1,1,120,0,0.658884," ","integrate(x^3/(a+b*exp(d*x+c)),x, algorithm=""fricas"")","\frac{d^{4} x^{4} - 12 \, d^{2} x^{2} {\rm Li}_2\left(-\frac{b e^{\left(d x + c\right)} + a}{a} + 1\right) + 4 \, c^{3} \log\left(b e^{\left(d x + c\right)} + a\right) + 24 \, d x {\rm polylog}\left(3, -\frac{b e^{\left(d x + c\right)}}{a}\right) - 4 \, {\left(d^{3} x^{3} + c^{3}\right)} \log\left(\frac{b e^{\left(d x + c\right)} + a}{a}\right) - 24 \, {\rm polylog}\left(4, -\frac{b e^{\left(d x + c\right)}}{a}\right)}{4 \, a d^{4}}"," ",0,"1/4*(d^4*x^4 - 12*d^2*x^2*dilog(-(b*e^(d*x + c) + a)/a + 1) + 4*c^3*log(b*e^(d*x + c) + a) + 24*d*x*polylog(3, -b*e^(d*x + c)/a) - 4*(d^3*x^3 + c^3)*log((b*e^(d*x + c) + a)/a) - 24*polylog(4, -b*e^(d*x + c)/a))/(a*d^4)","C",0
2,1,100,0,0.602662," ","integrate(x^2/(a+b*exp(d*x+c)),x, algorithm=""fricas"")","\frac{d^{3} x^{3} - 6 \, d x {\rm Li}_2\left(-\frac{b e^{\left(d x + c\right)} + a}{a} + 1\right) - 3 \, c^{2} \log\left(b e^{\left(d x + c\right)} + a\right) - 3 \, {\left(d^{2} x^{2} - c^{2}\right)} \log\left(\frac{b e^{\left(d x + c\right)} + a}{a}\right) + 6 \, {\rm polylog}\left(3, -\frac{b e^{\left(d x + c\right)}}{a}\right)}{3 \, a d^{3}}"," ",0,"1/3*(d^3*x^3 - 6*d*x*dilog(-(b*e^(d*x + c) + a)/a + 1) - 3*c^2*log(b*e^(d*x + c) + a) - 3*(d^2*x^2 - c^2)*log((b*e^(d*x + c) + a)/a) + 6*polylog(3, -b*e^(d*x + c)/a))/(a*d^3)","C",0
3,1,72,0,0.632513," ","integrate(x/(a+b*exp(d*x+c)),x, algorithm=""fricas"")","\frac{d^{2} x^{2} + 2 \, c \log\left(b e^{\left(d x + c\right)} + a\right) - 2 \, {\left(d x + c\right)} \log\left(\frac{b e^{\left(d x + c\right)} + a}{a}\right) - 2 \, {\rm Li}_2\left(-\frac{b e^{\left(d x + c\right)} + a}{a} + 1\right)}{2 \, a d^{2}}"," ",0,"1/2*(d^2*x^2 + 2*c*log(b*e^(d*x + c) + a) - 2*(d*x + c)*log((b*e^(d*x + c) + a)/a) - 2*dilog(-(b*e^(d*x + c) + a)/a + 1))/(a*d^2)","A",0
4,1,24,0,0.716283," ","integrate(1/(a+b*exp(d*x+c)),x, algorithm=""fricas"")","\frac{d x - \log\left(b e^{\left(d x + c\right)} + a\right)}{a d}"," ",0,"(d*x - log(b*e^(d*x + c) + a))/(a*d)","A",0
5,0,0,0,0.576658," ","integrate(1/(a+b*exp(d*x+c))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x e^{\left(d x + c\right)} + a x}, x\right)"," ",0,"integral(1/(b*x*e^(d*x + c) + a*x), x)","F",0
6,0,0,0,0.566227," ","integrate(1/(a+b*exp(d*x+c))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b x^{2} e^{\left(d x + c\right)} + a x^{2}}, x\right)"," ",0,"integral(1/(b*x^2*e^(d*x + c) + a*x^2), x)","F",0
7,1,23,0,0.601105," ","integrate(1/(a+b*exp(-d*x+c)),x, algorithm=""fricas"")","\frac{d x + \log\left(b e^{\left(-d x + c\right)} + a\right)}{a d}"," ",0,"(d*x + log(b*e^(-d*x + c) + a))/(a*d)","A",0
8,1,25,0,0.789896," ","integrate(1/(a+b*exp(-d*x-c)),x, algorithm=""fricas"")","\frac{d x + \log\left(b e^{\left(-d x - c\right)} + a\right)}{a d}"," ",0,"(d*x + log(b*e^(-d*x - c) + a))/(a*d)","A",0
9,1,330,0,0.555493," ","integrate(x^3/(a+b*exp(d*x+c))^2,x, algorithm=""fricas"")","\frac{a d^{4} x^{4} - a c^{4} - 4 \, a c^{3} - 12 \, {\left(a d^{2} x^{2} - 2 \, a d x + {\left(b d^{2} x^{2} - 2 \, b d x\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-\frac{b e^{\left(d x + c\right)} + a}{a} + 1\right) + {\left(b d^{4} x^{4} - 4 \, b d^{3} x^{3} - b c^{4} - 4 \, b c^{3}\right)} e^{\left(d x + c\right)} + 4 \, {\left(a c^{3} + 3 \, a c^{2} + {\left(b c^{3} + 3 \, b c^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(b e^{\left(d x + c\right)} + a\right) - 4 \, {\left(a d^{3} x^{3} - 3 \, a d^{2} x^{2} + a c^{3} + 3 \, a c^{2} + {\left(b d^{3} x^{3} - 3 \, b d^{2} x^{2} + b c^{3} + 3 \, b c^{2}\right)} e^{\left(d x + c\right)}\right)} \log\left(\frac{b e^{\left(d x + c\right)} + a}{a}\right) - 24 \, {\left(b e^{\left(d x + c\right)} + a\right)} {\rm polylog}\left(4, -\frac{b e^{\left(d x + c\right)}}{a}\right) + 24 \, {\left(a d x + {\left(b d x - b\right)} e^{\left(d x + c\right)} - a\right)} {\rm polylog}\left(3, -\frac{b e^{\left(d x + c\right)}}{a}\right)}{4 \, {\left(a^{2} b d^{4} e^{\left(d x + c\right)} + a^{3} d^{4}\right)}}"," ",0,"1/4*(a*d^4*x^4 - a*c^4 - 4*a*c^3 - 12*(a*d^2*x^2 - 2*a*d*x + (b*d^2*x^2 - 2*b*d*x)*e^(d*x + c))*dilog(-(b*e^(d*x + c) + a)/a + 1) + (b*d^4*x^4 - 4*b*d^3*x^3 - b*c^4 - 4*b*c^3)*e^(d*x + c) + 4*(a*c^3 + 3*a*c^2 + (b*c^3 + 3*b*c^2)*e^(d*x + c))*log(b*e^(d*x + c) + a) - 4*(a*d^3*x^3 - 3*a*d^2*x^2 + a*c^3 + 3*a*c^2 + (b*d^3*x^3 - 3*b*d^2*x^2 + b*c^3 + 3*b*c^2)*e^(d*x + c))*log((b*e^(d*x + c) + a)/a) - 24*(b*e^(d*x + c) + a)*polylog(4, -b*e^(d*x + c)/a) + 24*(a*d*x + (b*d*x - b)*e^(d*x + c) - a)*polylog(3, -b*e^(d*x + c)/a))/(a^2*b*d^4*e^(d*x + c) + a^3*d^4)","C",0
10,1,263,0,0.669994," ","integrate(x^2/(a+b*exp(d*x+c))^2,x, algorithm=""fricas"")","\frac{a d^{3} x^{3} + a c^{3} + 3 \, a c^{2} - 6 \, {\left(a d x + {\left(b d x - b\right)} e^{\left(d x + c\right)} - a\right)} {\rm Li}_2\left(-\frac{b e^{\left(d x + c\right)} + a}{a} + 1\right) + {\left(b d^{3} x^{3} - 3 \, b d^{2} x^{2} + b c^{3} + 3 \, b c^{2}\right)} e^{\left(d x + c\right)} - 3 \, {\left(a c^{2} + 2 \, a c + {\left(b c^{2} + 2 \, b c\right)} e^{\left(d x + c\right)}\right)} \log\left(b e^{\left(d x + c\right)} + a\right) - 3 \, {\left(a d^{2} x^{2} - a c^{2} - 2 \, a d x - 2 \, a c + {\left(b d^{2} x^{2} - b c^{2} - 2 \, b d x - 2 \, b c\right)} e^{\left(d x + c\right)}\right)} \log\left(\frac{b e^{\left(d x + c\right)} + a}{a}\right) + 6 \, {\left(b e^{\left(d x + c\right)} + a\right)} {\rm polylog}\left(3, -\frac{b e^{\left(d x + c\right)}}{a}\right)}{3 \, {\left(a^{2} b d^{3} e^{\left(d x + c\right)} + a^{3} d^{3}\right)}}"," ",0,"1/3*(a*d^3*x^3 + a*c^3 + 3*a*c^2 - 6*(a*d*x + (b*d*x - b)*e^(d*x + c) - a)*dilog(-(b*e^(d*x + c) + a)/a + 1) + (b*d^3*x^3 - 3*b*d^2*x^2 + b*c^3 + 3*b*c^2)*e^(d*x + c) - 3*(a*c^2 + 2*a*c + (b*c^2 + 2*b*c)*e^(d*x + c))*log(b*e^(d*x + c) + a) - 3*(a*d^2*x^2 - a*c^2 - 2*a*d*x - 2*a*c + (b*d^2*x^2 - b*c^2 - 2*b*d*x - 2*b*c)*e^(d*x + c))*log((b*e^(d*x + c) + a)/a) + 6*(b*e^(d*x + c) + a)*polylog(3, -b*e^(d*x + c)/a))/(a^2*b*d^3*e^(d*x + c) + a^3*d^3)","C",0
11,1,176,0,0.534854," ","integrate(x/(a+b*exp(d*x+c))^2,x, algorithm=""fricas"")","\frac{a d^{2} x^{2} - a c^{2} - 2 \, a c - 2 \, {\left(b e^{\left(d x + c\right)} + a\right)} {\rm Li}_2\left(-\frac{b e^{\left(d x + c\right)} + a}{a} + 1\right) + {\left(b d^{2} x^{2} - b c^{2} - 2 \, b d x - 2 \, b c\right)} e^{\left(d x + c\right)} + 2 \, {\left(a c + {\left(b c + b\right)} e^{\left(d x + c\right)} + a\right)} \log\left(b e^{\left(d x + c\right)} + a\right) - 2 \, {\left(a d x + a c + {\left(b d x + b c\right)} e^{\left(d x + c\right)}\right)} \log\left(\frac{b e^{\left(d x + c\right)} + a}{a}\right)}{2 \, {\left(a^{2} b d^{2} e^{\left(d x + c\right)} + a^{3} d^{2}\right)}}"," ",0,"1/2*(a*d^2*x^2 - a*c^2 - 2*a*c - 2*(b*e^(d*x + c) + a)*dilog(-(b*e^(d*x + c) + a)/a + 1) + (b*d^2*x^2 - b*c^2 - 2*b*d*x - 2*b*c)*e^(d*x + c) + 2*(a*c + (b*c + b)*e^(d*x + c) + a)*log(b*e^(d*x + c) + a) - 2*(a*d*x + a*c + (b*d*x + b*c)*e^(d*x + c))*log((b*e^(d*x + c) + a)/a))/(a^2*b*d^2*e^(d*x + c) + a^3*d^2)","A",0
12,1,60,0,0.815597," ","integrate(1/(a+b*exp(d*x+c))^2,x, algorithm=""fricas"")","\frac{b d x e^{\left(d x + c\right)} + a d x - {\left(b e^{\left(d x + c\right)} + a\right)} \log\left(b e^{\left(d x + c\right)} + a\right) + a}{a^{2} b d e^{\left(d x + c\right)} + a^{3} d}"," ",0,"(b*d*x*e^(d*x + c) + a*d*x - (b*e^(d*x + c) + a)*log(b*e^(d*x + c) + a) + a)/(a^2*b*d*e^(d*x + c) + a^3*d)","A",0
13,0,0,0,0.658524," ","integrate(1/(a+b*exp(d*x+c))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a b x e^{\left(d x + c\right)} + a^{2} x}, x\right)"," ",0,"integral(1/(b^2*x*e^(2*d*x + 2*c) + 2*a*b*x*e^(d*x + c) + a^2*x), x)","F",0
14,0,0,0,0.750729," ","integrate(1/(a+b*exp(d*x+c))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} x^{2} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a b x^{2} e^{\left(d x + c\right)} + a^{2} x^{2}}, x\right)"," ",0,"integral(1/(b^2*x^2*e^(2*d*x + 2*c) + 2*a*b*x^2*e^(d*x + c) + a^2*x^2), x)","F",0
15,1,65,0,0.528225," ","integrate(1/(a+b*exp(-d*x+c))^2,x, algorithm=""fricas"")","\frac{b d x e^{\left(-d x + c\right)} + a d x + {\left(b e^{\left(-d x + c\right)} + a\right)} \log\left(b e^{\left(-d x + c\right)} + a\right) - a}{a^{2} b d e^{\left(-d x + c\right)} + a^{3} d}"," ",0,"(b*d*x*e^(-d*x + c) + a*d*x + (b*e^(-d*x + c) + a)*log(b*e^(-d*x + c) + a) - a)/(a^2*b*d*e^(-d*x + c) + a^3*d)","A",0
16,1,73,0,0.544268," ","integrate(1/(a+b*exp(-d*x-c))^2,x, algorithm=""fricas"")","\frac{b d x e^{\left(-d x - c\right)} + a d x + {\left(b e^{\left(-d x - c\right)} + a\right)} \log\left(b e^{\left(-d x - c\right)} + a\right) - a}{a^{2} b d e^{\left(-d x - c\right)} + a^{3} d}"," ",0,"(b*d*x*e^(-d*x - c) + a*d*x + (b*e^(-d*x - c) + a)*log(b*e^(-d*x - c) + a) - a)/(a^2*b*d*e^(-d*x - c) + a^3*d)","A",0
17,1,702,0,0.861334," ","integrate(x^3/(a+b*exp(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{2} d^{4} x^{4} - a^{2} c^{4} - 6 \, a^{2} c^{3} - 6 \, a^{2} c^{2} - 12 \, {\left(a^{2} d^{2} x^{2} - 3 \, a^{2} d x + a^{2} + {\left(b^{2} d^{2} x^{2} - 3 \, b^{2} d x + b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(a b d^{2} x^{2} - 3 \, a b d x + a b\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-\frac{b e^{\left(d x + c\right)} + a}{a} + 1\right) + {\left(b^{2} d^{4} x^{4} - 6 \, b^{2} d^{3} x^{3} - b^{2} c^{4} + 6 \, b^{2} d^{2} x^{2} - 6 \, b^{2} c^{3} - 6 \, b^{2} c^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(a b d^{4} x^{4} - 4 \, a b d^{3} x^{3} - a b c^{4} + 3 \, a b d^{2} x^{2} - 6 \, a b c^{3} - 6 \, a b c^{2}\right)} e^{\left(d x + c\right)} + 2 \, {\left(2 \, a^{2} c^{3} + 9 \, a^{2} c^{2} + 6 \, a^{2} c + {\left(2 \, b^{2} c^{3} + 9 \, b^{2} c^{2} + 6 \, b^{2} c\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(2 \, a b c^{3} + 9 \, a b c^{2} + 6 \, a b c\right)} e^{\left(d x + c\right)}\right)} \log\left(b e^{\left(d x + c\right)} + a\right) - 2 \, {\left(2 \, a^{2} d^{3} x^{3} - 9 \, a^{2} d^{2} x^{2} + 2 \, a^{2} c^{3} + 9 \, a^{2} c^{2} + 6 \, a^{2} d x + 6 \, a^{2} c + {\left(2 \, b^{2} d^{3} x^{3} - 9 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{3} + 9 \, b^{2} c^{2} + 6 \, b^{2} d x + 6 \, b^{2} c\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(2 \, a b d^{3} x^{3} - 9 \, a b d^{2} x^{2} + 2 \, a b c^{3} + 9 \, a b c^{2} + 6 \, a b d x + 6 \, a b c\right)} e^{\left(d x + c\right)}\right)} \log\left(\frac{b e^{\left(d x + c\right)} + a}{a}\right) - 24 \, {\left(b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a b e^{\left(d x + c\right)} + a^{2}\right)} {\rm polylog}\left(4, -\frac{b e^{\left(d x + c\right)}}{a}\right) + 12 \, {\left(2 \, a^{2} d x - 3 \, a^{2} + {\left(2 \, b^{2} d x - 3 \, b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(2 \, a b d x - 3 \, a b\right)} e^{\left(d x + c\right)}\right)} {\rm polylog}\left(3, -\frac{b e^{\left(d x + c\right)}}{a}\right)}{4 \, {\left(a^{3} b^{2} d^{4} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a^{4} b d^{4} e^{\left(d x + c\right)} + a^{5} d^{4}\right)}}"," ",0,"1/4*(a^2*d^4*x^4 - a^2*c^4 - 6*a^2*c^3 - 6*a^2*c^2 - 12*(a^2*d^2*x^2 - 3*a^2*d*x + a^2 + (b^2*d^2*x^2 - 3*b^2*d*x + b^2)*e^(2*d*x + 2*c) + 2*(a*b*d^2*x^2 - 3*a*b*d*x + a*b)*e^(d*x + c))*dilog(-(b*e^(d*x + c) + a)/a + 1) + (b^2*d^4*x^4 - 6*b^2*d^3*x^3 - b^2*c^4 + 6*b^2*d^2*x^2 - 6*b^2*c^3 - 6*b^2*c^2)*e^(2*d*x + 2*c) + 2*(a*b*d^4*x^4 - 4*a*b*d^3*x^3 - a*b*c^4 + 3*a*b*d^2*x^2 - 6*a*b*c^3 - 6*a*b*c^2)*e^(d*x + c) + 2*(2*a^2*c^3 + 9*a^2*c^2 + 6*a^2*c + (2*b^2*c^3 + 9*b^2*c^2 + 6*b^2*c)*e^(2*d*x + 2*c) + 2*(2*a*b*c^3 + 9*a*b*c^2 + 6*a*b*c)*e^(d*x + c))*log(b*e^(d*x + c) + a) - 2*(2*a^2*d^3*x^3 - 9*a^2*d^2*x^2 + 2*a^2*c^3 + 9*a^2*c^2 + 6*a^2*d*x + 6*a^2*c + (2*b^2*d^3*x^3 - 9*b^2*d^2*x^2 + 2*b^2*c^3 + 9*b^2*c^2 + 6*b^2*d*x + 6*b^2*c)*e^(2*d*x + 2*c) + 2*(2*a*b*d^3*x^3 - 9*a*b*d^2*x^2 + 2*a*b*c^3 + 9*a*b*c^2 + 6*a*b*d*x + 6*a*b*c)*e^(d*x + c))*log((b*e^(d*x + c) + a)/a) - 24*(b^2*e^(2*d*x + 2*c) + 2*a*b*e^(d*x + c) + a^2)*polylog(4, -b*e^(d*x + c)/a) + 12*(2*a^2*d*x - 3*a^2 + (2*b^2*d*x - 3*b^2)*e^(2*d*x + 2*c) + 2*(2*a*b*d*x - 3*a*b)*e^(d*x + c))*polylog(3, -b*e^(d*x + c)/a))/(a^3*b^2*d^4*e^(2*d*x + 2*c) + 2*a^4*b*d^4*e^(d*x + c) + a^5*d^4)","C",0
