1,1,12,0,0.0168879,"\int \frac{e^x}{4+6 e^x} \, dx","Int[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",2,2,13,0.1538,1,"{2246, 31}"
2,1,12,0,0.0197353,"\int \frac{e^x}{a+b e^x} \, dx","Int[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",2,2,13,0.1538,1,"{2246, 31}"
3,1,24,0,0.0692306,"\int \frac{e^{d x}}{a+b e^{c+d x}} \, dx","Int[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",3,3,19,0.1579,1,"{2247, 2246, 31}"
4,1,19,0,0.0359485,"\int \frac{e^{c+d x}}{a+b e^{c+d x}} \, dx","Int[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",2,2,21,0.09524,1,"{2246, 31}"
5,1,20,0,0.019931,"\int e^x \left(a+b e^x\right)^n \, dx","Int[E^x*(a + b*E^x)^n,x]","\frac{\left(a+b e^x\right)^{n+1}}{b (n+1)}","\frac{\left(a+b e^x\right)^{n+1}}{b (n+1)}",1,"(a + b*E^x)^(1 + n)/(b*(1 + n))","A",2,2,13,0.1538,1,"{2246, 32}"
6,1,32,0,0.0696912,"\int e^{d x} \left(a+b e^{c+d x}\right)^n \, dx","Int[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+1)}","\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)/(b*d*E^c*(1 + n))","A",3,3,19,0.1579,1,"{2247, 2246, 32}"
7,1,27,0,0.0350901,"\int e^{c+d x} \left(a+b e^{c+d x}\right)^n \, dx","Int[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+1)}","\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*(1 + n))","A",2,2,21,0.09524,1,"{2246, 32}"
8,1,16,0,0.0205769,"\int \frac{F^x}{a+b F^x} \, dx","Int[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",2,2,13,0.1538,1,"{2246, 31}"
9,1,28,0,0.0707328,"\int \frac{F^{d x}}{a+b F^{c+d x}} \, dx","Int[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",3,3,19,0.1579,1,"{2247, 2246, 31}"
10,1,23,0,0.0358378,"\int \frac{F^{c+d x}}{a+b F^{c+d x}} \, dx","Int[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",2,2,21,0.09524,1,"{2246, 31}"
11,1,24,0,0.0229501,"\int F^x \left(a+b F^x\right)^n \, dx","Int[F^x*(a + b*F^x)^n,x]","\frac{\left(a+b F^x\right)^{n+1}}{b (n+1) \log (F)}","\frac{\left(a+b F^x\right)^{n+1}}{b (n+1) \log (F)}",1,"(a + b*F^x)^(1 + n)/(b*(1 + n)*Log[F])","A",2,2,13,0.1538,1,"{2246, 32}"
12,1,36,0,0.0734713,"\int F^{d x} \left(a+b F^{c+d x}\right)^n \, dx","Int[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+1) \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)/(b*d*F^c*(1 + n)*Log[F])","A",3,3,19,0.1579,1,"{2247, 2246, 32}"
13,1,31,0,0.0351259,"\int F^{c+d x} \left(a+b F^{c+d x}\right)^n \, dx","Int[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+1) \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*(1 + n)*Log[F])","A",2,2,21,0.09524,1,"{2246, 32}"
14,1,25,0,0.0373275,"\int \left(e^x\right)^n \left(a+b \left(e^x\right)^n\right)^p \, dx","Int[(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+1)}","\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*(1 + p))","A",2,2,17,0.1176,1,"{2246, 32}"
15,1,37,0,0.0589087,"\int e^{n x} \left(a+b \left(e^x\right)^n\right)^p \, dx","Int[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+1)}","\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))/(b*(E^x)^n*n*(1 + p))","A",3,3,17,0.1765,1,"{2247, 2246, 32}"
16,1,41,0,0.0646444,"\int \left(F^{e (c+d x)}\right)^n \left(a+b \left(F^{e (c+d x)}\right)^n\right)^p \, dx","Int[(F^(e*(c + d*x)))^n*(a + b*(F^(e*(c + d*x)))^n)^p,x]","\frac{\left(a+b \left(F^{e (c+d x)}\right)^n\right)^{p+1}}{b d e n (p+1) \log (F)}","\frac{\left(a+b \left(F^{e (c+d x)}\right)^n\right)^{p+1}}{b d e n (p+1) \log (F)}",1,"(a + b*(F^(e*(c + d*x)))^n)^(1 + p)/(b*d*e*n*(1 + p)*Log[F])","A",2,2,29,0.06897,1,"{2246, 32}"
17,1,80,0,0.1346392,"\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","Int[(a + b*(F^(e*(c + d*x)))^n)^p*(G^(h*(f + g*x)))^((d*e*n*Log[F])/(g*h*Log[G])),x]","\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)}","\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,"((a + b*(F^(e*(c + d*x)))^n)^(1 + p)*(G^(h*(f + g*x)))^((d*e*n*Log[F])/(g*h*Log[G])))/(b*d*e*(F^(e*(c + d*x)))^n*n*(1 + p)*Log[F])","A",3,3,44,0.06818,1,"{2247, 2246, 32}"
18,1,22,0,0.0320372,"\int \frac{e^{2 x}}{a+b e^x} \, dx","Int[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",3,2,15,0.1333,1,"{2248, 43}"
19,1,27,0,0.0337294,"\int \frac{e^{2 x}}{\left(a+b e^x\right)^2} \, dx","Int[E^(2*x)/(a + b*E^x)^2,x]","\frac{a}{b^2 \left(a+b e^x\right)}+\frac{\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/(b^2*(a + b*E^x)) + Log[a + b*E^x]/b^2","A",3,2,15,0.1333,1,"{2248, 43}"
20,1,21,0,0.0226021,"\int \frac{e^{2 x}}{\left(a+b e^x\right)^3} \, dx","Int[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",2,2,15,0.1333,1,"{2248, 37}"
21,1,34,0,0.0359505,"\int \frac{e^{2 x}}{\left(a+b e^x\right)^4} \, dx","Int[E^(2*x)/(a + b*E^x)^4,x]","\frac{a}{3 b^2 \left(a+b e^x\right)^3}-\frac{1}{2 b^2 \left(a+b e^x\right)^2}","\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,"a/(3*b^2*(a + b*E^x)^3) - 1/(2*b^2*(a + b*E^x)^2)","A",3,2,15,0.1333,1,"{2248, 43}"
22,1,31,0,0.0338813,"\int \frac{e^{4 x}}{a+b e^{2 x}} \, dx","Int[E^(4*x)/(a + b*E^(2*x)),x]","\frac{e^{2 x}}{2 b}-\frac{a \log \left(a+b e^{2 x}\right)}{2 b^2}","\frac{e^{2 x}}{2 b}-\frac{a \log \left(a+b e^{2 x}\right)}{2 b^2}",1,"E^(2*x)/(2*b) - (a*Log[a + b*E^(2*x)])/(2*b^2)","A",3,2,17,0.1176,1,"{2248, 43}"
23,1,37,0,0.037703,"\int \frac{e^{4 x}}{\left(a+b e^{2 x}\right)^2} \, dx","Int[E^(4*x)/(a + b*E^(2*x))^2,x]","\frac{a}{2 b^2 \left(a+b e^{2 x}\right)}+\frac{\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/(2*b^2*(a + b*E^(2*x))) + Log[a + b*E^(2*x)]/(2*b^2)","A",3,2,17,0.1176,1,"{2248, 43}"
24,1,23,0,0.0267732,"\int \frac{e^{4 x}}{\left(a+b e^{2 x}\right)^3} \, dx","Int[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",2,2,17,0.1176,1,"{2248, 37}"
25,1,38,0,0.0366779,"\int \frac{e^{4 x}}{\left(a+b e^{2 x}\right)^4} \, dx","Int[E^(4*x)/(a + b*E^(2*x))^4,x]","\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}","\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,"a/(6*b^2*(a + b*E^(2*x))^3) - 1/(4*b^2*(a + b*E^(2*x))^2)","A",3,2,17,0.1176,1,"{2248, 43}"
26,1,42,0,0.0478876,"\int \frac{e^{4 x}}{\left(a+b e^{2 x}\right)^{2/3}} \, dx","Int[E^(4*x)/(a + b*E^(2*x))^(2/3),x]","\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}","\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*a*(a + b*E^(2*x))^(1/3))/(2*b^2) + (3*(a + b*E^(2*x))^(4/3))/(8*b^2)","A",3,2,19,0.1053,1,"{2248, 43}"
27,1,16,0,0.0185339,"\int e^{-n x} \left(a+b e^{n x}\right) \, dx","Int[(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",3,2,16,0.1250,1,"{2248, 43}"
28,1,32,0,0.0342845,"\int e^{-n x} \left(a+b e^{n x}\right)^2 \, dx","Int[(a + b*E^(n*x))^2/E^(n*x),x]","-\frac{a^2 e^{-n x}}{n}+2 a b x+\frac{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)*n)) + (b^2*E^(n*x))/n + 2*a*b*x","A",3,2,18,0.1111,1,"{2248, 43}"
29,1,52,0,0.0416476,"\int e^{-n x} \left(a+b e^{n x}\right)^3 \, dx","Int[(a + b*E^(n*x))^3/E^(n*x),x]","3 a^2 b x-\frac{a^3 e^{-n x}}{n}+\frac{3 a b^2 e^{n x}}{n}+\frac{b^3 e^{2 n x}}{2 n}","3 a^2 b x-\frac{a^3 e^{-n x}}{n}+\frac{3 a b^2 e^{n x}}{n}+\frac{b^3 e^{2 n x}}{2 n}",1,"-(a^3/(E^(n*x)*n)) + (3*a*b^2*E^(n*x))/n + (b^3*E^(2*n*x))/(2*n) + 3*a^2*b*x","A",3,2,18,0.1111,1,"{2248, 43}"
30,1,40,0,0.0438791,"\int \frac{e^{-n x}}{a+b e^{n x}} \, dx","Int[1/(E^(n*x)*(a + b*E^(n*x))),x]","\frac{b \log \left(a+b e^{n x}\right)}{a^2 n}-\frac{b x}{a^2}-\frac{e^{-n x}}{a 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,"-(1/(a*E^(n*x)*n)) - (b*x)/a^2 + (b*Log[a + b*E^(n*x)])/(a^2*n)","A",3,2,18,0.1111,1,"{2248, 44}"
31,1,61,0,0.0572723,"\int \frac{e^{-n x}}{\left(a+b e^{n x}\right)^2} \, dx","Int[1/(E^(n*x)*(a + b*E^(n*x))^2),x]","-\frac{b}{a^2 n \left(a+b e^{n x}\right)}+\frac{2 b \log \left(a+b e^{n x}\right)}{a^3 n}-\frac{2 b x}{a^3}-\frac{e^{-n x}}{a^2 n}","-\frac{b}{a^2 n \left(a+b e^{n x}\right)}+\frac{2 b \log \left(a+b e^{n x}\right)}{a^3 n}-\frac{2 b x}{a^3}-\frac{e^{-n x}}{a^2 n}",1,"-(1/(a^2*E^(n*x)*n)) - b/(a^2*(a + b*E^(n*x))*n) - (2*b*x)/a^3 + (2*b*Log[a + b*E^(n*x)])/(a^3*n)","A",3,2,18,0.1111,1,"{2248, 44}"
32,1,83,0,0.0683861,"\int \frac{e^{-n x}}{\left(a+b e^{n x}\right)^3} \, dx","Int[1/(E^(n*x)*(a + b*E^(n*x))^3),x]","-\frac{2 b}{a^3 n \left(a+b e^{n x}\right)}-\frac{b}{2 a^2 n \left(a+b e^{n x}\right)^2}+\frac{3 b \log \left(a+b e^{n x}\right)}{a^4 n}-\frac{3 b x}{a^4}-\frac{e^{-n x}}{a^3 n}","-\frac{2 b}{a^3 n \left(a+b e^{n x}\right)}-\frac{b}{2 a^2 n \left(a+b e^{n x}\right)^2}+\frac{3 b \log \left(a+b e^{n x}\right)}{a^4 n}-\frac{3 b x}{a^4}-\frac{e^{-n x}}{a^3 n}",1,"-(1/(a^3*E^(n*x)*n)) - b/(2*a^2*(a + b*E^(n*x))^2*n) - (2*b)/(a^3*(a + b*E^(n*x))*n) - (3*b*x)/a^4 + (3*b*Log[a + b*E^(n*x)])/(a^4*n)","A",3,2,18,0.1111,1,"{2248, 44}"
33,1,50,0,0.077644,"\int \frac{f^{a+b x}}{c+d f^{e+2 b x}} \, dx","Int[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",2,2,22,0.09091,1,"{2249, 205}"
34,1,34,0,0.0811105,"\int \frac{f^{a+2 b x}}{c+d f^{e+2 b x}} \, dx","Int[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",3,3,23,0.1304,1,"{2247, 2246, 31}"
35,1,88,0,0.067568,"\int \frac{f^{a+3 b x}}{c+d f^{e+2 b x}} \, dx","Int[f^(a + 3*b*x)/(c + d*f^(e + 2*b*x)),x]","\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)}","\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^((2*a - 3*e)/2 + (e + 2*b*x)/2)/(b*d*Log[f]) - (Sqrt[c]*f^(a - (3*e)/2)*ArcTan[(Sqrt[d]*f^((e + 2*b*x)/2))/Sqrt[c]])/(b*d^(3/2)*Log[f])","A",3,3,23,0.1304,1,"{2248, 321, 205}"
36,1,61,0,0.060494,"\int \frac{f^{a+4 b x}}{c+d f^{e+2 b x}} \, dx","Int[f^(a + 4*b*x)/(c + d*f^(e + 2*b*x)),x]","\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)}","\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 - e + 2*b*x)/(2*b*d*Log[f]) - (c*f^(a - 2*e)*Log[c + d*f^(e + 2*b*x)])/(2*b*d^2*Log[f])","A",3,2,23,0.08696,1,"{2248, 43}"
37,1,127,0,0.079692,"\int \frac{f^{a+5 b x}}{c+d f^{e+2 b x}} \, dx","Int[f^(a + 5*b*x)/(c + d*f^(e + 2*b*x)),x]","\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)}","\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,"-((c*f^((2*a - 5*e)/2 + (e + 2*b*x)/2))/(b*d^2*Log[f])) + f^((2*a - 5*e)/2 + (3*(e + 2*b*x))/2)/(3*b*d*Log[f]) + (c^(3/2)*f^(a - (5*e)/2)*ArcTan[(Sqrt[d]*f^((e + 2*b*x)/2))/Sqrt[c]])/(b*d^(5/2)*Log[f])","A",4,3,23,0.1304,1,"{2248, 302, 205}"
38,1,4,0,0.0173531,"\int \frac{e^x}{1+e^{2 x}} \, dx","Int[E^x/(1 + E^(2*x)),x]","\tan ^{-1}\left(e^x\right)","\tan ^{-1}\left(e^x\right)",1,"ArcTan[E^x]","A",2,2,13,0.1538,1,"{2249, 203}"
39,1,4,0,0.0194058,"\int \frac{e^x}{1-e^{2 x}} \, dx","Int[E^x/(1 - E^(2*x)),x]","\tanh ^{-1}\left(e^x\right)","\tanh ^{-1}\left(e^x\right)",1,"ArcTanh[E^x]","A",2,2,15,0.1333,1,"{2249, 206}"
40,1,27,0,0.0581555,"\int \frac{e^x x}{1-e^{2 x}} \, dx","Int[(E^x*x)/(1 - E^(2*x)),x]","\frac{1}{2} \text{PolyLog}\left(2,-e^x\right)-\frac{1}{2} \text{PolyLog}\left(2,e^x\right)+x \tanh ^{-1}\left(e^x\right)","\frac{1}{2} \text{PolyLog}\left(2,-e^x\right)-\frac{1}{2} \text{PolyLog}\left(2,e^x\right)+x \tanh ^{-1}\left(e^x\right)",1,"x*ArcTanh[E^x] + PolyLog[2, -E^x]/2 - PolyLog[2, E^x]/2","A",3,5,16,0.3125,1,"{2249, 206, 2245, 2282, 5912}"
41,1,40,0,0.1004041,"\int \frac{e^x x^2}{1-e^{2 x}} \, dx","Int[(E^x*x^2)/(1 - E^(2*x)),x]","x \text{PolyLog}\left(2,-e^x\right)-x \text{PolyLog}\left(2,e^x\right)-\text{PolyLog}\left(3,-e^x\right)+\text{PolyLog}\left(3,e^x\right)+x^2 \tanh ^{-1}\left(e^x\right)","x \text{PolyLog}\left(2,-e^x\right)-x \text{PolyLog}\left(2,e^x\right)-\text{PolyLog}\left(3,-e^x\right)+\text{PolyLog}\left(3,e^x\right)+x^2 \tanh ^{-1}\left(e^x\right)",1,"x^2*ArcTanh[E^x] + x*PolyLog[2, -E^x] - x*PolyLog[2, E^x] - PolyLog[3, -E^x] + PolyLog[3, E^x]","A",8,7,18,0.3889,1,"{2249, 206, 2245, 6213, 2531, 2282, 6589}"
42,1,69,0,0.1210562,"\int \frac{e^x x^3}{1-e^{2 x}} \, dx","Int[(E^x*x^3)/(1 - E^(2*x)),x]","\frac{3}{2} x^2 \text{PolyLog}\left(2,-e^x\right)-\frac{3}{2} x^2 \text{PolyLog}\left(2,e^x\right)-3 x \text{PolyLog}\left(3,-e^x\right)+3 x \text{PolyLog}\left(3,e^x\right)+3 \text{PolyLog}\left(4,-e^x\right)-3 \text{PolyLog}\left(4,e^x\right)+x^3 \tanh ^{-1}\left(e^x\right)","\frac{3}{2} x^2 \text{PolyLog}\left(2,-e^x\right)-\frac{3}{2} x^2 \text{PolyLog}\left(2,e^x\right)-3 x \text{PolyLog}\left(3,-e^x\right)+3 x \text{PolyLog}\left(3,e^x\right)+3 \text{PolyLog}\left(4,-e^x\right)-3 \text{PolyLog}\left(4,e^x\right)+x^3 \tanh ^{-1}\left(e^x\right)",1,"x^3*ArcTanh[E^x] + (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",10,8,18,0.4444,1,"{2249, 206, 2245, 6213, 2531, 6609, 2282, 6589}"
43,1,30,0,0.029278,"\int \frac{f^x}{a+b f^{2 x}} \, dx","Int[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",2,2,15,0.1333,1,"{2249, 205}"
44,1,110,0,0.1060203,"\int \frac{f^x x}{a+b f^{2 x}} \, dx","Int[(f^x*x)/(a + b*f^(2*x)),x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,\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)}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,\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,"(x*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]) - ((I/2)*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^2) + ((I/2)*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^2)","A",6,7,16,0.4375,1,"{2249, 205, 2245, 12, 2282, 4848, 2391}"
45,1,184,0,0.1786647,"\int \frac{f^x x^2}{a+b f^{2 x}} \, dx","Int[(f^x*x^2)/(a + b*f^(2*x)),x]","-\frac{i x \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i x \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{i \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}+\frac{x^2 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (f)}","-\frac{i x \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i x \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{i \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}+\frac{x^2 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"(x^2*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]) - (I*x*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^2) + (I*x*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^2) + (I*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^3) - (I*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^3)","A",9,8,18,0.4444,1,"{2249, 205, 2245, 12, 5143, 2531, 2282, 6589}"
46,1,268,0,0.2299598,"\int \frac{f^x x^3}{a+b f^{2 x}} \, dx","Int[(f^x*x^3)/(a + b*f^(2*x)),x]","-\frac{3 i x^2 \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{3 i x^2 \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{3 i x \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{3 i \text{PolyLog}\left(4,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{3 i \text{PolyLog}\left(4,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{x^3 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (f)}","-\frac{3 i x^2 \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{3 i x^2 \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{3 i x \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{3 i \text{PolyLog}\left(4,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{3 i \text{PolyLog}\left(4,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{x^3 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"(x^3*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]) - (((3*I)/2)*x^2*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^2) + (((3*I)/2)*x^2*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^2) + ((3*I)*x*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^3) - ((3*I)*x*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^3) - ((3*I)*PolyLog[4, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^4) + ((3*I)*PolyLog[4, (I*Sqrt[b]*f^x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Log[f]^4)","A",11,9,18,0.5000,1,"{2249, 205, 2245, 12, 5143, 2531, 6609, 2282, 6589}"
47,1,59,0,0.0394861,"\int \frac{f^x}{\left(a+b f^{2 x}\right)^2} \, dx","Int[f^x/(a + b*f^(2*x))^2,x]","\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)}","\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/(2*a*(a + b*f^(2*x))*Log[f]) + ArcTan[(Sqrt[b]*f^x)/Sqrt[a]]/(2*a^(3/2)*Sqrt[b]*Log[f])","A",3,3,15,0.2000,1,"{2249, 199, 205}"
48,1,172,0,0.1583765,"\int \frac{f^x x}{\left(a+b f^{2 x}\right)^2} \, dx","Int[(f^x*x)/(a + b*f^(2*x))^2,x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,\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)}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,\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,"-ArcTan[(Sqrt[b]*f^x)/Sqrt[a]]/(2*a^(3/2)*Sqrt[b]*Log[f]^2) + (f^x*x)/(2*a*(a + b*f^(2*x))*Log[f]) + (x*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[b]*Log[f]) - ((I/4)*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^2) + ((I/4)*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^2)","A",8,7,16,0.4375,1,"{2249, 199, 205, 2245, 2282, 4848, 2391}"
49,1,333,0,0.3649249,"\int \frac{f^x x^2}{\left(a+b f^{2 x}\right)^2} \, dx","Int[(f^x*x^2)/(a + b*f^(2*x))^2,x]","-\frac{i x \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{i x \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^2(f)}-\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{i \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{i \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(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)}","-\frac{i x \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{i x \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^2(f)}-\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{i \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{i \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(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,"-((x*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^2)) + (f^x*x^2)/(2*a*(a + b*f^(2*x))*Log[f]) + (x^2*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[b]*Log[f]) + ((I/2)*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^3) - ((I/2)*x*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^2) - ((I/2)*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^3) + ((I/2)*x*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^2) + ((I/2)*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^3) - ((I/2)*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^3)","A",16,12,18,0.6667,1,"{2249, 199, 205, 2245, 14, 12, 2282, 4848, 2391, 5143, 2531, 6589}"
50,1,501,0,0.5138205,"\int \frac{f^x x^3}{\left(a+b f^{2 x}\right)^2} \, dx","Int[(f^x*x^3)/(a + b*f^(2*x))^2,x]","-\frac{3 i x^2 \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{3 i x^2 \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{3 i x \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{3 i x \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{3 i \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(f)}-\frac{3 i x \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{3 i \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(f)}-\frac{3 i \text{PolyLog}\left(4,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(f)}+\frac{3 i \text{PolyLog}\left(4,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(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 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log (f)}+\frac{x^3 f^x}{2 a \log (f) \left(a+b f^{2 x}\right)}","-\frac{3 i x^2 \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{3 i x^2 \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{3/2} \sqrt{b} \log ^2(f)}+\frac{3 i x \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{3 i x \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}-\frac{3 i \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(f)}-\frac{3 i x \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^3(f)}+\frac{3 i \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(f)}-\frac{3 i \text{PolyLog}\left(4,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(f)}+\frac{3 i \text{PolyLog}\left(4,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log ^4(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 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b} \log (f)}+\frac{x^3 f^x}{2 a \log (f) \left(a+b f^{2 x}\right)}",1,"(-3*x^2*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[b]*Log[f]^2) + (f^x*x^3)/(2*a*(a + b*f^(2*x))*Log[f]) + (x^3*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[b]*Log[f]) + (((3*I)/2)*x*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^3) - (((3*I)/4)*x^2*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^2) - (((3*I)/2)*x*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^3) + (((3*I)/4)*x^2*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^2) - (((3*I)/2)*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^4) + (((3*I)/2)*x*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^3) + (((3*I)/2)*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^4) - (((3*I)/2)*x*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^3) - (((3*I)/2)*PolyLog[4, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^4) + (((3*I)/2)*PolyLog[4, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Log[f]^4)","A",21,11,18,0.6111,1,"{2249, 199, 205, 2245, 14, 12, 5143, 2531, 2282, 6589, 6609}"
51,1,84,0,0.0510675,"\int \frac{f^x}{\left(a+b f^{2 x}\right)^3} \, dx","Int[f^x/(a + b*f^(2*x))^3,x]","\frac{3 f^x}{8 a^2 \log (f) \left(a+b f^{2 x}\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log (f)}+\frac{f^x}{4 a \log (f) \left(a+b f^{2 x}\right)^2}","\frac{3 f^x}{8 a^2 \log (f) \left(a+b f^{2 x}\right)}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log (f)}+\frac{f^x}{4 a \log (f) \left(a+b f^{2 x}\right)^2}",1,"f^x/(4*a*(a + b*f^(2*x))^2*Log[f]) + (3*f^x)/(8*a^2*(a + b*f^(2*x))*Log[f]) + (3*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*Log[f])","A",4,3,15,0.2000,1,"{2249, 199, 205}"
52,1,223,0,0.2170517,"\int \frac{f^x x}{\left(a+b f^{2 x}\right)^3} \, dx","Int[(f^x*x)/(a + b*f^(2*x))^3,x]","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b} \log ^2(f)}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b} \log ^2(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{\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{x f^x}{4 a \log (f) \left(a+b f^{2 x}\right)^2}","-\frac{3 i \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b} \log ^2(f)}+\frac{3 i \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{16 a^{5/2} \sqrt{b} \log ^2(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{\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{x f^x}{4 a \log (f) \left(a+b f^{2 x}\right)^2}",1,"-f^x/(8*a^2*(a + b*f^(2*x))*Log[f]^2) - ArcTan[(Sqrt[b]*f^x)/Sqrt[a]]/(2*a^(5/2)*Sqrt[b]*Log[f]^2) + (f^x*x)/(4*a*(a + b*f^(2*x))^2*Log[f]) + (3*f^x*x)/(8*a^2*(a + b*f^(2*x))*Log[f]) + (3*x*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*Log[f]) - (((3*I)/16)*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(5/2)*Sqrt[b]*Log[f]^2) + (((3*I)/16)*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(5/2)*Sqrt[b]*Log[f]^2)","A",11,7,16,0.4375,1,"{2249, 199, 205, 2245, 2282, 4848, 2391}"
53,1,420,0,0.5823671,"\int \frac{f^x x^2}{\left(a+b f^{2 x}\right)^3} \, dx","Int[(f^x*x^2)/(a + b*f^(2*x))^3,x]","-\frac{3 i x \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b} \log ^3(f)}+\frac{3 i x \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^2(f)}-\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b} \log ^3(f)}+\frac{3 i \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^3(f)}-\frac{3 i \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^3(f)}+\frac{3 x^2 f^x}{8 a^2 \log (f) \left(a+b f^{2 x}\right)}+\frac{3 x^2 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log (f)}-\frac{x f^x}{4 a^2 \log ^2(f) \left(a+b f^{2 x}\right)}-\frac{x \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{a^{5/2} \sqrt{b} \log ^2(f)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b} \log ^3(f)}+\frac{x^2 f^x}{4 a \log (f) \left(a+b f^{2 x}\right)^2}","-\frac{3 i x \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b} \log ^3(f)}+\frac{3 i x \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^2(f)}-\frac{i \text{PolyLog}\left(2,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b} \log ^3(f)}+\frac{3 i \text{PolyLog}\left(3,-\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^3(f)}-\frac{3 i \text{PolyLog}\left(3,\frac{i \sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log ^3(f)}+\frac{3 x^2 f^x}{8 a^2 \log (f) \left(a+b f^{2 x}\right)}+\frac{3 x^2 \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{b} \log (f)}-\frac{x f^x}{4 a^2 \log ^2(f) \left(a+b f^{2 x}\right)}-\frac{x \tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{a^{5/2} \sqrt{b} \log ^2(f)}+\frac{\tan ^{-1}\left(\frac{\sqrt{b} f^x}{\sqrt{a}}\right)}{4 a^{5/2} \sqrt{b} \log ^3(f)}+\frac{x^2 f^x}{4 a \log (f) \left(a+b f^{2 x}\right)^2}",1,"ArcTan[(Sqrt[b]*f^x)/Sqrt[a]]/(4*a^(5/2)*Sqrt[b]*Log[f]^3) - (f^x*x)/(4*a^2*(a + b*f^(2*x))*Log[f]^2) - (x*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(a^(5/2)*Sqrt[b]*Log[f]^2) + (f^x*x^2)/(4*a*(a + b*f^(2*x))^2*Log[f]) + (3*f^x*x^2)/(8*a^2*(a + b*f^(2*x))*Log[f]) + (3*x^2*ArcTan[(Sqrt[b]*f^x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[b]*Log[f]) + ((I/2)*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(5/2)*Sqrt[b]*Log[f]^3) - (((3*I)/8)*x*PolyLog[2, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(5/2)*Sqrt[b]*Log[f]^2) - ((I/2)*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(5/2)*Sqrt[b]*Log[f]^3) + (((3*I)/8)*x*PolyLog[2, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(5/2)*Sqrt[b]*Log[f]^2) + (((3*I)/8)*PolyLog[3, ((-I)*Sqrt[b]*f^x)/Sqrt[a]])/(a^(5/2)*Sqrt[b]*Log[f]^3) - (((3*I)/8)*PolyLog[3, (I*Sqrt[b]*f^x)/Sqrt[a]])/(a^(5/2)*Sqrt[b]*Log[f]^3)","A",24,12,18,0.6667,1,"{2249, 199, 205, 2245, 14, 2282, 4848, 2391, 12, 5143, 2531, 6589}"
54,1,30,0,0.0211419,"\int \frac{1}{b f^{-x}+a f^x} \, dx","Int[(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",2,2,15,0.1333,1,"{2282, 205}"
55,1,110,0,0.0952606,"\int \frac{x}{b f^{-x}+a f^x} \, dx","Int[x/(b/f^x + a*f^x),x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,\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)}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,\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,"(x*ArcTan[(Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]) - ((I/2)*PolyLog[2, ((-I)*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^2) + ((I/2)*PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^2)","A",6,6,17,0.3529,1,"{2282, 205, 2266, 12, 4848, 2391}"
56,1,184,0,0.1670249,"\int \frac{x^2}{b f^{-x}+a f^x} \, dx","Int[x^2/(b/f^x + a*f^x),x]","-\frac{i x \text{PolyLog}\left(2,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i x \text{PolyLog}\left(2,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(3,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{i \text{PolyLog}\left(3,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}+\frac{x^2 \tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log (f)}","-\frac{i x \text{PolyLog}\left(2,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i x \text{PolyLog}\left(2,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^2(f)}+\frac{i \text{PolyLog}\left(3,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{i \text{PolyLog}\left(3,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}+\frac{x^2 \tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"(x^2*ArcTan[(Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]) - (I*x*PolyLog[2, ((-I)*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^2) + (I*x*PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^2) + (I*PolyLog[3, ((-I)*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^3) - (I*PolyLog[3, (I*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^3)","A",9,7,19,0.3684,1,"{2282, 205, 2266, 12, 5143, 2531, 6589}"
57,1,268,0,0.2195381,"\int \frac{x^3}{b f^{-x}+a f^x} \, dx","Int[x^3/(b/f^x + a*f^x),x]","-\frac{3 i x^2 \text{PolyLog}\left(2,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{3 i x^2 \text{PolyLog}\left(2,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{3 i x \text{PolyLog}\left(3,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{PolyLog}\left(3,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{3 i \text{PolyLog}\left(4,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{3 i \text{PolyLog}\left(4,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{x^3 \tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log (f)}","-\frac{3 i x^2 \text{PolyLog}\left(2,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{3 i x^2 \text{PolyLog}\left(2,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{2 \sqrt{a} \sqrt{b} \log ^2(f)}+\frac{3 i x \text{PolyLog}\left(3,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{3 i x \text{PolyLog}\left(3,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^3(f)}-\frac{3 i \text{PolyLog}\left(4,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{3 i \text{PolyLog}\left(4,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log ^4(f)}+\frac{x^3 \tan ^{-1}\left(\frac{\sqrt{a} f^x}{\sqrt{b}}\right)}{\sqrt{a} \sqrt{b} \log (f)}",1,"(x^3*ArcTan[(Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]) - (((3*I)/2)*x^2*PolyLog[2, ((-I)*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^2) + (((3*I)/2)*x^2*PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^2) + ((3*I)*x*PolyLog[3, ((-I)*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^3) - ((3*I)*x*PolyLog[3, (I*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^3) - ((3*I)*PolyLog[4, ((-I)*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^4) + ((3*I)*PolyLog[4, (I*Sqrt[a]*f^x)/Sqrt[b]])/(Sqrt[a]*Sqrt[b]*Log[f]^4)","A",11,8,19,0.4211,1,"{2282, 205, 2266, 12, 5143, 2531, 6609, 6589}"
58,1,22,0,0.0199484,"\int \frac{1}{\left(b f^{-x}+a f^x\right)^2} \, dx","Int[(b/f^x + a*f^x)^(-2),x]","-\frac{1}{2 a \log (f) \left(a f^{2 x}+b\right)}","-\frac{1}{2 a \log (f) \left(a f^{2 x}+b\right)}",1,"-1/(2*a*(b + a*f^(2*x))*Log[f])","A",2,2,15,0.1333,1,"{2282, 261}"
59,1,63,0,0.0783578,"\int \frac{x}{\left(b f^{-x}+a f^x\right)^2} \, dx","Int[x/(b/f^x + a*f^x)^2,x]","-\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)}","-\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,"x/(2*a*b*Log[f]) - x/(2*a*(b + a*f^(2*x))*Log[f]) - Log[b + a*f^(2*x)]/(4*a*b*Log[f]^2)","A",6,6,17,0.3529,1,"{2283, 2191, 2282, 36, 29, 31}"
60,1,98,0,0.169159,"\int \frac{x^2}{\left(b f^{-x}+a f^x\right)^2} \, dx","Int[x^2/(b/f^x + a*f^x)^2,x]","-\frac{\text{PolyLog}\left(2,-\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)}","-\frac{\text{PolyLog}\left(2,-\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,"x^2/(2*a*b*Log[f]) - x^2/(2*a*(b + a*f^(2*x))*Log[f]) - (x*Log[1 + (a*f^(2*x))/b])/(2*a*b*Log[f]^2) - PolyLog[2, -((a*f^(2*x))/b)]/(4*a*b*Log[f]^3)","A",6,6,19,0.3158,1,"{2283, 2191, 2184, 2190, 2279, 2391}"
61,1,128,0,0.2254855,"\int \frac{x^3}{\left(b f^{-x}+a f^x\right)^2} \, dx","Int[x^3/(b/f^x + a*f^x)^2,x]","-\frac{3 x \text{PolyLog}\left(2,-\frac{a f^{2 x}}{b}\right)}{4 a b \log ^3(f)}+\frac{3 \text{PolyLog}\left(3,-\frac{a f^{2 x}}{b}\right)}{8 a b \log ^4(f)}-\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 \log (f) \left(a f^{2 x}+b\right)}+\frac{x^3}{2 a b \log (f)}","-\frac{3 x \text{PolyLog}\left(2,-\frac{a f^{2 x}}{b}\right)}{4 a b \log ^3(f)}+\frac{3 \text{PolyLog}\left(3,-\frac{a f^{2 x}}{b}\right)}{8 a b \log ^4(f)}-\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 \log (f) \left(a f^{2 x}+b\right)}+\frac{x^3}{2 a b \log (f)}",1,"x^3/(2*a*b*Log[f]) - x^3/(2*a*(b + a*f^(2*x))*Log[f]) - (3*x^2*Log[1 + (a*f^(2*x))/b])/(4*a*b*Log[f]^2) - (3*x*PolyLog[2, -((a*f^(2*x))/b)])/(4*a*b*Log[f]^3) + (3*PolyLog[3, -((a*f^(2*x))/b)])/(8*a*b*Log[f]^4)","A",7,7,19,0.3684,1,"{2283, 2191, 2184, 2190, 2531, 2282, 6589}"
62,1,87,0,0.0463815,"\int \frac{1}{\left(b f^{-x}+a f^x\right)^3} \, dx","Int[(b/f^x + a*f^x)^(-3),x]","\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}","\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,"-f^x/(4*a*(b + a*f^(2*x))^2*Log[f]) + f^x/(8*a*b*(b + a*f^(2*x))*Log[f]) + ArcTan[(Sqrt[a]*f^x)/Sqrt[b]]/(8*a^(3/2)*b^(3/2)*Log[f])","A",4,4,15,0.2667,1,"{2282, 288, 199, 205}"
63,1,196,0,0.5028887,"\int \frac{x}{\left(b f^{-x}+a f^x\right)^3} \, dx","Int[x/(b/f^x + a*f^x)^3,x]","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{16 a^{3/2} b^{3/2} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,\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}","-\frac{i \text{PolyLog}\left(2,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{16 a^{3/2} b^{3/2} \log ^2(f)}+\frac{i \text{PolyLog}\left(2,\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,"f^x/(8*a*b*(b + a*f^(2*x))*Log[f]^2) - (f^x*x)/(4*a*(b + a*f^(2*x))^2*Log[f]) + (f^x*x)/(8*a*b*(b + a*f^(2*x))*Log[f]) + (x*ArcTan[(Sqrt[a]*f^x)/Sqrt[b]])/(8*a^(3/2)*b^(3/2)*Log[f]) - ((I/16)*PolyLog[2, ((-I)*Sqrt[a]*f^x)/Sqrt[b]])/(a^(3/2)*b^(3/2)*Log[f]^2) + ((I/16)*PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]])/(a^(3/2)*b^(3/2)*Log[f]^2)","A",22,9,17,0.5294,1,"{2283, 2254, 2249, 199, 205, 2245, 2282, 4848, 2391}"
64,1,316,0,1.1633189,"\int \frac{x^2}{\left(b f^{-x}+a f^x\right)^3} \, dx","Int[x^2/(b/f^x + a*f^x)^3,x]","-\frac{i x \text{PolyLog}\left(2,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^2(f)}+\frac{i x \text{PolyLog}\left(2,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^2(f)}+\frac{i \text{PolyLog}\left(3,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^3(f)}-\frac{i \text{PolyLog}\left(3,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^3(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)}","-\frac{i x \text{PolyLog}\left(2,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^2(f)}+\frac{i x \text{PolyLog}\left(2,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^2(f)}+\frac{i \text{PolyLog}\left(3,-\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^3(f)}-\frac{i \text{PolyLog}\left(3,\frac{i \sqrt{a} f^x}{\sqrt{b}}\right)}{8 a^{3/2} b^{3/2} \log ^3(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,"-ArcTan[(Sqrt[a]*f^x)/Sqrt[b]]/(4*a^(3/2)*b^(3/2)*Log[f]^3) + (f^x*x)/(4*a*b*(b + a*f^(2*x))*Log[f]^2) - (f^x*x^2)/(4*a*(b + a*f^(2*x))^2*Log[f]) + (f^x*x^2)/(8*a*b*(b + a*f^(2*x))*Log[f]) + (x^2*ArcTan[(Sqrt[a]*f^x)/Sqrt[b]])/(8*a^(3/2)*b^(3/2)*Log[f]) - ((I/8)*x*PolyLog[2, ((-I)*Sqrt[a]*f^x)/Sqrt[b]])/(a^(3/2)*b^(3/2)*Log[f]^2) + ((I/8)*x*PolyLog[2, (I*Sqrt[a]*f^x)/Sqrt[b]])/(a^(3/2)*b^(3/2)*Log[f]^2) + ((I/8)*PolyLog[3, ((-I)*Sqrt[a]*f^x)/Sqrt[b]])/(a^(3/2)*b^(3/2)*Log[f]^3) - ((I/8)*PolyLog[3, (I*Sqrt[a]*f^x)/Sqrt[b]])/(a^(3/2)*b^(3/2)*Log[f]^3)","A",43,14,19,0.7368,1,"{2283, 2254, 2249, 199, 205, 2245, 14, 2282, 4848, 2391, 12, 5143, 2531, 6589}"
65,1,95,0,0.1805608,"\int f^{a+b x+c x^2} g^{d+e x+f x^2} \, dx","Int[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{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)}}","\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*Log[f] + e*Log[g] + 2*x*(c*Log[f] + f*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",3,3,25,0.1200,1,"{2287, 2234, 2204}"
66,1,106,0,0.0930117,"\int F^{e (c+d x)} \left(a+b G^{h (f+g x)}\right)^n \, dx","Int[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 \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)}","\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)))^n*Hypergeometric2F1[-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)])/(d*e*(1 + (b*G^(h*(f + g*x)))/a)^n*Log[F])","A",2,2,25,0.08000,1,"{2252, 2251}"
67,1,75,0,0.1345291,"\int \frac{F^{e (c+d x)} H^{t (r+s x)}}{a+b F^{e (c+d x)}} \, dx","Int[(F^(e*(c + d*x))*H^(t*(r + s*x)))/(a + b*F^(e*(c + d*x))),x]","\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)}","\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))*Hypergeometric2F1[1, -((s*t*Log[H])/(d*e*Log[F])), 1 - (s*t*Log[H])/(d*e*Log[F]), -(a/(b*F^(e*(c + d*x))))])/(b*s*t*Log[H])","A",2,2,34,0.05882,1,"{2256, 2251}"
68,1,85,0,0.1320623,"\int \frac{F^{e (f+d x)} H^{t (r+s x)}}{a+b F^{e (c+d x)}} \, dx","Int[(F^(e*(f + d*x))*H^(t*(r + s*x)))/(a + b*F^(e*(c + d*x))),x]","\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)}","\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,"(H^(t*(r + s*x))*Hypergeometric2F1[1, -((s*t*Log[H])/(d*e*Log[F])), 1 - (s*t*Log[H])/(d*e*Log[F]), -(a/(b*F^(e*(c + d*x))))])/(b*F^(e*(c - f))*s*t*Log[H])","A",2,2,34,0.05882,1,"{2256, 2251}"
69,1,46,0,0.0239831,"\int f^{a+b x^2} x^m \, dx","Int[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)} \text{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)} \text{Gamma}\left(\frac{m+1}{2},-b x^2 \log (f)\right)",1,"-(f^a*x^(1 + m)*Gamma[(1 + m)/2, -(b*x^2*Log[f])]*(-(b*x^2*Log[f]))^((-1 - m)/2))/2","A",1,1,13,0.07692,1,"{2218}"
70,1,24,0,0.0254629,"\int f^{a+b x^2} x^{11} \, dx","Int[f^(a + b*x^2)*x^11,x]","-\frac{f^a \text{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,"-(f^a*Gamma[6, -(b*x^2*Log[f])])/(2*b^6*Log[f]^6)","C",1,1,13,0.07692,1,"{2218}"
71,1,24,0,0.0240763,"\int f^{a+b x^2} x^9 \, dx","Int[f^(a + b*x^2)*x^9,x]","\frac{f^a \text{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",1,1,13,0.07692,1,"{2218}"
72,1,86,0,0.0929452,"\int f^{a+b x^2} x^7 \, dx","Int[f^(a + b*x^2)*x^7,x]","-\frac{3 x^4 f^{a+b x^2}}{2 b^2 \log ^2(f)}+\frac{3 x^2 f^{a+b x^2}}{b^3 \log ^3(f)}-\frac{3 f^{a+b x^2}}{b^4 \log ^4(f)}+\frac{x^6 f^{a+b x^2}}{2 b \log (f)}","-\frac{3 x^4 f^{a+b x^2}}{2 b^2 \log ^2(f)}+\frac{3 x^2 f^{a+b x^2}}{b^3 \log ^3(f)}-\frac{3 f^{a+b x^2}}{b^4 \log ^4(f)}+\frac{x^6 f^{a+b x^2}}{2 b \log (f)}",1,"(-3*f^(a + b*x^2))/(b^4*Log[f]^4) + (3*f^(a + b*x^2)*x^2)/(b^3*Log[f]^3) - (3*f^(a + b*x^2)*x^4)/(2*b^2*Log[f]^2) + (f^(a + b*x^2)*x^6)/(2*b*Log[f])","A",4,2,13,0.1538,1,"{2212, 2209}"
73,1,62,0,0.0628613,"\int f^{a+b x^2} x^5 \, dx","Int[f^(a + b*x^2)*x^5,x]","-\frac{x^2 f^{a+b x^2}}{b^2 \log ^2(f)}+\frac{f^{a+b x^2}}{b^3 \log ^3(f)}+\frac{x^4 f^{a+b x^2}}{2 b \log (f)}","-\frac{x^2 f^{a+b x^2}}{b^2 \log ^2(f)}+\frac{f^{a+b x^2}}{b^3 \log ^3(f)}+\frac{x^4 f^{a+b x^2}}{2 b \log (f)}",1,"f^(a + b*x^2)/(b^3*Log[f]^3) - (f^(a + b*x^2)*x^2)/(b^2*Log[f]^2) + (f^(a + b*x^2)*x^4)/(2*b*Log[f])","A",3,2,13,0.1538,1,"{2212, 2209}"
74,1,44,0,0.0380601,"\int f^{a+b x^2} x^3 \, dx","Int[f^(a + b*x^2)*x^3,x]","\frac{x^2 f^{a+b x^2}}{2 b \log (f)}-\frac{f^{a+b x^2}}{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)/(2*b^2*Log[f]^2) + (f^(a + b*x^2)*x^2)/(2*b*Log[f])","A",2,2,13,0.1538,1,"{2212, 2209}"
75,1,20,0,0.0129456,"\int f^{a+b x^2} x \, dx","Int[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",1,1,11,0.09091,1,"{2209}"
76,1,15,0,0.0212704,"\int \frac{f^{a+b x^2}}{x} \, dx","Int[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",1,1,13,0.07692,1,"{2210}"
77,1,35,0,0.0448627,"\int \frac{f^{a+b x^2}}{x^3} \, dx","Int[f^(a + b*x^2)/x^3,x]","\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}","\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 + b*x^2)/(2*x^2) + (b*f^a*ExpIntegralEi[b*x^2*Log[f]]*Log[f])/2","A",2,2,13,0.1538,1,"{2214, 2210}"
78,1,58,0,0.0659541,"\int \frac{f^{a+b x^2}}{x^5} \, dx","Int[f^(a + b*x^2)/x^5,x]","\frac{1}{4} b^2 f^a \log ^2(f) \text{Ei}\left(b x^2 \log (f)\right)-\frac{f^{a+b x^2}}{4 x^4}-\frac{b \log (f) f^{a+b x^2}}{4 x^2}","\frac{1}{4} b^2 f^a \log ^2(f) \text{Ei}\left(b x^2 \log (f)\right)-\frac{f^{a+b x^2}}{4 x^4}-\frac{b \log (f) f^{a+b x^2}}{4 x^2}",1,"-f^(a + b*x^2)/(4*x^4) - (b*f^(a + b*x^2)*Log[f])/(4*x^2) + (b^2*f^a*ExpIntegralEi[b*x^2*Log[f]]*Log[f]^2)/4","A",3,2,13,0.1538,1,"{2214, 2210}"
