Optimal. Leaf size=27 \[ x+\log ^2\left (20 \left (4 e^{-e^{4-\frac {7 x}{3}}}+\log (x)\right )^2\right ) \]
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Rubi [F] time = 3.29, 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 {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{3 x \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx\\ &=\frac {1}{3} \int \frac {12 x+3 e^{e^{\frac {1}{3} (12-7 x)}} x \log (x)+\left (12 e^{e^{\frac {1}{3} (12-7 x)}}+112 e^{\frac {1}{3} (12-7 x)} x\right ) \log \left (e^{-2 e^{\frac {1}{3} (12-7 x)}} \left (320+160 e^{e^{\frac {1}{3} (12-7 x)}} \log (x)+20 e^{2 e^{\frac {1}{3} (12-7 x)}} \log ^2(x)\right )\right )}{x \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx\\ &=\frac {1}{3} \int \left (\frac {112 e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)}+\frac {3 \left (4 x+e^{e^{4-\frac {7 x}{3}}} x \log (x)+4 e^{e^{4-\frac {7 x}{3}}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )\right )}{x \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )}\right ) \, dx\\ &=\frac {112}{3} \int \frac {e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)} \, dx+\int \frac {4 x+e^{e^{4-\frac {7 x}{3}}} x \log (x)+4 e^{e^{4-\frac {7 x}{3}}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx\\ &=\frac {112}{3} \int \frac {e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)} \, dx+\int \left (-\frac {16 \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x) \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )}+\frac {x \log (x)+4 \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x)}\right ) \, dx\\ &=-\left (16 \int \frac {\log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x) \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx\right )+\frac {112}{3} \int \frac {e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)} \, dx+\int \frac {x \log (x)+4 \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x)} \, dx\\ &=-\left (16 \int \frac {\log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x) \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx\right )+\frac {112}{3} \int \frac {e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)} \, dx+\int \left (1+\frac {4 \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x)}\right ) \, dx\\ &=x+4 \int \frac {\log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x)} \, dx-16 \int \frac {\log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{x \log (x) \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )} \, dx+\frac {112}{3} \int \frac {e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )}{4+e^{e^{4-\frac {7 x}{3}}} \log (x)} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [B] time = 0.32, size = 166, normalized size = 6.15 \begin {gather*} -4 e^{8-\frac {14 x}{3}}+x+\log ^2\left (\left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )-4 e^{4-\frac {7 x}{3}} \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )+\log \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right ) \left (8 e^{4-\frac {7 x}{3}}-4 \log \left (\left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )+4 \log \left (20 e^{-2 e^{4-\frac {7 x}{3}}} \left (4+e^{e^{4-\frac {7 x}{3}}} \log (x)\right )^2\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.98, size = 43, normalized size = 1.59 \begin {gather*} \log \left (20 \, {\left (e^{\left (2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \relax (x)^{2} + 8 \, e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \relax (x) + 16\right )} e^{\left (-2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )}\right )^{2} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {3 \, x e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \relax (x) + 4 \, {\left (28 \, x e^{\left (-\frac {7}{3} \, x + 4\right )} + 3 \, e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )}\right )} \log \left (20 \, {\left (e^{\left (2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \relax (x)^{2} + 8 \, e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \relax (x) + 16\right )} e^{\left (-2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )}\right ) + 12 \, x}{3 \, {\left (x e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \relax (x) + 4 \, x\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.13, size = 0, normalized size = 0.00 \[\int \frac {\left (12 \,{\mathrm e}^{{\mathrm e}^{-\frac {7 x}{3}+4}}+112 x \,{\mathrm e}^{-\frac {7 x}{3}+4}\right ) \ln \left (\left (20 \ln \relax (x )^{2} {\mathrm e}^{2 \,{\mathrm e}^{-\frac {7 x}{3}+4}}+160 \ln \relax (x ) {\mathrm e}^{{\mathrm e}^{-\frac {7 x}{3}+4}}+320\right ) {\mathrm e}^{-2 \,{\mathrm e}^{-\frac {7 x}{3}+4}}\right )+3 x \ln \relax (x ) {\mathrm e}^{{\mathrm e}^{-\frac {7 x}{3}+4}}+12 x}{3 x \ln \relax (x ) {\mathrm e}^{{\mathrm e}^{-\frac {7 x}{3}+4}}+12 x}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{3} \, \int \frac {3 \, x e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \relax (x) + 4 \, {\left (28 \, x e^{\left (-\frac {7}{3} \, x + 4\right )} + 3 \, e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )}\right )} \log \left (20 \, {\left (e^{\left (2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \relax (x)^{2} + 8 \, e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \relax (x) + 16\right )} e^{\left (-2 \, e^{\left (-\frac {7}{3} \, x + 4\right )}\right )}\right ) + 12 \, x}{x e^{\left (e^{\left (-\frac {7}{3} \, x + 4\right )}\right )} \log \relax (x) + 4 \, x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.88, size = 36, normalized size = 1.33 \begin {gather*} {\ln \left (20\,{\ln \relax (x)}^2+160\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^4}{{\left ({\mathrm {e}}^x\right )}^{7/3}}}\,\ln \relax (x)+320\,{\mathrm {e}}^{-\frac {2\,{\mathrm {e}}^4}{{\left ({\mathrm {e}}^x\right )}^{7/3}}}\right )}^2+x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 2.62, size = 51, normalized size = 1.89 \begin {gather*} x + \log {\left (\left (20 e^{2 e^{4 - \frac {7 x}{3}}} \log {\relax (x )}^{2} + 160 e^{e^{4 - \frac {7 x}{3}}} \log {\relax (x )} + 320\right ) e^{- 2 e^{4 - \frac {7 x}{3}}} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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