Optimal. Leaf size=17 \[ \frac {\log (x)}{4}-\frac {1}{4} \log (3 x+2) \]
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Rubi [A] time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.273, Rules used = {36, 29, 31} \begin {gather*} \frac {\log (x)}{4}-\frac {1}{4} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 31
Rule 36
Rubi steps
\begin {align*} \int \frac {1}{x (4+6 x)} \, dx &=\frac {1}{4} \int \frac {1}{x} \, dx-\frac {3}{2} \int \frac {1}{4+6 x} \, dx\\ &=\frac {\log (x)}{4}-\frac {1}{4} \log (2+3 x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} \frac {\log (x)}{4}-\frac {1}{4} \log (3 x+2) \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x (4+6 x)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.16, size = 13, normalized size = 0.76 \begin {gather*} -\frac {1}{4} \, \log \left (3 \, x + 2\right ) + \frac {1}{4} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.01, size = 15, normalized size = 0.88 \begin {gather*} -\frac {1}{4} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {1}{4} \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 14, normalized size = 0.82 \begin {gather*} \frac {\ln \relax (x )}{4}-\frac {\ln \left (3 x +2\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.29, size = 13, normalized size = 0.76 \begin {gather*} -\frac {1}{4} \, \log \left (3 \, x + 2\right ) + \frac {1}{4} \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.14, size = 10, normalized size = 0.59 \begin {gather*} -\frac {\ln \left (\frac {4}{x}+6\right )}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 12, normalized size = 0.71 \begin {gather*} \frac {\log {\relax (x )}}{4} - \frac {\log {\left (x + \frac {2}{3} \right )}}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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