*(c + d*x)^2)*(c + d*x)^4*Log[F] + 4*b^(3/2)*(d*e - c*f)^5*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Log[F]^(3/2) + (8*f^5*F^(b*(c + d*x)^2)*(1 - b*(c + d*x)^2*Log[F]))/(b*Log[F])))/(8*b^2*d^6*Log[F]^2)","A",1
383,1,220,389,0.4510976,"\int F^{a+b (c+d x)^2} (e+f x)^4 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(e + f*x)^4,x]","\frac{F^a \left(\sqrt{\pi } \left(4 b^2 \log ^2(F) (d e-c f)^4-12 b f^2 \log (F) (d e-c f)^2+3 f^4\right) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)+2 \sqrt{b} f \sqrt{\log (F)} F^{b (c+d x)^2} \left(2 b \log (F) \left(-c^3 f^3+c^2 d f^2 (4 e+f x)-c d^2 f \left(6 e^2+4 e f x+f^2 x^2\right)+d^3 \left(4 e^3+6 e^2 f x+4 e f^2 x^2+f^3 x^3\right)\right)+f^2 (5 c f-8 d e-3 d f x)\right)\right)}{8 b^{5/2} d^5 \log ^{\frac{5}{2}}(F)}","-\frac{3 \sqrt{\pi } f^2 F^a (d e-c f)^2 \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 b^{3/2} d^5 \log ^{\frac{3}{2}}(F)}+\frac{3 \sqrt{\pi } f^4 F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{8 b^{5/2} d^5 \log ^{\frac{5}{2}}(F)}-\frac{2 f^3 (d e-c f) F^{a+b (c+d x)^2}}{b^2 d^5 \log ^2(F)}-\frac{3 f^4 (c+d x) F^{a+b (c+d x)^2}}{4 b^2 d^5 \log ^2(F)}+\frac{\sqrt{\pi } F^a (d e-c f)^4 \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 \sqrt{b} d^5 \sqrt{\log (F)}}+\frac{2 f^3 (c+d x)^2 (d e-c f) F^{a+b (c+d x)^2}}{b d^5 \log (F)}+\frac{3 f^2 (c+d x) (d e-c f)^2 F^{a+b (c+d x)^2}}{b d^5 \log (F)}+\frac{2 f (d e-c f)^3 F^{a+b (c+d x)^2}}{b d^5 \log (F)}+\frac{f^4 (c+d x)^3 F^{a+b (c+d x)^2}}{2 b d^5 \log (F)}",1,"(F^a*(2*Sqrt[b]*f*F^(b*(c + d*x)^2)*Sqrt[Log[F]]*(f^2*(-8*d*e + 5*c*f - 3*d*f*x) + 2*b*(-(c^3*f^3) + c^2*d*f^2*(4*e + f*x) - c*d^2*f*(6*e^2 + 4*e*f*x + f^2*x^2) + d^3*(4*e^3 + 6*e^2*f*x + 4*e*f^2*x^2 + f^3*x^3))*Log[F]) + Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*(3*f^4 - 12*b*f^2*(d*e - c*f)^2*Log[F] + 4*b^2*(d*e - c*f)^4*Log[F]^2)))/(8*b^(5/2)*d^5*Log[F]^(5/2))","A",1
384,1,148,258,0.2592943,"\int F^{a+b (c+d x)^2} (e+f x)^3 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(e + f*x)^3,x]","\frac{F^a \left(2 f F^{b (c+d x)^2} \left(b \log (F) \left(c^2 f^2-c d f (3 e+f x)+d^2 \left(3 e^2+3 e f x+f^2 x^2\right)\right)-f^2\right)+\sqrt{\pi } \sqrt{b} \sqrt{\log (F)} (d e-c f) \left(2 b \log (F) (d e-c f)^2-3 f^2\right) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)\right)}{4 b^2 d^4 \log ^2(F)}","-\frac{3 \sqrt{\pi } f^2 F^a (d e-c f) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{4 b^{3/2} d^4 \log ^{\frac{3}{2}}(F)}-\frac{f^3 F^{a+b (c+d x)^2}}{2 b^2 d^4 \log ^2(F)}+\frac{\sqrt{\pi } F^a (d e-c f)^3 \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 \sqrt{b} d^4 \sqrt{\log (F)}}+\frac{3 f^2 (c+d x) (d e-c f) F^{a+b (c+d x)^2}}{2 b d^4 \log (F)}+\frac{3 f (d e-c f)^2 F^{a+b (c+d x)^2}}{2 b d^4 \log (F)}+\frac{f^3 (c+d x)^2 F^{a+b (c+d x)^2}}{2 b d^4 \log (F)}",1,"(F^a*(Sqrt[b]*(d*e - c*f)*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Sqrt[Log[F]]*(-3*f^2 + 2*b*(d*e - c*f)^2*Log[F]) + 2*f*F^(b*(c + d*x)^2)*(-f^2 + b*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2))*Log[F])))/(4*b^2*d^4*Log[F]^2)","A",1
385,1,105,170,0.2255952,"\int F^{a+b (c+d x)^2} (e+f x)^2 \, dx","Integrate[F^(a + b*(c + d*x)^2)*(e + f*x)^2,x]","\frac{F^a \left(\sqrt{\pi } \left(2 b \log (F) (d e-c f)^2-f^2\right) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)+2 \sqrt{b} f \sqrt{\log (F)} F^{b (c+d x)^2} (-c f+2 d e+d f x)\right)}{4 b^{3/2} d^3 \log ^{\frac{3}{2}}(F)}","-\frac{\sqrt{\pi } f^2 F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{4 b^{3/2} d^3 \log ^{\frac{3}{2}}(F)}+\frac{\sqrt{\pi } F^a (d e-c f)^2 \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 \sqrt{b} d^3 \sqrt{\log (F)}}+\frac{f (d e-c f) F^{a+b (c+d x)^2}}{b d^3 \log (F)}+\frac{f^2 (c+d x) F^{a+b (c+d x)^2}}{2 b d^3 \log (F)}",1,"(F^a*(2*Sqrt[b]*f*F^(b*(c + d*x)^2)*(2*d*e - c*f + d*f*x)*Sqrt[Log[F]] + Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*(-f^2 + 2*b*(d*e - c*f)^2*Log[F])))/(4*b^(3/2)*d^3*Log[F]^(3/2))","A",1
386,1,74,81,0.0701007,"\int F^{a+b (c+d x)^2} (e+f x) \, dx","Integrate[F^(a + b*(c + d*x)^2)*(e + f*x),x]","\frac{F^a \left(\sqrt{\pi } \sqrt{b} \sqrt{\log (F)} (d e-c f) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)+f F^{b (c+d x)^2}\right)}{2 b d^2 \log (F)}","\frac{\sqrt{\pi } F^a (d e-c f) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 \sqrt{b} d^2 \sqrt{\log (F)}}+\frac{f F^{a+b (c+d x)^2}}{2 b d^2 \log (F)}",1,"(F^a*(f*F^(b*(c + d*x)^2) + Sqrt[b]*(d*e - c*f)*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Sqrt[Log[F]]))/(2*b*d^2*Log[F])","A",1
387,1,44,44,0.0060201,"\int F^{a+b (c+d x)^2} \, dx","Integrate[F^(a + b*(c + d*x)^2),x]","\frac{\sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 \sqrt{b} d \sqrt{\log (F)}}","\frac{\sqrt{\pi } F^a \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{2 \sqrt{b} d \sqrt{\log (F)}}",1,"(F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(2*Sqrt[b]*d*Sqrt[Log[F]])","A",1
388,0,0,24,0.2916985,"\int \frac{F^{a+b (c+d x)^2}}{e+f x} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(e + f*x),x]","\int \frac{F^{a+b (c+d x)^2}}{e+f x} \, dx","\text{Int}\left(\frac{F^{a+b (c+d x)^2}}{e+f x},x\right)",0,"Integrate[F^(a + b*(c + d*x)^2)/(e + f*x), x]","A",-1
389,0,0,109,0.7768313,"\int \frac{F^{a+b (c+d x)^2}}{(e+f x)^2} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(e + f*x)^2,x]","\int \frac{F^{a+b (c+d x)^2}}{(e+f x)^2} \, dx","-\frac{2 b d \log (F) (d e-c f) \text{Int}\left(\frac{F^{a+b (c+d x)^2}}{e+f x},x\right)}{f^2}-\frac{F^{a+b (c+d x)^2}}{f (e+f x)}+\frac{\sqrt{\pi } \sqrt{b} d F^a \sqrt{\log (F)} \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{f^2}",0,"Integrate[F^(a + b*(c + d*x)^2)/(e + f*x)^2, x]","A",-1
390,0,0,200,1.1602393,"\int \frac{F^{a+b (c+d x)^2}}{(e+f x)^3} \, dx","Integrate[F^(a + b*(c + d*x)^2)/(e + f*x)^3,x]","\int \frac{F^{a+b (c+d x)^2}}{(e+f x)^3} \, dx","\frac{2 b^2 d^2 \log ^2(F) (d e-c f)^2 \text{Int}\left(\frac{F^{a+b (c+d x)^2}}{e+f x},x\right)}{f^4}+\frac{b d^2 \log (F) \text{Int}\left(\frac{F^{a+b (c+d x)^2}}{e+f x},x\right)}{f^2}-\frac{\sqrt{\pi } b^{3/2} d^2 F^a \log ^{\frac{3}{2}}(F) (d e-c f) \text{erfi}\left(\sqrt{b} \sqrt{\log (F)} (c+d x)\right)}{f^4}+\frac{b d \log (F) (d e-c f) F^{a+b (c+d x)^2}}{f^3 (e+f x)}-\frac{F^{a+b (c+d x)^2}}{2 f (e+f x)^2}",0,"Integrate[F^(a + b*(c + d*x)^2)/(e + f*x)^3, x]","A",-1
391,1,167,177,0.2020009,"\int e^{e (c+d x)^3} (a+b x)^3 \, dx","Integrate[E^(e*(c + d*x)^3)*(a + b*x)^3,x]","\frac{-\frac{3 b^2 (b c-a d) e^{e (c+d x)^3}}{e}-\frac{3 b (c+d x)^2 (b c-a d)^2 \Gamma \left(\frac{2}{3},-e (c+d x)^3\right)}{\left(-e (c+d x)^3\right)^{2/3}}+\frac{(c+d x) (b c-a d)^3 \Gamma \left(\frac{1}{3},-e (c+d x)^3\right)}{\sqrt[3]{-e (c+d x)^3}}+\frac{b^3 (c+d x) \Gamma \left(\frac{4}{3},-e (c+d x)^3\right)}{e \sqrt[3]{-e (c+d x)^3}}}{3 d^4}","-\frac{b^2 (b c-a d) e^{e (c+d x)^3}}{d^4 e}-\frac{b (c+d x)^2 (b c-a d)^2 \Gamma \left(\frac{2}{3},-e (c+d x)^3\right)}{d^4 \left(-e (c+d x)^3\right)^{2/3}}+\frac{(c+d x) (b c-a d)^3 \Gamma \left(\frac{1}{3},-e (c+d x)^3\right)}{3 d^4 \sqrt[3]{-e (c+d x)^3}}-\frac{b^3 (c+d x)^4 \Gamma \left(\frac{4}{3},-e (c+d x)^3\right)}{3 d^4 \left(-e (c+d x)^3\right)^{4/3}}",1,"((-3*b^2*(b*c - a*d)*E^(e*(c + d*x)^3))/e + ((b*c - a*d)^3*(c + d*x)*Gamma[1/3, -(e*(c + d*x)^3)])/(-(e*(c + d*x)^3))^(1/3) - (3*b*(b*c - a*d)^2*(c + d*x)^2*Gamma[2/3, -(e*(c + d*x)^3)])/(-(e*(c + d*x)^3))^(2/3) + (b^3*(c + d*x)*Gamma[4/3, -(e*(c + d*x)^3)])/(e*(-(e*(c + d*x)^3))^(1/3)))/(3*d^4)","A",1
392,1,117,126,0.0849125,"\int e^{e (c+d x)^3} (a+b x)^2 \, dx","Integrate[E^(e*(c + d*x)^3)*(a + b*x)^2,x]","\frac{\frac{2 b (c+d x)^2 (b c-a d) \Gamma \left(\frac{2}{3},-e (c+d x)^3\right)}{\left(-e (c+d x)^3\right)^{2/3}}-\frac{(c+d x) (b c-a d)^2 \Gamma \left(\frac{1}{3},-e (c+d x)^3\right)}{\sqrt[3]{-e (c+d x)^3}}+\frac{b^2 e^{e (c+d x)^3}}{e}}{3 d^3}","\frac{2 b (c+d x)^2 (b c-a d) \Gamma \left(\frac{2}{3},-e (c+d x)^3\right)}{3 d^3 \left(-e (c+d x)^3\right)^{2/3}}-\frac{(c+d x) (b c-a d)^2 \Gamma \left(\frac{1}{3},-e (c+d x)^3\right)}{3 d^3 \sqrt[3]{-e (c+d x)^3}}+\frac{b^2 e^{e (c+d x)^3}}{3 d^3 e}",1,"((b^2*E^(e*(c + d*x)^3))/e - ((b*c - a*d)^2*(c + d*x)*Gamma[1/3, -(e*(c + d*x)^3)])/(-(e*(c + d*x)^3))^(1/3) + (2*b*(b*c - a*d)*(c + d*x)^2*Gamma[2/3, -(e*(c + d*x)^3)])/(-(e*(c + d*x)^3))^(2/3))/(3*d^3)","A",1
393,1,86,92,0.0633807,"\int e^{e (c+d x)^3} (a+b x) \, dx","Integrate[E^(e*(c + d*x)^3)*(a + b*x),x]","-\frac{(c+d x) \left(b (c+d x) \Gamma \left(\frac{2}{3},-e (c+d x)^3\right)-(b c-a d) \sqrt[3]{-e (c+d x)^3} \Gamma \left(\frac{1}{3},-e (c+d x)^3\right)\right)}{3 d^2 \left(-e (c+d x)^3\right)^{2/3}}","\frac{(c+d x) (b c-a d) \Gamma \left(\frac{1}{3},-e (c+d x)^3\right)}{3 d^2 \sqrt[3]{-e (c+d x)^3}}-\frac{b (c+d x)^2 \Gamma \left(\frac{2}{3},-e (c+d x)^3\right)}{3 d^2 \left(-e (c+d x)^3\right)^{2/3}}",1,"-1/3*((c + d*x)*(-((b*c - a*d)*(-(e*(c + d*x)^3))^(1/3)*Gamma[1/3, -(e*(c + d*x)^3)]) + b*(c + d*x)*Gamma[2/3, -(e*(c + d*x)^3)]))/(d^2*(-(e*(c + d*x)^3))^(2/3))","A",1
394,1,40,40,0.0064622,"\int e^{e (c+d x)^3} \, dx","Integrate[E^(e*(c + d*x)^3),x]","-\frac{(c+d x) \Gamma \left(\frac{1}{3},-e (c+d x)^3\right)}{3 d \sqrt[3]{-e (c+d x)^3}}","-\frac{(c+d x) \Gamma \left(\frac{1}{3},-e (c+d x)^3\right)}{3 d \sqrt[3]{-e (c+d x)^3}}",1,"-1/3*((c + d*x)*Gamma[1/3, -(e*(c + d*x)^3)])/(d*(-(e*(c + d*x)^3))^(1/3))","A",1
395,0,0,22,0.3889262,"\int \frac{e^{e (c+d x)^3}}{a+b x} \, dx","Integrate[E^(e*(c + d*x)^3)/(a + b*x),x]","\int \frac{e^{e (c+d x)^3}}{a+b x} \, dx","\text{Int}\left(\frac{e^{e (c+d x)^3}}{a+b x},x\right)",0,"Integrate[E^(e*(c + d*x)^3)/(a + b*x), x]","A",-1
396,0,0,153,2.0621217,"\int \frac{e^{e (c+d x)^3}}{(a+b x)^2} \, dx","Integrate[E^(e*(c + d*x)^3)/(a + b*x)^2,x]","\int \frac{e^{e (c+d x)^3}}{(a+b x)^2} \, dx","\frac{3 d e (b c-a d)^2 \text{Int}\left(\frac{e^{e (c+d x)^3}}{a+b x},x\right)}{b^3}-\frac{d e (c+d x) (b c-a d) \Gamma \left(\frac{1}{3},-e (c+d x)^3\right)}{b^3 \sqrt[3]{-e (c+d x)^3}}-\frac{e^{e (c+d x)^3}}{b (a+b x)}-\frac{d e (c+d x)^2 \Gamma \left(\frac{2}{3},-e (c+d x)^3\right)}{b^2 \left(-e (c+d x)^3\right)^{2/3}}",0,"Integrate[E^(e*(c + d*x)^3)/(a + b*x)^2, x]","A",-1
397,1,66,71,0.1318638,"\int \frac{F^{a+\frac{b}{c+d x}}}{e+f x} \, dx","Integrate[F^(a + b/(c + d*x))/(e + f*x),x]","\frac{F^a \left(F^{\frac{b f}{c f-d e}} \text{Ei}\left(\frac{b d (e+f x) \log (F)}{(d e-c f) (c+d x)}\right)-\text{Ei}\left(\frac{b \log (F)}{c+d x}\right)\right)}{f}","\frac{F^{a-\frac{b f}{d e-c f}} \text{Ei}\left(\frac{b d (e+f x) \log (F)}{(d e-c f) (c+d x)}\right)}{f}-\frac{F^a \text{Ei}\left(\frac{b \log (F)}{c+d x}\right)}{f}",1,"(F^a*(-ExpIntegralEi[(b*Log[F])/(c + d*x)] + F^((b*f)/(-(d*e) + c*f))*ExpIntegralEi[(b*d*(e + f*x)*Log[F])/((d*e - c*f)*(c + d*x))]))/f","A",1
398,1,116,116,0.3279267,"\int \frac{F^{a+\frac{b}{c+d x}}}{(e+f x)^2} \, dx","Integrate[F^(a + b/(c + d*x))/(e + f*x)^2,x]","-\frac{b d \log (F) F^{a+\frac{b f}{c f-d e}} \text{Ei}\left(\frac{b \log (F)}{c+d x}-\frac{b f \log (F)}{c f-d e}\right)}{(d e-c f)^2}+\frac{d F^{a+\frac{b}{c+d x}}}{f (d e-c f)}-\frac{F^{a+\frac{b}{c+d x}}}{f (e+f x)}","-\frac{b d \log (F) F^{a-\frac{b f}{d e-c f}} \text{Ei}\left(\frac{b d (e+f x) \log (F)}{(d e-c f) (c+d x)}\right)}{(d e-c f)^2}+\frac{d F^{a+\frac{b}{c+d x}}}{f (d e-c f)}-\frac{F^{a+\frac{b}{c+d x}}}{f (e+f x)}",1,"(d*F^(a + b/(c + d*x)))/(f*(d*e - c*f)) - F^(a + b/(c + d*x))/(f*(e + f*x)) - (b*d*F^(a + (b*f)/(-(d*e) + c*f))*ExpIntegralEi[-((b*f*Log[F])/(-(d*e) + c*f)) + (b*Log[F])/(c + d*x)]*Log[F])/(d*e - c*f)^2","A",1
399,0,0,267,0.8237065,"\int \frac{F^{a+\frac{b}{c+d x}}}{(e+f x)^3} \, dx","Integrate[F^(a + b/(c + d*x))/(e + f*x)^3,x]","\int \frac{F^{a+\frac{b}{c+d x}}}{(e+f x)^3} \, dx","\frac{b^2 d^2 f \log ^2(F) F^{a-\frac{b f}{d e-c f}} \text{Ei}\left(\frac{b d (e+f x) \log (F)}{(d e-c f) (c+d x)}\right)}{2 (d e-c f)^4}-\frac{b d^2 \log (F) F^{a-\frac{b f}{d e-c f}} \text{Ei}\left(\frac{b d (e+f x) \log (F)}{(d e-c f) (c+d x)}\right)}{(d e-c f)^3}+\frac{d^2 F^{a+\frac{b}{c+d x}}}{2 f (d e-c f)^2}-\frac{b d^2 \log (F) F^{a+\frac{b}{c+d x}}}{2 (d e-c f)^3}-\frac{F^{a+\frac{b}{c+d x}}}{2 f (e+f x)^2}+\frac{b d \log (F) F^{a+\frac{b}{c+d x}}}{2 (e+f x) (d e-c f)^2}",1,"Integrate[F^(a + b/(c + d*x))/(e + f*x)^3, x]","F",-1
400,0,0,460,0.6277764,"\int \frac{F^{a+\frac{b}{c+d x}}}{(e+f x)^4} \, dx","Integrate[F^(a + b/(c + d*x))/(e + f*x)^4,x]","\int \frac{F^{a+\frac{b}{c+d x}}}{(e+f x)^4} \, dx","-\frac{b^3 d^3 f^2 \log ^3(F) F^{a-\frac{b f}{d e-c f}} \text{Ei}\left(\frac{b d (e+f x) \log (F)}{(d e-c f) (c+d x)}\right)}{6 (d e-c f)^6}+\frac{b^2 d^3 f \log ^2(F) F^{a-\frac{b f}{d e-c f}} \text{Ei}\left(\frac{b d (e+f x) \log (F)}{(d e-c f) (c+d x)}\right)}{(d e-c f)^5}+\frac{b^2 d^3 f \log ^2(F) F^{a+\frac{b}{c+d x}}}{6 (d e-c f)^5}-\frac{b^2 d^2 f \log ^2(F) F^{a+\frac{b}{c+d x}}}{6 (e+f x) (d e-c f)^4}-\frac{b d^3 \log (F) F^{a-\frac{b f}{d e-c f}} \text{Ei}\left(\frac{b d (e+f x) \log (F)}{(d e-c f) (c+d x)}\right)}{(d e-c f)^4}+\frac{d^3 F^{a+\frac{b}{c+d x}}}{3 f (d e-c f)^3}-\frac{5 b d^3 \log (F) F^{a+\frac{b}{c+d x}}}{6 (d e-c f)^4}+\frac{2 b d^2 \log (F) F^{a+\frac{b}{c+d x}}}{3 (e+f x) (d e-c f)^3}-\frac{F^{a+\frac{b}{c+d x}}}{3 f (e+f x)^3}+\frac{b d \log (F) F^{a+\frac{b}{c+d x}}}{6 (e+f x)^2 (d e-c f)^2}",1,"Integrate[F^(a + b/(c + d*x))/(e + f*x)^4, x]","F",-1
401,1,468,346,0.5014765,"\int e^{\frac{e}{c+d x}} (a+b x)^4 \, dx","Integrate[E^(e/(c + d*x))*(a + b*x)^4,x]","\frac{d x e^{\frac{e}{c+d x}} \left(120 a^4 d^4+240 a^3 b d^3 (d x+e)+120 a^2 b^2 d^2 \left(-4 c e+2 d^2 x^2+d e x+e^2\right)+20 a b^3 d \left(18 c^2 e-2 c e (3 d x+5 e)+6 d^3 x^3+2 d^2 e x^2+d e^2 x+e^3\right)+b^4 \left(-96 c^3 e+2 c^2 e (18 d x+43 e)-2 c e \left(8 d^2 x^2+7 d e x+9 e^2\right)+24 d^4 x^4+6 d^3 e x^3+2 d^2 e^2 x^2+d e^3 x+e^4\right)\right)-e \left(120 a^4 d^4-240 a^3 b d^3 (2 c-e)+120 a^2 b^2 d^2 \left(6 c^2-6 c e+e^2\right)-20 a b^3 d \left(24 c^3-36 c^2 e+12 c e^2-e^3\right)+b^4 \left(120 c^4-240 c^3 e+120 c^2 e^2-20 c e^3+e^4\right)\right) \text{Ei}\left(\frac{e}{c+d x}\right)}{120 d^5}+\frac{c e^{\frac{e}{c+d x}} \left(120 a^4 d^4-240 a^3 b d^3 (c-e)+120 a^2 b^2 d^2 \left(2 c^2-5 c e+e^2\right)-20 a b^3 d \left(6 c^3-26 c^2 e+11 c e^2-e^3\right)+b^4 \left(24 c^4-154 c^3 e+102 c^2 e^2-19 c e^3+e^4\right)\right)}{120 d^5}","-\frac{4 b^3 e^4 (b c-a d) \Gamma \left(-4,-\frac{e}{c+d x}\right)}{d^5}-\frac{b^2 e^3 (b c-a d)^2 \text{Ei}\left(\frac{e}{c+d x}\right)}{d^5}+\frac{b^2 e^2 (c+d x) (b c-a d)^2 e^{\frac{e}{c+d x}}}{d^5}+\frac{b^2 e (c+d x)^2 (b c-a d)^2 e^{\frac{e}{c+d x}}}{d^5}+\frac{2 b^2 (c+d x)^3 (b c-a d)^2 e^{\frac{e}{c+d x}}}{d^5}+\frac{2 b e^2 (b c-a d)^3 \text{Ei}\left(\frac{e}{c+d x}\right)}{d^5}-\frac{e (b c-a d)^4 \text{Ei}\left(\frac{e}{c+d x}\right)}{d^5}-\frac{2 b e (c+d x) (b c-a d)^3 e^{\frac{e}{c+d x}}}{d^5}-\frac{2 b (c+d x)^2 (b c-a d)^3 e^{\frac{e}{c+d x}}}{d^5}+\frac{(c+d x) (b c-a d)^4 e^{\frac{e}{c+d x}}}{d^5}-\frac{b^4 e^5 \Gamma \left(-5,-\frac{e}{c+d x}\right)}{d^5}",1,"(c*(120*a^4*d^4 - 240*a^3*b*d^3*(c - e) + 120*a^2*b^2*d^2*(2*c^2 - 5*c*e + e^2) - 20*a*b^3*d*(6*c^3 - 26*c^2*e + 11*c*e^2 - e^3) + b^4*(24*c^4 - 154*c^3*e + 102*c^2*e^2 - 19*c*e^3 + e^4))*E^(e/(c + d*x)))/(120*d^5) + (d*E^(e/(c + d*x))*x*(120*a^4*d^4 + 240*a^3*b*d^3*(e + d*x) + 120*a^2*b^2*d^2*(-4*c*e + e^2 + d*e*x + 2*d^2*x^2) + 20*a*b^3*d*(18*c^2*e + e^3 + d*e^2*x + 2*d^2*e*x^2 + 6*d^3*x^3 - 2*c*e*(5*e + 3*d*x)) + b^4*(-96*c^3*e + e^4 + d*e^3*x + 2*d^2*e^2*x^2 + 6*d^3*e*x^3 + 24*d^4*x^4 + 2*c^2*e*(43*e + 18*d*x) - 2*c*e*(9*e^2 + 7*d*e*x + 8*d^2*x^2))) - e*(120*a^4*d^4 - 240*a^3*b*d^3*(2*c - e) + 120*a^2*b^2*d^2*(6*c^2 - 6*c*e + e^2) - 20*a*b^3*d*(24*c^3 - 36*c^2*e + 12*c*e^2 - e^3) + b^4*(120*c^4 - 240*c^3*e + 120*c^2*e^2 - 20*c*e^3 + e^4))*ExpIntegralEi[e/(c + d*x)])/(120*d^5)","A",1
402,1,292,320,0.3321789,"\int e^{\frac{e}{c+d x}} (a+b x)^3 \, dx","Integrate[E^(e/(c + d*x))*(a + b*x)^3,x]","\frac{d x e^{\frac{e}{c+d x}} \left(24 a^3 d^3+36 a^2 b d^2 (d x+e)+12 a b^2 d \left(-4 c e+2 d^2 x^2+d e x+e^2\right)+b^3 \left(18 c^2 e-2 c e (3 d x+5 e)+6 d^3 x^3+2 d^2 e x^2+d e^2 x+e^3\right)\right)-e \left(24 a^3 d^3+36 a^2 b d^2 (e-2 c)+12 a b^2 d \left(6 c^2-6 c e+e^2\right)+b^3 \left(-24 c^3+36 c^2 e-12 c e^2+e^3\right)\right) \text{Ei}\left(\frac{e}{c+d x}\right)}{24 d^4}-\frac{c e^{\frac{e}{c+d x}} \left(-24 a^3 d^3+36 a^2 b d^2 (c-e)-12 a b^2 d \left(2 c^2-5 c e+e^2\right)+b^3 \left(6 c^3-26 c^2 e+11 c e^2-e^3\right)\right)}{24 d^4}","\frac{b^2 e^3 (b c-a d) \text{Ei}\left(\frac{e}{c+d x}\right)}{2 d^4}-\frac{b^2 e^2 (c+d x) (b c-a d) e^{\frac{e}{c+d x}}}{2 d^4}-\frac{b^2 e (c+d x)^2 (b c-a d) e^{\frac{e}{c+d x}}}{2 d^4}-\frac{b^2 (c+d x)^3 (b c-a d) e^{\frac{e}{c+d x}}}{d^4}-\frac{3 b e^2 (b c-a d)^2 \text{Ei}\left(\frac{e}{c+d x}\right)}{2 d^4}+\frac{e (b c-a d)^3 \text{Ei}\left(\frac{e}{c+d x}\right)}{d^4}+\frac{3 b e (c+d x) (b c-a d)^2 e^{\frac{e}{c+d x}}}{2 d^4}+\frac{3 b (c+d x)^2 (b c-a d)^2 e^{\frac{e}{c+d x}}}{2 d^4}-\frac{(c+d x) (b c-a d)^3 e^{\frac{e}{c+d x}}}{d^4}+\frac{b^3 e^4 \Gamma \left(-4,-\frac{e}{c+d x}\right)}{d^4}",1,"-1/24*(c*(-24*a^3*d^3 + 36*a^2*b*d^2*(c - e) - 12*a*b^2*d*(2*c^2 - 5*c*e + e^2) + b^3*(6*c^3 - 26*c^2*e + 11*c*e^2 - e^3))*E^(e/(c + d*x)))/d^4 + (d*E^(e/(c + d*x))*x*(24*a^3*d^3 + 36*a^2*b*d^2*(e + d*x) + 12*a*b^2*d*(-4*c*e + e^2 + d*e*x + 2*d^2*x^2) + b^3*(18*c^2*e + e^3 + d*e^2*x + 2*d^2*e*x^2 + 6*d^3*x^3 - 2*c*e*(5*e + 3*d*x))) - e*(24*a^3*d^3 + 36*a^2*b*d^2*(-2*c + e) + 12*a*b^2*d*(6*c^2 - 6*c*e + e^2) + b^3*(-24*c^3 + 36*c^2*e - 12*c*e^2 + e^3))*ExpIntegralEi[e/(c + d*x)])/(24*d^4)","A",1
403,1,170,255,0.2123475,"\int e^{\frac{e}{c+d x}} (a+b x)^2 \, dx","Integrate[E^(e/(c + d*x))*(a + b*x)^2,x]","\frac{d x e^{\frac{e}{c+d x}} \left(6 a^2 d^2+6 a b d (d x+e)+b^2 \left(-4 c e+2 d^2 x^2+d e x+e^2\right)\right)-e \left(6 a^2 d^2+6 a b d (e-2 c)+b^2 \left(6 c^2-6 c e+e^2\right)\right) \text{Ei}\left(\frac{e}{c+d x}\right)}{6 d^3}+\frac{c e^{\frac{e}{c+d x}} \left(6 a^2 d^2+6 a b d (e-c)+b^2 \left(2 c^2-5 c e+e^2\right)\right)}{6 d^3}","\frac{b e^2 (b c-a d) \text{Ei}\left(\frac{e}{c+d x}\right)}{d^3}-\frac{e (b c-a d)^2 \text{Ei}\left(\frac{e}{c+d x}\right)}{d^3}-\frac{b e (c+d x) (b c-a d) e^{\frac{e}{c+d x}}}{d^3}-\frac{b (c+d x)^2 (b c-a d) e^{\frac{e}{c+d x}}}{d^3}+\frac{(c+d x) (b c-a d)^2 e^{\frac{e}{c+d x}}}{d^3}-\frac{b^2 e^3 \text{Ei}\left(\frac{e}{c+d x}\right)}{6 d^3}+\frac{b^2 e^2 (c+d x) e^{\frac{e}{c+d x}}}{6 d^3}+\frac{b^2 e (c+d x)^2 e^{\frac{e}{c+d x}}}{6 d^3}+\frac{b^2 (c+d x)^3 e^{\frac{e}{c+d x}}}{3 d^3}",1,"(c*(6*a^2*d^2 + 6*a*b*d*(-c + e) + b^2*(2*c^2 - 5*c*e + e^2))*E^(e/(c + d*x)))/(6*d^3) + (d*E^(e/(c + d*x))*x*(6*a^2*d^2 + 6*a*b*d*(e + d*x) + b^2*(-4*c*e + e^2 + d*e*x + 2*d^2*x^2)) - e*(6*a^2*d^2 + 6*a*b*d*(-2*c + e) + b^2*(6*c^2 - 6*c*e + e^2))*ExpIntegralEi[e/(c + d*x)])/(6*d^3)","A",1
404,1,91,125,0.0971504,"\int e^{\frac{e}{c+d x}} (a+b x) \, dx","Integrate[E^(e/(c + d*x))*(a + b*x),x]","\frac{d x e^{\frac{e}{c+d x}} (2 a d+b (d x+e))-e (2 a d+b (e-2 c)) \text{Ei}\left(\frac{e}{c+d x}\right)}{2 d^2}+\frac{c e^{\frac{e}{c+d x}} (2 a d+b (e-c))}{2 d^2}","\frac{e (b c-a d) \text{Ei}\left(\frac{e}{c+d x}\right)}{d^2}-\frac{(c+d x) (b c-a d) e^{\frac{e}{c+d x}}}{d^2}-\frac{b e^2 \text{Ei}\left(\frac{e}{c+d x}\right)}{2 d^2}+\frac{b e (c+d x) e^{\frac{e}{c+d x}}}{2 d^2}+\frac{b (c+d x)^2 e^{\frac{e}{c+d x}}}{2 d^2}",1,"(c*(2*a*d + b*(-c + e))*E^(e/(c + d*x)))/(2*d^2) + (d*E^(e/(c + d*x))*x*(2*a*d + b*(e + d*x)) - e*(2*a*d + b*(-2*c + e))*ExpIntegralEi[e/(c + d*x)])/(2*d^2)","A",1
405,1,37,37,0.0133372,"\int e^{\frac{e}{c+d x}} \, dx","Integrate[E^(e/(c + d*x)),x]","\frac{(c+d x) e^{\frac{e}{c+d x}}}{d}-\frac{e \text{Ei}\left(\frac{e}{c+d x}\right)}{d}","\frac{(c+d x) e^{\frac{e}{c+d x}}}{d}-\frac{e \text{Ei}\left(\frac{e}{c+d x}\right)}{d}",1,"(E^(e/(c + d*x))*(c + d*x))/d - (e*ExpIntegralEi[e/(c + d*x)])/d","A",1
406,1,56,62,0.0660448,"\int \frac{e^{\frac{e}{c+d x}}}{a+b x} \, dx","Integrate[E^(e/(c + d*x))/(a + b*x),x]","\frac{e^{\frac{b e}{b c-a d}} \text{Ei}\left(e \left(\frac{b}{a d-b c}+\frac{1}{c+d x}\right)\right)-\text{Ei}\left(\frac{e}{c+d x}\right)}{b}","\frac{e^{\frac{b e}{b c-a d}} \text{Ei}\left(-\frac{d e (a+b x)}{(b c-a d) (c+d x)}\right)}{b}-\frac{\text{Ei}\left(\frac{e}{c+d x}\right)}{b}",1,"(-ExpIntegralEi[e/(c + d*x)] + E^((b*e)/(b*c - a*d))*ExpIntegralEi[e*(b/(-(b*c) + a*d) + (c + d*x)^(-1))])/b","A",1
407,1,105,107,0.1710915,"\int \frac{e^{\frac{e}{c+d x}}}{(a+b x)^2} \, dx","Integrate[E^(e/(c + d*x))/(a + b*x)^2,x]","-\frac{d e e^{\frac{b e}{b c-a d}} \text{Ei}\left(\frac{e}{c+d x}-\frac{b e}{b c-a d}\right)}{(a d-b c)^2}-\frac{d e^{\frac{e}{c+d x}}}{b (b c-a d)}-\frac{e^{\frac{e}{c+d x}}}{b (a+b x)}","-\frac{d e e^{\frac{b e}{b c-a d}} \text{Ei}\left(-\frac{d e (a+b x)}{(b c-a d) (c+d x)}\right)}{(b c-a d)^2}-\frac{d e^{\frac{e}{c+d x}}}{b (b c-a d)}-\frac{e^{\frac{e}{c+d x}}}{b (a+b x)}",1,"-((d*E^(e/(c + d*x)))/(b*(b*c - a*d))) - E^(e/(c + d*x))/(b*(a + b*x)) - (d*e*E^((b*e)/(b*c - a*d))*ExpIntegralEi[-((b*e)/(b*c - a*d)) + e/(c + d*x)])/(-(b*c) + a*d)^2","A",1
408,0,0,240,0.4764382,"\int \frac{e^{\frac{e}{c+d x}}}{(a+b x)^3} \, dx","Integrate[E^(e/(c + d*x))/(a + b*x)^3,x]","\int \frac{e^{\frac{e}{c+d x}}}{(a+b x)^3} \, dx","\frac{b d^2 e^2 e^{\frac{b e}{b c-a d}} \text{Ei}\left(-\frac{d e (a+b x)}{(b c-a d) (c+d x)}\right)}{2 (b c-a d)^4}+\frac{d^2 e e^{\frac{b e}{b c-a d}} \text{Ei}\left(-\frac{d e (a+b x)}{(b c-a d) (c+d x)}\right)}{(b c-a d)^3}+\frac{d^2 e e^{\frac{e}{c+d x}}}{2 (b c-a d)^3}+\frac{d^2 e^{\frac{e}{c+d x}}}{2 b (b c-a d)^2}+\frac{d e e^{\frac{e}{c+d x}}}{2 (a+b x) (b c-a d)^2}-\frac{e^{\frac{e}{c+d x}}}{2 b (a+b x)^2}",1,"Integrate[E^(e/(c + d*x))/(a + b*x)^3, x]","F",-1
409,1,243,322,0.3366107,"\int e^{\frac{e}{(c+d x)^2}} (a+b x)^3 \, dx","Integrate[E^(e/(c + d*x)^2)*(a + b*x)^3,x]","\frac{4 \sqrt{\pi } \sqrt{e} (b c-a d) \left(a^2 d^2-2 a b c d+b^2 \left(c^2+2 e\right)\right) \text{erfi}\left(\frac{\sqrt{e}}{c+d x}\right)-b e \left(6 a^2 d^2-12 a b c d+b^2 \left(6 c^2+e\right)\right) \text{Ei}\left(\frac{e}{(c+d x)^2}\right)+d x e^{\frac{e}{(c+d x)^2}} \left(4 a^3 d^3+6 a^2 b d^3 x+4 a b^2 d \left(d^2 x^2+2 e\right)+b^3 \left(-6 c e+d^3 x^3+d e x\right)\right)}{4 d^4}-\frac{c e^{\frac{e}{(c+d x)^2}} \left(-4 a^3 d^3+6 a^2 b c d^2-4 a b^2 d \left(c^2+2 e\right)+b^3 \left(c^3+7 c e\right)\right)}{4 d^4}","\frac{2 \sqrt{\pi } b^2 e^{3/2} (b c-a d) \text{erfi}\left(\frac{\sqrt{e}}{c+d x}\right)}{d^4}-\frac{b^2 (c+d x)^3 (b c-a d) e^{\frac{e}{(c+d x)^2}}}{d^4}-\frac{2 b^2 e (c+d x) (b c-a d) e^{\frac{e}{(c+d x)^2}}}{d^4}+\frac{\sqrt{\pi } \sqrt{e} (b c-a d)^3 \text{erfi}\left(\frac{\sqrt{e}}{c+d x}\right)}{d^4}-\frac{3 b e (b c-a d)^2 \text{Ei}\left(\frac{e}{(c+d x)^2}\right)}{2 d^4}+\frac{3 b (c+d x)^2 (b c-a d)^2 e^{\frac{e}{(c+d x)^2}}}{2 d^4}-\frac{(c+d x) (b c-a d)^3 e^{\frac{e}{(c+d x)^2}}}{d^4}-\frac{b^3 e^2 \text{Ei}\left(\frac{e}{(c+d x)^2}\right)}{4 d^4}+\frac{b^3 (c+d x)^4 e^{\frac{e}{(c+d x)^2}}}{4 d^4}+\frac{b^3 e (c+d x)^2 e^{\frac{e}{(c+d x)^2}}}{4 d^4}",1,"-1/4*(c*(6*a^2*b*c*d^2 - 4*a^3*d^3 - 4*a*b^2*d*(c^2 + 2*e) + b^3*(c^3 + 7*c*e))*E^(e/(c + d*x)^2))/d^4 + (d*E^(e/(c + d*x)^2)*x*(4*a^3*d^3 + 6*a^2*b*d^3*x + 4*a*b^2*d*(2*e + d^2*x^2) + b^3*(-6*c*e + d*e*x + d^3*x^3)) + 4*(b*c - a*d)*Sqrt[e]*(-2*a*b*c*d + a^2*d^2 + b^2*(c^2 + 2*e))*Sqrt[Pi]*Erfi[Sqrt[e]/(c + d*x)] - b*e*(-12*a*b*c*d + 6*a^2*d^2 + b^2*(6*c^2 + e))*ExpIntegralEi[e/(c + d*x)^2])/(4*d^4)","A",1
410,1,176,215,0.2130609,"\int e^{\frac{e}{(c+d x)^2}} (a+b x)^2 \, dx","Integrate[E^(e/(c + d*x)^2)*(a + b*x)^2,x]","\frac{-\sqrt{\pi } \sqrt{e} \left(3 a^2 d^2-6 a b c d+b^2 \left(3 c^2+2 e\right)\right) \text{erfi}\left(\frac{\sqrt{e}}{c+d x}\right)+d x e^{\frac{e}{(c+d x)^2}} \left(3 a^2 d^2+3 a b d^2 x+b^2 \left(d^2 x^2+2 e\right)\right)+3 b e (b c-a d) \text{Ei}\left(\frac{e}{(c+d x)^2}\right)}{3 d^3}+\frac{c e^{\frac{e}{(c+d x)^2}} \left(3 a^2 d^2-3 a b c d+b^2 \left(c^2+2 e\right)\right)}{3 d^3}","-\frac{\sqrt{\pi } \sqrt{e} (b c-a d)^2 \text{erfi}\left(\frac{\sqrt{e}}{c+d x}\right)}{d^3}+\frac{b e (b c-a d) \text{Ei}\left(\frac{e}{(c+d x)^2}\right)}{d^3}-\frac{b (c+d x)^2 (b c-a d) e^{\frac{e}{(c+d x)^2}}}{d^3}+\frac{(c+d x) (b c-a d)^2 e^{\frac{e}{(c+d x)^2}}}{d^3}-\frac{2 \sqrt{\pi } b^2 e^{3/2} \text{erfi}\left(\frac{\sqrt{e}}{c+d x}\right)}{3 d^3}+\frac{b^2 (c+d x)^3 e^{\frac{e}{(c+d x)^2}}}{3 d^3}+\frac{2 b^2 e (c+d x) e^{\frac{e}{(c+d x)^2}}}{3 d^3}",1,"(c*(-3*a*b*c*d + 3*a^2*d^2 + b^2*(c^2 + 2*e))*E^(e/(c + d*x)^2))/(3*d^3) + (d*E^(e/(c + d*x)^2)*x*(3*a^2*d^2 + 3*a*b*d^2*x + b^2*(2*e + d^2*x^2)) - Sqrt[e]*(-6*a*b*c*d + 3*a^2*d^2 + b^2*(3*c^2 + 2*e))*Sqrt[Pi]*Erfi[Sqrt[e]/(c + d*x)] + 3*b*(b*c - a*d)*e*ExpIntegralEi[e/(c + d*x)^2])/(3*d^3)","A",1
411,1,85,111,0.1267377,"\int e^{\frac{e}{(c+d x)^2}} (a+b x) \, dx","Integrate[E^(e/(c + d*x)^2)*(a + b*x),x]","-\frac{2 \sqrt{\pi } \sqrt{e} (a d-b c) \text{erfi}\left(\frac{\sqrt{e}}{c+d x}\right)+(c+d x) e^{\frac{e}{(c+d x)^2}} (-2 a d+b c-b d x)+b e \text{Ei}\left(\frac{e}{(c+d x)^2}\right)}{2 d^2}","\frac{\sqrt{\pi } \sqrt{e} (b c-a d) \text{erfi}\left(\frac{\sqrt{e}}{c+d x}\right)}{d^2}-\frac{(c+d x) (b c-a d) e^{\frac{e}{(c+d x)^2}}}{d^2}-\frac{b e \text{Ei}\left(\frac{e}{(c+d x)^2}\right)}{2 d^2}+\frac{b (c+d x)^2 e^{\frac{e}{(c+d x)^2}}}{2 d^2}",1,"-1/2*(E^(e/(c + d*x)^2)*(c + d*x)*(b*c - 2*a*d - b*d*x) + 2*(-(b*c) + a*d)*Sqrt[e]*Sqrt[Pi]*Erfi[Sqrt[e]/(c + d*x)] + b*e*ExpIntegralEi[e/(c + d*x)^2])/d^2","A",1
412,1,50,50,0.0230623,"\int e^{\frac{e}{(c+d x)^2}} \, dx","Integrate[E^(e/(c + d*x)^2),x]","\frac{(c+d x) e^{\frac{e}{(c+d x)^2}}}{d}-\frac{\sqrt{\pi } \sqrt{e} \text{erfi}\left(\frac{\sqrt{e}}{c+d x}\right)}{d}","\frac{(c+d x) e^{\frac{e}{(c+d x)^2}}}{d}-\frac{\sqrt{\pi } \sqrt{e} \text{erfi}\left(\frac{\sqrt{e}}{c+d x}\right)}{d}",1,"(E^(e/(c + d*x)^2)*(c + d*x))/d - (Sqrt[e]*Sqrt[Pi]*Erfi[Sqrt[e]/(c + d*x)])/d","A",1
413,0,0,22,0.0443984,"\int \frac{e^{\frac{e}{(c+d x)^2}}}{a+b x} \, dx","Integrate[E^(e/(c + d*x)^2)/(a + b*x),x]","\int \frac{e^{\frac{e}{(c+d x)^2}}}{a+b x} \, dx","\text{Int}\left(\frac{e^{\frac{e}{(c+d x)^2}}}{a+b x},x\right)",0,"Integrate[E^(e/(c + d*x)^2)/(a + b*x), x]","A",-1
414,0,0,22,0.3299253,"\int \frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^2} \, dx","Integrate[E^(e/(c + d*x)^2)/(a + b*x)^2,x]","\int \frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^2} \, dx","\text{Int}\left(\frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^2},x\right)",0,"Integrate[E^(e/(c + d*x)^2)/(a + b*x)^2, x]","A",-1
415,0,0,22,0.0880279,"\int \frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^3} \, dx","Integrate[E^(e/(c + d*x)^2)/(a + b*x)^3,x]","\int \frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^3} \, dx","\text{Int}\left(\frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^3},x\right)",0,"Integrate[E^(e/(c + d*x)^2)/(a + b*x)^3, x]","A",-1