79,1,81,0,0.09055,"\int \frac{f^{a+b x^2}}{x^7} \, dx","Int[f^(a + b*x^2)/x^7,x]","\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}","\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*x^2)/(6*x^6) - (b*f^(a + b*x^2)*Log[f])/(12*x^4) - (b^2*f^(a + b*x^2)*Log[f]^2)/(12*x^2) + (b^3*f^a*ExpIntegralEi[b*x^2*Log[f]]*Log[f]^3)/12","A",4,2,13,0.1538,1,"{2214, 2210}"
80,1,24,0,0.0221914,"\int \frac{f^{a+b x^2}}{x^9} \, dx","Int[f^(a + b*x^2)/x^9,x]","-\frac{1}{2} b^4 f^a \log ^4(f) \text{Gamma}\left(-4,-b x^2 \log (f)\right)","-\frac{1}{2} b^4 f^a \log ^4(f) \text{Gamma}\left(-4,-b x^2 \log (f)\right)",1,"-(b^4*f^a*Gamma[-4, -(b*x^2*Log[f])]*Log[f]^4)/2","A",1,1,13,0.07692,1,"{2218}"
81,1,24,0,0.0228089,"\int \frac{f^{a+b x^2}}{x^{11}} \, dx","Int[f^(a + b*x^2)/x^11,x]","\frac{1}{2} b^5 f^a \log ^5(f) \text{Gamma}\left(-5,-b x^2 \log (f)\right)","\frac{1}{2} b^5 f^a \log ^5(f) \text{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",1,1,13,0.07692,1,"{2218}"
82,1,34,0,0.0225019,"\int f^{a+b x^2} x^{12} \, dx","Int[f^(a + b*x^2)*x^12,x]","-\frac{x^{13} f^a \text{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 \text{Gamma}\left(\frac{13}{2},-b x^2 \log (f)\right)}{2 \left(-b x^2 \log (f)\right)^{13/2}}",1,"-(f^a*x^13*Gamma[13/2, -(b*x^2*Log[f])])/(2*(-(b*x^2*Log[f]))^(13/2))","A",1,1,13,0.07692,1,"{2218}"
83,1,34,0,0.0225988,"\int f^{a+b x^2} x^{10} \, dx","Int[f^(a + b*x^2)*x^10,x]","-\frac{x^{11} f^a \text{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 \text{Gamma}\left(\frac{11}{2},-b x^2 \log (f)\right)}{2 \left(-b x^2 \log (f)\right)^{11/2}}",1,"-(f^a*x^11*Gamma[11/2, -(b*x^2*Log[f])])/(2*(-(b*x^2*Log[f]))^(11/2))","A",1,1,13,0.07692,1,"{2218}"
84,1,128,0,0.1423988,"\int f^{a+b x^2} x^8 \, dx","Int[f^(a + b*x^2)*x^8,x]","\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{7 x^5 f^{a+b x^2}}{4 b^2 \log ^2(f)}+\frac{35 x^3 f^{a+b x^2}}{8 b^3 \log ^3(f)}-\frac{105 x f^{a+b x^2}}{16 b^4 \log ^4(f)}+\frac{x^7 f^{a+b x^2}}{2 b \log (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{7 x^5 f^{a+b x^2}}{4 b^2 \log ^2(f)}+\frac{35 x^3 f^{a+b x^2}}{8 b^3 \log ^3(f)}-\frac{105 x f^{a+b x^2}}{16 b^4 \log ^4(f)}+\frac{x^7 f^{a+b x^2}}{2 b \log (f)}",1,"(105*f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]])/(32*b^(9/2)*Log[f]^(9/2)) - (105*f^(a + b*x^2)*x)/(16*b^4*Log[f]^4) + (35*f^(a + b*x^2)*x^3)/(8*b^3*Log[f]^3) - (7*f^(a + b*x^2)*x^5)/(4*b^2*Log[f]^2) + (f^(a + b*x^2)*x^7)/(2*b*Log[f])","A",5,2,13,0.1538,1,"{2212, 2204}"
85,1,105,0,0.0875476,"\int f^{a+b x^2} x^6 \, dx","Int[f^(a + b*x^2)*x^6,x]","-\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{5 x^3 f^{a+b x^2}}{4 b^2 \log ^2(f)}+\frac{15 x f^{a+b x^2}}{8 b^3 \log ^3(f)}+\frac{x^5 f^{a+b x^2}}{2 b \log (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{5 x^3 f^{a+b x^2}}{4 b^2 \log ^2(f)}+\frac{15 x f^{a+b x^2}}{8 b^3 \log ^3(f)}+\frac{x^5 f^{a+b x^2}}{2 b \log (f)}",1,"(-15*f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]])/(16*b^(7/2)*Log[f]^(7/2)) + (15*f^(a + b*x^2)*x)/(8*b^3*Log[f]^3) - (5*f^(a + b*x^2)*x^3)/(4*b^2*Log[f]^2) + (f^(a + b*x^2)*x^5)/(2*b*Log[f])","A",4,2,13,0.1538,1,"{2212, 2204}"
86,1,82,0,0.0593823,"\int f^{a+b x^2} x^4 \, dx","Int[f^(a + b*x^2)*x^4,x]","\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)}","\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,"(3*f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]])/(8*b^(5/2)*Log[f]^(5/2)) - (3*f^(a + b*x^2)*x)/(4*b^2*Log[f]^2) + (f^(a + b*x^2)*x^3)/(2*b*Log[f])","A",3,2,13,0.1538,1,"{2212, 2204}"
87,1,59,0,0.0344495,"\int f^{a+b x^2} x^2 \, dx","Int[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,"-(f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]])/(4*b^(3/2)*Log[f]^(3/2)) + (f^(a + b*x^2)*x)/(2*b*Log[f])","A",2,2,13,0.1538,1,"{2212, 2204}"
88,1,37,0,0.006949,"\int f^{a+b x^2} \, dx","Int[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",1,1,9,0.1111,1,"{2204}"
89,1,49,0,0.0314357,"\int \frac{f^{a+b x^2}}{x^2} \, dx","Int[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",2,2,13,0.1538,1,"{2214, 2204}"
90,1,73,0,0.0548927,"\int \frac{f^{a+b x^2}}{x^4} \, dx","Int[f^(a + b*x^2)/x^4,x]","\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{f^{a+b x^2}}{3 x^3}-\frac{2 b \log (f) f^{a+b x^2}}{3 x}","\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{f^{a+b x^2}}{3 x^3}-\frac{2 b \log (f) f^{a+b x^2}}{3 x}",1,"-f^(a + b*x^2)/(3*x^3) - (2*b*f^(a + b*x^2)*Log[f])/(3*x) + (2*b^(3/2)*f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]]*Log[f]^(3/2))/3","A",3,2,13,0.1538,1,"{2214, 2204}"
91,1,96,0,0.0805698,"\int \frac{f^{a+b x^2}}{x^6} \, dx","Int[f^(a + b*x^2)/x^6,x]","\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}","\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 + b*x^2)/(5*x^5) - (2*b*f^(a + b*x^2)*Log[f])/(15*x^3) - (4*b^2*f^(a + b*x^2)*Log[f]^2)/(15*x) + (4*b^(5/2)*f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]]*Log[f]^(5/2))/15","A",4,2,13,0.1538,1,"{2214, 2204}"
92,1,119,0,0.1078716,"\int \frac{f^{a+b x^2}}{x^8} \, dx","Int[f^(a + b*x^2)/x^8,x]","\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}","\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 + b*x^2)/(7*x^7) - (2*b*f^(a + b*x^2)*Log[f])/(35*x^5) - (4*b^2*f^(a + b*x^2)*Log[f]^2)/(105*x^3) - (8*b^3*f^(a + b*x^2)*Log[f]^3)/(105*x) + (8*b^(7/2)*f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x*Sqrt[Log[f]]]*Log[f]^(7/2))/105","A",5,2,13,0.1538,1,"{2214, 2204}"
93,1,34,0,0.0206185,"\int \frac{f^{a+b x^2}}{x^{10}} \, dx","Int[f^(a + b*x^2)/x^10,x]","-\frac{f^a \left(-b x^2 \log (f)\right)^{9/2} \text{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} \text{Gamma}\left(-\frac{9}{2},-b x^2 \log (f)\right)}{2 x^9}",1,"-(f^a*Gamma[-9/2, -(b*x^2*Log[f])]*(-(b*x^2*Log[f]))^(9/2))/(2*x^9)","A",1,1,13,0.07692,1,"{2218}"
94,1,34,0,0.0208784,"\int \frac{f^{a+b x^2}}{x^{12}} \, dx","Int[f^(a + b*x^2)/x^12,x]","-\frac{f^a \left(-b x^2 \log (f)\right)^{11/2} \text{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} \text{Gamma}\left(-\frac{11}{2},-b x^2 \log (f)\right)}{2 x^{11}}",1,"-(f^a*Gamma[-11/2, -(b*x^2*Log[f])]*(-(b*x^2*Log[f]))^(11/2))/(2*x^11)","A",1,1,13,0.07692,1,"{2218}"
95,1,46,0,0.0214375,"\int f^{a+b x^3} x^m \, dx","Int[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)} \text{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)} \text{Gamma}\left(\frac{m+1}{3},-b x^3 \log (f)\right)",1,"-(f^a*x^(1 + m)*Gamma[(1 + m)/3, -(b*x^3*Log[f])]*(-(b*x^3*Log[f]))^((-1 - m)/3))/3","A",1,1,13,0.07692,1,"{2218}"
96,1,24,0,0.0224891,"\int f^{a+b x^3} x^{17} \, dx","Int[f^(a + b*x^3)*x^17,x]","-\frac{f^a \text{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,"-(f^a*Gamma[6, -(b*x^3*Log[f])])/(3*b^6*Log[f]^6)","C",1,1,13,0.07692,1,"{2218}"
97,1,24,0,0.0231564,"\int f^{a+b x^3} x^{14} \, dx","Int[f^(a + b*x^3)*x^14,x]","\frac{f^a \text{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",1,1,13,0.07692,1,"{2218}"
98,1,84,0,0.0950641,"\int f^{a+b x^3} x^{11} \, dx","Int[f^(a + b*x^3)*x^11,x]","-\frac{x^6 f^{a+b x^3}}{b^2 \log ^2(f)}+\frac{2 x^3 f^{a+b x^3}}{b^3 \log ^3(f)}-\frac{2 f^{a+b x^3}}{b^4 \log ^4(f)}+\frac{x^9 f^{a+b x^3}}{3 b \log (f)}","-\frac{x^6 f^{a+b x^3}}{b^2 \log ^2(f)}+\frac{2 x^3 f^{a+b x^3}}{b^3 \log ^3(f)}-\frac{2 f^{a+b x^3}}{b^4 \log ^4(f)}+\frac{x^9 f^{a+b x^3}}{3 b \log (f)}",1,"(-2*f^(a + b*x^3))/(b^4*Log[f]^4) + (2*f^(a + b*x^3)*x^3)/(b^3*Log[f]^3) - (f^(a + b*x^3)*x^6)/(b^2*Log[f]^2) + (f^(a + b*x^3)*x^9)/(3*b*Log[f])","A",4,2,13,0.1538,1,"{2212, 2209}"
99,1,67,0,0.0702023,"\int f^{a+b x^3} x^8 \, dx","Int[f^(a + b*x^3)*x^8,x]","-\frac{2 x^3 f^{a+b x^3}}{3 b^2 \log ^2(f)}+\frac{2 f^{a+b x^3}}{3 b^3 \log ^3(f)}+\frac{x^6 f^{a+b x^3}}{3 b \log (f)}","-\frac{2 x^3 f^{a+b x^3}}{3 b^2 \log ^2(f)}+\frac{2 f^{a+b x^3}}{3 b^3 \log ^3(f)}+\frac{x^6 f^{a+b x^3}}{3 b \log (f)}",1,"(2*f^(a + b*x^3))/(3*b^3*Log[f]^3) - (2*f^(a + b*x^3)*x^3)/(3*b^2*Log[f]^2) + (f^(a + b*x^3)*x^6)/(3*b*Log[f])","A",3,2,13,0.1538,1,"{2212, 2209}"
100,1,44,0,0.0439159,"\int f^{a+b x^3} x^5 \, dx","Int[f^(a + b*x^3)*x^5,x]","\frac{x^3 f^{a+b x^3}}{3 b \log (f)}-\frac{f^{a+b x^3}}{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)/(3*b^2*Log[f]^2) + (f^(a + b*x^3)*x^3)/(3*b*Log[f])","A",2,2,13,0.1538,1,"{2212, 2209}"
101,1,20,0,0.0220422,"\int f^{a+b x^3} x^2 \, dx","Int[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",1,1,13,0.07692,1,"{2209}"
102,1,15,0,0.0206387,"\int \frac{f^{a+b x^3}}{x} \, dx","Int[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",1,1,13,0.07692,1,"{2210}"
103,1,35,0,0.0420116,"\int \frac{f^{a+b x^3}}{x^4} \, dx","Int[f^(a + b*x^3)/x^4,x]","\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}","\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 + b*x^3)/(3*x^3) + (b*f^a*ExpIntegralEi[b*x^3*Log[f]]*Log[f])/3","A",2,2,13,0.1538,1,"{2214, 2210}"
104,1,58,0,0.0658597,"\int \frac{f^{a+b x^3}}{x^7} \, dx","Int[f^(a + b*x^3)/x^7,x]","\frac{1}{6} b^2 f^a \log ^2(f) \text{Ei}\left(b x^3 \log (f)\right)-\frac{f^{a+b x^3}}{6 x^6}-\frac{b \log (f) f^{a+b x^3}}{6 x^3}","\frac{1}{6} b^2 f^a \log ^2(f) \text{Ei}\left(b x^3 \log (f)\right)-\frac{f^{a+b x^3}}{6 x^6}-\frac{b \log (f) f^{a+b x^3}}{6 x^3}",1,"-f^(a + b*x^3)/(6*x^6) - (b*f^(a + b*x^3)*Log[f])/(6*x^3) + (b^2*f^a*ExpIntegralEi[b*x^3*Log[f]]*Log[f]^2)/6","A",3,2,13,0.1538,1,"{2214, 2210}"
105,1,81,0,0.0897108,"\int \frac{f^{a+b x^3}}{x^{10}} \, dx","Int[f^(a + b*x^3)/x^10,x]","\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}","\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*x^3)/(9*x^9) - (b*f^(a + b*x^3)*Log[f])/(18*x^6) - (b^2*f^(a + b*x^3)*Log[f]^2)/(18*x^3) + (b^3*f^a*ExpIntegralEi[b*x^3*Log[f]]*Log[f]^3)/18","A",4,2,13,0.1538,1,"{2214, 2210}"
106,1,24,0,0.0209979,"\int \frac{f^{a+b x^3}}{x^{13}} \, dx","Int[f^(a + b*x^3)/x^13,x]","-\frac{1}{3} b^4 f^a \log ^4(f) \text{Gamma}\left(-4,-b x^3 \log (f)\right)","-\frac{1}{3} b^4 f^a \log ^4(f) \text{Gamma}\left(-4,-b x^3 \log (f)\right)",1,"-(b^4*f^a*Gamma[-4, -(b*x^3*Log[f])]*Log[f]^4)/3","A",1,1,13,0.07692,1,"{2218}"
107,1,24,0,0.0209877,"\int \frac{f^{a+b x^3}}{x^{16}} \, dx","Int[f^(a + b*x^3)/x^16,x]","\frac{1}{3} b^5 f^a \log ^5(f) \text{Gamma}\left(-5,-b x^3 \log (f)\right)","\frac{1}{3} b^5 f^a \log ^5(f) \text{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",1,1,13,0.07692,1,"{2218}"
108,1,34,0,0.0229117,"\int f^{a+b x^3} x^4 \, dx","Int[f^(a + b*x^3)*x^4,x]","-\frac{x^5 f^a \text{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 \text{Gamma}\left(\frac{5}{3},-b x^3 \log (f)\right)}{3 \left(-b x^3 \log (f)\right)^{5/3}}",1,"-(f^a*x^5*Gamma[5/3, -(b*x^3*Log[f])])/(3*(-(b*x^3*Log[f]))^(5/3))","A",1,1,13,0.07692,1,"{2218}"
109,1,34,0,0.0224622,"\int f^{a+b x^3} x^3 \, dx","Int[f^(a + b*x^3)*x^3,x]","-\frac{x^4 f^a \text{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 \text{Gamma}\left(\frac{4}{3},-b x^3 \log (f)\right)}{3 \left(-b x^3 \log (f)\right)^{4/3}}",1,"-(f^a*x^4*Gamma[4/3, -(b*x^3*Log[f])])/(3*(-(b*x^3*Log[f]))^(4/3))","A",1,1,13,0.07692,1,"{2218}"
110,1,34,0,0.013284,"\int f^{a+b x^3} x \, dx","Int[f^(a + b*x^3)*x,x]","-\frac{x^2 f^a \text{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 \text{Gamma}\left(\frac{2}{3},-b x^3 \log (f)\right)}{3 \left(-b x^3 \log (f)\right)^{2/3}}",1,"-(f^a*x^2*Gamma[2/3, -(b*x^3*Log[f])])/(3*(-(b*x^3*Log[f]))^(2/3))","A",1,1,11,0.09091,1,"{2218}"
111,1,32,0,0.0038035,"\int f^{a+b x^3} \, dx","Int[f^(a + b*x^3),x]","-\frac{x f^a \text{Gamma}\left(\frac{1}{3},-b x^3 \log (f)\right)}{3 \sqrt[3]{-b x^3 \log (f)}}","-\frac{x f^a \text{Gamma}\left(\frac{1}{3},-b x^3 \log (f)\right)}{3 \sqrt[3]{-b x^3 \log (f)}}",1,"-(f^a*x*Gamma[1/3, -(b*x^3*Log[f])])/(3*(-(b*x^3*Log[f]))^(1/3))","A",1,1,9,0.1111,1,"{2208}"
112,1,34,0,0.0216656,"\int \frac{f^{a+b x^3}}{x^2} \, dx","Int[f^(a + b*x^3)/x^2,x]","-\frac{f^a \sqrt[3]{-b x^3 \log (f)} \text{Gamma}\left(-\frac{1}{3},-b x^3 \log (f)\right)}{3 x}","-\frac{f^a \sqrt[3]{-b x^3 \log (f)} \text{Gamma}\left(-\frac{1}{3},-b x^3 \log (f)\right)}{3 x}",1,"-(f^a*Gamma[-1/3, -(b*x^3*Log[f])]*(-(b*x^3*Log[f]))^(1/3))/(3*x)","A",1,1,13,0.07692,1,"{2218}"
113,1,34,0,0.0208568,"\int \frac{f^{a+b x^3}}{x^3} \, dx","Int[f^(a + b*x^3)/x^3,x]","-\frac{f^a \left(-b x^3 \log (f)\right)^{2/3} \text{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} \text{Gamma}\left(-\frac{2}{3},-b x^3 \log (f)\right)}{3 x^2}",1,"-(f^a*Gamma[-2/3, -(b*x^3*Log[f])]*(-(b*x^3*Log[f]))^(2/3))/(3*x^2)","A",1,1,13,0.07692,1,"{2218}"
114,1,11,0,0.0143383,"\int e^{4 x^3} x^2 \, dx","Int[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",1,1,11,0.09091,1,"{2209}"
115,1,35,0,0.0179775,"\int f^{a+\frac{b}{x}} x^m \, dx","Int[f^(a + b/x)*x^m,x]","f^a x^{m+1} \left(-\frac{b \log (f)}{x}\right)^{m+1} \text{Gamma}\left(-m-1,-\frac{b \log (f)}{x}\right)","f^a x^{m+1} \left(-\frac{b \log (f)}{x}\right)^{m+1} \text{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",1,1,13,0.07692,1,"{2218}"
116,1,22,0,0.0189867,"\int f^{a+\frac{b}{x}} x^4 \, dx","Int[f^(a + b/x)*x^4,x]","-b^5 f^a \log ^5(f) \text{Gamma}\left(-5,-\frac{b \log (f)}{x}\right)","-b^5 f^a \log ^5(f) \text{Gamma}\left(-5,-\frac{b \log (f)}{x}\right)",1,"-(b^5*f^a*Gamma[-5, -((b*Log[f])/x)]*Log[f]^5)","A",1,1,13,0.07692,1,"{2218}"
117,1,21,0,0.0198408,"\int f^{a+\frac{b}{x}} x^3 \, dx","Int[f^(a + b/x)*x^3,x]","b^4 f^a \log ^4(f) \text{Gamma}\left(-4,-\frac{b \log (f)}{x}\right)","b^4 f^a \log ^4(f) \text{Gamma}\left(-4,-\frac{b \log (f)}{x}\right)",1,"b^4*f^a*Gamma[-4, -((b*Log[f])/x)]*Log[f]^4","A",1,1,13,0.07692,1,"{2218}"
118,1,79,0,0.0592223,"\int f^{a+\frac{b}{x}} x^2 \, dx","Int[f^(a + b/x)*x^2,x]","-\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}}","-\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/x)*x^3)/3 + (b*f^(a + b/x)*x^2*Log[f])/6 + (b^2*f^(a + b/x)*x*Log[f]^2)/6 - (b^3*f^a*ExpIntegralEi[(b*Log[f])/x]*Log[f]^3)/6","A",4,3,13,0.2308,1,"{2214, 2206, 2210}"
119,1,56,0,0.0349944,"\int f^{a+\frac{b}{x}} x \, dx","Int[f^(a + b/x)*x,x]","-\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}}","-\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/x)*x^2)/2 + (b*f^(a + b/x)*x*Log[f])/2 - (b^2*f^a*ExpIntegralEi[(b*Log[f])/x]*Log[f]^2)/2","A",3,3,11,0.2727,1,"{2214, 2206, 2210}"
120,1,28,0,0.022346,"\int f^{a+\frac{b}{x}} \, dx","Int[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",2,2,9,0.2222,1,"{2206, 2210}"
121,1,13,0,0.0183578,"\int \frac{f^{a+\frac{b}{x}}}{x} \, dx","Int[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",1,1,13,0.07692,1,"{2210}"
122,1,18,0,0.018051,"\int \frac{f^{a+\frac{b}{x}}}{x^2} \, dx","Int[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",1,1,13,0.07692,1,"{2209}"
123,1,39,0,0.0364967,"\int \frac{f^{a+\frac{b}{x}}}{x^3} \, dx","Int[f^(a + b/x)/x^3,x]","\frac{f^{a+\frac{b}{x}}}{b^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x}}}{b x \log (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)/(b^2*Log[f]^2) - f^(a + b/x)/(b*x*Log[f])","A",2,2,13,0.1538,1,"{2212, 2209}"
124,1,61,0,0.0604829,"\int \frac{f^{a+\frac{b}{x}}}{x^4} \, dx","Int[f^(a + b/x)/x^4,x]","\frac{2 f^{a+\frac{b}{x}}}{b^2 x \log ^2(f)}-\frac{2 f^{a+\frac{b}{x}}}{b^3 \log ^3(f)}-\frac{f^{a+\frac{b}{x}}}{b x^2 \log (f)}","\frac{2 f^{a+\frac{b}{x}}}{b^2 x \log ^2(f)}-\frac{2 f^{a+\frac{b}{x}}}{b^3 \log ^3(f)}-\frac{f^{a+\frac{b}{x}}}{b x^2 \log (f)}",1,"(-2*f^(a + b/x))/(b^3*Log[f]^3) + (2*f^(a + b/x))/(b^2*x*Log[f]^2) - f^(a + b/x)/(b*x^2*Log[f])","A",3,2,13,0.1538,1,"{2212, 2209}"
125,1,82,0,0.0815529,"\int \frac{f^{a+\frac{b}{x}}}{x^5} \, dx","Int[f^(a + b/x)/x^5,x]","\frac{3 f^{a+\frac{b}{x}}}{b^2 x^2 \log ^2(f)}-\frac{6 f^{a+\frac{b}{x}}}{b^3 x \log ^3(f)}+\frac{6 f^{a+\frac{b}{x}}}{b^4 \log ^4(f)}-\frac{f^{a+\frac{b}{x}}}{b x^3 \log (f)}","\frac{3 f^{a+\frac{b}{x}}}{b^2 x^2 \log ^2(f)}-\frac{6 f^{a+\frac{b}{x}}}{b^3 x \log ^3(f)}+\frac{6 f^{a+\frac{b}{x}}}{b^4 \log ^4(f)}-\frac{f^{a+\frac{b}{x}}}{b x^3 \log (f)}",1,"(6*f^(a + b/x))/(b^4*Log[f]^4) - (6*f^(a + b/x))/(b^3*x*Log[f]^3) + (3*f^(a + b/x))/(b^2*x^2*Log[f]^2) - f^(a + b/x)/(b*x^3*Log[f])","A",4,2,13,0.1538,1,"{2212, 2209}"
126,1,22,0,0.0183533,"\int \frac{f^{a+\frac{b}{x}}}{x^6} \, dx","Int[f^(a + b/x)/x^6,x]","-\frac{f^a \text{Gamma}\left(5,-\frac{b \log (f)}{x}\right)}{b^5 \log ^5(f)}","-\frac{f^{a+\frac{b}{x}} \left(12 b^2 x^2 \log ^2(f)-4 b^3 x \log ^3(f)+b^4 \log ^4(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",1,1,13,0.07692,1,"{2218}"
127,1,21,0,0.0190488,"\int \frac{f^{a+\frac{b}{x}}}{x^7} \, dx","Int[f^(a + b/x)/x^7,x]","\frac{f^a \text{Gamma}\left(6,-\frac{b \log (f)}{x}\right)}{b^6 \log ^6(f)}","\frac{f^{a+\frac{b}{x}} \left(60 b^2 x^3 \log ^2(f)-20 b^3 x^2 \log ^3(f)+5 b^4 x \log ^4(f)-b^5 \log ^5(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",1,1,13,0.07692,1,"{2218}"
128,1,46,0,0.0236666,"\int f^{a+\frac{b}{x^2}} x^m \, dx","Int[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}} \text{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}} \text{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",1,1,13,0.07692,1,"{2218}"
129,1,24,0,0.0247295,"\int f^{a+\frac{b}{x^2}} x^9 \, dx","Int[f^(a + b/x^2)*x^9,x]","-\frac{1}{2} b^5 f^a \log ^5(f) \text{Gamma}\left(-5,-\frac{b \log (f)}{x^2}\right)","-\frac{1}{2} b^5 f^a \log ^5(f) \text{Gamma}\left(-5,-\frac{b \log (f)}{x^2}\right)",1,"-(b^5*f^a*Gamma[-5, -((b*Log[f])/x^2)]*Log[f]^5)/2","A",1,1,13,0.07692,1,"{2218}"
130,1,24,0,0.0246971,"\int f^{a+\frac{b}{x^2}} x^7 \, dx","Int[f^(a + b/x^2)*x^7,x]","\frac{1}{2} b^4 f^a \log ^4(f) \text{Gamma}\left(-4,-\frac{b \log (f)}{x^2}\right)","\frac{1}{2} b^4 f^a \log ^4(f) \text{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",1,1,13,0.07692,1,"{2218}"
131,1,81,0,0.0892356,"\int f^{a+\frac{b}{x^2}} x^5 \, dx","Int[f^(a + b/x^2)*x^5,x]","-\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}}","-\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/x^2)*x^6)/6 + (b*f^(a + b/x^2)*x^4*Log[f])/12 + (b^2*f^(a + b/x^2)*x^2*Log[f]^2)/12 - (b^3*f^a*ExpIntegralEi[(b*Log[f])/x^2]*Log[f]^3)/12","A",4,2,13,0.1538,1,"{2214, 2210}"
132,1,58,0,0.062517,"\int f^{a+\frac{b}{x^2}} x^3 \, dx","Int[f^(a + b/x^2)*x^3,x]","-\frac{1}{4} b^2 f^a \log ^2(f) \text{Ei}\left(\frac{b \log (f)}{x^2}\right)+\frac{1}{4} x^4 f^{a+\frac{b}{x^2}}+\frac{1}{4} b x^2 \log (f) f^{a+\frac{b}{x^2}}","-\frac{1}{4} b^2 f^a \log ^2(f) \text{Ei}\left(\frac{b \log (f)}{x^2}\right)+\frac{1}{4} x^4 f^{a+\frac{b}{x^2}}+\frac{1}{4} b x^2 \log (f) f^{a+\frac{b}{x^2}}",1,"(f^(a + b/x^2)*x^4)/4 + (b*f^(a + b/x^2)*x^2*Log[f])/4 - (b^2*f^a*ExpIntegralEi[(b*Log[f])/x^2]*Log[f]^2)/4","A",3,2,13,0.1538,1,"{2214, 2210}"
133,1,35,0,0.0359106,"\int f^{a+\frac{b}{x^2}} x \, dx","Int[f^(a + b/x^2)*x,x]","\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)","\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 + b/x^2)*x^2)/2 - (b*f^a*ExpIntegralEi[(b*Log[f])/x^2]*Log[f])/2","A",2,2,11,0.1818,1,"{2214, 2210}"
134,1,15,0,0.0234397,"\int \frac{f^{a+\frac{b}{x^2}}}{x} \, dx","Int[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,"-(f^a*ExpIntegralEi[(b*Log[f])/x^2])/2","A",1,1,13,0.07692,1,"{2210}"
135,1,20,0,0.0214927,"\int \frac{f^{a+\frac{b}{x^2}}}{x^3} \, dx","Int[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,"-f^(a + b/x^2)/(2*b*Log[f])","A",1,1,13,0.07692,1,"{2209}"
136,1,44,0,0.0451656,"\int \frac{f^{a+\frac{b}{x^2}}}{x^5} \, dx","Int[f^(a + b/x^2)/x^5,x]","\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)}","\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)/(2*b^2*Log[f]^2) - f^(a + b/x^2)/(2*b*x^2*Log[f])","A",2,2,13,0.1538,1,"{2212, 2209}"
137,1,62,0,0.0693236,"\int \frac{f^{a+\frac{b}{x^2}}}{x^7} \, dx","Int[f^(a + b/x^2)/x^7,x]","\frac{f^{a+\frac{b}{x^2}}}{b^2 x^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x^2}}}{b^3 \log ^3(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^4 \log (f)}","\frac{f^{a+\frac{b}{x^2}}}{b^2 x^2 \log ^2(f)}-\frac{f^{a+\frac{b}{x^2}}}{b^3 \log ^3(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^4 \log (f)}",1,"-(f^(a + b/x^2)/(b^3*Log[f]^3)) + f^(a + b/x^2)/(b^2*x^2*Log[f]^2) - f^(a + b/x^2)/(2*b*x^4*Log[f])","A",3,2,13,0.1538,1,"{2212, 2209}"
138,1,86,0,0.0957998,"\int \frac{f^{a+\frac{b}{x^2}}}{x^9} \, dx","Int[f^(a + b/x^2)/x^9,x]","\frac{3 f^{a+\frac{b}{x^2}}}{2 b^2 x^4 \log ^2(f)}-\frac{3 f^{a+\frac{b}{x^2}}}{b^3 x^2 \log ^3(f)}+\frac{3 f^{a+\frac{b}{x^2}}}{b^4 \log ^4(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^6 \log (f)}","\frac{3 f^{a+\frac{b}{x^2}}}{2 b^2 x^4 \log ^2(f)}-\frac{3 f^{a+\frac{b}{x^2}}}{b^3 x^2 \log ^3(f)}+\frac{3 f^{a+\frac{b}{x^2}}}{b^4 \log ^4(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^6 \log (f)}",1,"(3*f^(a + b/x^2))/(b^4*Log[f]^4) - (3*f^(a + b/x^2))/(b^3*x^2*Log[f]^3) + (3*f^(a + b/x^2))/(2*b^2*x^4*Log[f]^2) - f^(a + b/x^2)/(2*b*x^6*Log[f])","A",4,2,13,0.1538,1,"{2212, 2209}"
139,1,24,0,0.022182,"\int \frac{f^{a+\frac{b}{x^2}}}{x^{11}} \, dx","Int[f^(a + b/x^2)/x^11,x]","-\frac{f^a \text{Gamma}\left(5,-\frac{b \log (f)}{x^2}\right)}{2 b^5 \log ^5(f)}","-\frac{f^{a+\frac{b}{x^2}} \left(12 b^2 x^4 \log ^2(f)-4 b^3 x^2 \log ^3(f)+b^4 \log ^4(f)-24 b x^6 \log (f)+24 x^8\right)}{2 b^5 x^8 \log ^5(f)}",1,"-(f^a*Gamma[5, -((b*Log[f])/x^2)])/(2*b^5*Log[f]^5)","C",1,1,13,0.07692,1,"{2218}"
140,1,24,0,0.0240109,"\int \frac{f^{a+\frac{b}{x^2}}}{x^{13}} \, dx","Int[f^(a + b/x^2)/x^13,x]","\frac{f^a \text{Gamma}\left(6,-\frac{b \log (f)}{x^2}\right)}{2 b^6 \log ^6(f)}","\frac{f^{a+\frac{b}{x^2}} \left(60 b^2 x^6 \log ^2(f)-20 b^3 x^4 \log ^3(f)+5 b^4 x^2 \log ^4(f)-b^5 \log ^5(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",1,1,13,0.07692,1,"{2218}"
141,1,34,0,0.0241223,"\int f^{a+\frac{b}{x^2}} x^{10} \, dx","Int[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} \text{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} \text{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",1,1,13,0.07692,1,"{2218}"
142,1,34,0,0.0236792,"\int f^{a+\frac{b}{x^2}} x^8 \, dx","Int[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} \text{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} \text{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",1,1,13,0.07692,1,"{2218}"
143,1,119,0,0.1253172,"\int f^{a+\frac{b}{x^2}} x^6 \, dx","Int[f^(a + b/x^2)*x^6,x]","-\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}}","-\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 + b/x^2)*x^7)/7 + (2*b*f^(a + b/x^2)*x^5*Log[f])/35 + (4*b^2*f^(a + b/x^2)*x^3*Log[f]^2)/105 + (8*b^3*f^(a + b/x^2)*x*Log[f]^3)/105 - (8*b^(7/2)*f^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x]*Log[f]^(7/2))/105","A",6,4,13,0.3077,1,"{2214, 2206, 2211, 2204}"
144,1,96,0,0.0881798,"\int f^{a+\frac{b}{x^2}} x^4 \, dx","Int[f^(a + b/x^2)*x^4,x]","-\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}}","-\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 + b/x^2)*x^5)/5 + (2*b*f^(a + b/x^2)*x^3*Log[f])/15 + (4*b^2*f^(a + b/x^2)*x*Log[f]^2)/15 - (4*b^(5/2)*f^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x]*Log[f]^(5/2))/15","A",5,4,13,0.3077,1,"{2214, 2206, 2211, 2204}"
145,1,73,0,0.0608214,"\int f^{a+\frac{b}{x^2}} x^2 \, dx","Int[f^(a + b/x^2)*x^2,x]","-\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{1}{3} x^3 f^{a+\frac{b}{x^2}}+\frac{2}{3} b x \log (f) f^{a+\frac{b}{x^2}}","-\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{1}{3} x^3 f^{a+\frac{b}{x^2}}+\frac{2}{3} b x \log (f) f^{a+\frac{b}{x^2}}",1,"(f^(a + b/x^2)*x^3)/3 + (2*b*f^(a + b/x^2)*x*Log[f])/3 - (2*b^(3/2)*f^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x]*Log[f]^(3/2))/3","A",4,4,13,0.3077,1,"{2214, 2206, 2211, 2204}"
146,1,49,0,0.0342323,"\int f^{a+\frac{b}{x^2}} \, dx","Int[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",3,3,9,0.3333,1,"{2206, 2211, 2204}"
147,1,39,0,0.0274652,"\int \frac{f^{a+\frac{b}{x^2}}}{x^2} \, dx","Int[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,"-(f^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x])/(2*Sqrt[b]*Sqrt[Log[f]])","A",2,2,13,0.1538,1,"{2211, 2204}"
148,1,63,0,0.0526033,"\int \frac{f^{a+\frac{b}{x^2}}}{x^4} \, dx","Int[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",3,3,13,0.2308,1,"{2212, 2211, 2204}"
149,1,86,0,0.0790159,"\int \frac{f^{a+\frac{b}{x^2}}}{x^6} \, dx","Int[f^(a + b/x^2)/x^6,x]","-\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)}","-\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)) + (3*f^(a + b/x^2))/(4*b^2*x*Log[f]^2) - f^(a + b/x^2)/(2*b*x^3*Log[f])","A",4,3,13,0.2308,1,"{2212, 2211, 2204}"
150,1,109,0,0.1124018,"\int \frac{f^{a+\frac{b}{x^2}}}{x^8} \, dx","Int[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{5 f^{a+\frac{b}{x^2}}}{4 b^2 x^3 \log ^2(f)}-\frac{15 f^{a+\frac{b}{x^2}}}{8 b^3 x \log ^3(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^5 \log (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{5 f^{a+\frac{b}{x^2}}}{4 b^2 x^3 \log ^2(f)}-\frac{15 f^{a+\frac{b}{x^2}}}{8 b^3 x \log ^3(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)) - (15*f^(a + b/x^2))/(8*b^3*x*Log[f]^3) + (5*f^(a + b/x^2))/(4*b^2*x^3*Log[f]^2) - f^(a + b/x^2)/(2*b*x^5*Log[f])","A",5,3,13,0.2308,1,"{2212, 2211, 2204}"
151,1,132,0,0.1600329,"\int \frac{f^{a+\frac{b}{x^2}}}{x^{10}} \, dx","Int[f^(a + b/x^2)/x^10,x]","-\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{7 f^{a+\frac{b}{x^2}}}{4 b^2 x^5 \log ^2(f)}-\frac{35 f^{a+\frac{b}{x^2}}}{8 b^3 x^3 \log ^3(f)}+\frac{105 f^{a+\frac{b}{x^2}}}{16 b^4 x \log ^4(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^7 \log (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{7 f^{a+\frac{b}{x^2}}}{4 b^2 x^5 \log ^2(f)}-\frac{35 f^{a+\frac{b}{x^2}}}{8 b^3 x^3 \log ^3(f)}+\frac{105 f^{a+\frac{b}{x^2}}}{16 b^4 x \log ^4(f)}-\frac{f^{a+\frac{b}{x^2}}}{2 b x^7 \log (f)}",1,"(-105*f^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[f]])/x])/(32*b^(9/2)*Log[f]^(9/2)) + (105*f^(a + b/x^2))/(16*b^4*x*Log[f]^4) - (35*f^(a + b/x^2))/(8*b^3*x^3*Log[f]^3) + (7*f^(a + b/x^2))/(4*b^2*x^5*Log[f]^2) - f^(a + b/x^2)/(2*b*x^7*Log[f])","A",6,3,13,0.2308,1,"{2212, 2211, 2204}"
152,1,34,0,0.0256291,"\int \frac{f^{a+\frac{b}{x^2}}}{x^{12}} \, dx","Int[f^(a + b/x^2)/x^12,x]","\frac{f^a \text{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 \text{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",1,1,13,0.07692,1,"{2218}"
153,1,34,0,0.0240466,"\int \frac{f^{a+\frac{b}{x^2}}}{x^{14}} \, dx","Int[f^(a + b/x^2)/x^14,x]","\frac{f^a \text{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 \text{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",1,1,13,0.07692,1,"{2218}"
154,1,46,0,0.0250903,"\int f^{a+\frac{b}{x^3}} x^m \, dx","Int[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}} \text{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}} \text{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",1,1,13,0.07692,1,"{2218}"
155,1,24,0,0.0279187,"\int f^{a+\frac{b}{x^3}} x^{14} \, dx","Int[f^(a + b/x^3)*x^14,x]","-\frac{1}{3} b^5 f^a \log ^5(f) \text{Gamma}\left(-5,-\frac{b \log (f)}{x^3}\right)","-\frac{1}{3} b^5 f^a \log ^5(f) \text{Gamma}\left(-5,-\frac{b \log (f)}{x^3}\right)",1,"-(b^5*f^a*Gamma[-5, -((b*Log[f])/x^3)]*Log[f]^5)/3","A",1,1,13,0.07692,1,"{2218}"
156,1,24,0,0.0330287,"\int f^{a+\frac{b}{x^3}} x^{11} \, dx","Int[f^(a + b/x^3)*x^11,x]","\frac{1}{3} b^4 f^a \log ^4(f) \text{Gamma}\left(-4,-\frac{b \log (f)}{x^3}\right)","\frac{1}{3} b^4 f^a \log ^4(f) \text{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",1,1,13,0.07692,1,"{2218}"
157,1,81,0,0.1147183,"\int f^{a+\frac{b}{x^3}} x^8 \, dx","Int[f^(a + b/x^3)*x^8,x]","-\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}}","-\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/x^3)*x^9)/9 + (b*f^(a + b/x^3)*x^6*Log[f])/18 + (b^2*f^(a + b/x^3)*x^3*Log[f]^2)/18 - (b^3*f^a*ExpIntegralEi[(b*Log[f])/x^3]*Log[f]^3)/18","A",4,2,13,0.1538,1,"{2214, 2210}"
158,1,58,0,0.0760661,"\int f^{a+\frac{b}{x^3}} x^5 \, dx","Int[f^(a + b/x^3)*x^5,x]","-\frac{1}{6} b^2 f^a \log ^2(f) \text{Ei}\left(\frac{b \log (f)}{x^3}\right)+\frac{1}{6} x^6 f^{a+\frac{b}{x^3}}+\frac{1}{6} b x^3 \log (f) f^{a+\frac{b}{x^3}}","-\frac{1}{6} b^2 f^a \log ^2(f) \text{Ei}\left(\frac{b \log (f)}{x^3}\right)+\frac{1}{6} x^6 f^{a+\frac{b}{x^3}}+\frac{1}{6} b x^3 \log (f) f^{a+\frac{b}{x^3}}",1,"(f^(a + b/x^3)*x^6)/6 + (b*f^(a + b/x^3)*x^3*Log[f])/6 - (b^2*f^a*ExpIntegralEi[(b*Log[f])/x^3]*Log[f]^2)/6","A",3,2,13,0.1538,1,"{2214, 2210}"
159,1,35,0,0.0481365,"\int f^{a+\frac{b}{x^3}} x^2 \, dx","Int[f^(a + b/x^3)*x^2,x]","\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)","\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 + b/x^3)*x^3)/3 - (b*f^a*ExpIntegralEi[(b*Log[f])/x^3]*Log[f])/3","A",2,2,13,0.1538,1,"{2214, 2210}"
160,1,15,0,0.0223782,"\int \frac{f^{a+\frac{b}{x^3}}}{x} \, dx","Int[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,"-(f^a*ExpIntegralEi[(b*Log[f])/x^3])/3","A",1,1,13,0.07692,1,"{2210}"
161,1,20,0,0.0215353,"\int \frac{f^{a+\frac{b}{x^3}}}{x^4} \, dx","Int[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,"-f^(a + b/x^3)/(3*b*Log[f])","A",1,1,13,0.07692,1,"{2209}"
162,1,44,0,0.04618,"\int \frac{f^{a+\frac{b}{x^3}}}{x^7} \, dx","Int[f^(a + b/x^3)/x^7,x]","\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)}","\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)/(3*b^2*Log[f]^2) - f^(a + b/x^3)/(3*b*x^3*Log[f])","A",2,2,13,0.1538,1,"{2212, 2209}"
163,1,67,0,0.0703232,"\int \frac{f^{a+\frac{b}{x^3}}}{x^{10}} \, dx","Int[f^(a + b/x^3)/x^10,x]","\frac{2 f^{a+\frac{b}{x^3}}}{3 b^2 x^3 \log ^2(f)}-\frac{2 f^{a+\frac{b}{x^3}}}{3 b^3 \log ^3(f)}-\frac{f^{a+\frac{b}{x^3}}}{3 b x^6 \log (f)}","\frac{2 f^{a+\frac{b}{x^3}}}{3 b^2 x^3 \log ^2(f)}-\frac{2 f^{a+\frac{b}{x^3}}}{3 b^3 \log ^3(f)}-\frac{f^{a+\frac{b}{x^3}}}{3 b x^6 \log (f)}",1,"(-2*f^(a + b/x^3))/(3*b^3*Log[f]^3) + (2*f^(a + b/x^3))/(3*b^2*x^3*Log[f]^2) - f^(a + b/x^3)/(3*b*x^6*Log[f])","A",3,2,13,0.1538,1,"{2212, 2209}"
164,1,83,0,0.0942408,"\int \frac{f^{a+\frac{b}{x^3}}}{x^{13}} \, dx","Int[f^(a + b/x^3)/x^13,x]","\frac{f^{a+\frac{b}{x^3}}}{b^2 x^6 \log ^2(f)}-\frac{2 f^{a+\frac{b}{x^3}}}{b^3 x^3 \log ^3(f)}+\frac{2 f^{a+\frac{b}{x^3}}}{b^4 \log ^4(f)}-\frac{f^{a+\frac{b}{x^3}}}{3 b x^9 \log (f)}","\frac{f^{a+\frac{b}{x^3}}}{b^2 x^6 \log ^2(f)}-\frac{2 f^{a+\frac{b}{x^3}}}{b^3 x^3 \log ^3(f)}+\frac{2 f^{a+\frac{b}{x^3}}}{b^4 \log ^4(f)}-\frac{f^{a+\frac{b}{x^3}}}{3 b x^9 \log (f)}",1,"(2*f^(a + b/x^3))/(b^4*Log[f]^4) - (2*f^(a + b/x^3))/(b^3*x^3*Log[f]^3) + f^(a + b/x^3)/(b^2*x^6*Log[f]^2) - f^(a + b/x^3)/(3*b*x^9*Log[f])","A",4,2,13,0.1538,1,"{2212, 2209}"
165,1,24,0,0.0226648,"\int \frac{f^{a+\frac{b}{x^3}}}{x^{16}} \, dx","Int[f^(a + b/x^3)/x^16,x]","-\frac{f^a \text{Gamma}\left(5,-\frac{b \log (f)}{x^3}\right)}{3 b^5 \log ^5(f)}","-\frac{f^{a+\frac{b}{x^3}} \left(12 b^2 x^6 \log ^2(f)-4 b^3 x^3 \log ^3(f)+b^4 \log ^4(f)-24 b x^9 \log (f)+24 x^{12}\right)}{3 b^5 x^{12} \log ^5(f)}",1,"-(f^a*Gamma[5, -((b*Log[f])/x^3)])/(3*b^5*Log[f]^5)","C",1,1,13,0.07692,1,"{2218}"
166,1,24,0,0.0228049,"\int \frac{f^{a+\frac{b}{x^3}}}{x^{19}} \, dx","Int[f^(a + b/x^3)/x^19,x]","\frac{f^a \text{Gamma}\left(6,-\frac{b \log (f)}{x^3}\right)}{3 b^6 \log ^6(f)}","\frac{f^{a+\frac{b}{x^3}} \left(60 b^2 x^9 \log ^2(f)-20 b^3 x^6 \log ^3(f)+5 b^4 x^3 \log ^4(f)-b^5 \log ^5(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",1,1,13,0.07692,1,"{2218}"
167,1,34,0,0.0252712,"\int f^{a+\frac{b}{x^3}} x^4 \, dx","Int[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} \text{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} \text{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",1,1,13,0.07692,1,"{2218}"
168,1,34,0,0.0247654,"\int f^{a+\frac{b}{x^3}} x^3 \, dx","Int[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} \text{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} \text{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",1,1,13,0.07692,1,"{2218}"
169,1,34,0,0.0142921,"\int f^{a+\frac{b}{x^3}} x \, dx","Int[f^(a + b/x^3)*x,x]","\frac{1}{3} x^2 f^a \left(-\frac{b \log (f)}{x^3}\right)^{2/3} \text{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} \text{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",1,1,11,0.09091,1,"{2218}"
170,1,32,0,0.0047191,"\int f^{a+\frac{b}{x^3}} \, dx","Int[f^(a + b/x^3),x]","\frac{1}{3} x f^a \sqrt[3]{-\frac{b \log (f)}{x^3}} \text{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}} \text{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",1,1,9,0.1111,1,"{2208}"
171,1,34,0,0.0236808,"\int \frac{f^{a+\frac{b}{x^3}}}{x^2} \, dx","Int[f^(a + b/x^3)/x^2,x]","\frac{f^a \text{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 \text{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",1,1,13,0.07692,1,"{2218}"
172,1,34,0,0.0222683,"\int \frac{f^{a+\frac{b}{x^3}}}{x^3} \, dx","Int[f^(a + b/x^3)/x^3,x]","\frac{f^a \text{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 \text{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",1,1,13,0.07692,1,"{2218}"
173,1,34,0,0.0230954,"\int \frac{f^{a+\frac{b}{x^3}}}{x^5} \, dx","Int[f^(a + b/x^3)/x^5,x]","\frac{f^a \text{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 \text{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",1,1,13,0.07692,1,"{2218}"
174,1,46,0,0.0264467,"\int f^{a+b x^n} x^m \, dx","Int[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}} \text{Gamma}\left(\frac{m+1}{n},-b \log (f) x^n\right)}{n}","-\frac{f^a x^{m+1} \left(-b \log (f) x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-b \log (f) x^n\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",1,1,13,0.07692,1,"{2218}"
175,1,39,0,0.0253167,"\int f^{a+b x^n} x^3 \, dx","Int[f^(a + b*x^n)*x^3,x]","-\frac{x^4 f^a \left(-b \log (f) x^n\right)^{-4/n} \text{Gamma}\left(\frac{4}{n},-b \log (f) x^n\right)}{n}","-\frac{x^4 f^a \left(-b \log (f) x^n\right)^{-4/n} \text{Gamma}\left(\frac{4}{n},-b \log (f) x^n\right)}{n}",1,"-((f^a*x^4*Gamma[4/n, -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^(4/n)))","A",1,1,13,0.07692,1,"{2218}"
176,1,39,0,0.0252264,"\int f^{a+b x^n} x^2 \, dx","Int[f^(a + b*x^n)*x^2,x]","-\frac{x^3 f^a \left(-b \log (f) x^n\right)^{-3/n} \text{Gamma}\left(\frac{3}{n},-b \log (f) x^n\right)}{n}","-\frac{x^3 f^a \left(-b \log (f) x^n\right)^{-3/n} \text{Gamma}\left(\frac{3}{n},-b \log (f) x^n\right)}{n}",1,"-((f^a*x^3*Gamma[3/n, -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^(3/n)))","A",1,1,13,0.07692,1,"{2218}"
177,1,39,0,0.0145723,"\int f^{a+b x^n} x \, dx","Int[f^(a + b*x^n)*x,x]","-\frac{x^2 f^a \left(-b \log (f) x^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{n},-b \log (f) x^n\right)}{n}","-\frac{x^2 f^a \left(-b \log (f) x^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{n},-b \log (f) x^n\right)}{n}",1,"-((f^a*x^2*Gamma[2/n, -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^(2/n)))","A",1,1,11,0.09091,1,"{2218}"
178,1,35,0,0.0043448,"\int f^{a+b x^n} \, dx","Int[f^(a + b*x^n),x]","-\frac{x f^a \left(-b \log (f) x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-b \log (f) x^n\right)}{n}","-\frac{x f^a \left(-b \log (f) x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-b \log (f) x^n\right)}{n}",1,"-((f^a*x*Gamma[n^(-1), -(b*x^n*Log[f])])/(n*(-(b*x^n*Log[f]))^n^(-1)))","A",1,1,9,0.1111,1,"{2208}"
179,1,15,0,0.0231667,"\int \frac{f^{a+b x^n}}{x} \, dx","Int[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",1,1,13,0.07692,1,"{2210}"
180,1,37,0,0.0238832,"\int \frac{f^{a+b x^n}}{x^2} \, dx","Int[f^(a + b*x^n)/x^2,x]","-\frac{f^a \left(-b \log (f) x^n\right)^{\frac{1}{n}} \text{Gamma}\left(-\frac{1}{n},-b \log (f) x^n\right)}{n x}","-\frac{f^a \left(-b \log (f) x^n\right)^{\frac{1}{n}} \text{Gamma}\left(-\frac{1}{n},-b \log (f) x^n\right)}{n x}",1,"-((f^a*Gamma[-n^(-1), -(b*x^n*Log[f])]*(-(b*x^n*Log[f]))^n^(-1))/(n*x))","A",1,1,13,0.07692,1,"{2218}"
181,1,39,0,0.0246527,"\int \frac{f^{a+b x^n}}{x^3} \, dx","Int[f^(a + b*x^n)/x^3,x]","-\frac{f^a \left(-b \log (f) x^n\right)^{2/n} \text{Gamma}\left(-\frac{2}{n},-b \log (f) x^n\right)}{n x^2}","-\frac{f^a \left(-b \log (f) x^n\right)^{2/n} \text{Gamma}\left(-\frac{2}{n},-b \log (f) x^n\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",1,1,13,0.07692,1,"{2218}"
182,1,39,0,0.0241303,"\int \frac{f^{a+b x^n}}{x^4} \, dx","Int[f^(a + b*x^n)/x^4,x]","-\frac{f^a \left(-b \log (f) x^n\right)^{3/n} \text{Gamma}\left(-\frac{3}{n},-b \log (f) x^n\right)}{n x^3}","-\frac{f^a \left(-b \log (f) x^n\right)^{3/n} \text{Gamma}\left(-\frac{3}{n},-b \log (f) x^n\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",1,1,13,0.07692,1,"{2218}"
183,1,71,0,0.075849,"\int f^{a+b x^n} x^{-1+3 n} \, dx","Int[f^(a + b*x^n)*x^(-1 + 3*n),x]","-\frac{2 x^n f^{a+b x^n}}{b^2 n \log ^2(f)}+\frac{2 f^{a+b x^n}}{b^3 n \log ^3(f)}+\frac{x^{2 n} f^{a+b x^n}}{b n \log (f)}","-\frac{2 x^n f^{a+b x^n}}{b^2 n \log ^2(f)}+\frac{2 f^{a+b x^n}}{b^3 n \log ^3(f)}+\frac{x^{2 n} f^{a+b x^n}}{b n \log (f)}",1,"(2*f^(a + b*x^n))/(b^3*n*Log[f]^3) - (2*f^(a + b*x^n)*x^n)/(b^2*n*Log[f]^2) + (f^(a + b*x^n)*x^(2*n))/(b*n*Log[f])","A",3,2,17,0.1176,1,"{2213, 2209}"
184,1,45,0,0.048403,"\int f^{a+b x^n} x^{-1+2 n} \, dx","Int[f^(a + b*x^n)*x^(-1 + 2*n),x]","\frac{x^n f^{a+b x^n}}{b n \log (f)}-\frac{f^{a+b x^n}}{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 + b*x^n)/(b^2*n*Log[f]^2)) + (f^(a + b*x^n)*x^n)/(b*n*Log[f])","A",2,2,17,0.1176,1,"{2213, 2209}"
185,1,20,0,0.0231736,"\int f^{a+b x^n} x^{-1+n} \, dx","Int[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",1,1,15,0.06667,1,"{2209}"
186,1,15,0,0.0229328,"\int \frac{f^{a+b x^n}}{x} \, dx","Int[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",1,1,13,0.07692,1,"{2210}"
187,1,38,0,0.0486405,"\int f^{a+b x^n} x^{-1-n} \, dx","Int[f^(a + b*x^n)*x^(-1 - n),x]","\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}","\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,"-(f^(a + b*x^n)/(n*x^n)) + (b*f^a*ExpIntegralEi[b*x^n*Log[f]]*Log[f])/n","A",2,2,17,0.1176,1,"{2215, 2210}"
188,1,71,0,0.0752343,"\int f^{a+b x^n} x^{-1-2 n} \, dx","Int[f^(a + b*x^n)*x^(-1 - 2*n),x]","\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}","\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,"-f^(a + b*x^n)/(2*n*x^(2*n)) - (b*f^(a + b*x^n)*Log[f])/(2*n*x^n) + (b^2*f^a*ExpIntegralEi[b*x^n*Log[f]]*Log[f]^2)/(2*n)","A",3,2,17,0.1176,1,"{2215, 2210}"
189,1,104,0,0.1102449,"\int f^{a+b x^n} x^{-1+\frac{5 n}{2}} \, dx","Int[f^(a + b*x^n)*x^(-1 + (5*n)/2),x]","\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)}","\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,"(3*f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x^(n/2)*Sqrt[Log[f]]])/(4*b^(5/2)*n*Log[f]^(5/2)) - (3*f^(a + b*x^n)*x^(n/2))/(2*b^2*n*Log[f]^2) + (f^(a + b*x^n)*x^((3*n)/2))/(b*n*Log[f])","A",4,3,19,0.1579,1,"{2213, 2211, 2204}"
190,1,74,0,0.065467,"\int f^{a+b x^n} x^{-1+\frac{3 n}{2}} \, dx","Int[f^(a + b*x^n)*x^(-1 + (3*n)/2),x]","\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)}","\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*Sqrt[Pi]*Erfi[Sqrt[b]*x^(n/2)*Sqrt[Log[f]]])/(2*b^(3/2)*n*Log[f]^(3/2)) + (f^(a + b*x^n)*x^(n/2))/(b*n*Log[f])","A",3,3,19,0.1579,1,"{2213, 2211, 2204}"
