Optimal. Leaf size=15 \[ -\frac{1}{3} \left (4-x^2\right )^{3/2} \]
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Rubi [A] time = 0.0022245, 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} \[ -\frac{1}{3} \left (4-x^2\right )^{3/2} \]
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*}
Mathematica [A] time = 0.0015562, size = 15, normalized size = 1. \[ -\frac{1}{3} \left (4-x^2\right )^{3/2} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 18, normalized size = 1.2 \begin{align*}{\frac{ \left ( -2+x \right ) \left ( 2+x \right ) }{3}\sqrt{-{x}^{2}+4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.919963, size = 15, normalized size = 1. \begin{align*} -\frac{1}{3} \,{\left (-x^{2} + 4\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.00834, size = 41, normalized size = 2.73 \begin{align*} \frac{1}{3} \,{\left (x^{2} - 4\right )} \sqrt{-x^{2} + 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 0.180193, size = 24, normalized size = 1.6 \begin{align*} \frac{x^{2} \sqrt{4 - x^{2}}}{3} - \frac{4 \sqrt{4 - x^{2}}}{3} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.07207, size = 15, normalized size = 1. \begin{align*} -\frac{1}{3} \,{\left (-x^{2} + 4\right )}^{\frac{3}{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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