1,1,110,0,0.1893638,"\int \frac{x^3}{a+b e^{c+d x}} \, dx","Int[x^3/(a + b*E^(c + d*x)),x]","-\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a d^2}+\frac{6 x \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a d^3}-\frac{6 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a}\right)}{a d^4}-\frac{x^3 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a d}+\frac{x^4}{4 a}","-\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a d^2}+\frac{6 x \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a d^3}-\frac{6 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a}\right)}{a d^4}-\frac{x^3 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a d}+\frac{x^4}{4 a}",1,"x^4/(4*a) - (x^3*Log[1 + (b*E^(c + d*x))/a])/(a*d) - (3*x^2*PolyLog[2, -((b*E^(c + d*x))/a)])/(a*d^2) + (6*x*PolyLog[3, -((b*E^(c + d*x))/a)])/(a*d^3) - (6*PolyLog[4, -((b*E^(c + d*x))/a)])/(a*d^4)","A",6,6,17,0.3529,1,"{2184, 2190, 2531, 6609, 2282, 6589}"
2,1,84,0,0.1677539,"\int \frac{x^2}{a+b e^{c+d x}} \, dx","Int[x^2/(a + b*E^(c + d*x)),x]","-\frac{2 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a d^2}+\frac{2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a d^3}-\frac{x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a d}+\frac{x^3}{3 a}","-\frac{2 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a d^2}+\frac{2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a d^3}-\frac{x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a d}+\frac{x^3}{3 a}",1,"x^3/(3*a) - (x^2*Log[1 + (b*E^(c + d*x))/a])/(a*d) - (2*x*PolyLog[2, -((b*E^(c + d*x))/a)])/(a*d^2) + (2*PolyLog[3, -((b*E^(c + d*x))/a)])/(a*d^3)","A",5,5,17,0.2941,1,"{2184, 2190, 2531, 2282, 6589}"
3,1,58,0,0.0991882,"\int \frac{x}{a+b e^{c+d x}} \, dx","Int[x/(a + b*E^(c + d*x)),x]","-\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a d^2}-\frac{x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a d}+\frac{x^2}{2 a}","-\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a d^2}-\frac{x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a d}+\frac{x^2}{2 a}",1,"x^2/(2*a) - (x*Log[1 + (b*E^(c + d*x))/a])/(a*d) - PolyLog[2, -((b*E^(c + d*x))/a)]/(a*d^2)","A",4,4,15,0.2667,1,"{2184, 2190, 2279, 2391}"
4,1,26,0,0.0175739,"\int \frac{1}{a+b e^{c+d x}} \, dx","Int[(a + b*E^(c + d*x))^(-1),x]","\frac{x}{a}-\frac{\log \left(a+b e^{c+d x}\right)}{a d}","\frac{x}{a}-\frac{\log \left(a+b e^{c+d x}\right)}{a d}",1,"x/a - Log[a + b*E^(c + d*x)]/(a*d)","A",4,4,13,0.3077,1,"{2282, 36, 29, 31}"
5,0,0,0,0.04806,"\int \frac{1}{\left(a+b e^{c+d x}\right) x} \, dx","Int[1/((a + b*E^(c + d*x))*x),x]","\int \frac{1}{\left(a+b e^{c+d x}\right) x} \, dx","\text{Int}\left(\frac{1}{x \left(a+b e^{c+d x}\right)},x\right)",0,"Defer[Int][1/((a + b*E^(c + d*x))*x), x]","A",0,0,0,0,-1,"{}"
6,0,0,0,0.0453303,"\int \frac{1}{\left(a+b e^{c+d x}\right) x^2} \, dx","Int[1/((a + b*E^(c + d*x))*x^2),x]","\int \frac{1}{\left(a+b e^{c+d x}\right) x^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b e^{c+d x}\right)},x\right)",0,"Defer[Int][1/((a + b*E^(c + d*x))*x^2), x]","A",0,0,0,0,-1,"{}"
7,1,26,0,0.0208319,"\int \frac{1}{a+b e^{c-d x}} \, dx","Int[(a + b*E^(c - d*x))^(-1),x]","\frac{\log \left(a+b e^{c-d x}\right)}{a d}+\frac{x}{a}","\frac{\log \left(a+b e^{c-d x}\right)}{a d}+\frac{x}{a}",1,"x/a + Log[a + b*E^(c - d*x)]/(a*d)","A",4,4,14,0.2857,1,"{2282, 36, 29, 31}"
8,1,28,0,0.022578,"\int \frac{1}{a+b e^{-c-d x}} \, dx","Int[(a + b*E^(-c - d*x))^(-1),x]","\frac{\log \left(a+b e^{-c-d x}\right)}{a d}+\frac{x}{a}","\frac{\log \left(a+b e^{-c-d x}\right)}{a d}+\frac{x}{a}",1,"x/a + Log[a + b*E^(-c - d*x)]/(a*d)","A",4,4,16,0.2500,1,"{2282, 36, 29, 31}"
9,1,217,0,0.5065806,"\int \frac{x^3}{\left(a+b e^{c+d x}\right)^2} \, dx","Int[x^3/(a + b*E^(c + d*x))^2,x]","-\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^2}+\frac{6 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}+\frac{6 x \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}-\frac{6 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^4}-\frac{6 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^4}+\frac{3 x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^2 d^2}-\frac{x^3 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^2 d}-\frac{x^3}{a^2 d}+\frac{x^4}{4 a^2}+\frac{x^3}{a d \left(a+b e^{c+d x}\right)}","-\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^2}+\frac{6 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}+\frac{6 x \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}-\frac{6 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^4}-\frac{6 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^4}+\frac{3 x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^2 d^2}-\frac{x^3 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^2 d}-\frac{x^3}{a^2 d}+\frac{x^4}{4 a^2}+\frac{x^3}{a d \left(a+b e^{c+d x}\right)}",1,"-(x^3/(a^2*d)) + x^3/(a*d*(a + b*E^(c + d*x))) + x^4/(4*a^2) + (3*x^2*Log[1 + (b*E^(c + d*x))/a])/(a^2*d^2) - (x^3*Log[1 + (b*E^(c + d*x))/a])/(a^2*d) + (6*x*PolyLog[2, -((b*E^(c + d*x))/a)])/(a^2*d^3) - (3*x^2*PolyLog[2, -((b*E^(c + d*x))/a)])/(a^2*d^2) - (6*PolyLog[3, -((b*E^(c + d*x))/a)])/(a^2*d^4) + (6*x*PolyLog[3, -((b*E^(c + d*x))/a)])/(a^2*d^3) - (6*PolyLog[4, -((b*E^(c + d*x))/a)])/(a^2*d^4)","A",13,8,17,0.4706,1,"{2185, 2184, 2190, 2531, 6609, 2282, 6589, 2191}"
10,1,165,0,0.399357,"\int \frac{x^2}{\left(a+b e^{c+d x}\right)^2} \, dx","Int[x^2/(a + b*E^(c + d*x))^2,x]","-\frac{2 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^2}+\frac{2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}+\frac{2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}+\frac{2 x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^2 d^2}-\frac{x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^2 d}-\frac{x^2}{a^2 d}+\frac{x^3}{3 a^2}+\frac{x^2}{a d \left(a+b e^{c+d x}\right)}","-\frac{2 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^2}+\frac{2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}+\frac{2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}+\frac{2 x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^2 d^2}-\frac{x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^2 d}-\frac{x^2}{a^2 d}+\frac{x^3}{3 a^2}+\frac{x^2}{a d \left(a+b e^{c+d x}\right)}",1,"-(x^2/(a^2*d)) + x^2/(a*d*(a + b*E^(c + d*x))) + x^3/(3*a^2) + (2*x*Log[1 + (b*E^(c + d*x))/a])/(a^2*d^2) - (x^2*Log[1 + (b*E^(c + d*x))/a])/(a^2*d) + (2*PolyLog[2, -((b*E^(c + d*x))/a)])/(a^2*d^3) - (2*x*PolyLog[2, -((b*E^(c + d*x))/a)])/(a^2*d^2) + (2*PolyLog[3, -((b*E^(c + d*x))/a)])/(a^2*d^3)","A",11,9,17,0.5294,1,"{2185, 2184, 2190, 2531, 2282, 6589, 2191, 2279, 2391}"
11,1,107,0,0.2014001,"\int \frac{x}{\left(a+b e^{c+d x}\right)^2} \, dx","Int[x/(a + b*E^(c + d*x))^2,x]","-\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^2}+\frac{\log \left(a+b e^{c+d x}\right)}{a^2 d^2}-\frac{x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^2 d}-\frac{x}{a^2 d}+\frac{x^2}{2 a^2}+\frac{x}{a d \left(a+b e^{c+d x}\right)}","-\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^2 d^2}+\frac{\log \left(a+b e^{c+d x}\right)}{a^2 d^2}-\frac{x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^2 d}-\frac{x}{a^2 d}+\frac{x^2}{2 a^2}+\frac{x}{a d \left(a+b e^{c+d x}\right)}",1,"-(x/(a^2*d)) + x/(a*d*(a + b*E^(c + d*x))) + x^2/(2*a^2) + Log[a + b*E^(c + d*x)]/(a^2*d^2) - (x*Log[1 + (b*E^(c + d*x))/a])/(a^2*d) - PolyLog[2, -((b*E^(c + d*x))/a)]/(a^2*d^2)","A",10,10,15,0.6667,1,"{2185, 2184, 2190, 2279, 2391, 2191, 2282, 36, 29, 31}"
12,1,46,0,0.0328909,"\int \frac{1}{\left(a+b e^{c+d x}\right)^2} \, dx","Int[(a + b*E^(c + d*x))^(-2),x]","-\frac{\log \left(a+b e^{c+d x}\right)}{a^2 d}+\frac{x}{a^2}+\frac{1}{a d \left(a+b e^{c+d x}\right)}","-\frac{\log \left(a+b e^{c+d x}\right)}{a^2 d}+\frac{x}{a^2}+\frac{1}{a d \left(a+b e^{c+d x}\right)}",1,"1/(a*d*(a + b*E^(c + d*x))) + x/a^2 - Log[a + b*E^(c + d*x)]/(a^2*d)","A",3,2,13,0.1538,1,"{2282, 44}"
13,0,0,0,0.0465358,"\int \frac{1}{\left(a+b e^{c+d x}\right)^2 x} \, dx","Int[1/((a + b*E^(c + d*x))^2*x),x]","\int \frac{1}{\left(a+b e^{c+d x}\right)^2 x} \, dx","\text{Int}\left(\frac{1}{x \left(a+b e^{c+d x}\right)^2},x\right)",0,"Defer[Int][1/((a + b*E^(c + d*x))^2*x), x]","A",0,0,0,0,-1,"{}"
14,0,0,0,0.0436893,"\int \frac{1}{\left(a+b e^{c+d x}\right)^2 x^2} \, dx","Int[1/((a + b*E^(c + d*x))^2*x^2),x]","\int \frac{1}{\left(a+b e^{c+d x}\right)^2 x^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b e^{c+d x}\right)^2},x\right)",0,"Defer[Int][1/((a + b*E^(c + d*x))^2*x^2), x]","A",0,0,0,0,-1,"{}"
15,1,48,0,0.0343803,"\int \frac{1}{\left(a+b e^{c-d x}\right)^2} \, dx","Int[(a + b*E^(c - d*x))^(-2),x]","\frac{\log \left(a+b e^{c-d x}\right)}{a^2 d}+\frac{x}{a^2}-\frac{1}{a d \left(a+b e^{c-d x}\right)}","\frac{\log \left(a+b e^{c-d x}\right)}{a^2 d}+\frac{x}{a^2}-\frac{1}{a d \left(a+b e^{c-d x}\right)}",1,"-(1/(a*d*(a + b*E^(c - d*x)))) + x/a^2 + Log[a + b*E^(c - d*x)]/(a^2*d)","A",3,2,14,0.1429,1,"{2282, 44}"
16,1,52,0,0.0347173,"\int \frac{1}{\left(a+b e^{-c-d x}\right)^2} \, dx","Int[(a + b*E^(-c - d*x))^(-2),x]","\frac{\log \left(a+b e^{-c-d x}\right)}{a^2 d}+\frac{x}{a^2}-\frac{1}{a d \left(a+b e^{-c-d x}\right)}","\frac{\log \left(a+b e^{-c-d x}\right)}{a^2 d}+\frac{x}{a^2}-\frac{1}{a d \left(a+b e^{-c-d x}\right)}",1,"-(1/(a*d*(a + b*E^(-c - d*x)))) + x/a^2 + Log[a + b*E^(-c - d*x)]/(a^2*d)","A",3,2,16,0.1250,1,"{2282, 44}"
17,1,333,0,1.0778042,"\int \frac{x^3}{\left(a+b e^{c+d x}\right)^3} \, dx","Int[x^3/(a + b*E^(c + d*x))^3,x]","-\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^2}+\frac{9 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}+\frac{6 x \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}-\frac{3 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^4}-\frac{9 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^4}-\frac{6 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^4}-\frac{3 x^2}{2 a^2 d^2 \left(a+b e^{c+d x}\right)}+\frac{9 x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{2 a^3 d^2}-\frac{3 x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d^3}+\frac{x^3}{a^2 d \left(a+b e^{c+d x}\right)}-\frac{x^3 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d}+\frac{3 x^2}{2 a^3 d^2}-\frac{3 x^3}{2 a^3 d}+\frac{x^4}{4 a^3}+\frac{x^3}{2 a d \left(a+b e^{c+d x}\right)^2}","-\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^2}+\frac{9 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}+\frac{6 x \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}-\frac{3 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^4}-\frac{9 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^4}-\frac{6 \text{PolyLog}\left(4,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^4}-\frac{3 x^2}{2 a^2 d^2 \left(a+b e^{c+d x}\right)}+\frac{9 x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{2 a^3 d^2}-\frac{3 x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d^3}+\frac{x^3}{a^2 d \left(a+b e^{c+d x}\right)}-\frac{x^3 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d}+\frac{3 x^2}{2 a^3 d^2}-\frac{3 x^3}{2 a^3 d}+\frac{x^4}{4 a^3}+\frac{x^3}{2 a d \left(a+b e^{c+d x}\right)^2}",1,"(3*x^2)/(2*a^3*d^2) - (3*x^2)/(2*a^2*d^2*(a + b*E^(c + d*x))) - (3*x^3)/(2*a^3*d) + x^3/(2*a*d*(a + b*E^(c + d*x))^2) + x^3/(a^2*d*(a + b*E^(c + d*x))) + x^4/(4*a^3) - (3*x*Log[1 + (b*E^(c + d*x))/a])/(a^3*d^3) + (9*x^2*Log[1 + (b*E^(c + d*x))/a])/(2*a^3*d^2) - (x^3*Log[1 + (b*E^(c + d*x))/a])/(a^3*d) - (3*PolyLog[2, -((b*E^(c + d*x))/a)])/(a^3*d^4) + (9*x*PolyLog[2, -((b*E^(c + d*x))/a)])/(a^3*d^3) - (3*x^2*PolyLog[2, -((b*E^(c + d*x))/a)])/(a^3*d^2) - (9*PolyLog[3, -((b*E^(c + d*x))/a)])/(a^3*d^4) + (6*x*PolyLog[3, -((b*E^(c + d*x))/a)])/(a^3*d^3) - (6*PolyLog[4, -((b*E^(c + d*x))/a)])/(a^3*d^4)","A",26,10,17,0.5882,1,"{2185, 2184, 2190, 2531, 6609, 2282, 6589, 2191, 2279, 2391}"
