Optimal. Leaf size=17 \[ \frac{17}{3} \log (3 x+2)-6 \log (x+1) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0060647, antiderivative size = 17, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.111, Rules used = {632, 31} \[ \frac{17}{3} \log (3 x+2)-6 \log (x+1) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 632
Rule 31
Rubi steps
\begin{align*} \int \frac{5-x}{2+5 x+3 x^2} \, dx &=17 \int \frac{1}{2+3 x} \, dx-18 \int \frac{1}{3+3 x} \, dx\\ &=-6 \log (1+x)+\frac{17}{3} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0053466, size = 17, normalized size = 1. \[ \frac{17}{3} \log (3 x+2)-6 \log (x+1) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.005, size = 16, normalized size = 0.9 \begin{align*} -6\,\ln \left ( 1+x \right ) +{\frac{17\,\ln \left ( 2+3\,x \right ) }{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.23148, size = 20, normalized size = 1.18 \begin{align*} \frac{17}{3} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.32441, size = 46, normalized size = 2.71 \begin{align*} \frac{17}{3} \, \log \left (3 \, x + 2\right ) - 6 \, \log \left (x + 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.114983, size = 15, normalized size = 0.88 \begin{align*} \frac{17 \log{\left (x + \frac{2}{3} \right )}}{3} - 6 \log{\left (x + 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.15783, size = 23, normalized size = 1.35 \begin{align*} \frac{17}{3} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - 6 \, \log \left ({\left | x + 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]