Optimal. Leaf size=5 \[ \log (3+\log (x)) \]
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Rubi [A]
time = 0.01, antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2339, 29}
\begin {gather*} \log (\log (x)+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2339
Rubi steps
\begin {align*} \int \frac {1}{x (3+\log (x))} \, dx &=\text {Subst}\left (\int \frac {1}{x} \, dx,x,3+\log (x)\right )\\ &=\log (3+\log (x))\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 5, normalized size = 1.00 \begin {gather*} \log (3+\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 6, normalized size = 1.20
method | result | size |
derivativedivides | \(\ln \left (3+\ln \left (x \right )\right )\) | \(6\) |
default | \(\ln \left (3+\ln \left (x \right )\right )\) | \(6\) |
norman | \(\ln \left (3+\ln \left (x \right )\right )\) | \(6\) |
risch | \(\ln \left (3+\ln \left (x \right )\right )\) | \(6\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 5, normalized size = 1.00 \begin {gather*} \log \left (\log \left (x\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 5, normalized size = 1.00 \begin {gather*} \log \left (\log \left (x\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 5, normalized size = 1.00 \begin {gather*} \log {\left (\log {\left (x \right )} + 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 22 vs.
\(2 (5) = 10\).
time = 3.73, size = 22, normalized size = 4.40 \begin {gather*} \frac {1}{2} \, \log \left (\frac {1}{4} \, \pi ^{2} {\left (\mathrm {sgn}\left (x\right ) - 1\right )}^{2} + {\left (\log \left ({\left | x \right |}\right ) + 3\right )}^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.42, size = 5, normalized size = 1.00 \begin {gather*} \ln \left (\ln \left (x\right )+3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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