Optimal. Leaf size=9 \[ \frac {x^{a x}}{a} \]
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Rubi [A] time = 0.02, antiderivative size = 9, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.01, size = 9, normalized size = 1.00 \[ \frac {x^{a x}}{a} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 9, normalized size = 1.00 \[ \frac {x^{a x}}{a} \]
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 \[ \int x^{a x} \log \relax (x) + x^{a x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 11, normalized size = 1.22 \[ \frac {{\mathrm e}^{a x \ln \relax (x )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.82, size = 9, normalized size = 1.00 \[ \frac {x^{a x}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.37, size = 9, normalized size = 1.00 \[ \frac {x^{a\,x}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.26, size = 10, normalized size = 1.11 \[ \begin {cases} \frac {x^{a x}}{a} & \text {for}\: a \neq 0 \\x \log {\relax (x )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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