Optimal. Leaf size=26 \[ \frac {x^{m+1} \log (x)}{m+1}-\frac {x^{m+1}}{(m+1)^2} \]
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Rubi [A] time = 0.01, antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2304} \[ \frac {x^{m+1} \log (x)}{m+1}-\frac {x^{m+1}}{(m+1)^2} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin {align*} \int x^m \log (x) \, dx &=-\frac {x^{1+m}}{(1+m)^2}+\frac {x^{1+m} \log (x)}{1+m}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 0.73 \[ \frac {x^{m+1} ((m+1) \log (x)-1)}{(m+1)^2} \]
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x^m \log (x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.15, size = 25, normalized size = 0.96 \[ \frac {{\left ({\left (m + 1\right )} x \log \relax (x) - x\right )} x^{m}}{m^{2} + 2 \, m + 1} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int x^{m} \log \relax (x)\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 19, normalized size = 0.73
method | result | size |
risch | \(\frac {x \left (m \ln \relax (x )+\ln \relax (x )-1\right ) x^{m}}{\left (1+m \right )^{2}}\) | \(19\) |
norman | \(\frac {x \ln \relax (x ) {\mathrm e}^{m \ln \relax (x )}}{1+m}-\frac {x \,{\mathrm e}^{m \ln \relax (x )}}{m^{2}+2 m +1}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 26, normalized size = 1.00 \[ \frac {x^{m + 1} \log \relax (x)}{m + 1} - \frac {x^{m + 1}}{{\left (m + 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.40, size = 32, normalized size = 1.23 \[ \left \{\begin {array}{cl} \frac {{\ln \relax (x)}^2}{2} & \text {\ if\ \ }m=-1\\ \frac {x^{m+1}\,\left (\ln \relax (x)\,\left (m+1\right )-1\right )}{{\left (m+1\right )}^2} & \text {\ if\ \ }m\neq -1 \end {array}\right . \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.76, size = 56, normalized size = 2.15 \[ \begin {cases} \frac {m x x^{m} \log {\relax (x )}}{m^{2} + 2 m + 1} + \frac {x x^{m} \log {\relax (x )}}{m^{2} + 2 m + 1} - \frac {x x^{m}}{m^{2} + 2 m + 1} & \text {for}\: m \neq -1 \\\frac {\log {\relax (x )}^{2}}{2} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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