Optimal. Leaf size=12 \[ 2 \log \left (1-\sqrt{x}\right ) \]
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Rubi [A] time = 0.003826, antiderivative size = 12, normalized size of antiderivative = 1., 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 1593
Rule 260
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*}
Mathematica [A] time = 0.0022968, size = 12, normalized size = 1. \[ 2 \log \left (1-\sqrt{x}\right ) \]
Antiderivative was successfully verified.
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Maple [A] time = 0.003, size = 12, normalized size = 1. \begin{align*} \ln \left ( -1+x \right ) -2\,{\it Artanh} \left ( \sqrt{x} \right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.04106, size = 11, normalized size = 0.92 \begin{align*} 2 \, \log \left (\sqrt{x} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0.82284, size = 27, normalized size = 2.25 \begin{align*} 2 \, \log \left (\sqrt{x} - 1\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.152274, size = 8, normalized size = 0.67 \begin{align*} 2 \log{\left (\sqrt{x} - 1 \right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.17205, size = 12, normalized size = 1. \begin{align*} 2 \, \log \left ({\left | \sqrt{x} - 1 \right |}\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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