Integrand size = 11, antiderivative size = 12 \[ \int \frac {1}{-\sqrt {x}+x} \, dx=2 \log \left (1-\sqrt {x}\right ) \]
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Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {1607, 266} \[ \int \frac {1}{-\sqrt {x}+x} \, dx=2 \log \left (1-\sqrt {x}\right ) \]
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Rule 266
Rule 1607
Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{\left (-1+\sqrt {x}\right ) \sqrt {x}} \, dx \\ & = 2 \log \left (1-\sqrt {x}\right ) \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{-\sqrt {x}+x} \, dx=2 \log \left (-1+\sqrt {x}\right ) \]
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Time = 1.72 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75
method | result | size |
derivativedivides | \(2 \ln \left (\sqrt {x}-1\right )\) | \(9\) |
meijerg | \(2 \ln \left (1-\sqrt {x}\right )\) | \(11\) |
default | \(\ln \left (-1+x \right )-2 \,\operatorname {arctanh}\left (\sqrt {x}\right )\) | \(12\) |
trager | \(\ln \left (2 \sqrt {x}-1-x \right )\) | \(12\) |
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none
Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {1}{-\sqrt {x}+x} \, dx=2 \, \log \left (\sqrt {x} - 1\right ) \]
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Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {1}{-\sqrt {x}+x} \, dx=2 \log {\left (\sqrt {x} - 1 \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {1}{-\sqrt {x}+x} \, dx=2 \, \log \left (\sqrt {x} - 1\right ) \]
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none
Time = 0.28 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75 \[ \int \frac {1}{-\sqrt {x}+x} \, dx=2 \, \log \left ({\left | \sqrt {x} - 1 \right |}\right ) \]
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Time = 0.09 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {1}{-\sqrt {x}+x} \, dx=2\,\ln \left (\sqrt {x}-1\right ) \]
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