1,1,112,110,0.0119249,"\int \frac{x^3}{a+b e^{c+d x}} \, dx","Integrate[x^3/(a + b*E^(c + d*x)),x]","\frac{6 \text{Li}_4\left(-\frac{a e^{-c-d x}}{b}\right)}{a d^4}+\frac{6 x \text{Li}_3\left(-\frac{a e^{-c-d x}}{b}\right)}{a d^3}+\frac{3 x^2 \text{Li}_2\left(-\frac{a e^{-c-d x}}{b}\right)}{a d^2}-\frac{x^3 \log \left(\frac{a e^{-c-d x}}{b}+1\right)}{a d}","-\frac{6 \text{Li}_4\left(-\frac{b e^{c+d x}}{a}\right)}{a d^4}+\frac{6 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{a d^3}-\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a d^2}-\frac{x^3 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a d}+\frac{x^4}{4 a}",1,"-((x^3*Log[1 + (a*E^(-c - d*x))/b])/(a*d)) + (3*x^2*PolyLog[2, -((a*E^(-c - d*x))/b)])/(a*d^2) + (6*x*PolyLog[3, -((a*E^(-c - d*x))/b)])/(a*d^3) + (6*PolyLog[4, -((a*E^(-c - d*x))/b)])/(a*d^4)","A",1
2,1,83,84,0.0068372,"\int \frac{x^2}{a+b e^{c+d x}} \, dx","Integrate[x^2/(a + b*E^(c + d*x)),x]","\frac{2 \text{Li}_3\left(-\frac{a e^{-c-d x}}{b}\right)}{a d^3}+\frac{2 x \text{Li}_2\left(-\frac{a e^{-c-d x}}{b}\right)}{a d^2}-\frac{x^2 \log \left(\frac{a e^{-c-d x}}{b}+1\right)}{a d}","\frac{2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{a d^3}-\frac{2 x \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a d^2}-\frac{x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a d}+\frac{x^3}{3 a}",1,"-((x^2*Log[1 + (a*E^(-c - d*x))/b])/(a*d)) + (2*x*PolyLog[2, -((a*E^(-c - d*x))/b)])/(a*d^2) + (2*PolyLog[3, -((a*E^(-c - d*x))/b)])/(a*d^3)","A",1
3,1,53,58,0.0034382,"\int \frac{x}{a+b e^{c+d x}} \, dx","Integrate[x/(a + b*E^(c + d*x)),x]","\frac{\text{Li}_2\left(-\frac{a e^{-c-d x}}{b}\right)}{a d^2}-\frac{x \log \left(\frac{a e^{-c-d x}}{b}+1\right)}{a d}","-\frac{\text{Li}_2\left(-\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*Log[1 + (a*E^(-c - d*x))/b])/(a*d)) + PolyLog[2, -((a*E^(-c - d*x))/b)]/(a*d^2)","A",1
4,1,26,26,0.004007,"\int \frac{1}{a+b e^{c+d x}} \, dx","Integrate[(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",1
5,0,0,20,0.0446991,"\int \frac{1}{\left(a+b e^{c+d x}\right) x} \, dx","Integrate[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,"Integrate[1/((a + b*E^(c + d*x))*x), x]","A",-1
6,0,0,20,0.1309288,"\int \frac{1}{\left(a+b e^{c+d x}\right) x^2} \, dx","Integrate[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,"Integrate[1/((a + b*E^(c + d*x))*x^2), x]","A",-1
7,1,21,26,0.0169063,"\int \frac{1}{a+b e^{c-d x}} \, dx","Integrate[(a + b*E^(c - d*x))^(-1),x]","\frac{\log \left(a e^{d x}+b e^c\right)}{a d}","\frac{\log \left(a+b e^{c-d x}\right)}{a d}+\frac{x}{a}",1,"Log[b*E^c + a*E^(d*x)]/(a*d)","A",1
8,1,19,28,0.0158374,"\int \frac{1}{a+b e^{-c-d x}} \, dx","Integrate[(a + b*E^(-c - d*x))^(-1),x]","\frac{\log \left(a e^{c+d x}+b\right)}{a d}","\frac{\log \left(a+b e^{-c-d x}\right)}{a d}+\frac{x}{a}",1,"Log[b + a*E^(c + d*x)]/(a*d)","A",1
9,1,158,217,0.2430886,"\int \frac{x^3}{\left(a+b e^{c+d x}\right)^2} \, dx","Integrate[x^3/(a + b*E^(c + d*x))^2,x]","\frac{\frac{24 (d x-1) \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{d^4}-\frac{24 \text{Li}_4\left(-\frac{b e^{c+d x}}{a}\right)}{d^4}-\frac{12 x (d x-2) \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{d^3}+\frac{12 x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{d^2}+\frac{4 a x^3}{a d+b d e^{c+d x}}-\frac{4 x^3 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{d}-\frac{4 x^3}{d}+x^4}{4 a^2}","-\frac{6 \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{a^2 d^4}-\frac{6 \text{Li}_4\left(-\frac{b e^{c+d x}}{a}\right)}{a^2 d^4}+\frac{6 x \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}+\frac{6 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}-\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a^2 d^2}+\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,"((-4*x^3)/d + (4*a*x^3)/(a*d + b*d*E^(c + d*x)) + x^4 + (12*x^2*Log[1 + (b*E^(c + d*x))/a])/d^2 - (4*x^3*Log[1 + (b*E^(c + d*x))/a])/d - (12*x*(-2 + d*x)*PolyLog[2, -((b*E^(c + d*x))/a)])/d^3 + (24*(-1 + d*x)*PolyLog[3, -((b*E^(c + d*x))/a)])/d^4 - (24*PolyLog[4, -((b*E^(c + d*x))/a)])/d^4)/(4*a^2)","A",1
10,1,113,165,0.2444039,"\int \frac{x^2}{\left(a+b e^{c+d x}\right)^2} \, dx","Integrate[x^2/(a + b*E^(c + d*x))^2,x]","\frac{\frac{d^2 x^2 \left(a d x+b (d x-3) e^{c+d x}\right)}{a+b e^{c+d x}}+(6-6 d x) \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)+6 \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)-3 d x (d x-2) \log \left(\frac{b e^{c+d x}}{a}+1\right)}{3 a^2 d^3}","\frac{2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}+\frac{2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{a^2 d^3}-\frac{2 x \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a^2 d^2}+\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,"((d^2*x^2*(a*d*x + b*E^(c + d*x)*(-3 + d*x)))/(a + b*E^(c + d*x)) - 3*d*x*(-2 + d*x)*Log[1 + (b*E^(c + d*x))/a] + (6 - 6*d*x)*PolyLog[2, -((b*E^(c + d*x))/a)] + 6*PolyLog[3, -((b*E^(c + d*x))/a)])/(3*a^2*d^3)","A",1
11,1,85,107,0.1182714,"\int \frac{x}{\left(a+b e^{c+d x}\right)^2} \, dx","Integrate[x/(a + b*E^(c + d*x))^2,x]","\frac{-2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)+\frac{d x \left(a d x+b (d x-2) e^{c+d x}\right)}{a+b e^{c+d x}}-2 (d x-1) \log \left(\frac{b e^{c+d x}}{a}+1\right)}{2 a^2 d^2}","-\frac{\text{Li}_2\left(-\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,"((d*x*(a*d*x + b*E^(c + d*x)*(-2 + d*x)))/(a + b*E^(c + d*x)) - 2*(-1 + d*x)*Log[1 + (b*E^(c + d*x))/a] - 2*PolyLog[2, -((b*E^(c + d*x))/a)])/(2*a^2*d^2)","A",1
12,1,40,46,0.0393891,"\int \frac{1}{\left(a+b e^{c+d x}\right)^2} \, dx","Integrate[(a + b*E^(c + d*x))^(-2),x]","\frac{\frac{a}{a+b e^{c+d x}}-\log \left(a+b e^{c+d x}\right)+d x}{a^2 d}","-\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,"(a/(a + b*E^(c + d*x)) + d*x - Log[a + b*E^(c + d*x)])/(a^2*d)","A",1
13,0,0,20,0.8161726,"\int \frac{1}{\left(a+b e^{c+d x}\right)^2 x} \, dx","Integrate[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,"Integrate[1/((a + b*E^(c + d*x))^2*x), x]","A",-1
14,0,0,20,0.6358954,"\int \frac{1}{\left(a+b e^{c+d x}\right)^2 x^2} \, dx","Integrate[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,"Integrate[1/((a + b*E^(c + d*x))^2*x^2), x]","A",-1
15,1,42,48,0.0549933,"\int \frac{1}{\left(a+b e^{c-d x}\right)^2} \, dx","Integrate[(a + b*E^(c - d*x))^(-2),x]","\frac{\frac{b e^c}{a e^{d x}+b e^c}+\log \left(a e^{d x}+b e^c\right)}{a^2 d}","\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,"((b*E^c)/(b*E^c + a*E^(d*x)) + Log[b*E^c + a*E^(d*x)])/(a^2*d)","A",1
16,1,35,52,0.0584066,"\int \frac{1}{\left(a+b e^{-c-d x}\right)^2} \, dx","Integrate[(a + b*E^(-c - d*x))^(-2),x]","\frac{\frac{b}{a e^{c+d x}+b}+\log \left(a e^{c+d x}+b\right)}{a^2 d}","\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,"(b/(b + a*E^(c + d*x)) + Log[b + a*E^(c + d*x)])/(a^2*d)","A",1