191,1,43,0,0.0363298,"\int f^{a+b x^n} x^{-1+\frac{n}{2}} \, dx","Int[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",2,2,19,0.1053,1,"{2211, 2204}"
192,1,66,0,0.0652999,"\int f^{a+b x^n} x^{-1-\frac{n}{2}} \, dx","Int[f^(a + b*x^n)*x^(-1 - n/2),x]","\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}","\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,"(-2*f^(a + b*x^n))/(n*x^(n/2)) + (2*Sqrt[b]*f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x^(n/2)*Sqrt[Log[f]]]*Sqrt[Log[f]])/n","A",3,3,19,0.1579,1,"{2215, 2211, 2204}"
193,1,96,0,0.0955575,"\int f^{a+b x^n} x^{-1-\frac{3 n}{2}} \, dx","Int[f^(a + b*x^n)*x^(-1 - (3*n)/2),x]","\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}","\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,"(-2*f^(a + b*x^n))/(3*n*x^((3*n)/2)) - (4*b*f^(a + b*x^n)*Log[f])/(3*n*x^(n/2)) + (4*b^(3/2)*f^a*Sqrt[Pi]*Erfi[Sqrt[b]*x^(n/2)*Sqrt[Log[f]]]*Log[f]^(3/2))/(3*n)","A",4,3,19,0.1579,1,"{2215, 2211, 2204}"
194,1,16,0,0.0075144,"\int e^{-0.1 x} x \, dx","Int[x/E^(0.1*x),x]","-10. e^{-0.1 x} x-100. e^{-0.1 x}","-10. e^{-0.1 x} x-100. e^{-0.1 x}",1,"-100./E^(0.1*x) - (10.*x)/E^(0.1*x)","A",2,2,7,0.2857,1,"{2176, 2194}"
195,1,203,0,0.2289495,"\int f^{c (a+b x)^2} x^3 \, dx","Int[f^(c*(a + b*x)^2)*x^3,x]","-\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)}","-\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,"-f^(c*(a + b*x)^2)/(2*b^4*c^2*Log[f]^2) + (3*a*Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]])/(4*b^4*c^(3/2)*Log[f]^(3/2)) + (3*a^2*f^(c*(a + b*x)^2))/(2*b^4*c*Log[f]) - (3*a*f^(c*(a + b*x)^2)*(a + b*x))/(2*b^4*c*Log[f]) + (f^(c*(a + b*x)^2)*(a + b*x)^2)/(2*b^4*c*Log[f]) - (a^3*Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]])/(2*b^4*Sqrt[c]*Sqrt[Log[f]])","A",8,4,15,0.2667,1,"{2226, 2204, 2209, 2212}"
196,1,140,0,0.1294262,"\int f^{c (a+b x)^2} x^2 \, dx","Int[f^(c*(a + b*x)^2)*x^2,x]","\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)}","\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,"-(Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]])/(4*b^3*c^(3/2)*Log[f]^(3/2)) - (a*f^(c*(a + b*x)^2))/(b^3*c*Log[f]) + (f^(c*(a + b*x)^2)*(a + b*x))/(2*b^3*c*Log[f]) + (a^2*Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]])/(2*b^3*Sqrt[c]*Sqrt[Log[f]])","A",6,4,15,0.2667,1,"{2226, 2204, 2209, 2212}"
197,1,68,0,0.0579059,"\int f^{c (a+b x)^2} x \, dx","Int[f^(c*(a + b*x)^2)*x,x]","\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)}}","\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)/(2*b^2*c*Log[f]) - (a*Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]])/(2*b^2*Sqrt[c]*Sqrt[Log[f]])","A",4,3,13,0.2308,1,"{2226, 2204, 2209}"
198,1,41,0,0.0078993,"\int f^{c (a+b x)^2} \, dx","Int[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",1,1,11,0.09091,1,"{2204}"
199,0,0,0,0.0257867,"\int \frac{f^{c (a+b x)^2}}{x} \, dx","Int[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,"Defer[Int][f^(c*(a + b*x)^2)/x, x]","A",0,0,0,0,-1,"{}"
200,0,0,0,0.0579473,"\int \frac{f^{c (a+b x)^2}}{x^2} \, dx","Int[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,"-(f^(c*(a + b*x)^2)/x) + b*Sqrt[c]*Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]]*Sqrt[Log[f]] + 2*a*b*c*Log[f]*Defer[Int][f^(c*(a + b*x)^2)/x, x]","A",0,0,0,0,-1,"{}"
201,0,0,0,0.0971859,"\int \frac{f^{c (a+b x)^2}}{x^3} \, dx","Int[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,"-f^(c*(a + b*x)^2)/(2*x^2) - (a*b*c*f^(c*(a + b*x)^2)*Log[f])/x + a*b^2*c^(3/2)*Sqrt[Pi]*Erfi[Sqrt[c]*(a + b*x)*Sqrt[Log[f]]]*Log[f]^(3/2) + b^2*c*Log[f]*Defer[Int][f^(c*(a + b*x)^2)/x, x] + 2*a^2*b^2*c^2*Log[f]^2*Defer[Int][f^(c*(a + b*x)^2)/x, x]","A",0,0,0,0,-1,"{}"
202,1,120,0,0.0889143,"\int f^{c (a+b x)^3} x^2 \, dx","Int[f^(c*(a + b*x)^3)*x^2,x]","-\frac{a^2 (a+b x) \text{Gamma}\left(\frac{1}{3},-c \log (f) (a+b x)^3\right)}{3 b^3 \sqrt[3]{-c \log (f) (a+b x)^3}}+\frac{2 a (a+b x)^2 \text{Gamma}\left(\frac{2}{3},-c \log (f) (a+b x)^3\right)}{3 b^3 \left(-c \log (f) (a+b x)^3\right)^{2/3}}+\frac{f^{c (a+b x)^3}}{3 b^3 c \log (f)}","-\frac{a^2 (a+b x) \text{Gamma}\left(\frac{1}{3},-c \log (f) (a+b x)^3\right)}{3 b^3 \sqrt[3]{-c \log (f) (a+b x)^3}}+\frac{2 a (a+b x)^2 \text{Gamma}\left(\frac{2}{3},-c \log (f) (a+b x)^3\right)}{3 b^3 \left(-c \log (f) (a+b x)^3\right)^{2/3}}+\frac{f^{c (a+b x)^3}}{3 b^3 c \log (f)}",1,"f^(c*(a + b*x)^3)/(3*b^3*c*Log[f]) + (2*a*(a + b*x)^2*Gamma[2/3, -(c*(a + b*x)^3*Log[f])])/(3*b^3*(-(c*(a + b*x)^3*Log[f]))^(2/3)) - (a^2*(a + b*x)*Gamma[1/3, -(c*(a + b*x)^3*Log[f])])/(3*b^3*(-(c*(a + b*x)^3*Log[f]))^(1/3))","A",5,4,15,0.2667,1,"{2226, 2208, 2218, 2209}"
203,1,92,0,0.0494645,"\int f^{c (a+b x)^3} x \, dx","Int[f^(c*(a + b*x)^3)*x,x]","\frac{a (a+b x) \text{Gamma}\left(\frac{1}{3},-c \log (f) (a+b x)^3\right)}{3 b^2 \sqrt[3]{-c \log (f) (a+b x)^3}}-\frac{(a+b x)^2 \text{Gamma}\left(\frac{2}{3},-c \log (f) (a+b x)^3\right)}{3 b^2 \left(-c \log (f) (a+b x)^3\right)^{2/3}}","\frac{a (a+b x) \text{Gamma}\left(\frac{1}{3},-c \log (f) (a+b x)^3\right)}{3 b^2 \sqrt[3]{-c \log (f) (a+b x)^3}}-\frac{(a+b x)^2 \text{Gamma}\left(\frac{2}{3},-c \log (f) (a+b x)^3\right)}{3 b^2 \left(-c \log (f) (a+b x)^3\right)^{2/3}}",1,"-((a + b*x)^2*Gamma[2/3, -(c*(a + b*x)^3*Log[f])])/(3*b^2*(-(c*(a + b*x)^3*Log[f]))^(2/3)) + (a*(a + b*x)*Gamma[1/3, -(c*(a + b*x)^3*Log[f])])/(3*b^2*(-(c*(a + b*x)^3*Log[f]))^(1/3))","A",4,3,13,0.2308,1,"{2226, 2208, 2218}"
204,1,44,0,0.0055393,"\int f^{c (a+b x)^3} \, dx","Int[f^(c*(a + b*x)^3),x]","-\frac{(a+b x) \text{Gamma}\left(\frac{1}{3},-c \log (f) (a+b x)^3\right)}{3 b \sqrt[3]{-c \log (f) (a+b x)^3}}","-\frac{(a+b x) \text{Gamma}\left(\frac{1}{3},-c \log (f) (a+b x)^3\right)}{3 b \sqrt[3]{-c \log (f) (a+b x)^3}}",1,"-((a + b*x)*Gamma[1/3, -(c*(a + b*x)^3*Log[f])])/(3*b*(-(c*(a + b*x)^3*Log[f]))^(1/3))","A",1,1,11,0.09091,1,"{2208}"
205,0,0,0,0.0168283,"\int \frac{f^{c (a+b x)^3}}{x} \, dx","Int[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,"Defer[Int][f^(c*(a + b*x)^3)/x, x]","A",0,0,0,0,-1,"{}"
206,0,0,0,0.3023439,"\int \frac{f^{c (a+b x)^3}}{x^2} \, dx","Int[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{a b c \log (f) (a+b x) \text{Gamma}\left(\frac{1}{3},-c \log (f) (a+b x)^3\right)}{\sqrt[3]{-c \log (f) (a+b x)^3}}-\frac{b c \log (f) (a+b x)^2 \text{Gamma}\left(\frac{2}{3},-c \log (f) (a+b x)^3\right)}{\left(-c \log (f) (a+b x)^3\right)^{2/3}}-\frac{f^{c (a+b x)^3}}{x}",0,"-(f^(c*(a + b*x)^3)/x) - (b*c*(a + b*x)^2*Gamma[2/3, -(c*(a + b*x)^3*Log[f])]*Log[f])/(-(c*(a + b*x)^3*Log[f]))^(2/3) - (a*b*c*(a + b*x)*Gamma[1/3, -(c*(a + b*x)^3*Log[f])]*Log[f])/(-(c*(a + b*x)^3*Log[f]))^(1/3) + 3*a^2*b*c*Log[f]*Defer[Int][f^(c*(a + b*x)^3)/x, x]","A",0,0,0,0,-1,"{}"
207,0,0,0,0.4486822,"\int \frac{f^{c (a+b x)^3}}{x^3} \, dx","Int[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)-\frac{3 a^3 b^2 c^2 \log ^2(f) (a+b x) \text{Gamma}\left(\frac{1}{3},-c \log (f) (a+b x)^3\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 \text{Gamma}\left(\frac{2}{3},-c \log (f) (a+b x)^3\right)}{2 \left(-c \log (f) (a+b x)^3\right)^{2/3}}+3 a b^2 c \log (f) \text{Int}\left(\frac{f^{c (a+b x)^3}}{x},x\right)-\frac{b^2 c \log (f) (a+b x) \text{Gamma}\left(\frac{1}{3},-c \log (f) (a+b x)^3\right)}{2 \sqrt[3]{-c \log (f) (a+b x)^3}}-\frac{3 a^2 b c \log (f) f^{c (a+b x)^3}}{2 x}-\frac{f^{c (a+b x)^3}}{2 x^2}",0,"-f^(c*(a + b*x)^3)/(2*x^2) - (3*a^2*b*c*f^(c*(a + b*x)^3)*Log[f])/(2*x) - (3*a^2*b^2*c^2*(a + b*x)^2*Gamma[2/3, -(c*(a + b*x)^3*Log[f])]*Log[f]^2)/(2*(-(c*(a + b*x)^3*Log[f]))^(2/3)) - (b^2*c*(a + b*x)*Gamma[1/3, -(c*(a + b*x)^3*Log[f])]*Log[f])/(2*(-(c*(a + b*x)^3*Log[f]))^(1/3)) - (3*a^3*b^2*c^2*(a + b*x)*Gamma[1/3, -(c*(a + b*x)^3*Log[f])]*Log[f]^2)/(2*(-(c*(a + b*x)^3*Log[f]))^(1/3)) + 3*a*b^2*c*Log[f]*Defer[Int][f^(c*(a + b*x)^3)/x, x] + (9*a^4*b^2*c^2*Log[f]^2*Defer[Int][f^(c*(a + b*x)^3)/x, x])/2","A",0,0,0,0,-1,"{}"
208,1,183,0,0.1832037,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^4 \, dx","Int[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^4,x]","\frac{4 a^3 (a+b x)^2 \text{Gamma}\left(\frac{2}{3},-(a+b x)^3\right)}{3 b^5 \left(-(a+b x)^3\right)^{2/3}}-\frac{a^4 (a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b^5 \sqrt[3]{-(a+b x)^3}}-\frac{(a+b x)^5 \text{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 \text{Gamma}\left(\frac{4}{3},-(a+b x)^3\right)}{3 b^5 \left(-(a+b x)^3\right)^{4/3}}+\frac{2 a^2 e^{(a+b x)^3}}{b^5}","\frac{4 a^3 (a+b x)^2 \text{Gamma}\left(\frac{2}{3},-(a+b x)^3\right)}{3 b^5 \left(-(a+b x)^3\right)^{2/3}}-\frac{a^4 (a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b^5 \sqrt[3]{-(a+b x)^3}}-\frac{(a+b x)^5 \text{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 \text{Gamma}\left(\frac{4}{3},-(a+b x)^3\right)}{3 b^5 \left(-(a+b x)^3\right)^{4/3}}+\frac{2 a^2 e^{(a+b x)^3}}{b^5}",1,"(2*a^2*E^(a + b*x)^3)/b^5 - (a^4*(a + b*x)*Gamma[1/3, -(a + b*x)^3])/(3*b^5*(-(a + b*x)^3)^(1/3)) + (4*a^3*(a + b*x)^2*Gamma[2/3, -(a + b*x)^3])/(3*b^5*(-(a + b*x)^3)^(2/3)) + (4*a*(a + b*x)^4*Gamma[4/3, -(a + b*x)^3])/(3*b^5*(-(a + b*x)^3)^(4/3)) - ((a + b*x)^5*Gamma[5/3, -(a + b*x)^3])/(3*b^5*(-(a + b*x)^3)^(5/3))","A",8,5,33,0.1515,1,"{2227, 2226, 2208, 2218, 2209}"
209,1,138,0,0.1493387,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^3 \, dx","Int[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^3,x]","-\frac{a^2 (a+b x)^2 \text{Gamma}\left(\frac{2}{3},-(a+b x)^3\right)}{b^4 \left(-(a+b x)^3\right)^{2/3}}+\frac{a^3 (a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b^4 \sqrt[3]{-(a+b x)^3}}-\frac{(a+b x)^4 \text{Gamma}\left(\frac{4}{3},-(a+b x)^3\right)}{3 b^4 \left(-(a+b x)^3\right)^{4/3}}-\frac{a e^{(a+b x)^3}}{b^4}","-\frac{a^2 (a+b x)^2 \text{Gamma}\left(\frac{2}{3},-(a+b x)^3\right)}{b^4 \left(-(a+b x)^3\right)^{2/3}}+\frac{a^3 (a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b^4 \sqrt[3]{-(a+b x)^3}}-\frac{(a+b x)^4 \text{Gamma}\left(\frac{4}{3},-(a+b x)^3\right)}{3 b^4 \left(-(a+b x)^3\right)^{4/3}}-\frac{a e^{(a+b x)^3}}{b^4}",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",7,5,33,0.1515,1,"{2227, 2226, 2208, 2218, 2209}"
210,1,99,0,0.1209526,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^2 \, dx","Int[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^2,x]","-\frac{a^2 (a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b^3 \sqrt[3]{-(a+b x)^3}}+\frac{2 a (a+b x)^2 \text{Gamma}\left(\frac{2}{3},-(a+b x)^3\right)}{3 b^3 \left(-(a+b x)^3\right)^{2/3}}+\frac{e^{(a+b x)^3}}{3 b^3}","-\frac{a^2 (a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b^3 \sqrt[3]{-(a+b x)^3}}+\frac{2 a (a+b x)^2 \text{Gamma}\left(\frac{2}{3},-(a+b x)^3\right)}{3 b^3 \left(-(a+b x)^3\right)^{2/3}}+\frac{e^{(a+b x)^3}}{3 b^3}",1,"E^(a + b*x)^3/(3*b^3) - (a^2*(a + b*x)*Gamma[1/3, -(a + b*x)^3])/(3*b^3*(-(a + b*x)^3)^(1/3)) + (2*a*(a + b*x)^2*Gamma[2/3, -(a + b*x)^3])/(3*b^3*(-(a + b*x)^3)^(2/3))","A",6,5,33,0.1515,1,"{2227, 2226, 2208, 2218, 2209}"
211,1,80,0,0.0684645,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x \, dx","Int[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x,x]","\frac{a (a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b^2 \sqrt[3]{-(a+b x)^3}}-\frac{(a+b x)^2 \text{Gamma}\left(\frac{2}{3},-(a+b x)^3\right)}{3 b^2 \left(-(a+b x)^3\right)^{2/3}}","\frac{a (a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b^2 \sqrt[3]{-(a+b x)^3}}-\frac{(a+b x)^2 \text{Gamma}\left(\frac{2}{3},-(a+b x)^3\right)}{3 b^2 \left(-(a+b x)^3\right)^{2/3}}",1,"(a*(a + b*x)*Gamma[1/3, -(a + b*x)^3])/(3*b^2*(-(a + b*x)^3)^(1/3)) - ((a + b*x)^2*Gamma[2/3, -(a + b*x)^3])/(3*b^2*(-(a + b*x)^3)^(2/3))","A",5,4,31,0.1290,1,"{2227, 2226, 2208, 2218}"
212,1,38,0,0.0085331,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} \, dx","Int[E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3),x]","-\frac{(a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b \sqrt[3]{-(a+b x)^3}}","-\frac{(a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b \sqrt[3]{-(a+b x)^3}}",1,"-((a + b*x)*Gamma[1/3, -(a + b*x)^3])/(3*b*(-(a + b*x)^3)^(1/3))","A",2,2,29,0.06897,1,"{2227, 2208}"
213,0,0,0,0.0931069,"\int \frac{e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3}}{x} \, dx","Int[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^{3 a^2 b x+a^3+3 a b^2 x^2+b^3 x^3}}{x},x\right)",0,"Defer[Int][E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)/x, x]","A",0,0,0,0,-1,"{}"
214,0,0,0,0.0923404,"\int e^{a^3+3 a^2 b x+3 a b^2 x^2+b^3 x^3} x^m \, dx","Int[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^{3 a^2 b x+a^3+3 a b^2 x^2+b^3 x^3},x\right)",0,"Defer[Int][E^(a^3 + 3*a^2*b*x + 3*a*b^2*x^2 + b^3*x^3)*x^m, x]","A",0,0,0,0,-1,"{}"
215,1,40,0,0.0123375,"\int e^{\sqrt{5+3 x}} \, dx","Int[E^Sqrt[5 + 3*x],x]","\frac{2}{3} e^{\sqrt{3 x+5}} \sqrt{3 x+5}-\frac{2}{3} e^{\sqrt{3 x+5}}","\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])/3 + (2*E^Sqrt[5 + 3*x]*Sqrt[5 + 3*x])/3","A",3,3,11,0.2727,1,"{2207, 2176, 2194}"
216,1,291,0,0.2884907,"\int f^{\frac{c}{a+b x}} x^4 \, dx","Int[f^(c/(a + b*x))*x^4,x]","-\frac{c^5 \log ^5(f) \text{Gamma}\left(-5,-\frac{c \log (f)}{a+b x}\right)}{b^5}-\frac{4 a c^4 \log ^4(f) \text{Gamma}\left(-4,-\frac{c \log (f)}{a+b x}\right)}{b^5}-\frac{a^2 c^3 \log ^3(f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{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{a^2 c^2 \log ^2(f) (a+b x) f^{\frac{c}{a+b x}}}{b^5}-\frac{a^4 c \log (f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^5}+\frac{2 a^2 (a+b x)^3 f^{\frac{c}{a+b x}}}{b^5}-\frac{2 a^3 (a+b x)^2 f^{\frac{c}{a+b x}}}{b^5}+\frac{a^4 (a+b x) 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{2 a^3 c \log (f) (a+b x) f^{\frac{c}{a+b x}}}{b^5}","-\frac{c^5 \log ^5(f) \text{Gamma}\left(-5,-\frac{c \log (f)}{a+b x}\right)}{b^5}-\frac{4 a c^4 \log ^4(f) \text{Gamma}\left(-4,-\frac{c \log (f)}{a+b x}\right)}{b^5}-\frac{a^2 c^3 \log ^3(f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{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{a^2 c^2 \log ^2(f) (a+b x) f^{\frac{c}{a+b x}}}{b^5}-\frac{a^4 c \log (f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^5}+\frac{2 a^2 (a+b x)^3 f^{\frac{c}{a+b x}}}{b^5}-\frac{2 a^3 (a+b x)^2 f^{\frac{c}{a+b x}}}{b^5}+\frac{a^4 (a+b x) 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{2 a^3 c \log (f) (a+b x) f^{\frac{c}{a+b x}}}{b^5}",1,"(a^4*f^(c/(a + b*x))*(a + b*x))/b^5 - (2*a^3*f^(c/(a + b*x))*(a + b*x)^2)/b^5 + (2*a^2*f^(c/(a + b*x))*(a + b*x)^3)/b^5 - (2*a^3*c*f^(c/(a + b*x))*(a + b*x)*Log[f])/b^5 + (a^2*c*f^(c/(a + b*x))*(a + b*x)^2*Log[f])/b^5 - (a^4*c*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f])/b^5 + (a^2*c^2*f^(c/(a + b*x))*(a + b*x)*Log[f]^2)/b^5 + (2*a^3*c^2*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]^2)/b^5 - (a^2*c^3*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]^3)/b^5 - (4*a*c^4*Gamma[-4, -((c*Log[f])/(a + b*x))]*Log[f]^4)/b^5 - (c^5*Gamma[-5, -((c*Log[f])/(a + b*x))]*Log[f]^5)/b^5","A",13,5,15,0.3333,1,"{2226, 2206, 2210, 2214, 2218}"
217,1,269,0,0.2542997,"\int f^{\frac{c}{a+b x}} x^3 \, dx","Int[f^(c/(a + b*x))*x^3,x]","\frac{c^4 \log ^4(f) \text{Gamma}\left(-4,-\frac{c \log (f)}{a+b x}\right)}{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{a^3 c \log (f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^4}+\frac{3 a^2 (a+b x)^2 f^{\frac{c}{a+b x}}}{2 b^4}-\frac{a^3 (a+b x) f^{\frac{c}{a+b x}}}{b^4}+\frac{3 a^2 c \log (f) (a+b x) f^{\frac{c}{a+b x}}}{2 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}","\frac{c^4 \log ^4(f) \text{Gamma}\left(-4,-\frac{c \log (f)}{a+b x}\right)}{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{a^3 c \log (f) \text{Ei}\left(\frac{c \log (f)}{a+b x}\right)}{b^4}+\frac{3 a^2 (a+b x)^2 f^{\frac{c}{a+b x}}}{2 b^4}-\frac{a^3 (a+b x) f^{\frac{c}{a+b x}}}{b^4}+\frac{3 a^2 c \log (f) (a+b x) f^{\frac{c}{a+b x}}}{2 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,"-((a^3*f^(c/(a + b*x))*(a + b*x))/b^4) + (3*a^2*f^(c/(a + b*x))*(a + b*x)^2)/(2*b^4) - (a*f^(c/(a + b*x))*(a + b*x)^3)/b^4 + (3*a^2*c*f^(c/(a + b*x))*(a + b*x)*Log[f])/(2*b^4) - (a*c*f^(c/(a + b*x))*(a + b*x)^2*Log[f])/(2*b^4) + (a^3*c*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f])/b^4 - (a*c^2*f^(c/(a + b*x))*(a + b*x)*Log[f]^2)/(2*b^4) - (3*a^2*c^2*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]^2)/(2*b^4) + (a*c^3*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]^3)/(2*b^4) + (c^4*Gamma[-4, -((c*Log[f])/(a + b*x))]*Log[f]^4)/b^4","A",12,5,15,0.3333,1,"{2226, 2206, 2210, 2214, 2218}"
218,1,229,0,0.2234101,"\int f^{\frac{c}{a+b x}} x^2 \, dx","Int[f^(c/(a + b*x))*x^2,x]","-\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}","-\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^2*f^(c/(a + b*x))*(a + b*x))/b^3 - (a*f^(c/(a + b*x))*(a + b*x)^2)/b^3 + (f^(c/(a + b*x))*(a + b*x)^3)/(3*b^3) - (a*c*f^(c/(a + b*x))*(a + b*x)*Log[f])/b^3 + (c*f^(c/(a + b*x))*(a + b*x)^2*Log[f])/(6*b^3) - (a^2*c*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f])/b^3 + (c^2*f^(c/(a + b*x))*(a + b*x)*Log[f]^2)/(6*b^3) + (a*c^2*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]^2)/b^3 - (c^3*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]^3)/(6*b^3)","A",11,4,15,0.2667,1,"{2226, 2206, 2210, 2214}"
219,1,120,0,0.1162326,"\int f^{\frac{c}{a+b x}} x \, dx","Int[f^(c/(a + b*x))*x,x]","-\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}","-\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,"-((a*f^(c/(a + b*x))*(a + b*x))/b^2) + (f^(c/(a + b*x))*(a + b*x)^2)/(2*b^2) + (c*f^(c/(a + b*x))*(a + b*x)*Log[f])/(2*b^2) + (a*c*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f])/b^2 - (c^2*ExpIntegralEi[(c*Log[f])/(a + b*x)]*Log[f]^2)/(2*b^2)","A",7,4,13,0.3077,1,"{2226, 2206, 2210, 2214}"
220,1,41,0,0.0292191,"\int f^{\frac{c}{a+b x}} \, dx","Int[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",2,2,11,0.1818,1,"{2206, 2210}"
221,1,41,0,0.1311478,"\int \frac{f^{\frac{c}{a+b x}}}{x} \, dx","Int[f^(c/(a + b*x))/x,x]","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)","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*(a + b*x)))]","A",4,4,15,0.2667,1,"{2222, 2210, 2228, 2178}"
222,1,68,0,0.3966301,"\int \frac{f^{\frac{c}{a+b x}}}{x^2} \, dx","Int[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 (a+b x)}\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*(a + b*x)))]*Log[f])/a^2","A",9,7,15,0.4667,1,"{2223, 6742, 2222, 2210, 2228, 2178, 2209}"
223,1,166,0,0.7183315,"\int \frac{f^{\frac{c}{a+b x}}}{x^3} \, dx","Int[f^(c/(a + b*x))/x^3,x]","\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 f^{\frac{c}{a+b x}}}{2 a^2}+\frac{b^2 c \log (f) f^{\frac{c}{a+b x}}}{2 a^3}+\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}","\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 f^{\frac{c}{a+b x}}}{2 a^2}+\frac{b^2 c \log (f) f^{\frac{c}{a+b x}}}{2 a^3}+\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^2) - f^(c/(a + b*x))/(2*x^2) + (b^2*c*f^(c/(a + b*x))*Log[f])/(2*a^3) + (b*c*f^(c/(a + b*x))*Log[f])/(2*a^2*x) + (b^2*c*f^(c/a)*ExpIntegralEi[-((b*c*x*Log[f])/(a*(a + b*x)))]*Log[f])/a^3 + (b^2*c^2*f^(c/a)*ExpIntegralEi[-((b*c*x*Log[f])/(a*(a + b*x)))]*Log[f]^2)/(2*a^4)","A",18,7,15,0.4667,1,"{2223, 6742, 2222, 2210, 2228, 2178, 2209}"
224,1,415,0,0.4354339,"\int f^{\frac{c}{(a+b x)^2}} x^4 \, dx","Int[f^(c/(a + b*x)^2)*x^4,x]","-\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{\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{2 a^3 c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)}{b^5}+\frac{2 a^2 (a+b x)^3 f^{\frac{c}{(a+b x)^2}}}{b^5}-\frac{2 a^3 (a+b x)^2 f^{\frac{c}{(a+b x)^2}}}{b^5}+\frac{a^4 (a+b x) 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}","-\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{\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{2 a^3 c \log (f) \text{Ei}\left(\frac{c \log (f)}{(a+b x)^2}\right)}{b^5}+\frac{2 a^2 (a+b x)^3 f^{\frac{c}{(a+b x)^2}}}{b^5}-\frac{2 a^3 (a+b x)^2 f^{\frac{c}{(a+b x)^2}}}{b^5}+\frac{a^4 (a+b x) 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^4*f^(c/(a + b*x)^2)*(a + b*x))/b^5 - (2*a^3*f^(c/(a + b*x)^2)*(a + b*x)^2)/b^5 + (2*a^2*f^(c/(a + b*x)^2)*(a + b*x)^3)/b^5 - (a*f^(c/(a + b*x)^2)*(a + b*x)^4)/b^5 + (f^(c/(a + b*x)^2)*(a + b*x)^5)/(5*b^5) - (a^4*Sqrt[c]*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Sqrt[Log[f]])/b^5 + (4*a^2*c*f^(c/(a + b*x)^2)*(a + b*x)*Log[f])/b^5 - (a*c*f^(c/(a + b*x)^2)*(a + b*x)^2*Log[f])/b^5 + (2*c*f^(c/(a + b*x)^2)*(a + b*x)^3*Log[f])/(15*b^5) + (2*a^3*c*ExpIntegralEi[(c*Log[f])/(a + b*x)^2]*Log[f])/b^5 - (4*a^2*c^(3/2)*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Log[f]^(3/2))/b^5 + (4*c^2*f^(c/(a + b*x)^2)*(a + b*x)*Log[f]^2)/(15*b^5) + (a*c^2*ExpIntegralEi[(c*Log[f])/(a + b*x)^2]*Log[f]^2)/b^5 - (4*c^(5/2)*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Log[f]^(5/2))/(15*b^5)","A",19,6,15,0.4000,1,"{2226, 2206, 2211, 2204, 2214, 2210}"
225,1,291,0,0.303768,"\int f^{\frac{c}{(a+b x)^2}} x^3 \, dx","Int[f^(c/(a + b*x)^2)*x^3,x]","\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{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{a^3 (a+b x) f^{\frac{c}{(a+b x)^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}","\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{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{a^3 (a+b x) f^{\frac{c}{(a+b x)^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,"-((a^3*f^(c/(a + b*x)^2)*(a + b*x))/b^4) + (3*a^2*f^(c/(a + b*x)^2)*(a + b*x)^2)/(2*b^4) - (a*f^(c/(a + b*x)^2)*(a + b*x)^3)/b^4 + (f^(c/(a + b*x)^2)*(a + b*x)^4)/(4*b^4) + (a^3*Sqrt[c]*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Sqrt[Log[f]])/b^4 - (2*a*c*f^(c/(a + b*x)^2)*(a + b*x)*Log[f])/b^4 + (c*f^(c/(a + b*x)^2)*(a + b*x)^2*Log[f])/(4*b^4) - (3*a^2*c*ExpIntegralEi[(c*Log[f])/(a + b*x)^2]*Log[f])/(2*b^4) + (2*a*c^(3/2)*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Log[f]^(3/2))/b^4 - (c^2*ExpIntegralEi[(c*Log[f])/(a + b*x)^2]*Log[f]^2)/(4*b^4)","A",14,6,15,0.4000,1,"{2226, 2206, 2211, 2204, 2214, 2210}"
226,1,206,0,0.2149248,"\int f^{\frac{c}{(a+b x)^2}} x^2 \, dx","Int[f^(c/(a + b*x)^2)*x^2,x]","-\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}","-\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^2*f^(c/(a + b*x)^2)*(a + b*x))/b^3 - (a*f^(c/(a + b*x)^2)*(a + b*x)^2)/b^3 + (f^(c/(a + b*x)^2)*(a + b*x)^3)/(3*b^3) - (a^2*Sqrt[c]*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Sqrt[Log[f]])/b^3 + (2*c*f^(c/(a + b*x)^2)*(a + b*x)*Log[f])/(3*b^3) + (a*c*ExpIntegralEi[(c*Log[f])/(a + b*x)^2]*Log[f])/b^3 - (2*c^(3/2)*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Log[f]^(3/2))/(3*b^3)","A",11,6,15,0.4000,1,"{2226, 2206, 2211, 2204, 2214, 2210}"
227,1,111,0,0.1189639,"\int f^{\frac{c}{(a+b x)^2}} x \, dx","Int[f^(c/(a + b*x)^2)*x,x]","\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}","\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,"-((a*f^(c/(a + b*x)^2)*(a + b*x))/b^2) + (f^(c/(a + b*x)^2)*(a + b*x)^2)/(2*b^2) + (a*Sqrt[c]*Sqrt[Pi]*Erfi[(Sqrt[c]*Sqrt[Log[f]])/(a + b*x)]*Sqrt[Log[f]])/b^2 - (c*ExpIntegralEi[(c*Log[f])/(a + b*x)^2]*Log[f])/(2*b^2)","A",7,6,13,0.4615,1,"{2226, 2206, 2211, 2204, 2214, 2210}"
228,1,62,0,0.0393502,"\int f^{\frac{c}{(a+b x)^2}} \, dx","Int[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",3,3,11,0.2727,1,"{2206, 2211, 2204}"
229,0,0,0,0.0180934,"\int \frac{f^{\frac{c}{(a+b x)^2}}}{x} \, dx","Int[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,"Defer[Int][f^(c/(a + b*x)^2)/x, x]","A",0,0,0,0,-1,"{}"
230,0,0,0,0.0425695,"\int \frac{f^{\frac{c}{(a+b x)^2}}}{x^2} \, dx","Int[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,"Defer[Int][f^(c/(a + b*x)^2)/x^2, x]","A",0,0,0,0,-1,"{}"
231,0,0,0,0.0380722,"\int \frac{f^{\frac{c}{(a+b x)^2}}}{x^3} \, dx","Int[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,"Defer[Int][f^(c/(a + b*x)^2)/x^3, x]","A",0,0,0,0,-1,"{}"
232,1,239,0,0.2007148,"\int f^{\frac{c}{(a+b x)^3}} x^4 \, dx","Int[f^(c/(a + b*x)^3)*x^4,x]","-\frac{4 a^3 (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \text{Gamma}\left(-\frac{2}{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}} \text{Gamma}\left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^5}+\frac{(a+b x)^5 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{5/3} \text{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} \text{Gamma}\left(-\frac{4}{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{4 a^3 (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \text{Gamma}\left(-\frac{2}{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}} \text{Gamma}\left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^5}+\frac{(a+b x)^5 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{5/3} \text{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} \text{Gamma}\left(-\frac{4}{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}",1,"(2*a^2*f^(c/(a + b*x)^3)*(a + b*x)^3)/b^5 - (2*a^2*c*ExpIntegralEi[(c*Log[f])/(a + b*x)^3]*Log[f])/b^5 + (a^4*(a + b*x)*Gamma[-1/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(1/3))/(3*b^5) - (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))/(3*b^5) - (4*a*(a + b*x)^4*Gamma[-4/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(4/3))/(3*b^5) + ((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",8,5,15,0.3333,1,"{2226, 2208, 2218, 2214, 2210}"
233,1,184,0,0.1493281,"\int f^{\frac{c}{(a+b x)^3}} x^3 \, dx","Int[f^(c/(a + b*x)^3)*x^3,x]","\frac{a^2 (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \text{Gamma}\left(-\frac{2}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{b^4}-\frac{a^3 (a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \text{Gamma}\left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^4}+\frac{(a+b x)^4 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{4/3} \text{Gamma}\left(-\frac{4}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 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^2 (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \text{Gamma}\left(-\frac{2}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{b^4}-\frac{a^3 (a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \text{Gamma}\left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^4}+\frac{(a+b x)^4 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{4/3} \text{Gamma}\left(-\frac{4}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 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}",1,"-((a*f^(c/(a + b*x)^3)*(a + b*x)^3)/b^4) + (a*c*ExpIntegralEi[(c*Log[f])/(a + b*x)^3]*Log[f])/b^4 - (a^3*(a + b*x)*Gamma[-1/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(1/3))/(3*b^4) + (a^2*(a + b*x)^2*Gamma[-2/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(2/3))/b^4 + ((a + b*x)^4*Gamma[-4/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(4/3))/(3*b^4)","A",7,5,15,0.3333,1,"{2226, 2208, 2218, 2214, 2210}"
234,1,142,0,0.1178228,"\int f^{\frac{c}{(a+b x)^3}} x^2 \, dx","Int[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}} \text{Gamma}\left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^3}-\frac{2 a (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \text{Gamma}\left(-\frac{2}{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{a^2 (a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \text{Gamma}\left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^3}-\frac{2 a (a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \text{Gamma}\left(-\frac{2}{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}",1,"(f^(c/(a + b*x)^3)*(a + b*x)^3)/(3*b^3) - (c*ExpIntegralEi[(c*Log[f])/(a + b*x)^3]*Log[f])/(3*b^3) + (a^2*(a + b*x)*Gamma[-1/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(1/3))/(3*b^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",6,5,15,0.3333,1,"{2226, 2208, 2218, 2214, 2210}"
235,1,92,0,0.0518568,"\int f^{\frac{c}{(a+b x)^3}} x \, dx","Int[f^(c/(a + b*x)^3)*x,x]","\frac{(a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \text{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}} \text{Gamma}\left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^2}","\frac{(a+b x)^2 \left(-\frac{c \log (f)}{(a+b x)^3}\right)^{2/3} \text{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}} \text{Gamma}\left(-\frac{1}{3},-\frac{c \log (f)}{(a+b x)^3}\right)}{3 b^2}",1,"-(a*(a + b*x)*Gamma[-1/3, -((c*Log[f])/(a + b*x)^3)]*(-((c*Log[f])/(a + b*x)^3))^(1/3))/(3*b^2) + ((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^2)","A",4,3,13,0.2308,1,"{2226, 2208, 2218}"
236,1,44,0,0.0054403,"\int f^{\frac{c}{(a+b x)^3}} \, dx","Int[f^(c/(a + b*x)^3),x]","\frac{(a+b x) \sqrt[3]{-\frac{c \log (f)}{(a+b x)^3}} \text{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}} \text{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",1,1,11,0.09091,1,"{2208}"
237,0,0,0,0.0179304,"\int \frac{f^{\frac{c}{(a+b x)^3}}}{x} \, dx","Int[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,"Defer[Int][f^(c/(a + b*x)^3)/x, x]","A",0,0,0,0,-1,"{}"
238,0,0,0,0.0433816,"\int \frac{f^{\frac{c}{(a+b x)^3}}}{x^2} \, dx","Int[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,"Defer[Int][f^(c/(a + b*x)^3)/x^2, x]","A",0,0,0,0,-1,"{}"
239,0,0,0,0.0383083,"\int \frac{f^{\frac{c}{(a+b x)^3}}}{x^3} \, dx","Int[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,"Defer[Int][f^(c/(a + b*x)^3)/x^3, x]","A",0,0,0,0,-1,"{}"
240,0,0,0,0.0468174,"\int f^{c (a+b x)^3} x^m \, dx","Int[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,"Defer[Int][f^(c*(a + b*x)^3)*x^m, x]","A",0,0,0,0,-1,"{}"
241,0,0,0,0.0556472,"\int f^{c (a+b x)^2} x^m \, dx","Int[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,"Defer[Int][f^(a^2*c + 2*a*b*c*x + b^2*c*x^2)*x^m, x]","A",0,0,0,0,-1,"{}"
242,1,41,0,0.0217245,"\int f^{c (a+b x)} x^m \, dx","Int[f^(c*(a + b*x))*x^m,x]","\frac{x^m f^{a c} (-b c x \log (f))^{-m} \text{Gamma}(m+1,-b c x \log (f))}{b c \log (f)}","\frac{x^m f^{a c} (-b c x \log (f))^{-m} \text{Gamma}(m+1,-b c x \log (f))}{b c \log (f)}",1,"(f^(a*c)*x^m*Gamma[1 + m, -(b*c*x*Log[f])])/(b*c*Log[f]*(-(b*c*x*Log[f]))^m)","A",1,1,13,0.07692,1,"{2181}"
243,0,0,0,0.0391837,"\int f^{\frac{c}{a+b x}} x^m \, dx","Int[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,"Defer[Int][f^(c/(a + b*x))*x^m, x]","A",0,0,0,0,-1,"{}"
244,0,0,0,0.0415169,"\int f^{\frac{c}{(a+b x)^2}} x^m \, dx","Int[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,"Defer[Int][f^(c/(a + b*x)^2)*x^m, x]","A",0,0,0,0,-1,"{}"
245,0,0,0,0.0427128,"\int f^{\frac{c}{(a+b x)^3}} x^m \, dx","Int[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,"Defer[Int][f^(c/(a + b*x)^3)*x^m, x]","A",0,0,0,0,-1,"{}"
246,0,0,0,0.0520335,"\int f^{c (a+b x)^n} x^m \, dx","Int[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,"Defer[Int][f^(c*(a + b*x)^n)*x^m, x]","A",0,0,0,0,-1,"{}"
247,1,207,0,0.1572035,"\int f^{c (a+b x)^n} x^3 \, dx","Int[f^(c*(a + b*x)^n)*x^3,x]","-\frac{3 a^2 (a+b x)^2 \left(-c \log (f) (a+b x)^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{n},-c \log (f) (a+b x)^n\right)}{b^4 n}+\frac{a^3 (a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-c \log (f) (a+b x)^n\right)}{b^4 n}-\frac{(a+b x)^4 \left(-c \log (f) (a+b x)^n\right)^{-4/n} \text{Gamma}\left(\frac{4}{n},-c \log (f) (a+b x)^n\right)}{b^4 n}+\frac{3 a (a+b x)^3 \left(-c \log (f) (a+b x)^n\right)^{-3/n} \text{Gamma}\left(\frac{3}{n},-c \log (f) (a+b x)^n\right)}{b^4 n}","-\frac{3 a^2 (a+b x)^2 \left(-c \log (f) (a+b x)^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{n},-c \log (f) (a+b x)^n\right)}{b^4 n}+\frac{a^3 (a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-c \log (f) (a+b x)^n\right)}{b^4 n}-\frac{(a+b x)^4 \left(-c \log (f) (a+b x)^n\right)^{-4/n} \text{Gamma}\left(\frac{4}{n},-c \log (f) (a+b x)^n\right)}{b^4 n}+\frac{3 a (a+b x)^3 \left(-c \log (f) (a+b x)^n\right)^{-3/n} \text{Gamma}\left(\frac{3}{n},-c \log (f) (a+b x)^n\right)}{b^4 n}",1,"-(((a + b*x)^4*Gamma[4/n, -(c*(a + b*x)^n*Log[f])])/(b^4*n*(-(c*(a + b*x)^n*Log[f]))^(4/n))) + (3*a*(a + b*x)^3*Gamma[3/n, -(c*(a + b*x)^n*Log[f])])/(b^4*n*(-(c*(a + b*x)^n*Log[f]))^(3/n)) - (3*a^2*(a + b*x)^2*Gamma[2/n, -(c*(a + b*x)^n*Log[f])])/(b^4*n*(-(c*(a + b*x)^n*Log[f]))^(2/n)) + (a^3*(a + b*x)*Gamma[n^(-1), -(c*(a + b*x)^n*Log[f])])/(b^4*n*(-(c*(a + b*x)^n*Log[f]))^n^(-1))","A",6,3,15,0.2000,1,"{2226, 2208, 2218}"
248,1,154,0,0.1084355,"\int f^{c (a+b x)^n} x^2 \, dx","Int[f^(c*(a + b*x)^n)*x^2,x]","-\frac{a^2 (a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-c \log (f) (a+b x)^n\right)}{b^3 n}-\frac{(a+b x)^3 \left(-c \log (f) (a+b x)^n\right)^{-3/n} \text{Gamma}\left(\frac{3}{n},-c \log (f) (a+b x)^n\right)}{b^3 n}+\frac{2 a (a+b x)^2 \left(-c \log (f) (a+b x)^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{n},-c \log (f) (a+b x)^n\right)}{b^3 n}","-\frac{a^2 (a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-c \log (f) (a+b x)^n\right)}{b^3 n}-\frac{(a+b x)^3 \left(-c \log (f) (a+b x)^n\right)^{-3/n} \text{Gamma}\left(\frac{3}{n},-c \log (f) (a+b x)^n\right)}{b^3 n}+\frac{2 a (a+b x)^2 \left(-c \log (f) (a+b x)^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{n},-c \log (f) (a+b x)^n\right)}{b^3 n}",1,"-(((a + b*x)^3*Gamma[3/n, -(c*(a + b*x)^n*Log[f])])/(b^3*n*(-(c*(a + b*x)^n*Log[f]))^(3/n))) + (2*a*(a + b*x)^2*Gamma[2/n, -(c*(a + b*x)^n*Log[f])])/(b^3*n*(-(c*(a + b*x)^n*Log[f]))^(2/n)) - (a^2*(a + b*x)*Gamma[n^(-1), -(c*(a + b*x)^n*Log[f])])/(b^3*n*(-(c*(a + b*x)^n*Log[f]))^n^(-1))","A",5,3,15,0.2000,1,"{2226, 2208, 2218}"
249,1,99,0,0.0584529,"\int f^{c (a+b x)^n} x \, dx","Int[f^(c*(a + b*x)^n)*x,x]","\frac{a (a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-c \log (f) (a+b x)^n\right)}{b^2 n}-\frac{(a+b x)^2 \left(-c \log (f) (a+b x)^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{n},-c \log (f) (a+b x)^n\right)}{b^2 n}","\frac{a (a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-c \log (f) (a+b x)^n\right)}{b^2 n}-\frac{(a+b x)^2 \left(-c \log (f) (a+b x)^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{n},-c \log (f) (a+b x)^n\right)}{b^2 n}",1,"-(((a + b*x)^2*Gamma[2/n, -(c*(a + b*x)^n*Log[f])])/(b^2*n*(-(c*(a + b*x)^n*Log[f]))^(2/n))) + (a*(a + b*x)*Gamma[n^(-1), -(c*(a + b*x)^n*Log[f])])/(b^2*n*(-(c*(a + b*x)^n*Log[f]))^n^(-1))","A",4,3,13,0.2308,1,"{2226, 2208, 2218}"
250,1,47,0,0.0057907,"\int f^{c (a+b x)^n} \, dx","Int[f^(c*(a + b*x)^n),x]","-\frac{(a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-c \log (f) (a+b x)^n\right)}{b n}","-\frac{(a+b x) \left(-c \log (f) (a+b x)^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-c \log (f) (a+b x)^n\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",1,1,11,0.09091,1,"{2208}"
251,0,0,0,0.0224096,"\int \frac{f^{c (a+b x)^n}}{x} \, dx","Int[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,"Defer[Int][f^(c*(a + b*x)^n)/x, x]","A",0,0,0,0,-1,"{}"
252,0,0,0,0.0457516,"\int \frac{f^{c (a+b x)^n}}{x^2} \, dx","Int[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,"Defer[Int][f^(c*(a + b*x)^n)/x^2, x]","A",0,0,0,0,-1,"{}"
253,0,0,0,0.0449138,"\int \frac{f^{c (a+b x)^n}}{x^3} \, dx","Int[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,"Defer[Int][f^(c*(a + b*x)^n)/x^3, x]","A",0,0,0,0,-1,"{}"
254,1,61,0,0.0650038,"\int F^{a+b (c+d x)^2} (c+d x)^m \, dx","Int[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)} \text{Gamma}\left(\frac{m+1}{2},-b \log (F) (c+d x)^2\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)} \text{Gamma}\left(\frac{m+1}{2},-b \log (F) (c+d x)^2\right)}{2 d}",1,"-(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))/(2*d)","A",1,1,21,0.04762,1,"{2218}"
255,1,31,0,0.0726111,"\int F^{a+b (c+d x)^2} (c+d x)^{11} \, dx","Int[F^(a + b*(c + d*x)^2)*(c + d*x)^11,x]","-\frac{F^a \text{Gamma}\left(6,-b \log (F) (c+d x)^2\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,"-(F^a*Gamma[6, -(b*(c + d*x)^2*Log[F])])/(2*b^6*d*Log[F]^6)","C",1,1,21,0.04762,1,"{2218}"
256,1,31,0,0.0693239,"\int F^{a+b (c+d x)^2} (c+d x)^9 \, dx","Int[F^(a + b*(c + d*x)^2)*(c + d*x)^9,x]","\frac{F^a \text{Gamma}\left(5,-b \log (F) (c+d x)^2\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",1,1,21,0.04762,1,"{2218}"
257,1,126,0,0.2555396,"\int F^{a+b (c+d x)^2} (c+d x)^7 \, dx","Int[F^(a + b*(c + d*x)^2)*(c + d*x)^7,x]","-\frac{3 (c+d x)^4 F^{a+b (c+d x)^2}}{2 b^2 d \log ^2(F)}+\frac{3 (c+d x)^2 F^{a+b (c+d x)^2}}{b^3 d \log ^3(F)}-\frac{3 F^{a+b (c+d x)^2}}{b^4 d \log ^4(F)}+\frac{(c+d x)^6 F^{a+b (c+d x)^2}}{2 b d \log (F)}","-\frac{3 (c+d x)^4 F^{a+b (c+d x)^2}}{2 b^2 d \log ^2(F)}+\frac{3 (c+d x)^2 F^{a+b (c+d x)^2}}{b^3 d \log ^3(F)}-\frac{3 F^{a+b (c+d x)^2}}{b^4 d \log ^4(F)}+\frac{(c+d x)^6 F^{a+b (c+d x)^2}}{2 b d \log (F)}",1,"(-3*F^(a + b*(c + d*x)^2))/(b^4*d*Log[F]^4) + (3*F^(a + b*(c + d*x)^2)*(c + d*x)^2)/(b^3*d*Log[F]^3) - (3*F^(a + b*(c + d*x)^2)*(c + d*x)^4)/(2*b^2*d*Log[F]^2) + (F^(a + b*(c + d*x)^2)*(c + d*x)^6)/(2*b*d*Log[F])","A",4,2,21,0.09524,1,"{2212, 2209}"
258,1,91,0,0.1759587,"\int F^{a+b (c+d x)^2} (c+d x)^5 \, dx","Int[F^(a + b*(c + d*x)^2)*(c + d*x)^5,x]","-\frac{(c+d x)^2 F^{a+b (c+d x)^2}}{b^2 d \log ^2(F)}+\frac{F^{a+b (c+d x)^2}}{b^3 d \log ^3(F)}+\frac{(c+d x)^4 F^{a+b (c+d x)^2}}{2 b d \log (F)}","-\frac{(c+d x)^2 F^{a+b (c+d x)^2}}{b^2 d \log ^2(F)}+\frac{F^{a+b (c+d x)^2}}{b^3 d \log ^3(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)/(b^3*d*Log[F]^3) - (F^(a + b*(c + d*x)^2)*(c + d*x)^2)/(b^2*d*Log[F]^2) + (F^(a + b*(c + d*x)^2)*(c + d*x)^4)/(2*b*d*Log[F])","A",3,2,21,0.09524,1,"{2212, 2209}"
259,1,62,0,0.1047326,"\int F^{a+b (c+d x)^2} (c+d x)^3 \, dx","Int[F^(a + b*(c + d*x)^2)*(c + d*x)^3,x]","\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)}","\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)/(2*b^2*d*Log[F]^2) + (F^(a + b*(c + d*x)^2)*(c + d*x)^2)/(2*b*d*Log[F])","A",2,2,21,0.09524,1,"{2212, 2209}"
260,1,27,0,0.0362265,"\int F^{a+b (c+d x)^2} (c+d x) \, dx","Int[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",1,1,19,0.05263,1,"{2209}"
261,1,22,0,0.0676199,"\int \frac{F^{a+b (c+d x)^2}}{c+d x} \, dx","Int[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",1,1,21,0.04762,1,"{2210}"
262,1,53,0,0.1320282,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^3} \, dx","Int[F^(a + b*(c + d*x)^2)/(c + d*x)^3,x]","\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}","\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 + b*(c + d*x)^2)/(2*d*(c + d*x)^2) + (b*F^a*ExpIntegralEi[b*(c + d*x)^2*Log[F]]*Log[F])/(2*d)","A",2,2,21,0.09524,1,"{2214, 2210}"
263,1,87,0,0.1980219,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^5} \, dx","Int[F^(a + b*(c + d*x)^2)/(c + d*x)^5,x]","\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}","\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*(c + d*x)^2)/(4*d*(c + d*x)^4) - (b*F^(a + b*(c + d*x)^2)*Log[F])/(4*d*(c + d*x)^2) + (b^2*F^a*ExpIntegralEi[b*(c + d*x)^2*Log[F]]*Log[F]^2)/(4*d)","A",3,2,21,0.09524,1,"{2214, 2210}"
264,1,121,0,0.25758,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^7} \, dx","Int[F^(a + b*(c + d*x)^2)/(c + d*x)^7,x]","\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}","\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*(c + d*x)^2)/(6*d*(c + d*x)^6) - (b*F^(a + b*(c + d*x)^2)*Log[F])/(12*d*(c + d*x)^4) - (b^2*F^(a + b*(c + d*x)^2)*Log[F]^2)/(12*d*(c + d*x)^2) + (b^3*F^a*ExpIntegralEi[b*(c + d*x)^2*Log[F]]*Log[F]^3)/(12*d)","A",4,2,21,0.09524,1,"{2214, 2210}"
