1,0,0,0,0.000000," ","integrate(x**3/(a+b*exp(d*x+c)),x)","\int \frac{x^{3}}{a + b e^{c} e^{d x}}\, dx"," ",0,"Integral(x**3/(a + b*exp(c)*exp(d*x)), x)","F",0
2,0,0,0,0.000000," ","integrate(x**2/(a+b*exp(d*x+c)),x)","\int \frac{x^{2}}{a + b e^{c} e^{d x}}\, dx"," ",0,"Integral(x**2/(a + b*exp(c)*exp(d*x)), x)","F",0
3,0,0,0,0.000000," ","integrate(x/(a+b*exp(d*x+c)),x)","\int \frac{x}{a + b e^{c} e^{d x}}\, dx"," ",0,"Integral(x/(a + b*exp(c)*exp(d*x)), x)","F",0
4,1,17,0,0.122818," ","integrate(1/(a+b*exp(d*x+c)),x)","\frac{x}{a} - \frac{\log{\left(\frac{a}{b} + e^{c + d x} \right)}}{a d}"," ",0,"x/a - log(a/b + exp(c + d*x))/(a*d)","A",0
5,0,0,0,0.000000," ","integrate(1/(a+b*exp(d*x+c))/x,x)","\int \frac{1}{x \left(a + b e^{c} e^{d x}\right)}\, dx"," ",0,"Integral(1/(x*(a + b*exp(c)*exp(d*x))), x)","F",0
6,0,0,0,0.000000," ","integrate(1/(a+b*exp(d*x+c))/x**2,x)","\int \frac{1}{x^{2} \left(a + b e^{c} e^{d x}\right)}\, dx"," ",0,"Integral(1/(x**2*(a + b*exp(c)*exp(d*x))), x)","F",0
7,1,17,0,0.126906," ","integrate(1/(a+b*exp(-d*x+c)),x)","\frac{x}{a} + \frac{\log{\left(\frac{a}{b} + e^{c - d x} \right)}}{a d}"," ",0,"x/a + log(a/b + exp(c - d*x))/(a*d)","A",0
8,1,19,0,0.131995," ","integrate(1/(a+b*exp(-d*x-c)),x)","\frac{x}{a} + \frac{\log{\left(\frac{a}{b} + e^{- c - d x} \right)}}{a d}"," ",0,"x/a + log(a/b + exp(-c - d*x))/(a*d)","A",0
9,0,0,0,0.000000," ","integrate(x**3/(a+b*exp(d*x+c))**2,x)","\frac{x^{3}}{a^{2} d + a b d e^{c + d x}} + \frac{\int \left(- \frac{3 x^{2}}{a + b e^{c} e^{d x}}\right)\, dx + \int \frac{d x^{3}}{a + b e^{c} e^{d x}}\, dx}{a d}"," ",0,"x**3/(a**2*d + a*b*d*exp(c + d*x)) + (Integral(-3*x**2/(a + b*exp(c)*exp(d*x)), x) + Integral(d*x**3/(a + b*exp(c)*exp(d*x)), x))/(a*d)","F",0
10,0,0,0,0.000000," ","integrate(x**2/(a+b*exp(d*x+c))**2,x)","\frac{x^{2}}{a^{2} d + a b d e^{c + d x}} + \frac{\int \left(- \frac{2 x}{a + b e^{c} e^{d x}}\right)\, dx + \int \frac{d x^{2}}{a + b e^{c} e^{d x}}\, dx}{a d}"," ",0,"x**2/(a**2*d + a*b*d*exp(c + d*x)) + (Integral(-2*x/(a + b*exp(c)*exp(d*x)), x) + Integral(d*x**2/(a + b*exp(c)*exp(d*x)), x))/(a*d)","F",0
11,0,0,0,0.000000," ","integrate(x/(a+b*exp(d*x+c))**2,x)","\frac{x}{a^{2} d + a b d e^{c + d x}} + \frac{\int \frac{d x}{a + b e^{c} e^{d x}}\, dx + \int \left(- \frac{1}{a + b e^{c} e^{d x}}\right)\, dx}{a d}"," ",0,"x/(a**2*d + a*b*d*exp(c + d*x)) + (Integral(d*x/(a + b*exp(c)*exp(d*x)), x) + Integral(-1/(a + b*exp(c)*exp(d*x)), x))/(a*d)","F",0
12,1,39,0,0.149202," ","integrate(1/(a+b*exp(d*x+c))**2,x)","\frac{1}{a^{2} d + a b d e^{c + d x}} + \frac{x}{a^{2}} - \frac{\log{\left(\frac{a}{b} + e^{c + d x} \right)}}{a^{2} d}"," ",0,"1/(a**2*d + a*b*d*exp(c + d*x)) + x/a**2 - log(a/b + exp(c + d*x))/(a**2*d)","A",0
13,0,0,0,0.000000," ","integrate(1/(a+b*exp(d*x+c))**2/x,x)","\frac{1}{a^{2} d x + a b d x e^{c + d x}} + \frac{\int \frac{d x}{a x^{2} + b x^{2} e^{c} e^{d x}}\, dx + \int \frac{1}{a x^{2} + b x^{2} e^{c} e^{d x}}\, dx}{a d}"," ",0,"1/(a**2*d*x + a*b*d*x*exp(c + d*x)) + (Integral(d*x/(a*x**2 + b*x**2*exp(c)*exp(d*x)), x) + Integral(1/(a*x**2 + b*x**2*exp(c)*exp(d*x)), x))/(a*d)","F",0
14,0,0,0,0.000000," ","integrate(1/(a+b*exp(d*x+c))**2/x**2,x)","\frac{1}{a^{2} d x^{2} + a b d x^{2} e^{c + d x}} + \frac{\int \frac{d x}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx + \int \frac{2}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx}{a d}"," ",0,"1/(a**2*d*x**2 + a*b*d*x**2*exp(c + d*x)) + (Integral(d*x/(a*x**3 + b*x**3*exp(c)*exp(d*x)), x) + Integral(2/(a*x**3 + b*x**3*exp(c)*exp(d*x)), x))/(a*d)","F",0
15,1,39,0,0.157919," ","integrate(1/(a+b*exp(-d*x+c))**2,x)","- \frac{1}{a^{2} d + a b d e^{c - d x}} + \frac{x}{a^{2}} + \frac{\log{\left(\frac{a}{b} + e^{c - d x} \right)}}{a^{2} d}"," ",0,"-1/(a**2*d + a*b*d*exp(c - d*x)) + x/a**2 + log(a/b + exp(c - d*x))/(a**2*d)","A",0
16,1,42,0,0.167591," ","integrate(1/(a+b*exp(-d*x-c))**2,x)","- \frac{1}{a^{2} d + a b d e^{- c - d x}} + \frac{x}{a^{2}} + \frac{\log{\left(\frac{a}{b} + e^{- c - d x} \right)}}{a^{2} d}"," ",0,"-1/(a**2*d + a*b*d*exp(-c - d*x)) + x/a**2 + log(a/b + exp(-c - d*x))/(a**2*d)","A",0
17,0,0,0,0.000000," ","integrate(x**3/(a+b*exp(d*x+c))**3,x)","\frac{3 a d x^{3} - 3 a x^{2} + \left(2 b d x^{3} - 3 b x^{2}\right) e^{c + d x}}{2 a^{4} d^{2} + 4 a^{3} b d^{2} e^{c + d x} + 2 a^{2} b^{2} d^{2} e^{2 c + 2 d x}} + \frac{\int \frac{6 x}{a + b e^{c} e^{d x}}\, dx + \int \left(- \frac{9 d x^{2}}{a + b e^{c} e^{d x}}\right)\, dx + \int \frac{2 d^{2} x^{3}}{a + b e^{c} e^{d x}}\, dx}{2 a^{2} d^{2}}"," ",0,"(3*a*d*x**3 - 3*a*x**2 + (2*b*d*x**3 - 3*b*x**2)*exp(c + d*x))/(2*a**4*d**2 + 4*a**3*b*d**2*exp(c + d*x) + 2*a**2*b**2*d**2*exp(2*c + 2*d*x)) + (Integral(6*x/(a + b*exp(c)*exp(d*x)), x) + Integral(-9*d*x**2/(a + b*exp(c)*exp(d*x)), x) + Integral(2*d**2*x**3/(a + b*exp(c)*exp(d*x)), x))/(2*a**2*d**2)","F",0
18,0,0,0,0.000000," ","integrate(x**2/(a+b*exp(d*x+c))**3,x)","\frac{3 a d x^{2} - 2 a x + \left(2 b d x^{2} - 2 b x\right) e^{c + d x}}{2 a^{4} d^{2} + 4 a^{3} b d^{2} e^{c + d x} + 2 a^{2} b^{2} d^{2} e^{2 c + 2 d x}} + \frac{\int \left(- \frac{3 d x}{a + b e^{c} e^{d x}}\right)\, dx + \int \frac{d^{2} x^{2}}{a + b e^{c} e^{d x}}\, dx + \int \frac{1}{a + b e^{c} e^{d x}}\, dx}{a^{2} d^{2}}"," ",0,"(3*a*d*x**2 - 2*a*x + (2*b*d*x**2 - 2*b*x)*exp(c + d*x))/(2*a**4*d**2 + 4*a**3*b*d**2*exp(c + d*x) + 2*a**2*b**2*d**2*exp(2*c + 2*d*x)) + (Integral(-3*d*x/(a + b*exp(c)*exp(d*x)), x) + Integral(d**2*x**2/(a + b*exp(c)*exp(d*x)), x) + Integral(1/(a + b*exp(c)*exp(d*x)), x))/(a**2*d**2)","F",0
19,0,0,0,0.000000," ","integrate(x/(a+b*exp(d*x+c))**3,x)","\frac{3 a d x - a + \left(2 b d x - b\right) e^{c + d x}}{2 a^{4} d^{2} + 4 a^{3} b d^{2} e^{c + d x} + 2 a^{2} b^{2} d^{2} e^{2 c + 2 d x}} + \frac{\int \frac{2 d x}{a + b e^{c} e^{d x}}\, dx + \int \left(- \frac{3}{a + b e^{c} e^{d x}}\right)\, dx}{2 a^{2} d}"," ",0,"(3*a*d*x - a + (2*b*d*x - b)*exp(c + d*x))/(2*a**4*d**2 + 4*a**3*b*d**2*exp(c + d*x) + 2*a**2*b**2*d**2*exp(2*c + 2*d*x)) + (Integral(2*d*x/(a + b*exp(c)*exp(d*x)), x) + Integral(-3/(a + b*exp(c)*exp(d*x)), x))/(2*a**2*d)","F",0
20,1,76,0,0.187537," ","integrate(1/(a+b*exp(d*x+c))**3,x)","\frac{3 a + 2 b e^{c + d x}}{2 a^{4} d + 4 a^{3} b d e^{c + d x} + 2 a^{2} b^{2} d e^{2 c + 2 d x}} + \frac{x}{a^{3}} - \frac{\log{\left(\frac{a}{b} + e^{c + d x} \right)}}{a^{3} d}"," ",0,"(3*a + 2*b*exp(c + d*x))/(2*a**4*d + 4*a**3*b*d*exp(c + d*x) + 2*a**2*b**2*d*exp(2*c + 2*d*x)) + x/a**3 - log(a/b + exp(c + d*x))/(a**3*d)","A",0
21,0,0,0,0.000000," ","integrate(1/(a+b*exp(d*x+c))**3/x,x)","\frac{3 a d x + a + \left(2 b d x + b\right) e^{c + d x}}{2 a^{4} d^{2} x^{2} + 4 a^{3} b d^{2} x^{2} e^{c + d x} + 2 a^{2} b^{2} d^{2} x^{2} e^{2 c + 2 d x}} + \frac{\int \frac{3 d x}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx + \int \frac{2 d^{2} x^{2}}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx + \int \frac{2}{a x^{3} + b x^{3} e^{c} e^{d x}}\, dx}{2 a^{2} d^{2}}"," ",0,"(3*a*d*x + a + (2*b*d*x + b)*exp(c + d*x))/(2*a**4*d**2*x**2 + 4*a**3*b*d**2*x**2*exp(c + d*x) + 2*a**2*b**2*d**2*x**2*exp(2*c + 2*d*x)) + (Integral(3*d*x/(a*x**3 + b*x**3*exp(c)*exp(d*x)), x) + Integral(2*d**2*x**2/(a*x**3 + b*x**3*exp(c)*exp(d*x)), x) + Integral(2/(a*x**3 + b*x**3*exp(c)*exp(d*x)), x))/(2*a**2*d**2)","F",0
22,0,0,0,0.000000," ","integrate(1/(a+b*exp(d*x+c))**3/x**2,x)","\frac{3 a d x + 2 a + \left(2 b d x + 2 b\right) e^{c + d x}}{2 a^{4} d^{2} x^{3} + 4 a^{3} b d^{2} x^{3} e^{c + d x} + 2 a^{2} b^{2} d^{2} x^{3} e^{2 c + 2 d x}} + \frac{\int \frac{3 d x}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx + \int \frac{d^{2} x^{2}}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx + \int \frac{3}{a x^{4} + b x^{4} e^{c} e^{d x}}\, dx}{a^{2} d^{2}}"," ",0,"(3*a*d*x + 2*a + (2*b*d*x + 2*b)*exp(c + d*x))/(2*a**4*d**2*x**3 + 4*a**3*b*d**2*x**3*exp(c + d*x) + 2*a**2*b**2*d**2*x**3*exp(2*c + 2*d*x)) + (Integral(3*d*x/(a*x**4 + b*x**4*exp(c)*exp(d*x)), x) + Integral(d**2*x**2/(a*x**4 + b*x**4*exp(c)*exp(d*x)), x) + Integral(3/(a*x**4 + b*x**4*exp(c)*exp(d*x)), x))/(a**2*d**2)","F",0
