Optimal. Leaf size=12 \[ \frac{\log ^{n+1}(x)}{n+1} \]
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Rubi [A] time = 0.0174533, antiderivative size = 12, 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} \[ \frac{\log ^{n+1}(x)}{n+1} \]
Antiderivative was successfully verified.
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Rule 2302
Rule 30
Rubi steps
\begin{align*} \int \frac{\log ^n(x)}{x} \, dx &=\operatorname{Subst}\left (\int x^n \, dx,x,\log (x)\right )\\ &=\frac{\log ^{1+n}(x)}{1+n}\\ \end{align*}
Mathematica [A] time = 0.0033826, size = 12, normalized size = 1. \[ \frac{\log ^{n+1}(x)}{n+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 13, normalized size = 1.1 \begin{align*}{\frac{ \left ( \ln \left ( x \right ) \right ) ^{1+n}}{1+n}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.40761, size = 34, normalized size = 2.83 \begin{align*} \frac{\log \left (x\right )^{n} \log \left (x\right )}{n + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.865165, size = 15, normalized size = 1.25 \begin{align*} \begin{cases} \frac{\log{\left (x \right )}^{n + 1}}{n + 1} & \text{for}\: n \neq -1 \\\log{\left (\log{\left (x \right )} \right )} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13295, size = 16, normalized size = 1.33 \begin{align*} \frac{\log \left (x\right )^{n + 1}}{n + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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