Optimal. Leaf size=13 \[ -\left (a x^n\right )^{-1/n} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.133, Rules used = {15, 30} \[ -\left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin {align*} \int \frac {\left (a x^n\right )^{-1/n}}{x} \, dx &=\left (x \left (a x^n\right )^{-1/n}\right ) \int \frac {1}{x^2} \, dx\\ &=-\left (a x^n\right )^{-1/n}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \[ -\left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 12, normalized size = 0.92 \[ -\frac {1}{a^{\left (\frac {1}{n}\right )} x} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 13, normalized size = 1.00 \[ -\frac {1}{\left (a x^{n}\right )^{\left (\frac {1}{n}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 1.08 \[ -\left (a \,x^{n}\right )^{-\frac {1}{n}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.50, size = 18, normalized size = 1.38 \[ -\frac {1}{a^{\left (\frac {1}{n}\right )} {\left (x^{n}\right )}^{\left (\frac {1}{n}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.02, size = 13, normalized size = 1.00 \[ -\frac {1}{{\left (a\,x^n\right )}^{1/n}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.31, size = 32, normalized size = 2.46 \[ \begin {cases} - a^{- \frac {1}{n}} \left (x^{n}\right )^{- \frac {1}{n}} & \text {for}\: a \neq 0^{n} \\- \left (0^{n}\right )^{- \frac {1}{n}} \left (x^{n}\right )^{- \frac {1}{n}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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