23,1,78,0,0.198649," ","integrate(1/(a+b*exp(-d*x+c))**3,x)","\frac{- 3 a - 2 b e^{c - d x}}{2 a^{4} d + 4 a^{3} b d e^{c - d x} + 2 a^{2} b^{2} d e^{2 c - 2 d x}} + \frac{x}{a^{3}} + \frac{\log{\left(\frac{a}{b} + e^{c - d x} \right)}}{a^{3} d}"," ",0,"(-3*a - 2*b*exp(c - d*x))/(2*a**4*d + 4*a**3*b*d*exp(c - d*x) + 2*a**2*b**2*d*exp(2*c - 2*d*x)) + x/a**3 + log(a/b + exp(c - d*x))/(a**3*d)","A",0
24,1,85,0,0.204779," ","integrate(1/(a+b*exp(-d*x-c))**3,x)","\frac{- 3 a - 2 b e^{- c - d x}}{2 a^{4} d + 4 a^{3} b d e^{- c - d x} + 2 a^{2} b^{2} d e^{- 2 c - 2 d x}} + \frac{x}{a^{3}} + \frac{\log{\left(\frac{a}{b} + e^{- c - d x} \right)}}{a^{3} d}"," ",0,"(-3*a - 2*b*exp(-c - d*x))/(2*a**4*d + 4*a**3*b*d*exp(-c - d*x) + 2*a**2*b**2*d*exp(-2*c - 2*d*x)) + x/a**3 + log(a/b + exp(-c - d*x))/(a**3*d)","A",0
25,1,332,0,0.277517," ","integrate((a+b*(F**(g*(f*x+e)))**n)*(d*x+c)**3,x)","a c^{3} x + \frac{3 a c^{2} d x^{2}}{2} + a c d^{2} x^{3} + \frac{a d^{3} x^{4}}{4} + \begin{cases} \frac{\left(b c^{3} f^{3} g^{3} n^{3} \log{\left(F \right)}^{3} + 3 b c^{2} d f^{3} g^{3} n^{3} x \log{\left(F \right)}^{3} - 3 b c^{2} d f^{2} g^{2} n^{2} \log{\left(F \right)}^{2} + 3 b c d^{2} f^{3} g^{3} n^{3} x^{2} \log{\left(F \right)}^{3} - 6 b c d^{2} f^{2} g^{2} n^{2} x \log{\left(F \right)}^{2} + 6 b c d^{2} f g n \log{\left(F \right)} + b d^{3} f^{3} g^{3} n^{3} x^{3} \log{\left(F \right)}^{3} - 3 b d^{3} f^{2} g^{2} n^{2} x^{2} \log{\left(F \right)}^{2} + 6 b d^{3} f g n x \log{\left(F \right)} - 6 b d^{3}\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{f^{4} g^{4} n^{4} \log{\left(F \right)}^{4}} & \text{for}\: f^{4} g^{4} n^{4} \log{\left(F \right)}^{4} \neq 0 \\b c^{3} x + \frac{3 b c^{2} d x^{2}}{2} + b c d^{2} x^{3} + \frac{b d^{3} x^{4}}{4} & \text{otherwise} \end{cases}"," ",0,"a*c**3*x + 3*a*c**2*d*x**2/2 + a*c*d**2*x**3 + a*d**3*x**4/4 + Piecewise(((b*c**3*f**3*g**3*n**3*log(F)**3 + 3*b*c**2*d*f**3*g**3*n**3*x*log(F)**3 - 3*b*c**2*d*f**2*g**2*n**2*log(F)**2 + 3*b*c*d**2*f**3*g**3*n**3*x**2*log(F)**3 - 6*b*c*d**2*f**2*g**2*n**2*x*log(F)**2 + 6*b*c*d**2*f*g*n*log(F) + b*d**3*f**3*g**3*n**3*x**3*log(F)**3 - 3*b*d**3*f**2*g**2*n**2*x**2*log(F)**2 + 6*b*d**3*f*g*n*x*log(F) - 6*b*d**3)*(F**(g*(e + f*x)))**n/(f**4*g**4*n**4*log(F)**4), Ne(f**4*g**4*n**4*log(F)**4, 0)), (b*c**3*x + 3*b*c**2*d*x**2/2 + b*c*d**2*x**3 + b*d**3*x**4/4, True))","A",0
26,1,196,0,0.220237," ","integrate((a+b*(F**(g*(f*x+e)))**n)*(d*x+c)**2,x)","a c^{2} x + a c d x^{2} + \frac{a d^{2} x^{3}}{3} + \begin{cases} \frac{\left(b c^{2} f^{2} g^{2} n^{2} \log{\left(F \right)}^{2} + 2 b c d f^{2} g^{2} n^{2} x \log{\left(F \right)}^{2} - 2 b c d f g n \log{\left(F \right)} + b d^{2} f^{2} g^{2} n^{2} x^{2} \log{\left(F \right)}^{2} - 2 b d^{2} f g n x \log{\left(F \right)} + 2 b d^{2}\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{f^{3} g^{3} n^{3} \log{\left(F \right)}^{3}} & \text{for}\: f^{3} g^{3} n^{3} \log{\left(F \right)}^{3} \neq 0 \\b c^{2} x + b c d x^{2} + \frac{b d^{2} x^{3}}{3} & \text{otherwise} \end{cases}"," ",0,"a*c**2*x + a*c*d*x**2 + a*d**2*x**3/3 + Piecewise(((b*c**2*f**2*g**2*n**2*log(F)**2 + 2*b*c*d*f**2*g**2*n**2*x*log(F)**2 - 2*b*c*d*f*g*n*log(F) + b*d**2*f**2*g**2*n**2*x**2*log(F)**2 - 2*b*d**2*f*g*n*x*log(F) + 2*b*d**2)*(F**(g*(e + f*x)))**n/(f**3*g**3*n**3*log(F)**3), Ne(f**3*g**3*n**3*log(F)**3, 0)), (b*c**2*x + b*c*d*x**2 + b*d**2*x**3/3, True))","A",0
27,1,94,0,0.169902," ","integrate((a+b*(F**(g*(f*x+e)))**n)*(d*x+c),x)","a c x + \frac{a d x^{2}}{2} + \begin{cases} \frac{\left(b c f g n \log{\left(F \right)} + b d f g n x \log{\left(F \right)} - b d\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{f^{2} g^{2} n^{2} \log{\left(F \right)}^{2}} & \text{for}\: f^{2} g^{2} n^{2} \log{\left(F \right)}^{2} \neq 0 \\b c x + \frac{b d x^{2}}{2} & \text{otherwise} \end{cases}"," ",0,"a*c*x + a*d*x**2/2 + Piecewise(((b*c*f*g*n*log(F) + b*d*f*g*n*x*log(F) - b*d)*(F**(g*(e + f*x)))**n/(f**2*g**2*n**2*log(F)**2), Ne(f**2*g**2*n**2*log(F)**2, 0)), (b*c*x + b*d*x**2/2, True))","A",0
28,1,32,0,0.124804," ","integrate(a+b*(F**(g*(f*x+e)))**n,x)","a x + \begin{cases} \frac{b \left(F^{g \left(e + f x\right)}\right)^{n}}{f g n \log{\left(F \right)}} & \text{for}\: f g n \log{\left(F \right)} \neq 0 \\b x & \text{otherwise} \end{cases}"," ",0,"a*x + Piecewise((b*(F**(g*(e + f*x)))**n/(f*g*n*log(F)), Ne(f*g*n*log(F), 0)), (b*x, True))","A",0
29,0,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)/(d*x+c),x)","\int \frac{a + b \left(F^{e g} F^{f g x}\right)^{n}}{c + d x}\, dx"," ",0,"Integral((a + b*(F**(e*g)*F**(f*g*x))**n)/(c + d*x), x)","F",0
30,0,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)/(d*x+c)**2,x)","\int \frac{a + b \left(F^{e g} F^{f g x}\right)^{n}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral((a + b*(F**(e*g)*F**(f*g*x))**n)/(c + d*x)**2, x)","F",0
31,0,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)/(d*x+c)**3,x)","\int \frac{a + b \left(F^{e g} F^{f g x}\right)^{n}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral((a + b*(F**(e*g)*F**(f*g*x))**n)/(c + d*x)**3, x)","F",0
32,1,709,0,0.475714," ","integrate((a+b*(F**(g*(f*x+e)))**n)**2*(d*x+c)**3,x)","a^{2} c^{3} x + \frac{3 a^{2} c^{2} d x^{2}}{2} + a^{2} c d^{2} x^{3} + \frac{a^{2} d^{3} x^{4}}{4} + \begin{cases} \frac{\left(4 b^{2} c^{3} f^{7} g^{7} n^{7} \log{\left(F \right)}^{7} + 12 b^{2} c^{2} d f^{7} g^{7} n^{7} x \log{\left(F \right)}^{7} - 6 b^{2} c^{2} d f^{6} g^{6} n^{6} \log{\left(F \right)}^{6} + 12 b^{2} c d^{2} f^{7} g^{7} n^{7} x^{2} \log{\left(F \right)}^{7} - 12 b^{2} c d^{2} f^{6} g^{6} n^{6} x \log{\left(F \right)}^{6} + 6 b^{2} c d^{2} f^{5} g^{5} n^{5} \log{\left(F \right)}^{5} + 4 b^{2} d^{3} f^{7} g^{7} n^{7} x^{3} \log{\left(F \right)}^{7} - 6 b^{2} d^{3} f^{6} g^{6} n^{6} x^{2} \log{\left(F \right)}^{6} + 6 b^{2} d^{3} f^{5} g^{5} n^{5} x \log{\left(F \right)}^{5} - 3 b^{2} d^{3} f^{4} g^{4} n^{4} \log{\left(F \right)}^{4}\right) \left(F^{g \left(e + f x\right)}\right)^{2 n} + \left(16 a b c^{3} f^{7} g^{7} n^{7} \log{\left(F \right)}^{7} + 48 a b c^{2} d f^{7} g^{7} n^{7} x \log{\left(F \right)}^{7} - 48 a b c^{2} d f^{6} g^{6} n^{6} \log{\left(F \right)}^{6} + 48 a b c d^{2} f^{7} g^{7} n^{7} x^{2} \log{\left(F \right)}^{7} - 96 a b c d^{2} f^{6} g^{6} n^{6} x \log{\left(F \right)}^{6} + 96 a b c d^{2} f^{5} g^{5} n^{5} \log{\left(F \right)}^{5} + 16 a b d^{3} f^{7} g^{7} n^{7} x^{3} \log{\left(F \right)}^{7} - 48 a b d^{3} f^{6} g^{6} n^{6} x^{2} \log{\left(F \right)}^{6} + 96 a b d^{3} f^{5} g^{5} n^{5} x \log{\left(F \right)}^{5} - 96 a b d^{3} f^{4} g^{4} n^{4} \log{\left(F \right)}^{4}\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{8 f^{8} g^{8} n^{8} \log{\left(F \right)}^{8}} & \text{for}\: 8 f^{8} g^{8} n^{8} \log{\left(F \right)}^{8} \neq 0 \\x^{4} \left(\frac{a b d^{3}}{2} + \frac{b^{2} d^{3}}{4}\right) + x^{3} \left(2 a b c d^{2} + b^{2} c d^{2}\right) + x^{2} \left(3 a b c^{2} d + \frac{3 b^{2} c^{2} d}{2}\right) + x \left(2 a b c^{3} + b^{2} c^{3}\right) & \text{otherwise} \end{cases}"," ",0,"a**2*c**3*x + 3*a**2*c**2*d*x**2/2 + a**2*c*d**2*x**3 + a**2*d**3*x**4/4 + Piecewise((((4*b**2*c**3*f**7*g**7*n**7*log(F)**7 + 12*b**2*c**2*d*f**7*g**7*n**7*x*log(F)**7 - 6*b**2*c**2*d*f**6*g**6*n**6*log(F)**6 + 12*b**2*c*d**2*f**7*g**7*n**7*x**2*log(F)**7 - 12*b**2*c*d**2*f**6*g**6*n**6*x*log(F)**6 + 6*b**2*c*d**2*f**5*g**5*n**5*log(F)**5 + 4*b**2*d**3*f**7*g**7*n**7*x**3*log(F)**7 - 6*b**2*d**3*f**6*g**6*n**6*x**2*log(F)**6 + 6*b**2*d**3*f**5*g**5*n**5*x*log(F)**5 - 3*b**2*d**3*f**4*g**4*n**4*log(F)**4)*(F**(g*(e + f*x)))**(2*n) + (16*a*b*c**3*f**7*g**7*n**7*log(F)**7 + 48*a*b*c**2*d*f**7*g**7*n**7*x*log(F)**7 - 48*a*b*c**2*d*f**6*g**6*n**6*log(F)**6 + 48*a*b*c*d**2*f**7*g**7*n**7*x**2*log(F)**7 - 96*a*b*c*d**2*f**6*g**6*n**6*x*log(F)**6 + 96*a*b*c*d**2*f**5*g**5*n**5*log(F)**5 + 16*a*b*d**3*f**7*g**7*n**7*x**3*log(F)**7 - 48*a*b*d**3*f**6*g**6*n**6*x**2*log(F)**6 + 96*a*b*d**3*f**5*g**5*n**5*x*log(F)**5 - 96*a*b*d**3*f**4*g**4*n**4*log(F)**4)*(F**(g*(e + f*x)))**n)/(8*f**8*g**8*n**8*log(F)**8), Ne(8*f**8*g**8*n**8*log(F)**8, 0)), (x**4*(a*b*d**3/2 + b**2*d**3/4) + x**3*(2*a*b*c*d**2 + b**2*c*d**2) + x**2*(3*a*b*c**2*d + 3*b**2*c**2*d/2) + x*(2*a*b*c**3 + b**2*c**3), True))","A",0