18,1,243,0,0.7642865,"\int \frac{x^2}{\left(a+b e^{c+d x}\right)^3} \, dx","Int[x^2/(a + b*E^(c + d*x))^3,x]","-\frac{2 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^2}+\frac{3 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}+\frac{2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}-\frac{x}{a^2 d^2 \left(a+b e^{c+d x}\right)}+\frac{3 x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d^2}-\frac{\log \left(a+b e^{c+d x}\right)}{a^3 d^3}+\frac{x^2}{a^2 d \left(a+b e^{c+d x}\right)}-\frac{x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d}+\frac{x}{a^3 d^2}-\frac{3 x^2}{2 a^3 d}+\frac{x^3}{3 a^3}+\frac{x^2}{2 a d \left(a+b e^{c+d x}\right)^2}","-\frac{2 x \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^2}+\frac{3 \text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}+\frac{2 \text{PolyLog}\left(3,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}-\frac{x}{a^2 d^2 \left(a+b e^{c+d x}\right)}+\frac{3 x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d^2}-\frac{\log \left(a+b e^{c+d x}\right)}{a^3 d^3}+\frac{x^2}{a^2 d \left(a+b e^{c+d x}\right)}-\frac{x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d}+\frac{x}{a^3 d^2}-\frac{3 x^2}{2 a^3 d}+\frac{x^3}{3 a^3}+\frac{x^2}{2 a d \left(a+b e^{c+d x}\right)^2}",1,"x/(a^3*d^2) - x/(a^2*d^2*(a + b*E^(c + d*x))) - (3*x^2)/(2*a^3*d) + x^2/(2*a*d*(a + b*E^(c + d*x))^2) + x^2/(a^2*d*(a + b*E^(c + d*x))) + x^3/(3*a^3) - Log[a + b*E^(c + d*x)]/(a^3*d^3) + (3*x*Log[1 + (b*E^(c + d*x))/a])/(a^3*d^2) - (x^2*Log[1 + (b*E^(c + d*x))/a])/(a^3*d) + (3*PolyLog[2, -((b*E^(c + d*x))/a)])/(a^3*d^3) - (2*x*PolyLog[2, -((b*E^(c + d*x))/a)])/(a^3*d^2) + (2*PolyLog[3, -((b*E^(c + d*x))/a)])/(a^3*d^3)","A",23,12,17,0.7059,1,"{2185, 2184, 2190, 2531, 2282, 6589, 2191, 2279, 2391, 36, 29, 31}"
19,1,159,0,0.3315017,"\int \frac{x}{\left(a+b e^{c+d x}\right)^3} \, dx","Int[x/(a + b*E^(c + d*x))^3,x]","-\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^2}-\frac{1}{2 a^2 d^2 \left(a+b e^{c+d x}\right)}+\frac{3 \log \left(a+b e^{c+d x}\right)}{2 a^3 d^2}+\frac{x}{a^2 d \left(a+b e^{c+d x}\right)}-\frac{x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d}-\frac{3 x}{2 a^3 d}+\frac{x^2}{2 a^3}+\frac{x}{2 a d \left(a+b e^{c+d x}\right)^2}","-\frac{\text{PolyLog}\left(2,-\frac{b e^{c+d x}}{a}\right)}{a^3 d^2}-\frac{1}{2 a^2 d^2 \left(a+b e^{c+d x}\right)}+\frac{3 \log \left(a+b e^{c+d x}\right)}{2 a^3 d^2}+\frac{x}{a^2 d \left(a+b e^{c+d x}\right)}-\frac{x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d}-\frac{3 x}{2 a^3 d}+\frac{x^2}{2 a^3}+\frac{x}{2 a d \left(a+b e^{c+d x}\right)^2}",1,"-1/(2*a^2*d^2*(a + b*E^(c + d*x))) - (3*x)/(2*a^3*d) + x/(2*a*d*(a + b*E^(c + d*x))^2) + x/(a^2*d*(a + b*E^(c + d*x))) + x^2/(2*a^3) + (3*Log[a + b*E^(c + d*x)])/(2*a^3*d^2) - (x*Log[1 + (b*E^(c + d*x))/a])/(a^3*d) - PolyLog[2, -((b*E^(c + d*x))/a)]/(a^3*d^2)","A",15,11,15,0.7333,1,"{2185, 2184, 2190, 2279, 2391, 2191, 2282, 36, 29, 31, 44}"
20,1,69,0,0.0418567,"\int \frac{1}{\left(a+b e^{c+d x}\right)^3} \, dx","Int[(a + b*E^(c + d*x))^(-3),x]","\frac{1}{a^2 d \left(a+b e^{c+d x}\right)}-\frac{\log \left(a+b e^{c+d x}\right)}{a^3 d}+\frac{x}{a^3}+\frac{1}{2 a d \left(a+b e^{c+d x}\right)^2}","\frac{1}{a^2 d \left(a+b e^{c+d x}\right)}-\frac{\log \left(a+b e^{c+d x}\right)}{a^3 d}+\frac{x}{a^3}+\frac{1}{2 a d \left(a+b e^{c+d x}\right)^2}",1,"1/(2*a*d*(a + b*E^(c + d*x))^2) + 1/(a^2*d*(a + b*E^(c + d*x))) + x/a^3 - Log[a + b*E^(c + d*x)]/(a^3*d)","A",3,2,13,0.1538,1,"{2282, 44}"
21,0,0,0,0.0452978,"\int \frac{1}{\left(a+b e^{c+d x}\right)^3 x} \, dx","Int[1/((a + b*E^(c + d*x))^3*x),x]","\int \frac{1}{\left(a+b e^{c+d x}\right)^3 x} \, dx","\text{Int}\left(\frac{1}{x \left(a+b e^{c+d x}\right)^3},x\right)",0,"Defer[Int][1/((a + b*E^(c + d*x))^3*x), x]","A",0,0,0,0,-1,"{}"
22,0,0,0,0.0436581,"\int \frac{1}{\left(a+b e^{c+d x}\right)^3 x^2} \, dx","Int[1/((a + b*E^(c + d*x))^3*x^2),x]","\int \frac{1}{\left(a+b e^{c+d x}\right)^3 x^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b e^{c+d x}\right)^3},x\right)",0,"Defer[Int][1/((a + b*E^(c + d*x))^3*x^2), x]","A",0,0,0,0,-1,"{}"
23,1,72,0,0.0439052,"\int \frac{1}{\left(a+b e^{c-d x}\right)^3} \, dx","Int[(a + b*E^(c - d*x))^(-3),x]","-\frac{1}{a^2 d \left(a+b e^{c-d x}\right)}+\frac{\log \left(a+b e^{c-d x}\right)}{a^3 d}+\frac{x}{a^3}-\frac{1}{2 a d \left(a+b e^{c-d x}\right)^2}","-\frac{1}{a^2 d \left(a+b e^{c-d x}\right)}+\frac{\log \left(a+b e^{c-d x}\right)}{a^3 d}+\frac{x}{a^3}-\frac{1}{2 a d \left(a+b e^{c-d x}\right)^2}",1,"-1/(2*a*d*(a + b*E^(c - d*x))^2) - 1/(a^2*d*(a + b*E^(c - d*x))) + x/a^3 + Log[a + b*E^(c - d*x)]/(a^3*d)","A",3,2,14,0.1429,1,"{2282, 44}"
24,1,78,0,0.0467423,"\int \frac{1}{\left(a+b e^{-c-d x}\right)^3} \, dx","Int[(a + b*E^(-c - d*x))^(-3),x]","-\frac{1}{a^2 d \left(a+b e^{-c-d x}\right)}+\frac{\log \left(a+b e^{-c-d x}\right)}{a^3 d}+\frac{x}{a^3}-\frac{1}{2 a d \left(a+b e^{-c-d x}\right)^2}","-\frac{1}{a^2 d \left(a+b e^{-c-d x}\right)}+\frac{\log \left(a+b e^{-c-d x}\right)}{a^3 d}+\frac{x}{a^3}-\frac{1}{2 a d \left(a+b e^{-c-d x}\right)^2}",1,"-1/(2*a*d*(a + b*E^(-c - d*x))^2) - 1/(a^2*d*(a + b*E^(-c - d*x))) + x/a^3 + Log[a + b*E^(-c - d*x)]/(a^3*d)","A",3,2,16,0.1250,1,"{2282, 44}"
25,1,153,0,0.2381074,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)^3 \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^3,x]","\frac{a (c+d x)^4}{4 d}+\frac{6 b d^2 (c+d x) \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}-\frac{3 b d (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{b (c+d x)^3 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{6 b d^3 \left(F^{e g+f g x}\right)^n}{f^4 g^4 n^4 \log ^4(F)}","\frac{a (c+d x)^4}{4 d}+\frac{6 b d^2 (c+d x) \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}-\frac{3 b d (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{b (c+d x)^3 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{6 b d^3 \left(F^{e g+f g x}\right)^n}{f^4 g^4 n^4 \log ^4(F)}",1,"(a*(c + d*x)^4)/(4*d) - (6*b*d^3*(F^(e*g + f*g*x))^n)/(f^4*g^4*n^4*Log[F]^4) + (6*b*d^2*(F^(e*g + f*g*x))^n*(c + d*x))/(f^3*g^3*n^3*Log[F]^3) - (3*b*d*(F^(e*g + f*g*x))^n*(c + d*x)^2)/(f^2*g^2*n^2*Log[F]^2) + (b*(F^(e*g + f*g*x))^n*(c + d*x)^3)/(f*g*n*Log[F])","A",6,3,23,0.1304,1,"{2183, 2176, 2194}"
26,1,115,0,0.1544421,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)^2 \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^2,x]","\frac{a (c+d x)^3}{3 d}-\frac{2 b d (c+d x) \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{b (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}+\frac{2 b d^2 \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}","\frac{a (c+d x)^3}{3 d}-\frac{2 b d (c+d x) \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{b (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}+\frac{2 b d^2 \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}",1,"(a*(c + d*x)^3)/(3*d) + (2*b*d^2*(F^(e*g + f*g*x))^n)/(f^3*g^3*n^3*Log[F]^3) - (2*b*d*(F^(e*g + f*g*x))^n*(c + d*x))/(f^2*g^2*n^2*Log[F]^2) + (b*(F^(e*g + f*g*x))^n*(c + d*x)^2)/(f*g*n*Log[F])","A",5,3,23,0.1304,1,"{2183, 2176, 2194}"
27,1,77,0,0.07627,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x) \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)*(c + d*x),x]","\frac{a (c+d x)^2}{2 d}+\frac{b (c+d x) \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{b d \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}","\frac{a (c+d x)^2}{2 d}+\frac{b (c+d x) \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{b d \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}",1,"(a*(c + d*x)^2)/(2*d) - (b*d*(F^(e*g + f*g*x))^n)/(f^2*g^2*n^2*Log[F]^2) + (b*(F^(e*g + f*g*x))^n*(c + d*x))/(f*g*n*Log[F])","A",4,3,21,0.1429,1,"{2183, 2176, 2194}"
28,1,30,0,0.0158124,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) \, dx","Int[a + b*(F^(g*(e + f*x)))^n,x]","a x+\frac{b \left(F^{g (e+f x)}\right)^n}{f g n \log (F)}","a x+\frac{b \left(F^{g (e+f x)}\right)^n}{f g n \log (F)}",1,"a*x + (b*(F^(g*(e + f*x)))^n)/(f*g*n*Log[F])","A",2,1,15,0.06667,1,"{2194}"
29,1,68,0,0.1342002,"\int \frac{a+b \left(F^{g (e+f x)}\right)^n}{c+d x} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)/(c + d*x),x]","\frac{a \log (c+d x)}{d}+\frac{b \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d}","\frac{a \log (c+d x)}{d}+\frac{b \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d}",1,"(b*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d])/d + (a*Log[c + d*x])/d","A",4,3,23,0.1304,1,"{2183, 2182, 2178}"
30,1,100,0,0.17428,"\int \frac{a+b \left(F^{g (e+f x)}\right)^n}{(c+d x)^2} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)/(c + d*x)^2,x]","-\frac{a}{d (c+d x)}+\frac{b f g n \log (F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{b \left(F^{e g+f g x}\right)^n}{d (c+d x)}","-\frac{a}{d (c+d x)}+\frac{b f g n \log (F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{b \left(F^{e g+f g x}\right)^n}{d (c+d x)}",1,"-(a/(d*(c + d*x))) - (b*(F^(e*g + f*g*x))^n)/(d*(c + d*x)) + (b*f*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*g*n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F])/d^2","A",5,4,23,0.1739,1,"{2183, 2177, 2182, 2178}"
