Optimal. Leaf size=17 \[ -2 \log (2-x)+3 \log (3-x) \]
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Rubi [A]
time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, 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 = {646, 31}
\begin {gather*} 3 \log (3-x)-2 \log (2-x) \end {gather*}
Antiderivative was successfully verified.
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Rule 31
Rule 646
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*}
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Mathematica [A]
time = 0.00, size = 17, normalized size = 1.00 \begin {gather*} -2 \log (2-x)+3 \log (3-x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.64, size = 14, normalized size = 0.82
method | result | size |
default | \(3 \ln \left (x -3\right )-2 \ln \left (x -2\right )\) | \(14\) |
norman | \(3 \ln \left (x -3\right )-2 \ln \left (x -2\right )\) | \(14\) |
risch | \(3 \ln \left (x -3\right )-2 \ln \left (x -2\right )\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 13, normalized size = 0.76 \begin {gather*} -2 \, \log \left (x - 2\right ) + 3 \, \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 4.04, size = 13, normalized size = 0.76 \begin {gather*} -2 \, \log \left (x - 2\right ) + 3 \, \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 12, normalized size = 0.71 \begin {gather*} 3 \log {\left (x - 3 \right )} - 2 \log {\left (x - 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.99, size = 15, normalized size = 0.88 \begin {gather*} -2 \, \log \left ({\left | x - 2 \right |}\right ) + 3 \, \log \left ({\left | x - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 13, normalized size = 0.76 \begin {gather*} 3\,\ln \left (x-3\right )-2\,\ln \left (x-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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