33,1,439,0,0.367769," ","integrate((a+b*(F**(g*(f*x+e)))**n)**2*(d*x+c)**2,x)","a^{2} c^{2} x + a^{2} c d x^{2} + \frac{a^{2} d^{2} x^{3}}{3} + \begin{cases} \frac{\left(2 b^{2} c^{2} f^{5} g^{5} n^{5} \log{\left(F \right)}^{5} + 4 b^{2} c d f^{5} g^{5} n^{5} x \log{\left(F \right)}^{5} - 2 b^{2} c d f^{4} g^{4} n^{4} \log{\left(F \right)}^{4} + 2 b^{2} d^{2} f^{5} g^{5} n^{5} x^{2} \log{\left(F \right)}^{5} - 2 b^{2} d^{2} f^{4} g^{4} n^{4} x \log{\left(F \right)}^{4} + b^{2} d^{2} f^{3} g^{3} n^{3} \log{\left(F \right)}^{3}\right) \left(F^{g \left(e + f x\right)}\right)^{2 n} + \left(8 a b c^{2} f^{5} g^{5} n^{5} \log{\left(F \right)}^{5} + 16 a b c d f^{5} g^{5} n^{5} x \log{\left(F \right)}^{5} - 16 a b c d f^{4} g^{4} n^{4} \log{\left(F \right)}^{4} + 8 a b d^{2} f^{5} g^{5} n^{5} x^{2} \log{\left(F \right)}^{5} - 16 a b d^{2} f^{4} g^{4} n^{4} x \log{\left(F \right)}^{4} + 16 a b d^{2} f^{3} g^{3} n^{3} \log{\left(F \right)}^{3}\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{4 f^{6} g^{6} n^{6} \log{\left(F \right)}^{6}} & \text{for}\: 4 f^{6} g^{6} n^{6} \log{\left(F \right)}^{6} \neq 0 \\x^{3} \left(\frac{2 a b d^{2}}{3} + \frac{b^{2} d^{2}}{3}\right) + x^{2} \left(2 a b c d + b^{2} c d\right) + x \left(2 a b c^{2} + b^{2} c^{2}\right) & \text{otherwise} \end{cases}"," ",0,"a**2*c**2*x + a**2*c*d*x**2 + a**2*d**2*x**3/3 + Piecewise((((2*b**2*c**2*f**5*g**5*n**5*log(F)**5 + 4*b**2*c*d*f**5*g**5*n**5*x*log(F)**5 - 2*b**2*c*d*f**4*g**4*n**4*log(F)**4 + 2*b**2*d**2*f**5*g**5*n**5*x**2*log(F)**5 - 2*b**2*d**2*f**4*g**4*n**4*x*log(F)**4 + b**2*d**2*f**3*g**3*n**3*log(F)**3)*(F**(g*(e + f*x)))**(2*n) + (8*a*b*c**2*f**5*g**5*n**5*log(F)**5 + 16*a*b*c*d*f**5*g**5*n**5*x*log(F)**5 - 16*a*b*c*d*f**4*g**4*n**4*log(F)**4 + 8*a*b*d**2*f**5*g**5*n**5*x**2*log(F)**5 - 16*a*b*d**2*f**4*g**4*n**4*x*log(F)**4 + 16*a*b*d**2*f**3*g**3*n**3*log(F)**3)*(F**(g*(e + f*x)))**n)/(4*f**6*g**6*n**6*log(F)**6), Ne(4*f**6*g**6*n**6*log(F)**6, 0)), (x**3*(2*a*b*d**2/3 + b**2*d**2/3) + x**2*(2*a*b*c*d + b**2*c*d) + x*(2*a*b*c**2 + b**2*c**2), True))","A",0
34,1,233,0,0.271918," ","integrate((a+b*(F**(g*(f*x+e)))**n)**2*(d*x+c),x)","a^{2} c x + \frac{a^{2} d x^{2}}{2} + \begin{cases} \frac{\left(2 b^{2} c f^{3} g^{3} n^{3} \log{\left(F \right)}^{3} + 2 b^{2} d f^{3} g^{3} n^{3} x \log{\left(F \right)}^{3} - b^{2} d f^{2} g^{2} n^{2} \log{\left(F \right)}^{2}\right) \left(F^{g \left(e + f x\right)}\right)^{2 n} + \left(8 a b c f^{3} g^{3} n^{3} \log{\left(F \right)}^{3} + 8 a b d f^{3} g^{3} n^{3} x \log{\left(F \right)}^{3} - 8 a b d f^{2} g^{2} n^{2} \log{\left(F \right)}^{2}\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{4 f^{4} g^{4} n^{4} \log{\left(F \right)}^{4}} & \text{for}\: 4 f^{4} g^{4} n^{4} \log{\left(F \right)}^{4} \neq 0 \\x^{2} \left(a b d + \frac{b^{2} d}{2}\right) + x \left(2 a b c + b^{2} c\right) & \text{otherwise} \end{cases}"," ",0,"a**2*c*x + a**2*d*x**2/2 + Piecewise((((2*b**2*c*f**3*g**3*n**3*log(F)**3 + 2*b**2*d*f**3*g**3*n**3*x*log(F)**3 - b**2*d*f**2*g**2*n**2*log(F)**2)*(F**(g*(e + f*x)))**(2*n) + (8*a*b*c*f**3*g**3*n**3*log(F)**3 + 8*a*b*d*f**3*g**3*n**3*x*log(F)**3 - 8*a*b*d*f**2*g**2*n**2*log(F)**2)*(F**(g*(e + f*x)))**n)/(4*f**4*g**4*n**4*log(F)**4), Ne(4*f**4*g**4*n**4*log(F)**4, 0)), (x**2*(a*b*d + b**2*d/2) + x*(2*a*b*c + b**2*c), True))","A",0
35,1,94,0,0.176913," ","integrate((a+b*(F**(g*(f*x+e)))**n)**2,x)","a^{2} x + \begin{cases} \frac{4 a b f g n \left(F^{g \left(e + f x\right)}\right)^{n} \log{\left(F \right)} + b^{2} f g n \left(F^{g \left(e + f x\right)}\right)^{2 n} \log{\left(F \right)}}{2 f^{2} g^{2} n^{2} \log{\left(F \right)}^{2}} & \text{for}\: 2 f^{2} g^{2} n^{2} \log{\left(F \right)}^{2} \neq 0 \\x \left(2 a b + b^{2}\right) & \text{otherwise} \end{cases}"," ",0,"a**2*x + Piecewise(((4*a*b*f*g*n*(F**(g*(e + f*x)))**n*log(F) + b**2*f*g*n*(F**(g*(e + f*x)))**(2*n)*log(F))/(2*f**2*g**2*n**2*log(F)**2), Ne(2*f**2*g**2*n**2*log(F)**2, 0)), (x*(2*a*b + b**2), True))","A",0
36,0,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)**2/(d*x+c),x)","\int \frac{\left(a + b \left(F^{e g} F^{f g x}\right)^{n}\right)^{2}}{c + d x}\, dx"," ",0,"Integral((a + b*(F**(e*g)*F**(f*g*x))**n)**2/(c + d*x), x)","F",0
37,0,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)**2/(d*x+c)**2,x)","\int \frac{\left(a + b \left(F^{e g} F^{f g x}\right)^{n}\right)^{2}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral((a + b*(F**(e*g)*F**(f*g*x))**n)**2/(c + d*x)**2, x)","F",0
38,0,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)**2/(d*x+c)**3,x)","\int \frac{\left(a + b \left(F^{e g} F^{f g x}\right)^{n}\right)^{2}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral((a + b*(F**(e*g)*F**(f*g*x))**n)**2/(c + d*x)**3, x)","F",0
39,1,1074,0,0.653101," ","integrate((a+b*(F**(g*(f*x+e)))**n)**3*(d*x+c)**3,x)","a^{3} c^{3} x + \frac{3 a^{3} c^{2} d x^{2}}{2} + a^{3} c d^{2} x^{3} + \frac{a^{3} d^{3} x^{4}}{4} + \begin{cases} \frac{\left(72 b^{3} c^{3} f^{11} g^{11} n^{11} \log{\left(F \right)}^{11} + 216 b^{3} c^{2} d f^{11} g^{11} n^{11} x \log{\left(F \right)}^{11} - 72 b^{3} c^{2} d f^{10} g^{10} n^{10} \log{\left(F \right)}^{10} + 216 b^{3} c d^{2} f^{11} g^{11} n^{11} x^{2} \log{\left(F \right)}^{11} - 144 b^{3} c d^{2} f^{10} g^{10} n^{10} x \log{\left(F \right)}^{10} + 48 b^{3} c d^{2} f^{9} g^{9} n^{9} \log{\left(F \right)}^{9} + 72 b^{3} d^{3} f^{11} g^{11} n^{11} x^{3} \log{\left(F \right)}^{11} - 72 b^{3} d^{3} f^{10} g^{10} n^{10} x^{2} \log{\left(F \right)}^{10} + 48 b^{3} d^{3} f^{9} g^{9} n^{9} x \log{\left(F \right)}^{9} - 16 b^{3} d^{3} f^{8} g^{8} n^{8} \log{\left(F \right)}^{8}\right) \left(F^{g \left(e + f x\right)}\right)^{3 n} + \left(324 a b^{2} c^{3} f^{11} g^{11} n^{11} \log{\left(F \right)}^{11} + 972 a b^{2} c^{2} d f^{11} g^{11} n^{11} x \log{\left(F \right)}^{11} - 486 a b^{2} c^{2} d f^{10} g^{10} n^{10} \log{\left(F \right)}^{10} + 972 a b^{2} c d^{2} f^{11} g^{11} n^{11} x^{2} \log{\left(F \right)}^{11} - 972 a b^{2} c d^{2} f^{10} g^{10} n^{10} x \log{\left(F \right)}^{10} + 486 a b^{2} c d^{2} f^{9} g^{9} n^{9} \log{\left(F \right)}^{9} + 324 a b^{2} d^{3} f^{11} g^{11} n^{11} x^{3} \log{\left(F \right)}^{11} - 486 a b^{2} d^{3} f^{10} g^{10} n^{10} x^{2} \log{\left(F \right)}^{10} + 486 a b^{2} d^{3} f^{9} g^{9} n^{9} x \log{\left(F \right)}^{9} - 243 a b^{2} d^{3} f^{8} g^{8} n^{8} \log{\left(F \right)}^{8}\right) \left(F^{g \left(e + f x\right)}\right)^{2 n} + \left(648 a^{2} b c^{3} f^{11} g^{11} n^{11} \log{\left(F \right)}^{11} + 1944 a^{2} b c^{2} d f^{11} g^{11} n^{11} x \log{\left(F \right)}^{11} - 1944 a^{2} b c^{2} d f^{10} g^{10} n^{10} \log{\left(F \right)}^{10} + 1944 a^{2} b c d^{2} f^{11} g^{11} n^{11} x^{2} \log{\left(F \right)}^{11} - 3888 a^{2} b c d^{2} f^{10} g^{10} n^{10} x \log{\left(F \right)}^{10} + 3888 a^{2} b c d^{2} f^{9} g^{9} n^{9} \log{\left(F \right)}^{9} + 648 a^{2} b