Optimal. Leaf size=12 \[ \frac {\log ^{p+1}(x)}{p+1} \]
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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} \[ \frac {\log ^{p+1}(x)}{p+1} \]
Antiderivative was successfully verified.
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Rule 30
Rule 2302
Rubi steps
\begin {align*} \int \frac {\log ^p(x)}{x} \, dx &=\operatorname {Subst}\left (\int x^p \, dx,x,\log (x)\right )\\ &=\frac {\log ^{1+p}(x)}{1+p}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ \frac {\log ^{p+1}(x)}{p+1} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 12, normalized size = 1.00 \[ \frac {\log \relax (x)^{p} \log \relax (x)}{p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.23, size = 12, normalized size = 1.00 \[ \frac {\log \relax (x)^{p + 1}}{p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 13, normalized size = 1.08 \[ \frac {\ln \relax (x )^{p +1}}{p +1} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 12, normalized size = 1.00 \[ \frac {\log \relax (x)^{p + 1}}{p + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 22, normalized size = 1.83 \[ \left \{\begin {array}{cl} \ln \left (\ln \relax (x)\right ) & \text {\ if\ \ }p=-1\\ \frac {{\ln \relax (x)}^{p+1}}{p+1} & \text {\ if\ \ }p\neq -1 \end {array}\right . \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.88, size = 15, normalized size = 1.25 \[ \begin {cases} \frac {\log {\relax (x )}^{p + 1}}{p + 1} & \text {for}\: p \neq -1 \\\log {\left (\log {\relax (x )} \right )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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