Integrand size = 9, antiderivative size = 12 \[ \int \sqrt {\frac {b}{x^3}} \, dx=-2 \sqrt {\frac {b}{x^3}} x \]
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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} \[ \int \sqrt {\frac {b}{x^3}} \, dx=-2 x \sqrt {\frac {b}{x^3}} \]
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Rule 15
Rule 30
Rubi steps \begin{align*} \text {integral}& = \left (\sqrt {\frac {b}{x^3}} x^{3/2}\right ) \int \frac {1}{x^{3/2}} \, dx \\ & = -2 \sqrt {\frac {b}{x^3}} x \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \sqrt {\frac {b}{x^3}} \, dx=-2 \sqrt {\frac {b}{x^3}} x \]
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Time = 0.05 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92
method | result | size |
gosper | \(-2 x \sqrt {\frac {b}{x^{3}}}\) | \(11\) |
default | \(-2 x \sqrt {\frac {b}{x^{3}}}\) | \(11\) |
trager | \(-2 x \sqrt {\frac {b}{x^{3}}}\) | \(11\) |
risch | \(-2 x \sqrt {\frac {b}{x^{3}}}\) | \(11\) |
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none
Time = 0.26 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \sqrt {\frac {b}{x^3}} \, dx=-2 \, x \sqrt {\frac {b}{x^{3}}} \]
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Time = 0.13 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00 \[ \int \sqrt {\frac {b}{x^3}} \, dx=- 2 x \sqrt {\frac {b}{x^{3}}} \]
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none
Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \sqrt {\frac {b}{x^3}} \, dx=-2 \, x \sqrt {\frac {b}{x^{3}}} \]
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none
Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.67 \[ \int \sqrt {\frac {b}{x^3}} \, dx=-\frac {2 \, b}{\sqrt {b x}} \]
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Time = 5.46 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \sqrt {\frac {b}{x^3}} \, dx=-2\,x\,\sqrt {\frac {b}{x^3}} \]
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