Optimal. Leaf size=15 \[ -\frac {1}{3} \left (4-x^2\right )^{3/2} \]
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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} \[ -\frac {1}{3} \left (4-x^2\right )^{3/2} \]
Antiderivative was successfully verified.
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Rule 261
Rubi steps
\begin {align*} \int x \sqrt {4-x^2} \, dx &=-\frac {1}{3} \left (4-x^2\right )^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 15, normalized size = 1.00 \[ -\frac {1}{3} \left (4-x^2\right )^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 16, normalized size = 1.07 \[ \frac {1}{3} \, {\left (x^{2} - 4\right )} \sqrt {-x^{2} + 4} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 11, normalized size = 0.73 \[ -\frac {1}{3} \, {\left (-x^{2} + 4\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 18, normalized size = 1.20 \[ \frac {\left (x -2\right ) \left (x +2\right ) \sqrt {-x^{2}+4}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 11, normalized size = 0.73 \[ -\frac {1}{3} \, {\left (-x^{2} + 4\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 11, normalized size = 0.73 \[ -\frac {{\left (4-x^2\right )}^{3/2}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.21, size = 24, normalized size = 1.60 \[ \frac {x^{2} \sqrt {4 - x^{2}}}{3} - \frac {4 \sqrt {4 - x^{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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