Optimal. Leaf size=15 \[ -\frac{1}{12} \left (9-4 x^2\right )^{3/2} \]
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Rubi [A] time = 0.0023749, antiderivative size = 15, 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} \[ -\frac{1}{12} \left (9-4 x^2\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int x \sqrt{9-4 x^2} \, dx &=-\frac{1}{12} \left (9-4 x^2\right )^{3/2}\\ \end{align*}
Mathematica [A] time = 0.0017305, size = 15, normalized size = 1. \[ -\frac{1}{12} \left (9-4 x^2\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 22, normalized size = 1.5 \begin{align*}{\frac{ \left ( -3+2\,x \right ) \left ( 3+2\,x \right ) }{12}\sqrt{-4\,{x}^{2}+9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 2.80043, size = 15, normalized size = 1. \begin{align*} -\frac{1}{12} \,{\left (-4 \, x^{2} + 9\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.49731, size = 47, normalized size = 3.13 \begin{align*} \frac{1}{12} \,{\left (4 \, x^{2} - 9\right )} \sqrt{-4 \, x^{2} + 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.187359, size = 27, normalized size = 1.8 \begin{align*} \frac{x^{2} \sqrt{9 - 4 x^{2}}}{3} - \frac{3 \sqrt{9 - 4 x^{2}}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 2.69025, size = 15, normalized size = 1. \begin{align*} -\frac{1}{12} \,{\left (-4 \, x^{2} + 9\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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