3.99.34 \(\int \frac {-8 x^3-8 x^4+8 x^5+e^{e^2} (8 x^3-8 x^4)+(-16 x^3+16 e^{e^2} x^3-16 x^4) \log (\frac {5 e^x}{-3 x+3 e^{e^2} x-3 x^2})}{(-1+e^{e^2}-x) \log ^3(\frac {5 e^x}{-3 x+3 e^{e^2} x-3 x^2})} \, dx\)

Optimal. Leaf size=33 \[ 4 \left (-2+\frac {x^4}{\log ^2\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )}\right ) \]

________________________________________________________________________________________

Rubi [F]  time = 2.31, 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 {-8 x^3-8 x^4+8 x^5+e^{e^2} \left (8 x^3-8 x^4\right )+\left (-16 x^3+16 e^{e^2} x^3-16 x^4\right ) \log \left (\frac {5 e^x}{-3 x+3 e^{e^2} x-3 x^2}\right )}{\left (-1+e^{e^2}-x\right ) \log ^3\left (\frac {5 e^x}{-3 x+3 e^{e^2} x-3 x^2}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-8*x^3 - 8*x^4 + 8*x^5 + E^E^2*(8*x^3 - 8*x^4) + (-16*x^3 + 16*E^E^2*x^3 - 16*x^4)*Log[(5*E^x)/(-3*x + 3*
E^E^2*x - 3*x^2)])/((-1 + E^E^2 - x)*Log[(5*E^x)/(-3*x + 3*E^E^2*x - 3*x^2)]^3),x]

[Out]

-8*(1 - E^E^2)^3*Defer[Int][Log[(5*E^x)/(3*(-1 + E^E^2 - x)*x)]^(-3), x] - 8*(1 - E^E^2)^4*Defer[Int][1/((-1 +
E^E^2 - x)*Log[(5*E^x)/(3*(-1 + E^E^2 - x)*x)]^3), x] + 8*(1 - E^E^2)^2*Defer[Int][x/Log[(5*E^x)/(3*(-1 + E^E
^2 - x)*x)]^3, x] - 8*(1 - E^E^2)*Defer[Int][x^2/Log[(5*E^x)/(3*(-1 + E^E^2 - x)*x)]^3, x] + 16*Defer[Int][x^3
/Log[(5*E^x)/(3*(-1 + E^E^2 - x)*x)]^3, x] - 8*Defer[Int][x^4/Log[(5*E^x)/(3*(-1 + E^E^2 - x)*x)]^3, x] + 16*D
efer[Int][(x^3*Log[(-5*E^x)/(3*x*(1 - E^E^2 + x))])/Log[(5*E^x)/(3*(-1 + E^E^2 - x)*x)]^3, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8 x^3+8 x^4-8 x^5-e^{e^2} \left (8 x^3-8 x^4\right )-\left (-16 x^3+16 e^{e^2} x^3-16 x^4\right ) \log \left (\frac {5 e^x}{-3 x+3 e^{e^2} x-3 x^2}\right )}{\left (1-e^{e^2}+x\right ) \log ^3\left (\frac {5 e^x}{\left (3 \left (-1+e^{e^2}\right )-3 x\right ) x}\right )} \, dx\\ &=\int \left (\frac {8 x^3 \left (1-e^{e^2}+\left (1+e^{e^2}\right ) x-x^2\right )}{\left (1-e^{e^2}+x\right ) \log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )}+\frac {16 x^3 \log \left (-\frac {5 e^x}{3 x \left (1-e^{e^2}+x\right )}\right )}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )}\right ) \, dx\\ &=8 \int \frac {x^3 \left (1-e^{e^2}+\left (1+e^{e^2}\right ) x-x^2\right )}{\left (1-e^{e^2}+x\right ) \log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )} \, dx+16 \int \frac {x^3 \log \left (-\frac {5 e^x}{3 x \left (1-e^{e^2}+x\right )}\right )}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )} \, dx\\ &=8 \int \left (\frac {\left (-1+e^{e^2}\right )^3}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )}-\frac {\left (-1+e^{e^2}\right )^4}{\left (-1+e^{e^2}-x\right ) \log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )}+\frac {\left (-1+e^{e^2}\right )^2 x}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )}+\frac {\left (-1+e^{e^2}\right ) x^2}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )}+\frac {2 x^3}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )}-\frac {x^4}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )}\right ) \, dx+16 \int \frac {x^3 \log \left (-\frac {5 e^x}{3 x \left (1-e^{e^2}+x\right )}\right )}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )} \, dx\\ &=-\left (8 \int \frac {x^4}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )} \, dx\right )+16 \int \frac {x^3}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )} \, dx+16 \int \frac {x^3 \log \left (-\frac {5 e^x}{3 x \left (1-e^{e^2}+x\right )}\right )}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )} \, dx-\left (8 \left (1-e^{e^2}\right )\right ) \int \frac {x^2}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )} \, dx+\left (8 \left (1-e^{e^2}\right )^2\right ) \int \frac {x}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )} \, dx-\left (8 \left (1-e^{e^2}\right )^3\right ) \int \frac {1}{\log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )} \, dx-\left (8 \left (1-e^{e^2}\right )^4\right ) \int \frac {1}{\left (-1+e^{e^2}-x\right ) \log ^3\left (\frac {5 e^x}{3 \left (-1+e^{e^2}-x\right ) x}\right )} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.08, size = 30, normalized size = 0.91 \begin {gather*} \frac {4 x^4}{\log ^2\left (-\frac {5 e^x}{3 x \left (1-e^{e^2}+x\right )}\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-8*x^3 - 8*x^4 + 8*x^5 + E^E^2*(8*x^3 - 8*x^4) + (-16*x^3 + 16*E^E^2*x^3 - 16*x^4)*Log[(5*E^x)/(-3*
x + 3*E^E^2*x - 3*x^2)])/((-1 + E^E^2 - x)*Log[(5*E^x)/(-3*x + 3*E^E^2*x - 3*x^2)]^3),x]

