Optimal. Leaf size=12 \[ 2 x \sqrt{\frac{b}{x}} \]
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Rubi [A] time = 0.001497, antiderivative size = 12, 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} \[ 2 x \sqrt{\frac{b}{x}} \]
Antiderivative was successfully verified.
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Rule 15
Rule 30
Rubi steps
\begin{align*} \int \sqrt{\frac{b}{x}} \, dx &=\left (\sqrt{\frac{b}{x}} \sqrt{x}\right ) \int \frac{1}{\sqrt{x}} \, dx\\ &=2 \sqrt{\frac{b}{x}} x\\ \end{align*}
Mathematica [A] time = 0.0011144, size = 12, normalized size = 1. \[ 2 x \sqrt{\frac{b}{x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.001, size = 11, normalized size = 0.9 \begin{align*} 2\,x\sqrt{{\frac{b}{x}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.983577, size = 14, normalized size = 1.17 \begin{align*} 2 \, x \sqrt{\frac{b}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.69507, size = 20, normalized size = 1.67 \begin{align*} 2 \, x \sqrt{\frac{b}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.18345, size = 14, normalized size = 1.17 \begin{align*} 2 \sqrt{b} x \sqrt{\frac{1}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.20002, size = 12, normalized size = 1. \begin{align*} 2 \, \sqrt{b x} \mathrm{sgn}\left (x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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