416,1,195,206,0.1939564,"\int e^{\frac{e}{(c+d x)^3}} (a+b x)^3 \, dx","Integrate[E^(e/(c + d*x)^3)*(a + b*x)^3,x]","\frac{3 b^2 e (b c-a d) \text{Ei}\left(\frac{e}{(c+d x)^3}\right)-3 b^2 (c+d x)^3 (b c-a d) e^{\frac{e}{(c+d x)^3}}+3 b (c+d x)^2 (b c-a d)^2 \left(-\frac{e}{(c+d x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{e}{(c+d x)^3}\right)-(c+d x) (b c-a d)^3 \sqrt[3]{-\frac{e}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{e}{(c+d x)^3}\right)+b^3 (c+d x)^4 \left(-\frac{e}{(c+d x)^3}\right)^{4/3} \Gamma \left(-\frac{4}{3},-\frac{e}{(c+d x)^3}\right)}{3 d^4}","\frac{b^2 e (b c-a d) \text{Ei}\left(\frac{e}{(c+d x)^3}\right)}{d^4}-\frac{b^2 (c+d x)^3 (b c-a d) e^{\frac{e}{(c+d x)^3}}}{d^4}+\frac{b (c+d x)^2 (b c-a d)^2 \left(-\frac{e}{(c+d x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{e}{(c+d x)^3}\right)}{d^4}-\frac{(c+d x) (b c-a d)^3 \sqrt[3]{-\frac{e}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{e}{(c+d x)^3}\right)}{3 d^4}+\frac{b^3 (c+d x)^4 \left(-\frac{e}{(c+d x)^3}\right)^{4/3} \Gamma \left(-\frac{4}{3},-\frac{e}{(c+d x)^3}\right)}{3 d^4}",1,"(-3*b^2*(b*c - a*d)*E^(e/(c + d*x)^3)*(c + d*x)^3 + 3*b^2*(b*c - a*d)*e*ExpIntegralEi[e/(c + d*x)^3] + b^3*(-(e/(c + d*x)^3))^(4/3)*(c + d*x)^4*Gamma[-4/3, -(e/(c + d*x)^3)] + 3*b*(b*c - a*d)^2*(-(e/(c + d*x)^3))^(2/3)*(c + d*x)^2*Gamma[-2/3, -(e/(c + d*x)^3)] - (b*c - a*d)^3*(-(e/(c + d*x)^3))^(1/3)*(c + d*x)*Gamma[-1/3, -(e/(c + d*x)^3)])/(3*d^4)","A",1
417,1,136,151,0.0799558,"\int e^{\frac{e}{(c+d x)^3}} (a+b x)^2 \, dx","Integrate[E^(e/(c + d*x)^3)*(a + b*x)^2,x]","\frac{-2 b (c+d x)^2 (b c-a d) \left(-\frac{e}{(c+d x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{e}{(c+d x)^3}\right)+(c+d x) (b c-a d)^2 \sqrt[3]{-\frac{e}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{e}{(c+d x)^3}\right)-b^2 e \text{Ei}\left(\frac{e}{(c+d x)^3}\right)+b^2 (c+d x)^3 e^{\frac{e}{(c+d x)^3}}}{3 d^3}","-\frac{2 b (c+d x)^2 (b c-a d) \left(-\frac{e}{(c+d x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{e}{(c+d x)^3}\right)}{3 d^3}+\frac{(c+d x) (b c-a d)^2 \sqrt[3]{-\frac{e}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{e}{(c+d x)^3}\right)}{3 d^3}-\frac{b^2 e \text{Ei}\left(\frac{e}{(c+d x)^3}\right)}{3 d^3}+\frac{b^2 (c+d x)^3 e^{\frac{e}{(c+d x)^3}}}{3 d^3}",1,"(b^2*E^(e/(c + d*x)^3)*(c + d*x)^3 - b^2*e*ExpIntegralEi[e/(c + d*x)^3] - 2*b*(b*c - a*d)*(-(e/(c + d*x)^3))^(2/3)*(c + d*x)^2*Gamma[-2/3, -(e/(c + d*x)^3)] + (b*c - a*d)^2*(-(e/(c + d*x)^3))^(1/3)*(c + d*x)*Gamma[-1/3, -(e/(c + d*x)^3)])/(3*d^3)","A",1
418,1,85,92,0.0911767,"\int e^{\frac{e}{(c+d x)^3}} (a+b x) \, dx","Integrate[E^(e/(c + d*x)^3)*(a + b*x),x]","\frac{(c+d x) \left((a d-b c) \sqrt[3]{-\frac{e}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{e}{(c+d x)^3}\right)+b (c+d x) \left(-\frac{e}{(c+d x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{e}{(c+d x)^3}\right)\right)}{3 d^2}","\frac{b (c+d x)^2 \left(-\frac{e}{(c+d x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{e}{(c+d x)^3}\right)}{3 d^2}-\frac{(c+d x) (b c-a d) \sqrt[3]{-\frac{e}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{e}{(c+d x)^3}\right)}{3 d^2}",1,"((c + d*x)*(b*(-(e/(c + d*x)^3))^(2/3)*(c + d*x)*Gamma[-2/3, -(e/(c + d*x)^3)] + (-(b*c) + a*d)*(-(e/(c + d*x)^3))^(1/3)*Gamma[-1/3, -(e/(c + d*x)^3)]))/(3*d^2)","A",1
419,1,40,40,0.0061466,"\int e^{\frac{e}{(c+d x)^3}} \, dx","Integrate[E^(e/(c + d*x)^3),x]","\frac{(c+d x) \sqrt[3]{-\frac{e}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{e}{(c+d x)^3}\right)}{3 d}","\frac{(c+d x) \sqrt[3]{-\frac{e}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{e}{(c+d x)^3}\right)}{3 d}",1,"((-(e/(c + d*x)^3))^(1/3)*(c + d*x)*Gamma[-1/3, -(e/(c + d*x)^3)])/(3*d)","A",1
420,0,0,22,0.0337994,"\int \frac{e^{\frac{e}{(c+d x)^3}}}{a+b x} \, dx","Integrate[E^(e/(c + d*x)^3)/(a + b*x),x]","\int \frac{e^{\frac{e}{(c+d x)^3}}}{a+b x} \, dx","\text{Int}\left(\frac{e^{\frac{e}{(c+d x)^3}}}{a+b x},x\right)",0,"Integrate[E^(e/(c + d*x)^3)/(a + b*x), x]","A",-1
421,0,0,22,0.3588384,"\int \frac{e^{\frac{e}{(c+d x)^3}}}{(a+b x)^2} \, dx","Integrate[E^(e/(c + d*x)^3)/(a + b*x)^2,x]","\int \frac{e^{\frac{e}{(c+d x)^3}}}{(a+b x)^2} \, dx","\text{Int}\left(\frac{e^{\frac{e}{(c+d x)^3}}}{(a+b x)^2},x\right)",0,"Integrate[E^(e/(c + d*x)^3)/(a + b*x)^2, x]","A",-1
422,1,103,104,0.3189532,"\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{g+h x} \, dx","Integrate[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x),x]","\frac{F^{\frac{b f}{d}+e} \left(F^{\frac{f h (b c-a d)}{d (d g-c h)}} \text{Ei}\left(\frac{(b c-a d) f (g+h x) \log (F)}{(c h-d g) (c+d x)}\right)-\text{Ei}\left(\frac{(a d f-b c f) \log (F)}{d (c+d x)}\right)\right)}{h}","\frac{F^{\frac{f (b g-a h)}{d g-c h}+e} \text{Ei}\left(-\frac{(b c-a d) f (g+h x) \log (F)}{(d g-c h) (c+d x)}\right)}{h}-\frac{F^{\frac{b f}{d}+e} \text{Ei}\left(-\frac{(b c-a d) f \log (F)}{d (c+d x)}\right)}{h}",1,"(F^(e + (b*f)/d)*(-ExpIntegralEi[((-(b*c*f) + a*d*f)*Log[F])/(d*(c + d*x))] + F^(((b*c - a*d)*f*h)/(d*(d*g - c*h)))*ExpIntegralEi[((b*c - a*d)*f*(g + h*x)*Log[F])/((-(d*g) + c*h)*(c + d*x))]))/h","A",1
423,0,0,159,1.189006,"\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{(g+h x)^2} \, dx","Integrate[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x)^2,x]","\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{(g+h x)^2} \, dx","\frac{f \log (F) (b c-a d) F^{\frac{f (b g-a h)}{d g-c h}+e} \text{Ei}\left(-\frac{(b c-a d) f (g+h x) \log (F)}{(d g-c h) (c+d x)}\right)}{(d g-c h)^2}+\frac{d F^{-\frac{f (b c-a d)}{d (c+d x)}+\frac{b f}{d}+e}}{h (d g-c h)}-\frac{F^{\frac{f (a+b x)}{c+d x}+e}}{h (g+h x)}",1,"Integrate[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x)^2, x]","F",-1
424,0,0,366,0.5220805,"\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{(g+h x)^3} \, dx","Integrate[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x)^3,x]","\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{(g+h x)^3} \, dx","\frac{d^2 F^{-\frac{f (b c-a d)}{d (c+d x)}+\frac{b f}{d}+e}}{2 h (d g-c h)^2}+\frac{f^2 h \log ^2(F) (b c-a d)^2 F^{\frac{f (b g-a h)}{d g-c h}+e} \text{Ei}\left(-\frac{(b c-a d) f (g+h x) \log (F)}{(d g-c h) (c+d x)}\right)}{2 (d g-c h)^4}+\frac{d f \log (F) (b c-a d) F^{\frac{f (b g-a h)}{d g-c h}+e} \text{Ei}\left(-\frac{(b c-a d) f (g+h x) \log (F)}{(d g-c h) (c+d x)}\right)}{(d g-c h)^3}-\frac{F^{\frac{f (a+b x)}{c+d x}+e}}{2 h (g+h x)^2}+\frac{d f \log (F) (b c-a d) F^{-\frac{f (b c-a d)}{d (c+d x)}+\frac{b f}{d}+e}}{2 (d g-c h)^3}-\frac{f \log (F) (b c-a d) F^{\frac{f (a+b x)}{c+d x}+e}}{2 (g+h x) (d g-c h)^2}",1,"Integrate[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x)^3, x]","F",-1
425,0,0,634,0.9868636,"\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{(g+h x)^4} \, dx","Integrate[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x)^4,x]","\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{(g+h x)^4} \, dx","\frac{d^3 F^{-\frac{f (b c-a d)}{d (c+d x)}+\frac{b f}{d}+e}}{3 h (d g-c h)^3}+\frac{d^2 f \log (F) (b c-a d) F^{\frac{f (b g-a h)}{d g-c h}+e} \text{Ei}\left(-\frac{(b c-a d) f (g+h x) \log (F)}{(d g-c h) (c+d x)}\right)}{(d g-c h)^4}+\frac{5 d^2 f \log (F) (b c-a d) F^{-\frac{f (b c-a d)}{d (c+d x)}+\frac{b f}{d}+e}}{6 (d g-c h)^4}+\frac{f^3 h^2 \log ^3(F) (b c-a d)^3 F^{\frac{f (b g-a h)}{d g-c h}+e} \text{Ei}\left(-\frac{(b c-a d) f (g+h x) \log (F)}{(d g-c h) (c+d x)}\right)}{6 (d g-c h)^6}+\frac{d f^2 h \log ^2(F) (b c-a d)^2 F^{\frac{f (b g-a h)}{d g-c h}+e} \text{Ei}\left(-\frac{(b c-a d) f (g+h x) \log (F)}{(d g-c h) (c+d x)}\right)}{(d g-c h)^5}+\frac{d f^2 h \log ^2(F) (b c-a d)^2 F^{-\frac{f (b c-a d)}{d (c+d x)}+\frac{b f}{d}+e}}{6 (d g-c h)^5}-\frac{f^2 h \log ^2(F) (b c-a d)^2 F^{\frac{f (a+b x)}{c+d x}+e}}{6 (g+h x) (d g-c h)^4}-\frac{F^{\frac{f (a+b x)}{c+d x}+e}}{3 h (g+h x)^3}-\frac{2 d f \log (F) (b c-a d) F^{\frac{f (a+b x)}{c+d x}+e}}{3 (g+h x) (d g-c h)^3}-\frac{f \log (F) (b c-a d) F^{\frac{f (a+b x)}{c+d x}+e}}{6 (g+h x)^2 (d g-c h)^2}",1,"Integrate[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x)^4, x]","F",-1
426,1,122,217,0.1799833,"\int f^{a+b x+c x^2} x^3 \, dx","Integrate[f^(a + b*x + c*x^2)*x^3,x]","\frac{f^{a-\frac{b^2}{4 c}} \left(2 \sqrt{c} f^{\frac{(b+2 c x)^2}{4 c}} \left(\log (f) \left(b^2-2 b c x+4 c^2 x^2\right)-4 c\right)+\sqrt{\pi } b \sqrt{\log (f)} \left(6 c-b^2 \log (f)\right) \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)\right)}{16 c^{7/2} \log ^2(f)}","\frac{3 \sqrt{\pi } b f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{8 c^{5/2} \log ^{\frac{3}{2}}(f)}+\frac{b^2 f^{a+b x+c x^2}}{8 c^3 \log (f)}-\frac{\sqrt{\pi } b^3 f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{16 c^{7/2} \sqrt{\log (f)}}-\frac{f^{a+b x+c x^2}}{2 c^2 \log ^2(f)}-\frac{b x f^{a+b x+c x^2}}{4 c^2 \log (f)}+\frac{x^2 f^{a+b x+c x^2}}{2 c \log (f)}",1,"(f^(a - b^2/(4*c))*(b*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]]*(6*c - b^2*Log[f]) + 2*Sqrt[c]*f^((b + 2*c*x)^2/(4*c))*(-4*c + (b^2 - 2*b*c*x + 4*c^2*x^2)*Log[f])))/(16*c^(7/2)*Log[f]^2)","A",1
427,1,104,164,0.1245104,"\int f^{a+b x+c x^2} x^2 \, dx","Integrate[f^(a + b*x + c*x^2)*x^2,x]","\frac{f^{a-\frac{b^2}{4 c}} \left(\sqrt{\pi } \left(b^2 \log (f)-2 c\right) \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)-2 \sqrt{c} \sqrt{\log (f)} (b-2 c x) f^{\frac{(b+2 c x)^2}{4 c}}\right)}{8 c^{5/2} \log ^{\frac{3}{2}}(f)}","-\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 c^{3/2} \log ^{\frac{3}{2}}(f)}+\frac{\sqrt{\pi } b^2 f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{8 c^{5/2} \sqrt{\log (f)}}-\frac{b f^{a+b x+c x^2}}{4 c^2 \log (f)}+\frac{x f^{a+b x+c x^2}}{2 c \log (f)}",1,"(f^(a - b^2/(4*c))*(-2*Sqrt[c]*f^((b + 2*c*x)^2/(4*c))*(b - 2*c*x)*Sqrt[Log[f]] + Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*(-2*c + b^2*Log[f])))/(8*c^(5/2)*Log[f]^(3/2))","A",1
428,1,81,81,0.0688333,"\int f^{a+b x+c x^2} x \, dx","Integrate[f^(a + b*x + c*x^2)*x,x]","\frac{f^{a+b x+c x^2}}{2 c \log (f)}-\frac{\sqrt{\pi } b f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 c^{3/2} \sqrt{\log (f)}}","\frac{f^{a+b x+c x^2}}{2 c \log (f)}-\frac{\sqrt{\pi } b f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 c^{3/2} \sqrt{\log (f)}}",1,"f^(a + b*x + c*x^2)/(2*c*Log[f]) - (b*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(4*c^(3/2)*Sqrt[Log[f]])","A",1
429,1,56,56,0.014367,"\int f^{a+b x+c x^2} \, dx","Integrate[f^(a + b*x + c*x^2),x]","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{2 \sqrt{c} \sqrt{\log (f)}}","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{2 \sqrt{c} \sqrt{\log (f)}}",1,"(f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(2*Sqrt[c]*Sqrt[Log[f]])","A",1
430,0,0,19,0.1167294,"\int \frac{f^{a+b x+c x^2}}{x} \, dx","Integrate[f^(a + b*x + c*x^2)/x,x]","\int \frac{f^{a+b x+c x^2}}{x} \, dx","\text{Int}\left(\frac{f^{a+b x+c x^2}}{x},x\right)",0,"Integrate[f^(a + b*x + c*x^2)/x, x]","A",-1
431,0,0,94,0.2728977,"\int \frac{f^{a+b x+c x^2}}{x^2} \, dx","Integrate[f^(a + b*x + c*x^2)/x^2,x]","\int \frac{f^{a+b x+c x^2}}{x^2} \, dx","b \log (f) \text{Int}\left(\frac{f^{a+b x+c x^2}}{x},x\right)+\sqrt{\pi } \sqrt{c} \sqrt{\log (f)} f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)-\frac{f^{a+b x+c x^2}}{x}",0,"Integrate[f^(a + b*x + c*x^2)/x^2, x]","A",-1
432,1,91,181,0.2263374,"\int e^{a+b x-c x^2} x^3 \, dx","Integrate[E^(a + b*x - c*x^2)*x^3,x]","-\frac{e^a \left(\sqrt{\pi } b \left(b^2+6 c\right) e^{\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)+2 \sqrt{c} e^{x (b-c x)} \left(b^2+2 b c x+4 c \left(c x^2+1\right)\right)\right)}{16 c^{7/2}}","-\frac{3 \sqrt{\pi } b e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{8 c^{5/2}}-\frac{b^2 e^{a+b x-c x^2}}{8 c^3}-\frac{\sqrt{\pi } b^3 e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{16 c^{7/2}}-\frac{b x e^{a+b x-c x^2}}{4 c^2}-\frac{e^{a+b x-c x^2}}{2 c^2}-\frac{x^2 e^{a+b x-c x^2}}{2 c}",1,"-1/16*(E^a*(2*Sqrt[c]*E^(x*(b - c*x))*(b^2 + 2*b*c*x + 4*c*(1 + c*x^2)) + b*(b^2 + 6*c)*E^(b^2/(4*c))*Sqrt[Pi]*Erf[(b - 2*c*x)/(2*Sqrt[c])]))/c^(7/2)","A",1
433,1,79,134,0.1180981,"\int e^{a+b x-c x^2} x^2 \, dx","Integrate[E^(a + b*x - c*x^2)*x^2,x]","\frac{e^a \left(\sqrt{\pi } \left(b^2+2 c\right) e^{\frac{b^2}{4 c}} \text{erf}\left(\frac{2 c x-b}{2 \sqrt{c}}\right)-2 \sqrt{c} e^{x (b-c x)} (b+2 c x)\right)}{8 c^{5/2}}","-\frac{\sqrt{\pi } b^2 e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{8 c^{5/2}}-\frac{\sqrt{\pi } e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{4 c^{3/2}}-\frac{b e^{a+b x-c x^2}}{4 c^2}-\frac{x e^{a+b x-c x^2}}{2 c}",1,"(E^a*(-2*Sqrt[c]*E^(x*(b - c*x))*(b + 2*c*x) + (b^2 + 2*c)*E^(b^2/(4*c))*Sqrt[Pi]*Erf[(-b + 2*c*x)/(2*Sqrt[c])]))/(8*c^(5/2))","A",1
434,1,68,66,0.049451,"\int e^{a+b x-c x^2} x \, dx","Integrate[E^(a + b*x - c*x^2)*x,x]","\frac{\sqrt{\pi } b e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{2 c x-b}{2 \sqrt{c}}\right)}{4 c^{3/2}}-\frac{e^{a+b x-c x^2}}{2 c}","-\frac{\sqrt{\pi } b e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{4 c^{3/2}}-\frac{e^{a+b x-c x^2}}{2 c}",1,"-1/2*E^(a + b*x - c*x^2)/c + (b*E^(a + b^2/(4*c))*Sqrt[Pi]*Erf[(-b + 2*c*x)/(2*Sqrt[c])])/(4*c^(3/2))","A",1
435,1,46,44,0.0129236,"\int e^{a+b x-c x^2} \, dx","Integrate[E^(a + b*x - c*x^2),x]","\frac{\sqrt{\pi } e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{2 c x-b}{2 \sqrt{c}}\right)}{2 \sqrt{c}}","-\frac{\sqrt{\pi } e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)}{2 \sqrt{c}}",1,"(E^(a + b^2/(4*c))*Sqrt[Pi]*Erf[(-b + 2*c*x)/(2*Sqrt[c])])/(2*Sqrt[c])","A",1
436,0,0,20,0.1256134,"\int \frac{e^{a+b x-c x^2}}{x} \, dx","Integrate[E^(a + b*x - c*x^2)/x,x]","\int \frac{e^{a+b x-c x^2}}{x} \, dx","\text{Int}\left(\frac{e^{a+b x-c x^2}}{x},x\right)",0,"Integrate[E^(a + b*x - c*x^2)/x, x]","A",-1
437,0,0,82,0.2270139,"\int \frac{e^{a+b x-c x^2}}{x^2} \, dx","Integrate[E^(a + b*x - c*x^2)/x^2,x]","\int \frac{e^{a+b x-c x^2}}{x^2} \, dx","b \text{Int}\left(\frac{e^{a+b x-c x^2}}{x},x\right)+\sqrt{\pi } \sqrt{c} e^{a+\frac{b^2}{4 c}} \text{erf}\left(\frac{b-2 c x}{2 \sqrt{c}}\right)-\frac{e^{a+b x-c x^2}}{x}",0,"Integrate[E^(a + b*x - c*x^2)/x^2, x]","A",-1
438,1,191,297,0.3575398,"\int e^{(a+b x) (c+d x)} x^3 \, dx","Integrate[E^((a + b*x)*(c + d*x))*x^3,x]","\frac{e^{-\frac{(b c-a d)^2}{4 b d}} \left(2 \sqrt{b} \sqrt{d} e^{\frac{(a d+b (c+2 d x))^2}{4 b d}} \left(a^2 d^2-2 b d (-a c+a d x+2)+b^2 \left(c^2-2 c d x+4 d^2 x^2\right)\right)-\sqrt{\pi } \left(a^3 d^3+3 b^2 c d (a c-2)+3 a b d^2 (a c-2)+b^3 c^3\right) \text{erfi}\left(\frac{a d+b (c+2 d x)}{2 \sqrt{b} \sqrt{d}}\right)\right)}{16 b^{7/2} d^{7/2}}","-\frac{\sqrt{\pi } e^{-\frac{(b c-a d)^2}{4 b d}} (a d+b c)^3 \text{erfi}\left(\frac{a d+b c+2 b d x}{2 \sqrt{b} \sqrt{d}}\right)}{16 b^{7/2} d^{7/2}}+\frac{3 \sqrt{\pi } e^{-\frac{(b c-a d)^2}{4 b d}} (a d+b c) \text{erfi}\left(\frac{a d+b c+2 b d x}{2 \sqrt{b} \sqrt{d}}\right)}{8 b^{5/2} d^{5/2}}+\frac{(a d+b c)^2 e^{x (a d+b c)+a c+b d x^2}}{8 b^3 d^3}-\frac{x (a d+b c) e^{x (a d+b c)+a c+b d x^2}}{4 b^2 d^2}-\frac{e^{x (a d+b c)+a c+b d x^2}}{2 b^2 d^2}+\frac{x^2 e^{x (a d+b c)+a c+b d x^2}}{2 b d}",1,"(2*Sqrt[b]*Sqrt[d]*E^((a*d + b*(c + 2*d*x))^2/(4*b*d))*(a^2*d^2 - 2*b*d*(2 - a*c + a*d*x) + b^2*(c^2 - 2*c*d*x + 4*d^2*x^2)) - (b^3*c^3 + 3*b^2*c*(-2 + a*c)*d + 3*a*b*(-2 + a*c)*d^2 + a^3*d^3)*Sqrt[Pi]*Erfi[(a*d + b*(c + 2*d*x))/(2*Sqrt[b]*Sqrt[d])])/(16*b^(7/2)*d^(7/2)*E^((b*c - a*d)^2/(4*b*d)))","A",1
439,1,144,216,0.1836803,"\int e^{(a+b x) (c+d x)} x^2 \, dx","Integrate[E^((a + b*x)*(c + d*x))*x^2,x]","\frac{e^{-\frac{(b c-a d)^2}{4 b d}} \left(\sqrt{\pi } \left(a^2 d^2+2 b d (a c-1)+b^2 c^2\right) \text{erfi}\left(\frac{a d+b (c+2 d x)}{2 \sqrt{b} \sqrt{d}}\right)-2 \sqrt{b} \sqrt{d} e^{\frac{(a d+b (c+2 d x))^2}{4 b d}} (a d+b (c-2 d x))\right)}{8 b^{5/2} d^{5/2}}","\frac{\sqrt{\pi } e^{-\frac{(b c-a d)^2}{4 b d}} (a d+b c)^2 \text{erfi}\left(\frac{a d+b c+2 b d x}{2 \sqrt{b} \sqrt{d}}\right)}{8 b^{5/2} d^{5/2}}-\frac{\sqrt{\pi } e^{-\frac{(b c-a d)^2}{4 b d}} \text{erfi}\left(\frac{a d+b c+2 b d x}{2 \sqrt{b} \sqrt{d}}\right)}{4 b^{3/2} d^{3/2}}-\frac{(a d+b c) e^{x (a d+b c)+a c+b d x^2}}{4 b^2 d^2}+\frac{x e^{x (a d+b c)+a c+b d x^2}}{2 b d}",1,"(-2*Sqrt[b]*Sqrt[d]*E^((a*d + b*(c + 2*d*x))^2/(4*b*d))*(a*d + b*(c - 2*d*x)) + (b^2*c^2 + 2*b*(-1 + a*c)*d + a^2*d^2)*Sqrt[Pi]*Erfi[(a*d + b*(c + 2*d*x))/(2*Sqrt[b]*Sqrt[d])])/(8*b^(5/2)*d^(5/2)*E^((b*c - a*d)^2/(4*b*d)))","A",1
440,1,116,107,0.0940869,"\int e^{(a+b x) (c+d x)} x \, dx","Integrate[E^((a + b*x)*(c + d*x))*x,x]","\frac{e^{-\frac{(b c-a d)^2}{4 b d}} \left(2 \sqrt{b} \sqrt{d} e^{\frac{(a d+b (c+2 d x))^2}{4 b d}}-\sqrt{\pi } (a d+b c) \text{erfi}\left(\frac{a d+b (c+2 d x)}{2 \sqrt{b} \sqrt{d}}\right)\right)}{4 b^{3/2} d^{3/2}}","\frac{e^{x (a d+b c)+a c+b d x^2}}{2 b d}-\frac{\sqrt{\pi } (a d+b c) e^{-\frac{(b c-a d)^2}{4 b d}} \text{erfi}\left(\frac{a d+b c+2 b d x}{2 \sqrt{b} \sqrt{d}}\right)}{4 b^{3/2} d^{3/2}}",1,"(2*Sqrt[b]*Sqrt[d]*E^((a*d + b*(c + 2*d*x))^2/(4*b*d)) - (b*c + a*d)*Sqrt[Pi]*Erfi[(a*d + b*(c + 2*d*x))/(2*Sqrt[b]*Sqrt[d])])/(4*b^(3/2)*d^(3/2)*E^((b*c - a*d)^2/(4*b*d)))","A",1
441,1,68,68,0.0168557,"\int e^{(a+b x) (c+d x)} \, dx","Integrate[E^((a + b*x)*(c + d*x)),x]","\frac{\sqrt{\pi } e^{-\frac{(b c-a d)^2}{4 b d}} \text{erfi}\left(\frac{a d+b (c+2 d x)}{2 \sqrt{b} \sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}","\frac{\sqrt{\pi } e^{-\frac{(b c-a d)^2}{4 b d}} \text{erfi}\left(\frac{a d+b c+2 b d x}{2 \sqrt{b} \sqrt{d}}\right)}{2 \sqrt{b} \sqrt{d}}",1,"(Sqrt[Pi]*Erfi[(a*d + b*(c + 2*d*x))/(2*Sqrt[b]*Sqrt[d])])/(2*Sqrt[b]*Sqrt[d]*E^((b*c - a*d)^2/(4*b*d)))","A",1
442,0,0,28,0.5575831,"\int \frac{e^{(a+b x) (c+d x)}}{x} \, dx","Integrate[E^((a + b*x)*(c + d*x))/x,x]","\int \frac{e^{(a+b x) (c+d x)}}{x} \, dx","\text{Int}\left(\frac{e^{x (a d+b c)+a c+b d x^2}}{x},x\right)",0,"Integrate[E^((a + b*x)*(c + d*x))/x, x]","A",-1
443,0,0,128,0.3798759,"\int \frac{e^{(a+b x) (c+d x)}}{x^2} \, dx","Integrate[E^((a + b*x)*(c + d*x))/x^2,x]","\int \frac{e^{(a+b x) (c+d x)}}{x^2} \, dx","(a d+b c) \text{Int}\left(\frac{e^{x (a d+b c)+a c+b d x^2}}{x},x\right)+\sqrt{\pi } \sqrt{b} \sqrt{d} e^{-\frac{(b c-a d)^2}{4 b d}} \text{erfi}\left(\frac{a d+b c+2 b d x}{2 \sqrt{b} \sqrt{d}}\right)-\frac{e^{x (a d+b c)+a c+b d x^2}}{x}",0,"Integrate[E^((a + b*x)*(c + d*x))/x^2, x]","A",-1
444,1,169,266,0.2900811,"\int f^{a+b x+c x^2} (d+e x)^3 \, dx","Integrate[f^(a + b*x + c*x^2)*(d + e*x)^3,x]","\frac{f^{a-\frac{b^2}{4 c}} \left(2 \sqrt{c} e f^{\frac{(b+2 c x)^2}{4 c}} \left(\log (f) \left(b^2 e^2-2 b c e (3 d+e x)+4 c^2 \left(3 d^2+3 d e x+e^2 x^2\right)\right)-4 c e^2\right)+\sqrt{\pi } \sqrt{\log (f)} (2 c d-b e) \left(\log (f) (b e-2 c d)^2-6 c e^2\right) \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)\right)}{16 c^{7/2} \log ^2(f)}","-\frac{3 \sqrt{\pi } e^2 f^{a-\frac{b^2}{4 c}} (2 c d-b e) \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{8 c^{5/2} \log ^{\frac{3}{2}}(f)}+\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} (2 c d-b e)^3 \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{16 c^{7/2} \sqrt{\log (f)}}+\frac{e (2 c d-b e)^2 f^{a+b x+c x^2}}{8 c^3 \log (f)}+\frac{e (d+e x) (2 c d-b e) f^{a+b x+c x^2}}{4 c^2 \log (f)}-\frac{e^3 f^{a+b x+c x^2}}{2 c^2 \log ^2(f)}+\frac{e (d+e x)^2 f^{a+b x+c x^2}}{2 c \log (f)}",1,"(f^(a - b^2/(4*c))*((2*c*d - b*e)*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]]*(-6*c*e^2 + (-2*c*d + b*e)^2*Log[f]) + 2*Sqrt[c]*e*f^((b + 2*c*x)^2/(4*c))*(-4*c*e^2 + (b^2*e^2 - 2*b*c*e*(3*d + e*x) + 4*c^2*(3*d^2 + 3*d*e*x + e^2*x^2))*Log[f])))/(16*c^(7/2)*Log[f]^2)","A",1
445,1,123,189,0.1880859,"\int f^{a+b x+c x^2} (d+e x)^2 \, dx","Integrate[f^(a + b*x + c*x^2)*(d + e*x)^2,x]","\frac{f^{a-\frac{b^2}{4 c}} \left(\sqrt{\pi } \left(\log (f) (b e-2 c d)^2-2 c e^2\right) \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)+2 \sqrt{c} e \sqrt{\log (f)} f^{\frac{(b+2 c x)^2}{4 c}} (-b e+4 c d+2 c e x)\right)}{8 c^{5/2} \log ^{\frac{3}{2}}(f)}","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} (2 c d-b e)^2 \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{8 c^{5/2} \sqrt{\log (f)}}-\frac{\sqrt{\pi } e^2 f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 c^{3/2} \log ^{\frac{3}{2}}(f)}+\frac{e (2 c d-b e) f^{a+b x+c x^2}}{4 c^2 \log (f)}+\frac{e (d+e x) f^{a+b x+c x^2}}{2 c \log (f)}",1,"(f^(a - b^2/(4*c))*(2*Sqrt[c]*e*f^((b + 2*c*x)^2/(4*c))*(4*c*d - b*e + 2*c*e*x)*Sqrt[Log[f]] + Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*(-2*c*e^2 + (-2*c*d + b*e)^2*Log[f])))/(8*c^(5/2)*Log[f]^(3/2))","A",1
446,1,96,90,0.1050608,"\int f^{a+b x+c x^2} (d+e x) \, dx","Integrate[f^(a + b*x + c*x^2)*(d + e*x),x]","\frac{f^{a-\frac{b^2}{4 c}} \left(\sqrt{\pi } \sqrt{\log (f)} (2 c d-b e) \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)+2 \sqrt{c} e f^{\frac{(b+2 c x)^2}{4 c}}\right)}{4 c^{3/2} \log (f)}","\frac{\sqrt{\pi } f^{a-\frac{b^2}{4 c}} (2 c d-b e) \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 c^{3/2} \sqrt{\log (f)}}+\frac{e f^{a+b x+c x^2}}{2 c \log (f)}",1,"(f^(a - b^2/(4*c))*(2*Sqrt[c]*e*f^((b + 2*c*x)^2/(4*c)) + (2*c*d - b*e)*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]]))/(4*c^(3/2)*Log[f])","A",1
447,0,0,23,0.2176921,"\int \frac{f^{a+b x+c x^2}}{d+e x} \, dx","Integrate[f^(a + b*x + c*x^2)/(d + e*x),x]","\int \frac{f^{a+b x+c x^2}}{d+e x} \, dx","\text{Int}\left(\frac{f^{a+b x+c x^2}}{d+e x},x\right)",0,"Integrate[f^(a + b*x + c*x^2)/(d + e*x), x]","A",-1
448,0,0,120,0.5941183,"\int \frac{f^{a+b x+c x^2}}{(d+e x)^2} \, dx","Integrate[f^(a + b*x + c*x^2)/(d + e*x)^2,x]","\int \frac{f^{a+b x+c x^2}}{(d+e x)^2} \, dx","-\frac{\log (f) (2 c d-b e) \text{Int}\left(\frac{f^{a+b x+c x^2}}{d+e x},x\right)}{e^2}+\frac{\sqrt{\pi } \sqrt{c} \sqrt{\log (f)} f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{e^2}-\frac{f^{a+b x+c x^2}}{e (d+e x)}",0,"Integrate[f^(a + b*x + c*x^2)/(d + e*x)^2, x]","A",-1
449,0,0,207,0.8517331,"\int \frac{f^{a+b x+c x^2}}{(d+e x)^3} \, dx","Integrate[f^(a + b*x + c*x^2)/(d + e*x)^3,x]","\int \frac{f^{a+b x+c x^2}}{(d+e x)^3} \, dx","\frac{\log ^2(f) (2 c d-b e)^2 \text{Int}\left(\frac{f^{a+b x+c x^2}}{d+e x},x\right)}{2 e^4}+\frac{c \log (f) \text{Int}\left(\frac{f^{a+b x+c x^2}}{d+e x},x\right)}{e^2}-\frac{\sqrt{\pi } \sqrt{c} \log ^{\frac{3}{2}}(f) f^{a-\frac{b^2}{4 c}} (2 c d-b e) \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{2 e^4}+\frac{\log (f) (2 c d-b e) f^{a+b x+c x^2}}{2 e^3 (d+e x)}-\frac{f^{a+b x+c x^2}}{2 e (d+e x)^2}",0,"Integrate[f^(a + b*x + c*x^2)/(d + e*x)^3, x]","A",-1
450,1,31,45,0.1273177,"\int f^{a+b x+c x^2} (b+2 c x)^3 \, dx","Integrate[f^(a + b*x + c*x^2)*(b + 2*c*x)^3,x]","\frac{f^{a+x (b+c x)} \left(\log (f) (b+2 c x)^2-4 c\right)}{\log ^2(f)}","\frac{(b+2 c x)^2 f^{a+b x+c x^2}}{\log (f)}-\frac{4 c f^{a+b x+c x^2}}{\log ^2(f)}",1,"(f^(a + x*(b + c*x))*(-4*c + (b + 2*c*x)^2*Log[f]))/Log[f]^2","A",1
451,1,86,78,0.1105086,"\int f^{a+b x+c x^2} (b+2 c x)^2 \, dx","Integrate[f^(a + b*x + c*x^2)*(b + 2*c*x)^2,x]","\frac{f^{a-\frac{b^2}{4 c}} \left(\sqrt{\log (f)} (b+2 c x) f^{\frac{(b+2 c x)^2}{4 c}}-\sqrt{\pi } \sqrt{c} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)\right)}{\log ^{\frac{3}{2}}(f)}","\frac{(b+2 c x) f^{a+b x+c x^2}}{\log (f)}-\frac{\sqrt{\pi } \sqrt{c} f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{\log ^{\frac{3}{2}}(f)}",1,"(f^(a - b^2/(4*c))*(-(Sqrt[c]*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]) + f^((b + 2*c*x)^2/(4*c))*(b + 2*c*x)*Sqrt[Log[f]]))/Log[f]^(3/2)","A",1
452,1,17,17,0.0398766,"\int f^{a+b x+c x^2} (b+2 c x) \, dx","Integrate[f^(a + b*x + c*x^2)*(b + 2*c*x),x]","\frac{f^{a+b x+c x^2}}{\log (f)}","\frac{f^{a+b x+c x^2}}{\log (f)}",1,"f^(a + b*x + c*x^2)/Log[f]","A",1
453,1,39,39,0.0539612,"\int \frac{f^{a+b x+c x^2}}{b+2 c x} \, dx","Integrate[f^(a + b*x + c*x^2)/(b + 2*c*x),x]","\frac{f^{a-\frac{b^2}{4 c}} \text{Ei}\left(\frac{(b+2 c x)^2 \log (f)}{4 c}\right)}{4 c}","\frac{f^{a-\frac{b^2}{4 c}} \text{Ei}\left(\frac{(b+2 c x)^2 \log (f)}{4 c}\right)}{4 c}",1,"(f^(a - b^2/(4*c))*ExpIntegralEi[((b + 2*c*x)^2*Log[f])/(4*c)])/(4*c)","A",1
454,1,96,84,0.1071415,"\int \frac{f^{a+b x+c x^2}}{(b+2 c x)^2} \, dx","Integrate[f^(a + b*x + c*x^2)/(b + 2*c*x)^2,x]","\frac{f^{a-\frac{b^2}{4 c}} \left(\sqrt{\pi } \sqrt{\log (f)} (b+2 c x) \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)-2 \sqrt{c} f^{\frac{(b+2 c x)^2}{4 c}}\right)}{4 c^{3/2} (b+2 c x)}","\frac{\sqrt{\pi } \sqrt{\log (f)} f^{a-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 c^{3/2}}-\frac{f^{a+b x+c x^2}}{2 c (b+2 c x)}",1,"(f^(a - b^2/(4*c))*(-2*Sqrt[c]*f^((b + 2*c*x)^2/(4*c)) + Sqrt[Pi]*(b + 2*c*x)*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]]))/(4*c^(3/2)*(b + 2*c*x))","A",1
455,1,79,69,0.0937761,"\int \frac{f^{a+b x+c x^2}}{(b+2 c x)^3} \, dx","Integrate[f^(a + b*x + c*x^2)/(b + 2*c*x)^3,x]","\frac{f^{a-\frac{b^2}{4 c}} \left(\log (f) (b+2 c x)^2 \text{Ei}\left(\frac{(b+2 c x)^2 \log (f)}{4 c}\right)-4 c f^{\frac{(b+2 c x)^2}{4 c}}\right)}{16 c^2 (b+2 c x)^2}","\frac{\log (f) f^{a-\frac{b^2}{4 c}} \text{Ei}\left(\frac{(b+2 c x)^2 \log (f)}{4 c}\right)}{16 c^2}-\frac{f^{a+b x+c x^2}}{4 c (b+2 c x)^2}",1,"(f^(a - b^2/(4*c))*(-4*c*f^((b + 2*c*x)^2/(4*c)) + (b + 2*c*x)^2*ExpIntegralEi[((b + 2*c*x)^2*Log[f])/(4*c)]*Log[f]))/(16*c^2*(b + 2*c*x)^2)","A",1
456,1,29,43,0.0968815,"\int f^{b x+c x^2} (b+2 c x)^3 \, dx","Integrate[f^(b*x + c*x^2)*(b + 2*c*x)^3,x]","\frac{f^{x (b+c x)} \left(\log (f) (b+2 c x)^2-4 c\right)}{\log ^2(f)}","\frac{(b+2 c x)^2 f^{b x+c x^2}}{\log (f)}-\frac{4 c f^{b x+c x^2}}{\log ^2(f)}",1,"(f^(x*(b + c*x))*(-4*c + (b + 2*c*x)^2*Log[f]))/Log[f]^2","A",1
457,1,84,75,0.0677433,"\int f^{b x+c x^2} (b+2 c x)^2 \, dx","Integrate[f^(b*x + c*x^2)*(b + 2*c*x)^2,x]","\frac{f^{-\frac{b^2}{4 c}} \left(\sqrt{\log (f)} (b+2 c x) f^{\frac{(b+2 c x)^2}{4 c}}-\sqrt{\pi } \sqrt{c} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)\right)}{\log ^{\frac{3}{2}}(f)}","\frac{(b+2 c x) f^{b x+c x^2}}{\log (f)}-\frac{\sqrt{\pi } \sqrt{c} f^{-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{\log ^{\frac{3}{2}}(f)}",1,"(-(Sqrt[c]*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]) + f^((b + 2*c*x)^2/(4*c))*(b + 2*c*x)*Sqrt[Log[f]])/(f^(b^2/(4*c))*Log[f]^(3/2))","A",1
458,1,16,16,0.0267747,"\int f^{b x+c x^2} (b+2 c x) \, dx","Integrate[f^(b*x + c*x^2)*(b + 2*c*x),x]","\frac{f^{b x+c x^2}}{\log (f)}","\frac{f^{b x+c x^2}}{\log (f)}",1,"f^(b*x + c*x^2)/Log[f]","A",1
459,1,37,37,0.0400835,"\int \frac{f^{b x+c x^2}}{b+2 c x} \, dx","Integrate[f^(b*x + c*x^2)/(b + 2*c*x),x]","\frac{f^{-\frac{b^2}{4 c}} \text{Ei}\left(\frac{(b+2 c x)^2 \log (f)}{4 c}\right)}{4 c}","\frac{f^{-\frac{b^2}{4 c}} \text{Ei}\left(\frac{(b+2 c x)^2 \log (f)}{4 c}\right)}{4 c}",1,"ExpIntegralEi[((b + 2*c*x)^2*Log[f])/(4*c)]/(4*c*f^(b^2/(4*c)))","A",1
460,1,94,81,0.0575808,"\int \frac{f^{b x+c x^2}}{(b+2 c x)^2} \, dx","Integrate[f^(b*x + c*x^2)/(b + 2*c*x)^2,x]","\frac{f^{-\frac{b^2}{4 c}} \left(\sqrt{\pi } \sqrt{\log (f)} (b+2 c x) \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)-2 \sqrt{c} f^{\frac{(b+2 c x)^2}{4 c}}\right)}{4 c^{3/2} (b+2 c x)}","\frac{\sqrt{\pi } \sqrt{\log (f)} f^{-\frac{b^2}{4 c}} \text{erfi}\left(\frac{\sqrt{\log (f)} (b+2 c x)}{2 \sqrt{c}}\right)}{4 c^{3/2}}-\frac{f^{b x+c x^2}}{2 c (b+2 c x)}",1,"(-2*Sqrt[c]*f^((b + 2*c*x)^2/(4*c)) + Sqrt[Pi]*(b + 2*c*x)*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]])/(4*c^(3/2)*f^(b^2/(4*c))*(b + 2*c*x))","A",1
461,1,77,66,0.0689775,"\int \frac{f^{b x+c x^2}}{(b+2 c x)^3} \, dx","Integrate[f^(b*x + c*x^2)/(b + 2*c*x)^3,x]","\frac{f^{-\frac{b^2}{4 c}} \left(\log (f) (b+2 c x)^2 \text{Ei}\left(\frac{(b+2 c x)^2 \log (f)}{4 c}\right)-4 c f^{\frac{(b+2 c x)^2}{4 c}}\right)}{16 c^2 (b+2 c x)^2}","\frac{\log (f) f^{-\frac{b^2}{4 c}} \text{Ei}\left(\frac{(b+2 c x)^2 \log (f)}{4 c}\right)}{16 c^2}-\frac{f^{b x+c x^2}}{4 c (b+2 c x)^2}",1,"(-4*c*f^((b + 2*c*x)^2/(4*c)) + (b + 2*c*x)^2*ExpIntegralEi[((b + 2*c*x)^2*Log[f])/(4*c)]*Log[f])/(16*c^2*f^(b^2/(4*c))*(b + 2*c*x)^2)","A",1
