Optimal. Leaf size=12 \[ 2 \log \left (1-\sqrt {x}\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1593, 260} \[ 2 \log \left (1-\sqrt {x}\right ) \]
Antiderivative was successfully verified.
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Rule 260
Rule 1593
Rubi steps
\begin {align*} \int \frac {1}{-\sqrt {x}+x} \, dx &=\int \frac {1}{\left (-1+\sqrt {x}\right ) \sqrt {x}} \, dx\\ &=2 \log \left (1-\sqrt {x}\right )\\ \end {align*}
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Mathematica [A] time = 0.00, size = 12, normalized size = 1.00 \[ 2 \log \left (1-\sqrt {x}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.39, size = 8, normalized size = 0.67 \[ 2 \, \log \left (\sqrt {x} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 9, normalized size = 0.75 \[ 2 \, \log \left ({\left | \sqrt {x} - 1 \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 12, normalized size = 1.00 \[ -2 \arctanh \left (\sqrt {x}\right )+\ln \left (x -1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 8, normalized size = 0.67 \[ 2 \, \log \left (\sqrt {x} - 1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 8, normalized size = 0.67 \[ 2\,\ln \left (\sqrt {x}-1\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.18, size = 8, normalized size = 0.67 \[ 2 \log {\left (\sqrt {x} - 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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