Integrand size = 7, antiderivative size = 12 \[ \int \frac {1}{(b x)^{2/3}} \, dx=\frac {3 \sqrt [3]{b x}}{b} \]
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Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {32} \[ \int \frac {1}{(b x)^{2/3}} \, dx=\frac {3 \sqrt [3]{b x}}{b} \]
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Rule 32
Rubi steps \begin{align*} \text {integral}& = \frac {3 \sqrt [3]{b x}}{b} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{(b x)^{2/3}} \, dx=\frac {3 x}{(b x)^{2/3}} \]
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Time = 0.04 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.75
method | result | size |
gosper | \(\frac {3 x}{\left (b x \right )^{\frac {2}{3}}}\) | \(9\) |
risch | \(\frac {3 x}{\left (b x \right )^{\frac {2}{3}}}\) | \(9\) |
derivativedivides | \(\frac {3 \left (b x \right )^{\frac {1}{3}}}{b}\) | \(11\) |
default | \(\frac {3 \left (b x \right )^{\frac {1}{3}}}{b}\) | \(11\) |
trager | \(\frac {3 \left (b x \right )^{\frac {1}{3}}}{b}\) | \(11\) |
pseudoelliptic | \(\frac {3 \left (b x \right )^{\frac {1}{3}}}{b}\) | \(11\) |
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none
Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{(b x)^{2/3}} \, dx=\frac {3 \, \left (b x\right )^{\frac {1}{3}}}{b} \]
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Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \frac {1}{(b x)^{2/3}} \, dx=\frac {3 \sqrt [3]{b x}}{b} \]
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none
Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{(b x)^{2/3}} \, dx=\frac {3 \, \left (b x\right )^{\frac {1}{3}}}{b} \]
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none
Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{(b x)^{2/3}} \, dx=\frac {3 \, \left (b x\right )^{\frac {1}{3}}}{b} \]
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Time = 0.01 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{(b x)^{2/3}} \, dx=\frac {3\,{\left (b\,x\right )}^{1/3}}{b} \]
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