Optimal. Leaf size=13 \[ \frac{1}{8} \log \left (4 \log ^2(x)+1\right ) \]
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Rubi [A] time = 0.0243466, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {203, 260} \[ \frac{1}{8} \log \left (4 \log ^2(x)+1\right ) \]
Antiderivative was successfully verified.
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Rule 203
Rule 260
Rubi steps
\begin{align*} \int \frac{\log (x)}{x+4 x \log ^2(x)} \, dx &=\operatorname{Subst}\left (\int \frac{x}{1+4 x^2} \, dx,x,\log (x)\right )\\ &=\frac{1}{8} \log \left (1+4 \log ^2(x)\right )\\ \end{align*}
Mathematica [A] time = 0.0082652, size = 13, normalized size = 1. \[ \frac{1}{8} \log \left (4 \log ^2(x)+1\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 12, normalized size = 0.9 \begin{align*}{\frac{\ln \left ( 1+4\, \left ( \ln \left ( x \right ) \right ) ^{2} \right ) }{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.19732, size = 12, normalized size = 0.92 \begin{align*} \frac{1}{8} \, \log \left (\log \left (x\right )^{2} + \frac{1}{4}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.12501, size = 34, normalized size = 2.62 \begin{align*} \frac{1}{8} \, \log \left (4 \, \log \left (x\right )^{2} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.115593, size = 10, normalized size = 0.77 \begin{align*} \frac{\log{\left (\log{\left (x \right )}^{2} + \frac{1}{4} \right )}}{8} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.33486, size = 15, normalized size = 1.15 \begin{align*} \frac{1}{8} \, \log \left (4 \, \log \left (x\right )^{2} + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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