462,1,133,145,0.2896144,"\int \frac{e^{a+b x}}{x^2 \left(c+d x^2\right)} \, dx","Integrate[E^(a + b*x)/(x^2*(c + d*x^2)),x]","\frac{e^a \left(i \sqrt{d} x e^{\frac{i b \sqrt{c}}{\sqrt{d}}} \text{Ei}\left(b \left(x-\frac{i \sqrt{c}}{\sqrt{d}}\right)\right)-i \sqrt{d} x e^{-\frac{i b \sqrt{c}}{\sqrt{d}}} \text{Ei}\left(b \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)\right)+2 b \sqrt{c} x \text{Ei}(b x)-2 \sqrt{c} e^{b x}\right)}{2 c^{3/2} x}","\frac{\sqrt{d} e^{a+\frac{b \sqrt{-c}}{\sqrt{d}}} \text{Ei}\left(-\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{\sqrt{d}}\right)}{2 (-c)^{3/2}}-\frac{\sqrt{d} e^{a-\frac{b \sqrt{-c}}{\sqrt{d}}} \text{Ei}\left(\frac{b \left(\sqrt{d} x+\sqrt{-c}\right)}{\sqrt{d}}\right)}{2 (-c)^{3/2}}+\frac{e^a b \text{Ei}(b x)}{c}-\frac{e^{a+b x}}{c x}",1,"(E^a*(-2*Sqrt[c]*E^(b*x) + 2*b*Sqrt[c]*x*ExpIntegralEi[b*x] + I*Sqrt[d]*E^((I*b*Sqrt[c])/Sqrt[d])*x*ExpIntegralEi[b*(((-I)*Sqrt[c])/Sqrt[d] + x)] - (I*Sqrt[d]*x*ExpIntegralEi[b*((I*Sqrt[c])/Sqrt[d] + x)])/E^((I*b*Sqrt[c])/Sqrt[d])))/(2*c^(3/2)*x)","C",1
463,1,93,111,0.1261466,"\int \frac{e^{a+b x}}{x \left(c+d x^2\right)} \, dx","Integrate[E^(a + b*x)/(x*(c + d*x^2)),x]","\frac{e^a \left(2 \text{Ei}(b x)-e^{-\frac{i b \sqrt{c}}{\sqrt{d}}} \left(e^{\frac{2 i b \sqrt{c}}{\sqrt{d}}} \text{Ei}\left(b \left(x-\frac{i \sqrt{c}}{\sqrt{d}}\right)\right)+\text{Ei}\left(b \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)\right)\right)\right)}{2 c}","-\frac{e^{a+\frac{b \sqrt{-c}}{\sqrt{d}}} \text{Ei}\left(-\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{\sqrt{d}}\right)}{2 c}-\frac{e^{a-\frac{b \sqrt{-c}}{\sqrt{d}}} \text{Ei}\left(\frac{b \left(\sqrt{d} x+\sqrt{-c}\right)}{\sqrt{d}}\right)}{2 c}+\frac{e^a \text{Ei}(b x)}{c}",1,"(E^a*(2*ExpIntegralEi[b*x] - (E^(((2*I)*b*Sqrt[c])/Sqrt[d])*ExpIntegralEi[b*(((-I)*Sqrt[c])/Sqrt[d] + x)] + ExpIntegralEi[b*((I*Sqrt[c])/Sqrt[d] + x)])/E^((I*b*Sqrt[c])/Sqrt[d])))/(2*c)","C",1
464,1,94,118,0.0568457,"\int \frac{e^{a+b x}}{c+d x^2} \, dx","Integrate[E^(a + b*x)/(c + d*x^2),x]","-\frac{i e^{a-\frac{i b \sqrt{c}}{\sqrt{d}}} \left(e^{\frac{2 i b \sqrt{c}}{\sqrt{d}}} \text{Ei}\left(b \left(x-\frac{i \sqrt{c}}{\sqrt{d}}\right)\right)-\text{Ei}\left(b \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)\right)\right)}{2 \sqrt{c} \sqrt{d}}","\frac{e^{a+\frac{b \sqrt{-c}}{\sqrt{d}}} \text{Ei}\left(-\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{\sqrt{d}}\right)}{2 \sqrt{-c} \sqrt{d}}-\frac{e^{a-\frac{b \sqrt{-c}}{\sqrt{d}}} \text{Ei}\left(\frac{b \left(\sqrt{d} x+\sqrt{-c}\right)}{\sqrt{d}}\right)}{2 \sqrt{-c} \sqrt{d}}",1,"((-1/2*I)*E^(a - (I*b*Sqrt[c])/Sqrt[d])*(E^(((2*I)*b*Sqrt[c])/Sqrt[d])*ExpIntegralEi[b*(((-I)*Sqrt[c])/Sqrt[d] + x)] - ExpIntegralEi[b*((I*Sqrt[c])/Sqrt[d] + x)]))/(Sqrt[c]*Sqrt[d])","C",1
465,1,83,100,0.0619407,"\int \frac{e^{a+b x} x}{c+d x^2} \, dx","Integrate[(E^(a + b*x)*x)/(c + d*x^2),x]","\frac{e^{a-\frac{i b \sqrt{c}}{\sqrt{d}}} \left(e^{\frac{2 i b \sqrt{c}}{\sqrt{d}}} \text{Ei}\left(b \left(x-\frac{i \sqrt{c}}{\sqrt{d}}\right)\right)+\text{Ei}\left(b \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)\right)\right)}{2 d}","\frac{e^{a+\frac{b \sqrt{-c}}{\sqrt{d}}} \text{Ei}\left(-\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{\sqrt{d}}\right)}{2 d}+\frac{e^{a-\frac{b \sqrt{-c}}{\sqrt{d}}} \text{Ei}\left(\frac{b \left(\sqrt{d} x+\sqrt{-c}\right)}{\sqrt{d}}\right)}{2 d}",1,"(E^(a - (I*b*Sqrt[c])/Sqrt[d])*(E^(((2*I)*b*Sqrt[c])/Sqrt[d])*ExpIntegralEi[b*(((-I)*Sqrt[c])/Sqrt[d] + x)] + ExpIntegralEi[b*((I*Sqrt[c])/Sqrt[d] + x)]))/(2*d)","C",1
466,1,120,132,0.1313065,"\int \frac{e^{a+b x} x^2}{c+d x^2} \, dx","Integrate[(E^(a + b*x)*x^2)/(c + d*x^2),x]","\frac{e^a \left(i b \sqrt{c} e^{\frac{i b \sqrt{c}}{\sqrt{d}}} \text{Ei}\left(b \left(x-\frac{i \sqrt{c}}{\sqrt{d}}\right)\right)-i b \sqrt{c} e^{-\frac{i b \sqrt{c}}{\sqrt{d}}} \text{Ei}\left(b \left(x+\frac{i \sqrt{c}}{\sqrt{d}}\right)\right)+2 \sqrt{d} e^{b x}\right)}{2 b d^{3/2}}","\frac{\sqrt{-c} e^{a+\frac{b \sqrt{-c}}{\sqrt{d}}} \text{Ei}\left(-\frac{b \left(\sqrt{-c}-\sqrt{d} x\right)}{\sqrt{d}}\right)}{2 d^{3/2}}-\frac{\sqrt{-c} e^{a-\frac{b \sqrt{-c}}{\sqrt{d}}} \text{Ei}\left(\frac{b \left(\sqrt{d} x+\sqrt{-c}\right)}{\sqrt{d}}\right)}{2 d^{3/2}}+\frac{e^{a+b x}}{b d}",1,"(E^a*(2*Sqrt[d]*E^(b*x) + I*b*Sqrt[c]*E^((I*b*Sqrt[c])/Sqrt[d])*ExpIntegralEi[b*(((-I)*Sqrt[c])/Sqrt[d] + x)] - (I*b*Sqrt[c]*ExpIntegralEi[b*((I*Sqrt[c])/Sqrt[d] + x)])/E^((I*b*Sqrt[c])/Sqrt[d])))/(2*b*d^(3/2))","C",1
467,1,232,212,1.1412742,"\int \frac{e^{d+e x}}{x^2 \left(a+b x+c x^2\right)} \, dx","Integrate[E^(d + e*x)/(x^2*(a + b*x + c*x^2)),x]","\frac{e^d \left(\frac{e^{-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \left(x \left(b \sqrt{b^2-4 a c}-2 a c+b^2\right) e^{\frac{e \sqrt{b^2-4 a c}}{c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)+x \left(b \sqrt{b^2-4 a c}+2 a c-b^2\right) \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)-2 a \sqrt{b^2-4 a c} e^{\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c}}\right)}{x \sqrt{b^2-4 a c}}-2 (b-a e) \text{Ei}(e x)\right)}{2 a^2}","\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) e^{d-\frac{e \left(b-\sqrt{b^2-4 a c}\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)}{2 a^2}+\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) e^{d-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)}{2 a^2}-\frac{b e^d \text{Ei}(e x)}{a^2}+\frac{e^d e \text{Ei}(e x)}{a}-\frac{e^{d+e x}}{a x}",1,"(E^d*(-2*(b - a*e)*ExpIntegralEi[e*x] + (-2*a*Sqrt[b^2 - 4*a*c]*E^((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)) + (b^2 - 2*a*c + b*Sqrt[b^2 - 4*a*c])*E^((Sqrt[b^2 - 4*a*c]*e)/c)*x*ExpIntegralEi[(e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)] + (-b^2 + 2*a*c + b*Sqrt[b^2 - 4*a*c])*x*ExpIntegralEi[(e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)])/(Sqrt[b^2 - 4*a*c]*E^(((b + Sqrt[b^2 - 4*a*c])*e)/(2*c))*x)))/(2*a^2)","A",1
468,1,163,169,0.5727109,"\int \frac{e^{d+e x}}{x \left(a+b x+c x^2\right)} \, dx","Integrate[E^(d + e*x)/(x*(a + b*x + c*x^2)),x]","\frac{e^d \left(\frac{e^{-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \left(\left(b-\sqrt{b^2-4 a c}\right) \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)-\left(\sqrt{b^2-4 a c}+b\right) e^{\frac{e \sqrt{b^2-4 a c}}{c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)\right)}{\sqrt{b^2-4 a c}}+2 \text{Ei}(e x)\right)}{2 a}","-\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) e^{d-\frac{e \left(b-\sqrt{b^2-4 a c}\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)}{2 a}-\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) e^{d-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)}{2 a}+\frac{e^d \text{Ei}(e x)}{a}",1,"(E^d*(2*ExpIntegralEi[e*x] + (-((b + Sqrt[b^2 - 4*a*c])*E^((Sqrt[b^2 - 4*a*c]*e)/c)*ExpIntegralEi[(e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)]) + (b - Sqrt[b^2 - 4*a*c])*ExpIntegralEi[(e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)])/(Sqrt[b^2 - 4*a*c]*E^(((b + Sqrt[b^2 - 4*a*c])*e)/(2*c)))))/(2*a)","A",1
469,1,127,138,0.1458841,"\int \frac{e^{d+e x}}{a+b x+c x^2} \, dx","Integrate[E^(d + e*x)/(a + b*x + c*x^2),x]","\frac{e^{\frac{e \left(\sqrt{b^2-4 a c}-b\right)}{2 c}+d} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)-e^{d-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)}{\sqrt{b^2-4 a c}}","\frac{e^{d-\frac{e \left(b-\sqrt{b^2-4 a c}\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)}{\sqrt{b^2-4 a c}}-\frac{e^{d-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)}{\sqrt{b^2-4 a c}}",1,"(E^(d + ((-b + Sqrt[b^2 - 4*a*c])*e)/(2*c))*ExpIntegralEi[(e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)] - E^(d - ((b + Sqrt[b^2 - 4*a*c])*e)/(2*c))*ExpIntegralEi[(e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)])/Sqrt[b^2 - 4*a*c]","A",1
470,1,153,158,0.1886845,"\int \frac{e^{d+e x} x}{a+b x+c x^2} \, dx","Integrate[(E^(d + e*x)*x)/(a + b*x + c*x^2),x]","\frac{e^{d-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \left(\left(\sqrt{b^2-4 a c}-b\right) e^{\frac{e \sqrt{b^2-4 a c}}{c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)+\left(\sqrt{b^2-4 a c}+b\right) \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)\right)}{2 c \sqrt{b^2-4 a c}}","\frac{\left(1-\frac{b}{\sqrt{b^2-4 a c}}\right) e^{d-\frac{e \left(b-\sqrt{b^2-4 a c}\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)}{2 c}+\frac{\left(\frac{b}{\sqrt{b^2-4 a c}}+1\right) e^{d-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)}{2 c}",1,"(E^(d - ((b + Sqrt[b^2 - 4*a*c])*e)/(2*c))*((-b + Sqrt[b^2 - 4*a*c])*E^((Sqrt[b^2 - 4*a*c]*e)/c)*ExpIntegralEi[(e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)] + (b + Sqrt[b^2 - 4*a*c])*ExpIntegralEi[(e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)]))/(2*c*Sqrt[b^2 - 4*a*c])","A",1
471,1,217,186,0.5324237,"\int \frac{e^{d+e x} x^2}{a+b x+c x^2} \, dx","Integrate[(E^(d + e*x)*x^2)/(a + b*x + c*x^2),x]","-\frac{e^{d-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \left(e \left(b \sqrt{b^2-4 a c}+2 a c-b^2\right) e^{\frac{e \sqrt{b^2-4 a c}}{c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)+e \left(b \sqrt{b^2-4 a c}-2 a c+b^2\right) \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)-2 c \sqrt{b^2-4 a c} e^{\frac{e \left(\sqrt{b^2-4 a c}+b+2 c x\right)}{2 c}}\right)}{2 c^2 e \sqrt{b^2-4 a c}}","-\frac{\left(b-\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}\right) e^{d-\frac{e \left(b-\sqrt{b^2-4 a c}\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)}{2 c^2}-\frac{\left(\frac{b^2-2 a c}{\sqrt{b^2-4 a c}}+b\right) e^{d-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)}{2 c^2}+\frac{e^{d+e x}}{c e}",1,"-1/2*(E^(d - ((b + Sqrt[b^2 - 4*a*c])*e)/(2*c))*(-2*c*Sqrt[b^2 - 4*a*c]*E^((e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)) + (-b^2 + 2*a*c + b*Sqrt[b^2 - 4*a*c])*e*E^((Sqrt[b^2 - 4*a*c]*e)/c)*ExpIntegralEi[(e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)] + (b^2 - 2*a*c + b*Sqrt[b^2 - 4*a*c])*e*ExpIntegralEi[(e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)]))/(c^2*Sqrt[b^2 - 4*a*c]*e)","A",1
472,1,268,232,0.6529717,"\int \frac{e^{d+e x} x^3}{a+b x+c x^2} \, dx","Integrate[(E^(d + e*x)*x^3)/(a + b*x + c*x^2),x]","\frac{e^{d-\frac{b e}{c}} \left(-2 c \sqrt{b^2-4 a c} e^{e \left(\frac{b}{c}+x\right)} (b e+c (-e) x+c)+e^2 \left(b^2 \sqrt{b^2-4 a c}-a c \sqrt{b^2-4 a c}+3 a b c-b^3\right) e^{\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)+e^2 \left(b^2 \sqrt{b^2-4 a c}-a c \sqrt{b^2-4 a c}-3 a b c+b^3\right) e^{\frac{e \left(b-\sqrt{b^2-4 a c}\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)\right)}{2 c^3 e^2 \sqrt{b^2-4 a c}}","\frac{\left(-\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) e^{d-\frac{e \left(b-\sqrt{b^2-4 a c}\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x-\sqrt{b^2-4 a c}\right)}{2 c}\right)}{2 c^3}+\frac{\left(\frac{b \left(b^2-3 a c\right)}{\sqrt{b^2-4 a c}}-a c+b^2\right) e^{d-\frac{e \left(\sqrt{b^2-4 a c}+b\right)}{2 c}} \text{Ei}\left(\frac{e \left(b+2 c x+\sqrt{b^2-4 a c}\right)}{2 c}\right)}{2 c^3}-\frac{b e^{d+e x}}{c^2 e}-\frac{e^{d+e x}}{c e^2}+\frac{x e^{d+e x}}{c e}",1,"(E^(d - (b*e)/c)*(-2*c*Sqrt[b^2 - 4*a*c]*E^(e*(b/c + x))*(c + b*e - c*e*x) + (-b^3 + 3*a*b*c + b^2*Sqrt[b^2 - 4*a*c] - a*c*Sqrt[b^2 - 4*a*c])*e^2*E^(((b + Sqrt[b^2 - 4*a*c])*e)/(2*c))*ExpIntegralEi[(e*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)] + (b^3 - 3*a*b*c + b^2*Sqrt[b^2 - 4*a*c] - a*c*Sqrt[b^2 - 4*a*c])*e^2*E^(((b - Sqrt[b^2 - 4*a*c])*e)/(2*c))*ExpIntegralEi[(e*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/(2*c)]))/(2*c^3*Sqrt[b^2 - 4*a*c]*e^2)","A",1
473,1,27,30,0.0195579,"\int \frac{4^x}{a+2^x b} \, dx","Integrate[4^x/(a + 2^x*b),x]","\frac{\frac{2^x}{b}-\frac{a \log \left(a+b 2^x\right)}{b^2}}{\log (2)}","\frac{2^x}{b \log (2)}-\frac{a \log \left(a+b 2^x\right)}{b^2 \log (2)}",1,"(2^x/b - (a*Log[a + 2^x*b])/b^2)/Log[2]","A",1
474,1,27,30,0.0121168,"\int \frac{2^{2 x}}{a+2^x b} \, dx","Integrate[2^(2*x)/(a + 2^x*b),x]","\frac{\frac{2^x}{b}-\frac{a \log \left(a+b 2^x\right)}{b^2}}{\log (2)}","\frac{2^x}{b \log (2)}-\frac{a \log \left(a+b 2^x\right)}{b^2 \log (2)}",1,"(2^x/b - (a*Log[a + 2^x*b])/b^2)/Log[2]","A",1
475,1,26,32,0.0233744,"\int \frac{4^x}{a-2^x b} \, dx","Integrate[4^x/(a - 2^x*b),x]","-\frac{a \log \left(a-b 2^x\right)+b 2^x}{b^2 \log (2)}","-\frac{a \log \left(a-b 2^x\right)}{b^2 \log (2)}-\frac{2^x}{b \log (2)}",1,"-((2^x*b + a*Log[a - 2^x*b])/(b^2*Log[2]))","A",1
476,1,26,32,0.0139613,"\int \frac{2^{2 x}}{a-2^x b} \, dx","Integrate[2^(2*x)/(a - 2^x*b),x]","-\frac{a \log \left(a-b 2^x\right)+b 2^x}{b^2 \log (2)}","-\frac{a \log \left(a-b 2^x\right)}{b^2 \log (2)}-\frac{2^x}{b \log (2)}",1,"-((2^x*b + a*Log[a - 2^x*b])/(b^2*Log[2]))","A",1
477,1,36,58,0.0336888,"\int \frac{4^x}{a+2^{-x} b} \, dx","Integrate[4^x/(a + b/2^x),x]","\frac{2 b^2 \log \left(a 2^x+b\right)+a 2^x \left(a 2^x-2 b\right)}{a^3 \log (4)}","\frac{b^2 x}{a^3}+\frac{b^2 \log \left(a+b 2^{-x}\right)}{a^3 \log (2)}-\frac{b 2^x}{a^2 \log (2)}+\frac{2^{2 x-1}}{a \log (2)}",1,"(2^x*a*(2^x*a - 2*b) + 2*b^2*Log[2^x*a + b])/(a^3*Log[4])","A",1
478,1,36,58,0.0188395,"\int \frac{2^{2 x}}{a+2^{-x} b} \, dx","Integrate[2^(2*x)/(a + b/2^x),x]","\frac{2 b^2 \log \left(a 2^x+b\right)+a 2^x \left(a 2^x-2 b\right)}{a^3 \log (4)}","\frac{b^2 x}{a^3}+\frac{b^2 \log \left(a+b 2^{-x}\right)}{a^3 \log (2)}-\frac{b 2^x}{a^2 \log (2)}+\frac{2^{2 x-1}}{a \log (2)}",1,"(2^x*a*(2^x*a - 2*b) + 2*b^2*Log[2^x*a + b])/(a^3*Log[4])","A",1
479,1,38,58,0.0307282,"\int \frac{4^x}{a-2^{-x} b} \, dx","Integrate[4^x/(a - b/2^x),x]","\frac{2 b^2 \log \left(a 2^x-b\right)+a 2^x \left(a 2^x+2 b\right)}{a^3 \log (4)}","\frac{b^2 x}{a^3}+\frac{b^2 \log \left(a-b 2^{-x}\right)}{a^3 \log (2)}+\frac{b 2^x}{a^2 \log (2)}+\frac{2^{2 x-1}}{a \log (2)}",1,"(2^x*a*(2^x*a + 2*b) + 2*b^2*Log[2^x*a - b])/(a^3*Log[4])","A",1
480,1,38,58,0.0177903,"\int \frac{2^{2 x}}{a-2^{-x} b} \, dx","Integrate[2^(2*x)/(a - b/2^x),x]","\frac{2 b^2 \log \left(a 2^x-b\right)+a 2^x \left(a 2^x+2 b\right)}{a^3 \log (4)}","\frac{b^2 x}{a^3}+\frac{b^2 \log \left(a-b 2^{-x}\right)}{a^3 \log (2)}+\frac{b 2^x}{a^2 \log (2)}+\frac{2^{2 x-1}}{a \log (2)}",1,"(2^x*a*(2^x*a + 2*b) + 2*b^2*Log[2^x*a - b])/(a^3*Log[4])","A",1
481,1,30,30,0.007752,"\int \frac{2^x}{a+4^x b} \, dx","Integrate[2^x/(a + 4^x*b),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (2)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (2)}",1,"ArcTan[(2^x*Sqrt[b])/Sqrt[a]]/(Sqrt[a]*Sqrt[b]*Log[2])","A",1
482,1,30,30,0.0044116,"\int \frac{2^x}{a+2^{2 x} b} \, dx","Integrate[2^x/(a + 2^(2*x)*b),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (2)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (2)}",1,"ArcTan[(2^x*Sqrt[b])/Sqrt[a]]/(Sqrt[a]*Sqrt[b]*Log[2])","A",1
483,1,30,30,0.0071106,"\int \frac{2^x}{a-4^x b} \, dx","Integrate[2^x/(a - 4^x*b),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (2)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (2)}",1,"ArcTanh[(2^x*Sqrt[b])/Sqrt[a]]/(Sqrt[a]*Sqrt[b]*Log[2])","A",1
484,1,30,30,0.0054433,"\int \frac{2^x}{a-2^{2 x} b} \, dx","Integrate[2^x/(a - 2^(2*x)*b),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (2)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (2)}",1,"ArcTanh[(2^x*Sqrt[b])/Sqrt[a]]/(Sqrt[a]*Sqrt[b]*Log[2])","A",1
485,1,40,43,0.020954,"\int \frac{2^x}{a+4^{-x} b} \, dx","Integrate[2^x/(a + b/4^x),x]","\frac{\frac{2^x}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} 2^x}{\sqrt{b}}\right)}{a^{3/2}}}{\log (2)}","\frac{2^x}{a \log (2)}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} 2^x}{\sqrt{b}}\right)}{a^{3/2} \log (2)}",1,"(2^x/a - (Sqrt[b]*ArcTan[(2^x*Sqrt[a])/Sqrt[b]])/a^(3/2))/Log[2]","A",1
486,1,40,43,0.0085559,"\int \frac{2^x}{a+2^{-2 x} b} \, dx","Integrate[2^x/(a + b/2^(2*x)),x]","\frac{\frac{2^x}{a}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} 2^x}{\sqrt{b}}\right)}{a^{3/2}}}{\log (2)}","\frac{2^x}{a \log (2)}-\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{a} 2^x}{\sqrt{b}}\right)}{a^{3/2} \log (2)}",1,"(2^x/a - (Sqrt[b]*ArcTan[(2^x*Sqrt[a])/Sqrt[b]])/a^(3/2))/Log[2]","A",1
487,1,40,43,0.0190317,"\int \frac{2^x}{a-4^{-x} b} \, dx","Integrate[2^x/(a - b/4^x),x]","\frac{\frac{2^x}{a}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a} 2^x}{\sqrt{b}}\right)}{a^{3/2}}}{\log (2)}","\frac{2^x}{a \log (2)}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a} 2^x}{\sqrt{b}}\right)}{a^{3/2} \log (2)}",1,"(2^x/a - (Sqrt[b]*ArcTanh[(2^x*Sqrt[a])/Sqrt[b]])/a^(3/2))/Log[2]","A",1
488,1,40,43,0.0093007,"\int \frac{2^x}{a-2^{-2 x} b} \, dx","Integrate[2^x/(a - b/2^(2*x)),x]","\frac{\frac{2^x}{a}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a} 2^x}{\sqrt{b}}\right)}{a^{3/2}}}{\log (2)}","\frac{2^x}{a \log (2)}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{a} 2^x}{\sqrt{b}}\right)}{a^{3/2} \log (2)}",1,"(2^x/a - (Sqrt[b]*ArcTanh[(2^x*Sqrt[a])/Sqrt[b]])/a^(3/2))/Log[2]","A",1
489,1,33,31,0.0123417,"\int \frac{2^x}{\sqrt{a+4^x b}} \, dx","Integrate[2^x/Sqrt[a + 4^x*b],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a+b 2^{2 x}}}\right)}{\sqrt{b} \log (2)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a+b 4^x}}\right)}{\sqrt{b} \log (2)}",1,"ArcTanh[(2^x*Sqrt[b])/Sqrt[a + 2^(2*x)*b]]/(Sqrt[b]*Log[2])","A",1
490,1,33,31,0.0047329,"\int \frac{2^x}{\sqrt{a+2^{2 x} b}} \, dx","Integrate[2^x/Sqrt[a + 2^(2*x)*b],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a+b 2^{2 x}}}\right)}{\sqrt{b} \log (2)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a+b 4^x}}\right)}{\sqrt{b} \log (2)}",1,"ArcTanh[(2^x*Sqrt[b])/Sqrt[a + 2^(2*x)*b]]/(Sqrt[b]*Log[2])","A",1
491,1,34,32,0.0138222,"\int \frac{2^x}{\sqrt{a-4^x b}} \, dx","Integrate[2^x/Sqrt[a - 4^x*b],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a-b 2^{2 x}}}\right)}{\sqrt{b} \log (2)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a-b 4^x}}\right)}{\sqrt{b} \log (2)}",1,"ArcTan[(2^x*Sqrt[b])/Sqrt[a - 2^(2*x)*b]]/(Sqrt[b]*Log[2])","A",1
492,1,34,32,0.0047908,"\int \frac{2^x}{\sqrt{a-2^{2 x} b}} \, dx","Integrate[2^x/Sqrt[a - 2^(2*x)*b],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a-b 2^{2 x}}}\right)}{\sqrt{b} \log (2)}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a-b 4^x}}\right)}{\sqrt{b} \log (2)}",1,"ArcTan[(2^x*Sqrt[b])/Sqrt[a - 2^(2*x)*b]]/(Sqrt[b]*Log[2])","A",1
493,1,35,24,0.0320997,"\int \frac{2^x}{\sqrt{a+4^{-x} b}} \, dx","Integrate[2^x/Sqrt[a + b/4^x],x]","\frac{2^{-x} \left(a 2^{2 x}+b\right)}{a \log (2) \sqrt{a+b 2^{-2 x}}}","\frac{2^x \sqrt{a+b 2^{-2 x}}}{a \log (2)}",1,"(2^(2*x)*a + b)/(2^x*a*Sqrt[a + b/2^(2*x)]*Log[2])","A",1
494,1,35,24,0.0067574,"\int \frac{2^x}{\sqrt{a+2^{-2 x} b}} \, dx","Integrate[2^x/Sqrt[a + b/2^(2*x)],x]","\frac{2^{-x} \left(a 2^{2 x}+b\right)}{a \log (2) \sqrt{a+b 2^{-2 x}}}","\frac{2^x \sqrt{a+b 2^{-2 x}}}{a \log (2)}",1,"(2^(2*x)*a + b)/(2^x*a*Sqrt[a + b/2^(2*x)]*Log[2])","A",1
495,1,38,25,0.0322369,"\int \frac{2^x}{\sqrt{a-4^{-x} b}} \, dx","Integrate[2^x/Sqrt[a - b/4^x],x]","\frac{2^{-x} \left(a 2^{2 x}-b\right)}{a \log (2) \sqrt{a-b 2^{-2 x}}}","\frac{2^x \sqrt{a-b 2^{-2 x}}}{a \log (2)}",1,"(2^(2*x)*a - b)/(2^x*a*Sqrt[a - b/2^(2*x)]*Log[2])","A",1
496,1,38,25,0.0074233,"\int \frac{2^x}{\sqrt{a-2^{-2 x} b}} \, dx","Integrate[2^x/Sqrt[a - b/2^(2*x)],x]","\frac{2^{-x} \left(a 2^{2 x}-b\right)}{a \log (2) \sqrt{a-b 2^{-2 x}}}","\frac{2^x \sqrt{a-b 2^{-2 x}}}{a \log (2)}",1,"(2^(2*x)*a - b)/(2^x*a*Sqrt[a - b/2^(2*x)]*Log[2])","A",1
497,1,29,44,0.023013,"\int \frac{4^x}{\sqrt{a+2^x b}} \, dx","Integrate[4^x/Sqrt[a + 2^x*b],x]","\frac{2 \left(b 2^x-2 a\right) \sqrt{a+b 2^x}}{b^2 \log (8)}","\frac{2 \left(a+b 2^x\right)^{3/2}}{3 b^2 \log (2)}-\frac{2 a \sqrt{a+b 2^x}}{b^2 \log (2)}",1,"(2*(-2*a + 2^x*b)*Sqrt[a + 2^x*b])/(b^2*Log[8])","A",1
498,1,29,44,0.0123272,"\int \frac{2^{2 x}}{\sqrt{a+2^x b}} \, dx","Integrate[2^(2*x)/Sqrt[a + 2^x*b],x]","\frac{2 \left(b 2^x-2 a\right) \sqrt{a+b 2^x}}{b^2 \log (8)}","\frac{2 \left(a+b 2^x\right)^{3/2}}{3 b^2 \log (2)}-\frac{2 a \sqrt{a+b 2^x}}{b^2 \log (2)}",1,"(2*(-2*a + 2^x*b)*Sqrt[a + 2^x*b])/(b^2*Log[8])","A",1
499,1,30,46,0.0244524,"\int \frac{4^x}{\sqrt{a-2^x b}} \, dx","Integrate[4^x/Sqrt[a - 2^x*b],x]","-\frac{2 \sqrt{a-b 2^x} \left(2 a+b 2^x\right)}{b^2 \log (8)}","\frac{2 \left(a-b 2^x\right)^{3/2}}{3 b^2 \log (2)}-\frac{2 a \sqrt{a-b 2^x}}{b^2 \log (2)}",1,"(-2*Sqrt[a - 2^x*b]*(2*a + 2^x*b))/(b^2*Log[8])","A",1
500,1,30,46,0.0127708,"\int \frac{2^{2 x}}{\sqrt{a-2^x b}} \, dx","Integrate[2^(2*x)/Sqrt[a - 2^x*b],x]","-\frac{2 \sqrt{a-b 2^x} \left(2 a+b 2^x\right)}{b^2 \log (8)}","\frac{2 \left(a-b 2^x\right)^{3/2}}{3 b^2 \log (2)}-\frac{2 a \sqrt{a-b 2^x}}{b^2 \log (2)}",1,"(-2*Sqrt[a - 2^x*b]*(2*a + 2^x*b))/(b^2*Log[8])","A",1
501,1,111,93,0.0908696,"\int \frac{4^x}{\sqrt{a+2^{-x} b}} \, dx","Integrate[4^x/Sqrt[a + b/2^x],x]","\frac{2^{-\frac{x}{2}-2} \left(\sqrt{a} 2^{x/2} \left(a^2 2^{2 x+1}-a b 2^x-3 b^2\right)+3 b^2 \sqrt{a 2^x+b} \tanh ^{-1}\left(\frac{\sqrt{a} 2^{x/2}}{\sqrt{a 2^x+b}}\right)\right)}{a^{5/2} \log (2) \sqrt{a+b 2^{-x}}}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b 2^{-x}}}{\sqrt{a}}\right)}{4 a^{5/2} \log (2)}-\frac{3 b 2^{x-2} \sqrt{a+b 2^{-x}}}{a^2 \log (2)}+\frac{2^{2 x-1} \sqrt{a+b 2^{-x}}}{a \log (2)}",1,"(2^(-2 - x/2)*(2^(x/2)*Sqrt[a]*(2^(1 + 2*x)*a^2 - 2^x*a*b - 3*b^2) + 3*b^2*Sqrt[2^x*a + b]*ArcTanh[(2^(x/2)*Sqrt[a])/Sqrt[2^x*a + b]]))/(a^(5/2)*Sqrt[a + b/2^x]*Log[2])","A",1
502,1,111,93,0.0355061,"\int \frac{2^{2 x}}{\sqrt{a+2^{-x} b}} \, dx","Integrate[2^(2*x)/Sqrt[a + b/2^x],x]","\frac{2^{-\frac{x}{2}-2} \left(\sqrt{a} 2^{x/2} \left(a^2 2^{2 x+1}-a b 2^x-3 b^2\right)+3 b^2 \sqrt{a 2^x+b} \tanh ^{-1}\left(\frac{\sqrt{a} 2^{x/2}}{\sqrt{a 2^x+b}}\right)\right)}{a^{5/2} \log (2) \sqrt{a+b 2^{-x}}}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b 2^{-x}}}{\sqrt{a}}\right)}{4 a^{5/2} \log (2)}-\frac{3 b 2^{x-2} \sqrt{a+b 2^{-x}}}{a^2 \log (2)}+\frac{2^{2 x-1} \sqrt{a+b 2^{-x}}}{a \log (2)}",1,"(2^(-2 - x/2)*(2^(x/2)*Sqrt[a]*(2^(1 + 2*x)*a^2 - 2^x*a*b - 3*b^2) + 3*b^2*Sqrt[2^x*a + b]*ArcTanh[(2^(x/2)*Sqrt[a])/Sqrt[2^x*a + b]]))/(a^(5/2)*Sqrt[a + b/2^x]*Log[2])","A",1
503,1,115,96,0.0821198,"\int \frac{4^x}{\sqrt{a-2^{-x} b}} \, dx","Integrate[4^x/Sqrt[a - b/2^x],x]","\frac{2^{-\frac{x}{2}-2} \left(\sqrt{a} 2^{x/2} \left(a^2 2^{2 x+1}+a b 2^x-3 b^2\right)+3 b^2 \sqrt{a 2^x-b} \tanh ^{-1}\left(\frac{\sqrt{a} 2^{x/2}}{\sqrt{a 2^x-b}}\right)\right)}{a^{5/2} \log (2) \sqrt{a-b 2^{-x}}}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a-b 2^{-x}}}{\sqrt{a}}\right)}{4 a^{5/2} \log (2)}+\frac{3 b 2^{x-2} \sqrt{a-b 2^{-x}}}{a^2 \log (2)}+\frac{2^{2 x-1} \sqrt{a-b 2^{-x}}}{a \log (2)}",1,"(2^(-2 - x/2)*(2^(x/2)*Sqrt[a]*(2^(1 + 2*x)*a^2 + 2^x*a*b - 3*b^2) + 3*Sqrt[2^x*a - b]*b^2*ArcTanh[(2^(x/2)*Sqrt[a])/Sqrt[2^x*a - b]]))/(a^(5/2)*Sqrt[a - b/2^x]*Log[2])","A",1
504,1,115,96,0.0132686,"\int \frac{2^{2 x}}{\sqrt{a-2^{-x} b}} \, dx","Integrate[2^(2*x)/Sqrt[a - b/2^x],x]","\frac{2^{-\frac{x}{2}-2} \left(\sqrt{a} 2^{x/2} \left(a^2 2^{2 x+1}+a b 2^x-3 b^2\right)+3 b^2 \sqrt{a 2^x-b} \tanh ^{-1}\left(\frac{\sqrt{a} 2^{x/2}}{\sqrt{a 2^x-b}}\right)\right)}{a^{5/2} \log (2) \sqrt{a-b 2^{-x}}}","\frac{3 b^2 \tanh ^{-1}\left(\frac{\sqrt{a-b 2^{-x}}}{\sqrt{a}}\right)}{4 a^{5/2} \log (2)}+\frac{3 b 2^{x-2} \sqrt{a-b 2^{-x}}}{a^2 \log (2)}+\frac{2^{2 x-1} \sqrt{a-b 2^{-x}}}{a \log (2)}",1,"(2^(-2 - x/2)*(2^(x/2)*Sqrt[a]*(2^(1 + 2*x)*a^2 + 2^x*a*b - 3*b^2) + 3*Sqrt[2^x*a - b]*b^2*ArcTanh[(2^(x/2)*Sqrt[a])/Sqrt[2^x*a - b]]))/(a^(5/2)*Sqrt[a - b/2^x]*Log[2])","A",1
505,1,17,17,0.0173806,"\int \frac{1}{1+2 e^x+e^{2 x}} \, dx","Integrate[(1 + 2*E^x + E^(2*x))^(-1),x]","x+\frac{1}{e^x+1}-\log \left(e^x+1\right)","x+\frac{1}{e^x+1}-\log \left(e^x+1\right)",1,"(1 + E^x)^(-1) + x - Log[1 + E^x]","A",1
506,1,24,24,0.0111215,"\int \frac{1}{2+3 e^x+e^{2 x}} \, dx","Integrate[(2 + 3*E^x + E^(2*x))^(-1),x]","\frac{x}{2}-\log \left(e^x+1\right)+\frac{1}{2} \log \left(e^x+2\right)","\frac{x}{2}-\log \left(e^x+1\right)+\frac{1}{2} \log \left(e^x+2\right)",1,"x/2 - Log[1 + E^x] + Log[2 + E^x]/2","A",1
507,1,44,56,0.0253675,"\int \frac{1}{-1+e^x+e^{2 x}} \, dx","Integrate[(-1 + E^x + E^(2*x))^(-1),x]","-x+\frac{1}{2} \log \left(-e^x-e^{2 x}+1\right)-\frac{\tanh ^{-1}\left(\frac{2 e^x+1}{\sqrt{5}}\right)}{\sqrt{5}}","-x+\frac{1}{10} \left(5+\sqrt{5}\right) \log \left(2 e^x+1-\sqrt{5}\right)+\frac{1}{10} \left(5-\sqrt{5}\right) \log \left(2 e^x+1+\sqrt{5}\right)",1,"-x - ArcTanh[(1 + 2*E^x)/Sqrt[5]]/Sqrt[5] + Log[1 - E^x - E^(2*x)]/2","A",1
508,1,44,44,0.0185036,"\int \frac{1}{3+3 e^x+e^{2 x}} \, dx","Integrate[(3 + 3*E^x + E^(2*x))^(-1),x]","\frac{x}{3}-\frac{1}{6} \log \left(3 e^x+e^{2 x}+3\right)-\frac{\tan ^{-1}\left(\frac{2 e^x+3}{\sqrt{3}}\right)}{\sqrt{3}}","\frac{x}{3}-\frac{1}{6} \log \left(3 e^x+e^{2 x}+3\right)-\frac{\tan ^{-1}\left(\frac{2 e^x+3}{\sqrt{3}}\right)}{\sqrt{3}}",1,"x/3 - ArcTan[(3 + 2*E^x)/Sqrt[3]]/Sqrt[3] - Log[3 + 3*E^x + E^(2*x)]/6","A",1
509,1,66,67,0.1084494,"\int \frac{1}{a+b e^x+c e^{2 x}} \, dx","Integrate[(a + b*E^x + c*E^(2*x))^(-1),x]","-\frac{\frac{2 b \tan ^{-1}\left(\frac{b+2 c e^x}{\sqrt{4 a c-b^2}}\right)}{\sqrt{4 a c-b^2}}+\log \left(a+e^x \left(b+c e^x\right)\right)-2 x}{2 a}","\frac{b \tanh ^{-1}\left(\frac{b+2 c e^x}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c}}-\frac{\log \left(a+b e^x+c e^{2 x}\right)}{2 a}+\frac{x}{a}",1,"-1/2*(-2*x + (2*b*ArcTan[(b + 2*c*E^x)/Sqrt[-b^2 + 4*a*c]])/Sqrt[-b^2 + 4*a*c] + Log[a + E^x*(b + c*E^x)])/a","A",1
510,1,38,44,0.062447,"\int \frac{x}{1+2 e^x+e^{2 x}} \, dx","Integrate[x/(1 + 2*E^x + E^(2*x)),x]","-\text{Li}_2\left(-e^x\right)+\frac{1}{2} x \left(x+\frac{2}{e^x+1}-2\right)-(x-1) \log \left(e^x+1\right)","-\text{Li}_2\left(-e^x\right)+\frac{x^2}{2}+\frac{x}{e^x+1}-x-x \log \left(e^x+1\right)+\log \left(e^x+1\right)",1,"(x*(-2 + 2/(1 + E^x) + x))/2 - (-1 + x)*Log[1 + E^x] - PolyLog[2, -E^x]","A",1
511,1,49,54,0.0042079,"\int \frac{x}{2+3 e^x+e^{2 x}} \, dx","Integrate[x/(2 + 3*E^x + E^(2*x)),x]","-\frac{1}{2} \text{Li}_2\left(-2 e^{-x}\right)+\text{Li}_2\left(-e^{-x}\right)-x \log \left(e^{-x}+1\right)+\frac{1}{2} x \log \left(2 e^{-x}+1\right)","-\text{Li}_2\left(-e^x\right)+\frac{1}{2} \text{Li}_2\left(-\frac{e^x}{2}\right)+\frac{x^2}{4}+\frac{1}{2} x \log \left(\frac{e^x}{2}+1\right)-x \log \left(e^x+1\right)",1,"-(x*Log[1 + E^(-x)]) + (x*Log[1 + 2/E^x])/2 - PolyLog[2, -2/E^x]/2 + PolyLog[2, -E^(-x)]","A",1
512,1,120,180,0.1063771,"\int \frac{x}{-1+e^x+e^{2 x}} \, dx","Integrate[x/(-1 + E^x + E^(2*x)),x]","\frac{-\left(1+\sqrt{5}\right) \text{Li}_2\left(\frac{1}{2} \left(-1+\sqrt{5}\right) e^{-x}\right)-\left(\sqrt{5}-1\right) \text{Li}_2\left(-\frac{1}{2} \left(1+\sqrt{5}\right) e^{-x}\right)+\left(1+\sqrt{5}\right) x \log \left(1-\frac{1}{2} \left(\sqrt{5}-1\right) e^{-x}\right)+\left(\sqrt{5}-1\right) x \log \left(\frac{1}{2} \left(1+\sqrt{5}\right) e^{-x}+1\right)}{2 \sqrt{5}}","-\frac{2 \text{Li}_2\left(-\frac{2 e^x}{1-\sqrt{5}}\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}+\frac{2 \text{Li}_2\left(-\frac{2 e^x}{1+\sqrt{5}}\right)}{\sqrt{5} \left(1+\sqrt{5}\right)}-\frac{x^2}{\sqrt{5} \left(1+\sqrt{5}\right)}+\frac{x^2}{\sqrt{5} \left(1-\sqrt{5}\right)}-\frac{2 x \log \left(\frac{2 e^x}{1-\sqrt{5}}+1\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}+\frac{2 x \log \left(\frac{2 e^x}{1+\sqrt{5}}+1\right)}{\sqrt{5} \left(1+\sqrt{5}\right)}",1,"((1 + Sqrt[5])*x*Log[1 - (-1 + Sqrt[5])/(2*E^x)] + (-1 + Sqrt[5])*x*Log[1 + (1 + Sqrt[5])/(2*E^x)] - (1 + Sqrt[5])*PolyLog[2, (-1 + Sqrt[5])/(2*E^x)] - (-1 + Sqrt[5])*PolyLog[2, -1/2*(1 + Sqrt[5])/E^x])/(2*Sqrt[5])","A",1
