Optimal. Leaf size=9 \[ 4+\log (x+x \log (x)) \]
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Rubi [A] time = 0.02, antiderivative size = 8, normalized size of antiderivative = 0.89, number of steps used = 3, number of rules used = 1, integrand size = 13, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {43} \begin {gather*} \log (x)+\log (\log (x)+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {2+x}{1+x} \, dx,x,\log (x)\right )\\ &=\operatorname {Subst}\left (\int \left (1+\frac {1}{1+x}\right ) \, dx,x,\log (x)\right )\\ &=\log (x)+\log (1+\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 8, normalized size = 0.89 \begin {gather*} \log (x)+\log (1+\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 8, normalized size = 0.89 \begin {gather*} \log \relax (x) + \log \left (\log \relax (x) + 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.24, size = 25, normalized size = 2.78 \begin {gather*} \frac {1}{2} \, \log \left (\frac {1}{4} \, \pi ^{2} {\left (\mathrm {sgn}\relax (x) - 1\right )}^{2} + {\left (\log \left ({\left | x \right |}\right ) + 1\right )}^{2}\right ) + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 8, normalized size = 0.89
method | result | size |
derivativedivides | \(\ln \left (x \ln \relax (x )+x \right )\) | \(8\) |
default | \(\ln \left (x \ln \relax (x )+x \right )\) | \(8\) |
norman | \(\ln \relax (x )+\ln \left (\ln \relax (x )+1\right )\) | \(9\) |
risch | \(\ln \relax (x )+\ln \left (\ln \relax (x )+1\right )\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.65, size = 7, normalized size = 0.78 \begin {gather*} \log \left (x \log \relax (x) + x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.77, size = 8, normalized size = 0.89 \begin {gather*} \ln \left (\ln \relax (x)+1\right )+\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 = 8, normalized size = 0.89 \begin {gather*} \log {\relax (x )} + \log {\left (\log {\relax (x )} + 1 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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