Optimal. Leaf size=19 \[ \frac{3 x}{(3-2 n) \left (b x^n\right )^{2/3}} \]
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Rubi [A] time = 0.0054536, antiderivative size = 19, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac{3 x}{(3-2 n) \left (b x^n\right )^{2/3}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\left (b x^n\right )^{2/3}} \, dx &=\frac{x^{2 n/3} \int x^{-2 n/3} \, dx}{\left (b x^n\right )^{2/3}}\\ &=\frac{3 x}{(3-2 n) \left (b x^n\right )^{2/3}}\\ \end{align*}
Mathematica [A] time = 0.0053653, size = 20, normalized size = 1.05 \[ \frac{x}{\left (1-\frac{2 n}{3}\right ) \left (b x^n\right )^{2/3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 18, normalized size = 1. \begin{align*} -3\,{\frac{x}{ \left ( 2\,n-3 \right ) \left ( b{x}^{n} \right ) ^{2/3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: ValueError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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 (b x^{n}\right )^{\frac{2}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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