Integrand size = 15, antiderivative size = 19 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=\frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \]
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Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {14} \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=\frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \]
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Rule 14
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{\sqrt [3]{x}}-\sqrt [6]{x}\right ) \, dx \\ & = \frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=\frac {3 x^{2/3}}{2}-\frac {6 x^{7/6}}{7} \]
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Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63
method | result | size |
derivativedivides | \(\frac {3 x^{\frac {2}{3}}}{2}-\frac {6 x^{\frac {7}{6}}}{7}\) | \(12\) |
default | \(\frac {3 x^{\frac {2}{3}}}{2}-\frac {6 x^{\frac {7}{6}}}{7}\) | \(12\) |
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none
Time = 0.28 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=-\frac {6}{7} \, x^{\frac {7}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} \]
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Time = 0.38 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=- \frac {6 x^{\frac {7}{6}}}{7} + \frac {3 x^{\frac {2}{3}}}{2} \]
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none
Time = 0.18 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=-\frac {6}{7} \, x^{\frac {7}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} \]
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none
Time = 0.32 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.58 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=-\frac {6}{7} \, x^{\frac {7}{6}} + \frac {3}{2} \, x^{\frac {2}{3}} \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.63 \[ \int \frac {1-\sqrt {x}}{\sqrt [3]{x}} \, dx=-\frac {3\,x^{2/3}\,\left (4\,\sqrt {x}-7\right )}{14} \]
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