17,1,241,333,0.2539129,"\int \frac{x^3}{\left(a+b e^{c+d x}\right)^3} \, dx","Integrate[x^3/(a + b*E^(c + d*x))^3,x]","\frac{\frac{2 a^2 x^3}{d \left(a+b e^{c+d x}\right)^2}+\frac{12 (2 d x-3) \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{d^4}-\frac{24 \text{Li}_4\left(-\frac{b e^{c+d x}}{a}\right)}{d^4}-\frac{12 x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{d^3}-\frac{6 a x^2}{d^2 \left(a+b e^{c+d x}\right)}+\frac{18 x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{d^2}-\frac{12 \left(d^2 x^2-3 d x+1\right) \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{d^4}+\frac{4 a x^3}{a d+b d e^{c+d x}}-\frac{4 x^3 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{d}+\frac{6 x^2}{d^2}-\frac{6 x^3}{d}+x^4}{4 a^3}","-\frac{3 \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a^3 d^4}-\frac{9 \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{a^3 d^4}-\frac{6 \text{Li}_4\left(-\frac{b e^{c+d x}}{a}\right)}{a^3 d^4}+\frac{9 x \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}+\frac{6 x \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}-\frac{3 x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d^3}-\frac{3 x^2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a^3 d^2}+\frac{9 x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{2 a^3 d^2}-\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{3 x^2}{2 a^2 d^2 \left(a+b e^{c+d x}\right)}+\frac{x^3}{a^2 d \left(a+b e^{c+d x}\right)}+\frac{x^3}{2 a d \left(a+b e^{c+d x}\right)^2}",1,"((6*x^2)/d^2 - (6*a*x^2)/(d^2*(a + b*E^(c + d*x))) - (6*x^3)/d + (2*a^2*x^3)/(d*(a + b*E^(c + d*x))^2) + (4*a*x^3)/(a*d + b*d*E^(c + d*x)) + x^4 - (12*x*Log[1 + (b*E^(c + d*x))/a])/d^3 + (18*x^2*Log[1 + (b*E^(c + d*x))/a])/d^2 - (4*x^3*Log[1 + (b*E^(c + d*x))/a])/d - (12*(1 - 3*d*x + d^2*x^2)*PolyLog[2, -((b*E^(c + d*x))/a)])/d^4 + (12*(-3 + 2*d*x)*PolyLog[3, -((b*E^(c + d*x))/a)])/d^4 - (24*PolyLog[4, -((b*E^(c + d*x))/a)])/d^4)/(4*a^3)","A",1
18,1,203,243,0.1896445,"\int \frac{x^2}{\left(a+b e^{c+d x}\right)^3} \, dx","Integrate[x^2/(a + b*E^(c + d*x))^3,x]","\frac{\frac{3 a^2 x^2}{d \left(a+b e^{c+d x}\right)^2}-\frac{6 (2 d x-3) \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{d^3}+\frac{12 \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{d^3}-\frac{6 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{d^3}-\frac{6 a x}{d^2 \left(a+b e^{c+d x}\right)}+\frac{18 x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{d^2}+\frac{6 a x^2}{a d+b d e^{c+d x}}-\frac{6 x^2 \log \left(\frac{b e^{c+d x}}{a}+1\right)}{d}+\frac{6 x}{d^2}-\frac{9 x^2}{d}+2 x^3}{6 a^3}","\frac{3 \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}+\frac{2 \text{Li}_3\left(-\frac{b e^{c+d x}}{a}\right)}{a^3 d^3}-\frac{\log \left(a+b e^{c+d x}\right)}{a^3 d^3}-\frac{2 x \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a^3 d^2}+\frac{3 x \log \left(\frac{b e^{c+d x}}{a}+1\right)}{a^3 d^2}-\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}{a^2 d^2 \left(a+b e^{c+d x}\right)}+\frac{x^2}{a^2 d \left(a+b e^{c+d x}\right)}+\frac{x^2}{2 a d \left(a+b e^{c+d x}\right)^2}",1,"((6*x)/d^2 - (6*a*x)/(d^2*(a + b*E^(c + d*x))) - (9*x^2)/d + (3*a^2*x^2)/(d*(a + b*E^(c + d*x))^2) + (6*a*x^2)/(a*d + b*d*E^(c + d*x)) + 2*x^3 - (6*Log[1 + (b*E^(c + d*x))/a])/d^3 + (18*x*Log[1 + (b*E^(c + d*x))/a])/d^2 - (6*x^2*Log[1 + (b*E^(c + d*x))/a])/d - (6*(-3 + 2*d*x)*PolyLog[2, -((b*E^(c + d*x))/a)])/d^3 + (12*PolyLog[3, -((b*E^(c + d*x))/a)])/d^3)/(6*a^3)","A",1
19,1,120,159,0.1475447,"\int \frac{x}{\left(a+b e^{c+d x}\right)^3} \, dx","Integrate[x/(a + b*E^(c + d*x))^3,x]","\frac{\frac{d x \left(d x-2 \log \left(\frac{b e^{c+d x}}{a}+1\right)\right)-2 \text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a}+\frac{a d x}{\left(a+b e^{c+d x}\right)^2}+\frac{2 d x-1}{a+b e^{c+d x}}+\frac{3 \log \left(\frac{b e^{c+d x}}{a}+1\right)-3 d x}{a}}{2 a^2 d^2}","-\frac{\text{Li}_2\left(-\frac{b e^{c+d x}}{a}\right)}{a^3 d^2}+\frac{3 \log \left(a+b e^{c+d x}\right)}{2 a^3 d^2}-\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{1}{2 a^2 d^2 \left(a+b e^{c+d x}\right)}+\frac{x}{a^2 d \left(a+b e^{c+d x}\right)}+\frac{x}{2 a d \left(a+b e^{c+d x}\right)^2}",1,"((a*d*x)/(a + b*E^(c + d*x))^2 + (-1 + 2*d*x)/(a + b*E^(c + d*x)) + (-3*d*x + 3*Log[1 + (b*E^(c + d*x))/a])/a + (d*x*(d*x - 2*Log[1 + (b*E^(c + d*x))/a]) - 2*PolyLog[2, -((b*E^(c + d*x))/a)])/a)/(2*a^2*d^2)","A",1
20,1,62,69,0.0615491,"\int \frac{1}{\left(a+b e^{c+d x}\right)^3} \, dx","Integrate[(a + b*E^(c + d*x))^(-3),x]","\frac{\frac{a^2}{\left(a+b e^{c+d x}\right)^2}+\frac{2 a}{a+b e^{c+d x}}-2 \log \left(a+b e^{c+d x}\right)+2 d x}{2 a^3 d}","-\frac{\log \left(a+b e^{c+d x}\right)}{a^3 d}+\frac{x}{a^3}+\frac{1}{a^2 d \left(a+b e^{c+d x}\right)}+\frac{1}{2 a d \left(a+b e^{c+d x}\right)^2}",1,"(a^2/(a + b*E^(c + d*x))^2 + (2*a)/(a + b*E^(c + d*x)) + 2*d*x - 2*Log[a + b*E^(c + d*x)])/(2*a^3*d)","A",1
21,0,0,20,1.0040135,"\int \frac{1}{\left(a+b e^{c+d x}\right)^3 x} \, dx","Integrate[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,"Integrate[1/((a + b*E^(c + d*x))^3*x), x]","A",-1
22,0,0,20,0.7773339,"\int \frac{1}{\left(a+b e^{c+d x}\right)^3 x^2} \, dx","Integrate[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,"Integrate[1/((a + b*E^(c + d*x))^3*x^2), x]","A",-1
23,1,62,72,0.0928707,"\int \frac{1}{\left(a+b e^{c-d x}\right)^3} \, dx","Integrate[(a + b*E^(c - d*x))^(-3),x]","\frac{\frac{b e^c \left(4 a e^{d x}+3 b e^c\right)}{\left(a e^{d x}+b e^c\right)^2}+2 \log \left(a e^{d x}+b e^c\right)}{2 a^3 d}","\frac{\log \left(a+b e^{c-d x}\right)}{a^3 d}+\frac{x}{a^3}-\frac{1}{a^2 d \left(a+b e^{c-d x}\right)}-\frac{1}{2 a d \left(a+b e^{c-d x}\right)^2}",1,"((b*E^c*(3*b*E^c + 4*a*E^(d*x)))/(b*E^c + a*E^(d*x))^2 + 2*Log[b*E^c + a*E^(d*x)])/(2*a^3*d)","A",1
24,1,54,78,0.0955293,"\int \frac{1}{\left(a+b e^{-c-d x}\right)^3} \, dx","Integrate[(a + b*E^(-c - d*x))^(-3),x]","\frac{\frac{b \left(4 a e^{c+d x}+3 b\right)}{\left(a e^{c+d x}+b\right)^2}+2 \log \left(a e^{c+d x}+b\right)}{2 a^3 d}","\frac{\log \left(a+b e^{-c-d x}\right)}{a^3 d}+\frac{x}{a^3}-\frac{1}{a^2 d \left(a+b e^{-c-d x}\right)}-\frac{1}{2 a d \left(a+b e^{-c-d x}\right)^2}",1,"((b*(3*b + 4*a*E^(c + d*x)))/(b + a*E^(c + d*x))^2 + 2*Log[b + a*E^(c + d*x)])/(2*a^3*d)","A",1