18,1,521,0,0.821281," ","integrate(x^2/(a+b*exp(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, a^{2} d^{3} x^{3} + 2 \, a^{2} c^{3} + 9 \, a^{2} c^{2} + 6 \, a^{2} c - 6 \, {\left(2 \, a^{2} d x - 3 \, a^{2} + {\left(2 \, b^{2} d x - 3 \, b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(2 \, a b d x - 3 \, a b\right)} e^{\left(d x + c\right)}\right)} {\rm Li}_2\left(-\frac{b e^{\left(d x + c\right)} + a}{a} + 1\right) + {\left(2 \, b^{2} d^{3} x^{3} - 9 \, b^{2} d^{2} x^{2} + 2 \, b^{2} c^{3} + 9 \, b^{2} c^{2} + 6 \, b^{2} d x + 6 \, b^{2} c\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(2 \, a b d^{3} x^{3} - 6 \, a b d^{2} x^{2} + 2 \, a b c^{3} + 9 \, a b c^{2} + 3 \, a b d x + 6 \, a b c\right)} e^{\left(d x + c\right)} - 6 \, {\left(a^{2} c^{2} + 3 \, a^{2} c + a^{2} + {\left(b^{2} c^{2} + 3 \, b^{2} c + b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(a b c^{2} + 3 \, a b c + a b\right)} e^{\left(d x + c\right)}\right)} \log\left(b e^{\left(d x + c\right)} + a\right) - 6 \, {\left(a^{2} d^{2} x^{2} - a^{2} c^{2} - 3 \, a^{2} d x - 3 \, a^{2} c + {\left(b^{2} d^{2} x^{2} - b^{2} c^{2} - 3 \, b^{2} d x - 3 \, b^{2} c\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(a b d^{2} x^{2} - a b c^{2} - 3 \, a b d x - 3 \, a b c\right)} e^{\left(d x + c\right)}\right)} \log\left(\frac{b e^{\left(d x + c\right)} + a}{a}\right) + 12 \, {\left(b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a b e^{\left(d x + c\right)} + a^{2}\right)} {\rm polylog}\left(3, -\frac{b e^{\left(d x + c\right)}}{a}\right)}{6 \, {\left(a^{3} b^{2} d^{3} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a^{4} b d^{3} e^{\left(d x + c\right)} + a^{5} d^{3}\right)}}"," ",0,"1/6*(2*a^2*d^3*x^3 + 2*a^2*c^3 + 9*a^2*c^2 + 6*a^2*c - 6*(2*a^2*d*x - 3*a^2 + (2*b^2*d*x - 3*b^2)*e^(2*d*x + 2*c) + 2*(2*a*b*d*x - 3*a*b)*e^(d*x + c))*dilog(-(b*e^(d*x + c) + a)/a + 1) + (2*b^2*d^3*x^3 - 9*b^2*d^2*x^2 + 2*b^2*c^3 + 9*b^2*c^2 + 6*b^2*d*x + 6*b^2*c)*e^(2*d*x + 2*c) + 2*(2*a*b*d^3*x^3 - 6*a*b*d^2*x^2 + 2*a*b*c^3 + 9*a*b*c^2 + 3*a*b*d*x + 6*a*b*c)*e^(d*x + c) - 6*(a^2*c^2 + 3*a^2*c + a^2 + (b^2*c^2 + 3*b^2*c + b^2)*e^(2*d*x + 2*c) + 2*(a*b*c^2 + 3*a*b*c + a*b)*e^(d*x + c))*log(b*e^(d*x + c) + a) - 6*(a^2*d^2*x^2 - a^2*c^2 - 3*a^2*d*x - 3*a^2*c + (b^2*d^2*x^2 - b^2*c^2 - 3*b^2*d*x - 3*b^2*c)*e^(2*d*x + 2*c) + 2*(a*b*d^2*x^2 - a*b*c^2 - 3*a*b*d*x - 3*a*b*c)*e^(d*x + c))*log((b*e^(d*x + c) + a)/a) + 12*(b^2*e^(2*d*x + 2*c) + 2*a*b*e^(d*x + c) + a^2)*polylog(3, -b*e^(d*x + c)/a))/(a^3*b^2*d^3*e^(2*d*x + 2*c) + 2*a^4*b*d^3*e^(d*x + c) + a^5*d^3)","C",0
19,1,338,0,0.736067," ","integrate(x/(a+b*exp(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{2} d^{2} x^{2} - a^{2} c^{2} - 3 \, a^{2} c - a^{2} - 2 \, {\left(b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a b e^{\left(d x + c\right)} + a^{2}\right)} {\rm Li}_2\left(-\frac{b e^{\left(d x + c\right)} + a}{a} + 1\right) + {\left(b^{2} d^{2} x^{2} - b^{2} c^{2} - 3 \, b^{2} d x - 3 \, b^{2} c\right)} e^{\left(2 \, d x + 2 \, c\right)} + {\left(2 \, a b d^{2} x^{2} - 2 \, a b c^{2} - 4 \, a b d x - 6 \, a b c - a b\right)} e^{\left(d x + c\right)} + {\left(2 \, a^{2} c + 3 \, a^{2} + {\left(2 \, b^{2} c + 3 \, b^{2}\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(2 \, a b c + 3 \, a b\right)} e^{\left(d x + c\right)}\right)} \log\left(b e^{\left(d x + c\right)} + a\right) - 2 \, {\left(a^{2} d x + a^{2} c + {\left(b^{2} d x + b^{2} c\right)} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, {\left(a b d x + a b c\right)} e^{\left(d x + c\right)}\right)} \log\left(\frac{b e^{\left(d x + c\right)} + a}{a}\right)}{2 \, {\left(a^{3} b^{2} d^{2} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a^{4} b d^{2} e^{\left(d x + c\right)} + a^{5} d^{2}\right)}}"," ",0,"1/2*(a^2*d^2*x^2 - a^2*c^2 - 3*a^2*c - a^2 - 2*(b^2*e^(2*d*x + 2*c) + 2*a*b*e^(d*x + c) + a^2)*dilog(-(b*e^(d*x + c) + a)/a + 1) + (b^2*d^2*x^2 - b^2*c^2 - 3*b^2*d*x - 3*b^2*c)*e^(2*d*x + 2*c) + (2*a*b*d^2*x^2 - 2*a*b*c^2 - 4*a*b*d*x - 6*a*b*c - a*b)*e^(d*x + c) + (2*a^2*c + 3*a^2 + (2*b^2*c + 3*b^2)*e^(2*d*x + 2*c) + 2*(2*a*b*c + 3*a*b)*e^(d*x + c))*log(b*e^(d*x + c) + a) - 2*(a^2*d*x + a^2*c + (b^2*d*x + b^2*c)*e^(2*d*x + 2*c) + 2*(a*b*d*x + a*b*c)*e^(d*x + c))*log((b*e^(d*x + c) + a)/a))/(a^3*b^2*d^2*e^(2*d*x + 2*c) + 2*a^4*b*d^2*e^(d*x + c) + a^5*d^2)","B",0
20,1,127,0,0.530473," ","integrate(1/(a+b*exp(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} d x e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a^{2} d x + 3 \, a^{2} + 2 \, {\left(2 \, a b d x + a b\right)} e^{\left(d x + c\right)} - 2 \, {\left(b^{2} e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a b e^{\left(d x + c\right)} + a^{2}\right)} \log\left(b e^{\left(d x + c\right)} + a\right)}{2 \, {\left(a^{3} b^{2} d e^{\left(2 \, d x + 2 \, c\right)} + 2 \, a^{4} b d e^{\left(d x + c\right)} + a^{5} d\right)}}"," ",0,"1/2*(2*b^2*d*x*e^(2*d*x + 2*c) + 2*a^2*d*x + 3*a^2 + 2*(2*a*b*d*x + a*b)*e^(d*x + c) - 2*(b^2*e^(2*d*x + 2*c) + 2*a*b*e^(d*x + c) + a^2)*log(b*e^(d*x + c) + a))/(a^3*b^2*d*e^(2*d*x + 2*c) + 2*a^4*b*d*e^(d*x + c) + a^5*d)","A",0
21,0,0,0,0.510373," ","integrate(1/(a+b*exp(d*x+c))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x e^{\left(3 \, d x + 3 \, c\right)} + 3 \, a b^{2} x e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a^{2} b x e^{\left(d x + c\right)} + a^{3} x}, x\right)"," ",0,"integral(1/(b^3*x*e^(3*d*x + 3*c) + 3*a*b^2*x*e^(2*d*x + 2*c) + 3*a^2*b*x*e^(d*x + c) + a^3*x), x)","F",0
22,0,0,0,0.524571," ","integrate(1/(a+b*exp(d*x+c))^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} x^{2} e^{\left(3 \, d x + 3 \, c\right)} + 3 \, a b^{2} x^{2} e^{\left(2 \, d x + 2 \, c\right)} + 3 \, a^{2} b x^{2} e^{\left(d x + c\right)} + a^{3} x^{2}}, x\right)"," ",0,"integral(1/(b^3*x^2*e^(3*d*x + 3*c) + 3*a*b^2*x^2*e^(2*d*x + 2*c) + 3*a^2*b*x^2*e^(d*x + c) + a^3*x^2), x)","F",0
23,1,132,0,0.592349," ","integrate(1/(a+b*exp(-d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} d x e^{\left(-2 \, d x + 2 \, c\right)} + 2 \, a^{2} d x - 3 \, a^{2} + 2 \, {\left(2 \, a b d x - a b\right)} e^{\left(-d x + c\right)} + 2 \, {\left(2 \, a b e^{\left(-d x + c\right)} + b^{2} e^{\left(-2 \, d x + 2 \, c\right)} + a^{2}\right)} \log\left(b e^{\left(-d x + c\right)} + a\right)}{2 \, {\left(2 \, a^{4} b d e^{\left(-d x + c\right)} + a^{3} b^{2} d e^{\left(-2 \, d x + 2 \, c\right)} + a^{5} d\right)}}"," ",0,"1/2*(2*b^2*d*x*e^(-2*d*x + 2*c) + 2*a^2*d*x - 3*a^2 + 2*(2*a*b*d*x - a*b)*e^(-d*x + c) + 2*(2*a*b*e^(-d*x + c) + b^2*e^(-2*d*x + 2*c) + a^2)*log(b*e^(-d*x + c) + a))/(2*a^4*b*d*e^(-d*x + c) + a^3*b^2*d*e^(-2*d*x + 2*c) + a^5*d)","A",0
24,1,140,0,0.734116," ","integrate(1/(a+b*exp(-d*x-c))^3,x, algorithm=""fricas"")","\frac{2 \, b^{2} d x e^{\left(-2 \, d x - 2 \, c\right)} + 2 \, a^{2} d x - 3 \, a^{2} + 2 \, {\left(2 \, a b d x - a b\right)} e^{\left(-d x - c\right)} + 2 \, {\left(2 \, a b e^{\left(-d x - c\right)} + b^{2} e^{\left(-2 \, d x - 2 \, c\right)} + a^{2}\right)} \log\left(b e^{\left(-d x - c\right)} + a\right)}{2 \, {\left(2 \, a^{4} b d e^{\left(-d x - c\right)} + a^{3} b^{2} d e^{\left(-2 \, d x - 2 \, c\right)} + a^{5} d\right)}}"," ",0,"1/2*(2*b^2*d*x*e^(-2*d*x - 2*c) + 2*a^2*d*x - 3*a^2 + 2*(2*a*b*d*x - a*b)*e^(-d*x - c) + 2*(2*a*b*e^(-d*x - c) + b^2*e^(-2*d*x - 2*c) + a^2)*log(b*e^(-d*x - c) + a))/(2*a^4*b*d*e^(-d*x - c) + a^3*b^2*d*e^(-2*d*x - 2*c) + a^5*d)","A",0
25,1,267,0,0.645929," ","integrate((a+b*(F^(g*(f*x+e)))^n)*(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(a d^{3} f^{4} g^{4} n^{4} x^{4} + 4 \, a c d^{2} f^{4} g^{4} n^{4} x^{3} + 6 \, a c^{2} d f^{4} g^{4} n^{4} x^{2} + 4 \, a c^{3} f^{4} g^{4} n^{4} x\right)} \log\left(F\right)^{4} - 4 \, {\left(6 \, b d^{3} - {\left(b d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, b c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, b c^{2} d f^{3} g^{3} n^{3} x + b c^{3} f^{3} g^{3} n^{3}\right)} \log\left(F\right)^{3} + 3 \, {\left(b d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, b c d^{2} f^{2} g^{2} n^{2} x + b c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 6 \, {\left(b d^{3} f g n x + b c d^{2} f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{4 \, f^{4} g^{4} n^{4} \log\left(F\right)^{4}}"," ",0,"1/4*((a*d^3*f^4*g^4*n^4*x^4 + 4*a*c*d^2*f^4*g^4*n^4*x^3 + 6*a*c^2*d*f^4*g^4*n^4*x^2 + 4*a*c^3*f^4*g^4*n^4*x)*log(F)^4 - 4*(6*b*d^3 - (b*d^3*f^3*g^3*n^3*x^3 + 3*b*c*d^2*f^3*g^3*n^3*x^2 + 3*b*c^2*d*f^3*g^3*n^3*x + b*c^3*f^3*g^3*n^3)*log(F)^3 + 3*(b*d^3*f^2*g^2*n^2*x^2 + 2*b*c*d^2*f^2*g^2*n^2*x + b*c^2*d*f^2*g^2*n^2)*log(F)^2 - 6*(b*d^3*f*g*n*x + b*c*d^2*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(f^4*g^4*n^4*log(F)^4)","A",0
26,1,166,0,0.490481," ","integrate((a+b*(F^(g*(f*x+e)))^n)*(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(a d^{2} f^{3} g^{3} n^{3} x^{3} + 3 \, a c d f^{3} g^{3} n^{3} x^{2} + 3 \, a c^{2} f^{3} g^{3} n^{3} x\right)} \log\left(F\right)^{3} + 3 \, {\left(2 \, b d^{2} + {\left(b d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, b c d f^{2} g^{2} n^{2} x + b c^{2} f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(b d^{2} f g n x + b c d f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{3 \, f^{3} g^{3} n^{3} \log\left(F\right)^{3}}"," ",0,"1/3*((a*d^2*f^3*g^3*n^3*x^3 + 3*a*c*d*f^3*g^3*n^3*x^2 + 3*a*c^2*f^3*g^3*n^3*x)*log(F)^3 + 3*(2*b*d^2 + (b*d^2*f^2*g^2*n^2*x^2 + 2*b*c*d*f^2*g^2*n^2*x + b*c^2*f^2*g^2*n^2)*log(F)^2 - 2*(b*d^2*f*g*n*x + b*c*d*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(f^3*g^3*n^3*log(F)^3)","A",0
27,1,87,0,0.613482," ","integrate((a+b*(F^(g*(f*x+e)))^n)*(d*x+c),x, algorithm=""fricas"")","\frac{{\left(a d f^{2} g^{2} n^{2} x^{2} + 2 \, a c f^{2} g^{2} n^{2} x\right)} \log\left(F\right)^{2} - 2 \, {\left(b d - {\left(b d f g n x + b c f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{2 \, f^{2} g^{2} n^{2} \log\left(F\right)^{2}}"," ",0,"1/2*((a*d*f^2*g^2*n^2*x^2 + 2*a*c*f^2*g^2*n^2*x)*log(F)^2 - 2*(b*d - (b*d*f*g*n*x + b*c*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(f^2*g^2*n^2*log(F)^2)","A",0
28,1,37,0,0.417620," ","integrate(a+b*(F^(g*(f*x+e)))^n,x, algorithm=""fricas"")","\frac{a f g n x \log\left(F\right) + F^{f g n x + e g n} b}{f g n \log\left(F\right)}"," ",0,"(a*f*g*n*x*log(F) + F^(f*g*n*x + e*g*n)*b)/(f*g*n*log(F))","A",0
29,1,50,0,0.431991," ","integrate((a+b*(F^(g*(f*x+e)))^n)/(d*x+c),x, algorithm=""fricas"")","\frac{F^{\frac{{\left(d e - c f\right)} g n}{d}} b {\rm Ei}\left(\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + a \log\left(d x + c\right)}{d}"," ",0,"(F^((d*e - c*f)*g*n/d)*b*Ei((d*f*g*n*x + c*f*g*n)*log(F)/d) + a*log(d*x + c))/d","A",0
30,1,87,0,0.438254," ","integrate((a+b*(F^(g*(f*x+e)))^n)/(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(b d f g n x + b c f g n\right)} F^{\frac{{\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right) - F^{f g n x + e g n} b d - a d}{d^{3} x + c d^{2}}"," ",0,"((b*d*f*g*n*x + b*c*f*g*n)*F^((d*e - c*f)*g*n/d)*Ei((d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F) - F^(f*g*n*x + e*g*n)*b*d - a*d)/(d^3*x + c*d^2)","A",0
31,1,160,0,0.440183," ","integrate((a+b*(F^(g*(f*x+e)))^n)/(d*x+c)^3,x, algorithm=""fricas"")","\frac{{\left(b d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, b c d f^{2} g^{2} n^{2} x + b c^{2} f^{2} g^{2} n^{2}\right)} F^{\frac{{\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right)^{2} - a d^{2} - {\left(b d^{2} + {\left(b d^{2} f g n x + b c d f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{2 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/2*((b*d^2*f^2*g^2*n^2*x^2 + 2*b*c*d*f^2*g^2*n^2*x + b*c^2*f^2*g^2*n^2)*F^((d*e - c*f)*g*n/d)*Ei((d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F)^2 - a*d^2 - (b*d^2 + (b*d^2*f*g*n*x + b*c*d*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
32,1,482,0,0.442960," ","integrate((a+b*(F^(g*(f*x+e)))^n)^2*(d*x+c)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} d^{3} f^{4} g^{4} n^{4} x^{4} + 4 \, a^{2} c d^{2} f^{4} g^{4} n^{4} x^{3} + 6 \, a^{2} c^{2} d f^{4} g^{4} n^{4} x^{2} + 4 \, a^{2} c^{3} f^{4} g^{4} n^{4} x\right)} \log\left(F\right)^{4} - {\left(3 \, b^{2} d^{3} - 4 \, {\left(b^{2} d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, b^{2} c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, b^{2} c^{2} d f^{3} g^{3} n^{3} x + b^{2} c^{3} f^{3} g^{3} n^{3}\right)} \log\left(F\right)^{3} + 6 \, {\left(b^{2} d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{2} c d^{2} f^{2} g^{2} n^{2} x + b^{2} c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 6 \, {\left(b^{2} d^{3} f g n x + b^{2} c d^{2} f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} - 16 \, {\left(6 \, a b d^{3} - {\left(a b d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, a b c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, a b c^{2} d f^{3} g^{3} n^{3} x + a b c^{3} f^{3} g^{3} n^{3}\right)} \log\left(F\right)^{3} + 3 \, {\left(a b d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a b c d^{2} f^{2} g^{2} n^{2} x + a b c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 6 \, {\left(a b d^{3} f g n x + a b c d^{2} f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{8 \, f^{4} g^{4} n^{4} \log\left(F\right)^{4}}"," ",0,"1/8*(2*(a^2*d^3*f^4*g^4*n^4*x^4 + 4*a^2*c*d^2*f^4*g^4*n^4*x^3 + 6*a^2*c^2*d*f^4*g^4*n^4*x^2 + 4*a^2*c^3*f^4*g^4*n^4*x)*log(F)^4 - (3*b^2*d^3 - 4*(b^2*d^3*f^3*g^3*n^3*x^3 + 3*b^2*c*d^2*f^3*g^3*n^3*x^2 + 3*b^2*c^2*d*f^3*g^3*n^3*x + b^2*c^3*f^3*g^3*n^3)*log(F)^3 + 6*(b^2*d^3*f^2*g^2*n^2*x^2 + 2*b^2*c*d^2*f^2*g^2*n^2*x + b^2*c^2*d*f^2*g^2*n^2)*log(F)^2 - 6*(b^2*d^3*f*g*n*x + b^2*c*d^2*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) - 16*(6*a*b*d^3 - (a*b*d^3*f^3*g^3*n^3*x^3 + 3*a*b*c*d^2*f^3*g^3*n^3*x^2 + 3*a*b*c^2*d*f^3*g^3*n^3*x + a*b*c^3*f^3*g^3*n^3)*log(F)^3 + 3*(a*b*d^3*f^2*g^2*n^2*x^2 + 2*a*b*c*d^2*f^2*g^2*n^2*x + a*b*c^2*d*f^2*g^2*n^2)*log(F)^2 - 6*(a*b*d^3*f*g*n*x + a*b*c*d^2*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(f^4*g^4*n^4*log(F)^4)","A",0
