Optimal. Leaf size=13 \[ \log (1-x)+3 \log (x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0057979, antiderivative size = 13, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.062, Rules used = {72} \[ \log (1-x)+3 \log (x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 72
Rubi steps
\begin{align*} \int \frac{-1+4 x}{(-1+x) (2+x)} \, dx &=\int \left (\frac{1}{-1+x}+\frac{3}{2+x}\right ) \, dx\\ &=\log (1-x)+3 \log (2+x)\\ \end{align*}
Mathematica [A] time = 0.0038172, size = 13, normalized size = 1. \[ \log (1-x)+3 \log (x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.004, size = 12, normalized size = 0.9 \begin{align*} 3\,\ln \left ( 2+x \right ) +\ln \left ( -1+x \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.918911, size = 15, normalized size = 1.15 \begin{align*} 3 \, \log \left (x + 2\right ) + \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.9185, size = 36, normalized size = 2.77 \begin{align*} 3 \, \log \left (x + 2\right ) + \log \left (x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.094259, size = 10, normalized size = 0.77 \begin{align*} \log{\left (x - 1 \right )} + 3 \log{\left (x + 2 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.05401, size = 18, normalized size = 1.38 \begin{align*} 3 \, \log \left ({\left | x + 2 \right |}\right ) + \log \left ({\left | x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]