25,1,130,153,0.2782632,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)^3 \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^3,x]","a c^3 x+\frac{3}{2} a c^2 d x^2+a c d^2 x^3+\frac{1}{4} a d^3 x^4+\frac{b \left(F^{g (e+f x)}\right)^n \left(6 d^2 f g n \log (F) (c+d x)+f^3 g^3 n^3 \log ^3(F) (c+d x)^3-3 d f^2 g^2 n^2 \log ^2(F) (c+d x)^2-6 d^3\right)}{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^3*x + (3*a*c^2*d*x^2)/2 + a*c*d^2*x^3 + (a*d^3*x^4)/4 + (b*(F^(g*(e + f*x)))^n*(-6*d^3 + 6*d^2*f*g*n*(c + d*x)*Log[F] - 3*d*f^2*g^2*n^2*(c + d*x)^2*Log[F]^2 + f^3*g^3*n^3*(c + d*x)^3*Log[F]^3))/(f^4*g^4*n^4*Log[F]^4)","A",1
26,1,91,115,0.1692696,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)^2 \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^2,x]","a c^2 x+a c d x^2+\frac{1}{3} a d^2 x^3+\frac{b \left(F^{g (e+f x)}\right)^n \left(f^2 g^2 n^2 \log ^2(F) (c+d x)^2-2 d f g n \log (F) (c+d x)+2 d^2\right)}{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^2*x + a*c*d*x^2 + (a*d^2*x^3)/3 + (b*(F^(g*(e + f*x)))^n*(2*d^2 - 2*d*f*g*n*(c + d*x)*Log[F] + f^2*g^2*n^2*(c + d*x)^2*Log[F]^2))/(f^3*g^3*n^3*Log[F]^3)","A",1
27,1,73,77,0.1669888,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x) \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)*(c + d*x),x]","\frac{1}{2} a x (2 c+d x)+\frac{b (c+d x) \left(F^{g (e+f x)}\right)^n}{f g n \log (F)}-\frac{b d \left(F^{g (e+f 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*x*(2*c + d*x))/2 - (b*d*(F^(g*(e + f*x)))^n)/(f^2*g^2*n^2*Log[F]^2) + (b*(F^(g*(e + f*x)))^n*(c + d*x))/(f*g*n*Log[F])","A",1
28,1,30,30,0.0264438,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) \, dx","Integrate[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",1
29,1,56,68,0.1502797,"\int \frac{a+b \left(F^{g (e+f x)}\right)^n}{c+d x} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)/(c + d*x),x]","\frac{a \log (c+d x)+b \left(F^{g (e+f x)}\right)^n F^{-\frac{f g n (c+d x)}{d}} \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^(g*(e + f*x)))^n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d])/F^((f*g*n*(c + d*x))/d) + a*Log[c + d*x])/d","A",1
30,1,78,100,0.2784071,"\int \frac{a+b \left(F^{g (e+f x)}\right)^n}{(c+d x)^2} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)/(c + d*x)^2,x]","\frac{b f g n \log (F) \left(F^{g (e+f x)}\right)^n F^{-\frac{f g n (c+d x)}{d}} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)-\frac{d \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{c+d x}}{d^2}","-\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,"(-((d*(a + b*(F^(g*(e + f*x)))^n))/(c + d*x)) + (b*f*(F^(g*(e + f*x)))^n*g*n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F])/F^((f*g*n*(c + d*x))/d))/d^2","A",1
31,1,111,147,0.3332158,"\int \frac{a+b \left(F^{g (e+f x)}\right)^n}{(c+d x)^3} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)/(c + d*x)^3,x]","-\frac{a d^2-b f^2 g^2 n^2 \log ^2(F) (c+d x)^2 \left(F^{g (e+f x)}\right)^n F^{-\frac{f g n (c+d x)}{d}} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)+b d \left(F^{g (e+f x)}\right)^n (f g n \log (F) (c+d x)+d)}{2 d^3 (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,"-1/2*(a*d^2 - (b*f^2*(F^(g*(e + f*x)))^n*g^2*n^2*(c + d*x)^2*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/F^((f*g*n*(c + d*x))/d) + b*d*(F^(g*(e + f*x)))^n*(d + f*g*n*(c + d*x)*Log[F]))/(d^3*(c + d*x)^2)","A",1
32,1,239,322,0.5579107,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)^3 \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)^3,x]","a^2 c^3 x+\frac{3}{2} a^2 c^2 d x^2+a^2 c d^2 x^3+\frac{1}{4} a^2 d^3 x^4+\frac{2 a b \left(F^{g (e+f x)}\right)^n \left(6 d^2 f g n \log (F) (c+d x)+f^3 g^3 n^3 \log ^3(F) (c+d x)^3-3 d f^2 g^2 n^2 \log ^2(F) (c+d x)^2-6 d^3\right)}{f^4 g^4 n^4 \log ^4(F)}+\frac{b^2 \left(F^{g (e+f x)}\right)^{2 n} \left(6 d^2 f g n \log (F) (c+d x)+4 f^3 g^3 n^3 \log ^3(F) (c+d x)^3-6 d f^2 g^2 n^2 \log ^2(F) (c+d x)^2-3 d^3\right)}{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^3*x + (3*a^2*c^2*d*x^2)/2 + a^2*c*d^2*x^3 + (a^2*d^3*x^4)/4 + (2*a*b*(F^(g*(e + f*x)))^n*(-6*d^3 + 6*d^2*f*g*n*(c + d*x)*Log[F] - 3*d*f^2*g^2*n^2*(c + d*x)^2*Log[F]^2 + f^3*g^3*n^3*(c + d*x)^3*Log[F]^3))/(f^4*g^4*n^4*Log[F]^4) + (b^2*(F^(g*(e + f*x)))^(2*n)*(-3*d^3 + 6*d^2*f*g*n*(c + d*x)*Log[F] - 6*d*f^2*g^2*n^2*(c + d*x)^2*Log[F]^2 + 4*f^3*g^3*n^3*(c + d*x)^3*Log[F]^3))/(8*f^4*g^4*n^4*Log[F]^4)","A",1
33,1,171,239,0.3696145,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)^2 \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)^2,x]","a^2 c^2 x+a^2 c d x^2+\frac{1}{3} a^2 d^2 x^3+\frac{2 a b \left(F^{g (e+f x)}\right)^n \left(f^2 g^2 n^2 \log ^2(F) (c+d x)^2-2 d f g n \log (F) (c+d x)+2 d^2\right)}{f^3 g^3 n^3 \log ^3(F)}+\frac{b^2 \left(F^{g (e+f x)}\right)^{2 n} \left(2 f^2 g^2 n^2 \log ^2(F) (c+d x)^2-2 d f g n \log (F) (c+d x)+d^2\right)}{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^2*x + a^2*c*d*x^2 + (a^2*d^2*x^3)/3 + (2*a*b*(F^(g*(e + f*x)))^n*(2*d^2 - 2*d*f*g*n*(c + d*x)*Log[F] + f^2*g^2*n^2*(c + d*x)^2*Log[F]^2))/(f^3*g^3*n^3*Log[F]^3) + (b^2*(F^(g*(e + f*x)))^(2*n)*(d^2 - 2*d*f*g*n*(c + d*x)*Log[F] + 2*f^2*g^2*n^2*(c + d*x)^2*Log[F]^2))/(4*f^3*g^3*n^3*Log[F]^3)","A",1
34,1,117,156,0.2629071,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x) \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x),x]","\frac{2 a^2 f^2 g^2 n^2 x \log ^2(F) (2 c+d x)+2 b f g n \log (F) (c+d x) \left(F^{g (e+f x)}\right)^n \left(4 a+b \left(F^{g (e+f x)}\right)^n\right)-b d \left(F^{g (e+f x)}\right)^n \left(8 a+b \left(F^{g (e+f x)}\right)^n\right)}{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,"(-(b*d*(F^(g*(e + f*x)))^n*(8*a + b*(F^(g*(e + f*x)))^n)) + 2*b*f*(F^(g*(e + f*x)))^n*(4*a + b*(F^(g*(e + f*x)))^n)*g*n*(c + d*x)*Log[F] + 2*a^2*f^2*g^2*n^2*x*(2*c + d*x)*Log[F]^2)/(4*f^2*g^2*n^2*Log[F]^2)","A",1
35,1,52,67,0.0380337,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^2,x]","a^2 x+\frac{b \left(F^{g (e+f x)}\right)^n \left(4 a+b \left(F^{g (e+f x)}\right)^n\right)}{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 + (b*(F^(g*(e + f*x)))^n*(4*a + b*(F^(g*(e + f*x)))^n))/(2*f*g*n*Log[F])","A",1
36,1,108,134,0.3148702,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}{c+d x} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^2/(c + d*x),x]","\frac{a^2 \log (c+d x)+2 a b \left(F^{g (e+f x)}\right)^n F^{-\frac{f g n (c+d x)}{d}} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)+b^2 \left(F^{g (e+f x)}\right)^{2 n} F^{-\frac{2 f g n (c+d x)}{d}} \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^(g*(e + f*x)))^n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d])/F^((f*g*n*(c + d*x))/d) + (b^2*(F^(g*(e + f*x)))^(2*n)*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d])/F^((2*f*g*n*(c + d*x))/d) + a^2*Log[c + d*x])/d","A",1
