Optimal. Leaf size=9 \[ \frac{x^{a x}}{a} \]
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Rubi [A] time = 0.021677, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {2553} \[ \frac{x^{a x}}{a} \]
Antiderivative was successfully verified.
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Rule 2553
Rubi steps
\begin{align*} \int \left (x^{a x}+x^{a x} \log (x)\right ) \, dx &=\int x^{a x} \, dx+\int x^{a x} \log (x) \, dx\\ &=\frac{x^{a x}}{a}\\ \end{align*}
Mathematica [A] time = 0.0133085, size = 9, normalized size = 1. \[ \frac{x^{a x}}{a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.013, size = 11, normalized size = 1.2 \begin{align*}{\frac{{{\rm e}^{ax\ln \left ( x \right ) }}}{a}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.23197, size = 12, normalized size = 1.33 \begin{align*} \frac{x^{a x}}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.14332, size = 15, normalized size = 1.67 \begin{align*} \frac{x^{a x}}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.298313, size = 10, normalized size = 1.11 \begin{align*} \begin{cases} \frac{x^{a x}}{a} & \text{for}\: a \neq 0 \\x \log{\left (x \right )} & \text{otherwise} \end{cases} \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^{a x} \log \left (x\right ) + x^{a x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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