Optimal. Leaf size=18 \[ \frac{3 \left (a+b x^2\right )^{5/3}}{10 b} \]
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Rubi [A] time = 0.0036006, 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} \[ \frac{3 \left (a+b x^2\right )^{5/3}}{10 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x \left (a+b x^2\right )^{2/3} \, dx &=\frac{3 \left (a+b x^2\right )^{5/3}}{10 b}\\ \end{align*}
Mathematica [A] time = 0.0033351, size = 18, normalized size = 1. \[ \frac{3 \left (a+b x^2\right )^{5/3}}{10 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 15, normalized size = 0.8 \begin{align*}{\frac{3}{10\,b} \left ( b{x}^{2}+a \right ) ^{{\frac{5}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.06763, size = 19, normalized size = 1.06 \begin{align*} \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{5}{3}}}{10 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.73614, size = 35, normalized size = 1.94 \begin{align*} \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{5}{3}}}{10 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.358824, size = 42, normalized size = 2.33 \begin{align*} \begin{cases} \frac{3 a \left (a + b x^{2}\right )^{\frac{2}{3}}}{10 b} + \frac{3 x^{2} \left (a + b x^{2}\right )^{\frac{2}{3}}}{10} & \text{for}\: b \neq 0 \\\frac{a^{\frac{2}{3}} x^{2}}{2} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.45134, size = 19, normalized size = 1.06 \begin{align*} \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{5}{3}}}{10 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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