265,1,31,0,0.062995,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^9} \, dx","Int[F^(a + b*(c + d*x)^2)/(c + d*x)^9,x]","-\frac{b^4 F^a \log ^4(F) \text{Gamma}\left(-4,-b \log (F) (c+d x)^2\right)}{2 d}","-\frac{b^4 F^a \log ^4(F) \text{Gamma}\left(-4,-b \log (F) (c+d x)^2\right)}{2 d}",1,"-(b^4*F^a*Gamma[-4, -(b*(c + d*x)^2*Log[F])]*Log[F]^4)/(2*d)","A",1,1,21,0.04762,1,"{2218}"
266,1,31,0,0.0642407,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^{11}} \, dx","Int[F^(a + b*(c + d*x)^2)/(c + d*x)^11,x]","\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-b \log (F) (c+d x)^2\right)}{2 d}","\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-b \log (F) (c+d x)^2\right)}{2 d}",1,"(b^5*F^a*Gamma[-5, -(b*(c + d*x)^2*Log[F])]*Log[F]^5)/(2*d)","A",1,1,21,0.04762,1,"{2218}"
267,1,49,0,0.0656325,"\int F^{a+b (c+d x)^2} (c+d x)^{12} \, dx","Int[F^(a + b*(c + d*x)^2)*(c + d*x)^12,x]","-\frac{F^a (c+d x)^{13} \text{Gamma}\left(\frac{13}{2},-b \log (F) (c+d x)^2\right)}{2 d \left(-b \log (F) (c+d x)^2\right)^{13/2}}","-\frac{F^a (c+d x)^{13} \text{Gamma}\left(\frac{13}{2},-b \log (F) (c+d x)^2\right)}{2 d \left(-b \log (F) (c+d x)^2\right)^{13/2}}",1,"-(F^a*(c + d*x)^13*Gamma[13/2, -(b*(c + d*x)^2*Log[F])])/(2*d*(-(b*(c + d*x)^2*Log[F]))^(13/2))","A",1,1,21,0.04762,1,"{2218}"
268,1,49,0,0.0669821,"\int F^{a+b (c+d x)^2} (c+d x)^{10} \, dx","Int[F^(a + b*(c + d*x)^2)*(c + d*x)^10,x]","-\frac{F^a (c+d x)^{11} \text{Gamma}\left(\frac{11}{2},-b \log (F) (c+d x)^2\right)}{2 d \left(-b \log (F) (c+d x)^2\right)^{11/2}}","-\frac{F^a (c+d x)^{11} \text{Gamma}\left(\frac{11}{2},-b \log (F) (c+d x)^2\right)}{2 d \left(-b \log (F) (c+d x)^2\right)^{11/2}}",1,"-(F^a*(c + d*x)^11*Gamma[11/2, -(b*(c + d*x)^2*Log[F])])/(2*d*(-(b*(c + d*x)^2*Log[F]))^(11/2))","A",1,1,21,0.04762,1,"{2218}"
269,1,179,0,0.3312874,"\int F^{a+b (c+d x)^2} (c+d x)^8 \, dx","Int[F^(a + b*(c + d*x)^2)*(c + d*x)^8,x]","\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{7 (c+d x)^5 F^{a+b (c+d x)^2}}{4 b^2 d \log ^2(F)}+\frac{35 (c+d x)^3 F^{a+b (c+d x)^2}}{8 b^3 d \log ^3(F)}-\frac{105 (c+d x) F^{a+b (c+d x)^2}}{16 b^4 d \log ^4(F)}+\frac{(c+d x)^7 F^{a+b (c+d x)^2}}{2 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{7 (c+d x)^5 F^{a+b (c+d x)^2}}{4 b^2 d \log ^2(F)}+\frac{35 (c+d x)^3 F^{a+b (c+d x)^2}}{8 b^3 d \log ^3(F)}-\frac{105 (c+d x) F^{a+b (c+d x)^2}}{16 b^4 d \log ^4(F)}+\frac{(c+d x)^7 F^{a+b (c+d x)^2}}{2 b d \log (F)}",1,"(105*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(32*b^(9/2)*d*Log[F]^(9/2)) - (105*F^(a + b*(c + d*x)^2)*(c + d*x))/(16*b^4*d*Log[F]^4) + (35*F^(a + b*(c + d*x)^2)*(c + d*x)^3)/(8*b^3*d*Log[F]^3) - (7*F^(a + b*(c + d*x)^2)*(c + d*x)^5)/(4*b^2*d*Log[F]^2) + (F^(a + b*(c + d*x)^2)*(c + d*x)^7)/(2*b*d*Log[F])","A",5,2,21,0.09524,1,"{2212, 2204}"
270,1,145,0,0.2301779,"\int F^{a+b (c+d x)^2} (c+d x)^6 \, dx","Int[F^(a + b*(c + d*x)^2)*(c + d*x)^6,x]","-\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{5 (c+d x)^3 F^{a+b (c+d x)^2}}{4 b^2 d \log ^2(F)}+\frac{15 (c+d x) F^{a+b (c+d x)^2}}{8 b^3 d \log ^3(F)}+\frac{(c+d x)^5 F^{a+b (c+d x)^2}}{2 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{5 (c+d x)^3 F^{a+b (c+d x)^2}}{4 b^2 d \log ^2(F)}+\frac{15 (c+d x) F^{a+b (c+d x)^2}}{8 b^3 d \log ^3(F)}+\frac{(c+d x)^5 F^{a+b (c+d x)^2}}{2 b d \log (F)}",1,"(-15*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(16*b^(7/2)*d*Log[F]^(7/2)) + (15*F^(a + b*(c + d*x)^2)*(c + d*x))/(8*b^3*d*Log[F]^3) - (5*F^(a + b*(c + d*x)^2)*(c + d*x)^3)/(4*b^2*d*Log[F]^2) + (F^(a + b*(c + d*x)^2)*(c + d*x)^5)/(2*b*d*Log[F])","A",4,2,21,0.09524,1,"{2212, 2204}"
271,1,111,0,0.1538235,"\int F^{a+b (c+d x)^2} (c+d x)^4 \, dx","Int[F^(a + b*(c + d*x)^2)*(c + d*x)^4,x]","\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)}","\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,"(3*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(8*b^(5/2)*d*Log[F]^(5/2)) - (3*F^(a + b*(c + d*x)^2)*(c + d*x))/(4*b^2*d*Log[F]^2) + (F^(a + b*(c + d*x)^2)*(c + d*x)^3)/(2*b*d*Log[F])","A",3,2,21,0.09524,1,"{2212, 2204}"
272,1,77,0,0.0817664,"\int F^{a+b (c+d x)^2} (c+d x)^2 \, dx","Int[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,"-(F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(4*b^(3/2)*d*Log[F]^(3/2)) + (F^(a + b*(c + d*x)^2)*(c + d*x))/(2*b*d*Log[F])","A",2,2,21,0.09524,1,"{2212, 2204}"
273,1,44,0,0.0106032,"\int F^{a+b (c+d x)^2} \, dx","Int[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",1,1,13,0.07692,1,"{2204}"
274,1,67,0,0.0792093,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^2} \, dx","Int[F^(a + b*(c + d*x)^2)/(c + d*x)^2,x]","\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)}","\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 + b*(c + d*x)^2)/(d*(c + d*x))) + (Sqrt[b]*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Sqrt[Log[F]])/d","A",2,2,21,0.09524,1,"{2214, 2204}"
275,1,102,0,0.145172,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^4} \, dx","Int[F^(a + b*(c + d*x)^2)/(c + d*x)^4,x]","\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)}","\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 + b*(c + d*x)^2)/(3*d*(c + d*x)^3) - (2*b*F^(a + b*(c + d*x)^2)*Log[F])/(3*d*(c + d*x)) + (2*b^(3/2)*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Log[F]^(3/2))/(3*d)","A",3,2,21,0.09524,1,"{2214, 2204}"
276,1,136,0,0.2185944,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^6} \, dx","Int[F^(a + b*(c + d*x)^2)/(c + d*x)^6,x]","\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}","\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 + b*(c + d*x)^2)/(5*d*(c + d*x)^5) - (2*b*F^(a + b*(c + d*x)^2)*Log[F])/(15*d*(c + d*x)^3) - (4*b^2*F^(a + b*(c + d*x)^2)*Log[F]^2)/(15*d*(c + d*x)) + (4*b^(5/2)*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Log[F]^(5/2))/(15*d)","A",4,2,21,0.09524,1,"{2214, 2204}"
277,1,170,0,0.2859712,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^8} \, dx","Int[F^(a + b*(c + d*x)^2)/(c + d*x)^8,x]","\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}","\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 + b*(c + d*x)^2)/(7*d*(c + d*x)^7) - (2*b*F^(a + b*(c + d*x)^2)*Log[F])/(35*d*(c + d*x)^5) - (4*b^2*F^(a + b*(c + d*x)^2)*Log[F]^2)/(105*d*(c + d*x)^3) - (8*b^3*F^(a + b*(c + d*x)^2)*Log[F]^3)/(105*d*(c + d*x)) + (8*b^(7/2)*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Log[F]^(7/2))/(105*d)","A",5,2,21,0.09524,1,"{2214, 2204}"
278,1,49,0,0.0613516,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^{10}} \, dx","Int[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} \text{Gamma}\left(-\frac{9}{2},-b \log (F) (c+d x)^2\right)}{2 d (c+d x)^9}","-\frac{F^a \left(-b \log (F) (c+d x)^2\right)^{9/2} \text{Gamma}\left(-\frac{9}{2},-b \log (F) (c+d x)^2\right)}{2 d (c+d x)^9}",1,"-(F^a*Gamma[-9/2, -(b*(c + d*x)^2*Log[F])]*(-(b*(c + d*x)^2*Log[F]))^(9/2))/(2*d*(c + d*x)^9)","A",1,1,21,0.04762,1,"{2218}"
279,1,49,0,0.0619664,"\int \frac{F^{a+b (c+d x)^2}}{(c+d x)^{12}} \, dx","Int[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} \text{Gamma}\left(-\frac{11}{2},-b \log (F) (c+d x)^2\right)}{2 d (c+d x)^{11}}","-\frac{F^a \left(-b \log (F) (c+d x)^2\right)^{11/2} \text{Gamma}\left(-\frac{11}{2},-b \log (F) (c+d x)^2\right)}{2 d (c+d x)^{11}}",1,"-(F^a*Gamma[-11/2, -(b*(c + d*x)^2*Log[F])]*(-(b*(c + d*x)^2*Log[F]))^(11/2))/(2*d*(c + d*x)^11)","A",1,1,21,0.04762,1,"{2218}"
280,1,61,0,0.061417,"\int F^{a+b (c+d x)^3} (c+d x)^m \, dx","Int[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)} \text{Gamma}\left(\frac{m+1}{3},-b \log (F) (c+d x)^3\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)} \text{Gamma}\left(\frac{m+1}{3},-b \log (F) (c+d x)^3\right)}{3 d}",1,"-(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))/(3*d)","A",1,1,21,0.04762,1,"{2218}"
281,1,31,0,0.0669175,"\int F^{a+b (c+d x)^3} (c+d x)^{17} \, dx","Int[F^(a + b*(c + d*x)^3)*(c + d*x)^17,x]","-\frac{F^a \text{Gamma}\left(6,-b \log (F) (c+d x)^3\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,"-(F^a*Gamma[6, -(b*(c + d*x)^3*Log[F])])/(3*b^6*d*Log[F]^6)","C",1,1,21,0.04762,1,"{2218}"
282,1,31,0,0.0670609,"\int F^{a+b (c+d x)^3} (c+d x)^{14} \, dx","Int[F^(a + b*(c + d*x)^3)*(c + d*x)^14,x]","\frac{F^a \text{Gamma}\left(5,-b \log (F) (c+d x)^3\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",1,1,21,0.04762,1,"{2218}"
283,1,124,0,0.2837232,"\int F^{a+b (c+d x)^3} (c+d x)^{11} \, dx","Int[F^(a + b*(c + d*x)^3)*(c + d*x)^11,x]","-\frac{(c+d x)^6 F^{a+b (c+d x)^3}}{b^2 d \log ^2(F)}+\frac{2 (c+d x)^3 F^{a+b (c+d x)^3}}{b^3 d \log ^3(F)}-\frac{2 F^{a+b (c+d x)^3}}{b^4 d \log ^4(F)}+\frac{(c+d x)^9 F^{a+b (c+d x)^3}}{3 b d \log (F)}","-\frac{(c+d x)^6 F^{a+b (c+d x)^3}}{b^2 d \log ^2(F)}+\frac{2 (c+d x)^3 F^{a+b (c+d x)^3}}{b^3 d \log ^3(F)}-\frac{2 F^{a+b (c+d x)^3}}{b^4 d \log ^4(F)}+\frac{(c+d x)^9 F^{a+b (c+d x)^3}}{3 b d \log (F)}",1,"(-2*F^(a + b*(c + d*x)^3))/(b^4*d*Log[F]^4) + (2*F^(a + b*(c + d*x)^3)*(c + d*x)^3)/(b^3*d*Log[F]^3) - (F^(a + b*(c + d*x)^3)*(c + d*x)^6)/(b^2*d*Log[F]^2) + (F^(a + b*(c + d*x)^3)*(c + d*x)^9)/(3*b*d*Log[F])","A",4,2,21,0.09524,1,"{2212, 2209}"
284,1,96,0,0.2087191,"\int F^{a+b (c+d x)^3} (c+d x)^8 \, dx","Int[F^(a + b*(c + d*x)^3)*(c + d*x)^8,x]","-\frac{2 (c+d x)^3 F^{a+b (c+d x)^3}}{3 b^2 d \log ^2(F)}+\frac{2 F^{a+b (c+d x)^3}}{3 b^3 d \log ^3(F)}+\frac{(c+d x)^6 F^{a+b (c+d x)^3}}{3 b d \log (F)}","-\frac{2 (c+d x)^3 F^{a+b (c+d x)^3}}{3 b^2 d \log ^2(F)}+\frac{2 F^{a+b (c+d x)^3}}{3 b^3 d \log ^3(F)}+\frac{(c+d x)^6 F^{a+b (c+d x)^3}}{3 b d \log (F)}",1,"(2*F^(a + b*(c + d*x)^3))/(3*b^3*d*Log[F]^3) - (2*F^(a + b*(c + d*x)^3)*(c + d*x)^3)/(3*b^2*d*Log[F]^2) + (F^(a + b*(c + d*x)^3)*(c + d*x)^6)/(3*b*d*Log[F])","A",3,2,21,0.09524,1,"{2212, 2209}"
285,1,62,0,0.1381399,"\int F^{a+b (c+d x)^3} (c+d x)^5 \, dx","Int[F^(a + b*(c + d*x)^3)*(c + d*x)^5,x]","\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)}","\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)/(3*b^2*d*Log[F]^2) + (F^(a + b*(c + d*x)^3)*(c + d*x)^3)/(3*b*d*Log[F])","A",2,2,21,0.09524,1,"{2212, 2209}"
286,1,27,0,0.0672355,"\int F^{a+b (c+d x)^3} (c+d x)^2 \, dx","Int[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",1,1,21,0.04762,1,"{2209}"
287,1,22,0,0.0658895,"\int \frac{F^{a+b (c+d x)^3}}{c+d x} \, dx","Int[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",1,1,21,0.04762,1,"{2210}"
288,1,53,0,0.1254061,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^4} \, dx","Int[F^(a + b*(c + d*x)^3)/(c + d*x)^4,x]","\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}","\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 + b*(c + d*x)^3)/(3*d*(c + d*x)^3) + (b*F^a*ExpIntegralEi[b*(c + d*x)^3*Log[F]]*Log[F])/(3*d)","A",2,2,21,0.09524,1,"{2214, 2210}"
289,1,87,0,0.1927935,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^7} \, dx","Int[F^(a + b*(c + d*x)^3)/(c + d*x)^7,x]","\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}","\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*(c + d*x)^3)/(6*d*(c + d*x)^6) - (b*F^(a + b*(c + d*x)^3)*Log[F])/(6*d*(c + d*x)^3) + (b^2*F^a*ExpIntegralEi[b*(c + d*x)^3*Log[F]]*Log[F]^2)/(6*d)","A",3,2,21,0.09524,1,"{2214, 2210}"
290,1,121,0,0.2595708,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^{10}} \, dx","Int[F^(a + b*(c + d*x)^3)/(c + d*x)^10,x]","\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}","\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*(c + d*x)^3)/(9*d*(c + d*x)^9) - (b*F^(a + b*(c + d*x)^3)*Log[F])/(18*d*(c + d*x)^6) - (b^2*F^(a + b*(c + d*x)^3)*Log[F]^2)/(18*d*(c + d*x)^3) + (b^3*F^a*ExpIntegralEi[b*(c + d*x)^3*Log[F]]*Log[F]^3)/(18*d)","A",4,2,21,0.09524,1,"{2214, 2210}"
291,1,31,0,0.0614399,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^{13}} \, dx","Int[F^(a + b*(c + d*x)^3)/(c + d*x)^13,x]","-\frac{b^4 F^a \log ^4(F) \text{Gamma}\left(-4,-b \log (F) (c+d x)^3\right)}{3 d}","-\frac{b^4 F^a \log ^4(F) \text{Gamma}\left(-4,-b \log (F) (c+d x)^3\right)}{3 d}",1,"-(b^4*F^a*Gamma[-4, -(b*(c + d*x)^3*Log[F])]*Log[F]^4)/(3*d)","A",1,1,21,0.04762,1,"{2218}"
292,1,31,0,0.0615456,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^{16}} \, dx","Int[F^(a + b*(c + d*x)^3)/(c + d*x)^16,x]","\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-b \log (F) (c+d x)^3\right)}{3 d}","\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-b \log (F) (c+d x)^3\right)}{3 d}",1,"(b^5*F^a*Gamma[-5, -(b*(c + d*x)^3*Log[F])]*Log[F]^5)/(3*d)","A",1,1,21,0.04762,1,"{2218}"
293,1,49,0,0.0638079,"\int F^{a+b (c+d x)^3} (c+d x)^3 \, dx","Int[F^(a + b*(c + d*x)^3)*(c + d*x)^3,x]","-\frac{F^a (c+d x)^4 \text{Gamma}\left(\frac{4}{3},-b \log (F) (c+d x)^3\right)}{3 d \left(-b \log (F) (c+d x)^3\right)^{4/3}}","-\frac{F^a (c+d x)^4 \text{Gamma}\left(\frac{4}{3},-b \log (F) (c+d x)^3\right)}{3 d \left(-b \log (F) (c+d x)^3\right)^{4/3}}",1,"-(F^a*(c + d*x)^4*Gamma[4/3, -(b*(c + d*x)^3*Log[F])])/(3*d*(-(b*(c + d*x)^3*Log[F]))^(4/3))","A",1,1,21,0.04762,1,"{2218}"
294,1,49,0,0.0411224,"\int F^{a+b (c+d x)^3} (c+d x) \, dx","Int[F^(a + b*(c + d*x)^3)*(c + d*x),x]","-\frac{F^a (c+d x)^2 \text{Gamma}\left(\frac{2}{3},-b \log (F) (c+d x)^3\right)}{3 d \left(-b \log (F) (c+d x)^3\right)^{2/3}}","-\frac{F^a (c+d x)^2 \text{Gamma}\left(\frac{2}{3},-b \log (F) (c+d x)^3\right)}{3 d \left(-b \log (F) (c+d x)^3\right)^{2/3}}",1,"-(F^a*(c + d*x)^2*Gamma[2/3, -(b*(c + d*x)^3*Log[F])])/(3*d*(-(b*(c + d*x)^3*Log[F]))^(2/3))","A",1,1,19,0.05263,1,"{2218}"
295,1,47,0,0.0070726,"\int F^{a+b (c+d x)^3} \, dx","Int[F^(a + b*(c + d*x)^3),x]","-\frac{F^a (c+d x) \text{Gamma}\left(\frac{1}{3},-b \log (F) (c+d x)^3\right)}{3 d \sqrt[3]{-b \log (F) (c+d x)^3}}","-\frac{F^a (c+d x) \text{Gamma}\left(\frac{1}{3},-b \log (F) (c+d x)^3\right)}{3 d \sqrt[3]{-b \log (F) (c+d x)^3}}",1,"-(F^a*(c + d*x)*Gamma[1/3, -(b*(c + d*x)^3*Log[F])])/(3*d*(-(b*(c + d*x)^3*Log[F]))^(1/3))","A",1,1,13,0.07692,1,"{2208}"
296,1,49,0,0.0643983,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^2} \, dx","Int[F^(a + b*(c + d*x)^3)/(c + d*x)^2,x]","-\frac{F^a \sqrt[3]{-b \log (F) (c+d x)^3} \text{Gamma}\left(-\frac{1}{3},-b \log (F) (c+d x)^3\right)}{3 d (c+d x)}","-\frac{F^a \sqrt[3]{-b \log (F) (c+d x)^3} \text{Gamma}\left(-\frac{1}{3},-b \log (F) (c+d x)^3\right)}{3 d (c+d x)}",1,"-(F^a*Gamma[-1/3, -(b*(c + d*x)^3*Log[F])]*(-(b*(c + d*x)^3*Log[F]))^(1/3))/(3*d*(c + d*x))","A",1,1,21,0.04762,1,"{2218}"
297,1,49,0,0.0629146,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^3} \, dx","Int[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} \text{Gamma}\left(-\frac{2}{3},-b \log (F) (c+d x)^3\right)}{3 d (c+d x)^2}","-\frac{F^a \left(-b \log (F) (c+d x)^3\right)^{2/3} \text{Gamma}\left(-\frac{2}{3},-b \log (F) (c+d x)^3\right)}{3 d (c+d x)^2}",1,"-(F^a*Gamma[-2/3, -(b*(c + d*x)^3*Log[F])]*(-(b*(c + d*x)^3*Log[F]))^(2/3))/(3*d*(c + d*x)^2)","A",1,1,21,0.04762,1,"{2218}"
298,1,49,0,0.0626988,"\int \frac{F^{a+b (c+d x)^3}}{(c+d x)^5} \, dx","Int[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} \text{Gamma}\left(-\frac{4}{3},-b \log (F) (c+d x)^3\right)}{3 d (c+d x)^4}","-\frac{F^a \left(-b \log (F) (c+d x)^3\right)^{4/3} \text{Gamma}\left(-\frac{4}{3},-b \log (F) (c+d x)^3\right)}{3 d (c+d x)^4}",1,"-(F^a*Gamma[-4/3, -(b*(c + d*x)^3*Log[F])]*(-(b*(c + d*x)^3*Log[F]))^(4/3))/(3*d*(c + d*x)^4)","A",1,1,21,0.04762,1,"{2218}"
299,1,64,0,0.0324213,"\int f^{a+b \sqrt{c+d x}} \, dx","Int[f^(a + b*Sqrt[c + d*x]),x]","\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)}","\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]))/(b^2*d*Log[f]^2) + (2*f^(a + b*Sqrt[c + d*x])*Sqrt[c + d*x])/(b*d*Log[f])","A",3,3,15,0.2000,1,"{2207, 2176, 2194}"
300,1,100,0,0.0640819,"\int f^{a+b \sqrt[3]{c+d x}} \, dx","Int[f^(a + b*(c + d*x)^(1/3)),x]","-\frac{6 \sqrt[3]{c+d x} f^{a+b \sqrt[3]{c+d x}}}{b^2 d \log ^2(f)}+\frac{6 f^{a+b \sqrt[3]{c+d x}}}{b^3 d \log ^3(f)}+\frac{3 (c+d x)^{2/3} f^{a+b \sqrt[3]{c+d x}}}{b d \log (f)}","-\frac{6 \sqrt[3]{c+d x} f^{a+b \sqrt[3]{c+d x}}}{b^2 d \log ^2(f)}+\frac{6 f^{a+b \sqrt[3]{c+d x}}}{b^3 d \log ^3(f)}+\frac{3 (c+d x)^{2/3} f^{a+b \sqrt[3]{c+d x}}}{b d \log (f)}",1,"(6*f^(a + b*(c + d*x)^(1/3)))/(b^3*d*Log[f]^3) - (6*f^(a + b*(c + d*x)^(1/3))*(c + d*x)^(1/3))/(b^2*d*Log[f]^2) + (3*f^(a + b*(c + d*x)^(1/3))*(c + d*x)^(2/3))/(b*d*Log[f])","A",4,3,15,0.2000,1,"{2207, 2176, 2194}"
301,1,50,0,0.0437885,"\int F^{a+\frac{b}{c+d x}} (c+d x)^m \, dx","Int[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} \text{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} \text{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",1,1,21,0.04762,1,"{2218}"
302,1,29,0,0.0446677,"\int F^{a+\frac{b}{c+d x}} (c+d x)^4 \, dx","Int[F^(a + b/(c + d*x))*(c + d*x)^4,x]","-\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-\frac{b \log (F)}{c+d x}\right)}{d}","-\frac{b^5 F^a \log ^5(F) \text{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",1,1,21,0.04762,1,"{2218}"
303,1,28,0,0.0441052,"\int F^{a+\frac{b}{c+d x}} (c+d x)^3 \, dx","Int[F^(a + b/(c + d*x))*(c + d*x)^3,x]","\frac{b^4 F^a \log ^4(F) \text{Gamma}\left(-4,-\frac{b \log (F)}{c+d x}\right)}{d}","\frac{b^4 F^a \log ^4(F) \text{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",1,1,21,0.04762,1,"{2218}"
304,1,119,0,0.1325491,"\int F^{a+\frac{b}{c+d x}} (c+d x)^2 \, dx","Int[F^(a + b/(c + d*x))*(c + d*x)^2,x]","-\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}","-\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/(c + d*x))*(c + d*x)^3)/(3*d) + (b*F^(a + b/(c + d*x))*(c + d*x)^2*Log[F])/(6*d) + (b^2*F^(a + b/(c + d*x))*(c + d*x)*Log[F]^2)/(6*d) - (b^3*F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)]*Log[F]^3)/(6*d)","A",4,3,21,0.1429,1,"{2214, 2206, 2210}"
305,1,85,0,0.0798134,"\int F^{a+\frac{b}{c+d x}} (c+d x) \, dx","Int[F^(a + b/(c + d*x))*(c + d*x),x]","-\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}","-\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/(c + d*x))*(c + d*x)^2)/(2*d) + (b*F^(a + b/(c + d*x))*(c + d*x)*Log[F])/(2*d) - (b^2*F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)]*Log[F]^2)/(2*d)","A",3,3,19,0.1579,1,"{2214, 2206, 2210}"
306,1,46,0,0.0519797,"\int F^{a+\frac{b}{c+d x}} \, dx","Int[F^(a + b/(c + d*x)),x]","\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}","\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 + b/(c + d*x))*(c + d*x))/d - (b*F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)]*Log[F])/d","A",2,2,13,0.1538,1,"{2206, 2210}"
307,1,20,0,0.0438938,"\int \frac{F^{a+\frac{b}{c+d x}}}{c+d x} \, dx","Int[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",1,1,21,0.04762,1,"{2210}"
308,1,25,0,0.0423626,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^2} \, dx","Int[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",1,1,21,0.04762,1,"{2209}"
309,1,57,0,0.0849565,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^3} \, dx","Int[F^(a + b/(c + d*x))/(c + d*x)^3,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)}","\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))/(b^2*d*Log[F]^2) - F^(a + b/(c + d*x))/(b*d*(c + d*x)*Log[F])","A",2,2,21,0.09524,1,"{2212, 2209}"
310,1,90,0,0.1330948,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^4} \, dx","Int[F^(a + b/(c + d*x))/(c + d*x)^4,x]","\frac{2 F^{a+\frac{b}{c+d x}}}{b^2 d \log ^2(F) (c+d x)}-\frac{2 F^{a+\frac{b}{c+d x}}}{b^3 d \log ^3(F)}-\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F) (c+d x)^2}","\frac{2 F^{a+\frac{b}{c+d x}}}{b^2 d \log ^2(F) (c+d x)}-\frac{2 F^{a+\frac{b}{c+d x}}}{b^3 d \log ^3(F)}-\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F) (c+d x)^2}",1,"(-2*F^(a + b/(c + d*x)))/(b^3*d*Log[F]^3) + (2*F^(a + b/(c + d*x)))/(b^2*d*(c + d*x)*Log[F]^2) - F^(a + b/(c + d*x))/(b*d*(c + d*x)^2*Log[F])","A",3,2,21,0.09524,1,"{2212, 2209}"
311,1,122,0,0.1851301,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^5} \, dx","Int[F^(a + b/(c + d*x))/(c + d*x)^5,x]","\frac{3 F^{a+\frac{b}{c+d x}}}{b^2 d \log ^2(F) (c+d x)^2}-\frac{6 F^{a+\frac{b}{c+d x}}}{b^3 d \log ^3(F) (c+d x)}+\frac{6 F^{a+\frac{b}{c+d x}}}{b^4 d \log ^4(F)}-\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F) (c+d x)^3}","\frac{3 F^{a+\frac{b}{c+d x}}}{b^2 d \log ^2(F) (c+d x)^2}-\frac{6 F^{a+\frac{b}{c+d x}}}{b^3 d \log ^3(F) (c+d x)}+\frac{6 F^{a+\frac{b}{c+d x}}}{b^4 d \log ^4(F)}-\frac{F^{a+\frac{b}{c+d x}}}{b d \log (F) (c+d x)^3}",1,"(6*F^(a + b/(c + d*x)))/(b^4*d*Log[F]^4) - (6*F^(a + b/(c + d*x)))/(b^3*d*(c + d*x)*Log[F]^3) + (3*F^(a + b/(c + d*x)))/(b^2*d*(c + d*x)^2*Log[F]^2) - F^(a + b/(c + d*x))/(b*d*(c + d*x)^3*Log[F])","A",4,2,21,0.09524,1,"{2212, 2209}"
312,1,29,0,0.0485709,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^6} \, dx","Int[F^(a + b/(c + d*x))/(c + d*x)^6,x]","-\frac{F^a \text{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(12 b^2 \log ^2(F) (c+d x)^2-4 b^3 \log ^3(F) (c+d x)+b^4 \log ^4(F)-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",1,1,21,0.04762,1,"{2218}"
313,1,28,0,0.0533513,"\int \frac{F^{a+\frac{b}{c+d x}}}{(c+d x)^7} \, dx","Int[F^(a + b/(c + d*x))/(c + d*x)^7,x]","\frac{F^a \text{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(60 b^2 \log ^2(F) (c+d x)^3-20 b^3 \log ^3(F) (c+d x)^2+5 b^4 \log ^4(F) (c+d x)-b^5 \log ^5(F)-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",1,1,21,0.04762,1,"{2218}"
314,1,61,0,0.0536999,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^m \, dx","Int[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}} \text{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}} \text{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",1,1,21,0.04762,1,"{2218}"
315,1,31,0,0.0519668,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^9 \, dx","Int[F^(a + b/(c + d*x)^2)*(c + d*x)^9,x]","-\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}","-\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}",1,"-(b^5*F^a*Gamma[-5, -((b*Log[F])/(c + d*x)^2)]*Log[F]^5)/(2*d)","A",1,1,21,0.04762,1,"{2218}"
316,1,31,0,0.0505083,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^7 \, dx","Int[F^(a + b/(c + d*x)^2)*(c + d*x)^7,x]","\frac{b^4 F^a \log ^4(F) \text{Gamma}\left(-4,-\frac{b \log (F)}{(c+d x)^2}\right)}{2 d}","\frac{b^4 F^a \log ^4(F) \text{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",1,1,21,0.04762,1,"{2218}"
317,1,121,0,0.1856477,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^5 \, dx","Int[F^(a + b/(c + d*x)^2)*(c + d*x)^5,x]","-\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}","-\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 + b/(c + d*x)^2)*(c + d*x)^6)/(6*d) + (b*F^(a + b/(c + d*x)^2)*(c + d*x)^4*Log[F])/(12*d) + (b^2*F^(a + b/(c + d*x)^2)*(c + d*x)^2*Log[F]^2)/(12*d) - (b^3*F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)^2]*Log[F]^3)/(12*d)","A",4,2,21,0.09524,1,"{2214, 2210}"
318,1,87,0,0.124042,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^3 \, dx","Int[F^(a + b/(c + d*x)^2)*(c + d*x)^3,x]","-\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}","-\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 + b/(c + d*x)^2)*(c + d*x)^4)/(4*d) + (b*F^(a + b/(c + d*x)^2)*(c + d*x)^2*Log[F])/(4*d) - (b^2*F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)^2]*Log[F]^2)/(4*d)","A",3,2,21,0.09524,1,"{2214, 2210}"
319,1,53,0,0.0713583,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x) \, dx","Int[F^(a + b/(c + d*x)^2)*(c + d*x),x]","\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}","\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 + b/(c + d*x)^2)*(c + d*x)^2)/(2*d) - (b*F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)^2]*Log[F])/(2*d)","A",2,2,19,0.1053,1,"{2214, 2210}"
320,1,22,0,0.0447805,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{c+d x} \, dx","Int[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,"-(F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)^2])/(2*d)","A",1,1,21,0.04762,1,"{2210}"
321,1,27,0,0.042856,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^3} \, dx","Int[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,"-F^(a + b/(c + d*x)^2)/(2*b*d*Log[F])","A",1,1,21,0.04762,1,"{2209}"
322,1,62,0,0.0866581,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^5} \, dx","Int[F^(a + b/(c + d*x)^2)/(c + d*x)^5,x]","\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}","\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)/(2*b^2*d*Log[F]^2) - F^(a + b/(c + d*x)^2)/(2*b*d*(c + d*x)^2*Log[F])","A",2,2,21,0.09524,1,"{2212, 2209}"
323,1,91,0,0.1370924,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^7} \, dx","Int[F^(a + b/(c + d*x)^2)/(c + d*x)^7,x]","\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}}}{b^3 d \log ^3(F)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^4}","\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}}}{b^3 d \log ^3(F)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^4}",1,"-(F^(a + b/(c + d*x)^2)/(b^3*d*Log[F]^3)) + F^(a + b/(c + d*x)^2)/(b^2*d*(c + d*x)^2*Log[F]^2) - F^(a + b/(c + d*x)^2)/(2*b*d*(c + d*x)^4*Log[F])","A",3,2,21,0.09524,1,"{2212, 2209}"
324,1,126,0,0.191042,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^9} \, dx","Int[F^(a + b/(c + d*x)^2)/(c + d*x)^9,x]","\frac{3 F^{a+\frac{b}{(c+d x)^2}}}{2 b^2 d \log ^2(F) (c+d x)^4}-\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}}}{b^4 d \log ^4(F)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^6}","\frac{3 F^{a+\frac{b}{(c+d x)^2}}}{2 b^2 d \log ^2(F) (c+d x)^4}-\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}}}{b^4 d \log ^4(F)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^6}",1,"(3*F^(a + b/(c + d*x)^2))/(b^4*d*Log[F]^4) - (3*F^(a + b/(c + d*x)^2))/(b^3*d*(c + d*x)^2*Log[F]^3) + (3*F^(a + b/(c + d*x)^2))/(2*b^2*d*(c + d*x)^4*Log[F]^2) - F^(a + b/(c + d*x)^2)/(2*b*d*(c + d*x)^6*Log[F])","A",4,2,21,0.09524,1,"{2212, 2209}"
325,1,31,0,0.0449171,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{11}} \, dx","Int[F^(a + b/(c + d*x)^2)/(c + d*x)^11,x]","-\frac{F^a \text{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(12 b^2 \log ^2(F) (c+d x)^4-4 b^3 \log ^3(F) (c+d x)^2+b^4 \log ^4(F)-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,"-(F^a*Gamma[5, -((b*Log[F])/(c + d*x)^2)])/(2*b^5*d*Log[F]^5)","C",1,1,21,0.04762,1,"{2218}"
326,1,31,0,0.0456741,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{13}} \, dx","Int[F^(a + b/(c + d*x)^2)/(c + d*x)^13,x]","\frac{F^a \text{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(60 b^2 \log ^2(F) (c+d x)^6-20 b^3 \log ^3(F) (c+d x)^4+5 b^4 \log ^4(F) (c+d x)^2-b^5 \log ^5(F)-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",1,1,21,0.04762,1,"{2218}"
327,1,49,0,0.0484642,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^{10} \, dx","Int[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} \text{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} \text{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",1,1,21,0.04762,1,"{2218}"
328,1,49,0,0.0493251,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^8 \, dx","Int[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} \text{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} \text{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",1,1,21,0.04762,1,"{2218}"
329,1,170,0,0.233666,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^6 \, dx","Int[F^(a + b/(c + d*x)^2)*(c + d*x)^6,x]","-\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}","-\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 + b/(c + d*x)^2)*(c + d*x)^7)/(7*d) + (2*b*F^(a + b/(c + d*x)^2)*(c + d*x)^5*Log[F])/(35*d) + (4*b^2*F^(a + b/(c + d*x)^2)*(c + d*x)^3*Log[F]^2)/(105*d) + (8*b^3*F^(a + b/(c + d*x)^2)*(c + d*x)*Log[F]^3)/(105*d) - (8*b^(7/2)*F^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)]*Log[F]^(7/2))/(105*d)","A",6,4,21,0.1905,1,"{2214, 2206, 2211, 2204}"
330,1,136,0,0.168491,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^4 \, dx","Int[F^(a + b/(c + d*x)^2)*(c + d*x)^4,x]","-\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}","-\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 + b/(c + d*x)^2)*(c + d*x)^5)/(5*d) + (2*b*F^(a + b/(c + d*x)^2)*(c + d*x)^3*Log[F])/(15*d) + (4*b^2*F^(a + b/(c + d*x)^2)*(c + d*x)*Log[F]^2)/(15*d) - (4*b^(5/2)*F^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)]*Log[F]^(5/2))/(15*d)","A",5,4,21,0.1905,1,"{2214, 2206, 2211, 2204}"
331,1,102,0,0.1160434,"\int F^{a+\frac{b}{(c+d x)^2}} (c+d x)^2 \, dx","Int[F^(a + b/(c + d*x)^2)*(c + d*x)^2,x]","-\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}","-\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 + b/(c + d*x)^2)*(c + d*x)^3)/(3*d) + (2*b*F^(a + b/(c + d*x)^2)*(c + d*x)*Log[F])/(3*d) - (2*b^(3/2)*F^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)]*Log[F]^(3/2))/(3*d)","A",4,4,21,0.1905,1,"{2214, 2206, 2211, 2204}"
332,1,67,0,0.0635389,"\int F^{a+\frac{b}{(c+d x)^2}} \, dx","Int[F^(a + b/(c + d*x)^2),x]","\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}","\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 + b/(c + d*x)^2)*(c + d*x))/d - (Sqrt[b]*F^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)]*Sqrt[Log[F]])/d","A",3,3,13,0.2308,1,"{2206, 2211, 2204}"
333,1,46,0,0.054265,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^2} \, dx","Int[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,"-(F^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)])/(2*Sqrt[b]*d*Sqrt[Log[F]])","A",2,2,21,0.09524,1,"{2211, 2204}"
334,1,81,0,0.1021348,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^4} \, dx","Int[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",3,3,21,0.1429,1,"{2212, 2211, 2204}"
335,1,115,0,0.1507262,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^6} \, dx","Int[F^(a + b/(c + d*x)^2)/(c + d*x)^6,x]","-\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}","-\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,"(-3*F^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)])/(8*b^(5/2)*d*Log[F]^(5/2)) + (3*F^(a + b/(c + d*x)^2))/(4*b^2*d*(c + d*x)*Log[F]^2) - F^(a + b/(c + d*x)^2)/(2*b*d*(c + d*x)^3*Log[F])","A",4,3,21,0.1429,1,"{2212, 2211, 2204}"
336,1,149,0,0.2077208,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^8} \, dx","Int[F^(a + b/(c + d*x)^2)/(c + d*x)^8,x]","\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{5 F^{a+\frac{b}{(c+d x)^2}}}{4 b^2 d \log ^2(F) (c+d x)^3}-\frac{15 F^{a+\frac{b}{(c+d x)^2}}}{8 b^3 d \log ^3(F) (c+d x)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^5}","\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{5 F^{a+\frac{b}{(c+d x)^2}}}{4 b^2 d \log ^2(F) (c+d x)^3}-\frac{15 F^{a+\frac{b}{(c+d x)^2}}}{8 b^3 d \log ^3(F) (c+d x)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^5}",1,"(15*F^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)])/(16*b^(7/2)*d*Log[F]^(7/2)) - (15*F^(a + b/(c + d*x)^2))/(8*b^3*d*(c + d*x)*Log[F]^3) + (5*F^(a + b/(c + d*x)^2))/(4*b^2*d*(c + d*x)^3*Log[F]^2) - F^(a + b/(c + d*x)^2)/(2*b*d*(c + d*x)^5*Log[F])","A",5,3,21,0.1429,1,"{2212, 2211, 2204}"
337,1,183,0,0.264987,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{10}} \, dx","Int[F^(a + b/(c + d*x)^2)/(c + d*x)^10,x]","-\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{7 F^{a+\frac{b}{(c+d x)^2}}}{4 b^2 d \log ^2(F) (c+d x)^5}-\frac{35 F^{a+\frac{b}{(c+d x)^2}}}{8 b^3 d \log ^3(F) (c+d x)^3}+\frac{105 F^{a+\frac{b}{(c+d x)^2}}}{16 b^4 d \log ^4(F) (c+d x)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^7}","-\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{7 F^{a+\frac{b}{(c+d x)^2}}}{4 b^2 d \log ^2(F) (c+d x)^5}-\frac{35 F^{a+\frac{b}{(c+d x)^2}}}{8 b^3 d \log ^3(F) (c+d x)^3}+\frac{105 F^{a+\frac{b}{(c+d x)^2}}}{16 b^4 d \log ^4(F) (c+d x)}-\frac{F^{a+\frac{b}{(c+d x)^2}}}{2 b d \log (F) (c+d x)^7}",1,"(-105*F^a*Sqrt[Pi]*Erfi[(Sqrt[b]*Sqrt[Log[F]])/(c + d*x)])/(32*b^(9/2)*d*Log[F]^(9/2)) + (105*F^(a + b/(c + d*x)^2))/(16*b^4*d*(c + d*x)*Log[F]^4) - (35*F^(a + b/(c + d*x)^2))/(8*b^3*d*(c + d*x)^3*Log[F]^3) + (7*F^(a + b/(c + d*x)^2))/(4*b^2*d*(c + d*x)^5*Log[F]^2) - F^(a + b/(c + d*x)^2)/(2*b*d*(c + d*x)^7*Log[F])","A",6,3,21,0.1429,1,"{2212, 2211, 2204}"
338,1,49,0,0.0453887,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{12}} \, dx","Int[F^(a + b/(c + d*x)^2)/(c + d*x)^12,x]","\frac{F^a \text{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 \text{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",1,1,21,0.04762,1,"{2218}"
339,1,49,0,0.0453299,"\int \frac{F^{a+\frac{b}{(c+d x)^2}}}{(c+d x)^{14}} \, dx","Int[F^(a + b/(c + d*x)^2)/(c + d*x)^14,x]","\frac{F^a \text{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 \text{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",1,1,21,0.04762,1,"{2218}"
340,1,61,0,0.0446864,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^m \, dx","Int[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}} \text{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}} \text{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",1,1,21,0.04762,1,"{2218}"
341,1,31,0,0.0463526,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^{14} \, dx","Int[F^(a + b/(c + d*x)^3)*(c + d*x)^14,x]","-\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}","-\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}",1,"-(b^5*F^a*Gamma[-5, -((b*Log[F])/(c + d*x)^3)]*Log[F]^5)/(3*d)","A",1,1,21,0.04762,1,"{2218}"
342,1,31,0,0.0463236,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^{11} \, dx","Int[F^(a + b/(c + d*x)^3)*(c + d*x)^11,x]","\frac{b^4 F^a \log ^4(F) \text{Gamma}\left(-4,-\frac{b \log (F)}{(c+d x)^3}\right)}{3 d}","\frac{b^4 F^a \log ^4(F) \text{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",1,1,21,0.04762,1,"{2218}"
343,1,121,0,0.1910085,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^8 \, dx","Int[F^(a + b/(c + d*x)^3)*(c + d*x)^8,x]","-\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}","-\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 + b/(c + d*x)^3)*(c + d*x)^9)/(9*d) + (b*F^(a + b/(c + d*x)^3)*(c + d*x)^6*Log[F])/(18*d) + (b^2*F^(a + b/(c + d*x)^3)*(c + d*x)^3*Log[F]^2)/(18*d) - (b^3*F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)^3]*Log[F]^3)/(18*d)","A",4,2,21,0.09524,1,"{2214, 2210}"
344,1,87,0,0.1391984,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^5 \, dx","Int[F^(a + b/(c + d*x)^3)*(c + d*x)^5,x]","-\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}","-\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 + b/(c + d*x)^3)*(c + d*x)^6)/(6*d) + (b*F^(a + b/(c + d*x)^3)*(c + d*x)^3*Log[F])/(6*d) - (b^2*F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)^3]*Log[F]^2)/(6*d)","A",3,2,21,0.09524,1,"{2214, 2210}"
345,1,53,0,0.0910202,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^2 \, dx","Int[F^(a + b/(c + d*x)^3)*(c + d*x)^2,x]","\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}","\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 + b/(c + d*x)^3)*(c + d*x)^3)/(3*d) - (b*F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)^3]*Log[F])/(3*d)","A",2,2,21,0.09524,1,"{2214, 2210}"
346,1,22,0,0.0435177,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{c+d x} \, dx","Int[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,"-(F^a*ExpIntegralEi[(b*Log[F])/(c + d*x)^3])/(3*d)","A",1,1,21,0.04762,1,"{2210}"
347,1,27,0,0.0425225,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^4} \, dx","Int[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,"-F^(a + b/(c + d*x)^3)/(3*b*d*Log[F])","A",1,1,21,0.04762,1,"{2209}"
348,1,62,0,0.0867742,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^7} \, dx","Int[F^(a + b/(c + d*x)^3)/(c + d*x)^7,x]","\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}","\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)/(3*b^2*d*Log[F]^2) - F^(a + b/(c + d*x)^3)/(3*b*d*(c + d*x)^3*Log[F])","A",2,2,21,0.09524,1,"{2212, 2209}"
349,1,96,0,0.1348242,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^{10}} \, dx","Int[F^(a + b/(c + d*x)^3)/(c + d*x)^10,x]","\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{3 b^2 d \log ^2(F) (c+d x)^3}-\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{3 b^3 d \log ^3(F)}-\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F) (c+d x)^6}","\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{3 b^2 d \log ^2(F) (c+d x)^3}-\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{3 b^3 d \log ^3(F)}-\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F) (c+d x)^6}",1,"(-2*F^(a + b/(c + d*x)^3))/(3*b^3*d*Log[F]^3) + (2*F^(a + b/(c + d*x)^3))/(3*b^2*d*(c + d*x)^3*Log[F]^2) - F^(a + b/(c + d*x)^3)/(3*b*d*(c + d*x)^6*Log[F])","A",3,2,21,0.09524,1,"{2212, 2209}"
350,1,123,0,0.1856929,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^{13}} \, dx","Int[F^(a + b/(c + d*x)^3)/(c + d*x)^13,x]","\frac{F^{a+\frac{b}{(c+d x)^3}}}{b^2 d \log ^2(F) (c+d x)^6}-\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{b^3 d \log ^3(F) (c+d x)^3}+\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{b^4 d \log ^4(F)}-\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F) (c+d x)^9}","\frac{F^{a+\frac{b}{(c+d x)^3}}}{b^2 d \log ^2(F) (c+d x)^6}-\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{b^3 d \log ^3(F) (c+d x)^3}+\frac{2 F^{a+\frac{b}{(c+d x)^3}}}{b^4 d \log ^4(F)}-\frac{F^{a+\frac{b}{(c+d x)^3}}}{3 b d \log (F) (c+d x)^9}",1,"(2*F^(a + b/(c + d*x)^3))/(b^4*d*Log[F]^4) - (2*F^(a + b/(c + d*x)^3))/(b^3*d*(c + d*x)^3*Log[F]^3) + F^(a + b/(c + d*x)^3)/(b^2*d*(c + d*x)^6*Log[F]^2) - F^(a + b/(c + d*x)^3)/(3*b*d*(c + d*x)^9*Log[F])","A",4,2,21,0.09524,1,"{2212, 2209}"
351,1,31,0,0.0440779,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^{16}} \, dx","Int[F^(a + b/(c + d*x)^3)/(c + d*x)^16,x]","-\frac{F^a \text{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(12 b^2 \log ^2(F) (c+d x)^6-4 b^3 \log ^3(F) (c+d x)^3+b^4 \log ^4(F)-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,"-(F^a*Gamma[5, -((b*Log[F])/(c + d*x)^3)])/(3*b^5*d*Log[F]^5)","C",1,1,21,0.04762,1,"{2218}"
352,1,31,0,0.0449279,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^{19}} \, dx","Int[F^(a + b/(c + d*x)^3)/(c + d*x)^19,x]","\frac{F^a \text{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(60 b^2 \log ^2(F) (c+d x)^9-20 b^3 \log ^3(F) (c+d x)^6+5 b^4 \log ^4(F) (c+d x)^3-b^5 \log ^5(F)-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",1,1,21,0.04762,1,"{2218}"
353,1,49,0,0.0479236,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x)^3 \, dx","Int[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} \text{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} \text{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",1,1,21,0.04762,1,"{2218}"
354,1,49,0,0.0273341,"\int F^{a+\frac{b}{(c+d x)^3}} (c+d x) \, dx","Int[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} \text{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} \text{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",1,1,19,0.05263,1,"{2218}"
355,1,47,0,0.0068177,"\int F^{a+\frac{b}{(c+d x)^3}} \, dx","Int[F^(a + b/(c + d*x)^3),x]","\frac{F^a (c+d x) \sqrt[3]{-\frac{b \log (F)}{(c+d x)^3}} \text{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}} \text{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",1,1,13,0.07692,1,"{2208}"
