Optimal. Leaf size=18 \[ -\frac {52}{25}+e^5+2 x+\log (x-\log (\log (2))) \]
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Rubi [A]
time = 0.01, antiderivative size = 12, normalized size of antiderivative = 0.67, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {45}
\begin {gather*} 2 x+\log (x-\log (\log (2))) \end {gather*}
Antiderivative was successfully verified.
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Rule 45
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (2+\frac {1}{x-\log (\log (2))}\right ) \, dx\\ &=2 x+\log (x-\log (\log (2)))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 18, normalized size = 1.00 \begin {gather*} 2 (x-\log (\log (2)))+\log (x-\log (\log (2))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 1.30, size = 13, normalized size = 0.72
method | result | size |
default | \(2 x +\ln \left (x -\ln \left (\ln \left (2\right )\right )\right )\) | \(13\) |
norman | \(2 x +\ln \left (\ln \left (\ln \left (2\right )\right )-x \right )\) | \(13\) |
risch | \(2 x +\ln \left (x -\ln \left (\ln \left (2\right )\right )\right )\) | \(13\) |
meijerg | \(-2 \ln \left (\ln \left (2\right )\right ) \ln \left (1-\frac {x}{\ln \left (\ln \left (2\right )\right )}\right )-2 \ln \left (\ln \left (2\right )\right ) \left (-\frac {x}{\ln \left (\ln \left (2\right )\right )}-\ln \left (1-\frac {x}{\ln \left (\ln \left (2\right )\right )}\right )\right )+\ln \left (1-\frac {x}{\ln \left (\ln \left (2\right )\right )}\right )\) | \(56\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 12, normalized size = 0.67 \begin {gather*} 2 \, x + \log \left (x - \log \left (\log \left (2\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 12, normalized size = 0.67 \begin {gather*} 2 \, x + \log \left (x - \log \left (\log \left (2\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 10, normalized size = 0.56 \begin {gather*} 2 x + \log {\left (x - \log {\left (\log {\left (2 \right )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 13, normalized size = 0.72 \begin {gather*} 2 \, x + \log \left ({\left | x - \log \left (\log \left (2\right )\right ) \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 12, normalized size = 0.67 \begin {gather*} 2\,x+\ln \left (x-\ln \left (\ln \left (2\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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