31,1,147,0,0.2396076,"\int \frac{a+b \left(F^{g (e+f x)}\right)^n}{(c+d x)^3} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)/(c + d*x)^3,x]","-\frac{a}{2 d (c+d x)^2}+\frac{b f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{2 d^3}-\frac{b f g n \log (F) \left(F^{e g+f g x}\right)^n}{2 d^2 (c+d x)}-\frac{b \left(F^{e g+f g x}\right)^n}{2 d (c+d x)^2}","-\frac{a}{2 d (c+d x)^2}+\frac{b f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{2 d^3}-\frac{b f g n \log (F) \left(F^{e g+f g x}\right)^n}{2 d^2 (c+d x)}-\frac{b \left(F^{e g+f g x}\right)^n}{2 d (c+d x)^2}",1,"-a/(2*d*(c + d*x)^2) - (b*(F^(e*g + f*g*x))^n)/(2*d*(c + d*x)^2) - (b*f*(F^(e*g + f*g*x))^n*g*n*Log[F])/(2*d^2*(c + d*x)) + (b*f^2*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*g^2*n^2*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/(2*d^3)","A",6,4,23,0.1739,1,"{2183, 2177, 2182, 2178}"
32,1,322,0,0.4864867,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)^3 \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)^3,x]","\frac{a^2 (c+d x)^4}{4 d}+\frac{12 a b d^2 (c+d x) \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}-\frac{6 a b d (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{2 a b (c+d x)^3 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{12 a b d^3 \left(F^{e g+f g x}\right)^n}{f^4 g^4 n^4 \log ^4(F)}+\frac{3 b^2 d^2 (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{4 f^3 g^3 n^3 \log ^3(F)}-\frac{3 b^2 d (c+d x)^2 \left(F^{e g+f g x}\right)^{2 n}}{4 f^2 g^2 n^2 \log ^2(F)}+\frac{b^2 (c+d x)^3 \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}-\frac{3 b^2 d^3 \left(F^{e g+f g x}\right)^{2 n}}{8 f^4 g^4 n^4 \log ^4(F)}","\frac{a^2 (c+d x)^4}{4 d}+\frac{12 a b d^2 (c+d x) \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}-\frac{6 a b d (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{2 a b (c+d x)^3 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{12 a b d^3 \left(F^{e g+f g x}\right)^n}{f^4 g^4 n^4 \log ^4(F)}+\frac{3 b^2 d^2 (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{4 f^3 g^3 n^3 \log ^3(F)}-\frac{3 b^2 d (c+d x)^2 \left(F^{e g+f g x}\right)^{2 n}}{4 f^2 g^2 n^2 \log ^2(F)}+\frac{b^2 (c+d x)^3 \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}-\frac{3 b^2 d^3 \left(F^{e g+f g x}\right)^{2 n}}{8 f^4 g^4 n^4 \log ^4(F)}",1,"(a^2*(c + d*x)^4)/(4*d) - (12*a*b*d^3*(F^(e*g + f*g*x))^n)/(f^4*g^4*n^4*Log[F]^4) - (3*b^2*d^3*(F^(e*g + f*g*x))^(2*n))/(8*f^4*g^4*n^4*Log[F]^4) + (12*a*b*d^2*(F^(e*g + f*g*x))^n*(c + d*x))/(f^3*g^3*n^3*Log[F]^3) + (3*b^2*d^2*(F^(e*g + f*g*x))^(2*n)*(c + d*x))/(4*f^3*g^3*n^3*Log[F]^3) - (6*a*b*d*(F^(e*g + f*g*x))^n*(c + d*x)^2)/(f^2*g^2*n^2*Log[F]^2) - (3*b^2*d*(F^(e*g + f*g*x))^(2*n)*(c + d*x)^2)/(4*f^2*g^2*n^2*Log[F]^2) + (2*a*b*(F^(e*g + f*g*x))^n*(c + d*x)^3)/(f*g*n*Log[F]) + (b^2*(F^(e*g + f*g*x))^(2*n)*(c + d*x)^3)/(2*f*g*n*Log[F])","A",10,3,25,0.1200,1,"{2183, 2176, 2194}"
33,1,239,0,0.3204853,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)^2 \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)^2,x]","\frac{a^2 (c+d x)^3}{3 d}-\frac{4 a b d (c+d x) \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{2 a b (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}+\frac{4 a b d^2 \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}-\frac{b^2 d (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{2 f^2 g^2 n^2 \log ^2(F)}+\frac{b^2 (c+d x)^2 \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}+\frac{b^2 d^2 \left(F^{e g+f g x}\right)^{2 n}}{4 f^3 g^3 n^3 \log ^3(F)}","\frac{a^2 (c+d x)^3}{3 d}-\frac{4 a b d (c+d x) \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{2 a b (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}+\frac{4 a b d^2 \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}-\frac{b^2 d (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{2 f^2 g^2 n^2 \log ^2(F)}+\frac{b^2 (c+d x)^2 \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}+\frac{b^2 d^2 \left(F^{e g+f g x}\right)^{2 n}}{4 f^3 g^3 n^3 \log ^3(F)}",1,"(a^2*(c + d*x)^3)/(3*d) + (4*a*b*d^2*(F^(e*g + f*g*x))^n)/(f^3*g^3*n^3*Log[F]^3) + (b^2*d^2*(F^(e*g + f*g*x))^(2*n))/(4*f^3*g^3*n^3*Log[F]^3) - (4*a*b*d*(F^(e*g + f*g*x))^n*(c + d*x))/(f^2*g^2*n^2*Log[F]^2) - (b^2*d*(F^(e*g + f*g*x))^(2*n)*(c + d*x))/(2*f^2*g^2*n^2*Log[F]^2) + (2*a*b*(F^(e*g + f*g*x))^n*(c + d*x)^2)/(f*g*n*Log[F]) + (b^2*(F^(e*g + f*g*x))^(2*n)*(c + d*x)^2)/(2*f*g*n*Log[F])","A",8,3,25,0.1200,1,"{2183, 2176, 2194}"
34,1,156,0,0.1569362,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x) \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x),x]","\frac{a^2 (c+d x)^2}{2 d}+\frac{2 a b (c+d x) \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{2 a b d \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{b^2 (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}-\frac{b^2 d \left(F^{e g+f g x}\right)^{2 n}}{4 f^2 g^2 n^2 \log ^2(F)}","\frac{a^2 (c+d x)^2}{2 d}+\frac{2 a b (c+d x) \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{2 a b d \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{b^2 (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}-\frac{b^2 d \left(F^{e g+f g x}\right)^{2 n}}{4 f^2 g^2 n^2 \log ^2(F)}",1,"(a^2*(c + d*x)^2)/(2*d) - (2*a*b*d*(F^(e*g + f*g*x))^n)/(f^2*g^2*n^2*Log[F]^2) - (b^2*d*(F^(e*g + f*g*x))^(2*n))/(4*f^2*g^2*n^2*Log[F]^2) + (2*a*b*(F^(e*g + f*g*x))^n*(c + d*x))/(f*g*n*Log[F]) + (b^2*(F^(e*g + f*g*x))^(2*n)*(c + d*x))/(2*f*g*n*Log[F])","A",6,3,23,0.1304,1,"{2183, 2176, 2194}"
35,1,67,0,0.0366563,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^2,x]","a^2 x+\frac{2 a b \left(F^{g (e+f x)}\right)^n}{f g n \log (F)}+\frac{b^2 \left(F^{g (e+f x)}\right)^{2 n}}{2 f g n \log (F)}","a^2 x+\frac{2 a b \left(F^{g (e+f x)}\right)^n}{f g n \log (F)}+\frac{b^2 \left(F^{g (e+f x)}\right)^{2 n}}{2 f g n \log (F)}",1,"a^2*x + (2*a*b*(F^(g*(e + f*x)))^n)/(f*g*n*Log[F]) + (b^2*(F^(g*(e + f*x)))^(2*n))/(2*f*g*n*Log[F])","A",4,3,17,0.1765,1,"{2282, 266, 43}"
36,1,134,0,0.2540948,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}{c+d x} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^2/(c + d*x),x]","\frac{a^2 \log (c+d x)}{d}+\frac{2 a b \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d}+\frac{b^2 \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d}","\frac{a^2 \log (c+d x)}{d}+\frac{2 a b \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d}+\frac{b^2 \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d}",1,"(2*a*b*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d])/d + (b^2*F^(2*(e - (c*f)/d)*g*n - 2*g*n*(e + f*x))*(F^(e*g + f*g*x))^(2*n)*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d])/d + (a^2*Log[c + d*x])/d","A",6,3,25,0.1200,1,"{2183, 2182, 2178}"
37,1,202,0,0.3414214,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}{(c+d x)^2} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^2/(c + d*x)^2,x]","-\frac{a^2}{d (c+d x)}+\frac{2 a b f g n \log (F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{2 a b \left(F^{e g+f g x}\right)^n}{d (c+d x)}+\frac{2 b^2 f g n \log (F) \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{b^2 \left(F^{e g+f g x}\right)^{2 n}}{d (c+d x)}","-\frac{a^2}{d (c+d x)}+\frac{2 a b f g n \log (F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{2 a b \left(F^{e g+f g x}\right)^n}{d (c+d x)}+\frac{2 b^2 f g n \log (F) \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{b^2 \left(F^{e g+f g x}\right)^{2 n}}{d (c+d x)}",1,"-(a^2/(d*(c + d*x))) - (2*a*b*(F^(e*g + f*g*x))^n)/(d*(c + d*x)) - (b^2*(F^(e*g + f*g*x))^(2*n))/(d*(c + d*x)) + (2*a*b*f*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*g*n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F])/d^2 + (2*b^2*f*F^(2*(e - (c*f)/d)*g*n - 2*g*n*(e + f*x))*(F^(e*g + f*g*x))^(2*n)*g*n*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d]*Log[F])/d^2","A",8,4,25,0.1600,1,"{2183, 2177, 2182, 2178}"
38,1,286,0,0.474569,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}{(c+d x)^3} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^2/(c + d*x)^3,x]","-\frac{a^2}{2 d (c+d x)^2}+\frac{a b f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d^3}-\frac{a b f g n \log (F) \left(F^{e g+f g x}\right)^n}{d^2 (c+d x)}-\frac{a b \left(F^{e g+f g x}\right)^n}{d (c+d x)^2}+\frac{2 b^2 f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d^3}-\frac{b^2 f g n \log (F) \left(F^{e g+f g x}\right)^{2 n}}{d^2 (c+d x)}-\frac{b^2 \left(F^{e g+f g x}\right)^{2 n}}{2 d (c+d x)^2}","-\frac{a^2}{2 d (c+d x)^2}+\frac{a b f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d^3}-\frac{a b f g n \log (F) \left(F^{e g+f g x}\right)^n}{d^2 (c+d x)}-\frac{a b \left(F^{e g+f g x}\right)^n}{d (c+d x)^2}+\frac{2 b^2 f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d^3}-\frac{b^2 f g n \log (F) \left(F^{e g+f g x}\right)^{2 n}}{d^2 (c+d x)}-\frac{b^2 \left(F^{e g+f g x}\right)^{2 n}}{2 d (c+d x)^2}",1,"-a^2/(2*d*(c + d*x)^2) - (a*b*(F^(e*g + f*g*x))^n)/(d*(c + d*x)^2) - (b^2*(F^(e*g + f*g*x))^(2*n))/(2*d*(c + d*x)^2) - (a*b*f*(F^(e*g + f*g*x))^n*g*n*Log[F])/(d^2*(c + d*x)) - (b^2*f*(F^(e*g + f*g*x))^(2*n)*g*n*Log[F])/(d^2*(c + d*x)) + (a*b*f^2*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*g^2*n^2*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/d^3 + (2*b^2*f^2*F^(2*(e - (c*f)/d)*g*n - 2*g*n*(e + f*x))*(F^(e*g + f*g*x))^(2*n)*g^2*n^2*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/d^3","A",10,4,25,0.1600,1,"{2183, 2177, 2182, 2178}"