356,1,49,0,0.0456179,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^2} \, dx","Int[F^(a + b/(c + d*x)^3)/(c + d*x)^2,x]","\frac{F^a \text{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 \text{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",1,1,21,0.04762,1,"{2218}"
357,1,49,0,0.0438045,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^3} \, dx","Int[F^(a + b/(c + d*x)^3)/(c + d*x)^3,x]","\frac{F^a \text{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 \text{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",1,1,21,0.04762,1,"{2218}"
358,1,49,0,0.0435577,"\int \frac{F^{a+\frac{b}{(c+d x)^3}}}{(c+d x)^5} \, dx","Int[F^(a + b/(c + d*x)^3)/(c + d*x)^5,x]","\frac{F^a \text{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 \text{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",1,1,21,0.04762,1,"{2218}"
359,1,61,0,0.034471,"\int F^{a+b (c+d x)^n} (c+d x)^m \, dx","Int[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}} \text{Gamma}\left(\frac{m+1}{n},-b \log (F) (c+d x)^n\right)}{d n}","-\frac{F^a (c+d x)^{m+1} \left(-b \log (F) (c+d x)^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-b \log (F) (c+d x)^n\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",1,1,21,0.04762,1,"{2218}"
360,1,54,0,0.0361046,"\int F^{a+b (c+d x)^n} (c+d x)^3 \, dx","Int[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} \text{Gamma}\left(\frac{4}{n},-b \log (F) (c+d x)^n\right)}{d n}","-\frac{F^a (c+d x)^4 \left(-b \log (F) (c+d x)^n\right)^{-4/n} \text{Gamma}\left(\frac{4}{n},-b \log (F) (c+d x)^n\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",1,1,21,0.04762,1,"{2218}"
361,1,54,0,0.0357216,"\int F^{a+b (c+d x)^n} (c+d x)^2 \, dx","Int[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} \text{Gamma}\left(\frac{3}{n},-b \log (F) (c+d x)^n\right)}{d n}","-\frac{F^a (c+d x)^3 \left(-b \log (F) (c+d x)^n\right)^{-3/n} \text{Gamma}\left(\frac{3}{n},-b \log (F) (c+d x)^n\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",1,1,21,0.04762,1,"{2218}"
362,1,54,0,0.0207883,"\int F^{a+b (c+d x)^n} (c+d x) \, dx","Int[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} \text{Gamma}\left(\frac{2}{n},-b \log (F) (c+d x)^n\right)}{d n}","-\frac{F^a (c+d x)^2 \left(-b \log (F) (c+d x)^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{n},-b \log (F) (c+d x)^n\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",1,1,19,0.05263,1,"{2218}"
363,1,50,0,0.0065579,"\int F^{a+b (c+d x)^n} \, dx","Int[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} \text{Gamma}\left(\frac{1}{n},-b \log (F) (c+d x)^n\right)}{d n}","-\frac{F^a (c+d x) \left(-b \log (F) (c+d x)^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-b \log (F) (c+d x)^n\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",1,1,13,0.07692,1,"{2208}"
364,1,22,0,0.0349404,"\int \frac{F^{a+b (c+d x)^n}}{c+d x} \, dx","Int[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",1,1,21,0.04762,1,"{2210}"
365,1,52,0,0.0345223,"\int \frac{F^{a+b (c+d x)^n}}{(c+d x)^2} \, dx","Int[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}} \text{Gamma}\left(-\frac{1}{n},-b \log (F) (c+d x)^n\right)}{d n (c+d x)}","-\frac{F^a \left(-b \log (F) (c+d x)^n\right)^{\frac{1}{n}} \text{Gamma}\left(-\frac{1}{n},-b \log (F) (c+d x)^n\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",1,1,21,0.04762,1,"{2218}"
366,1,54,0,0.0347216,"\int \frac{F^{a+b (c+d x)^n}}{(c+d x)^3} \, dx","Int[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} \text{Gamma}\left(-\frac{2}{n},-b \log (F) (c+d x)^n\right)}{d n (c+d x)^2}","-\frac{F^a \left(-b \log (F) (c+d x)^n\right)^{2/n} \text{Gamma}\left(-\frac{2}{n},-b \log (F) (c+d x)^n\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",1,1,21,0.04762,1,"{2218}"
367,1,54,0,0.0367762,"\int \frac{F^{a+b (c+d x)^n}}{(c+d x)^4} \, dx","Int[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} \text{Gamma}\left(-\frac{3}{n},-b \log (F) (c+d x)^n\right)}{d n (c+d x)^3}","-\frac{F^a \left(-b \log (F) (c+d x)^n\right)^{3/n} \text{Gamma}\left(-\frac{3}{n},-b \log (F) (c+d x)^n\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",1,1,21,0.04762,1,"{2218}"
368,1,32,0,0.0375697,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+6 n} \, dx","Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 6*n),x]","-\frac{F^a \text{Gamma}\left(6,-b \log (F) (c+d x)^n\right)}{b^6 d n \log ^6(F)}","-\frac{F^{a+b (c+d x)^n} \left(60 b^2 \log ^2(F) (c+d x)^{2 n}-20 b^3 \log ^3(F) (c+d x)^{3 n}+5 b^4 \log ^4(F) (c+d x)^{4 n}-b^5 \log ^5(F) (c+d x)^{5 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",1,1,25,0.04000,1,"{2218}"
369,1,31,0,0.0396707,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+5 n} \, dx","Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 5*n),x]","\frac{F^a \text{Gamma}\left(5,-b \log (F) (c+d x)^n\right)}{b^5 d n \log ^5(F)}","\frac{F^{a+b (c+d x)^n} \left(12 b^2 \log ^2(F) (c+d x)^{2 n}-4 b^3 \log ^3(F) (c+d x)^{3 n}+b^4 \log ^4(F) (c+d x)^{4 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",1,1,25,0.04000,1,"{2218}"
370,1,137,0,0.1678544,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+4 n} \, dx","Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 4*n),x]","\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{6 F^{a+b (c+d x)^n}}{b^4 d n \log ^4(F)}+\frac{(c+d x)^{3 n} F^{a+b (c+d x)^n}}{b d n \log (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{6 F^{a+b (c+d x)^n}}{b^4 d n \log ^4(F)}+\frac{(c+d x)^{3 n} F^{a+b (c+d x)^n}}{b d n \log (F)}",1,"(-6*F^(a + b*(c + d*x)^n))/(b^4*d*n*Log[F]^4) + (6*F^(a + b*(c + d*x)^n)*(c + d*x)^n)/(b^3*d*n*Log[F]^3) - (3*F^(a + b*(c + d*x)^n)*(c + d*x)^(2*n))/(b^2*d*n*Log[F]^2) + (F^(a + b*(c + d*x)^n)*(c + d*x)^(3*n))/(b*d*n*Log[F])","A",4,2,25,0.08000,1,"{2213, 2209}"
371,1,100,0,0.1195266,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+3 n} \, dx","Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 3*n),x]","-\frac{2 (c+d x)^n F^{a+b (c+d x)^n}}{b^2 d n \log ^2(F)}+\frac{2 F^{a+b (c+d x)^n}}{b^3 d n \log ^3(F)}+\frac{(c+d x)^{2 n} F^{a+b (c+d x)^n}}{b d n \log (F)}","-\frac{2 (c+d x)^n F^{a+b (c+d x)^n}}{b^2 d n \log ^2(F)}+\frac{2 F^{a+b (c+d x)^n}}{b^3 d n \log ^3(F)}+\frac{(c+d x)^{2 n} F^{a+b (c+d x)^n}}{b d n \log (F)}",1,"(2*F^(a + b*(c + d*x)^n))/(b^3*d*n*Log[F]^3) - (2*F^(a + b*(c + d*x)^n)*(c + d*x)^n)/(b^2*d*n*Log[F]^2) + (F^(a + b*(c + d*x)^n)*(c + d*x)^(2*n))/(b*d*n*Log[F])","A",3,2,25,0.08000,1,"{2213, 2209}"
372,1,63,0,0.074351,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+2 n} \, dx","Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 + 2*n),x]","\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)}","\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 + b*(c + d*x)^n)/(b^2*d*n*Log[F]^2)) + (F^(a + b*(c + d*x)^n)*(c + d*x)^n)/(b*d*n*Log[F])","A",2,2,25,0.08000,1,"{2213, 2209}"
373,1,27,0,0.037157,"\int F^{a+b (c+d x)^n} (c+d x)^{-1+n} \, dx","Int[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",1,1,23,0.04348,1,"{2209}"
374,1,22,0,0.0358306,"\int \frac{F^{a+b (c+d x)^n}}{c+d x} \, dx","Int[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",1,1,21,0.04762,1,"{2210}"
375,1,56,0,0.0725984,"\int F^{a+b (c+d x)^n} (c+d x)^{-1-n} \, dx","Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 - n),x]","\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}","\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,"-(F^(a + b*(c + d*x)^n)/(d*n*(c + d*x)^n)) + (b*F^a*ExpIntegralEi[b*(c + d*x)^n*Log[F]]*Log[F])/(d*n)","A",2,2,25,0.08000,1,"{2215, 2210}"
376,1,100,0,0.1140209,"\int F^{a+b (c+d x)^n} (c+d x)^{-1-2 n} \, dx","Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 - 2*n),x]","\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}","\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,"-F^(a + b*(c + d*x)^n)/(2*d*n*(c + d*x)^(2*n)) - (b*F^(a + b*(c + d*x)^n)*Log[F])/(2*d*n*(c + d*x)^n) + (b^2*F^a*ExpIntegralEi[b*(c + d*x)^n*Log[F]]*Log[F]^2)/(2*d*n)","A",3,2,25,0.08000,1,"{2215, 2210}"
377,1,139,0,0.1644644,"\int F^{a+b (c+d x)^n} (c+d x)^{-1-3 n} \, dx","Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 - 3*n),x]","\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}","\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,"-F^(a + b*(c + d*x)^n)/(3*d*n*(c + d*x)^(3*n)) - (b*F^(a + b*(c + d*x)^n)*Log[F])/(6*d*n*(c + d*x)^(2*n)) - (b^2*F^(a + b*(c + d*x)^n)*Log[F]^2)/(6*d*n*(c + d*x)^n) + (b^3*F^a*ExpIntegralEi[b*(c + d*x)^n*Log[F]]*Log[F]^3)/(6*d*n)","A",4,2,25,0.08000,1,"{2215, 2210}"
378,1,32,0,0.0427772,"\int F^{a+b (c+d x)^n} (c+d x)^{-1-4 n} \, dx","Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 - 4*n),x]","-\frac{b^4 F^a \log ^4(F) \text{Gamma}\left(-4,-b \log (F) (c+d x)^n\right)}{d n}","-\frac{b^4 F^a \log ^4(F) \text{Gamma}\left(-4,-b \log (F) (c+d x)^n\right)}{d n}",1,"-((b^4*F^a*Gamma[-4, -(b*(c + d*x)^n*Log[F])]*Log[F]^4)/(d*n))","A",1,1,25,0.04000,1,"{2218}"
379,1,31,0,0.0392378,"\int F^{a+b (c+d x)^n} (c+d x)^{-1-5 n} \, dx","Int[F^(a + b*(c + d*x)^n)*(c + d*x)^(-1 - 5*n),x]","\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-b \log (F) (c+d x)^n\right)}{d n}","\frac{b^5 F^a \log ^5(F) \text{Gamma}\left(-5,-b \log (F) (c+d x)^n\right)}{d n}",1,"(b^5*F^a*Gamma[-5, -(b*(c + d*x)^n*Log[F])]*Log[F]^5)/(d*n)","A",1,1,25,0.04000,1,"{2218}"
380,1,47,0,0.0651868,"\int F^{c (a+b x)^n} (a+b x)^{-1+\frac{n}{2}} \, dx","Int[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",2,2,25,0.08000,1,"{2211, 2204}"
381,1,47,0,0.0484519,"\int F^{-c (a+b x)^n} (a+b x)^{-1+\frac{n}{2}} \, dx","Int[(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",2,2,26,0.07692,1,"{2211, 2205}"
382,1,518,0,0.9433331,"\int F^{a+b (c+d x)^2} (e+f x)^5 \, dx","Int[F^(a + b*(c + d*x)^2)*(e + f*x)^5,x]","-\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{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 f^3 (d e-c f)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(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{f^5 (c+d x)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(F)}+\frac{f^5 F^{a+b (c+d x)^2}}{b^3 d^6 \log ^3(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)}","-\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{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 f^3 (d e-c f)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(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{f^5 (c+d x)^2 F^{a+b (c+d x)^2}}{b^2 d^6 \log ^2(F)}+\frac{f^5 F^{a+b (c+d x)^2}}{b^3 d^6 \log ^3(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^5*F^(a + b*(c + d*x)^2))/(b^3*d^6*Log[F]^3) + (15*f^4*(d*e - c*f)*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(8*b^(5/2)*d^6*Log[F]^(5/2)) - (5*f^3*(d*e - c*f)^2*F^(a + b*(c + d*x)^2))/(b^2*d^6*Log[F]^2) - (15*f^4*(d*e - c*f)*F^(a + b*(c + d*x)^2)*(c + d*x))/(4*b^2*d^6*Log[F]^2) - (f^5*F^(a + b*(c + d*x)^2)*(c + d*x)^2)/(b^2*d^6*Log[F]^2) - (5*f^2*(d*e - c*f)^3*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(2*b^(3/2)*d^6*Log[F]^(3/2)) + (5*f*(d*e - c*f)^4*F^(a + b*(c + d*x)^2))/(2*b*d^6*Log[F]) + (5*f^2*(d*e - c*f)^3*F^(a + b*(c + d*x)^2)*(c + d*x))/(b*d^6*Log[F]) + (5*f^3*(d*e - c*f)^2*F^(a + b*(c + d*x)^2)*(c + d*x)^2)/(b*d^6*Log[F]) + (5*f^4*(d*e - c*f)*F^(a + b*(c + d*x)^2)*(c + d*x)^3)/(2*b*d^6*Log[F]) + (f^5*F^(a + b*(c + d*x)^2)*(c + d*x)^4)/(2*b*d^6*Log[F]) + ((d*e - c*f)^5*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(2*Sqrt[b]*d^6*Sqrt[Log[F]])","A",14,4,21,0.1905,1,"{2226, 2204, 2209, 2212}"
383,1,389,0,0.6536447,"\int F^{a+b (c+d x)^2} (e+f x)^4 \, dx","Int[F^(a + b*(c + d*x)^2)*(e + f*x)^4,x]","-\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{2 f^3 (d e-c f) F^{a+b (c+d x)^2}}{b^2 d^5 \log ^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{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)}","-\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{2 f^3 (d e-c f) F^{a+b (c+d x)^2}}{b^2 d^5 \log ^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{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,"(3*f^4*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(8*b^(5/2)*d^5*Log[F]^(5/2)) - (2*f^3*(d*e - c*f)*F^(a + b*(c + d*x)^2))/(b^2*d^5*Log[F]^2) - (3*f^4*F^(a + b*(c + d*x)^2)*(c + d*x))/(4*b^2*d^5*Log[F]^2) - (3*f^2*(d*e - c*f)^2*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(2*b^(3/2)*d^5*Log[F]^(3/2)) + (2*f*(d*e - c*f)^3*F^(a + b*(c + d*x)^2))/(b*d^5*Log[F]) + (3*f^2*(d*e - c*f)^2*F^(a + b*(c + d*x)^2)*(c + d*x))/(b*d^5*Log[F]) + (2*f^3*(d*e - c*f)*F^(a + b*(c + d*x)^2)*(c + d*x)^2)/(b*d^5*Log[F]) + (f^4*F^(a + b*(c + d*x)^2)*(c + d*x)^3)/(2*b*d^5*Log[F]) + ((d*e - c*f)^4*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(2*Sqrt[b]*d^5*Sqrt[Log[F]])","A",11,4,21,0.1905,1,"{2226, 2204, 2209, 2212}"
384,1,258,0,0.4356179,"\int F^{a+b (c+d x)^2} (e+f x)^3 \, dx","Int[F^(a + b*(c + d*x)^2)*(e + f*x)^3,x]","-\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)}","-\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^3*F^(a + b*(c + d*x)^2))/(2*b^2*d^4*Log[F]^2) - (3*f^2*(d*e - c*f)*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(4*b^(3/2)*d^4*Log[F]^(3/2)) + (3*f*(d*e - c*f)^2*F^(a + b*(c + d*x)^2))/(2*b*d^4*Log[F]) + (3*f^2*(d*e - c*f)*F^(a + b*(c + d*x)^2)*(c + d*x))/(2*b*d^4*Log[F]) + (f^3*F^(a + b*(c + d*x)^2)*(c + d*x)^2)/(2*b*d^4*Log[F]) + ((d*e - c*f)^3*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(2*Sqrt[b]*d^4*Sqrt[Log[F]])","A",8,4,21,0.1905,1,"{2226, 2204, 2209, 2212}"
385,1,170,0,0.3142877,"\int F^{a+b (c+d x)^2} (e+f x)^2 \, dx","Int[F^(a + b*(c + d*x)^2)*(e + f*x)^2,x]","-\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)}","-\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^2*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(4*b^(3/2)*d^3*Log[F]^(3/2)) + (f*(d*e - c*f)*F^(a + b*(c + d*x)^2))/(b*d^3*Log[F]) + (f^2*F^(a + b*(c + d*x)^2)*(c + d*x))/(2*b*d^3*Log[F]) + ((d*e - c*f)^2*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(2*Sqrt[b]*d^3*Sqrt[Log[F]])","A",6,4,21,0.1905,1,"{2226, 2204, 2209, 2212}"
386,1,81,0,0.1465044,"\int F^{a+b (c+d x)^2} (e+f x) \, dx","Int[F^(a + b*(c + d*x)^2)*(e + f*x),x]","\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)}","\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*F^(a + b*(c + d*x)^2))/(2*b*d^2*Log[F]) + ((d*e - c*f)*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]])/(2*Sqrt[b]*d^2*Sqrt[Log[F]])","A",4,3,19,0.1579,1,"{2226, 2204, 2209}"
387,1,44,0,0.0122826,"\int F^{a+b (c+d x)^2} \, dx","Int[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",1,1,13,0.07692,1,"{2204}"
388,0,0,0,0.0685714,"\int \frac{F^{a+b (c+d x)^2}}{e+f x} \, dx","Int[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,"Defer[Int][F^(a + b*(c + d*x)^2)/(e + f*x), x]","A",0,0,0,0,-1,"{}"
389,0,0,0,0.1564015,"\int \frac{F^{a+b (c+d x)^2}}{(e+f x)^2} \, dx","Int[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,"-(F^(a + b*(c + d*x)^2)/(f*(e + f*x))) + (Sqrt[b]*d*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Sqrt[Log[F]])/f^2 - (2*b*d*(d*e - c*f)*Log[F]*Defer[Int][F^(a + b*(c + d*x)^2)/(e + f*x), x])/f^2","A",0,0,0,0,-1,"{}"
390,0,0,0,0.3138754,"\int \frac{F^{a+b (c+d x)^2}}{(e+f x)^3} \, dx","Int[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,"-F^(a + b*(c + d*x)^2)/(2*f*(e + f*x)^2) + (b*d*(d*e - c*f)*F^(a + b*(c + d*x)^2)*Log[F])/(f^3*(e + f*x)) - (b^(3/2)*d^2*(d*e - c*f)*F^a*Sqrt[Pi]*Erfi[Sqrt[b]*(c + d*x)*Sqrt[Log[F]]]*Log[F]^(3/2))/f^4 + (b*d^2*Log[F]*Defer[Int][F^(a + b*(c + d*x)^2)/(e + f*x), x])/f^2 + (2*b^2*d^2*(d*e - c*f)^2*Log[F]^2*Defer[Int][F^(a + b*(c + d*x)^2)/(e + f*x), x])/f^4","A",0,0,0,0,-1,"{}"
391,1,177,0,0.1559747,"\int e^{e (c+d x)^3} (a+b x)^3 \, dx","Int[E^(e*(c + d*x)^3)*(a + b*x)^3,x]","-\frac{b (c+d x)^2 (b c-a d)^2 \text{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 \text{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 \text{Gamma}\left(\frac{4}{3},-e (c+d x)^3\right)}{3 d^4 \left(-e (c+d x)^3\right)^{4/3}}-\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 \text{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 \text{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 \text{Gamma}\left(\frac{4}{3},-e (c+d x)^3\right)}{3 d^4 \left(-e (c+d x)^3\right)^{4/3}}-\frac{b^2 (b c-a d) e^{e (c+d x)^3}}{d^4 e}",1,"-((b^2*(b*c - a*d)*E^(e*(c + d*x)^3))/(d^4*e)) + ((b*c - a*d)^3*(c + d*x)*Gamma[1/3, -(e*(c + d*x)^3)])/(3*d^4*(-(e*(c + d*x)^3))^(1/3)) - (b*(b*c - a*d)^2*(c + d*x)^2*Gamma[2/3, -(e*(c + d*x)^3)])/(d^4*(-(e*(c + d*x)^3))^(2/3)) - (b^3*(c + d*x)^4*Gamma[4/3, -(e*(c + d*x)^3)])/(3*d^4*(-(e*(c + d*x)^3))^(4/3))","A",6,4,19,0.2105,1,"{2226, 2208, 2218, 2209}"
392,1,126,0,0.1067005,"\int e^{e (c+d x)^3} (a+b x)^2 \, dx","Int[E^(e*(c + d*x)^3)*(a + b*x)^2,x]","\frac{2 b (c+d x)^2 (b c-a d) \text{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 \text{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}","\frac{2 b (c+d x)^2 (b c-a d) \text{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 \text{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))/(3*d^3*e) - ((b*c - a*d)^2*(c + d*x)*Gamma[1/3, -(e*(c + d*x)^3)])/(3*d^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)])/(3*d^3*(-(e*(c + d*x)^3))^(2/3))","A",5,4,19,0.2105,1,"{2226, 2208, 2218, 2209}"
393,1,92,0,0.0602533,"\int e^{e (c+d x)^3} (a+b x) \, dx","Int[E^(e*(c + d*x)^3)*(a + b*x),x]","\frac{(c+d x) (b c-a d) \text{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 \text{Gamma}\left(\frac{2}{3},-e (c+d x)^3\right)}{3 d^2 \left(-e (c+d x)^3\right)^{2/3}}","\frac{(c+d x) (b c-a d) \text{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 \text{Gamma}\left(\frac{2}{3},-e (c+d x)^3\right)}{3 d^2 \left(-e (c+d x)^3\right)^{2/3}}",1,"((b*c - a*d)*(c + d*x)*Gamma[1/3, -(e*(c + d*x)^3)])/(3*d^2*(-(e*(c + d*x)^3))^(1/3)) - (b*(c + d*x)^2*Gamma[2/3, -(e*(c + d*x)^3)])/(3*d^2*(-(e*(c + d*x)^3))^(2/3))","A",4,3,17,0.1765,1,"{2226, 2208, 2218}"
394,1,40,0,0.0051903,"\int e^{e (c+d x)^3} \, dx","Int[E^(e*(c + d*x)^3),x]","-\frac{(c+d x) \text{Gamma}\left(\frac{1}{3},-e (c+d x)^3\right)}{3 d \sqrt[3]{-e (c+d x)^3}}","-\frac{(c+d x) \text{Gamma}\left(\frac{1}{3},-e (c+d x)^3\right)}{3 d \sqrt[3]{-e (c+d x)^3}}",1,"-((c + d*x)*Gamma[1/3, -(e*(c + d*x)^3)])/(3*d*(-(e*(c + d*x)^3))^(1/3))","A",1,1,11,0.09091,1,"{2208}"
395,0,0,0,0.0226154,"\int \frac{e^{e (c+d x)^3}}{a+b x} \, dx","Int[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,"Defer[Int][E^(e*(c + d*x)^3)/(a + b*x), x]","A",0,0,0,0,-1,"{}"
396,0,0,0,0.3503155,"\int \frac{e^{e (c+d x)^3}}{(a+b x)^2} \, dx","Int[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) \text{Gamma}\left(\frac{1}{3},-e (c+d x)^3\right)}{b^3 \sqrt[3]{-e (c+d x)^3}}-\frac{d e (c+d x)^2 \text{Gamma}\left(\frac{2}{3},-e (c+d x)^3\right)}{b^2 \left(-e (c+d x)^3\right)^{2/3}}-\frac{e^{e (c+d x)^3}}{b (a+b x)}",0,"-(E^(e*(c + d*x)^3)/(b*(a + b*x))) - (d*(b*c - a*d)*e*(c + d*x)*Gamma[1/3, -(e*(c + d*x)^3)])/(b^3*(-(e*(c + d*x)^3))^(1/3)) - (d*e*(c + d*x)^2*Gamma[2/3, -(e*(c + d*x)^3)])/(b^2*(-(e*(c + d*x)^3))^(2/3)) + (3*d*(b*c - a*d)^2*e*Defer[Int][E^(e*(c + d*x)^3)/(a + b*x), x])/b^3","A",0,0,0,0,-1,"{}"
397,1,71,0,0.4050281,"\int \frac{F^{a+\frac{b}{c+d x}}}{e+f x} \, dx","Int[F^(a + b/(c + d*x))/(e + f*x),x]","\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}","\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) + (F^(a - (b*f)/(d*e - c*f))*ExpIntegralEi[(b*d*(e + f*x)*Log[F])/((d*e - c*f)*(c + d*x))])/f","A",4,4,21,0.1905,1,"{2222, 2210, 2228, 2178}"
398,1,116,0,1.010753,"\int \frac{F^{a+\frac{b}{c+d x}}}{(e+f x)^2} \, dx","Int[F^(a + b/(c + d*x))/(e + f*x)^2,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)}","-\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*d*(e + f*x)*Log[F])/((d*e - c*f)*(c + d*x))]*Log[F])/(d*e - c*f)^2","A",9,7,21,0.3333,1,"{2223, 6742, 2209, 2210, 2222, 2228, 2178}"
399,1,267,0,1.913994,"\int \frac{F^{a+\frac{b}{c+d x}}}{(e+f x)^3} \, dx","Int[F^(a + b/(c + d*x))/(e + f*x)^3,x]","\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}","\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,"(d^2*F^(a + b/(c + d*x)))/(2*f*(d*e - c*f)^2) - F^(a + b/(c + d*x))/(2*f*(e + f*x)^2) - (b*d^2*F^(a + b/(c + d*x))*Log[F])/(2*(d*e - c*f)^3) + (b*d*F^(a + b/(c + d*x))*Log[F])/(2*(d*e - c*f)^2*(e + f*x)) - (b*d^2*F^(a - (b*f)/(d*e - c*f))*ExpIntegralEi[(b*d*(e + f*x)*Log[F])/((d*e - c*f)*(c + d*x))]*Log[F])/(d*e - c*f)^3 + (b^2*d^2*f*F^(a - (b*f)/(d*e - c*f))*ExpIntegralEi[(b*d*(e + f*x)*Log[F])/((d*e - c*f)*(c + d*x))]*Log[F]^2)/(2*(d*e - c*f)^4)","A",18,7,21,0.3333,1,"{2223, 6742, 2209, 2210, 2222, 2228, 2178}"
400,1,460,0,3.7510583,"\int \frac{F^{a+\frac{b}{c+d x}}}{(e+f x)^4} \, dx","Int[F^(a + b/(c + d*x))/(e + f*x)^4,x]","-\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^2 f \log ^2(F) F^{a+\frac{b}{c+d x}}}{6 (e+f x) (d e-c f)^4}+\frac{b^2 d^3 f \log ^2(F) F^{a+\frac{b}{c+d x}}}{6 (d e-c f)^5}-\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{2 b d^2 \log (F) F^{a+\frac{b}{c+d x}}}{3 (e+f x) (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{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}","-\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^2 f \log ^2(F) F^{a+\frac{b}{c+d x}}}{6 (e+f x) (d e-c f)^4}+\frac{b^2 d^3 f \log ^2(F) F^{a+\frac{b}{c+d x}}}{6 (d e-c f)^5}-\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{2 b d^2 \log (F) F^{a+\frac{b}{c+d x}}}{3 (e+f x) (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{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,"(d^3*F^(a + b/(c + d*x)))/(3*f*(d*e - c*f)^3) - F^(a + b/(c + d*x))/(3*f*(e + f*x)^3) - (5*b*d^3*F^(a + b/(c + d*x))*Log[F])/(6*(d*e - c*f)^4) + (b*d*F^(a + b/(c + d*x))*Log[F])/(6*(d*e - c*f)^2*(e + f*x)^2) + (2*b*d^2*F^(a + b/(c + d*x))*Log[F])/(3*(d*e - c*f)^3*(e + f*x)) - (b*d^3*F^(a - (b*f)/(d*e - c*f))*ExpIntegralEi[(b*d*(e + f*x)*Log[F])/((d*e - c*f)*(c + d*x))]*Log[F])/(d*e - c*f)^4 + (b^2*d^3*f*F^(a + b/(c + d*x))*Log[F]^2)/(6*(d*e - c*f)^5) - (b^2*d^2*f*F^(a + b/(c + d*x))*Log[F]^2)/(6*(d*e - c*f)^4*(e + f*x)) + (b^2*d^3*f*F^(a - (b*f)/(d*e - c*f))*ExpIntegralEi[(b*d*(e + f*x)*Log[F])/((d*e - c*f)*(c + d*x))]*Log[F]^2)/(d*e - c*f)^5 - (b^3*d^3*f^2*F^(a - (b*f)/(d*e - c*f))*ExpIntegralEi[(b*d*(e + f*x)*Log[F])/((d*e - c*f)*(c + d*x))]*Log[F]^3)/(6*(d*e - c*f)^6)","A",36,7,21,0.3333,1,"{2223, 6742, 2209, 2210, 2222, 2228, 2178}"
401,1,346,0,0.3617788,"\int e^{\frac{e}{c+d x}} (a+b x)^4 \, dx","Int[E^(e/(c + d*x))*(a + b*x)^4,x]","-\frac{4 b^3 e^4 (b c-a d) \text{Gamma}\left(-4,-\frac{e}{c+d x}\right)}{d^5}-\frac{b^4 e^5 \text{Gamma}\left(-5,-\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{4 b^3 e^4 (b c-a d) \text{Gamma}\left(-4,-\frac{e}{c+d x}\right)}{d^5}-\frac{b^4 e^5 \text{Gamma}\left(-5,-\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}",1,"((b*c - a*d)^4*E^(e/(c + d*x))*(c + d*x))/d^5 - (2*b*(b*c - a*d)^3*e*E^(e/(c + d*x))*(c + d*x))/d^5 + (b^2*(b*c - a*d)^2*e^2*E^(e/(c + d*x))*(c + d*x))/d^5 - (2*b*(b*c - a*d)^3*E^(e/(c + d*x))*(c + d*x)^2)/d^5 + (b^2*(b*c - a*d)^2*e*E^(e/(c + d*x))*(c + d*x)^2)/d^5 + (2*b^2*(b*c - a*d)^2*E^(e/(c + d*x))*(c + d*x)^3)/d^5 - ((b*c - a*d)^4*e*ExpIntegralEi[e/(c + d*x)])/d^5 + (2*b*(b*c - a*d)^3*e^2*ExpIntegralEi[e/(c + d*x)])/d^5 - (b^2*(b*c - a*d)^2*e^3*ExpIntegralEi[e/(c + d*x)])/d^5 - (b^4*e^5*Gamma[-5, -(e/(c + d*x))])/d^5 - (4*b^3*(b*c - a*d)*e^4*Gamma[-4, -(e/(c + d*x))])/d^5","A",13,5,19,0.2632,1,"{2226, 2206, 2210, 2214, 2218}"
402,1,320,0,0.3170496,"\int e^{\frac{e}{c+d x}} (a+b x)^3 \, dx","Int[E^(e/(c + d*x))*(a + b*x)^3,x]","\frac{b^3 e^4 \text{Gamma}\left(-4,-\frac{e}{c+d x}\right)}{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 \text{Gamma}\left(-4,-\frac{e}{c+d x}\right)}{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}",1,"-(((b*c - a*d)^3*E^(e/(c + d*x))*(c + d*x))/d^4) + (3*b*(b*c - a*d)^2*e*E^(e/(c + d*x))*(c + d*x))/(2*d^4) - (b^2*(b*c - a*d)*e^2*E^(e/(c + d*x))*(c + d*x))/(2*d^4) + (3*b*(b*c - a*d)^2*E^(e/(c + d*x))*(c + d*x)^2)/(2*d^4) - (b^2*(b*c - a*d)*e*E^(e/(c + d*x))*(c + d*x)^2)/(2*d^4) - (b^2*(b*c - a*d)*E^(e/(c + d*x))*(c + d*x)^3)/d^4 + ((b*c - a*d)^3*e*ExpIntegralEi[e/(c + d*x)])/d^4 - (3*b*(b*c - a*d)^2*e^2*ExpIntegralEi[e/(c + d*x)])/(2*d^4) + (b^2*(b*c - a*d)*e^3*ExpIntegralEi[e/(c + d*x)])/(2*d^4) + (b^3*e^4*Gamma[-4, -(e/(c + d*x))])/d^4","A",12,5,19,0.2632,1,"{2226, 2206, 2210, 2214, 2218}"
403,1,255,0,0.2561845,"\int e^{\frac{e}{c+d x}} (a+b x)^2 \, dx","Int[E^(e/(c + d*x))*(a + b*x)^2,x]","\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}","\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,"((b*c - a*d)^2*E^(e/(c + d*x))*(c + d*x))/d^3 - (b*(b*c - a*d)*e*E^(e/(c + d*x))*(c + d*x))/d^3 + (b^2*e^2*E^(e/(c + d*x))*(c + d*x))/(6*d^3) - (b*(b*c - a*d)*E^(e/(c + d*x))*(c + d*x)^2)/d^3 + (b^2*e*E^(e/(c + d*x))*(c + d*x)^2)/(6*d^3) + (b^2*E^(e/(c + d*x))*(c + d*x)^3)/(3*d^3) - ((b*c - a*d)^2*e*ExpIntegralEi[e/(c + d*x)])/d^3 + (b*(b*c - a*d)*e^2*ExpIntegralEi[e/(c + d*x)])/d^3 - (b^2*e^3*ExpIntegralEi[e/(c + d*x)])/(6*d^3)","A",11,4,19,0.2105,1,"{2226, 2206, 2210, 2214}"
404,1,125,0,0.1284174,"\int e^{\frac{e}{c+d x}} (a+b x) \, dx","Int[E^(e/(c + d*x))*(a + b*x),x]","\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}","\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,"-(((b*c - a*d)*E^(e/(c + d*x))*(c + d*x))/d^2) + (b*e*E^(e/(c + d*x))*(c + d*x))/(2*d^2) + (b*E^(e/(c + d*x))*(c + d*x)^2)/(2*d^2) + ((b*c - a*d)*e*ExpIntegralEi[e/(c + d*x)])/d^2 - (b*e^2*ExpIntegralEi[e/(c + d*x)])/(2*d^2)","A",7,4,17,0.2353,1,"{2226, 2206, 2210, 2214}"
405,1,37,0,0.0301463,"\int e^{\frac{e}{c+d x}} \, dx","Int[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",2,2,11,0.1818,1,"{2206, 2210}"
406,1,62,0,0.2025668,"\int \frac{e^{\frac{e}{c+d x}}}{a+b x} \, dx","Int[E^(e/(c + d*x))/(a + b*x),x]","\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}","\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)]/b) + (E^((b*e)/(b*c - a*d))*ExpIntegralEi[-((d*e*(a + b*x))/((b*c - a*d)*(c + d*x)))])/b","A",4,4,19,0.2105,1,"{2222, 2210, 2228, 2178}"
407,1,107,0,0.5445278,"\int \frac{e^{\frac{e}{c+d x}}}{(a+b x)^2} \, dx","Int[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{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)}","-\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[-((d*e*(a + b*x))/((b*c - a*d)*(c + d*x)))])/(b*c - a*d)^2","A",9,7,19,0.3684,1,"{2223, 6742, 2222, 2210, 2228, 2178, 2209}"
408,1,240,0,1.036562,"\int \frac{e^{\frac{e}{c+d x}}}{(a+b x)^3} \, dx","Int[E^(e/(c + d*x))/(a + b*x)^3,x]","\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}","\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,"(d^2*E^(e/(c + d*x)))/(2*b*(b*c - a*d)^2) + (d^2*e*E^(e/(c + d*x)))/(2*(b*c - a*d)^3) - E^(e/(c + d*x))/(2*b*(a + b*x)^2) + (d*e*E^(e/(c + d*x)))/(2*(b*c - a*d)^2*(a + b*x)) + (d^2*e*E^((b*e)/(b*c - a*d))*ExpIntegralEi[-((d*e*(a + b*x))/((b*c - a*d)*(c + d*x)))])/(b*c - a*d)^3 + (b*d^2*e^2*E^((b*e)/(b*c - a*d))*ExpIntegralEi[-((d*e*(a + b*x))/((b*c - a*d)*(c + d*x)))])/(2*(b*c - a*d)^4)","A",18,7,19,0.3684,1,"{2223, 6742, 2222, 2210, 2228, 2178, 2209}"
409,1,322,0,0.3387774,"\int e^{\frac{e}{(c+d x)^2}} (a+b x)^3 \, dx","Int[E^(e/(c + d*x)^2)*(a + b*x)^3,x]","\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}","\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,"-(((b*c - a*d)^3*E^(e/(c + d*x)^2)*(c + d*x))/d^4) - (2*b^2*(b*c - a*d)*e*E^(e/(c + d*x)^2)*(c + d*x))/d^4 + (3*b*(b*c - a*d)^2*E^(e/(c + d*x)^2)*(c + d*x)^2)/(2*d^4) + (b^3*e*E^(e/(c + d*x)^2)*(c + d*x)^2)/(4*d^4) - (b^2*(b*c - a*d)*E^(e/(c + d*x)^2)*(c + d*x)^3)/d^4 + (b^3*E^(e/(c + d*x)^2)*(c + d*x)^4)/(4*d^4) + ((b*c - a*d)^3*Sqrt[e]*Sqrt[Pi]*Erfi[Sqrt[e]/(c + d*x)])/d^4 + (2*b^2*(b*c - a*d)*e^(3/2)*Sqrt[Pi]*Erfi[Sqrt[e]/(c + d*x)])/d^4 - (3*b*(b*c - a*d)^2*e*ExpIntegralEi[e/(c + d*x)^2])/(2*d^4) - (b^3*e^2*ExpIntegralEi[e/(c + d*x)^2])/(4*d^4)","A",14,6,19,0.3158,1,"{2226, 2206, 2211, 2204, 2214, 2210}"
410,1,215,0,0.2332288,"\int e^{\frac{e}{(c+d x)^2}} (a+b x)^2 \, dx","Int[E^(e/(c + d*x)^2)*(a + b*x)^2,x]","-\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}","-\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,"((b*c - a*d)^2*E^(e/(c + d*x)^2)*(c + d*x))/d^3 + (2*b^2*e*E^(e/(c + d*x)^2)*(c + d*x))/(3*d^3) - (b*(b*c - a*d)*E^(e/(c + d*x)^2)*(c + d*x)^2)/d^3 + (b^2*E^(e/(c + d*x)^2)*(c + d*x)^3)/(3*d^3) - ((b*c - a*d)^2*Sqrt[e]*Sqrt[Pi]*Erfi[Sqrt[e]/(c + d*x)])/d^3 - (2*b^2*e^(3/2)*Sqrt[Pi]*Erfi[Sqrt[e]/(c + d*x)])/(3*d^3) + (b*(b*c - a*d)*e*ExpIntegralEi[e/(c + d*x)^2])/d^3","A",11,6,19,0.3158,1,"{2226, 2206, 2211, 2204, 2214, 2210}"
411,1,111,0,0.1294923,"\int e^{\frac{e}{(c+d x)^2}} (a+b x) \, dx","Int[E^(e/(c + d*x)^2)*(a + b*x),x]","\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}","\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,"-(((b*c - a*d)*E^(e/(c + d*x)^2)*(c + d*x))/d^2) + (b*E^(e/(c + d*x)^2)*(c + d*x)^2)/(2*d^2) + ((b*c - a*d)*Sqrt[e]*Sqrt[Pi]*Erfi[Sqrt[e]/(c + d*x)])/d^2 - (b*e*ExpIntegralEi[e/(c + d*x)^2])/(2*d^2)","A",7,6,17,0.3529,1,"{2226, 2206, 2211, 2204, 2214, 2210}"
412,1,50,0,0.0399308,"\int e^{\frac{e}{(c+d x)^2}} \, dx","Int[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",3,3,11,0.2727,1,"{2206, 2211, 2204}"
413,0,0,0,0.0230121,"\int \frac{e^{\frac{e}{(c+d x)^2}}}{a+b x} \, dx","Int[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,"Defer[Int][E^(e/(c + d*x)^2)/(a + b*x), x]","A",0,0,0,0,-1,"{}"
414,0,0,0,0.0575595,"\int \frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^2} \, dx","Int[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,"Defer[Int][E^(e/(c + d*x)^2)/(a + b*x)^2, x]","A",0,0,0,0,-1,"{}"
415,0,0,0,0.0530332,"\int \frac{e^{\frac{e}{(c+d x)^2}}}{(a+b x)^3} \, dx","Int[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,"Defer[Int][E^(e/(c + d*x)^2)/(a + b*x)^3, x]","A",0,0,0,0,-1,"{}"
416,1,206,0,0.189264,"\int e^{\frac{e}{(c+d x)^3}} (a+b x)^3 \, dx","Int[E^(e/(c + d*x)^3)*(a + b*x)^3,x]","\frac{b (c+d x)^2 (b c-a d)^2 \left(-\frac{e}{(c+d x)^3}\right)^{2/3} \text{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}} \text{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} \text{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} \text{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}} \text{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} \text{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}",1,"-((b^2*(b*c - a*d)*E^(e/(c + d*x)^3)*(c + d*x)^3)/d^4) + (b^2*(b*c - a*d)*e*ExpIntegralEi[e/(c + d*x)^3])/d^4 + (b^3*(-(e/(c + d*x)^3))^(4/3)*(c + d*x)^4*Gamma[-4/3, -(e/(c + d*x)^3)])/(3*d^4) + (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)])/d^4 - ((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",7,5,19,0.2632,1,"{2226, 2208, 2218, 2214, 2210}"
417,1,151,0,0.1331736,"\int e^{\frac{e}{(c+d x)^3}} (a+b x)^2 \, dx","Int[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} \text{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}} \text{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}","-\frac{2 b (c+d x)^2 (b c-a d) \left(-\frac{e}{(c+d x)^3}\right)^{2/3} \text{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}} \text{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)/(3*d^3) - (b^2*e*ExpIntegralEi[e/(c + d*x)^3])/(3*d^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)])/(3*d^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",6,5,19,0.2632,1,"{2226, 2208, 2218, 2214, 2210}"
418,1,92,0,0.0567096,"\int e^{\frac{e}{(c+d x)^3}} (a+b x) \, dx","Int[E^(e/(c + d*x)^3)*(a + b*x),x]","\frac{b (c+d x)^2 \left(-\frac{e}{(c+d x)^3}\right)^{2/3} \text{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}} \text{Gamma}\left(-\frac{1}{3},-\frac{e}{(c+d x)^3}\right)}{3 d^2}","\frac{b (c+d x)^2 \left(-\frac{e}{(c+d x)^3}\right)^{2/3} \text{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}} \text{Gamma}\left(-\frac{1}{3},-\frac{e}{(c+d x)^3}\right)}{3 d^2}",1,"(b*(-(e/(c + d*x)^3))^(2/3)*(c + d*x)^2*Gamma[-2/3, -(e/(c + d*x)^3)])/(3*d^2) - ((b*c - a*d)*(-(e/(c + d*x)^3))^(1/3)*(c + d*x)*Gamma[-1/3, -(e/(c + d*x)^3)])/(3*d^2)","A",4,3,17,0.1765,1,"{2226, 2208, 2218}"
419,1,40,0,0.0055857,"\int e^{\frac{e}{(c+d x)^3}} \, dx","Int[E^(e/(c + d*x)^3),x]","\frac{(c+d x) \sqrt[3]{-\frac{e}{(c+d x)^3}} \text{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}} \text{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",1,1,11,0.09091,1,"{2208}"
420,0,0,0,0.0222072,"\int \frac{e^{\frac{e}{(c+d x)^3}}}{a+b x} \, dx","Int[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,"Defer[Int][E^(e/(c + d*x)^3)/(a + b*x), x]","A",0,0,0,0,-1,"{}"
421,0,0,0,0.0573897,"\int \frac{e^{\frac{e}{(c+d x)^3}}}{(a+b x)^2} \, dx","Int[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,"Defer[Int][E^(e/(c + d*x)^3)/(a + b*x)^2, x]","A",0,0,0,0,-1,"{}"
422,1,104,0,1.0455923,"\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{g+h x} \, dx","Int[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x),x]","\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}","\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 - a*d)*f*Log[F])/(d*(c + d*x)))])/h) + (F^(e + (f*(b*g - a*h))/(d*g - c*h))*ExpIntegralEi[-(((b*c - a*d)*f*(g + h*x)*Log[F])/((d*g - c*h)*(c + d*x)))])/h","A",5,5,26,0.1923,1,"{2231, 2230, 2210, 2233, 2178}"
423,1,159,0,2.5586694,"\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{(g+h x)^2} \, dx","Int[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x)^2,x]","\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)}","\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,"(d*F^(e + (b*f)/d - ((b*c - a*d)*f)/(d*(c + d*x))))/(h*(d*g - c*h)) - F^(e + (f*(a + b*x))/(c + d*x))/(h*(g + h*x)) + ((b*c - a*d)*f*F^(e + (f*(b*g - a*h))/(d*g - c*h))*ExpIntegralEi[-(((b*c - a*d)*f*(g + h*x)*Log[F])/((d*g - c*h)*(c + d*x)))]*Log[F])/(d*g - c*h)^2","A",12,8,26,0.3077,1,"{2232, 6742, 2230, 2209, 2210, 2231, 2233, 2178}"
424,1,366,0,4.7574851,"\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{(g+h x)^3} \, dx","Int[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x)^3,x]","\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}","\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,"(d^2*F^(e + (b*f)/d - ((b*c - a*d)*f)/(d*(c + d*x))))/(2*h*(d*g - c*h)^2) - F^(e + (f*(a + b*x))/(c + d*x))/(2*h*(g + h*x)^2) + (d*(b*c - a*d)*f*F^(e + (b*f)/d - ((b*c - a*d)*f)/(d*(c + d*x)))*Log[F])/(2*(d*g - c*h)^3) - ((b*c - a*d)*f*F^(e + (f*(a + b*x))/(c + d*x))*Log[F])/(2*(d*g - c*h)^2*(g + h*x)) + (d*(b*c - a*d)*f*F^(e + (f*(b*g - a*h))/(d*g - c*h))*ExpIntegralEi[-(((b*c - a*d)*f*(g + h*x)*Log[F])/((d*g - c*h)*(c + d*x)))]*Log[F])/(d*g - c*h)^3 + ((b*c - a*d)^2*f^2*F^(e + (f*(b*g - a*h))/(d*g - c*h))*h*ExpIntegralEi[-(((b*c - a*d)*f*(g + h*x)*Log[F])/((d*g - c*h)*(c + d*x)))]*Log[F]^2)/(2*(d*g - c*h)^4)","A",24,8,26,0.3077,1,"{2232, 6742, 2230, 2209, 2210, 2231, 2233, 2178}"
425,1,634,0,9.4052368,"\int \frac{F^{e+\frac{f (a+b x)}{c+d x}}}{(g+h x)^4} \, dx","Int[F^(e + (f*(a + b*x))/(c + d*x))/(g + h*x)^4,x]","\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{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{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}","\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{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{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,"(d^3*F^(e + (b*f)/d - ((b*c - a*d)*f)/(d*(c + d*x))))/(3*h*(d*g - c*h)^3) - F^(e + (f*(a + b*x))/(c + d*x))/(3*h*(g + h*x)^3) + (5*d^2*(b*c - a*d)*f*F^(e + (b*f)/d - ((b*c - a*d)*f)/(d*(c + d*x)))*Log[F])/(6*(d*g - c*h)^4) - ((b*c - a*d)*f*F^(e + (f*(a + b*x))/(c + d*x))*Log[F])/(6*(d*g - c*h)^2*(g + h*x)^2) - (2*d*(b*c - a*d)*f*F^(e + (f*(a + b*x))/(c + d*x))*Log[F])/(3*(d*g - c*h)^3*(g + h*x)) + (d^2*(b*c - a*d)*f*F^(e + (f*(b*g - a*h))/(d*g - c*h))*ExpIntegralEi[-(((b*c - a*d)*f*(g + h*x)*Log[F])/((d*g - c*h)*(c + d*x)))]*Log[F])/(d*g - c*h)^4 + (d*(b*c - a*d)^2*f^2*F^(e + (b*f)/d - ((b*c - a*d)*f)/(d*(c + d*x)))*h*Log[F]^2)/(6*(d*g - c*h)^5) - ((b*c - a*d)^2*f^2*F^(e + (f*(a + b*x))/(c + d*x))*h*Log[F]^2)/(6*(d*g - c*h)^4*(g + h*x)) + (d*(b*c - a*d)^2*f^2*F^(e + (f*(b*g - a*h))/(d*g - c*h))*h*ExpIntegralEi[-(((b*c - a*d)*f*(g + h*x)*Log[F])/((d*g - c*h)*(c + d*x)))]*Log[F]^2)/(d*g - c*h)^5 + ((b*c - a*d)^3*f^3*F^(e + (f*(b*g - a*h))/(d*g - c*h))*h^2*ExpIntegralEi[-(((b*c - a*d)*f*(g + h*x)*Log[F])/((d*g - c*h)*(c + d*x)))]*Log[F]^3)/(6*(d*g - c*h)^6)","A",48,8,26,0.3077,1,"{2232, 6742, 2230, 2209, 2210, 2231, 2233, 2178}"
426,1,217,0,0.2308306,"\int f^{a+b x+c x^2} x^3 \, dx","Int[f^(a + b*x + c*x^2)*x^3,x]","\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{\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{b^2 f^{a+b x+c x^2}}{8 c^3 \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)}","\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{\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{b^2 f^{a+b x+c x^2}}{8 c^3 \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*x + c*x^2)/(2*c^2*Log[f]^2) + (3*b*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(8*c^(5/2)*Log[f]^(3/2)) + (b^2*f^(a + b*x + c*x^2))/(8*c^3*Log[f]) - (b*f^(a + b*x + c*x^2)*x)/(4*c^2*Log[f]) + (f^(a + b*x + c*x^2)*x^2)/(2*c*Log[f]) - (b^3*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(16*c^(7/2)*Sqrt[Log[f]])","A",10,4,16,0.2500,1,"{2241, 2240, 2234, 2204}"
427,1,164,0,0.0925418,"\int f^{a+b x+c x^2} x^2 \, dx","Int[f^(a + b*x + c*x^2)*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)}{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)}","-\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))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(4*c^(3/2)*Log[f]^(3/2)) - (b*f^(a + b*x + c*x^2))/(4*c^2*Log[f]) + (f^(a + b*x + c*x^2)*x)/(2*c*Log[f]) + (b^2*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(8*c^(5/2)*Sqrt[Log[f]])","A",6,4,16,0.2500,1,"{2241, 2240, 2234, 2204}"
428,1,81,0,0.0383484,"\int f^{a+b x+c x^2} x \, dx","Int[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",3,3,14,0.2143,1,"{2240, 2234, 2204}"
429,1,56,0,0.0149092,"\int f^{a+b x+c x^2} \, dx","Int[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",2,2,12,0.1667,1,"{2234, 2204}"
430,0,0,0,0.0254935,"\int \frac{f^{a+b x+c x^2}}{x} \, dx","Int[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,"Defer[Int][f^(a + b*x + c*x^2)/x, x]","A",0,0,0,0,-1,"{}"
431,0,0,0,0.0759386,"\int \frac{f^{a+b x+c x^2}}{x^2} \, dx","Int[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,"-(f^(a + b*x + c*x^2)/x) + Sqrt[c]*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]] + b*Log[f]*Defer[Int][f^(a + b*x + c*x^2)/x, x]","A",0,0,0,0,-1,"{}"
432,1,181,0,0.1787448,"\int e^{a+b x-c x^2} x^3 \, dx","Int[E^(a + b*x - c*x^2)*x^3,x]","-\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{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{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}","-\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{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{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,"-(b^2*E^(a + b*x - c*x^2))/(8*c^3) - E^(a + b*x - c*x^2)/(2*c^2) - (b*E^(a + b*x - c*x^2)*x)/(4*c^2) - (E^(a + b*x - c*x^2)*x^2)/(2*c) - (b^3*E^(a + b^2/(4*c))*Sqrt[Pi]*Erf[(b - 2*c*x)/(2*Sqrt[c])])/(16*c^(7/2)) - (3*b*E^(a + b^2/(4*c))*Sqrt[Pi]*Erf[(b - 2*c*x)/(2*Sqrt[c])])/(8*c^(5/2))","A",10,4,17,0.2353,1,"{2241, 2240, 2234, 2205}"
