Optimal. Leaf size=21 \[ \frac{x}{9 \sqrt{3-x} \sqrt{x+3}} \]
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Rubi [A] time = 0.0016875, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {39} \[ \frac{x}{9 \sqrt{3-x} \sqrt{x+3}} \]
Antiderivative was successfully verified.
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Rule 39
Rubi steps
\begin{align*} \int \frac{1}{(3-x)^{3/2} (3+x)^{3/2}} \, dx &=\frac{x}{9 \sqrt{3-x} \sqrt{3+x}}\\ \end{align*}
Mathematica [A] time = 0.0043093, size = 16, normalized size = 0.76 \[ \frac{x}{9 \sqrt{9-x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 16, normalized size = 0.8 \begin{align*}{\frac{x}{9}{\frac{1}{\sqrt{3-x}}}{\frac{1}{\sqrt{3+x}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.984483, size = 16, normalized size = 0.76 \begin{align*} \frac{x}{9 \, \sqrt{-x^{2} + 9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.48049, size = 58, normalized size = 2.76 \begin{align*} -\frac{\sqrt{x + 3} x \sqrt{-x + 3}}{9 \,{\left (x^{2} - 9\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.84558, size = 73, normalized size = 3.48 \begin{align*} \begin{cases} \frac{1}{9 \sqrt{-1 + \frac{6}{x + 3}}} - \frac{1}{3 \sqrt{-1 + \frac{6}{x + 3}} \left (x + 3\right )} & \text{for}\: \frac{6}{\left |{x + 3}\right |} > 1 \\- \frac{i \sqrt{1 - \frac{6}{x + 3}} \left (x + 3\right )}{9 x - 27} + \frac{3 i \sqrt{1 - \frac{6}{x + 3}}}{9 x - 27} & \text{otherwise} \end{cases} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.07454, size = 84, normalized size = 4. \begin{align*} \frac{\sqrt{6} - \sqrt{-x + 3}}{36 \, \sqrt{x + 3}} - \frac{\sqrt{x + 3} \sqrt{-x + 3}}{18 \,{\left (x - 3\right )}} - \frac{\sqrt{x + 3}}{36 \,{\left (\sqrt{6} - \sqrt{-x + 3}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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