Optimal. Leaf size=15 \[ -\frac {1}{12} \left (-4 x^2-9\right )^{3/2} \]
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Rubi [A] time = 0.00, antiderivative size = 15, 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} \[ -\frac {1}{12} \left (-4 x^2-9\right )^{3/2} \]
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*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ -\frac {1}{12} \left (-4 x^2-9\right )^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.99, size = 18, normalized size = 1.20 \[ \frac {1}{12} \, {\left (4 \, x^{2} + 9\right )} \sqrt {-4 \, x^{2} - 9} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.08, size = 12, normalized size = 0.80 \[ \frac {1}{12} \, {\left (4 \, x^{2} + 9\right )}^{\frac {3}{2}} i \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 12, normalized size = 0.80 \[ -\frac {\left (-4 x^{2}-9\right )^{\frac {3}{2}}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.31, size = 11, normalized size = 0.73 \[ -\frac {1}{12} \, {\left (-4 \, x^{2} - 9\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 11, normalized size = 0.73 \[ -\frac {{\left (-4\,x^2-9\right )}^{3/2}}{12} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.22, size = 31, normalized size = 2.07 \[ \frac {x^{2} \sqrt {- 4 x^{2} - 9}}{3} + \frac {3 \sqrt {- 4 x^{2} - 9}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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