Optimal. Leaf size=5 \[ \log (\log (x)+3) \]
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Rubi [A] time = 0.0178284, antiderivative size = 5, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2, Rules used = {2302, 29} \[ \log (\log (x)+3) \]
Antiderivative was successfully verified.
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Rule 2302
Rule 29
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*}
Mathematica [A] time = 0.0091176, size = 5, normalized size = 1. \[ \log (\log (x)+3) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 6, normalized size = 1.2 \begin{align*} \ln \left ( 3+\ln \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.08247, size = 7, normalized size = 1.4 \begin{align*} \log \left (\log \left (x\right ) + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.98059, size = 23, normalized size = 4.6 \begin{align*} \log \left (\log \left (x\right ) + 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.095218, size = 5, normalized size = 1. \begin{align*} \log{\left (\log{\left (x \right )} + 3 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.27814, size = 30, normalized size = 6. \begin{align*} \frac{1}{2} \, \log \left (\frac{1}{4} \, \pi ^{2}{\left (\mathrm{sgn}\left (x\right ) - 1\right )}^{2} +{\left (\log \left ({\left | x \right |}\right ) + 3\right )}^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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