Optimal. Leaf size=17 \[ 2 \sqrt {x} \log (x)-4 \sqrt {x} \]
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Rubi [A] time = 0.01, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2304} \[ 2 \sqrt {x} \log (x)-4 \sqrt {x} \]
Antiderivative was successfully verified.
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Rule 2304
Rubi steps
\begin {align*} \int \frac {\log (x)}{\sqrt {x}} \, dx &=-4 \sqrt {x}+2 \sqrt {x} \log (x)\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.65 \[ 2 \sqrt {x} (\log (x)-2) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 9, normalized size = 0.53 \[ 2 \, \sqrt {x} {\left (\log \relax (x) - 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 13, normalized size = 0.76 \[ 2 \, \sqrt {x} \log \relax (x) - 4 \, \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 14, normalized size = 0.82 \[ 2 \sqrt {x}\, \ln \relax (x )-4 \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 13, normalized size = 0.76 \[ 2 \, \sqrt {x} \log \relax (x) - 4 \, \sqrt {x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 9, normalized size = 0.53 \[ 2\,\sqrt {x}\,\left (\ln \relax (x)-2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.74, size = 60, normalized size = 3.53 \[ \begin {cases} 2 \sqrt {x} \log {\relax (x )} - 4 \sqrt {x} & \text {for}\: \left |{x}\right | < 1 \\- 2 \sqrt {x} \log {\left (\frac {1}{x} \right )} - 4 \sqrt {x} & \text {for}\: \frac {1}{\left |{x}\right |} < 1 \\- {G_{3, 3}^{2, 1}\left (\begin {matrix} 1 & \frac {3}{2}, \frac {3}{2} \\\frac {1}{2}, \frac {1}{2} & 0 \end {matrix} \middle | {x} \right )} + {G_{3, 3}^{0, 3}\left (\begin {matrix} \frac {3}{2}, \frac {3}{2}, 1 & \\ & \frac {1}{2}, \frac {1}{2}, 0 \end {matrix} \middle | {x} \right )} & \text {otherwise} \end {cases} \]
Verification of antiderivative is not currently implemented for this CAS.
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