d^{3} f^{11} g^{11} n^{11} x^{3} \log{\left(F \right)}^{11} - 1944 a^{2} b d^{3} f^{10} g^{10} n^{10} x^{2} \log{\left(F \right)}^{10} + 3888 a^{2} b d^{3} f^{9} g^{9} n^{9} x \log{\left(F \right)}^{9} - 3888 a^{2} b d^{3} f^{8} g^{8} n^{8} \log{\left(F \right)}^{8}\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{216 f^{12} g^{12} n^{12} \log{\left(F \right)}^{12}} & \text{for}\: 216 f^{12} g^{12} n^{12} \log{\left(F \right)}^{12} \neq 0 \\x^{4} \left(\frac{3 a^{2} b d^{3}}{4} + \frac{3 a b^{2} d^{3}}{4} + \frac{b^{3} d^{3}}{4}\right) + x^{3} \left(3 a^{2} b c d^{2} + 3 a b^{2} c d^{2} + b^{3} c d^{2}\right) + x^{2} \left(\frac{9 a^{2} b c^{2} d}{2} + \frac{9 a b^{2} c^{2} d}{2} + \frac{3 b^{3} c^{2} d}{2}\right) + x \left(3 a^{2} b c^{3} + 3 a b^{2} c^{3} + b^{3} c^{3}\right) & \text{otherwise} \end{cases}"," ",0,"a**3*c**3*x + 3*a**3*c**2*d*x**2/2 + a**3*c*d**2*x**3 + a**3*d**3*x**4/4 + Piecewise((((72*b**3*c**3*f**11*g**11*n**11*log(F)**11 + 216*b**3*c**2*d*f**11*g**11*n**11*x*log(F)**11 - 72*b**3*c**2*d*f**10*g**10*n**10*log(F)**10 + 216*b**3*c*d**2*f**11*g**11*n**11*x**2*log(F)**11 - 144*b**3*c*d**2*f**10*g**10*n**10*x*log(F)**10 + 48*b**3*c*d**2*f**9*g**9*n**9*log(F)**9 + 72*b**3*d**3*f**11*g**11*n**11*x**3*log(F)**11 - 72*b**3*d**3*f**10*g**10*n**10*x**2*log(F)**10 + 48*b**3*d**3*f**9*g**9*n**9*x*log(F)**9 - 16*b**3*d**3*f**8*g**8*n**8*log(F)**8)*(F**(g*(e + f*x)))**(3*n) + (324*a*b**2*c**3*f**11*g**11*n**11*log(F)**11 + 972*a*b**2*c**2*d*f**11*g**11*n**11*x*log(F)**11 - 486*a*b**2*c**2*d*f**10*g**10*n**10*log(F)**10 + 972*a*b**2*c*d**2*f**11*g**11*n**11*x**2*log(F)**11 - 972*a*b**2*c*d**2*f**10*g**10*n**10*x*log(F)**10 + 486*a*b**2*c*d**2*f**9*g**9*n**9*log(F)**9 + 324*a*b**2*d**3*f**11*g**11*n**11*x**3*log(F)**11 - 486*a*b**2*d**3*f**10*g**10*n**10*x**2*log(F)**10 + 486*a*b**2*d**3*f**9*g**9*n**9*x*log(F)**9 - 243*a*b**2*d**3*f**8*g**8*n**8*log(F)**8)*(F**(g*(e + f*x)))**(2*n) + (648*a**2*b*c**3*f**11*g**11*n**11*log(F)**11 + 1944*a**2*b*c**2*d*f**11*g**11*n**11*x*log(F)**11 - 1944*a**2*b*c**2*d*f**10*g**10*n**10*log(F)**10 + 1944*a**2*b*c*d**2*f**11*g**11*n**11*x**2*log(F)**11 - 3888*a**2*b*c*d**2*f**10*g**10*n**10*x*log(F)**10 + 3888*a**2*b*c*d**2*f**9*g**9*n**9*log(F)**9 + 648*a**2*b*d**3*f**11*g**11*n**11*x**3*log(F)**11 - 1944*a**2*b*d**3*f**10*g**10*n**10*x**2*log(F)**10 + 3888*a**2*b*d**3*f**9*g**9*n**9*x*log(F)**9 - 3888*a**2*b*d**3*f**8*g**8*n**8*log(F)**8)*(F**(g*(e + f*x)))**n)/(216*f**12*g**12*n**12*log(F)**12), Ne(216*f**12*g**12*n**12*log(F)**12, 0)), (x**4*(3*a**2*b*d**3/4 + 3*a*b**2*d**3/4 + b**3*d**3/4) + x**3*(3*a**2*b*c*d**2 + 3*a*b**2*c*d**2 + b**3*c*d**2) + x**2*(9*a**2*b*c**2*d/2 + 9*a*b**2*c**2*d/2 + 3*b**3*c**2*d/2) + x*(3*a**2*b*c**3 + 3*a*b**2*c**3 + b**3*c**3), True))","A",0
40,1,653,0,0.479332," ","integrate((a+b*(F**(g*(f*x+e)))**n)**3*(d*x+c)**2,x)","a^{3} c^{2} x + a^{3} c d x^{2} + \frac{a^{3} d^{2} x^{3}}{3} + \begin{cases} \frac{\left(36 b^{3} c^{2} f^{8} g^{8} n^{8} \log{\left(F \right)}^{8} + 72 b^{3} c d f^{8} g^{8} n^{8} x \log{\left(F \right)}^{8} - 24 b^{3} c d f^{7} g^{7} n^{7} \log{\left(F \right)}^{7} + 36 b^{3} d^{2} f^{8} g^{8} n^{8} x^{2} \log{\left(F \right)}^{8} - 24 b^{3} d^{2} f^{7} g^{7} n^{7} x \log{\left(F \right)}^{7} + 8 b^{3} d^{2} f^{6} g^{6} n^{6} \log{\left(F \right)}^{6}\right) \left(F^{g \left(e + f x\right)}\right)^{3 n} + \left(162 a b^{2} c^{2} f^{8} g^{8} n^{8} \log{\left(F \right)}^{8} + 324 a b^{2} c d f^{8} g^{8} n^{8} x \log{\left(F \right)}^{8} - 162 a b^{2} c d f^{7} g^{7} n^{7} \log{\left(F \right)}^{7} + 162 a b^{2} d^{2} f^{8} g^{8} n^{8} x^{2} \log{\left(F \right)}^{8} - 162 a b^{2} d^{2} f^{7} g^{7} n^{7} x \log{\left(F \right)}^{7} + 81 a b^{2} d^{2} f^{6} g^{6} n^{6} \log{\left(F \right)}^{6}\right) \left(F^{g \left(e + f x\right)}\right)^{2 n} + \left(324 a^{2} b c^{2} f^{8} g^{8} n^{8} \log{\left(F \right)}^{8} + 648 a^{2} b c d f^{8} g^{8} n^{8} x \log{\left(F \right)}^{8} - 648 a^{2} b c d f^{7} g^{7} n^{7} \log{\left(F \right)}^{7} + 324 a^{2} b d^{2} f^{8} g^{8} n^{8} x^{2} \log{\left(F \right)}^{8} - 648 a^{2} b d^{2} f^{7} g^{7} n^{7} x \log{\left(F \right)}^{7} + 648 a^{2} b d^{2} f^{6} g^{6} n^{6} \log{\left(F \right)}^{6}\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{108 f^{9} g^{9} n^{9} \log{\left(F \right)}^{9}} & \text{for}\: 108 f^{9} g^{9} n^{9} \log{\left(F \right)}^{9} \neq 0 \\x^{3} \left(a^{2} b d^{2} + a b^{2} d^{2} + \frac{b^{3} d^{2}}{3}\right) + x^{2} \left(3 a^{2} b c d + 3 a b^{2} c d + b^{3} c d\right) + x \left(3 a^{2} b c^{2} + 3 a b^{2} c^{2} + b^{3} c^{2}\right) & \text{otherwise} \end{cases}"," ",0,"a**3*c**2*x + a**3*c*d*x**2 + a**3*d**2*x**3/3 + Piecewise((((36*b**3*c**2*f**8*g**8*n**8*log(F)**8 + 72*b**3*c*d*f**8*g**8*n**8*x*log(F)**8 - 24*b**3*c*d*f**7*g**7*n**7*log(F)**7 + 36*b**3*d**2*f**8*g**8*n**8*x**2*log(F)**8 - 24*b**3*d**2*f**7*g**7*n**7*x*log(F)**7 + 8*b**3*d**2*f**6*g**6*n**6*log(F)**6)*(F**(g*(e + f*x)))**(3*n) + (162*a*b**2*c**2*f**8*g**8*n**8*log(F)**8 + 324*a*b**2*c*d*f**8*g**8*n**8*x*log(F)**8 - 162*a*b**2*c*d*f**7*g**7*n**7*log(F)**7 + 162*a*b**2*d**2*f**8*g**8*n**8*x**2*log(F)**8 - 162*a*b**2*d**2*f**7*g**7*n**7*x*log(F)**7 + 81*a*b**2*d**2*f**6*g**6*n**6*log(F)**6)*(F**(g*(e + f*x)))**(2*n) + (324*a**2*b*c**2*f**8*g**8*n**8*log(F)**8 + 648*a**2*b*c*d*f**8*g**8*n**8*x*log(F)**8 - 648*a**2*b*c*d*f**7*g**7*n**7*log(F)**7 + 324*a**2*b*d**2*f**8*g**8*n**8*x**2*log(F)**8 - 648*a**2*b*d**2*f**7*g**7*n**7*x*log(F)**7 + 648*a**2*b*d**2*f**6*g**6*n**6*log(F)**6)*(F**(g*(e + f*x)))**n)/(108*f**9*g**9*n**9*log(F)**9), Ne(108*f**9*g**9*n**9*log(F)**9, 0)), (x**3*(a**2*b*d**2 + a*b**2*d**2 + b**3*d**2/3) + x**2*(3*a**2*b*c*d + 3*a*b**2*c*d + b**3*c*d) + x*(3*a**2*b*c**2 + 3*a*b**2*c**2 + b**3*c**2), True))","A",0
41,1,350,0,0.340467," ","integrate((a+b*(F**(g*(f*x+e)))**n)**3*(d*x+c),x)","a^{3} c x + \frac{a^{3} d x^{2}}{2} + \begin{cases} \frac{\left(12 b^{3} c f^{5} g^{5} n^{5} \log{\left(F \right)}^{5} + 12 b^{3} d f^{5} g^{5} n^{5} x \log{\left(F \right)}^{5} - 4 b^{3} d f^{4} g^{4} n^{4} \log{\left(F \right)}^{4}\right) \left(F^{g \left(e + f x\right)}\right)^{3 n} + \left(54 a b^{2} c f^{5} g^{5} n^{5} \log{\left(F \right)}^{5} + 54 a b^{2} d f^{5} g^{5} n^{5} x \log{\left(F \right)}^{5} - 27 a b^{2} d f^{4} g^{4} n^{4} \log{\left(F \right)}^{4}\right) \left(F^{g \left(e + f x\right)}\right)^{2 n} + \left(108 a^{2} b c f^{5} g^{5} n^{5} \log{\left(F \right)}^{5} + 108 a^{2} b d f^{5} g^{5} n^{5} x \log{\left(F \right)}^{5} - 108 a^{2} b d f^{4} g^{4} n^{4} \log{\left(F \right)}^{4}\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{36 f^{6} g^{6} n^{6} \log{\left(F \right)}^{6}} & \text{for}\: 36 f^{6} g^{6} n^{6} \log{\left(F \right)}^{6} \neq 0 \\x^{2} \left(\frac{3 a^{2} b d}{2} + \frac{3 a b^{2} d}{2} + \frac{b^{3} d}{2}\right) + x \left(3 a^{2} b c + 3 a b^{2} c + b^{3} c\right) & \text{otherwise} \end{cases}"," ",0,"a**3*c*x + a**3*d*x**2/2 + Piecewise((((12*b**3*c*f**5*g**5*n**5*log(F)**5 + 12*b**3*d*f**5*g**5*n**5*x*log(F)**5 - 4*b**3*d*f**4*g**4*n**4*log(F)**4)*(F**(g*(e + f*x)))**(3*n) + (54*a*b**2*c*f**5*g**5*n**5*log(F)**5 + 54*a*b**2*d*f**5*g**5*n**5*x*log(F)**5 - 27*a*b**2*d*f**4*g**4*n**4*log(F)**4)*(F**(g*(e + f*x)))**(2*n) + (108*a**2*b*c*f**5*g**5*n**5*log(F)**5 + 108*a**2*b*d*f**5*g**5*n**5*x*log(F)**5 - 108*a**2*b*d*f**4*g**4*n**4*log(F)**4)*(F**(g*(e + f*x)))**n)/(36*f**6*g**6*n**6*log(F)**6), Ne(36*f**6*g**6*n**6*log(F)**6, 0)), (x**2*(3*a**2*b*d/2 + 3*a*b**2*d/2 + b**3*d/2) + x*(3*a**2*b*c + 3*a*b**2*c + b**3*c), True))","A",0