33,1,287,0,0.424948," ","integrate((a+b*(F^(g*(f*x+e)))^n)^2*(d*x+c)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(a^{2} d^{2} f^{3} g^{3} n^{3} x^{3} + 3 \, a^{2} c d f^{3} g^{3} n^{3} x^{2} + 3 \, a^{2} c^{2} f^{3} g^{3} n^{3} x\right)} \log\left(F\right)^{3} + 3 \, {\left(b^{2} d^{2} + 2 \, {\left(b^{2} d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{2} c d f^{2} g^{2} n^{2} x + b^{2} c^{2} f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(b^{2} d^{2} f g n x + b^{2} c d f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 24 \, {\left(2 \, a b d^{2} + {\left(a b d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, a b c d f^{2} g^{2} n^{2} x + a b c^{2} f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(a b d^{2} f g n x + a b c d f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{12 \, f^{3} g^{3} n^{3} \log\left(F\right)^{3}}"," ",0,"1/12*(4*(a^2*d^2*f^3*g^3*n^3*x^3 + 3*a^2*c*d*f^3*g^3*n^3*x^2 + 3*a^2*c^2*f^3*g^3*n^3*x)*log(F)^3 + 3*(b^2*d^2 + 2*(b^2*d^2*f^2*g^2*n^2*x^2 + 2*b^2*c*d*f^2*g^2*n^2*x + b^2*c^2*f^2*g^2*n^2)*log(F)^2 - 2*(b^2*d^2*f*g*n*x + b^2*c*d*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 24*(2*a*b*d^2 + (a*b*d^2*f^2*g^2*n^2*x^2 + 2*a*b*c*d*f^2*g^2*n^2*x + a*b*c^2*f^2*g^2*n^2)*log(F)^2 - 2*(a*b*d^2*f*g*n*x + a*b*c*d*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(f^3*g^3*n^3*log(F)^3)","A",0
34,1,139,0,0.437922," ","integrate((a+b*(F^(g*(f*x+e)))^n)^2*(d*x+c),x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} d f^{2} g^{2} n^{2} x^{2} + 2 \, a^{2} c f^{2} g^{2} n^{2} x\right)} \log\left(F\right)^{2} - {\left(b^{2} d - 2 \, {\left(b^{2} d f g n x + b^{2} c f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} - 8 \, {\left(a b d - {\left(a b d f g n x + a b c f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{4 \, f^{2} g^{2} n^{2} \log\left(F\right)^{2}}"," ",0,"1/4*(2*(a^2*d*f^2*g^2*n^2*x^2 + 2*a^2*c*f^2*g^2*n^2*x)*log(F)^2 - (b^2*d - 2*(b^2*d*f*g*n*x + b^2*c*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) - 8*(a*b*d - (a*b*d*f*g*n*x + a*b*c*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(f^2*g^2*n^2*log(F)^2)","A",0
35,1,61,0,0.424201," ","integrate((a+b*(F^(g*(f*x+e)))^n)^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} f g n x \log\left(F\right) + 4 \, F^{f g n x + e g n} a b + F^{2 \, f g n x + 2 \, e g n} b^{2}}{2 \, f g n \log\left(F\right)}"," ",0,"1/2*(2*a^2*f*g*n*x*log(F) + 4*F^(f*g*n*x + e*g*n)*a*b + F^(2*f*g*n*x + 2*e*g*n)*b^2)/(f*g*n*log(F))","A",0
36,1,95,0,0.436434," ","integrate((a+b*(F^(g*(f*x+e)))^n)^2/(d*x+c),x, algorithm=""fricas"")","\frac{F^{\frac{2 \, {\left(d e - c f\right)} g n}{d}} b^{2} {\rm Ei}\left(\frac{2 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + 2 \, F^{\frac{{\left(d e - c f\right)} g n}{d}} a b {\rm Ei}\left(\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + a^{2} \log\left(d x + c\right)}{d}"," ",0,"(F^(2*(d*e - c*f)*g*n/d)*b^2*Ei(2*(d*f*g*n*x + c*f*g*n)*log(F)/d) + 2*F^((d*e - c*f)*g*n/d)*a*b*Ei((d*f*g*n*x + c*f*g*n)*log(F)/d) + a^2*log(d*x + c))/d","A",0
37,1,171,0,0.434673," ","integrate((a+b*(F^(g*(f*x+e)))^n)^2/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{2 \, F^{f g n x + e g n} a b d + F^{2 \, f g n x + 2 \, e g n} b^{2} d - 2 \, {\left(b^{2} d f g n x + b^{2} c f g n\right)} F^{\frac{2 \, {\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{2 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right) - 2 \, {\left(a b d f g n x + a b c f g n\right)} F^{\frac{{\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right) + a^{2} d}{d^{3} x + c d^{2}}"," ",0,"-(2*F^(f*g*n*x + e*g*n)*a*b*d + F^(2*f*g*n*x + 2*e*g*n)*b^2*d - 2*(b^2*d*f*g*n*x + b^2*c*f*g*n)*F^(2*(d*e - c*f)*g*n/d)*Ei(2*(d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F) - 2*(a*b*d*f*g*n*x + a*b*c*f*g*n)*F^((d*e - c*f)*g*n/d)*Ei((d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F) + a^2*d)/(d^3*x + c*d^2)","A",0
38,1,314,0,0.440093," ","integrate((a+b*(F^(g*(f*x+e)))^n)^2/(d*x+c)^3,x, algorithm=""fricas"")","\frac{4 \, {\left(b^{2} d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{2} c d f^{2} g^{2} n^{2} x + b^{2} c^{2} f^{2} g^{2} n^{2}\right)} F^{\frac{2 \, {\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{2 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right)^{2} + 2 \, {\left(a b d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, a b c d f^{2} g^{2} n^{2} x + a b c^{2} f^{2} g^{2} n^{2}\right)} F^{\frac{{\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right)^{2} - a^{2} d^{2} - {\left(b^{2} d^{2} + 2 \, {\left(b^{2} d^{2} f g n x + b^{2} c d f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} - 2 \, {\left(a b d^{2} + {\left(a b d^{2} f g n x + a b c d f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{2 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"1/2*(4*(b^2*d^2*f^2*g^2*n^2*x^2 + 2*b^2*c*d*f^2*g^2*n^2*x + b^2*c^2*f^2*g^2*n^2)*F^(2*(d*e - c*f)*g*n/d)*Ei(2*(d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F)^2 + 2*(a*b*d^2*f^2*g^2*n^2*x^2 + 2*a*b*c*d*f^2*g^2*n^2*x + a*b*c^2*f^2*g^2*n^2)*F^((d*e - c*f)*g*n/d)*Ei((d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F)^2 - a^2*d^2 - (b^2*d^2 + 2*(b^2*d^2*f*g*n*x + b^2*c*d*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) - 2*(a*b*d^2 + (a*b*d^2*f*g*n*x + a*b*c*d*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
39,1,708,0,0.445031," ","integrate((a+b*(F^(g*(f*x+e)))^n)^3*(d*x+c)^3,x, algorithm=""fricas"")","\frac{54 \, {\left(a^{3} d^{3} f^{4} g^{4} n^{4} x^{4} + 4 \, a^{3} c d^{2} f^{4} g^{4} n^{4} x^{3} + 6 \, a^{3} c^{2} d f^{4} g^{4} n^{4} x^{2} + 4 \, a^{3} c^{3} f^{4} g^{4} n^{4} x\right)} \log\left(F\right)^{4} - 8 \, {\left(2 \, b^{3} d^{3} - 9 \, {\left(b^{3} d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, b^{3} c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, b^{3} c^{2} d f^{3} g^{3} n^{3} x + b^{3} c^{3} f^{3} g^{3} n^{3}\right)} \log\left(F\right)^{3} + 9 \, {\left(b^{3} d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{3} c d^{2} f^{2} g^{2} n^{2} x + b^{3} c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 6 \, {\left(b^{3} d^{3} f g n x + b^{3} c d^{2} f g n\right)} \log\left(F\right)\right)} F^{3 \, f g n x + 3 \, e g n} - 81 \, {\left(3 \, a b^{2} d^{3} - 4 \, {\left(a b^{2} d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, a b^{2} c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, a b^{2} c^{2} d f^{3} g^{3} n^{3} x + a b^{2} c^{3} f^{3} g^{3} n^{3}\right)} \log\left(F\right)^{3} + 6 \, {\left(a b^{2} d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a b^{2} c d^{2} f^{2} g^{2} n^{2} x + a b^{2} c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 6 \, {\left(a b^{2} d^{3} f g n x + a b^{2} c d^{2} f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} - 648 \, {\left(6 \, a^{2} b d^{3} - {\left(a^{2} b d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, a^{2} b c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, a^{2} b c^{2} d f^{3} g^{3} n^{3} x + a^{2} b c^{3} f^{3} g^{3} n^{3}\right)} \log\left(F\right)^{3} + 3 \, {\left(a^{2} b d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a^{2} b c d^{2} f^{2} g^{2} n^{2} x + a^{2} b c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 6 \, {\left(a^{2} b d^{3} f g n x + a^{2} b c d^{2} f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{216 \, f^{4} g^{4} n^{4} \log\left(F\right)^{4}}"," ",0,"1/216*(54*(a^3*d^3*f^4*g^4*n^4*x^4 + 4*a^3*c*d^2*f^4*g^4*n^4*x^3 + 6*a^3*c^2*d*f^4*g^4*n^4*x^2 + 4*a^3*c^3*f^4*g^4*n^4*x)*log(F)^4 - 8*(2*b^3*d^3 - 9*(b^3*d^3*f^3*g^3*n^3*x^3 + 3*b^3*c*d^2*f^3*g^3*n^3*x^2 + 3*b^3*c^2*d*f^3*g^3*n^3*x + b^3*c^3*f^3*g^3*n^3)*log(F)^3 + 9*(b^3*d^3*f^2*g^2*n^2*x^2 + 2*b^3*c*d^2*f^2*g^2*n^2*x + b^3*c^2*d*f^2*g^2*n^2)*log(F)^2 - 6*(b^3*d^3*f*g*n*x + b^3*c*d^2*f*g*n)*log(F))*F^(3*f*g*n*x + 3*e*g*n) - 81*(3*a*b^2*d^3 - 4*(a*b^2*d^3*f^3*g^3*n^3*x^3 + 3*a*b^2*c*d^2*f^3*g^3*n^3*x^2 + 3*a*b^2*c^2*d*f^3*g^3*n^3*x + a*b^2*c^3*f^3*g^3*n^3)*log(F)^3 + 6*(a*b^2*d^3*f^2*g^2*n^2*x^2 + 2*a*b^2*c*d^2*f^2*g^2*n^2*x + a*b^2*c^2*d*f^2*g^2*n^2)*log(F)^2 - 6*(a*b^2*d^3*f*g*n*x + a*b^2*c*d^2*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) - 648*(6*a^2*b*d^3 - (a^2*b*d^3*f^3*g^3*n^3*x^3 + 3*a^2*b*c*d^2*f^3*g^3*n^3*x^2 + 3*a^2*b*c^2*d*f^3*g^3*n^3*x + a^2*b*c^3*f^3*g^3*n^3)*log(F)^3 + 3*(a^2*b*d^3*f^2*g^2*n^2*x^2 + 2*a^2*b*c*d^2*f^2*g^2*n^2*x + a^2*b*c^2*d*f^2*g^2*n^2)*log(F)^2 - 6*(a^2*b*d^3*f*g*n*x + a^2*b*c*d^2*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(f^4*g^4*n^4*log(F)^4)","A",0
40,1,414,0,0.431108," ","integrate((a+b*(F^(g*(f*x+e)))^n)^3*(d*x+c)^2,x, algorithm=""fricas"")","\frac{36 \, {\left(a^{3} d^{2} f^{3} g^{3} n^{3} x^{3} + 3 \, a^{3} c d f^{3} g^{3} n^{3} x^{2} + 3 \, a^{3} c^{2} f^{3} g^{3} n^{3} x\right)} \log\left(F\right)^{3} + 4 \, {\left(2 \, b^{3} d^{2} + 9 \, {\left(b^{3} d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{3} c d f^{2} g^{2} n^{2} x + b^{3} c^{2} f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 6 \, {\left(b^{3} d^{2} f g n x + b^{3} c d f g n\right)} \log\left(F\right)\right)} F^{3 \, f g n x + 3 \, e g n} + 81 \, {\left(a b^{2} d^{2} + 2 \, {\left(a b^{2} d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, a b^{2} c d f^{2} g^{2} n^{2} x + a b^{2} c^{2} f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(a b^{2} d^{2} f g n x + a b^{2} c d f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 324 \, {\left(2 \, a^{2} b d^{2} + {\left(a^{2} b d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, a^{2} b c d f^{2} g^{2} n^{2} x + a^{2} b c^{2} f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(a^{2} b d^{2} f g n x + a^{2} b c d f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{108 \, f^{3} g^{3} n^{3} \log\left(F\right)^{3}}"," ",0,"1/108*(36*(a^3*d^2*f^3*g^3*n^3*x^3 + 3*a^3*c*d*f^3*g^3*n^3*x^2 + 3*a^3*c^2*f^3*g^3*n^3*x)*log(F)^3 + 4*(2*b^3*d^2 + 9*(b^3*d^2*f^2*g^2*n^2*x^2 + 2*b^3*c*d*f^2*g^2*n^2*x + b^3*c^2*f^2*g^2*n^2)*log(F)^2 - 6*(b^3*d^2*f*g*n*x + b^3*c*d*f*g*n)*log(F))*F^(3*f*g*n*x + 3*e*g*n) + 81*(a*b^2*d^2 + 2*(a*b^2*d^2*f^2*g^2*n^2*x^2 + 2*a*b^2*c*d*f^2*g^2*n^2*x + a*b^2*c^2*f^2*g^2*n^2)*log(F)^2 - 2*(a*b^2*d^2*f*g*n*x + a*b^2*c*d*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 324*(2*a^2*b*d^2 + (a^2*b*d^2*f^2*g^2*n^2*x^2 + 2*a^2*b*c*d*f^2*g^2*n^2*x + a^2*b*c^2*f^2*g^2*n^2)*log(F)^2 - 2*(a^2*b*d^2*f*g*n*x + a^2*b*c*d*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(f^3*g^3*n^3*log(F)^3)","A",0
41,1,192,0,0.443573," ","integrate((a+b*(F^(g*(f*x+e)))^n)^3*(d*x+c),x, algorithm=""fricas"")","\frac{18 \, {\left(a^{3} d f^{2} g^{2} n^{2} x^{2} + 2 \, a^{3} c f^{2} g^{2} n^{2} x\right)} \log\left(F\right)^{2} - 4 \, {\left(b^{3} d - 3 \, {\left(b^{3} d f g n x + b^{3} c f g n\right)} \log\left(F\right)\right)} F^{3 \, f g n x + 3 \, e g n} - 27 \, {\left(a b^{2} d - 2 \, {\left(a b^{2} d f g n x + a b^{2} c f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} - 108 \, {\left(a^{2} b d - {\left(a^{2} b d f g n x + a^{2} b c f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{36 \, f^{2} g^{2} n^{2} \log\left(F\right)^{2}}"," ",0,"1/36*(18*(a^3*d*f^2*g^2*n^2*x^2 + 2*a^3*c*f^2*g^2*n^2*x)*log(F)^2 - 4*(b^3*d - 3*(b^3*d*f*g*n*x + b^3*c*f*g*n)*log(F))*F^(3*f*g*n*x + 3*e*g*n) - 27*(a*b^2*d - 2*(a*b^2*d*f*g*n*x + a*b^2*c*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) - 108*(a^2*b*d - (a^2*b*d*f*g*n*x + a^2*b*c*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(f^2*g^2*n^2*log(F)^2)","A",0
42,1,84,0,0.438259," ","integrate((a+b*(F^(g*(f*x+e)))^n)^3,x, algorithm=""fricas"")","\frac{6 \, a^{3} f g n x \log\left(F\right) + 18 \, F^{f g n x + e g n} a^{2} b + 9 \, F^{2 \, f g n x + 2 \, e g n} a b^{2} + 2 \, F^{3 \, f g n x + 3 \, e g n} b^{3}}{6 \, f g n \log\left(F\right)}"," ",0,"1/6*(6*a^3*f*g*n*x*log(F) + 18*F^(f*g*n*x + e*g*n)*a^2*b + 9*F^(2*f*g*n*x + 2*e*g*n)*a*b^2 + 2*F^(3*f*g*n*x + 3*e*g*n)*b^3)/(f*g*n*log(F))","A",0
43,1,140,0,0.440796," ","integrate((a+b*(F^(g*(f*x+e)))^n)^3/(d*x+c),x, algorithm=""fricas"")","\frac{F^{\frac{3 \, {\left(d e - c f\right)} g n}{d}} b^{3} {\rm Ei}\left(\frac{3 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + 3 \, F^{\frac{2 \, {\left(d e - c f\right)} g n}{d}} a b^{2} {\rm Ei}\left(\frac{2 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + 3 \, F^{\frac{{\left(d e - c f\right)} g n}{d}} a^{2} b {\rm Ei}\left(\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + a^{3} \log\left(d x + c\right)}{d}"," ",0,"(F^(3*(d*e - c*f)*g*n/d)*b^3*Ei(3*(d*f*g*n*x + c*f*g*n)*log(F)/d) + 3*F^(2*(d*e - c*f)*g*n/d)*a*b^2*Ei(2*(d*f*g*n*x + c*f*g*n)*log(F)/d) + 3*F^((d*e - c*f)*g*n/d)*a^2*b*Ei((d*f*g*n*x + c*f*g*n)*log(F)/d) + a^3*log(d*x + c))/d","A",0
