Optimal. Leaf size=3 \[ \sin ^{-1}(\log (x)) \]
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Rubi [A] time = 0.03, antiderivative size = 3, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {216} \[ \sin ^{-1}(\log (x)) \]
Antiderivative was successfully verified.
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Rule 216
Rubi steps
\begin {align*} \int \frac {1}{x \sqrt {1-\log ^2(x)}} \, dx &=\operatorname {Subst}\left (\int \frac {1}{\sqrt {1-x^2}} \, dx,x,\log (x)\right )\\ &=\sin ^{-1}(\log (x))\\ \end {align*}
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Mathematica [A] time = 0.02, size = 3, normalized size = 1.00 \[ \sin ^{-1}(\log (x)) \]
Antiderivative was successfully verified.
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fricas [B] time = 0.43, size = 20, normalized size = 6.67 \[ -2 \, \arctan \left (\frac {\sqrt {-\log \relax (x)^{2} + 1} - 1}{\log \relax (x)}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 3, normalized size = 1.00 \[ \arcsin \left (\log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 4, normalized size = 1.33 \[ \arcsin \left (\ln \relax (x )\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.98, size = 3, normalized size = 1.00 \[ \arcsin \left (\log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.39, size = 3, normalized size = 1.00 \[ \mathrm {asin}\left (\ln \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \sqrt {- \left (\log {\relax (x )} - 1\right ) \left (\log {\relax (x )} + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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