42,1,153,0,0.208730," ","integrate((a+b*(F**(g*(f*x+e)))**n)**3,x)","a^{3} x + \begin{cases} \frac{18 a^{2} b f^{2} g^{2} n^{2} \left(F^{g \left(e + f x\right)}\right)^{n} \log{\left(F \right)}^{2} + 9 a b^{2} f^{2} g^{2} n^{2} \left(F^{g \left(e + f x\right)}\right)^{2 n} \log{\left(F \right)}^{2} + 2 b^{3} f^{2} g^{2} n^{2} \left(F^{g \left(e + f x\right)}\right)^{3 n} \log{\left(F \right)}^{2}}{6 f^{3} g^{3} n^{3} \log{\left(F \right)}^{3}} & \text{for}\: 6 f^{3} g^{3} n^{3} \log{\left(F \right)}^{3} \neq 0 \\x \left(3 a^{2} b + 3 a b^{2} + b^{3}\right) & \text{otherwise} \end{cases}"," ",0,"a**3*x + Piecewise(((18*a**2*b*f**2*g**2*n**2*(F**(g*(e + f*x)))**n*log(F)**2 + 9*a*b**2*f**2*g**2*n**2*(F**(g*(e + f*x)))**(2*n)*log(F)**2 + 2*b**3*f**2*g**2*n**2*(F**(g*(e + f*x)))**(3*n)*log(F)**2)/(6*f**3*g**3*n**3*log(F)**3), Ne(6*f**3*g**3*n**3*log(F)**3, 0)), (x*(3*a**2*b + 3*a*b**2 + b**3), True))","A",0
43,0,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)**3/(d*x+c),x)","\int \frac{\left(a + b \left(F^{e g} F^{f g x}\right)^{n}\right)^{3}}{c + d x}\, dx"," ",0,"Integral((a + b*(F**(e*g)*F**(f*g*x))**n)**3/(c + d*x), x)","F",0
44,0,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)**3/(d*x+c)**2,x)","\int \frac{\left(a + b \left(F^{e g} F^{f g x}\right)^{n}\right)^{3}}{\left(c + d x\right)^{2}}\, dx"," ",0,"Integral((a + b*(F**(e*g)*F**(f*g*x))**n)**3/(c + d*x)**2, x)","F",0
45,0,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)**3/(d*x+c)**3,x)","\int \frac{\left(a + b \left(F^{e g} F^{f g x}\right)^{n}\right)^{3}}{\left(c + d x\right)^{3}}\, dx"," ",0,"Integral((a + b*(F**(e*g)*F**(f*g*x))**n)**3/(c + d*x)**3, x)","F",0
46,0,0,0,0.000000," ","integrate((d*x+c)**3/(a+b*(F**(g*(f*x+e)))**n),x)","\int \frac{\left(c + d x\right)^{3}}{a + b \left(F^{e g} F^{f g x}\right)^{n}}\, dx"," ",0,"Integral((c + d*x)**3/(a + b*(F**(e*g)*F**(f*g*x))**n), x)","F",0
47,0,0,0,0.000000," ","integrate((d*x+c)**2/(a+b*(F**(g*(f*x+e)))**n),x)","\int \frac{\left(c + d x\right)^{2}}{a + b \left(F^{e g} F^{f g x}\right)^{n}}\, dx"," ",0,"Integral((c + d*x)**2/(a + b*(F**(e*g)*F**(f*g*x))**n), x)","F",0
48,0,0,0,0.000000," ","integrate((d*x+c)/(a+b*(F**(g*(f*x+e)))**n),x)","\int \frac{c + d x}{a + b \left(F^{e g} F^{f g x}\right)^{n}}\, dx"," ",0,"Integral((c + d*x)/(a + b*(F**(e*g)*F**(f*g*x))**n), x)","F",0
49,1,27,0,0.155282," ","integrate(1/(a+b*(F**(g*(f*x+e)))**n),x)","\frac{x}{a} - \frac{\log{\left(\frac{a}{b} + \left(F^{g \left(e + f x\right)}\right)^{n} \right)}}{a f g n \log{\left(F \right)}}"," ",0,"x/a - log(a/b + (F**(g*(e + f*x)))**n)/(a*f*g*n*log(F))","A",0
50,0,0,0,0.000000," ","integrate(1/(a+b*(F**(g*(f*x+e)))**n)/(d*x+c),x)","\int \frac{1}{\left(a + b \left(F^{e g} F^{f g x}\right)^{n}\right) \left(c + d x\right)}\, dx"," ",0,"Integral(1/((a + b*(F**(e*g)*F**(f*g*x))**n)*(c + d*x)), x)","F",0
51,-1,0,0,0.000000," ","integrate(1/(a+b*(F**(g*(f*x+e)))**n)/(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,0,0,0,0.000000," ","integrate((d*x+c)**3/(a+b*(F**(g*(f*x+e)))**n)**2,x)","\frac{c^{3} + 3 c^{2} d x + 3 c d^{2} x^{2} + d^{3} x^{3}}{a^{2} f g n \log{\left(F \right)} + a b f g n \left(F^{g \left(e + f x\right)}\right)^{n} \log{\left(F \right)}} + \frac{\int \left(- \frac{3 c^{2} d}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \left(- \frac{3 d^{3} x^{2}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \left(- \frac{6 c d^{2} x}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \frac{c^{3} f g n \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{d^{3} f g n x^{3} \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{3 c d^{2} f g n x^{2} \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{3 c^{2} d f g n x \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx}{a f g n \log{\left(F \right)}}"," ",0,"(c**3 + 3*c**2*d*x + 3*c*d**2*x**2 + d**3*x**3)/(a**2*f*g*n*log(F) + a*b*f*g*n*(F**(g*(e + f*x)))**n*log(F)) + (Integral(-3*c**2*d/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(-3*d**3*x**2/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(-6*c*d**2*x/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(c**3*f*g*n*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(d**3*f*g*n*x**3*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(3*c*d**2*f*g*n*x**2*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(3*c**2*d*f*g*n*x*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x))/(a*f*g*n*log(F))","F",0
53,0,0,0,0.000000," ","integrate((d*x+c)**2/(a+b*(F**(g*(f*x+e)))**n)**2,x)","\frac{c^{2} + 2 c d x + d^{2} x^{2}}{a^{2} f g n \log{\left(F \right)} + a b f g n \left(F^{g \left(e + f x\right)}\right)^{n} \log{\left(F \right)}} + \frac{\int \left(- \frac{2 c d}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \left(- \frac{2 d^{2} x}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \frac{c^{2} f g n \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{d^{2} f g n x^{2} \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{2 c d f g n x \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx}{a f g n \log{\left(F \right)}}"," ",0,"(c**2 + 2*c*d*x + d**2*x**2)/(a**2*f*g*n*log(F) + a*b*f*g*n*(F**(g*(e + f*x)))**n*log(F)) + (Integral(-2*c*d/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(-2*d**2*x/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(c**2*f*g*n*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(d**2*f*g*n*x**2*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(2*c*d*f*g*n*x*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x))/(a*f*g*n*log(F))","F",0
54,0,0,0,0.000000," ","integrate((d*x+c)/(a+b*(F**(g*(f*x+e)))**n)**2,x)","\frac{c + d x}{a^{2} f g n \log{\left(F \right)} + a b f g n \left(F^{g \left(e + f x\right)}\right)^{n} \log{\left(F \right)}} + \frac{\int \left(- \frac{d}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \frac{c f g n \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{d f g n x \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx}{a f g n \log{\left(F \right)}}"," ",0,"(c + d*x)/(a**2*f*g*n*log(F) + a*b*f*g*n*(F**(g*(e + f*x)))**n*log(F)) + (Integral(-d/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(c*f*g*n*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(d*f*g*n*x*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x))/(a*f*g*n*log(F))","F",0
55,1,66,0,0.189507," ","integrate(1/(a+b*(F**(g*(f*x+e)))**n)**2,x)","\frac{1}{a^{2} f g n \log{\left(F \right)} + a b f g n \left(F^{g \left(e + f x\right)}\right)^{n} \log{\left(F \right)}} + \frac{x}{a^{2}} - \frac{\log{\left(\frac{a}{b} + \left(F^{g \left(e + f x\right)}\right)^{n} \right)}}{a^{2} f g n \log{\left(F \right)}}"," ",0,"1/(a**2*f*g*n*log(F) + a*b*f*g*n*(F**(g*(e + f*x)))**n*log(F)) + x/a**2 - log(a/b + (F**(g*(e + f*x)))**n)/(a**2*f*g*n*log(F))","A",0
56,0,0,0,0.000000," ","integrate(1/(a+b*(F**(g*(f*x+e)))**n)**2/(d*x+c),x)","\frac{1}{a^{2} c f g n \log{\left(F \right)} + a^{2} d f g n x \log{\left(F \right)} + \left(a b c f g n \log{\left(F \right)} + a b d f g n x \log{\left(F \right)}\right) \left(F^{g \left(e + f x\right)}\right)^{n}} + \frac{\int \frac{d}{a c^{2} + 2 a c d x + a d^{2} x^{2} + b c^{2} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + 2 b c d x e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + b d^{2} x^{2} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{c f g n \log{\left(F \right)}}{a c^{2} + 2 a c d x + a d^{2} x^{2} + b c^{2} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + 2 b c d x e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + b d^{2} x^{2} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{d f g n x \log{\left(F \right)}}{a c^{2} + 2 a c d x + a d^{2} x^{2} + b c^{2} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + 2 b c d x e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + b d^{2} x^{2} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx}{a f g n \log{\left(F \right)}}"," ",0,"1/(a**2*c*f*g*n*log(F) + a**2*d*f*g*n*x*log(F) + (a*b*c*f*g*n*log(F) + a*b*d*f*g*n*x*log(F))*(F**(g*(e + f*x)))**n) + (Integral(d/(a*c**2 + 2*a*c*d*x + a*d**2*x**2 + b*c**2*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + 2*b*c*d*x*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + b*d**2*x**2*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(c*f*g*n*log(F)/(a*c**2 + 2*a*c*d*x + a*d**2*x**2 + b*c**2*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + 2*b*c*d*x*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + b*d**2*x**2*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(d*f*g*n*x*log(F)/(a*c**2 + 2*a*c*d*x + a*d**2*x**2 + b*c**2*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + 2*b*c*d*x*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + b*d**2*x**2*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x))/(a*f*g*n*log(F))","F",0
