Optimal. Leaf size=23 \[ \frac{2 \sqrt{b x+c x^2}}{c \sqrt{x}} \]
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Rubi [A] time = 0.0068375, antiderivative size = 23, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 19, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.053, Rules used = {648} \[ \frac{2 \sqrt{b x+c x^2}}{c \sqrt{x}} \]
Antiderivative was successfully verified.
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Rule 648
Rubi steps
\begin{align*} \int \frac{\sqrt{x}}{\sqrt{b x+c x^2}} \, dx &=\frac{2 \sqrt{b x+c x^2}}{c \sqrt{x}}\\ \end{align*}
Mathematica [A] time = 0.008983, size = 21, normalized size = 0.91 \[ \frac{2 \sqrt{x (b+c x)}}{c \sqrt{x}} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.045, size = 25, normalized size = 1.1 \begin{align*} 2\,{\frac{ \left ( cx+b \right ) \sqrt{x}}{c\sqrt{c{x}^{2}+bx}}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.18947, size = 16, normalized size = 0.7 \begin{align*} \frac{2 \, \sqrt{c x + b}}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.99411, size = 45, normalized size = 1.96 \begin{align*} \frac{2 \, \sqrt{c x^{2} + b x}}{c \sqrt{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{\sqrt{x}}{\sqrt{x \left (b + c x\right )}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.26256, size = 28, normalized size = 1.22 \begin{align*} \frac{2 \, \sqrt{c x + b}}{c} - \frac{2 \, \sqrt{b}}{c} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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