[Out]

(4*x^4)/Log[(-5*E^x)/(3*x*(1 - E^E^2 + x))]^2

________________________________________________________________________________________

fricas [A]  time = 0.81, size = 25, normalized size = 0.76 \begin {gather*} \frac {4 \, x^{4}}{\log \left (-\frac {5 \, e^{x}}{3 \, {\left (x^{2} - x e^{\left (e^{2}\right )} + x\right )}}\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x^3*exp(exp(2))-16*x^4-16*x^3)*log(5*exp(x)/(3*x*exp(exp(2))-3*x^2-3*x))+(-8*x^4+8*x^3)*exp(exp
(2))+8*x^5-8*x^4-8*x^3)/(exp(exp(2))-x-1)/log(5*exp(x)/(3*x*exp(exp(2))-3*x^2-3*x))^3,x, algorithm="fricas")

[Out]

4*x^4/log(-5/3*e^x/(x^2 - x*e^(e^2) + x))^2

________________________________________________________________________________________

giac [A]  time = 0.49, size = 48, normalized size = 1.45 \begin {gather*} \frac {4 \, x^{4}}{x^{2} + 2 \, x \log \left (-\frac {5}{3 \, {\left (x^{2} - x e^{\left (e^{2}\right )} + x\right )}}\right ) + \log \left (-\frac {5}{3 \, {\left (x^{2} - x e^{\left (e^{2}\right )} + x\right )}}\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x^3*exp(exp(2))-16*x^4-16*x^3)*log(5*exp(x)/(3*x*exp(exp(2))-3*x^2-3*x))+(-8*x^4+8*x^3)*exp(exp
(2))+8*x^5-8*x^4-8*x^3)/(exp(exp(2))-x-1)/log(5*exp(x)/(3*x*exp(exp(2))-3*x^2-3*x))^3,x, algorithm="giac")

[Out]

4*x^4/(x^2 + 2*x*log(-5/3/(x^2 - x*e^(e^2) + x)) + log(-5/3/(x^2 - x*e^(e^2) + x))^2)