57,0,0,0,0.000000," ","integrate(1/(a+b*(F**(g*(f*x+e)))**n)**2/(d*x+c)**2,x)","\frac{1}{a^{2} c^{2} f g n \log{\left(F \right)} + 2 a^{2} c d f g n x \log{\left(F \right)} + a^{2} d^{2} f g n x^{2} \log{\left(F \right)} + \left(a b c^{2} f g n \log{\left(F \right)} + 2 a b c d f g n x \log{\left(F \right)} + a b d^{2} f g n x^{2} \log{\left(F \right)}\right) \left(F^{g \left(e + f x\right)}\right)^{n}} + \frac{\int \frac{2 d}{a c^{3} + 3 a c^{2} d x + 3 a c d^{2} x^{2} + a d^{3} x^{3} + b c^{3} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + 3 b c^{2} d x e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + 3 b c d^{2} x^{2} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + b d^{3} x^{3} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{c f g n \log{\left(F \right)}}{a c^{3} + 3 a c^{2} d x + 3 a c d^{2} x^{2} + a d^{3} x^{3} + b c^{3} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + 3 b c^{2} d x e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + 3 b c d^{2} x^{2} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + b d^{3} x^{3} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{d f g n x \log{\left(F \right)}}{a c^{3} + 3 a c^{2} d x + 3 a c d^{2} x^{2} + a d^{3} x^{3} + b c^{3} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + 3 b c^{2} d x e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + 3 b c d^{2} x^{2} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}} + b d^{3} x^{3} e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx}{a f g n \log{\left(F \right)}}"," ",0,"1/(a**2*c**2*f*g*n*log(F) + 2*a**2*c*d*f*g*n*x*log(F) + a**2*d**2*f*g*n*x**2*log(F) + (a*b*c**2*f*g*n*log(F) + 2*a*b*c*d*f*g*n*x*log(F) + a*b*d**2*f*g*n*x**2*log(F))*(F**(g*(e + f*x)))**n) + (Integral(2*d/(a*c**3 + 3*a*c**2*d*x + 3*a*c*d**2*x**2 + a*d**3*x**3 + b*c**3*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + 3*b*c**2*d*x*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + 3*b*c*d**2*x**2*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + b*d**3*x**3*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(c*f*g*n*log(F)/(a*c**3 + 3*a*c**2*d*x + 3*a*c*d**2*x**2 + a*d**3*x**3 + b*c**3*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + 3*b*c**2*d*x*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + 3*b*c*d**2*x**2*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + b*d**3*x**3*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(d*f*g*n*x*log(F)/(a*c**3 + 3*a*c**2*d*x + 3*a*c*d**2*x**2 + a*d**3*x**3 + b*c**3*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + 3*b*c**2*d*x*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + 3*b*c*d**2*x**2*exp(e*g*n*log(F))*exp(f*g*n*x*log(F)) + b*d**3*x**3*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x))/(a*f*g*n*log(F))","F",0
58,0,0,0,0.000000," ","integrate((d*x+c)**3/(a+b*(F**(g*(f*x+e)))**n)**3,x)","\frac{3 a c^{3} f g n \log{\left(F \right)} + 9 a c^{2} d f g n x \log{\left(F \right)} - 3 a c^{2} d + 9 a c d^{2} f g n x^{2} \log{\left(F \right)} - 6 a c d^{2} x + 3 a d^{3} f g n x^{3} \log{\left(F \right)} - 3 a d^{3} x^{2} + \left(2 b c^{3} f g n \log{\left(F \right)} + 6 b c^{2} d f g n x \log{\left(F \right)} - 3 b c^{2} d + 6 b c d^{2} f g n x^{2} \log{\left(F \right)} - 6 b c d^{2} x + 2 b d^{3} f g n x^{3} \log{\left(F \right)} - 3 b d^{3} x^{2}\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{2 a^{4} f^{2} g^{2} n^{2} \log{\left(F \right)}^{2} + 4 a^{3} b f^{2} g^{2} n^{2} \left(F^{g \left(e + f x\right)}\right)^{n} \log{\left(F \right)}^{2} + 2 a^{2} b^{2} f^{2} g^{2} n^{2} \left(F^{g \left(e + f x\right)}\right)^{2 n} \log{\left(F \right)}^{2}} + \frac{\int \frac{6 c d^{2}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{6 d^{3} x}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{2 c^{3} f^{2} g^{2} n^{2} \log{\left(F \right)}^{2}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \left(- \frac{9 c^{2} d f g n \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \left(- \frac{9 d^{3} f g n x^{2} \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \frac{2 d^{3} f^{2} g^{2} n^{2} x^{3} \log{\left(F \right)}^{2}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \left(- \frac{18 c d^{2} f g n x \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \frac{6 c d^{2} f^{2} g^{2} n^{2} x^{2} \log{\left(F \right)}^{2}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{6 c^{2} d f^{2} g^{2} n^{2} x \log{\left(F \right)}^{2}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx}{2 a^{2} f^{2} g^{2} n^{2} \log{\left(F \right)}^{2}}"," ",0,"(3*a*c**3*f*g*n*log(F) + 9*a*c**2*d*f*g*n*x*log(F) - 3*a*c**2*d + 9*a*c*d**2*f*g*n*x**2*log(F) - 6*a*c*d**2*x + 3*a*d**3*f*g*n*x**3*log(F) - 3*a*d**3*x**2 + (2*b*c**3*f*g*n*log(F) + 6*b*c**2*d*f*g*n*x*log(F) - 3*b*c**2*d + 6*b*c*d**2*f*g*n*x**2*log(F) - 6*b*c*d**2*x + 2*b*d**3*f*g*n*x**3*log(F) - 3*b*d**3*x**2)*(F**(g*(e + f*x)))**n)/(2*a**4*f**2*g**2*n**2*log(F)**2 + 4*a**3*b*f**2*g**2*n**2*(F**(g*(e + f*x)))**n*log(F)**2 + 2*a**2*b**2*f**2*g**2*n**2*(F**(g*(e + f*x)))**(2*n)*log(F)**2) + (Integral(6*c*d**2/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(6*d**3*x/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(2*c**3*f**2*g**2*n**2*log(F)**2/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(-9*c**2*d*f*g*n*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(-9*d**3*f*g*n*x**2*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(2*d**3*f**2*g**2*n**2*x**3*log(F)**2/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(-18*c*d**2*f*g*n*x*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(6*c*d**2*f**2*g**2*n**2*x**2*log(F)**2/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(6*c**2*d*f**2*g**2*n**2*x*log(F)**2/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x))/(2*a**2*f**2*g**2*n**2*log(F)**2)","F",0
59,0,0,0,0.000000," ","integrate((d*x+c)**2/(a+b*(F**(g*(f*x+e)))**n)**3,x)","\frac{3 a c^{2} f g n \log{\left(F \right)} + 6 a c d f g n x \log{\left(F \right)} - 2 a c d + 3 a d^{2} f g n x^{2} \log{\left(F \right)} - 2 a d^{2} x + \left(2 b c^{2} f g n \log{\left(F \right)} + 4 b c d f g n x \log{\left(F \right)} - 2 b c d + 2 b d^{2} f g n x^{2} \log{\left(F \right)} - 2 b d^{2} x\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{2 a^{4} f^{2} g^{2} n^{2} \log{\left(F \right)}^{2} + 4 a^{3} b f^{2} g^{2} n^{2} \left(F^{g \left(e + f x\right)}\right)^{n} \log{\left(F \right)}^{2} + 2 a^{2} b^{2} f^{2} g^{2} n^{2} \left(F^{g \left(e + f x\right)}\right)^{2 n} \log{\left(F \right)}^{2}} + \frac{\int \frac{d^{2}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{c^{2} f^{2} g^{2} n^{2} \log{\left(F \right)}^{2}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \left(- \frac{3 c d f g n \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \left(- \frac{3 d^{2} f g n x \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \frac{d^{2} f^{2} g^{2} n^{2} x^{2} \log{\left(F \right)}^{2}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{2 c d f^{2} g^{2} n^{2} x \log{\left(F \right)}^{2}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx}{a^{2} f^{2} g^{2} n^{2} \log{\left(F \right)}^{2}}"," ",0,"(3*a*c**2*f*g*n*log(F) + 6*a*c*d*f*g*n*x*log(F) - 2*a*c*d + 3*a*d**2*f*g*n*x**2*log(F) - 2*a*d**2*x + (2*b*c**2*f*g*n*log(F) + 4*b*c*d*f*g*n*x*log(F) - 2*b*c*d + 2*b*d**2*f*g*n*x**2*log(F) - 2*b*d**2*x)*(F**(g*(e + f*x)))**n)/(2*a**4*f**2*g**2*n**2*log(F)**2 + 4*a**3*b*f**2*g**2*n**2*(F**(g*(e + f*x)))**n*log(F)**2 + 2*a**2*b**2*f**2*g**2*n**2*(F**(g*(e + f*x)))**(2*n)*log(F)**2) + (Integral(d**2/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(c**2*f**2*g**2*n**2*log(F)**2/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(-3*c*d*f*g*n*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(-3*d**2*f*g*n*x*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(d**2*f**2*g**2*n**2*x**2*log(F)**2/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(2*c*d*f**2*g**2*n**2*x*log(F)**2/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x))/(a**2*f**2*g**2*n**2*log(F)**2)","F",0
