Optimal. Leaf size=10 \[ \log \left (16 x^4 \log ^2(x)\right ) \]
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Rubi [A] time = 0.04, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2365, 43} \begin {gather*} 4 \log (x)+2 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rule 2365
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {2+4 x}{x} \, dx,x,\log (x)\right )\\ &=\operatorname {Subst}\left (\int \left (4+\frac {2}{x}\right ) \, dx,x,\log (x)\right )\\ &=4 \log (x)+2 \log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} 4 \log (x)+2 \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.46, size = 10, normalized size = 1.00 \begin {gather*} 4 \, \log \relax (x) + 2 \, \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 11, normalized size = 1.10 \begin {gather*} 4 \, \log \relax (x) + 2 \, \log \left ({\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 = 0.02, size = 11, normalized size = 1.10
method | result | size |
derivativedivides | \(4 \ln \relax (x )+2 \ln \left (\ln \relax (x )\right )\) | \(11\) |
default | \(4 \ln \relax (x )+2 \ln \left (\ln \relax (x )\right )\) | \(11\) |
norman | \(4 \ln \relax (x )+2 \ln \left (\ln \relax (x )\right )\) | \(11\) |
risch | \(4 \ln \relax (x )+2 \ln \left (\ln \relax (x )\right )\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 10, normalized size = 1.00 \begin {gather*} 4 \, \log \relax (x) + 2 \, \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.73, size = 10, normalized size = 1.00 \begin {gather*} 2\,\ln \left (\ln \relax (x)\right )+4\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 10, normalized size = 1.00 \begin {gather*} 4 \log {\relax (x )} + 2 \log {\left (\log {\relax (x )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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