39,1,496,0,0.7051356,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)^3 \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^3,x]","\frac{18 a^2 b d^2 (c+d x) \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}-\frac{9 a^2 b d (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{3 a^2 b (c+d x)^3 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{18 a^2 b d^3 \left(F^{e g+f g x}\right)^n}{f^4 g^4 n^4 \log ^4(F)}+\frac{a^3 (c+d x)^4}{4 d}+\frac{9 a b^2 d^2 (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{4 f^3 g^3 n^3 \log ^3(F)}-\frac{9 a b^2 d (c+d x)^2 \left(F^{e g+f g x}\right)^{2 n}}{4 f^2 g^2 n^2 \log ^2(F)}+\frac{3 a b^2 (c+d x)^3 \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}-\frac{9 a b^2 d^3 \left(F^{e g+f g x}\right)^{2 n}}{8 f^4 g^4 n^4 \log ^4(F)}+\frac{2 b^3 d^2 (c+d x) \left(F^{e g+f g x}\right)^{3 n}}{9 f^3 g^3 n^3 \log ^3(F)}-\frac{b^3 d (c+d x)^2 \left(F^{e g+f g x}\right)^{3 n}}{3 f^2 g^2 n^2 \log ^2(F)}+\frac{b^3 (c+d x)^3 \left(F^{e g+f g x}\right)^{3 n}}{3 f g n \log (F)}-\frac{2 b^3 d^3 \left(F^{e g+f g x}\right)^{3 n}}{27 f^4 g^4 n^4 \log ^4(F)}","\frac{18 a^2 b d^2 (c+d x) \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}-\frac{9 a^2 b d (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{3 a^2 b (c+d x)^3 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{18 a^2 b d^3 \left(F^{e g+f g x}\right)^n}{f^4 g^4 n^4 \log ^4(F)}+\frac{a^3 (c+d x)^4}{4 d}+\frac{9 a b^2 d^2 (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{4 f^3 g^3 n^3 \log ^3(F)}-\frac{9 a b^2 d (c+d x)^2 \left(F^{e g+f g x}\right)^{2 n}}{4 f^2 g^2 n^2 \log ^2(F)}+\frac{3 a b^2 (c+d x)^3 \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}-\frac{9 a b^2 d^3 \left(F^{e g+f g x}\right)^{2 n}}{8 f^4 g^4 n^4 \log ^4(F)}+\frac{2 b^3 d^2 (c+d x) \left(F^{e g+f g x}\right)^{3 n}}{9 f^3 g^3 n^3 \log ^3(F)}-\frac{b^3 d (c+d x)^2 \left(F^{e g+f g x}\right)^{3 n}}{3 f^2 g^2 n^2 \log ^2(F)}+\frac{b^3 (c+d x)^3 \left(F^{e g+f g x}\right)^{3 n}}{3 f g n \log (F)}-\frac{2 b^3 d^3 \left(F^{e g+f g x}\right)^{3 n}}{27 f^4 g^4 n^4 \log ^4(F)}",1,"(a^3*(c + d*x)^4)/(4*d) - (18*a^2*b*d^3*(F^(e*g + f*g*x))^n)/(f^4*g^4*n^4*Log[F]^4) - (9*a*b^2*d^3*(F^(e*g + f*g*x))^(2*n))/(8*f^4*g^4*n^4*Log[F]^4) - (2*b^3*d^3*(F^(e*g + f*g*x))^(3*n))/(27*f^4*g^4*n^4*Log[F]^4) + (18*a^2*b*d^2*(F^(e*g + f*g*x))^n*(c + d*x))/(f^3*g^3*n^3*Log[F]^3) + (9*a*b^2*d^2*(F^(e*g + f*g*x))^(2*n)*(c + d*x))/(4*f^3*g^3*n^3*Log[F]^3) + (2*b^3*d^2*(F^(e*g + f*g*x))^(3*n)*(c + d*x))/(9*f^3*g^3*n^3*Log[F]^3) - (9*a^2*b*d*(F^(e*g + f*g*x))^n*(c + d*x)^2)/(f^2*g^2*n^2*Log[F]^2) - (9*a*b^2*d*(F^(e*g + f*g*x))^(2*n)*(c + d*x)^2)/(4*f^2*g^2*n^2*Log[F]^2) - (b^3*d*(F^(e*g + f*g*x))^(3*n)*(c + d*x)^2)/(3*f^2*g^2*n^2*Log[F]^2) + (3*a^2*b*(F^(e*g + f*g*x))^n*(c + d*x)^3)/(f*g*n*Log[F]) + (3*a*b^2*(F^(e*g + f*g*x))^(2*n)*(c + d*x)^3)/(2*f*g*n*Log[F]) + (b^3*(F^(e*g + f*g*x))^(3*n)*(c + d*x)^3)/(3*f*g*n*Log[F])","A",14,3,25,0.1200,1,"{2183, 2176, 2194}"
40,1,366,0,0.4642526,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)^2 \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^2,x]","-\frac{6 a^2 b d (c+d x) \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{3 a^2 b (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}+\frac{6 a^2 b d^2 \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}+\frac{a^3 (c+d x)^3}{3 d}-\frac{3 a b^2 d (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{2 f^2 g^2 n^2 \log ^2(F)}+\frac{3 a b^2 (c+d x)^2 \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}+\frac{3 a b^2 d^2 \left(F^{e g+f g x}\right)^{2 n}}{4 f^3 g^3 n^3 \log ^3(F)}-\frac{2 b^3 d (c+d x) \left(F^{e g+f g x}\right)^{3 n}}{9 f^2 g^2 n^2 \log ^2(F)}+\frac{b^3 (c+d x)^2 \left(F^{e g+f g x}\right)^{3 n}}{3 f g n \log (F)}+\frac{2 b^3 d^2 \left(F^{e g+f g x}\right)^{3 n}}{27 f^3 g^3 n^3 \log ^3(F)}","-\frac{6 a^2 b d (c+d x) \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{3 a^2 b (c+d x)^2 \left(F^{e g+f g x}\right)^n}{f g n \log (F)}+\frac{6 a^2 b d^2 \left(F^{e g+f g x}\right)^n}{f^3 g^3 n^3 \log ^3(F)}+\frac{a^3 (c+d x)^3}{3 d}-\frac{3 a b^2 d (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{2 f^2 g^2 n^2 \log ^2(F)}+\frac{3 a b^2 (c+d x)^2 \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}+\frac{3 a b^2 d^2 \left(F^{e g+f g x}\right)^{2 n}}{4 f^3 g^3 n^3 \log ^3(F)}-\frac{2 b^3 d (c+d x) \left(F^{e g+f g x}\right)^{3 n}}{9 f^2 g^2 n^2 \log ^2(F)}+\frac{b^3 (c+d x)^2 \left(F^{e g+f g x}\right)^{3 n}}{3 f g n \log (F)}+\frac{2 b^3 d^2 \left(F^{e g+f g x}\right)^{3 n}}{27 f^3 g^3 n^3 \log ^3(F)}",1,"(a^3*(c + d*x)^3)/(3*d) + (6*a^2*b*d^2*(F^(e*g + f*g*x))^n)/(f^3*g^3*n^3*Log[F]^3) + (3*a*b^2*d^2*(F^(e*g + f*g*x))^(2*n))/(4*f^3*g^3*n^3*Log[F]^3) + (2*b^3*d^2*(F^(e*g + f*g*x))^(3*n))/(27*f^3*g^3*n^3*Log[F]^3) - (6*a^2*b*d*(F^(e*g + f*g*x))^n*(c + d*x))/(f^2*g^2*n^2*Log[F]^2) - (3*a*b^2*d*(F^(e*g + f*g*x))^(2*n)*(c + d*x))/(2*f^2*g^2*n^2*Log[F]^2) - (2*b^3*d*(F^(e*g + f*g*x))^(3*n)*(c + d*x))/(9*f^2*g^2*n^2*Log[F]^2) + (3*a^2*b*(F^(e*g + f*g*x))^n*(c + d*x)^2)/(f*g*n*Log[F]) + (3*a*b^2*(F^(e*g + f*g*x))^(2*n)*(c + d*x)^2)/(2*f*g*n*Log[F]) + (b^3*(F^(e*g + f*g*x))^(3*n)*(c + d*x)^2)/(3*f*g*n*Log[F])","A",11,3,25,0.1200,1,"{2183, 2176, 2194}"
41,1,236,0,0.2394982,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x) \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x),x]","\frac{3 a^2 b (c+d x) \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{3 a^2 b d \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{a^3 (c+d x)^2}{2 d}+\frac{3 a b^2 (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}-\frac{3 a b^2 d \left(F^{e g+f g x}\right)^{2 n}}{4 f^2 g^2 n^2 \log ^2(F)}+\frac{b^3 (c+d x) \left(F^{e g+f g x}\right)^{3 n}}{3 f g n \log (F)}-\frac{b^3 d \left(F^{e g+f g x}\right)^{3 n}}{9 f^2 g^2 n^2 \log ^2(F)}","\frac{3 a^2 b (c+d x) \left(F^{e g+f g x}\right)^n}{f g n \log (F)}-\frac{3 a^2 b d \left(F^{e g+f g x}\right)^n}{f^2 g^2 n^2 \log ^2(F)}+\frac{a^3 (c+d x)^2}{2 d}+\frac{3 a b^2 (c+d x) \left(F^{e g+f g x}\right)^{2 n}}{2 f g n \log (F)}-\frac{3 a b^2 d \left(F^{e g+f g x}\right)^{2 n}}{4 f^2 g^2 n^2 \log ^2(F)}+\frac{b^3 (c+d x) \left(F^{e g+f g x}\right)^{3 n}}{3 f g n \log (F)}-\frac{b^3 d \left(F^{e g+f g x}\right)^{3 n}}{9 f^2 g^2 n^2 \log ^2(F)}",1,"(a^3*(c + d*x)^2)/(2*d) - (3*a^2*b*d*(F^(e*g + f*g*x))^n)/(f^2*g^2*n^2*Log[F]^2) - (3*a*b^2*d*(F^(e*g + f*g*x))^(2*n))/(4*f^2*g^2*n^2*Log[F]^2) - (b^3*d*(F^(e*g + f*g*x))^(3*n))/(9*f^2*g^2*n^2*Log[F]^2) + (3*a^2*b*(F^(e*g + f*g*x))^n*(c + d*x))/(f*g*n*Log[F]) + (3*a*b^2*(F^(e*g + f*g*x))^(2*n)*(c + d*x))/(2*f*g*n*Log[F]) + (b^3*(F^(e*g + f*g*x))^(3*n)*(c + d*x))/(3*f*g*n*Log[F])","A",8,3,23,0.1304,1,"{2183, 2176, 2194}"
42,1,103,0,0.0493079,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^3,x]","\frac{3 a^2 b \left(F^{g (e+f x)}\right)^n}{f g n \log (F)}+a^3 x+\frac{3 a b^2 \left(F^{g (e+f x)}\right)^{2 n}}{2 f g n \log (F)}+\frac{b^3 \left(F^{g (e+f x)}\right)^{3 n}}{3 f g n \log (F)}","\frac{3 a^2 b \left(F^{g (e+f x)}\right)^n}{f g n \log (F)}+a^3 x+\frac{3 a b^2 \left(F^{g (e+f x)}\right)^{2 n}}{2 f g n \log (F)}+\frac{b^3 \left(F^{g (e+f x)}\right)^{3 n}}{3 f g n \log (F)}",1,"a^3*x + (3*a^2*b*(F^(g*(e + f*x)))^n)/(f*g*n*Log[F]) + (3*a*b^2*(F^(g*(e + f*x)))^(2*n))/(2*f*g*n*Log[F]) + (b^3*(F^(g*(e + f*x)))^(3*n))/(3*f*g*n*Log[F])","A",4,3,17,0.1765,1,"{2282, 266, 43}"
43,1,200,0,0.3538001,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3}{c+d x} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^3/(c + d*x),x]","\frac{3 a^2 b \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d}+\frac{a^3 \log (c+d x)}{d}+\frac{3 a b^2 \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d}+\frac{b^3 \left(F^{e g+f g x}\right)^{3 n} F^{3 g n \left(e-\frac{c f}{d}\right)-3 g n (e+f x)} \text{Ei}\left(\frac{3 f g n (c+d x) \log (F)}{d}\right)}{d}","\frac{3 a^2 b \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d}+\frac{a^3 \log (c+d x)}{d}+\frac{3 a b^2 \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d}+\frac{b^3 \left(F^{e g+f g x}\right)^{3 n} F^{3 g n \left(e-\frac{c f}{d}\right)-3 g n (e+f x)} \text{Ei}\left(\frac{3 f g n (c+d x) \log (F)}{d}\right)}{d}",1,"(3*a^2*b*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d])/d + (3*a*b^2*F^(2*(e - (c*f)/d)*g*n - 2*g*n*(e + f*x))*(F^(e*g + f*g*x))^(2*n)*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d])/d + (b^3*F^(3*(e - (c*f)/d)*g*n - 3*g*n*(e + f*x))*(F^(e*g + f*g*x))^(3*n)*ExpIntegralEi[(3*f*g*n*(c + d*x)*Log[F])/d])/d + (a^3*Log[c + d*x])/d","A",8,3,25,0.1200,1,"{2183, 2182, 2178}"
44,1,305,0,0.4908956,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3}{(c+d x)^2} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^3/(c + d*x)^2,x]","\frac{3 a^2 b f g n \log (F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{3 a^2 b \left(F^{e g+f g x}\right)^n}{d (c+d x)}-\frac{a^3}{d (c+d x)}+\frac{6 a b^2 f g n \log (F) \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{3 a b^2 \left(F^{e g+f g x}\right)^{2 n}}{d (c+d x)}+\frac{3 b^3 f g n \log (F) \left(F^{e g+f g x}\right)^{3 n} F^{3 g n \left(e-\frac{c f}{d}\right)-3 g n (e+f x)} \text{Ei}\left(\frac{3 f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{b^3 \left(F^{e g+f g x}\right)^{3 n}}{d (c+d x)}","\frac{3 a^2 b f g n \log (F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{3 a^2 b \left(F^{e g+f g x}\right)^n}{d (c+d x)}-\frac{a^3}{d (c+d x)}+\frac{6 a b^2 f g n \log (F) \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{3 a b^2 \left(F^{e g+f g x}\right)^{2 n}}{d (c+d x)}+\frac{3 b^3 f g n \log (F) \left(F^{e g+f g x}\right)^{3 n} F^{3 g n \left(e-\frac{c f}{d}\right)-3 g n (e+f x)} \text{Ei}\left(\frac{3 f g n (c+d x) \log (F)}{d}\right)}{d^2}-\frac{b^3 \left(F^{e g+f g x}\right)^{3 n}}{d (c+d x)}",1,"-(a^3/(d*(c + d*x))) - (3*a^2*b*(F^(e*g + f*g*x))^n)/(d*(c + d*x)) - (3*a*b^2*(F^(e*g + f*g*x))^(2*n))/(d*(c + d*x)) - (b^3*(F^(e*g + f*g*x))^(3*n))/(d*(c + d*x)) + (3*a^2*b*f*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*g*n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F])/d^2 + (6*a*b^2*f*F^(2*(e - (c*f)/d)*g*n - 2*g*n*(e + f*x))*(F^(e*g + f*g*x))^(2*n)*g*n*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d]*Log[F])/d^2 + (3*b^3*f*F^(3*(e - (c*f)/d)*g*n - 3*g*n*(e + f*x))*(F^(e*g + f*g*x))^(3*n)*g*n*ExpIntegralEi[(3*f*g*n*(c + d*x)*Log[F])/d]*Log[F])/d^2","A",11,4,25,0.1600,1,"{2183, 2177, 2182, 2178}"
45,1,447,0,0.6948769,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3}{(c+d x)^3} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^3/(c + d*x)^3,x]","\frac{3 a^2 b f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{2 d^3}-\frac{3 a^2 b f g n \log (F) \left(F^{e g+f g x}\right)^n}{2 d^2 (c+d x)}-\frac{3 a^2 b \left(F^{e g+f g x}\right)^n}{2 d (c+d x)^2}-\frac{a^3}{2 d (c+d x)^2}+\frac{6 a b^2 f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d^3}-\frac{3 a b^2 f g n \log (F) \left(F^{e g+f g x}\right)^{2 n}}{d^2 (c+d x)}-\frac{3 a b^2 \left(F^{e g+f g x}\right)^{2 n}}{2 d (c+d x)^2}+\frac{9 b^3 f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^{3 n} F^{3 g n \left(e-\frac{c f}{d}\right)-3 g n (e+f x)} \text{Ei}\left(\frac{3 f g n (c+d x) \log (F)}{d}\right)}{2 d^3}-\frac{3 b^3 f g n \log (F) \left(F^{e g+f g x}\right)^{3 n}}{2 d^2 (c+d x)}-\frac{b^3 \left(F^{e g+f g x}\right)^{3 n}}{2 d (c+d x)^2}","\frac{3 a^2 b f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)}{2 d^3}-\frac{3 a^2 b f g n \log (F) \left(F^{e g+f g x}\right)^n}{2 d^2 (c+d x)}-\frac{3 a^2 b \left(F^{e g+f g x}\right)^n}{2 d (c+d x)^2}-\frac{a^3}{2 d (c+d x)^2}+\frac{6 a b^2 f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d^3}-\frac{3 a b^2 f g n \log (F) \left(F^{e g+f g x}\right)^{2 n}}{d^2 (c+d x)}-\frac{3 a b^2 \left(F^{e g+f g x}\right)^{2 n}}{2 d (c+d x)^2}+\frac{9 b^3 f^2 g^2 n^2 \log ^2(F) \left(F^{e g+f g x}\right)^{3 n} F^{3 g n \left(e-\frac{c f}{d}\right)-3 g n (e+f x)} \text{Ei}\left(\frac{3 f g n (c+d x) \log (F)}{d}\right)}{2 d^3}-\frac{3 b^3 f g n \log (F) \left(F^{e g+f g x}\right)^{3 n}}{2 d^2 (c+d x)}-\frac{b^3 \left(F^{e g+f g x}\right)^{3 n}}{2 d (c+d x)^2}",1,"-a^3/(2*d*(c + d*x)^2) - (3*a^2*b*(F^(e*g + f*g*x))^n)/(2*d*(c + d*x)^2) - (3*a*b^2*(F^(e*g + f*g*x))^(2*n))/(2*d*(c + d*x)^2) - (b^3*(F^(e*g + f*g*x))^(3*n))/(2*d*(c + d*x)^2) - (3*a^2*b*f*(F^(e*g + f*g*x))^n*g*n*Log[F])/(2*d^2*(c + d*x)) - (3*a*b^2*f*(F^(e*g + f*g*x))^(2*n)*g*n*Log[F])/(d^2*(c + d*x)) - (3*b^3*f*(F^(e*g + f*g*x))^(3*n)*g*n*Log[F])/(2*d^2*(c + d*x)) + (3*a^2*b*f^2*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*g^2*n^2*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/(2*d^3) + (6*a*b^2*f^2*F^(2*(e - (c*f)/d)*g*n - 2*g*n*(e + f*x))*(F^(e*g + f*g*x))^(2*n)*g^2*n^2*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/d^3 + (9*b^3*f^2*F^(3*(e - (c*f)/d)*g*n - 3*g*n*(e + f*x))*(F^(e*g + f*g*x))^(3*n)*g^2*n^2*ExpIntegralEi[(3*f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/(2*d^3)","A",14,4,25,0.1600,1,"{2183, 2177, 2182, 2178}"
