Integrand size = 5, antiderivative size = 9 \[ \int \sqrt [3]{x} \, dx=\frac {3 x^{4/3}}{4} \]
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Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {30} \[ \int \sqrt [3]{x} \, dx=\frac {3 x^{4/3}}{4} \]
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Rule 30
Rubi steps \begin{align*} \text {integral}& = \frac {3 x^{4/3}}{4} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \sqrt [3]{x} \, dx=\frac {3 x^{4/3}}{4} \]
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Time = 0.01 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67
method | result | size |
gosper | \(\frac {3 x^{\frac {4}{3}}}{4}\) | \(6\) |
derivativedivides | \(\frac {3 x^{\frac {4}{3}}}{4}\) | \(6\) |
default | \(\frac {3 x^{\frac {4}{3}}}{4}\) | \(6\) |
trager | \(\frac {3 x^{\frac {4}{3}}}{4}\) | \(6\) |
risch | \(\frac {3 x^{\frac {4}{3}}}{4}\) | \(6\) |
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none
Time = 0.22 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \sqrt [3]{x} \, dx=\frac {3}{4} \, x^{\frac {4}{3}} \]
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Time = 0.05 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \sqrt [3]{x} \, dx=\frac {3 x^{\frac {4}{3}}}{4} \]
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none
Time = 0.21 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \sqrt [3]{x} \, dx=\frac {3}{4} \, x^{\frac {4}{3}} \]
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none
Time = 0.46 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \sqrt [3]{x} \, dx=\frac {3}{4} \, x^{\frac {4}{3}} \]
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Time = 0.04 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int \sqrt [3]{x} \, dx=\frac {3\,x^{4/3}}{4} \]
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