Optimal. Leaf size=17 \[ 3 \log (3-x)-2 \log (2-x) \]
________________________________________________________________________________________
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 = {632, 31} \begin {gather*} 3 \log (3-x)-2 \log (2-x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 31
Rule 632
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 = 0.00, size = 17, normalized size = 1.00 \begin {gather*} 3 \log (3-x)-2 \log (2-x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{6-5 x+x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.39, 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.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.17, 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.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.06, size = 14, normalized size = 0.82 \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.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.84, 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.
[In]
[Out]
________________________________________________________________________________________
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.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, 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.
[In]
[Out]
________________________________________________________________________________________