Optimal. Leaf size=12 \[ \log (3-x)-\frac{1}{x} \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0106617, antiderivative size = 12, normalized size of antiderivative = 1., 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} \[ \log (3-x)-\frac{1}{x} \]
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 = 0.0029219, size = 12, normalized size = 1. \[ \log (3-x)-\frac{1}{x} \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 11, normalized size = 0.9 \begin{align*} \ln \left ( -3+x \right ) -{x}^{-1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.98342, size = 14, normalized size = 1.17 \begin{align*} -\frac{1}{x} + \log \left (x - 3\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.42738, size = 30, normalized size = 2.5 \begin{align*} \frac{x \log \left (x - 3\right ) - 1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.084146, size = 7, normalized size = 0.58 \begin{align*} \log{\left (x - 3 \right )} - \frac{1}{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.14268, size = 15, normalized size = 1.25 \begin{align*} -\frac{1}{x} + \log \left ({\left | x - 3 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]