Optimal. Leaf size=3 \[ \tan ^{-1}(\log (x)) \]
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Rubi [A] time = 0.0200639, antiderivative size = 3, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.083, Rules used = {203} \[ \tan ^{-1}(\log (x)) \]
Antiderivative was successfully verified.
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Rule 203
Rubi steps
\begin{align*} \int \frac{1}{x \left (1+\log ^2(x)\right )} \, dx &=\operatorname{Subst}\left (\int \frac{1}{1+x^2} \, dx,x,\log (x)\right )\\ &=\tan ^{-1}(\log (x))\\ \end{align*}
Mathematica [A] time = 0.0116724, size = 3, normalized size = 1. \[ \tan ^{-1}(\log (x)) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.004, size = 4, normalized size = 1.3 \begin{align*} \arctan \left ( \ln \left ( x \right ) \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.605, size = 4, normalized size = 1.33 \begin{align*} \arctan \left (\log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.01827, size = 22, normalized size = 7.33 \begin{align*} \arctan \left (\log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.136765, size = 15, normalized size = 5. \begin{align*} \operatorname{RootSum}{\left (4 z^{2} + 1, \left ( i \mapsto i \log{\left (2 i + \log{\left (x \right )} \right )} \right )\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.27133, size = 4, normalized size = 1.33 \begin{align*} \arctan \left (\log \left (x\right )\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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