Optimal. Leaf size=8 \[ \frac{\log ^3(x)}{3} \]
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Rubi [A] time = 0.0116141, antiderivative size = 8, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {2302, 30} \[ \frac{\log ^3(x)}{3} \]
Antiderivative was successfully verified.
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Rule 2302
Rule 30
Rubi steps
\begin{align*} \int \frac{\log ^2(x)}{x} \, dx &=\operatorname{Subst}\left (\int x^2 \, dx,x,\log (x)\right )\\ &=\frac{\log ^3(x)}{3}\\ \end{align*}
Mathematica [A] time = 0.0009859, size = 8, normalized size = 1. \[ \frac{\log ^3(x)}{3} \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 7, normalized size = 0.9 \begin{align*}{\frac{ \left ( \ln \left ( x \right ) \right ) ^{3}}{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.940217, size = 8, normalized size = 1. \begin{align*} \frac{1}{3} \, \log \left (x\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.00398, size = 19, normalized size = 2.38 \begin{align*} \frac{1}{3} \, \log \left (x\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.08174, size = 5, normalized size = 0.62 \begin{align*} \frac{\log{\left (x \right )}^{3}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09391, size = 8, normalized size = 1. \begin{align*} \frac{1}{3} \, \log \left (x\right )^{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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