Optimal. Leaf size=18 \[ -\frac{3}{2 b \sqrt [3]{a+b x^2}} \]
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Rubi [A] time = 0.0035819, antiderivative size = 18, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {261} \[ -\frac{3}{2 b \sqrt [3]{a+b x^2}} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\left (a+b x^2\right )^{4/3}} \, dx &=-\frac{3}{2 b \sqrt [3]{a+b x^2}}\\ \end{align*}
Mathematica [A] time = 0.0026457, size = 18, normalized size = 1. \[ -\frac{3}{2 b \sqrt [3]{a+b x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 15, normalized size = 0.8 \begin{align*} -{\frac{3}{2\,b}{\frac{1}{\sqrt [3]{b{x}^{2}+a}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.53318, size = 19, normalized size = 1.06 \begin{align*} -\frac{3}{2 \,{\left (b x^{2} + a\right )}^{\frac{1}{3}} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.72524, size = 54, normalized size = 3. \begin{align*} -\frac{3 \,{\left (b x^{2} + a\right )}^{\frac{2}{3}}}{2 \,{\left (b^{2} x^{2} + a b\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.603189, size = 26, normalized size = 1.44 \begin{align*} \begin{cases} - \frac{3}{2 b \sqrt [3]{a + b x^{2}}} & \text{for}\: b \neq 0 \\\frac{x^{2}}{2 a^{\frac{4}{3}}} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.32453, size = 19, normalized size = 1.06 \begin{align*} -\frac{3}{2 \,{\left (b x^{2} + a\right )}^{\frac{1}{3}} b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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