Optimal. Leaf size=21 \[ \frac {x}{9 \sqrt {3-x} \sqrt {x+3}} \]
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Rubi [A] time = 0.00, antiderivative size = 21, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 16, normalized size = 0.76 \[ \frac {x}{9 \sqrt {9-x^2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.43, size = 22, normalized size = 1.05 \[ -\frac {\sqrt {x + 3} x \sqrt {-x + 3}}{9 \, {\left (x^{2} - 9\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.90, size = 62, normalized size = 2.95 \[ \frac {\sqrt {6} - \sqrt {-x + 3}}{36 \, \sqrt {x + 3}} - \frac {\sqrt {x + 3} \sqrt {-x + 3}}{18 \, {\left (x - 3\right )}} - \frac {\sqrt {x + 3}}{36 \, {\left (\sqrt {6} - \sqrt {-x + 3}\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 16, normalized size = 0.76 \[ \frac {x}{9 \sqrt {-x +3}\, \sqrt {x +3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.37, size = 12, normalized size = 0.57 \[ \frac {x}{9 \, \sqrt {-x^{2} + 9}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.36, size = 22, normalized size = 1.05 \[ -\frac {x\,\sqrt {3-x}}{\left (9\,x-27\right )\,\sqrt {x+3}} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.80, size = 73, normalized size = 3.48 \[ \begin {cases} \frac {1}{9 \sqrt {-1 + \frac {6}{x + 3}}} - \frac {1}{3 \sqrt {-1 + \frac {6}{x + 3}} \left (x + 3\right )} & \text {for}\: \frac {6}{\left |{x + 3}\right |} > 1 \\\frac {i \sqrt {1 - \frac {6}{x + 3}} \left (x + 3\right )}{27 - 9 x} - \frac {3 i \sqrt {1 - \frac {6}{x + 3}}}{27 - 9 x} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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