Optimal. Leaf size=18 \[ \frac {3 \sqrt [3]{a+b x^2}}{2 b} \]
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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} \[ \frac {3 \sqrt [3]{a+b x^2}}{2 b} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int \frac {x}{\left (a+b x^2\right )^{2/3}} \, dx &=\frac {3 \sqrt [3]{a+b x^2}}{2 b}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {3 \sqrt [3]{a+b x^2}}{2 b} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 14, normalized size = 0.78 \[ \frac {3 \, {\left (b x^{2} + a\right )}^{\frac {1}{3}}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.57, size = 14, normalized size = 0.78 \[ \frac {3 \, {\left (b x^{2} + a\right )}^{\frac {1}{3}}}{2 \, b} \]
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 \[ \frac {3 \left (b \,x^{2}+a \right )^{\frac {1}{3}}}{2 b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.24, size = 14, normalized size = 0.78 \[ \frac {3 \, {\left (b x^{2} + a\right )}^{\frac {1}{3}}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.69, size = 14, normalized size = 0.78 \[ \frac {3\,{\left (b\,x^2+a\right )}^{1/3}}{2\,b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 24, normalized size = 1.33 \[ \begin {cases} \frac {3 \sqrt [3]{a + b x^{2}}}{2 b} & \text {for}\: b \neq 0 \\\frac {x^{2}}{2 a^{\frac {2}{3}}} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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