Integrand size = 22, antiderivative size = 14 \[ \int \frac {2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx=2 \sqrt {-1+x}+2 \log (x) \]
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Time = 0.11 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {6820} \[ \int \frac {2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx=2 \sqrt {x-1}+2 \log (x) \]
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Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{\sqrt {-1+x}}+\frac {2}{x}\right ) \, dx \\ & = 2 \sqrt {-1+x}+2 \log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx=2 \sqrt {-1+x}+2 \log (x) \]
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Time = 1.10 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93
method | result | size |
derivativedivides | \(2 \ln \left (x \right )+2 \sqrt {x -1}\) | \(13\) |
default | \(2 \ln \left (x \right )+2 \sqrt {x -1}\) | \(13\) |
trager | \(2 \sqrt {x -1}-2 \ln \left (\frac {1}{x}\right )\) | \(15\) |
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none
Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx=2 \, \sqrt {x - 1} + 2 \, \log \left (x\right ) \]
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Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx=2 \sqrt {x - 1} + 2 \log {\left (x \right )} \]
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none
Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx=2 \, \sqrt {x - 1} + 2 \, \log \left (x\right ) \]
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none
Time = 0.31 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx=2 \, \sqrt {x - 1} + 2 \, \log \left (x\right ) \]
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Time = 20.38 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {2 \sqrt {-1+x}+x}{\sqrt {-1+x} x} \, dx=2\,\ln \left (x\right )+2\,\sqrt {x-1} \]
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