Optimal. Leaf size=14 \[ \frac{2 x}{3 \sqrt{\frac{b}{x}}} \]
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Rubi [A] time = 0.0015289, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222, Rules used = {15, 30} \[ \frac{2 x}{3 \sqrt{\frac{b}{x}}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{\frac{b}{x}}} \, dx &=\frac{\int \sqrt{x} \, dx}{\sqrt{\frac{b}{x}} \sqrt{x}}\\ &=\frac{2 x}{3 \sqrt{\frac{b}{x}}}\\ \end{align*}
Mathematica [A] time = 0.0015514, size = 14, normalized size = 1. \[ \frac{2 x}{3 \sqrt{\frac{b}{x}}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 11, normalized size = 0.8 \begin{align*}{\frac{2\,x}{3}{\frac{1}{\sqrt{{\frac{b}{x}}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.953574, size = 14, normalized size = 1. \begin{align*} \frac{2 \, x}{3 \, \sqrt{\frac{b}{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.73286, size = 28, normalized size = 2. \begin{align*} \frac{2 \, x^{2} \sqrt{\frac{b}{x}}}{3 \, b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.519949, size = 15, normalized size = 1.07 \begin{align*} \frac{2 x}{3 \sqrt{b} \sqrt{\frac{1}{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19693, size = 20, normalized size = 1.43 \begin{align*} \frac{2 \, \sqrt{b x} x}{3 \, b \mathrm{sgn}\left (x\right )} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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