3.65.85 \(\int \frac {-x+x^2+(x^2-x^3) \log (5)+(x^2-x^3 \log (5)) \log (x)+e^{-e^{e^5 x}+x} (1-x-x \log (x))+(e^{-e^{e^5 x}+x} (-x+x^2+e^{5+e^5 x} (x-x^2)) \log (x)+(x-x^2+(-2 x^2+2 x^3) \log (5)) \log (x)) \log ((-1+x) \log (x))}{(-x+x^2) \log (x) \log ^2((-1+x) \log (x))} \, dx\)

Optimal. Leaf size=33 \[ \frac {e^{-e^{e^5 x}+x}-x+x^2 \log (5)}{\log ((-1+x) \log (x))} \]

________________________________________________________________________________________

Rubi [F]  time = 10.39, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {-x+x^2+\left (x^2-x^3\right ) \log (5)+\left (x^2-x^3 \log (5)\right ) \log (x)+e^{-e^{e^5 x}+x} (1-x-x \log (x))+\left (e^{-e^{e^5 x}+x} \left (-x+x^2+e^{5+e^5 x} \left (x-x^2\right )\right ) \log (x)+\left (x-x^2+\left (-2 x^2+2 x^3\right ) \log (5)\right ) \log (x)\right ) \log ((-1+x) \log (x))}{\left (-x+x^2\right ) \log (x) \log ^2((-1+x) \log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-x + x^2 + (x^2 - x^3)*Log[5] + (x^2 - x^3*Log[5])*Log[x] + E^(-E^(E^5*x) + x)*(1 - x - x*Log[x]) + (E^(-
E^(E^5*x) + x)*(-x + x^2 + E^(5 + E^5*x)*(x - x^2))*Log[x] + (x - x^2 + (-2*x^2 + 2*x^3)*Log[5])*Log[x])*Log[(
-1 + x)*Log[x]])/((-x + x^2)*Log[x]*Log[(-1 + x)*Log[x]]^2),x]

[Out]

