Optimal. Leaf size=31 \[ -\frac {1}{8 x^2}+\frac {3}{8 x}+\frac {9 \log (x)}{16}-\frac {9}{16} \log (3 x+2) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 31, normalized size of antiderivative = 1.00, 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} \[ -\frac {1}{8 x^2}+\frac {3}{8 x}+\frac {9 \log (x)}{16}-\frac {9}{16} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 44
Rubi steps
\begin {align*} \int \frac {1}{x^3 (4+6 x)} \, dx &=\int \left (\frac {1}{4 x^3}-\frac {3}{8 x^2}+\frac {9}{16 x}-\frac {27}{16 (2+3 x)}\right ) \, dx\\ &=-\frac {1}{8 x^2}+\frac {3}{8 x}+\frac {9 \log (x)}{16}-\frac {9}{16} \log (2+3 x)\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 31, normalized size = 1.00 \[ -\frac {1}{8 x^2}+\frac {3}{8 x}+\frac {9 \log (x)}{16}-\frac {9}{16} \log (3 x+2) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.52, size = 28, normalized size = 0.90 \[ -\frac {9 \, x^{2} \log \left (3 \, x + 2\right ) - 9 \, x^{2} \log \relax (x) - 6 \, x + 2}{16 \, x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 1.07, size = 25, normalized size = 0.81 \[ \frac {3 \, x - 1}{8 \, x^{2}} - \frac {9}{16} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {9}{16} \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.01, size = 24, normalized size = 0.77 \[ \frac {9 \ln \relax (x )}{16}-\frac {9 \ln \left (3 x +2\right )}{16}+\frac {3}{8 x}-\frac {1}{8 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 1.29, size = 23, normalized size = 0.74 \[ \frac {3 \, x - 1}{8 \, x^{2}} - \frac {9}{16} \, \log \left (3 \, x + 2\right ) + \frac {9}{16} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.04, size = 18, normalized size = 0.58 \[ \frac {\frac {3\,x}{8}-\frac {1}{8}}{x^2}-\frac {9\,\mathrm {atanh}\left (3\,x+1\right )}{8} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.15, size = 26, normalized size = 0.84 \[ \frac {9 \log {\relax (x )}}{16} - \frac {9 \log {\left (x + \frac {2}{3} \right )}}{16} + \frac {3 x - 1}{8 x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________