Optimal. Leaf size=19 \[ \log \left (\frac {-21+x-\log (x)+\frac {1}{5} \log (\log (x))}{x}\right ) \]
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Rubi [A]
time = 0.29, antiderivative size = 20, normalized size of antiderivative = 1.05, number of steps
used = 4, number of rules used = 3, integrand size = 49, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {6873, 6874,
6816} \begin {gather*} \log (-5 x+5 \log (x)-\log (\log (x))+105)-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6816
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-1-100 \log (x)-5 \log ^2(x)+\log (x) \log (\log (x))}{x \log (x) (105-5 x+5 \log (x)-\log (\log (x)))} \, dx\\ &=\int \left (-\frac {1}{x}+\frac {1-5 \log (x)+5 x \log (x)}{x \log (x) (-105+5 x-5 \log (x)+\log (\log (x)))}\right ) \, dx\\ &=-\log (x)+\int \frac {1-5 \log (x)+5 x \log (x)}{x \log (x) (-105+5 x-5 \log (x)+\log (\log (x)))} \, dx\\ &=-\log (x)+\log (105-5 x+5 \log (x)-\log (\log (x)))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 20, normalized size = 1.05 \begin {gather*} -\log (x)+\log (105-5 x+5 \log (x)-\log (\log (x))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.32, size = 21, normalized size = 1.11
method | result | size |
risch | \(-\ln \left (x \right )+\ln \left (5 x -5 \ln \left (x \right )+\ln \left (\ln \left (x \right )\right )-105\right )\) | \(19\) |
default | \(-\ln \left (x \right )+\ln \left (5 \ln \left (x \right )-\ln \left (\ln \left (x \right )\right )-5 x +105\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 18, normalized size = 0.95 \begin {gather*} \log \left (5 \, x - 5 \, \log \left (x\right ) + \log \left (\log \left (x\right )\right ) - 105\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 18, normalized size = 0.95 \begin {gather*} \log \left (5 \, x - 5 \, \log \left (x\right ) + \log \left (\log \left (x\right )\right ) - 105\right ) - \log \left (x\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 = 1.00 \begin {gather*} - \log {\left (x \right )} + \log {\left (5 x - 5 \log {\left (x \right )} + \log {\left (\log {\left (x \right )} \right )} - 105 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 20, normalized size = 1.05 \begin {gather*} -\log \left (x\right ) + \log \left (-5 \, x + 5 \, \log \left (x\right ) - \log \left (\log \left (x\right )\right ) + 105\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.76, size = 18, normalized size = 0.95 \begin {gather*} \ln \left (5\,x+\ln \left (\ln \left (x\right )\right )-5\,\ln \left (x\right )-105\right )-\ln \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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