37,1,136,202,0.6846719,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}{(c+d x)^2} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^2/(c + d*x)^2,x]","\frac{2 a b f g n \log (F) \left(F^{g (e+f x)}\right)^n F^{-\frac{f g n (c+d x)}{d}} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)-\frac{d \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}{c+d x}+2 b^2 f g n \log (F) \left(F^{g (e+f x)}\right)^{2 n} F^{-\frac{2 f g n (c+d x)}{d}} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)}{d^2}","-\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,"(-((d*(a + b*(F^(g*(e + f*x)))^n)^2)/(c + d*x)) + (2*a*b*f*(F^(g*(e + f*x)))^n*g*n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F])/F^((f*g*n*(c + d*x))/d) + (2*b^2*f*(F^(g*(e + f*x)))^(2*n)*g*n*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d]*Log[F])/F^((2*f*g*n*(c + d*x))/d))/d^2","A",1
38,1,217,286,0.7298957,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}{(c+d x)^3} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^2/(c + d*x)^3,x]","-\frac{a^2 d^2-2 a b f^2 g^2 n^2 \log ^2(F) (c+d x)^2 \left(F^{g (e+f x)}\right)^n F^{-\frac{f g n (c+d x)}{d}} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)+2 a b d \left(F^{g (e+f x)}\right)^n (f g n \log (F) (c+d x)+d)-4 b^2 f^2 g^2 n^2 \log ^2(F) (c+d x)^2 \left(F^{g (e+f x)}\right)^{2 n} F^{-\frac{2 f g n (c+d x)}{d}} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)+b^2 d \left(F^{g (e+f x)}\right)^{2 n} (2 f g n \log (F) (c+d x)+d)}{2 d^3 (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,"-1/2*(a^2*d^2 - (2*a*b*f^2*(F^(g*(e + f*x)))^n*g^2*n^2*(c + d*x)^2*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/F^((f*g*n*(c + d*x))/d) - (4*b^2*f^2*(F^(g*(e + f*x)))^(2*n)*g^2*n^2*(c + d*x)^2*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/F^((2*f*g*n*(c + d*x))/d) + 2*a*b*d*(F^(g*(e + f*x)))^n*(d + f*g*n*(c + d*x)*Log[F]) + b^2*d*(F^(g*(e + f*x)))^(2*n)*(d + 2*f*g*n*(c + d*x)*Log[F]))/(d^3*(c + d*x)^2)","A",1
39,1,341,496,0.7431908,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)^3 \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^3,x]","a^3 c^3 x+\frac{3}{2} a^3 c^2 d x^2+a^3 c d^2 x^3+\frac{1}{4} a^3 d^3 x^4+\frac{3 a^2 b \left(F^{g (e+f x)}\right)^n \left(6 d^2 f g n \log (F) (c+d x)+f^3 g^3 n^3 \log ^3(F) (c+d x)^3-3 d f^2 g^2 n^2 \log ^2(F) (c+d x)^2-6 d^3\right)}{f^4 g^4 n^4 \log ^4(F)}+\frac{3 a b^2 \left(F^{g (e+f x)}\right)^{2 n} \left(6 d^2 f g n \log (F) (c+d x)+4 f^3 g^3 n^3 \log ^3(F) (c+d x)^3-6 d f^2 g^2 n^2 \log ^2(F) (c+d x)^2-3 d^3\right)}{8 f^4 g^4 n^4 \log ^4(F)}+\frac{b^3 \left(F^{g (e+f x)}\right)^{3 n} \left(6 d^2 f g n \log (F) (c+d x)+9 f^3 g^3 n^3 \log ^3(F) (c+d x)^3-9 d f^2 g^2 n^2 \log ^2(F) (c+d x)^2-2 d^3\right)}{27 f^4 g^4 n^4 \log ^4(F)}","\frac{a^3 (c+d x)^4}{4 d}+\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{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^3*x + (3*a^3*c^2*d*x^2)/2 + a^3*c*d^2*x^3 + (a^3*d^3*x^4)/4 + (3*a^2*b*(F^(g*(e + f*x)))^n*(-6*d^3 + 6*d^2*f*g*n*(c + d*x)*Log[F] - 3*d*f^2*g^2*n^2*(c + d*x)^2*Log[F]^2 + f^3*g^3*n^3*(c + d*x)^3*Log[F]^3))/(f^4*g^4*n^4*Log[F]^4) + (3*a*b^2*(F^(g*(e + f*x)))^(2*n)*(-3*d^3 + 6*d^2*f*g*n*(c + d*x)*Log[F] - 6*d*f^2*g^2*n^2*(c + d*x)^2*Log[F]^2 + 4*f^3*g^3*n^3*(c + d*x)^3*Log[F]^3))/(8*f^4*g^4*n^4*Log[F]^4) + (b^3*(F^(g*(e + f*x)))^(3*n)*(-2*d^3 + 6*d^2*f*g*n*(c + d*x)*Log[F] - 9*d*f^2*g^2*n^2*(c + d*x)^2*Log[F]^2 + 9*f^3*g^3*n^3*(c + d*x)^3*Log[F]^3))/(27*f^4*g^4*n^4*Log[F]^4)","A",1
40,1,248,366,0.5304038,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)^2 \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^2,x]","a^3 c^2 x+a^3 c d x^2+\frac{1}{3} a^3 d^2 x^3+\frac{3 a^2 b \left(F^{g (e+f x)}\right)^n \left(f^2 g^2 n^2 \log ^2(F) (c+d x)^2-2 d f g n \log (F) (c+d x)+2 d^2\right)}{f^3 g^3 n^3 \log ^3(F)}+\frac{3 a b^2 \left(F^{g (e+f x)}\right)^{2 n} \left(2 f^2 g^2 n^2 \log ^2(F) (c+d x)^2-2 d f g n \log (F) (c+d x)+d^2\right)}{4 f^3 g^3 n^3 \log ^3(F)}+\frac{b^3 \left(F^{g (e+f x)}\right)^{3 n} \left(9 f^2 g^2 n^2 \log ^2(F) (c+d x)^2-6 d f g n \log (F) (c+d x)+2 d^2\right)}{27 f^3 g^3 n^3 \log ^3(F)}","\frac{a^3 (c+d x)^3}{3 d}-\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{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^2*x + a^3*c*d*x^2 + (a^3*d^2*x^3)/3 + (3*a^2*b*(F^(g*(e + f*x)))^n*(2*d^2 - 2*d*f*g*n*(c + d*x)*Log[F] + f^2*g^2*n^2*(c + d*x)^2*Log[F]^2))/(f^3*g^3*n^3*Log[F]^3) + (3*a*b^2*(F^(g*(e + f*x)))^(2*n)*(d^2 - 2*d*f*g*n*(c + d*x)*Log[F] + 2*f^2*g^2*n^2*(c + d*x)^2*Log[F]^2))/(4*f^3*g^3*n^3*Log[F]^3) + (b^3*(F^(g*(e + f*x)))^(3*n)*(2*d^2 - 6*d*f*g*n*(c + d*x)*Log[F] + 9*f^2*g^2*n^2*(c + d*x)^2*Log[F]^2))/(27*f^3*g^3*n^3*Log[F]^3)","A",1
41,1,161,236,0.3754707,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x) \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x),x]","\frac{18 a^3 f^2 g^2 n^2 x \log ^2(F) (2 c+d x)+6 b f g n \log (F) (c+d x) \left(F^{g (e+f x)}\right)^n \left(18 a^2+9 a b \left(F^{g (e+f x)}\right)^n+2 b^2 \left(F^{g (e+f x)}\right)^{2 n}\right)-b d \left(F^{g (e+f x)}\right)^n \left(108 a^2+27 a b \left(F^{g (e+f x)}\right)^n+4 b^2 \left(F^{g (e+f x)}\right)^{2 n}\right)}{36 f^2 g^2 n^2 \log ^2(F)}","\frac{a^3 (c+d x)^2}{2 d}+\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{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,"(-(b*d*(F^(g*(e + f*x)))^n*(108*a^2 + 27*a*b*(F^(g*(e + f*x)))^n + 4*b^2*(F^(g*(e + f*x)))^(2*n))) + 6*b*f*(F^(g*(e + f*x)))^n*(18*a^2 + 9*a*b*(F^(g*(e + f*x)))^n + 2*b^2*(F^(g*(e + f*x)))^(2*n))*g*n*(c + d*x)*Log[F] + 18*a^3*f^2*g^2*n^2*x*(2*c + d*x)*Log[F]^2)/(36*f^2*g^2*n^2*Log[F]^2)","A",1
42,1,74,103,0.0501045,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^3,x]","a^3 x+\frac{b \left(F^{g (e+f x)}\right)^n \left(18 a^2+9 a b \left(F^{g (e+f x)}\right)^n+2 b^2 \left(F^{g (e+f x)}\right)^{2 n}\right)}{6 f g n \log (F)}","a^3 x+\frac{3 a^2 b \left(F^{g (e+f x)}\right)^n}{f g n \log (F)}+\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 + (b*(F^(g*(e + f*x)))^n*(18*a^2 + 9*a*b*(F^(g*(e + f*x)))^n + 2*b^2*(F^(g*(e + f*x)))^(2*n)))/(6*f*g*n*Log[F])","A",1
43,1,160,200,0.4984753,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3}{c+d x} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^3/(c + d*x),x]","\frac{a^3 \log (c+d x)+3 a^2 b \left(F^{g (e+f x)}\right)^n F^{-\frac{f g n (c+d x)}{d}} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)+3 a b^2 \left(F^{g (e+f x)}\right)^{2 n} F^{-\frac{2 f g n (c+d x)}{d}} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)+b^3 \left(F^{g (e+f x)}\right)^{3 n} F^{-\frac{3 f g n (c+d x)}{d}} \text{Ei}\left(\frac{3 f g n (c+d x) \log (F)}{d}\right)}{d}","\frac{a^3 \log (c+d x)}{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{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^(g*(e + f*x)))^n*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d])/F^((f*g*n*(c + d*x))/d) + (3*a*b^2*(F^(g*(e + f*x)))^(2*n)*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d])/F^((2*f*g*n*(c + d*x))/d) + (b^3*(F^(g*(e + f*x)))^(3*n)*ExpIntegralEi[(3*f*g*n*(c + d*x)*Log[F])/d])/F^((3*f*g*n*(c + d*x))/d) + a^3*Log[c + d*x])/d","A",1
