Optimal. Leaf size=30 \[ (-2+x)^2 \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right ) \]
________________________________________________________________________________________
Rubi [F] time = 8.08, 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 {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{\left (x^2+x \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (16-12 x^2+4 x^3+e^3 \left (-16 x^2-16 x^3+28 x^4-8 x^5\right )+e^3 \left (-16 x-16 x^2+28 x^3-8 x^4\right ) \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+\left (-4 x^2+2 x^3+\left (-4 x+2 x^2\right ) \log (x)\right ) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right ) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{x (x+\log (x)) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx\\ &=\int \frac {2 (2-x) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right ) \left (\frac {2 (-2+x) \left (-1-x+e^3 x^2+2 e^3 x^3+e^3 x (1+2 x) \log (x)\right )}{\log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )}-x (x+\log (x)) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )\right )}{x (x+\log (x))} \, dx\\ &=2 \int \frac {(2-x) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right ) \left (\frac {2 (-2+x) \left (-1-x+e^3 x^2+2 e^3 x^3+e^3 x (1+2 x) \log (x)\right )}{\log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )}-x (x+\log (x)) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )\right )}{x (x+\log (x))} \, dx\\ &=2 \int \left (-\frac {2 (-2+x)^2 \left (-1-x+e^3 x^2+2 e^3 x^3+e^3 x \log (x)+2 e^3 x^2 \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{x (x+\log (x)) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )}+(-2+x) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )\right ) \, dx\\ &=2 \int (-2+x) \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right ) \, dx-4 \int \frac {(-2+x)^2 \left (-1-x+e^3 x^2+2 e^3 x^3+e^3 x \log (x)+2 e^3 x^2 \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{x (x+\log (x)) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx\\ &=2 \int \left (-2 \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )+x \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )\right ) \, dx-4 \int \left (-\frac {4 \left (-1-x+e^3 x^2+2 e^3 x^3+e^3 x \log (x)+2 e^3 x^2 \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )}+\frac {4 \left (-1-x+e^3 x^2+2 e^3 x^3+e^3 x \log (x)+2 e^3 x^2 \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{x (x+\log (x)) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )}+\frac {x \left (-1-x+e^3 x^2+2 e^3 x^3+e^3 x \log (x)+2 e^3 x^2 \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )}\right ) \, dx\\ &=2 \int x \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right ) \, dx-4 \int \frac {x \left (-1-x+e^3 x^2+2 e^3 x^3+e^3 x \log (x)+2 e^3 x^2 \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx-4 \int \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right ) \, dx+16 \int \frac {\left (-1-x+e^3 x^2+2 e^3 x^3+e^3 x \log (x)+2 e^3 x^2 \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{(x+\log (x)) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx-16 \int \frac {\left (-1-x+e^3 x^2+2 e^3 x^3+e^3 x \log (x)+2 e^3 x^2 \log (x)\right ) \log \left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right )}{x (x+\log (x)) \log \left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.18, size = 30, normalized size = 1.00 \begin {gather*} (-2+x)^2 \log ^2\left (\log ^2\left (e^{-e^3 \left (2+x+x^2\right )} (x+\log (x))\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.62, size = 43, normalized size = 1.43 \begin {gather*} {\left (x^{2} - 4 \, x + 4\right )} \log \left (\log \left (x e^{\left (-{\left (x^{2} + x + 2\right )} e^{3}\right )} + e^{\left (-{\left (x^{2} + x + 2\right )} e^{3}\right )} \log \relax (x)\right )^{2}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [F] time = 0.14, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (2 x^{2}-4 x \right ) \ln \relax (x )+2 x^{3}-4 x^{2}\right ) \ln \left (\left (x +\ln \relax (x )\right ) {\mathrm e}^{-\left (x^{2}+x +2\right ) {\mathrm e}^{3}}\right ) \ln \left (\ln \left (\left (x +\ln \relax (x )\right ) {\mathrm e}^{-\left (x^{2}+x +2\right ) {\mathrm e}^{3}}\right )^{2}\right )^{2}+\left (\left (-8 x^{4}+28 x^{3}-16 x^{2}-16 x \right ) {\mathrm e}^{3} \ln \relax (x )+\left (-8 x^{5}+28 x^{4}-16 x^{3}-16 x^{2}\right ) {\mathrm e}^{3}+4 x^{3}-12 x^{2}+16\right ) \ln \left (\ln \left (\left (x +\ln \relax (x )\right ) {\mathrm e}^{-\left (x^{2}+x +2\right ) {\mathrm e}^{3}}\right )^{2}\right )}{\left (x \ln \relax (x )+x^{2}\right ) \ln \left (\left (x +\ln \relax (x )\right ) {\mathrm e}^{-\left (x^{2}+x +2\right ) {\mathrm e}^{3}}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.69, size = 35, normalized size = 1.17 \begin {gather*} 4 \, {\left (x^{2} - 4 \, x + 4\right )} \log \left (x^{2} e^{3} + x e^{3} + 2 \, e^{3} - \log \left (x + \log \relax (x)\right )\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 3.26, size = 36, normalized size = 1.20 \begin {gather*} {\ln \left ({\ln \left ({\mathrm {e}}^{-x^2\,{\mathrm {e}}^3}\,{\mathrm {e}}^{-2\,{\mathrm {e}}^3}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^3}\,\left (x+\ln \relax (x)\right )\right )}^2\right )}^2\,{\left (x-2\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 19.14, size = 31, normalized size = 1.03 \begin {gather*} \left (x^{2} - 4 x + 4\right ) \log {\left (\log {\left (\left (x + \log {\relax (x )}\right ) e^{- \left (x^{2} + x + 2\right ) e^{3}} \right )}^{2} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________