Optimal. Leaf size=17 \[ 3 \log (3-x)-2 \log (2-x) \]
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Rubi [A] time = 0.00531, antiderivative size = 17, 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 = {632, 31} \[ 3 \log (3-x)-2 \log (2-x) \]
Antiderivative was successfully verified.
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Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{x}{6-5 x+x^2} \, dx &=-\left (2 \int \frac{1}{-2+x} \, dx\right )+3 \int \frac{1}{-3+x} \, dx\\ &=-2 \log (2-x)+3 \log (3-x)\\ \end{align*}
Mathematica [A] time = 0.003102, size = 17, normalized size = 1. \[ 3 \log (3-x)-2 \log (2-x) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.046, size = 14, normalized size = 0.8 \begin{align*} 3\,\ln \left ( -3+x \right ) -2\,\ln \left ( -2+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.949461, size = 18, normalized size = 1.06 \begin{align*} -2 \, \log \left (x - 2\right ) + 3 \, \log \left (x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 2.69446, size = 41, normalized size = 2.41 \begin{align*} -2 \, \log \left (x - 2\right ) + 3 \, \log \left (x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.096094, size = 12, normalized size = 0.71 \begin{align*} 3 \log{\left (x - 3 \right )} - 2 \log{\left (x - 2 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.09749, size = 20, normalized size = 1.18 \begin{align*} -2 \, \log \left ({\left | x - 2 \right |}\right ) + 3 \, \log \left ({\left | x - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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