60,0,0,0,0.000000," ","integrate((d*x+c)/(a+b*(F**(g*(f*x+e)))**n)**3,x)","\frac{3 a c f g n \log{\left(F \right)} + 3 a d f g n x \log{\left(F \right)} - a d + \left(2 b c f g n \log{\left(F \right)} + 2 b d f g n x \log{\left(F \right)} - b d\right) \left(F^{g \left(e + f x\right)}\right)^{n}}{2 a^{4} f^{2} g^{2} n^{2} \log{\left(F \right)}^{2} + 4 a^{3} b f^{2} g^{2} n^{2} \left(F^{g \left(e + f x\right)}\right)^{n} \log{\left(F \right)}^{2} + 2 a^{2} b^{2} f^{2} g^{2} n^{2} \left(F^{g \left(e + f x\right)}\right)^{2 n} \log{\left(F \right)}^{2}} + \frac{\int \left(- \frac{3 d}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\right)\, dx + \int \frac{2 c f g n \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx + \int \frac{2 d f g n x \log{\left(F \right)}}{a + b e^{e g n \log{\left(F \right)}} e^{f g n x \log{\left(F \right)}}}\, dx}{2 a^{2} f g n \log{\left(F \right)}}"," ",0,"(3*a*c*f*g*n*log(F) + 3*a*d*f*g*n*x*log(F) - a*d + (2*b*c*f*g*n*log(F) + 2*b*d*f*g*n*x*log(F) - b*d)*(F**(g*(e + f*x)))**n)/(2*a**4*f**2*g**2*n**2*log(F)**2 + 4*a**3*b*f**2*g**2*n**2*(F**(g*(e + f*x)))**n*log(F)**2 + 2*a**2*b**2*f**2*g**2*n**2*(F**(g*(e + f*x)))**(2*n)*log(F)**2) + (Integral(-3*d/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(2*c*f*g*n*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x) + Integral(2*d*f*g*n*x*log(F)/(a + b*exp(e*g*n*log(F))*exp(f*g*n*x*log(F))), x))/(2*a**2*f*g*n*log(F))","F",0
61,1,116,0,0.240938," ","integrate(1/(a+b*(F**(g*(f*x+e)))**n)**3,x)","\frac{3 a + 2 b \left(F^{g \left(e + f x\right)}\right)^{n}}{2 a^{4} f g n \log{\left(F \right)} + 4 a^{3} b f g n \left(F^{g \left(e + f x\right)}\right)^{n} \log{\left(F \right)} + 2 a^{2} b^{2} f g n \left(F^{g \left(e + f x\right)}\right)^{2 n} \log{\left(F \right)}} + \frac{x}{a^{3}} - \frac{\log{\left(\frac{a}{b} + \left(F^{g \left(e + f x\right)}\right)^{n} \right)}}{a^{3} f g n \log{\left(F \right)}}"," ",0,"(3*a + 2*b*(F**(g*(e + f*x)))**n)/(2*a**4*f*g*n*log(F) + 4*a**3*b*f*g*n*(F**(g*(e + f*x)))**n*log(F) + 2*a**2*b**2*f*g*n*(F**(g*(e + f*x)))**(2*n)*log(F)) + x/a**3 - log(a/b + (F**(g*(e + f*x)))**n)/(a**3*f*g*n*log(F))","A",0
62,-1,0,0,0.000000," ","integrate(1/(a+b*(F**(g*(f*x+e)))**n)**3/(d*x+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate(1/(a+b*(F**(g*(f*x+e)))**n)**3/(d*x+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,1,85,0,2.135414," ","integrate((a+b*exp(x))*(d*x+c)**(1/2),x)","\frac{2 a \left(c + d x\right)^{\frac{3}{2}}}{3 d} - \frac{\sqrt{\pi} b \sqrt{d} e^{- \frac{c}{d}} \operatorname{erfi}{\left(\frac{\sqrt{c + d x}}{d \sqrt{\frac{1}{d}}} \right)}}{2} + \frac{b \sqrt{c + d x} e^{- \frac{c}{d}} e^{\frac{c}{d} + x}}{\sqrt{d} \sqrt{\frac{1}{d}}}"," ",0,"2*a*(c + d*x)**(3/2)/(3*d) - sqrt(pi)*b*sqrt(d)*exp(-c/d)*erfi(sqrt(c + d*x)/(d*sqrt(1/d)))/2 + b*sqrt(c + d*x)*exp(-c/d)*exp(c/d + x)/(sqrt(d)*sqrt(1/d))","A",0
65,1,184,0,3.212994," ","integrate((a+b*exp(x))**2*(d*x+c)**(1/2),x)","\frac{2 a^{2} \left(c + d x\right)^{\frac{3}{2}}}{3 d} - \sqrt{\pi} a b \sqrt{d} e^{- \frac{c}{d}} \operatorname{erfi}{\left(\frac{\sqrt{c + d x}}{d \sqrt{\frac{1}{d}}} \right)} + \frac{2 a b \sqrt{c + d x} e^{- \frac{c}{d}} e^{\frac{c}{d} + x}}{\sqrt{d} \sqrt{\frac{1}{d}}} - \frac{\sqrt{2} \sqrt{\pi} b^{2} \sqrt{d} e^{- \frac{2 c}{d}} \operatorname{erfi}{\left(\frac{\sqrt{2} \sqrt{c + d x}}{d \sqrt{\frac{1}{d}}} \right)}}{8} + \frac{b^{2} \sqrt{c + d x} e^{- \frac{2 c}{d}} e^{\frac{2 c}{d} + 2 x}}{2 \sqrt{d} \sqrt{\frac{1}{d}}}"," ",0,"2*a**2*(c + d*x)**(3/2)/(3*d) - sqrt(pi)*a*b*sqrt(d)*exp(-c/d)*erfi(sqrt(c + d*x)/(d*sqrt(1/d))) + 2*a*b*sqrt(c + d*x)*exp(-c/d)*exp(c/d + x)/(sqrt(d)*sqrt(1/d)) - sqrt(2)*sqrt(pi)*b**2*sqrt(d)*exp(-2*c/d)*erfi(sqrt(2)*sqrt(c + d*x)/(d*sqrt(1/d)))/8 + b**2*sqrt(c + d*x)*exp(-2*c/d)*exp(2*c/d + 2*x)/(2*sqrt(d)*sqrt(1/d))","A",0
66,1,291,0,4.360077," ","integrate((a+b*exp(x))**3*(d*x+c)**(1/2),x)","\frac{2 a^{3} \left(c + d x\right)^{\frac{3}{2}}}{3 d} - \frac{3 \sqrt{\pi} a^{2} b \sqrt{d} e^{- \frac{c}{d}} \operatorname{erfi}{\left(\frac{\sqrt{c + d x}}{d \sqrt{\frac{1}{d}}} \right)}}{2} + \frac{3 a^{2} b \sqrt{c + d x} e^{- \frac{c}{d}} e^{\frac{c}{d} + x}}{\sqrt{d} \sqrt{\frac{1}{d}}} - \frac{3 \sqrt{2} \sqrt{\pi} a b^{2} \sqrt{d} e^{- \frac{2 c}{d}} \operatorname{erfi}{\left(\frac{\sqrt{2} \sqrt{c + d x}}{d \sqrt{\frac{1}{d}}} \right)}}{8} + \frac{3 a b^{2} \sqrt{c + d x} e^{- \frac{2 c}{d}} e^{\frac{2 c}{d} + 2 x}}{2 \sqrt{d} \sqrt{\frac{1}{d}}} - \frac{\sqrt{3} \sqrt{\pi} b^{3} \sqrt{d} e^{- \frac{3 c}{d}} \operatorname{erfi}{\left(\frac{\sqrt{3} \sqrt{c + d x}}{d \sqrt{\frac{1}{d}}} \right)}}{18} + \frac{b^{3} \sqrt{c + d x} e^{- \frac{3 c}{d}} e^{\frac{3 c}{d} + 3 x}}{3 \sqrt{d} \sqrt{\frac{1}{d}}}"," ",0,"2*a**3*(c + d*x)**(3/2)/(3*d) - 3*sqrt(pi)*a**2*b*sqrt(d)*exp(-c/d)*erfi(sqrt(c + d*x)/(d*sqrt(1/d)))/2 + 3*a**2*b*sqrt(c + d*x)*exp(-c/d)*exp(c/d + x)/(sqrt(d)*sqrt(1/d)) - 3*sqrt(2)*sqrt(pi)*a*b**2*sqrt(d)*exp(-2*c/d)*erfi(sqrt(2)*sqrt(c + d*x)/(d*sqrt(1/d)))/8 + 3*a*b**2*sqrt(c + d*x)*exp(-2*c/d)*exp(2*c/d + 2*x)/(2*sqrt(d)*sqrt(1/d)) - sqrt(3)*sqrt(pi)*b**3*sqrt(d)*exp(-3*c/d)*erfi(sqrt(3)*sqrt(c + d*x)/(d*sqrt(1/d)))/18 + b**3*sqrt(c + d*x)*exp(-3*c/d)*exp(3*c/d + 3*x)/(3*sqrt(d)*sqrt(1/d))","A",0
67,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(a+b*exp(x)),x)","\int \frac{\sqrt{c + d x}}{a + b e^{x}}\, dx"," ",0,"Integral(sqrt(c + d*x)/(a + b*exp(x)), x)","F",0
68,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(a+b*exp(x))**2,x)","\int \frac{\sqrt{c + d x}}{\left(a + b e^{x}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c + d*x)/(a + b*exp(x))**2, x)","F",0
69,0,0,0,0.000000," ","integrate((d*x+c)**(1/2)/(a+b*exp(x))**3,x)","\int \frac{\sqrt{c + d x}}{\left(a + b e^{x}\right)^{3}}\, dx"," ",0,"Integral(sqrt(c + d*x)/(a + b*exp(x))**3, x)","F",0
70,-1,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)**3*(d*x+c)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)**2*(d*x+c)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)*(d*x+c)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate((d*x+c)**m/(a+b*(F**(g*(f*x+e)))**n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate((d*x+c)**m/(a+b*(F**(g*(f*x+e)))**n)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate((a+b*(F**(g*(f*x+e)))**n)**p*(d*x+c)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,0,0,0,0.000000," ","integrate(F**(d*x+c)*x**3/(a+b*F**(d*x+c)),x)","\int \frac{F^{c + d x} x^{3}}{F^{c} F^{d x} b + a}\, dx"," ",0,"Integral(F**(c + d*x)*x**3/(F**c*F**(d*x)*b + a), x)","F",0
77,0,0,0,0.000000," ","integrate(F**(d*x+c)*x**2/(a+b*F**(d*x+c)),x)","\int \frac{F^{c + d x} x^{2}}{F^{c} F^{d x} b + a}\, dx"," ",0,"Integral(F**(c + d*x)*x**2/(F**c*F**(d*x)*b + a), x)","F",0