513,1,144,204,0.0954657,"\int \frac{x}{3+3 e^x+e^{2 x}} \, dx","Integrate[x/(3 + 3*E^x + E^(2*x)),x]","\frac{\left(\sqrt{3}+3 i\right) \text{Li}_2\left(-\frac{1}{2} i \left(-3 i+\sqrt{3}\right) e^{-x}\right)+\left(\sqrt{3}-3 i\right) \text{Li}_2\left(\frac{1}{2} i \left(3 i+\sqrt{3}\right) e^{-x}\right)-x \left(\left(\sqrt{3}-3 i\right) \log \left(1+\frac{1}{2} \left(3-i \sqrt{3}\right) e^{-x}\right)+\left(\sqrt{3}+3 i\right) \log \left(1+\frac{1}{2} \left(3+i \sqrt{3}\right) e^{-x}\right)\right)}{6 \sqrt{3}}","-\frac{2 \text{Li}_2\left(-\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}+\frac{2 \text{Li}_2\left(-\frac{2 e^x}{3+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+3 i\right)}+\frac{x^2}{\sqrt{3} \left(\sqrt{3}+3 i\right)}-\frac{x^2}{\sqrt{3} \left(-\sqrt{3}+3 i\right)}-\frac{2 x \log \left(1+\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}+\frac{2 x \log \left(1+\frac{2 e^x}{3+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+3 i\right)}",1,"(-(x*((-3*I + Sqrt[3])*Log[1 + (3 - I*Sqrt[3])/(2*E^x)] + (3*I + Sqrt[3])*Log[1 + (3 + I*Sqrt[3])/(2*E^x)])) + (3*I + Sqrt[3])*PolyLog[2, ((-1/2*I)*(-3*I + Sqrt[3]))/E^x] + (-3*I + Sqrt[3])*PolyLog[2, ((I/2)*(3*I + Sqrt[3]))/E^x])/(6*Sqrt[3])","A",1
514,1,205,276,0.2228041,"\int \frac{x}{a+b e^x+c e^{2 x}} \, dx","Integrate[x/(a + b*E^x + c*E^(2*x)),x]","\frac{-\left(\sqrt{b^2-4 a c}+b\right) \text{Li}_2\left(\frac{2 c e^x}{\sqrt{b^2-4 a c}-b}\right)+\left(b-\sqrt{b^2-4 a c}\right) \text{Li}_2\left(-\frac{2 c e^x}{b+\sqrt{b^2-4 a c}}\right)+x \left(x \sqrt{b^2-4 a c}-\left(\sqrt{b^2-4 a c}+b\right) \log \left(\frac{2 c e^x}{b-\sqrt{b^2-4 a c}}+1\right)+\left(b-\sqrt{b^2-4 a c}\right) \log \left(\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}+1\right)\right)}{2 a \sqrt{b^2-4 a c}}","\frac{2 c \text{Li}_2\left(-\frac{2 c e^x}{b-\sqrt{b^2-4 a c}}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}+\frac{2 c \text{Li}_2\left(-\frac{2 c e^x}{b+\sqrt{b^2-4 a c}}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{c x^2}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{c x^2}{b \sqrt{b^2-4 a c}-4 a c+b^2}+\frac{2 c x \log \left(\frac{2 c e^x}{b-\sqrt{b^2-4 a c}}+1\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}+\frac{2 c x \log \left(\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}+1\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}",1,"(x*(Sqrt[b^2 - 4*a*c]*x - (b + Sqrt[b^2 - 4*a*c])*Log[1 + (2*c*E^x)/(b - Sqrt[b^2 - 4*a*c])] + (b - Sqrt[b^2 - 4*a*c])*Log[1 + (2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])]) - (b + Sqrt[b^2 - 4*a*c])*PolyLog[2, (2*c*E^x)/(-b + Sqrt[b^2 - 4*a*c])] + (b - Sqrt[b^2 - 4*a*c])*PolyLog[2, (-2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])])/(2*a*Sqrt[b^2 - 4*a*c])","A",1
515,1,57,72,0.0988627,"\int \frac{x^2}{1+2 e^x+e^{2 x}} \, dx","Integrate[x^2/(1 + 2*E^x + E^(2*x)),x]","-2 (x-1) \text{Li}_2\left(-e^x\right)+2 \text{Li}_3\left(-e^x\right)+\frac{\left(e^x (x-3)+x\right) x^2}{3 \left(e^x+1\right)}-(x-2) x \log \left(e^x+1\right)","-2 x \text{Li}_2\left(-e^x\right)+2 \text{Li}_2\left(-e^x\right)+2 \text{Li}_3\left(-e^x\right)+\frac{x^3}{3}+\frac{x^2}{e^x+1}-x^2-x^2 \log \left(e^x+1\right)+2 x \log \left(e^x+1\right)",1,"(x^2*(E^x*(-3 + x) + x))/(3*(1 + E^x)) - (-2 + x)*x*Log[1 + E^x] - 2*(-1 + x)*PolyLog[2, -E^x] + 2*PolyLog[3, -E^x]","A",1
516,1,77,77,0.0096953,"\int \frac{x^2}{2+3 e^x+e^{2 x}} \, dx","Integrate[x^2/(2 + 3*E^x + E^(2*x)),x]","-x \text{Li}_2\left(-2 e^{-x}\right)+2 x \text{Li}_2\left(-e^{-x}\right)-\text{Li}_3\left(-2 e^{-x}\right)+2 \text{Li}_3\left(-e^{-x}\right)+x^2 \left(-\log \left(e^{-x}+1\right)\right)+\frac{1}{2} x^2 \log \left(2 e^{-x}+1\right)","-2 x \text{Li}_2\left(-e^x\right)+x \text{Li}_2\left(-\frac{e^x}{2}\right)+2 \text{Li}_3\left(-e^x\right)-\text{Li}_3\left(-\frac{e^x}{2}\right)+\frac{x^3}{6}+\frac{1}{2} x^2 \log \left(\frac{e^x}{2}+1\right)-x^2 \log \left(e^x+1\right)",1,"-(x^2*Log[1 + E^(-x)]) + (x^2*Log[1 + 2/E^x])/2 - x*PolyLog[2, -2/E^x] + 2*x*PolyLog[2, -E^(-x)] - PolyLog[3, -2/E^x] + 2*PolyLog[3, -E^(-x)]","A",1
517,1,172,259,0.1541813,"\int \frac{x^2}{-1+e^x+e^{2 x}} \, dx","Integrate[x^2/(-1 + E^x + E^(2*x)),x]","\frac{2 \left(-\frac{2 \left(x \text{Li}_2\left(\frac{1}{2} \left(-1+\sqrt{5}\right) e^{-x}\right)+\text{Li}_3\left(\frac{1}{2} \left(-1+\sqrt{5}\right) e^{-x}\right)\right)}{\sqrt{5}-1}-\frac{2 \left(x \text{Li}_2\left(-\frac{1}{2} \left(1+\sqrt{5}\right) e^{-x}\right)+\text{Li}_3\left(-\frac{1}{2} \left(1+\sqrt{5}\right) e^{-x}\right)\right)}{1+\sqrt{5}}+\frac{x^2 \log \left(1-\frac{1}{2} \left(\sqrt{5}-1\right) e^{-x}\right)}{\sqrt{5}-1}+\frac{x^2 \log \left(\frac{1}{2} \left(1+\sqrt{5}\right) e^{-x}+1\right)}{1+\sqrt{5}}\right)}{\sqrt{5}}","-\frac{4 x \text{Li}_2\left(-\frac{2 e^x}{1-\sqrt{5}}\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}+\frac{4 x \text{Li}_2\left(-\frac{2 e^x}{1+\sqrt{5}}\right)}{\sqrt{5} \left(1+\sqrt{5}\right)}+\frac{4 \text{Li}_3\left(-\frac{2 e^x}{1-\sqrt{5}}\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}-\frac{4 \text{Li}_3\left(-\frac{2 e^x}{1+\sqrt{5}}\right)}{\sqrt{5} \left(1+\sqrt{5}\right)}-\frac{2 x^3}{3 \sqrt{5} \left(1+\sqrt{5}\right)}+\frac{2 x^3}{3 \sqrt{5} \left(1-\sqrt{5}\right)}-\frac{2 x^2 \log \left(\frac{2 e^x}{1-\sqrt{5}}+1\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}+\frac{2 x^2 \log \left(\frac{2 e^x}{1+\sqrt{5}}+1\right)}{\sqrt{5} \left(1+\sqrt{5}\right)}",1,"(2*((x^2*Log[1 - (-1 + Sqrt[5])/(2*E^x)])/(-1 + Sqrt[5]) + (x^2*Log[1 + (1 + Sqrt[5])/(2*E^x)])/(1 + Sqrt[5]) - (2*(x*PolyLog[2, (-1 + Sqrt[5])/(2*E^x)] + PolyLog[3, (-1 + Sqrt[5])/(2*E^x)]))/(-1 + Sqrt[5]) - (2*(x*PolyLog[2, -1/2*(1 + Sqrt[5])/E^x] + PolyLog[3, -1/2*(1 + Sqrt[5])/E^x]))/(1 + Sqrt[5])))/Sqrt[5]","A",1
518,1,216,293,0.191686,"\int \frac{x^2}{3+3 e^x+e^{2 x}} \, dx","Integrate[x^2/(3 + 3*E^x + E^(2*x)),x]","\frac{2 i \left(\frac{2 \left(x \text{Li}_2\left(-\frac{1}{2} i \left(-3 i+\sqrt{3}\right) e^{-x}\right)+\text{Li}_3\left(-\frac{1}{2} i \left(-3 i+\sqrt{3}\right) e^{-x}\right)\right)}{3+i \sqrt{3}}-\frac{2 i \left(x \text{Li}_2\left(\frac{1}{2} i \left(3 i+\sqrt{3}\right) e^{-x}\right)+\text{Li}_3\left(\frac{1}{2} i \left(3 i+\sqrt{3}\right) e^{-x}\right)\right)}{\sqrt{3}+3 i}+\frac{i x^2 \log \left(1+\frac{1}{2} \left(3-i \sqrt{3}\right) e^{-x}\right)}{\sqrt{3}+3 i}+\frac{i x^2 \log \left(1+\frac{1}{2} \left(3+i \sqrt{3}\right) e^{-x}\right)}{\sqrt{3}-3 i}\right)}{\sqrt{3}}","-\frac{4 x \text{Li}_2\left(-\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}+\frac{4 x \text{Li}_2\left(-\frac{2 e^x}{3+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+3 i\right)}+\frac{4 \text{Li}_3\left(-\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}-\frac{4 \text{Li}_3\left(-\frac{2 e^x}{3+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+3 i\right)}+\frac{2 x^3}{3 \sqrt{3} \left(\sqrt{3}+3 i\right)}-\frac{2 x^3}{3 \sqrt{3} \left(-\sqrt{3}+3 i\right)}-\frac{2 x^2 \log \left(1+\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}+\frac{2 x^2 \log \left(1+\frac{2 e^x}{3+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+3 i\right)}",1,"((2*I)*((I*x^2*Log[1 + (3 - I*Sqrt[3])/(2*E^x)])/(3*I + Sqrt[3]) + (I*x^2*Log[1 + (3 + I*Sqrt[3])/(2*E^x)])/(-3*I + Sqrt[3]) + (2*(x*PolyLog[2, ((-1/2*I)*(-3*I + Sqrt[3]))/E^x] + PolyLog[3, ((-1/2*I)*(-3*I + Sqrt[3]))/E^x]))/(3 + I*Sqrt[3]) - ((2*I)*(x*PolyLog[2, ((I/2)*(3*I + Sqrt[3]))/E^x] + PolyLog[3, ((I/2)*(3*I + Sqrt[3]))/E^x]))/(3*I + Sqrt[3])))/Sqrt[3]","A",1
519,1,407,391,0.1852076,"\int \frac{x^2}{a+b e^x+c e^{2 x}} \, dx","Integrate[x^2/(a + b*E^x + c*E^(2*x)),x]","\frac{-6 x \left(\sqrt{b^2-4 a c}+b\right) \text{Li}_2\left(\frac{2 c e^x}{\sqrt{b^2-4 a c}-b}\right)+6 x \left(b-\sqrt{b^2-4 a c}\right) \text{Li}_2\left(-\frac{2 c e^x}{b+\sqrt{b^2-4 a c}}\right)+6 b \text{Li}_3\left(\frac{2 c e^x}{\sqrt{b^2-4 a c}-b}\right)+6 \sqrt{b^2-4 a c} \text{Li}_3\left(\frac{2 c e^x}{\sqrt{b^2-4 a c}-b}\right)-6 b \text{Li}_3\left(-\frac{2 c e^x}{b+\sqrt{b^2-4 a c}}\right)+6 \sqrt{b^2-4 a c} \text{Li}_3\left(-\frac{2 c e^x}{b+\sqrt{b^2-4 a c}}\right)+2 x^3 \sqrt{b^2-4 a c}-3 b x^2 \log \left(\frac{2 c e^x}{b-\sqrt{b^2-4 a c}}+1\right)-3 x^2 \sqrt{b^2-4 a c} \log \left(\frac{2 c e^x}{b-\sqrt{b^2-4 a c}}+1\right)+3 b x^2 \log \left(\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}+1\right)-3 x^2 \sqrt{b^2-4 a c} \log \left(\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}+1\right)}{6 a \sqrt{b^2-4 a c}}","\frac{4 c x \text{Li}_2\left(-\frac{2 c e^x}{b-\sqrt{b^2-4 a c}}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}+\frac{4 c x \text{Li}_2\left(-\frac{2 c e^x}{b+\sqrt{b^2-4 a c}}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{4 c \text{Li}_3\left(-\frac{2 c e^x}{b-\sqrt{b^2-4 a c}}\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{4 c \text{Li}_3\left(-\frac{2 c e^x}{b+\sqrt{b^2-4 a c}}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{2 c x^3}{3 \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}-\frac{2 c x^3}{3 \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}+\frac{2 c x^2 \log \left(\frac{2 c e^x}{b-\sqrt{b^2-4 a c}}+1\right)}{-b \sqrt{b^2-4 a c}-4 a c+b^2}+\frac{2 c x^2 \log \left(\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}+1\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}",1,"(2*Sqrt[b^2 - 4*a*c]*x^3 - 3*b*x^2*Log[1 + (2*c*E^x)/(b - Sqrt[b^2 - 4*a*c])] - 3*Sqrt[b^2 - 4*a*c]*x^2*Log[1 + (2*c*E^x)/(b - Sqrt[b^2 - 4*a*c])] + 3*b*x^2*Log[1 + (2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])] - 3*Sqrt[b^2 - 4*a*c]*x^2*Log[1 + (2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])] - 6*(b + Sqrt[b^2 - 4*a*c])*x*PolyLog[2, (2*c*E^x)/(-b + Sqrt[b^2 - 4*a*c])] + 6*(b - Sqrt[b^2 - 4*a*c])*x*PolyLog[2, (-2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])] + 6*b*PolyLog[3, (2*c*E^x)/(-b + Sqrt[b^2 - 4*a*c])] + 6*Sqrt[b^2 - 4*a*c]*PolyLog[3, (2*c*E^x)/(-b + Sqrt[b^2 - 4*a*c])] - 6*b*PolyLog[3, (-2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])] + 6*Sqrt[b^2 - 4*a*c]*PolyLog[3, (-2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])])/(6*a*Sqrt[b^2 - 4*a*c])","A",1
520,1,37,40,0.0357871,"\int \frac{1}{1+2 f^{c+d x}+f^{2 c+2 d x}} \, dx","Integrate[(1 + 2*f^(c + d*x) + f^(2*c + 2*d*x))^(-1),x]","\frac{\frac{1}{f^{c+d x}+1}-\log \left(f^{c+d x}+1\right)+d x \log (f)}{d \log (f)}","-\frac{\log \left(f^{c+d x}+1\right)}{d \log (f)}+\frac{1}{d \log (f) \left(f^{c+d x}+1\right)}+x",1,"((1 + f^(c + d*x))^(-1) + d*x*Log[f] - Log[1 + f^(c + d*x)])/(d*Log[f])","A",1
521,1,93,94,0.1494921,"\int \frac{1}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx","Integrate[(a + b*f^(c + d*x) + c*f^(2*c + 2*d*x))^(-1),x]","-\frac{\frac{2 b \tan ^{-1}\left(\frac{b+2 c f^{c+d x}}{\sqrt{4 a c-b^2}}\right)}{d \log (f) \sqrt{4 a c-b^2}}+\frac{\log \left(a+f^{c+d x} \left(b+c f^{c+d x}\right)\right)}{d \log (f)}-2 x}{2 a}","\frac{b \tanh ^{-1}\left(\frac{b+2 c f^{c+d x}}{\sqrt{b^2-4 a c}}\right)}{a d \log (f) \sqrt{b^2-4 a c}}-\frac{\log \left(a+b f^{c+d x}+c f^{2 c+2 d x}\right)}{2 a d \log (f)}+\frac{x}{a}",1,"-1/2*(-2*x + (2*b*ArcTan[(b + 2*c*f^(c + d*x))/Sqrt[-b^2 + 4*a*c]])/(Sqrt[-b^2 + 4*a*c]*d*Log[f]) + Log[a + f^(c + d*x)*(b + c*f^(c + d*x))]/(d*Log[f]))/a","A",1
522,1,93,94,0.1501614,"\int \frac{1}{a+b f^{g+h x}+c f^{2 (g+h x)}} \, dx","Integrate[(a + b*f^(g + h*x) + c*f^(2*(g + h*x)))^(-1),x]","-\frac{\frac{2 b \tan ^{-1}\left(\frac{b+2 c f^{g+h x}}{\sqrt{4 a c-b^2}}\right)}{h \log (f) \sqrt{4 a c-b^2}}+\frac{\log \left(a+f^{g+h x} \left(b+c f^{g+h x}\right)\right)}{h \log (f)}-2 x}{2 a}","\frac{b \tanh ^{-1}\left(\frac{b+2 c f^{g+h x}}{\sqrt{b^2-4 a c}}\right)}{a h \log (f) \sqrt{b^2-4 a c}}-\frac{\log \left(a+b f^{g+h x}+c f^{2 g+2 h x}\right)}{2 a h \log (f)}+\frac{x}{a}",1,"-1/2*(-2*x + (2*b*ArcTan[(b + 2*c*f^(g + h*x))/Sqrt[-b^2 + 4*a*c]])/(Sqrt[-b^2 + 4*a*c]*h*Log[f]) + Log[a + f^(g + h*x)*(b + c*f^(g + h*x))]/(h*Log[f]))/a","A",1
523,1,88,96,0.1801446,"\int \frac{x}{1+2 f^{c+d x}+f^{2 c+2 d x}} \, dx","Integrate[x/(1 + 2*f^(c + d*x) + f^(2*c + 2*d*x)),x]","-\frac{\text{Li}_2\left(-f^{c+d x}\right)}{d^2 \log ^2(f)}+\frac{\log \left(f^{c+d x}+1\right)}{d^2 \log ^2(f)}+\frac{1}{2} x \left(\frac{2}{d \log (f) f^{c+d x}+d \log (f)}+x\right)-\frac{x \left(\log \left(f^{c+d x}+1\right)+1\right)}{d \log (f)}","-\frac{\text{Li}_2\left(-f^{c+d x}\right)}{d^2 \log ^2(f)}+\frac{\log \left(f^{c+d x}+1\right)}{d^2 \log ^2(f)}-\frac{x \log \left(f^{c+d x}+1\right)}{d \log (f)}+\frac{x}{d \log (f) \left(f^{c+d x}+1\right)}-\frac{x}{d \log (f)}+\frac{x^2}{2}",1,"(x*(x + 2/(d*Log[f] + d*f^(c + d*x)*Log[f])))/2 + Log[1 + f^(c + d*x)]/(d^2*Log[f]^2) - (x*(1 + Log[1 + f^(c + d*x)]))/(d*Log[f]) - PolyLog[2, -f^(c + d*x)]/(d^2*Log[f]^2)","A",1
524,0,0,338,5.3286785,"\int \frac{x}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx","Integrate[x/(a + b*f^(c + d*x) + c*f^(2*c + 2*d*x)),x]","\int \frac{x}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx","-\frac{2 c \text{Li}_2\left(-\frac{2 c f^{c+d x}}{b-\sqrt{b^2-4 a c}}\right)}{d^2 \log ^2(f) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}+\frac{2 c \text{Li}_2\left(-\frac{2 c f^{c+d x}}{b+\sqrt{b^2-4 a c}}\right)}{d^2 \log ^2(f) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}-\frac{2 c x \log \left(\frac{2 c f^{c+d x}}{b-\sqrt{b^2-4 a c}}+1\right)}{d \log (f) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}+\frac{2 c x \log \left(\frac{2 c f^{c+d x}}{\sqrt{b^2-4 a c}+b}+1\right)}{d \log (f) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}-\frac{c x^2}{-b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{c x^2}{b \sqrt{b^2-4 a c}-4 a c+b^2}",1,"Integrate[x/(a + b*f^(c + d*x) + c*f^(2*c + 2*d*x)), x]","F",-1
525,1,123,145,0.2369451,"\int \frac{x^2}{1+2 f^{c+d x}+f^{2 c+2 d x}} \, dx","Integrate[x^2/(1 + 2*f^(c + d*x) + f^(2*c + 2*d*x)),x]","\frac{-\frac{3 d^2 x^2 \log ^2(f) \left(f^{c+d x}+\left(f^{c+d x}+1\right) \log \left(f^{c+d x}+1\right)\right)}{f^{c+d x}+1}+6 \text{Li}_3\left(-f^{c+d x}\right)+(6-6 d x \log (f)) \text{Li}_2\left(-f^{c+d x}\right)+6 d x \log (f) \log \left(f^{c+d x}+1\right)+d^3 x^3 \log ^3(f)}{3 d^3 \log ^3(f)}","\frac{2 \text{Li}_2\left(-f^{c+d x}\right)}{d^3 \log ^3(f)}+\frac{2 \text{Li}_3\left(-f^{c+d x}\right)}{d^3 \log ^3(f)}-\frac{2 x \text{Li}_2\left(-f^{c+d x}\right)}{d^2 \log ^2(f)}+\frac{2 x \log \left(f^{c+d x}+1\right)}{d^2 \log ^2(f)}-\frac{x^2 \log \left(f^{c+d x}+1\right)}{d \log (f)}+\frac{x^2}{d \log (f) \left(f^{c+d x}+1\right)}-\frac{x^2}{d \log (f)}+\frac{x^3}{3}",1,"(d^3*x^3*Log[f]^3 + 6*d*x*Log[f]*Log[1 + f^(c + d*x)] - (3*d^2*x^2*Log[f]^2*(f^(c + d*x) + (1 + f^(c + d*x))*Log[1 + f^(c + d*x)]))/(1 + f^(c + d*x)) + (6 - 6*d*x*Log[f])*PolyLog[2, -f^(c + d*x)] + 6*PolyLog[3, -f^(c + d*x)])/(3*d^3*Log[f]^3)","A",1
526,0,0,484,2.8298931,"\int \frac{x^2}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx","Integrate[x^2/(a + b*f^(c + d*x) + c*f^(2*c + 2*d*x)),x]","\int \frac{x^2}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx","\frac{4 c \text{Li}_3\left(-\frac{2 c f^{c+d x}}{b-\sqrt{b^2-4 a c}}\right)}{d^3 \log ^3(f) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{4 c \text{Li}_3\left(-\frac{2 c f^{c+d x}}{b+\sqrt{b^2-4 a c}}\right)}{d^3 \log ^3(f) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}-\frac{4 c x \text{Li}_2\left(-\frac{2 c f^{c+d x}}{b-\sqrt{b^2-4 a c}}\right)}{d^2 \log ^2(f) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}+\frac{4 c x \text{Li}_2\left(-\frac{2 c f^{c+d x}}{b+\sqrt{b^2-4 a c}}\right)}{d^2 \log ^2(f) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}-\frac{2 c x^2 \log \left(\frac{2 c f^{c+d x}}{b-\sqrt{b^2-4 a c}}+1\right)}{d \log (f) \sqrt{b^2-4 a c} \left(b-\sqrt{b^2-4 a c}\right)}+\frac{2 c x^2 \log \left(\frac{2 c f^{c+d x}}{\sqrt{b^2-4 a c}+b}+1\right)}{d \log (f) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}-\frac{2 c x^3}{3 \left(-b \sqrt{b^2-4 a c}-4 a c+b^2\right)}-\frac{2 c x^3}{3 \left(b \sqrt{b^2-4 a c}-4 a c+b^2\right)}",1,"Integrate[x^2/(a + b*f^(c + d*x) + c*f^(2*c + 2*d*x)), x]","F",-1
527,1,102,103,0.1579496,"\int \frac{d+e f^{g+h x}}{a+b f^{g+h x}+c f^{2 g+2 h x}} \, dx","Integrate[(d + e*f^(g + h*x))/(a + b*f^(g + h*x) + c*f^(2*g + 2*h*x)),x]","-\frac{\frac{2 (b d-2 a e) \tan ^{-1}\left(\frac{b+2 c f^{g+h x}}{\sqrt{4 a c-b^2}}\right)}{h \log (f) \sqrt{4 a c-b^2}}+\frac{d \log \left(a+f^{g+h x} \left(b+c f^{g+h x}\right)\right)}{h \log (f)}-2 d x}{2 a}","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c f^{g+h x}}{\sqrt{b^2-4 a c}}\right)}{a h \log (f) \sqrt{b^2-4 a c}}-\frac{d \log \left(a+b f^{g+h x}+c f^{2 g+2 h x}\right)}{2 a h \log (f)}+\frac{d x}{a}",1,"-1/2*(-2*d*x + (2*(b*d - 2*a*e)*ArcTan[(b + 2*c*f^(g + h*x))/Sqrt[-b^2 + 4*a*c]])/(Sqrt[-b^2 + 4*a*c]*h*Log[f]) + (d*Log[a + f^(g + h*x)*(b + c*f^(g + h*x))])/(h*Log[f]))/a","A",1
528,1,102,103,0.0340416,"\int \frac{d+e f^{g+h x}}{a+b f^{g+h x}+c f^{2 (g+h x)}} \, dx","Integrate[(d + e*f^(g + h*x))/(a + b*f^(g + h*x) + c*f^(2*(g + h*x))),x]","-\frac{\frac{2 (b d-2 a e) \tan ^{-1}\left(\frac{b+2 c f^{g+h x}}{\sqrt{4 a c-b^2}}\right)}{h \log (f) \sqrt{4 a c-b^2}}+\frac{d \log \left(a+f^{g+h x} \left(b+c f^{g+h x}\right)\right)}{h \log (f)}-2 d x}{2 a}","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c f^{g+h x}}{\sqrt{b^2-4 a c}}\right)}{a h \log (f) \sqrt{b^2-4 a c}}-\frac{d \log \left(a+b f^{g+h x}+c f^{2 g+2 h x}\right)}{2 a h \log (f)}+\frac{d x}{a}",1,"-1/2*(-2*d*x + (2*(b*d - 2*a*e)*ArcTan[(b + 2*c*f^(g + h*x))/Sqrt[-b^2 + 4*a*c]])/(Sqrt[-b^2 + 4*a*c]*h*Log[f]) + (d*Log[a + f^(g + h*x)*(b + c*f^(g + h*x))])/(h*Log[f]))/a","A",1
529,1,9,9,0.0080938,"\int \frac{1}{2+e^{-x}+e^x} \, dx","Integrate[(2 + E^(-x) + E^x)^(-1),x]","-\frac{1}{e^x+1}","-\frac{1}{e^x+1}",1,"-(1 + E^x)^(-1)","A",1
530,1,20,20,0.0274919,"\int \frac{x}{2+e^{-x}+e^x} \, dx","Integrate[x/(2 + E^(-x) + E^x),x]","-\frac{x}{e^x+1}+x-\log \left(e^x+1\right)","-\frac{x}{e^x+1}+x-\log \left(e^x+1\right)",1,"x - x/(1 + E^x) - Log[1 + E^x]","A",1
531,1,33,34,0.047276,"\int \frac{x^2}{2+e^{-x}+e^x} \, dx","Integrate[x^2/(2 + E^(-x) + E^x),x]","x \left(\frac{e^x x}{e^x+1}-2 \log \left(e^x+1\right)\right)-2 \text{Li}_2\left(-e^x\right)","-2 \text{Li}_2\left(-e^x\right)-\frac{x^2}{e^x+1}+x^2-2 x \log \left(e^x+1\right)",1,"x*((E^x*x)/(1 + E^x) - 2*Log[1 + E^x]) - 2*PolyLog[2, -E^x]","A",1
532,1,20,20,0.0180944,"\int \frac{1}{2+f^{-c-d x}+f^{c+d x}} \, dx","Integrate[(2 + f^(-c - d*x) + f^(c + d*x))^(-1),x]","-\frac{1}{d \log (f) \left(f^{c+d x}+1\right)}","-\frac{1}{d \log (f) \left(f^{c+d x}+1\right)}",1,"-(1/(d*(1 + f^(c + d*x))*Log[f]))","A",1
533,1,44,50,0.0665185,"\int \frac{x}{2+f^{-c-d x}+f^{c+d x}} \, dx","Integrate[x/(2 + f^(-c - d*x) + f^(c + d*x)),x]","\frac{\frac{d x \log (f) f^{c+d x}}{f^{c+d x}+1}-\log \left(f^{c+d x}+1\right)}{d^2 \log ^2(f)}","-\frac{\log \left(f^{c+d x}+1\right)}{d^2 \log ^2(f)}-\frac{x}{d \log (f) \left(f^{c+d x}+1\right)}+\frac{x}{d \log (f)}",1,"((d*f^(c + d*x)*x*Log[f])/(1 + f^(c + d*x)) - Log[1 + f^(c + d*x)])/(d^2*Log[f]^2)","A",1
534,1,63,75,0.1154978,"\int \frac{x^2}{2+f^{-c-d x}+f^{c+d x}} \, dx","Integrate[x^2/(2 + f^(-c - d*x) + f^(c + d*x)),x]","\frac{d x \log (f) \left(\frac{d x \log (f) f^{c+d x}}{f^{c+d x}+1}-2 \log \left(f^{c+d x}+1\right)\right)-2 \text{Li}_2\left(-f^{c+d x}\right)}{d^3 \log ^3(f)}","-\frac{2 \text{Li}_2\left(-f^{c+d x}\right)}{d^3 \log ^3(f)}-\frac{2 x \log \left(f^{c+d x}+1\right)}{d^2 \log ^2(f)}-\frac{x^2}{d \log (f) \left(f^{c+d x}+1\right)}+\frac{x^2}{d \log (f)}",1,"(d*x*Log[f]*((d*f^(c + d*x)*x*Log[f])/(1 + f^(c + d*x)) - 2*Log[1 + f^(c + d*x)]) - 2*PolyLog[2, -f^(c + d*x)])/(d^3*Log[f]^3)","A",1
535,1,13,13,0.0107597,"\int \frac{1}{2+3^{-x}+3^x} \, dx","Integrate[(2 + 3^(-x) + 3^x)^(-1),x]","-\frac{1}{\left(3^x+1\right) \log (3)}","-\frac{1}{\left(3^x+1\right) \log (3)}",1,"-(1/((1 + 3^x)*Log[3]))","A",1
536,1,16,23,0.011283,"\int \frac{1}{1-e^{-x}+2 e^x} \, dx","Integrate[(1 - E^(-x) + 2*E^x)^(-1),x]","-\frac{2}{3} \tanh ^{-1}\left(\frac{1}{3} \left(4 e^x+1\right)\right)","\frac{1}{3} \log \left(1-2 e^x\right)-\frac{1}{3} \log \left(e^x+1\right)",1,"(-2*ArcTanh[(1 + 4*E^x)/3])/3","A",1
537,1,36,36,0.0247666,"\int \frac{1}{a+b e^{-x}+c e^x} \, dx","Integrate[(a + b/E^x + c*E^x)^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{a+2 c e^x}{\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}","-\frac{2 \tanh ^{-1}\left(\frac{a+2 c e^x}{\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}",1,"(-2*ArcTanh[(a + 2*c*E^x)/Sqrt[a^2 - 4*b*c]])/Sqrt[a^2 - 4*b*c]","A",1
538,1,123,159,0.068702,"\int \frac{x}{a+b e^{-x}+c e^x} \, dx","Integrate[x/(a + b/E^x + c*E^x),x]","\frac{\text{Li}_2\left(\frac{2 c e^x}{\sqrt{a^2-4 b c}-a}\right)-\text{Li}_2\left(-\frac{2 c e^x}{a+\sqrt{a^2-4 b c}}\right)+x \left(\log \left(\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}+1\right)-\log \left(\frac{2 c e^x}{\sqrt{a^2-4 b c}+a}+1\right)\right)}{\sqrt{a^2-4 b c}}","\frac{\text{Li}_2\left(-\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}-\frac{\text{Li}_2\left(-\frac{2 c e^x}{a+\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}+\frac{x \log \left(\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}+1\right)}{\sqrt{a^2-4 b c}}-\frac{x \log \left(\frac{2 c e^x}{\sqrt{a^2-4 b c}+a}+1\right)}{\sqrt{a^2-4 b c}}",1,"(x*(Log[1 + (2*c*E^x)/(a - Sqrt[a^2 - 4*b*c])] - Log[1 + (2*c*E^x)/(a + Sqrt[a^2 - 4*b*c])]) + PolyLog[2, (2*c*E^x)/(-a + Sqrt[a^2 - 4*b*c])] - PolyLog[2, (-2*c*E^x)/(a + Sqrt[a^2 - 4*b*c])])/Sqrt[a^2 - 4*b*c]","A",1
539,1,185,244,0.038496,"\int \frac{x^2}{a+b e^{-x}+c e^x} \, dx","Integrate[x^2/(a + b/E^x + c*E^x),x]","\frac{2 x \text{Li}_2\left(\frac{2 c e^x}{\sqrt{a^2-4 b c}-a}\right)-2 x \text{Li}_2\left(-\frac{2 c e^x}{a+\sqrt{a^2-4 b c}}\right)-2 \text{Li}_3\left(\frac{2 c e^x}{\sqrt{a^2-4 b c}-a}\right)+2 \text{Li}_3\left(-\frac{2 c e^x}{a+\sqrt{a^2-4 b c}}\right)+x^2 \log \left(\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}+1\right)-x^2 \log \left(\frac{2 c e^x}{\sqrt{a^2-4 b c}+a}+1\right)}{\sqrt{a^2-4 b c}}","\frac{2 x \text{Li}_2\left(-\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}-\frac{2 x \text{Li}_2\left(-\frac{2 c e^x}{a+\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}-\frac{2 \text{Li}_3\left(-\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}+\frac{2 \text{Li}_3\left(-\frac{2 c e^x}{a+\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}+\frac{x^2 \log \left(\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}+1\right)}{\sqrt{a^2-4 b c}}-\frac{x^2 \log \left(\frac{2 c e^x}{\sqrt{a^2-4 b c}+a}+1\right)}{\sqrt{a^2-4 b c}}",1,"(x^2*Log[1 + (2*c*E^x)/(a - Sqrt[a^2 - 4*b*c])] - x^2*Log[1 + (2*c*E^x)/(a + Sqrt[a^2 - 4*b*c])] + 2*x*PolyLog[2, (2*c*E^x)/(-a + Sqrt[a^2 - 4*b*c])] - 2*x*PolyLog[2, (-2*c*E^x)/(a + Sqrt[a^2 - 4*b*c])] - 2*PolyLog[3, (2*c*E^x)/(-a + Sqrt[a^2 - 4*b*c])] + 2*PolyLog[3, (-2*c*E^x)/(a + Sqrt[a^2 - 4*b*c])])/Sqrt[a^2 - 4*b*c]","A",1
540,1,47,47,0.0552824,"\int \frac{1}{a+b f^{-c-d x}+c f^{c+d x}} \, dx","Integrate[(a + b*f^(-c - d*x) + c*f^(c + d*x))^(-1),x]","-\frac{2 \tanh ^{-1}\left(\frac{a+2 c f^{c+d x}}{\sqrt{a^2-4 b c}}\right)}{d \log (f) \sqrt{a^2-4 b c}}","-\frac{2 \tanh ^{-1}\left(\frac{a+2 c f^{c+d x}}{\sqrt{a^2-4 b c}}\right)}{d \log (f) \sqrt{a^2-4 b c}}",1,"(-2*ArcTanh[(a + 2*c*f^(c + d*x))/Sqrt[a^2 - 4*b*c]])/(Sqrt[a^2 - 4*b*c]*d*Log[f])","A",1
541,0,0,203,0.4611452,"\int \frac{x}{a+b f^{-c-d x}+c f^{c+d x}} \, dx","Integrate[x/(a + b*f^(-c - d*x) + c*f^(c + d*x)),x]","\int \frac{x}{a+b f^{-c-d x}+c f^{c+d x}} \, dx","\frac{\text{Li}_2\left(-\frac{2 c f^{c+d x}}{a-\sqrt{a^2-4 b c}}\right)}{d^2 \log ^2(f) \sqrt{a^2-4 b c}}-\frac{\text{Li}_2\left(-\frac{2 c f^{c+d x}}{a+\sqrt{a^2-4 b c}}\right)}{d^2 \log ^2(f) \sqrt{a^2-4 b c}}+\frac{x \log \left(\frac{2 c f^{c+d x}}{a-\sqrt{a^2-4 b c}}+1\right)}{d \log (f) \sqrt{a^2-4 b c}}-\frac{x \log \left(\frac{2 c f^{c+d x}}{\sqrt{a^2-4 b c}+a}+1\right)}{d \log (f) \sqrt{a^2-4 b c}}",1,"Integrate[x/(a + b*f^(-c - d*x) + c*f^(c + d*x)), x]","F",-1
542,0,0,310,0.1979377,"\int \frac{x^2}{a+b f^{-c-d x}+c f^{c+d x}} \, dx","Integrate[x^2/(a + b*f^(-c - d*x) + c*f^(c + d*x)),x]","\int \frac{x^2}{a+b f^{-c-d x}+c f^{c+d x}} \, dx","-\frac{2 \text{Li}_3\left(-\frac{2 c f^{c+d x}}{a-\sqrt{a^2-4 b c}}\right)}{d^3 \log ^3(f) \sqrt{a^2-4 b c}}+\frac{2 \text{Li}_3\left(-\frac{2 c f^{c+d x}}{a+\sqrt{a^2-4 b c}}\right)}{d^3 \log ^3(f) \sqrt{a^2-4 b c}}+\frac{2 x \text{Li}_2\left(-\frac{2 c f^{c+d x}}{a-\sqrt{a^2-4 b c}}\right)}{d^2 \log ^2(f) \sqrt{a^2-4 b c}}-\frac{2 x \text{Li}_2\left(-\frac{2 c f^{c+d x}}{a+\sqrt{a^2-4 b c}}\right)}{d^2 \log ^2(f) \sqrt{a^2-4 b c}}+\frac{x^2 \log \left(\frac{2 c f^{c+d x}}{a-\sqrt{a^2-4 b c}}+1\right)}{d \log (f) \sqrt{a^2-4 b c}}-\frac{x^2 \log \left(\frac{2 c f^{c+d x}}{\sqrt{a^2-4 b c}+a}+1\right)}{d \log (f) \sqrt{a^2-4 b c}}",1,"Integrate[x^2/(a + b*f^(-c - d*x) + c*f^(c + d*x)), x]","F",-1
543,0,0,53,0.6794903,"\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)^n}{d f+(e f+d g) x+e g x^2} \, dx","Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))^n/(d*f + (e*f + d*g)*x + e*g*x^2),x]","\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)^n}{d f+(e f+d g) x+e g x^2} \, dx","\text{Int}\left(\frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)^n}{x (d g+e f)+d f+e g x^2},x\right)",0,"Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))^n/(d*f + (e*f + d*g)*x + e*g*x^2), x]","A",-1
544,0,0,154,1.6427624,"\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)^3}{d f+(e f+d g) x+e g x^2} \, dx","Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))^3/(d*f + (e*f + d*g)*x + e*g*x^2),x]","\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)^3}{d f+(e f+d g) x+e g x^2} \, dx","\frac{2 a^3 \log \left(\frac{\sqrt{d+e x}}{\sqrt{f+g x}}\right)}{e f-d g}+\frac{6 a^2 b \text{Ei}\left(\frac{c \sqrt{d+e x} \log (F)}{\sqrt{f+g x}}\right)}{e f-d g}+\frac{6 a b^2 \text{Ei}\left(\frac{2 c \sqrt{d+e x} \log (F)}{\sqrt{f+g x}}\right)}{e f-d g}+\frac{2 b^3 \text{Ei}\left(\frac{3 c \sqrt{d+e x} \log (F)}{\sqrt{f+g x}}\right)}{e f-d g}",1,"Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))^3/(d*f + (e*f + d*g)*x + e*g*x^2), x]","F",-1
545,0,0,112,1.3853185,"\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)^2}{d f+(e f+d g) x+e g x^2} \, dx","Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))^2/(d*f + (e*f + d*g)*x + e*g*x^2),x]","\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)^2}{d f+(e f+d g) x+e g x^2} \, dx","\frac{2 a^2 \log \left(\frac{\sqrt{d+e x}}{\sqrt{f+g x}}\right)}{e f-d g}+\frac{4 a b \text{Ei}\left(\frac{c \sqrt{d+e x} \log (F)}{\sqrt{f+g x}}\right)}{e f-d g}+\frac{2 b^2 \text{Ei}\left(\frac{2 c \sqrt{d+e x} \log (F)}{\sqrt{f+g x}}\right)}{e f-d g}",1,"Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))^2/(d*f + (e*f + d*g)*x + e*g*x^2), x]","F",-1
546,0,0,70,0.5239775,"\int \frac{a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}}{d f+(e f+d g) x+e g x^2} \, dx","Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))/(d*f + (e*f + d*g)*x + e*g*x^2),x]","\int \frac{a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}}{d f+(e f+d g) x+e g x^2} \, dx","\frac{2 a \log \left(\frac{\sqrt{d+e x}}{\sqrt{f+g x}}\right)}{e f-d g}+\frac{2 b \text{Ei}\left(\frac{c \sqrt{d+e x} \log (F)}{\sqrt{f+g x}}\right)}{e f-d g}",1,"Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))/(d*f + (e*f + d*g)*x + e*g*x^2), x]","F",-1
547,1,26,36,0.0106625,"\int \frac{1}{d f+(e f+d g) x+e g x^2} \, dx","Integrate[(d*f + (e*f + d*g)*x + e*g*x^2)^(-1),x]","\frac{\log (d+e x)-\log (f+g x)}{e f-d g}","\frac{\log (d+e x)}{e f-d g}-\frac{\log (f+g x)}{e f-d g}",1,"(Log[d + e*x] - Log[f + g*x])/(e*f - d*g)","A",1