44,1,250,305,1.3249922,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3}{(c+d x)^2} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^3/(c + d*x)^2,x]","-\frac{a^3 d-3 a^2 b f g n \log (F) (c+d x) \left(F^{g (e+f x)}\right)^n F^{-\frac{f g n (c+d x)}{d}} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)+3 a^2 b d \left(F^{g (e+f x)}\right)^n-6 a b^2 f g n \log (F) (c+d x) \left(F^{g (e+f x)}\right)^{2 n} F^{-\frac{2 f g n (c+d x)}{d}} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)+3 a b^2 d \left(F^{g (e+f x)}\right)^{2 n}-3 b^3 f g n \log (F) (c+d x) \left(F^{g (e+f x)}\right)^{3 n} F^{-\frac{3 f g n (c+d x)}{d}} \text{Ei}\left(\frac{3 f g n (c+d x) \log (F)}{d}\right)+b^3 d \left(F^{g (e+f x)}\right)^{3 n}}{d^2 (c+d x)}","-\frac{a^3}{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{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 + 3*a^2*b*d*(F^(g*(e + f*x)))^n + 3*a*b^2*d*(F^(g*(e + f*x)))^(2*n) + b^3*d*(F^(g*(e + f*x)))^(3*n) - (3*a^2*b*f*(F^(g*(e + f*x)))^n*g*n*(c + d*x)*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F])/F^((f*g*n*(c + d*x))/d) - (6*a*b^2*f*(F^(g*(e + f*x)))^(2*n)*g*n*(c + d*x)*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d]*Log[F])/F^((2*f*g*n*(c + d*x))/d) - (3*b^3*f*(F^(g*(e + f*x)))^(3*n)*g*n*(c + d*x)*ExpIntegralEi[(3*f*g*n*(c + d*x)*Log[F])/d]*Log[F])/F^((3*f*g*n*(c + d*x))/d))/(d^2*(c + d*x)))","A",1
45,1,325,447,1.0589245,"\int \frac{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3}{(c+d x)^3} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^3/(c + d*x)^3,x]","-\frac{a^3 d^2-3 a^2 b f^2 g^2 n^2 \log ^2(F) (c+d x)^2 \left(F^{g (e+f x)}\right)^n F^{-\frac{f g n (c+d x)}{d}} \text{Ei}\left(\frac{f g n (c+d x) \log (F)}{d}\right)+3 a^2 b d \left(F^{g (e+f x)}\right)^n (f g n \log (F) (c+d x)+d)-12 a b^2 f^2 g^2 n^2 \log ^2(F) (c+d x)^2 \left(F^{g (e+f x)}\right)^{2 n} F^{-\frac{2 f g n (c+d x)}{d}} \text{Ei}\left(\frac{2 f g n (c+d x) \log (F)}{d}\right)+3 a b^2 d \left(F^{g (e+f x)}\right)^{2 n} (2 f g n \log (F) (c+d x)+d)-9 b^3 f^2 g^2 n^2 \log ^2(F) (c+d x)^2 \left(F^{g (e+f x)}\right)^{3 n} F^{-\frac{3 f g n (c+d x)}{d}} \text{Ei}\left(\frac{3 f g n (c+d x) \log (F)}{d}\right)+b^3 d \left(F^{g (e+f x)}\right)^{3 n} (3 f g n \log (F) (c+d x)+d)}{2 d^3 (c+d x)^2}","-\frac{a^3}{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{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,"-1/2*(a^3*d^2 - (3*a^2*b*f^2*(F^(g*(e + f*x)))^n*g^2*n^2*(c + d*x)^2*ExpIntegralEi[(f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/F^((f*g*n*(c + d*x))/d) - (12*a*b^2*f^2*(F^(g*(e + f*x)))^(2*n)*g^2*n^2*(c + d*x)^2*ExpIntegralEi[(2*f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/F^((2*f*g*n*(c + d*x))/d) - (9*b^3*f^2*(F^(g*(e + f*x)))^(3*n)*g^2*n^2*(c + d*x)^2*ExpIntegralEi[(3*f*g*n*(c + d*x)*Log[F])/d]*Log[F]^2)/F^((3*f*g*n*(c + d*x))/d) + 3*a^2*b*d*(F^(g*(e + f*x)))^n*(d + f*g*n*(c + d*x)*Log[F]) + 3*a*b^2*d*(F^(g*(e + f*x)))^(2*n)*(d + 2*f*g*n*(c + d*x)*Log[F]) + b^3*d*(F^(g*(e + f*x)))^(3*n)*(d + 3*f*g*n*(c + d*x)*Log[F]))/(d^3*(c + d*x)^2)","A",1
46,1,166,192,0.1118797,"\int \frac{(c+d x)^3}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","Integrate[(c + d*x)^3/(a + b*(F^(g*(e + f*x)))^n),x]","\frac{\frac{3 d \left(f^2 g^2 n^2 \log ^2(F) (c+d x)^2 \text{Li}_2\left(-\frac{a \left(F^{g (e+f x)}\right)^{-n}}{b}\right)+2 d \left(f g n \log (F) (c+d x) \text{Li}_3\left(-\frac{a \left(F^{g (e+f x)}\right)^{-n}}{b}\right)+d \text{Li}_4\left(-\frac{a \left(F^{g (e+f x)}\right)^{-n}}{b}\right)\right)\right)}{f^3 g^3 n^3 \log ^3(F)}-(c+d x)^3 \log \left(\frac{a \left(F^{g (e+f x)}\right)^{-n}}{b}+1\right)}{a f g n \log (F)}","\frac{6 d^2 (c+d x) \text{Li}_3\left(-\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{Li}_2\left(-\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)^3 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a f g n \log (F)}-\frac{6 d^3 \text{Li}_4\left(-\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)^4}{4 a d}",1,"(-((c + d*x)^3*Log[1 + a/(b*(F^(g*(e + f*x)))^n)]) + (3*d*(f^2*g^2*n^2*(c + d*x)^2*Log[F]^2*PolyLog[2, -(a/(b*(F^(g*(e + f*x)))^n))] + 2*d*(f*g*n*(c + d*x)*Log[F]*PolyLog[3, -(a/(b*(F^(g*(e + f*x)))^n))] + d*PolyLog[4, -(a/(b*(F^(g*(e + f*x)))^n))])))/(f^3*g^3*n^3*Log[F]^3))/(a*f*g*n*Log[F])","A",1
47,1,121,145,0.0346978,"\int \frac{(c+d x)^2}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","Integrate[(c + d*x)^2/(a + b*(F^(g*(e + f*x)))^n),x]","\frac{-f^2 g^2 n^2 \log ^2(F) (c+d x)^2 \log \left(\frac{a \left(F^{g (e+f x)}\right)^{-n}}{b}+1\right)+2 d f g n \log (F) (c+d x) \text{Li}_2\left(-\frac{a \left(F^{g (e+f x)}\right)^{-n}}{b}\right)+2 d^2 \text{Li}_3\left(-\frac{a \left(F^{g (e+f x)}\right)^{-n}}{b}\right)}{a f^3 g^3 n^3 \log ^3(F)}","-\frac{2 d (c+d x) \text{Li}_2\left(-\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)^2 \log \left(\frac{b \left(F^{g (e+f x)}\right)^n}{a}+1\right)}{a f g n \log (F)}+\frac{2 d^2 \text{Li}_3\left(-\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)^3}{3 a d}",1,"(-(f^2*g^2*n^2*(c + d*x)^2*Log[F]^2*Log[1 + a/(b*(F^(g*(e + f*x)))^n)]) + 2*d*f*g*n*(c + d*x)*Log[F]*PolyLog[2, -(a/(b*(F^(g*(e + f*x)))^n))] + 2*d^2*PolyLog[3, -(a/(b*(F^(g*(e + f*x)))^n))])/(a*f^3*g^3*n^3*Log[F]^3)","A",1
48,1,74,98,0.0115452,"\int \frac{c+d x}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","Integrate[(c + d*x)/(a + b*(F^(g*(e + f*x)))^n),x]","\frac{d \text{Li}_2\left(-\frac{a \left(F^{g (e+f x)}\right)^{-n}}{b}\right)-f g n \log (F) (c+d x) \log \left(\frac{a \left(F^{g (e+f x)}\right)^{-n}}{b}+1\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{d \text{Li}_2\left(-\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)^2}{2 a d}",1,"(-(f*g*n*(c + d*x)*Log[F]*Log[1 + a/(b*(F^(g*(e + f*x)))^n)]) + d*PolyLog[2, -(a/(b*(F^(g*(e + f*x)))^n))])/(a*f^2*g^2*n^2*Log[F]^2)","A",1
49,1,40,40,0.0080756,"\int \frac{1}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","Integrate[(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",1
50,0,0,29,0.1338058,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)} \, dx","Integrate[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,"Integrate[1/((a + b*(F^(g*(e + f*x)))^n)*(c + d*x)), x]","A",-1
51,0,0,29,0.3848732,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)^2} \, dx","Integrate[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,"Integrate[1/((a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^2), x]","A",-1
