Optimal. Leaf size=45 \[ -\frac{9}{32 x^2}+\frac{1}{8 x^3}-\frac{1}{16 x^4}+\frac{27}{32 x}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (3 x+2) \]
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Rubi [A] time = 0.0117359, antiderivative size = 45, 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} \[ -\frac{9}{32 x^2}+\frac{1}{8 x^3}-\frac{1}{16 x^4}+\frac{27}{32 x}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (3 x+2) \]
Antiderivative was successfully verified.
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Rule 44
Rubi steps
\begin{align*} \int \frac{1}{x^5 (4+6 x)} \, dx &=\int \left (\frac{1}{4 x^5}-\frac{3}{8 x^4}+\frac{9}{16 x^3}-\frac{27}{32 x^2}+\frac{81}{64 x}-\frac{243}{64 (2+3 x)}\right ) \, dx\\ &=-\frac{1}{16 x^4}+\frac{1}{8 x^3}-\frac{9}{32 x^2}+\frac{27}{32 x}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (2+3 x)\\ \end{align*}
Mathematica [A] time = 0.0031462, size = 45, normalized size = 1. \[ -\frac{9}{32 x^2}+\frac{1}{8 x^3}-\frac{1}{16 x^4}+\frac{27}{32 x}+\frac{81 \log (x)}{64}-\frac{81}{64} \log (3 x+2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.006, size = 34, normalized size = 0.8 \begin{align*} -{\frac{1}{16\,{x}^{4}}}+{\frac{1}{8\,{x}^{3}}}-{\frac{9}{32\,{x}^{2}}}+{\frac{27}{32\,x}}+{\frac{81\,\ln \left ( x \right ) }{64}}-{\frac{81\,\ln \left ( 2+3\,x \right ) }{64}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02507, size = 45, normalized size = 1. \begin{align*} \frac{27 \, x^{3} - 9 \, x^{2} + 4 \, x - 2}{32 \, x^{4}} - \frac{81}{64} \, \log \left (3 \, x + 2\right ) + \frac{81}{64} \, \log \left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.69802, size = 104, normalized size = 2.31 \begin{align*} -\frac{81 \, x^{4} \log \left (3 \, x + 2\right ) - 81 \, x^{4} \log \left (x\right ) - 54 \, x^{3} + 18 \, x^{2} - 8 \, x + 4}{64 \, x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.193303, size = 36, normalized size = 0.8 \begin{align*} \frac{81 \log{\left (x \right )}}{64} - \frac{81 \log{\left (x + \frac{2}{3} \right )}}{64} + \frac{27 x^{3} - 9 x^{2} + 4 x - 2}{32 x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.2037, size = 47, normalized size = 1.04 \begin{align*} \frac{27 \, x^{3} - 9 \, x^{2} + 4 \, x - 2}{32 \, x^{4}} - \frac{81}{64} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac{81}{64} \, \log \left ({\left | x \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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