Integrand size = 9, antiderivative size = 13 \[ \int \sqrt [3]{\frac {b}{x^3}} \, dx=\sqrt [3]{\frac {b}{x^3}} x \log (x) \]
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Time = 0.00 (sec) , antiderivative size = 13, 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, 29} \[ \int \sqrt [3]{\frac {b}{x^3}} \, dx=x \sqrt [3]{\frac {b}{x^3}} \log (x) \]
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Rule 15
Rule 29
Rubi steps \begin{align*} \text {integral}& = \left (\sqrt [3]{\frac {b}{x^3}} x\right ) \int \frac {1}{x} \, dx \\ & = \sqrt [3]{\frac {b}{x^3}} x \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.00 \[ \int \sqrt [3]{\frac {b}{x^3}} \, dx=\sqrt [3]{\frac {b}{x^3}} x \log (x) \]
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Time = 0.04 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92
method | result | size |
risch | \(\left (\frac {b}{x^{3}}\right )^{\frac {1}{3}} x \ln \left (x \right )\) | \(12\) |
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none
Time = 0.26 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85 \[ \int \sqrt [3]{\frac {b}{x^3}} \, dx=x \left (\frac {b}{x^{3}}\right )^{\frac {1}{3}} \log \left (x\right ) \]
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Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.92 \[ \int \sqrt [3]{\frac {b}{x^3}} \, dx=x \sqrt [3]{\frac {b}{x^{3}}} \log {\left (x \right )} \]
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none
Time = 0.18 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85 \[ \int \sqrt [3]{\frac {b}{x^3}} \, dx=x \left (\frac {b}{x^{3}}\right )^{\frac {1}{3}} \log \left (x\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 1, normalized size of antiderivative = 0.08 \[ \int \sqrt [3]{\frac {b}{x^3}} \, dx=+\infty \]
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Timed out. \[ \int \sqrt [3]{\frac {b}{x^3}} \, dx=\int {\left (\frac {b}{x^3}\right )}^{1/3} \,d x \]
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