46,1,192,0,0.3258703,"\int \frac{(c+d x)^3}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","Int[(c + d*x)^3/(a + b*(F^(g*(e + f*x)))^n),x]","\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^3 g^3 n^3 \log ^3(F)}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^2 g^2 n^2 \log ^2(F)}-\frac{6 d^3 \text{PolyLog}\left(4,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^4 g^4 n^4 \log ^4(F)}-\frac{(c+d x)^3 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a f g n \log (F)}+\frac{(c+d x)^4}{4 a d}","\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^3 g^3 n^3 \log ^3(F)}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^2 g^2 n^2 \log ^2(F)}-\frac{6 d^3 \text{PolyLog}\left(4,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^4 g^4 n^4 \log ^4(F)}-\frac{(c+d x)^3 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a f g n \log (F)}+\frac{(c+d x)^4}{4 a d}",1,"(c + d*x)^4/(4*a*d) - ((c + d*x)^3*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a*f*g*n*Log[F]) - (3*d*(c + d*x)^2*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a*f^2*g^2*n^2*Log[F]^2) + (6*d^2*(c + d*x)*PolyLog[3, -((b*(F^(g*(e + f*x)))^n)/a)])/(a*f^3*g^3*n^3*Log[F]^3) - (6*d^3*PolyLog[4, -((b*(F^(g*(e + f*x)))^n)/a)])/(a*f^4*g^4*n^4*Log[F]^4)","A",6,6,25,0.2400,1,"{2184, 2190, 2531, 6609, 2282, 6589}"
47,1,145,0,0.2756882,"\int \frac{(c+d x)^2}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","Int[(c + d*x)^2/(a + b*(F^(g*(e + f*x)))^n),x]","-\frac{2 d (c+d x) \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^2 g^2 n^2 \log ^2(F)}+\frac{2 d^2 \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^3 g^3 n^3 \log ^3(F)}-\frac{(c+d x)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a f g n \log (F)}+\frac{(c+d x)^3}{3 a d}","-\frac{2 d (c+d x) \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^2 g^2 n^2 \log ^2(F)}+\frac{2 d^2 \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^3 g^3 n^3 \log ^3(F)}-\frac{(c+d x)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a f g n \log (F)}+\frac{(c+d x)^3}{3 a d}",1,"(c + d*x)^3/(3*a*d) - ((c + d*x)^2*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a*f*g*n*Log[F]) - (2*d*(c + d*x)*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a*f^2*g^2*n^2*Log[F]^2) + (2*d^2*PolyLog[3, -((b*(F^(g*(e + f*x)))^n)/a)])/(a*f^3*g^3*n^3*Log[F]^3)","A",5,5,25,0.2000,1,"{2184, 2190, 2531, 2282, 6589}"
48,1,98,0,0.1565126,"\int \frac{c+d x}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","Int[(c + d*x)/(a + b*(F^(g*(e + f*x)))^n),x]","-\frac{d \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^2 g^2 n^2 \log ^2(F)}-\frac{(c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a f g n \log (F)}+\frac{(c+d x)^2}{2 a d}","-\frac{d \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a f^2 g^2 n^2 \log ^2(F)}-\frac{(c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a f g n \log (F)}+\frac{(c+d x)^2}{2 a d}",1,"(c + d*x)^2/(2*a*d) - ((c + d*x)*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a*f*g*n*Log[F]) - (d*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a*f^2*g^2*n^2*Log[F]^2)","A",4,4,23,0.1739,1,"{2184, 2190, 2279, 2391}"
49,1,40,0,0.0300728,"\int \frac{1}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^(-1),x]","\frac{x}{a}-\frac{\log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a f g n \log (F)}","\frac{x}{a}-\frac{\log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a f g n \log (F)}",1,"x/a - Log[a + b*(F^(g*(e + f*x)))^n]/(a*f*g*n*Log[F])","A",5,5,17,0.2941,1,"{2282, 266, 36, 29, 31}"
50,0,0,0,0.1372536,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)} \, dx","Int[1/((a + b*(F^(g*(e + f*x)))^n)*(c + d*x)),x]","\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)} \, dx","\text{Int}\left(\frac{1}{(c+d x) \left(a+b \left(F^{e g+f g x}\right)^n\right)},x\right)",0,"Defer[Int][1/((a + b*(F^(e*g + f*g*x))^n)*(c + d*x)), x]","A",0,0,0,0,-1,"{}"
51,0,0,0,0.1278805,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)^2} \, dx","Int[1/((a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^2),x]","\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 \left(a+b \left(F^{e g+f g x}\right)^n\right)},x\right)",0,"Defer[Int][1/((a + b*(F^(e*g + f*g*x))^n)*(c + d*x)^2), x]","A",0,0,0,0,-1,"{}"
52,1,388,0,0.8668118,"\int \frac{(c+d x)^3}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","Int[(c + d*x)^3/(a + b*(F^(g*(e + f*x)))^n)^2,x]","\frac{6 d^2 (c+d x) \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^3 g^3 n^3 \log ^3(F)}+\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^3 g^3 n^3 \log ^3(F)}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}-\frac{6 d^3 \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^4 g^4 n^4 \log ^4(F)}-\frac{6 d^3 \text{PolyLog}\left(4,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^4 g^4 n^4 \log ^4(F)}+\frac{3 d (c+d x)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}-\frac{(c+d x)^3 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^2 f g n \log (F)}-\frac{(c+d x)^3}{a^2 f g n \log (F)}+\frac{(c+d x)^4}{4 a^2 d}+\frac{(c+d x)^3}{a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}","\frac{6 d^2 (c+d x) \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^3 g^3 n^3 \log ^3(F)}+\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^3 g^3 n^3 \log ^3(F)}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}-\frac{6 d^3 \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^4 g^4 n^4 \log ^4(F)}-\frac{6 d^3 \text{PolyLog}\left(4,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^4 g^4 n^4 \log ^4(F)}+\frac{3 d (c+d x)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}-\frac{(c+d x)^3 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^2 f g n \log (F)}-\frac{(c+d x)^3}{a^2 f g n \log (F)}+\frac{(c+d x)^4}{4 a^2 d}+\frac{(c+d x)^3}{a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}",1,"(c + d*x)^4/(4*a^2*d) - (c + d*x)^3/(a^2*f*g*n*Log[F]) + (c + d*x)^3/(a*f*(a + b*(F^(g*(e + f*x)))^n)*g*n*Log[F]) + (3*d*(c + d*x)^2*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a^2*f^2*g^2*n^2*Log[F]^2) - ((c + d*x)^3*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a^2*f*g*n*Log[F]) + (6*d^2*(c + d*x)*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^2*f^3*g^3*n^3*Log[F]^3) - (3*d*(c + d*x)^2*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^2*f^2*g^2*n^2*Log[F]^2) - (6*d^3*PolyLog[3, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^2*f^4*g^4*n^4*Log[F]^4) + (6*d^2*(c + d*x)*PolyLog[3, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^2*f^3*g^3*n^3*Log[F]^3) - (6*d^3*PolyLog[4, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^2*f^4*g^4*n^4*Log[F]^4)","A",13,8,25,0.3200,1,"{2185, 2184, 2190, 2531, 6609, 2282, 6589, 2191}"
53,1,294,0,0.6713428,"\int \frac{(c+d x)^2}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","Int[(c + d*x)^2/(a + b*(F^(g*(e + f*x)))^n)^2,x]","-\frac{2 d (c+d x) \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}+\frac{2 d^2 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^3 g^3 n^3 \log ^3(F)}+\frac{2 d^2 \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^3 g^3 n^3 \log ^3(F)}+\frac{2 d (c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}-\frac{(c+d x)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^2 f g n \log (F)}-\frac{(c+d x)^2}{a^2 f g n \log (F)}+\frac{(c+d x)^3}{3 a^2 d}+\frac{(c+d x)^2}{a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}","-\frac{2 d (c+d x) \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}+\frac{2 d^2 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^3 g^3 n^3 \log ^3(F)}+\frac{2 d^2 \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^3 g^3 n^3 \log ^3(F)}+\frac{2 d (c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}-\frac{(c+d x)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^2 f g n \log (F)}-\frac{(c+d x)^2}{a^2 f g n \log (F)}+\frac{(c+d x)^3}{3 a^2 d}+\frac{(c+d x)^2}{a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}",1,"(c + d*x)^3/(3*a^2*d) - (c + d*x)^2/(a^2*f*g*n*Log[F]) + (c + d*x)^2/(a*f*(a + b*(F^(g*(e + f*x)))^n)*g*n*Log[F]) + (2*d*(c + d*x)*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a^2*f^2*g^2*n^2*Log[F]^2) - ((c + d*x)^2*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a^2*f*g*n*Log[F]) + (2*d^2*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^2*f^3*g^3*n^3*Log[F]^3) - (2*d*(c + d*x)*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^2*f^2*g^2*n^2*Log[F]^2) + (2*d^2*PolyLog[3, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^2*f^3*g^3*n^3*Log[F]^3)","A",11,9,25,0.3600,1,"{2185, 2184, 2190, 2531, 2282, 6589, 2191, 2279, 2391}"
54,1,191,0,0.3404359,"\int \frac{c+d x}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","Int[(c + d*x)/(a + b*(F^(g*(e + f*x)))^n)^2,x]","-\frac{d \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}-\frac{(c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^2 f g n \log (F)}+\frac{d \log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}+\frac{(c+d x)^2}{2 a^2 d}-\frac{d x}{a^2 f g n \log (F)}+\frac{c+d x}{a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}","-\frac{d \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}-\frac{(c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^2 f g n \log (F)}+\frac{d \log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a^2 f^2 g^2 n^2 \log ^2(F)}+\frac{(c+d x)^2}{2 a^2 d}-\frac{d x}{a^2 f g n \log (F)}+\frac{c+d x}{a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}",1,"(c + d*x)^2/(2*a^2*d) - (d*x)/(a^2*f*g*n*Log[F]) + (c + d*x)/(a*f*(a + b*(F^(g*(e + f*x)))^n)*g*n*Log[F]) + (d*Log[a + b*(F^(g*(e + f*x)))^n])/(a^2*f^2*g^2*n^2*Log[F]^2) - ((c + d*x)*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a^2*f*g*n*Log[F]) - (d*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^2*f^2*g^2*n^2*Log[F]^2)","A",11,11,23,0.4783,1,"{2185, 2184, 2190, 2279, 2391, 2191, 2282, 266, 36, 29, 31}"