433,1,134,0,0.0821288,"\int e^{a+b x-c x^2} x^2 \, dx","Int[E^(a + b*x - c*x^2)*x^2,x]","-\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}","-\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,"-(b*E^(a + b*x - c*x^2))/(4*c^2) - (E^(a + b*x - c*x^2)*x)/(2*c) - (b^2*E^(a + b^2/(4*c))*Sqrt[Pi]*Erf[(b - 2*c*x)/(2*Sqrt[c])])/(8*c^(5/2)) - (E^(a + b^2/(4*c))*Sqrt[Pi]*Erf[(b - 2*c*x)/(2*Sqrt[c])])/(4*c^(3/2))","A",6,4,17,0.2353,1,"{2241, 2240, 2234, 2205}"
434,1,66,0,0.0323039,"\int e^{a+b x-c x^2} x \, dx","Int[E^(a + b*x - c*x^2)*x,x]","-\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}","-\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,"-E^(a + b*x - c*x^2)/(2*c) - (b*E^(a + b^2/(4*c))*Sqrt[Pi]*Erf[(b - 2*c*x)/(2*Sqrt[c])])/(4*c^(3/2))","A",3,3,15,0.2000,1,"{2240, 2234, 2205}"
435,1,44,0,0.0107908,"\int e^{a+b x-c x^2} \, dx","Int[E^(a + b*x - c*x^2),x]","-\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}}","-\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",2,2,13,0.1538,1,"{2234, 2205}"
436,0,0,0,0.0276418,"\int \frac{e^{a+b x-c x^2}}{x} \, dx","Int[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,"Defer[Int][E^(a + b*x - c*x^2)/x, x]","A",0,0,0,0,-1,"{}"
437,0,0,0,0.0705695,"\int \frac{e^{a+b x-c x^2}}{x^2} \, dx","Int[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,"-(E^(a + b*x - c*x^2)/x) + Sqrt[c]*E^(a + b^2/(4*c))*Sqrt[Pi]*Erf[(b - 2*c*x)/(2*Sqrt[c])] + b*Defer[Int][E^(a + b*x - c*x^2)/x, x]","A",0,0,0,0,-1,"{}"
438,1,297,0,0.6358603,"\int e^{(a+b x) (c+d x)} x^3 \, dx","Int[E^((a + b*x)*(c + d*x))*x^3,x]","-\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}","-\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,"-E^(a*c + (b*c + a*d)*x + b*d*x^2)/(2*b^2*d^2) + ((b*c + a*d)^2*E^(a*c + (b*c + a*d)*x + b*d*x^2))/(8*b^3*d^3) - ((b*c + a*d)*E^(a*c + (b*c + a*d)*x + b*d*x^2)*x)/(4*b^2*d^2) + (E^(a*c + (b*c + a*d)*x + b*d*x^2)*x^2)/(2*b*d) + (3*(b*c + a*d)*Sqrt[Pi]*Erfi[(b*c + a*d + 2*b*d*x)/(2*Sqrt[b]*Sqrt[d])])/(8*b^(5/2)*d^(5/2)*E^((b*c - a*d)^2/(4*b*d))) - ((b*c + a*d)^3*Sqrt[Pi]*Erfi[(b*c + a*d + 2*b*d*x)/(2*Sqrt[b]*Sqrt[d])])/(16*b^(7/2)*d^(7/2)*E^((b*c - a*d)^2/(4*b*d)))","A",11,5,17,0.2941,1,"{2244, 2241, 2240, 2234, 2204}"
439,1,216,0,0.2713861,"\int e^{(a+b x) (c+d x)} x^2 \, dx","Int[E^((a + b*x)*(c + d*x))*x^2,x]","\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}","\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,"-((b*c + a*d)*E^(a*c + (b*c + a*d)*x + b*d*x^2))/(4*b^2*d^2) + (E^(a*c + (b*c + a*d)*x + b*d*x^2)*x)/(2*b*d) - (Sqrt[Pi]*Erfi[(b*c + a*d + 2*b*d*x)/(2*Sqrt[b]*Sqrt[d])])/(4*b^(3/2)*d^(3/2)*E^((b*c - a*d)^2/(4*b*d))) + ((b*c + a*d)^2*Sqrt[Pi]*Erfi[(b*c + a*d + 2*b*d*x)/(2*Sqrt[b]*Sqrt[d])])/(8*b^(5/2)*d^(5/2)*E^((b*c - a*d)^2/(4*b*d)))","A",7,5,17,0.2941,1,"{2244, 2241, 2240, 2234, 2204}"
440,1,107,0,0.1041867,"\int e^{(a+b x) (c+d x)} x \, dx","Int[E^((a + b*x)*(c + d*x))*x,x]","\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}}","\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,"E^(a*c + (b*c + a*d)*x + b*d*x^2)/(2*b*d) - ((b*c + a*d)*Sqrt[Pi]*Erfi[(b*c + a*d + 2*b*d*x)/(2*Sqrt[b]*Sqrt[d])])/(4*b^(3/2)*d^(3/2)*E^((b*c - a*d)^2/(4*b*d)))","A",4,4,15,0.2667,1,"{2244, 2240, 2234, 2204}"
441,1,68,0,0.0254584,"\int e^{(a+b x) (c+d x)} \, dx","Int[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 b 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[(b*c + a*d + 2*b*d*x)/(2*Sqrt[b]*Sqrt[d])])/(2*Sqrt[b]*Sqrt[d]*E^((b*c - a*d)^2/(4*b*d)))","A",3,3,13,0.2308,1,"{2235, 2234, 2204}"
442,0,0,0,0.138539,"\int \frac{e^{(a+b x) (c+d x)}}{x} \, dx","Int[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,"Defer[Int][E^(a*c + (b*c + a*d)*x + b*d*x^2)/x, x]","A",0,0,0,0,-1,"{}"
443,0,0,0,0.2645861,"\int \frac{e^{(a+b x) (c+d x)}}{x^2} \, dx","Int[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,"-(E^(a*c + (b*c + a*d)*x + b*d*x^2)/x) + (Sqrt[b]*Sqrt[d]*Sqrt[Pi]*Erfi[(b*c + a*d + 2*b*d*x)/(2*Sqrt[b]*Sqrt[d])])/E^((b*c - a*d)^2/(4*b*d)) + (b*c + a*d)*Defer[Int][E^(a*c + (b*c + a*d)*x + b*d*x^2)/x, x]","A",0,0,0,0,-1,"{}"
444,1,266,0,0.3237496,"\int f^{a+b x+c x^2} (d+e x)^3 \, dx","Int[f^(a + b*x + c*x^2)*(d + e*x)^3,x]","-\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)}","-\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,"-(e^3*f^(a + b*x + c*x^2))/(2*c^2*Log[f]^2) - (3*e^2*(2*c*d - b*e)*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(8*c^(5/2)*Log[f]^(3/2)) + (e*(2*c*d - b*e)^2*f^(a + b*x + c*x^2))/(8*c^3*Log[f]) + (e*(2*c*d - b*e)*f^(a + b*x + c*x^2)*(d + e*x))/(4*c^2*Log[f]) + (e*f^(a + b*x + c*x^2)*(d + e*x)^2)/(2*c*Log[f]) + ((2*c*d - b*e)^3*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(16*c^(7/2)*Sqrt[Log[f]])","A",10,4,20,0.2000,1,"{2241, 2240, 2234, 2204}"
445,1,189,0,0.1080719,"\int f^{a+b x+c x^2} (d+e x)^2 \, dx","Int[f^(a + b*x + c*x^2)*(d + e*x)^2,x]","\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)}","\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,"-(e^2*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(4*c^(3/2)*Log[f]^(3/2)) + (e*(2*c*d - b*e)*f^(a + b*x + c*x^2))/(4*c^2*Log[f]) + (e*f^(a + b*x + c*x^2)*(d + e*x))/(2*c*Log[f]) + ((2*c*d - b*e)^2*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/(8*c^(5/2)*Sqrt[Log[f]])","A",6,4,20,0.2000,1,"{2241, 2240, 2234, 2204}"
446,1,90,0,0.0411925,"\int f^{a+b x+c x^2} (d+e x) \, dx","Int[f^(a + b*x + c*x^2)*(d + e*x),x]","\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)}","\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,"(e*f^(a + b*x + c*x^2))/(2*c*Log[f]) + ((2*c*d - b*e)*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",3,3,18,0.1667,1,"{2240, 2234, 2204}"
447,0,0,0,0.0305396,"\int \frac{f^{a+b x+c x^2}}{d+e x} \, dx","Int[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,"Defer[Int][f^(a + b*x + c*x^2)/(d + e*x), x]","A",0,0,0,0,-1,"{}"
448,0,0,0,0.1031325,"\int \frac{f^{a+b x+c x^2}}{(d+e x)^2} \, dx","Int[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,"-(f^(a + b*x + c*x^2)/(e*(d + e*x))) + (Sqrt[c]*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]])/e^2 - ((2*c*d - b*e)*Log[f]*Defer[Int][f^(a + b*x + c*x^2)/(d + e*x), x])/e^2","A",0,0,0,0,-1,"{}"
449,0,0,0,0.2080533,"\int \frac{f^{a+b x+c x^2}}{(d+e x)^3} \, dx","Int[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,"-f^(a + b*x + c*x^2)/(2*e*(d + e*x)^2) + ((2*c*d - b*e)*f^(a + b*x + c*x^2)*Log[f])/(2*e^3*(d + e*x)) - (Sqrt[c]*(2*c*d - b*e)*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Log[f]^(3/2))/(2*e^4) + (c*Log[f]*Defer[Int][f^(a + b*x + c*x^2)/(d + e*x), x])/e^2 + ((2*c*d - b*e)^2*Log[f]^2*Defer[Int][f^(a + b*x + c*x^2)/(d + e*x), x])/(2*e^4)","A",0,0,0,0,-1,"{}"
450,1,45,0,0.0556069,"\int f^{a+b x+c x^2} (b+2 c x)^3 \, dx","Int[f^(a + b*x + c*x^2)*(b + 2*c*x)^3,x]","\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)}","\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,"(-4*c*f^(a + b*x + c*x^2))/Log[f]^2 + (f^(a + b*x + c*x^2)*(b + 2*c*x)^2)/Log[f]","A",2,2,21,0.09524,1,"{2237, 2236}"
451,1,78,0,0.0555783,"\int f^{a+b x+c x^2} (b+2 c x)^2 \, dx","Int[f^(a + b*x + c*x^2)*(b + 2*c*x)^2,x]","\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)}","\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,"-((Sqrt[c]*f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])])/Log[f]^(3/2)) + (f^(a + b*x + c*x^2)*(b + 2*c*x))/Log[f]","A",3,3,21,0.1429,1,"{2237, 2234, 2204}"
452,1,17,0,0.0174103,"\int f^{a+b x+c x^2} (b+2 c x) \, dx","Int[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",1,1,19,0.05263,1,"{2236}"
453,1,39,0,0.0371917,"\int \frac{f^{a+b x+c x^2}}{b+2 c x} \, dx","Int[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",1,1,21,0.04762,1,"{2238}"
454,1,84,0,0.0551733,"\int \frac{f^{a+b x+c x^2}}{(b+2 c x)^2} \, dx","Int[f^(a + b*x + c*x^2)/(b + 2*c*x)^2,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)}","\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*x + c*x^2)/(2*c*(b + 2*c*x)) + (f^(a - b^2/(4*c))*Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]])/(4*c^(3/2))","A",3,3,21,0.1429,1,"{2239, 2234, 2204}"
455,1,69,0,0.0706892,"\int \frac{f^{a+b x+c x^2}}{(b+2 c x)^3} \, dx","Int[f^(a + b*x + c*x^2)/(b + 2*c*x)^3,x]","\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}","\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*x + c*x^2)/(4*c*(b + 2*c*x)^2) + (f^(a - b^2/(4*c))*ExpIntegralEi[((b + 2*c*x)^2*Log[f])/(4*c)]*Log[f])/(16*c^2)","A",2,2,21,0.09524,1,"{2239, 2238}"
456,1,43,0,0.0433466,"\int f^{b x+c x^2} (b+2 c x)^3 \, dx","Int[f^(b*x + c*x^2)*(b + 2*c*x)^3,x]","\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)}","\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,"(-4*c*f^(b*x + c*x^2))/Log[f]^2 + (f^(b*x + c*x^2)*(b + 2*c*x)^2)/Log[f]","A",2,2,20,0.1000,1,"{2237, 2236}"
457,1,75,0,0.0575022,"\int f^{b x+c x^2} (b+2 c x)^2 \, dx","Int[f^(b*x + c*x^2)*(b + 2*c*x)^2,x]","\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)}","\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/(4*c))*Log[f]^(3/2))) + (f^(b*x + c*x^2)*(b + 2*c*x))/Log[f]","A",3,3,20,0.1500,1,"{2237, 2234, 2204}"
458,1,16,0,0.0141611,"\int f^{b x+c x^2} (b+2 c x) \, dx","Int[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",1,1,18,0.05556,1,"{2236}"
459,1,37,0,0.0294125,"\int \frac{f^{b x+c x^2}}{b+2 c x} \, dx","Int[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",1,1,20,0.05000,1,"{2238}"
460,1,81,0,0.0485183,"\int \frac{f^{b x+c x^2}}{(b+2 c x)^2} \, dx","Int[f^(b*x + c*x^2)/(b + 2*c*x)^2,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)}","\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,"-f^(b*x + c*x^2)/(2*c*(b + 2*c*x)) + (Sqrt[Pi]*Erfi[((b + 2*c*x)*Sqrt[Log[f]])/(2*Sqrt[c])]*Sqrt[Log[f]])/(4*c^(3/2)*f^(b^2/(4*c)))","A",3,3,20,0.1500,1,"{2239, 2234, 2204}"
461,1,66,0,0.0632942,"\int \frac{f^{b x+c x^2}}{(b+2 c x)^3} \, dx","Int[f^(b*x + c*x^2)/(b + 2*c*x)^3,x]","\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}","\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,"-f^(b*x + 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)))","A",2,2,20,0.1000,1,"{2239, 2238}"
462,1,145,0,0.3518703,"\int \frac{e^{a+b x}}{x^2 \left(c+d x^2\right)} \, dx","Int[E^(a + b*x)/(x^2*(c + d*x^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}","\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 + b*x)/(c*x)) + (b*E^a*ExpIntegralEi[b*x])/c + (Sqrt[d]*E^(a + (b*Sqrt[-c])/Sqrt[d])*ExpIntegralEi[-((b*(Sqrt[-c] - Sqrt[d]*x))/Sqrt[d])])/(2*(-c)^(3/2)) - (Sqrt[d]*E^(a - (b*Sqrt[-c])/Sqrt[d])*ExpIntegralEi[(b*(Sqrt[-c] + Sqrt[d]*x))/Sqrt[d]])/(2*(-c)^(3/2))","A",8,4,20,0.2000,1,"{2271, 2177, 2178, 2269}"
463,1,111,0,0.2466971,"\int \frac{e^{a+b x}}{x \left(c+d x^2\right)} \, dx","Int[E^(a + b*x)/(x*(c + d*x^2)),x]","-\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}","-\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*ExpIntegralEi[b*x])/c - (E^(a + (b*Sqrt[-c])/Sqrt[d])*ExpIntegralEi[-((b*(Sqrt[-c] - Sqrt[d]*x))/Sqrt[d])])/(2*c) - (E^(a - (b*Sqrt[-c])/Sqrt[d])*ExpIntegralEi[(b*(Sqrt[-c] + Sqrt[d]*x))/Sqrt[d]])/(2*c)","A",7,2,20,0.1000,1,"{2271, 2178}"
464,1,118,0,0.1190934,"\int \frac{e^{a+b x}}{c+d x^2} \, dx","Int[E^(a + b*x)/(c + d*x^2),x]","\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}}","\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,"(E^(a + (b*Sqrt[-c])/Sqrt[d])*ExpIntegralEi[-((b*(Sqrt[-c] - Sqrt[d]*x))/Sqrt[d])])/(2*Sqrt[-c]*Sqrt[d]) - (E^(a - (b*Sqrt[-c])/Sqrt[d])*ExpIntegralEi[(b*(Sqrt[-c] + Sqrt[d]*x))/Sqrt[d]])/(2*Sqrt[-c]*Sqrt[d])","A",4,2,17,0.1176,1,"{2269, 2178}"
465,1,100,0,0.1288418,"\int \frac{e^{a+b x} x}{c+d x^2} \, dx","Int[(E^(a + b*x)*x)/(c + d*x^2),x]","\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}","\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 + (b*Sqrt[-c])/Sqrt[d])*ExpIntegralEi[-((b*(Sqrt[-c] - Sqrt[d]*x))/Sqrt[d])])/(2*d) + (E^(a - (b*Sqrt[-c])/Sqrt[d])*ExpIntegralEi[(b*(Sqrt[-c] + Sqrt[d]*x))/Sqrt[d]])/(2*d)","A",4,2,18,0.1111,1,"{2271, 2178}"
466,1,132,0,0.23545,"\int \frac{e^{a+b x} x^2}{c+d x^2} \, dx","Int[(E^(a + b*x)*x^2)/(c + d*x^2),x]","\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}","\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 + b*x)/(b*d) + (Sqrt[-c]*E^(a + (b*Sqrt[-c])/Sqrt[d])*ExpIntegralEi[-((b*(Sqrt[-c] - Sqrt[d]*x))/Sqrt[d])])/(2*d^(3/2)) - (Sqrt[-c]*E^(a - (b*Sqrt[-c])/Sqrt[d])*ExpIntegralEi[(b*(Sqrt[-c] + Sqrt[d]*x))/Sqrt[d]])/(2*d^(3/2))","A",7,4,20,0.2000,1,"{2271, 2194, 2269, 2178}"
467,1,212,0,0.6200858,"\int \frac{e^{d+e x}}{x^2 \left(a+b x+c x^2\right)} \, dx","Int[E^(d + e*x)/(x^2*(a + b*x + c*x^2)),x]","\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}","\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 + e*x)/(a*x)) - (b*E^d*ExpIntegralEi[e*x])/a^2 + (e*E^d*ExpIntegralEi[e*x])/a + ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*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)])/(2*a^2) + ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*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)])/(2*a^2)","A",9,3,23,0.1304,1,"{2270, 2177, 2178}"
468,1,169,0,0.4112151,"\int \frac{e^{d+e x}}{x \left(a+b x+c x^2\right)} \, dx","Int[E^(d + e*x)/(x*(a + b*x + c*x^2)),x]","-\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}","-\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*ExpIntegralEi[e*x])/a - ((1 + b/Sqrt[b^2 - 4*a*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)])/(2*a) - ((1 - b/Sqrt[b^2 - 4*a*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)])/(2*a)","A",7,2,23,0.08696,1,"{2270, 2178}"
469,1,138,0,0.1942632,"\int \frac{e^{d+e x}}{a+b x+c x^2} \, dx","Int[E^(d + e*x)/(a + b*x + c*x^2),x]","\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}}","\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)])/Sqrt[b^2 - 4*a*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",4,2,20,0.1000,1,"{2268, 2178}"
470,1,158,0,0.214408,"\int \frac{e^{d+e x} x}{a+b x+c x^2} \, dx","Int[(E^(d + e*x)*x)/(a + b*x + c*x^2),x]","\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}","\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,"((1 - b/Sqrt[b^2 - 4*a*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)])/(2*c) + ((1 + b/Sqrt[b^2 - 4*a*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)])/(2*c)","A",4,2,21,0.09524,1,"{2270, 2178}"
471,1,186,0,0.4078887,"\int \frac{e^{d+e x} x^2}{a+b x+c x^2} \, dx","Int[(E^(d + e*x)*x^2)/(a + b*x + c*x^2),x]","-\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}","-\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,"E^(d + e*x)/(c*e) - ((b - (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*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)])/(2*c^2) - ((b + (b^2 - 2*a*c)/Sqrt[b^2 - 4*a*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)])/(2*c^2)","A",7,3,23,0.1304,1,"{2270, 2194, 2178}"
472,1,232,0,0.5095393,"\int \frac{e^{d+e x} x^3}{a+b x+c x^2} \, dx","Int[(E^(d + e*x)*x^3)/(a + b*x + c*x^2),x]","\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}","\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 + e*x)/(c*e^2)) - (b*E^(d + e*x))/(c^2*e) + (E^(d + e*x)*x)/(c*e) + ((b^2 - a*c - (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*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)])/(2*c^3) + ((b^2 - a*c + (b*(b^2 - 3*a*c))/Sqrt[b^2 - 4*a*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)])/(2*c^3)","A",9,4,23,0.1739,1,"{2270, 2194, 2176, 2178}"
473,1,30,0,0.0372135,"\int \frac{4^x}{a+2^x b} \, dx","Int[4^x/(a + 2^x*b),x]","\frac{2^x}{b \log (2)}-\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*Log[2]) - (a*Log[a + 2^x*b])/(b^2*Log[2])","A",3,2,13,0.1538,1,"{2248, 43}"
474,1,30,0,0.0337079,"\int \frac{2^{2 x}}{a+2^x b} \, dx","Int[2^(2*x)/(a + 2^x*b),x]","\frac{2^x}{b \log (2)}-\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*Log[2]) - (a*Log[a + 2^x*b])/(b^2*Log[2])","A",3,2,15,0.1333,1,"{2248, 43}"
475,1,32,0,0.038245,"\int \frac{4^x}{a-2^x b} \, dx","Int[4^x/(a - 2^x*b),x]","-\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)}-\frac{2^x}{b \log (2)}",1,"-(2^x/(b*Log[2])) - (a*Log[a - 2^x*b])/(b^2*Log[2])","A",3,2,14,0.1429,1,"{2248, 43}"
476,1,32,0,0.0354631,"\int \frac{2^{2 x}}{a-2^x b} \, dx","Int[2^(2*x)/(a - 2^x*b),x]","-\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)}-\frac{2^x}{b \log (2)}",1,"-(2^x/(b*Log[2])) - (a*Log[a - 2^x*b])/(b^2*Log[2])","A",3,2,16,0.1250,1,"{2248, 43}"
477,1,58,0,0.0578888,"\int \frac{4^x}{a+2^{-x} b} \, dx","Int[4^x/(a + b/2^x),x]","\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)}","\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,"(b^2*x)/a^3 + 2^(-1 + 2*x)/(a*Log[2]) - (2^x*b)/(a^2*Log[2]) + (b^2*Log[a + b/2^x])/(a^3*Log[2])","A",3,2,15,0.1333,1,"{2248, 44}"
478,1,58,0,0.0508679,"\int \frac{2^{2 x}}{a+2^{-x} b} \, dx","Int[2^(2*x)/(a + b/2^x),x]","\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)}","\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,"(b^2*x)/a^3 + 2^(-1 + 2*x)/(a*Log[2]) - (2^x*b)/(a^2*Log[2]) + (b^2*Log[a + b/2^x])/(a^3*Log[2])","A",3,2,17,0.1176,1,"{2248, 44}"
479,1,58,0,0.0540729,"\int \frac{4^x}{a-2^{-x} b} \, dx","Int[4^x/(a - b/2^x),x]","\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)}","\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,"(b^2*x)/a^3 + 2^(-1 + 2*x)/(a*Log[2]) + (2^x*b)/(a^2*Log[2]) + (b^2*Log[a - b/2^x])/(a^3*Log[2])","A",3,2,16,0.1250,1,"{2248, 44}"
480,1,58,0,0.0520763,"\int \frac{2^{2 x}}{a-2^{-x} b} \, dx","Int[2^(2*x)/(a - b/2^x),x]","\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)}","\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,"(b^2*x)/a^3 + 2^(-1 + 2*x)/(a*Log[2]) + (2^x*b)/(a^2*Log[2]) + (b^2*Log[a - b/2^x])/(a^3*Log[2])","A",3,2,18,0.1111,1,"{2248, 44}"
481,1,30,0,0.0295758,"\int \frac{2^x}{a+4^x b} \, dx","Int[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",2,2,13,0.1538,1,"{2249, 205}"
482,1,30,0,0.0288414,"\int \frac{2^x}{a+2^{2 x} b} \, dx","Int[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",2,2,15,0.1333,1,"{2249, 205}"
483,1,30,0,0.028477,"\int \frac{2^x}{a-4^x b} \, dx","Int[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",2,2,14,0.1429,1,"{2249, 208}"
484,1,30,0,0.0301893,"\int \frac{2^x}{a-2^{2 x} b} \, dx","Int[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",2,2,16,0.1250,1,"{2249, 208}"
485,1,43,0,0.0431895,"\int \frac{2^x}{a+4^{-x} b} \, dx","Int[2^x/(a + b/4^x),x]","\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)}","\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*Log[2]) - (Sqrt[b]*ArcTan[(2^x*Sqrt[a])/Sqrt[b]])/(a^(3/2)*Log[2])","A",4,4,15,0.2667,1,"{2249, 193, 321, 205}"
486,1,43,0,0.0400896,"\int \frac{2^x}{a+2^{-2 x} b} \, dx","Int[2^x/(a + b/2^(2*x)),x]","\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)}","\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*Log[2]) - (Sqrt[b]*ArcTan[(2^x*Sqrt[a])/Sqrt[b]])/(a^(3/2)*Log[2])","A",4,4,15,0.2667,1,"{2249, 193, 321, 205}"
487,1,43,0,0.0432581,"\int \frac{2^x}{a-4^{-x} b} \, dx","Int[2^x/(a - b/4^x),x]","\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)}","\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*Log[2]) - (Sqrt[b]*ArcTanh[(2^x*Sqrt[a])/Sqrt[b]])/(a^(3/2)*Log[2])","A",4,4,16,0.2500,1,"{2249, 193, 321, 208}"
488,1,43,0,0.0432004,"\int \frac{2^x}{a-2^{-2 x} b} \, dx","Int[2^x/(a - b/2^(2*x)),x]","\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)}","\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*Log[2]) - (Sqrt[b]*ArcTanh[(2^x*Sqrt[a])/Sqrt[b]])/(a^(3/2)*Log[2])","A",4,4,16,0.2500,1,"{2249, 193, 321, 208}"
489,1,31,0,0.0391978,"\int \frac{2^x}{\sqrt{a+4^x b}} \, dx","Int[2^x/Sqrt[a + 4^x*b],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a+b 4^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 + 4^x*b]]/(Sqrt[b]*Log[2])","A",3,3,15,0.2000,1,"{2249, 217, 206}"
490,1,31,0,0.0375751,"\int \frac{2^x}{\sqrt{a+2^{2 x} b}} \, dx","Int[2^x/Sqrt[a + 2^(2*x)*b],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a+b 4^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 + 4^x*b]]/(Sqrt[b]*Log[2])","A",3,3,17,0.1765,1,"{2249, 217, 206}"
491,1,32,0,0.0398257,"\int \frac{2^x}{\sqrt{a-4^x b}} \, dx","Int[2^x/Sqrt[a - 4^x*b],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a-b 4^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 - 4^x*b]]/(Sqrt[b]*Log[2])","A",3,3,16,0.1875,1,"{2249, 217, 203}"
492,1,32,0,0.0396528,"\int \frac{2^x}{\sqrt{a-2^{2 x} b}} \, dx","Int[2^x/Sqrt[a - 2^(2*x)*b],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} 2^x}{\sqrt{a-b 4^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 - 4^x*b]]/(Sqrt[b]*Log[2])","A",3,3,18,0.1667,1,"{2249, 217, 203}"
493,1,24,0,0.0479708,"\int \frac{2^x}{\sqrt{a+4^{-x} b}} \, dx","Int[2^x/Sqrt[a + b/4^x],x]","\frac{2^x \sqrt{a+b 2^{-2 x}}}{a \log (2)}","\frac{2^x \sqrt{a+b 2^{-2 x}}}{a \log (2)}",1,"(2^x*Sqrt[a + b/2^(2*x)])/(a*Log[2])","A",2,2,17,0.1176,1,"{2249, 191}"
494,1,24,0,0.0471247,"\int \frac{2^x}{\sqrt{a+2^{-2 x} b}} \, dx","Int[2^x/Sqrt[a + b/2^(2*x)],x]","\frac{2^x \sqrt{a+b 2^{-2 x}}}{a \log (2)}","\frac{2^x \sqrt{a+b 2^{-2 x}}}{a \log (2)}",1,"(2^x*Sqrt[a + b/2^(2*x)])/(a*Log[2])","A",2,2,17,0.1176,1,"{2249, 191}"
495,1,25,0,0.0504276,"\int \frac{2^x}{\sqrt{a-4^{-x} b}} \, dx","Int[2^x/Sqrt[a - b/4^x],x]","\frac{2^x \sqrt{a-b 2^{-2 x}}}{a \log (2)}","\frac{2^x \sqrt{a-b 2^{-2 x}}}{a \log (2)}",1,"(2^x*Sqrt[a - b/2^(2*x)])/(a*Log[2])","A",2,2,18,0.1111,1,"{2249, 191}"
496,1,25,0,0.0500951,"\int \frac{2^x}{\sqrt{a-2^{-2 x} b}} \, dx","Int[2^x/Sqrt[a - b/2^(2*x)],x]","\frac{2^x \sqrt{a-b 2^{-2 x}}}{a \log (2)}","\frac{2^x \sqrt{a-b 2^{-2 x}}}{a \log (2)}",1,"(2^x*Sqrt[a - b/2^(2*x)])/(a*Log[2])","A",2,2,18,0.1111,1,"{2249, 191}"
497,1,44,0,0.040342,"\int \frac{4^x}{\sqrt{a+2^x b}} \, dx","Int[4^x/Sqrt[a + 2^x*b],x]","\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)}","\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*a*Sqrt[a + 2^x*b])/(b^2*Log[2]) + (2*(a + 2^x*b)^(3/2))/(3*b^2*Log[2])","A",3,2,15,0.1333,1,"{2248, 43}"
498,1,44,0,0.0410894,"\int \frac{2^{2 x}}{\sqrt{a+2^x b}} \, dx","Int[2^(2*x)/Sqrt[a + 2^x*b],x]","\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)}","\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*a*Sqrt[a + 2^x*b])/(b^2*Log[2]) + (2*(a + 2^x*b)^(3/2))/(3*b^2*Log[2])","A",3,2,17,0.1176,1,"{2248, 43}"
499,1,46,0,0.0433091,"\int \frac{4^x}{\sqrt{a-2^x b}} \, dx","Int[4^x/Sqrt[a - 2^x*b],x]","\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)}","\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*a*Sqrt[a - 2^x*b])/(b^2*Log[2]) + (2*(a - 2^x*b)^(3/2))/(3*b^2*Log[2])","A",3,2,16,0.1250,1,"{2248, 43}"
500,1,46,0,0.0436841,"\int \frac{2^{2 x}}{\sqrt{a-2^x b}} \, dx","Int[2^(2*x)/Sqrt[a - 2^x*b],x]","\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)}","\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*a*Sqrt[a - 2^x*b])/(b^2*Log[2]) + (2*(a - 2^x*b)^(3/2))/(3*b^2*Log[2])","A",3,2,18,0.1111,1,"{2248, 43}"
501,1,93,0,0.0743125,"\int \frac{4^x}{\sqrt{a+2^{-x} b}} \, dx","Int[4^x/Sqrt[a + b/2^x],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)}","\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^(-1 + 2*x)*Sqrt[a + b/2^x])/(a*Log[2]) - (3*2^(-2 + x)*b*Sqrt[a + b/2^x])/(a^2*Log[2]) + (3*b^2*ArcTanh[Sqrt[a + b/2^x]/Sqrt[a]])/(4*a^(5/2)*Log[2])","A",5,4,17,0.2353,1,"{2248, 51, 63, 208}"
502,1,93,0,0.0729013,"\int \frac{2^{2 x}}{\sqrt{a+2^{-x} b}} \, dx","Int[2^(2*x)/Sqrt[a + b/2^x],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)}","\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^(-1 + 2*x)*Sqrt[a + b/2^x])/(a*Log[2]) - (3*2^(-2 + x)*b*Sqrt[a + b/2^x])/(a^2*Log[2]) + (3*b^2*ArcTanh[Sqrt[a + b/2^x]/Sqrt[a]])/(4*a^(5/2)*Log[2])","A",5,4,19,0.2105,1,"{2248, 51, 63, 208}"
503,1,96,0,0.0757727,"\int \frac{4^x}{\sqrt{a-2^{-x} b}} \, dx","Int[4^x/Sqrt[a - b/2^x],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)}","\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^(-1 + 2*x)*Sqrt[a - b/2^x])/(a*Log[2]) + (3*2^(-2 + x)*b*Sqrt[a - b/2^x])/(a^2*Log[2]) + (3*b^2*ArcTanh[Sqrt[a - b/2^x]/Sqrt[a]])/(4*a^(5/2)*Log[2])","A",5,4,18,0.2222,1,"{2248, 51, 63, 208}"
504,1,96,0,0.0774554,"\int \frac{2^{2 x}}{\sqrt{a-2^{-x} b}} \, dx","Int[2^(2*x)/Sqrt[a - b/2^x],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)}","\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^(-1 + 2*x)*Sqrt[a - b/2^x])/(a*Log[2]) + (3*2^(-2 + x)*b*Sqrt[a - b/2^x])/(a^2*Log[2]) + (3*b^2*ArcTanh[Sqrt[a - b/2^x]/Sqrt[a]])/(4*a^(5/2)*Log[2])","A",5,4,20,0.2000,1,"{2248, 51, 63, 208}"
505,1,17,0,0.0147249,"\int \frac{1}{1+2 e^x+e^{2 x}} \, dx","Int[(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",3,2,14,0.1429,1,"{2282, 44}"
506,1,24,0,0.0198411,"\int \frac{1}{2+3 e^x+e^{2 x}} \, dx","Int[(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",6,5,14,0.3571,1,"{2282, 705, 29, 632, 31}"
507,1,56,0,0.0316725,"\int \frac{1}{-1+e^x+e^{2 x}} \, dx","Int[(-1 + E^x + E^(2*x))^(-1),x]","-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)","-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 + ((5 + Sqrt[5])*Log[1 - Sqrt[5] + 2*E^x])/10 + ((5 - Sqrt[5])*Log[1 + Sqrt[5] + 2*E^x])/10","A",6,5,12,0.4167,1,"{2282, 705, 29, 632, 31}"
508,1,44,0,0.036331,"\int \frac{1}{3+3 e^x+e^{2 x}} \, dx","Int[(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",7,7,14,0.5000,1,"{2282, 705, 29, 634, 618, 204, 628}"
509,1,67,0,0.0646843,"\int \frac{1}{a+b e^x+c e^{2 x}} \, dx","Int[(a + b*E^x + c*E^(2*x))^(-1),x]","\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}","\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,"x/a + (b*ArcTanh[(b + 2*c*E^x)/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]) - Log[a + b*E^x + c*E^(2*x)]/(2*a)","A",7,7,16,0.4375,1,"{2282, 705, 29, 634, 618, 206, 628}"
510,1,44,0,0.1276699,"\int \frac{x}{1+2 e^x+e^{2 x}} \, dx","Int[x/(1 + 2*E^x + E^(2*x)),x]","-\text{PolyLog}\left(2,-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)","-\text{PolyLog}\left(2,-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 + x/(1 + E^x) + x^2/2 + Log[1 + E^x] - x*Log[1 + E^x] - PolyLog[2, -E^x]","A",11,11,16,0.6875,1,"{6688, 2185, 2184, 2190, 2279, 2391, 2191, 2282, 36, 29, 31}"
511,1,54,0,0.1240276,"\int \frac{x}{2+3 e^x+e^{2 x}} \, dx","Int[x/(2 + 3*E^x + E^(2*x)),x]","-\text{PolyLog}\left(2,-e^x\right)+\frac{1}{2} \text{PolyLog}\left(2,-\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)","-\text{PolyLog}\left(2,-e^x\right)+\frac{1}{2} \text{PolyLog}\left(2,-\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^2/4 + (x*Log[1 + E^x/2])/2 - x*Log[1 + E^x] - PolyLog[2, -E^x] + PolyLog[2, -E^x/2]/2","A",9,5,16,0.3125,1,"{2263, 2184, 2190, 2279, 2391}"
512,1,180,0,0.1880711,"\int \frac{x}{-1+e^x+e^{2 x}} \, dx","Int[x/(-1 + E^x + E^(2*x)),x]","-\frac{2 \text{PolyLog}\left(2,-\frac{2 e^x}{1-\sqrt{5}}\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}+\frac{2 \text{PolyLog}\left(2,-\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)}","-\frac{2 \text{PolyLog}\left(2,-\frac{2 e^x}{1-\sqrt{5}}\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}+\frac{2 \text{PolyLog}\left(2,-\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,"x^2/(Sqrt[5]*(1 - Sqrt[5])) - x^2/(Sqrt[5]*(1 + Sqrt[5])) - (2*x*Log[1 + (2*E^x)/(1 - Sqrt[5])])/(Sqrt[5]*(1 - Sqrt[5])) + (2*x*Log[1 + (2*E^x)/(1 + Sqrt[5])])/(Sqrt[5]*(1 + Sqrt[5])) - (2*PolyLog[2, (-2*E^x)/(1 - Sqrt[5])])/(Sqrt[5]*(1 - Sqrt[5])) + (2*PolyLog[2, (-2*E^x)/(1 + Sqrt[5])])/(Sqrt[5]*(1 + Sqrt[5]))","A",9,5,14,0.3571,1,"{2263, 2184, 2190, 2279, 2391}"
513,1,204,0,0.1953669,"\int \frac{x}{3+3 e^x+e^{2 x}} \, dx","Int[x/(3 + 3*E^x + E^(2*x)),x]","-\frac{2 \text{PolyLog}\left(2,-\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}+\frac{2 \text{PolyLog}\left(2,-\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)}","-\frac{2 \text{PolyLog}\left(2,-\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}+\frac{2 \text{PolyLog}\left(2,-\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^2/(Sqrt[3]*(3*I - Sqrt[3]))) + x^2/(Sqrt[3]*(3*I + Sqrt[3])) - (2*x*Log[1 + (2*E^x)/(3 - I*Sqrt[3])])/(Sqrt[3]*(3*I + Sqrt[3])) + (2*x*Log[1 + (2*E^x)/(3 + I*Sqrt[3])])/(Sqrt[3]*(3*I - Sqrt[3])) - (2*PolyLog[2, (-2*E^x)/(3 - I*Sqrt[3])])/(Sqrt[3]*(3*I + Sqrt[3])) + (2*PolyLog[2, (-2*E^x)/(3 + I*Sqrt[3])])/(Sqrt[3]*(3*I - Sqrt[3]))","A",9,5,16,0.3125,1,"{2263, 2184, 2190, 2279, 2391}"
514,1,276,0,0.4294951,"\int \frac{x}{a+b e^x+c e^{2 x}} \, dx","Int[x/(a + b*E^x + c*E^(2*x)),x]","\frac{2 c \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}\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}","\frac{2 c \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}\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,"-((c*x^2)/(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])) - (c*x^2)/(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c]) + (2*c*x*Log[1 + (2*c*E^x)/(b - Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c]) + (2*c*x*Log[1 + (2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c]) + (2*c*PolyLog[2, (-2*c*E^x)/(b - Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c]) + (2*c*PolyLog[2, (-2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])","A",9,5,18,0.2778,1,"{2263, 2184, 2190, 2279, 2391}"
515,1,72,0,0.2295008,"\int \frac{x^2}{1+2 e^x+e^{2 x}} \, dx","Int[x^2/(1 + 2*E^x + E^(2*x)),x]","-2 x \text{PolyLog}\left(2,-e^x\right)+2 \text{PolyLog}\left(2,-e^x\right)+2 \text{PolyLog}\left(3,-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)","-2 x \text{PolyLog}\left(2,-e^x\right)+2 \text{PolyLog}\left(2,-e^x\right)+2 \text{PolyLog}\left(3,-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 + x^2/(1 + E^x) + x^3/3 + 2*x*Log[1 + E^x] - x^2*Log[1 + E^x] + 2*PolyLog[2, -E^x] - 2*x*PolyLog[2, -E^x] + 2*PolyLog[3, -E^x]","A",12,10,18,0.5556,1,"{6688, 2185, 2184, 2190, 2531, 2282, 6589, 2191, 2279, 2391}"
516,1,77,0,0.2223416,"\int \frac{x^2}{2+3 e^x+e^{2 x}} \, dx","Int[x^2/(2 + 3*E^x + E^(2*x)),x]","-2 x \text{PolyLog}\left(2,-e^x\right)+x \text{PolyLog}\left(2,-\frac{e^x}{2}\right)+2 \text{PolyLog}\left(3,-e^x\right)-\text{PolyLog}\left(3,-\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)","-2 x \text{PolyLog}\left(2,-e^x\right)+x \text{PolyLog}\left(2,-\frac{e^x}{2}\right)+2 \text{PolyLog}\left(3,-e^x\right)-\text{PolyLog}\left(3,-\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^3/6 + (x^2*Log[1 + E^x/2])/2 - x^2*Log[1 + E^x] - 2*x*PolyLog[2, -E^x] + x*PolyLog[2, -E^x/2] + 2*PolyLog[3, -E^x] - PolyLog[3, -E^x/2]","A",11,6,18,0.3333,1,"{2263, 2184, 2190, 2531, 2282, 6589}"
517,1,259,0,0.2962717,"\int \frac{x^2}{-1+e^x+e^{2 x}} \, dx","Int[x^2/(-1 + E^x + E^(2*x)),x]","-\frac{4 x \text{PolyLog}\left(2,-\frac{2 e^x}{1-\sqrt{5}}\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}+\frac{4 x \text{PolyLog}\left(2,-\frac{2 e^x}{1+\sqrt{5}}\right)}{\sqrt{5} \left(1+\sqrt{5}\right)}+\frac{4 \text{PolyLog}\left(3,-\frac{2 e^x}{1-\sqrt{5}}\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}-\frac{4 \text{PolyLog}\left(3,-\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)}","-\frac{4 x \text{PolyLog}\left(2,-\frac{2 e^x}{1-\sqrt{5}}\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}+\frac{4 x \text{PolyLog}\left(2,-\frac{2 e^x}{1+\sqrt{5}}\right)}{\sqrt{5} \left(1+\sqrt{5}\right)}+\frac{4 \text{PolyLog}\left(3,-\frac{2 e^x}{1-\sqrt{5}}\right)}{\sqrt{5} \left(1-\sqrt{5}\right)}-\frac{4 \text{PolyLog}\left(3,-\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^3)/(3*Sqrt[5]*(1 - Sqrt[5])) - (2*x^3)/(3*Sqrt[5]*(1 + Sqrt[5])) - (2*x^2*Log[1 + (2*E^x)/(1 - Sqrt[5])])/(Sqrt[5]*(1 - Sqrt[5])) + (2*x^2*Log[1 + (2*E^x)/(1 + Sqrt[5])])/(Sqrt[5]*(1 + Sqrt[5])) - (4*x*PolyLog[2, (-2*E^x)/(1 - Sqrt[5])])/(Sqrt[5]*(1 - Sqrt[5])) + (4*x*PolyLog[2, (-2*E^x)/(1 + Sqrt[5])])/(Sqrt[5]*(1 + Sqrt[5])) + (4*PolyLog[3, (-2*E^x)/(1 - Sqrt[5])])/(Sqrt[5]*(1 - Sqrt[5])) - (4*PolyLog[3, (-2*E^x)/(1 + Sqrt[5])])/(Sqrt[5]*(1 + Sqrt[5]))","A",11,6,16,0.3750,1,"{2263, 2184, 2190, 2531, 2282, 6589}"
518,1,293,0,0.3089993,"\int \frac{x^2}{3+3 e^x+e^{2 x}} \, dx","Int[x^2/(3 + 3*E^x + E^(2*x)),x]","-\frac{4 x \text{PolyLog}\left(2,-\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}+\frac{4 x \text{PolyLog}\left(2,-\frac{2 e^x}{3+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+3 i\right)}+\frac{4 \text{PolyLog}\left(3,-\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}-\frac{4 \text{PolyLog}\left(3,-\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)}","-\frac{4 x \text{PolyLog}\left(2,-\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}+\frac{4 x \text{PolyLog}\left(2,-\frac{2 e^x}{3+i \sqrt{3}}\right)}{\sqrt{3} \left(-\sqrt{3}+3 i\right)}+\frac{4 \text{PolyLog}\left(3,-\frac{2 e^x}{3-i \sqrt{3}}\right)}{\sqrt{3} \left(\sqrt{3}+3 i\right)}-\frac{4 \text{PolyLog}\left(3,-\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*x^3)/(3*Sqrt[3]*(3*I - Sqrt[3])) + (2*x^3)/(3*Sqrt[3]*(3*I + Sqrt[3])) - (2*x^2*Log[1 + (2*E^x)/(3 - I*Sqrt[3])])/(Sqrt[3]*(3*I + Sqrt[3])) + (2*x^2*Log[1 + (2*E^x)/(3 + I*Sqrt[3])])/(Sqrt[3]*(3*I - Sqrt[3])) - (4*x*PolyLog[2, (-2*E^x)/(3 - I*Sqrt[3])])/(Sqrt[3]*(3*I + Sqrt[3])) + (4*x*PolyLog[2, (-2*E^x)/(3 + I*Sqrt[3])])/(Sqrt[3]*(3*I - Sqrt[3])) + (4*PolyLog[3, (-2*E^x)/(3 - I*Sqrt[3])])/(Sqrt[3]*(3*I + Sqrt[3])) - (4*PolyLog[3, (-2*E^x)/(3 + I*Sqrt[3])])/(Sqrt[3]*(3*I - Sqrt[3]))","A",11,6,18,0.3333,1,"{2263, 2184, 2190, 2531, 2282, 6589}"
519,1,391,0,0.6653025,"\int \frac{x^2}{a+b e^x+c e^{2 x}} \, dx","Int[x^2/(a + b*E^x + c*E^(2*x)),x]","\frac{4 c x \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{4 c \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}\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}","\frac{4 c x \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}\right)}{b \sqrt{b^2-4 a c}-4 a c+b^2}-\frac{4 c \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{2 c e^x}{\sqrt{b^2-4 a c}+b}\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*c*x^3)/(3*(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])) - (2*c*x^3)/(3*(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])) + (2*c*x^2*Log[1 + (2*c*E^x)/(b - Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c]) + (2*c*x^2*Log[1 + (2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c]) + (4*c*x*PolyLog[2, (-2*c*E^x)/(b - Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c]) + (4*c*x*PolyLog[2, (-2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c]) - (4*c*PolyLog[3, (-2*c*E^x)/(b - Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c]) - (4*c*PolyLog[3, (-2*c*E^x)/(b + Sqrt[b^2 - 4*a*c])])/(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])","A",11,6,20,0.3000,1,"{2263, 2184, 2190, 2531, 2282, 6589}"
520,1,40,0,0.0265826,"\int \frac{1}{1+2 f^{c+d x}+f^{2 c+2 d x}} \, dx","Int[(1 + 2*f^(c + d*x) + f^(2*c + 2*d*x))^(-1),x]","-\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","-\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,"x + 1/(d*(1 + f^(c + d*x))*Log[f]) - Log[1 + f^(c + d*x)]/(d*Log[f])","A",3,2,23,0.08696,1,"{2282, 44}"
521,1,94,0,0.1080364,"\int \frac{1}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx","Int[(a + b*f^(c + d*x) + c*f^(2*c + 2*d*x))^(-1),x]","\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}","\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,"x/a + (b*ArcTanh[(b + 2*c*f^(c + d*x))/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]*d*Log[f]) - Log[a + b*f^(c + d*x) + c*f^(2*c + 2*d*x)]/(2*a*d*Log[f])","A",7,7,25,0.2800,1,"{2282, 705, 29, 634, 618, 206, 628}"
522,1,94,0,0.0926453,"\int \frac{1}{a+b f^{g+h x}+c f^{2 (g+h x)}} \, dx","Int[(a + b*f^(g + h*x) + c*f^(2*(g + h*x)))^(-1),x]","\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}","\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,"x/a + (b*ArcTanh[(b + 2*c*f^(g + h*x))/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]*h*Log[f]) - Log[a + b*f^(g + h*x) + c*f^(2*g + 2*h*x)]/(2*a*h*Log[f])","A",7,7,24,0.2917,1,"{2282, 705, 29, 634, 618, 206, 628}"
523,1,96,0,0.2675432,"\int \frac{x}{1+2 f^{c+d x}+f^{2 c+2 d x}} \, dx","Int[x/(1 + 2*f^(c + d*x) + f^(2*c + 2*d*x)),x]","-\frac{\text{PolyLog}\left(2,-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}","-\frac{\text{PolyLog}\left(2,-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^2/2 - x/(d*Log[f]) + x/(d*(1 + f^(c + d*x))*Log[f]) + Log[1 + f^(c + d*x)]/(d^2*Log[f]^2) - (x*Log[1 + f^(c + d*x)])/(d*Log[f]) - PolyLog[2, -f^(c + d*x)]/(d^2*Log[f]^2)","A",11,11,25,0.4400,1,"{6688, 2185, 2184, 2190, 2279, 2391, 2191, 2282, 36, 29, 31}"
524,1,338,0,0.6857549,"\int \frac{x}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx","Int[x/(a + b*f^(c + d*x) + c*f^(2*c + 2*d*x)),x]","-\frac{2 c \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c f^{c+d x}}{\sqrt{b^2-4 a c}+b}\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}","-\frac{2 c \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c f^{c+d x}}{\sqrt{b^2-4 a c}+b}\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,"-((c*x^2)/(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])) - (c*x^2)/(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c]) - (2*c*x*Log[1 + (2*c*f^(c + d*x))/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*d*Log[f]) + (2*c*x*Log[1 + (2*c*f^(c + d*x))/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*d*Log[f]) - (2*c*PolyLog[2, (-2*c*f^(c + d*x))/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*d^2*Log[f]^2) + (2*c*PolyLog[2, (-2*c*f^(c + d*x))/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*d^2*Log[f]^2)","A",9,5,27,0.1852,1,"{2263, 2184, 2190, 2279, 2391}"
525,1,145,0,0.4207117,"\int \frac{x^2}{1+2 f^{c+d x}+f^{2 c+2 d x}} \, dx","Int[x^2/(1 + 2*f^(c + d*x) + f^(2*c + 2*d*x)),x]","-\frac{2 x \text{PolyLog}\left(2,-f^{c+d x}\right)}{d^2 \log ^2(f)}+\frac{2 \text{PolyLog}\left(2,-f^{c+d x}\right)}{d^3 \log ^3(f)}+\frac{2 \text{PolyLog}\left(3,-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 \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}","-\frac{2 x \text{PolyLog}\left(2,-f^{c+d x}\right)}{d^2 \log ^2(f)}+\frac{2 \text{PolyLog}\left(2,-f^{c+d x}\right)}{d^3 \log ^3(f)}+\frac{2 \text{PolyLog}\left(3,-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 \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,"x^3/3 - x^2/(d*Log[f]) + x^2/(d*(1 + f^(c + d*x))*Log[f]) + (2*x*Log[1 + f^(c + d*x)])/(d^2*Log[f]^2) - (x^2*Log[1 + f^(c + d*x)])/(d*Log[f]) + (2*PolyLog[2, -f^(c + d*x)])/(d^3*Log[f]^3) - (2*x*PolyLog[2, -f^(c + d*x)])/(d^2*Log[f]^2) + (2*PolyLog[3, -f^(c + d*x)])/(d^3*Log[f]^3)","A",12,10,27,0.3704,1,"{6688, 2185, 2184, 2190, 2531, 2282, 6589, 2191, 2279, 2391}"
