Optimal. Leaf size=18 \[ \frac {10 \log (2 \log (4))}{3 x (x+\log (x))} \]
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Rubi [A]
time = 0.11, antiderivative size = 16, normalized size of antiderivative = 0.89, number of steps
used = 4, number of rules used = 3, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 6820, 6819}
\begin {gather*} \frac {10 \log (\log (16))}{3 x (x+\log (x))} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6819
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (\log (16)) \int \frac {-10-20 x-10 \log (x)}{3 x^4+6 x^3 \log (x)+3 x^2 \log ^2(x)} \, dx\\ &=\log (\log (16)) \int \frac {10 (-1-2 x-\log (x))}{3 x^2 (x+\log (x))^2} \, dx\\ &=\frac {1}{3} (10 \log (\log (16))) \int \frac {-1-2 x-\log (x)}{x^2 (x+\log (x))^2} \, dx\\ &=\frac {10 \log (\log (16))}{3 x (x+\log (x))}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 16, normalized size = 0.89 \begin {gather*} \frac {10 \log (\log (16))}{3 x (x+\log (x))} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 17, normalized size = 0.94
method | result | size |
default | \(\frac {10 \ln \left (4 \ln \left (2\right )\right )}{3 \left (x +\ln \left (x \right )\right ) x}\) | \(17\) |
risch | \(\frac {\frac {20 \ln \left (2\right )}{3}+\frac {10 \ln \left (\ln \left (2\right )\right )}{3}}{\left (x +\ln \left (x \right )\right ) x}\) | \(20\) |
norman | \(\frac {\frac {20 \ln \left (2\right )}{3}+\frac {10 \ln \left (\ln \left (2\right )\right )}{3}}{\left (x +\ln \left (x \right )\right ) x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 17, normalized size = 0.94 \begin {gather*} \frac {10 \, \log \left (4 \, \log \left (2\right )\right )}{3 \, {\left (x^{2} + x \log \left (x\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 17, normalized size = 0.94 \begin {gather*} \frac {10 \, \log \left (4 \, \log \left (2\right )\right )}{3 \, {\left (x^{2} + x \log \left (x\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 22, normalized size = 1.22 \begin {gather*} \frac {10 \log {\left (\log {\left (2 \right )} \right )} + 20 \log {\left (2 \right )}}{3 x^{2} + 3 x \log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 17, normalized size = 0.94 \begin {gather*} \frac {10 \, \log \left (4 \, \log \left (2\right )\right )}{3 \, {\left (x^{2} + x \log \left (x\right )\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.66, size = 18, normalized size = 1.00 \begin {gather*} \frac {10\,\ln \left (\ln \left (16\right )\right )}{3\,x\,\ln \left (x\right )+3\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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