548,0,0,53,0.3922114,"\int \frac{1}{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right) \left(d f+(e f+d g) x+e g x^2\right)} \, dx","Integrate[1/((a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))*(d*f + (e*f + d*g)*x + e*g*x^2)),x]","\int \frac{1}{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right) \left(d f+(e f+d g) x+e g x^2\right)} \, dx","\text{Int}\left(\frac{1}{\left(x (d g+e f)+d f+e g x^2\right) \left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)},x\right)",0,"Integrate[1/((a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))*(d*f + (e*f + d*g)*x + e*g*x^2)), x]","A",-1
549,0,0,53,1.2665009,"\int \frac{1}{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)^2 \left(d f+(e f+d g) x+e g x^2\right)} \, dx","Integrate[1/((a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))^2*(d*f + (e*f + d*g)*x + e*g*x^2)),x]","\int \frac{1}{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)^2 \left(d f+(e f+d g) x+e g x^2\right)} \, dx","\text{Int}\left(\frac{1}{\left(x (d g+e f)+d f+e g x^2\right) \left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{f+g x}}}\right)^2},x\right)",0,"Integrate[1/((a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))^2*(d*f + (e*f + d*g)*x + e*g*x^2)), x]","A",-1
550,0,0,50,0.7259627,"\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)^n}{d^2-e^2 x^2} \, dx","Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^n/(d^2 - e^2*x^2),x]","\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)^n}{d^2-e^2 x^2} \, dx","\text{Int}\left(\frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)^n}{d^2-e^2 x^2},x\right)",0,"Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^n/(d^2 - e^2*x^2), x]","A",-1
551,0,0,152,1.3435811,"\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)^3}{d^2-e^2 x^2} \, dx","Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^3/(d^2 - e^2*x^2),x]","\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)^3}{d^2-e^2 x^2} \, dx","\frac{a^3 \log \left(\frac{\sqrt{d+e x}}{\sqrt{d f-e f x}}\right)}{d e}+\frac{3 a^2 b \text{Ei}\left(\frac{c \sqrt{d+e x} \log (F)}{\sqrt{d f-e f x}}\right)}{d e}+\frac{3 a b^2 \text{Ei}\left(\frac{2 c \sqrt{d+e x} \log (F)}{\sqrt{d f-e f x}}\right)}{d e}+\frac{b^3 \text{Ei}\left(\frac{3 c \sqrt{d+e x} \log (F)}{\sqrt{d f-e f x}}\right)}{d e}",1,"Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^3/(d^2 - e^2*x^2), x]","F",-1
552,0,0,110,1.3048952,"\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)^2}{d^2-e^2 x^2} \, dx","Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^2/(d^2 - e^2*x^2),x]","\int \frac{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)^2}{d^2-e^2 x^2} \, dx","\frac{a^2 \log \left(\frac{\sqrt{d+e x}}{\sqrt{d f-e f x}}\right)}{d e}+\frac{2 a b \text{Ei}\left(\frac{c \sqrt{d+e x} \log (F)}{\sqrt{d f-e f x}}\right)}{d e}+\frac{b^2 \text{Ei}\left(\frac{2 c \sqrt{d+e x} \log (F)}{\sqrt{d f-e f x}}\right)}{d e}",1,"Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^2/(d^2 - e^2*x^2), x]","F",-1
553,0,0,68,0.463913,"\int \frac{a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}}{d^2-e^2 x^2} \, dx","Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))/(d^2 - e^2*x^2),x]","\int \frac{a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}}{d^2-e^2 x^2} \, dx","\frac{a \log \left(\frac{\sqrt{d+e x}}{\sqrt{d f-e f x}}\right)}{d e}+\frac{b \text{Ei}\left(\frac{c \sqrt{d+e x} \log (F)}{\sqrt{d f-e f x}}\right)}{d e}",1,"Integrate[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))/(d^2 - e^2*x^2), x]","F",-1
554,1,14,14,0.0031274,"\int \frac{1}{d^2-e^2 x^2} \, dx","Integrate[(d^2 - e^2*x^2)^(-1),x]","\frac{\tanh ^{-1}\left(\frac{e x}{d}\right)}{d e}","\frac{\tanh ^{-1}\left(\frac{e x}{d}\right)}{d e}",1,"ArcTanh[(e*x)/d]/(d*e)","A",1
555,0,0,50,0.4807492,"\int \frac{1}{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right) \left(d^2-e^2 x^2\right)} \, dx","Integrate[1/((a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))*(d^2 - e^2*x^2)),x]","\int \frac{1}{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right) \left(d^2-e^2 x^2\right)} \, dx","\text{Int}\left(\frac{1}{\left(d^2-e^2 x^2\right) \left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)},x\right)",0,"Integrate[1/((a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))*(d^2 - e^2*x^2)), x]","A",-1
556,0,0,50,1.3955249,"\int \frac{1}{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)^2 \left(d^2-e^2 x^2\right)} \, dx","Integrate[1/((a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^2*(d^2 - e^2*x^2)),x]","\int \frac{1}{\left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)^2 \left(d^2-e^2 x^2\right)} \, dx","\text{Int}\left(\frac{1}{\left(d^2-e^2 x^2\right) \left(a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}\right)^2},x\right)",0,"Integrate[1/((a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^2*(d^2 - e^2*x^2)), x]","A",-1
557,1,77,77,0.321383,"\int \frac{\left(F^{\frac{\sqrt{1-a x}}{\sqrt{1+a x}}}\right)^n}{1-a^2 x^2} \, dx","Integrate[(F^(Sqrt[1 - a*x]/Sqrt[1 + a*x]))^n/(1 - a^2*x^2),x]","-\frac{F^{-\frac{n \sqrt{1-a x}}{\sqrt{a x+1}}} \left(F^{\frac{\sqrt{1-a x}}{\sqrt{a x+1}}}\right)^n \text{Ei}\left(\frac{n \sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}","-\frac{F^{-\frac{n \sqrt{1-a x}}{\sqrt{a x+1}}} \left(F^{\frac{\sqrt{1-a x}}{\sqrt{a x+1}}}\right)^n \text{Ei}\left(\frac{n \sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}",1,"-(((F^(Sqrt[1 - a*x]/Sqrt[1 + a*x]))^n*ExpIntegralEi[(n*Sqrt[1 - a*x]*Log[F])/Sqrt[1 + a*x]])/(a*F^((n*Sqrt[1 - a*x])/Sqrt[1 + a*x])))","A",1
558,1,29,29,0.2582985,"\int \frac{F^{\frac{3 \sqrt{1-a x}}{\sqrt{1+a x}}}}{1-a^2 x^2} \, dx","Integrate[F^((3*Sqrt[1 - a*x])/Sqrt[1 + a*x])/(1 - a^2*x^2),x]","-\frac{\text{Ei}\left(\frac{3 \sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}","-\frac{\text{Ei}\left(\frac{3 \sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}",1,"-(ExpIntegralEi[(3*Sqrt[1 - a*x]*Log[F])/Sqrt[1 + a*x]]/a)","A",1
559,1,29,29,0.2548668,"\int \frac{F^{\frac{2 \sqrt{1-a x}}{\sqrt{1+a x}}}}{1-a^2 x^2} \, dx","Integrate[F^((2*Sqrt[1 - a*x])/Sqrt[1 + a*x])/(1 - a^2*x^2),x]","-\frac{\text{Ei}\left(\frac{2 \sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}","-\frac{\text{Ei}\left(\frac{2 \sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}",1,"-(ExpIntegralEi[(2*Sqrt[1 - a*x]*Log[F])/Sqrt[1 + a*x]]/a)","A",1
560,1,28,28,0.2381271,"\int \frac{F^{\frac{\sqrt{1-a x}}{\sqrt{1+a x}}}}{1-a^2 x^2} \, dx","Integrate[F^(Sqrt[1 - a*x]/Sqrt[1 + a*x])/(1 - a^2*x^2),x]","-\frac{\text{Ei}\left(\frac{\sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}","-\frac{\text{Ei}\left(\frac{\sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}",1,"-(ExpIntegralEi[(Sqrt[1 - a*x]*Log[F])/Sqrt[1 + a*x]]/a)","A",1
561,1,29,29,0.2493499,"\int \frac{F^{-\frac{\sqrt{1-a x}}{\sqrt{1+a x}}}}{1-a^2 x^2} \, dx","Integrate[1/(F^(Sqrt[1 - a*x]/Sqrt[1 + a*x])*(1 - a^2*x^2)),x]","-\frac{\text{Ei}\left(-\frac{\sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}","-\frac{\text{Ei}\left(-\frac{\sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}",1,"-(ExpIntegralEi[-((Sqrt[1 - a*x]*Log[F])/Sqrt[1 + a*x])]/a)","A",1
562,1,29,29,0.299463,"\int \frac{F^{-\frac{2 \sqrt{1-a x}}{\sqrt{1+a x}}}}{1-a^2 x^2} \, dx","Integrate[1/(F^((2*Sqrt[1 - a*x])/Sqrt[1 + a*x])*(1 - a^2*x^2)),x]","-\frac{\text{Ei}\left(-\frac{2 \sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}","-\frac{\text{Ei}\left(-\frac{2 \sqrt{1-a x} \log (F)}{\sqrt{a x+1}}\right)}{a}",1,"-(ExpIntegralEi[(-2*Sqrt[1 - a*x]*Log[F])/Sqrt[1 + a*x]]/a)","A",1
563,1,35,49,0.0328248,"\int a^x b^x x^2 \, dx","Integrate[a^x*b^x*x^2,x]","\frac{a^x b^x \left(x^2 (\log (a)+\log (b))^2-2 x (\log (a)+\log (b))+2\right)}{(\log (a)+\log (b))^3}","\frac{x^2 a^x b^x}{\log (a)+\log (b)}-\frac{2 x a^x b^x}{(\log (a)+\log (b))^2}+\frac{2 a^x b^x}{(\log (a)+\log (b))^3}",1,"(a^x*b^x*(2 - 2*x*(Log[a] + Log[b]) + x^2*(Log[a] + Log[b])^2))/(Log[a] + Log[b])^3","A",1
564,1,26,31,0.0168639,"\int a^x b^x x \, dx","Integrate[a^x*b^x*x,x]","a^x b^x \left(\frac{x}{\log (a)+\log (b)}-\frac{1}{(\log (a)+\log (b))^2}\right)","\frac{x a^x b^x}{\log (a)+\log (b)}-\frac{a^x b^x}{(\log (a)+\log (b))^2}",1,"a^x*b^x*(-(Log[a] + Log[b])^(-2) + x/(Log[a] + Log[b]))","A",1
565,1,14,14,0.0060934,"\int a^x b^x \, dx","Integrate[a^x*b^x,x]","\frac{a^x b^x}{\log (a)+\log (b)}","\frac{a^x b^x}{\log (a)+\log (b)}",1,"(a^x*b^x)/(Log[a] + Log[b])","A",1
566,1,10,8,0.0122156,"\int \frac{a^x b^x}{x} \, dx","Integrate[(a^x*b^x)/x,x]","\text{Ei}(x \log (a)+x \log (b))","\text{Ei}(x (\log (a)+\log (b)))",1,"ExpIntegralEi[x*Log[a] + x*Log[b]]","A",1
567,0,0,26,0.0525584,"\int \frac{a^x b^x}{x^2} \, dx","Integrate[(a^x*b^x)/x^2,x]","\int \frac{a^x b^x}{x^2} \, dx","(\log (a)+\log (b)) \text{Ei}(x (\log (a)+\log (b)))-\frac{a^x b^x}{x}",1,"Integrate[(a^x*b^x)/x^2, x]","F",-1
568,0,0,51,0.0639085,"\int \frac{a^x b^x}{x^3} \, dx","Integrate[(a^x*b^x)/x^3,x]","\int \frac{a^x b^x}{x^3} \, dx","-\frac{a^x b^x}{2 x^2}-\frac{a^x b^x (\log (a)+\log (b))}{2 x}+\frac{1}{2} (\log (a)+\log (b))^2 \text{Ei}(x (\log (a)+\log (b)))",1,"Integrate[(a^x*b^x)/x^3, x]","F",-1
569,1,21,19,0.016905,"\int a^x b^x c^x \, dx","Integrate[a^x*b^x*c^x,x]","\frac{e^{x (\log (a)+\log (b)+\log (c))}}{\log (a)+\log (b)+\log (c)}","\frac{a^x b^x c^x}{\log (a)+\log (b)+\log (c)}",1,"E^(x*(Log[a] + Log[b] + Log[c]))/(Log[a] + Log[b] + Log[c])","A",1
570,1,18,18,0.0172683,"\int a^x b^{-x} \, dx","Integrate[a^x/b^x,x]","\frac{a^x b^{-x}}{\log (a)-\log (b)}","\frac{a^x b^{-x}}{\log (a)-\log (b)}",1,"a^x/(b^x*(Log[a] - Log[b]))","A",1
571,1,43,61,0.0317971,"\int a^x b^{-x} x^2 \, dx","Integrate[(a^x*x^2)/b^x,x]","\frac{a^x b^{-x} \left(x^2 (\log (a)-\log (b))^2-2 x (\log (a)-\log (b))+2\right)}{(\log (a)-\log (b))^3}","\frac{x^2 a^x b^{-x}}{\log (a)-\log (b)}-\frac{2 x a^x b^{-x}}{(\log (a)-\log (b))^2}+\frac{2 a^x b^{-x}}{(\log (a)-\log (b))^3}",1,"(a^x*(2 - 2*x*(Log[a] - Log[b]) + x^2*(Log[a] - Log[b])^2))/(b^x*(Log[a] - Log[b])^3)","A",1
572,1,2441,770,4.6752087,"\int \frac{\left(d+e e^{h+i x}\right) (f+g x)^3}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx","Integrate[((d + e*E^(h + i*x))*(f + g*x)^3)/(a + b*E^(h + i*x) + c*E^(2*h + 2*i*x)),x]","\text{Result too large to show}","\frac{6 g^2 (f+g x) \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{Li}_3\left(-\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}\right)}{i^3 \left(b-\sqrt{b^2-4 a c}\right)}+\frac{6 g^2 (f+g x) \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \text{Li}_3\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right)}{i^3 \left(\sqrt{b^2-4 a c}+b\right)}-\frac{3 g (f+g x)^2 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{Li}_2\left(-\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}\right)}{i^2 \left(b-\sqrt{b^2-4 a c}\right)}-\frac{3 g (f+g x)^2 \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \text{Li}_2\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right)}{i^2 \left(\sqrt{b^2-4 a c}+b\right)}-\frac{(f+g x)^3 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}+1\right)}{i \left(b-\sqrt{b^2-4 a c}\right)}-\frac{(f+g x)^3 \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}+1\right)}{i \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(f+g x)^4 \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right)}{4 g \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(f+g x)^4 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right)}{4 g \left(b-\sqrt{b^2-4 a c}\right)}-\frac{6 g^3 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{Li}_4\left(-\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}\right)}{i^4 \left(b-\sqrt{b^2-4 a c}\right)}-\frac{6 g^3 \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \text{Li}_4\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right)}{i^4 \left(\sqrt{b^2-4 a c}+b\right)}",1,"-1/4*(-4*Sqrt[-(b^2 - 4*a*c)^2]*d*f^3*i^4*x - 6*Sqrt[-(b^2 - 4*a*c)^2]*d*f^2*g*i^4*x^2 - 4*Sqrt[-(b^2 - 4*a*c)^2]*d*f*g^2*i^4*x^3 - Sqrt[-(b^2 - 4*a*c)^2]*d*g^3*i^4*x^4 + 4*b*Sqrt[b^2 - 4*a*c]*d*f^3*i^3*ArcTan[(b + 2*c*E^(h + i*x))/Sqrt[-b^2 + 4*a*c]] + 8*a*Sqrt[-b^2 + 4*a*c]*e*f^3*i^3*ArcTanh[(b + 2*c*E^(h + i*x))/Sqrt[b^2 - 4*a*c]] + 6*Sqrt[-(b^2 - 4*a*c)^2]*d*f^2*g*i^3*x*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + 6*b*Sqrt[-b^2 + 4*a*c]*d*f^2*g*i^3*x*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] - 12*a*Sqrt[-b^2 + 4*a*c]*e*f^2*g*i^3*x*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + 6*Sqrt[-(b^2 - 4*a*c)^2]*d*f*g^2*i^3*x^2*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + 6*b*Sqrt[-b^2 + 4*a*c]*d*f*g^2*i^3*x^2*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] - 12*a*Sqrt[-b^2 + 4*a*c]*e*f*g^2*i^3*x^2*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + 2*Sqrt[-(b^2 - 4*a*c)^2]*d*g^3*i^3*x^3*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + 2*b*Sqrt[-b^2 + 4*a*c]*d*g^3*i^3*x^3*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] - 4*a*Sqrt[-b^2 + 4*a*c]*e*g^3*i^3*x^3*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + 6*Sqrt[-(b^2 - 4*a*c)^2]*d*f^2*g*i^3*x*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 6*b*Sqrt[-b^2 + 4*a*c]*d*f^2*g*i^3*x*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 12*a*Sqrt[-b^2 + 4*a*c]*e*f^2*g*i^3*x*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 6*Sqrt[-(b^2 - 4*a*c)^2]*d*f*g^2*i^3*x^2*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 6*b*Sqrt[-b^2 + 4*a*c]*d*f*g^2*i^3*x^2*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 12*a*Sqrt[-b^2 + 4*a*c]*e*f*g^2*i^3*x^2*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 2*Sqrt[-(b^2 - 4*a*c)^2]*d*g^3*i^3*x^3*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 2*b*Sqrt[-b^2 + 4*a*c]*d*g^3*i^3*x^3*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 4*a*Sqrt[-b^2 + 4*a*c]*e*g^3*i^3*x^3*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 2*Sqrt[-(b^2 - 4*a*c)^2]*d*f^3*i^3*Log[a + E^(h + i*x)*(b + c*E^(h + i*x))] + 6*(Sqrt[-(b^2 - 4*a*c)^2]*d + b*Sqrt[-b^2 + 4*a*c]*d - 2*a*Sqrt[-b^2 + 4*a*c]*e)*g*i^2*(f + g*x)^2*PolyLog[2, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] + 6*(Sqrt[-(b^2 - 4*a*c)^2]*d - b*Sqrt[-b^2 + 4*a*c]*d + 2*a*Sqrt[-b^2 + 4*a*c]*e)*g*i^2*(f + g*x)^2*PolyLog[2, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 12*Sqrt[-(b^2 - 4*a*c)^2]*d*f*g^2*i*PolyLog[3, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] - 12*b*Sqrt[-b^2 + 4*a*c]*d*f*g^2*i*PolyLog[3, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] + 24*a*Sqrt[-b^2 + 4*a*c]*e*f*g^2*i*PolyLog[3, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] - 12*Sqrt[-(b^2 - 4*a*c)^2]*d*g^3*i*x*PolyLog[3, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] - 12*b*Sqrt[-b^2 + 4*a*c]*d*g^3*i*x*PolyLog[3, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] + 24*a*Sqrt[-b^2 + 4*a*c]*e*g^3*i*x*PolyLog[3, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] - 12*Sqrt[-(b^2 - 4*a*c)^2]*d*f*g^2*i*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 12*b*Sqrt[-b^2 + 4*a*c]*d*f*g^2*i*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 24*a*Sqrt[-b^2 + 4*a*c]*e*f*g^2*i*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 12*Sqrt[-(b^2 - 4*a*c)^2]*d*g^3*i*x*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 12*b*Sqrt[-b^2 + 4*a*c]*d*g^3*i*x*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 24*a*Sqrt[-b^2 + 4*a*c]*e*g^3*i*x*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 12*Sqrt[-(b^2 - 4*a*c)^2]*d*g^3*PolyLog[4, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] + 12*b*Sqrt[-b^2 + 4*a*c]*d*g^3*PolyLog[4, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] - 24*a*Sqrt[-b^2 + 4*a*c]*e*g^3*PolyLog[4, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] + 12*Sqrt[-(b^2 - 4*a*c)^2]*d*g^3*PolyLog[4, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 12*b*Sqrt[-b^2 + 4*a*c]*d*g^3*PolyLog[4, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 24*a*Sqrt[-b^2 + 4*a*c]*e*g^3*PolyLog[4, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/(a*Sqrt[-(b^2 - 4*a*c)^2]*i^4)","B",1
573,1,1412,599,2.6836376,"\int \frac{\left(d+e e^{h+i x}\right) (f+g x)^2}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx","Integrate[((d + e*E^(h + i*x))*(f + g*x)^2)/(a + b*E^(h + i*x) + c*E^(2*h + 2*i*x)),x]","-\frac{-2 \sqrt{-\left(b^2-4 a c\right)^2} d g^2 x^3 i^3-6 \sqrt{-\left(b^2-4 a c\right)^2} d f g x^2 i^3-6 \sqrt{-\left(b^2-4 a c\right)^2} d f^2 x i^3+6 b \sqrt{b^2-4 a c} d f^2 \tan ^{-1}\left(\frac{b+2 c e^{h+i x}}{\sqrt{4 a c-b^2}}\right) i^2+12 a \sqrt{4 a c-b^2} e f^2 \tanh ^{-1}\left(\frac{b+2 c e^{h+i x}}{\sqrt{b^2-4 a c}}\right) i^2+3 \sqrt{-\left(b^2-4 a c\right)^2} d g^2 x^2 \log \left(\frac{2 e^{h+i x} c}{b-\sqrt{b^2-4 a c}}+1\right) i^2+3 b \sqrt{4 a c-b^2} d g^2 x^2 \log \left(\frac{2 e^{h+i x} c}{b-\sqrt{b^2-4 a c}}+1\right) i^2-6 a \sqrt{4 a c-b^2} e g^2 x^2 \log \left(\frac{2 e^{h+i x} c}{b-\sqrt{b^2-4 a c}}+1\right) i^2+6 \sqrt{-\left(b^2-4 a c\right)^2} d f g x \log \left(\frac{2 e^{h+i x} c}{b-\sqrt{b^2-4 a c}}+1\right) i^2+6 b \sqrt{4 a c-b^2} d f g x \log \left(\frac{2 e^{h+i x} c}{b-\sqrt{b^2-4 a c}}+1\right) i^2-12 a \sqrt{4 a c-b^2} e f g x \log \left(\frac{2 e^{h+i x} c}{b-\sqrt{b^2-4 a c}}+1\right) i^2+3 \sqrt{-\left(b^2-4 a c\right)^2} d g^2 x^2 \log \left(\frac{2 e^{h+i x} c}{b+\sqrt{b^2-4 a c}}+1\right) i^2-3 b \sqrt{4 a c-b^2} d g^2 x^2 \log \left(\frac{2 e^{h+i x} c}{b+\sqrt{b^2-4 a c}}+1\right) i^2+6 a \sqrt{4 a c-b^2} e g^2 x^2 \log \left(\frac{2 e^{h+i x} c}{b+\sqrt{b^2-4 a c}}+1\right) i^2+6 \sqrt{-\left(b^2-4 a c\right)^2} d f g x \log \left(\frac{2 e^{h+i x} c}{b+\sqrt{b^2-4 a c}}+1\right) i^2-6 b \sqrt{4 a c-b^2} d f g x \log \left(\frac{2 e^{h+i x} c}{b+\sqrt{b^2-4 a c}}+1\right) i^2+12 a \sqrt{4 a c-b^2} e f g x \log \left(\frac{2 e^{h+i x} c}{b+\sqrt{b^2-4 a c}}+1\right) i^2+3 \sqrt{-\left(b^2-4 a c\right)^2} d f^2 \log \left(a+e^{h+i x} \left(b+c e^{h+i x}\right)\right) i^2+6 \left(\sqrt{-\left(b^2-4 a c\right)^2} d+b \sqrt{4 a c-b^2} d-2 a \sqrt{4 a c-b^2} e\right) g (f+g x) \text{Li}_2\left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}-b}\right) i+6 \left(\sqrt{-\left(b^2-4 a c\right)^2} d-b \sqrt{4 a c-b^2} d+2 a \sqrt{4 a c-b^2} e\right) g (f+g x) \text{Li}_2\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right) i-6 \sqrt{-\left(b^2-4 a c\right)^2} d g^2 \text{Li}_3\left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}-b}\right)-6 b \sqrt{4 a c-b^2} d g^2 \text{Li}_3\left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}-b}\right)+12 a \sqrt{4 a c-b^2} e g^2 \text{Li}_3\left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}-b}\right)-6 \sqrt{-\left(b^2-4 a c\right)^2} d g^2 \text{Li}_3\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right)+6 b \sqrt{4 a c-b^2} d g^2 \text{Li}_3\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right)-12 a \sqrt{4 a c-b^2} e g^2 \text{Li}_3\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right)}{6 a \sqrt{-\left(b^2-4 a c\right)^2} i^3}","-\frac{2 g (f+g x) \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{Li}_2\left(-\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}\right)}{i^2 \left(b-\sqrt{b^2-4 a c}\right)}-\frac{2 g (f+g x) \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \text{Li}_2\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right)}{i^2 \left(\sqrt{b^2-4 a c}+b\right)}-\frac{(f+g x)^2 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}+1\right)}{i \left(b-\sqrt{b^2-4 a c}\right)}-\frac{(f+g x)^2 \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}+1\right)}{i \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(f+g x)^3 \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right)}{3 g \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(f+g x)^3 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right)}{3 g \left(b-\sqrt{b^2-4 a c}\right)}+\frac{2 g^2 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{Li}_3\left(-\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}\right)}{i^3 \left(b-\sqrt{b^2-4 a c}\right)}+\frac{2 g^2 \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \text{Li}_3\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right)}{i^3 \left(\sqrt{b^2-4 a c}+b\right)}",1,"-1/6*(-6*Sqrt[-(b^2 - 4*a*c)^2]*d*f^2*i^3*x - 6*Sqrt[-(b^2 - 4*a*c)^2]*d*f*g*i^3*x^2 - 2*Sqrt[-(b^2 - 4*a*c)^2]*d*g^2*i^3*x^3 + 6*b*Sqrt[b^2 - 4*a*c]*d*f^2*i^2*ArcTan[(b + 2*c*E^(h + i*x))/Sqrt[-b^2 + 4*a*c]] + 12*a*Sqrt[-b^2 + 4*a*c]*e*f^2*i^2*ArcTanh[(b + 2*c*E^(h + i*x))/Sqrt[b^2 - 4*a*c]] + 6*Sqrt[-(b^2 - 4*a*c)^2]*d*f*g*i^2*x*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + 6*b*Sqrt[-b^2 + 4*a*c]*d*f*g*i^2*x*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] - 12*a*Sqrt[-b^2 + 4*a*c]*e*f*g*i^2*x*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + 3*Sqrt[-(b^2 - 4*a*c)^2]*d*g^2*i^2*x^2*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + 3*b*Sqrt[-b^2 + 4*a*c]*d*g^2*i^2*x^2*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] - 6*a*Sqrt[-b^2 + 4*a*c]*e*g^2*i^2*x^2*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + 6*Sqrt[-(b^2 - 4*a*c)^2]*d*f*g*i^2*x*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 6*b*Sqrt[-b^2 + 4*a*c]*d*f*g*i^2*x*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 12*a*Sqrt[-b^2 + 4*a*c]*e*f*g*i^2*x*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 3*Sqrt[-(b^2 - 4*a*c)^2]*d*g^2*i^2*x^2*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 3*b*Sqrt[-b^2 + 4*a*c]*d*g^2*i^2*x^2*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 6*a*Sqrt[-b^2 + 4*a*c]*e*g^2*i^2*x^2*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 3*Sqrt[-(b^2 - 4*a*c)^2]*d*f^2*i^2*Log[a + E^(h + i*x)*(b + c*E^(h + i*x))] + 6*(Sqrt[-(b^2 - 4*a*c)^2]*d + b*Sqrt[-b^2 + 4*a*c]*d - 2*a*Sqrt[-b^2 + 4*a*c]*e)*g*i*(f + g*x)*PolyLog[2, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] + 6*(Sqrt[-(b^2 - 4*a*c)^2]*d - b*Sqrt[-b^2 + 4*a*c]*d + 2*a*Sqrt[-b^2 + 4*a*c]*e)*g*i*(f + g*x)*PolyLog[2, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 6*Sqrt[-(b^2 - 4*a*c)^2]*d*g^2*PolyLog[3, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] - 6*b*Sqrt[-b^2 + 4*a*c]*d*g^2*PolyLog[3, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] + 12*a*Sqrt[-b^2 + 4*a*c]*e*g^2*PolyLog[3, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] - 6*Sqrt[-(b^2 - 4*a*c)^2]*d*g^2*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 6*b*Sqrt[-b^2 + 4*a*c]*d*g^2*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - 12*a*Sqrt[-b^2 + 4*a*c]*e*g^2*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/(a*Sqrt[-(b^2 - 4*a*c)^2]*i^3)","B",1
574,1,677,428,1.750629,"\int \frac{\left(d+e e^{h+i x}\right) (f+g x)}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx","Integrate[((d + e*E^(h + i*x))*(f + g*x))/(a + b*E^(h + i*x) + c*E^(2*h + 2*i*x)),x]","-\frac{i \left(d f \sqrt{-\left(b^2-4 a c\right)^2} \log \left(a+e^{h+i x} \left(b+c e^{h+i x}\right)\right)+2 b d f \sqrt{b^2-4 a c} \tan ^{-1}\left(\frac{b+2 c e^{h+i x}}{\sqrt{4 a c-b^2}}\right)-2 d f i x \sqrt{-\left(b^2-4 a c\right)^2}+d g x \sqrt{-\left(b^2-4 a c\right)^2} \log \left(\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}+1\right)+b d g x \sqrt{4 a c-b^2} \log \left(\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}+1\right)+d g x \sqrt{-\left(b^2-4 a c\right)^2} \log \left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}+1\right)-b d g x \sqrt{4 a c-b^2} \log \left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}+1\right)+d g i x^2 \left(-\sqrt{-\left(b^2-4 a c\right)^2}\right)+4 a e f \sqrt{4 a c-b^2} \tanh ^{-1}\left(\frac{b+2 c e^{h+i x}}{\sqrt{b^2-4 a c}}\right)-2 a e g x \sqrt{4 a c-b^2} \log \left(\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}+1\right)+2 a e g x \sqrt{4 a c-b^2} \log \left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}+1\right)\right)+g \left(d \sqrt{-\left(b^2-4 a c\right)^2}+b d \sqrt{4 a c-b^2}-2 a e \sqrt{4 a c-b^2}\right) \text{Li}_2\left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}-b}\right)+g \left(d \sqrt{-\left(b^2-4 a c\right)^2}-b d \sqrt{4 a c-b^2}+2 a e \sqrt{4 a c-b^2}\right) \text{Li}_2\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right)}{2 a i^2 \sqrt{-\left(b^2-4 a c\right)^2}}","-\frac{(f+g x) \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \log \left(\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}+1\right)}{i \left(b-\sqrt{b^2-4 a c}\right)}-\frac{(f+g x) \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \log \left(\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}+1\right)}{i \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(f+g x)^2 \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right)}{2 g \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(f+g x)^2 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right)}{2 g \left(b-\sqrt{b^2-4 a c}\right)}-\frac{g \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{Li}_2\left(-\frac{2 c e^{h+i x}}{b-\sqrt{b^2-4 a c}}\right)}{i^2 \left(b-\sqrt{b^2-4 a c}\right)}-\frac{g \left(e-\frac{2 c d-b e}{\sqrt{b^2-4 a c}}\right) \text{Li}_2\left(-\frac{2 c e^{h+i x}}{b+\sqrt{b^2-4 a c}}\right)}{i^2 \left(\sqrt{b^2-4 a c}+b\right)}",1,"-1/2*(i*(-2*Sqrt[-(b^2 - 4*a*c)^2]*d*f*i*x - Sqrt[-(b^2 - 4*a*c)^2]*d*g*i*x^2 + 2*b*Sqrt[b^2 - 4*a*c]*d*f*ArcTan[(b + 2*c*E^(h + i*x))/Sqrt[-b^2 + 4*a*c]] + 4*a*Sqrt[-b^2 + 4*a*c]*e*f*ArcTanh[(b + 2*c*E^(h + i*x))/Sqrt[b^2 - 4*a*c]] + Sqrt[-(b^2 - 4*a*c)^2]*d*g*x*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + b*Sqrt[-b^2 + 4*a*c]*d*g*x*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] - 2*a*Sqrt[-b^2 + 4*a*c]*e*g*x*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])] + Sqrt[-(b^2 - 4*a*c)^2]*d*g*x*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] - b*Sqrt[-b^2 + 4*a*c]*d*g*x*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + 2*a*Sqrt[-b^2 + 4*a*c]*e*g*x*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])] + Sqrt[-(b^2 - 4*a*c)^2]*d*f*Log[a + E^(h + i*x)*(b + c*E^(h + i*x))]) + (Sqrt[-(b^2 - 4*a*c)^2]*d + b*Sqrt[-b^2 + 4*a*c]*d - 2*a*Sqrt[-b^2 + 4*a*c]*e)*g*PolyLog[2, (2*c*E^(h + i*x))/(-b + Sqrt[b^2 - 4*a*c])] + (Sqrt[-(b^2 - 4*a*c)^2]*d - b*Sqrt[-b^2 + 4*a*c]*d + 2*a*Sqrt[-b^2 + 4*a*c]*e)*g*PolyLog[2, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/(a*Sqrt[-(b^2 - 4*a*c)^2]*i^2)","A",1
575,1,94,95,0.1699798,"\int \frac{d+e e^{h+i x}}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx","Integrate[(d + e*E^(h + i*x))/(a + b*E^(h + i*x) + c*E^(2*h + 2*i*x)),x]","-\frac{\frac{2 (b d-2 a e) \tan ^{-1}\left(\frac{b+2 c e^{h+i x}}{\sqrt{4 a c-b^2}}\right)}{i \sqrt{4 a c-b^2}}+\frac{d \log \left(a+e^{h+i x} \left(b+c e^{h+i x}\right)\right)}{i}-2 d x}{2 a}","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c e^{h+i x}}{\sqrt{b^2-4 a c}}\right)}{a i \sqrt{b^2-4 a c}}-\frac{d \log \left(a+b e^{h+i x}+c e^{2 h+2 i x}\right)}{2 a i}+\frac{d x}{a}",1,"-1/2*(-2*d*x + (2*(b*d - 2*a*e)*ArcTan[(b + 2*c*E^(h + i*x))/Sqrt[-b^2 + 4*a*c]])/(Sqrt[-b^2 + 4*a*c]*i) + (d*Log[a + E^(h + i*x)*(b + c*E^(h + i*x))])/i)/a","A",1
576,0,0,84,0.4363928,"\int \frac{d+e e^{h+i x}}{\left(a+b e^{h+i x}+c e^{2 h+2 i x}\right) (f+g x)} \, dx","Integrate[(d + e*E^(h + i*x))/((a + b*E^(h + i*x) + c*E^(2*h + 2*i*x))*(f + g*x)),x]","\int \frac{d+e e^{h+i x}}{\left(a+b e^{h+i x}+c e^{2 h+2 i x}\right) (f+g x)} \, dx","d \text{Int}\left(\frac{1}{(f+g x) \left(a+b e^{h+i x}+c e^{2 h+2 i x}\right)},x\right)+e \text{Int}\left(\frac{e^{h+i x}}{(f+g x) \left(a+b e^{h+i x}+c e^{2 h+2 i x}\right)},x\right)",0,"Integrate[(d + e*E^(h + i*x))/((a + b*E^(h + i*x) + c*E^(2*h + 2*i*x))*(f + g*x)), x]","A",-1
