Optimal. Leaf size=23 \[ -\frac{1}{6} (2-3 x) \sqrt{-9 x^2+12 x-4} \]
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Rubi [A] time = 0.0026217, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.071, Rules used = {609} \[ -\frac{1}{6} (2-3 x) \sqrt{-9 x^2+12 x-4} \]
Antiderivative was successfully verified.
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Rule 609
Rubi steps
\begin{align*} \int \sqrt{-4+12 x-9 x^2} \, dx &=-\frac{1}{6} (2-3 x) \sqrt{-4+12 x-9 x^2}\\ \end{align*}
Mathematica [A] time = 0.0076881, size = 27, normalized size = 1.17 \[ \frac{\sqrt{-(2-3 x)^2} x (3 x-4)}{6 x-4} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.066, size = 27, normalized size = 1.2 \begin{align*}{\frac{x \left ( 3\,x-4 \right ) }{-4+6\,x}\sqrt{- \left ( -2+3\,x \right ) ^{2}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.69619, size = 41, normalized size = 1.78 \begin{align*} \frac{1}{2} \, \sqrt{-9 \, x^{2} + 12 \, x - 4} x - \frac{1}{3} \, \sqrt{-9 \, x^{2} + 12 \, x - 4} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [C] time = 2.04588, size = 26, normalized size = 1.13 \begin{align*} \frac{3}{2} i \, x^{2} - 2 i \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \sqrt{- \left (3 x - 2\right )^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [C] time = 1.33137, size = 35, normalized size = 1.52 \begin{align*} -\frac{1}{2} i \,{\left (3 \, x^{2} - 4 \, x\right )} \mathrm{sgn}\left (-3 \, x + 2\right ) - \frac{2}{3} i \, \mathrm{sgn}\left (-3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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