Optimal. Leaf size=18 \[ \frac{3 \left (a+b x^2\right )^{7/3}}{14 b} \]
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Rubi [A] time = 0.0038096, 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} \[ \frac{3 \left (a+b x^2\right )^{7/3}}{14 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x \left (a+b x^2\right )^{4/3} \, dx &=\frac{3 \left (a+b x^2\right )^{7/3}}{14 b}\\ \end{align*}
Mathematica [A] time = 0.0044949, size = 18, normalized size = 1. \[ \frac{3 \left (a+b x^2\right )^{7/3}}{14 b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 15, normalized size = 0.8 \begin{align*}{\frac{3}{14\,b} \left ( b{x}^{2}+a \right ) ^{{\frac{7}{3}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.85676, size = 19, normalized size = 1.06 \begin{align*} \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{7}{3}}}{14 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] time = 1.82185, size = 73, normalized size = 4.06 \begin{align*} \frac{3 \,{\left (b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right )}{\left (b x^{2} + a\right )}^{\frac{1}{3}}}{14 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.34041, size = 65, normalized size = 3.61 \begin{align*} \begin{cases} \frac{3 a^{2} \sqrt [3]{a + b x^{2}}}{14 b} + \frac{3 a x^{2} \sqrt [3]{a + b x^{2}}}{7} + \frac{3 b x^{4} \sqrt [3]{a + b x^{2}}}{14} & \text{for}\: b \neq 0 \\\frac{a^{\frac{4}{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 = 2.65785, size = 19, normalized size = 1.06 \begin{align*} \frac{3 \,{\left (b x^{2} + a\right )}^{\frac{7}{3}}}{14 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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