577,0,0,84,6.0076256,"\int \frac{d+e e^{h+i x}}{\left(a+b e^{h+i x}+c e^{2 h+2 i x}\right) (f+g x)^2} \, dx","Integrate[(d + e*E^(h + i*x))/((a + b*E^(h + i*x) + c*E^(2*h + 2*i*x))*(f + g*x)^2),x]","\int \frac{d+e e^{h+i x}}{\left(a+b e^{h+i x}+c e^{2 h+2 i x}\right) (f+g x)^2} \, dx","d \text{Int}\left(\frac{1}{(f+g x)^2 \left(a+b e^{h+i x}+c e^{2 h+2 i x}\right)},x\right)+e \text{Int}\left(\frac{e^{h+i x}}{(f+g x)^2 \left(a+b e^{h+i x}+c e^{2 h+2 i x}\right)},x\right)",0,"Integrate[(d + e*E^(h + i*x))/((a + b*E^(h + i*x) + c*E^(2*h + 2*i*x))*(f + g*x)^2), x]","A",-1
578,1,398,150,0.4329218,"\int \frac{\left(b e-a e e^{c+d x}\right) x}{b e-2 a e e^{c+d x}-b e e^{2 (c+d x)}} \, dx","Integrate[((b*e - a*e*E^(c + d*x))*x)/(b*e - 2*a*e*E^(c + d*x) - b*e*E^(2*(c + d*x))),x]","\frac{\left(\sqrt{a^2+b^2}+a\right) \text{Li}_2\left(\frac{\left(\sqrt{a^2+b^2}-a\right) e^{-c-d x}}{b}\right)+\left(\sqrt{a^2+b^2}-a\right) \text{Li}_2\left(-\frac{\left(a+\sqrt{a^2+b^2}\right) e^{-c-d x}}{b}\right)+a \text{Li}_2\left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}-a}\right)-a \text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)-a d x \log \left(\frac{\left(a-\sqrt{a^2+b^2}\right) e^{-c-d x}}{b}+1\right)-d x \sqrt{a^2+b^2} \log \left(\frac{\left(a-\sqrt{a^2+b^2}\right) e^{-c-d x}}{b}+1\right)+a d x \log \left(\frac{\left(\sqrt{a^2+b^2}+a\right) e^{-c-d x}}{b}+1\right)-d x \sqrt{a^2+b^2} \log \left(\frac{\left(\sqrt{a^2+b^2}+a\right) e^{-c-d x}}{b}+1\right)+a d x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)-a d x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{2 d^2 \sqrt{a^2+b^2}}","-\frac{\text{Li}_2\left(-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{2 d^2}-\frac{\text{Li}_2\left(-\frac{b e^{c+d x}}{a+\sqrt{a^2+b^2}}\right)}{2 d^2}-\frac{x \log \left(\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}+1\right)}{2 d}-\frac{x \log \left(\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}+1\right)}{2 d}+\frac{x^2}{2}",1,"(-(a*d*x*Log[1 + ((a - Sqrt[a^2 + b^2])*E^(-c - d*x))/b]) - Sqrt[a^2 + b^2]*d*x*Log[1 + ((a - Sqrt[a^2 + b^2])*E^(-c - d*x))/b] + a*d*x*Log[1 + ((a + Sqrt[a^2 + b^2])*E^(-c - d*x))/b] - Sqrt[a^2 + b^2]*d*x*Log[1 + ((a + Sqrt[a^2 + b^2])*E^(-c - d*x))/b] + a*d*x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])] - a*d*x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])] + (a + Sqrt[a^2 + b^2])*PolyLog[2, ((-a + Sqrt[a^2 + b^2])*E^(-c - d*x))/b] + (-a + Sqrt[a^2 + b^2])*PolyLog[2, -(((a + Sqrt[a^2 + b^2])*E^(-c - d*x))/b)] + a*PolyLog[2, (b*E^(c + d*x))/(-a + Sqrt[a^2 + b^2])] - a*PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))])/(2*Sqrt[a^2 + b^2]*d^2)","B",1
579,1,85,65,0.1801721,"\int F^{a+b \log \left(c+d x^n\right)} x^2 \, dx","Integrate[F^(a + b*Log[c + d*x^n])*x^2,x]","-\frac{x^3 \left(-\frac{d x^n}{c}\right)^{-3/n} \left(c+d x^n\right) F^{a+b \log \left(c+d x^n\right)} \, _2F_1\left(\frac{n-3}{n},b \log (F)+1;b \log (F)+2;\frac{d x^n}{c}+1\right)}{c n (b \log (F)+1)}","\frac{1}{3} x^3 F^a \left(c+d x^n\right)^{b \log (F)} \left(\frac{d x^n}{c}+1\right)^{-b \log (F)} \, _2F_1\left(\frac{3}{n},-b \log (F);\frac{n+3}{n};-\frac{d x^n}{c}\right)",1,"-((F^(a + b*Log[c + d*x^n])*x^3*(c + d*x^n)*Hypergeometric2F1[(-3 + n)/n, 1 + b*Log[F], 2 + b*Log[F], 1 + (d*x^n)/c])/(c*n*(-((d*x^n)/c))^(3/n)*(1 + b*Log[F])))","A",1
580,1,85,65,0.1133696,"\int F^{a+b \log \left(c+d x^n\right)} x \, dx","Integrate[F^(a + b*Log[c + d*x^n])*x,x]","-\frac{x^2 \left(-\frac{d x^n}{c}\right)^{-2/n} \left(c+d x^n\right) F^{a+b \log \left(c+d x^n\right)} \, _2F_1\left(\frac{n-2}{n},b \log (F)+1;b \log (F)+2;\frac{d x^n}{c}+1\right)}{c n (b \log (F)+1)}","\frac{1}{2} x^2 F^a \left(c+d x^n\right)^{b \log (F)} \left(\frac{d x^n}{c}+1\right)^{-b \log (F)} \, _2F_1\left(\frac{2}{n},-b \log (F);\frac{n+2}{n};-\frac{d x^n}{c}\right)",1,"-((F^(a + b*Log[c + d*x^n])*x^2*(c + d*x^n)*Hypergeometric2F1[(-2 + n)/n, 1 + b*Log[F], 2 + b*Log[F], 1 + (d*x^n)/c])/(c*n*(-((d*x^n)/c))^(2/n)*(1 + b*Log[F])))","A",1
581,1,83,56,0.0922,"\int F^{a+b \log \left(c+d x^n\right)} \, dx","Integrate[F^(a + b*Log[c + d*x^n]),x]","-\frac{x \left(-\frac{d x^n}{c}\right)^{-1/n} \left(c+d x^n\right) F^{a+b \log \left(c+d x^n\right)} \, _2F_1\left(\frac{n-1}{n},b \log (F)+1;b \log (F)+2;\frac{d x^n}{c}+1\right)}{c n (b \log (F)+1)}","x F^a \left(c+d x^n\right)^{b \log (F)} \left(\frac{d x^n}{c}+1\right)^{-b \log (F)} \, _2F_1\left(\frac{1}{n},-b \log (F);1+\frac{1}{n};-\frac{d x^n}{c}\right)",1,"-((F^(a + b*Log[c + d*x^n])*x*(c + d*x^n)*Hypergeometric2F1[(-1 + n)/n, 1 + b*Log[F], 2 + b*Log[F], 1 + (d*x^n)/c])/(c*n*(-((d*x^n)/c))^n^(-1)*(1 + b*Log[F])))","A",1
582,1,50,57,0.1057163,"\int \frac{F^{a+b \log \left(c+d x^n\right)}}{x} \, dx","Integrate[F^(a + b*Log[c + d*x^n])/x,x]","-\frac{F^{a+b \log \left(c+d x^n\right)} \left(\, _2F_1\left(1,b \log (F);b \log (F)+1;\frac{d x^n}{c}+1\right)-1\right)}{b n \log (F)}","-\frac{F^a \left(c+d x^n\right)^{b \log (F)+1} \, _2F_1\left(1,b \log (F)+1;b \log (F)+2;\frac{d x^n}{c}+1\right)}{c n (b \log (F)+1)}",1,"-((F^(a + b*Log[c + d*x^n])*(-1 + Hypergeometric2F1[1, b*Log[F], 1 + b*Log[F], 1 + (d*x^n)/c]))/(b*n*Log[F]))","A",1
583,1,81,66,0.1229372,"\int \frac{F^{a+b \log \left(c+d x^n\right)}}{x^2} \, dx","Integrate[F^(a + b*Log[c + d*x^n])/x^2,x]","-\frac{\left(-\frac{d x^n}{c}\right)^{\frac{1}{n}} \left(c+d x^n\right) F^{a+b \log \left(c+d x^n\right)} \, _2F_1\left(1+\frac{1}{n},b \log (F)+1;b \log (F)+2;\frac{d x^n}{c}+1\right)}{c n x (b \log (F)+1)}","-\frac{F^a \left(c+d x^n\right)^{b \log (F)} \left(\frac{d x^n}{c}+1\right)^{-b \log (F)} \, _2F_1\left(-\frac{1}{n},-b \log (F);-\frac{1-n}{n};-\frac{d x^n}{c}\right)}{x}",1,"-((F^(a + b*Log[c + d*x^n])*(-((d*x^n)/c))^n^(-1)*(c + d*x^n)*Hypergeometric2F1[1 + n^(-1), 1 + b*Log[F], 2 + b*Log[F], 1 + (d*x^n)/c])/(c*n*x*(1 + b*Log[F])))","A",1
584,1,85,68,0.1235678,"\int \frac{F^{a+b \log \left(c+d x^n\right)}}{x^3} \, dx","Integrate[F^(a + b*Log[c + d*x^n])/x^3,x]","-\frac{\left(-\frac{d x^n}{c}\right)^{2/n} \left(c+d x^n\right) F^{a+b \log \left(c+d x^n\right)} \, _2F_1\left(\frac{n+2}{n},b \log (F)+1;b \log (F)+2;\frac{d x^n}{c}+1\right)}{c n x^2 (b \log (F)+1)}","-\frac{F^a \left(c+d x^n\right)^{b \log (F)} \left(\frac{d x^n}{c}+1\right)^{-b \log (F)} \, _2F_1\left(-\frac{2}{n},-b \log (F);-\frac{2-n}{n};-\frac{d x^n}{c}\right)}{2 x^2}",1,"-((F^(a + b*Log[c + d*x^n])*(-((d*x^n)/c))^(2/n)*(c + d*x^n)*Hypergeometric2F1[(2 + n)/n, 1 + b*Log[F], 2 + b*Log[F], 1 + (d*x^n)/c])/(c*n*x^2*(1 + b*Log[F])))","A",1
585,1,94,77,0.166129,"\int F^{a+b \log \left(c+d x^n\right)} (d x)^m \, dx","Integrate[F^(a + b*Log[c + d*x^n])*(d*x)^m,x]","-\frac{x (d x)^m \left(c+d x^n\right) \left(-\frac{d x^n}{c}\right)^{-\frac{m+1}{n}} F^{a+b \log \left(c+d x^n\right)} \, _2F_1\left(1-\frac{m+1}{n},b \log (F)+1;b \log (F)+2;\frac{d x^n}{c}+1\right)}{c n (b \log (F)+1)}","\frac{F^a (d x)^{m+1} \left(c+d x^n\right)^{b \log (F)} \left(\frac{d x^n}{c}+1\right)^{-b \log (F)} \, _2F_1\left(\frac{m+1}{n},-b \log (F);\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{d (m+1)}",1,"-((F^(a + b*Log[c + d*x^n])*x*(d*x)^m*(c + d*x^n)*Hypergeometric2F1[1 - (1 + m)/n, 1 + b*Log[F], 2 + b*Log[F], 1 + (d*x^n)/c])/(c*n*(-((d*x^n)/c))^((1 + m)/n)*(1 + b*Log[F])))","A",1
586,0,0,76,0.0903409,"\int e^{\log ^2\left((d+e x)^n\right)} (d+e x)^m \, dx","Integrate[E^Log[(d + e*x)^n]^2*(d + e*x)^m,x]","\int e^{\log ^2\left((d+e x)^n\right)} (d+e x)^m \, dx","\frac{\sqrt{\pi } e^{-\frac{(m+1)^2}{4 n^2}} (d+e x)^{m+1} \left((d+e x)^n\right)^{-\frac{m+1}{n}} \text{erfi}\left(\frac{2 n \log \left((d+e x)^n\right)+m+1}{2 n}\right)}{2 e n}",1,"Integrate[E^Log[(d + e*x)^n]^2*(d + e*x)^m, x]","F",-1
587,0,0,137,0.1666686,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (d g+e g x)^m \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(d*g + e*g*x)^m,x]","\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (d g+e g x)^m \, dx","\frac{\sqrt{\pi } F^{a f} (d g+e g x)^{m+1} e^{-\frac{(m+1)^2}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-\frac{m+1}{n}} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+m+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} g n \sqrt{\log (F)}}",1,"Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(d*g + e*g*x)^m, x]","F",-1
588,1,123,123,0.2484601,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (d g+e g x)^2 \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(d*g + e*g*x)^2,x]","\frac{\sqrt{\pi } g^2 F^{a f} (d+e x)^3 e^{-\frac{9}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-3/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+3}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } g^2 F^{a f} (d+e x)^3 e^{-\frac{9}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-3/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+3}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} n \sqrt{\log (F)}}",1,"(F^(a*f)*g^2*Sqrt[Pi]*(d + e*x)^3*Erfi[(3 + 2*b*f*n*Log[F]*Log[c*(d + e*x)^n])/(2*Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])])/(2*Sqrt[b]*e*E^(9/(4*b*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^(3/n)*Sqrt[Log[F]])","A",1
589,1,115,115,0.5600484,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (d g+e g x) \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(d*g + e*g*x),x]","\frac{\sqrt{\pi } g F^{a f} (d+e x)^2 e^{-\frac{1}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-2/n} \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)+1}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } g F^{a f} (d+e x)^2 e^{-\frac{1}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-2/n} \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)+1}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} n \sqrt{\log (F)}}",1,"(F^(a*f)*g*Sqrt[Pi]*(d + e*x)^2*Erfi[(1 + b*f*n*Log[F]*Log[c*(d + e*x)^n])/(Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])])/(2*Sqrt[b]*e*E^(1/(b*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^(2/n)*Sqrt[Log[F]])","A",1
590,1,118,118,0.1087702,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2)),x]","\frac{\sqrt{\pi } F^{a f} (d+e x) e^{-\frac{1}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-1/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } F^{a f} (d+e x) e^{-\frac{1}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-1/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} n \sqrt{\log (F)}}",1,"(F^(a*f)*Sqrt[Pi]*(d + e*x)*Erfi[(1 + 2*b*f*n*Log[F]*Log[c*(d + e*x)^n])/(2*Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])])/(2*Sqrt[b]*e*E^(1/(4*b*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^n^(-1)*Sqrt[Log[F]])","A",1
591,1,67,67,0.0508956,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{d g+e g x} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(d*g + e*g*x),x]","\frac{\sqrt{\pi } F^{a f} \text{erfi}\left(\sqrt{b} \sqrt{f} \sqrt{\log (F)} \log \left(c (d+e x)^n\right)\right)}{2 \sqrt{b} e \sqrt{f} g n \sqrt{\log (F)}}","\frac{\sqrt{\pi } F^{a f} \text{erfi}\left(\sqrt{b} \sqrt{f} \sqrt{\log (F)} \log \left(c (d+e x)^n\right)\right)}{2 \sqrt{b} e \sqrt{f} g n \sqrt{\log (F)}}",1,"(F^(a*f)*Sqrt[Pi]*Erfi[Sqrt[b]*Sqrt[f]*Sqrt[Log[F]]*Log[c*(d + e*x)^n]])/(2*Sqrt[b]*e*Sqrt[f]*g*n*Sqrt[Log[F]])","A",1
592,1,121,121,0.2125125,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(d g+e g x)^2} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(d*g + e*g*x)^2,x]","\frac{\sqrt{\pi } F^{a f} e^{-\frac{1}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)-1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} g^2 n \sqrt{\log (F)} (d+e x)}","-\frac{\sqrt{\pi } F^{a f} e^{-\frac{1}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{erfi}\left(\frac{1-2 b f n \log (F) \log \left(c (d+e x)^n\right)}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} g^2 n \sqrt{\log (F)} (d+e x)}",1,"(F^(a*f)*Sqrt[Pi]*(c*(d + e*x)^n)^n^(-1)*Erfi[(-1 + 2*b*f*n*Log[F]*Log[c*(d + e*x)^n])/(2*Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])])/(2*Sqrt[b]*e*E^(1/(4*b*f*n^2*Log[F]))*Sqrt[f]*g^2*n*(d + e*x)*Sqrt[Log[F]])","A",1
593,1,117,118,0.2132582,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(d g+e g x)^3} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(d*g + e*g*x)^3,x]","\frac{\sqrt{\pi } F^{a f} e^{-\frac{1}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{2/n} \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)-1}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} g^3 n \sqrt{\log (F)} (d+e x)^2}","-\frac{\sqrt{\pi } F^{a f} e^{-\frac{1}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{2/n} \text{erfi}\left(\frac{1-b f n \log (F) \log \left(c (d+e x)^n\right)}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} g^3 n \sqrt{\log (F)} (d+e x)^2}",1,"(F^(a*f)*Sqrt[Pi]*(c*(d + e*x)^n)^(2/n)*Erfi[(-1 + b*f*n*Log[F]*Log[c*(d + e*x)^n])/(Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])])/(2*Sqrt[b]*e*E^(1/(b*f*n^2*Log[F]))*Sqrt[f]*g^3*n*(d + e*x)^2*Sqrt[Log[F]])","A",1
594,0,0,31,1.817047,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x)^m \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(g + h*x)^m,x]","\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x)^m \, dx","\text{Int}\left((g+h x)^m F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)},x\right)",0,"Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(g + h*x)^m, x]","A",-1
595,1,396,502,1.5927928,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x)^3 \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(g + h*x)^3,x]","\frac{\sqrt{\pi } F^{a f} (d+e x) e^{-\frac{4}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-4/n} \left((e g-d h) e^{\frac{7}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \left((e g-d h)^2 e^{\frac{2}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{2/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)+3 h^2 (d+e x)^2 \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+3}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)\right)+3 h (d+e x) (e g-d h)^2 e^{\frac{3}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{2/n} \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)+1}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)+h^3 (d+e x)^3 \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)+2}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)\right)}{2 \sqrt{b} e^4 \sqrt{f} n \sqrt{\log (F)}}","\frac{3 \sqrt{\pi } h^2 F^{a f} (d+e x)^3 (e g-d h) e^{-\frac{9}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-3/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+3}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e^4 \sqrt{f} n \sqrt{\log (F)}}+\frac{3 \sqrt{\pi } h F^{a f} (d+e x)^2 (e g-d h)^2 e^{-\frac{1}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-2/n} \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)+1}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e^4 \sqrt{f} n \sqrt{\log (F)}}+\frac{\sqrt{\pi } F^{a f} (d+e x) (e g-d h)^3 e^{-\frac{1}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-1/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e^4 \sqrt{f} n \sqrt{\log (F)}}+\frac{\sqrt{\pi } h^3 F^{a f} (d+e x)^4 e^{-\frac{4}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-4/n} \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)+2}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e^4 \sqrt{f} n \sqrt{\log (F)}}",1,"(F^(a*f)*Sqrt[Pi]*(d + e*x)*(3*E^(3/(b*f*n^2*Log[F]))*h*(e*g - d*h)^2*(d + e*x)*(c*(d + e*x)^n)^(2/n)*Erfi[(1 + b*f*n*Log[F]*Log[c*(d + e*x)^n])/(Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])] + h^3*(d + e*x)^3*Erfi[(2 + b*f*n*Log[F]*Log[c*(d + e*x)^n])/(Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])] + E^(7/(4*b*f*n^2*Log[F]))*(e*g - d*h)*(c*(d + e*x)^n)^n^(-1)*(E^(2/(b*f*n^2*Log[F]))*(e*g - d*h)^2*(c*(d + e*x)^n)^(2/n)*Erfi[(1 + 2*b*f*n*Log[F]*Log[c*(d + e*x)^n])/(2*Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])] + 3*h^2*(d + e*x)^2*Erfi[(3 + 2*b*f*n*Log[F]*Log[c*(d + e*x)^n])/(2*Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])])))/(2*Sqrt[b]*e^4*E^(4/(b*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^(4/n)*Sqrt[Log[F]])","A",1
596,1,303,372,0.8147411,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x)^2 \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(g + h*x)^2,x]","\frac{\sqrt{\pi } F^{a f} (d+e x) e^{-\frac{9}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-3/n} \left((e g-d h)^2 e^{\frac{2}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{2/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)-2 h (d+e x) (d h-e g) e^{\frac{5}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)+1}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)+h^2 (d+e x)^2 \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+3}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)\right)}{2 \sqrt{b} e^3 \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } h F^{a f} (d+e x)^2 (e g-d h) e^{-\frac{1}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-2/n} \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)+1}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{\sqrt{b} e^3 \sqrt{f} n \sqrt{\log (F)}}+\frac{\sqrt{\pi } F^{a f} (d+e x) (e g-d h)^2 e^{-\frac{1}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-1/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e^3 \sqrt{f} n \sqrt{\log (F)}}+\frac{\sqrt{\pi } h^2 F^{a f} (d+e x)^3 e^{-\frac{9}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-3/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+3}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e^3 \sqrt{f} n \sqrt{\log (F)}}",1,"(F^(a*f)*Sqrt[Pi]*(d + e*x)*(-2*E^(5/(4*b*f*n^2*Log[F]))*h*(-(e*g) + d*h)*(d + e*x)*(c*(d + e*x)^n)^n^(-1)*Erfi[(1 + b*f*n*Log[F]*Log[c*(d + e*x)^n])/(Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])] + E^(2/(b*f*n^2*Log[F]))*(e*g - d*h)^2*(c*(d + e*x)^n)^(2/n)*Erfi[(1 + 2*b*f*n*Log[F]*Log[c*(d + e*x)^n])/(2*Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])] + h^2*(d + e*x)^2*Erfi[(3 + 2*b*f*n*Log[F]*Log[c*(d + e*x)^n])/(2*Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])]))/(2*Sqrt[b]*e^3*E^(9/(4*b*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^(3/n)*Sqrt[Log[F]])","A",1
597,1,204,242,0.3851765,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x) \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(g + h*x),x]","\frac{\sqrt{\pi } F^{a f} (d+e x) e^{-\frac{1}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-2/n} \left((e g-d h) e^{\frac{3}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{\frac{1}{n}} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)+h (d+e x) \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)+1}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)\right)}{2 \sqrt{b} e^2 \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } F^{a f} (d+e x) (e g-d h) e^{-\frac{1}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-1/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e^2 \sqrt{f} n \sqrt{\log (F)}}+\frac{\sqrt{\pi } h F^{a f} (d+e x)^2 e^{-\frac{1}{b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-2/n} \text{erfi}\left(\frac{b f n \log (F) \log \left(c (d+e x)^n\right)+1}{\sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e^2 \sqrt{f} n \sqrt{\log (F)}}",1,"(F^(a*f)*Sqrt[Pi]*(d + e*x)*(h*(d + e*x)*Erfi[(1 + b*f*n*Log[F]*Log[c*(d + e*x)^n])/(Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])] + E^(3/(4*b*f*n^2*Log[F]))*(e*g - d*h)*(c*(d + e*x)^n)^n^(-1)*Erfi[(1 + 2*b*f*n*Log[F]*Log[c*(d + e*x)^n])/(2*Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])]))/(2*Sqrt[b]*e^2*E^(1/(b*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^(2/n)*Sqrt[Log[F]])","A",1
598,1,118,118,0.0249301,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2)),x]","\frac{\sqrt{\pi } F^{a f} (d+e x) e^{-\frac{1}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-1/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } F^{a f} (d+e x) e^{-\frac{1}{4 b f n^2 \log (F)}} \left(c (d+e x)^n\right)^{-1/n} \text{erfi}\left(\frac{2 b f n \log (F) \log \left(c (d+e x)^n\right)+1}{2 \sqrt{b} \sqrt{f} n \sqrt{\log (F)}}\right)}{2 \sqrt{b} e \sqrt{f} n \sqrt{\log (F)}}",1,"(F^(a*f)*Sqrt[Pi]*(d + e*x)*Erfi[(1 + 2*b*f*n*Log[F]*Log[c*(d + e*x)^n])/(2*Sqrt[b]*Sqrt[f]*n*Sqrt[Log[F]])])/(2*Sqrt[b]*e*E^(1/(4*b*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^n^(-1)*Sqrt[Log[F]])","A",1
599,0,0,31,0.5226133,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{g+h x} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(g + h*x),x]","\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{g+h x} \, dx","\text{Int}\left(\frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{g+h x},x\right)",0,"Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(g + h*x), x]","A",-1
600,0,0,31,2.6314045,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(g+h x)^2} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(g + h*x)^2,x]","\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(g+h x)^2} \, dx","\text{Int}\left(\frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(g+h x)^2},x\right)",0,"Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(g + h*x)^2, x]","A",-1
601,0,0,31,3.4205553,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(g+h x)^3} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(g + h*x)^3,x]","\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(g+h x)^3} \, dx","\text{Int}\left(\frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(g+h x)^3},x\right)",0,"Integrate[F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(g + h*x)^3, x]","A",-1
602,0,0,153,0.2501998,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (d g+e g x)^m \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(d*g + e*g*x)^m,x]","\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (d g+e g x)^m \, dx","\frac{\sqrt{\pi } F^{a^2 f} (d+e x) (d g+e g x)^m \left(c (d+e x)^n\right)^{-\frac{m+1}{n}} \exp \left(-\frac{(2 a b f n \log (F)+m+1)^2}{4 b^2 f n^2 \log (F)}\right) \text{erfi}\left(\frac{2 a b f n \log (F)+2 b^2 f n \log (F) \log \left(c (d+e x)^n\right)+m+1}{2 b \sqrt{f} n \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} n \sqrt{\log (F)}}",1,"Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(d*g + e*g*x)^m, x]","F",-1
603,1,129,133,0.3574932,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (d g+e g x)^2 \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(d*g + e*g*x)^2,x]","\frac{\sqrt{\pi } g^2 \text{erfi}\left(\frac{2 b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+3}{2 b \sqrt{f} n \sqrt{\log (F)}}\right) \exp \left(-\frac{3 \left(4 b f n \log (F) \left(a+b \left(\log \left(c (d+e x)^n\right)-n \log (d+e x)\right)\right)+3\right)}{4 b^2 f n^2 \log (F)}\right)}{2 b e \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } g^2 (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \exp \left(-\frac{3 (4 a b f n \log (F)+3)}{4 b^2 f n^2 \log (F)}\right) \text{erfi}\left(\frac{2 a b f \log (F)+2 b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{3}{n}}{2 b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} n \sqrt{\log (F)}}",1,"(g^2*Sqrt[Pi]*Erfi[(3 + 2*b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(2*b*Sqrt[f]*n*Sqrt[Log[F]])])/(2*b*e*E^((3*(3 + 4*b*f*n*Log[F]*(a + b*(-(n*Log[d + e*x]) + Log[c*(d + e*x)^n]))))/(4*b^2*f*n^2*Log[F]))*Sqrt[f]*n*Sqrt[Log[F]])","A",1
604,1,120,122,0.7261101,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (d g+e g x) \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(d*g + e*g*x),x]","\frac{\sqrt{\pi } g (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} e^{-\frac{2 a b f n \log (F)+1}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+1}{b \sqrt{f} n \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } g (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} e^{-\frac{2 a b f n \log (F)+1}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{a b f \log (F)+b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} n \sqrt{\log (F)}}",1,"(g*Sqrt[Pi]*(d + e*x)^2*Erfi[(1 + b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(b*Sqrt[f]*n*Sqrt[Log[F]])])/(2*b*e*E^((1 + 2*a*b*f*n*Log[F])/(b^2*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^(2/n)*Sqrt[Log[F]])","A",1
605,1,123,126,0.0975922,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2),x]","\frac{\sqrt{\pi } (d+e x) \left(c (d+e x)^n\right)^{-1/n} e^{-\frac{4 a b f n \log (F)+1}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+1}{2 b \sqrt{f} n \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } (d+e x) \left(c (d+e x)^n\right)^{-1/n} e^{-\frac{4 a b f n \log (F)+1}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 a b f \log (F)+2 b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{2 b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} n \sqrt{\log (F)}}",1,"(Sqrt[Pi]*(d + e*x)*Erfi[(1 + 2*b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(2*b*Sqrt[f]*n*Sqrt[Log[F]])])/(2*b*e*E^((1 + 4*a*b*f*n*Log[F])/(4*b^2*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^n^(-1)*Sqrt[Log[F]])","A",1
606,1,59,70,0.0480789,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{d g+e g x} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(d*g + e*g*x),x]","\frac{\sqrt{\pi } \text{erfi}\left(\sqrt{f} \sqrt{\log (F)} \left(a+b \log \left(c (d+e x)^n\right)\right)\right)}{2 b e \sqrt{f} g n \sqrt{\log (F)}}","\frac{\sqrt{\pi } \text{erfi}\left(a \sqrt{f} \sqrt{\log (F)}+b \sqrt{f} \sqrt{\log (F)} \log \left(c (d+e x)^n\right)\right)}{2 b e \sqrt{f} g n \sqrt{\log (F)}}",1,"(Sqrt[Pi]*Erfi[Sqrt[f]*Sqrt[Log[F]]*(a + b*Log[c*(d + e*x)^n])])/(2*b*e*Sqrt[f]*g*n*Sqrt[Log[F]])","A",1
607,1,126,128,0.2622165,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(d g+e g x)^2} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(d*g + e*g*x)^2,x]","\frac{\sqrt{\pi } \left(c (d+e x)^n\right)^{\frac{1}{n}} e^{\frac{4 a b f n \log (F)-1}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)-1}{2 b \sqrt{f} n \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} g^2 n \sqrt{\log (F)} (d+e x)}","-\frac{\sqrt{\pi } \left(c (d+e x)^n\right)^{\frac{1}{n}} e^{\frac{a}{b n}-\frac{1}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{-2 a b f \log (F)-2 b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{2 b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} g^2 n \sqrt{\log (F)} (d+e x)}",1,"(E^((-1 + 4*a*b*f*n*Log[F])/(4*b^2*f*n^2*Log[F]))*Sqrt[Pi]*(c*(d + e*x)^n)^n^(-1)*Erfi[(-1 + 2*b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(2*b*Sqrt[f]*n*Sqrt[Log[F]])])/(2*b*e*Sqrt[f]*g^2*n*(d + e*x)*Sqrt[Log[F]])","A",1
608,1,121,126,0.3168771,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(d g+e g x)^3} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(d*g + e*g*x)^3,x]","\frac{\sqrt{\pi } \left(c (d+e x)^n\right)^{2/n} e^{\frac{2 a b f n \log (F)-1}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)-1}{b \sqrt{f} n \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} g^3 n \sqrt{\log (F)} (d+e x)^2}","-\frac{\sqrt{\pi } \left(c (d+e x)^n\right)^{2/n} e^{-\frac{1-2 a b f n \log (F)}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{-a b f \log (F)+b^2 (-f) \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} g^3 n \sqrt{\log (F)} (d+e x)^2}",1,"(E^((-1 + 2*a*b*f*n*Log[F])/(b^2*f*n^2*Log[F]))*Sqrt[Pi]*(c*(d + e*x)^n)^(2/n)*Erfi[(-1 + b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(b*Sqrt[f]*n*Sqrt[Log[F]])])/(2*b*e*Sqrt[f]*g^3*n*(d + e*x)^2*Sqrt[Log[F]])","A",1
609,0,0,31,1.4220974,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x)^m \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(g + h*x)^m,x]","\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x)^m \, dx","\text{Int}\left((g+h x)^m F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2},x\right)",0,"Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(g + h*x)^m, x]","A",-1
