Optimal. Leaf size=15 \[ \log \left (\log \left (x-\frac {5+\log (2 x)}{x}\right )\right ) \]
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Rubi [A]
time = 0.09, antiderivative size = 18, normalized size of antiderivative = 1.20, number of steps
used = 1, number of rules used = 1, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6816}
\begin {gather*} \log \left (\log \left (-\frac {-x^2+\log (2 x)+5}{x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log \left (\log \left (-\frac {5-x^2+\log (2 x)}{x}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 17, normalized size = 1.13 \begin {gather*} \log \left (\log \left (\frac {-5+x^2-\log (2 x)}{x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.70, size = 0, normalized size = 0.00 \[\int \frac {-\ln \left (2 x \right )-x^{2}-4}{\left (x \ln \left (2 x \right )-x^{3}+5 x \right ) \ln \left (\frac {-\ln \left (2 x \right )+x^{2}-5}{x}\right )}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 20, normalized size = 1.33 \begin {gather*} \log \left (\log \left (x^{2} - \log \left (2\right ) - \log \left (x\right ) - 5\right ) - \log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 17, normalized size = 1.13 \begin {gather*} \log \left (\log \left (\frac {x^{2} - \log \left (2 \, x\right ) - 5}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.18, size = 14, normalized size = 0.93 \begin {gather*} \log {\left (\log {\left (\frac {x^{2} - \log {\left (2 x \right )} - 5}{x} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [F]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.13, size = 18, normalized size = 1.20 \begin {gather*} \ln \left (\ln \left (-\frac {\ln \left (2\,x\right )-x^2+5}{x}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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