Optimal. Leaf size=11 \[ \frac {1}{3} \sin ^{-1}\left (\frac {3 \log (x)}{2}\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 11, 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} \[ \frac {1}{3} \sin ^{-1}\left (\frac {3 \log (x)}{2}\right ) \]
Antiderivative was successfully verified.
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Rule 216
Rubi steps
\begin {align*} \int \frac {1}{x \sqrt {4-9 \log ^2(x)}} \, dx &=\operatorname {Subst}\left (\int \frac {1}{\sqrt {4-9 x^2}} \, dx,x,\log (x)\right )\\ &=\frac {1}{3} \sin ^{-1}\left (\frac {3 \log (x)}{2}\right )\\ \end {align*}
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Mathematica [A] time = 0.02, size = 11, normalized size = 1.00 \[ \frac {1}{3} \sin ^{-1}\left (\frac {3 \log (x)}{2}\right ) \]
Antiderivative was successfully verified.
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fricas [B] time = 1.51, size = 21, normalized size = 1.91 \[ -\frac {2}{3} \, \arctan \left (\frac {\sqrt {-9 \, \log \relax (x)^{2} + 4} - 2}{3 \, \log \relax (x)}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.23, size = 7, normalized size = 0.64 \[ \frac {1}{3} \, \arcsin \left (\frac {3}{2} \, \log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 8, normalized size = 0.73 \[ \frac {\arcsin \left (\frac {3 \ln \relax (x )}{2}\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.22, size = 7, normalized size = 0.64 \[ \frac {1}{3} \, \arcsin \left (\frac {3}{2} \, \log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.40, size = 7, normalized size = 0.64 \[ \frac {\mathrm {asin}\left (\frac {3\,\ln \relax (x)}{2}\right )}{3} \]
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 \[ \int \frac {1}{x \sqrt {- \left (3 \log {\relax (x )} - 2\right ) \left (3 \log {\relax (x )} + 2\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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