Optimal. Leaf size=15 \[ 64 \log ^2(1+e-\log (16)) \log (\log (x)) \]
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Rubi [A]
time = 0.01, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.158, Rules used = {12, 2339, 29}
\begin {gather*} 64 \log ^2(1+e-\log (16)) \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 29
Rule 2339
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (64 \log ^2(1+e-\log (16))\right ) \int \frac {1}{x \log (x)} \, dx\\ &=\left (64 \log ^2(1+e-\log (16))\right ) \text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=64 \log ^2(1+e-\log (16)) \log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 15, normalized size = 1.00 \begin {gather*} 64 \log ^2(1+e-\log (16)) \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 17, normalized size = 1.13
method | result | size |
derivativedivides | \(64 \ln \left (\ln \left (x \right )\right ) \ln \left (-4 \ln \left (2\right )+1+{\mathrm e}\right )^{2}\) | \(17\) |
default | \(64 \ln \left (\ln \left (x \right )\right ) \ln \left (-4 \ln \left (2\right )+1+{\mathrm e}\right )^{2}\) | \(17\) |
norman | \(64 \ln \left (\ln \left (x \right )\right ) \ln \left (-4 \ln \left (2\right )+1+{\mathrm e}\right )^{2}\) | \(17\) |
risch | \(64 \ln \left (\ln \left (x \right )\right ) \ln \left (-4 \ln \left (2\right )+1+{\mathrm e}\right )^{2}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 16, normalized size = 1.07 \begin {gather*} 64 \, \log \left (e - 4 \, \log \left (2\right ) + 1\right )^{2} \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 16, normalized size = 1.07 \begin {gather*} 64 \, \log \left (e - 4 \, \log \left (2\right ) + 1\right )^{2} \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 19, normalized size = 1.27 \begin {gather*} 64 \log {\left (- 4 \log {\left (2 \right )} + 1 + e \right )}^{2} \log {\left (\log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 17, normalized size = 1.13 \begin {gather*} 64 \, \log \left (e - 4 \, \log \left (2\right ) + 1\right )^{2} \log \left ({\left | \log \left (x\right ) \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.73, size = 16, normalized size = 1.07 \begin {gather*} 64\,\ln \left (\ln \left (x\right )\right )\,{\ln \left (\mathrm {e}-\ln \left (16\right )+1\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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