44,1,259,0,0.434496," ","integrate((a+b*(F^(g*(f*x+e)))^n)^3/(d*x+c)^2,x, algorithm=""fricas"")","-\frac{3 \, F^{f g n x + e g n} a^{2} b d + 3 \, F^{2 \, f g n x + 2 \, e g n} a b^{2} d + F^{3 \, f g n x + 3 \, e g n} b^{3} d + a^{3} d - 3 \, {\left(b^{3} d f g n x + b^{3} c f g n\right)} F^{\frac{3 \, {\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{3 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right) - 6 \, {\left(a b^{2} d f g n x + a b^{2} c f g n\right)} F^{\frac{2 \, {\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{2 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right) - 3 \, {\left(a^{2} b d f g n x + a^{2} b c f g n\right)} F^{\frac{{\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right)}{d^{3} x + c d^{2}}"," ",0,"-(3*F^(f*g*n*x + e*g*n)*a^2*b*d + 3*F^(2*f*g*n*x + 2*e*g*n)*a*b^2*d + F^(3*f*g*n*x + 3*e*g*n)*b^3*d + a^3*d - 3*(b^3*d*f*g*n*x + b^3*c*f*g*n)*F^(3*(d*e - c*f)*g*n/d)*Ei(3*(d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F) - 6*(a*b^2*d*f*g*n*x + a*b^2*c*f*g*n)*F^(2*(d*e - c*f)*g*n/d)*Ei(2*(d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F) - 3*(a^2*b*d*f*g*n*x + a^2*b*c*f*g*n)*F^((d*e - c*f)*g*n/d)*Ei((d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F))/(d^3*x + c*d^2)","A",0
45,1,475,0,0.445332," ","integrate((a+b*(F^(g*(f*x+e)))^n)^3/(d*x+c)^3,x, algorithm=""fricas"")","-\frac{a^{3} d^{2} - 9 \, {\left(b^{3} d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{3} c d f^{2} g^{2} n^{2} x + b^{3} c^{2} f^{2} g^{2} n^{2}\right)} F^{\frac{3 \, {\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{3 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right)^{2} - 12 \, {\left(a b^{2} d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, a b^{2} c d f^{2} g^{2} n^{2} x + a b^{2} c^{2} f^{2} g^{2} n^{2}\right)} F^{\frac{2 \, {\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{2 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right)^{2} - 3 \, {\left(a^{2} b d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, a^{2} b c d f^{2} g^{2} n^{2} x + a^{2} b c^{2} f^{2} g^{2} n^{2}\right)} F^{\frac{{\left(d e - c f\right)} g n}{d}} {\rm Ei}\left(\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) \log\left(F\right)^{2} + {\left(b^{3} d^{2} + 3 \, {\left(b^{3} d^{2} f g n x + b^{3} c d f g n\right)} \log\left(F\right)\right)} F^{3 \, f g n x + 3 \, e g n} + 3 \, {\left(a b^{2} d^{2} + 2 \, {\left(a b^{2} d^{2} f g n x + a b^{2} c d f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 3 \, {\left(a^{2} b d^{2} + {\left(a^{2} b d^{2} f g n x + a^{2} b c d f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n}}{2 \, {\left(d^{5} x^{2} + 2 \, c d^{4} x + c^{2} d^{3}\right)}}"," ",0,"-1/2*(a^3*d^2 - 9*(b^3*d^2*f^2*g^2*n^2*x^2 + 2*b^3*c*d*f^2*g^2*n^2*x + b^3*c^2*f^2*g^2*n^2)*F^(3*(d*e - c*f)*g*n/d)*Ei(3*(d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F)^2 - 12*(a*b^2*d^2*f^2*g^2*n^2*x^2 + 2*a*b^2*c*d*f^2*g^2*n^2*x + a*b^2*c^2*f^2*g^2*n^2)*F^(2*(d*e - c*f)*g*n/d)*Ei(2*(d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F)^2 - 3*(a^2*b*d^2*f^2*g^2*n^2*x^2 + 2*a^2*b*c*d*f^2*g^2*n^2*x + a^2*b*c^2*f^2*g^2*n^2)*F^((d*e - c*f)*g*n/d)*Ei((d*f*g*n*x + c*f*g*n)*log(F)/d)*log(F)^2 + (b^3*d^2 + 3*(b^3*d^2*f*g*n*x + b^3*c*d*f*g*n)*log(F))*F^(3*f*g*n*x + 3*e*g*n) + 3*(a*b^2*d^2 + 2*(a*b^2*d^2*f*g*n*x + a*b^2*c*d*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 3*(a^2*b*d^2 + (a^2*b*d^2*f*g*n*x + a^2*b*c*d*f*g*n)*log(F))*F^(f*g*n*x + e*g*n))/(d^5*x^2 + 2*c*d^4*x + c^2*d^3)","A",0
46,1,413,0,0.457270," ","integrate((d*x+c)^3/(a+b*(F^(g*(f*x+e)))^n),x, algorithm=""fricas"")","\frac{4 \, {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2} - c^{3} f^{3}\right)} g^{3} n^{3} \log\left(F^{f g n x + e g n} b + a\right) \log\left(F\right)^{3} + {\left(d^{3} f^{4} g^{4} n^{4} x^{4} + 4 \, c d^{2} f^{4} g^{4} n^{4} x^{3} + 6 \, c^{2} d f^{4} g^{4} n^{4} x^{2} + 4 \, c^{3} f^{4} g^{4} n^{4} x\right)} \log\left(F\right)^{4} - 4 \, {\left(d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, c^{2} d f^{3} g^{3} n^{3} x + {\left(d^{3} e^{3} - 3 \, c d^{2} e^{2} f + 3 \, c^{2} d e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} \log\left(\frac{F^{f g n x + e g n} b + a}{a}\right) - 12 \, {\left(d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, c d^{2} f^{2} g^{2} n^{2} x + c^{2} d f^{2} g^{2} n^{2}\right)} {\rm Li}_2\left(-\frac{F^{f g n x + e g n} b + a}{a} + 1\right) \log\left(F\right)^{2} - 24 \, d^{3} {\rm polylog}\left(4, -\frac{F^{f g n x + e g n} b}{a}\right) + 24 \, {\left(d^{3} f g n x + c d^{2} f g n\right)} \log\left(F\right) {\rm polylog}\left(3, -\frac{F^{f g n x + e g n} b}{a}\right)}{4 \, a f^{4} g^{4} n^{4} \log\left(F\right)^{4}}"," ",0,"1/4*(4*(d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2 - c^3*f^3)*g^3*n^3*log(F^(f*g*n*x + e*g*n)*b + a)*log(F)^3 + (d^3*f^4*g^4*n^4*x^4 + 4*c*d^2*f^4*g^4*n^4*x^3 + 6*c^2*d*f^4*g^4*n^4*x^2 + 4*c^3*f^4*g^4*n^4*x)*log(F)^4 - 4*(d^3*f^3*g^3*n^3*x^3 + 3*c*d^2*f^3*g^3*n^3*x^2 + 3*c^2*d*f^3*g^3*n^3*x + (d^3*e^3 - 3*c*d^2*e^2*f + 3*c^2*d*e*f^2)*g^3*n^3)*log(F)^3*log((F^(f*g*n*x + e*g*n)*b + a)/a) - 12*(d^3*f^2*g^2*n^2*x^2 + 2*c*d^2*f^2*g^2*n^2*x + c^2*d*f^2*g^2*n^2)*dilog(-(F^(f*g*n*x + e*g*n)*b + a)/a + 1)*log(F)^2 - 24*d^3*polylog(4, -F^(f*g*n*x + e*g*n)*b/a) + 24*(d^3*f*g*n*x + c*d^2*f*g*n)*log(F)*polylog(3, -F^(f*g*n*x + e*g*n)*b/a))/(a*f^4*g^4*n^4*log(F)^4)","C",0
47,1,271,0,0.458096," ","integrate((d*x+c)^2/(a+b*(F^(g*(f*x+e)))^n),x, algorithm=""fricas"")","-\frac{3 \, {\left(d^{2} e^{2} - 2 \, c d e f + c^{2} f^{2}\right)} g^{2} n^{2} \log\left(F^{f g n x + e g n} b + a\right) \log\left(F\right)^{2} - {\left(d^{2} f^{3} g^{3} n^{3} x^{3} + 3 \, c d f^{3} g^{3} n^{3} x^{2} + 3 \, c^{2} f^{3} g^{3} n^{3} x\right)} \log\left(F\right)^{3} + 3 \, {\left(d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, c d f^{2} g^{2} n^{2} x - {\left(d^{2} e^{2} - 2 \, c d e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} \log\left(\frac{F^{f g n x + e g n} b + a}{a}\right) + 6 \, {\left(d^{2} f g n x + c d f g n\right)} {\rm Li}_2\left(-\frac{F^{f g n x + e g n} b + a}{a} + 1\right) \log\left(F\right) - 6 \, d^{2} {\rm polylog}\left(3, -\frac{F^{f g n x + e g n} b}{a}\right)}{3 \, a f^{3} g^{3} n^{3} \log\left(F\right)^{3}}"," ",0,"-1/3*(3*(d^2*e^2 - 2*c*d*e*f + c^2*f^2)*g^2*n^2*log(F^(f*g*n*x + e*g*n)*b + a)*log(F)^2 - (d^2*f^3*g^3*n^3*x^3 + 3*c*d*f^3*g^3*n^3*x^2 + 3*c^2*f^3*g^3*n^3*x)*log(F)^3 + 3*(d^2*f^2*g^2*n^2*x^2 + 2*c*d*f^2*g^2*n^2*x - (d^2*e^2 - 2*c*d*e*f)*g^2*n^2)*log(F)^2*log((F^(f*g*n*x + e*g*n)*b + a)/a) + 6*(d^2*f*g*n*x + c*d*f*g*n)*dilog(-(F^(f*g*n*x + e*g*n)*b + a)/a + 1)*log(F) - 6*d^2*polylog(3, -F^(f*g*n*x + e*g*n)*b/a))/(a*f^3*g^3*n^3*log(F)^3)","C",0
48,1,147,0,0.420582," ","integrate((d*x+c)/(a+b*(F^(g*(f*x+e)))^n),x, algorithm=""fricas"")","\frac{2 \, {\left(d e - c f\right)} g n \log\left(F^{f g n x + e g n} b + a\right) \log\left(F\right) + {\left(d f^{2} g^{2} n^{2} x^{2} + 2 \, c f^{2} g^{2} n^{2} x\right)} \log\left(F\right)^{2} - 2 \, {\left(d f g n x + d e g n\right)} \log\left(F\right) \log\left(\frac{F^{f g n x + e g n} b + a}{a}\right) - 2 \, d {\rm Li}_2\left(-\frac{F^{f g n x + e g n} b + a}{a} + 1\right)}{2 \, a f^{2} g^{2} n^{2} \log\left(F\right)^{2}}"," ",0,"1/2*(2*(d*e - c*f)*g*n*log(F^(f*g*n*x + e*g*n)*b + a)*log(F) + (d*f^2*g^2*n^2*x^2 + 2*c*f^2*g^2*n^2*x)*log(F)^2 - 2*(d*f*g*n*x + d*e*g*n)*log(F)*log((F^(f*g*n*x + e*g*n)*b + a)/a) - 2*d*dilog(-(F^(f*g*n*x + e*g*n)*b + a)/a + 1))/(a*f^2*g^2*n^2*log(F)^2)","A",0
49,1,44,0,0.456690," ","integrate(1/(a+b*(F^(g*(f*x+e)))^n),x, algorithm=""fricas"")","\frac{f g n x \log\left(F\right) - \log\left(F^{f g n x + e g n} b + a\right)}{a f g n \log\left(F\right)}"," ",0,"(f*g*n*x*log(F) - log(F^(f*g*n*x + e*g*n)*b + a))/(a*f*g*n*log(F))","A",0
50,0,0,0,0.470611," ","integrate(1/(a+b*(F^(g*(f*x+e)))^n)/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d x + {\left(b d x + b c\right)} {\left(F^{f g x + e g}\right)}^{n} + a c}, x\right)"," ",0,"integral(1/(a*d*x + (b*d*x + b*c)*(F^(f*g*x + e*g))^n + a*c), x)","F",0
51,0,0,0,0.434977," ","integrate(1/(a+b*(F^(g*(f*x+e)))^n)/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a d^{2} x^{2} + 2 \, a c d x + a c^{2} + {\left(b d^{2} x^{2} + 2 \, b c d x + b c^{2}\right)} {\left(F^{f g x + e g}\right)}^{n}}, x\right)"," ",0,"integral(1/(a*d^2*x^2 + 2*a*c*d*x + a*c^2 + (b*d^2*x^2 + 2*b*c*d*x + b*c^2)*(F^(f*g*x + e*g))^n), x)","F",0
52,1,1390,0,0.490771," ","integrate((d*x+c)^3/(a+b*(F^(g*(f*x+e)))^n)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} g^{3} n^{3} \log\left(F\right)^{3} - {\left(a d^{3} f^{4} g^{4} n^{4} x^{4} + 4 \, a c d^{2} f^{4} g^{4} n^{4} x^{3} + 6 \, a c^{2} d f^{4} g^{4} n^{4} x^{2} + 4 \, a c^{3} f^{4} g^{4} n^{4} x - {\left(a d^{3} e^{4} - 4 \, a c d^{2} e^{3} f + 6 \, a c^{2} d e^{2} f^{2} - 4 \, a c^{3} e f^{3}\right)} g^{4} n^{4}\right)} \log\left(F\right)^{4} - {\left({\left(b d^{3} f^{4} g^{4} n^{4} x^{4} + 4 \, b c d^{2} f^{4} g^{4} n^{4} x^{3} + 6 \, b c^{2} d f^{4} g^{4} n^{4} x^{2} + 4 \, b c^{3} f^{4} g^{4} n^{4} x - {\left(b d^{3} e^{4} - 4 \, b c d^{2} e^{3} f + 6 \, b c^{2} d e^{2} f^{2} - 4 \, b c^{3} e f^{3}\right)} g^{4} n^{4}\right)} \log\left(F\right)^{4} - 4 \, {\left(b d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, b c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, b c^{2} d f^{3} g^{3} n^{3} x + {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3}\right)} F^{f g n x + e g n} + 12 \, {\left({\left(a d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a c d^{2} f^{2} g^{2} n^{2} x + a c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} + {\left({\left(b d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, b c d^{2} f^{2} g^{2} n^{2} x + b c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(b d^{3} f g n x + b c d^{2} f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} - 2 \, {\left(a d^{3} f g n x + a c d^{2} f g n\right)} \log\left(F\right)\right)} {\rm Li}_2\left(-\frac{F^{f g n x + e g n} b + a}{a} + 1\right) - 4 \, {\left({\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2} - a c^{3} f^{3}\right)} g^{3} n^{3} \log\left(F\right)^{3} + 3 \, {\left(a d^{3} e^{2} - 2 \, a c d^{2} e f + a c^{2} d f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + {\left({\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2} - b c^{3} f^{3}\right)} g^{3} n^{3} \log\left(F\right)^{3} + 3 \, {\left(b d^{3} e^{2} - 2 \, b c d^{2} e f + b c^{2} d f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2}\right)} F^{f g n x + e g n}\right)} \log\left(F^{f g n x + e g n} b + a\right) + 4 \, {\left({\left(a d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, a c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, a c^{2} d f^{3} g^{3} n^{3} x + {\left(a d^{3} e^{3} - 3 \, a c d^{2} e^{2} f + 3 \, a c^{2} d e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} - 3 \, {\left(a d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a c d^{2} f^{2} g^{2} n^{2} x - {\left(a d^{3} e^{2} - 2 \, a c d^{2} e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} + {\left({\left(b d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, b c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, b c^{2} d f^{3} g^{3} n^{3} x + {\left(b d^{3} e^{3} - 3 \, b c d^{2} e^{2} f + 3 \, b c^{2} d e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} - 3 \, {\left(b d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, b c d^{2} f^{2} g^{2} n^{2} x - {\left(b d^{3} e^{2} - 2 \, b c d^{2} e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2}\right)} F^{f g n x + e g n}\right)} \log\left(\frac{F^{f g n x + e g n} b + a}{a}\right) + 24 \, {\left(F^{f g n x + e g n} b d^{3} + a d^{3}\right)} {\rm polylog}\left(4, -\frac{F^{f g n x + e g n} b}{a}\right) + 24 \, {\left(a d^{3} + {\left(b d^{3} - {\left(b d^{3} f g n x + b c d^{2} f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} - {\left(a d^{3} f g n x + a c d^{2} f g n\right)} \log\left(F\right)\right)} {\rm polylog}\left(3, -\frac{F^{f g n x + e g n} b}{a}\right)}{4 \, {\left(F^{f g n x + e g n} a^{2} b f^{4} g^{4} n^{4} \log\left(F\right)^{4} + a^{3} f^{4} g^{4} n^{4} \log\left(F\right)^{4}\right)}}"," ",0,"-1/4*(4*(a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*g^3*n^3*log(F)^3 - (a*d^3*f^4*g^4*n^4*x^4 + 4*a*c*d^2*f^4*g^4*n^4*x^3 + 6*a*c^2*d*f^4*g^4*n^4*x^2 + 4*a*c^3*f^4*g^4*n^4*x - (a*d^3*e^4 - 4*a*c*d^2*e^3*f + 6*a*c^2*d*e^2*f^2 - 4*a*c^3*e*f^3)*g^4*n^4)*log(F)^4 - ((b*d^3*f^4*g^4*n^4*x^4 + 4*b*c*d^2*f^4*g^4*n^4*x^3 + 6*b*c^2*d*f^4*g^4*n^4*x^2 + 4*b*c^3*f^4*g^4*n^4*x - (b*d^3*e^4 - 4*b*c*d^2*e^3*f + 6*b*c^2*d*e^2*f^2 - 4*b*c^3*e*f^3)*g^4*n^4)*log(F)^4 - 4*(b*d^3*f^3*g^3*n^3*x^3 + 3*b*c*d^2*f^3*g^3*n^3*x^2 + 3*b*c^2*d*f^3*g^3*n^3*x + (b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*g^3*n^3)*log(F)^3)*F^(f*g*n*x + e*g*n) + 12*((a*d^3*f^2*g^2*n^2*x^2 + 2*a*c*d^2*f^2*g^2*n^2*x + a*c^2*d*f^2*g^2*n^2)*log(F)^2 + ((b*d^3*f^2*g^2*n^2*x^2 + 2*b*c*d^2*f^2*g^2*n^2*x + b*c^2*d*f^2*g^2*n^2)*log(F)^2 - 2*(b*d^3*f*g*n*x + b*c*d^2*f*g*n)*log(F))*F^(f*g*n*x + e*g*n) - 2*(a*d^3*f*g*n*x + a*c*d^2*f*g*n)*log(F))*dilog(-(F^(f*g*n*x + e*g*n)*b + a)/a + 1) - 4*((a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2 - a*c^3*f^3)*g^3*n^3*log(F)^3 + 3*(a*d^3*e^2 - 2*a*c*d^2*e*f + a*c^2*d*f^2)*g^2*n^2*log(F)^2 + ((b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2 - b*c^3*f^3)*g^3*n^3*log(F)^3 + 3*(b*d^3*e^2 - 2*b*c*d^2*e*f + b*c^2*d*f^2)*g^2*n^2*log(F)^2)*F^(f*g*n*x + e*g*n))*log(F^(f*g*n*x + e*g*n)*b + a) + 4*((a*d^3*f^3*g^3*n^3*x^3 + 3*a*c*d^2*f^3*g^3*n^3*x^2 + 3*a*c^2*d*f^3*g^3*n^3*x + (a*d^3*e^3 - 3*a*c*d^2*e^2*f + 3*a*c^2*d*e*f^2)*g^3*n^3)*log(F)^3 - 3*(a*d^3*f^2*g^2*n^2*x^2 + 2*a*c*d^2*f^2*g^2*n^2*x - (a*d^3*e^2 - 2*a*c*d^2*e*f)*g^2*n^2)*log(F)^2 + ((b*d^3*f^3*g^3*n^3*x^3 + 3*b*c*d^2*f^3*g^3*n^3*x^2 + 3*b*c^2*d*f^3*g^3*n^3*x + (b*d^3*e^3 - 3*b*c*d^2*e^2*f + 3*b*c^2*d*e*f^2)*g^3*n^3)*log(F)^3 - 3*(b*d^3*f^2*g^2*n^2*x^2 + 2*b*c*d^2*f^2*g^2*n^2*x - (b*d^3*e^2 - 2*b*c*d^2*e*f)*g^2*n^2)*log(F)^2)*F^(f*g*n*x + e*g*n))*log((F^(f*g*n*x + e*g*n)*b + a)/a) + 24*(F^(f*g*n*x + e*g*n)*b*d^3 + a*d^3)*polylog(4, -F^(f*g*n*x + e*g*n)*b/a) + 24*(a*d^3 + (b*d^3 - (b*d^3*f*g*n*x + b*c*d^2*f*g*n)*log(F))*F^(f*g*n*x + e*g*n) - (a*d^3*f*g*n*x + a*c*d^2*f*g*n)*log(F))*polylog(3, -F^(f*g*n*x + e*g*n)*b/a))/(F^(f*g*n*x + e*g*n)*a^2*b*f^4*g^4*n^4*log(F)^4 + a^3*f^4*g^4*n^4*log(F)^4)","C",0
