Optimal. Leaf size=12 \[ \frac {\log ^{n+1}(x)}{n+1} \]
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Rubi [A] time = 0.02, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2302, 30} \[ \frac {\log ^{n+1}(x)}{n+1} \]
Antiderivative was successfully verified.
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Rule 30
Rule 2302
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*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ \frac {\log ^{n+1}(x)}{n+1} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\log ^n(x)}{x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.05, size = 12, normalized size = 1.00 \[ \frac {\log \relax (x)^{n} \log \relax (x)}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.61, size = 12, normalized size = 1.00 \[ \frac {\log \relax (x)^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 13, normalized size = 1.08
method | result | size |
derivativedivides | \(\frac {\ln \relax (x )^{1+n}}{1+n}\) | \(13\) |
default | \(\frac {\ln \relax (x )^{1+n}}{1+n}\) | \(13\) |
risch | \(\frac {\ln \relax (x ) \ln \relax (x )^{n}}{1+n}\) | \(13\) |
norman | \(\frac {\ln \relax (x ) {\mathrm e}^{n \ln \left (\ln \relax (x )\right )}}{1+n}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 12, normalized size = 1.00 \[ \frac {\log \relax (x)^{n + 1}}{n + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.33, size = 22, normalized size = 1.83 \[ \left \{\begin {array}{cl} \ln \left (\ln \relax (x)\right ) & \text {\ if\ \ }n=-1\\ \frac {{\ln \relax (x)}^{n+1}}{n+1} & \text {\ if\ \ }n\neq -1 \end {array}\right . \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.89, size = 15, normalized size = 1.25 \[ \begin {cases} \frac {\log {\relax (x )}^{n + 1}}{n + 1} & \text {for}\: n \neq -1 \\\log {\left (\log {\relax (x )} \right )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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