Integrand size = 9, antiderivative size = 12 \[ \int \frac {1}{\sqrt [3]{b x^2}} \, dx=\frac {3 x}{\sqrt [3]{b x^2}} \]
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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} \[ \int \frac {1}{\sqrt [3]{b x^2}} \, dx=\frac {3 x}{\sqrt [3]{b x^2}} \]
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Rule 15
Rule 30
Rubi steps \begin{align*} \text {integral}& = \frac {x^{2/3} \int \frac {1}{x^{2/3}} \, dx}{\sqrt [3]{b x^2}} \\ & = \frac {3 x}{\sqrt [3]{b x^2}} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \frac {1}{\sqrt [3]{b x^2}} \, dx=\frac {3 x}{\sqrt [3]{b x^2}} \]
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Time = 0.04 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92
method | result | size |
gosper | \(\frac {3 x}{\left (b \,x^{2}\right )^{\frac {1}{3}}}\) | \(11\) |
risch | \(\frac {3 x}{\left (b \,x^{2}\right )^{\frac {1}{3}}}\) | \(11\) |
trager | \(\frac {3 \left (b \,x^{2}\right )^{\frac {2}{3}}}{b x}\) | \(16\) |
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none
Time = 0.26 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.25 \[ \int \frac {1}{\sqrt [3]{b x^2}} \, dx=\frac {3 \, \left (b x^{2}\right )^{\frac {2}{3}}}{b x} \]
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Time = 0.17 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{\sqrt [3]{b x^2}} \, dx=\frac {3 x}{\sqrt [3]{b x^{2}}} \]
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none
Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{\sqrt [3]{b x^2}} \, dx=\frac {3 \, x}{\left (b x^{2}\right )^{\frac {1}{3}}} \]
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none
Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \frac {1}{\sqrt [3]{b x^2}} \, dx=\frac {3 \, x}{\left (b x^{2}\right )^{\frac {1}{3}}} \]
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Time = 5.73 (sec) , antiderivative size = 13, normalized size of antiderivative = 1.08 \[ \int \frac {1}{\sqrt [3]{b x^2}} \, dx=\frac {3\,{\left (x^4\right )}^{1/3}}{b^{1/3}\,x} \]
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