78,0,0,0,0.000000," ","integrate(F**(d*x+c)*x/(a+b*F**(d*x+c)),x)","\int \frac{F^{c + d x} x}{F^{c} F^{d x} b + a}\, dx"," ",0,"Integral(F**(c + d*x)*x/(F**c*F**(d*x)*b + a), x)","F",0
79,1,17,0,0.137864," ","integrate(F**(d*x+c)/(a+b*F**(d*x+c)),x)","\frac{\log{\left(F^{c + d x} + \frac{a}{b} \right)}}{b d \log{\left(F \right)}}"," ",0,"log(F**(c + d*x) + a/b)/(b*d*log(F))","A",0
80,0,0,0,0.000000," ","integrate(F**(d*x+c)/(a+b*F**(d*x+c))/x,x)","\int \frac{F^{c + d x}}{x \left(F^{c} F^{d x} b + a\right)}\, dx"," ",0,"Integral(F**(c + d*x)/(x*(F**c*F**(d*x)*b + a)), x)","F",0
81,0,0,0,0.000000," ","integrate(F**(d*x+c)/(a+b*F**(d*x+c))/x**2,x)","\int \frac{F^{c + d x}}{x^{2} \left(F^{c} F^{d x} b + a\right)}\, dx"," ",0,"Integral(F**(c + d*x)/(x**2*(F**c*F**(d*x)*b + a)), x)","F",0
82,0,0,0,0.000000," ","integrate(F**(d*x+c)*x**3/(a+b*F**(d*x+c))**2,x)","- \frac{x^{3}}{F^{c + d x} b^{2} d \log{\left(F \right)} + a b d \log{\left(F \right)}} + \frac{3 \int \frac{x^{2}}{a + b e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\, dx}{b d \log{\left(F \right)}}"," ",0,"-x**3/(F**(c + d*x)*b**2*d*log(F) + a*b*d*log(F)) + 3*Integral(x**2/(a + b*exp(c*log(F))*exp(d*x*log(F))), x)/(b*d*log(F))","F",0
83,0,0,0,0.000000," ","integrate(F**(d*x+c)*x**2/(a+b*F**(d*x+c))**2,x)","- \frac{x^{2}}{F^{c + d x} b^{2} d \log{\left(F \right)} + a b d \log{\left(F \right)}} + \frac{2 \int \frac{x}{a + b e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\, dx}{b d \log{\left(F \right)}}"," ",0,"-x**2/(F**(c + d*x)*b**2*d*log(F) + a*b*d*log(F)) + 2*Integral(x/(a + b*exp(c*log(F))*exp(d*x*log(F))), x)/(b*d*log(F))","F",0
84,1,58,0,0.183156," ","integrate(F**(d*x+c)*x/(a+b*F**(d*x+c))**2,x)","- \frac{x}{F^{c + d x} b^{2} d \log{\left(F \right)} + a b d \log{\left(F \right)}} + \frac{x}{a b d \log{\left(F \right)}} - \frac{\log{\left(F^{c + d x} + \frac{a}{b} \right)}}{a b d^{2} \log{\left(F \right)}^{2}}"," ",0,"-x/(F**(c + d*x)*b**2*d*log(F) + a*b*d*log(F)) + x/(a*b*d*log(F)) - log(F**(c + d*x) + a/b)/(a*b*d**2*log(F)**2)","A",0
85,1,26,0,0.123079," ","integrate(F**(d*x+c)/(a+b*F**(d*x+c))**2,x)","- \frac{1}{F^{c + d x} b^{2} d \log{\left(F \right)} + a b d \log{\left(F \right)}}"," ",0,"-1/(F**(c + d*x)*b**2*d*log(F) + a*b*d*log(F))","A",0
86,0,0,0,0.000000," ","integrate(F**(d*x+c)/(a+b*F**(d*x+c))**2/x,x)","- \frac{1}{F^{c + d x} b^{2} d x \log{\left(F \right)} + a b d x \log{\left(F \right)}} - \frac{\int \frac{1}{a x^{2} + b x^{2} e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\, dx}{b d \log{\left(F \right)}}"," ",0,"-1/(F**(c + d*x)*b**2*d*x*log(F) + a*b*d*x*log(F)) - Integral(1/(a*x**2 + b*x**2*exp(c*log(F))*exp(d*x*log(F))), x)/(b*d*log(F))","F",0
87,0,0,0,0.000000," ","integrate(F**(d*x+c)/(a+b*F**(d*x+c))**2/x**2,x)","- \frac{1}{F^{c + d x} b^{2} d x^{2} \log{\left(F \right)} + a b d x^{2} \log{\left(F \right)}} - \frac{2 \int \frac{1}{a x^{3} + b x^{3} e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\, dx}{b d \log{\left(F \right)}}"," ",0,"-1/(F**(c + d*x)*b**2*d*x**2*log(F) + a*b*d*x**2*log(F)) - 2*Integral(1/(a*x**3 + b*x**3*exp(c*log(F))*exp(d*x*log(F))), x)/(b*d*log(F))","F",0
88,0,0,0,0.000000," ","integrate(F**(d*x+c)*x**3/(a+b*F**(d*x+c))**3,x)","\frac{3 F^{c + d x} b x^{2} - a d x^{3} \log{\left(F \right)} + 3 a x^{2}}{4 F^{c + d x} a^{2} b^{2} d^{2} \log{\left(F \right)}^{2} + 2 F^{2 c + 2 d x} a b^{3} d^{2} \log{\left(F \right)}^{2} + 2 a^{3} b d^{2} \log{\left(F \right)}^{2}} + \frac{3 \left(\int \left(- \frac{2 x}{a + b e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\right)\, dx + \int \frac{d x^{2} \log{\left(F \right)}}{a + b e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\, dx\right)}{2 a b d^{2} \log{\left(F \right)}^{2}}"," ",0,"(3*F**(c + d*x)*b*x**2 - a*d*x**3*log(F) + 3*a*x**2)/(4*F**(c + d*x)*a**2*b**2*d**2*log(F)**2 + 2*F**(2*c + 2*d*x)*a*b**3*d**2*log(F)**2 + 2*a**3*b*d**2*log(F)**2) + 3*(Integral(-2*x/(a + b*exp(c*log(F))*exp(d*x*log(F))), x) + Integral(d*x**2*log(F)/(a + b*exp(c*log(F))*exp(d*x*log(F))), x))/(2*a*b*d**2*log(F)**2)","F",0
89,0,0,0,0.000000," ","integrate(F**(d*x+c)*x**2/(a+b*F**(d*x+c))**3,x)","\frac{2 F^{c + d x} b x - a d x^{2} \log{\left(F \right)} + 2 a x}{4 F^{c + d x} a^{2} b^{2} d^{2} \log{\left(F \right)}^{2} + 2 F^{2 c + 2 d x} a b^{3} d^{2} \log{\left(F \right)}^{2} + 2 a^{3} b d^{2} \log{\left(F \right)}^{2}} + \frac{\int \frac{d x \log{\left(F \right)}}{a + b e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\, dx + \int \left(- \frac{1}{a + b e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\right)\, dx}{a b d^{2} \log{\left(F \right)}^{2}}"," ",0,"(2*F**(c + d*x)*b*x - a*d*x**2*log(F) + 2*a*x)/(4*F**(c + d*x)*a**2*b**2*d**2*log(F)**2 + 2*F**(2*c + 2*d*x)*a*b**3*d**2*log(F)**2 + 2*a**3*b*d**2*log(F)**2) + (Integral(d*x*log(F)/(a + b*exp(c*log(F))*exp(d*x*log(F))), x) + Integral(-1/(a + b*exp(c*log(F))*exp(d*x*log(F))), x))/(a*b*d**2*log(F)**2)","F",0
90,1,122,0,0.225816," ","integrate(F**(d*x+c)*x/(a+b*F**(d*x+c))**3,x)","\frac{F^{c + d x} b - a d x \log{\left(F \right)} + a}{4 F^{c + d x} a^{2} b^{2} d^{2} \log{\left(F \right)}^{2} + 2 F^{2 c + 2 d x} a b^{3} d^{2} \log{\left(F \right)}^{2} + 2 a^{3} b d^{2} \log{\left(F \right)}^{2}} + \frac{x}{2 a^{2} b d \log{\left(F \right)}} - \frac{\log{\left(F^{c + d x} + \frac{a}{b} \right)}}{2 a^{2} b d^{2} \log{\left(F \right)}^{2}}"," ",0,"(F**(c + d*x)*b - a*d*x*log(F) + a)/(4*F**(c + d*x)*a**2*b**2*d**2*log(F)**2 + 2*F**(2*c + 2*d*x)*a*b**3*d**2*log(F)**2 + 2*a**3*b*d**2*log(F)**2) + x/(2*a**2*b*d*log(F)) - log(F**(c + d*x) + a/b)/(2*a**2*b*d**2*log(F)**2)","A",0
91,1,53,0,0.152545," ","integrate(F**(d*x+c)/(a+b*F**(d*x+c))**3,x)","- \frac{1}{4 F^{c + d x} a b^{2} d \log{\left(F \right)} + 2 F^{2 c + 2 d x} b^{3} d \log{\left(F \right)} + 2 a^{2} b d \log{\left(F \right)}}"," ",0,"-1/(4*F**(c + d*x)*a*b**2*d*log(F) + 2*F**(2*c + 2*d*x)*b**3*d*log(F) + 2*a**2*b*d*log(F))","B",0
92,0,0,0,0.000000," ","integrate(F**(d*x+c)/(a+b*F**(d*x+c))**3/x,x)","\frac{- F^{c + d x} b - a d x \log{\left(F \right)} - a}{4 F^{c + d x} a^{2} b^{2} d^{2} x^{2} \log{\left(F \right)}^{2} + 2 F^{2 c + 2 d x} a b^{3} d^{2} x^{2} \log{\left(F \right)}^{2} + 2 a^{3} b d^{2} x^{2} \log{\left(F \right)}^{2}} - \frac{\int \frac{d x \log{\left(F \right)}}{a x^{3} + b x^{3} e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\, dx + \int \frac{2}{a x^{3} + b x^{3} e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\, dx}{2 a b d^{2} \log{\left(F \right)}^{2}}"," ",0,"(-F**(c + d*x)*b - a*d*x*log(F) - a)/(4*F**(c + d*x)*a**2*b**2*d**2*x**2*log(F)**2 + 2*F**(2*c + 2*d*x)*a*b**3*d**2*x**2*log(F)**2 + 2*a**3*b*d**2*x**2*log(F)**2) - (Integral(d*x*log(F)/(a*x**3 + b*x**3*exp(c*log(F))*exp(d*x*log(F))), x) + Integral(2/(a*x**3 + b*x**3*exp(c*log(F))*exp(d*x*log(F))), x))/(2*a*b*d**2*log(F)**2)","F",0
93,0,0,0,0.000000," ","integrate(F**(d*x+c)/(a+b*F**(d*x+c))**3/x**2,x)","\frac{- 2 F^{c + d x} b - a d x \log{\left(F \right)} - 2 a}{4 F^{c + d x} a^{2} b^{2} d^{2} x^{3} \log{\left(F \right)}^{2} + 2 F^{2 c + 2 d x} a b^{3} d^{2} x^{3} \log{\left(F \right)}^{2} + 2 a^{3} b d^{2} x^{3} \log{\left(F \right)}^{2}} - \frac{\int \frac{d x \log{\left(F \right)}}{a x^{4} + b x^{4} e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\, dx + \int \frac{3}{a x^{4} + b x^{4} e^{c \log{\left(F \right)}} e^{d x \log{\left(F \right)}}}\, dx}{a b d^{2} \log{\left(F \right)}^{2}}"," ",0,"(-2*F**(c + d*x)*b - a*d*x*log(F) - 2*a)/(4*F**(c + d*x)*a**2*b**2*d**2*x**3*log(F)**2 + 2*F**(2*c + 2*d*x)*a*b**3*d**2*x**3*log(F)**2 + 2*a**3*b*d**2*x**3*log(F)**2) - (Integral(d*x*log(F)/(a*x**4 + b*x**4*exp(c*log(F))*exp(d*x*log(F))), x) + Integral(3/(a*x**4 + b*x**4*exp(c*log(F))*exp(d*x*log(F))), x))/(a*b*d**2*log(F)**2)","F",0
