Optimal. Leaf size=38 \[ \frac{3}{16 x^2}-\frac{1}{12 x^3}-\frac{9}{16 x}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2) \]
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Rubi [A] time = 0.0117281, antiderivative size = 38, 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} \[ \frac{3}{16 x^2}-\frac{1}{12 x^3}-\frac{9}{16 x}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 44
Rubi steps
\begin{align*} \int \frac{1}{x^4 (4+6 x)} \, dx &=\int \left (\frac{1}{4 x^4}-\frac{3}{8 x^3}+\frac{9}{16 x^2}-\frac{27}{32 x}+\frac{81}{32 (2+3 x)}\right ) \, dx\\ &=-\frac{1}{12 x^3}+\frac{3}{16 x^2}-\frac{9}{16 x}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0065298, size = 38, normalized size = 1. \[ \frac{3}{16 x^2}-\frac{1}{12 x^3}-\frac{9}{16 x}-\frac{27 \log (x)}{32}+\frac{27}{32} \log (3 x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.005, size = 29, normalized size = 0.8 \begin{align*} -{\frac{1}{12\,{x}^{3}}}+{\frac{3}{16\,{x}^{2}}}-{\frac{9}{16\,x}}-{\frac{27\,\ln \left ( x \right ) }{32}}+{\frac{27\,\ln \left ( 2+3\,x \right ) }{32}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.03935, size = 38, normalized size = 1. \begin{align*} -\frac{27 \, x^{2} - 9 \, x + 4}{48 \, x^{3}} + \frac{27}{32} \, \log \left (3 \, x + 2\right ) - \frac{27}{32} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.79884, size = 92, normalized size = 2.42 \begin{align*} \frac{81 \, x^{3} \log \left (3 \, x + 2\right ) - 81 \, x^{3} \log \left (x\right ) - 54 \, x^{2} + 18 \, x - 8}{96 \, x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.21336, size = 31, normalized size = 0.82 \begin{align*} - \frac{27 \log{\left (x \right )}}{32} + \frac{27 \log{\left (x + \frac{2}{3} \right )}}{32} - \frac{27 x^{2} - 9 x + 4}{48 x^{3}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14213, size = 41, normalized size = 1.08 \begin{align*} -\frac{27 \, x^{2} - 9 \, x + 4}{48 \, x^{3}} + \frac{27}{32} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac{27}{32} \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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