Optimal. Leaf size=13 \[ \log \left (\frac {e^{-2 x} x}{\log (\log (x))}\right ) \]
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Rubi [A] time = 0.16, antiderivative size = 12, normalized size of antiderivative = 0.92, number of steps used = 5, number of rules used = 3, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.115, Rules used = {6688, 2302, 29} \begin {gather*} -2 x+\log (x)-\log (\log (\log (x))) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2302
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2+\frac {1}{x}-\frac {1}{x \log (x) \log (\log (x))}\right ) \, dx\\ &=-2 x+\log (x)-\int \frac {1}{x \log (x) \log (\log (x))} \, dx\\ &=-2 x+\log (x)-\operatorname {Subst}\left (\int \frac {1}{x \log (x)} \, dx,x,\log (x)\right )\\ &=-2 x+\log (x)-\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (\log (x))\right )\\ &=-2 x+\log (x)-\log (\log (\log (x)))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 12, normalized size = 0.92 \begin {gather*} -2 x+\log (x)-\log (\log (\log (x))) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 12, normalized size = 0.92 \begin {gather*} -2 \, x + \log \relax (x) - \log \left (\log \left (\log \relax (x)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 12, normalized size = 0.92 \begin {gather*} -2 \, x + \log \relax (x) - \log \left (\log \left (\log \relax (x)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 13, normalized size = 1.00
method | result | size |
default | \(\ln \relax (x )-2 x -\ln \left (\ln \left (\ln \relax (x )\right )\right )\) | \(13\) |
norman | \(\ln \relax (x )-2 x -\ln \left (\ln \left (\ln \relax (x )\right )\right )\) | \(13\) |
risch | \(\ln \relax (x )-2 x -\ln \left (\ln \left (\ln \relax (x )\right )\right )\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 12, normalized size = 0.92 \begin {gather*} -2 \, x + \log \relax (x) - \log \left (\log \left (\log \relax (x)\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.30, size = 12, normalized size = 0.92 \begin {gather*} \ln \relax (x)-\ln \left (\ln \left (\ln \relax (x)\right )\right )-2\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.25, size = 12, normalized size = 0.92 \begin {gather*} - 2 x + \log {\relax (x )} - \log {\left (\log {\left (\log {\relax (x )} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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