(1 - Log[5])*Defer[Int][Log[(-1 + x)*Log[x]]^(-2), x] + (1 - Log[5])*Defer[Int][1/((-1 + x)*Log[(-1 + x)*Log[x
]]^2), x] - Defer[Int][E^(-E^(E^5*x) + x)/((-1 + x)*Log[(-1 + x)*Log[x]]^2), x] - Log[5]*Defer[Int][x/Log[(-1
+ x)*Log[x]]^2, x] + Defer[Int][1/(Log[x]*Log[(-1 + x)*Log[x]]^2), x] - Defer[Int][E^(-E^(E^5*x) + x)/(x*Log[x
]*Log[(-1 + x)*Log[x]]^2), x] - Log[5]*Defer[Int][x/(Log[x]*Log[(-1 + x)*Log[x]]^2), x] - Defer[Int][Log[(-1 +
x)*Log[x]]^(-1), x] + Defer[Int][E^(-E^(E^5*x) + x)/Log[(-1 + x)*Log[x]], x] - Defer[Int][E^(5 - E^(E^5*x) +
(1 + E^5)*x)/Log[(-1 + x)*Log[x]], x] + Log[25]*Defer[Int][x/Log[(-1 + x)*Log[x]], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-x+x^2+\left (x^2-x^3\right ) \log (5)+\left (x^2-x^3 \log (5)\right ) \log (x)+e^{-e^{e^5 x}+x} (1-x-x \log (x))+\left (e^{-e^{e^5 x}+x} \left (-x+x^2+e^{5+e^5 x} \left (x-x^2\right )\right ) \log (x)+\left (x-x^2+\left (-2 x^2+2 x^3\right ) \log (5)\right ) \log (x)\right ) \log ((-1+x) \log (x))}{(-1+x) x \log (x) \log ^2((-1+x) \log (x))} \, dx\\ &=\int \left (-\frac {x (-1+x \log (5))}{(-1+x) \log ^2((-1+x) \log (x))}-\frac {1}{(-1+x) \log (x) \log ^2((-1+x) \log (x))}+\frac {x}{(-1+x) \log (x) \log ^2((-1+x) \log (x))}-\frac {x \log (5)}{\log (x) \log ^2((-1+x) \log (x))}-\frac {e^{-e^{e^5 x}+x} (-1+x+x \log (x))}{(-1+x) x \log (x) \log ^2((-1+x) \log (x))}-\frac {e^{5-e^{e^5 x}+\left (1+e^5\right ) x}}{\log ((-1+x) \log (x))}-\frac {e^{-e^{e^5 x}+x}}{(-1+x) \log ((-1+x) \log (x))}+\frac {e^{-e^{e^5 x}+x} x}{(-1+x) \log ((-1+x) \log (x))}+\frac {-1+x \log (25)}{\log ((-1+x) \log (x))}\right ) \, dx\\ &=-\left (\log (5) \int \frac {x}{\log (x) \log ^2((-1+x) \log (x))} \, dx\right )-\int \frac {x (-1+x \log (5))}{(-1+x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {1}{(-1+x) \log (x) \log ^2((-1+x) \log (x))} \, dx+\int \frac {x}{(-1+x) \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x} (-1+x+x \log (x))}{(-1+x) x \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {e^{5-e^{e^5 x}+\left (1+e^5\right ) x}}{\log ((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x}}{(-1+x) \log ((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x} x}{(-1+x) \log ((-1+x) \log (x))} \, dx+\int \frac {-1+x \log (25)}{\log ((-1+x) \log (x))} \, dx\\ &=-\left (\log (5) \int \frac {x}{\log (x) \log ^2((-1+x) \log (x))} \, dx\right )-\int \left (-\frac {1-\log (5)}{\log ^2((-1+x) \log (x))}+\frac {-1+\log (5)}{(-1+x) \log ^2((-1+x) \log (x))}+\frac {x \log (5)}{\log ^2((-1+x) \log (x))}\right ) \, dx+\int \left (\frac {1}{\log (x) \log ^2((-1+x) \log (x))}+\frac {1}{(-1+x) \log (x) \log ^2((-1+x) \log (x))}\right ) \, dx-\int \left (\frac {e^{-e^{e^5 x}+x} (1-x-x \log (x))}{x \log (x) \log ^2((-1+x) \log (x))}+\frac {e^{-e^{e^5 x}+x} (-1+x+x \log (x))}{(-1+x) \log (x) \log ^2((-1+x) \log (x))}\right ) \, dx+\int \left (\frac {e^{-e^{e^5 x}+x}}{\log ((-1+x) \log (x))}+\frac {e^{-e^{e^5 x}+x}}{(-1+x) \log ((-1+x) \log (x))}\right ) \, dx+\int \left (-\frac {1}{\log ((-1+x) \log (x))}+\frac {x \log (25)}{\log ((-1+x) \log (x))}\right ) \, dx-\int \frac {1}{(-1+x) \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {e^{5-e^{e^5 x}+\left (1+e^5\right ) x}}{\log ((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x}}{(-1+x) \log ((-1+x) \log (x))} \, dx\\ &=-\left ((-1+\log (5)) \int \frac {1}{\log ^2((-1+x) \log (x))} \, dx\right )-(-1+\log (5)) \int \frac {1}{(-1+x) \log ^2((-1+x) \log (x))} \, dx-\log (5) \int \frac {x}{\log ^2((-1+x) \log (x))} \, dx-\log (5) \int \frac {x}{\log (x) \log ^2((-1+x) \log (x))} \, dx+\log (25) \int \frac {x}{\log ((-1+x) \log (x))} \, dx+\int \frac {1}{\log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x} (1-x-x \log (x))}{x \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x} (-1+x+x \log (x))}{(-1+x) \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {1}{\log ((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x}}{\log ((-1+x) \log (x))} \, dx-\int \frac {e^{5-e^{e^5 x}+\left (1+e^5\right ) x}}{\log ((-1+x) \log (x))} \, dx\\ &=-\left ((-1+\log (5)) \int \frac {1}{\log ^2((-1+x) \log (x))} \, dx\right )-(-1+\log (5)) \int \frac {1}{(-1+x) \log ^2((-1+x) \log (x))} \, dx-\log (5) \int \frac {x}{\log ^2((-1+x) \log (x))} \, dx-\log (5) \int \frac {x}{\log (x) \log ^2((-1+x) \log (x))} \, dx+\log (25) \int \frac {x}{\log ((-1+x) \log (x))} \, dx-\int \left (-\frac {e^{-e^{e^5 x}+x}}{\log ^2((-1+x) \log (x))}-\frac {e^{-e^{e^5 x}+x}}{\log (x) \log ^2((-1+x) \log (x))}+\frac {e^{-e^{e^5 x}+x}}{x \log (x) \log ^2((-1+x) \log (x))}\right ) \, dx-\int \left (\frac {e^{-e^{e^5 x}+x} x}{(-1+x) \log ^2((-1+x) \log (x))}-\frac {e^{-e^{e^5 x}+x}}{(-1+x) \log (x) \log ^2((-1+x) \log (x))}+\frac {e^{-e^{e^5 x}+x} x}{(-1+x) \log (x) \log ^2((-1+x) \log (x))}\right ) \, dx+\int \frac {1}{\log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {1}{\log ((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x}}{\log ((-1+x) \log (x))} \, dx-\int \frac {e^{5-e^{e^5 x}+\left (1+e^5\right ) x}}{\log ((-1+x) \log (x))} \, dx\\ &=-\left ((-1+\log (5)) \int \frac {1}{\log ^2((-1+x) \log (x))} \, dx\right )-(-1+\log (5)) \int \frac {1}{(-1+x) \log ^2((-1+x) \log (x))} \, dx-\log (5) \int \frac {x}{\log ^2((-1+x) \log (x))} \, dx-\log (5) \int \frac {x}{\log (x) \log ^2((-1+x) \log (x))} \, dx+\log (25) \int \frac {x}{\log ((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x}}{\log ^2((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x} x}{(-1+x) \log ^2((-1+x) \log (x))} \, dx+\int \frac {1}{\log (x) \log ^2((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x}}{\log (x) \log ^2((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x}}{(-1+x) \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x}}{x \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x} x}{(-1+x) \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {1}{\log ((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x}}{\log ((-1+x) \log (x))} \, dx-\int \frac {e^{5-e^{e^5 x}+\left (1+e^5\right ) x}}{\log ((-1+x) \log (x))} \, dx\\ &=-\left ((-1+\log (5)) \int \frac {1}{\log ^2((-1+x) \log (x))} \, dx\right )-(-1+\log (5)) \int \frac {1}{(-1+x) \log ^2((-1+x) \log (x))} \, dx-\log (5) \int \frac {x}{\log ^2((-1+x) \log (x))} \, dx-\log (5) \int \frac {x}{\log (x) \log ^2((-1+x) \log (x))} \, dx+\log (25) \int \frac {x}{\log ((-1+x) \log (x))} \, dx-\int \left (\frac {e^{-e^{e^5 x}+x}}{\log ^2((-1+x) \log (x))}+\frac {e^{-e^{e^5 x}+x}}{(-1+x) \log ^2((-1+x) \log (x))}\right ) \, dx-\int \left (\frac {e^{-e^{e^5 x}+x}}{\log (x) \log ^2((-1+x) \log (x))}+\frac {e^{-e^{e^5 x}+x}}{(-1+x) \log (x) \log ^2((-1+x) \log (x))}\right ) \, dx+\int \frac {e^{-e^{e^5 x}+x}}{\log ^2((-1+x) \log (x))} \, dx+\int \frac {1}{\log (x) \log ^2((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x}}{\log (x) \log ^2((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x}}{(-1+x) \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x}}{x \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {1}{\log ((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x}}{\log ((-1+x) \log (x))} \, dx-\int \frac {e^{5-e^{e^5 x}+\left (1+e^5\right ) x}}{\log ((-1+x) \log (x))} \, dx\\ &=-\left ((-1+\log (5)) \int \frac {1}{\log ^2((-1+x) \log (x))} \, dx\right )-(-1+\log (5)) \int \frac {1}{(-1+x) \log ^2((-1+x) \log (x))} \, dx-\log (5) \int \frac {x}{\log ^2((-1+x) \log (x))} \, dx-\log (5) \int \frac {x}{\log (x) \log ^2((-1+x) \log (x))} \, dx+\log (25) \int \frac {x}{\log ((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x}}{(-1+x) \log ^2((-1+x) \log (x))} \, dx+\int \frac {1}{\log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {e^{-e^{e^5 x}+x}}{x \log (x) \log ^2((-1+x) \log (x))} \, dx-\int \frac {1}{\log ((-1+x) \log (x))} \, dx+\int \frac {e^{-e^{e^5 x}+x}}{\log ((-1+x) \log (x))} \, dx-\int \frac {e^{5-e^{e^5 x}+\left (1+e^5\right ) x}}{\log ((-1+x) \log (x))} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.64, size = 33, normalized size = 1.00 \begin {gather*} \frac {e^{-e^{e^5 x}+x}-x+x^2 \log (5)}{\log ((-1+x) \log (x))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-x + x^2 + (x^2 - x^3)*Log[5] + (x^2 - x^3*Log[5])*Log[x] + E^(-E^(E^5*x) + x)*(1 - x - x*Log[x]) +
(E^(-E^(E^5*x) + x)*(-x + x^2 + E^(5 + E^5*x)*(x - x^2))*Log[x] + (x - x^2 + (-2*x^2 + 2*x^3)*Log[5])*Log[x])
*Log[(-1 + x)*Log[x]])/((-x + x^2)*Log[x]*Log[(-1 + x)*Log[x]]^2),x]

