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} \[ x^2 \left (a x^n\right )^{-1/n} \]
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 \[ x^2 \left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 9, normalized size = 0.60 \[ \frac {x}{a^{\left (\frac {1}{n}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 9, normalized size = 0.60 \[ \frac {x}{a^{\left (\frac {1}{n}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.02, 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 = 1.46, size = 20, normalized size = 1.33 \[ \frac {x^{2}}{a^{\left (\frac {1}{n}\right )} {\left (x^{n}\right )}^{\left (\frac {1}{n}\right )}} \]
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 \[ \frac {x^2}{{\left (a\,x^n\right )}^{1/n}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.01, size = 56, normalized size = 3.73 \[ \begin {cases} a^{- \frac {1}{n}} x^{2} \left (x^{n}\right )^{- \frac {1}{n}} & \text {for}\: a \neq 0^{n} \\- \frac {x^{2}}{0^{n} \tilde {\infty }^{n} \left (0^{n}\right )^{\frac {1}{n}} \left (x^{n}\right )^{\frac {1}{n}} - 2 \left (0^{n}\right )^{\frac {1}{n}} \left (x^{n}\right )^{\frac {1}{n}}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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