Optimal. Leaf size=17 \[ \log (x)-\log \left (5 e^{2 x} \log (2 x)\right ) \]
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Rubi [A]
time = 0.06, antiderivative size = 13, normalized size of antiderivative = 0.76, number of steps
used = 4, number of rules used = 3, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.136, Rules used = {6820, 2339, 29}
\begin {gather*} -2 x+\log (x)-\log (\log (2 x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2339
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2+\frac {1}{x}-\frac {1}{x \log (2 x)}\right ) \, dx\\ &=-2 x+\log (x)-\int \frac {1}{x \log (2 x)} \, dx\\ &=-2 x+\log (x)-\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (2 x)\right )\\ &=-2 x+\log (x)-\log (\log (2 x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 13, normalized size = 0.76 \begin {gather*} -2 x+\log (x)-\log (\log (2 x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.28, size = 16, normalized size = 0.94
method | result | size |
risch | \(\ln \left (x \right )-2 x -\ln \left (\ln \left (2 x \right )\right )\) | \(14\) |
derivativedivides | \(-2 x +\ln \left (2 x \right )-\ln \left (\ln \left (2 x \right )\right )\) | \(16\) |
default | \(-2 x +\ln \left (2 x \right )-\ln \left (\ln \left (2 x \right )\right )\) | \(16\) |
norman | \(-2 x +\ln \left (2 x \right )-\ln \left (\ln \left (2 x \right )\right )\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 13, normalized size = 0.76 \begin {gather*} -2 \, x + \log \left (x\right ) - \log \left (\log \left (2 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 15, normalized size = 0.88 \begin {gather*} -2 \, x + \log \left (2 \, x\right ) - \log \left (\log \left (2 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 12, normalized size = 0.71 \begin {gather*} - 2 x + \log {\left (x \right )} - \log {\left (\log {\left (2 x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 13, normalized size = 0.76 \begin {gather*} -2 \, x + \log \left (x\right ) - \log \left (\log \left (2 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.09, size = 13, normalized size = 0.76 \begin {gather*} \ln \left (x\right )-\ln \left (\ln \left (2\,x\right )\right )-2\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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