[Out]

(E^(-E^(E^5*x) + x) - x + x^2*Log[5])/Log[(-1 + x)*Log[x]]

________________________________________________________________________________________

fricas [A]  time = 0.73, size = 38, normalized size = 1.15 \begin {gather*} \frac {x^{2} \log \relax (5) - x + e^{\left ({\left (x e^{5} - e^{\left (x e^{5} + 5\right )}\right )} e^{\left (-5\right )}\right )}}{\log \left ({\left (x - 1\right )} \log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-x^2+x)*exp(5)*exp(x*exp(5))+x^2-x)*log(x)*exp(x-exp(x*exp(5)))+((2*x^3-2*x^2)*log(5)-x^2+x)*log
(x))*log((x-1)*log(x))+(-x*log(x)-x+1)*exp(x-exp(x*exp(5)))+(-x^3*log(5)+x^2)*log(x)+(-x^3+x^2)*log(5)+x^2-x)/
(x^2-x)/log(x)/log((x-1)*log(x))^2,x, algorithm="fricas")

[Out]

(x^2*log(5) - x + e^((x*e^5 - e^(x*e^5 + 5))*e^(-5)))/log((x - 1)*log(x))

________________________________________________________________________________________

giac [A]  time = 0.27, size = 33, normalized size = 1.00 \begin {gather*} \frac {x^{2} \log \relax (5) - x + e^{\left (x - e^{\left (x e^{5}\right )}\right )}}{\log \left (x \log \relax (x) - \log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-x^2+x)*exp(5)*exp(x*exp(5))+x^2-x)*log(x)*exp(x-exp(x*exp(5)))+((2*x^3-2*x^2)*log(5)-x^2+x)*log
(x))*log((x-1)*log(x))+(-x*log(x)-x+1)*exp(x-exp(x*exp(5)))+(-x^3*log(5)+x^2)*log(x)+(-x^3+x^2)*log(5)+x^2-x)/
(x^2-x)/log(x)/log((x-1)*log(x))^2,x, algorithm="giac")

[Out]

(x^2*log(5) - x + e^(x - e^(x*e^5)))/log(x*log(x) - log(x))

________________________________________________________________________________________

maple [C]  time = 0.50, size = 118, normalized size = 3.58

method	result	size
risch	\(\frac {2 i \left (x^{2} \ln \relax (5)+{\mathrm e}^{x -{\mathrm e}^{x \,{\mathrm e}^{5}}}-x \right )}{\pi \mathrm {csgn}\left (i \ln \relax (x ) \left (x -1\right )\right )^{3}-\pi \mathrm {csgn}\left (i \ln \relax (x ) \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i \ln \relax (x )\right )-\pi \mathrm {csgn}\left (i \ln \relax (x ) \left (x -1\right )\right )^{2} \mathrm {csgn}\left (i \left (x -1\right )\right )+\pi \,\mathrm {csgn}\left (i \ln \relax (x ) \left (x -1\right )\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i \left (x -1\right )\right )+2 i \ln \left (\ln \relax (x )\right )+2 i \ln \left (x -1\right )}\)	\(118\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-x^2+x)*exp(5)*exp(x*exp(5))+x^2-x)*ln(x)*exp(x-exp(x*exp(5)))+((2*x^3-2*x^2)*ln(5)-x^2+x)*ln(x))*ln((
x-1)*ln(x))+(-x*ln(x)-x+1)*exp(x-exp(x*exp(5)))+(-x^3*ln(5)+x^2)*ln(x)+(-x^3+x^2)*ln(5)+x^2-x)/(x^2-x)/ln(x)/l
n((x-1)*ln(x))^2,x,method=_RETURNVERBOSE)

[Out]

2*I*(x^2*ln(5)+exp(x-exp(x*exp(5)))-x)/(Pi*csgn(I*ln(x)*(x-1))^3-Pi*csgn(I*ln(x)*(x-1))^2*csgn(I*ln(x))-Pi*csg
n(I*ln(x)*(x-1))^2*csgn(I*(x-1))+Pi*csgn(I*ln(x)*(x-1))*csgn(I*ln(x))*csgn(I*(x-1))+2*I*ln(ln(x))+2*I*ln(x-1))

