Optimal. Leaf size=12 \[ -\frac{3 x}{\left (b x^2\right )^{2/3}} \]
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Rubi [A] time = 0.0013542, antiderivative size = 12, 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} \[ -\frac{3 x}{\left (b x^2\right )^{2/3}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\left (b x^2\right )^{2/3}} \, dx &=\frac{x^{4/3} \int \frac{1}{x^{4/3}} \, dx}{\left (b x^2\right )^{2/3}}\\ &=-\frac{3 x}{\left (b x^2\right )^{2/3}}\\ \end{align*}
Mathematica [A] time = 0.0012241, size = 12, normalized size = 1. \[ -\frac{3 x}{\left (b x^2\right )^{2/3}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.9 \begin{align*} -3\,{\frac{x}{ \left ( b{x}^{2} \right ) ^{2/3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.960016, size = 14, normalized size = 1.17 \begin{align*} -\frac{3 \, x}{\left (b x^{2}\right )^{\frac{2}{3}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.74738, size = 32, normalized size = 2.67 \begin{align*} -\frac{3 \, \left (b x^{2}\right )^{\frac{1}{3}}}{b x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.571284, size = 15, normalized size = 1.25 \begin{align*} - \frac{3 x}{b^{\frac{2}{3}} \left (x^{2}\right )^{\frac{2}{3}}} \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^{2}\right )^{\frac{2}{3}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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