Optimal. Leaf size=24 \[ -\frac{1}{4 x}-\frac{3 \log (x)}{8}+\frac{3}{8} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.0078345, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {44} \[ -\frac{1}{4 x}-\frac{3 \log (x)}{8}+\frac{3}{8} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 44
Rubi steps
\begin{align*} \int \frac{1}{x^2 (4+6 x)} \, dx &=\int \left (\frac{1}{4 x^2}-\frac{3}{8 x}+\frac{9}{8 (2+3 x)}\right ) \, dx\\ &=-\frac{1}{4 x}-\frac{3 \log (x)}{8}+\frac{3}{8} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0026833, size = 24, normalized size = 1. \[ -\frac{1}{4 x}-\frac{3 \log (x)}{8}+\frac{3}{8} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A] time = 0.007, size = 19, normalized size = 0.8 \begin{align*} -{\frac{1}{4\,x}}-{\frac{3\,\ln \left ( x \right ) }{8}}+{\frac{3\,\ln \left ( 2+3\,x \right ) }{8}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A] time = 1.03344, size = 24, normalized size = 1. \begin{align*} -\frac{1}{4 \, x} + \frac{3}{8} \, \log \left (3 \, x + 2\right ) - \frac{3}{8} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A] time = 1.7301, size = 58, normalized size = 2.42 \begin{align*} \frac{3 \, x \log \left (3 \, x + 2\right ) - 3 \, x \log \left (x\right ) - 2}{8 \, x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A] time = 0.123414, size = 20, normalized size = 0.83 \begin{align*} - \frac{3 \log{\left (x \right )}}{8} + \frac{3 \log{\left (x + \frac{2}{3} \right )}}{8} - \frac{1}{4 x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A] time = 1.17741, size = 27, normalized size = 1.12 \begin{align*} -\frac{1}{4 \, x} + \frac{3}{8} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{3}{8} \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]