Optimal. Leaf size=12 \[ \log (3-x)-\frac {1}{x} \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {893} \begin {gather*} \log (3-x)-\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 893
Rubi steps
\begin {align*} \int \frac {-3+x+x^2}{(-3+x) x^2} \, dx &=\int \left (\frac {1}{-3+x}+\frac {1}{x^2}\right ) \, dx\\ &=-\frac {1}{x}+\log (3-x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \begin {gather*} \log (3-x)-\frac {1}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {-3+x+x^2}{(-3+x) x^2} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.23, size = 12, normalized size = 1.00 \begin {gather*} \frac {x \log \left (x - 3\right ) - 1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.42, size = 11, normalized size = 0.92 \begin {gather*} -\frac {1}{x} + \log \left ({\left | x - 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.00, size = 11, normalized size = 0.92 \begin {gather*} \ln \left (x -3\right )-\frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.75, size = 10, normalized size = 0.83 \begin {gather*} -\frac {1}{x} + \log \left (x - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 10, normalized size = 0.83 \begin {gather*} \ln \left (x-3\right )-\frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.09, size = 7, normalized size = 0.58 \begin {gather*} \log {\left (x - 3 \right )} - \frac {1}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________