Optimal. Leaf size=18 \[ \frac {3 \left (a+b x^2\right )^{7/3}}{14 b} \]
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Rubi [A] time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {3 \left (a+b x^2\right )^{7/3}}{14 b} \]
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 32, normalized size = 1.78 \[ \frac {3 \, {\left (b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right )} {\left (b x^{2} + a\right )}^{\frac {1}{3}}}{14 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.63, size = 14, normalized size = 0.78 \[ \frac {3 \, {\left (b x^{2} + a\right )}^{\frac {7}{3}}}{14 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.83 \[ \frac {3 \left (b \,x^{2}+a \right )^{\frac {7}{3}}}{14 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 14, normalized size = 0.78 \[ \frac {3 \, {\left (b x^{2} + a\right )}^{\frac {7}{3}}}{14 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.99, size = 14, normalized size = 0.78 \[ \frac {3\,{\left (b\,x^2+a\right )}^{7/3}}{14\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.37, size = 65, normalized size = 3.61 \[ \begin {cases} \frac {3 a^{2} \sqrt [3]{a + b x^{2}}}{14 b} + \frac {3 a x^{2} \sqrt [3]{a + b x^{2}}}{7} + \frac {3 b x^{4} \sqrt [3]{a + b x^{2}}}{14} & \text {for}\: b \neq 0 \\\frac {a^{\frac {4}{3}} x^{2}}{2} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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