Optimal. Leaf size=25 \[ \frac {4}{\frac {x}{16}+\log (x)-\log \left (\frac {5 x^2}{4+x}\right )} \]
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Rubi [A]
time = 0.24, antiderivative size = 23, normalized size of antiderivative = 0.92, number of steps
used = 3, number of rules used = 3, integrand size = 108, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.028, Rules used = {6820, 12,
6818} \begin {gather*} \frac {64}{-16 \log \left (\frac {5 x^2}{x+4}\right )+x+16 \log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6818
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {64 \left (64-4 x-x^2\right )}{x (4+x) \left (x+16 \log (x)-16 \log \left (\frac {5 x^2}{4+x}\right )\right )^2} \, dx\\ &=64 \int \frac {64-4 x-x^2}{x (4+x) \left (x+16 \log (x)-16 \log \left (\frac {5 x^2}{4+x}\right )\right )^2} \, dx\\ &=\frac {64}{x+16 \log (x)-16 \log \left (\frac {5 x^2}{4+x}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 23, normalized size = 0.92 \begin {gather*} \frac {64}{x+16 \log (x)-16 \log \left (\frac {5 x^2}{4+x}\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 13.88, size = 174, normalized size = 6.96
method | result | size |
default | \(-\frac {64}{-8 i \pi \,\mathrm {csgn}\left (\frac {i}{4+x}\right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i x^{2}}{4+x}\right )+8 i \pi \,\mathrm {csgn}\left (\frac {i}{4+x}\right ) \mathrm {csgn}\left (\frac {i x^{2}}{4+x}\right )^{2}-8 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+16 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-8 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+8 i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i x^{2}}{4+x}\right )^{2}-8 i \pi \mathrm {csgn}\left (\frac {i x^{2}}{4+x}\right )^{3}+16 \ln \left (5\right )+16 \ln \left (x \right )-x -16 \ln \left (4+x \right )}\) | \(174\) |
risch | \(-\frac {64}{-8 i \pi \,\mathrm {csgn}\left (\frac {i}{4+x}\right ) \mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i x^{2}}{4+x}\right )+8 i \pi \,\mathrm {csgn}\left (\frac {i}{4+x}\right ) \mathrm {csgn}\left (\frac {i x^{2}}{4+x}\right )^{2}-8 i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+16 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-8 i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+8 i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (\frac {i x^{2}}{4+x}\right )^{2}-8 i \pi \mathrm {csgn}\left (\frac {i x^{2}}{4+x}\right )^{3}+16 \ln \left (5\right )+16 \ln \left (x \right )-x -16 \ln \left (4+x \right )}\) | \(174\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.54, size = 20, normalized size = 0.80 \begin {gather*} \frac {64}{x - 16 \, \log \left (5\right ) + 16 \, \log \left (x + 4\right ) - 16 \, \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 23, normalized size = 0.92 \begin {gather*} \frac {64}{x + 16 \, \log \left (x\right ) - 16 \, \log \left (\frac {5 \, x^{2}}{x + 4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 19, normalized size = 0.76 \begin {gather*} - \frac {4}{- \frac {x}{16} - \log {\left (x \right )} + \log {\left (\frac {5 x^{2}}{x + 4} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.45, size = 20, normalized size = 0.80 \begin {gather*} \frac {64}{x - 16 \, \log \left (5\right ) + 16 \, \log \left (x + 4\right ) - 16 \, \log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.77, size = 23, normalized size = 0.92 \begin {gather*} \frac {64}{x-16\,\ln \left (\frac {5\,x^2}{x+4}\right )+16\,\ln \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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