Integrand size = 9, antiderivative size = 11 \[ \int \left (1-\sqrt {x}\right ) \, dx=x-\frac {2 x^{3/2}}{3} \]
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Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (1-\sqrt {x}\right ) \, dx=x-\frac {2 x^{3/2}}{3} \]
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Rubi steps \begin{align*} \text {integral}& = x-\frac {2 x^{3/2}}{3} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \left (1-\sqrt {x}\right ) \, dx=x-\frac {2 x^{3/2}}{3} \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73
method | result | size |
derivativedivides | \(x -\frac {2 x^{\frac {3}{2}}}{3}\) | \(8\) |
default | \(x -\frac {2 x^{\frac {3}{2}}}{3}\) | \(8\) |
risch | \(x -\frac {2 x^{\frac {3}{2}}}{3}\) | \(8\) |
parts | \(x -\frac {2 x^{\frac {3}{2}}}{3}\) | \(8\) |
trager | \(x -1-\frac {2 x^{\frac {3}{2}}}{3}\) | \(9\) |
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Time = 0.28 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \left (1-\sqrt {x}\right ) \, dx=-\frac {2}{3} \, x^{\frac {3}{2}} + x \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \left (1-\sqrt {x}\right ) \, dx=- \frac {2 x^{\frac {3}{2}}}{3} + x \]
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none
Time = 0.18 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \left (1-\sqrt {x}\right ) \, dx=-\frac {2}{3} \, x^{\frac {3}{2}} + x \]
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none
Time = 0.31 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \left (1-\sqrt {x}\right ) \, dx=-\frac {2}{3} \, x^{\frac {3}{2}} + x \]
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Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \left (1-\sqrt {x}\right ) \, dx=x-\frac {2\,x^{3/2}}{3} \]
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