55,1,74,0,0.0494327,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^(-2),x]","-\frac{\log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a^2 f g n \log (F)}+\frac{x}{a^2}+\frac{1}{a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}","-\frac{\log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a^2 f g n \log (F)}+\frac{x}{a^2}+\frac{1}{a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}",1,"x/a^2 + 1/(a*f*(a + b*(F^(g*(e + f*x)))^n)*g*n*Log[F]) - Log[a + b*(F^(g*(e + f*x)))^n]/(a^2*f*g*n*Log[F])","A",4,3,17,0.1765,1,"{2282, 266, 44}"
56,0,0,0,0.1267819,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)} \, dx","Int[1/((a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)),x]","\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)} \, dx","\text{Int}\left(\frac{1}{(c+d x) \left(a+b \left(F^{e g+f g x}\right)^n\right)^2},x\right)",0,"Defer[Int][1/((a + b*(F^(e*g + f*g*x))^n)^2*(c + d*x)), x]","A",0,0,0,0,-1,"{}"
57,0,0,0,0.1199087,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)^2} \, dx","Int[1/((a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)^2),x]","\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 \left(a+b \left(F^{e g+f g x}\right)^n\right)^2},x\right)",0,"Defer[Int][1/((a + b*(F^(e*g + f*g*x))^n)^2*(c + d*x)^2), x]","A",0,0,0,0,-1,"{}"
58,1,594,0,1.9008297,"\int \frac{(c+d x)^3}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","Int[(c + d*x)^3/(a + b*(F^(g*(e + f*x)))^n)^3,x]","\frac{9 d^2 (c+d x) \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{3 d^3 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^4 g^4 n^4 \log ^4(F)}-\frac{9 d^3 \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^4 g^4 n^4 \log ^4(F)}-\frac{6 d^3 \text{PolyLog}\left(4,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^4 g^4 n^4 \log ^4(F)}-\frac{3 d^2 (c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac{9 d (c+d x)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{3 d (c+d x)^2}{2 a^2 f^2 g^2 n^2 \log ^2(F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}-\frac{(c+d x)^3 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^3 f g n \log (F)}+\frac{(c+d x)^3}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\frac{3 d (c+d x)^2}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{3 (c+d x)^3}{2 a^3 f g n \log (F)}+\frac{(c+d x)^4}{4 a^3 d}+\frac{(c+d x)^3}{2 a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}","\frac{9 d^2 (c+d x) \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac{6 d^2 (c+d x) \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac{3 d (c+d x)^2 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{3 d^3 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^4 g^4 n^4 \log ^4(F)}-\frac{9 d^3 \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^4 g^4 n^4 \log ^4(F)}-\frac{6 d^3 \text{PolyLog}\left(4,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^4 g^4 n^4 \log ^4(F)}-\frac{3 d^2 (c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac{9 d (c+d x)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{3 d (c+d x)^2}{2 a^2 f^2 g^2 n^2 \log ^2(F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}-\frac{(c+d x)^3 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^3 f g n \log (F)}+\frac{(c+d x)^3}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\frac{3 d (c+d x)^2}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{3 (c+d x)^3}{2 a^3 f g n \log (F)}+\frac{(c+d x)^4}{4 a^3 d}+\frac{(c+d x)^3}{2 a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}",1,"(c + d*x)^4/(4*a^3*d) + (3*d*(c + d*x)^2)/(2*a^3*f^2*g^2*n^2*Log[F]^2) - (3*d*(c + d*x)^2)/(2*a^2*f^2*(a + b*(F^(g*(e + f*x)))^n)*g^2*n^2*Log[F]^2) - (3*(c + d*x)^3)/(2*a^3*f*g*n*Log[F]) + (c + d*x)^3/(2*a*f*(a + b*(F^(g*(e + f*x)))^n)^2*g*n*Log[F]) + (c + d*x)^3/(a^2*f*(a + b*(F^(g*(e + f*x)))^n)*g*n*Log[F]) - (3*d^2*(c + d*x)*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a^3*f^3*g^3*n^3*Log[F]^3) + (9*d*(c + d*x)^2*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(2*a^3*f^2*g^2*n^2*Log[F]^2) - ((c + d*x)^3*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a^3*f*g*n*Log[F]) - (3*d^3*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^3*f^4*g^4*n^4*Log[F]^4) + (9*d^2*(c + d*x)*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^3*f^3*g^3*n^3*Log[F]^3) - (3*d*(c + d*x)^2*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^3*f^2*g^2*n^2*Log[F]^2) - (9*d^3*PolyLog[3, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^3*f^4*g^4*n^4*Log[F]^4) + (6*d^2*(c + d*x)*PolyLog[3, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^3*f^3*g^3*n^3*Log[F]^3) - (6*d^3*PolyLog[4, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^3*f^4*g^4*n^4*Log[F]^4)","A",26,10,25,0.4000,1,"{2185, 2184, 2190, 2531, 6609, 2282, 6589, 2191, 2279, 2391}"
59,1,439,0,1.3189513,"\int \frac{(c+d x)^2}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","Int[(c + d*x)^2/(a + b*(F^(g*(e + f*x)))^n)^3,x]","-\frac{2 d (c+d x) \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^2 g^2 n^2 \log ^2(F)}+\frac{3 d^2 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac{2 d^2 \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac{3 d (c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{d (c+d x)}{a^2 f^2 g^2 n^2 \log ^2(F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}-\frac{(c+d x)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^3 f g n \log (F)}+\frac{(c+d x)^2}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}-\frac{d^2 \log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac{3 (c+d x)^2}{2 a^3 f g n \log (F)}+\frac{(c+d x)^3}{3 a^3 d}+\frac{d^2 x}{a^3 f^2 g^2 n^2 \log ^2(F)}+\frac{(c+d x)^2}{2 a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}","-\frac{2 d (c+d x) \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^2 g^2 n^2 \log ^2(F)}+\frac{3 d^2 \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac{2 d^2 \text{PolyLog}\left(3,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}+\frac{3 d (c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{d (c+d x)}{a^2 f^2 g^2 n^2 \log ^2(F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}-\frac{(c+d x)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^3 f g n \log (F)}+\frac{(c+d x)^2}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}-\frac{d^2 \log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}-\frac{3 (c+d x)^2}{2 a^3 f g n \log (F)}+\frac{(c+d x)^3}{3 a^3 d}+\frac{d^2 x}{a^3 f^2 g^2 n^2 \log ^2(F)}+\frac{(c+d x)^2}{2 a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}",1,"(c + d*x)^3/(3*a^3*d) + (d^2*x)/(a^3*f^2*g^2*n^2*Log[F]^2) - (d*(c + d*x))/(a^2*f^2*(a + b*(F^(g*(e + f*x)))^n)*g^2*n^2*Log[F]^2) - (3*(c + d*x)^2)/(2*a^3*f*g*n*Log[F]) + (c + d*x)^2/(2*a*f*(a + b*(F^(g*(e + f*x)))^n)^2*g*n*Log[F]) + (c + d*x)^2/(a^2*f*(a + b*(F^(g*(e + f*x)))^n)*g*n*Log[F]) - (d^2*Log[a + b*(F^(g*(e + f*x)))^n])/(a^3*f^3*g^3*n^3*Log[F]^3) + (3*d*(c + d*x)*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a^3*f^2*g^2*n^2*Log[F]^2) - ((c + d*x)^2*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a^3*f*g*n*Log[F]) + (3*d^2*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^3*f^3*g^3*n^3*Log[F]^3) - (2*d*(c + d*x)*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^3*f^2*g^2*n^2*Log[F]^2) + (2*d^2*PolyLog[3, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^3*f^3*g^3*n^3*Log[F]^3)","A",24,13,25,0.5200,1,"{2185, 2184, 2190, 2531, 2282, 6589, 2191, 2279, 2391, 266, 36, 29, 31}"
60,1,276,0,0.5637784,"\int \frac{c+d x}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","Int[(c + d*x)/(a + b*(F^(g*(e + f*x)))^n)^3,x]","-\frac{d \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{(c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^3 f g n \log (F)}+\frac{c+d x}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\frac{3 d \log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{d}{2 a^2 f^2 g^2 n^2 \log ^2(F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\frac{(c+d x)^2}{2 a^3 d}-\frac{3 d x}{2 a^3 f g n \log (F)}+\frac{c+d x}{2 a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}","-\frac{d \text{PolyLog}\left(2,-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{(c+d x) \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a^3 f g n \log (F)}+\frac{c+d x}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\frac{3 d \log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{2 a^3 f^2 g^2 n^2 \log ^2(F)}-\frac{d}{2 a^2 f^2 g^2 n^2 \log ^2(F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\frac{(c+d x)^2}{2 a^3 d}-\frac{3 d x}{2 a^3 f g n \log (F)}+\frac{c+d x}{2 a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}",1,"(c + d*x)^2/(2*a^3*d) - d/(2*a^2*f^2*(a + b*(F^(g*(e + f*x)))^n)*g^2*n^2*Log[F]^2) - (3*d*x)/(2*a^3*f*g*n*Log[F]) + (c + d*x)/(2*a*f*(a + b*(F^(g*(e + f*x)))^n)^2*g*n*Log[F]) + (c + d*x)/(a^2*f*(a + b*(F^(g*(e + f*x)))^n)*g*n*Log[F]) + (3*d*Log[a + b*(F^(g*(e + f*x)))^n])/(2*a^3*f^2*g^2*n^2*Log[F]^2) - ((c + d*x)*Log[1 + (b*(F^(g*(e + f*x)))^n)/a])/(a^3*f*g*n*Log[F]) - (d*PolyLog[2, -((b*(F^(g*(e + f*x)))^n)/a)])/(a^3*f^2*g^2*n^2*Log[F]^2)","A",17,12,23,0.5217,1,"{2185, 2184, 2190, 2279, 2391, 2191, 2282, 266, 36, 29, 31, 44}"
61,1,111,0,0.063461,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^(-3),x]","-\frac{\log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a^3 f g n \log (F)}+\frac{1}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\frac{x}{a^3}+\frac{1}{2 a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}","-\frac{\log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a^3 f g n \log (F)}+\frac{1}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\frac{x}{a^3}+\frac{1}{2 a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}",1,"x/a^3 + 1/(2*a*f*(a + b*(F^(g*(e + f*x)))^n)^2*g*n*Log[F]) + 1/(a^2*f*(a + b*(F^(g*(e + f*x)))^n)*g*n*Log[F]) - Log[a + b*(F^(g*(e + f*x)))^n]/(a^3*f*g*n*Log[F])","A",4,3,17,0.1765,1,"{2282, 266, 44}"
62,0,0,0,0.1275399,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)} \, dx","Int[1/((a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)),x]","\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)} \, dx","\text{Int}\left(\frac{1}{(c+d x) \left(a+b \left(F^{e g+f g x}\right)^n\right)^3},x\right)",0,"Defer[Int][1/((a + b*(F^(e*g + f*g*x))^n)^3*(c + d*x)), x]","A",0,0,0,0,-1,"{}"