610,1,434,535,2.4235757,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x)^3 \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(g + h*x)^3,x]","\frac{\sqrt{\pi } (d+e x) \left(c (d+e x)^n\right)^{-4/n} e^{-\frac{4 (a b f n \log (F)+1)}{b^2 f n^2 \log (F)}} \left((e g-d h) \left(c (d+e x)^n\right)^{\frac{1}{n}} e^{\frac{4 a b f n \log (F)+7}{4 b^2 f n^2 \log (F)}} \left((e g-d h)^2 \left(c (d+e x)^n\right)^{2/n} e^{\frac{2 a b f n \log (F)+2}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+1}{2 b \sqrt{f} n \sqrt{\log (F)}}\right)+3 h^2 (d+e x)^2 \text{erfi}\left(\frac{2 b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+3}{2 b \sqrt{f} n \sqrt{\log (F)}}\right)\right)+3 h (d+e x) (e g-d h)^2 \left(c (d+e x)^n\right)^{2/n} e^{\frac{2 a b f n \log (F)+3}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+1}{b \sqrt{f} n \sqrt{\log (F)}}\right)+h^3 (d+e x)^3 \text{erfi}\left(\frac{b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+2}{b \sqrt{f} n \sqrt{\log (F)}}\right)\right)}{2 b e^4 \sqrt{f} n \sqrt{\log (F)}}","\frac{3 \sqrt{\pi } h^2 (d+e x)^3 (e g-d h) \left(c (d+e x)^n\right)^{-3/n} \exp \left(-\frac{3 (4 a b f n \log (F)+3)}{4 b^2 f n^2 \log (F)}\right) \text{erfi}\left(\frac{2 a b f \log (F)+2 b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{3}{n}}{2 b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e^4 \sqrt{f} n \sqrt{\log (F)}}+\frac{3 \sqrt{\pi } h (d+e x)^2 (e g-d h)^2 \left(c (d+e x)^n\right)^{-2/n} e^{-\frac{2 a b f n \log (F)+1}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{a b f \log (F)+b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e^4 \sqrt{f} n \sqrt{\log (F)}}+\frac{\sqrt{\pi } (d+e x) (e g-d h)^3 \left(c (d+e x)^n\right)^{-1/n} e^{-\frac{4 a b f n \log (F)+1}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 a b f \log (F)+2 b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{2 b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e^4 \sqrt{f} n \sqrt{\log (F)}}+\frac{\sqrt{\pi } h^3 (d+e x)^4 \left(c (d+e x)^n\right)^{-4/n} e^{-\frac{4 (a b f n \log (F)+1)}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{a b f \log (F)+b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{2}{n}}{b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e^4 \sqrt{f} n \sqrt{\log (F)}}",1,"(Sqrt[Pi]*(d + e*x)*(3*E^((3 + 2*a*b*f*n*Log[F])/(b^2*f*n^2*Log[F]))*h*(e*g - d*h)^2*(d + e*x)*(c*(d + e*x)^n)^(2/n)*Erfi[(1 + b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(b*Sqrt[f]*n*Sqrt[Log[F]])] + h^3*(d + e*x)^3*Erfi[(2 + b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(b*Sqrt[f]*n*Sqrt[Log[F]])] + E^((7 + 4*a*b*f*n*Log[F])/(4*b^2*f*n^2*Log[F]))*(e*g - d*h)*(c*(d + e*x)^n)^n^(-1)*(E^((2 + 2*a*b*f*n*Log[F])/(b^2*f*n^2*Log[F]))*(e*g - d*h)^2*(c*(d + e*x)^n)^(2/n)*Erfi[(1 + 2*b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(2*b*Sqrt[f]*n*Sqrt[Log[F]])] + 3*h^2*(d + e*x)^2*Erfi[(3 + 2*b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(2*b*Sqrt[f]*n*Sqrt[Log[F]])])))/(2*b*e^4*E^((4*(1 + a*b*f*n*Log[F]))/(b^2*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^(4/n)*Sqrt[Log[F]])","A",1
611,1,331,397,1.142066,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x)^2 \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(g + h*x)^2,x]","\frac{\sqrt{\pi } (d+e x) \left(c (d+e x)^n\right)^{-3/n} \exp \left(-\frac{3 (4 a b f n \log (F)+3)}{4 b^2 f n^2 \log (F)}\right) \left((e g-d h)^2 \left(c (d+e x)^n\right)^{2/n} e^{\frac{2 a b f n \log (F)+2}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+1}{2 b \sqrt{f} n \sqrt{\log (F)}}\right)-2 h (d+e x) (d h-e g) \left(c (d+e x)^n\right)^{\frac{1}{n}} e^{\frac{4 a b f n \log (F)+5}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+1}{b \sqrt{f} n \sqrt{\log (F)}}\right)+h^2 (d+e x)^2 \text{erfi}\left(\frac{2 b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+3}{2 b \sqrt{f} n \sqrt{\log (F)}}\right)\right)}{2 b e^3 \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } h^2 (d+e x)^3 \left(c (d+e x)^n\right)^{-3/n} \exp \left(-\frac{3 (4 a b f n \log (F)+3)}{4 b^2 f n^2 \log (F)}\right) \text{erfi}\left(\frac{2 a b f \log (F)+2 b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{3}{n}}{2 b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e^3 \sqrt{f} n \sqrt{\log (F)}}+\frac{\sqrt{\pi } h (d+e x)^2 (e g-d h) \left(c (d+e x)^n\right)^{-2/n} e^{-\frac{2 a b f n \log (F)+1}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{a b f \log (F)+b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{b \sqrt{f} \sqrt{\log (F)}}\right)}{b e^3 \sqrt{f} n \sqrt{\log (F)}}+\frac{\sqrt{\pi } (d+e x) (e g-d h)^2 \left(c (d+e x)^n\right)^{-1/n} e^{-\frac{4 a b f n \log (F)+1}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 a b f \log (F)+2 b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{2 b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e^3 \sqrt{f} n \sqrt{\log (F)}}",1,"(Sqrt[Pi]*(d + e*x)*(-2*E^((5 + 4*a*b*f*n*Log[F])/(4*b^2*f*n^2*Log[F]))*h*(-(e*g) + d*h)*(d + e*x)*(c*(d + e*x)^n)^n^(-1)*Erfi[(1 + b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(b*Sqrt[f]*n*Sqrt[Log[F]])] + E^((2 + 2*a*b*f*n*Log[F])/(b^2*f*n^2*Log[F]))*(e*g - d*h)^2*(c*(d + e*x)^n)^(2/n)*Erfi[(1 + 2*b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(2*b*Sqrt[f]*n*Sqrt[Log[F]])] + h^2*(d + e*x)^2*Erfi[(3 + 2*b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(2*b*Sqrt[f]*n*Sqrt[Log[F]])]))/(2*b*e^3*E^((3*(3 + 4*a*b*f*n*Log[F]))/(4*b^2*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^(3/n)*Sqrt[Log[F]])","A",1
612,1,221,257,0.5158117,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x) \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(g + h*x),x]","\frac{\sqrt{\pi } (d+e x) \left(c (d+e x)^n\right)^{-2/n} e^{-\frac{2 a b f n \log (F)+1}{b^2 f n^2 \log (F)}} \left((e g-d h) \left(c (d+e x)^n\right)^{\frac{1}{n}} e^{\frac{4 a b f n \log (F)+3}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+1}{2 b \sqrt{f} n \sqrt{\log (F)}}\right)+h (d+e x) \text{erfi}\left(\frac{b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+1}{b \sqrt{f} n \sqrt{\log (F)}}\right)\right)}{2 b e^2 \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } (d+e x) (e g-d h) \left(c (d+e x)^n\right)^{-1/n} e^{-\frac{4 a b f n \log (F)+1}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 a b f \log (F)+2 b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{2 b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e^2 \sqrt{f} n \sqrt{\log (F)}}+\frac{\sqrt{\pi } h (d+e x)^2 \left(c (d+e x)^n\right)^{-2/n} e^{-\frac{2 a b f n \log (F)+1}{b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{a b f \log (F)+b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e^2 \sqrt{f} n \sqrt{\log (F)}}",1,"(Sqrt[Pi]*(d + e*x)*(h*(d + e*x)*Erfi[(1 + b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(b*Sqrt[f]*n*Sqrt[Log[F]])] + E^((3 + 4*a*b*f*n*Log[F])/(4*b^2*f*n^2*Log[F]))*(e*g - d*h)*(c*(d + e*x)^n)^n^(-1)*Erfi[(1 + 2*b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(2*b*Sqrt[f]*n*Sqrt[Log[F]])]))/(2*b*e^2*E^((1 + 2*a*b*f*n*Log[F])/(b^2*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^(2/n)*Sqrt[Log[F]])","A",1
613,1,123,126,0.0653545,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2),x]","\frac{\sqrt{\pi } (d+e x) \left(c (d+e x)^n\right)^{-1/n} e^{-\frac{4 a b f n \log (F)+1}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 b f n \log (F) \left(a+b \log \left(c (d+e x)^n\right)\right)+1}{2 b \sqrt{f} n \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} n \sqrt{\log (F)}}","\frac{\sqrt{\pi } (d+e x) \left(c (d+e x)^n\right)^{-1/n} e^{-\frac{4 a b f n \log (F)+1}{4 b^2 f n^2 \log (F)}} \text{erfi}\left(\frac{2 a b f \log (F)+2 b^2 f \log (F) \log \left(c (d+e x)^n\right)+\frac{1}{n}}{2 b \sqrt{f} \sqrt{\log (F)}}\right)}{2 b e \sqrt{f} n \sqrt{\log (F)}}",1,"(Sqrt[Pi]*(d + e*x)*Erfi[(1 + 2*b*f*n*Log[F]*(a + b*Log[c*(d + e*x)^n]))/(2*b*Sqrt[f]*n*Sqrt[Log[F]])])/(2*b*e*E^((1 + 4*a*b*f*n*Log[F])/(4*b^2*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^n^(-1)*Sqrt[Log[F]])","A",1
614,0,0,31,0.994752,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{g+h x} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x),x]","\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{g+h x} \, dx","\text{Int}\left(\frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{g+h x},x\right)",0,"Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x), x]","A",-1
615,0,0,31,4.6522639,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(g+h x)^2} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x)^2,x]","\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(g+h x)^2} \, dx","\text{Int}\left(\frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(g+h x)^2},x\right)",0,"Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x)^2, x]","A",-1
616,0,0,31,7.1119219,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(g+h x)^3} \, dx","Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x)^3,x]","\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(g+h x)^3} \, dx","\text{Int}\left(\frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(g+h x)^3},x\right)",0,"Integrate[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x)^3, x]","A",-1
617,1,17,17,0.0566937,"\int F^{a+b x+c x^3} \left(b+3 c x^2\right) \, dx","Integrate[F^(a + b*x + c*x^3)*(b + 3*c*x^2),x]","\frac{F^{a+b x+c x^3}}{\log (F)}","\frac{F^{a+b x+c x^3}}{\log (F)}",1,"F^(a + b*x + c*x^3)/Log[F]","A",1
618,1,19,20,0.4155963,"\int \frac{F^{\frac{1}{a+b x+c x^2}} (b+2 c x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(F^(a + b*x + c*x^2)^(-1)*(b + 2*c*x))/(a + b*x + c*x^2)^2,x]","-\frac{F^{\frac{1}{a+x (b+c x)}}}{\log (F)}","-\frac{F^{\frac{1}{a+b x+c x^2}}}{\log (F)}",1,"-(F^(a + x*(b + c*x))^(-1)/Log[F])","A",1
619,1,44,49,0.0521588,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^m \, dx","Integrate[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^m,x]","(-a-x (b+c x))^{-m} (a+x (b+c x))^m \Gamma (m+1,-a-x (b+c x))","\left(-a-b x-c x^2\right)^{-m} \left(a+b x+c x^2\right)^m \Gamma \left(m+1,-c x^2-b x-a\right)",1,"((a + x*(b + c*x))^m*Gamma[1 + m, -a - x*(b + c*x)])/(-a - x*(b + c*x))^m","A",1
620,1,49,90,0.0378477,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^3 \, dx","Integrate[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^3,x]","e^{a+x (b+c x)} \left((a+x (b+c x))^3-3 (a+x (b+c x))^2+6 (a+x (b+c x))-6\right)","e^{a+b x+c x^2} \left(a+b x+c x^2\right)^3-3 e^{a+b x+c x^2} \left(a+b x+c x^2\right)^2+6 e^{a+b x+c x^2} \left(a+b x+c x^2\right)-6 e^{a+b x+c x^2}",1,"E^(a + x*(b + c*x))*(-6 + 6*(a + x*(b + c*x)) - 3*(a + x*(b + c*x))^2 + (a + x*(b + c*x))^3)","A",1
621,1,36,64,0.033101,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^2 \, dx","Integrate[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^2,x]","e^{a+x (b+c x)} \left((a+x (b+c x))^2-2 (a+x (b+c x))+2\right)","e^{a+b x+c x^2} \left(a+b x+c x^2\right)^2-2 e^{a+b x+c x^2} \left(a+b x+c x^2\right)+2 e^{a+b x+c x^2}",1,"E^(a + x*(b + c*x))*(2 - 2*(a + x*(b + c*x)) + (a + x*(b + c*x))^2)","A",1
622,1,23,38,0.0294266,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right) \, dx","Integrate[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2),x]","e^{a+x (b+c x)} \left(a+b x+c x^2-1\right)","e^{a+b x+c x^2} \left(a+b x+c x^2\right)-e^{a+b x+c x^2}",1,"E^(a + x*(b + c*x))*(-1 + a + b*x + c*x^2)","A",1
623,1,12,12,0.0387132,"\int e^{a+b x+c x^2} (b+2 c x) \, dx","Integrate[E^(a + b*x + c*x^2)*(b + 2*c*x),x]","e^{a+b x+c x^2}","e^{a+b x+c x^2}",1,"E^(a + b*x + c*x^2)","A",1
624,1,10,11,0.0249471,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{a+b x+c x^2} \, dx","Integrate[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2),x]","\text{Ei}(a+x (b+c x))","\text{Ei}\left(a+b x+c x^2\right)",1,"ExpIntegralEi[a + x*(b + c*x)]","A",1
625,1,35,38,0.0546113,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^2} \, dx","Integrate[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^2,x]","\text{Ei}(a+x (b+c x))-\frac{e^{a+x (b+c x)}}{a+x (b+c x)}","\text{Ei}\left(c x^2+b x+a\right)-\frac{e^{a+b x+c x^2}}{a+b x+c x^2}",1,"-(E^(a + x*(b + c*x))/(a + x*(b + c*x))) + ExpIntegralEi[a + x*(b + c*x)]","A",1
626,1,50,72,0.0709122,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^3} \, dx","Integrate[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^3,x]","\frac{1}{2} \left(\text{Ei}(a+x (b+c x))-\frac{e^{a+x (b+c x)} \left(a+b x+c x^2+1\right)}{(a+x (b+c x))^2}\right)","\frac{1}{2} \text{Ei}\left(c x^2+b x+a\right)-\frac{e^{a+b x+c x^2}}{2 \left(a+b x+c x^2\right)}-\frac{e^{a+b x+c x^2}}{2 \left(a+b x+c x^2\right)^2}",1,"(-((E^(a + x*(b + c*x))*(1 + a + b*x + c*x^2))/(a + x*(b + c*x))^2) + ExpIntegralEi[a + x*(b + c*x)])/2","A",1
627,1,47,142,0.2020975,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^{7/2} \, dx","Integrate[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(7/2),x]","-\frac{\sqrt{a+x (b+c x)} \Gamma \left(\frac{9}{2},-a-x (b+c x)\right)}{\sqrt{-a-x (b+c x)}}","\frac{105}{16} \sqrt{\pi } \text{erfi}\left(\sqrt{a+b x+c x^2}\right)+e^{a+b x+c x^2} \left(a+b x+c x^2\right)^{7/2}-\frac{7}{2} e^{a+b x+c x^2} \left(a+b x+c x^2\right)^{5/2}+\frac{35}{4} e^{a+b x+c x^2} \left(a+b x+c x^2\right)^{3/2}-\frac{105}{8} e^{a+b x+c x^2} \sqrt{a+b x+c x^2}",1,"-((Sqrt[a + x*(b + c*x)]*Gamma[9/2, -a - x*(b + c*x)])/Sqrt[-a - x*(b + c*x)])","A",1
628,1,46,112,0.1270024,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^{5/2} \, dx","Integrate[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{\sqrt{a+x (b+c x)} \Gamma \left(\frac{7}{2},-a-x (b+c x)\right)}{\sqrt{-a-x (b+c x)}}","-\frac{15}{8} \sqrt{\pi } \text{erfi}\left(\sqrt{a+b x+c x^2}\right)+e^{a+b x+c x^2} \left(a+b x+c x^2\right)^{5/2}-\frac{5}{2} e^{a+b x+c x^2} \left(a+b x+c x^2\right)^{3/2}+\frac{15}{4} e^{a+b x+c x^2} \sqrt{a+b x+c x^2}",1,"(Sqrt[a + x*(b + c*x)]*Gamma[7/2, -a - x*(b + c*x)])/Sqrt[-a - x*(b + c*x)]","A",1
629,1,47,82,0.1132731,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \, dx","Integrate[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2),x]","-\frac{\sqrt{a+x (b+c x)} \Gamma \left(\frac{5}{2},-a-x (b+c x)\right)}{\sqrt{-a-x (b+c x)}}","\frac{3}{4} \sqrt{\pi } \text{erfi}\left(\sqrt{a+b x+c x^2}\right)+e^{a+b x+c x^2} \left(a+b x+c x^2\right)^{3/2}-\frac{3}{2} e^{a+b x+c x^2} \sqrt{a+b x+c x^2}",1,"-((Sqrt[a + x*(b + c*x)]*Gamma[5/2, -a - x*(b + c*x)])/Sqrt[-a - x*(b + c*x)])","A",1
630,1,46,52,0.048185,"\int e^{a+b x+c x^2} (b+2 c x) \sqrt{a+b x+c x^2} \, dx","Integrate[E^(a + b*x + c*x^2)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+x (b+c x)} \Gamma \left(\frac{3}{2},-a-x (b+c x)\right)}{\sqrt{-a-x (b+c x)}}","e^{a+b x+c x^2} \sqrt{a+b x+c x^2}-\frac{1}{2} \sqrt{\pi } \text{erfi}\left(\sqrt{a+b x+c x^2}\right)",1,"(Sqrt[a + x*(b + c*x)]*Gamma[3/2, -a - x*(b + c*x)])/Sqrt[-a - x*(b + c*x)]","A",1
631,1,46,21,0.0613424,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\sqrt{a+b x+c x^2}} \, dx","Integrate[(E^(a + b*x + c*x^2)*(b + 2*c*x))/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{-a-x (b+c x)} \Gamma \left(\frac{1}{2},-a-x (b+c x)\right)}{\sqrt{a+x (b+c x)}}","\sqrt{\pi } \text{erfi}\left(\sqrt{a+b x+c x^2}\right)",1,"(Sqrt[-a - x*(b + c*x)]*Gamma[1/2, -a - x*(b + c*x)])/Sqrt[a + x*(b + c*x)]","B",1
632,1,62,51,0.0994803,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Integrate[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{-a-x (b+c x)} \Gamma \left(\frac{1}{2},-a-x (b+c x)\right)-2 e^{a+x (b+c x)}}{\sqrt{a+x (b+c x)}}","2 \sqrt{\pi } \text{erfi}\left(\sqrt{a+b x+c x^2}\right)-\frac{2 e^{a+b x+c x^2}}{\sqrt{a+b x+c x^2}}",1,"(-2*E^(a + x*(b + c*x)) + 2*Sqrt[-a - x*(b + c*x)]*Gamma[1/2, -a - x*(b + c*x)])/Sqrt[a + x*(b + c*x)]","A",1
633,1,77,85,0.1284293,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Integrate[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \left(e^{a+x (b+c x)} (2 (a+x (b+c x))+1)+2 (-a-x (b+c x))^{3/2} \Gamma \left(\frac{1}{2},-a-x (b+c x)\right)\right)}{3 (a+x (b+c x))^{3/2}}","\frac{4}{3} \sqrt{\pi } \text{erfi}\left(\sqrt{a+b x+c x^2}\right)-\frac{4 e^{a+b x+c x^2}}{3 \sqrt{a+b x+c x^2}}-\frac{2 e^{a+b x+c x^2}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(E^(a + x*(b + c*x))*(1 + 2*(a + x*(b + c*x))) + 2*(-a - x*(b + c*x))^(3/2)*Gamma[1/2, -a - x*(b + c*x)]))/(3*(a + x*(b + c*x))^(3/2))","A",1
634,1,91,115,0.1766219,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Integrate[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^(7/2),x]","\frac{8 (-a-x (b+c x))^{5/2} \Gamma \left(\frac{1}{2},-a-x (b+c x)\right)-2 e^{a+x (b+c x)} \left(4 (a+x (b+c x))^2+2 (a+x (b+c x))+3\right)}{15 (a+x (b+c x))^{5/2}}","\frac{8}{15} \sqrt{\pi } \text{erfi}\left(\sqrt{a+b x+c x^2}\right)-\frac{8 e^{a+b x+c x^2}}{15 \sqrt{a+b x+c x^2}}-\frac{4 e^{a+b x+c x^2}}{15 \left(a+b x+c x^2\right)^{3/2}}-\frac{2 e^{a+b x+c x^2}}{5 \left(a+b x+c x^2\right)^{5/2}}",1,"(-2*E^(a + x*(b + c*x))*(3 + 2*(a + x*(b + c*x)) + 4*(a + x*(b + c*x))^2) + 8*(-a - x*(b + c*x))^(5/2)*Gamma[1/2, -a - x*(b + c*x)])/(15*(a + x*(b + c*x))^(5/2))","A",1
635,1,103,145,0.2413632,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^{9/2}} \, dx","Integrate[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^(9/2),x]","-\frac{2 \left(e^{a+x (b+c x)} \left(8 (a+x (b+c x))^3+4 (a+x (b+c x))^2+6 (a+x (b+c x))+15\right)+8 (-a-x (b+c x))^{7/2} \Gamma \left(\frac{1}{2},-a-x (b+c x)\right)\right)}{105 (a+x (b+c x))^{7/2}}","\frac{16}{105} \sqrt{\pi } \text{erfi}\left(\sqrt{a+b x+c x^2}\right)-\frac{16 e^{a+b x+c x^2}}{105 \sqrt{a+b x+c x^2}}-\frac{8 e^{a+b x+c x^2}}{105 \left(a+b x+c x^2\right)^{3/2}}-\frac{4 e^{a+b x+c x^2}}{35 \left(a+b x+c x^2\right)^{5/2}}-\frac{2 e^{a+b x+c x^2}}{7 \left(a+b x+c x^2\right)^{7/2}}",1,"(-2*(E^(a + x*(b + c*x))*(15 + 6*(a + x*(b + c*x)) + 4*(a + x*(b + c*x))^2 + 8*(a + x*(b + c*x))^3) + 8*(-a - x*(b + c*x))^(7/2)*Gamma[1/2, -a - x*(b + c*x)]))/(105*(a + x*(b + c*x))^(7/2))","A",1
636,1,42,8,0.0182034,"\int \frac{e^{-x}}{\sqrt{1-e^{-2 x}}} \, dx","Integrate[1/(E^x*Sqrt[1 - E^(-2*x)]),x]","\frac{e^{-x} \sqrt{e^{2 x}-1} \tan ^{-1}\left(\sqrt{e^{2 x}-1}\right)}{\sqrt{1-e^{-2 x}}}","-\sin ^{-1}\left(e^{-x}\right)",1,"(Sqrt[-1 + E^(2*x)]*ArcTan[Sqrt[-1 + E^(2*x)]])/(E^x*Sqrt[1 - E^(-2*x)])","B",1
637,1,12,12,0.00274,"\int \frac{e^x}{4+e^{2 x}} \, dx","Integrate[E^x/(4 + E^(2*x)),x]","\frac{1}{2} \tan ^{-1}\left(\frac{e^x}{2}\right)","\frac{1}{2} \tan ^{-1}\left(\frac{e^x}{2}\right)",1,"ArcTan[E^x/2]/2","A",1
638,1,4,4,0.0031631,"\int \frac{e^x}{1-e^{2 x}} \, dx","Integrate[E^x/(1 - E^(2*x)),x]","\tanh ^{-1}\left(e^x\right)","\tanh ^{-1}\left(e^x\right)",1,"ArcTanh[E^x]","A",1
639,1,20,20,0.0063449,"\int \frac{e^x}{3-4 e^{2 x}} \, dx","Integrate[E^x/(3 - 4*E^(2*x)),x]","\frac{\tanh ^{-1}\left(\frac{2 e^x}{\sqrt{3}}\right)}{2 \sqrt{3}}","\frac{\tanh ^{-1}\left(\frac{2 e^x}{\sqrt{3}}\right)}{2 \sqrt{3}}",1,"ArcTanh[(2*E^x)/Sqrt[3]]/(2*Sqrt[3])","A",1
640,1,36,36,0.0151191,"\int e^x \sqrt{3-4 e^{2 x}} \, dx","Integrate[E^x*Sqrt[3 - 4*E^(2*x)],x]","\frac{1}{4} \left(2 e^x \sqrt{3-4 e^{2 x}}+3 \sin ^{-1}\left(\frac{2 e^x}{\sqrt{3}}\right)\right)","\frac{1}{2} e^x \sqrt{3-4 e^{2 x}}+\frac{3}{4} \sin ^{-1}\left(\frac{2 e^x}{\sqrt{3}}\right)",1,"(2*E^x*Sqrt[3 - 4*E^(2*x)] + 3*ArcSin[(2*E^x)/Sqrt[3]])/4","A",1
641,1,14,22,0.0021328,"\int e^{x^2} x^3 \, dx","Integrate[E^x^2*x^3,x]","\frac{1}{2} e^{x^2} \left(x^2-1\right)","\frac{1}{2} e^{x^2} x^2-\frac{e^{x^2}}{2}",1,"(E^x^2*(-1 + x^2))/2","A",1
642,1,26,29,0.0117075,"\int e^x \sqrt{1-e^{2 x}} \, dx","Integrate[E^x*Sqrt[1 - E^(2*x)],x]","\frac{1}{2} \left(e^x \sqrt{1-e^{2 x}}+\sin ^{-1}\left(e^x\right)\right)","\frac{1}{2} e^x \sqrt{1-e^{2 x}}+\frac{1}{2} \sin ^{-1}\left(e^x\right)",1,"(E^x*Sqrt[1 - E^(2*x)] + ArcSin[E^x])/2","A",1
643,1,14,14,0.0092259,"\int \frac{e^x}{\sqrt{1+e^x+e^{2 x}}} \, dx","Integrate[E^x/Sqrt[1 + E^x + E^(2*x)],x]","\sinh ^{-1}\left(\frac{2 e^x+1}{\sqrt{3}}\right)","\sinh ^{-1}\left(\frac{2 e^x+1}{\sqrt{3}}\right)",1,"ArcSinh[(1 + 2*E^x)/Sqrt[3]]","A",1
644,1,12,12,0.0026211,"\int \frac{e^x}{-4+e^{2 x}} \, dx","Integrate[E^x/(-4 + E^(2*x)),x]","-\frac{1}{2} \tanh ^{-1}\left(\frac{e^x}{2}\right)","-\frac{1}{2} \tanh ^{-1}\left(\frac{e^x}{2}\right)",1,"-1/2*ArcTanh[E^x/2]","A",1
645,1,13,13,0.0023489,"\int e^{2-x^2} x \, dx","Integrate[E^(2 - x^2)*x,x]","-\frac{1}{2} e^{2-x^2}","-\frac{1}{2} e^{2-x^2}",1,"-1/2*E^(2 - x^2)","A",1
646,1,16,16,0.0054072,"\int \left(e^x-x^e\right) \, dx","Integrate[E^x - x^E,x]","e^x-\frac{x^{1+e}}{1+e}","e^x-\frac{x^{1+e}}{1+e}",1,"E^x - x^(1 + E)/(1 + E)","A",1
647,1,18,18,0.0088759,"\int \frac{-1+e^{2 x}}{3+e^{2 x}} \, dx","Integrate[(-1 + E^(2*x))/(3 + E^(2*x)),x]","\frac{2}{3} \log \left(e^{2 x}+3\right)-\frac{x}{3}","\frac{2}{3} \log \left(e^{2 x}+3\right)-\frac{x}{3}",1,"-1/3*x + (2*Log[3 + E^(2*x)])/3","A",1
648,1,4,4,0.0044006,"\int \frac{e^x}{\sqrt{1-e^{2 x}}} \, dx","Integrate[E^x/Sqrt[1 - E^(2*x)],x]","\sin ^{-1}\left(e^x\right)","\sin ^{-1}\left(e^x\right)",1,"ArcSin[E^x]","A",1
649,1,10,10,0.0030615,"\int \frac{e^{2 x}}{1+e^{4 x}} \, dx","Integrate[E^(2*x)/(1 + E^(4*x)),x]","\frac{1}{2} \tan ^{-1}\left(e^{2 x}\right)","\frac{1}{2} \tan ^{-1}\left(e^{2 x}\right)",1,"ArcTan[E^(2*x)]/2","A",1
650,1,23,27,0.0196067,"\int \frac{1}{-3 e^x+e^{2 x}} \, dx","Integrate[(-3*E^x + E^(2*x))^(-1),x]","\frac{1}{9} \left(-x+3 e^{-x}+\log \left(3-e^x\right)\right)","-\frac{x}{9}+\frac{e^{-x}}{3}+\frac{1}{9} \log \left(3-e^x\right)",1,"(3/E^x - x + Log[3 - E^x])/9","A",1
651,1,12,12,0.0106031,"\int \frac{e^x \left(-2+e^x\right)}{1+e^x} \, dx","Integrate[(E^x*(-2 + E^x))/(1 + E^x),x]","e^x-3 \log \left(e^x+1\right)","e^x-3 \log \left(e^x+1\right)",1,"E^x - 3*Log[1 + E^x]","A",1
652,1,6,6,0.0022054,"\int \frac{e^x}{-1+e^{2 x}} \, dx","Integrate[E^x/(-1 + E^(2*x)),x]","-\tanh ^{-1}\left(e^x\right)","-\tanh ^{-1}\left(e^x\right)",1,"-ArcTanh[E^x]","A",1
653,1,4,4,0.0026972,"\int \frac{e^x}{1+e^{2 x}} \, dx","Integrate[E^x/(1 + E^(2*x)),x]","\tan ^{-1}\left(e^x\right)","\tan ^{-1}\left(e^x\right)",1,"ArcTan[E^x]","A",1
654,1,14,12,0.0088189,"\int \frac{e^{-x}+e^x}{-e^{-x}+e^x} \, dx","Integrate[(E^(-x) + E^x)/(-E^(-x) + E^x),x]","\log \left(1-e^{2 x}\right)-x","\log \left(e^{-x}-e^x\right)",1,"-x + Log[1 - E^(2*x)]","A",1
655,1,12,10,0.0082514,"\int \frac{-e^{-x}+e^x}{e^{-x}+e^x} \, dx","Integrate[(-E^(-x) + E^x)/(E^(-x) + E^x),x]","\log \left(e^{2 x}+1\right)-x","\log \left(e^{-x}+e^x\right)",1,"-x + Log[1 + E^(2*x)]","A",1
656,1,18,18,0.0088912,"\int \frac{e^{-2 x}+e^{2 x}}{-e^{-2 x}+e^{2 x}} \, dx","Integrate[(E^(-2*x) + E^(2*x))/(-E^(-2*x) + E^(2*x)),x]","\frac{1}{2} \log \left(1-e^{4 x}\right)-x","\frac{1}{2} \log \left(1-e^{4 x}\right)-x",1,"-x + Log[1 - E^(4*x)]/2","A",1
657,1,4,4,0.0037298,"\int \frac{e^x}{\sqrt{1+e^{2 x}}} \, dx","Integrate[E^x/Sqrt[1 + E^(2*x)],x]","\sinh ^{-1}\left(e^x\right)","\sinh ^{-1}\left(e^x\right)",1,"ArcSinh[E^x]","A",1
658,1,11,11,0.0035066,"\int \frac{e^{\sqrt{4+x}}}{\sqrt{4+x}} \, dx","Integrate[E^Sqrt[4 + x]/Sqrt[4 + x],x]","2 e^{\sqrt{x+4}}","2 e^{\sqrt{x+4}}",1,"2*E^Sqrt[4 + x]","A",1
659,1,18,18,0.016655,"\int \frac{x}{\sqrt{-1+e^{2 x^2}}} \, dx","Integrate[x/Sqrt[-1 + E^(2*x^2)],x]","\frac{1}{2} \tan ^{-1}\left(\sqrt{e^{2 x^2}-1}\right)","\frac{1}{2} \tan ^{-1}\left(\sqrt{e^{2 x^2}-1}\right)",1,"ArcTan[Sqrt[-1 + E^(2*x^2)]]/2","A",1
660,1,30,31,0.0103942,"\int e^x \sqrt{9+e^{2 x}} \, dx","Integrate[E^x*Sqrt[9 + E^(2*x)],x]","\frac{1}{2} \left(e^x \sqrt{e^{2 x}+9}+9 \sinh ^{-1}\left(\frac{e^x}{3}\right)\right)","\frac{1}{2} e^x \sqrt{e^{2 x}+9}+\frac{9}{2} \sinh ^{-1}\left(\frac{e^x}{3}\right)",1,"(E^x*Sqrt[9 + E^(2*x)] + 9*ArcSinh[E^x/3])/2","A",1
661,1,24,27,0.0092598,"\int e^x \sqrt{1+e^{2 x}} \, dx","Integrate[E^x*Sqrt[1 + E^(2*x)],x]","\frac{1}{2} \left(e^x \sqrt{e^{2 x}+1}+\sinh ^{-1}\left(e^x\right)\right)","\frac{1}{2} e^x \sqrt{e^{2 x}+1}+\frac{1}{2} \sinh ^{-1}\left(e^x\right)",1,"(E^x*Sqrt[1 + E^(2*x)] + ArcSinh[E^x])/2","A",1
662,1,10,10,0.0160921,"\int \frac{e^{x^2} x}{1+e^{2 x^2}} \, dx","Integrate[(E^x^2*x)/(1 + E^(2*x^2)),x]","\frac{1}{2} \tan ^{-1}\left(e^{x^2}\right)","\frac{1}{2} \tan ^{-1}\left(e^{x^2}\right)",1,"ArcTan[E^x^2]/2","A",1
663,1,13,28,0.0014907,"\int e^{x^{3/2}} x^2 \, dx","Integrate[E^x^(3/2)*x^2,x]","-\frac{2}{3} \Gamma \left(2,-x^{3/2}\right)","\frac{2}{3} e^{x^{3/2}} x^{3/2}-\frac{2 e^{x^{3/2}}}{3}",1,"(-2*Gamma[2, -x^(3/2)])/3","C",1
664,1,16,16,0.0044636,"\int \frac{e^x}{\sqrt{-3+e^{2 x}}} \, dx","Integrate[E^x/Sqrt[-3 + E^(2*x)],x]","\tanh ^{-1}\left(\frac{e^x}{\sqrt{e^{2 x}-3}}\right)","\tanh ^{-1}\left(\frac{e^x}{\sqrt{e^{2 x}-3}}\right)",1,"ArcTanh[E^x/Sqrt[-3 + E^(2*x)]]","A",1
665,1,12,12,0.0037105,"\int \frac{e^x}{16-e^{2 x}} \, dx","Integrate[E^x/(16 - E^(2*x)),x]","\frac{1}{4} \tanh ^{-1}\left(\frac{e^x}{4}\right)","\frac{1}{4} \tanh ^{-1}\left(\frac{e^x}{4}\right)",1,"ArcTanh[E^x/4]/4","A",1
666,1,10,10,0.0037957,"\int \frac{e^{5 x}}{1+e^{10 x}} \, dx","Integrate[E^(5*x)/(1 + E^(10*x)),x]","\frac{1}{5} \tan ^{-1}\left(e^{5 x}\right)","\frac{1}{5} \tan ^{-1}\left(e^{5 x}\right)",1,"ArcTan[E^(5*x)]/5","A",1
667,1,14,14,0.0051036,"\int \frac{e^{4 x}}{\sqrt{16+e^{8 x}}} \, dx","Integrate[E^(4*x)/Sqrt[16 + E^(8*x)],x]","\frac{1}{4} \sinh ^{-1}\left(\frac{e^{4 x}}{4}\right)","\frac{1}{4} \sinh ^{-1}\left(\frac{e^{4 x}}{4}\right)",1,"ArcSinh[E^(4*x)/4]/4","A",1
668,1,28,35,0.0554397,"\int e^{4 x^3} x^2 \cos \left(7 x^3\right) \, dx","Integrate[E^(4*x^3)*x^2*Cos[7*x^3],x]","\frac{1}{195} e^{4 x^3} \left(7 \sin \left(7 x^3\right)+4 \cos \left(7 x^3\right)\right)","\frac{7}{195} e^{4 x^3} \sin \left(7 x^3\right)+\frac{4}{195} e^{4 x^3} \cos \left(7 x^3\right)",1,"(E^(4*x^3)*(4*Cos[7*x^3] + 7*Sin[7*x^3]))/195","A",1
669,1,11,11,0.001838,"\int e^{1+x^2} x \, dx","Integrate[E^(1 + x^2)*x,x]","\frac{e^{x^2+1}}{2}","\frac{e^{x^2+1}}{2}",1,"E^(1 + x^2)/2","A",1
670,1,11,11,0.0017988,"\int e^{1+x^3} x^2 \, dx","Integrate[E^(1 + x^3)*x^2,x]","\frac{e^{x^3+1}}{3}","\frac{e^{x^3+1}}{3}",1,"E^(1 + x^3)/3","A",1
671,1,9,9,0.0018848,"\int \frac{e^{\sqrt{x}}}{\sqrt{x}} \, dx","Integrate[E^Sqrt[x]/Sqrt[x],x]","2 e^{\sqrt{x}}","2 e^{\sqrt{x}}",1,"2*E^Sqrt[x]","A",1
672,1,9,9,0.002021,"\int \frac{e^{\sqrt[3]{x}}}{x^{2/3}} \, dx","Integrate[E^x^(1/3)/x^(2/3),x]","3 e^{\sqrt[3]{x}}","3 e^{\sqrt[3]{x}}",1,"3*E^x^(1/3)","A",1
673,1,34,68,0.0227432,"\int e^{3 x} \left(-8+2 x^3+x^5\right) \, dx","Integrate[E^(3*x)*(-8 + 2*x^3 + x^5),x]","\frac{1}{243} e^{3 x} \left(81 x^5-135 x^4+342 x^3-342 x^2+228 x-724\right)","\frac{1}{3} e^{3 x} x^5-\frac{5}{9} e^{3 x} x^4+\frac{38}{27} e^{3 x} x^3-\frac{38}{27} e^{3 x} x^2+\frac{76}{81} e^{3 x} x-\frac{724 e^{3 x}}{243}",1,"(E^(3*x)*(-724 + 228*x - 342*x^2 + 342*x^3 - 135*x^4 + 81*x^5))/243","A",1
674,1,26,28,0.015146,"\int \left(e^x+x\right)^2 \, dx","Integrate[(E^x + x)^2,x]","\frac{x^3}{3}+\frac{e^{2 x}}{2}+e^x (2 x-2)","\frac{x^3}{3}+2 e^x x-2 e^x+\frac{e^{2 x}}{2}",1,"E^(2*x)/2 + x^3/3 + E^x*(-2 + 2*x)","A",1
675,1,23,26,0.0116093,"\int e^{-4 x} \left(e^x+e^{2 x}+e^{3 x}\right) \, dx","Integrate[(E^x + E^(2*x) + E^(3*x))/E^(4*x),x]","-\frac{1}{6} e^{-3 x} \left(3 e^x+6 e^{2 x}+2\right)","-\frac{1}{3} e^{-3 x}-\frac{e^{-2 x}}{2}-e^{-x}",1,"-1/6*(2 + 3*E^x + 6*E^(2*x))/E^(3*x)","A",1
676,1,9,9,0.0078052,"\int \frac{e^x}{1+2 e^x+e^{2 x}} \, dx","Integrate[E^x/(1 + 2*E^x + E^(2*x)),x]","-\frac{1}{e^x+1}","-\frac{1}{e^x+1}",1,"-(1 + E^x)^(-1)","A",1
677,1,20,27,0.0269229,"\int e^{-x} \cos (3 x) \, dx","Integrate[Cos[3*x]/E^x,x]","-\frac{1}{10} e^{-x} (\cos (3 x)-3 \sin (3 x))","\frac{3}{10} e^{-x} \sin (3 x)-\frac{1}{10} e^{-x} \cos (3 x)",1,"-1/10*(Cos[3*x] - 3*Sin[3*x])/E^x","A",1
