Optimal. Leaf size=45 \[ -\frac {1}{16 x^4}+\frac {1}{8 x^3}-\frac {9}{32 x^2}+\frac {27}{32 x}+\frac {81 \log (x)}{64}-\frac {81}{64} \log (3 x+2) \]
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Rubi [A] time = 0.01, antiderivative size = 45, 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} \[ -\frac {9}{32 x^2}+\frac {1}{8 x^3}-\frac {1}{16 x^4}+\frac {27}{32 x}+\frac {81 \log (x)}{64}-\frac {81}{64} \log (3 x+2) \]
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*}
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Mathematica [A] time = 0.00, size = 45, normalized size = 1.00 \[ -\frac {1}{16 x^4}+\frac {1}{8 x^3}-\frac {9}{32 x^2}+\frac {27}{32 x}+\frac {81 \log (x)}{64}-\frac {81}{64} \log (3 x+2) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.48, size = 38, normalized size = 0.84 \[ -\frac {81 \, x^{4} \log \left (3 \, x + 2\right ) - 81 \, x^{4} \log \relax (x) - 54 \, x^{3} + 18 \, x^{2} - 8 \, x + 4}{64 \, x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.14, size = 35, normalized size = 0.78 \[ \frac {27 \, x^{3} - 9 \, x^{2} + 4 \, x - 2}{32 \, x^{4}} - \frac {81}{64} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) + \frac {81}{64} \, \log \left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.01, size = 34, normalized size = 0.76 \[ \frac {81 \ln \relax (x )}{64}-\frac {81 \ln \left (3 x +2\right )}{64}+\frac {27}{32 x}-\frac {9}{32 x^{2}}+\frac {1}{8 x^{3}}-\frac {1}{16 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.32, size = 33, normalized size = 0.73 \[ \frac {27 \, x^{3} - 9 \, x^{2} + 4 \, x - 2}{32 \, x^{4}} - \frac {81}{64} \, \log \left (3 \, x + 2\right ) + \frac {81}{64} \, \log \relax (x) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 28, normalized size = 0.62 \[ \frac {\frac {27\,x^3}{32}-\frac {9\,x^2}{32}+\frac {x}{8}-\frac {1}{16}}{x^4}-\frac {81\,\mathrm {atanh}\left (3\,x+1\right )}{32} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 36, normalized size = 0.80 \[ \frac {81 \log {\relax (x )}}{64} - \frac {81 \log {\left (x + \frac {2}{3} \right )}}{64} + \frac {27 x^{3} - 9 x^{2} + 4 x - 2}{32 x^{4}} \]
Verification of antiderivative is not currently implemented for this CAS.
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