526,1,484,0,0.8747199,"\int \frac{x^2}{a+b f^{c+d x}+c f^{2 c+2 d x}} \, dx","Int[x^2/(a + b*f^(c + d*x) + c*f^(2*c + 2*d*x)),x]","-\frac{4 c x \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c f^{c+d x}}{\sqrt{b^2-4 a c}+b}\right)}{d^2 \log ^2(f) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{4 c \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{2 c f^{c+d x}}{\sqrt{b^2-4 a c}+b}\right)}{d^3 \log ^3(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)}","-\frac{4 c x \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c f^{c+d x}}{\sqrt{b^2-4 a c}+b}\right)}{d^2 \log ^2(f) \sqrt{b^2-4 a c} \left(\sqrt{b^2-4 a c}+b\right)}+\frac{4 c \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{2 c f^{c+d x}}{\sqrt{b^2-4 a c}+b}\right)}{d^3 \log ^3(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,"(-2*c*x^3)/(3*(b^2 - 4*a*c - b*Sqrt[b^2 - 4*a*c])) - (2*c*x^3)/(3*(b^2 - 4*a*c + b*Sqrt[b^2 - 4*a*c])) - (2*c*x^2*Log[1 + (2*c*f^(c + d*x))/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*d*Log[f]) + (2*c*x^2*Log[1 + (2*c*f^(c + d*x))/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*d*Log[f]) - (4*c*x*PolyLog[2, (-2*c*f^(c + d*x))/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*d^2*Log[f]^2) + (4*c*x*PolyLog[2, (-2*c*f^(c + d*x))/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*d^2*Log[f]^2) + (4*c*PolyLog[3, (-2*c*f^(c + d*x))/(b - Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b - Sqrt[b^2 - 4*a*c])*d^3*Log[f]^3) - (4*c*PolyLog[3, (-2*c*f^(c + d*x))/(b + Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(b + Sqrt[b^2 - 4*a*c])*d^3*Log[f]^3)","A",11,6,29,0.2069,1,"{2263, 2184, 2190, 2531, 2282, 6589}"
527,1,103,0,0.1565652,"\int \frac{d+e f^{g+h x}}{a+b f^{g+h x}+c f^{2 g+2 h x}} \, dx","Int[(d + e*f^(g + h*x))/(a + b*f^(g + h*x) + c*f^(2*g + 2*h*x)),x]","\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}","\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,"(d*x)/a + ((b*d - 2*a*e)*ArcTanh[(b + 2*c*f^(g + h*x))/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]*h*Log[f]) - (d*Log[a + b*f^(g + h*x) + c*f^(2*g + 2*h*x)])/(2*a*h*Log[f])","A",7,6,37,0.1622,1,"{2282, 800, 634, 618, 206, 628}"
528,1,103,0,0.1413645,"\int \frac{d+e f^{g+h x}}{a+b f^{g+h x}+c f^{2 (g+h x)}} \, dx","Int[(d + e*f^(g + h*x))/(a + b*f^(g + h*x) + c*f^(2*(g + h*x))),x]","\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}","\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,"(d*x)/a + ((b*d - 2*a*e)*ArcTanh[(b + 2*c*f^(g + h*x))/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]*h*Log[f]) - (d*Log[a + b*f^(g + h*x) + c*f^(2*g + 2*h*x)])/(2*a*h*Log[f])","A",7,6,36,0.1667,1,"{2282, 800, 634, 618, 206, 628}"
529,1,9,0,0.0108058,"\int \frac{1}{2+e^{-x}+e^x} \, dx","Int[(2 + E^(-x) + E^x)^(-1),x]","-\frac{1}{e^x+1}","-\frac{1}{e^x+1}",1,"-(1 + E^x)^(-1)","A",2,2,12,0.1667,1,"{2282, 32}"
530,1,20,0,0.1344801,"\int \frac{x}{2+e^{-x}+e^x} \, dx","Int[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",7,7,14,0.5000,1,"{2267, 6688, 2191, 2282, 36, 29, 31}"
531,1,34,0,0.2495054,"\int \frac{x^2}{2+e^{-x}+e^x} \, dx","Int[x^2/(2 + E^(-x) + E^x),x]","-2 \text{PolyLog}\left(2,-e^x\right)-\frac{x^2}{e^x+1}+x^2-2 x \log \left(e^x+1\right)","-2 \text{PolyLog}\left(2,-e^x\right)-\frac{x^2}{e^x+1}+x^2-2 x \log \left(e^x+1\right)",1,"x^2 - x^2/(1 + E^x) - 2*x*Log[1 + E^x] - 2*PolyLog[2, -E^x]","A",7,7,16,0.4375,1,"{2267, 6688, 2191, 2184, 2190, 2279, 2391}"
532,1,20,0,0.0203003,"\int \frac{1}{2+f^{-c-d x}+f^{c+d x}} \, dx","Int[(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",2,2,21,0.09524,1,"{2282, 32}"
533,1,50,0,0.2881481,"\int \frac{x}{2+f^{-c-d x}+f^{c+d x}} \, dx","Int[x/(2 + f^(-c - d*x) + f^(c + d*x)),x]","-\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)}","-\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,"x/(d*Log[f]) - x/(d*(1 + f^(c + d*x))*Log[f]) - Log[1 + f^(c + d*x)]/(d^2*Log[f]^2)","A",7,7,23,0.3043,1,"{2267, 6688, 2191, 2282, 36, 29, 31}"
534,1,75,0,0.4909362,"\int \frac{x^2}{2+f^{-c-d x}+f^{c+d x}} \, dx","Int[x^2/(2 + f^(-c - d*x) + f^(c + d*x)),x]","-\frac{2 \text{PolyLog}\left(2,-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)}","-\frac{2 \text{PolyLog}\left(2,-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,"x^2/(d*Log[f]) - x^2/(d*(1 + f^(c + d*x))*Log[f]) - (2*x*Log[1 + f^(c + d*x)])/(d^2*Log[f]^2) - (2*PolyLog[2, -f^(c + d*x)])/(d^3*Log[f]^3)","A",7,7,25,0.2800,1,"{2267, 6688, 2191, 2184, 2190, 2279, 2391}"
535,1,13,0,0.0120727,"\int \frac{1}{2+3^{-x}+3^x} \, dx","Int[(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",2,2,12,0.1667,1,"{2282, 32}"
536,1,23,0,0.0192433,"\int \frac{1}{1-e^{-x}+2 e^x} \, dx","Int[(1 - E^(-x) + 2*E^x)^(-1),x]","\frac{1}{3} \log \left(1-2 e^x\right)-\frac{1}{3} \log \left(e^x+1\right)","\frac{1}{3} \log \left(1-2 e^x\right)-\frac{1}{3} \log \left(e^x+1\right)",1,"Log[1 - 2*E^x]/3 - Log[1 + E^x]/3","A",4,3,16,0.1875,1,"{2282, 616, 31}"
537,1,36,0,0.0568149,"\int \frac{1}{a+b e^{-x}+c e^x} \, dx","Int[(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",4,4,16,0.2500,1,"{2282, 1386, 618, 206}"
538,1,159,0,0.3039147,"\int \frac{x}{a+b e^{-x}+c e^x} \, dx","Int[x/(a + b/E^x + c*E^x),x]","\frac{\text{PolyLog}\left(2,-\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}-\frac{\text{PolyLog}\left(2,-\frac{2 c e^x}{\sqrt{a^2-4 b c}+a}\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}}","\frac{\text{PolyLog}\left(2,-\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}-\frac{\text{PolyLog}\left(2,-\frac{2 c e^x}{\sqrt{a^2-4 b c}+a}\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])])/Sqrt[a^2 - 4*b*c] - (x*Log[1 + (2*c*E^x)/(a + Sqrt[a^2 - 4*b*c])])/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] - PolyLog[2, (-2*c*E^x)/(a + Sqrt[a^2 - 4*b*c])]/Sqrt[a^2 - 4*b*c]","A",8,5,18,0.2778,1,"{2267, 2264, 2190, 2279, 2391}"
539,1,244,0,0.498767,"\int \frac{x^2}{a+b e^{-x}+c e^x} \, dx","Int[x^2/(a + b/E^x + c*E^x),x]","\frac{2 x \text{PolyLog}\left(2,-\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}-\frac{2 x \text{PolyLog}\left(2,-\frac{2 c e^x}{\sqrt{a^2-4 b c}+a}\right)}{\sqrt{a^2-4 b c}}-\frac{2 \text{PolyLog}\left(3,-\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}+\frac{2 \text{PolyLog}\left(3,-\frac{2 c e^x}{\sqrt{a^2-4 b c}+a}\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}}","\frac{2 x \text{PolyLog}\left(2,-\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}-\frac{2 x \text{PolyLog}\left(2,-\frac{2 c e^x}{\sqrt{a^2-4 b c}+a}\right)}{\sqrt{a^2-4 b c}}-\frac{2 \text{PolyLog}\left(3,-\frac{2 c e^x}{a-\sqrt{a^2-4 b c}}\right)}{\sqrt{a^2-4 b c}}+\frac{2 \text{PolyLog}\left(3,-\frac{2 c e^x}{\sqrt{a^2-4 b c}+a}\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])])/Sqrt[a^2 - 4*b*c] - (x^2*Log[1 + (2*c*E^x)/(a + Sqrt[a^2 - 4*b*c])])/Sqrt[a^2 - 4*b*c] + (2*x*PolyLog[2, (-2*c*E^x)/(a - Sqrt[a^2 - 4*b*c])])/Sqrt[a^2 - 4*b*c] - (2*x*PolyLog[2, (-2*c*E^x)/(a + Sqrt[a^2 - 4*b*c])])/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] + (2*PolyLog[3, (-2*c*E^x)/(a + Sqrt[a^2 - 4*b*c])])/Sqrt[a^2 - 4*b*c]","A",10,6,20,0.3000,1,"{2267, 2264, 2190, 2531, 2282, 6589}"
540,1,47,0,0.0641623,"\int \frac{1}{a+b f^{-c-d x}+c f^{c+d x}} \, dx","Int[(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",4,4,25,0.1600,1,"{2282, 1386, 618, 206}"
541,1,203,0,0.4067332,"\int \frac{x}{a+b f^{-c-d x}+c f^{c+d x}} \, dx","Int[x/(a + b*f^(-c - d*x) + c*f^(c + d*x)),x]","\frac{\text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c f^{c+d x}}{\sqrt{a^2-4 b c}+a}\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}}","\frac{\text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c f^{c+d x}}{\sqrt{a^2-4 b c}+a}\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,"(x*Log[1 + (2*c*f^(c + d*x))/(a - Sqrt[a^2 - 4*b*c])])/(Sqrt[a^2 - 4*b*c]*d*Log[f]) - (x*Log[1 + (2*c*f^(c + d*x))/(a + Sqrt[a^2 - 4*b*c])])/(Sqrt[a^2 - 4*b*c]*d*Log[f]) + PolyLog[2, (-2*c*f^(c + d*x))/(a - Sqrt[a^2 - 4*b*c])]/(Sqrt[a^2 - 4*b*c]*d^2*Log[f]^2) - PolyLog[2, (-2*c*f^(c + d*x))/(a + Sqrt[a^2 - 4*b*c])]/(Sqrt[a^2 - 4*b*c]*d^2*Log[f]^2)","A",8,5,27,0.1852,1,"{2267, 2264, 2190, 2279, 2391}"
542,1,310,0,0.6596286,"\int \frac{x^2}{a+b f^{-c-d x}+c f^{c+d x}} \, dx","Int[x^2/(a + b*f^(-c - d*x) + c*f^(c + d*x)),x]","\frac{2 x \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c f^{c+d x}}{\sqrt{a^2-4 b c}+a}\right)}{d^2 \log ^2(f) \sqrt{a^2-4 b c}}-\frac{2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{2 c f^{c+d x}}{\sqrt{a^2-4 b c}+a}\right)}{d^3 \log ^3(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}}","\frac{2 x \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c f^{c+d x}}{\sqrt{a^2-4 b c}+a}\right)}{d^2 \log ^2(f) \sqrt{a^2-4 b c}}-\frac{2 \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{2 c f^{c+d x}}{\sqrt{a^2-4 b c}+a}\right)}{d^3 \log ^3(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,"(x^2*Log[1 + (2*c*f^(c + d*x))/(a - Sqrt[a^2 - 4*b*c])])/(Sqrt[a^2 - 4*b*c]*d*Log[f]) - (x^2*Log[1 + (2*c*f^(c + d*x))/(a + Sqrt[a^2 - 4*b*c])])/(Sqrt[a^2 - 4*b*c]*d*Log[f]) + (2*x*PolyLog[2, (-2*c*f^(c + d*x))/(a - Sqrt[a^2 - 4*b*c])])/(Sqrt[a^2 - 4*b*c]*d^2*Log[f]^2) - (2*x*PolyLog[2, (-2*c*f^(c + d*x))/(a + Sqrt[a^2 - 4*b*c])])/(Sqrt[a^2 - 4*b*c]*d^2*Log[f]^2) - (2*PolyLog[3, (-2*c*f^(c + d*x))/(a - Sqrt[a^2 - 4*b*c])])/(Sqrt[a^2 - 4*b*c]*d^3*Log[f]^3) + (2*PolyLog[3, (-2*c*f^(c + d*x))/(a + Sqrt[a^2 - 4*b*c])])/(Sqrt[a^2 - 4*b*c]*d^3*Log[f]^3)","A",10,6,29,0.2069,1,"{2267, 2264, 2190, 2531, 2282, 6589}"
543,0,0,0,0.1492285,"\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","Int[(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,"Defer[Int][(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",0,0,0,0,-1,"{}"
544,1,154,0,0.2648089,"\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","Int[(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]","\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{2 a^3 \log \left(\frac{\sqrt{d+e x}}{\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}","\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{2 a^3 \log \left(\frac{\sqrt{d+e x}}{\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,"(6*a^2*b*ExpIntegralEi[(c*Sqrt[d + e*x]*Log[F])/Sqrt[f + g*x]])/(e*f - d*g) + (6*a*b^2*ExpIntegralEi[(2*c*Sqrt[d + e*x]*Log[F])/Sqrt[f + g*x]])/(e*f - d*g) + (2*b^3*ExpIntegralEi[(3*c*Sqrt[d + e*x]*Log[F])/Sqrt[f + g*x]])/(e*f - d*g) + (2*a^3*Log[Sqrt[d + e*x]/Sqrt[f + g*x]])/(e*f - d*g)","A",6,3,50,0.06000,1,"{2290, 2183, 2178}"
545,1,112,0,0.2272897,"\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","Int[(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]","\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}","\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,"(4*a*b*ExpIntegralEi[(c*Sqrt[d + e*x]*Log[F])/Sqrt[f + g*x]])/(e*f - d*g) + (2*b^2*ExpIntegralEi[(2*c*Sqrt[d + e*x]*Log[F])/Sqrt[f + g*x]])/(e*f - d*g) + (2*a^2*Log[Sqrt[d + e*x]/Sqrt[f + g*x]])/(e*f - d*g)","A",5,3,50,0.06000,1,"{2290, 2183, 2178}"
546,1,70,0,0.1223791,"\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","Int[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[f + g*x]))/(d*f + (e*f + d*g)*x + e*g*x^2),x]","\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}","\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,"(2*b*ExpIntegralEi[(c*Sqrt[d + e*x]*Log[F])/Sqrt[f + g*x]])/(e*f - d*g) + (2*a*Log[Sqrt[d + e*x]/Sqrt[f + g*x]])/(e*f - d*g)","A",4,3,48,0.06250,1,"{2290, 14, 2178}"
547,1,36,0,0.0145575,"\int \frac{1}{d f+(e f+d g) x+e g x^2} \, dx","Int[(d*f + (e*f + d*g)*x + e*g*x^2)^(-1),x]","\frac{\log (d+e x)}{e f-d g}-\frac{\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]/(e*f - d*g) - Log[f + g*x]/(e*f - d*g)","A",3,2,21,0.09524,1,"{616, 31}"
548,0,0,0,0.1522229,"\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","Int[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,"Defer[Int][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",0,0,0,0,-1,"{}"
549,0,0,0,0.1489084,"\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","Int[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,"Defer[Int][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",0,0,0,0,-1,"{}"
550,0,0,0,0.2295375,"\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","Int[(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,"Defer[Int][(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^n/(d^2 - e^2*x^2), x]","A",0,0,0,0,-1,"{}"
551,1,152,0,0.3269861,"\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","Int[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^3/(d^2 - e^2*x^2),x]","\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{a^3 \log \left(\frac{\sqrt{d+e x}}{\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}","\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{a^3 \log \left(\frac{\sqrt{d+e x}}{\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,"(3*a^2*b*ExpIntegralEi[(c*Sqrt[d + e*x]*Log[F])/Sqrt[d*f - e*f*x]])/(d*e) + (3*a*b^2*ExpIntegralEi[(2*c*Sqrt[d + e*x]*Log[F])/Sqrt[d*f - e*f*x]])/(d*e) + (b^3*ExpIntegralEi[(3*c*Sqrt[d + e*x]*Log[F])/Sqrt[d*f - e*f*x]])/(d*e) + (a^3*Log[Sqrt[d + e*x]/Sqrt[d*f - e*f*x]])/(d*e)","A",6,3,47,0.06383,1,"{2291, 2183, 2178}"
552,1,110,0,0.3031616,"\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","Int[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^2/(d^2 - e^2*x^2),x]","\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}","\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,"(2*a*b*ExpIntegralEi[(c*Sqrt[d + e*x]*Log[F])/Sqrt[d*f - e*f*x]])/(d*e) + (b^2*ExpIntegralEi[(2*c*Sqrt[d + e*x]*Log[F])/Sqrt[d*f - e*f*x]])/(d*e) + (a^2*Log[Sqrt[d + e*x]/Sqrt[d*f - e*f*x]])/(d*e)","A",5,3,47,0.06383,1,"{2291, 2183, 2178}"
553,1,68,0,0.1795808,"\int \frac{a+b F^{\frac{c \sqrt{d+e x}}{\sqrt{d f-e f x}}}}{d^2-e^2 x^2} \, dx","Int[(a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))/(d^2 - e^2*x^2),x]","\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}","\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,"(b*ExpIntegralEi[(c*Sqrt[d + e*x]*Log[F])/Sqrt[d*f - e*f*x]])/(d*e) + (a*Log[Sqrt[d + e*x]/Sqrt[d*f - e*f*x]])/(d*e)","A",4,3,45,0.06667,1,"{2291, 14, 2178}"
554,1,14,0,0.0078265,"\int \frac{1}{d^2-e^2 x^2} \, dx","Int[(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",1,1,14,0.07143,1,"{208}"
555,0,0,0,0.2325101,"\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","Int[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,"Defer[Int][1/((a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))*(d^2 - e^2*x^2)), x]","A",0,0,0,0,-1,"{}"
556,0,0,0,0.2248542,"\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","Int[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,"Defer[Int][1/((a + b*F^((c*Sqrt[d + e*x])/Sqrt[d*f - e*f*x]))^2*(d^2 - e^2*x^2)), x]","A",0,0,0,0,-1,"{}"
557,1,77,0,0.2405743,"\int \frac{\left(F^{\frac{\sqrt{1-a x}}{\sqrt{1+a x}}}\right)^n}{1-a^2 x^2} \, dx","Int[(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",3,3,37,0.08108,1,"{2281, 2291, 2178}"
558,1,29,0,0.1064505,"\int \frac{F^{\frac{3 \sqrt{1-a x}}{\sqrt{1+a x}}}}{1-a^2 x^2} \, dx","Int[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",2,2,36,0.05556,1,"{2291, 2178}"
559,1,29,0,0.1077932,"\int \frac{F^{\frac{2 \sqrt{1-a x}}{\sqrt{1+a x}}}}{1-a^2 x^2} \, dx","Int[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",2,2,36,0.05556,1,"{2291, 2178}"
560,1,28,0,0.0958213,"\int \frac{F^{\frac{\sqrt{1-a x}}{\sqrt{1+a x}}}}{1-a^2 x^2} \, dx","Int[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",2,2,35,0.05714,1,"{2291, 2178}"
561,1,29,0,0.1041846,"\int \frac{F^{-\frac{\sqrt{1-a x}}{\sqrt{1+a x}}}}{1-a^2 x^2} \, dx","Int[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",2,2,36,0.05556,1,"{2291, 2178}"
562,1,29,0,0.1048066,"\int \frac{F^{-\frac{2 \sqrt{1-a x}}{\sqrt{1+a x}}}}{1-a^2 x^2} \, dx","Int[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",2,2,36,0.05556,1,"{2291, 2178}"
563,1,49,0,0.0638647,"\int a^x b^x x^2 \, dx","Int[a^x*b^x*x^2,x]","\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}","\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,"(2*a^x*b^x)/(Log[a] + Log[b])^3 - (2*a^x*b^x*x)/(Log[a] + Log[b])^2 + (a^x*b^x*x^2)/(Log[a] + Log[b])","A",4,3,10,0.3000,1,"{2287, 2176, 2194}"
564,1,31,0,0.0286941,"\int a^x b^x x \, dx","Int[a^x*b^x*x,x]","\frac{x a^x b^x}{\log (a)+\log (b)}-\frac{a^x b^x}{(\log (a)+\log (b))^2}","\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) + (a^x*b^x*x)/(Log[a] + Log[b])","A",3,3,8,0.3750,1,"{2287, 2176, 2194}"
565,1,14,0,0.0123337,"\int a^x b^x \, dx","Int[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",2,2,7,0.2857,1,"{2287, 2194}"
566,1,8,0,0.0416269,"\int \frac{a^x b^x}{x} \, dx","Int[(a^x*b^x)/x,x]","\text{Ei}(x (\log (a)+\log (b)))","\text{Ei}(x (\log (a)+\log (b)))",1,"ExpIntegralEi[x*(Log[a] + Log[b])]","A",2,2,10,0.2000,1,"{2287, 2178}"
567,1,26,0,0.0619315,"\int \frac{a^x b^x}{x^2} \, dx","Int[(a^x*b^x)/x^2,x]","(\log (a)+\log (b)) \text{Ei}(x (\log (a)+\log (b)))-\frac{a^x b^x}{x}","(\log (a)+\log (b)) \text{Ei}(x (\log (a)+\log (b)))-\frac{a^x b^x}{x}",1,"-((a^x*b^x)/x) + ExpIntegralEi[x*(Log[a] + Log[b])]*(Log[a] + Log[b])","A",3,3,10,0.3000,1,"{2287, 2177, 2178}"
568,1,51,0,0.0853705,"\int \frac{a^x b^x}{x^3} \, dx","Int[(a^x*b^x)/x^3,x]","-\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)))","-\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,"-(a^x*b^x)/(2*x^2) - (a^x*b^x*(Log[a] + Log[b]))/(2*x) + (ExpIntegralEi[x*(Log[a] + Log[b])]*(Log[a] + Log[b])^2)/2","A",4,3,10,0.3000,1,"{2287, 2177, 2178}"
569,1,19,0,0.0410007,"\int a^x b^x c^x \, dx","Int[a^x*b^x*c^x,x]","\frac{a^x b^x c^x}{\log (a)+\log (b)+\log (c)}","\frac{a^x b^x c^x}{\log (a)+\log (b)+\log (c)}",1,"(a^x*b^x*c^x)/(Log[a] + Log[b] + Log[c])","A",3,2,10,0.2000,1,"{2287, 2194}"
570,1,18,0,0.0211684,"\int a^x b^{-x} \, dx","Int[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",2,2,9,0.2222,1,"{2287, 2194}"
571,1,61,0,0.0697103,"\int a^x b^{-x} x^2 \, dx","Int[(a^x*x^2)/b^x,x]","\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}","\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,"(2*a^x)/(b^x*(Log[a] - Log[b])^3) - (2*a^x*x)/(b^x*(Log[a] - Log[b])^2) + (a^x*x^2)/(b^x*(Log[a] - Log[b]))","A",4,3,12,0.2500,1,"{2287, 2176, 2194}"
572,1,770,0,1.373989,"\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","Int[((d + e*E^(h + i*x))*(f + g*x)^3)/(a + b*E^(h + i*x) + c*E^(2*h + 2*i*x)),x]","\frac{6 g^2 (f+g x) \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\right)}{i^2 \left(\sqrt{b^2-4 a c}+b\right)}-\frac{6 g^3 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\right)}{i^4 \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^2 (f+g x) \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\right)}{i^2 \left(\sqrt{b^2-4 a c}+b\right)}-\frac{6 g^3 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{PolyLog}\left(4,-\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{PolyLog}\left(4,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\right)}{i^4 \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)}",1,"((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)^4)/(4*(b + Sqrt[b^2 - 4*a*c])*g) + ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)^4)/(4*(b - Sqrt[b^2 - 4*a*c])*g) - ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)^3*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*i) - ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)^3*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*i) - (3*(e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g*(f + g*x)^2*PolyLog[2, (-2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*i^2) - (3*(e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g*(f + g*x)^2*PolyLog[2, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*i^2) + (6*(e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g^2*(f + g*x)*PolyLog[3, (-2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*i^3) + (6*(e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g^2*(f + g*x)*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*i^3) - (6*(e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g^3*PolyLog[4, (-2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*i^4) - (6*(e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g^3*PolyLog[4, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*i^4)","A",13,7,44,0.1591,1,"{2265, 2184, 2190, 2531, 6609, 2282, 6589}"
573,1,599,0,1.0022164,"\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","Int[((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 g (f+g x) \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\right)}{i^2 \left(\sqrt{b^2-4 a c}+b\right)}+\frac{2 g^2 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\right)}{i^3 \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 (f+g x) \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\right)}{i^2 \left(\sqrt{b^2-4 a c}+b\right)}+\frac{2 g^2 \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{PolyLog}\left(3,-\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{PolyLog}\left(3,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\right)}{i^3 \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)}",1,"((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)^3)/(3*(b + Sqrt[b^2 - 4*a*c])*g) + ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)^3)/(3*(b - Sqrt[b^2 - 4*a*c])*g) - ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)^2*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*i) - ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)^2*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*i) - (2*(e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g*(f + g*x)*PolyLog[2, (-2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*i^2) - (2*(e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g*(f + g*x)*PolyLog[2, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*i^2) + (2*(e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g^2*PolyLog[3, (-2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*i^3) + (2*(e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g^2*PolyLog[3, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*i^3)","A",11,6,44,0.1364,1,"{2265, 2184, 2190, 2531, 2282, 6589}"
574,1,428,0,0.5825166,"\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","Int[((d + e*E^(h + i*x))*(f + g*x))/(a + b*E^(h + i*x) + c*E^(2*h + 2*i*x)),x]","-\frac{g \left(\frac{2 c d-b e}{\sqrt{b^2-4 a c}}+e\right) \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\right)}{i^2 \left(\sqrt{b^2-4 a c}+b\right)}-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\frac{2 c e^{h+i x}}{\sqrt{b^2-4 a c}+b}\right)}{i^2 \left(\sqrt{b^2-4 a c}+b\right)}-\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)}",1,"((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)^2)/(2*(b + Sqrt[b^2 - 4*a*c])*g) + ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)^2)/(2*(b - Sqrt[b^2 - 4*a*c])*g) - ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)*Log[1 + (2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*i) - ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*(f + g*x)*Log[1 + (2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*i) - ((e + (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g*PolyLog[2, (-2*c*E^(h + i*x))/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*i^2) - ((e - (2*c*d - b*e)/Sqrt[b^2 - 4*a*c])*g*PolyLog[2, (-2*c*E^(h + i*x))/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*i^2)","A",9,5,42,0.1190,1,"{2265, 2184, 2190, 2279, 2391}"
575,1,95,0,0.1514672,"\int \frac{d+e e^{h+i x}}{a+b e^{h+i x}+c e^{2 h+2 i x}} \, dx","Int[(d + e*E^(h + i*x))/(a + b*E^(h + i*x) + c*E^(2*h + 2*i*x)),x]","\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}","\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,"(d*x)/a + ((b*d - 2*a*e)*ArcTanh[(b + 2*c*E^(h + i*x))/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]*i) - (d*Log[a + b*E^(h + i*x) + c*E^(2*h + 2*i*x)])/(2*a*i)","A",7,6,37,0.1622,1,"{2282, 800, 634, 618, 206, 628}"
576,0,0,0,1.017874,"\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","Int[(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,"d*Defer[Int][1/((a + b*E^(h + i*x) + c*E^(2*h + 2*i*x))*(f + g*x)), x] + e*Defer[Int][E^(h + i*x)/((a + b*E^(h + i*x) + c*E^(2*h + 2*i*x))*(f + g*x)), x]","A",0,0,0,0,-1,"{}"
577,0,0,0,0.8698542,"\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","Int[(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,"d*Defer[Int][1/((a + b*E^(h + i*x) + c*E^(2*h + 2*i*x))*(f + g*x)^2), x] + e*Defer[Int][E^(h + i*x)/((a + b*E^(h + i*x) + c*E^(2*h + 2*i*x))*(f + g*x)^2), x]","A",0,0,0,0,-1,"{}"
578,1,150,0,0.6724398,"\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","Int[((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{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{2 d^2}-\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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}","-\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a-\sqrt{a^2+b^2}}\right)}{2 d^2}-\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{\sqrt{a^2+b^2}+a}\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,"x^2/2 - (x*Log[1 + (b*E^(c + d*x))/(a - Sqrt[a^2 + b^2])])/(2*d) - (x*Log[1 + (b*E^(c + d*x))/(a + Sqrt[a^2 + b^2])])/(2*d) - PolyLog[2, -((b*E^(c + d*x))/(a - Sqrt[a^2 + b^2]))]/(2*d^2) - PolyLog[2, -((b*E^(c + d*x))/(a + Sqrt[a^2 + b^2]))]/(2*d^2)","A",9,5,47,0.1064,1,"{2265, 2184, 2190, 2279, 2391}"
579,1,65,0,0.0492867,"\int F^{a+b \log \left(c+d x^n\right)} x^2 \, dx","Int[F^(a + b*Log[c + d*x^n])*x^2,x]","\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)","\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*x^3*(c + d*x^n)^(b*Log[F])*Hypergeometric2F1[3/n, -(b*Log[F]), (3 + n)/n, -((d*x^n)/c)])/(3*(1 + (d*x^n)/c)^(b*Log[F]))","A",4,4,18,0.2222,1,"{2274, 12, 365, 364}"
580,1,65,0,0.0331369,"\int F^{a+b \log \left(c+d x^n\right)} x \, dx","Int[F^(a + b*Log[c + d*x^n])*x,x]","\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)","\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*x^2*(c + d*x^n)^(b*Log[F])*Hypergeometric2F1[2/n, -(b*Log[F]), (2 + n)/n, -((d*x^n)/c)])/(2*(1 + (d*x^n)/c)^(b*Log[F]))","A",4,4,16,0.2500,1,"{2274, 12, 365, 364}"
581,1,56,0,0.0216632,"\int F^{a+b \log \left(c+d x^n\right)} \, dx","Int[F^(a + b*Log[c + d*x^n]),x]","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)","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*x*(c + d*x^n)^(b*Log[F])*Hypergeometric2F1[n^(-1), -(b*Log[F]), 1 + n^(-1), -((d*x^n)/c)])/(1 + (d*x^n)/c)^(b*Log[F])","A",4,4,14,0.2857,1,"{2274, 12, 246, 245}"
582,1,57,0,0.0638044,"\int \frac{F^{a+b \log \left(c+d x^n\right)}}{x} \, dx","Int[F^(a + b*Log[c + d*x^n])/x,x]","-\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)}","-\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*(c + d*x^n)^(1 + b*Log[F])*Hypergeometric2F1[1, 1 + b*Log[F], 2 + b*Log[F], 1 + (d*x^n)/c])/(c*n*(1 + b*Log[F])))","A",4,4,18,0.2222,1,"{2274, 12, 266, 65}"
583,1,66,0,0.0450553,"\int \frac{F^{a+b \log \left(c+d x^n\right)}}{x^2} \, dx","Int[F^(a + b*Log[c + d*x^n])/x^2,x]","-\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}","-\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*(c + d*x^n)^(b*Log[F])*Hypergeometric2F1[-n^(-1), -(b*Log[F]), -((1 - n)/n), -((d*x^n)/c)])/(x*(1 + (d*x^n)/c)^(b*Log[F])))","A",4,4,18,0.2222,1,"{2274, 12, 365, 364}"
584,1,68,0,0.0449979,"\int \frac{F^{a+b \log \left(c+d x^n\right)}}{x^3} \, dx","Int[F^(a + b*Log[c + d*x^n])/x^3,x]","-\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}","-\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*(c + d*x^n)^(b*Log[F])*Hypergeometric2F1[-2/n, -(b*Log[F]), -((2 - n)/n), -((d*x^n)/c)])/(2*x^2*(1 + (d*x^n)/c)^(b*Log[F]))","A",4,4,18,0.2222,1,"{2274, 12, 365, 364}"
585,1,77,0,0.0547465,"\int F^{a+b \log \left(c+d x^n\right)} (d x)^m \, dx","Int[F^(a + b*Log[c + d*x^n])*(d*x)^m,x]","\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)}","\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*(d*x)^(1 + m)*(c + d*x^n)^(b*Log[F])*Hypergeometric2F1[(1 + m)/n, -(b*Log[F]), (1 + m + n)/n, -((d*x^n)/c)])/(d*(1 + m)*(1 + (d*x^n)/c)^(b*Log[F]))","A",4,4,20,0.2000,1,"{2274, 12, 365, 364}"
586,1,76,0,0.1569267,"\int e^{\log ^2\left((d+e x)^n\right)} (d+e x)^m \, dx","Int[E^Log[(d + e*x)^n]^2*(d + e*x)^m,x]","\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}","\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,"(Sqrt[Pi]*(d + e*x)^(1 + m)*Erfi[(1 + m + 2*n*Log[(d + e*x)^n])/(2*n)])/(2*e*E^((1 + m)^2/(4*n^2))*n*((d + e*x)^n)^((1 + m)/n))","A",4,3,20,0.1500,1,"{2276, 2234, 2204}"
587,1,136,0,0.3896829,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (d g+e g x)^m \, dx","Int[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(d*g + e*g*x)^m,x]","\frac{\sqrt{\pi } F^{a f} (g (d+e 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)}}","\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,"(F^(a*f)*Sqrt[Pi]*(g*(d + e*x))^(1 + m)*Erfi[(1 + m + 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 + m)^2/(4*b*f*n^2*Log[F]))*Sqrt[f]*g*n*(c*(d + e*x)^n)^((1 + m)/n)*Sqrt[Log[F]])","A",4,3,31,0.09677,1,"{2276, 2234, 2204}"
588,1,123,0,0.2493056,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (d g+e g x)^2 \, dx","Int[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",5,4,31,0.1290,1,"{12, 2276, 2234, 2204}"
589,1,115,0,0.207366,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (d g+e g x) \, dx","Int[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",5,4,29,0.1379,1,"{12, 2276, 2234, 2204}"
590,1,118,0,0.1265913,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} \, dx","Int[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",4,3,20,0.1500,1,"{2275, 2234, 2204}"
591,1,67,0,0.1440662,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{d g+e g x} \, dx","Int[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",4,3,31,0.09677,1,"{12, 2276, 2204}"
592,1,121,0,0.2339332,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(d g+e g x)^2} \, dx","Int[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{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)}","-\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",5,4,31,0.1290,1,"{12, 2276, 2234, 2204}"
593,1,118,0,0.2306705,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(d g+e g x)^3} \, dx","Int[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{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}","-\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",5,4,31,0.1290,1,"{12, 2276, 2234, 2204}"
594,0,0,0,0.0762954,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x)^m \, dx","Int[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,"Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(g + h*x)^m, x]","A",0,0,0,0,-1,"{}"
595,0,0,0,0.3763675,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x)^3 \, dx","Int[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(g + h*x)^3,x]","\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x)^3 \, dx","\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)*g^3*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]]) + 3*g^2*h*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n]^2))*x, x] + 3*g*h^2*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n]^2))*x^2, x] + h^3*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n]^2))*x^3, x]","F",0,0,0,0,-1,"{}"
596,0,0,0,0.3061636,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x)^2 \, dx","Int[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(g + h*x)^2,x]","\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x)^2 \, dx","\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)*g^2*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]]) + 2*g*h*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n]^2))*x, x] + h^2*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n]^2))*x^2, x]","F",0,0,0,0,-1,"{}"
597,0,0,0,0.2295301,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x) \, dx","Int[F^(f*(a + b*Log[c*(d + e*x)^n]^2))*(g + h*x),x]","\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} (g+h x) \, dx","\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)*g*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]]) + h*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n]^2))*x, x]","F",0,0,0,0,-1,"{}"
598,1,118,0,0.0938932,"\int F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)} \, dx","Int[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",4,3,20,0.1500,1,"{2275, 2234, 2204}"
599,0,0,0,0.0836023,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{g+h x} \, dx","Int[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,"Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(g + h*x), x]","A",0,0,0,0,-1,"{}"
600,0,0,0,0.0852799,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(g+h x)^2} \, dx","Int[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,"Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(g + h*x)^2, x]","A",0,0,0,0,-1,"{}"
601,0,0,0,0.0834928,"\int \frac{F^{f \left(a+b \log ^2\left(c (d+e x)^n\right)\right)}}{(g+h x)^3} \, dx","Int[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,"Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n]^2))/(g + h*x)^3, x]","A",0,0,0,0,-1,"{}"
602,1,152,0,0.7570045,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (d g+e g x)^m \, dx","Int[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(d*g + e*g*x)^m,x]","\frac{\sqrt{\pi } F^{a^2 f} (d+e x) (g (d+e 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)}}","\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,"(F^(a^2*f)*Sqrt[Pi]*(d + e*x)*(g*(d + e*x))^m*Erfi[(1 + m + 2*a*b*f*n*Log[F] + 2*b^2*f*n*Log[F]*Log[c*(d + e*x)^n])/(2*b*Sqrt[f]*n*Sqrt[Log[F]])])/(2*b*e*E^((1 + m + 2*a*b*f*n*Log[F])^2/(4*b^2*f*n^2*Log[F]))*Sqrt[f]*n*(c*(d + e*x)^n)^((1 + m)/n)*Sqrt[Log[F]])","A",8,7,31,0.2258,1,"{2278, 2274, 15, 20, 2276, 2234, 2204}"
603,1,133,0,0.4107366,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (d g+e g x)^2 \, dx","Int[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(d*g + e*g*x)^2,x]","\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)}}","\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]*(d + e*x)^3*Erfi[(3/n + 2*a*b*f*Log[F] + 2*b^2*f*Log[F]*Log[c*(d + e*x)^n])/(2*b*Sqrt[f]*Sqrt[Log[F]])])/(2*b*e*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",8,7,31,0.2258,1,"{12, 2278, 2274, 15, 2276, 2234, 2204}"
604,1,122,0,0.3694189,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (d g+e g x) \, dx","Int[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{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)}}","\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[(n^(-1) + a*b*f*Log[F] + b^2*f*Log[F]*Log[c*(d + e*x)^n])/(b*Sqrt[f]*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",8,7,29,0.2414,1,"{12, 2278, 2274, 15, 2276, 2234, 2204}"
605,1,126,0,0.232463,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[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 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)}}","\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[(n^(-1) + 2*a*b*f*Log[F] + 2*b^2*f*Log[F]*Log[c*(d + e*x)^n])/(2*b*Sqrt[f]*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",7,6,20,0.3000,1,"{2277, 2274, 15, 2276, 2234, 2204}"
606,1,70,0,0.2677448,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{d g+e g x} \, dx","Int[F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(d*g + e*g*x),x]","\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)}}","\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[a*Sqrt[f]*Sqrt[Log[F]] + b*Sqrt[f]*Sqrt[Log[F]]*Log[c*(d + e*x)^n]])/(2*b*e*Sqrt[f]*g*n*Sqrt[Log[F]])","A",8,7,31,0.2258,1,"{12, 2278, 2274, 15, 2276, 2234, 2204}"
607,1,128,0,0.4118686,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(d g+e g x)^2} \, dx","Int[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{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)}","-\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^(a/(b*n) - 1/(4*b^2*f*n^2*Log[F]))*Sqrt[Pi]*(c*(d + e*x)^n)^n^(-1)*Erfi[(n^(-1) - 2*a*b*f*Log[F] - 2*b^2*f*Log[F]*Log[c*(d + e*x)^n])/(2*b*Sqrt[f]*Sqrt[Log[F]])])/(2*b*e*Sqrt[f]*g^2*n*(d + e*x)*Sqrt[Log[F]])","A",8,7,31,0.2258,1,"{12, 2278, 2274, 15, 2276, 2234, 2204}"
608,1,126,0,0.4052781,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(d g+e g x)^3} \, dx","Int[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{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}","-\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,"-(Sqrt[Pi]*(c*(d + e*x)^n)^(2/n)*Erfi[(n^(-1) - a*b*f*Log[F] - b^2*f*Log[F]*Log[c*(d + e*x)^n])/(b*Sqrt[f]*Sqrt[Log[F]])])/(2*b*e*E^((1 - 2*a*b*f*n*Log[F])/(b^2*f*n^2*Log[F]))*Sqrt[f]*g^3*n*(d + e*x)^2*Sqrt[Log[F]])","A",8,7,31,0.2258,1,"{12, 2278, 2274, 15, 2276, 2234, 2204}"
609,0,0,0,0.0886785,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x)^m \, dx","Int[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,"Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(g + h*x)^m, x]","A",0,0,0,0,-1,"{}"
610,0,0,0,0.4931987,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x)^3 \, dx","Int[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(g + h*x)^3,x]","\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x)^3 \, dx","\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,"(g^3*Sqrt[Pi]*(d + e*x)*Erfi[(n^(-1) + 2*a*b*f*Log[F] + 2*b^2*f*Log[F]*Log[c*(d + e*x)^n])/(2*b*Sqrt[f]*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]]) + 3*g^2*h*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)*x, x] + 3*g*h^2*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)*x^2, x] + h^3*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)*x^3, x]","F",0,0,0,0,-1,"{}"
611,0,0,0,0.367427,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x)^2 \, dx","Int[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(g + h*x)^2,x]","\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x)^2 \, dx","\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,"(g^2*Sqrt[Pi]*(d + e*x)*Erfi[(n^(-1) + 2*a*b*f*Log[F] + 2*b^2*f*Log[F]*Log[c*(d + e*x)^n])/(2*b*Sqrt[f]*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]]) + 2*g*h*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)*x, x] + h^2*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)*x^2, x]","F",0,0,0,0,-1,"{}"
612,0,0,0,0.305888,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x) \, dx","Int[F^(f*(a + b*Log[c*(d + e*x)^n])^2)*(g + h*x),x]","\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} (g+h x) \, dx","\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,"(g*Sqrt[Pi]*(d + e*x)*Erfi[(n^(-1) + 2*a*b*f*Log[F] + 2*b^2*f*Log[F]*Log[c*(d + e*x)^n])/(2*b*Sqrt[f]*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]]) + h*Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)*x, x]","F",0,0,0,0,-1,"{}"
613,1,126,0,0.1427265,"\int F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2} \, dx","Int[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 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)}}","\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[(n^(-1) + 2*a*b*f*Log[F] + 2*b^2*f*Log[F]*Log[c*(d + e*x)^n])/(2*b*Sqrt[f]*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",7,6,20,0.3000,1,"{2277, 2274, 15, 2276, 2234, 2204}"
614,0,0,0,0.0942562,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{g+h x} \, dx","Int[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,"Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x), x]","A",0,0,0,0,-1,"{}"
