Integrand size = 15, antiderivative size = 10 \[ \int \frac {1}{\left (1+\sqrt {x}\right ) \sqrt {x}} \, dx=2 \log \left (1+\sqrt {x}\right ) \]
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Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {266} \[ \int \frac {1}{\left (1+\sqrt {x}\right ) \sqrt {x}} \, dx=2 \log \left (\sqrt {x}+1\right ) \]
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Rule 266
Rubi steps \begin{align*} \text {integral}& = 2 \log \left (1+\sqrt {x}\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int \frac {1}{\left (1+\sqrt {x}\right ) \sqrt {x}} \, dx=2 \log \left (1+\sqrt {x}\right ) \]
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Time = 3.70 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90
method | result | size |
derivativedivides | \(2 \ln \left (\sqrt {x}+1\right )\) | \(9\) |
default | \(2 \ln \left (\sqrt {x}+1\right )\) | \(9\) |
meijerg | \(2 \ln \left (\sqrt {x}+1\right )\) | \(9\) |
trager | \(\ln \left (x +2 \sqrt {x}+1\right )\) | \(10\) |
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none
Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {1}{\left (1+\sqrt {x}\right ) \sqrt {x}} \, dx=2 \, \log \left (\sqrt {x} + 1\right ) \]
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Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {1}{\left (1+\sqrt {x}\right ) \sqrt {x}} \, dx=2 \log {\left (\sqrt {x} + 1 \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {1}{\left (1+\sqrt {x}\right ) \sqrt {x}} \, dx=2 \, \log \left (\sqrt {x} + 1\right ) \]
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none
Time = 0.29 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {1}{\left (1+\sqrt {x}\right ) \sqrt {x}} \, dx=2 \, \log \left (\sqrt {x} + 1\right ) \]
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Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {1}{\left (1+\sqrt {x}\right ) \sqrt {x}} \, dx=2\,\ln \left (\sqrt {x}+1\right ) \]
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