52,0,0,388,1.8144692,"\int \frac{(c+d x)^3}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","Integrate[(c + d*x)^3/(a + b*(F^(g*(e + f*x)))^n)^2,x]","\int \frac{(c+d x)^3}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","\frac{6 d^2 (c+d x) \text{Li}_2\left(-\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{Li}_3\left(-\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{Li}_2\left(-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^2 g^2 n^2 \log ^2(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{6 d^3 \text{Li}_3\left(-\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{Li}_4\left(-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^4 g^4 n^4 \log ^4(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,"Integrate[(c + d*x)^3/(a + b*(F^(g*(e + f*x)))^n)^2, x]","F",-1
53,0,0,294,1.1827972,"\int \frac{(c+d x)^2}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","Integrate[(c + d*x)^2/(a + b*(F^(g*(e + f*x)))^n)^2,x]","\int \frac{(c+d x)^2}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","-\frac{2 d (c+d x) \text{Li}_2\left(-\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 (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{2 d^2 \text{Li}_2\left(-\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{Li}_3\left(-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^3 g^3 n^3 \log ^3(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,"Integrate[(c + d*x)^2/(a + b*(F^(g*(e + f*x)))^n)^2, x]","F",-1
54,0,0,191,1.1310798,"\int \frac{c+d x}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","Integrate[(c + d*x)/(a + b*(F^(g*(e + f*x)))^n)^2,x]","\int \frac{c+d x}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","-\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 \text{Li}_2\left(-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^2 f^2 g^2 n^2 \log ^2(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,"Integrate[(c + d*x)/(a + b*(F^(g*(e + f*x)))^n)^2, x]","F",-1
55,1,62,74,0.0613042,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^(-2),x]","\frac{\frac{a}{a+b \left(F^{g (e+f x)}\right)^n}-\log \left(a+b \left(F^{g (e+f x)}\right)^n\right)+f g n x \log (F)}{a^2 f g n \log (F)}","-\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,"(a/(a + b*(F^(g*(e + f*x)))^n) + f*g*n*x*Log[F] - Log[a + b*(F^(g*(e + f*x)))^n])/(a^2*f*g*n*Log[F])","A",1
56,0,0,29,1.0149049,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)} \, dx","Integrate[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,"Integrate[1/((a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)), x]","A",-1
57,0,0,29,1.0523944,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)^2} \, dx","Integrate[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,"Integrate[1/((a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)^2), x]","A",-1
58,0,0,594,1.8135214,"\int \frac{(c+d x)^3}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","Integrate[(c + d*x)^3/(a + b*(F^(g*(e + f*x)))^n)^3,x]","\int \frac{(c+d x)^3}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","\frac{9 d^2 (c+d x) \text{Li}_2\left(-\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{Li}_3\left(-\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^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{3 d (c+d x)^2 \text{Li}_2\left(-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^2 g^2 n^2 \log ^2(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{(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{3 d^3 \text{Li}_2\left(-\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{Li}_3\left(-\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{Li}_4\left(-\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 (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{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}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\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,"Integrate[(c + d*x)^3/(a + b*(F^(g*(e + f*x)))^n)^3, x]","F",-1
59,0,0,439,1.3714047,"\int \frac{(c+d x)^2}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","Integrate[(c + d*x)^2/(a + b*(F^(g*(e + f*x)))^n)^3,x]","\int \frac{(c+d x)^2}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","-\frac{2 d (c+d x) \text{Li}_2\left(-\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 (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{(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{3 d^2 \text{Li}_2\left(-\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{Li}_3\left(-\frac{b \left(F^{g (e+f x)}\right)^n}{a}\right)}{a^3 f^3 g^3 n^3 \log ^3(F)}-\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{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}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\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,"Integrate[(c + d*x)^2/(a + b*(F^(g*(e + f*x)))^n)^3, x]","F",-1
60,0,0,276,0.9769295,"\int \frac{c+d x}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","Integrate[(c + d*x)/(a + b*(F^(g*(e + f*x)))^n)^3,x]","\int \frac{c+d x}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","-\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{d \text{Li}_2\left(-\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 \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{(c+d x)^2}{2 a^3 d}-\frac{3 d x}{2 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{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 a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}",1,"Integrate[(c + d*x)/(a + b*(F^(g*(e + f*x)))^n)^3, x]","F",-1
61,1,84,111,0.1073587,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3} \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^(-3),x]","\frac{\frac{a \left(3 a+2 b \left(F^{g (e+f x)}\right)^n\right)}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}-2 \log \left(a+b \left(F^{g (e+f x)}\right)^n\right)+2 f g n x \log (F)}{2 a^3 f g n \log (F)}","-\frac{\log \left(a+b \left(F^{g (e+f x)}\right)^n\right)}{a^3 f g n \log (F)}+\frac{x}{a^3}+\frac{1}{a^2 f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)}+\frac{1}{2 a f g n \log (F) \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2}",1,"((a*(3*a + 2*b*(F^(g*(e + f*x)))^n))/(a + b*(F^(g*(e + f*x)))^n)^2 + 2*f*g*n*x*Log[F] - 2*Log[a + b*(F^(g*(e + f*x)))^n])/(2*a^3*f*g*n*Log[F])","A",1
62,0,0,29,1.8666471,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)} \, dx","Integrate[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,"Integrate[1/((a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)), x]","A",-1
63,0,0,29,1.4896424,"\int \frac{1}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)^2} \, dx","Integrate[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,"Integrate[1/((a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^2), x]","A",-1
