Optimal. Leaf size=29 \[ -\frac {(2-3 x) \log (2-3 x)}{3 \sqrt {-9 x^2+12 x-4}} \]
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Rubi [A] time = 0.00, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {608, 31} \[ -\frac {(2-3 x) \log (2-3 x)}{3 \sqrt {-9 x^2+12 x-4}} \]
Antiderivative was successfully verified.
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Rule 31
Rule 608
Rubi steps
\begin {align*} \int \frac {1}{\sqrt {-4+12 x-9 x^2}} \, dx &=\frac {(6-9 x) \int \frac {1}{6-9 x} \, dx}{\sqrt {-4+12 x-9 x^2}}\\ &=-\frac {(2-3 x) \log (2-3 x)}{3 \sqrt {-4+12 x-9 x^2}}\\ \end {align*}
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Mathematica [A] time = 0.01, size = 28, normalized size = 0.97 \[ -\frac {(2-3 x) \log (2-3 x)}{3 \sqrt {-(2-3 x)^2}} \]
Antiderivative was successfully verified.
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fricas [C] time = 1.11, size = 6, normalized size = 0.21 \[ -\frac {1}{3} i \, \log \left (x - \frac {2}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [C] time = 0.45, size = 23, normalized size = 0.79 \[ \frac {i \, \log \left ({\left (-3 i \, x + 2 i\right )} \mathrm {sgn}\left (-3 \, x + 2\right )\right )}{3 \, \mathrm {sgn}\left (-3 \, x + 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 25, normalized size = 0.86 \[ \frac {\left (3 x -2\right ) \ln \left (3 x -2\right )}{3 \sqrt {-\left (3 x -2\right )^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 2.90, size = 6, normalized size = 0.21 \[ \frac {1}{3} i \, \log \left (x - \frac {2}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 15, normalized size = 0.52 \[ -\frac {\ln \left (2-3\,x\right )\,\mathrm {sign}\left (3\,x-2\right )\,1{}\mathrm {i}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{\sqrt {- \left (3 x - 2\right )^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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