Optimal. Leaf size=13 \[ \frac {\sin ^{-1}(2 x)}{2 \sqrt {6}} \]
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Rubi [A] time = 0.00, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 19, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.105, Rules used = {41, 216} \begin {gather*} \frac {\sin ^{-1}(2 x)}{2 \sqrt {6}} \end {gather*}
Antiderivative was successfully verified.
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Rule 41
Rule 216
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {3-6 x} \sqrt {2+4 x}} \, dx &=\int \frac {1}{\sqrt {6-24 x^2}} \, dx\\ &=\frac {\sin ^{-1}(2 x)}{2 \sqrt {6}}\\ \end {align*}
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Mathematica [A] time = 0.02, size = 13, normalized size = 1.00 \begin {gather*} \frac {\sin ^{-1}(2 x)}{2 \sqrt {6}} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [B] time = 0.59, size = 36, normalized size = 2.77 \begin {gather*} \sqrt {\frac {2}{3}} \tan ^{-1}\left (\frac {\sqrt {2 x+1}-\sqrt {2}}{\sqrt {1-2 x}}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 1.09, size = 28, normalized size = 2.15 \begin {gather*} -\frac {1}{12} \, \sqrt {6} \arctan \left (\frac {\sqrt {6} \sqrt {4 \, x + 2} \sqrt {-6 \, x + 3}}{12 \, x}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.88, size = 15, normalized size = 1.15 \begin {gather*} \frac {1}{6} \, \sqrt {6} \arcsin \left (\frac {1}{2} \, \sqrt {4 \, x + 2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.00, size = 37, normalized size = 2.85 \begin {gather*} \frac {\sqrt {\left (4 x +2\right ) \left (-6 x +3\right )}\, \sqrt {6}\, \arcsin \left (2 x \right )}{12 \sqrt {4 x +2}\, \sqrt {-6 x +3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.94, size = 9, normalized size = 0.69 \begin {gather*} \frac {1}{12} \, \sqrt {6} \arcsin \left (2 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 40, normalized size = 3.08 \begin {gather*} -\frac {\sqrt {6}\,\mathrm {atan}\left (\frac {\sqrt {24}\,\left (\sqrt {3}-\sqrt {3-6\,x}\right )}{6\,\left (\sqrt {2}-\sqrt {4\,x+2}\right )}\right )}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 3.35, size = 41, normalized size = 3.15 \begin {gather*} \begin {cases} - \frac {\sqrt {6} i \operatorname {acosh}{\left (\sqrt {x + \frac {1}{2}} \right )}}{6} & \text {for}\: \left |{x + \frac {1}{2}}\right | > 1 \\\frac {\sqrt {6} \operatorname {asin}{\left (\sqrt {x + \frac {1}{2}} \right )}}{6} & \text {otherwise} \end {cases} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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