Integrand size = 9, antiderivative size = 14 \[ \int \frac {1}{\left (\frac {b}{x^3}\right )^{2/3}} \, dx=\frac {x}{3 \left (\frac {b}{x^3}\right )^{2/3}} \]
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Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {15, 30} \[ \int \frac {1}{\left (\frac {b}{x^3}\right )^{2/3}} \, dx=\frac {x}{3 \left (\frac {b}{x^3}\right )^{2/3}} \]
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Rule 15
Rule 30
Rubi steps \begin{align*} \text {integral}& = \frac {\int x^2 \, dx}{\left (\frac {b}{x^3}\right )^{2/3} x^2} \\ & = \frac {x}{3 \left (\frac {b}{x^3}\right )^{2/3}} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {1}{\left (\frac {b}{x^3}\right )^{2/3}} \, dx=\frac {x}{3 \left (\frac {b}{x^3}\right )^{2/3}} \]
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Time = 0.04 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.79
method | result | size |
gosper | \(\frac {x}{3 \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}}\) | \(11\) |
risch | \(\frac {x}{3 \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}}\) | \(11\) |
trager | \(\frac {x \left (x^{2}+x +1\right ) \left (-1+x \right ) \left (\frac {b}{x^{3}}\right )^{\frac {1}{3}}}{3 b}\) | \(23\) |
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none
Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {1}{\left (\frac {b}{x^3}\right )^{2/3}} \, dx=\frac {x^{4} \left (\frac {b}{x^{3}}\right )^{\frac {1}{3}}}{3 \, b} \]
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Time = 0.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{\left (\frac {b}{x^3}\right )^{2/3}} \, dx=\frac {x}{3 \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}} \]
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none
Time = 0.19 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{\left (\frac {b}{x^3}\right )^{2/3}} \, dx=\frac {x}{3 \, \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}} \]
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none
Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{\left (\frac {b}{x^3}\right )^{2/3}} \, dx=\frac {x}{3 \, \left (\frac {b}{x^{3}}\right )^{\frac {2}{3}}} \]
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Time = 5.98 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07 \[ \int \frac {1}{\left (\frac {b}{x^3}\right )^{2/3}} \, dx=\frac {x^4\,{\left (\frac {b}{x^3}\right )}^{1/3}}{3\,b} \]
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