Optimal. Leaf size=25 \[ -5+\log (5)-\frac {2 x}{x+\log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )} \]
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Rubi [A]
time = 0.42, antiderivative size = 24, normalized size of antiderivative = 0.96, number of steps
used = 3, number of rules used = 3, integrand size = 136, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {6820, 6843,
32} \begin {gather*} \frac {2}{\frac {x}{\log \left (16 \log \left (\frac {x}{\log (x)}\right )-x\right )}+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 32
Rule 6820
Rule 6843
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {32+2 \log (x) \left (-16+x-\left (x-16 \log \left (\frac {x}{\log (x)}\right )\right ) \log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )\right )}{\log (x) \left (x-16 \log \left (\frac {x}{\log (x)}\right )\right ) \left (x+\log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )\right )^2} \, dx\\ &=-\left (2 \text {Subst}\left (\int \frac {1}{(1+x)^2} \, dx,x,\frac {x}{\log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )}\right )\right )\\ &=\frac {2}{1+\frac {x}{\log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\right )}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.18, size = 21, normalized size = 0.84 \begin {gather*} -\frac {2 x}{x+\log \left (-x+16 \log \left (\frac {x}{\log (x)}\right )\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 = 105.09, size = 72, normalized size = 2.88 \[-\frac {2 x}{x +\ln \left (-16 \ln \left (\ln \left (x \right )\right )+16 \ln \left (x \right )-8 i \pi \,\mathrm {csgn}\left (\frac {i x}{\ln \left (x \right )}\right ) \left (-\mathrm {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\mathrm {csgn}\left (\frac {i}{\ln \left (x \right )}\right )\right ) \left (-\mathrm {csgn}\left (\frac {i x}{\ln \left (x \right )}\right )+\mathrm {csgn}\left (i x \right )\right )-x \right )}\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 21, normalized size = 0.84 \begin {gather*} -\frac {2 \, x}{x + \log \left (-x + 16 \, \log \left (x\right ) - 16 \, \log \left (\log \left (x\right )\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 21, normalized size = 0.84 \begin {gather*} -\frac {2 \, x}{x + \log \left (-x + 16 \, \log \left (\frac {x}{\log \left (x\right )}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.30, size = 17, normalized size = 0.68 \begin {gather*} - \frac {2 x}{x + \log {\left (- x + 16 \log {\left (\frac {x}{\log {\left (x \right )}} \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.58, size = 21, normalized size = 0.84 \begin {gather*} -\frac {2 \, x}{x + \log \left (-x + 16 \, \log \left (x\right ) - 16 \, \log \left (\log \left (x\right )\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 8.09, size = 21, normalized size = 0.84 \begin {gather*} -\frac {2\,x}{x+\ln \left (16\,\ln \left (\frac {x}{\ln \left (x\right )}\right )-x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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