678,1,17,17,0.0138424,"\int \frac{e^{2 x}}{2+3 e^x+e^{2 x}} \, dx","Integrate[E^(2*x)/(2 + 3*E^x + E^(2*x)),x]","2 \log \left(e^x+2\right)-\log \left(e^x+1\right)","2 \log \left(e^x+2\right)-\log \left(e^x+1\right)",1,"-Log[1 + E^x] + 2*Log[2 + E^x]","A",1
679,1,12,12,0.0081884,"\int \frac{e^{2 x}}{1+e^x} \, dx","Integrate[E^(2*x)/(1 + E^x),x]","e^x-\log \left(e^x+1\right)","e^x-\log \left(e^x+1\right)",1,"E^x - Log[1 + E^x]","A",1
680,1,22,27,0.0290799,"\int e^{3 x} \cos (5 x) \, dx","Integrate[E^(3*x)*Cos[5*x],x]","\frac{1}{34} e^{3 x} (5 \sin (5 x)+3 \cos (5 x))","\frac{5}{34} e^{3 x} \sin (5 x)+\frac{3}{34} e^{3 x} \cos (5 x)",1,"(E^(3*x)*(3*Cos[5*x] + 5*Sin[5*x]))/34","A",1
681,1,5,5,0.005779,"\int e^x \text{sech}\left(e^x\right) \, dx","Integrate[E^x*Sech[E^x],x]","\tan ^{-1}\left(\sinh \left(e^x\right)\right)","\tan ^{-1}\left(\sinh \left(e^x\right)\right)",1,"ArcTan[Sinh[E^x]]","A",1
682,1,21,21,0.0157725,"\int \frac{e^{-x}}{1+2 e^x} \, dx","Integrate[1/(E^x*(1 + 2*E^x)),x]","-2 x-e^{-x}+2 \log \left(2 e^x+1\right)","-2 x-e^{-x}+2 \log \left(2 e^x+1\right)",1,"-E^(-x) - 2*x + 2*Log[1 + 2*E^x]","A",1
683,1,22,27,0.0422074,"\int e^x \cos (4+3 x) \, dx","Integrate[E^x*Cos[4 + 3*x],x]","\frac{1}{10} e^x (3 \sin (3 x+4)+\cos (3 x+4))","\frac{3}{10} e^x \sin (3 x+4)+\frac{1}{10} e^x \cos (3 x+4)",1,"(E^x*(Cos[4 + 3*x] + 3*Sin[4 + 3*x]))/10","A",1
684,1,34,34,0.0181842,"\int e^x \sec ^3\left(1-e^x\right) \, dx","Integrate[E^x*Sec[1 - E^x]^3,x]","-\frac{1}{2} \tanh ^{-1}\left(\sin \left(1-e^x\right)\right)-\frac{1}{2} \tan \left(1-e^x\right) \sec \left(1-e^x\right)","-\frac{1}{2} \tanh ^{-1}\left(\sin \left(1-e^x\right)\right)-\frac{1}{2} \tan \left(1-e^x\right) \sec \left(1-e^x\right)",1,"-1/2*ArcTanh[Sin[1 - E^x]] - (Sec[1 - E^x]*Tan[1 - E^x])/2","A",1
685,1,20,26,0.0219656,"\int \left(e^{-x}+e^x\right) x \, dx","Integrate[(E^(-x) + E^x)*x,x]","e^{-x} \left(e^{2 x} (x-1)-x-1\right)","-e^{-x} x+e^x x-e^{-x}-e^x",1,"(-1 + E^(2*x)*(-1 + x) - x)/E^x","A",1
686,1,10,15,0.0066237,"\int \frac{e^x}{2+3 e^x+e^{2 x}} \, dx","Integrate[E^x/(2 + 3*E^x + E^(2*x)),x]","-2 \tanh ^{-1}\left(2 e^x+3\right)","\log \left(e^x+1\right)-\log \left(e^x+2\right)",1,"-2*ArcTanh[3 + 2*E^x]","A",1
687,1,20,27,0.0109704,"\int \frac{e^{2 x}}{\sqrt[3]{1+e^x}} \, dx","Integrate[E^(2*x)/(1 + E^x)^(1/3),x]","\frac{3}{10} \left(e^x+1\right)^{2/3} \left(2 e^x-3\right)","\frac{3}{5} \left(e^x+1\right)^{5/3}-\frac{3}{2} \left(e^x+1\right)^{2/3}",1,"(3*(1 + E^x)^(2/3)*(-3 + 2*E^x))/10","A",1
688,1,20,27,0.0105901,"\int \frac{e^{2 x}}{\sqrt[4]{1+e^x}} \, dx","Integrate[E^(2*x)/(1 + E^x)^(1/4),x]","\frac{4}{21} \left(e^x+1\right)^{3/4} \left(3 e^x-4\right)","\frac{4}{7} \left(e^x+1\right)^{7/4}-\frac{4}{3} \left(e^x+1\right)^{3/4}",1,"(4*(1 + E^x)^(3/4)*(-4 + 3*E^x))/21","A",1
689,1,54,62,0.0416747,"\int \frac{-e^x+2 e^{2 x}}{\sqrt{-1-6 e^x+3 e^{2 x}}} \, dx","Integrate[(-E^x + 2*E^(2*x))/Sqrt[-1 - 6*E^x + 3*E^(2*x)],x]","\frac{2}{3} \sqrt{-6 e^x+3 e^{2 x}-1}+\frac{\tanh ^{-1}\left(\frac{e^x-1}{\sqrt{-2 e^x+e^{2 x}-\frac{1}{3}}}\right)}{\sqrt{3}}","\frac{2}{3} \sqrt{-6 e^x+3 e^{2 x}-1}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3} \left(1-e^x\right)}{\sqrt{-6 e^x+3 e^{2 x}-1}}\right)}{\sqrt{3}}",1,"(2*Sqrt[-1 - 6*E^x + 3*E^(2*x)])/3 + ArcTanh[(-1 + E^x)/Sqrt[-1/3 - 2*E^x + E^(2*x)]]/Sqrt[3]","A",1
690,1,12,19,0.0294367,"\int e^x \left(-5 x+x^2\right) \, dx","Integrate[E^x*(-5*x + x^2),x]","e^x \left(x^2-7 x+7\right)","e^x x^2-7 e^x x+7 e^x",1,"E^x*(7 - 7*x + x^2)","A",1
691,1,19,32,0.0302003,"\int e^{3 x} \left(-x+x^2\right) \, dx","Integrate[E^(3*x)*(-x + x^2),x]","\frac{1}{27} e^{3 x} \left(9 x^2-15 x+5\right)","\frac{1}{3} e^{3 x} x^2-\frac{5}{9} e^{3 x} x+\frac{5 e^{3 x}}{27}",1,"(E^(3*x)*(5 - 15*x + 9*x^2))/27","A",1
692,1,11,11,0.0444241,"\int e^{x^x} x^{2 x} (1+\log (x)) \, dx","Integrate[E^x^x*x^(2*x)*(1 + Log[x]),x]","e^{x^x} \left(x^x-1\right)","e^{x^x} \left(x^x-1\right)",1,"E^x^x*(-1 + x^x)","A",1
693,1,9,9,0.001107,"\int \frac{e^{5 x}+e^{7 x}}{e^{-x}+e^x} \, dx","Integrate[(E^(5*x) + E^(7*x))/(E^(-x) + E^x),x]","\frac{e^{6 x}}{6}","\frac{e^{6 x}}{6}",1,"E^(6*x)/6","A",1
694,1,9,9,0.0207474,"\int x^{-2-\frac{1}{x}} (1-\log (x)) \, dx","Integrate[x^(-2 - x^(-1))*(1 - Log[x]),x]","-x^{-1/x}","-x^{-1/x}",1,"-x^(-x^(-1))","A",1
695,1,25,25,0.0100837,"\int \left(a+b e^x\right)^2 \, dx","Integrate[(a + b*E^x)^2,x]","a^2 x+2 a b e^x+\frac{1}{2} b^2 e^{2 x}","a^2 x+2 a b e^x+\frac{1}{2} b^2 e^{2 x}",1,"2*a*b*E^x + (b^2*E^(2*x))/2 + a^2*x","A",1
696,1,40,40,0.0131838,"\int \left(a+b e^x\right)^3 \, dx","Integrate[(a + b*E^x)^3,x]","a^3 x+3 a^2 b e^x+\frac{3}{2} a b^2 e^{2 x}+\frac{1}{3} b^3 e^{3 x}","a^3 x+3 a^2 b e^x+\frac{3}{2} a b^2 e^{2 x}+\frac{1}{3} b^3 e^{3 x}",1,"3*a^2*b*E^x + (3*a*b^2*E^(2*x))/2 + (b^3*E^(3*x))/3 + a^3*x","A",1
697,1,53,53,0.0176592,"\int \left(a+b e^x\right)^4 \, dx","Integrate[(a + b*E^x)^4,x]","a^4 x+4 a^3 b e^x+3 a^2 b^2 e^{2 x}+\frac{4}{3} a b^3 e^{3 x}+\frac{1}{4} b^4 e^{4 x}","a^4 x+4 a^3 b e^x+3 a^2 b^2 e^{2 x}+\frac{4}{3} a b^3 e^{3 x}+\frac{1}{4} b^4 e^{4 x}",1,"4*a^3*b*E^x + 3*a^2*b^2*E^(2*x) + (4*a*b^3*E^(3*x))/3 + (b^4*E^(4*x))/4 + a^4*x","A",1
698,1,32,32,0.0130912,"\int \frac{1}{\sqrt{a+b e^{c+d x}}} \, dx","Integrate[1/Sqrt[a + b*E^(c + d*x)],x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b e^{c+d x}}}{\sqrt{a}}\right)}{\sqrt{a} d}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b e^{c+d x}}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(-2*ArcTanh[Sqrt[a + b*E^(c + d*x)]/Sqrt[a]])/(Sqrt[a]*d)","A",1
699,1,34,34,0.0131152,"\int \frac{1}{\sqrt{-a+b e^{c+d x}}} \, dx","Integrate[1/Sqrt[-a + b*E^(c + d*x)],x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b e^{c+d x}-a}}{\sqrt{a}}\right)}{\sqrt{a} d}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b e^{c+d x}-a}}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"(2*ArcTan[Sqrt[-a + b*E^(c + d*x)]/Sqrt[a]])/(Sqrt[a]*d)","A",1
700,1,51,53,0.0166232,"\int \sqrt{a+b e^{c+d x}} \, dx","Integrate[Sqrt[a + b*E^(c + d*x)],x]","\frac{2 \sqrt{a+b e^{c+d x}}-2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b e^{c+d x}}}{\sqrt{a}}\right)}{d}","\frac{2 \sqrt{a+b e^{c+d x}}}{d}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b e^{c+d x}}}{\sqrt{a}}\right)}{d}",1,"(2*Sqrt[a + b*E^(c + d*x)] - 2*Sqrt[a]*ArcTanh[Sqrt[a + b*E^(c + d*x)]/Sqrt[a]])/d","A",1
701,1,55,57,0.0178515,"\int \sqrt{-a+b e^{c+d x}} \, dx","Integrate[Sqrt[-a + b*E^(c + d*x)],x]","\frac{2 \sqrt{b e^{c+d x}-a}-2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b e^{c+d x}-a}}{\sqrt{a}}\right)}{d}","\frac{2 \sqrt{b e^{c+d x}-a}}{d}-\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b e^{c+d x}-a}}{\sqrt{a}}\right)}{d}",1,"(2*Sqrt[-a + b*E^(c + d*x)] - 2*Sqrt[a]*ArcTan[Sqrt[-a + b*E^(c + d*x)]/Sqrt[a]])/d","A",1
702,1,20,27,0.0244819,"\int e^{6 x} \sin (3 x) \, dx","Integrate[E^(6*x)*Sin[3*x],x]","-\frac{1}{15} e^{6 x} (\cos (3 x)-2 \sin (3 x))","\frac{2}{15} e^{6 x} \sin (3 x)-\frac{1}{15} e^{6 x} \cos (3 x)",1,"-1/15*(E^(6*x)*(Cos[3*x] - 2*Sin[3*x]))","A",1
703,1,10,10,0.006872,"\int \frac{e^{3 x}}{1+e^{2 x}} \, dx","Integrate[E^(3*x)/(1 + E^(2*x)),x]","e^x-\tan ^{-1}\left(e^x\right)","e^x-\tan ^{-1}\left(e^x\right)",1,"E^x - ArcTan[E^x]","A",1
704,1,10,10,0.0067994,"\int \frac{e^{3 x}}{-1+e^{2 x}} \, dx","Integrate[E^(3*x)/(-1 + E^(2*x)),x]","e^x-\tanh ^{-1}\left(e^x\right)","e^x-\tanh ^{-1}\left(e^x\right)",1,"E^x - ArcTanh[E^x]","A",1
705,1,18,18,0.0144981,"\int \frac{e^{-x}}{\sqrt{1+e^{2 x}}} \, dx","Integrate[1/(E^x*Sqrt[1 + E^(2*x)]),x]","-e^{-x} \sqrt{e^{2 x}+1}","-e^{-x} \sqrt{e^{2 x}+1}",1,"-(Sqrt[1 + E^(2*x)]/E^x)","A",1
706,1,19,20,0.0130783,"\int \frac{e^x}{-1-8 e^x+e^{2 x}} \, dx","Integrate[E^x/(-1 - 8*E^x + E^(2*x)),x]","-\frac{\tanh ^{-1}\left(\frac{e^x-4}{\sqrt{17}}\right)}{\sqrt{17}}","\frac{\tanh ^{-1}\left(\frac{4-e^x}{\sqrt{17}}\right)}{\sqrt{17}}",1,"-(ArcTanh[(-4 + E^x)/Sqrt[17]]/Sqrt[17])","A",1
707,1,24,44,0.0079667,"\int e^{7 x} x^3 \, dx","Integrate[E^(7*x)*x^3,x]","\frac{e^{7 x} \left(343 x^3-147 x^2+42 x-6\right)}{2401}","\frac{1}{7} e^{7 x} x^3-\frac{3}{49} e^{7 x} x^2+\frac{6}{343} e^{7 x} x-\frac{6 e^{7 x}}{2401}",1,"(E^(7*x)*(-6 + 42*x - 147*x^2 + 343*x^3))/2401","A",1
708,1,26,52,0.0103489,"\int e^{8-2 x} x^3 \, dx","Integrate[E^(8 - 2*x)*x^3,x]","-\frac{1}{8} e^{8-2 x} \left(4 x^3+6 x^2+6 x+3\right)","-\frac{1}{2} e^{8-2 x} x^3-\frac{3}{4} e^{8-2 x} x^2-\frac{3}{4} e^{8-2 x} x-\frac{3}{8} e^{8-2 x}",1,"-1/8*(E^(8 - 2*x)*(3 + 6*x + 6*x^2 + 4*x^3))","A",1
709,1,32,33,0.0124316,"\int e^x \sqrt{9-e^{2 x}} \, dx","Integrate[E^x*Sqrt[9 - E^(2*x)],x]","\frac{1}{2} \left(e^x \sqrt{9-e^{2 x}}+9 \sin ^{-1}\left(\frac{e^x}{3}\right)\right)","\frac{1}{2} e^x \sqrt{9-e^{2 x}}+\frac{9}{2} \sin ^{-1}\left(\frac{e^x}{3}\right)",1,"(E^x*Sqrt[9 - E^(2*x)] + 9*ArcSin[E^x/3])/2","A",1
710,1,33,50,0.0209854,"\int e^{6 x} \sqrt{9-e^{2 x}} \, dx","Integrate[E^(6*x)*Sqrt[9 - E^(2*x)],x]","-\frac{1}{35} \left(9-e^{2 x}\right)^{3/2} \left(36 e^{2 x}+5 e^{4 x}+216\right)","-\frac{1}{7} \left(9-e^{2 x}\right)^{7/2}+\frac{18}{5} \left(9-e^{2 x}\right)^{5/2}-27 \left(9-e^{2 x}\right)^{3/2}",1,"-1/35*((9 - E^(2*x))^(3/2)*(216 + 36*E^(2*x) + 5*E^(4*x)))","A",1
711,1,48,81,0.0277715,"\int \frac{e^{6 x}}{\left(9-e^x\right)^{5/2}} \, dx","Integrate[E^(6*x)/(9 - E^x)^(5/2),x]","-\frac{2 \left(-839808 e^x+23328 e^{2 x}+432 e^{3 x}+18 e^{4 x}+e^{5 x}+5038848\right)}{7 \left(9-e^x\right)^{3/2}}","\frac{2}{7} \left(9-e^x\right)^{7/2}-18 \left(9-e^x\right)^{5/2}+540 \left(9-e^x\right)^{3/2}-14580 \sqrt{9-e^x}-\frac{65610}{\sqrt{9-e^x}}+\frac{39366}{\left(9-e^x\right)^{3/2}}",1,"(-2*(5038848 - 839808*E^x + 23328*E^(2*x) + 432*E^(3*x) + 18*E^(4*x) + E^(5*x)))/(7*(9 - E^x)^(3/2))","A",1
712,1,55,55,0.0300338,"\int \left(2-7 e^{x^4}\right)^5 x^3 \, dx","Integrate[(2 - 7*E^x^4)^5*x^3,x]","8 x^4-140 e^{x^4}+490 e^{2 x^4}-\frac{3430 e^{3 x^4}}{3}+\frac{12005 e^{4 x^4}}{8}-\frac{16807 e^{5 x^4}}{20}","8 x^4-140 e^{x^4}+490 e^{2 x^4}-\frac{3430 e^{3 x^4}}{3}+\frac{12005 e^{4 x^4}}{8}-\frac{16807 e^{5 x^4}}{20}",1,"-140*E^x^4 + 490*E^(2*x^4) - (3430*E^(3*x^4))/3 + (12005*E^(4*x^4))/8 - (16807*E^(5*x^4))/20 + 8*x^4","A",1
713,1,32,35,0.028788,"\int e^{x^2} \sqrt{1-e^{2 x^2}} x \, dx","Integrate[E^x^2*Sqrt[1 - E^(2*x^2)]*x,x]","\frac{1}{4} \left(e^{x^2} \sqrt{1-e^{2 x^2}}+\sin ^{-1}\left(e^{x^2}\right)\right)","\frac{1}{4} e^{x^2} \sqrt{1-e^{2 x^2}}+\frac{1}{4} \sin ^{-1}\left(e^{x^2}\right)",1,"(E^x^2*Sqrt[1 - E^(2*x^2)] + ArcSin[E^x^2])/4","A",1
714,1,29,32,0.0246729,"\int e^{x^3} \left(1-e^{4 x^3}\right)^2 x^2 \, dx","Integrate[E^x^3*(1 - E^(4*x^3))^2*x^2,x]","\frac{1}{135} e^{x^3} \left(-18 e^{4 x^3}+5 e^{8 x^3}+45\right)","\frac{e^{x^3}}{3}-\frac{2 e^{5 x^3}}{15}+\frac{e^{9 x^3}}{27}",1,"(E^x^3*(45 - 18*E^(4*x^3) + 5*E^(8*x^3)))/135","A",1
715,1,5,5,0.0050602,"\int e^{e^x+x} \, dx","Integrate[E^(E^x + x),x]","e^{e^x}","e^{e^x}",1,"E^E^x","A",1
716,1,7,7,0.0123553,"\int e^{e^{e^x}+e^x+x} \, dx","Integrate[E^(E^E^x + E^x + x),x]","e^{e^{e^x}}","e^{e^{e^x}}",1,"E^E^E^x","A",1
717,1,20,22,0.0149901,"\int \left(e^{-x}+e^x\right)^2 \, dx","Integrate[(E^(-x) + E^x)^2,x]","\frac{1}{2} \left(4 x-e^{-2 x}+e^{2 x}\right)","2 x-\frac{e^{-2 x}}{2}+\frac{e^{2 x}}{2}",1,"(-E^(-2*x) + E^(2*x) + 4*x)/2","A",1
718,1,4,4,0.0028234,"\int \frac{1}{e^{-x}+e^x} \, dx","Integrate[(E^(-x) + E^x)^(-1),x]","\tan ^{-1}\left(e^x\right)","\tan ^{-1}\left(e^x\right)",1,"ArcTan[E^x]","A",1
719,1,13,13,0.0098048,"\int \frac{1}{\left(e^{-x}+e^x\right)^2} \, dx","Integrate[(E^(-x) + E^x)^(-2),x]","-\frac{1}{2 e^{2 x}+2}","-\frac{1}{2 \left(e^{2 x}+1\right)}",1,"-(2 + 2*E^(2*x))^(-1)","A",1
720,1,6,6,0.0041922,"\int \frac{1}{-e^{-x}+e^x} \, dx","Integrate[(-E^(-x) + E^x)^(-1),x]","-\tanh ^{-1}\left(e^x\right)","-\tanh ^{-1}\left(e^x\right)",1,"-ArcTanh[E^x]","A",1
721,1,11,15,0.0151322,"\int \frac{1}{\left(-e^{-x}+e^x\right)^2} \, dx","Integrate[(-E^(-x) + E^x)^(-2),x]","\frac{1}{2-2 e^{2 x}}","\frac{1}{2 \left(1-e^{2 x}\right)}",1,"(2 - 2*E^(2*x))^(-1)","A",1
722,1,22,22,0.0078995,"\int e^x \left(-e^{-x}+e^x\right)^2 \, dx","Integrate[E^x*(-E^(-x) + E^x)^2,x]","-e^{-x}-2 e^x+\frac{e^{3 x}}{3}","-e^{-x}-2 e^x+\frac{e^{3 x}}{3}",1,"-E^(-x) - 2*E^x + E^(3*x)/3","A",1
723,1,29,31,0.0145002,"\int e^x \left(-e^{-x}+e^x\right)^3 \, dx","Integrate[E^x*(-E^(-x) + E^x)^3,x]","\frac{1}{2} \left(6 x+e^{-2 x}-3 e^{2 x}+\frac{e^{4 x}}{2}\right)","3 x+\frac{e^{-2 x}}{2}-\frac{3 e^{2 x}}{2}+\frac{e^{4 x}}{4}",1,"(E^(-2*x) - 3*E^(2*x) + E^(4*x)/2 + 6*x)/2","A",1
724,1,21,22,0.0132522,"\int \frac{1+4^x}{1+2^x} \, dx","Integrate[(1 + 4^x)/(1 + 2^x),x]","\frac{2^x+x \log (2)-2 \log \left(2^x+1\right)}{\log (2)}","x-\frac{2 \log \left(2^x+1\right)}{\log (2)}+\frac{2^x}{\log (2)}",1,"(2^x + x*Log[2] - 2*Log[1 + 2^x])/Log[2]","A",1
725,1,23,34,0.0331178,"\int \frac{1+4^x}{1+2^{-x}} \, dx","Integrate[(1 + 4^x)/(1 + 2^(-x)),x]","\frac{2^x \left(2^x-2\right)+4 \log \left(2^x+1\right)}{\log (4)}","\frac{2 \log \left(2^x+1\right)}{\log (2)}-\frac{2^x}{\log (2)}+\frac{2^{2 x-1}}{\log (2)}",1,"(2^x*(-2 + 2^x) + 4*Log[1 + 2^x])/Log[4]","A",1
726,1,23,23,0.0867672,"\int \left(\frac{e^{(a+x)^2}}{x^2}-\frac{2 a e^{(a+x)^2}}{x}\right) \, dx","Integrate[E^(a + x)^2/x^2 - (2*a*E^(a + x)^2)/x,x]","\sqrt{\pi } \text{erfi}(a+x)-\frac{e^{(a+x)^2}}{x}","\sqrt{\pi } \text{erfi}(a+x)-\frac{e^{(a+x)^2}}{x}",1,"-(E^(a + x)^2/x) + Sqrt[Pi]*Erfi[a + x]","A",1
727,1,41,66,0.027555,"\int e^{-x^2} \left(x^4+x^6+x^8\right) \, dx","Integrate[(x^4 + x^6 + x^8)/E^x^2,x]","\frac{1}{32} \left(147 \sqrt{\pi } \text{erf}(x)-2 e^{-x^2} x \left(8 x^6+36 x^4+98 x^2+147\right)\right)","\frac{147}{32} \sqrt{\pi } \text{erf}(x)-\frac{147}{16} e^{-x^2} x-\frac{1}{2} e^{-x^2} x^7-\frac{9}{4} e^{-x^2} x^5-\frac{49}{8} e^{-x^2} x^3",1,"((-2*x*(147 + 98*x^2 + 36*x^4 + 8*x^6))/E^x^2 + 147*Sqrt[Pi]*Erf[x])/32","A",1
728,1,19,12,0.006227,"\int \frac{1}{-e^x+e^{3 x}} \, dx","Integrate[(-E^x + E^(3*x))^(-1),x]","e^{-x} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};e^{2 x}\right)","e^{-x}-\tanh ^{-1}\left(e^x\right)",1,"Hypergeometric2F1[-1/2, 1, 1/2, E^(2*x)]/E^x","C",1
729,1,12,16,0.0342354,"\int \frac{e^x \left(-5+x+x^2\right)}{(-1+x)^2} \, dx","Integrate[(E^x*(-5 + x + x^2))/(-1 + x)^2,x]","\frac{e^x (x+2)}{x-1}","e^x-\frac{3 e^x}{1-x}",1,"(E^x*(2 + x))/(-1 + x)","A",1
730,1,16,16,0.0346941,"\int \frac{e^{x^2} x^3}{\left(1+x^2\right)^2} \, dx","Integrate[(E^x^2*x^3)/(1 + x^2)^2,x]","\frac{e^{x^2}}{2 \left(x^2+1\right)}","\frac{e^{x^2}}{2 \left(x^2+1\right)}",1,"E^x^2/(2*(1 + x^2))","A",1
731,1,33,33,0.0166597,"\int \frac{e^{3 x}}{\sqrt{25+16 e^{2 x}}} \, dx","Integrate[E^(3*x)/Sqrt[25 + 16*E^(2*x)],x]","\frac{1}{32} e^x \sqrt{16 e^{2 x}+25}-\frac{25}{128} \sinh ^{-1}\left(\frac{4 e^x}{5}\right)","\frac{1}{32} e^x \sqrt{16 e^{2 x}+25}-\frac{25}{128} \sinh ^{-1}\left(\frac{4 e^x}{5}\right)",1,"(E^x*Sqrt[25 + 16*E^(2*x)])/32 - (25*ArcSinh[(4*E^x)/5])/128","A",1
732,1,11,11,0.0075245,"\int \frac{1+e^x}{\sqrt{e^x+x}} \, dx","Integrate[(1 + E^x)/Sqrt[E^x + x],x]","2 \sqrt{x+e^x}","2 \sqrt{x+e^x}",1,"2*Sqrt[E^x + x]","A",1
733,1,6,6,0.029127,"\int \frac{1+e^x}{e^x+x} \, dx","Integrate[(1 + E^x)/(E^x + x),x]","\log \left(x+e^x\right)","\log \left(x+e^x\right)",1,"Log[E^x + x]","A",1
734,1,19,19,0.0046467,"\int \frac{e^{x^2}}{x^2} \, dx","Integrate[E^x^2/x^2,x]","\sqrt{\pi } \text{erfi}(x)-\frac{e^{x^2}}{x}","\sqrt{\pi } \text{erfi}(x)-\frac{e^{x^2}}{x}",1,"-(E^x^2/x) + Sqrt[Pi]*Erfi[x]","A",1
735,1,16,19,0.014435,"\int \frac{e^{x^2} \left(1+4 x^4\right)}{x^2} \, dx","Integrate[(E^x^2*(1 + 4*x^4))/x^2,x]","\frac{e^{x^2} \left(2 x^2-1\right)}{x}","2 e^{x^2} x-\frac{e^{x^2}}{x}",1,"(E^x^2*(-1 + 2*x^2))/x","A",1
736,1,41,56,0.0455542,"\int \sqrt{f^x} (a+b x)^2 \, dx","Integrate[Sqrt[f^x]*(a + b*x)^2,x]","\frac{2 \sqrt{f^x} \left(\log ^2(f) (a+b x)^2-4 b \log (f) (a+b x)+8 b^2\right)}{\log ^3(f)}","-\frac{8 b \sqrt{f^x} (a+b x)}{\log ^2(f)}+\frac{2 \sqrt{f^x} (a+b x)^2}{\log (f)}+\frac{16 b^2 \sqrt{f^x}}{\log ^3(f)}",1,"(2*Sqrt[f^x]*(8*b^2 - 4*b*(a + b*x)*Log[f] + (a + b*x)^2*Log[f]^2))/Log[f]^3","A",1
737,1,12,15,0.0022009,"\int 3^{1+x^2} x \, dx","Integrate[3^(1 + x^2)*x,x]","\frac{3^{x^2+1}}{\log (9)}","\frac{3^{x^2+1}}{2 \log (3)}",1,"3^(1 + x^2)/Log[9]","A",1
738,1,14,14,0.0030651,"\int \frac{2^{\sqrt{x}}}{\sqrt{x}} \, dx","Integrate[2^Sqrt[x]/Sqrt[x],x]","\frac{2^{\sqrt{x}+1}}{\log (2)}","\frac{2^{\sqrt{x}+1}}{\log (2)}",1,"2^(1 + Sqrt[x])/Log[2]","A",1
739,1,11,11,0.0017961,"\int \frac{2^{\frac{1}{x}}}{x^2} \, dx","Integrate[2^x^(-1)/x^2,x]","-\frac{2^{\frac{1}{x}}}{\log (2)}","-\frac{2^{\frac{1}{x}}}{\log (2)}",1,"-(2^x^(-1)/Log[2])","A",1
740,1,20,20,0.0035326,"\int \left(2^{-x}+2^x\right) \, dx","Integrate[2^(-x) + 2^x,x]","\frac{2^x}{\log (2)}-\frac{2^{-x}}{\log (2)}","\frac{2^x}{\log (2)}-\frac{2^{-x}}{\log (2)}",1,"-(1/(2^x*Log[2])) + 2^x/Log[2]","A",1
741,1,19,32,0.020511,"\int e^{-4 x} \left(2-3 x+x^2\right) \, dx","Integrate[(2 - 3*x + x^2)/E^(4*x),x]","-\frac{1}{32} e^{-4 x} \left(8 x^2-20 x+11\right)","-\frac{1}{4} e^{-4 x} x^2+\frac{5}{8} e^{-4 x} x-\frac{11 e^{-4 x}}{32}",1,"-1/32*(11 - 20*x + 8*x^2)/E^(4*x)","A",1
742,1,33,33,0.0170593,"\int \left(k^{x/2}+x^{\sqrt{k}}\right) \, dx","Integrate[k^(x/2) + x^Sqrt[k],x]","\frac{2 k^{x/2}}{\log (k)}+\frac{x^{\sqrt{k}+1}}{\sqrt{k}+1}","\frac{2 k^{x/2}}{\log (k)}+\frac{x^{\sqrt{k}+1}}{\sqrt{k}+1}",1,"x^(1 + Sqrt[k])/(1 + Sqrt[k]) + (2*k^(x/2))/Log[k]","A",1
743,1,21,21,0.0030635,"\int \frac{10^{\sqrt{x}}}{\sqrt{x}} \, dx","Integrate[10^Sqrt[x]/Sqrt[x],x]","\frac{2^{\sqrt{x}+1} 5^{\sqrt{x}}}{\log (10)}","\frac{2^{\sqrt{x}+1} 5^{\sqrt{x}}}{\log (10)}",1,"(2^(1 + Sqrt[x])*5^Sqrt[x])/Log[10]","A",1
744,1,11,11,0.0051693,"\int \left(\frac{1}{\sqrt{e^x+x}}+\frac{e^x}{\sqrt{e^x+x}}\right) \, dx","Integrate[1/Sqrt[E^x + x] + E^x/Sqrt[E^x + x],x]","2 \sqrt{x+e^x}","2 \sqrt{x+e^x}",1,"2*Sqrt[E^x + x]","A",1
745,1,12,12,0.0963061,"\int \left(\frac{\left(1+e^x\right) x}{\sqrt{e^x+x}}+2 \sqrt{e^x+x}\right) \, dx","Integrate[((1 + E^x)*x)/Sqrt[E^x + x] + 2*Sqrt[E^x + x],x]","2 x \sqrt{x+e^x}","2 x \sqrt{x+e^x}",1,"2*x*Sqrt[E^x + x]","A",1
746,1,12,12,0.0456662,"\int \left(\frac{x}{\sqrt{e^x+x}}+\frac{e^x x}{\sqrt{e^x+x}}+2 \sqrt{e^x+x}\right) \, dx","Integrate[x/Sqrt[E^x + x] + (E^x*x)/Sqrt[E^x + x] + 2*Sqrt[E^x + x],x]","2 x \sqrt{x+e^x}","2 x \sqrt{x+e^x}",1,"2*x*Sqrt[E^x + x]","A",1
747,0,0,27,0.1588592,"\int \frac{\left(1+e^x\right) x}{\sqrt{e^x+x}} \, dx","Integrate[((1 + E^x)*x)/Sqrt[E^x + x],x]","\int \frac{\left(1+e^x\right) x}{\sqrt{e^x+x}} \, dx","2 x \sqrt{x+e^x}-2 \text{Int}\left(\sqrt{x+e^x},x\right)",0,"Integrate[((1 + E^x)*x)/Sqrt[E^x + x], x]","A",-1
748,0,0,27,0.0744643,"\int \left(\frac{x}{\sqrt{e^x+x}}+\frac{e^x x}{\sqrt{e^x+x}}\right) \, dx","Integrate[x/Sqrt[E^x + x] + (E^x*x)/Sqrt[E^x + x],x]","\int \left(\frac{x}{\sqrt{e^x+x}}+\frac{e^x x}{\sqrt{e^x+x}}\right) \, dx","2 x \sqrt{x+e^x}-2 \text{Int}\left(\sqrt{x+e^x},x\right)",0,"Integrate[x/Sqrt[E^x + x] + (E^x*x)/Sqrt[E^x + x], x]","A",-1
749,0,0,52,0.1018478,"\int \frac{e^x x}{\sqrt{e^x+x}} \, dx","Integrate[(E^x*x)/Sqrt[E^x + x],x]","\int \frac{e^x x}{\sqrt{e^x+x}} \, dx","-\text{Int}\left(\frac{1}{\sqrt{x+e^x}},x\right)-3 \text{Int}\left(\sqrt{x+e^x},x\right)+2 \sqrt{x+e^x} x+2 \sqrt{x+e^x}",0,"Integrate[(E^x*x)/Sqrt[E^x + x], x]","A",-1
750,1,20,20,0.1703509,"\int \left(\frac{x^2 \left(5 e^x+3 x^2\right)}{5 \sqrt{5 e^x+x^3}}+\frac{4}{5} x \sqrt{5 e^x+x^3}\right) \, dx","Integrate[(x^2*(5*E^x + 3*x^2))/(5*Sqrt[5*E^x + x^3]) + (4*x*Sqrt[5*E^x + x^3])/5,x]","\frac{2}{5} x^2 \sqrt{x^3+5 e^x}","\frac{2}{5} x^2 \sqrt{x^3+5 e^x}",1,"(2*x^2*Sqrt[5*E^x + x^3])/5","A",1
751,0,0,67,0.1906711,"\int \frac{e^x x^2}{\sqrt{5 e^x+x^3}} \, dx","Integrate[(E^x*x^2)/Sqrt[5*E^x + x^3],x]","\int \frac{e^x x^2}{\sqrt{5 e^x+x^3}} \, dx","-\frac{4}{5} \text{Int}\left(x \sqrt{x^3+5 e^x},x\right)-\frac{3}{5} \text{Int}\left(\frac{x^4}{\sqrt{x^3+5 e^x}},x\right)+\frac{2}{5} \sqrt{x^3+5 e^x} x^2",0,"Integrate[(E^x*x^2)/Sqrt[5*E^x + x^3], x]","A",-1
752,1,13,13,0.0089133,"\int -\frac{1+e^x}{\sqrt[3]{e^x+x}} \, dx","Integrate[-((1 + E^x)/(E^x + x)^(1/3)),x]","-\frac{3}{2} \left(x+e^x\right)^{2/3}","-\frac{3}{2} \left(x+e^x\right)^{2/3}",1,"(-3*(E^x + x)^(2/3))/2","A",1
753,1,13,13,0.0048726,"\int \left(-\frac{1}{\sqrt[3]{e^x+x}}+\frac{x}{\sqrt[3]{e^x+x}}-\left(e^x+x\right)^{2/3}\right) \, dx","Integrate[-(E^x + x)^(-1/3) + x/(E^x + x)^(1/3) - (E^x + x)^(2/3),x]","-\frac{3}{2} \left(x+e^x\right)^{2/3}","-\frac{3}{2} \left(x+e^x\right)^{2/3}",1,"(-3*(E^x + x)^(2/3))/2","A",1
754,0,0,38,0.0499296,"\int \frac{x}{\sqrt[3]{e^x+x}} \, dx","Integrate[x/(E^x + x)^(1/3),x]","\int \frac{x}{\sqrt[3]{e^x+x}} \, dx","\text{Int}\left(\frac{1}{\sqrt[3]{x+e^x}},x\right)+\text{Int}\left(\left(x+e^x\right)^{2/3},x\right)-\frac{3}{2} \left(x+e^x\right)^{2/3}",0,"Integrate[x/(E^x + x)^(1/3), x]","A",-1
755,1,12,12,0.0974269,"\int \frac{5 x+e^x (3+2 x)}{\sqrt[3]{e^x+x}} \, dx","Integrate[(5*x + E^x*(3 + 2*x))/(E^x + x)^(1/3),x]","3 x \left(x+e^x\right)^{2/3}","3 x \left(x+e^x\right)^{2/3}",1,"3*x*(E^x + x)^(2/3)","A",1
756,1,12,12,0.0510795,"\int \left(\frac{2 x}{\sqrt[3]{e^x+x}}+\frac{2 e^x x}{\sqrt[3]{e^x+x}}+3 \left(e^x+x\right)^{2/3}\right) \, dx","Integrate[(2*x)/(E^x + x)^(1/3) + (2*E^x*x)/(E^x + x)^(1/3) + 3*(E^x + x)^(2/3),x]","3 x \left(x+e^x\right)^{2/3}","3 x \left(x+e^x\right)^{2/3}",1,"3*x*(E^x + x)^(2/3)","A",1
757,1,31,31,0.0107099,"\int e^x \left(-e^{-x}+e^x\right) \left(e^{-x}+e^x\right)^2 \, dx","Integrate[E^x*(-E^(-x) + E^x)*(E^(-x) + E^x)^2,x]","-x+\frac{e^{-2 x}}{2}+\frac{e^{2 x}}{2}+\frac{e^{4 x}}{4}","-x+\frac{e^{-2 x}}{2}+\frac{e^{2 x}}{2}+\frac{e^{4 x}}{4}",1,"1/(2*E^(2*x)) + E^(2*x)/2 + E^(4*x)/4 - x","A",1
758,0,0,12,2.511802,"\int \frac{x}{e^x+x} \, dx","Integrate[x/(E^x + x),x]","\int \frac{x}{e^x+x} \, dx","\text{Int}\left(\frac{x}{x+e^x},x\right)",0,"Integrate[x/(E^x + x), x]","A",-1
759,0,0,16,0.0486024,"\int \frac{x^2}{\sqrt{e^x+x}} \, dx","Integrate[x^2/Sqrt[E^x + x],x]","\int \frac{x^2}{\sqrt{e^x+x}} \, dx","\text{Int}\left(\frac{x^2}{\sqrt{x+e^x}},x\right)",0,"Integrate[x^2/Sqrt[E^x + x], x]","A",-1
760,0,0,14,0.0177754,"\int \frac{e^x}{e^x+x} \, dx","Integrate[E^x/(E^x + x),x]","\int \frac{e^x}{e^x+x} \, dx","\text{Int}\left(\frac{e^x}{x+e^x},x\right)",0,"Integrate[E^x/(E^x + x), x]","A",-1
761,0,0,16,0.0339042,"\int \frac{e^x}{e^x+x^2} \, dx","Integrate[E^x/(E^x + x^2),x]","\int \frac{e^x}{e^x+x^2} \, dx","\text{Int}\left(\frac{e^x}{x^2+e^x},x\right)",0,"Integrate[E^x/(E^x + x^2), x]","A",-1
762,0,0,15,0.0457658,"\int \frac{\text{F0}(x)}{x+\text{F0}(x)} \, dx","Integrate[F0[x]/(x + F0[x]),x]","\int \frac{\text{F0}(x)}{x+\text{F0}(x)} \, dx","x-\text{Int}\left(\frac{x}{\text{F0}(x)+x},x\right)",0,"Integrate[F0[x]/(x + F0[x]), x]","A",-1
763,0,0,19,0.0520168,"\int \frac{\text{F0}(x)}{x^2+\text{F0}(x)} \, dx","Integrate[F0[x]/(x^2 + F0[x]),x]","\int \frac{\text{F0}(x)}{x^2+\text{F0}(x)} \, dx","x-\text{Int}\left(\frac{x^2}{\text{F0}(x)+x^2},x\right)",0,"Integrate[F0[x]/(x^2 + F0[x]), x]","A",-1
764,0,0,23,0.0212347,"\int \frac{\text{F0}(x)}{(x+\text{F0}(x))^2} \, dx","Integrate[F0[x]/(x + F0[x])^2,x]","\int \frac{\text{F0}(x)}{(x+\text{F0}(x))^2} \, dx","\text{Int}\left(\frac{1}{\text{F0}(x)+x},x\right)-\text{Int}\left(\frac{x}{(\text{F0}(x)+x)^2},x\right)",0,"Integrate[F0[x]/(x + F0[x])^2, x]","A",-1
765,0,0,29,0.0230729,"\int \frac{\text{F0}(x)}{\left(x^2+\text{F0}(x)\right)^2} \, dx","Integrate[F0[x]/(x^2 + F0[x])^2,x]","\int \frac{\text{F0}(x)}{\left(x^2+\text{F0}(x)\right)^2} \, dx","\text{Int}\left(\frac{1}{\text{F0}(x)+x^2},x\right)-\text{Int}\left(\frac{x^2}{\left(\text{F0}(x)+x^2\right)^2},x\right)",0,"Integrate[F0[x]/(x^2 + F0[x])^2, x]","A",-1
766,1,36,36,0.0462852,"\int \left(a F^{c+d x}\right)^m \left(b F^{e+f x}\right)^n \, dx","Integrate[(a*F^(c + d*x))^m*(b*F^(e + f*x))^n,x]","\frac{\left(a F^{c+d x}\right)^m \left(b F^{e+f x}\right)^n}{d m \log (F)+f n \log (F)}","\frac{\left(a F^{c+d x}\right)^m \left(b F^{e+f x}\right)^n}{\log (F) (d m+f n)}",1,"((a*F^(c + d*x))^m*(b*F^(e + f*x))^n)/(d*m*Log[F] + f*n*Log[F])","A",1
767,1,37,37,0.0178831,"\int e^{a+c+b x^n+d x^n} \, dx","Integrate[E^(a + c + b*x^n + d*x^n),x]","-\frac{x e^{a+c} \left(-\left((b+d) x^n\right)\right)^{-1/n} \Gamma \left(\frac{1}{n},-\left((b+d) x^n\right)\right)}{n}","-\frac{x e^{a+c} \left(-\left((b+d) x^n\right)\right)^{-1/n} \Gamma \left(\frac{1}{n},-\left((b+d) x^n\right)\right)}{n}",1,"-((E^(a + c)*x*Gamma[n^(-1), -((b + d)*x^n)])/(n*(-((b + d)*x^n))^n^(-1)))","A",1
768,1,50,50,0.0256383,"\int f^{a+b x^n} g^{c+d x^n} \, dx","Integrate[f^(a + b*x^n)*g^(c + d*x^n),x]","-\frac{x f^a g^c \left(-x^n (b \log (f)+d \log (g))\right)^{-1/n} \Gamma \left(\frac{1}{n},-x^n (b \log (f)+d \log (g))\right)}{n}","-\frac{x f^a g^c \left(-x^n (b \log (f)+d \log (g))\right)^{-1/n} \Gamma \left(\frac{1}{n},-x^n (b \log (f)+d \log (g))\right)}{n}",1,"-((f^a*g^c*x*Gamma[n^(-1), -(x^n*(b*Log[f] + d*Log[g]))])/(n*(-(x^n*(b*Log[f] + d*Log[g])))^n^(-1)))","A",1
769,1,37,37,0.0082794,"\int e^{x^n} x^m \, dx","Integrate[E^x^n*x^m,x]","-\frac{x^{m+1} \left(-x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-x^n\right)}{n}","-\frac{x^{m+1} \left(-x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-x^n\right)}{n}",1,"-((x^(1 + m)*Gamma[(1 + m)/n, -x^n])/(n*(-x^n)^((1 + m)/n)))","A",1
770,1,41,41,0.0089948,"\int f^{x^n} x^m \, dx","Integrate[f^x^n*x^m,x]","-\frac{x^{m+1} \left(\log (f) \left(-x^n\right)\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-x^n \log (f)\right)}{n}","-\frac{x^{m+1} \left(\log (f) \left(-x^n\right)\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-x^n \log (f)\right)}{n}",1,"-((x^(1 + m)*Gamma[(1 + m)/n, -(x^n*Log[f])])/(n*(-(x^n*Log[f]))^((1 + m)/n)))","A",1
771,1,52,52,0.0154838,"\int e^{(a+b x)^n} (a+b x)^m \, dx","Integrate[E^(a + b*x)^n*(a + b*x)^m,x]","-\frac{(a+b x)^{m+1} \left(-(a+b x)^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-(a+b x)^n\right)}{b n}","-\frac{(a+b x)^{m+1} \left(-(a+b x)^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-(a+b x)^n\right)}{b n}",1,"-(((a + b*x)^(1 + m)*Gamma[(1 + m)/n, -(a + b*x)^n])/(b*n*(-(a + b*x)^n)^((1 + m)/n)))","A",1
772,1,56,56,0.0139543,"\int f^{(a+b x)^n} (a+b x)^m \, dx","Integrate[f^(a + b*x)^n*(a + b*x)^m,x]","-\frac{(a+b x)^{m+1} \left(\log (f) \left(-(a+b x)^n\right)\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-(a+b x)^n \log (f)\right)}{b n}","-\frac{(a+b x)^{m+1} \left(\log (f) \left(-(a+b x)^n\right)\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-(a+b x)^n \log (f)\right)}{b n}",1,"-(((a + b*x)^(1 + m)*Gamma[(1 + m)/n, -((a + b*x)^n*Log[f])])/(b*n*(-((a + b*x)^n*Log[f]))^((1 + m)/n)))","A",1
773,1,74,80,0.0378623,"\int e^{(a+b x)^3} x \, dx","Integrate[E^(a + b*x)^3*x,x]","\frac{(a+b x) \left(a \sqrt[3]{-(a+b x)^3} \Gamma \left(\frac{1}{3},-(a+b x)^3\right)-(a+b x) \Gamma \left(\frac{2}{3},-(a+b x)^3\right)\right)}{3 b^2 \left(-(a+b x)^3\right)^{2/3}}","\frac{a (a+b x) \Gamma \left(\frac{1}{3},-(a+b x)^3\right)}{3 b^2 \sqrt[3]{-(a+b x)^3}}-\frac{(a+b x)^2 \Gamma \left(\frac{2}{3},-(a+b x)^3\right)}{3 b^2 \left(-(a+b x)^3\right)^{2/3}}",1,"((a + b*x)*(a*(-(a + b*x)^3)^(1/3)*Gamma[1/3, -(a + b*x)^3] - (a + b*x)*Gamma[2/3, -(a + b*x)^3]))/(3*b^2*(-(a + b*x)^3)^(2/3))","A",1
774,1,17,17,0.2395674,"\int \frac{5 x^2+3 \sqrt[3]{e^x+x}+e^x \left(3 x+2 x^2\right)}{x \sqrt[3]{e^x+x}} \, dx","Integrate[(5*x^2 + 3*(E^x + x)^(1/3) + E^x*(3*x + 2*x^2))/(x*(E^x + x)^(1/3)),x]","3 \left(x+e^x\right)^{2/3} x+3 \log (x)","3 \left(x+e^x\right)^{2/3} x+3 \log (x)",1,"3*x*(E^x + x)^(2/3) + 3*Log[x]","A",1