Optimal. Leaf size=16 \[ \frac{2 x}{3}-\frac{1}{9} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0063008, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.077, Rules used = {43} \[ \frac{2 x}{3}-\frac{1}{9} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rubi steps
\begin{align*} \int \frac{1+2 x}{2+3 x} \, dx &=\int \left (\frac{2}{3}-\frac{1}{3 (2+3 x)}\right ) \, dx\\ &=\frac{2 x}{3}-\frac{1}{9} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0027664, size = 17, normalized size = 1.06 \[ \frac{1}{9} (6 x-\log (3 x+2)+4) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.001, size = 13, normalized size = 0.8 \begin{align*}{\frac{2\,x}{3}}-{\frac{\ln \left ( 2+3\,x \right ) }{9}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 0.947144, size = 16, normalized size = 1. \begin{align*} \frac{2}{3} \, x - \frac{1}{9} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.51052, size = 35, normalized size = 2.19 \begin{align*} \frac{2}{3} \, x - \frac{1}{9} \, \log \left (3 \, x + 2\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.069165, size = 12, normalized size = 0.75 \begin{align*} \frac{2 x}{3} - \frac{\log{\left (3 x + 2 \right )}}{9} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.07865, size = 18, normalized size = 1.12 \begin{align*} \frac{2}{3} \, x - \frac{1}{9} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]