53,1,834,0,0.448662," ","integrate((d*x+c)^2/(a+b*(F^(g*(f*x+e)))^n)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + {\left(a d^{2} f^{3} g^{3} n^{3} x^{3} + 3 \, a c d f^{3} g^{3} n^{3} x^{2} + 3 \, a c^{2} f^{3} g^{3} n^{3} x + {\left(a d^{2} e^{3} - 3 \, a c d e^{2} f + 3 \, a c^{2} e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} + {\left({\left(b d^{2} f^{3} g^{3} n^{3} x^{3} + 3 \, b c d f^{3} g^{3} n^{3} x^{2} + 3 \, b c^{2} f^{3} g^{3} n^{3} x + {\left(b d^{2} e^{3} - 3 \, b c d e^{2} f + 3 \, b c^{2} e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} - 3 \, {\left(b d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, b c d f^{2} g^{2} n^{2} x - {\left(b d^{2} e^{2} - 2 \, b c d e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2}\right)} F^{f g n x + e g n} + 6 \, {\left(a d^{2} + {\left(b d^{2} - {\left(b d^{2} f g n x + b c d f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} - {\left(a d^{2} f g n x + a c d f g n\right)} \log\left(F\right)\right)} {\rm Li}_2\left(-\frac{F^{f g n x + e g n} b + a}{a} + 1\right) - 3 \, {\left({\left(a d^{2} e^{2} - 2 \, a c d e f + a c^{2} f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + 2 \, {\left(a d^{2} e - a c d f\right)} g n \log\left(F\right) + {\left({\left(b d^{2} e^{2} - 2 \, b c d e f + b c^{2} f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + 2 \, {\left(b d^{2} e - b c d f\right)} g n \log\left(F\right)\right)} F^{f g n x + e g n}\right)} \log\left(F^{f g n x + e g n} b + a\right) - 3 \, {\left({\left(a d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, a c d f^{2} g^{2} n^{2} x - {\left(a d^{2} e^{2} - 2 \, a c d e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} + {\left({\left(b d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, b c d f^{2} g^{2} n^{2} x - {\left(b d^{2} e^{2} - 2 \, b c d e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(b d^{2} f g n x + b d^{2} e g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} - 2 \, {\left(a d^{2} f g n x + a d^{2} e g n\right)} \log\left(F\right)\right)} \log\left(\frac{F^{f g n x + e g n} b + a}{a}\right) + 6 \, {\left(F^{f g n x + e g n} b d^{2} + a d^{2}\right)} {\rm polylog}\left(3, -\frac{F^{f g n x + e g n} b}{a}\right)}{3 \, {\left(F^{f g n x + e g n} a^{2} b f^{3} g^{3} n^{3} \log\left(F\right)^{3} + a^{3} f^{3} g^{3} n^{3} \log\left(F\right)^{3}\right)}}"," ",0,"1/3*(3*(a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*g^2*n^2*log(F)^2 + (a*d^2*f^3*g^3*n^3*x^3 + 3*a*c*d*f^3*g^3*n^3*x^2 + 3*a*c^2*f^3*g^3*n^3*x + (a*d^2*e^3 - 3*a*c*d*e^2*f + 3*a*c^2*e*f^2)*g^3*n^3)*log(F)^3 + ((b*d^2*f^3*g^3*n^3*x^3 + 3*b*c*d*f^3*g^3*n^3*x^2 + 3*b*c^2*f^3*g^3*n^3*x + (b*d^2*e^3 - 3*b*c*d*e^2*f + 3*b*c^2*e*f^2)*g^3*n^3)*log(F)^3 - 3*(b*d^2*f^2*g^2*n^2*x^2 + 2*b*c*d*f^2*g^2*n^2*x - (b*d^2*e^2 - 2*b*c*d*e*f)*g^2*n^2)*log(F)^2)*F^(f*g*n*x + e*g*n) + 6*(a*d^2 + (b*d^2 - (b*d^2*f*g*n*x + b*c*d*f*g*n)*log(F))*F^(f*g*n*x + e*g*n) - (a*d^2*f*g*n*x + a*c*d*f*g*n)*log(F))*dilog(-(F^(f*g*n*x + e*g*n)*b + a)/a + 1) - 3*((a*d^2*e^2 - 2*a*c*d*e*f + a*c^2*f^2)*g^2*n^2*log(F)^2 + 2*(a*d^2*e - a*c*d*f)*g*n*log(F) + ((b*d^2*e^2 - 2*b*c*d*e*f + b*c^2*f^2)*g^2*n^2*log(F)^2 + 2*(b*d^2*e - b*c*d*f)*g*n*log(F))*F^(f*g*n*x + e*g*n))*log(F^(f*g*n*x + e*g*n)*b + a) - 3*((a*d^2*f^2*g^2*n^2*x^2 + 2*a*c*d*f^2*g^2*n^2*x - (a*d^2*e^2 - 2*a*c*d*e*f)*g^2*n^2)*log(F)^2 + ((b*d^2*f^2*g^2*n^2*x^2 + 2*b*c*d*f^2*g^2*n^2*x - (b*d^2*e^2 - 2*b*c*d*e*f)*g^2*n^2)*log(F)^2 - 2*(b*d^2*f*g*n*x + b*d^2*e*g*n)*log(F))*F^(f*g*n*x + e*g*n) - 2*(a*d^2*f*g*n*x + a*d^2*e*g*n)*log(F))*log((F^(f*g*n*x + e*g*n)*b + a)/a) + 6*(F^(f*g*n*x + e*g*n)*b*d^2 + a*d^2)*polylog(3, -F^(f*g*n*x + e*g*n)*b/a))/(F^(f*g*n*x + e*g*n)*a^2*b*f^3*g^3*n^3*log(F)^3 + a^3*f^3*g^3*n^3*log(F)^3)","C",0
54,1,400,0,0.438457," ","integrate((d*x+c)/(a+b*(F^(g*(f*x+e)))^n)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a d e - a c f\right)} g n \log\left(F\right) - {\left(a d f^{2} g^{2} n^{2} x^{2} + 2 \, a c f^{2} g^{2} n^{2} x - {\left(a d e^{2} - 2 \, a c e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} - {\left({\left(b d f^{2} g^{2} n^{2} x^{2} + 2 \, b c f^{2} g^{2} n^{2} x - {\left(b d e^{2} - 2 \, b c e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(b d f g n x + b d e g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} + 2 \, {\left(F^{f g n x + e g n} b d + a d\right)} {\rm Li}_2\left(-\frac{F^{f g n x + e g n} b + a}{a} + 1\right) - 2 \, {\left({\left(a d e - a c f\right)} g n \log\left(F\right) + {\left({\left(b d e - b c f\right)} g n \log\left(F\right) + b d\right)} F^{f g n x + e g n} + a d\right)} \log\left(F^{f g n x + e g n} b + a\right) + 2 \, {\left({\left(b d f g n x + b d e g n\right)} F^{f g n x + e g n} \log\left(F\right) + {\left(a d f g n x + a d e g n\right)} \log\left(F\right)\right)} \log\left(\frac{F^{f g n x + e g n} b + a}{a}\right)}{2 \, {\left(F^{f g n x + e g n} a^{2} b f^{2} g^{2} n^{2} \log\left(F\right)^{2} + a^{3} f^{2} g^{2} n^{2} \log\left(F\right)^{2}\right)}}"," ",0,"-1/2*(2*(a*d*e - a*c*f)*g*n*log(F) - (a*d*f^2*g^2*n^2*x^2 + 2*a*c*f^2*g^2*n^2*x - (a*d*e^2 - 2*a*c*e*f)*g^2*n^2)*log(F)^2 - ((b*d*f^2*g^2*n^2*x^2 + 2*b*c*f^2*g^2*n^2*x - (b*d*e^2 - 2*b*c*e*f)*g^2*n^2)*log(F)^2 - 2*(b*d*f*g*n*x + b*d*e*g*n)*log(F))*F^(f*g*n*x + e*g*n) + 2*(F^(f*g*n*x + e*g*n)*b*d + a*d)*dilog(-(F^(f*g*n*x + e*g*n)*b + a)/a + 1) - 2*((a*d*e - a*c*f)*g*n*log(F) + ((b*d*e - b*c*f)*g*n*log(F) + b*d)*F^(f*g*n*x + e*g*n) + a*d)*log(F^(f*g*n*x + e*g*n)*b + a) + 2*((b*d*f*g*n*x + b*d*e*g*n)*F^(f*g*n*x + e*g*n)*log(F) + (a*d*f*g*n*x + a*d*e*g*n)*log(F))*log((F^(f*g*n*x + e*g*n)*b + a)/a))/(F^(f*g*n*x + e*g*n)*a^2*b*f^2*g^2*n^2*log(F)^2 + a^3*f^2*g^2*n^2*log(F)^2)","B",0
55,1,100,0,0.449022," ","integrate(1/(a+b*(F^(g*(f*x+e)))^n)^2,x, algorithm=""fricas"")","\frac{F^{f g n x + e g n} b f g n x \log\left(F\right) + a f g n x \log\left(F\right) - {\left(F^{f g n x + e g n} b + a\right)} \log\left(F^{f g n x + e g n} b + a\right) + a}{F^{f g n x + e g n} a^{2} b f g n \log\left(F\right) + a^{3} f g n \log\left(F\right)}"," ",0,"(F^(f*g*n*x + e*g*n)*b*f*g*n*x*log(F) + a*f*g*n*x*log(F) - (F^(f*g*n*x + e*g*n)*b + a)*log(F^(f*g*n*x + e*g*n)*b + a) + a)/(F^(f*g*n*x + e*g*n)*a^2*b*f*g*n*log(F) + a^3*f*g*n*log(F))","A",0
56,0,0,0,0.422577," ","integrate(1/(a+b*(F^(g*(f*x+e)))^n)^2/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d x + a^{2} c + {\left(b^{2} d x + b^{2} c\right)} {\left(F^{f g x + e g}\right)}^{2 \, n} + 2 \, {\left(a b d x + a b c\right)} {\left(F^{f g x + e g}\right)}^{n}}, x\right)"," ",0,"integral(1/(a^2*d*x + a^2*c + (b^2*d*x + b^2*c)*(F^(f*g*x + e*g))^(2*n) + 2*(a*b*d*x + a*b*c)*(F^(f*g*x + e*g))^n), x)","F",0
57,0,0,0,0.423368," ","integrate(1/(a+b*(F^(g*(f*x+e)))^n)^2/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} d^{2} x^{2} + 2 \, a^{2} c d x + a^{2} c^{2} + {\left(b^{2} d^{2} x^{2} + 2 \, b^{2} c d x + b^{2} c^{2}\right)} {\left(F^{f g x + e g}\right)}^{2 \, n} + 2 \, {\left(a b d^{2} x^{2} + 2 \, a b c d x + a b c^{2}\right)} {\left(F^{f g x + e g}\right)}^{n}}, x\right)"," ",0,"integral(1/(a^2*d^2*x^2 + 2*a^2*c*d*x + a^2*c^2 + (b^2*d^2*x^2 + 2*b^2*c*d*x + b^2*c^2)*(F^(f*g*x + e*g))^(2*n) + 2*(a*b*d^2*x^2 + 2*a*b*c*d*x + a*b*c^2)*(F^(f*g*x + e*g))^n), x)","F",0
58,1,2704,0,0.499989," ","integrate((d*x+c)^3/(a+b*(F^(g*(f*x+e)))^n)^3,x, algorithm=""fricas"")","-\frac{6 \, {\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - a^{2} c^{3} f^{3}\right)} g^{3} n^{3} \log\left(F\right)^{3} + 6 \, {\left(a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} - {\left(a^{2} d^{3} f^{4} g^{4} n^{4} x^{4} + 4 \, a^{2} c d^{2} f^{4} g^{4} n^{4} x^{3} + 6 \, a^{2} c^{2} d f^{4} g^{4} n^{4} x^{2} + 4 \, a^{2} c^{3} f^{4} g^{4} n^{4} x - {\left(a^{2} d^{3} e^{4} - 4 \, a^{2} c d^{2} e^{3} f + 6 \, a^{2} c^{2} d e^{2} f^{2} - 4 \, a^{2} c^{3} e f^{3}\right)} g^{4} n^{4}\right)} \log\left(F\right)^{4} - {\left({\left(b^{2} d^{3} f^{4} g^{4} n^{4} x^{4} + 4 \, b^{2} c d^{2} f^{4} g^{4} n^{4} x^{3} + 6 \, b^{2} c^{2} d f^{4} g^{4} n^{4} x^{2} + 4 \, b^{2} c^{3} f^{4} g^{4} n^{4} x - {\left(b^{2} d^{3} e^{4} - 4 \, b^{2} c d^{2} e^{3} f + 6 \, b^{2} c^{2} d e^{2} f^{2} - 4 \, b^{2} c^{3} e f^{3}\right)} g^{4} n^{4}\right)} \log\left(F\right)^{4} - 6 \, {\left(b^{2} d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, b^{2} c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, b^{2} c^{2} d f^{3} g^{3} n^{3} x + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} + 6 \, {\left(b^{2} d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{2} c d^{2} f^{2} g^{2} n^{2} x - {\left(b^{2} d^{3} e^{2} - 2 \, b^{2} c d^{2} e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2}\right)} F^{2 \, f g n x + 2 \, e g n} - 2 \, {\left({\left(a b d^{3} f^{4} g^{4} n^{4} x^{4} + 4 \, a b c d^{2} f^{4} g^{4} n^{4} x^{3} + 6 \, a b c^{2} d f^{4} g^{4} n^{4} x^{2} + 4 \, a b c^{3} f^{4} g^{4} n^{4} x - {\left(a b d^{3} e^{4} - 4 \, a b c d^{2} e^{3} f + 6 \, a b c^{2} d e^{2} f^{2} - 4 \, a b c^{3} e f^{3}\right)} g^{4} n^{4}\right)} \log\left(F\right)^{4} - 2 \, {\left(2 \, a b d^{3} f^{3} g^{3} n^{3} x^{3} + 6 \, a b c d^{2} f^{3} g^{3} n^{3} x^{2} + 6 \, a b c^{2} d f^{3} g^{3} n^{3} x + {\left(3 \, a b d^{3} e^{3} - 9 \, a b c d^{2} e^{2} f + 9 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} + 3 \, {\left(a b d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a b c d^{2} f^{2} g^{2} n^{2} x - {\left(2 \, a b d^{3} e^{2} - 4 \, a b c d^{2} e f + a b c^{2} d f^{2}\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2}\right)} F^{f g n x + e g n} + 12 \, {\left(a^{2} d^{3} + {\left(a^{2} d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a^{2} c d^{2} f^{2} g^{2} n^{2} x + a^{2} c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} + {\left(b^{2} d^{3} + {\left(b^{2} d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{2} c d^{2} f^{2} g^{2} n^{2} x + b^{2} c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 3 \, {\left(b^{2} d^{3} f g n x + b^{2} c d^{2} f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 2 \, {\left(a b d^{3} + {\left(a b d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a b c d^{2} f^{2} g^{2} n^{2} x + a b c^{2} d f^{2} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 3 \, {\left(a b d^{3} f g n x + a b c d^{2} f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} - 3 \, {\left(a^{2} d^{3} f g n x + a^{2} c d^{2} f g n\right)} \log\left(F\right)\right)} {\rm Li}_2\left(-\frac{F^{f g n x + e g n} b + a}{a} + 1\right) - 2 \, {\left(2 \, {\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2} - a^{2} c^{3} f^{3}\right)} g^{3} n^{3} \log\left(F\right)^{3} + 9 \, {\left(a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f + a^{2} c^{2} d f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + 6 \, {\left(a^{2} d^{3} e - a^{2} c d^{2} f\right)} g n \log\left(F\right) + {\left(2 \, {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2} - b^{2} c^{3} f^{3}\right)} g^{3} n^{3} \log\left(F\right)^{3} + 9 \, {\left(b^{2} d^{3} e^{2} - 2 \, b^{2} c d^{2} e f + b^{2} c^{2} d f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + 6 \, {\left(b^{2} d^{3} e - b^{2} c d^{2} f\right)} g n \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 2 \, {\left(2 \, {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2} - a b c^{3} f^{3}\right)} g^{3} n^{3} \log\left(F\right)^{3} + 9 \, {\left(a b d^{3} e^{2} - 2 \, a b c d^{2} e f + a b c^{2} d f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + 6 \, {\left(a b d^{3} e - a b c d^{2} f\right)} g n \log\left(F\right)\right)} F^{f g n x + e g n}\right)} \log\left(F^{f g n x + e g n} b + a\right) + 2 \, {\left(2 \, {\left(a^{2} d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, a^{2} c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, a^{2} c^{2} d f^{3} g^{3} n^{3} x + {\left(a^{2} d^{3} e^{3} - 3 \, a^{2} c d^{2} e^{2} f + 3 \, a^{2} c^{2} d e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} - 9 \, {\left(a^{2} d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a^{2} c d^{2} f^{2} g^{2} n^{2} x - {\left(a^{2} d^{3} e^{2} - 2 \, a^{2} c d^{2} e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} + {\left(2 \, {\left(b^{2} d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, b^{2} c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, b^{2} c^{2} d f^{3} g^{3} n^{3} x + {\left(b^{2} d^{3} e^{3} - 3 \, b^{2} c d^{2} e^{2} f + 3 \, b^{2} c^{2} d e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} - 9 \, {\left(b^{2} d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{2} c d^{2} f^{2} g^{2} n^{2} x - {\left(b^{2} d^{3} e^{2} - 2 \, b^{2} c d^{2} e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} + 6 \, {\left(b^{2} d^{3} f g n x + b^{2} d^{3} e g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 2 \, {\left(2 \, {\left(a b d^{3} f^{3} g^{3} n^{3} x^{3} + 3 \, a b c d^{2} f^{3} g^{3} n^{3} x^{2} + 3 \, a b c^{2} d f^{3} g^{3} n^{3} x + {\left(a b d^{3} e^{3} - 3 \, a b c d^{2} e^{2} f + 3 \, a b c^{2} d e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} - 9 \, {\left(a b d^{3} f^{2} g^{2} n^{2} x^{2} + 2 \, a b c d^{2} f^{2} g^{2} n^{2} x - {\left(a b d^{3} e^{2} - 2 \, a b c d^{2} e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} + 6 \, {\left(a b d^{3} f g n x + a b d^{3} e g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} + 6 \, {\left(a^{2} d^{3} f g n x + a^{2} d^{3} e g n\right)} \log\left(F\right)\right)} \log\left(\frac{F^{f g n x + e g n} b + a}{a}\right) + 24 \, {\left(2 \, F^{f g n x + e g n} a b d^{3} + F^{2 \, f g n x + 2 \, e g n} b^{2} d^{3} + a^{2} d^{3}\right)} {\rm polylog}\left(4, -\frac{F^{f g n x + e g n} b}{a}\right) + 12 \, {\left(3 \, a^{2} d^{3} + {\left(3 \, b^{2} d^{3} - 2 \, {\left(b^{2} d^{3} f g n x + b^{2} c d^{2} f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 2 \, {\left(3 \, a b d^{3} - 2 \, {\left(a b d^{3} f g n x + a b c d^{2} f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} - 2 \, {\left(a^{2} d^{3} f g n x + a^{2} c d^{2} f g n\right)} \log\left(F\right)\right)} {\rm polylog}\left(3, -\frac{F^{f g n x + e g n} b}{a}\right)}{4 \, {\left(2 \, F^{f g n x + e g n} a^{4} b f^{4} g^{4} n^{4} \log\left(F\right)^{4} + F^{2 \, f g n x + 2 \, e g n} a^{3} b^{2} f^{4} g^{4} n^{4} \log\left(F\right)^{4} + a^{5} f^{4} g^{4} n^{4} \log\left(F\right)^{4}\right)}}"," ",0,"-1/4*(6*(a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - a^2*c^3*f^3)*g^3*n^3*log(F)^3 + 6*(a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2)*g^2*n^2*log(F)^2 - (a^2*d^3*f^4*g^4*n^4*x^4 + 4*a^2*c*d^2*f^4*g^4*n^4*x^3 + 6*a^2*c^2*d*f^4*g^4*n^4*x^2 + 4*a^2*c^3*f^4*g^4*n^4*x - (a^2*d^3*e^4 - 4*a^2*c*d^2*e^3*f + 6*a^2*c^2*d*e^2*f^2 - 4*a^2*c^3*e*f^3)*g^4*n^4)*log(F)^4 - ((b^2*d^3*f^4*g^4*n^4*x^4 + 4*b^2*c*d^2*f^4*g^4*n^4*x^3 + 6*b^2*c^2*d*f^4*g^4*n^4*x^2 + 4*b^2*c^3*f^4*g^4*n^4*x - (b^2*d^3*e^4 - 4*b^2*c*d^2*e^3*f + 6*b^2*c^2*d*e^2*f^2 - 4*b^2*c^3*e*f^3)*g^4*n^4)*log(F)^4 - 6*(b^2*d^3*f^3*g^3*n^3*x^3 + 3*b^2*c*d^2*f^3*g^3*n^3*x^2 + 3*b^2*c^2*d*f^3*g^3*n^3*x + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2)*g^3*n^3)*log(F)^3 + 6*(b^2*d^3*f^2*g^2*n^2*x^2 + 2*b^2*c*d^2*f^2*g^2*n^2*x - (b^2*d^3*e^2 - 2*b^2*c*d^2*e*f)*g^2*n^2)*log(F)^2)*F^(2*f*g*n*x + 2*e*g*n) - 2*((a*b*d^3*f^4*g^4*n^4*x^4 + 4*a*b*c*d^2*f^4*g^4*n^4*x^3 + 6*a*b*c^2*d*f^4*g^4*n^4*x^2 + 4*a*b*c^3*f^4*g^4*n^4*x - (a*b*d^3*e^4 - 4*a*b*c*d^2*e^3*f + 6*a*b*c^2*d*e^2*f^2 - 4*a*b*c^3*e*f^3)*g^4*n^4)*log(F)^4 - 2*(2*a*b*d^3*f^3*g^3*n^3*x^3 + 6*a*b*c*d^2*f^3*g^3*n^3*x^2 + 6*a*b*c^2*d*f^3*g^3*n^3*x + (3*a*b*d^3*e^3 - 9*a*b*c*d^2*e^2*f + 9*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*g^3*n^3)*log(F)^3 + 3*(a*b*d^3*f^2*g^2*n^2*x^2 + 2*a*b*c*d^2*f^2*g^2*n^2*x - (2*a*b*d^3*e^2 - 4*a*b*c*d^2*e*f + a*b*c^2*d*f^2)*g^2*n^2)*log(F)^2)*F^(f*g*n*x + e*g*n) + 12*(a^2*d^3 + (a^2*d^3*f^2*g^2*n^2*x^2 + 2*a^2*c*d^2*f^2*g^2*n^2*x + a^2*c^2*d*f^2*g^2*n^2)*log(F)^2 + (b^2*d^3 + (b^2*d^3*f^2*g^2*n^2*x^2 + 2*b^2*c*d^2*f^2*g^2*n^2*x + b^2*c^2*d*f^2*g^2*n^2)*log(F)^2 - 3*(b^2*d^3*f*g*n*x + b^2*c*d^2*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 2*(a*b*d^3 + (a*b*d^3*f^2*g^2*n^2*x^2 + 2*a*b*c*d^2*f^2*g^2*n^2*x + a*b*c^2*d*f^2*g^2*n^2)*log(F)^2 - 3*(a*b*d^3*f*g*n*x + a*b*c*d^2*f*g*n)*log(F))*F^(f*g*n*x + e*g*n) - 3*(a^2*d^3*f*g*n*x + a^2*c*d^2*f*g*n)*log(F))*dilog(-(F^(f*g*n*x + e*g*n)*b + a)/a + 1) - 2*(2*(a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2 - a^2*c^3*f^3)*g^3*n^3*log(F)^3 + 9*(a^2*d^3*e^2 - 2*a^2*c*d^2*e*f + a^2*c^2*d*f^2)*g^2*n^2*log(F)^2 + 6*(a^2*d^3*e - a^2*c*d^2*f)*g*n*log(F) + (2*(b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2 - b^2*c^3*f^3)*g^3*n^3*log(F)^3 + 9*(b^2*d^3*e^2 - 2*b^2*c*d^2*e*f + b^2*c^2*d*f^2)*g^2*n^2*log(F)^2 + 6*(b^2*d^3*e - b^2*c*d^2*f)*g*n*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 2*(2*(a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2 - a*b*c^3*f^3)*g^3*n^3*log(F)^3 + 9*(a*b*d^3*e^2 - 2*a*b*c*d^2*e*f + a*b*c^2*d*f^2)*g^2*n^2*log(F)^2 + 6*(a*b*d^3*e - a*b*c*d^2*f)*g*n*log(F))*F^(f*g*n*x + e*g*n))*log(F^(f*g*n*x + e*g*n)*b + a) + 2*(2*(a^2*d^3*f^3*g^3*n^3*x^3 + 3*a^2*c*d^2*f^3*g^3*n^3*x^2 + 3*a^2*c^2*d*f^3*g^3*n^3*x + (a^2*d^3*e^3 - 3*a^2*c*d^2*e^2*f + 3*a^2*c^2*d*e*f^2)*g^3*n^3)*log(F)^3 - 9*(a^2*d^3*f^2*g^2*n^2*x^2 + 2*a^2*c*d^2*f^2*g^2*n^2*x - (a^2*d^3*e^2 - 2*a^2*c*d^2*e*f)*g^2*n^2)*log(F)^2 + (2*(b^2*d^3*f^3*g^3*n^3*x^3 + 3*b^2*c*d^2*f^3*g^3*n^3*x^2 + 3*b^2*c^2*d*f^3*g^3*n^3*x + (b^2*d^3*e^3 - 3*b^2*c*d^2*e^2*f + 3*b^2*c^2*d*e*f^2)*g^3*n^3)*log(F)^3 - 9*(b^2*d^3*f^2*g^2*n^2*x^2 + 2*b^2*c*d^2*f^2*g^2*n^2*x - (b^2*d^3*e^2 - 2*b^2*c*d^2*e*f)*g^2*n^2)*log(F)^2 + 6*(b^2*d^3*f*g*n*x + b^2*d^3*e*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 2*(2*(a*b*d^3*f^3*g^3*n^3*x^3 + 3*a*b*c*d^2*f^3*g^3*n^3*x^2 + 3*a*b*c^2*d*f^3*g^3*n^3*x + (a*b*d^3*e^3 - 3*a*b*c*d^2*e^2*f + 3*a*b*c^2*d*e*f^2)*g^3*n^3)*log(F)^3 - 9*(a*b*d^3*f^2*g^2*n^2*x^2 + 2*a*b*c*d^2*f^2*g^2*n^2*x - (a*b*d^3*e^2 - 2*a*b*c*d^2*e*f)*g^2*n^2)*log(F)^2 + 6*(a*b*d^3*f*g*n*x + a*b*d^3*e*g*n)*log(F))*F^(f*g*n*x + e*g*n) + 6*(a^2*d^3*f*g*n*x + a^2*d^3*e*g*n)*log(F))*log((F^(f*g*n*x + e*g*n)*b + a)/a) + 24*(2*F^(f*g*n*x + e*g*n)*a*b*d^3 + F^(2*f*g*n*x + 2*e*g*n)*b^2*d^3 + a^2*d^3)*polylog(4, -F^(f*g*n*x + e*g*n)*b/a) + 12*(3*a^2*d^3 + (3*b^2*d^3 - 2*(b^2*d^3*f*g*n*x + b^2*c*d^2*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 2*(3*a*b*d^3 - 2*(a*b*d^3*f*g*n*x + a*b*c*d^2*f*g*n)*log(F))*F^(f*g*n*x + e*g*n) - 2*(a^2*d^3*f*g*n*x + a^2*c*d^2*f*g*n)*log(F))*polylog(3, -F^(f*g*n*x + e*g*n)*b/a))/(2*F^(f*g*n*x + e*g*n)*a^4*b*f^4*g^4*n^4*log(F)^4 + F^(2*f*g*n*x + 2*e*g*n)*a^3*b^2*f^4*g^4*n^4*log(F)^4 + a^5*f^4*g^4*n^4*log(F)^4)","C",0
59,1,1518,0,0.472978," ","integrate((d*x+c)^2/(a+b*(F^(g*(f*x+e)))^n)^3,x, algorithm=""fricas"")","\frac{9 \, {\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f + a^{2} c^{2} f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + 6 \, {\left(a^{2} d^{2} e - a^{2} c d f\right)} g n \log\left(F\right) + 2 \, {\left(a^{2} d^{2} f^{3} g^{3} n^{3} x^{3} + 3 \, a^{2} c d f^{3} g^{3} n^{3} x^{2} + 3 \, a^{2} c^{2} f^{3} g^{3} n^{3} x + {\left(a^{2} d^{2} e^{3} - 3 \, a^{2} c d e^{2} f + 3 \, a^{2} c^{2} e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} + {\left(2 \, {\left(b^{2} d^{2} f^{3} g^{3} n^{3} x^{3} + 3 \, b^{2} c d f^{3} g^{3} n^{3} x^{2} + 3 \, b^{2} c^{2} f^{3} g^{3} n^{3} x + {\left(b^{2} d^{2} e^{3} - 3 \, b^{2} c d e^{2} f + 3 \, b^{2} c^{2} e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} - 9 \, {\left(b^{2} d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{2} c d f^{2} g^{2} n^{2} x - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} + 6 \, {\left(b^{2} d^{2} f g n x + b^{2} d^{2} e g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 2 \, {\left(2 \, {\left(a b d^{2} f^{3} g^{3} n^{3} x^{3} + 3 \, a b c d f^{3} g^{3} n^{3} x^{2} + 3 \, a b c^{2} f^{3} g^{3} n^{3} x + {\left(a b d^{2} e^{3} - 3 \, a b c d e^{2} f + 3 \, a b c^{2} e f^{2}\right)} g^{3} n^{3}\right)} \log\left(F\right)^{3} - 3 \, {\left(2 \, a b d^{2} f^{2} g^{2} n^{2} x^{2} + 4 \, a b c d f^{2} g^{2} n^{2} x - {\left(3 \, a b d^{2} e^{2} - 6 \, a b c d e f + a b c^{2} f^{2}\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} + 3 \, {\left(a b d^{2} f g n x + {\left(2 \, a b d^{2} e - a b c d f\right)} g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} + 6 \, {\left(3 \, a^{2} d^{2} + {\left(3 \, b^{2} d^{2} - 2 \, {\left(b^{2} d^{2} f g n x + b^{2} c d f g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 2 \, {\left(3 \, a b d^{2} - 2 \, {\left(a b d^{2} f g n x + a b c d f g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} - 2 \, {\left(a^{2} d^{2} f g n x + a^{2} c d f g n\right)} \log\left(F\right)\right)} {\rm Li}_2\left(-\frac{F^{f g n x + e g n} b + a}{a} + 1\right) - 6 \, {\left({\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f + a^{2} c^{2} f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + a^{2} d^{2} + 3 \, {\left(a^{2} d^{2} e - a^{2} c d f\right)} g n \log\left(F\right) + {\left({\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f + b^{2} c^{2} f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + b^{2} d^{2} + 3 \, {\left(b^{2} d^{2} e - b^{2} c d f\right)} g n \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 2 \, {\left({\left(a b d^{2} e^{2} - 2 \, a b c d e f + a b c^{2} f^{2}\right)} g^{2} n^{2} \log\left(F\right)^{2} + a b d^{2} + 3 \, {\left(a b d^{2} e - a b c d f\right)} g n \log\left(F\right)\right)} F^{f g n x + e g n}\right)} \log\left(F^{f g n x + e g n} b + a\right) - 6 \, {\left({\left(a^{2} d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, a^{2} c d f^{2} g^{2} n^{2} x - {\left(a^{2} d^{2} e^{2} - 2 \, a^{2} c d e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} + {\left({\left(b^{2} d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, b^{2} c d f^{2} g^{2} n^{2} x - {\left(b^{2} d^{2} e^{2} - 2 \, b^{2} c d e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 3 \, {\left(b^{2} d^{2} f g n x + b^{2} d^{2} e g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + 2 \, {\left({\left(a b d^{2} f^{2} g^{2} n^{2} x^{2} + 2 \, a b c d f^{2} g^{2} n^{2} x - {\left(a b d^{2} e^{2} - 2 \, a b c d e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 3 \, {\left(a b d^{2} f g n x + a b d^{2} e g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} - 3 \, {\left(a^{2} d^{2} f g n x + a^{2} d^{2} e g n\right)} \log\left(F\right)\right)} \log\left(\frac{F^{f g n x + e g n} b + a}{a}\right) + 12 \, {\left(2 \, F^{f g n x + e g n} a b d^{2} + F^{2 \, f g n x + 2 \, e g n} b^{2} d^{2} + a^{2} d^{2}\right)} {\rm polylog}\left(3, -\frac{F^{f g n x + e g n} b}{a}\right)}{6 \, {\left(2 \, F^{f g n x + e g n} a^{4} b f^{3} g^{3} n^{3} \log\left(F\right)^{3} + F^{2 \, f g n x + 2 \, e g n} a^{3} b^{2} f^{3} g^{3} n^{3} \log\left(F\right)^{3} + a^{5} f^{3} g^{3} n^{3} \log\left(F\right)^{3}\right)}}"," ",0,"1/6*(9*(a^2*d^2*e^2 - 2*a^2*c*d*e*f + a^2*c^2*f^2)*g^2*n^2*log(F)^2 + 6*(a^2*d^2*e - a^2*c*d*f)*g*n*log(F) + 2*(a^2*d^2*f^3*g^3*n^3*x^3 + 3*a^2*c*d*f^3*g^3*n^3*x^2 + 3*a^2*c^2*f^3*g^3*n^3*x + (a^2*d^2*e^3 - 3*a^2*c*d*e^2*f + 3*a^2*c^2*e*f^2)*g^3*n^3)*log(F)^3 + (2*(b^2*d^2*f^3*g^3*n^3*x^3 + 3*b^2*c*d*f^3*g^3*n^3*x^2 + 3*b^2*c^2*f^3*g^3*n^3*x + (b^2*d^2*e^3 - 3*b^2*c*d*e^2*f + 3*b^2*c^2*e*f^2)*g^3*n^3)*log(F)^3 - 9*(b^2*d^2*f^2*g^2*n^2*x^2 + 2*b^2*c*d*f^2*g^2*n^2*x - (b^2*d^2*e^2 - 2*b^2*c*d*e*f)*g^2*n^2)*log(F)^2 + 6*(b^2*d^2*f*g*n*x + b^2*d^2*e*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 2*(2*(a*b*d^2*f^3*g^3*n^3*x^3 + 3*a*b*c*d*f^3*g^3*n^3*x^2 + 3*a*b*c^2*f^3*g^3*n^3*x + (a*b*d^2*e^3 - 3*a*b*c*d*e^2*f + 3*a*b*c^2*e*f^2)*g^3*n^3)*log(F)^3 - 3*(2*a*b*d^2*f^2*g^2*n^2*x^2 + 4*a*b*c*d*f^2*g^2*n^2*x - (3*a*b*d^2*e^2 - 6*a*b*c*d*e*f + a*b*c^2*f^2)*g^2*n^2)*log(F)^2 + 3*(a*b*d^2*f*g*n*x + (2*a*b*d^2*e - a*b*c*d*f)*g*n)*log(F))*F^(f*g*n*x + e*g*n) + 6*(3*a^2*d^2 + (3*b^2*d^2 - 2*(b^2*d^2*f*g*n*x + b^2*c*d*f*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 2*(3*a*b*d^2 - 2*(a*b*d^2*f*g*n*x + a*b*c*d*f*g*n)*log(F))*F^(f*g*n*x + e*g*n) - 2*(a^2*d^2*f*g*n*x + a^2*c*d*f*g*n)*log(F))*dilog(-(F^(f*g*n*x + e*g*n)*b + a)/a + 1) - 6*((a^2*d^2*e^2 - 2*a^2*c*d*e*f + a^2*c^2*f^2)*g^2*n^2*log(F)^2 + a^2*d^2 + 3*(a^2*d^2*e - a^2*c*d*f)*g*n*log(F) + ((b^2*d^2*e^2 - 2*b^2*c*d*e*f + b^2*c^2*f^2)*g^2*n^2*log(F)^2 + b^2*d^2 + 3*(b^2*d^2*e - b^2*c*d*f)*g*n*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 2*((a*b*d^2*e^2 - 2*a*b*c*d*e*f + a*b*c^2*f^2)*g^2*n^2*log(F)^2 + a*b*d^2 + 3*(a*b*d^2*e - a*b*c*d*f)*g*n*log(F))*F^(f*g*n*x + e*g*n))*log(F^(f*g*n*x + e*g*n)*b + a) - 6*((a^2*d^2*f^2*g^2*n^2*x^2 + 2*a^2*c*d*f^2*g^2*n^2*x - (a^2*d^2*e^2 - 2*a^2*c*d*e*f)*g^2*n^2)*log(F)^2 + ((b^2*d^2*f^2*g^2*n^2*x^2 + 2*b^2*c*d*f^2*g^2*n^2*x - (b^2*d^2*e^2 - 2*b^2*c*d*e*f)*g^2*n^2)*log(F)^2 - 3*(b^2*d^2*f*g*n*x + b^2*d^2*e*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) + 2*((a*b*d^2*f^2*g^2*n^2*x^2 + 2*a*b*c*d*f^2*g^2*n^2*x - (a*b*d^2*e^2 - 2*a*b*c*d*e*f)*g^2*n^2)*log(F)^2 - 3*(a*b*d^2*f*g*n*x + a*b*d^2*e*g*n)*log(F))*F^(f*g*n*x + e*g*n) - 3*(a^2*d^2*f*g*n*x + a^2*d^2*e*g*n)*log(F))*log((F^(f*g*n*x + e*g*n)*b + a)/a) + 12*(2*F^(f*g*n*x + e*g*n)*a*b*d^2 + F^(2*f*g*n*x + 2*e*g*n)*b^2*d^2 + a^2*d^2)*polylog(3, -F^(f*g*n*x + e*g*n)*b/a))/(2*F^(f*g*n*x + e*g*n)*a^4*b*f^3*g^3*n^3*log(F)^3 + F^(2*f*g*n*x + 2*e*g*n)*a^3*b^2*f^3*g^3*n^3*log(F)^3 + a^5*f^3*g^3*n^3*log(F)^3)","C",0
