Optimal. Leaf size=28 \[ \frac{x}{6 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}} \]
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Rubi [A] time = 0.0019949, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {39} \[ \frac{x}{6 \sqrt{6} \sqrt{1-2 x} \sqrt{2 x+1}} \]
Antiderivative was successfully verified.
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Rule 39
Rubi steps
\begin{align*} \int \frac{1}{(3-6 x)^{3/2} (2+4 x)^{3/2}} \, dx &=\frac{x}{6 \sqrt{6} \sqrt{1-2 x} \sqrt{1+2 x}}\\ \end{align*}
Mathematica [A] time = 0.0156117, size = 16, normalized size = 0.57 \[ \frac{x}{6 \sqrt{6-24 x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 28, normalized size = 1. \begin{align*} -{ \left ( 2\,x-1 \right ) \left ( 1+2\,x \right ) x \left ( 3-6\,x \right ) ^{-{\frac{3}{2}}} \left ( 2+4\,x \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.963899, size = 16, normalized size = 0.57 \begin{align*} \frac{x}{6 \, \sqrt{-24 \, x^{2} + 6}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.55657, size = 68, normalized size = 2.43 \begin{align*} -\frac{\sqrt{4 \, x + 2} x \sqrt{-6 \, x + 3}}{36 \,{\left (4 \, x^{2} - 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] time = 1.05424, size = 96, normalized size = 3.43 \begin{align*} -\frac{\sqrt{6}{\left (\sqrt{-4 \, x + 2} - 2\right )}}{288 \, \sqrt{4 \, x + 2}} - \frac{\sqrt{6} \sqrt{4 \, x + 2} \sqrt{-4 \, x + 2}}{288 \,{\left (2 \, x - 1\right )}} + \frac{\sqrt{6} \sqrt{4 \, x + 2}}{288 \,{\left (\sqrt{-4 \, x + 2} - 2\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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