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 = 0.0098902, antiderivative size = 26, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0074999, 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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Maple [A] time = 0.007, size = 34, normalized size = 1.3 \begin{align*}{\frac{x\ln \left ( x \right ){{\rm e}^{\ln \left ( x \right ) p}}}{1+p}}-{\frac{x{{\rm e}^{\ln \left ( x \right ) p}}}{{p}^{2}+2\,p+1}} \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 = 1.91599, size = 59, normalized size = 2.27 \begin{align*} \frac{{\left ({\left (p + 1\right )} x \log \left (x\right ) - x\right )} x^{p}}{p^{2} + 2 \, p + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: TypeError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int x^{p} \log \left (x\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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