60,1,696,0,0.463941," ","integrate((d*x+c)/(a+b*(F^(g*(f*x+e)))^n)^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} d e - a^{2} c f\right)} g n \log\left(F\right) + a^{2} d - {\left(a^{2} d f^{2} g^{2} n^{2} x^{2} + 2 \, a^{2} c f^{2} g^{2} n^{2} x - {\left(a^{2} d e^{2} - 2 \, a^{2} c e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} - {\left({\left(b^{2} d f^{2} g^{2} n^{2} x^{2} + 2 \, b^{2} c f^{2} g^{2} n^{2} x - {\left(b^{2} d e^{2} - 2 \, b^{2} c e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} - 3 \, {\left(b^{2} d f g n x + b^{2} d e g n\right)} \log\left(F\right)\right)} F^{2 \, f g n x + 2 \, e g n} + {\left(a b d - 2 \, {\left(a b d f^{2} g^{2} n^{2} x^{2} + 2 \, a b c f^{2} g^{2} n^{2} x - {\left(a b d e^{2} - 2 \, a b c e f\right)} g^{2} n^{2}\right)} \log\left(F\right)^{2} + 2 \, {\left(2 \, a b d f g n x + {\left(3 \, a b d e - a b c f\right)} g n\right)} \log\left(F\right)\right)} F^{f g n x + e g n} + 2 \, {\left(2 \, F^{f g n x + e g n} a b d + F^{2 \, f g n x + 2 \, e g n} b^{2} d + a^{2} d\right)} {\rm Li}_2\left(-\frac{F^{f g n x + e g n} b + a}{a} + 1\right) - {\left(2 \, {\left(a^{2} d e - a^{2} c f\right)} g n \log\left(F\right) + 3 \, a^{2} d + {\left(2 \, {\left(b^{2} d e - b^{2} c f\right)} g n \log\left(F\right) + 3 \, b^{2} d\right)} F^{2 \, f g n x + 2 \, e g n} + 2 \, {\left(2 \, {\left(a b d e - a b c f\right)} g n \log\left(F\right) + 3 \, a b d\right)} F^{f g n x + e g n}\right)} \log\left(F^{f g n x + e g n} b + a\right) + 2 \, {\left({\left(b^{2} d f g n x + b^{2} d e g n\right)} F^{2 \, f g n x + 2 \, e g n} \log\left(F\right) + 2 \, {\left(a b d f g n x + a b d e g n\right)} F^{f g n x + e g n} \log\left(F\right) + {\left(a^{2} d f g n x + a^{2} d e g n\right)} \log\left(F\right)\right)} \log\left(\frac{F^{f g n x + e g n} b + a}{a}\right)}{2 \, {\left(2 \, F^{f g n x + e g n} a^{4} b f^{2} g^{2} n^{2} \log\left(F\right)^{2} + F^{2 \, f g n x + 2 \, e g n} a^{3} b^{2} f^{2} g^{2} n^{2} \log\left(F\right)^{2} + a^{5} f^{2} g^{2} n^{2} \log\left(F\right)^{2}\right)}}"," ",0,"-1/2*(3*(a^2*d*e - a^2*c*f)*g*n*log(F) + a^2*d - (a^2*d*f^2*g^2*n^2*x^2 + 2*a^2*c*f^2*g^2*n^2*x - (a^2*d*e^2 - 2*a^2*c*e*f)*g^2*n^2)*log(F)^2 - ((b^2*d*f^2*g^2*n^2*x^2 + 2*b^2*c*f^2*g^2*n^2*x - (b^2*d*e^2 - 2*b^2*c*e*f)*g^2*n^2)*log(F)^2 - 3*(b^2*d*f*g*n*x + b^2*d*e*g*n)*log(F))*F^(2*f*g*n*x + 2*e*g*n) + (a*b*d - 2*(a*b*d*f^2*g^2*n^2*x^2 + 2*a*b*c*f^2*g^2*n^2*x - (a*b*d*e^2 - 2*a*b*c*e*f)*g^2*n^2)*log(F)^2 + 2*(2*a*b*d*f*g*n*x + (3*a*b*d*e - a*b*c*f)*g*n)*log(F))*F^(f*g*n*x + e*g*n) + 2*(2*F^(f*g*n*x + e*g*n)*a*b*d + F^(2*f*g*n*x + 2*e*g*n)*b^2*d + a^2*d)*dilog(-(F^(f*g*n*x + e*g*n)*b + a)/a + 1) - (2*(a^2*d*e - a^2*c*f)*g*n*log(F) + 3*a^2*d + (2*(b^2*d*e - b^2*c*f)*g*n*log(F) + 3*b^2*d)*F^(2*f*g*n*x + 2*e*g*n) + 2*(2*(a*b*d*e - a*b*c*f)*g*n*log(F) + 3*a*b*d)*F^(f*g*n*x + e*g*n))*log(F^(f*g*n*x + e*g*n)*b + a) + 2*((b^2*d*f*g*n*x + b^2*d*e*g*n)*F^(2*f*g*n*x + 2*e*g*n)*log(F) + 2*(a*b*d*f*g*n*x + a*b*d*e*g*n)*F^(f*g*n*x + e*g*n)*log(F) + (a^2*d*f*g*n*x + a^2*d*e*g*n)*log(F))*log((F^(f*g*n*x + e*g*n)*b + a)/a))/(2*F^(f*g*n*x + e*g*n)*a^4*b*f^2*g^2*n^2*log(F)^2 + F^(2*f*g*n*x + 2*e*g*n)*a^3*b^2*f^2*g^2*n^2*log(F)^2 + a^5*f^2*g^2*n^2*log(F)^2)","B",0
61,1,190,0,0.435716," ","integrate(1/(a+b*(F^(g*(f*x+e)))^n)^3,x, algorithm=""fricas"")","\frac{2 \, F^{2 \, f g n x + 2 \, e g n} b^{2} f g n x \log\left(F\right) + 2 \, a^{2} f g n x \log\left(F\right) + 2 \, {\left(2 \, a b f g n x \log\left(F\right) + a b\right)} F^{f g n x + e g n} + 3 \, a^{2} - 2 \, {\left(2 \, F^{f g n x + e g n} a b + F^{2 \, f g n x + 2 \, e g n} b^{2} + a^{2}\right)} \log\left(F^{f g n x + e g n} b + a\right)}{2 \, {\left(2 \, F^{f g n x + e g n} a^{4} b f g n \log\left(F\right) + F^{2 \, f g n x + 2 \, e g n} a^{3} b^{2} f g n \log\left(F\right) + a^{5} f g n \log\left(F\right)\right)}}"," ",0,"1/2*(2*F^(2*f*g*n*x + 2*e*g*n)*b^2*f*g*n*x*log(F) + 2*a^2*f*g*n*x*log(F) + 2*(2*a*b*f*g*n*x*log(F) + a*b)*F^(f*g*n*x + e*g*n) + 3*a^2 - 2*(2*F^(f*g*n*x + e*g*n)*a*b + F^(2*f*g*n*x + 2*e*g*n)*b^2 + a^2)*log(F^(f*g*n*x + e*g*n)*b + a))/(2*F^(f*g*n*x + e*g*n)*a^4*b*f*g*n*log(F) + F^(2*f*g*n*x + 2*e*g*n)*a^3*b^2*f*g*n*log(F) + a^5*f*g*n*log(F))","A",0
62,0,0,0,0.433977," ","integrate(1/(a+b*(F^(g*(f*x+e)))^n)^3/(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{3} d x + a^{3} c + {\left(b^{3} d x + b^{3} c\right)} {\left(F^{f g x + e g}\right)}^{3 \, n} + 3 \, {\left(a b^{2} d x + a b^{2} c\right)} {\left(F^{f g x + e g}\right)}^{2 \, n} + 3 \, {\left(a^{2} b d x + a^{2} b c\right)} {\left(F^{f g x + e g}\right)}^{n}}, x\right)"," ",0,"integral(1/(a^3*d*x + a^3*c + (b^3*d*x + b^3*c)*(F^(f*g*x + e*g))^(3*n) + 3*(a*b^2*d*x + a*b^2*c)*(F^(f*g*x + e*g))^(2*n) + 3*(a^2*b*d*x + a^2*b*c)*(F^(f*g*x + e*g))^n), x)","F",0
63,0,0,0,0.429358," ","integrate(1/(a+b*(F^(g*(f*x+e)))^n)^3/(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{3} d^{2} x^{2} + 2 \, a^{3} c d x + a^{3} c^{2} + {\left(b^{3} d^{2} x^{2} + 2 \, b^{3} c d x + b^{3} c^{2}\right)} {\left(F^{f g x + e g}\right)}^{3 \, n} + 3 \, {\left(a b^{2} d^{2} x^{2} + 2 \, a b^{2} c d x + a b^{2} c^{2}\right)} {\left(F^{f g x + e g}\right)}^{2 \, n} + 3 \, {\left(a^{2} b d^{2} x^{2} + 2 \, a^{2} b c d x + a^{2} b c^{2}\right)} {\left(F^{f g x + e g}\right)}^{n}}, x\right)"," ",0,"integral(1/(a^3*d^2*x^2 + 2*a^3*c*d*x + a^3*c^2 + (b^3*d^2*x^2 + 2*b^3*c*d*x + b^3*c^2)*(F^(f*g*x + e*g))^(3*n) + 3*(a*b^2*d^2*x^2 + 2*a*b^2*c*d*x + a*b^2*c^2)*(F^(f*g*x + e*g))^(2*n) + 3*(a^2*b*d^2*x^2 + 2*a^2*b*c*d*x + a^2*b*c^2)*(F^(f*g*x + e*g))^n), x)","F",0
64,1,70,0,0.454362," ","integrate((a+b*exp(x))*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{\pi} b d^{2} \sqrt{-\frac{1}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{1}{d}}\right) e^{\left(-\frac{c}{d}\right)} + 2 \, {\left(2 \, a d x + 3 \, b d e^{x} + 2 \, a c\right)} \sqrt{d x + c}}{6 \, d}"," ",0,"1/6*(3*sqrt(pi)*b*d^2*sqrt(-1/d)*erf(sqrt(d*x + c)*sqrt(-1/d))*e^(-c/d) + 2*(2*a*d*x + 3*b*d*e^x + 2*a*c)*sqrt(d*x + c))/d","A",0
65,1,133,0,0.436296," ","integrate((a+b*exp(x))^2*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} \sqrt{\pi} b^{2} d^{2} \sqrt{-\frac{1}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{1}{d}}\right) e^{\left(-\frac{2 \, c}{d}\right)} + 24 \, \sqrt{\pi} a b d^{2} \sqrt{-\frac{1}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{1}{d}}\right) e^{\left(-\frac{c}{d}\right)} + 4 \, {\left(4 \, a^{2} d x + 3 \, b^{2} d e^{\left(2 \, x\right)} + 12 \, a b d e^{x} + 4 \, a^{2} c\right)} \sqrt{d x + c}}{24 \, d}"," ",0,"1/24*(3*sqrt(2)*sqrt(pi)*b^2*d^2*sqrt(-1/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-1/d))*e^(-2*c/d) + 24*sqrt(pi)*a*b*d^2*sqrt(-1/d)*erf(sqrt(d*x + c)*sqrt(-1/d))*e^(-c/d) + 4*(4*a^2*d*x + 3*b^2*d*e^(2*x) + 12*a*b*d*e^x + 4*a^2*c)*sqrt(d*x + c))/d","A",0
66,1,196,0,0.458270," ","integrate((a+b*exp(x))^3*(d*x+c)^(1/2),x, algorithm=""fricas"")","\frac{27 \, \sqrt{2} \sqrt{\pi} a b^{2} d^{2} \sqrt{-\frac{1}{d}} \operatorname{erf}\left(\sqrt{2} \sqrt{d x + c} \sqrt{-\frac{1}{d}}\right) e^{\left(-\frac{2 \, c}{d}\right)} + 4 \, \sqrt{3} \sqrt{\pi} b^{3} d^{2} \sqrt{-\frac{1}{d}} \operatorname{erf}\left(\sqrt{3} \sqrt{d x + c} \sqrt{-\frac{1}{d}}\right) e^{\left(-\frac{3 \, c}{d}\right)} + 108 \, \sqrt{\pi} a^{2} b d^{2} \sqrt{-\frac{1}{d}} \operatorname{erf}\left(\sqrt{d x + c} \sqrt{-\frac{1}{d}}\right) e^{\left(-\frac{c}{d}\right)} + 12 \, {\left(4 \, a^{3} d x + 2 \, b^{3} d e^{\left(3 \, x\right)} + 9 \, a b^{2} d e^{\left(2 \, x\right)} + 18 \, a^{2} b d e^{x} + 4 \, a^{3} c\right)} \sqrt{d x + c}}{72 \, d}"," ",0,"1/72*(27*sqrt(2)*sqrt(pi)*a*b^2*d^2*sqrt(-1/d)*erf(sqrt(2)*sqrt(d*x + c)*sqrt(-1/d))*e^(-2*c/d) + 4*sqrt(3)*sqrt(pi)*b^3*d^2*sqrt(-1/d)*erf(sqrt(3)*sqrt(d*x + c)*sqrt(-1/d))*e^(-3*c/d) + 108*sqrt(pi)*a^2*b*d^2*sqrt(-1/d)*erf(sqrt(d*x + c)*sqrt(-1/d))*e^(-c/d) + 12*(4*a^3*d*x + 2*b^3*d*e^(3*x) + 9*a*b^2*d*e^(2*x) + 18*a^2*b*d*e^x + 4*a^3*c)*sqrt(d*x + c))/d","A",0
67,0,0,0,0.454119," ","integrate((d*x+c)^(1/2)/(a+b*exp(x)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x + c}}{b e^{x} + a}, x\right)"," ",0,"integral(sqrt(d*x + c)/(b*e^x + a), x)","F",0
68,0,0,0,0.417825," ","integrate((d*x+c)^(1/2)/(a+b*exp(x))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x + c}}{b^{2} e^{\left(2 \, x\right)} + 2 \, a b e^{x} + a^{2}}, x\right)"," ",0,"integral(sqrt(d*x + c)/(b^2*e^(2*x) + 2*a*b*e^x + a^2), x)","F",0
69,0,0,0,0.426222," ","integrate((d*x+c)^(1/2)/(a+b*exp(x))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{d x + c}}{b^{3} e^{\left(3 \, x\right)} + 3 \, a b^{2} e^{\left(2 \, x\right)} + 3 \, a^{2} b e^{x} + a^{3}}, x\right)"," ",0,"integral(sqrt(d*x + c)/(b^3*e^(3*x) + 3*a*b^2*e^(2*x) + 3*a^2*b*e^x + a^3), x)","F",0
70,1,270,0,0.447403," ","integrate((a+b*(F^(g*(f*x+e)))^n)^3*(d*x+c)^m,x, algorithm=""fricas"")","\frac{18 \, {\left(a^{2} b d m + a^{2} b d\right)} e^{\left(\frac{{\left(d e - c f\right)} g n \log\left(F\right) - d m \log\left(-\frac{f g n \log\left(F\right)}{d}\right)}{d}\right)} \Gamma\left(m + 1, -\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + 9 \, {\left(a b^{2} d m + a b^{2} d\right)} e^{\left(\frac{2 \, {\left(d e - c f\right)} g n \log\left(F\right) - d m \log\left(-\frac{2 \, f g n \log\left(F\right)}{d}\right)}{d}\right)} \Gamma\left(m + 1, -\frac{2 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + 2 \, {\left(b^{3} d m + b^{3} d\right)} e^{\left(\frac{3 \, {\left(d e - c f\right)} g n \log\left(F\right) - d m \log\left(-\frac{3 \, f g n \log\left(F\right)}{d}\right)}{d}\right)} \Gamma\left(m + 1, -\frac{3 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + 6 \, {\left(a^{3} d f g n x + a^{3} c f g n\right)} {\left(d x + c\right)}^{m} \log\left(F\right)}{6 \, {\left(d f g m + d f g\right)} n \log\left(F\right)}"," ",0,"1/6*(18*(a^2*b*d*m + a^2*b*d)*e^(((d*e - c*f)*g*n*log(F) - d*m*log(-f*g*n*log(F)/d))/d)*gamma(m + 1, -(d*f*g*n*x + c*f*g*n)*log(F)/d) + 9*(a*b^2*d*m + a*b^2*d)*e^((2*(d*e - c*f)*g*n*log(F) - d*m*log(-2*f*g*n*log(F)/d))/d)*gamma(m + 1, -2*(d*f*g*n*x + c*f*g*n)*log(F)/d) + 2*(b^3*d*m + b^3*d)*e^((3*(d*e - c*f)*g*n*log(F) - d*m*log(-3*f*g*n*log(F)/d))/d)*gamma(m + 1, -3*(d*f*g*n*x + c*f*g*n)*log(F)/d) + 6*(a^3*d*f*g*n*x + a^3*c*f*g*n)*(d*x + c)^m*log(F))/((d*f*g*m + d*f*g)*n*log(F))","A",0
71,1,191,0,0.447875," ","integrate((a+b*(F^(g*(f*x+e)))^n)^2*(d*x+c)^m,x, algorithm=""fricas"")","\frac{4 \, {\left(a b d m + a b d\right)} e^{\left(\frac{{\left(d e - c f\right)} g n \log\left(F\right) - d m \log\left(-\frac{f g n \log\left(F\right)}{d}\right)}{d}\right)} \Gamma\left(m + 1, -\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + {\left(b^{2} d m + b^{2} d\right)} e^{\left(\frac{2 \, {\left(d e - c f\right)} g n \log\left(F\right) - d m \log\left(-\frac{2 \, f g n \log\left(F\right)}{d}\right)}{d}\right)} \Gamma\left(m + 1, -\frac{2 \, {\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + 2 \, {\left(a^{2} d f g n x + a^{2} c f g n\right)} {\left(d x + c\right)}^{m} \log\left(F\right)}{2 \, {\left(d f g m + d f g\right)} n \log\left(F\right)}"," ",0,"1/2*(4*(a*b*d*m + a*b*d)*e^(((d*e - c*f)*g*n*log(F) - d*m*log(-f*g*n*log(F)/d))/d)*gamma(m + 1, -(d*f*g*n*x + c*f*g*n)*log(F)/d) + (b^2*d*m + b^2*d)*e^((2*(d*e - c*f)*g*n*log(F) - d*m*log(-2*f*g*n*log(F)/d))/d)*gamma(m + 1, -2*(d*f*g*n*x + c*f*g*n)*log(F)/d) + 2*(a^2*d*f*g*n*x + a^2*c*f*g*n)*(d*x + c)^m*log(F))/((d*f*g*m + d*f*g)*n*log(F))","A",0
72,1,111,0,0.435065," ","integrate((a+b*(F^(g*(f*x+e)))^n)*(d*x+c)^m,x, algorithm=""fricas"")","\frac{{\left(b d m + b d\right)} e^{\left(\frac{{\left(d e - c f\right)} g n \log\left(F\right) - d m \log\left(-\frac{f g n \log\left(F\right)}{d}\right)}{d}\right)} \Gamma\left(m + 1, -\frac{{\left(d f g n x + c f g n\right)} \log\left(F\right)}{d}\right) + {\left(a d f g n x + a c f g n\right)} {\left(d x + c\right)}^{m} \log\left(F\right)}{{\left(d f g m + d f g\right)} n \log\left(F\right)}"," ",0,"((b*d*m + b*d)*e^(((d*e - c*f)*g*n*log(F) - d*m*log(-f*g*n*log(F)/d))/d)*gamma(m + 1, -(d*f*g*n*x + c*f*g*n)*log(F)/d) + (a*d*f*g*n*x + a*c*f*g*n)*(d*x + c)^m*log(F))/((d*f*g*m + d*f*g)*n*log(F))","A",0
73,0,0,0,0.441024," ","integrate((d*x+c)^m/(a+b*(F^(g*(f*x+e)))^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{{\left(F^{f g x + e g}\right)}^{n} b + a}, x\right)"," ",0,"integral((d*x + c)^m/((F^(f*g*x + e*g))^n*b + a), x)","F",0
74,0,0,0,0.424750," ","integrate((d*x+c)^m/(a+b*(F^(g*(f*x+e)))^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d x + c\right)}^{m}}{2 \, {\left(F^{f g x + e g}\right)}^{n} a b + {\left(F^{f g x + e g}\right)}^{2 \, n} b^{2} + a^{2}}, x\right)"," ",0,"integral((d*x + c)^m/(2*(F^(f*g*x + e*g))^n*a*b + (F^(f*g*x + e*g))^(2*n)*b^2 + a^2), x)","F",0
75,0,0,0,0.463075," ","integrate((a+b*(F^(g*(f*x+e)))^n)^p*(d*x+c)^m,x, algorithm=""fricas"")","{\rm integral}\left({\left({\left(F^{f g x + e g}\right)}^{n} b + a\right)}^{p} {\left(d x + c\right)}^{m}, x\right)"," ",0,"integral(((F^(f*g*x + e*g))^n*b + a)^p*(d*x + c)^m, x)","F",0
