Optimal. Leaf size=8 \[ 2 \sqrt {\log (x)} \]
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Rubi [A]
time = 0.01, antiderivative size = 8, 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, 30}
\begin {gather*} 2 \sqrt {\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 30
Rule 2339
Rubi steps
\begin {align*} \int \frac {1}{x \sqrt {\log (x)}} \, dx &=\text {Subst}\left (\int \frac {1}{\sqrt {x}} \, dx,x,\log (x)\right )\\ &=2 \sqrt {\log (x)}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} 2 \sqrt {\log (x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 7, normalized size = 0.88
method | result | size |
derivativedivides | \(2 \sqrt {\ln \left (x \right )}\) | \(7\) |
default | \(2 \sqrt {\ln \left (x \right )}\) | \(7\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 6, normalized size = 0.75 \begin {gather*} 2 \, \sqrt {\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 6, normalized size = 0.75 \begin {gather*} 2 \, \sqrt {\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.27, size = 7, normalized size = 0.88 \begin {gather*} 2 \sqrt {\log {\left (x \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 5.53, size = 6, normalized size = 0.75 \begin {gather*} 2 \, \sqrt {\log \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 6, normalized size = 0.75 \begin {gather*} 2\,\sqrt {\ln \left (x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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