Optimal. Leaf size=15 \[ -\frac{1}{4} \sqrt{-4 x^2-9} \]
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Rubi [A] time = 0.0022589, 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} \[ -\frac{1}{4} \sqrt{-4 x^2-9} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin{align*} \int \frac{x}{\sqrt{-9-4 x^2}} \, dx &=-\frac{1}{4} \sqrt{-9-4 x^2}\\ \end{align*}
Mathematica [A] time = 0.0014836, size = 15, normalized size = 1. \[ -\frac{1}{4} \sqrt{-4 x^2-9} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 12, normalized size = 0.8 \begin{align*} -{\frac{1}{4}\sqrt{-4\,{x}^{2}-9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.89684, size = 15, normalized size = 1. \begin{align*} -\frac{1}{4} \, \sqrt{-4 \, x^{2} - 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.20037, size = 31, normalized size = 2.07 \begin{align*} -\frac{1}{4} \, \sqrt{-4 \, x^{2} - 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.14674, size = 14, normalized size = 0.93 \begin{align*} - \frac{\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 = 2.40221, size = 15, normalized size = 1. \begin{align*} -\frac{1}{4} i \, \sqrt{4 \, x^{2} + 9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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