Optimal. Leaf size=21 \[ \frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}}}{a} \]
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Rubi [A] time = 0.005363, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059, Rules used = {264} \[ \frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}}}{a} \]
Antiderivative was successfully verified.
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Rule 264
Rubi steps
\begin{align*} \int \frac{1}{\sqrt{a+\frac{b}{x}} \sqrt{x}} \, dx &=\frac{2 \sqrt{a+\frac{b}{x}} \sqrt{x}}{a}\\ \end{align*}
Mathematica [A] time = 0.0089242, size = 21, normalized size = 1. \[ \frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}}}{a} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.002, size = 25, normalized size = 1.2 \begin{align*} 2\,{\frac{ax+b}{a\sqrt{x}}{\frac{1}{\sqrt{{\frac{ax+b}{x}}}}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.96491, size = 23, normalized size = 1.1 \begin{align*} \frac{2 \, \sqrt{a + \frac{b}{x}} \sqrt{x}}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.46166, size = 42, normalized size = 2. \begin{align*} \frac{2 \, \sqrt{x} \sqrt{\frac{a x + b}{x}}}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 2.08187, size = 17, normalized size = 0.81 \begin{align*} \frac{2 \sqrt{b} \sqrt{\frac{a x}{b} + 1}}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.15257, size = 28, normalized size = 1.33 \begin{align*} \frac{2 \, \sqrt{a x + b}}{a} - \frac{2 \, \sqrt{b}}{a} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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