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 = 26, normalized size = 0.90 \[ -\frac {(2-3 x) \log (2-3 x)}{3 \sqrt {(2-3 x)^2}} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.87, size = 8, normalized size = 0.28 \[ \frac {1}{3} \, \log \left (3 \, x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.46, size = 15, normalized size = 0.52 \[ \frac {1}{3} \, \log \left ({\left | 3 \, x - 2 \right |}\right ) \mathrm {sgn}\left (3 \, x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 23, normalized size = 0.79 \[ \frac {\left (3 x -2\right ) \ln \left (3 x -2\right )}{3 \sqrt {\left (3 x -2\right )^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 2.97, size = 6, normalized size = 0.21 \[ \frac {1}{3} \, \log \left (x - \frac {2}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.35, size = 14, normalized size = 0.48 \[ \frac {\ln \left (3\,x-2\right )\,\mathrm {sign}\left (3\,x-2\right )}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 7, normalized size = 0.24 \[ \frac {\log {\left (3 x - 2 \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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