Optimal. Leaf size=17 \[ 2 \sqrt{x} \log (x)-4 \sqrt{x} \]
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Rubi [A] time = 0.0066523, antiderivative size = 17, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0018617, size = 11, normalized size = 0.65 \[ 2 \sqrt{x} (\log (x)-2) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.007, size = 14, normalized size = 0.8 \begin{align*} -4\,\sqrt{x}+2\,\ln \left ( x \right ) \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.02922, size = 18, normalized size = 1.06 \begin{align*} 2 \, \sqrt{x} \log \left (x\right ) - 4 \, \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.81478, size = 32, normalized size = 1.88 \begin{align*} 2 \, \sqrt{x}{\left (\log \left (x\right ) - 2\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 1.8802, size = 60, normalized size = 3.53 \begin{align*} \begin{cases} 2 \sqrt{x} \log{\left (x \right )} - 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} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.31282, size = 18, normalized size = 1.06 \begin{align*} 2 \, \sqrt{x} \log \left (x\right ) - 4 \, \sqrt{x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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