Optimal. Leaf size=31 \[ -\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0143793, antiderivative size = 31, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.045, Rules used = {72} \[ -\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 72
Rubi steps
\begin{align*} \int \frac{1}{(1-2 x) (2+3 x) (3+5 x)} \, dx &=\int \left (-\frac{4}{77 (-1+2 x)}-\frac{9}{7 (2+3 x)}+\frac{25}{11 (3+5 x)}\right ) \, dx\\ &=-\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (2+3 x)+\frac{5}{11} \log (3+5 x)\\ \end{align*}
Mathematica [A] time = 0.0068216, size = 31, normalized size = 1. \[ -\frac{2}{77} \log (1-2 x)-\frac{3}{7} \log (3 x+2)+\frac{5}{11} \log (5 x+3) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.006, size = 26, normalized size = 0.8 \begin{align*} -{\frac{2\,\ln \left ( 2\,x-1 \right ) }{77}}-{\frac{3\,\ln \left ( 2+3\,x \right ) }{7}}+{\frac{5\,\ln \left ( 3+5\,x \right ) }{11}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.02492, size = 34, normalized size = 1.1 \begin{align*} \frac{5}{11} \, \log \left (5 \, x + 3\right ) - \frac{3}{7} \, \log \left (3 \, x + 2\right ) - \frac{2}{77} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.32895, size = 78, normalized size = 2.52 \begin{align*} \frac{5}{11} \, \log \left (5 \, x + 3\right ) - \frac{3}{7} \, \log \left (3 \, x + 2\right ) - \frac{2}{77} \, \log \left (2 \, x - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.133795, size = 29, normalized size = 0.94 \begin{align*} - \frac{2 \log{\left (x - \frac{1}{2} \right )}}{77} + \frac{5 \log{\left (x + \frac{3}{5} \right )}}{11} - \frac{3 \log{\left (x + \frac{2}{3} \right )}}{7} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.20787, size = 38, normalized size = 1.23 \begin{align*} \frac{5}{11} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac{3}{7} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{2}{77} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]