Optimal. Leaf size=11 \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 \log (x)}{2}\right ) \]
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Rubi [A] time = 0.0350316, antiderivative size = 11, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0188951, size = 11, normalized size = 1. \[ \frac{1}{3} \sin ^{-1}\left (\frac{3 \log (x)}{2}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.012, size = 8, normalized size = 0.7 \begin{align*}{\frac{1}{3}\arcsin \left ({\frac{3\,\ln \left ( x \right ) }{2}} \right ) } \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.64437, size = 9, normalized size = 0.82 \begin{align*} \frac{1}{3} \, \arcsin \left (\frac{3}{2} \, \log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 2.03161, size = 72, normalized size = 6.55 \begin{align*} -\frac{2}{3} \, \arctan \left (\frac{\sqrt{-9 \, \log \left (x\right )^{2} + 4} - 2}{3 \, \log \left (x\right )}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x \sqrt{- \left (3 \log{\left (x \right )} - 2\right ) \left (3 \log{\left (x \right )} + 2\right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19744, size = 9, normalized size = 0.82 \begin{align*} \frac{1}{3} \, \arcsin \left (\frac{3}{2} \, \log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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