Optimal. Leaf size=12 \[ \frac {2}{3} (\log (x)+1)^{3/2} \]
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Rubi [A] time = 0.03, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {2302, 30} \[ \frac {2}{3} (\log (x)+1)^{3/2} \]
Antiderivative was successfully verified.
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Rule 30
Rule 2302
Rubi steps
\begin {align*} \int \frac {\sqrt {1+\log (x)}}{x} \, dx &=\operatorname {Subst}\left (\int \sqrt {x} \, dx,x,1+\log (x)\right )\\ &=\frac {2}{3} (1+\log (x))^{3/2}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ \frac {2}{3} (\log (x)+1)^{3/2} \]
Antiderivative was successfully verified.
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fricas [A] time = 1.95, size = 8, normalized size = 0.67 \[ \frac {2}{3} \, {\left (\log \relax (x) + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 8, normalized size = 0.67 \[ \frac {2}{3} \, {\left (\log \relax (x) + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 9, normalized size = 0.75 \[ \frac {2 \left (\ln \relax (x )+1\right )^{\frac {3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.72, size = 8, normalized size = 0.67 \[ \frac {2}{3} \, {\left (\log \relax (x) + 1\right )}^{\frac {3}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.39, size = 13, normalized size = 1.08 \[ \sqrt {\ln \relax (x)+1}\,\left (\frac {2\,\ln \relax (x)}{3}+\frac {2}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.80, size = 10, normalized size = 0.83 \[ \frac {2 \left (\log {\relax (x )} + 1\right )^{\frac {3}{2}}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
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