Optimal. Leaf size=29 \[ \frac{x}{18 \sqrt{2} \sqrt{3-b x} \sqrt{b x+3}} \]
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Rubi [A] time = 0.0025479, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05, Rules used = {39} \[ \frac{x}{18 \sqrt{2} \sqrt{3-b x} \sqrt{b x+3}} \]
Antiderivative was successfully verified.
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Rule 39
Rubi steps
\begin{align*} \int \frac{1}{(6-2 b x)^{3/2} (3+b x)^{3/2}} \, dx &=\frac{x}{18 \sqrt{2} \sqrt{3-b x} \sqrt{3+b x}}\\ \end{align*}
Mathematica [A] time = 0.0177079, size = 19, normalized size = 0.66 \[ \frac{x}{18 \sqrt{18-2 b^2 x^2}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 24, normalized size = 0.8 \begin{align*} -{\frac{ \left ( bx-3 \right ) x}{9}{\frac{1}{\sqrt{bx+3}}} \left ( -2\,bx+6 \right ) ^{-{\frac{3}{2}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.969727, size = 20, normalized size = 0.69 \begin{align*} \frac{x}{18 \, \sqrt{-2 \, b^{2} x^{2} + 18}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.59389, size = 73, normalized size = 2.52 \begin{align*} -\frac{\sqrt{b x + 3} \sqrt{-2 \, b x + 6} x}{36 \,{\left (b^{2} x^{2} - 9\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 = 1.07303, size = 123, normalized size = 4.24 \begin{align*} \frac{\sqrt{2}{\left (\sqrt{6} - \sqrt{-b x + 3}\right )}}{144 \, \sqrt{b x + 3} b} - \frac{\sqrt{2} \sqrt{b x + 3} \sqrt{-b x + 3}}{72 \,{\left (b x - 3\right )} b} - \frac{\sqrt{2} \sqrt{b x + 3}}{144 \, b{\left (\sqrt{6} - \sqrt{-b x + 3}\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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