Optimal. Leaf size=15 \[ -\frac {1}{4} \sqrt {9-4 x^2} \]
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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} \[ -\frac {1}{4} \sqrt {9-4 x^2} \]
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*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ -\frac {1}{4} \sqrt {9-4 x^2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.98, size = 11, normalized size = 0.73 \[ -\frac {1}{4} \, \sqrt {-4 \, x^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.13, size = 11, normalized size = 0.73 \[ -\frac {1}{4} \, \sqrt {-4 \, x^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 22, normalized size = 1.47 \[ \frac {\left (2 x -3\right ) \left (2 x +3\right )}{4 \sqrt {-4 x^{2}+9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 11, normalized size = 0.73 \[ -\frac {1}{4} \, \sqrt {-4 \, x^{2} + 9} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.56, size = 11, normalized size = 0.73 \[ -\frac {\sqrt {\frac {9}{4}-x^2}}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 12, normalized size = 0.80 \[ - \frac {\sqrt {9 - 4 x^{2}}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
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