Optimal. Leaf size=15 \[ x^2 \left (a x^n\right )^{-1/n} \]
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Rubi [A]
time = 0.00, antiderivative size = 15, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 8}
\begin {gather*} x^2 \left (a x^n\right )^{-1/n} \end {gather*}
Antiderivative was successfully verified.
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Rule 8
Rule 15
Rubi steps
\begin {align*} \int x \left (a x^n\right )^{-1/n} \, dx &=\left (x \left (a x^n\right )^{-1/n}\right ) \int 1 \, dx\\ &=x^2 \left (a x^n\right )^{-1/n}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 15, normalized size = 1.00 \begin {gather*} x^2 \left (a x^n\right )^{-1/n} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.01, size = 0, normalized size = 0.00 \[\int x \left (a \,x^{n}\right )^{-\frac {1}{n}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 20, normalized size = 1.33 \begin {gather*} \frac {x^{2}}{a^{\left (\frac {1}{n}\right )} {\left (x^{n}\right )}^{\left (\frac {1}{n}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 9, normalized size = 0.60 \begin {gather*} \frac {x}{a^{\left (\frac {1}{n}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.33, size = 10, normalized size = 0.67 \begin {gather*} x^{2} \left (a x^{n}\right )^{- \frac {1}{n}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.88, size = 9, normalized size = 0.60 \begin {gather*} \frac {x}{a^{\left (\frac {1}{n}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.06, size = 15, normalized size = 1.00 \begin {gather*} \frac {x^2}{{\left (a\,x^n\right )}^{1/n}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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