Optimal. Leaf size=12 \[ \frac {2}{3} (1+\log (x))^{3/2} \]
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Rubi [A]
time = 0.02, 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 = {2339, 30}
\begin {gather*} \frac {2}{3} (\log (x)+1)^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Rule 30
Rule 2339
Rubi steps
\begin {align*} \int \frac {\sqrt {1+\log (x)}}{x} \, dx &=\text {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 \begin {gather*} \frac {2}{3} (1+\log (x))^{3/2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 9, normalized size = 0.75
method | result | size |
derivativedivides | \(\frac {2 \left (1+\ln \left (x \right )\right )^{\frac {3}{2}}}{3}\) | \(9\) |
default | \(\frac {2 \left (1+\ln \left (x \right )\right )^{\frac {3}{2}}}{3}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 8, normalized size = 0.67 \begin {gather*} \frac {2}{3} \, {\left (\log \left (x\right ) + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 8, normalized size = 0.67 \begin {gather*} \frac {2}{3} \, {\left (\log \left (x\right ) + 1\right )}^{\frac {3}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.38, size = 10, normalized size = 0.83 \begin {gather*} \frac {2 \left (\log {\left (x \right )} + 1\right )^{\frac {3}{2}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 4.45, size = 8, normalized size = 0.67 \begin {gather*} \frac {2}{3} \, {\left (\log \left (x\right ) + 1\right )}^{\frac {3}{2}} \end {gather*}
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 \begin {gather*} \sqrt {\ln \left (x\right )+1}\,\left (\frac {2\,\ln \left (x\right )}{3}+\frac {2}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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