________________________________________________________________________________________

maple [A]  time = 0.89, size = 30, normalized size = 0.91

method	result	size
default	\(\frac {4 x^{4}}{\ln \left (\frac {5 \,{\mathrm e}^{x}}{3 x \,{\mathrm e}^{{\mathrm e}^{2}}-3 x^{2}-3 x}\right )^{2}}\)	\(30\)
risch	\(-\frac {16 x^{4}}{\left (\pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{1-{\mathrm e}^{{\mathrm e}^{2}}+x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{x \left (1-{\mathrm e}^{{\mathrm e}^{2}}+x \right )}\right )-\pi \,\mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{x \left (1-{\mathrm e}^{{\mathrm e}^{2}}+x \right )}\right )^{2}+\pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (\frac {i}{1-{\mathrm e}^{{\mathrm e}^{2}}+x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{1-{\mathrm e}^{{\mathrm e}^{2}}+x}\right )-\pi \,\mathrm {csgn}\left (i {\mathrm e}^{x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{1-{\mathrm e}^{{\mathrm e}^{2}}+x}\right )^{2}+\pi \,\mathrm {csgn}\left (\frac {i}{1-{\mathrm e}^{{\mathrm e}^{2}}+x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{1-{\mathrm e}^{{\mathrm e}^{2}}+x}\right )^{2}-\pi \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{1-{\mathrm e}^{{\mathrm e}^{2}}+x}\right )^{3}+\pi \,\mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{1-{\mathrm e}^{{\mathrm e}^{2}}+x}\right ) \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{x \left (1-{\mathrm e}^{{\mathrm e}^{2}}+x \right )}\right )^{2}-\pi \mathrm {csgn}\left (\frac {i {\mathrm e}^{x}}{x \left (1-{\mathrm e}^{{\mathrm e}^{2}}+x \right )}\right )^{3}+2 i \ln \relax (5)-2 i \ln \relax (3)+2 i \ln \left ({\mathrm e}^{x}\right )-2 i \ln \relax (x )-2 i \ln \left ({\mathrm e}^{{\mathrm e}^{2}}-x -1\right )\right )^{2}}\)	\(300\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((16*x^3*exp(exp(2))-16*x^4-16*x^3)*ln(5*exp(x)/(3*x*exp(exp(2))-3*x^2-3*x))+(-8*x^4+8*x^3)*exp(exp(2))+8*
x^5-8*x^4-8*x^3)/(exp(exp(2))-x-1)/ln(5*exp(x)/(3*x*exp(exp(2))-3*x^2-3*x))^3,x,method=_RETURNVERBOSE)

[Out]

4*x^4/ln(5*exp(x)/(3*x*exp(exp(2))-3*x^2-3*x))^2

________________________________________________________________________________________

maxima [B]  time = 0.55, size = 85, normalized size = 2.58 \begin {gather*} \frac {4 \, x^{4}}{x^{2} + 2 \, x {\left (\log \relax (5) - \log \relax (3)\right )} + \log \relax (5)^{2} - 2 \, \log \relax (5) \log \relax (3) + \log \relax (3)^{2} - 2 \, {\left (x + \log \relax (5) - \log \relax (3)\right )} \log \relax (x) + \log \relax (x)^{2} - 2 \, {\left (x + \log \relax (5) - \log \relax (3) - \log \relax (x)\right )} \log \left (-x + e^{\left (e^{2}\right )} - 1\right ) + \log \left (-x + e^{\left (e^{2}\right )} - 1\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x^3*exp(exp(2))-16*x^4-16*x^3)*log(5*exp(x)/(3*x*exp(exp(2))-3*x^2-3*x))+(-8*x^4+8*x^3)*exp(exp
(2))+8*x^5-8*x^4-8*x^3)/(exp(exp(2))-x-1)/log(5*exp(x)/(3*x*exp(exp(2))-3*x^2-3*x))^3,x, algorithm="maxima")

[Out]