63,0,0,0,0.1208636,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)^2} \, dx","Int[1/((a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^2),x]","\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)^2} \, dx","\text{Int}\left(\frac{1}{(c+d x)^2 \left(a+b \left(F^{e g+f g x}\right)^n\right)^3},x\right)",0,"Defer[Int][1/((a + b*(F^(e*g + f*g*x))^n)^3*(c + d*x)^2), x]","A",0,0,0,0,-1,"{}"
64,1,71,0,0.0881561,"\int \left(a+b e^x\right) \sqrt{c+d x} \, dx","Int[(a + b*E^x)*Sqrt[c + d*x],x]","\frac{2 a (c+d x)^{3/2}}{3 d}-\frac{1}{2} \sqrt{\pi } b \sqrt{d} e^{-\frac{c}{d}} \text{Erfi}\left(\frac{\sqrt{c+d x}}{\sqrt{d}}\right)+b e^x \sqrt{c+d x}","\frac{2 a (c+d x)^{3/2}}{3 d}-\frac{1}{2} \sqrt{\pi } b \sqrt{d} e^{-\frac{c}{d}} \text{Erfi}\left(\frac{\sqrt{c+d x}}{\sqrt{d}}\right)+b e^x \sqrt{c+d x}",1,"b*E^x*Sqrt[c + d*x] + (2*a*(c + d*x)^(3/2))/(3*d) - (b*Sqrt[d]*Sqrt[Pi]*Erfi[Sqrt[c + d*x]/Sqrt[d]])/(2*E^(c/d))","A",5,4,17,0.2353,1,"{2183, 2176, 2180, 2204}"
65,1,145,0,0.1846144,"\int \left(a+b e^x\right)^2 \sqrt{c+d x} \, dx","Int[(a + b*E^x)^2*Sqrt[c + d*x],x]","\frac{2 a^2 (c+d x)^{3/2}}{3 d}-\sqrt{\pi } a b \sqrt{d} e^{-\frac{c}{d}} \text{Erfi}\left(\frac{\sqrt{c+d x}}{\sqrt{d}}\right)+2 a b e^x \sqrt{c+d x}-\frac{1}{4} \sqrt{\frac{\pi }{2}} b^2 \sqrt{d} e^{-\frac{2 c}{d}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c+d x}}{\sqrt{d}}\right)+\frac{1}{2} b^2 e^{2 x} \sqrt{c+d x}","\frac{2 a^2 (c+d x)^{3/2}}{3 d}-\sqrt{\pi } a b \sqrt{d} e^{-\frac{c}{d}} \text{Erfi}\left(\frac{\sqrt{c+d x}}{\sqrt{d}}\right)+2 a b e^x \sqrt{c+d x}-\frac{1}{4} \sqrt{\frac{\pi }{2}} b^2 \sqrt{d} e^{-\frac{2 c}{d}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c+d x}}{\sqrt{d}}\right)+\frac{1}{2} b^2 e^{2 x} \sqrt{c+d x}",1,"2*a*b*E^x*Sqrt[c + d*x] + (b^2*E^(2*x)*Sqrt[c + d*x])/2 + (2*a^2*(c + d*x)^(3/2))/(3*d) - (a*b*Sqrt[d]*Sqrt[Pi]*Erfi[Sqrt[c + d*x]/Sqrt[d]])/E^(c/d) - (b^2*Sqrt[d]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c + d*x])/Sqrt[d]])/(4*E^((2*c)/d))","A",8,4,19,0.2105,1,"{2183, 2176, 2180, 2204}"
66,1,224,0,0.263767,"\int \left(a+b e^x\right)^3 \sqrt{c+d x} \, dx","Int[(a + b*E^x)^3*Sqrt[c + d*x],x]","-\frac{3}{2} \sqrt{\pi } a^2 b \sqrt{d} e^{-\frac{c}{d}} \text{Erfi}\left(\frac{\sqrt{c+d x}}{\sqrt{d}}\right)+3 a^2 b e^x \sqrt{c+d x}+\frac{2 a^3 (c+d x)^{3/2}}{3 d}-\frac{3}{4} \sqrt{\frac{\pi }{2}} a b^2 \sqrt{d} e^{-\frac{2 c}{d}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c+d x}}{\sqrt{d}}\right)+\frac{3}{2} a b^2 e^{2 x} \sqrt{c+d x}-\frac{1}{6} \sqrt{\frac{\pi }{3}} b^3 \sqrt{d} e^{-\frac{3 c}{d}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{c+d x}}{\sqrt{d}}\right)+\frac{1}{3} b^3 e^{3 x} \sqrt{c+d x}","-\frac{3}{2} \sqrt{\pi } a^2 b \sqrt{d} e^{-\frac{c}{d}} \text{Erfi}\left(\frac{\sqrt{c+d x}}{\sqrt{d}}\right)+3 a^2 b e^x \sqrt{c+d x}+\frac{2 a^3 (c+d x)^{3/2}}{3 d}-\frac{3}{4} \sqrt{\frac{\pi }{2}} a b^2 \sqrt{d} e^{-\frac{2 c}{d}} \text{Erfi}\left(\frac{\sqrt{2} \sqrt{c+d x}}{\sqrt{d}}\right)+\frac{3}{2} a b^2 e^{2 x} \sqrt{c+d x}-\frac{1}{6} \sqrt{\frac{\pi }{3}} b^3 \sqrt{d} e^{-\frac{3 c}{d}} \text{Erfi}\left(\frac{\sqrt{3} \sqrt{c+d x}}{\sqrt{d}}\right)+\frac{1}{3} b^3 e^{3 x} \sqrt{c+d x}",1,"3*a^2*b*E^x*Sqrt[c + d*x] + (3*a*b^2*E^(2*x)*Sqrt[c + d*x])/2 + (b^3*E^(3*x)*Sqrt[c + d*x])/3 + (2*a^3*(c + d*x)^(3/2))/(3*d) - (3*a^2*b*Sqrt[d]*Sqrt[Pi]*Erfi[Sqrt[c + d*x]/Sqrt[d]])/(2*E^(c/d)) - (3*a*b^2*Sqrt[d]*Sqrt[Pi/2]*Erfi[(Sqrt[2]*Sqrt[c + d*x])/Sqrt[d]])/(4*E^((2*c)/d)) - (b^3*Sqrt[d]*Sqrt[Pi/3]*Erfi[(Sqrt[3]*Sqrt[c + d*x])/Sqrt[d]])/(6*E^((3*c)/d))","A",11,4,19,0.2105,1,"{2183, 2176, 2180, 2204}"
67,0,0,0,0.0402916,"\int \frac{\sqrt{c+d x}}{a+b e^x} \, dx","Int[Sqrt[c + d*x]/(a + b*E^x),x]","\int \frac{\sqrt{c+d x}}{a+b e^x} \, dx","\text{Int}\left(\frac{\sqrt{c+d x}}{a+b e^x},x\right)",0,"Defer[Int][Sqrt[c + d*x]/(a + b*E^x), x]","A",0,0,0,0,-1,"{}"
68,0,0,0,0.0395974,"\int \frac{\sqrt{c+d x}}{\left(a+b e^x\right)^2} \, dx","Int[Sqrt[c + d*x]/(a + b*E^x)^2,x]","\int \frac{\sqrt{c+d x}}{\left(a+b e^x\right)^2} \, dx","\text{Int}\left(\frac{\sqrt{c+d x}}{\left(a+b e^x\right)^2},x\right)",0,"Defer[Int][Sqrt[c + d*x]/(a + b*E^x)^2, x]","A",0,0,0,0,-1,"{}"
69,0,0,0,0.0387193,"\int \frac{\sqrt{c+d x}}{\left(a+b e^x\right)^3} \, dx","Int[Sqrt[c + d*x]/(a + b*E^x)^3,x]","\int \frac{\sqrt{c+d x}}{\left(a+b e^x\right)^3} \, dx","\text{Int}\left(\frac{\sqrt{c+d x}}{\left(a+b e^x\right)^3},x\right)",0,"Defer[Int][Sqrt[c + d*x]/(a + b*E^x)^3, x]","A",0,0,0,0,-1,"{}"
70,1,340,0,0.4674529,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)^m \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^m,x]","\frac{3 a^2 b (c+d x)^m \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{3 a b^2 2^{-m-1} (c+d x)^m \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{b^3 3^{-m-1} (c+d x)^m \left(F^{e g+f g x}\right)^{3 n} F^{3 g n \left(e-\frac{c f}{d}\right)-3 g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{3 f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{a^3 (c+d x)^{m+1}}{d (m+1)}","\frac{3 a^2 b (c+d x)^m \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{3 a b^2 2^{-m-1} (c+d x)^m \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{b^3 3^{-m-1} (c+d x)^m \left(F^{e g+f g x}\right)^{3 n} F^{3 g n \left(e-\frac{c f}{d}\right)-3 g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{3 f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{a^3 (c+d x)^{m+1}}{d (m+1)}",1,"(a^3*(c + d*x)^(1 + m))/(d*(1 + m)) + (3^(-1 - m)*b^3*F^(3*(e - (c*f)/d)*g*n - 3*g*n*(e + f*x))*(F^(e*g + f*g*x))^(3*n)*(c + d*x)^m*Gamma[1 + m, (-3*f*g*n*(c + d*x)*Log[F])/d])/(f*g*n*Log[F]*(-((f*g*n*(c + d*x)*Log[F])/d))^m) + (3*2^(-1 - m)*a*b^2*F^(2*(e - (c*f)/d)*g*n - 2*g*n*(e + f*x))*(F^(e*g + f*g*x))^(2*n)*(c + d*x)^m*Gamma[1 + m, (-2*f*g*n*(c + d*x)*Log[F])/d])/(f*g*n*Log[F]*(-((f*g*n*(c + d*x)*Log[F])/d))^m) + (3*a^2*b*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*(c + d*x)^m*Gamma[1 + m, -((f*g*n*(c + d*x)*Log[F])/d)])/(f*g*n*Log[F]*(-((f*g*n*(c + d*x)*Log[F])/d))^m)","A",8,3,25,0.1200,1,"{2183, 2182, 2181}"
71,1,228,0,0.2780439,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)^m \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)^m,x]","\frac{2 a b (c+d x)^m \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{b^2 2^{-m-1} (c+d x)^m \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{a^2 (c+d x)^{m+1}}{d (m+1)}","\frac{2 a b (c+d x)^m \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{b^2 2^{-m-1} (c+d x)^m \left(F^{e g+f g x}\right)^{2 n} F^{2 g n \left(e-\frac{c f}{d}\right)-2 g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{2 f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{a^2 (c+d x)^{m+1}}{d (m+1)}",1,"(a^2*(c + d*x)^(1 + m))/(d*(1 + m)) + (2^(-1 - m)*b^2*F^(2*(e - (c*f)/d)*g*n - 2*g*n*(e + f*x))*(F^(e*g + f*g*x))^(2*n)*(c + d*x)^m*Gamma[1 + m, (-2*f*g*n*(c + d*x)*Log[F])/d])/(f*g*n*Log[F]*(-((f*g*n*(c + d*x)*Log[F])/d))^m) + (2*a*b*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*(c + d*x)^m*Gamma[1 + m, -((f*g*n*(c + d*x)*Log[F])/d)])/(f*g*n*Log[F]*(-((f*g*n*(c + d*x)*Log[F])/d))^m)","A",6,3,25,0.1200,1,"{2183, 2182, 2181}"
72,1,116,0,0.1347529,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)^m \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^m,x]","\frac{b (c+d x)^m \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{a (c+d x)^{m+1}}{d (m+1)}","\frac{b (c+d x)^m \left(F^{e g+f g x}\right)^n F^{g n \left(e-\frac{c f}{d}\right)-g n (e+f x)} \left(-\frac{f g n \log (F) (c+d x)}{d}\right)^{-m} \text{Gamma}\left(m+1,-\frac{f g n \log (F) (c+d x)}{d}\right)}{f g n \log (F)}+\frac{a (c+d x)^{m+1}}{d (m+1)}",1,"(a*(c + d*x)^(1 + m))/(d*(1 + m)) + (b*F^((e - (c*f)/d)*g*n - g*n*(e + f*x))*(F^(e*g + f*g*x))^n*(c + d*x)^m*Gamma[1 + m, -((f*g*n*(c + d*x)*Log[F])/d)])/(f*g*n*Log[F]*(-((f*g*n*(c + d*x)*Log[F])/d))^m)","A",4,3,23,0.1304,1,"{2183, 2182, 2181}"
73,0,0,0,0.1225387,"\int \frac{(c+d x)^m}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","Int[(c + d*x)^m/(a + b*(F^(g*(e + f*x)))^n),x]","\int \frac{(c+d x)^m}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","\text{Int}\left(\frac{(c+d x)^m}{a+b \left(F^{e g+f g x}\right)^n},x\right)",0,"Defer[Int][(c + d*x)^m/(a + b*(F^(e*g + f*g*x))^n), x]","A",0,0,0,0,-1,"{}"
74,0,0,0,0.1195905,"\int \frac{(c+d x)^m}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","Int[(c + d*x)^m/(a + b*(F^(g*(e + f*x)))^n)^2,x]","\int \frac{(c+d x)^m}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","\text{Int}\left(\frac{(c+d x)^m}{\left(a+b \left(F^{e g+f g x}\right)^n\right)^2},x\right)",0,"Defer[Int][(c + d*x)^m/(a + b*(F^(e*g + f*g*x))^n)^2, x]","A",0,0,0,0,-1,"{}"
75,0,0,0,0.1187412,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^p (c+d x)^m \, dx","Int[(a + b*(F^(g*(e + f*x)))^n)^p*(c + d*x)^m,x]","\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^p (c+d x)^m \, dx","\text{Int}\left((c+d x)^m \left(a+b \left(F^{e g+f g x}\right)^n\right)^p,x\right)",0,"Defer[Int][(a + b*(F^(e*g + f*g*x))^n)^p*(c + d*x)^m, x]","A",0,0,0,0,-1,"{}"
76,1,115,0,0.1318181,"\int \frac{F^{c+d x} x^3}{a+b F^{c+d x}} \, dx","Int[(F^(c + d*x)*x^3)/(a + b*F^(c + d*x)),x]","\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{b d^2 \log ^2(F)}-\frac{6 x \text{PolyLog}\left(3,-\frac{b F^{c+d x}}{a}\right)}{b d^3 \log ^3(F)}+\frac{6 \text{PolyLog}\left(4,-\frac{b F^{c+d x}}{a}\right)}{b d^4 \log ^4(F)}+\frac{x^3 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{b d \log (F)}","\frac{3 x^2 \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{b d^2 \log ^2(F)}-\frac{6 x \text{PolyLog}\left(3,-\frac{b F^{c+d x}}{a}\right)}{b d^3 \log ^3(F)}+\frac{6 \text{PolyLog}\left(4,-\frac{b F^{c+d x}}{a}\right)}{b d^4 \log ^4(F)}+\frac{x^3 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{b d \log (F)}",1,"(x^3*Log[1 + (b*F^(c + d*x))/a])/(b*d*Log[F]) + (3*x^2*PolyLog[2, -((b*F^(c + d*x))/a)])/(b*d^2*Log[F]^2) - (6*x*PolyLog[3, -((b*F^(c + d*x))/a)])/(b*d^3*Log[F]^3) + (6*PolyLog[4, -((b*F^(c + d*x))/a)])/(b*d^4*Log[F]^4)","A",5,5,24,0.2083,1,"{2190, 2531, 6609, 2282, 6589}"
77,1,85,0,0.1093079,"\int \frac{F^{c+d x} x^2}{a+b F^{c+d x}} \, dx","Int[(F^(c + d*x)*x^2)/(a + b*F^(c + d*x)),x]","\frac{2 x \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{b d^2 \log ^2(F)}-\frac{2 \text{PolyLog}\left(3,-\frac{b F^{c+d x}}{a}\right)}{b d^3 \log ^3(F)}+\frac{x^2 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{b d \log (F)}","\frac{2 x \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{b d^2 \log ^2(F)}-\frac{2 \text{PolyLog}\left(3,-\frac{b F^{c+d x}}{a}\right)}{b d^3 \log ^3(F)}+\frac{x^2 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{b d \log (F)}",1,"(x^2*Log[1 + (b*F^(c + d*x))/a])/(b*d*Log[F]) + (2*x*PolyLog[2, -((b*F^(c + d*x))/a)])/(b*d^2*Log[F]^2) - (2*PolyLog[3, -((b*F^(c + d*x))/a)])/(b*d^3*Log[F]^3)","A",4,4,24,0.1667,1,"{2190, 2531, 2282, 6589}"
