Optimal. Leaf size=14 \[ \frac {4 \log (3)}{5 x^3 (4+x)} \]
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Rubi [A] time = 0.03, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 5, number of rules used = 4, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 1594, 27, 74} \begin {gather*} \frac {4 \log (3)}{5 x^3 (x+4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 74
Rule 1594
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (3) \int \frac {-48-16 x}{80 x^4+40 x^5+5 x^6} \, dx\\ &=\log (3) \int \frac {-48-16 x}{x^4 \left (80+40 x+5 x^2\right )} \, dx\\ &=\log (3) \int \frac {-48-16 x}{5 x^4 (4+x)^2} \, dx\\ &=\frac {1}{5} \log (3) \int \frac {-48-16 x}{x^4 (4+x)^2} \, dx\\ &=\frac {4 \log (3)}{5 x^3 (4+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} \frac {4 \log (3)}{5 x^3 (4+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 15, normalized size = 1.07 \begin {gather*} \frac {4 \, \log \relax (3)}{5 \, {\left (x^{4} + 4 \, x^{3}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.36, size = 23, normalized size = 1.64 \begin {gather*} -\frac {1}{80} \, {\left (\frac {1}{x + 4} - \frac {x^{2} - 4 \, x + 16}{x^{3}}\right )} \log \relax (3) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 13, normalized size = 0.93
method | result | size |
gosper | \(\frac {4 \ln \relax (3)}{5 x^{3} \left (4+x \right )}\) | \(13\) |
norman | \(\frac {4 \ln \relax (3)}{5 x^{3} \left (4+x \right )}\) | \(13\) |
risch | \(\frac {4 \ln \relax (3)}{5 x^{3} \left (4+x \right )}\) | \(13\) |
default | \(\frac {16 \ln \relax (3) \left (\frac {1}{16 x^{3}}-\frac {1}{64 x^{2}}+\frac {1}{256 x}-\frac {1}{256 \left (4+x \right )}\right )}{5}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 15, normalized size = 1.07 \begin {gather*} \frac {4 \, \log \relax (3)}{5 \, {\left (x^{4} + 4 \, x^{3}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 17, normalized size = 1.21 \begin {gather*} \frac {4\,\ln \relax (3)}{5\,\left (x^4+4\,x^3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 14, normalized size = 1.00 \begin {gather*} \frac {4 \log {\relax (3 )}}{5 x^{4} + 20 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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