Optimal. Leaf size=21 \[ \frac{1}{5} \log (2-x)-\frac{1}{5} \log (1-3 x) \]
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Rubi [A] time = 0.0055049, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 12, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167, Rules used = {616, 31} \[ \frac{1}{5} \log (2-x)-\frac{1}{5} \log (1-3 x) \]
Antiderivative was successfully verified.
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Rule 616
Rule 31
Rubi steps
\begin{align*} \int \frac{1}{2-7 x+3 x^2} \, dx &=\frac{3}{5} \int \frac{1}{-6+3 x} \, dx-\frac{3}{5} \int \frac{1}{-1+3 x} \, dx\\ &=-\frac{1}{5} \log (1-3 x)+\frac{1}{5} \log (2-x)\\ \end{align*}
Mathematica [A] time = 0.0029235, size = 21, normalized size = 1. \[ \frac{1}{5} \log (2-x)-\frac{1}{5} \log (1-3 x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 16, normalized size = 0.8 \begin{align*} -{\frac{\ln \left ( 3\,x-1 \right ) }{5}}+{\frac{\ln \left ( -2+x \right ) }{5}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.934454, size = 20, normalized size = 0.95 \begin{align*} -\frac{1}{5} \, \log \left (3 \, x - 1\right ) + \frac{1}{5} \, \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.77085, size = 49, normalized size = 2.33 \begin{align*} -\frac{1}{5} \, \log \left (3 \, x - 1\right ) + \frac{1}{5} \, \log \left (x - 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.089842, size = 14, normalized size = 0.67 \begin{align*} \frac{\log{\left (x - 2 \right )}}{5} - \frac{\log{\left (x - \frac{1}{3} \right )}}{5} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.04913, size = 23, normalized size = 1.1 \begin{align*} -\frac{1}{5} \, \log \left ({\left | 3 \, x - 1 \right |}\right ) + \frac{1}{5} \, \log \left ({\left | x - 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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