Optimal. Leaf size=26 \[ \frac {x^{p+1} \log (x)}{p+1}-\frac {x^{p+1}}{(p+1)^2} \]
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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} \[ \frac {x^{p+1} \log (x)}{p+1}-\frac {x^{p+1}}{(p+1)^2} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin {align*} \int x^p \log (x) \, dx &=-\frac {x^{1+p}}{(1+p)^2}+\frac {x^{1+p} \log (x)}{1+p}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 19, normalized size = 0.73 \[ \frac {x^{p+1} ((p+1) \log (x)-1)}{(p+1)^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 25, normalized size = 0.96 \[ \frac {{\left ({\left (p + 1\right )} x \log \relax (x) - x\right )} x^{p}}{p^{2} + 2 \, p + 1} \]
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 \[ \int x^{p} \log \relax (x)\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 34, normalized size = 1.31 \[ \frac {x \,{\mathrm e}^{p \ln \relax (x )} \ln \relax (x )}{p +1}-\frac {x \,{\mathrm e}^{p \ln \relax (x )}}{p^{2}+2 p +1} \]
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 \[ \frac {x^{p + 1} \log \relax (x)}{p + 1} - \frac {x^{p + 1}}{{\left (p + 1\right )}^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.24, size = 32, normalized size = 1.23 \[ \left \{\begin {array}{cl} \frac {{\ln \relax (x)}^2}{2} & \text {\ if\ \ }p=-1\\ \frac {x^{p+1}\,\left (\ln \relax (x)\,\left (p+1\right )-1\right )}{{\left (p+1\right )}^2} & \text {\ if\ \ }p\neq -1 \end {array}\right . \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.74, size = 56, normalized size = 2.15 \[ \begin {cases} \frac {p x x^{p} \log {\relax (x )}}{p^{2} + 2 p + 1} + \frac {x x^{p} \log {\relax (x )}}{p^{2} + 2 p + 1} - \frac {x x^{p}}{p^{2} + 2 p + 1} & \text {for}\: p \neq -1 \\\frac {\log {\relax (x )}^{2}}{2} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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