Optimal. Leaf size=13 \[ -\left (a x^n\right )^{-1/n} \]
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Rubi [A] time = 0.0016147, antiderivative size = 13, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0010883, size = 13, normalized size = 1. \[ -\left (a x^n\right )^{-1/n} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 14, normalized size = 1.1 \begin{align*} - \left ( \sqrt [n]{a{x}^{n}} \right ) ^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02555, size = 24, normalized size = 1.85 \begin{align*} -\frac{1}{a^{\left (\frac{1}{n}\right )}{\left (x^{n}\right )}^{\left (\frac{1}{n}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.7453, size = 22, normalized size = 1.69 \begin{align*} -\frac{1}{a^{\left (\frac{1}{n}\right )} x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.36858, size = 32, normalized size = 2.46 \begin{align*} \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} \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 \frac{1}{\left (a x^{n}\right )^{\left (\frac{1}{n}\right )} x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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