Optimal. Leaf size=27 \[ \frac {2}{27} (2-3 x)^{3/2}-\frac {4}{9} \sqrt {2-3 x} \]
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Rubi [A] time = 0.00, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {43} \[ \frac {2}{27} (2-3 x)^{3/2}-\frac {4}{9} \sqrt {2-3 x} \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \frac {x}{\sqrt {2-3 x}} \, dx &=\int \left (\frac {2}{3 \sqrt {2-3 x}}-\frac {1}{3} \sqrt {2-3 x}\right ) \, dx\\ &=-\frac {4}{9} \sqrt {2-3 x}+\frac {2}{27} (2-3 x)^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 0.67 \[ -\frac {2}{27} \sqrt {2-3 x} (3 x+4) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.41, size = 14, normalized size = 0.52 \[ -\frac {2}{27} \, {\left (3 \, x + 4\right )} \sqrt {-3 \, x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.01, size = 19, normalized size = 0.70 \[ \frac {2}{27} \, {\left (-3 \, x + 2\right )}^{\frac {3}{2}} - \frac {4}{9} \, \sqrt {-3 \, x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 15, normalized size = 0.56 \[ -\frac {2 \left (3 x +4\right ) \sqrt {-3 x +2}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.50, size = 19, normalized size = 0.70 \[ \frac {2}{27} \, {\left (-3 \, x + 2\right )}^{\frac {3}{2}} - \frac {4}{9} \, \sqrt {-3 \, x + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 14, normalized size = 0.52 \[ -\frac {2\,\sqrt {2-3\,x}\,\left (3\,x+4\right )}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.95, size = 61, normalized size = 2.26 \[ \begin {cases} - \frac {2 i x \sqrt {3 x - 2}}{9} - \frac {8 i \sqrt {3 x - 2}}{27} & \text {for}\: \frac {3 \left |{x}\right |}{2} > 1 \\- \frac {2 x \sqrt {2 - 3 x}}{9} - \frac {8 \sqrt {2 - 3 x}}{27} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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