64,1,71,71,0.1016332,"\int \left(a+b e^x\right) \sqrt{c+d x} \, dx","Integrate[(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",1
65,1,134,145,0.3244045,"\int \left(a+b e^x\right)^2 \sqrt{c+d x} \, dx","Integrate[(a + b*E^x)^2*Sqrt[c + d*x],x]","\frac{4 \sqrt{c+d x} \left(4 a^2 (c+d x)+12 a b d e^x+3 b^2 d e^{2 x}\right)-3 \sqrt{2 \pi } b^2 d^{3/2} e^{-\frac{2 c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{c+d x}}{\sqrt{d}}\right)}{24 d}-\sqrt{\pi } a b \sqrt{d} e^{-\frac{c}{d}} \text{erfi}\left(\frac{\sqrt{c+d x}}{\sqrt{d}}\right)","\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,"-((a*b*Sqrt[d]*Sqrt[Pi]*Erfi[Sqrt[c + d*x]/Sqrt[d]])/E^(c/d)) + (4*Sqrt[c + d*x]*(12*a*b*d*E^x + 3*b^2*d*E^(2*x) + 4*a^2*(c + d*x)) - (3*b^2*d^(3/2)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[c + d*x])/Sqrt[d]])/E^((2*c)/d))/(24*d)","A",1
66,1,196,224,0.7966962,"\int \left(a+b e^x\right)^3 \sqrt{c+d x} \, dx","Integrate[(a + b*E^x)^3*Sqrt[c + d*x],x]","-\frac{108 \sqrt{\pi } a^2 b d^{3/2} e^{-\frac{c}{d}} \text{erfi}\left(\frac{\sqrt{c+d x}}{\sqrt{d}}\right)-12 \sqrt{c+d x} \left(4 a^3 (c+d x)+18 a^2 b d e^x+9 a b^2 d e^{2 x}+2 b^3 d e^{3 x}\right)+27 \sqrt{2 \pi } a b^2 d^{3/2} e^{-\frac{2 c}{d}} \text{erfi}\left(\frac{\sqrt{2} \sqrt{c+d x}}{\sqrt{d}}\right)+4 \sqrt{3 \pi } b^3 d^{3/2} e^{-\frac{3 c}{d}} \text{erfi}\left(\frac{\sqrt{3} \sqrt{c+d x}}{\sqrt{d}}\right)}{72 d}","\frac{2 a^3 (c+d x)^{3/2}}{3 d}-\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{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,"-1/72*(-12*Sqrt[c + d*x]*(18*a^2*b*d*E^x + 9*a*b^2*d*E^(2*x) + 2*b^3*d*E^(3*x) + 4*a^3*(c + d*x)) + (108*a^2*b*d^(3/2)*Sqrt[Pi]*Erfi[Sqrt[c + d*x]/Sqrt[d]])/E^(c/d) + (27*a*b^2*d^(3/2)*Sqrt[2*Pi]*Erfi[(Sqrt[2]*Sqrt[c + d*x])/Sqrt[d]])/E^((2*c)/d) + (4*b^3*d^(3/2)*Sqrt[3*Pi]*Erfi[(Sqrt[3]*Sqrt[c + d*x])/Sqrt[d]])/E^((3*c)/d))/d","A",1
67,0,0,22,0.6833091,"\int \frac{\sqrt{c+d x}}{a+b e^x} \, dx","Integrate[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,"Integrate[Sqrt[c + d*x]/(a + b*E^x), x]","A",-1
68,0,0,22,1.2653304,"\int \frac{\sqrt{c+d x}}{\left(a+b e^x\right)^2} \, dx","Integrate[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,"Integrate[Sqrt[c + d*x]/(a + b*E^x)^2, x]","A",-1
69,0,0,22,2.3645411,"\int \frac{\sqrt{c+d x}}{\left(a+b e^x\right)^3} \, dx","Integrate[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,"Integrate[Sqrt[c + d*x]/(a + b*E^x)^3, x]","A",-1
70,0,0,340,0.3355444,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)^m \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^m,x]","\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^3 (c+d x)^m \, dx","\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} \Gamma \left(m+1,-\frac{f g n (c+d x) \log (F)}{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} \Gamma \left(m+1,-\frac{2 f g n (c+d x) \log (F)}{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} \Gamma \left(m+1,-\frac{3 f g n (c+d x) \log (F)}{d}\right)}{f g n \log (F)}",1,"Integrate[(a + b*(F^(g*(e + f*x)))^n)^3*(c + d*x)^m, x]","F",-1
71,0,0,228,0.215025,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)^m \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)^m,x]","\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^2 (c+d x)^m \, dx","\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} \Gamma \left(m+1,-\frac{f g n (c+d x) \log (F)}{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} \Gamma \left(m+1,-\frac{2 f g n (c+d x) \log (F)}{d}\right)}{f g n \log (F)}",1,"Integrate[(a + b*(F^(g*(e + f*x)))^n)^2*(c + d*x)^m, x]","F",-1
72,0,0,116,0.1231273,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)^m \, dx","Integrate[(a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^m,x]","\int \left(a+b \left(F^{g (e+f x)}\right)^n\right) (c+d x)^m \, dx","\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} \Gamma \left(m+1,-\frac{f g n (c+d x) \log (F)}{d}\right)}{f g n \log (F)}",1,"Integrate[(a + b*(F^(g*(e + f*x)))^n)*(c + d*x)^m, x]","F",-1
73,0,0,29,0.1077772,"\int \frac{(c+d x)^m}{a+b \left(F^{g (e+f x)}\right)^n} \, dx","Integrate[(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,"Integrate[(c + d*x)^m/(a + b*(F^(g*(e + f*x)))^n), x]","A",-1
74,0,0,29,0.1368906,"\int \frac{(c+d x)^m}{\left(a+b \left(F^{g (e+f x)}\right)^n\right)^2} \, dx","Integrate[(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,"Integrate[(c + d*x)^m/(a + b*(F^(g*(e + f*x)))^n)^2, x]","A",-1
75,0,0,29,0.2870857,"\int \left(a+b \left(F^{g (e+f x)}\right)^n\right)^p (c+d x)^m \, dx","Integrate[(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,"Integrate[(a + b*(F^(g*(e + f*x)))^n)^p*(c + d*x)^m, x]","A",-1
76,1,115,115,0.0129428,"\int \frac{F^{c+d x} x^3}{a+b F^{c+d x}} \, dx","Integrate[(F^(c + d*x)*x^3)/(a + b*F^(c + d*x)),x]","\frac{6 \text{Li}_4\left(-\frac{b F^{c+d x}}{a}\right)}{b d^4 \log ^4(F)}-\frac{6 x \text{Li}_3\left(-\frac{b F^{c+d x}}{a}\right)}{b d^3 \log ^3(F)}+\frac{3 x^2 \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{b d^2 \log ^2(F)}+\frac{x^3 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{b d \log (F)}","\frac{6 \text{Li}_4\left(-\frac{b F^{c+d x}}{a}\right)}{b d^4 \log ^4(F)}-\frac{6 x \text{Li}_3\left(-\frac{b F^{c+d x}}{a}\right)}{b d^3 \log ^3(F)}+\frac{3 x^2 \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{b d^2 \log ^2(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",1
77,1,85,85,0.0091862,"\int \frac{F^{c+d x} x^2}{a+b F^{c+d x}} \, dx","Integrate[(F^(c + d*x)*x^2)/(a + b*F^(c + d*x)),x]","-\frac{2 \text{Li}_3\left(-\frac{b F^{c+d x}}{a}\right)}{b d^3 \log ^3(F)}+\frac{2 x \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{b d^2 \log ^2(F)}+\frac{x^2 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{b d \log (F)}","-\frac{2 \text{Li}_3\left(-\frac{b F^{c+d x}}{a}\right)}{b d^3 \log ^3(F)}+\frac{2 x \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{b d^2 \log ^2(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",1
78,1,54,54,0.0059696,"\int \frac{F^{c+d x} x}{a+b F^{c+d x}} \, dx","Integrate[(F^(c + d*x)*x)/(a + b*F^(c + d*x)),x]","\frac{\text{Li}_2\left(-\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{Li}_2\left(-\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",1
79,1,23,23,0.0074556,"\int \frac{F^{c+d x}}{a+b F^{c+d x}} \, dx","Integrate[F^(c + d*x)/(a + b*F^(c + d*x)),x]","\frac{\log \left(a+b F^{c+d x}\right)}{b d \log (F)}","\frac{\log \left(a+b F^{c+d x}\right)}{b d \log (F)}",1,"Log[a + b*F^(c + d*x)]/(b*d*Log[F])","A",1
