Optimal. Leaf size=9 \[ -\log (1-\log (x)) \]
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Rubi [A] time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, 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 29
Rule 2302
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*}
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Mathematica [A] time = 0.01, size = 7, normalized size = 0.78 \[ -\log (\log (x)-1) \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x (1-\log (x))} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.03, size = 7, normalized size = 0.78 \[ -\log \left (\log \relax (x) - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 1.00, size = 22, normalized size = 2.44 \[ -\frac {1}{2} \, \log \left (\frac {1}{4} \, \pi ^{2} {\left (\mathrm {sgn}\relax (x) - 1\right )}^{2} + {\left (\log \left ({\left | x \right |}\right ) - 1\right )}^{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 8, normalized size = 0.89
method | result | size |
norman | \(-\ln \left (-1+\ln \relax (x )\right )\) | \(8\) |
risch | \(-\ln \left (-1+\ln \relax (x )\right )\) | \(8\) |
derivativedivides | \(-\ln \left (1-\ln \relax (x )\right )\) | \(10\) |
default | \(-\ln \left (1-\ln \relax (x )\right )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 7, normalized size = 0.78 \[ -\log \left (\log \relax (x) - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 7, normalized size = 0.78 \[ -\ln \left (\ln \relax (x)-1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 7, normalized size = 0.78 \[ - \log {\left (\log {\relax (x )} - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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