Optimal. Leaf size=5 \[ \log (\log (x)+3) \]
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Rubi [A] time = 0.02, antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2302, 29} \[ \log (\log (x)+3) \]
Antiderivative was successfully verified.
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Rule 29
Rule 2302
Rubi steps
\begin {align*} \int \frac {1}{x (3+\log (x))} \, dx &=\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,3+\log (x)\right )\\ &=\log (3+\log (x))\\ \end {align*}
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Mathematica [A] time = 0.01, size = 5, normalized size = 1.00 \[ \log (\log (x)+3) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.86, size = 5, normalized size = 1.00 \[ \log \left (\log \relax (x) + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.16, size = 22, normalized size = 4.40 \[ \frac {1}{2} \, \log \left (\frac {1}{4} \, \pi ^{2} {\left (\mathrm {sgn}\relax (x) - 1\right )}^{2} + {\left (\log \left ({\left | x \right |}\right ) + 3\right )}^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 6, normalized size = 1.20 \[ \ln \left (\ln \relax (x )+3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.62, size = 5, normalized size = 1.00 \[ \log \left (\log \relax (x) + 3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.42, size = 5, normalized size = 1.00 \[ \ln \left (\ln \relax (x)+3\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 5, normalized size = 1.00 \[ \log {\left (\log {\relax (x )} + 3 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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