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

________________________________________________________________________________________

mupad [B]  time = 6.94, size = 551, normalized size = 16.70 \begin {gather*} 80\,x-\frac {\frac {8\,x^4\,\left (x-{\mathrm {e}}^{{\mathrm {e}}^2}+1\right )}{x-{\mathrm {e}}^{{\mathrm {e}}^2}+x\,{\mathrm {e}}^{{\mathrm {e}}^2}-x^2+1}+\frac {8\,x^4\,\ln \left (-\frac {5\,{\mathrm {e}}^x}{3\,x-3\,x\,{\mathrm {e}}^{{\mathrm {e}}^2}+3\,x^2}\right )\,\left (x-{\mathrm {e}}^{{\mathrm {e}}^2}+1\right )\,\left (8\,x+4\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}-8\,{\mathrm {e}}^{{\mathrm {e}}^2}-3\,x\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}+6\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^2}-5\,x\,{\mathrm {e}}^{{\mathrm {e}}^2}+2\,x^2-3\,x^3+4\right )}{{\left (x-{\mathrm {e}}^{{\mathrm {e}}^2}+x\,{\mathrm {e}}^{{\mathrm {e}}^2}-x^2+1\right )}^3}}{\ln \left (-\frac {5\,{\mathrm {e}}^x}{3\,x-3\,x\,{\mathrm {e}}^{{\mathrm {e}}^2}+3\,x^2}\right )}+\frac {\left (24\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}+96\,{\mathrm {e}}^{{\mathrm {e}}^2}+264\right )\,x^5+\left (-288\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}-56\,{\mathrm {e}}^{3\,{\mathrm {e}}^2}-888\,{\mathrm {e}}^{{\mathrm {e}}^2}-432\right )\,x^4+\left (984\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}+280\,{\mathrm {e}}^{3\,{\mathrm {e}}^2}+32\,{\mathrm {e}}^{4\,{\mathrm {e}}^2}+968\,{\mathrm {e}}^{{\mathrm {e}}^2}-728\right )\,x^3+\left (1128\,{\mathrm {e}}^{{\mathrm {e}}^2}-456\,{\mathrm {e}}^{3\,{\mathrm {e}}^2}-96\,{\mathrm {e}}^{4\,{\mathrm {e}}^2}-840\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}+264\right )\,x^2+\left (304\,{\mathrm {e}}^{3\,{\mathrm {e}}^2}-336\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}+96\,{\mathrm {e}}^{4\,{\mathrm {e}}^2}-624\,{\mathrm {e}}^{{\mathrm {e}}^2}+560\right )\,x+384\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}-64\,{\mathrm {e}}^{3\,{\mathrm {e}}^2}-32\,{\mathrm {e}}^{4\,{\mathrm {e}}^2}-448\,{\mathrm {e}}^{{\mathrm {e}}^2}+160}{x^6+\left (-3\,{\mathrm {e}}^{{\mathrm {e}}^2}-3\right )\,x^5+\left (3\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}+9\,{\mathrm {e}}^{{\mathrm {e}}^2}\right )\,x^4+\left (5-{\mathrm {e}}^{3\,{\mathrm {e}}^2}-3\,{\mathrm {e}}^{{\mathrm {e}}^2}-9\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}\right )\,x^3+\left (6\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}+3\,{\mathrm {e}}^{3\,{\mathrm {e}}^2}-9\,{\mathrm {e}}^{{\mathrm {e}}^2}\right )\,x^2+\left (3\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}-3\,{\mathrm {e}}^{3\,{\mathrm {e}}^2}+3\,{\mathrm {e}}^{{\mathrm {e}}^2}-3\right )\,x-3\,{\mathrm {e}}^{2\,{\mathrm {e}}^2}+{\mathrm {e}}^{3\,{\mathrm {e}}^2}+3\,{\mathrm {e}}^{{\mathrm {e}}^2}-1}+24\,x^2+\frac {4\,x^4+\frac {8\,x^4\,\ln \left (-\frac {5\,{\mathrm {e}}^x}{3\,x-3\,x\,{\mathrm {e}}^{{\mathrm {e}}^2}+3\,x^2}\right )\,\left (x-{\mathrm {e}}^{{\mathrm {e}}^2}+1\right )}{x-{\mathrm {e}}^{{\mathrm {e}}^2}+x\,{\mathrm {e}}^{{\mathrm {e}}^2}-x^2+1}}{{\ln \left (-\frac {5\,{\mathrm {e}}^x}{3\,x-3\,x\,{\mathrm {e}}^{{\mathrm {e}}^2}+3\,x^2}\right )}^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(-(5*exp(x))/(3*x - 3*x*exp(exp(2)) + 3*x^2))*(16*x^3 - 16*x^3*exp(exp(2)) + 16*x^4) + 8*x^3 + 8*x^4 -
8*x^5 - exp(exp(2))*(8*x^3 - 8*x^4))/(log(-(5*exp(x))/(3*x - 3*x*exp(exp(2)) + 3*x^2))^3*(x - exp(exp(2)) + 1
)),x)

