Optimal. Leaf size=29 \[ -\frac{11}{14} \log (3-x)+\frac{3}{2} \log (5-x)+\frac{2}{7} \log (x+4) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0528289, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.048, Rules used = {1612} \[ -\frac{11}{14} \log (3-x)+\frac{3}{2} \log (5-x)+\frac{2}{7} \log (x+4) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 1612
Rubi steps
\begin{align*} \int \frac{2+x^2}{(-5+x) (-3+x) (4+x)} \, dx &=\int \left (\frac{3}{2 (-5+x)}-\frac{11}{14 (-3+x)}+\frac{2}{7 (4+x)}\right ) \, dx\\ &=-\frac{11}{14} \log (3-x)+\frac{3}{2} \log (5-x)+\frac{2}{7} \log (4+x)\\ \end{align*}
Mathematica [A] time = 0.0074461, size = 29, normalized size = 1. \[ -\frac{11}{14} \log (3-x)+\frac{3}{2} \log (5-x)+\frac{2}{7} \log (x+4) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.009, size = 20, normalized size = 0.7 \begin{align*} -{\frac{11\,\ln \left ( -3+x \right ) }{14}}+{\frac{2\,\ln \left ( 4+x \right ) }{7}}+{\frac{3\,\ln \left ( -5+x \right ) }{2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.971552, size = 26, normalized size = 0.9 \begin{align*} \frac{2}{7} \, \log \left (x + 4\right ) - \frac{11}{14} \, \log \left (x - 3\right ) + \frac{3}{2} \, \log \left (x - 5\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.5611, size = 70, normalized size = 2.41 \begin{align*} \frac{2}{7} \, \log \left (x + 4\right ) - \frac{11}{14} \, \log \left (x - 3\right ) + \frac{3}{2} \, \log \left (x - 5\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.130081, size = 24, normalized size = 0.83 \begin{align*} \frac{3 \log{\left (x - 5 \right )}}{2} - \frac{11 \log{\left (x - 3 \right )}}{14} + \frac{2 \log{\left (x + 4 \right )}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.15394, size = 30, normalized size = 1.03 \begin{align*} \frac{2}{7} \, \log \left ({\left | x + 4 \right |}\right ) - \frac{11}{14} \, \log \left ({\left | x - 3 \right |}\right ) + \frac{3}{2} \, \log \left ({\left | x - 5 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]