76,1,134,0,0.465048," ","integrate(F^(d*x+c)*x^3/(a+b*F^(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, d^{2} x^{2} {\rm Li}_2\left(-\frac{F^{d x + c} b + a}{a} + 1\right) \log\left(F\right)^{2} - c^{3} \log\left(F^{d x + c} b + a\right) \log\left(F\right)^{3} + {\left(d^{3} x^{3} + c^{3}\right)} \log\left(F\right)^{3} \log\left(\frac{F^{d x + c} b + a}{a}\right) - 6 \, d x \log\left(F\right) {\rm polylog}\left(3, -\frac{F^{d x + c} b}{a}\right) + 6 \, {\rm polylog}\left(4, -\frac{F^{d x + c} b}{a}\right)}{b d^{4} \log\left(F\right)^{4}}"," ",0,"(3*d^2*x^2*dilog(-(F^(d*x + c)*b + a)/a + 1)*log(F)^2 - c^3*log(F^(d*x + c)*b + a)*log(F)^3 + (d^3*x^3 + c^3)*log(F)^3*log((F^(d*x + c)*b + a)/a) - 6*d*x*log(F)*polylog(3, -F^(d*x + c)*b/a) + 6*polylog(4, -F^(d*x + c)*b/a))/(b*d^4*log(F)^4)","C",0
77,1,108,0,0.431826," ","integrate(F^(d*x+c)*x^2/(a+b*F^(d*x+c)),x, algorithm=""fricas"")","\frac{c^{2} \log\left(F^{d x + c} b + a\right) \log\left(F\right)^{2} + 2 \, d x {\rm Li}_2\left(-\frac{F^{d x + c} b + a}{a} + 1\right) \log\left(F\right) + {\left(d^{2} x^{2} - c^{2}\right)} \log\left(F\right)^{2} \log\left(\frac{F^{d x + c} b + a}{a}\right) - 2 \, {\rm polylog}\left(3, -\frac{F^{d x + c} b}{a}\right)}{b d^{3} \log\left(F\right)^{3}}"," ",0,"(c^2*log(F^(d*x + c)*b + a)*log(F)^2 + 2*d*x*dilog(-(F^(d*x + c)*b + a)/a + 1)*log(F) + (d^2*x^2 - c^2)*log(F)^2*log((F^(d*x + c)*b + a)/a) - 2*polylog(3, -F^(d*x + c)*b/a))/(b*d^3*log(F)^3)","C",0
78,1,75,0,0.453526," ","integrate(F^(d*x+c)*x/(a+b*F^(d*x+c)),x, algorithm=""fricas"")","-\frac{c \log\left(F^{d x + c} b + a\right) \log\left(F\right) - {\left(d x + c\right)} \log\left(F\right) \log\left(\frac{F^{d x + c} b + a}{a}\right) - {\rm Li}_2\left(-\frac{F^{d x + c} b + a}{a} + 1\right)}{b d^{2} \log\left(F\right)^{2}}"," ",0,"-(c*log(F^(d*x + c)*b + a)*log(F) - (d*x + c)*log(F)*log((F^(d*x + c)*b + a)/a) - dilog(-(F^(d*x + c)*b + a)/a + 1))/(b*d^2*log(F)^2)","A",0
79,1,23,0,0.414201," ","integrate(F^(d*x+c)/(a+b*F^(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(F^{d x + c} b + a\right)}{b d \log\left(F\right)}"," ",0,"log(F^(d*x + c)*b + a)/(b*d*log(F))","A",0
80,0,0,0,0.425038," ","integrate(F^(d*x+c)/(a+b*F^(d*x+c))/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{d x + c}}{F^{d x + c} b x + a x}, x\right)"," ",0,"integral(F^(d*x + c)/(F^(d*x + c)*b*x + a*x), x)","F",0
81,0,0,0,0.451908," ","integrate(F^(d*x+c)/(a+b*F^(d*x+c))/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{d x + c}}{F^{d x + c} b x^{2} + a x^{2}}, x\right)"," ",0,"integral(F^(d*x + c)/(F^(d*x + c)*b*x^2 + a*x^2), x)","F",0
82,1,246,0,0.456516," ","integrate(F^(d*x+c)*x^3/(a+b*F^(d*x+c))^2,x, algorithm=""fricas"")","\frac{a c^{3} \log\left(F\right)^{3} + {\left(b d^{3} x^{3} + b c^{3}\right)} F^{d x + c} \log\left(F\right)^{3} - 6 \, {\left(F^{d x + c} b d x \log\left(F\right) + a d x \log\left(F\right)\right)} {\rm Li}_2\left(-\frac{F^{d x + c} b + a}{a} + 1\right) - 3 \, {\left(F^{d x + c} b c^{2} \log\left(F\right)^{2} + a c^{2} \log\left(F\right)^{2}\right)} \log\left(F^{d x + c} b + a\right) - 3 \, {\left({\left(b d^{2} x^{2} - b c^{2}\right)} F^{d x + c} \log\left(F\right)^{2} + {\left(a d^{2} x^{2} - a c^{2}\right)} \log\left(F\right)^{2}\right)} \log\left(\frac{F^{d x + c} b + a}{a}\right) + 6 \, {\left(F^{d x + c} b + a\right)} {\rm polylog}\left(3, -\frac{F^{d x + c} b}{a}\right)}{F^{d x + c} a b^{2} d^{4} \log\left(F\right)^{4} + a^{2} b d^{4} \log\left(F\right)^{4}}"," ",0,"(a*c^3*log(F)^3 + (b*d^3*x^3 + b*c^3)*F^(d*x + c)*log(F)^3 - 6*(F^(d*x + c)*b*d*x*log(F) + a*d*x*log(F))*dilog(-(F^(d*x + c)*b + a)/a + 1) - 3*(F^(d*x + c)*b*c^2*log(F)^2 + a*c^2*log(F)^2)*log(F^(d*x + c)*b + a) - 3*((b*d^2*x^2 - b*c^2)*F^(d*x + c)*log(F)^2 + (a*d^2*x^2 - a*c^2)*log(F)^2)*log((F^(d*x + c)*b + a)/a) + 6*(F^(d*x + c)*b + a)*polylog(3, -F^(d*x + c)*b/a))/(F^(d*x + c)*a*b^2*d^4*log(F)^4 + a^2*b*d^4*log(F)^4)","C",0
83,1,186,0,0.421331," ","integrate(F^(d*x+c)*x^2/(a+b*F^(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a c^{2} \log\left(F\right)^{2} - {\left(b d^{2} x^{2} - b c^{2}\right)} F^{d x + c} \log\left(F\right)^{2} + 2 \, {\left(F^{d x + c} b + a\right)} {\rm Li}_2\left(-\frac{F^{d x + c} b + a}{a} + 1\right) - 2 \, {\left(F^{d x + c} b c \log\left(F\right) + a c \log\left(F\right)\right)} \log\left(F^{d x + c} b + a\right) + 2 \, {\left({\left(b d x + b c\right)} F^{d x + c} \log\left(F\right) + {\left(a d x + a c\right)} \log\left(F\right)\right)} \log\left(\frac{F^{d x + c} b + a}{a}\right)}{F^{d x + c} a b^{2} d^{3} \log\left(F\right)^{3} + a^{2} b d^{3} \log\left(F\right)^{3}}"," ",0,"-(a*c^2*log(F)^2 - (b*d^2*x^2 - b*c^2)*F^(d*x + c)*log(F)^2 + 2*(F^(d*x + c)*b + a)*dilog(-(F^(d*x + c)*b + a)/a + 1) - 2*(F^(d*x + c)*b*c*log(F) + a*c*log(F))*log(F^(d*x + c)*b + a) + 2*((b*d*x + b*c)*F^(d*x + c)*log(F) + (a*d*x + a*c)*log(F))*log((F^(d*x + c)*b + a)/a))/(F^(d*x + c)*a*b^2*d^3*log(F)^3 + a^2*b*d^3*log(F)^3)","A",0
84,1,74,0,0.429934," ","integrate(F^(d*x+c)*x/(a+b*F^(d*x+c))^2,x, algorithm=""fricas"")","\frac{F^{d x + c} b d x \log\left(F\right) - {\left(F^{d x + c} b + a\right)} \log\left(F^{d x + c} b + a\right)}{F^{d x + c} a b^{2} d^{2} \log\left(F\right)^{2} + a^{2} b d^{2} \log\left(F\right)^{2}}"," ",0,"(F^(d*x + c)*b*d*x*log(F) - (F^(d*x + c)*b + a)*log(F^(d*x + c)*b + a))/(F^(d*x + c)*a*b^2*d^2*log(F)^2 + a^2*b*d^2*log(F)^2)","A",0
85,1,25,0,0.428579," ","integrate(F^(d*x+c)/(a+b*F^(d*x+c))^2,x, algorithm=""fricas"")","-\frac{1}{F^{d x + c} b^{2} d \log\left(F\right) + a b d \log\left(F\right)}"," ",0,"-1/(F^(d*x + c)*b^2*d*log(F) + a*b*d*log(F))","A",0
86,0,0,0,0.431974," ","integrate(F^(d*x+c)/(a+b*F^(d*x+c))^2/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{d x + c}}{2 \, F^{d x + c} a b x + F^{2 \, d x + 2 \, c} b^{2} x + a^{2} x}, x\right)"," ",0,"integral(F^(d*x + c)/(2*F^(d*x + c)*a*b*x + F^(2*d*x + 2*c)*b^2*x + a^2*x), x)","F",0
87,0,0,0,0.424089," ","integrate(F^(d*x+c)/(a+b*F^(d*x+c))^2/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{d x + c}}{2 \, F^{d x + c} a b x^{2} + F^{2 \, d x + 2 \, c} b^{2} x^{2} + a^{2} x^{2}}, x\right)"," ",0,"integral(F^(d*x + c)/(2*F^(d*x + c)*a*b*x^2 + F^(2*d*x + 2*c)*b^2*x^2 + a^2*x^2), x)","F",0
88,1,577,0,0.450131," ","integrate(F^(d*x+c)*x^3/(a+b*F^(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{2} c^{3} \log\left(F\right)^{3} + 3 \, a^{2} c^{2} \log\left(F\right)^{2} + {\left({\left(b^{2} d^{3} x^{3} + b^{2} c^{3}\right)} \log\left(F\right)^{3} - 3 \, {\left(b^{2} d^{2} x^{2} - b^{2} c^{2}\right)} \log\left(F\right)^{2}\right)} F^{2 \, d x + 2 \, c} + {\left(2 \, {\left(a b d^{3} x^{3} + a b c^{3}\right)} \log\left(F\right)^{3} - 3 \, {\left(a b d^{2} x^{2} - 2 \, a b c^{2}\right)} \log\left(F\right)^{2}\right)} F^{d x + c} - 6 \, {\left(a^{2} d x \log\left(F\right) + {\left(b^{2} d x \log\left(F\right) - b^{2}\right)} F^{2 \, d x + 2 \, c} + 2 \, {\left(a b d x \log\left(F\right) - a b\right)} F^{d x + c} - a^{2}\right)} {\rm Li}_2\left(-\frac{F^{d x + c} b + a}{a} + 1\right) - 3 \, {\left(a^{2} c^{2} \log\left(F\right)^{2} + 2 \, a^{2} c \log\left(F\right) + {\left(b^{2} c^{2} \log\left(F\right)^{2} + 2 \, b^{2} c \log\left(F\right)\right)} F^{2 \, d x + 2 \, c} + 2 \, {\left(a b c^{2} \log\left(F\right)^{2} + 2 \, a b c \log\left(F\right)\right)} F^{d x + c}\right)} \log\left(F^{d x + c} b + a\right) - 3 \, {\left({\left(a^{2} d^{2} x^{2} - a^{2} c^{2}\right)} \log\left(F\right)^{2} + {\left({\left(b^{2} d^{2} x^{2} - b^{2} c^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(b^{2} d x + b^{2} c\right)} \log\left(F\right)\right)} F^{2 \, d x + 2 \, c} + 2 \, {\left({\left(a b d^{2} x^{2} - a b c^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(a b d x + a b c\right)} \log\left(F\right)\right)} F^{d x + c} - 2 \, {\left(a^{2} d x + a^{2} c\right)} \log\left(F\right)\right)} \log\left(\frac{F^{d x + c} b + a}{a}\right) + 6 \, {\left(2 \, F^{d x + c} a b + F^{2 \, d x + 2 \, c} b^{2} + a^{2}\right)} {\rm polylog}\left(3, -\frac{F^{d x + c} b}{a}\right)}{2 \, {\left(2 \, F^{d x + c} a^{3} b^{2} d^{4} \log\left(F\right)^{4} + F^{2 \, d x + 2 \, c} a^{2} b^{3} d^{4} \log\left(F\right)^{4} + a^{4} b d^{4} \log\left(F\right)^{4}\right)}}"," ",0,"1/2*(a^2*c^3*log(F)^3 + 3*a^2*c^2*log(F)^2 + ((b^2*d^3*x^3 + b^2*c^3)*log(F)^3 - 3*(b^2*d^2*x^2 - b^2*c^2)*log(F)^2)*F^(2*d*x + 2*c) + (2*(a*b*d^3*x^3 + a*b*c^3)*log(F)^3 - 3*(a*b*d^2*x^2 - 2*a*b*c^2)*log(F)^2)*F^(d*x + c) - 6*(a^2*d*x*log(F) + (b^2*d*x*log(F) - b^2)*F^(2*d*x + 2*c) + 2*(a*b*d*x*log(F) - a*b)*F^(d*x + c) - a^2)*dilog(-(F^(d*x + c)*b + a)/a + 1) - 3*(a^2*c^2*log(F)^2 + 2*a^2*c*log(F) + (b^2*c^2*log(F)^2 + 2*b^2*c*log(F))*F^(2*d*x + 2*c) + 2*(a*b*c^2*log(F)^2 + 2*a*b*c*log(F))*F^(d*x + c))*log(F^(d*x + c)*b + a) - 3*((a^2*d^2*x^2 - a^2*c^2)*log(F)^2 + ((b^2*d^2*x^2 - b^2*c^2)*log(F)^2 - 2*(b^2*d*x + b^2*c)*log(F))*F^(2*d*x + 2*c) + 2*((a*b*d^2*x^2 - a*b*c^2)*log(F)^2 - 2*(a*b*d*x + a*b*c)*log(F))*F^(d*x + c) - 2*(a^2*d*x + a^2*c)*log(F))*log((F^(d*x + c)*b + a)/a) + 6*(2*F^(d*x + c)*a*b + F^(2*d*x + 2*c)*b^2 + a^2)*polylog(3, -F^(d*x + c)*b/a))/(2*F^(d*x + c)*a^3*b^2*d^4*log(F)^4 + F^(2*d*x + 2*c)*a^2*b^3*d^4*log(F)^4 + a^4*b*d^4*log(F)^4)","C",0
89,1,379,0,0.440311," ","integrate(F^(d*x+c)*x^2/(a+b*F^(d*x+c))^3,x, algorithm=""fricas"")","-\frac{a^{2} c^{2} \log\left(F\right)^{2} + 2 \, a^{2} c \log\left(F\right) - {\left({\left(b^{2} d^{2} x^{2} - b^{2} c^{2}\right)} \log\left(F\right)^{2} - 2 \, {\left(b^{2} d x + b^{2} c\right)} \log\left(F\right)\right)} F^{2 \, d x + 2 \, c} - 2 \, {\left({\left(a b d^{2} x^{2} - a b c^{2}\right)} \log\left(F\right)^{2} - {\left(a b d x + 2 \, a b c\right)} \log\left(F\right)\right)} F^{d x + c} + 2 \, {\left(2 \, F^{d x + c} a b + F^{2 \, d x + 2 \, c} b^{2} + a^{2}\right)} {\rm Li}_2\left(-\frac{F^{d x + c} b + a}{a} + 1\right) - 2 \, {\left(a^{2} c \log\left(F\right) + {\left(b^{2} c \log\left(F\right) + b^{2}\right)} F^{2 \, d x + 2 \, c} + 2 \, {\left(a b c \log\left(F\right) + a b\right)} F^{d x + c} + a^{2}\right)} \log\left(F^{d x + c} b + a\right) + 2 \, {\left({\left(b^{2} d x + b^{2} c\right)} F^{2 \, d x + 2 \, c} \log\left(F\right) + 2 \, {\left(a b d x + a b c\right)} F^{d x + c} \log\left(F\right) + {\left(a^{2} d x + a^{2} c\right)} \log\left(F\right)\right)} \log\left(\frac{F^{d x + c} b + a}{a}\right)}{2 \, {\left(2 \, F^{d x + c} a^{3} b^{2} d^{3} \log\left(F\right)^{3} + F^{2 \, d x + 2 \, c} a^{2} b^{3} d^{3} \log\left(F\right)^{3} + a^{4} b d^{3} \log\left(F\right)^{3}\right)}}"," ",0,"-1/2*(a^2*c^2*log(F)^2 + 2*a^2*c*log(F) - ((b^2*d^2*x^2 - b^2*c^2)*log(F)^2 - 2*(b^2*d*x + b^2*c)*log(F))*F^(2*d*x + 2*c) - 2*((a*b*d^2*x^2 - a*b*c^2)*log(F)^2 - (a*b*d*x + 2*a*b*c)*log(F))*F^(d*x + c) + 2*(2*F^(d*x + c)*a*b + F^(2*d*x + 2*c)*b^2 + a^2)*dilog(-(F^(d*x + c)*b + a)/a + 1) - 2*(a^2*c*log(F) + (b^2*c*log(F) + b^2)*F^(2*d*x + 2*c) + 2*(a*b*c*log(F) + a*b)*F^(d*x + c) + a^2)*log(F^(d*x + c)*b + a) + 2*((b^2*d*x + b^2*c)*F^(2*d*x + 2*c)*log(F) + 2*(a*b*d*x + a*b*c)*F^(d*x + c)*log(F) + (a^2*d*x + a^2*c)*log(F))*log((F^(d*x + c)*b + a)/a))/(2*F^(d*x + c)*a^3*b^2*d^3*log(F)^3 + F^(2*d*x + 2*c)*a^2*b^3*d^3*log(F)^3 + a^4*b*d^3*log(F)^3)","B",0
90,1,148,0,0.432998," ","integrate(F^(d*x+c)*x/(a+b*F^(d*x+c))^3,x, algorithm=""fricas"")","\frac{F^{2 \, d x + 2 \, c} b^{2} d x \log\left(F\right) + {\left(2 \, a b d x \log\left(F\right) + a b\right)} F^{d x + c} + a^{2} - {\left(2 \, F^{d x + c} a b + F^{2 \, d x + 2 \, c} b^{2} + a^{2}\right)} \log\left(F^{d x + c} b + a\right)}{2 \, {\left(2 \, F^{d x + c} a^{3} b^{2} d^{2} \log\left(F\right)^{2} + F^{2 \, d x + 2 \, c} a^{2} b^{3} d^{2} \log\left(F\right)^{2} + a^{4} b d^{2} \log\left(F\right)^{2}\right)}}"," ",0,"1/2*(F^(2*d*x + 2*c)*b^2*d*x*log(F) + (2*a*b*d*x*log(F) + a*b)*F^(d*x + c) + a^2 - (2*F^(d*x + c)*a*b + F^(2*d*x + 2*c)*b^2 + a^2)*log(F^(d*x + c)*b + a))/(2*F^(d*x + c)*a^3*b^2*d^2*log(F)^2 + F^(2*d*x + 2*c)*a^2*b^3*d^2*log(F)^2 + a^4*b*d^2*log(F)^2)","A",0
91,1,46,0,0.409555," ","integrate(F^(d*x+c)/(a+b*F^(d*x+c))^3,x, algorithm=""fricas"")","-\frac{1}{2 \, {\left(2 \, F^{d x + c} a b^{2} d \log\left(F\right) + F^{2 \, d x + 2 \, c} b^{3} d \log\left(F\right) + a^{2} b d \log\left(F\right)\right)}}"," ",0,"-1/2/(2*F^(d*x + c)*a*b^2*d*log(F) + F^(2*d*x + 2*c)*b^3*d*log(F) + a^2*b*d*log(F))","A",0
92,0,0,0,0.420868," ","integrate(F^(d*x+c)/(a+b*F^(d*x+c))^3/x,x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{d x + c}}{3 \, F^{d x + c} a^{2} b x + 3 \, F^{2 \, d x + 2 \, c} a b^{2} x + F^{3 \, d x + 3 \, c} b^{3} x + a^{3} x}, x\right)"," ",0,"integral(F^(d*x + c)/(3*F^(d*x + c)*a^2*b*x + 3*F^(2*d*x + 2*c)*a*b^2*x + F^(3*d*x + 3*c)*b^3*x + a^3*x), x)","F",0
93,0,0,0,0.413115," ","integrate(F^(d*x+c)/(a+b*F^(d*x+c))^3/x^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{F^{d x + c}}{3 \, F^{d x + c} a^{2} b x^{2} + 3 \, F^{2 \, d x + 2 \, c} a b^{2} x^{2} + F^{3 \, d x + 3 \, c} b^{3} x^{2} + a^{3} x^{2}}, x\right)"," ",0,"integral(F^(d*x + c)/(3*F^(d*x + c)*a^2*b*x^2 + 3*F^(2*d*x + 2*c)*a*b^2*x^2 + F^(3*d*x + 3*c)*b^3*x^2 + a^3*x^2), x)","F",0
