Optimal. Leaf size=22 \[ \log \left (\frac {1}{45} \left (\frac {16}{3}-e^x-\log (\log (x+\log (x)))\right )\right ) \]
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Rubi [A]
time = 0.61, antiderivative size = 16, normalized size of antiderivative = 0.73, number of steps
used = 3, number of rules used = 3, integrand size = 88, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6820, 12, 6816}
\begin {gather*} \log \left (-3 e^x-3 \log (\log (x+\log (x)))+16\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6816
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3 \left (-1-x-e^x x (x+\log (x)) \log (x+\log (x))\right )}{x (x+\log (x)) \log (x+\log (x)) \left (16-3 e^x-3 \log (\log (x+\log (x)))\right )} \, dx\\ &=3 \int \frac {-1-x-e^x x (x+\log (x)) \log (x+\log (x))}{x (x+\log (x)) \log (x+\log (x)) \left (16-3 e^x-3 \log (\log (x+\log (x)))\right )} \, dx\\ &=\log \left (16-3 e^x-3 \log (\log (x+\log (x)))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 16, normalized size = 0.73 \begin {gather*} \log \left (-16+3 e^x+3 \log (\log (x+\log (x)))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 12, normalized size = 0.55
method | result | size |
risch | \(\ln \left ({\mathrm e}^{x}+\ln \left (\ln \left (x +\ln \left (x \right )\right )\right )-\frac {16}{3}\right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 11, normalized size = 0.50 \begin {gather*} \log \left (e^{x} + \log \left (\log \left (x + \log \left (x\right )\right )\right ) - \frac {16}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 15, normalized size = 0.68 \begin {gather*} \log \left (3 \, e^{x} + 3 \, \log \left (\log \left (x + \log \left (x\right )\right )\right ) - 16\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.53, size = 15, normalized size = 0.68 \begin {gather*} \log {\left (e^{x} + \log {\left (\log {\left (x + \log {\left (x \right )} \right )} \right )} - \frac {16}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.46, size = 15, normalized size = 0.68 \begin {gather*} \log \left (-3 \, e^{x} - 3 \, \log \left (\log \left (x + \log \left (x\right )\right )\right ) + 16\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.01, size = 11, normalized size = 0.50 \begin {gather*} \ln \left (\ln \left (\ln \left (x+\ln \left (x\right )\right )\right )+{\mathrm {e}}^x-\frac {16}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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