________________________________________________________________________________________

maxima [A]  time = 0.50, size = 31, normalized size = 0.94 \begin {gather*} \frac {x^{2} \log \relax (5) - x + e^{\left (x - e^{\left (x e^{5}\right )}\right )}}{\log \left (x - 1\right ) + \log \left (\log \relax (x)\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-x^2+x)*exp(5)*exp(x*exp(5))+x^2-x)*log(x)*exp(x-exp(x*exp(5)))+((2*x^3-2*x^2)*log(5)-x^2+x)*log
(x))*log((x-1)*log(x))+(-x*log(x)-x+1)*exp(x-exp(x*exp(5)))+(-x^3*log(5)+x^2)*log(x)+(-x^3+x^2)*log(5)+x^2-x)/
(x^2-x)/log(x)/log((x-1)*log(x))^2,x, algorithm="maxima")

[Out]

(x^2*log(5) - x + e^(x - e^(x*e^5)))/(log(x - 1) + log(log(x)))

________________________________________________________________________________________

mupad [B]  time = 4.89, size = 138, normalized size = 4.18 \begin {gather*} \frac {{\mathrm {e}}^{x-{\mathrm {e}}^{x\,{\mathrm {e}}^5}}}{\ln \left (\ln \relax (x)\,\left (x-1\right )\right )}-x\,\left (\ln \left (25\right )+1\right )+2\,x^2\,\ln \relax (5)+\frac {x\,\left (x\,\ln \relax (5)-1\right )-\frac {x\,\ln \left (\ln \relax (x)\,\left (x-1\right )\right )\,\ln \relax (x)\,\left (2\,x\,\ln \relax (5)-1\right )\,\left (x-1\right )}{x+x\,\ln \relax (x)-1}}{\ln \left (\ln \relax (x)\,\left (x-1\right )\right )}-\frac {x+2\,x\,\ln \relax (5)-2\,x^2\,\ln \relax (5)-2\,x^3\,\ln \relax (5)+2\,x^4\,\ln \relax (5)+x^2-x^3-1}{\left (x+1\right )\,\left (x+x\,\ln \relax (x)-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((x + exp(x - exp(x*exp(5)))*(x + x*log(x) - 1) + log(log(x)*(x - 1))*(log(x)*(log(5)*(2*x^2 - 2*x^3) - x +
x^2) - exp(x - exp(x*exp(5)))*log(x)*(x^2 - x + exp(5)*exp(x*exp(5))*(x - x^2))) - log(5)*(x^2 - x^3) + log(x
)*(x^3*log(5) - x^2) - x^2)/(log(log(x)*(x - 1))^2*log(x)*(x - x^2)),x)

[Out]

exp(x - exp(x*exp(5)))/log(log(x)*(x - 1)) - x*(log(25) + 1) + 2*x^2*log(5) + (x*(x*log(5) - 1) - (x*log(log(x
)*(x - 1))*log(x)*(2*x*log(5) - 1)*(x - 1))/(x + x*log(x) - 1))/log(log(x)*(x - 1)) - (x + 2*x*log(5) - 2*x^2*
log(5) - 2*x^3*log(5) + 2*x^4*log(5) + x^2 - x^3 - 1)/((x + 1)*(x + x*log(x) - 1))

________________________________________________________________________________________

sympy [A]  time = 1.90, size = 34, normalized size = 1.03 \begin {gather*} \frac {x^{2} \log {\relax (5 )} - x}{\log {\left (\left (x - 1\right ) \log {\relax (x )} \right )}} + \frac {e^{x - e^{x e^{5}}}}{\log {\left (\left (x - 1\right ) \log {\relax (x )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-x**2+x)*exp(5)*exp(x*exp(5))+x**2-x)*ln(x)*exp(x-exp(x*exp(5)))+((2*x**3-2*x**2)*ln(5)-x**2+x)*
ln(x))*ln((x-1)*ln(x))+(-x*ln(x)-x+1)*exp(x-exp(x*exp(5)))+(-x**3*ln(5)+x**2)*ln(x)+(-x**3+x**2)*ln(5)+x**2-x)
/(x**2-x)/ln(x)/ln((x-1)*ln(x))**2,x)

[Out]

(x**2*log(5) - x)/log((x - 1)*log(x)) + exp(x - exp(x*exp(5)))/log((x - 1)*log(x))

________________________________________________________________________________________