[Out]

80*x - ((8*x^4*(x - exp(exp(2)) + 1))/(x - exp(exp(2)) + x*exp(exp(2)) - x^2 + 1) + (8*x^4*log(-(5*exp(x))/(3*
x - 3*x*exp(exp(2)) + 3*x^2))*(x - exp(exp(2)) + 1)*(8*x + 4*exp(2*exp(2)) - 8*exp(exp(2)) - 3*x*exp(2*exp(2))
+ 6*x^2*exp(exp(2)) - 5*x*exp(exp(2)) + 2*x^2 - 3*x^3 + 4))/(x - exp(exp(2)) + x*exp(exp(2)) - x^2 + 1)^3)/lo
g(-(5*exp(x))/(3*x - 3*x*exp(exp(2)) + 3*x^2)) + (384*exp(2*exp(2)) - 64*exp(3*exp(2)) - 32*exp(4*exp(2)) - 44
8*exp(exp(2)) + x^5*(24*exp(2*exp(2)) + 96*exp(exp(2)) + 264) - x^2*(840*exp(2*exp(2)) + 456*exp(3*exp(2)) + 9
6*exp(4*exp(2)) - 1128*exp(exp(2)) - 264) + x^3*(984*exp(2*exp(2)) + 280*exp(3*exp(2)) + 32*exp(4*exp(2)) + 96
8*exp(exp(2)) - 728) - x^4*(288*exp(2*exp(2)) + 56*exp(3*exp(2)) + 888*exp(exp(2)) + 432) + x*(304*exp(3*exp(2
)) - 336*exp(2*exp(2)) + 96*exp(4*exp(2)) - 624*exp(exp(2)) + 560) + 160)/(exp(3*exp(2)) - 3*exp(2*exp(2)) + 3
*exp(exp(2)) + x^4*(3*exp(2*exp(2)) + 9*exp(exp(2))) + x*(3*exp(2*exp(2)) - 3*exp(3*exp(2)) + 3*exp(exp(2)) -
3) - x^3*(9*exp(2*exp(2)) + exp(3*exp(2)) + 3*exp(exp(2)) - 5) - x^5*(3*exp(exp(2)) + 3) + x^2*(6*exp(2*exp(2)
) + 3*exp(3*exp(2)) - 9*exp(exp(2))) + x^6 - 1) + 24*x^2 + (4*x^4 + (8*x^4*log(-(5*exp(x))/(3*x - 3*x*exp(exp(
2)) + 3*x^2))*(x - exp(exp(2)) + 1))/(x - exp(exp(2)) + x*exp(exp(2)) - x^2 + 1))/log(-(5*exp(x))/(3*x - 3*x*e
xp(exp(2)) + 3*x^2))^2

________________________________________________________________________________________

sympy [A]  time = 0.29, size = 29, normalized size = 0.88 \begin {gather*} \frac {4 x^{4}}{\log {\left (\frac {5 e^{x}}{- 3 x^{2} - 3 x + 3 x e^{e^{2}}} \right )}^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((16*x**3*exp(exp(2))-16*x**4-16*x**3)*ln(5*exp(x)/(3*x*exp(exp(2))-3*x**2-3*x))+(-8*x**4+8*x**3)*ex
p(exp(2))+8*x**5-8*x**4-8*x**3)/(exp(exp(2))-x-1)/ln(5*exp(x)/(3*x*exp(exp(2))-3*x**2-3*x))**3,x)

[Out]

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

________________________________________________________________________________________