Optimal. Leaf size=20 \[ -1+\log \left (2-2 x+\log \left (\frac {4 \log (\log (\log (5)))}{5 x}\right )\right ) \]
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Rubi [F]
time = 0.13, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-1-2 x}{2 x-2 x^2+x \log \left (\frac {4 \log (\log (\log (5)))}{5 x}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2}{-2+2 x-\log \left (\frac {4 \log (\log (\log (5)))}{5 x}\right )}+\frac {1}{x \left (-2+2 x-\log \left (\frac {4 \log (\log (\log (5)))}{5 x}\right )\right )}\right ) \, dx\\ &=2 \int \frac {1}{-2+2 x-\log \left (\frac {4 \log (\log (\log (5)))}{5 x}\right )} \, dx+\int \frac {1}{x \left (-2+2 x-\log \left (\frac {4 \log (\log (\log (5)))}{5 x}\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 18, normalized size = 0.90 \begin {gather*} \log \left (2-2 x+\log \left (\frac {4 \log (\log (\log (5)))}{5 x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(49\) vs.
\(2(18)=36\).
time = 0.25, size = 50, normalized size = 2.50
method | result | size |
risch | \(\ln \left (\ln \left (\frac {4 \ln \left (\ln \left (\ln \left (5\right )\right )\right )}{5 x}\right )+2-2 x \right )\) | \(17\) |
norman | \(\ln \left (2 x -\ln \left (\frac {4 \ln \left (\ln \left (\ln \left (5\right )\right )\right )}{5 x}\right )-2\right )\) | \(19\) |
derivativedivides | \(-\ln \left (\frac {4 \ln \left (\ln \left (\ln \left (5\right )\right )\right )}{5 x}\right )+\ln \left (-\frac {4 \ln \left (\frac {4 \ln \left (\ln \left (\ln \left (5\right )\right )\right )}{5 x}\right ) \ln \left (\ln \left (\ln \left (5\right )\right )\right )}{x}+8 \ln \left (\ln \left (\ln \left (5\right )\right )\right )-\frac {8 \ln \left (\ln \left (\ln \left (5\right )\right )\right )}{x}\right )\) | \(50\) |
default | \(-\ln \left (\frac {4 \ln \left (\ln \left (\ln \left (5\right )\right )\right )}{5 x}\right )+\ln \left (-\frac {4 \ln \left (\frac {4 \ln \left (\ln \left (\ln \left (5\right )\right )\right )}{5 x}\right ) \ln \left (\ln \left (\ln \left (5\right )\right )\right )}{x}+8 \ln \left (\ln \left (\ln \left (5\right )\right )\right )-\frac {8 \ln \left (\ln \left (\ln \left (5\right )\right )\right )}{x}\right )\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.51, size = 21, normalized size = 1.05 \begin {gather*} \log \left (2 \, x + \log \left (5\right ) - 2 \, \log \left (2\right ) + \log \left (x\right ) - \log \left (\log \left (\log \left (\log \left (5\right )\right )\right )\right ) - 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 16, normalized size = 0.80 \begin {gather*} \log \left (-2 \, x + \log \left (\frac {4 \, \log \left (\log \left (\log \left (5\right )\right )\right )}{5 \, x}\right ) + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 19, normalized size = 0.95 \begin {gather*} \log {\left (- 2 x + \log {\left (\frac {4 \log {\left (\log {\left (\log {\left (5 \right )} \right )} \right )}}{5 x} \right )} + 2 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 65 vs.
\(2 (18) = 36\).
time = 0.41, size = 65, normalized size = 3.25 \begin {gather*} \frac {\log \left (-\frac {4 \, \log \left (\frac {4 \, \log \left (\log \left (\log \left (5\right )\right )\right )}{5 \, x}\right ) \log \left (\log \left (\log \left (5\right )\right )\right )}{x} - \frac {8 \, \log \left (\log \left (\log \left (5\right )\right )\right )}{x} + 8 \, \log \left (\log \left (\log \left (5\right )\right )\right )\right ) \log \left (\log \left (\log \left (5\right )\right )\right ) - \log \left (\frac {4 \, \log \left (\log \left (\log \left (5\right )\right )\right )}{5 \, x}\right ) \log \left (\log \left (\log \left (5\right )\right )\right )}{\log \left (\log \left (\log \left (5\right )\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.60, size = 29, normalized size = 1.45 \begin {gather*} \ln \left (x-\frac {\ln \left (-\ln \left (\ln \left (\ln \left (5\right )\right )\right )\right )}{2}-\ln \left (2\right )+\frac {\ln \left (5\right )}{2}-\frac {\ln \left (-\frac {1}{x}\right )}{2}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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