80,0,0,27,0.0859041,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right) x} \, dx","Integrate[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,"Integrate[F^(c + d*x)/((a + b*F^(c + d*x))*x), x]","A",-1
81,0,0,27,0.0679268,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right) x^2} \, dx","Integrate[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,"Integrate[F^(c + d*x)/((a + b*F^(c + d*x))*x^2), x]","A",-1
82,1,137,140,0.1606981,"\int \frac{F^{c+d x} x^3}{\left(a+b F^{c+d x}\right)^2} \, dx","Integrate[(F^(c + d*x)*x^3)/(a + b*F^(c + d*x))^2,x]","\frac{3 \left(\frac{2 \text{Li}_3\left(-\frac{b F^{c+d x}}{a}\right)}{a d^3 \log ^3(F)}-\frac{2 x \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{a d^2 \log ^2(F)}-\frac{x^2 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{a d \log (F)}+\frac{x^3}{3 a}\right)}{b d \log (F)}-\frac{x^3}{b d \log (F) \left(a+b F^{c+d x}\right)}","\frac{6 \text{Li}_3\left(-\frac{b F^{c+d x}}{a}\right)}{a b d^4 \log ^4(F)}-\frac{6 x \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{a b d^3 \log ^3(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/(b*d*(a + b*F^(c + d*x))*Log[F])) + (3*(x^3/(3*a) - (x^2*Log[1 + (b*F^(c + d*x))/a])/(a*d*Log[F]) - (2*x*PolyLog[2, -((b*F^(c + d*x))/a)])/(a*d^2*Log[F]^2) + (2*PolyLog[3, -((b*F^(c + d*x))/a)])/(a*d^3*Log[F]^3)))/(b*d*Log[F])","A",1
83,1,103,107,0.0926007,"\int \frac{F^{c+d x} x^2}{\left(a+b F^{c+d x}\right)^2} \, dx","Integrate[(F^(c + d*x)*x^2)/(a + b*F^(c + d*x))^2,x]","\frac{d x \log (F) \left(b d x \log (F) F^{c+d x}-2 \left(a+b F^{c+d x}\right) \log \left(\frac{b F^{c+d x}}{a}+1\right)\right)-2 \left(a+b F^{c+d x}\right) \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{a b d^3 \log ^3(F) \left(a+b F^{c+d x}\right)}","-\frac{2 \text{Li}_2\left(-\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,"(d*x*Log[F]*(b*d*F^(c + d*x)*x*Log[F] - 2*(a + b*F^(c + d*x))*Log[1 + (b*F^(c + d*x))/a]) - 2*(a + b*F^(c + d*x))*PolyLog[2, -((b*F^(c + d*x))/a)])/(a*b*d^3*(a + b*F^(c + d*x))*Log[F]^3)","A",1
84,1,54,69,0.0705282,"\int \frac{F^{c+d x} x}{\left(a+b F^{c+d x}\right)^2} \, dx","Integrate[(F^(c + d*x)*x)/(a + b*F^(c + d*x))^2,x]","\frac{\frac{d x \log (F) F^{c+d x}}{a+b F^{c+d x}}-\frac{\log \left(a+b F^{c+d x}\right)}{b}}{a d^2 \log ^2(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,"((d*F^(c + d*x)*x*Log[F])/(a + b*F^(c + d*x)) - Log[a + b*F^(c + d*x)]/b)/(a*d^2*Log[F]^2)","A",1
85,1,25,25,0.0210188,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^2} \, dx","Integrate[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",1
86,0,0,61,0.1311824,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^2 x} \, dx","Integrate[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,"Integrate[F^(c + d*x)/((a + b*F^(c + d*x))^2*x), x]","A",-1
87,0,0,61,0.1608145,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^2 x^2} \, dx","Integrate[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,"Integrate[F^(c + d*x)/((a + b*F^(c + d*x))^2*x^2), x]","A",-1
88,1,220,261,0.3232175,"\int \frac{F^{c+d x} x^3}{\left(a+b F^{c+d x}\right)^3} \, dx","Integrate[(F^(c + d*x)*x^3)/(a + b*F^(c + d*x))^3,x]","\frac{d x \log (F) \left(b d^2 x^2 \log ^2(F) F^{c+d x} \left(2 a+b F^{c+d x}\right)+6 \left(a+b F^{c+d x}\right)^2 \log \left(\frac{b F^{c+d x}}{a}+1\right)-3 d x \log (F) \left(a+b F^{c+d x}\right) \left(\left(a+b F^{c+d x}\right) \log \left(\frac{b F^{c+d x}}{a}+1\right)+b F^{c+d x}\right)\right)+6 \left(a+b F^{c+d x}\right)^2 \text{Li}_3\left(-\frac{b F^{c+d x}}{a}\right)-6 (d x \log (F)-1) \left(a+b F^{c+d x}\right)^2 \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{2 a^2 b d^4 \log ^4(F) \left(a+b F^{c+d x}\right)^2}","\frac{3 \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^4 \log ^4(F)}+\frac{3 \text{Li}_3\left(-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^4 \log ^4(F)}-\frac{3 x \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^3 \log ^3(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 \log \left(\frac{b F^{c+d x}}{a}+1\right)}{2 a^2 b d^2 \log ^2(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,"(d*x*Log[F]*(b*d^2*F^(c + d*x)*(2*a + b*F^(c + d*x))*x^2*Log[F]^2 + 6*(a + b*F^(c + d*x))^2*Log[1 + (b*F^(c + d*x))/a] - 3*d*(a + b*F^(c + d*x))*x*Log[F]*(b*F^(c + d*x) + (a + b*F^(c + d*x))*Log[1 + (b*F^(c + d*x))/a])) - 6*(a + b*F^(c + d*x))^2*(-1 + d*x*Log[F])*PolyLog[2, -((b*F^(c + d*x))/a)] + 6*(a + b*F^(c + d*x))^2*PolyLog[3, -((b*F^(c + d*x))/a)])/(2*a^2*b*d^4*(a + b*F^(c + d*x))^2*Log[F]^4)","A",1
89,1,177,182,0.1659295,"\int \frac{F^{c+d x} x^2}{\left(a+b F^{c+d x}\right)^3} \, dx","Integrate[(F^(c + d*x)*x^2)/(a + b*F^(c + d*x))^3,x]","\frac{b d^2 x^2 \log ^2(F) F^{c+d x} \left(2 a+b F^{c+d x}\right)-2 \left(a+b F^{c+d x}\right)^2 \text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)+2 \left(a+b F^{c+d x}\right)^2 \log \left(\frac{b F^{c+d x}}{a}+1\right)-2 d x \log (F) \left(a+b F^{c+d x}\right) \left(\left(a+b F^{c+d x}\right) \log \left(\frac{b F^{c+d x}}{a}+1\right)+b F^{c+d x}\right)}{2 a^2 b d^3 \log ^3(F) \left(a+b F^{c+d x}\right)^2}","-\frac{\text{Li}_2\left(-\frac{b F^{c+d x}}{a}\right)}{a^2 b d^3 \log ^3(F)}+\frac{\log \left(a+b F^{c+d x}\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{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,"(b*d^2*F^(c + d*x)*(2*a + b*F^(c + d*x))*x^2*Log[F]^2 + 2*(a + b*F^(c + d*x))^2*Log[1 + (b*F^(c + d*x))/a] - 2*d*(a + b*F^(c + d*x))*x*Log[F]*(b*F^(c + d*x) + (a + b*F^(c + d*x))*Log[1 + (b*F^(c + d*x))/a]) - 2*(a + b*F^(c + d*x))^2*PolyLog[2, -((b*F^(c + d*x))/a)])/(2*a^2*b*d^3*(a + b*F^(c + d*x))^2*Log[F]^3)","A",1
90,1,98,106,0.0909146,"\int \frac{F^{c+d x} x}{\left(a+b F^{c+d x}\right)^3} \, dx","Integrate[(F^(c + d*x)*x)/(a + b*F^(c + d*x))^3,x]","\frac{b d x \log (F) F^{c+d x} \left(2 a+b F^{c+d x}\right)-\left(a+b F^{c+d x}\right) \left(\left(a+b F^{c+d x}\right) \log \left(a+b F^{c+d x}\right)-a\right)}{2 a^2 b d^2 \log ^2(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,"(b*d*F^(c + d*x)*(2*a + b*F^(c + d*x))*x*Log[F] - (a + b*F^(c + d*x))*(-a + (a + b*F^(c + d*x))*Log[a + b*F^(c + d*x)]))/(2*a^2*b*d^2*(a + b*F^(c + d*x))^2*Log[F]^2)","A",1
91,1,27,27,0.0274873,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^3} \, dx","Integrate[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*1/(b*d*(a + b*F^(c + d*x))^2*Log[F])","A",1
92,0,0,65,0.736224,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^3 x} \, dx","Integrate[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,"Integrate[F^(c + d*x)/((a + b*F^(c + d*x))^3*x), x]","A",-1
93,0,0,63,0.7756972,"\int \frac{F^{c+d x}}{\left(a+b F^{c+d x}\right)^3 x^2} \, dx","Integrate[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,"Integrate[F^(c + d*x)/((a + b*F^(c + d*x))^3*x^2), x]","A",-1