615,0,0,0,0.1024569,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(g+h x)^2} \, dx","Int[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,"Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x)^2, x]","A",0,0,0,0,-1,"{}"
616,0,0,0,0.0993224,"\int \frac{F^{f \left(a+b \log \left(c (d+e x)^n\right)\right)^2}}{(g+h x)^3} \, dx","Int[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,"Defer[Int][F^(f*(a + b*Log[c*(d + e*x)^n])^2)/(g + h*x)^3, x]","A",0,0,0,0,-1,"{}"
617,1,17,0,0.0520096,"\int F^{a+b x+c x^3} \left(b+3 c x^2\right) \, dx","Int[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",1,1,21,0.04762,1,"{6706}"
618,1,20,0,0.1661466,"\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","Int[(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+b x+c x^2}}}{\log (F)}","-\frac{F^{\frac{1}{a+b x+c x^2}}}{\log (F)}",1,"-(F^(a + b*x + c*x^2)^(-1)/Log[F])","A",1,1,33,0.03030,1,"{6706}"
619,1,49,0,0.1995967,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^m \, dx","Int[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^m,x]","\left(-a-b x-c x^2\right)^{-m} \left(a+b x+c x^2\right)^m \text{Gamma}\left(m+1,-a-b x-c x^2\right)","\left(-a-b x-c x^2\right)^{-m} \left(a+b x+c x^2\right)^m \text{Gamma}\left(m+1,-a-b x-c x^2\right)",1,"((a + b*x + c*x^2)^m*Gamma[1 + m, -a - b*x - c*x^2])/(-a - b*x - c*x^2)^m","A",2,2,31,0.06452,1,"{6707, 2181}"
620,1,90,0,0.1817028,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^3 \, dx","Int[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^3,x]","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}","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,"-6*E^(a + b*x + c*x^2) + 6*E^(a + b*x + c*x^2)*(a + b*x + c*x^2) - 3*E^(a + b*x + c*x^2)*(a + b*x + c*x^2)^2 + E^(a + b*x + c*x^2)*(a + b*x + c*x^2)^3","A",5,3,31,0.09677,1,"{6707, 2176, 2194}"
621,1,64,0,0.1606827,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^2 \, dx","Int[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^2,x]","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}","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,"2*E^(a + b*x + c*x^2) - 2*E^(a + b*x + c*x^2)*(a + b*x + c*x^2) + E^(a + b*x + c*x^2)*(a + b*x + c*x^2)^2","A",4,3,31,0.09677,1,"{6707, 2176, 2194}"
622,1,38,0,0.0956658,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right) \, dx","Int[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2),x]","e^{a+b x+c x^2} \left(a+b x+c x^2\right)-e^{a+b x+c x^2}","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 + b*x + c*x^2) + E^(a + b*x + c*x^2)*(a + b*x + c*x^2)","A",3,3,29,0.1034,1,"{6707, 2176, 2194}"
623,1,12,0,0.0192453,"\int e^{a+b x+c x^2} (b+2 c x) \, dx","Int[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",1,1,19,0.05263,1,"{2236}"
624,1,11,0,0.1765938,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{a+b x+c x^2} \, dx","Int[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2),x]","\text{Ei}\left(a+b x+c x^2\right)","\text{Ei}\left(a+b x+c x^2\right)",1,"ExpIntegralEi[a + b*x + c*x^2]","A",2,2,31,0.06452,1,"{6707, 2178}"
625,1,38,0,0.1970198,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^2} \, dx","Int[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^2,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}","\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 + b*x + c*x^2)/(a + b*x + c*x^2)) + ExpIntegralEi[a + b*x + c*x^2]","A",3,3,31,0.09677,1,"{6707, 2177, 2178}"
626,1,72,0,0.2411479,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^3} \, dx","Int[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^3,x]","\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}","\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 + b*x + c*x^2)/(2*(a + b*x + c*x^2)^2) - E^(a + b*x + c*x^2)/(2*(a + b*x + c*x^2)) + ExpIntegralEi[a + b*x + c*x^2]/2","A",4,3,31,0.09677,1,"{6707, 2177, 2178}"
627,1,142,0,0.6333174,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^{7/2} \, dx","Int[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(7/2),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}","\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,"(-105*E^(a + b*x + c*x^2)*Sqrt[a + b*x + c*x^2])/8 + (35*E^(a + b*x + c*x^2)*(a + b*x + c*x^2)^(3/2))/4 - (7*E^(a + b*x + c*x^2)*(a + b*x + c*x^2)^(5/2))/2 + E^(a + b*x + c*x^2)*(a + b*x + c*x^2)^(7/2) + (105*Sqrt[Pi]*Erfi[Sqrt[a + b*x + c*x^2]])/16","A",7,4,33,0.1212,1,"{6707, 2176, 2180, 2204}"
628,1,112,0,0.4570195,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2),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}","-\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,"(15*E^(a + b*x + c*x^2)*Sqrt[a + b*x + c*x^2])/4 - (5*E^(a + b*x + c*x^2)*(a + b*x + c*x^2)^(3/2))/2 + E^(a + b*x + c*x^2)*(a + b*x + c*x^2)^(5/2) - (15*Sqrt[Pi]*Erfi[Sqrt[a + b*x + c*x^2]])/8","A",6,4,33,0.1212,1,"{6707, 2176, 2180, 2204}"
629,1,82,0,0.3629432,"\int e^{a+b x+c x^2} (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[E^(a + b*x + c*x^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2),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}","\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,"(-3*E^(a + b*x + c*x^2)*Sqrt[a + b*x + c*x^2])/2 + E^(a + b*x + c*x^2)*(a + b*x + c*x^2)^(3/2) + (3*Sqrt[Pi]*Erfi[Sqrt[a + b*x + c*x^2]])/4","A",5,4,33,0.1212,1,"{6707, 2176, 2180, 2204}"
630,1,52,0,0.2349005,"\int e^{a+b x+c x^2} (b+2 c x) \sqrt{a+b x+c x^2} \, dx","Int[E^(a + b*x + c*x^2)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2],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)","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,"E^(a + b*x + c*x^2)*Sqrt[a + b*x + c*x^2] - (Sqrt[Pi]*Erfi[Sqrt[a + b*x + c*x^2]])/2","A",4,4,33,0.1212,1,"{6707, 2176, 2180, 2204}"
631,1,21,0,0.2639319,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\sqrt{a+b x+c x^2}} \, dx","Int[(E^(a + b*x + c*x^2)*(b + 2*c*x))/Sqrt[a + b*x + c*x^2],x]","\sqrt{\pi } \text{Erfi}\left(\sqrt{a+b x+c x^2}\right)","\sqrt{\pi } \text{Erfi}\left(\sqrt{a+b x+c x^2}\right)",1,"Sqrt[Pi]*Erfi[Sqrt[a + b*x + c*x^2]]","A",3,3,33,0.09091,1,"{6707, 2180, 2204}"
632,1,51,0,0.3148059,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^(3/2),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}}","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 + b*x + c*x^2))/Sqrt[a + b*x + c*x^2] + 2*Sqrt[Pi]*Erfi[Sqrt[a + b*x + c*x^2]]","A",4,4,33,0.1212,1,"{6707, 2177, 2180, 2204}"
633,1,85,0,0.3480269,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^(5/2),x]","\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}}","\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 + b*x + c*x^2))/(3*(a + b*x + c*x^2)^(3/2)) - (4*E^(a + b*x + c*x^2))/(3*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[Pi]*Erfi[Sqrt[a + b*x + c*x^2]])/3","A",5,4,33,0.1212,1,"{6707, 2177, 2180, 2204}"
634,1,115,0,0.3546599,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Int[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^(7/2),x]","\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}}","\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 + b*x + c*x^2))/(5*(a + b*x + c*x^2)^(5/2)) - (4*E^(a + b*x + c*x^2))/(15*(a + b*x + c*x^2)^(3/2)) - (8*E^(a + b*x + c*x^2))/(15*Sqrt[a + b*x + c*x^2]) + (8*Sqrt[Pi]*Erfi[Sqrt[a + b*x + c*x^2]])/15","A",6,4,33,0.1212,1,"{6707, 2177, 2180, 2204}"
635,1,145,0,0.3794057,"\int \frac{e^{a+b x+c x^2} (b+2 c x)}{\left(a+b x+c x^2\right)^{9/2}} \, dx","Int[(E^(a + b*x + c*x^2)*(b + 2*c*x))/(a + b*x + c*x^2)^(9/2),x]","\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}}","\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 + b*x + c*x^2))/(7*(a + b*x + c*x^2)^(7/2)) - (4*E^(a + b*x + c*x^2))/(35*(a + b*x + c*x^2)^(5/2)) - (8*E^(a + b*x + c*x^2))/(105*(a + b*x + c*x^2)^(3/2)) - (16*E^(a + b*x + c*x^2))/(105*Sqrt[a + b*x + c*x^2]) + (16*Sqrt[Pi]*Erfi[Sqrt[a + b*x + c*x^2]])/105","A",7,4,33,0.1212,1,"{6707, 2177, 2180, 2204}"
636,1,8,0,0.0284385,"\int \frac{e^{-x}}{\sqrt{1-e^{-2 x}}} \, dx","Int[1/(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",2,2,19,0.1053,1,"{2249, 216}"
637,1,12,0,0.0193594,"\int \frac{e^x}{4+e^{2 x}} \, dx","Int[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",2,2,13,0.1538,1,"{2249, 203}"
638,1,4,0,0.0196363,"\int \frac{e^x}{1-e^{2 x}} \, dx","Int[E^x/(1 - E^(2*x)),x]","\tanh ^{-1}\left(e^x\right)","\tanh ^{-1}\left(e^x\right)",1,"ArcTanh[E^x]","A",2,2,15,0.1333,1,"{2249, 206}"
639,1,20,0,0.0217914,"\int \frac{e^x}{3-4 e^{2 x}} \, dx","Int[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",2,2,15,0.1333,1,"{2249, 206}"
640,1,36,0,0.0288832,"\int e^x \sqrt{3-4 e^{2 x}} \, dx","Int[E^x*Sqrt[3 - 4*E^(2*x)],x]","\frac{1}{2} e^x \sqrt{3-4 e^{2 x}}+\frac{3}{4} \sin ^{-1}\left(\frac{2 e^x}{\sqrt{3}}\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,"(E^x*Sqrt[3 - 4*E^(2*x)])/2 + (3*ArcSin[(2*E^x)/Sqrt[3]])/4","A",3,3,17,0.1765,1,"{2249, 195, 216}"
641,1,22,0,0.021128,"\int e^{x^2} x^3 \, dx","Int[E^x^2*x^3,x]","\frac{1}{2} e^{x^2} x^2-\frac{e^{x^2}}{2}","\frac{1}{2} e^{x^2} x^2-\frac{e^{x^2}}{2}",1,"-E^x^2/2 + (E^x^2*x^2)/2","A",2,2,9,0.2222,1,"{2212, 2209}"
642,1,29,0,0.026527,"\int e^x \sqrt{1-e^{2 x}} \, dx","Int[E^x*Sqrt[1 - E^(2*x)],x]","\frac{1}{2} e^x \sqrt{1-e^{2 x}}+\frac{1}{2} \sin ^{-1}\left(e^x\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)])/2 + ArcSin[E^x]/2","A",3,3,17,0.1765,1,"{2249, 195, 216}"
643,1,14,0,0.0362688,"\int \frac{e^x}{\sqrt{1+e^x+e^{2 x}}} \, dx","Int[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",3,3,18,0.1667,1,"{2282, 619, 215}"
644,1,12,0,0.0198792,"\int \frac{e^x}{-4+e^{2 x}} \, dx","Int[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,"-ArcTanh[E^x/2]/2","A",2,2,13,0.1538,1,"{2249, 207}"
645,1,13,0,0.0093858,"\int e^{2-x^2} x \, dx","Int[E^(2 - x^2)*x,x]","-\frac{1}{2} e^{2-x^2}","-\frac{1}{2} e^{2-x^2}",1,"-E^(2 - x^2)/2","A",1,1,11,0.09091,1,"{2209}"
646,1,16,0,0.004769,"\int \left(e^x-x^e\right) \, dx","Int[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",2,1,9,0.1111,1,"{2194}"
647,1,18,0,0.0258383,"\int \frac{-1+e^{2 x}}{3+e^{2 x}} \, dx","Int[(-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,"-x/3 + (2*Log[3 + E^(2*x)])/3","A",3,2,17,0.1176,1,"{2282, 72}"
648,1,4,0,0.0226324,"\int \frac{e^x}{\sqrt{1-e^{2 x}}} \, dx","Int[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",2,2,17,0.1176,1,"{2249, 216}"
649,1,10,0,0.0204029,"\int \frac{e^{2 x}}{1+e^{4 x}} \, dx","Int[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",2,2,15,0.1333,1,"{2249, 203}"
650,1,27,0,0.0188416,"\int \frac{1}{-3 e^x+e^{2 x}} \, dx","Int[(-3*E^x + E^(2*x))^(-1),x]","-\frac{x}{9}+\frac{e^{-x}}{3}+\frac{1}{9} \log \left(3-e^x\right)","-\frac{x}{9}+\frac{e^{-x}}{3}+\frac{1}{9} \log \left(3-e^x\right)",1,"1/(3*E^x) - x/9 + Log[3 - E^x]/9","A",3,2,13,0.1538,1,"{2282, 44}"
651,1,12,0,0.0351896,"\int \frac{e^x \left(-2+e^x\right)}{1+e^x} \, dx","Int[(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",3,2,16,0.1250,1,"{2282, 43}"
652,1,6,0,0.0188114,"\int \frac{e^x}{-1+e^{2 x}} \, dx","Int[E^x/(-1 + E^(2*x)),x]","-\tanh ^{-1}\left(e^x\right)","-\tanh ^{-1}\left(e^x\right)",1,"-ArcTanh[E^x]","A",2,2,13,0.1538,1,"{2249, 207}"
653,1,4,0,0.0190307,"\int \frac{e^x}{1+e^{2 x}} \, dx","Int[E^x/(1 + E^(2*x)),x]","\tan ^{-1}\left(e^x\right)","\tan ^{-1}\left(e^x\right)",1,"ArcTan[E^x]","A",2,2,13,0.1538,1,"{2249, 203}"
654,1,14,0,0.0398882,"\int \frac{e^{-x}+e^x}{-e^{-x}+e^x} \, dx","Int[(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",4,3,23,0.1304,1,"{2282, 446, 72}"
655,1,12,0,0.0372131,"\int \frac{-e^{-x}+e^x}{e^{-x}+e^x} \, dx","Int[(-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",4,3,23,0.1304,1,"{2282, 446, 72}"
656,1,18,0,0.0444535,"\int \frac{e^{-2 x}+e^{2 x}}{-e^{-2 x}+e^{2 x}} \, dx","Int[(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",4,3,27,0.1111,1,"{2282, 446, 72}"
657,1,4,0,0.0214806,"\int \frac{e^x}{\sqrt{1+e^{2 x}}} \, dx","Int[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",2,2,15,0.1333,1,"{2249, 215}"
658,1,11,0,0.0237167,"\int \frac{e^{\sqrt{4+x}}}{\sqrt{4+x}} \, dx","Int[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",1,1,17,0.05882,1,"{2209}"
659,1,18,0,0.0605359,"\int \frac{x}{\sqrt{-1+e^{2 x^2}}} \, dx","Int[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",4,4,15,0.2667,1,"{6715, 2282, 63, 203}"
660,1,31,0,0.0250647,"\int e^x \sqrt{9+e^{2 x}} \, dx","Int[E^x*Sqrt[9 + E^(2*x)],x]","\frac{1}{2} e^x \sqrt{e^{2 x}+9}+\frac{9}{2} \sinh ^{-1}\left(\frac{e^x}{3}\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)])/2 + (9*ArcSinh[E^x/3])/2","A",3,3,15,0.2000,1,"{2249, 195, 215}"
661,1,27,0,0.022784,"\int e^x \sqrt{1+e^{2 x}} \, dx","Int[E^x*Sqrt[1 + E^(2*x)],x]","\frac{1}{2} e^x \sqrt{e^{2 x}+1}+\frac{1}{2} \sinh ^{-1}\left(e^x\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)])/2 + ArcSinh[E^x]/2","A",3,3,15,0.2000,1,"{2249, 195, 215}"
662,1,10,0,0.1264919,"\int \frac{e^{x^2} x}{1+e^{2 x^2}} \, dx","Int[(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",3,3,18,0.1667,1,"{6715, 2249, 203}"
663,1,28,0,0.0423121,"\int e^{x^{3/2}} x^2 \, dx","Int[E^x^(3/2)*x^2,x]","\frac{2}{3} e^{x^{3/2}} x^{3/2}-\frac{2 e^{x^{3/2}}}{3}","\frac{2}{3} e^{x^{3/2}} x^{3/2}-\frac{2 e^{x^{3/2}}}{3}",1,"(-2*E^x^(3/2))/3 + (2*E^x^(3/2)*x^(3/2))/3","A",3,3,11,0.2727,1,"{2216, 2212, 2209}"
664,1,16,0,0.0244502,"\int \frac{e^x}{\sqrt{-3+e^{2 x}}} \, dx","Int[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",3,3,15,0.2000,1,"{2249, 217, 206}"
665,1,12,0,0.0221998,"\int \frac{e^x}{16-e^{2 x}} \, dx","Int[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",2,2,15,0.1333,1,"{2249, 206}"
666,1,10,0,0.0208617,"\int \frac{e^{5 x}}{1+e^{10 x}} \, dx","Int[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",2,2,15,0.1333,1,"{2249, 203}"
667,1,14,0,0.0234841,"\int \frac{e^{4 x}}{\sqrt{16+e^{8 x}}} \, dx","Int[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",2,2,17,0.1176,1,"{2249, 215}"
668,1,35,0,0.1785501,"\int e^{4 x^3} x^2 \cos \left(7 x^3\right) \, dx","Int[E^(4*x^3)*x^2*Cos[7*x^3],x]","\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)","\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,"(4*E^(4*x^3)*Cos[7*x^3])/195 + (7*E^(4*x^3)*Sin[7*x^3])/195","A",2,2,17,0.1176,1,"{6715, 4433}"
669,1,11,0,0.008696,"\int e^{1+x^2} x \, dx","Int[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",1,1,9,0.1111,1,"{2209}"
670,1,11,0,0.0155205,"\int e^{1+x^3} x^2 \, dx","Int[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",1,1,11,0.09091,1,"{2209}"
671,1,9,0,0.0103662,"\int \frac{e^{\sqrt{x}}}{\sqrt{x}} \, dx","Int[E^Sqrt[x]/Sqrt[x],x]","2 e^{\sqrt{x}}","2 e^{\sqrt{x}}",1,"2*E^Sqrt[x]","A",1,1,13,0.07692,1,"{2209}"
672,1,9,0,0.0109865,"\int \frac{e^{\sqrt[3]{x}}}{x^{2/3}} \, dx","Int[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",1,1,13,0.07692,1,"{2209}"
673,1,68,0,0.1073935,"\int e^{3 x} \left(-8+2 x^3+x^5\right) \, dx","Int[E^(3*x)*(-8 + 2*x^3 + x^5),x]","\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}","\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,"(-724*E^(3*x))/243 + (76*E^(3*x)*x)/81 - (38*E^(3*x)*x^2)/27 + (38*E^(3*x)*x^3)/27 - (5*E^(3*x)*x^4)/9 + (E^(3*x)*x^5)/3","A",13,3,16,0.1875,1,"{2196, 2194, 2176}"
674,1,28,0,0.023869,"\int \left(e^x+x\right)^2 \, dx","Int[(E^x + x)^2,x]","\frac{x^3}{3}+2 e^x x-2 e^x+\frac{e^{2 x}}{2}","\frac{x^3}{3}+2 e^x x-2 e^x+\frac{e^{2 x}}{2}",1,"-2*E^x + E^(2*x)/2 + 2*E^x*x + x^3/3","A",5,3,7,0.4286,1,"{6742, 2194, 2176}"
675,1,26,0,0.0220473,"\int e^{-4 x} \left(e^x+e^{2 x}+e^{3 x}\right) \, dx","Int[(E^x + E^(2*x) + E^(3*x))/E^(4*x),x]","-\frac{1}{3} e^{-3 x}-\frac{e^{-2 x}}{2}-e^{-x}","-\frac{1}{3} e^{-3 x}-\frac{e^{-2 x}}{2}-e^{-x}",1,"-1/(3*E^(3*x)) - 1/(2*E^(2*x)) - E^(-x)","A",3,2,20,0.1000,1,"{2282, 14}"
676,1,9,0,0.0241844,"\int \frac{e^x}{1+2 e^x+e^{2 x}} \, dx","Int[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",2,2,18,0.1111,1,"{2282, 32}"
677,1,27,0,0.0103131,"\int e^{-x} \cos (3 x) \, dx","Int[Cos[3*x]/E^x,x]","\frac{3}{10} e^{-x} \sin (3 x)-\frac{1}{10} e^{-x} \cos (3 x)","\frac{3}{10} e^{-x} \sin (3 x)-\frac{1}{10} e^{-x} \cos (3 x)",1,"-Cos[3*x]/(10*E^x) + (3*Sin[3*x])/(10*E^x)","A",1,1,10,0.1000,1,"{4433}"
678,1,17,0,0.0320087,"\int \frac{e^{2 x}}{2+3 e^x+e^{2 x}} \, dx","Int[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",4,3,20,0.1500,1,"{2282, 632, 31}"
679,1,12,0,0.0224585,"\int \frac{e^{2 x}}{1+e^x} \, dx","Int[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",3,2,13,0.1538,1,"{2248, 43}"
680,1,27,0,0.0107157,"\int e^{3 x} \cos (5 x) \, dx","Int[E^(3*x)*Cos[5*x],x]","\frac{5}{34} e^{3 x} \sin (5 x)+\frac{3}{34} e^{3 x} \cos (5 x)","\frac{5}{34} e^{3 x} \sin (5 x)+\frac{3}{34} e^{3 x} \cos (5 x)",1,"(3*E^(3*x)*Cos[5*x])/34 + (5*E^(3*x)*Sin[5*x])/34","A",1,1,10,0.1000,1,"{4433}"
681,1,5,0,0.013739,"\int e^x \text{sech}\left(e^x\right) \, dx","Int[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",2,2,8,0.2500,1,"{2282, 3770}"
682,1,21,0,0.0252346,"\int \frac{e^{-x}}{1+2 e^x} \, dx","Int[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",3,2,15,0.1333,1,"{2248, 44}"
683,1,27,0,0.0099718,"\int e^x \cos (4+3 x) \, dx","Int[E^x*Cos[4 + 3*x],x]","\frac{3}{10} e^x \sin (3 x+4)+\frac{1}{10} e^x \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])/10 + (3*E^x*Sin[4 + 3*x])/10","A",1,1,10,0.1000,1,"{4433}"
684,1,34,0,0.0298723,"\int e^x \sec ^3\left(1-e^x\right) \, dx","Int[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,"-ArcTanh[Sin[1 - E^x]]/2 - (Sec[1 - E^x]*Tan[1 - E^x])/2","A",3,3,14,0.2143,1,"{2282, 3768, 3770}"
685,1,26,0,0.0174877,"\int \left(e^{-x}+e^x\right) x \, dx","Int[(E^(-x) + E^x)*x,x]","-e^{-x} x+e^x x-e^{-x}-e^x","-e^{-x} x+e^x x-e^{-x}-e^x",1,"-E^(-x) - E^x - x/E^x + E^x*x","A",6,3,11,0.2727,1,"{14, 2176, 2194}"
686,1,15,0,0.0289803,"\int \frac{e^x}{2+3 e^x+e^{2 x}} \, dx","Int[E^x/(2 + 3*E^x + E^(2*x)),x]","\log \left(e^x+1\right)-\log \left(e^x+2\right)","\log \left(e^x+1\right)-\log \left(e^x+2\right)",1,"Log[1 + E^x] - Log[2 + E^x]","A",4,3,18,0.1667,1,"{2282, 616, 31}"
687,1,27,0,0.0259199,"\int \frac{e^{2 x}}{\sqrt[3]{1+e^x}} \, dx","Int[E^(2*x)/(1 + E^x)^(1/3),x]","\frac{3}{5} \left(e^x+1\right)^{5/3}-\frac{3}{2} \left(e^x+1\right)^{2/3}","\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))/2 + (3*(1 + E^x)^(5/3))/5","A",3,2,15,0.1333,1,"{2248, 43}"
688,1,27,0,0.0258179,"\int \frac{e^{2 x}}{\sqrt[4]{1+e^x}} \, dx","Int[E^(2*x)/(1 + E^x)^(1/4),x]","\frac{4}{7} \left(e^x+1\right)^{7/4}-\frac{4}{3} \left(e^x+1\right)^{3/4}","\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))/3 + (4*(1 + E^x)^(7/4))/7","A",3,2,15,0.1333,1,"{2248, 43}"
689,1,62,0,0.052227,"\int \frac{-e^x+2 e^{2 x}}{\sqrt{-1-6 e^x+3 e^{2 x}}} \, dx","Int[(-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{\sqrt{3} \left(1-e^x\right)}{\sqrt{-6 e^x+3 e^{2 x}-1}}\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[(Sqrt[3]*(1 - E^x))/Sqrt[-1 - 6*E^x + 3*E^(2*x)]]/Sqrt[3]","A",4,4,32,0.1250,1,"{2282, 640, 621, 206}"
690,1,19,0,0.0429315,"\int e^x \left(-5 x+x^2\right) \, dx","Int[E^x*(-5*x + x^2),x]","e^x x^2-7 e^x x+7 e^x","e^x x^2-7 e^x x+7 e^x",1,"7*E^x - 7*E^x*x + E^x*x^2","A",8,4,11,0.3636,1,"{1593, 2196, 2176, 2194}"
691,1,32,0,0.0506393,"\int e^{3 x} \left(-x+x^2\right) \, dx","Int[E^(3*x)*(-x + x^2),x]","\frac{1}{3} e^{3 x} x^2-\frac{5}{9} e^{3 x} x+\frac{5 e^{3 x}}{27}","\frac{1}{3} e^{3 x} x^2-\frac{5}{9} e^{3 x} x+\frac{5 e^{3 x}}{27}",1,"(5*E^(3*x))/27 - (5*E^(3*x)*x)/9 + (E^(3*x)*x^2)/3","A",8,4,13,0.3077,1,"{1593, 2196, 2176, 2194}"
692,0,0,0,0.1450142,"\int e^{x^x} x^{2 x} (1+\log (x)) \, dx","Int[E^x^x*x^(2*x)*(1 + Log[x]),x]","\int e^{x^x} x^{2 x} (1+\log (x)) \, dx","e^{x^x} \left(x^x-1\right)",1,"Defer[Int][E^x^x*x^(2*x), x] + Log[x]*Defer[Int][E^x^x*x^(2*x), x] - Defer[Int][Defer[Int][E^x^x*x^(2*x), x]/x, x]","F",0,0,0,0,-1,"{}"
693,1,9,0,0.0258115,"\int \frac{e^{5 x}+e^{7 x}}{e^{-x}+e^x} \, dx","Int[(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",2,2,23,0.08696,1,"{2282, 30}"
694,0,0,0,0.0726652,"\int x^{-2-\frac{1}{x}} (1-\log (x)) \, dx","Int[x^(-2 - x^(-1))*(1 - Log[x]),x]","\int x^{-2-\frac{1}{x}} (1-\log (x)) \, dx","-x^{-1/x}",1,"Defer[Int][x^(-2 - x^(-1)), x] - Log[x]*Defer[Int][x^(-2 - x^(-1)), x] + Defer[Int][Defer[Int][x^(-2 - x^(-1)), x]/x, x]","F",0,0,0,0,-1,"{}"
695,1,25,0,0.0143958,"\int \left(a+b e^x\right)^2 \, dx","Int[(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",3,2,9,0.2222,1,"{2282, 43}"
696,1,40,0,0.0195108,"\int \left(a+b e^x\right)^3 \, dx","Int[(a + b*E^x)^3,x]","3 a^2 b e^x+a^3 x+\frac{3}{2} a b^2 e^{2 x}+\frac{1}{3} b^3 e^{3 x}","3 a^2 b e^x+a^3 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",3,2,9,0.2222,1,"{2282, 43}"
697,1,53,0,0.0264042,"\int \left(a+b e^x\right)^4 \, dx","Int[(a + b*E^x)^4,x]","3 a^2 b^2 e^{2 x}+4 a^3 b e^x+a^4 x+\frac{4}{3} a b^3 e^{3 x}+\frac{1}{4} b^4 e^{4 x}","3 a^2 b^2 e^{2 x}+4 a^3 b e^x+a^4 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",3,2,9,0.2222,1,"{2282, 43}"
698,1,32,0,0.0273548,"\int \frac{1}{\sqrt{a+b e^{c+d x}}} \, dx","Int[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",3,3,15,0.2000,1,"{2282, 63, 208}"
699,1,34,0,0.0294162,"\int \frac{1}{\sqrt{-a+b e^{c+d x}}} \, dx","Int[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",3,3,17,0.1765,1,"{2282, 63, 205}"
700,1,53,0,0.0348304,"\int \sqrt{a+b e^{c+d x}} \, dx","Int[Sqrt[a + b*E^(c + d*x)],x]","\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}","\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)])/d - (2*Sqrt[a]*ArcTanh[Sqrt[a + b*E^(c + d*x)]/Sqrt[a]])/d","A",4,4,15,0.2667,1,"{2282, 50, 63, 208}"
701,1,57,0,0.0355086,"\int \sqrt{-a+b e^{c+d x}} \, dx","Int[Sqrt[-a + b*E^(c + d*x)],x]","\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}","\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)])/d - (2*Sqrt[a]*ArcTan[Sqrt[-a + b*E^(c + d*x)]/Sqrt[a]])/d","A",4,4,17,0.2353,1,"{2282, 50, 63, 205}"
702,1,27,0,0.011199,"\int e^{6 x} \sin (3 x) \, dx","Int[E^(6*x)*Sin[3*x],x]","\frac{2}{15} e^{6 x} \sin (3 x)-\frac{1}{15} e^{6 x} \cos (3 x)","\frac{2}{15} e^{6 x} \sin (3 x)-\frac{1}{15} e^{6 x} \cos (3 x)",1,"-(E^(6*x)*Cos[3*x])/15 + (2*E^(6*x)*Sin[3*x])/15","A",1,1,10,0.1000,1,"{4432}"
703,1,10,0,0.0231388,"\int \frac{e^{3 x}}{1+e^{2 x}} \, dx","Int[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",3,3,15,0.2000,1,"{2248, 321, 203}"
704,1,10,0,0.0243592,"\int \frac{e^{3 x}}{-1+e^{2 x}} \, dx","Int[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",3,3,15,0.2000,1,"{2248, 321, 207}"
705,1,18,0,0.0255804,"\int \frac{e^{-x}}{\sqrt{1+e^{2 x}}} \, dx","Int[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",2,2,17,0.1176,1,"{2249, 191}"
706,1,20,0,0.0430682,"\int \frac{e^x}{-1-8 e^x+e^{2 x}} \, dx","Int[E^x/(-1 - 8*E^x + E^(2*x)),x]","\frac{\tanh ^{-1}\left(\frac{4-e^x}{\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",3,3,18,0.1667,1,"{2282, 618, 206}"
707,1,44,0,0.0348359,"\int e^{7 x} x^3 \, dx","Int[E^(7*x)*x^3,x]","\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}","\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,"(-6*E^(7*x))/2401 + (6*E^(7*x)*x)/343 - (3*E^(7*x)*x^2)/49 + (E^(7*x)*x^3)/7","A",4,2,9,0.2222,1,"{2176, 2194}"
708,1,52,0,0.0392965,"\int e^{8-2 x} x^3 \, dx","Int[E^(8 - 2*x)*x^3,x]","-\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}","-\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,"(-3*E^(8 - 2*x))/8 - (3*E^(8 - 2*x)*x)/4 - (3*E^(8 - 2*x)*x^2)/4 - (E^(8 - 2*x)*x^3)/2","A",4,2,11,0.1818,1,"{2176, 2194}"
709,1,33,0,0.0255834,"\int e^x \sqrt{9-e^{2 x}} \, dx","Int[E^x*Sqrt[9 - E^(2*x)],x]","\frac{1}{2} e^x \sqrt{9-e^{2 x}}+\frac{9}{2} \sin ^{-1}\left(\frac{e^x}{3}\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)])/2 + (9*ArcSin[E^x/3])/2","A",3,3,17,0.1765,1,"{2249, 195, 216}"
710,1,50,0,0.0362776,"\int e^{6 x} \sqrt{9-e^{2 x}} \, dx","Int[E^(6*x)*Sqrt[9 - E^(2*x)],x]","-\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}","-\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,"-27*(9 - E^(2*x))^(3/2) + (18*(9 - E^(2*x))^(5/2))/5 - (9 - E^(2*x))^(7/2)/7","A",3,2,19,0.1053,1,"{2248, 43}"
711,1,81,0,0.0451012,"\int \frac{e^{6 x}}{\left(9-e^x\right)^{5/2}} \, dx","Int[E^(6*x)/(9 - E^x)^(5/2),x]","\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}}","\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,"39366/(9 - E^x)^(3/2) - 65610/Sqrt[9 - E^x] - 14580*Sqrt[9 - E^x] + 540*(9 - E^x)^(3/2) - 18*(9 - E^x)^(5/2) + (2*(9 - E^x)^(7/2))/7","A",3,2,17,0.1176,1,"{2248, 43}"
712,1,55,0,0.0857752,"\int \left(2-7 e^{x^4}\right)^5 x^3 \, dx","Int[(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",4,3,15,0.2000,1,"{6715, 2282, 43}"
713,1,35,0,0.1603975,"\int e^{x^2} \sqrt{1-e^{2 x^2}} x \, dx","Int[E^x^2*Sqrt[1 - E^(2*x^2)]*x,x]","\frac{1}{4} e^{x^2} \sqrt{1-e^{2 x^2}}+\frac{1}{4} \sin ^{-1}\left(e^{x^2}\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)])/4 + ArcSin[E^x^2]/4","A",4,4,22,0.1818,1,"{6715, 2249, 195, 216}"
714,1,32,0,0.2087847,"\int e^{x^3} \left(1-e^{4 x^3}\right)^2 x^2 \, dx","Int[E^x^3*(1 - E^(4*x^3))^2*x^2,x]","\frac{e^{x^3}}{3}-\frac{2 e^{5 x^3}}{15}+\frac{e^{9 x^3}}{27}","\frac{e^{x^3}}{3}-\frac{2 e^{5 x^3}}{15}+\frac{e^{9 x^3}}{27}",1,"E^x^3/3 - (2*E^(5*x^3))/15 + E^(9*x^3)/27","A",4,3,22,0.1364,1,"{6715, 2249, 194}"
715,1,5,0,0.0053152,"\int e^{e^x+x} \, dx","Int[E^(E^x + x),x]","e^{e^x}","e^{e^x}",1,"E^E^x","A",2,2,7,0.2857,1,"{2282, 2194}"
716,1,7,0,0.0149321,"\int e^{e^{e^x}+e^x+x} \, dx","Int[E^(E^E^x + E^x + x),x]","e^{e^{e^x}}","e^{e^{e^x}}",1,"E^E^E^x","A",3,2,12,0.1667,1,"{2282, 2194}"
717,1,22,0,0.0181731,"\int \left(e^{-x}+e^x\right)^2 \, dx","Int[(E^(-x) + E^x)^2,x]","2 x-\frac{e^{-2 x}}{2}+\frac{e^{2 x}}{2}","2 x-\frac{e^{-2 x}}{2}+\frac{e^{2 x}}{2}",1,"-1/(2*E^(2*x)) + E^(2*x)/2 + 2*x","A",4,3,11,0.2727,1,"{2282, 266, 43}"
718,1,4,0,0.0106405,"\int \frac{1}{e^{-x}+e^x} \, dx","Int[(E^(-x) + E^x)^(-1),x]","\tan ^{-1}\left(e^x\right)","\tan ^{-1}\left(e^x\right)",1,"ArcTan[E^x]","A",2,2,11,0.1818,1,"{2282, 203}"
719,1,13,0,0.0124029,"\int \frac{1}{\left(e^{-x}+e^x\right)^2} \, dx","Int[(E^(-x) + E^x)^(-2),x]","-\frac{1}{2 \left(e^{2 x}+1\right)}","-\frac{1}{2 \left(e^{2 x}+1\right)}",1,"-1/(2*(1 + E^(2*x)))","A",2,2,11,0.1818,1,"{2282, 261}"
720,1,6,0,0.0103198,"\int \frac{1}{-e^{-x}+e^x} \, dx","Int[(-E^(-x) + E^x)^(-1),x]","-\tanh ^{-1}\left(e^x\right)","-\tanh ^{-1}\left(e^x\right)",1,"-ArcTanh[E^x]","A",2,2,13,0.1538,1,"{2282, 207}"
721,1,15,0,0.0139409,"\int \frac{1}{\left(-e^{-x}+e^x\right)^2} \, dx","Int[(-E^(-x) + E^x)^(-2),x]","\frac{1}{2 \left(1-e^{2 x}\right)}","\frac{1}{2 \left(1-e^{2 x}\right)}",1,"1/(2*(1 - E^(2*x)))","A",2,2,13,0.1538,1,"{2282, 261}"
722,1,22,0,0.0277052,"\int e^x \left(-e^{-x}+e^x\right)^2 \, dx","Int[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",3,2,17,0.1176,1,"{2282, 14}"
723,1,31,0,0.0366155,"\int e^x \left(-e^{-x}+e^x\right)^3 \, dx","Int[E^x*(-E^(-x) + E^x)^3,x]","3 x+\frac{e^{-2 x}}{2}-\frac{3 e^{2 x}}{2}+\frac{e^{4 x}}{4}","3 x+\frac{e^{-2 x}}{2}-\frac{3 e^{2 x}}{2}+\frac{e^{4 x}}{4}",1,"1/(2*E^(2*x)) - (3*E^(2*x))/2 + E^(4*x)/4 + 3*x","A",4,3,17,0.1765,1,"{2282, 266, 43}"
724,1,22,0,0.0267354,"\int \frac{1+4^x}{1+2^x} \, dx","Int[(1 + 4^x)/(1 + 2^x),x]","x-\frac{2 \log \left(2^x+1\right)}{\log (2)}+\frac{2^x}{\log (2)}","x-\frac{2 \log \left(2^x+1\right)}{\log (2)}+\frac{2^x}{\log (2)}",1,"x + 2^x/Log[2] - (2*Log[1 + 2^x])/Log[2]","A",3,2,13,0.1538,1,"{2282, 894}"
725,1,34,0,0.0312803,"\int \frac{1+4^x}{1+2^{-x}} \, dx","Int[(1 + 4^x)/(1 + 2^(-x)),x]","\frac{2 \log \left(2^x+1\right)}{\log (2)}-\frac{2^x}{\log (2)}+\frac{2^{2 x-1}}{\log (2)}","\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/Log[2]) + 2^(-1 + 2*x)/Log[2] + (2*Log[1 + 2^x])/Log[2]","A",3,2,15,0.1333,1,"{2282, 697}"
726,1,23,0,0.0481148,"\int \left(\frac{e^{(a+x)^2}}{x^2}-\frac{2 a e^{(a+x)^2}}{x}\right) \, dx","Int[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",3,2,25,0.08000,1,"{2220, 2204}"
727,1,66,0,0.1835378,"\int e^{-x^2} \left(x^4+x^6+x^8\right) \, dx","Int[(x^4 + x^6 + x^8)/E^x^2,x]","\frac{147}{32} \sqrt{\pi } \text{Erf}(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-\frac{147}{16} e^{-x^2} x","\frac{147}{32} \sqrt{\pi } \text{Erf}(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-\frac{147}{16} e^{-x^2} x",1,"(-147*x)/(16*E^x^2) - (49*x^3)/(8*E^x^2) - (9*x^5)/(4*E^x^2) - x^7/(2*E^x^2) + (147*Sqrt[Pi]*Erf[x])/32","A",15,4,18,0.2222,1,"{1594, 2226, 2212, 2205}"
728,1,12,0,0.0133264,"\int \frac{1}{-e^x+e^{3 x}} \, dx","Int[(-E^x + E^(3*x))^(-1),x]","e^{-x}-\tanh ^{-1}\left(e^x\right)","e^{-x}-\tanh ^{-1}\left(e^x\right)",1,"E^(-x) - ArcTanh[E^x]","A",3,3,13,0.2308,1,"{2282, 325, 207}"
729,1,16,0,0.0742178,"\int \frac{e^x \left(-5+x+x^2\right)}{(-1+x)^2} \, dx","Int[(E^x*(-5 + x + x^2))/(-1 + x)^2,x]","e^x-\frac{3 e^x}{1-x}","e^x-\frac{3 e^x}{1-x}",1,"E^x - (3*E^x)/(1 - x)","A",6,4,15,0.2667,1,"{2199, 2194, 2177, 2178}"
730,1,16,0,0.0576866,"\int \frac{e^{x^2} x^3}{\left(1+x^2\right)^2} \, dx","Int[(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",1,1,16,0.06250,1,"{2289}"
731,1,33,0,0.032377,"\int \frac{e^{3 x}}{\sqrt{25+16 e^{2 x}}} \, dx","Int[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",3,3,19,0.1579,1,"{2248, 321, 215}"
732,1,11,0,0.0252986,"\int \frac{1+e^x}{\sqrt{e^x+x}} \, dx","Int[(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",1,1,15,0.06667,1,"{6686}"
733,1,6,0,0.0195129,"\int \frac{1+e^x}{e^x+x} \, dx","Int[(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",1,1,13,0.07692,1,"{6684}"
734,1,19,0,0.0152378,"\int \frac{e^{x^2}}{x^2} \, dx","Int[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",2,2,9,0.2222,1,"{2214, 2204}"
735,1,19,0,0.1002369,"\int \frac{e^{x^2} \left(1+4 x^4\right)}{x^2} \, dx","Int[(E^x^2*(1 + 4*x^4))/x^2,x]","2 e^{x^2} x-\frac{e^{x^2}}{x}","2 e^{x^2} x-\frac{e^{x^2}}{x}",1,"-(E^x^2/x) + 2*E^x^2*x","A",6,4,16,0.2500,1,"{6742, 2214, 2204, 2212}"
736,1,56,0,0.0407702,"\int \sqrt{f^x} (a+b x)^2 \, dx","Int[Sqrt[f^x]*(a + b*x)^2,x]","-\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)}","-\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,"(16*b^2*Sqrt[f^x])/Log[f]^3 - (8*b*Sqrt[f^x]*(a + b*x))/Log[f]^2 + (2*Sqrt[f^x]*(a + b*x)^2)/Log[f]","A",3,2,15,0.1333,1,"{2176, 2194}"
737,1,15,0,0.0094084,"\int 3^{1+x^2} x \, dx","Int[3^(1 + x^2)*x,x]","\frac{3^{x^2+1}}{2 \log (3)}","\frac{3^{x^2+1}}{2 \log (3)}",1,"3^(1 + x^2)/(2*Log[3])","A",1,1,9,0.1111,1,"{2209}"
738,1,14,0,0.0105539,"\int \frac{2^{\sqrt{x}}}{\sqrt{x}} \, dx","Int[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",1,1,13,0.07692,1,"{2209}"
739,1,11,0,0.0109216,"\int \frac{2^{\frac{1}{x}}}{x^2} \, dx","Int[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",1,1,9,0.1111,1,"{2209}"
740,1,20,0,0.0062042,"\int \left(2^{-x}+2^x\right) \, dx","Int[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",3,1,9,0.1111,1,"{2194}"
741,1,32,0,0.0439118,"\int e^{-4 x} \left(2-3 x+x^2\right) \, dx","Int[(2 - 3*x + x^2)/E^(4*x),x]","-\frac{1}{4} e^{-4 x} x^2+\frac{5}{8} e^{-4 x} x-\frac{11 e^{-4 x}}{32}","-\frac{1}{4} e^{-4 x} x^2+\frac{5}{8} e^{-4 x} x-\frac{11 e^{-4 x}}{32}",1,"-11/(32*E^(4*x)) + (5*x)/(8*E^(4*x)) - x^2/(4*E^(4*x))","A",8,3,14,0.2143,1,"{2196, 2194, 2176}"
742,1,33,0,0.0090667,"\int \left(k^{x/2}+x^{\sqrt{k}}\right) \, dx","Int[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",2,1,15,0.06667,1,"{2194}"
743,1,21,0,0.0114011,"\int \frac{10^{\sqrt{x}}}{\sqrt{x}} \, dx","Int[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",1,1,13,0.07692,1,"{2209}"
744,1,11,0,0.0408029,"\int \left(\frac{1}{\sqrt{e^x+x}}+\frac{e^x}{\sqrt{e^x+x}}\right) \, dx","Int[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",2,1,23,0.04348,1,"{2261}"
745,1,12,0,0.2586044,"\int \left(\frac{\left(1+e^x\right) x}{\sqrt{e^x+x}}+2 \sqrt{e^x+x}\right) \, dx","Int[((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",6,3,28,0.1071,1,"{6742, 2273, 2262}"
746,1,12,0,0.130266,"\int \left(\frac{x}{\sqrt{e^x+x}}+\frac{e^x x}{\sqrt{e^x+x}}+2 \sqrt{e^x+x}\right) \, dx","Int[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",4,2,37,0.05405,1,"{2273, 2262}"
747,0,0,0,0.18311,"\int \frac{\left(1+e^x\right) x}{\sqrt{e^x+x}} \, dx","Int[((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,"2*x*Sqrt[E^x + x] - 2*Defer[Int][Sqrt[E^x + x], x]","A",0,0,0,0,-1,"{}"
748,0,0,0,0.1174169,"\int \left(\frac{x}{\sqrt{e^x+x}}+\frac{e^x x}{\sqrt{e^x+x}}\right) \, dx","Int[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,"2*x*Sqrt[E^x + x] - 2*Defer[Int][Sqrt[E^x + x], x]","A",0,0,0,0,-1,"{}"
749,0,0,0,0.0810275,"\int \frac{e^x x}{\sqrt{e^x+x}} \, dx","Int[(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,"2*Sqrt[E^x + x] + 2*x*Sqrt[E^x + x] - Defer[Int][1/Sqrt[E^x + x], x] - 3*Defer[Int][Sqrt[E^x + x], x]","A",0,0,0,0,-1,"{}"
750,1,20,0,0.5974824,"\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","Int[(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",4,2,50,0.04000,1,"{6742, 2262}"
751,0,0,0,0.1658706,"\int \frac{e^x x^2}{\sqrt{5 e^x+x^3}} \, dx","Int[(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{3}{5} \text{Int}\left(\frac{x^4}{\sqrt{x^3+5 e^x}},x\right)-\frac{4}{5} \text{Int}\left(x \sqrt{x^3+5 e^x},x\right)+\frac{2}{5} \sqrt{x^3+5 e^x} x^2",0,"(2*x^2*Sqrt[5*E^x + x^3])/5 - (3*Defer[Int][x^4/Sqrt[5*E^x + x^3], x])/5 - (4*Defer[Int][x*Sqrt[5*E^x + x^3], x])/5","A",0,0,0,0,-1,"{}"
752,1,13,0,0.024423,"\int -\frac{1+e^x}{\sqrt[3]{e^x+x}} \, dx","Int[-((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",1,1,16,0.06250,1,"{6686}"
753,1,13,0,0.0657407,"\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","Int[-(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",2,1,34,0.02941,1,"{2273}"
754,0,0,0,0.0396365,"\int \frac{x}{\sqrt[3]{e^x+x}} \, dx","Int[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,"(-3*(E^x + x)^(2/3))/2 + Defer[Int][(E^x + x)^(-1/3), x] + Defer[Int][(E^x + x)^(2/3), x]","A",0,0,0,0,-1,"{}"
755,1,12,0,0.3368844,"\int \frac{5 x+e^x (3+2 x)}{\sqrt[3]{e^x+x}} \, dx","Int[(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",8,4,23,0.1739,1,"{6742, 2273, 2261, 2262}"
756,1,12,0,0.1437654,"\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","Int[(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",4,2,39,0.05128,1,"{2273, 2262}"
757,1,31,0,0.0493072,"\int e^x \left(-e^{-x}+e^x\right) \left(e^{-x}+e^x\right)^2 \, dx","Int[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",3,2,26,0.07692,1,"{2282, 14}"
758,0,0,0,0.0290672,"\int \frac{x}{e^x+x} \, dx","Int[x/(E^x + x),x]","\int \frac{x}{e^x+x} \, dx","\text{Int}\left(\frac{x}{x+e^x},x\right)",0,"Defer[Int][x/(E^x + x), x]","A",0,0,0,0,-1,"{}"
759,0,0,0,0.0572397,"\int \frac{x^2}{\sqrt{e^x+x}} \, dx","Int[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,"Defer[Int][x^2/Sqrt[E^x + x], x]","A",0,0,0,0,-1,"{}"
760,0,0,0,0.0341178,"\int \frac{e^x}{e^x+x} \, dx","Int[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,"Defer[Int][E^x/(E^x + x), x]","A",0,0,0,0,-1,"{}"
761,0,0,0,0.0392725,"\int \frac{e^x}{e^x+x^2} \, dx","Int[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,"Defer[Int][E^x/(E^x + x^2), x]","A",0,0,0,0,-1,"{}"
762,0,0,0,0.0455445,"\int \frac{\text{F0}(x)}{x+\text{F0}(x)} \, dx","Int[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,"x - Defer[Int][x/(x + F0[x]), x]","A",0,0,0,0,-1,"{}"
763,0,0,0,0.0699767,"\int \frac{\text{F0}(x)}{x^2+\text{F0}(x)} \, dx","Int[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,"x - Defer[Int][x^2/(x^2 + F0[x]), x]","A",0,0,0,0,-1,"{}"
764,0,0,0,0.0561132,"\int \frac{\text{F0}(x)}{(x+\text{F0}(x))^2} \, dx","Int[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,"-Defer[Int][x/(x + F0[x])^2, x] + Defer[Int][(x + F0[x])^(-1), x]","A",0,0,0,0,-1,"{}"
765,0,0,0,0.0806389,"\int \frac{\text{F0}(x)}{\left(x^2+\text{F0}(x)\right)^2} \, dx","Int[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,"-Defer[Int][x^2/(x^2 + F0[x])^2, x] + Defer[Int][(x^2 + F0[x])^(-1), x]","A",0,0,0,0,-1,"{}"
766,1,36,0,0.0986903,"\int \left(a F^{c+d x}\right)^m \left(b F^{e+f x}\right)^n \, dx","Int[(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}{\log (F) (d m+f n)}","\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 + f*n)*Log[F])","A",4,3,23,0.1304,1,"{2281, 2227, 2194}"
767,1,37,0,0.0351137,"\int e^{a+c+b x^n+d x^n} \, dx","Int[E^(a + c + b*x^n + d*x^n),x]","-\frac{x e^{a+c} \left(-(b+d) x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-(b+d) x^n\right)}{n}","-\frac{x e^{a+c} \left(-(b+d) x^n\right)^{-1/n} \text{Gamma}\left(\frac{1}{n},-(b+d) x^n\right)}{n}",1,"-((E^(a + c)*x*Gamma[n^(-1), -((b + d)*x^n)])/(n*(-((b + d)*x^n))^n^(-1)))","A",2,2,15,0.1333,1,"{6741, 2208}"
768,1,50,0,0.0444385,"\int f^{a+b x^n} g^{c+d x^n} \, dx","Int[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} \text{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} \text{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",2,2,19,0.1053,1,"{2287, 2208}"
769,1,37,0,0.0169732,"\int e^{x^n} x^m \, dx","Int[E^x^n*x^m,x]","-\frac{x^{m+1} \left(-x^n\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},-x^n\right)}{n}","-\frac{x^{m+1} \left(-x^n\right)^{-\frac{m+1}{n}} \text{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",1,1,9,0.1111,1,"{2218}"
770,1,41,0,0.015585,"\int f^{x^n} x^m \, dx","Int[f^x^n*x^m,x]","-\frac{x^{m+1} \left(\log (f) \left(-x^n\right)\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},\log (f) \left(-x^n\right)\right)}{n}","-\frac{x^{m+1} \left(\log (f) \left(-x^n\right)\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},\log (f) \left(-x^n\right)\right)}{n}",1,"-((x^(1 + m)*Gamma[(1 + m)/n, -(x^n*Log[f])])/(n*(-(x^n*Log[f]))^((1 + m)/n)))","A",1,1,9,0.1111,1,"{2218}"
771,1,52,0,0.0263118,"\int e^{(a+b x)^n} (a+b x)^m \, dx","Int[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}} \text{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}} \text{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",1,1,17,0.05882,1,"{2218}"
772,1,56,0,0.0253398,"\int f^{(a+b x)^n} (a+b x)^m \, dx","Int[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}} \text{Gamma}\left(\frac{m+1}{n},\log (f) \left(-(a+b x)^n\right)\right)}{b n}","-\frac{(a+b x)^{m+1} \left(\log (f) \left(-(a+b x)^n\right)\right)^{-\frac{m+1}{n}} \text{Gamma}\left(\frac{m+1}{n},\log (f) \left(-(a+b x)^n\right)\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",1,1,17,0.05882,1,"{2218}"
773,1,80,0,0.0436073,"\int e^{(a+b x)^3} x \, dx","Int[E^(a + b*x)^3*x,x]","\frac{a (a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b^2 \sqrt[3]{-(a+b x)^3}}-\frac{(a+b x)^2 \text{Gamma}\left(\frac{2}{3},-(a+b x)^3\right)}{3 b^2 \left(-(a+b x)^3\right)^{2/3}}","\frac{a (a+b x) \text{Gamma}\left(\frac{1}{3},-(a+b x)^3\right)}{3 b^2 \sqrt[3]{-(a+b x)^3}}-\frac{(a+b x)^2 \text{Gamma}\left(\frac{2}{3},-(a+b x)^3\right)}{3 b^2 \left(-(a+b x)^3\right)^{2/3}}",1,"(a*(a + b*x)*Gamma[1/3, -(a + b*x)^3])/(3*b^2*(-(a + b*x)^3)^(1/3)) - ((a + b*x)^2*Gamma[2/3, -(a + b*x)^3])/(3*b^2*(-(a + b*x)^3)^(2/3))","A",4,3,11,0.2727,1,"{2226, 2208, 2218}"
774,1,17,0,0.635028,"\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","Int[(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",8,4,43,0.09302,1,"{6742, 2261, 2273, 2262}"