78,1,54,0,0.0642339,"\int \frac{F^{c+d x} x}{a+b F^{c+d x}} \, dx","Int[(F^(c + d*x)*x)/(a + b*F^(c + d*x)),x]","\frac{\text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{b d^2 \log ^2(F)}+\frac{x \log \left(\frac{b F^{c+d x}}{a}+1\right)}{b d \log (F)}","\frac{\text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{b d^2 \log ^2(F)}+\frac{x \log \left(\frac{b F^{c+d x}}{a}+1\right)}{b d \log (F)}",1,"(x*Log[1 + (b*F^(c + d*x))/a])/(b*d*Log[F]) + PolyLog[2, -((b*F^(c + d*x))/a)]/(b*d^2*Log[F]^2)","A",3,3,22,0.1364,1,"{2190, 2279, 2391}"
79,1,23,0,0.036539,"\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}"
80,0,0,0,0.0699827,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right) x} \, dx","Int[F^(c + d*x)/((a + b*F^(c + d*x))*x),x]","\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right) x} \, dx","\text{Int}\left(\frac{F^{c+d x}}{x \left(a+b F^{c+d x}\right)},x\right)",0,"Defer[Int][F^(c + d*x)/((a + b*F^(c + d*x))*x), x]","A",0,0,0,0,-1,"{}"
81,0,0,0,0.068707,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right) x^2} \, dx","Int[F^(c + d*x)/((a + b*F^(c + d*x))*x^2),x]","\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right) x^2} \, dx","\text{Int}\left(\frac{F^{c+d x}}{x^2 \left(a+b F^{c+d x}\right)},x\right)",0,"Defer[Int][F^(c + d*x)/((a + b*F^(c + d*x))*x^2), x]","A",0,0,0,0,-1,"{}"
82,1,140,0,0.2475189,"\int \frac{F^{c+d x} x^3}{\left(a+b F^{c+d x}\right)^2} \, dx","Int[(F^(c + d*x)*x^3)/(a + b*F^(c + d*x))^2,x]","-\frac{6 x \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{a b d^3 \log ^3(F)}+\frac{6 \text{PolyLog}\left(3,-\frac{b F^{c+d x}}{a}\right)}{a b d^4 \log ^4(F)}-\frac{3 x^2 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{a b d^2 \log ^2(F)}-\frac{x^3}{b d \log (F) \left(a+b F^{c+d x}\right)}+\frac{x^3}{a b d \log (F)}","-\frac{6 x \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{a b d^3 \log ^3(F)}+\frac{6 \text{PolyLog}\left(3,-\frac{b F^{c+d x}}{a}\right)}{a b d^4 \log ^4(F)}-\frac{3 x^2 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{a b d^2 \log ^2(F)}-\frac{x^3}{b d \log (F) \left(a+b F^{c+d x}\right)}+\frac{x^3}{a b d \log (F)}",1,"x^3/(a*b*d*Log[F]) - x^3/(b*d*(a + b*F^(c + d*x))*Log[F]) - (3*x^2*Log[1 + (b*F^(c + d*x))/a])/(a*b*d^2*Log[F]^2) - (6*x*PolyLog[2, -((b*F^(c + d*x))/a)])/(a*b*d^3*Log[F]^3) + (6*PolyLog[3, -((b*F^(c + d*x))/a)])/(a*b*d^4*Log[F]^4)","A",6,6,24,0.2500,1,"{2191, 2184, 2190, 2531, 2282, 6589}"
83,1,107,0,0.1811472,"\int \frac{F^{c+d x} x^2}{\left(a+b F^{c+d x}\right)^2} \, dx","Int[(F^(c + d*x)*x^2)/(a + b*F^(c + d*x))^2,x]","-\frac{2 \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{a b d^3 \log ^3(F)}-\frac{2 x \log \left(\frac{b F^{c+d x}}{a}+1\right)}{a b d^2 \log ^2(F)}-\frac{x^2}{b d \log (F) \left(a+b F^{c+d x}\right)}+\frac{x^2}{a b d \log (F)}","-\frac{2 \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{a b d^3 \log ^3(F)}-\frac{2 x \log \left(\frac{b F^{c+d x}}{a}+1\right)}{a b d^2 \log ^2(F)}-\frac{x^2}{b d \log (F) \left(a+b F^{c+d x}\right)}+\frac{x^2}{a b d \log (F)}",1,"x^2/(a*b*d*Log[F]) - x^2/(b*d*(a + b*F^(c + d*x))*Log[F]) - (2*x*Log[1 + (b*F^(c + d*x))/a])/(a*b*d^2*Log[F]^2) - (2*PolyLog[2, -((b*F^(c + d*x))/a)])/(a*b*d^3*Log[F]^3)","A",5,5,24,0.2083,1,"{2191, 2184, 2190, 2279, 2391}"
84,1,69,0,0.0738341,"\int \frac{F^{c+d x} x}{\left(a+b F^{c+d x}\right)^2} \, dx","Int[(F^(c + d*x)*x)/(a + b*F^(c + d*x))^2,x]","-\frac{\log \left(a+b F^{c+d x}\right)}{a b d^2 \log ^2(F)}-\frac{x}{b d \log (F) \left(a+b F^{c+d x}\right)}+\frac{x}{a b d \log (F)}","-\frac{\log \left(a+b F^{c+d x}\right)}{a b d^2 \log ^2(F)}-\frac{x}{b d \log (F) \left(a+b F^{c+d x}\right)}+\frac{x}{a b d \log (F)}",1,"x/(a*b*d*Log[F]) - x/(b*d*(a + b*F^(c + d*x))*Log[F]) - Log[a + b*F^(c + d*x)]/(a*b*d^2*Log[F]^2)","A",5,5,22,0.2273,1,"{2191, 2282, 36, 29, 31}"
85,1,25,0,0.0352445,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^2} \, dx","Int[F^(c + d*x)/(a + b*F^(c + d*x))^2,x]","-\frac{1}{b d \log (F) \left(a+b F^{c+d x}\right)}","-\frac{1}{b d \log (F) \left(a+b F^{c+d x}\right)}",1,"-(1/(b*d*(a + b*F^(c + d*x))*Log[F]))","A",2,2,21,0.09524,1,"{2246, 32}"
86,0,0,0,0.1182457,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^2 x} \, dx","Int[F^(c + d*x)/((a + b*F^(c + d*x))^2*x),x]","\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^2 x} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \left(a+b F^{c+d x}\right)},x\right)}{b d \log (F)}-\frac{1}{b d x \log (F) \left(a+b F^{c+d x}\right)}",0,"-(1/(b*d*(a + b*F^(c + d*x))*x*Log[F])) - Defer[Int][1/((a + b*F^(c + d*x))*x^2), x]/(b*d*Log[F])","A",0,0,0,0,-1,"{}"
87,0,0,0,0.117562,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^2 x^2} \, dx","Int[F^(c + d*x)/((a + b*F^(c + d*x))^2*x^2),x]","\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^2 x^2} \, dx","-\frac{2 \text{Int}\left(\frac{1}{x^3 \left(a+b F^{c+d x}\right)},x\right)}{b d \log (F)}-\frac{1}{b d x^2 \log (F) \left(a+b F^{c+d x}\right)}",0,"-(1/(b*d*(a + b*F^(c + d*x))*x^2*Log[F])) - (2*Defer[Int][1/((a + b*F^(c + d*x))*x^3), x])/(b*d*Log[F])","A",0,0,0,0,-1,"{}"
88,1,261,0,0.5036323,"\int \frac{F^{c+d x} x^3}{\left(a+b F^{c+d x}\right)^3} \, dx","Int[(F^(c + d*x)*x^3)/(a + b*F^(c + d*x))^3,x]","-\frac{3 x \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^3 \log ^3(F)}+\frac{3 \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^4 \log ^4(F)}+\frac{3 \text{PolyLog}\left(3,-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^4 \log ^4(F)}-\frac{3 x^2 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{2 a^2 b d^2 \log ^2(F)}+\frac{3 x \log \left(\frac{b F^{c+d x}}{a}+1\right)}{a^2 b d^3 \log ^3(F)}-\frac{3 x^2}{2 a^2 b d^2 \log ^2(F)}+\frac{x^3}{2 a^2 b d \log (F)}+\frac{3 x^2}{2 a b d^2 \log ^2(F) \left(a+b F^{c+d x}\right)}-\frac{x^3}{2 b d \log (F) \left(a+b F^{c+d x}\right)^2}","-\frac{3 x \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^3 \log ^3(F)}+\frac{3 \text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^4 \log ^4(F)}+\frac{3 \text{PolyLog}\left(3,-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^4 \log ^4(F)}-\frac{3 x^2 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{2 a^2 b d^2 \log ^2(F)}+\frac{3 x \log \left(\frac{b F^{c+d x}}{a}+1\right)}{a^2 b d^3 \log ^3(F)}-\frac{3 x^2}{2 a^2 b d^2 \log ^2(F)}+\frac{x^3}{2 a^2 b d \log (F)}+\frac{3 x^2}{2 a b d^2 \log ^2(F) \left(a+b F^{c+d x}\right)}-\frac{x^3}{2 b d \log (F) \left(a+b F^{c+d x}\right)^2}",1,"(-3*x^2)/(2*a^2*b*d^2*Log[F]^2) + (3*x^2)/(2*a*b*d^2*(a + b*F^(c + d*x))*Log[F]^2) + x^3/(2*a^2*b*d*Log[F]) - x^3/(2*b*d*(a + b*F^(c + d*x))^2*Log[F]) + (3*x*Log[1 + (b*F^(c + d*x))/a])/(a^2*b*d^3*Log[F]^3) - (3*x^2*Log[1 + (b*F^(c + d*x))/a])/(2*a^2*b*d^2*Log[F]^2) + (3*PolyLog[2, -((b*F^(c + d*x))/a)])/(a^2*b*d^4*Log[F]^4) - (3*x*PolyLog[2, -((b*F^(c + d*x))/a)])/(a^2*b*d^3*Log[F]^3) + (3*PolyLog[3, -((b*F^(c + d*x))/a)])/(a^2*b*d^4*Log[F]^4)","A",12,9,24,0.3750,1,"{2191, 2185, 2184, 2190, 2531, 2282, 6589, 2279, 2391}"
89,1,182,0,0.291422,"\int \frac{F^{c+d x} x^2}{\left(a+b F^{c+d x}\right)^3} \, dx","Int[(F^(c + d*x)*x^2)/(a + b*F^(c + d*x))^3,x]","-\frac{\text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^3 \log ^3(F)}-\frac{x \log \left(\frac{b F^{c+d x}}{a}+1\right)}{a^2 b d^2 \log ^2(F)}+\frac{\log \left(a+b F^{c+d x}\right)}{a^2 b d^3 \log ^3(F)}-\frac{x}{a^2 b d^2 \log ^2(F)}+\frac{x^2}{2 a^2 b d \log (F)}+\frac{x}{a b d^2 \log ^2(F) \left(a+b F^{c+d x}\right)}-\frac{x^2}{2 b d \log (F) \left(a+b F^{c+d x}\right)^2}","-\frac{\text{PolyLog}\left(2,-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^3 \log ^3(F)}-\frac{x \log \left(\frac{b F^{c+d x}}{a}+1\right)}{a^2 b d^2 \log ^2(F)}+\frac{\log \left(a+b F^{c+d x}\right)}{a^2 b d^3 \log ^3(F)}-\frac{x}{a^2 b d^2 \log ^2(F)}+\frac{x^2}{2 a^2 b d \log (F)}+\frac{x}{a b d^2 \log ^2(F) \left(a+b F^{c+d x}\right)}-\frac{x^2}{2 b d \log (F) \left(a+b F^{c+d x}\right)^2}",1,"-(x/(a^2*b*d^2*Log[F]^2)) + x/(a*b*d^2*(a + b*F^(c + d*x))*Log[F]^2) + x^2/(2*a^2*b*d*Log[F]) - x^2/(2*b*d*(a + b*F^(c + d*x))^2*Log[F]) + Log[a + b*F^(c + d*x)]/(a^2*b*d^3*Log[F]^3) - (x*Log[1 + (b*F^(c + d*x))/a])/(a^2*b*d^2*Log[F]^2) - PolyLog[2, -((b*F^(c + d*x))/a)]/(a^2*b*d^3*Log[F]^3)","A",11,10,24,0.4167,1,"{2191, 2185, 2184, 2190, 2279, 2391, 2282, 36, 29, 31}"
90,1,106,0,0.0885608,"\int \frac{F^{c+d x} x}{\left(a+b F^{c+d x}\right)^3} \, dx","Int[(F^(c + d*x)*x)/(a + b*F^(c + d*x))^3,x]","-\frac{\log \left(a+b F^{c+d x}\right)}{2 a^2 b d^2 \log ^2(F)}+\frac{x}{2 a^2 b d \log (F)}+\frac{1}{2 a b d^2 \log ^2(F) \left(a+b F^{c+d x}\right)}-\frac{x}{2 b d \log (F) \left(a+b F^{c+d x}\right)^2}","-\frac{\log \left(a+b F^{c+d x}\right)}{2 a^2 b d^2 \log ^2(F)}+\frac{x}{2 a^2 b d \log (F)}+\frac{1}{2 a b d^2 \log ^2(F) \left(a+b F^{c+d x}\right)}-\frac{x}{2 b d \log (F) \left(a+b F^{c+d x}\right)^2}",1,"1/(2*a*b*d^2*(a + b*F^(c + d*x))*Log[F]^2) + x/(2*a^2*b*d*Log[F]) - x/(2*b*d*(a + b*F^(c + d*x))^2*Log[F]) - Log[a + b*F^(c + d*x)]/(2*a^2*b*d^2*Log[F]^2)","A",4,3,22,0.1364,1,"{2191, 2282, 44}"
91,1,27,0,0.0345761,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^3} \, dx","Int[F^(c + d*x)/(a + b*F^(c + d*x))^3,x]","-\frac{1}{2 b d \log (F) \left(a+b F^{c+d x}\right)^2}","-\frac{1}{2 b d \log (F) \left(a+b F^{c+d x}\right)^2}",1,"-1/(2*b*d*(a + b*F^(c + d*x))^2*Log[F])","A",2,2,21,0.09524,1,"{2246, 32}"
92,0,0,0,0.1158077,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^3 x} \, dx","Int[F^(c + d*x)/((a + b*F^(c + d*x))^3*x),x]","\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^3 x} \, dx","-\frac{\text{Int}\left(\frac{1}{x^2 \left(a+b F^{c+d x}\right)^2},x\right)}{2 b d \log (F)}-\frac{1}{2 b d x \log (F) \left(a+b F^{c+d x}\right)^2}",0,"-1/(2*b*d*(a + b*F^(c + d*x))^2*x*Log[F]) - Defer[Int][1/((a + b*F^(c + d*x))^2*x^2), x]/(2*b*d*Log[F])","A",0,0,0,0,-1,"{}"
93,0,0,0,0.1131538,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^3 x^2} \, dx","Int[F^(c + d*x)/((a + b*F^(c + d*x))^3*x^2),x]","\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^3 x^2} \, dx","-\frac{\text{Int}\left(\frac{1}{x^3 \left(a+b F^{c+d x}\right)^2},x\right)}{b d \log (F)}-\frac{1}{2 b d x^2 \log (F) \left(a+b F^{c+d x}\right)^2}",0,"-1/(2*b*d*(a + b*F^(c + d*x))^2*x^2*Log[F]) - Defer[Int][1/((a + b*F^(c + d*x))^2*x^3), x]/(b*d*Log[F])","A",0,0,0,0,-1,"{}"