Integrand size = 13, antiderivative size = 9 \[ \int \frac {\sqrt {b x^2}}{x} \, dx=\sqrt {b x^2} \]
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Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {15, 8} \[ \int \frac {\sqrt {b x^2}}{x} \, dx=\sqrt {b x^2} \]
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Rule 8
Rule 15
Rubi steps \begin{align*} \text {integral}& = \frac {\sqrt {b x^2} \int 1 \, dx}{x} \\ & = \sqrt {b x^2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int \frac {\sqrt {b x^2}}{x} \, dx=\sqrt {b x^2} \]
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Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89
method | result | size |
derivativedivides | \(\sqrt {b \,x^{2}}\) | \(8\) |
default | \(\sqrt {b \,x^{2}}\) | \(8\) |
risch | \(\sqrt {b \,x^{2}}\) | \(8\) |
pseudoelliptic | \(\sqrt {b \,x^{2}}\) | \(8\) |
trager | \(\frac {\left (-1+x \right ) \sqrt {b \,x^{2}}}{x}\) | \(15\) |
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none
Time = 0.27 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {\sqrt {b x^2}}{x} \, dx=\sqrt {b x^{2}} \]
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Time = 0.06 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {\sqrt {b x^2}}{x} \, dx=\sqrt {b x^{2}} \]
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Exception generated. \[ \int \frac {\sqrt {b x^2}}{x} \, dx=\text {Exception raised: RuntimeError} \]
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none
Time = 0.28 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int \frac {\sqrt {b x^2}}{x} \, dx=\sqrt {b} x \mathrm {sgn}\left (x\right ) \]
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Time = 5.74 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int \frac {\sqrt {b x^2}}{x} \, dx=\sqrt {b}\,\left |x\right | \]
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