Optimal. Leaf size=27 \[ 5+\log \left (-e^9 x+\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right ) \]
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Rubi [F]
time = 2.68, 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 {4+e^4+x+\left (1+e^9 \left (-4-e^4-x\right )\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )}{e^9 \left (-4 x-e^4 x-x^2\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )+\left (4+e^4+x\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right ) \log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-4 \left (1+\frac {e^4}{4}\right )-x-\left (1+e^9 \left (-4-e^4-x\right )\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )}{\left (4+e^4+x\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )} \, dx\\ &=\int \left (-\frac {1-e^9 \left (4+e^4\right )}{\left (4+e^4+x\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )}+\frac {e^9 x}{\left (4+e^4+x\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )}+\frac {-4-e^4}{\left (4+e^4+x\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )}-\frac {x}{\left (4+e^4+x\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )}\right ) \, dx\\ &=e^9 \int \frac {x}{\left (4+e^4+x\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )} \, dx+\left (-4-e^4\right ) \int \frac {1}{\left (4+e^4+x\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )} \, dx+\left (-1+4 e^9+e^{13}\right ) \int \frac {1}{\left (4+e^4+x\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )} \, dx-\int \frac {x}{\left (4+e^4+x\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )} \, dx\\ &=e^9 \int \left (\frac {1}{e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )}+\frac {-4-e^4}{\left (4+e^4+x\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )}\right ) \, dx+\left (-4-e^4\right ) \int \frac {1}{\left (4+e^4+x\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )} \, dx+\left (-1+4 e^9+e^{13}\right ) \int \frac {1}{\left (4+e^4+x\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )} \, dx-\int \left (\frac {1}{\log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )}+\frac {-4-e^4}{\left (4+e^4+x\right ) \log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )}\right ) \, dx\\ &=e^9 \int \frac {1}{e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )} \, dx-\left (e^9 \left (4+e^4\right )\right ) \int \frac {1}{\left (4+e^4+x\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )} \, dx+\left (-1+4 e^9+e^{13}\right ) \int \frac {1}{\left (4+e^4+x\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )} \, dx-\int \frac {1}{\log \left (\frac {e^x}{4}\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right ) \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 26, normalized size = 0.96 \begin {gather*} \log \left (e^9 x-\log \left (\left (4+e^4+x\right ) \log \left (\log \left (\frac {e^x}{4}\right )\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 27.83, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (-{\mathrm e}^{4}-x -4\right ) {\mathrm e}^{9}+1\right ) \ln \left (\frac {{\mathrm e}^{x}}{4}\right ) \ln \left (\ln \left (\frac {{\mathrm e}^{x}}{4}\right )\right )+x +4+{\mathrm e}^{4}}{\left (x +4+{\mathrm e}^{4}\right ) \ln \left (\frac {{\mathrm e}^{x}}{4}\right ) \ln \left (\ln \left (\frac {{\mathrm e}^{x}}{4}\right )\right ) \ln \left (\left (x +4+{\mathrm e}^{4}\right ) \ln \left (\ln \left (\frac {{\mathrm e}^{x}}{4}\right )\right )\right )+\left (-x \,{\mathrm e}^{4}-x^{2}-4 x \right ) {\mathrm e}^{9} \ln \left (\frac {{\mathrm e}^{x}}{4}\right ) \ln \left (\ln \left (\frac {{\mathrm e}^{x}}{4}\right )\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.60, size = 21, normalized size = 0.78 \begin {gather*} \log \left (-x e^{9} + \log \left (x + e^{4} + 4\right ) + \log \left (\log \left (x - 2 \, \log \left (2\right )\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 21, normalized size = 0.78 \begin {gather*} \log \left (-x e^{9} + \log \left ({\left (x + e^{4} + 4\right )} \log \left (x - 2 \, \log \left (2\right )\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.47, size = 21, normalized size = 0.78 \begin {gather*} \log \left (-x e^{9} + \log \left (x + e^{4} + 4\right ) + \log \left (\log \left (x - 2 \, \log \left (2\right )\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 8.10, size = 21, normalized size = 0.78 \begin {gather*} \ln \left (\ln \left (\ln \left (x-\ln \left (4\right )\right )\,\left (x+{\mathrm {e}}^4+4\right )\right )-x\,{\mathrm {e}}^9\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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