Integrand size = 9, antiderivative size = 12 \[ \int \left (\frac {b}{x^2}\right )^{2/3} \, dx=-3 \left (\frac {b}{x^2}\right )^{2/3} x \]
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Time = 0.00 (sec) , antiderivative size = 12, 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} \[ \int \left (\frac {b}{x^2}\right )^{2/3} \, dx=-3 x \left (\frac {b}{x^2}\right )^{2/3} \]
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Rule 15
Rule 30
Rubi steps \begin{align*} \text {integral}& = \left (\left (\frac {b}{x^2}\right )^{2/3} x^{4/3}\right ) \int \frac {1}{x^{4/3}} \, dx \\ & = -3 \left (\frac {b}{x^2}\right )^{2/3} x \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (\frac {b}{x^2}\right )^{2/3} \, dx=-3 \left (\frac {b}{x^2}\right )^{2/3} x \]
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Time = 0.03 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92
method | result | size |
gosper | \(-3 \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}} x\) | \(11\) |
trager | \(-3 \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}} x\) | \(11\) |
risch | \(-3 \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}} x\) | \(11\) |
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none
Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (\frac {b}{x^2}\right )^{2/3} \, dx=-3 \, x \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}} \]
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Time = 0.16 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \left (\frac {b}{x^2}\right )^{2/3} \, dx=- 3 x \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}} \]
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none
Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (\frac {b}{x^2}\right )^{2/3} \, dx=-3 \, x \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}} \]
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none
Time = 0.27 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (\frac {b}{x^2}\right )^{2/3} \, dx=-3 \, x \left (\frac {b}{x^{2}}\right )^{\frac {2}{3}} \]
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Time = 5.32 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int \left (\frac {b}{x^2}\right )^{2/3} \, dx=-3\,b^{2/3}\,x\,{\left (\frac {1}{x^2}\right )}^{2/3} \]
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