Optimal. Leaf size=15 \[ -\frac{1}{12} \left (-4 x^2-9\right )^{3/2} \]
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Rubi [A] time = 0.0024286, 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} \[ -\frac{1}{12} \left (-4 x^2-9\right )^{3/2} \]
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 = 0.0016278, size = 15, normalized size = 1. \[ -\frac{1}{12} \left (-4 x^2-9\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 12, normalized size = 0.8 \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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Maxima [A] time = 2.09672, 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 = 1.26114, 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 = 0.203126, size = 31, normalized size = 2.07 \begin{align*} \frac{x^{2} \sqrt{- 4 x^{2} - 9}}{3} + \frac{3 \sqrt{- 4 x^{2} - 9}}{4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [C] time = 1.58329, size = 15, normalized size = 1. \begin{align*} \frac{1}{12} i \,{\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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