Optimal. Leaf size=9 \[ -\log (1-\log (x)) \]
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Rubi [A] time = 0.0202668, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {2302, 29} \[ -\log (1-\log (x)) \]
Antiderivative was successfully verified.
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Rule 2302
Rule 29
Rubi steps
\begin{align*} \int \frac{1}{x (1-\log (x))} \, dx &=-\operatorname{Subst}\left (\int \frac{1}{x} \, dx,x,1-\log (x)\right )\\ &=-\log (1-\log (x))\\ \end{align*}
Mathematica [A] time = 0.008645, size = 7, normalized size = 0.78 \[ -\log (\log (x)-1) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 10, normalized size = 1.1 \begin{align*} -\ln \left ( 1-\ln \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.926967, size = 9, normalized size = 1. \begin{align*} -\log \left (\log \left (x\right ) - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.29388, size = 24, normalized size = 2.67 \begin{align*} -\log \left (\log \left (x\right ) - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.0888, size = 7, normalized size = 0.78 \begin{align*} - \log{\left (\log{\left (x \right )} - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.06416, size = 30, normalized size = 3.33 \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 ) - 1\right )}^{2}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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